%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET732+4 : TPTP v8.1.2. Bugfixed v2.2.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 15:26:12 EDT 2023 % Result : Theorem 22.52s 3.84s % Output : Proof 27.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET732+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n008.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 14:16:32 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.13/1.28 Prover 1: Preprocessing ... % 4.13/1.28 Prover 4: Preprocessing ... % 4.57/1.32 Prover 2: Preprocessing ... % 4.57/1.32 Prover 6: Preprocessing ... % 4.57/1.32 Prover 0: Preprocessing ... % 4.57/1.32 Prover 5: Preprocessing ... % 4.57/1.33 Prover 3: Preprocessing ... % 9.79/2.06 Prover 5: Proving ... % 9.79/2.07 Prover 2: Proving ... % 10.23/2.11 Prover 1: Constructing countermodel ... % 10.23/2.15 Prover 6: Proving ... % 10.23/2.16 Prover 3: Constructing countermodel ... % 10.23/2.23 Prover 3: gave up % 10.23/2.23 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.23/2.25 Prover 1: gave up % 10.23/2.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.23/2.29 Prover 7: Preprocessing ... % 10.23/2.30 Prover 8: Preprocessing ... % 12.87/2.48 Prover 7: Warning: ignoring some quantifiers % 13.29/2.53 Prover 7: Constructing countermodel ... % 14.33/2.66 Prover 8: Warning: ignoring some quantifiers % 14.33/2.67 Prover 4: Constructing countermodel ... % 14.33/2.68 Prover 8: Constructing countermodel ... % 14.68/2.71 Prover 0: Proving ... % 15.20/2.87 Prover 8: gave up % 15.20/2.87 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 15.20/2.90 Prover 9: Preprocessing ... % 19.91/3.48 Prover 9: Constructing countermodel ... % 22.52/3.84 Prover 0: proved (3219ms) % 22.52/3.84 % 22.52/3.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.52/3.84 % 23.22/3.84 Prover 5: stopped % 23.22/3.84 Prover 9: stopped % 23.22/3.84 Prover 2: stopped % 23.22/3.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.22/3.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.22/3.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 23.22/3.84 Prover 6: stopped % 23.22/3.86 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 23.22/3.86 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 23.22/3.89 Prover 10: Preprocessing ... % 23.57/3.94 Prover 11: Preprocessing ... % 23.98/3.94 Prover 16: Preprocessing ... % 23.98/3.95 Prover 13: Preprocessing ... % 24.07/3.96 Prover 19: Preprocessing ... % 24.07/3.98 Prover 10: Warning: ignoring some quantifiers % 24.07/3.99 Prover 10: Constructing countermodel ... % 24.50/4.02 Prover 16: Warning: ignoring some quantifiers % 24.50/4.04 Prover 16: Constructing countermodel ... % 24.84/4.08 Prover 10: gave up % 24.84/4.10 Prover 13: Warning: ignoring some quantifiers % 24.84/4.12 Prover 13: Constructing countermodel ... % 25.54/4.16 Prover 4: Found proof (size 192) % 25.54/4.16 Prover 4: proved (3539ms) % 25.54/4.16 Prover 7: stopped % 25.54/4.16 Prover 16: stopped % 25.54/4.17 Prover 13: stopped % 25.82/4.22 Prover 19: Warning: ignoring some quantifiers % 25.82/4.23 Prover 19: Constructing countermodel ... % 26.11/4.24 Prover 19: stopped % 26.11/4.31 Prover 11: Constructing countermodel ... % 26.11/4.33 Prover 11: stopped % 26.11/4.33 % 26.11/4.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 26.11/4.33 % 26.11/4.34 % SZS output start Proof for theBenchmark % 26.11/4.35 Assumptions after simplification: % 26.11/4.35 --------------------------------- % 26.11/4.35 % 26.11/4.35 (equal_set) % 26.23/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 26.23/4.38 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 26.23/4.38 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 26.23/4.38 $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | ~ $i(v1) | % 26.23/4.38 ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & % 26.23/4.38 subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : % 26.23/4.38 ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 26.23/4.38 | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = % 26.23/4.38 v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 26.23/4.38 (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v0) = 0 & % 26.23/4.38 subset(v0, v1) = 0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) = % 26.23/4.38 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, % 26.23/4.38 v1) = v3 & subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] % 26.23/4.38 : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 26.23/4.38 any] : ? [v3: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = v2 & ( ~ % 26.23/4.38 (v2 = 0) | v3 = 0))) % 26.23/4.38 % 26.23/4.38 (image2) % 26.23/4.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 26.23/4.38 $i] : (v4 = 0 | ~ (image2(v0, v1) = v3) | ~ (apply(v0, v5, v2) = 0) | ~ % 26.23/4.38 (member(v2, v3) = v4) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.23/4.38 [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6)) & ! [v0: $i] : ! [v1: $i] % 26.23/4.38 : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: $i] : (v4 = 0 | ~ % 26.23/4.38 (image2(v0, v1) = v3) | ~ (member(v5, v1) = 0) | ~ (member(v2, v3) = v4) | % 26.23/4.38 ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) % 26.23/4.38 & apply(v0, v5, v2) = v6)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.23/4.38 [v3: $i] : ( ~ (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | % 26.23/4.38 ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v4, v2) = 0 & member(v4, v1) % 26.23/4.38 = 0 & $i(v4))) % 26.23/4.38 % 26.23/4.38 (injective) % 26.23/4.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.23/4.39 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) % 26.23/4.39 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 26.23/4.39 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 26.23/4.39 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 26.23/4.39 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 26.23/4.39 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 26.23/4.39 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, % 26.23/4.39 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 26.23/4.39 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v5) = % 26.23/4.39 v8 & member(v5, v2) = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = % 26.23/4.39 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.23/4.39 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = % 26.23/4.39 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v5) | ~ % 26.23/4.39 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 26.23/4.39 [v7: any] : ? [v8: any] : (apply(v0, v4, v5) = v8 & member(v5, v2) = v7 & % 26.23/4.39 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! % 26.23/4.39 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 26.23/4.39 : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ % 26.23/4.39 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 26.23/4.39 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.23/4.39 (apply(v0, v4, v5) = v7 & apply(v0, v3, v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 26.23/4.39 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 26.23/4.39 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.23/4.39 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 % 26.23/4.39 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & % 26.23/4.39 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 26.23/4.39 % 26.23/4.39 (maps) % 26.23/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.23/4.40 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ % 26.23/4.40 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.23/4.40 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 26.23/4.40 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 26.23/4.40 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 26.23/4.40 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, % 26.23/4.40 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~ % 26.23/4.40 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 26.23/4.40 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, % 26.23/4.40 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 26.23/4.40 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 26.23/4.40 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, % 26.23/4.40 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 26.23/4.40 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 26.23/4.40 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1) % 26.23/4.40 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: % 26.23/4.40 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 26.23/4.40 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | % 26.23/4.40 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 26.23/4.40 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & % 26.23/4.40 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! % 26.23/4.40 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | % 26.23/4.40 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 26.23/4.40 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] % 26.23/4.40 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 % 26.23/4.40 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) = % 26.23/4.40 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2) % 26.23/4.40 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) | % 26.23/4.40 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 = % 26.23/4.40 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, % 26.23/4.40 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, % 26.23/4.40 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 26.23/4.40 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) % 26.23/4.40 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, % 26.23/4.40 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4))) % 26.23/4.40 % 26.23/4.40 (one_to_one) % 26.23/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.23/4.40 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 26.23/4.40 any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2) % 26.23/4.40 = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.23/4.40 $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 26.23/4.40 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = % 26.23/4.40 v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! % 26.23/4.40 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (injective(v0, v1, % 26.23/4.40 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 26.23/4.40 any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v5 & ( ~ % 26.23/4.40 (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.23/4.40 $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.23/4.40 (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: $i] : ! % 26.23/4.40 [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 26.23/4.40 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) = % 26.23/4.40 v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : % 26.23/4.40 ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 26.23/4.40 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) = % 26.23/4.40 v4 & surjective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 26.23/4.40 % 26.23/4.40 (subset) % 26.23/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.23/4.40 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 26.23/4.40 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 26.23/4.40 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 26.23/4.40 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 26.23/4.40 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.23/4.40 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 26.23/4.40 ~ $i(v0) | member(v2, v1) = 0) % 26.23/4.40 % 26.23/4.40 (surjective) % 26.23/4.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.23/4.40 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 26.23/4.40 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4) % 26.23/4.40 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6)) % 26.23/4.40 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ % 26.23/4.40 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 26.23/4.40 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) % 26.23/4.40 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 26.23/4.40 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4))) % 26.23/4.40 % 26.23/4.40 (thII23) % 26.23/4.41 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 26.23/4.41 int] : ( ~ (v5 = 0) & image2(v0, v2) = v4 & one_to_one(v1, v2, v4) = v5 & % 26.23/4.41 injective(v0, v2, v3) = 0 & maps(v0, v2, v3) = 0 & subset(v4, v3) = 0 & % 26.23/4.41 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7: $i] : ! % 26.23/4.41 [v8: any] : ( ~ (apply(v1, v6, v7) = v8) | ~ $i(v7) | ~ $i(v6) | ? [v9: % 26.23/4.41 any] : ? [v10: any] : ? [v11: any] : (apply(v0, v6, v7) = v11 & % 26.23/4.41 member(v7, v4) = v10 & member(v6, v2) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0) % 26.23/4.41 | (( ~ (v11 = 0) | v8 = 0) & ( ~ (v8 = 0) | v11 = 0))))) & ! [v6: $i] % 26.23/4.41 : ! [v7: $i] : ! [v8: any] : ( ~ (apply(v0, v6, v7) = v8) | ~ $i(v7) | ~ % 26.23/4.41 $i(v6) | ? [v9: any] : ? [v10: any] : ? [v11: any] : (apply(v1, v6, v7) % 26.23/4.41 = v11 & member(v7, v4) = v10 & member(v6, v2) = v9 & ( ~ (v10 = 0) | ~ % 26.23/4.41 (v9 = 0) | (( ~ (v11 = 0) | v8 = 0) & ( ~ (v8 = 0) | v11 = 0)))))) % 26.23/4.41 % 26.23/4.41 (function-axioms) % 26.87/4.41 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 26.87/4.41 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 26.87/4.41 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 26.87/4.41 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 26.87/4.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.87/4.41 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 26.87/4.41 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 26.87/4.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.87/4.41 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 26.87/4.41 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 26.87/4.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.87/4.41 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 26.87/4.41 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 26.87/4.41 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 26.87/4.41 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 26.87/4.41 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 26.87/4.41 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.87/4.41 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 26.87/4.41 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 26.87/4.41 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 26.87/4.41 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 26.87/4.41 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 26.87/4.41 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 26.87/4.41 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 26.87/4.41 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 26.87/4.41 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.87/4.42 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 26.87/4.42 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 26.87/4.42 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 26.87/4.42 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 26.87/4.42 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 26.87/4.42 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 26.87/4.42 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.87/4.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 26.87/4.42 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 26.87/4.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 26.87/4.42 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 26.87/4.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.87/4.42 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 26.87/4.42 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 26.87/4.42 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 26.87/4.42 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 26.87/4.42 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 26.87/4.42 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 26.87/4.42 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 26.87/4.42 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.87/4.42 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 26.87/4.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.87/4.42 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 26.87/4.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 26.87/4.42 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 26.87/4.42 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 26.87/4.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 26.87/4.42 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 26.87/4.42 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 26.87/4.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 26.87/4.42 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 26.87/4.42 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.87/4.42 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 26.87/4.42 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 26.87/4.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 26.87/4.42 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 26.87/4.42 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 26.87/4.42 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 26.87/4.42 (power_set(v2) = v0)) % 26.87/4.42 % 26.87/4.42 Further assumptions not needed in the proof: % 26.87/4.42 -------------------------------------------- % 26.87/4.42 compose_function, compose_predicate, decreasing_function, difference, empty_set, % 26.87/4.42 equal_maps, identity, image3, increasing_function, intersection, % 26.87/4.42 inverse_function, inverse_image2, inverse_image3, inverse_predicate, % 26.87/4.42 isomorphism, power_set, product, singleton, sum, union, unordered_pair % 26.87/4.42 % 26.87/4.42 Those formulas are unsatisfiable: % 26.87/4.42 --------------------------------- % 26.87/4.42 % 26.87/4.42 Begin of proof % 26.87/4.42 | % 26.87/4.42 | ALPHA: (subset) implies: % 26.87/4.42 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 26.87/4.42 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2, % 26.87/4.42 | v1) = 0) % 26.87/4.42 | % 26.87/4.42 | ALPHA: (equal_set) implies: % 26.87/4.42 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 26.87/4.42 | $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, v1) = v3 & % 26.87/4.42 | subset(v1, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 26.87/4.42 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) = 0) | ~ $i(v1) | ~ % 26.87/4.42 | $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, v1) = v3 & % 26.87/4.42 | subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 26.87/4.42 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | % 26.87/4.42 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, % 26.87/4.42 | v1) = v3 & subset(v1, v0) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = % 26.87/4.42 | 0)))) % 26.87/4.42 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | % 26.87/4.42 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, % 26.87/4.42 | v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = % 26.87/4.42 | 0)))) % 26.87/4.42 | % 26.87/4.42 | ALPHA: (maps) implies: % 26.87/4.42 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, % 26.87/4.42 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 26.87/4.42 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 26.87/4.42 | member(v4, v2) = 0 & $i(v4))) % 26.87/4.42 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.87/4.42 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) % 26.87/4.42 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ % 26.87/4.42 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.87/4.42 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, % 26.87/4.42 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 26.87/4.42 | % 26.87/4.42 | ALPHA: (injective) implies: % 26.87/4.43 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.87/4.43 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 26.87/4.43 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, % 26.87/4.43 | v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, % 26.87/4.43 | v1) = 0 & member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 26.87/4.43 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.87/4.43 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, % 26.87/4.43 | v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ % 26.87/4.43 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.87/4.43 | ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3, % 26.87/4.43 | v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 26.87/4.43 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 26.87/4.43 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, % 26.87/4.43 | v4, v5) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | % 26.87/4.43 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 26.87/4.43 | [v7: any] : ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v5, v2) % 26.87/4.43 | = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 26.87/4.43 | 0)))) % 26.87/4.43 | % 26.87/4.43 | ALPHA: (surjective) implies: % 26.87/4.43 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.87/4.43 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.87/4.43 | ? [v4: $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ % 26.87/4.43 | (apply(v0, v5, v4) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = % 26.87/4.43 | 0) & member(v5, v1) = v6)) & ! [v5: $i] : ( ~ (member(v5, % 26.87/4.43 | v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & % 26.87/4.43 | apply(v0, v5, v4) = v6)))) % 26.87/4.43 | % 26.87/4.43 | ALPHA: (one_to_one) implies: % 26.87/4.43 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = % 26.87/4.43 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 26.87/4.43 | any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v3 % 26.87/4.43 | & ( ~ (v3 = 0) | v4 = 0))) % 26.87/4.43 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 26.87/4.43 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.87/4.43 | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = v4 & % 26.87/4.43 | surjective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) % 26.87/4.43 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 26.87/4.43 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.87/4.43 | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = v4 & % 26.87/4.43 | injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) % 26.87/4.43 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 26.87/4.43 | (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 26.87/4.43 | ? [v4: any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & % 26.87/4.43 | injective(v0, v1, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 26.87/4.43 | % 26.87/4.43 | ALPHA: (image2) implies: % 26.87/4.43 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 26.87/4.43 | (image2(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ % 26.87/4.43 | $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v4, v2) = 0 & % 26.87/4.43 | member(v4, v1) = 0 & $i(v4))) % 26.87/4.43 | % 26.87/4.43 | ALPHA: (function-axioms) implies: % 26.87/4.43 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.87/4.43 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 26.87/4.43 | v2) = v0)) % 26.87/4.44 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.87/4.44 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 26.87/4.44 | v2) = v0)) % 26.87/4.44 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.87/4.44 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 26.87/4.44 | ~ (apply(v4, v3, v2) = v0)) % 26.87/4.44 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.87/4.44 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (injective(v4, v3, v2) = % 26.87/4.44 | v1) | ~ (injective(v4, v3, v2) = v0)) % 26.87/4.44 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.87/4.44 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = % 26.87/4.44 | v1) | ~ (surjective(v4, v3, v2) = v0)) % 26.87/4.44 | % 26.87/4.44 | DELTA: instantiating (thII23) with fresh symbols all_32_0, all_32_1, all_32_2, % 26.87/4.44 | all_32_3, all_32_4, all_32_5 gives: % 26.87/4.44 | (22) ~ (all_32_0 = 0) & image2(all_32_5, all_32_3) = all_32_1 & % 26.87/4.44 | one_to_one(all_32_4, all_32_3, all_32_1) = all_32_0 & % 26.87/4.44 | injective(all_32_5, all_32_3, all_32_2) = 0 & maps(all_32_5, all_32_3, % 26.87/4.44 | all_32_2) = 0 & subset(all_32_1, all_32_2) = 0 & $i(all_32_1) & % 26.87/4.44 | $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & ! [v0: % 26.87/4.44 | $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_32_4, v0, v1) = % 26.87/4.44 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 26.87/4.44 | [v5: any] : (apply(all_32_5, v0, v1) = v5 & member(v1, all_32_1) = % 26.87/4.44 | v4 & member(v0, all_32_3) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ % 26.87/4.44 | (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! [v0: % 26.87/4.44 | $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_32_5, v0, v1) = % 26.87/4.44 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? % 26.87/4.44 | [v5: any] : (apply(all_32_4, v0, v1) = v5 & member(v1, all_32_1) = % 26.87/4.44 | v4 & member(v0, all_32_3) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ % 26.87/4.44 | (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) % 26.87/4.44 | % 26.87/4.44 | ALPHA: (22) implies: % 26.87/4.44 | (23) ~ (all_32_0 = 0) % 26.87/4.44 | (24) $i(all_32_5) % 26.87/4.44 | (25) $i(all_32_4) % 26.87/4.44 | (26) $i(all_32_3) % 26.87/4.44 | (27) $i(all_32_2) % 26.87/4.44 | (28) $i(all_32_1) % 26.87/4.44 | (29) subset(all_32_1, all_32_2) = 0 % 26.87/4.44 | (30) maps(all_32_5, all_32_3, all_32_2) = 0 % 26.87/4.44 | (31) injective(all_32_5, all_32_3, all_32_2) = 0 % 26.87/4.44 | (32) one_to_one(all_32_4, all_32_3, all_32_1) = all_32_0 % 26.87/4.44 | (33) image2(all_32_5, all_32_3) = all_32_1 % 26.87/4.44 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_32_5, v0, % 26.87/4.44 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] % 26.87/4.44 | : ? [v5: any] : (apply(all_32_4, v0, v1) = v5 & member(v1, % 26.87/4.44 | all_32_1) = v4 & member(v0, all_32_3) = v3 & ( ~ (v4 = 0) | ~ % 26.87/4.44 | (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) % 26.87/4.44 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (apply(all_32_4, v0, % 26.87/4.44 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] % 26.87/4.44 | : ? [v5: any] : (apply(all_32_5, v0, v1) = v5 & member(v1, % 26.87/4.44 | all_32_1) = v4 & member(v0, all_32_3) = v3 & ( ~ (v4 = 0) | ~ % 26.87/4.44 | (v3 = 0) | (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) % 26.87/4.44 | % 26.87/4.44 | GROUND_INST: instantiating (3) with all_32_2, all_32_1, simplifying with (27), % 26.87/4.44 | (28), (29) gives: % 26.87/4.44 | (36) ? [v0: any] : ? [v1: any] : (equal_set(all_32_2, all_32_1) = v1 & % 26.87/4.44 | subset(all_32_2, all_32_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 26.87/4.44 | % 26.87/4.44 | GROUND_INST: instantiating (2) with all_32_1, all_32_2, simplifying with (27), % 26.87/4.44 | (28), (29) gives: % 26.87/4.44 | (37) ? [v0: any] : ? [v1: any] : (equal_set(all_32_1, all_32_2) = v1 & % 26.87/4.44 | subset(all_32_2, all_32_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 26.87/4.44 | % 26.87/4.44 | GROUND_INST: instantiating (5) with all_32_2, all_32_1, 0, simplifying with % 26.87/4.44 | (27), (28), (29) gives: % 26.87/4.44 | (38) ? [v0: any] : ? [v1: any] : (equal_set(all_32_2, all_32_1) = v0 & % 26.87/4.44 | subset(all_32_2, all_32_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 26.87/4.44 | % 26.87/4.44 | GROUND_INST: instantiating (4) with all_32_1, all_32_2, 0, simplifying with % 26.87/4.44 | (27), (28), (29) gives: % 26.87/4.44 | (39) ? [v0: any] : ? [v1: any] : (equal_set(all_32_1, all_32_2) = v0 & % 26.87/4.44 | subset(all_32_2, all_32_1) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 26.87/4.44 | % 26.87/4.45 | GROUND_INST: instantiating (12) with all_32_5, all_32_3, all_32_2, simplifying % 26.87/4.45 | with (24), (26), (27), (31) gives: % 26.87/4.45 | (40) ? [v0: any] : ? [v1: any] : (one_to_one(all_32_5, all_32_3, % 26.87/4.45 | all_32_2) = v1 & surjective(all_32_5, all_32_3, all_32_2) = v0 & ( % 26.87/4.45 | ~ (v0 = 0) | v1 = 0)) % 26.87/4.45 | % 26.87/4.45 | GROUND_INST: instantiating (13) with all_32_5, all_32_3, all_32_2, 0, % 26.87/4.45 | simplifying with (24), (26), (27), (31) gives: % 26.87/4.45 | (41) ? [v0: any] : ? [v1: any] : (one_to_one(all_32_5, all_32_3, % 26.87/4.45 | all_32_2) = v0 & surjective(all_32_5, all_32_3, all_32_2) = v1 & ( % 26.87/4.45 | ~ (v0 = 0) | v1 = 0)) % 26.87/4.45 | % 26.87/4.45 | GROUND_INST: instantiating (15) with all_32_4, all_32_3, all_32_1, all_32_0, % 26.87/4.45 | simplifying with (25), (26), (28), (32) gives: % 26.87/4.45 | (42) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (surjective(all_32_4, % 26.87/4.45 | all_32_3, all_32_1) = v1 & injective(all_32_4, all_32_3, all_32_1) % 26.87/4.45 | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.87/4.45 | % 26.87/4.45 | DELTA: instantiating (41) with fresh symbols all_42_0, all_42_1 gives: % 26.87/4.45 | (43) one_to_one(all_32_5, all_32_3, all_32_2) = all_42_1 & % 26.87/4.45 | surjective(all_32_5, all_32_3, all_32_2) = all_42_0 & ( ~ (all_42_1 = % 26.87/4.45 | 0) | all_42_0 = 0) % 26.87/4.45 | % 26.87/4.45 | ALPHA: (43) implies: % 26.87/4.45 | (44) surjective(all_32_5, all_32_3, all_32_2) = all_42_0 % 26.87/4.45 | % 26.87/4.45 | DELTA: instantiating (38) with fresh symbols all_44_0, all_44_1 gives: % 26.87/4.45 | (45) equal_set(all_32_2, all_32_1) = all_44_1 & subset(all_32_2, all_32_1) % 26.87/4.45 | = all_44_0 & ( ~ (all_44_1 = 0) | all_44_0 = 0) % 26.87/4.45 | % 26.87/4.45 | ALPHA: (45) implies: % 26.87/4.45 | (46) subset(all_32_2, all_32_1) = all_44_0 % 26.87/4.45 | % 26.87/4.45 | DELTA: instantiating (40) with fresh symbols all_46_0, all_46_1 gives: % 26.87/4.45 | (47) one_to_one(all_32_5, all_32_3, all_32_2) = all_46_0 & % 26.87/4.45 | surjective(all_32_5, all_32_3, all_32_2) = all_46_1 & ( ~ (all_46_1 = % 26.87/4.45 | 0) | all_46_0 = 0) % 26.87/4.45 | % 26.87/4.45 | ALPHA: (47) implies: % 26.87/4.45 | (48) surjective(all_32_5, all_32_3, all_32_2) = all_46_1 % 26.87/4.45 | % 26.87/4.45 | DELTA: instantiating (39) with fresh symbols all_48_0, all_48_1 gives: % 26.87/4.45 | (49) equal_set(all_32_1, all_32_2) = all_48_1 & subset(all_32_2, all_32_1) % 26.87/4.45 | = all_48_0 & ( ~ (all_48_1 = 0) | all_48_0 = 0) % 26.87/4.45 | % 26.87/4.45 | ALPHA: (49) implies: % 26.87/4.45 | (50) subset(all_32_2, all_32_1) = all_48_0 % 26.87/4.45 | % 26.87/4.45 | DELTA: instantiating (37) with fresh symbols all_50_0, all_50_1 gives: % 26.87/4.45 | (51) equal_set(all_32_1, all_32_2) = all_50_0 & subset(all_32_2, all_32_1) % 26.87/4.45 | = all_50_1 & ( ~ (all_50_1 = 0) | all_50_0 = 0) % 26.87/4.45 | % 26.87/4.45 | ALPHA: (51) implies: % 26.87/4.45 | (52) subset(all_32_2, all_32_1) = all_50_1 % 26.87/4.45 | % 26.87/4.45 | DELTA: instantiating (36) with fresh symbols all_52_0, all_52_1 gives: % 26.87/4.45 | (53) equal_set(all_32_2, all_32_1) = all_52_0 & subset(all_32_2, all_32_1) % 26.87/4.45 | = all_52_1 & ( ~ (all_52_1 = 0) | all_52_0 = 0) % 26.87/4.45 | % 26.87/4.45 | ALPHA: (53) implies: % 26.87/4.45 | (54) subset(all_32_2, all_32_1) = all_52_1 % 26.87/4.45 | % 26.87/4.45 | BETA: splitting (42) gives: % 26.87/4.45 | % 26.87/4.45 | Case 1: % 26.87/4.45 | | % 26.87/4.45 | | (55) all_32_0 = 0 % 26.87/4.45 | | % 26.87/4.45 | | REDUCE: (23), (55) imply: % 26.87/4.45 | | (56) $false % 26.87/4.45 | | % 26.87/4.45 | | CLOSE: (56) is inconsistent. % 26.87/4.45 | | % 26.87/4.45 | Case 2: % 26.87/4.45 | | % 26.87/4.45 | | (57) ? [v0: any] : ? [v1: any] : (surjective(all_32_4, all_32_3, % 26.87/4.45 | | all_32_1) = v1 & injective(all_32_4, all_32_3, all_32_1) = v0 & % 26.87/4.45 | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.87/4.45 | | % 26.87/4.45 | | DELTA: instantiating (57) with fresh symbols all_58_0, all_58_1 gives: % 26.87/4.45 | | (58) surjective(all_32_4, all_32_3, all_32_1) = all_58_0 & % 26.87/4.45 | | injective(all_32_4, all_32_3, all_32_1) = all_58_1 & ( ~ (all_58_0 = % 26.87/4.45 | | 0) | ~ (all_58_1 = 0)) % 26.87/4.45 | | % 26.87/4.45 | | ALPHA: (58) implies: % 26.87/4.45 | | (59) injective(all_32_4, all_32_3, all_32_1) = all_58_1 % 26.87/4.45 | | (60) surjective(all_32_4, all_32_3, all_32_1) = all_58_0 % 26.87/4.45 | | (61) ~ (all_58_0 = 0) | ~ (all_58_1 = 0) % 26.87/4.45 | | % 26.87/4.45 | | GROUND_INST: instantiating (18) with all_50_1, all_52_1, all_32_1, all_32_2, % 26.87/4.45 | | simplifying with (52), (54) gives: % 26.87/4.45 | | (62) all_52_1 = all_50_1 % 26.87/4.45 | | % 26.87/4.45 | | GROUND_INST: instantiating (18) with all_48_0, all_52_1, all_32_1, all_32_2, % 26.87/4.45 | | simplifying with (50), (54) gives: % 26.87/4.45 | | (63) all_52_1 = all_48_0 % 26.87/4.45 | | % 26.87/4.45 | | GROUND_INST: instantiating (18) with all_44_0, all_52_1, all_32_1, all_32_2, % 26.87/4.45 | | simplifying with (46), (54) gives: % 26.87/4.45 | | (64) all_52_1 = all_44_0 % 26.87/4.45 | | % 26.87/4.45 | | GROUND_INST: instantiating (21) with all_42_0, all_46_1, all_32_2, all_32_3, % 26.87/4.45 | | all_32_5, simplifying with (44), (48) gives: % 26.87/4.45 | | (65) all_46_1 = all_42_0 % 26.87/4.45 | | % 26.87/4.45 | | COMBINE_EQS: (62), (64) imply: % 26.87/4.45 | | (66) all_50_1 = all_44_0 % 26.87/4.45 | | % 26.87/4.45 | | COMBINE_EQS: (62), (63) imply: % 26.87/4.45 | | (67) all_50_1 = all_48_0 % 26.87/4.45 | | % 26.87/4.45 | | COMBINE_EQS: (66), (67) imply: % 26.87/4.45 | | (68) all_48_0 = all_44_0 % 26.87/4.45 | | % 26.87/4.45 | | SIMP: (68) implies: % 26.87/4.45 | | (69) all_48_0 = all_44_0 % 26.87/4.45 | | % 26.87/4.45 | | GROUND_INST: instantiating (5) with all_32_1, all_32_2, all_44_0, % 26.87/4.45 | | simplifying with (27), (28), (46) gives: % 26.87/4.45 | | (70) ? [v0: any] : ? [v1: any] : (equal_set(all_32_1, all_32_2) = v0 & % 26.87/4.45 | | subset(all_32_1, all_32_2) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 26.87/4.45 | | all_44_0 = 0))) % 26.87/4.45 | | % 26.87/4.45 | | GROUND_INST: instantiating (4) with all_32_2, all_32_1, all_44_0, % 26.87/4.45 | | simplifying with (27), (28), (46) gives: % 26.87/4.45 | | (71) ? [v0: any] : ? [v1: any] : (equal_set(all_32_2, all_32_1) = v0 & % 26.87/4.45 | | subset(all_32_1, all_32_2) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 26.87/4.45 | | all_44_0 = 0))) % 26.87/4.45 | | % 26.87/4.45 | | GROUND_INST: instantiating (8) with all_32_4, all_32_3, all_32_1, all_58_1, % 26.87/4.45 | | simplifying with (25), (26), (28), (59) gives: % 26.87/4.46 | | (72) all_58_1 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = % 26.87/4.46 | | v0) & apply(all_32_4, v1, v2) = 0 & apply(all_32_4, v0, v2) = 0 % 26.87/4.46 | | & member(v2, all_32_1) = 0 & member(v1, all_32_3) = 0 & member(v0, % 26.87/4.46 | | all_32_3) = 0 & $i(v2) & $i(v1) & $i(v0)) % 26.87/4.46 | | % 26.87/4.46 | | GROUND_INST: instantiating (14) with all_32_5, all_32_3, all_32_2, all_42_0, % 26.87/4.46 | | simplifying with (24), (26), (27), (44) gives: % 26.87/4.46 | | (73) ? [v0: any] : ? [v1: any] : (one_to_one(all_32_5, all_32_3, % 26.87/4.46 | | all_32_2) = v0 & injective(all_32_5, all_32_3, all_32_2) = v1 & % 26.87/4.46 | | ( ~ (v0 = 0) | (v1 = 0 & all_42_0 = 0))) % 26.87/4.46 | | % 26.87/4.46 | | GROUND_INST: instantiating (11) with all_32_4, all_32_3, all_32_1, all_58_0, % 26.87/4.46 | | simplifying with (25), (26), (28), (60) gives: % 26.87/4.46 | | (74) all_58_0 = 0 | ? [v0: $i] : (member(v0, all_32_1) = 0 & $i(v0) & ! % 26.87/4.46 | | [v1: $i] : ( ~ (apply(all_32_4, v1, v0) = 0) | ~ $i(v1) | ? [v2: % 26.87/4.46 | | int] : ( ~ (v2 = 0) & member(v1, all_32_3) = v2)) & ! [v1: % 26.87/4.46 | | $i] : ( ~ (member(v1, all_32_3) = 0) | ~ $i(v1) | ? [v2: int] % 26.87/4.46 | | : ( ~ (v2 = 0) & apply(all_32_4, v1, v0) = v2))) % 26.87/4.46 | | % 26.87/4.46 | | DELTA: instantiating (73) with fresh symbols all_69_0, all_69_1 gives: % 27.09/4.46 | | (75) one_to_one(all_32_5, all_32_3, all_32_2) = all_69_1 & % 27.09/4.46 | | injective(all_32_5, all_32_3, all_32_2) = all_69_0 & ( ~ (all_69_1 = % 27.09/4.46 | | 0) | (all_69_0 = 0 & all_42_0 = 0)) % 27.09/4.46 | | % 27.09/4.46 | | ALPHA: (75) implies: % 27.09/4.46 | | (76) injective(all_32_5, all_32_3, all_32_2) = all_69_0 % 27.09/4.46 | | % 27.09/4.46 | | DELTA: instantiating (71) with fresh symbols all_71_0, all_71_1 gives: % 27.09/4.46 | | (77) equal_set(all_32_2, all_32_1) = all_71_1 & subset(all_32_1, % 27.09/4.46 | | all_32_2) = all_71_0 & ( ~ (all_71_1 = 0) | (all_71_0 = 0 & % 27.09/4.46 | | all_44_0 = 0)) % 27.09/4.46 | | % 27.09/4.46 | | ALPHA: (77) implies: % 27.09/4.46 | | (78) subset(all_32_1, all_32_2) = all_71_0 % 27.09/4.46 | | % 27.09/4.46 | | DELTA: instantiating (70) with fresh symbols all_73_0, all_73_1 gives: % 27.09/4.46 | | (79) equal_set(all_32_1, all_32_2) = all_73_1 & subset(all_32_1, % 27.09/4.46 | | all_32_2) = all_73_0 & ( ~ (all_73_1 = 0) | (all_73_0 = 0 & % 27.09/4.46 | | all_44_0 = 0)) % 27.09/4.46 | | % 27.09/4.46 | | ALPHA: (79) implies: % 27.09/4.46 | | (80) subset(all_32_1, all_32_2) = all_73_0 % 27.09/4.46 | | % 27.09/4.46 | | GROUND_INST: instantiating (18) with 0, all_73_0, all_32_2, all_32_1, % 27.09/4.46 | | simplifying with (29), (80) gives: % 27.09/4.46 | | (81) all_73_0 = 0 % 27.09/4.46 | | % 27.09/4.46 | | GROUND_INST: instantiating (18) with all_71_0, all_73_0, all_32_2, all_32_1, % 27.09/4.46 | | simplifying with (78), (80) gives: % 27.09/4.46 | | (82) all_73_0 = all_71_0 % 27.09/4.46 | | % 27.09/4.46 | | GROUND_INST: instantiating (20) with 0, all_69_0, all_32_2, all_32_3, % 27.09/4.46 | | all_32_5, simplifying with (31), (76) gives: % 27.09/4.46 | | (83) all_69_0 = 0 % 27.09/4.46 | | % 27.09/4.46 | | COMBINE_EQS: (81), (82) imply: % 27.09/4.46 | | (84) all_71_0 = 0 % 27.09/4.46 | | % 27.09/4.46 | | BETA: splitting (61) gives: % 27.09/4.46 | | % 27.09/4.46 | | Case 1: % 27.09/4.46 | | | % 27.09/4.46 | | | (85) ~ (all_58_0 = 0) % 27.09/4.46 | | | % 27.09/4.46 | | | BETA: splitting (74) gives: % 27.09/4.46 | | | % 27.09/4.46 | | | Case 1: % 27.09/4.46 | | | | % 27.09/4.46 | | | | (86) all_58_0 = 0 % 27.09/4.46 | | | | % 27.09/4.46 | | | | REDUCE: (85), (86) imply: % 27.09/4.46 | | | | (87) $false % 27.09/4.46 | | | | % 27.09/4.46 | | | | CLOSE: (87) is inconsistent. % 27.09/4.46 | | | | % 27.09/4.46 | | | Case 2: % 27.09/4.46 | | | | % 27.09/4.46 | | | | (88) ? [v0: $i] : (member(v0, all_32_1) = 0 & $i(v0) & ! [v1: $i] : % 27.09/4.46 | | | | ( ~ (apply(all_32_4, v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : % 27.09/4.46 | | | | ( ~ (v2 = 0) & member(v1, all_32_3) = v2)) & ! [v1: $i] : ( % 27.09/4.46 | | | | ~ (member(v1, all_32_3) = 0) | ~ $i(v1) | ? [v2: int] : ( % 27.09/4.46 | | | | ~ (v2 = 0) & apply(all_32_4, v1, v0) = v2))) % 27.09/4.46 | | | | % 27.09/4.46 | | | | DELTA: instantiating (88) with fresh symbol all_115_0 gives: % 27.09/4.46 | | | | (89) member(all_115_0, all_32_1) = 0 & $i(all_115_0) & ! [v0: $i] : % 27.09/4.46 | | | | ( ~ (apply(all_32_4, v0, all_115_0) = 0) | ~ $i(v0) | ? [v1: % 27.09/4.46 | | | | int] : ( ~ (v1 = 0) & member(v0, all_32_3) = v1)) & ! [v0: % 27.09/4.46 | | | | $i] : ( ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | ? [v1: % 27.09/4.46 | | | | int] : ( ~ (v1 = 0) & apply(all_32_4, v0, all_115_0) = v1)) % 27.09/4.46 | | | | % 27.09/4.46 | | | | ALPHA: (89) implies: % 27.09/4.46 | | | | (90) $i(all_115_0) % 27.09/4.46 | | | | (91) member(all_115_0, all_32_1) = 0 % 27.09/4.46 | | | | (92) ! [v0: $i] : ( ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | ? % 27.09/4.46 | | | | [v1: int] : ( ~ (v1 = 0) & apply(all_32_4, v0, all_115_0) = % 27.09/4.46 | | | | v1)) % 27.09/4.46 | | | | % 27.09/4.46 | | | | GROUND_INST: instantiating (16) with all_32_5, all_32_3, all_115_0, % 27.09/4.46 | | | | all_32_1, simplifying with (24), (26), (33), (90), (91) % 27.09/4.46 | | | | gives: % 27.09/4.46 | | | | (93) ? [v0: $i] : (apply(all_32_5, v0, all_115_0) = 0 & member(v0, % 27.09/4.46 | | | | all_32_3) = 0 & $i(v0)) % 27.09/4.46 | | | | % 27.09/4.46 | | | | DELTA: instantiating (93) with fresh symbol all_124_0 gives: % 27.09/4.46 | | | | (94) apply(all_32_5, all_124_0, all_115_0) = 0 & member(all_124_0, % 27.09/4.46 | | | | all_32_3) = 0 & $i(all_124_0) % 27.09/4.46 | | | | % 27.09/4.46 | | | | ALPHA: (94) implies: % 27.09/4.46 | | | | (95) $i(all_124_0) % 27.09/4.46 | | | | (96) member(all_124_0, all_32_3) = 0 % 27.09/4.46 | | | | (97) apply(all_32_5, all_124_0, all_115_0) = 0 % 27.09/4.46 | | | | % 27.09/4.46 | | | | GROUND_INST: instantiating (92) with all_124_0, simplifying with (95), % 27.09/4.46 | | | | (96) gives: % 27.09/4.46 | | | | (98) ? [v0: int] : ( ~ (v0 = 0) & apply(all_32_4, all_124_0, % 27.09/4.46 | | | | all_115_0) = v0) % 27.09/4.46 | | | | % 27.09/4.46 | | | | GROUND_INST: instantiating (34) with all_124_0, all_115_0, 0, % 27.09/4.46 | | | | simplifying with (90), (95), (97) gives: % 27.09/4.46 | | | | (99) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_4, % 27.09/4.46 | | | | all_124_0, all_115_0) = v2 & member(all_124_0, all_32_3) = % 27.09/4.46 | | | | v0 & member(all_115_0, all_32_1) = v1 & ( ~ (v1 = 0) | ~ (v0 % 27.09/4.46 | | | | = 0) | v2 = 0)) % 27.09/4.46 | | | | % 27.09/4.46 | | | | DELTA: instantiating (98) with fresh symbol all_131_0 gives: % 27.09/4.46 | | | | (100) ~ (all_131_0 = 0) & apply(all_32_4, all_124_0, all_115_0) = % 27.09/4.46 | | | | all_131_0 % 27.09/4.46 | | | | % 27.09/4.46 | | | | ALPHA: (100) implies: % 27.09/4.46 | | | | (101) ~ (all_131_0 = 0) % 27.09/4.46 | | | | (102) apply(all_32_4, all_124_0, all_115_0) = all_131_0 % 27.09/4.46 | | | | % 27.09/4.46 | | | | DELTA: instantiating (99) with fresh symbols all_137_0, all_137_1, % 27.09/4.46 | | | | all_137_2 gives: % 27.09/4.46 | | | | (103) apply(all_32_4, all_124_0, all_115_0) = all_137_0 & % 27.09/4.46 | | | | member(all_124_0, all_32_3) = all_137_2 & member(all_115_0, % 27.09/4.46 | | | | all_32_1) = all_137_1 & ( ~ (all_137_1 = 0) | ~ (all_137_2 = % 27.09/4.46 | | | | 0) | all_137_0 = 0) % 27.09/4.46 | | | | % 27.09/4.46 | | | | ALPHA: (103) implies: % 27.09/4.46 | | | | (104) member(all_115_0, all_32_1) = all_137_1 % 27.09/4.46 | | | | (105) member(all_124_0, all_32_3) = all_137_2 % 27.09/4.46 | | | | (106) apply(all_32_4, all_124_0, all_115_0) = all_137_0 % 27.09/4.47 | | | | (107) ~ (all_137_1 = 0) | ~ (all_137_2 = 0) | all_137_0 = 0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | GROUND_INST: instantiating (17) with 0, all_137_1, all_32_1, all_115_0, % 27.09/4.47 | | | | simplifying with (91), (104) gives: % 27.09/4.47 | | | | (108) all_137_1 = 0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | GROUND_INST: instantiating (17) with 0, all_137_2, all_32_3, all_124_0, % 27.09/4.47 | | | | simplifying with (96), (105) gives: % 27.09/4.47 | | | | (109) all_137_2 = 0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | GROUND_INST: instantiating (19) with all_131_0, all_137_0, all_115_0, % 27.09/4.47 | | | | all_124_0, all_32_4, simplifying with (102), (106) gives: % 27.09/4.47 | | | | (110) all_137_0 = all_131_0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | BETA: splitting (107) gives: % 27.09/4.47 | | | | % 27.09/4.47 | | | | Case 1: % 27.09/4.47 | | | | | % 27.09/4.47 | | | | | (111) ~ (all_137_1 = 0) % 27.09/4.47 | | | | | % 27.09/4.47 | | | | | REDUCE: (108), (111) imply: % 27.09/4.47 | | | | | (112) $false % 27.09/4.47 | | | | | % 27.09/4.47 | | | | | CLOSE: (112) is inconsistent. % 27.09/4.47 | | | | | % 27.09/4.47 | | | | Case 2: % 27.09/4.47 | | | | | % 27.09/4.47 | | | | | (113) ~ (all_137_2 = 0) | all_137_0 = 0 % 27.09/4.47 | | | | | % 27.09/4.47 | | | | | BETA: splitting (113) gives: % 27.09/4.47 | | | | | % 27.09/4.47 | | | | | Case 1: % 27.09/4.47 | | | | | | % 27.09/4.47 | | | | | | (114) ~ (all_137_2 = 0) % 27.09/4.47 | | | | | | % 27.09/4.47 | | | | | | REDUCE: (109), (114) imply: % 27.09/4.47 | | | | | | (115) $false % 27.09/4.47 | | | | | | % 27.09/4.47 | | | | | | CLOSE: (115) is inconsistent. % 27.09/4.47 | | | | | | % 27.09/4.47 | | | | | Case 2: % 27.09/4.47 | | | | | | % 27.09/4.47 | | | | | | (116) all_137_0 = 0 % 27.09/4.47 | | | | | | % 27.09/4.47 | | | | | | COMBINE_EQS: (110), (116) imply: % 27.09/4.47 | | | | | | (117) all_131_0 = 0 % 27.09/4.47 | | | | | | % 27.09/4.47 | | | | | | REDUCE: (101), (117) imply: % 27.09/4.47 | | | | | | (118) $false % 27.09/4.47 | | | | | | % 27.09/4.47 | | | | | | CLOSE: (118) is inconsistent. % 27.09/4.47 | | | | | | % 27.09/4.47 | | | | | End of split % 27.09/4.47 | | | | | % 27.09/4.47 | | | | End of split % 27.09/4.47 | | | | % 27.09/4.47 | | | End of split % 27.09/4.47 | | | % 27.09/4.47 | | Case 2: % 27.09/4.47 | | | % 27.09/4.47 | | | (119) ~ (all_58_1 = 0) % 27.09/4.47 | | | % 27.09/4.47 | | | BETA: splitting (72) gives: % 27.09/4.47 | | | % 27.09/4.47 | | | Case 1: % 27.09/4.47 | | | | % 27.09/4.47 | | | | (120) all_58_1 = 0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | REDUCE: (119), (120) imply: % 27.09/4.47 | | | | (121) $false % 27.09/4.47 | | | | % 27.09/4.47 | | | | CLOSE: (121) is inconsistent. % 27.09/4.47 | | | | % 27.09/4.47 | | | Case 2: % 27.09/4.47 | | | | % 27.09/4.47 | | | | (122) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & % 27.09/4.47 | | | | apply(all_32_4, v1, v2) = 0 & apply(all_32_4, v0, v2) = 0 & % 27.09/4.47 | | | | member(v2, all_32_1) = 0 & member(v1, all_32_3) = 0 & % 27.09/4.47 | | | | member(v0, all_32_3) = 0 & $i(v2) & $i(v1) & $i(v0)) % 27.09/4.47 | | | | % 27.09/4.47 | | | | DELTA: instantiating (122) with fresh symbols all_115_0, all_115_1, % 27.09/4.47 | | | | all_115_2 gives: % 27.09/4.47 | | | | (123) ~ (all_115_1 = all_115_2) & apply(all_32_4, all_115_1, % 27.09/4.47 | | | | all_115_0) = 0 & apply(all_32_4, all_115_2, all_115_0) = 0 & % 27.09/4.47 | | | | member(all_115_0, all_32_1) = 0 & member(all_115_1, all_32_3) = % 27.09/4.47 | | | | 0 & member(all_115_2, all_32_3) = 0 & $i(all_115_0) & % 27.09/4.47 | | | | $i(all_115_1) & $i(all_115_2) % 27.09/4.47 | | | | % 27.09/4.47 | | | | ALPHA: (123) implies: % 27.09/4.47 | | | | (124) ~ (all_115_1 = all_115_2) % 27.09/4.47 | | | | (125) $i(all_115_2) % 27.09/4.47 | | | | (126) $i(all_115_1) % 27.09/4.47 | | | | (127) $i(all_115_0) % 27.09/4.47 | | | | (128) member(all_115_2, all_32_3) = 0 % 27.09/4.47 | | | | (129) member(all_115_1, all_32_3) = 0 % 27.09/4.47 | | | | (130) member(all_115_0, all_32_1) = 0 % 27.09/4.47 | | | | (131) apply(all_32_4, all_115_2, all_115_0) = 0 % 27.09/4.47 | | | | (132) apply(all_32_4, all_115_1, all_115_0) = 0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | GROUND_INST: instantiating (6) with all_32_5, all_32_3, all_32_2, % 27.09/4.47 | | | | all_115_2, simplifying with (24), (26), (27), (30), (125), % 27.09/4.47 | | | | (128) gives: % 27.09/4.47 | | | | (133) ? [v0: $i] : (apply(all_32_5, all_115_2, v0) = 0 & member(v0, % 27.09/4.47 | | | | all_32_2) = 0 & $i(v0)) % 27.09/4.47 | | | | % 27.09/4.47 | | | | GROUND_INST: instantiating (6) with all_32_5, all_32_3, all_32_2, % 27.09/4.47 | | | | all_115_1, simplifying with (24), (26), (27), (30), (126), % 27.09/4.47 | | | | (129) gives: % 27.09/4.47 | | | | (134) ? [v0: $i] : (apply(all_32_5, all_115_1, v0) = 0 & member(v0, % 27.09/4.47 | | | | all_32_2) = 0 & $i(v0)) % 27.09/4.47 | | | | % 27.09/4.47 | | | | GROUND_INST: instantiating (1) with all_32_1, all_32_2, all_115_0, % 27.09/4.47 | | | | simplifying with (27), (28), (29), (127), (130) gives: % 27.09/4.47 | | | | (135) member(all_115_0, all_32_2) = 0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | GROUND_INST: instantiating (35) with all_115_2, all_115_0, 0, % 27.09/4.47 | | | | simplifying with (125), (127), (131) gives: % 27.09/4.47 | | | | (136) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_5, % 27.09/4.47 | | | | all_115_2, all_115_0) = v2 & member(all_115_0, all_32_1) = % 27.09/4.47 | | | | v1 & member(all_115_2, all_32_3) = v0 & ( ~ (v1 = 0) | ~ (v0 % 27.09/4.47 | | | | = 0) | v2 = 0)) % 27.09/4.47 | | | | % 27.09/4.47 | | | | GROUND_INST: instantiating (35) with all_115_1, all_115_0, 0, % 27.09/4.47 | | | | simplifying with (126), (127), (132) gives: % 27.09/4.47 | | | | (137) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_5, % 27.09/4.47 | | | | all_115_1, all_115_0) = v2 & member(all_115_0, all_32_1) = % 27.09/4.47 | | | | v1 & member(all_115_1, all_32_3) = v0 & ( ~ (v1 = 0) | ~ (v0 % 27.09/4.47 | | | | = 0) | v2 = 0)) % 27.09/4.47 | | | | % 27.09/4.47 | | | | DELTA: instantiating (134) with fresh symbol all_125_0 gives: % 27.09/4.47 | | | | (138) apply(all_32_5, all_115_1, all_125_0) = 0 & member(all_125_0, % 27.09/4.47 | | | | all_32_2) = 0 & $i(all_125_0) % 27.09/4.47 | | | | % 27.09/4.47 | | | | ALPHA: (138) implies: % 27.09/4.47 | | | | (139) $i(all_125_0) % 27.09/4.47 | | | | (140) member(all_125_0, all_32_2) = 0 % 27.09/4.47 | | | | (141) apply(all_32_5, all_115_1, all_125_0) = 0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | DELTA: instantiating (133) with fresh symbol all_127_0 gives: % 27.09/4.47 | | | | (142) apply(all_32_5, all_115_2, all_127_0) = 0 & member(all_127_0, % 27.09/4.47 | | | | all_32_2) = 0 & $i(all_127_0) % 27.09/4.47 | | | | % 27.09/4.47 | | | | ALPHA: (142) implies: % 27.09/4.47 | | | | (143) $i(all_127_0) % 27.09/4.47 | | | | (144) member(all_127_0, all_32_2) = 0 % 27.09/4.47 | | | | (145) apply(all_32_5, all_115_2, all_127_0) = 0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | DELTA: instantiating (137) with fresh symbols all_131_0, all_131_1, % 27.09/4.47 | | | | all_131_2 gives: % 27.09/4.47 | | | | (146) apply(all_32_5, all_115_1, all_115_0) = all_131_0 & % 27.09/4.47 | | | | member(all_115_0, all_32_1) = all_131_1 & member(all_115_1, % 27.09/4.47 | | | | all_32_3) = all_131_2 & ( ~ (all_131_1 = 0) | ~ (all_131_2 = % 27.09/4.47 | | | | 0) | all_131_0 = 0) % 27.09/4.47 | | | | % 27.09/4.47 | | | | ALPHA: (146) implies: % 27.09/4.47 | | | | (147) member(all_115_1, all_32_3) = all_131_2 % 27.09/4.47 | | | | (148) member(all_115_0, all_32_1) = all_131_1 % 27.09/4.47 | | | | (149) apply(all_32_5, all_115_1, all_115_0) = all_131_0 % 27.09/4.47 | | | | (150) ~ (all_131_1 = 0) | ~ (all_131_2 = 0) | all_131_0 = 0 % 27.09/4.47 | | | | % 27.09/4.47 | | | | DELTA: instantiating (136) with fresh symbols all_133_0, all_133_1, % 27.09/4.47 | | | | all_133_2 gives: % 27.09/4.47 | | | | (151) apply(all_32_5, all_115_2, all_115_0) = all_133_0 & % 27.09/4.47 | | | | member(all_115_0, all_32_1) = all_133_1 & member(all_115_2, % 27.09/4.47 | | | | all_32_3) = all_133_2 & ( ~ (all_133_1 = 0) | ~ (all_133_2 = % 27.09/4.47 | | | | 0) | all_133_0 = 0) % 27.09/4.47 | | | | % 27.09/4.47 | | | | ALPHA: (151) implies: % 27.09/4.47 | | | | (152) member(all_115_2, all_32_3) = all_133_2 % 27.09/4.47 | | | | (153) member(all_115_0, all_32_1) = all_133_1 % 27.09/4.47 | | | | (154) apply(all_32_5, all_115_2, all_115_0) = all_133_0 % 27.09/4.47 | | | | (155) ~ (all_133_1 = 0) | ~ (all_133_2 = 0) | all_133_0 = 0 % 27.09/4.47 | | | | % 27.09/4.48 | | | | GROUND_INST: instantiating (17) with 0, all_133_2, all_32_3, all_115_2, % 27.09/4.48 | | | | simplifying with (128), (152) gives: % 27.09/4.48 | | | | (156) all_133_2 = 0 % 27.09/4.48 | | | | % 27.09/4.48 | | | | GROUND_INST: instantiating (17) with 0, all_131_2, all_32_3, all_115_1, % 27.09/4.48 | | | | simplifying with (129), (147) gives: % 27.09/4.48 | | | | (157) all_131_2 = 0 % 27.09/4.48 | | | | % 27.09/4.48 | | | | GROUND_INST: instantiating (17) with 0, all_133_1, all_32_1, all_115_0, % 27.09/4.48 | | | | simplifying with (130), (153) gives: % 27.09/4.48 | | | | (158) all_133_1 = 0 % 27.09/4.48 | | | | % 27.09/4.48 | | | | GROUND_INST: instantiating (17) with all_131_1, all_133_1, all_32_1, % 27.09/4.48 | | | | all_115_0, simplifying with (148), (153) gives: % 27.09/4.48 | | | | (159) all_133_1 = all_131_1 % 27.09/4.48 | | | | % 27.09/4.48 | | | | COMBINE_EQS: (158), (159) imply: % 27.09/4.48 | | | | (160) all_131_1 = 0 % 27.09/4.48 | | | | % 27.09/4.48 | | | | BETA: splitting (155) gives: % 27.09/4.48 | | | | % 27.09/4.48 | | | | Case 1: % 27.09/4.48 | | | | | % 27.09/4.48 | | | | | (161) ~ (all_133_1 = 0) % 27.09/4.48 | | | | | % 27.09/4.48 | | | | | REDUCE: (158), (161) imply: % 27.09/4.48 | | | | | (162) $false % 27.09/4.48 | | | | | % 27.09/4.48 | | | | | CLOSE: (162) is inconsistent. % 27.09/4.48 | | | | | % 27.09/4.48 | | | | Case 2: % 27.09/4.48 | | | | | % 27.09/4.48 | | | | | (163) ~ (all_133_2 = 0) | all_133_0 = 0 % 27.09/4.48 | | | | | % 27.09/4.48 | | | | | BETA: splitting (163) gives: % 27.09/4.48 | | | | | % 27.09/4.48 | | | | | Case 1: % 27.09/4.48 | | | | | | % 27.09/4.48 | | | | | | (164) ~ (all_133_2 = 0) % 27.09/4.48 | | | | | | % 27.09/4.48 | | | | | | REDUCE: (156), (164) imply: % 27.09/4.48 | | | | | | (165) $false % 27.09/4.48 | | | | | | % 27.09/4.48 | | | | | | CLOSE: (165) is inconsistent. % 27.09/4.48 | | | | | | % 27.09/4.48 | | | | | Case 2: % 27.09/4.48 | | | | | | % 27.09/4.48 | | | | | | (166) all_133_0 = 0 % 27.09/4.48 | | | | | | % 27.09/4.48 | | | | | | REDUCE: (154), (166) imply: % 27.09/4.48 | | | | | | (167) apply(all_32_5, all_115_2, all_115_0) = 0 % 27.09/4.48 | | | | | | % 27.09/4.48 | | | | | | BETA: splitting (150) gives: % 27.09/4.48 | | | | | | % 27.09/4.48 | | | | | | Case 1: % 27.09/4.48 | | | | | | | % 27.09/4.48 | | | | | | | (168) ~ (all_131_1 = 0) % 27.09/4.48 | | | | | | | % 27.09/4.48 | | | | | | | REDUCE: (160), (168) imply: % 27.09/4.48 | | | | | | | (169) $false % 27.09/4.48 | | | | | | | % 27.09/4.48 | | | | | | | CLOSE: (169) is inconsistent. % 27.09/4.48 | | | | | | | % 27.09/4.48 | | | | | | Case 2: % 27.09/4.48 | | | | | | | % 27.09/4.48 | | | | | | | (170) ~ (all_131_2 = 0) | all_131_0 = 0 % 27.09/4.48 | | | | | | | % 27.09/4.48 | | | | | | | BETA: splitting (170) gives: % 27.09/4.48 | | | | | | | % 27.09/4.48 | | | | | | | Case 1: % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | (171) ~ (all_131_2 = 0) % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | REDUCE: (157), (171) imply: % 27.09/4.48 | | | | | | | | (172) $false % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | CLOSE: (172) is inconsistent. % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | Case 2: % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | (173) all_131_0 = 0 % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | REDUCE: (149), (173) imply: % 27.09/4.48 | | | | | | | | (174) apply(all_32_5, all_115_1, all_115_0) = 0 % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | GROUND_INST: instantiating (7) with all_32_5, all_32_3, % 27.09/4.48 | | | | | | | | all_32_2, all_115_1, all_125_0, all_115_0, % 27.09/4.48 | | | | | | | | simplifying with (24), (26), (27), (30), (126), % 27.09/4.48 | | | | | | | | (127), (129), (135), (139), (140) gives: % 27.09/4.48 | | | | | | | | (175) all_125_0 = all_115_0 | ? [v0: any] : ? [v1: any] : % 27.09/4.48 | | | | | | | | (apply(all_32_5, all_115_1, all_125_0) = v0 & % 27.09/4.48 | | | | | | | | apply(all_32_5, all_115_1, all_115_0) = v1 & ( ~ (v1 % 27.09/4.48 | | | | | | | | = 0) | ~ (v0 = 0))) % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | GROUND_INST: instantiating (9) with all_32_5, all_32_3, % 27.09/4.48 | | | | | | | | all_32_2, all_115_2, all_115_1, all_125_0, % 27.09/4.48 | | | | | | | | simplifying with (24), (26), (27), (31), (125), % 27.09/4.48 | | | | | | | | (126), (128), (129), (139), (140) gives: % 27.09/4.48 | | | | | | | | (176) all_115_1 = all_115_2 | ? [v0: any] : ? [v1: any] : % 27.09/4.48 | | | | | | | | (apply(all_32_5, all_115_1, all_125_0) = v1 & % 27.09/4.48 | | | | | | | | apply(all_32_5, all_115_2, all_125_0) = v0 & ( ~ (v1 % 27.09/4.48 | | | | | | | | = 0) | ~ (v0 = 0))) % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | GROUND_INST: instantiating (9) with all_32_5, all_32_3, % 27.09/4.48 | | | | | | | | all_32_2, all_115_1, all_115_2, all_125_0, % 27.09/4.48 | | | | | | | | simplifying with (24), (26), (27), (31), (125), % 27.09/4.48 | | | | | | | | (126), (128), (129), (139), (140) gives: % 27.09/4.48 | | | | | | | | (177) all_115_1 = all_115_2 | ? [v0: any] : ? [v1: any] : % 27.09/4.48 | | | | | | | | (apply(all_32_5, all_115_1, all_125_0) = v0 & % 27.09/4.48 | | | | | | | | apply(all_32_5, all_115_2, all_125_0) = v1 & ( ~ (v1 % 27.09/4.48 | | | | | | | | = 0) | ~ (v0 = 0))) % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | GROUND_INST: instantiating (9) with all_32_5, all_32_3, % 27.09/4.48 | | | | | | | | all_32_2, all_115_2, all_115_1, all_127_0, % 27.09/4.48 | | | | | | | | simplifying with (24), (26), (27), (31), (125), % 27.09/4.48 | | | | | | | | (126), (128), (129), (143), (144) gives: % 27.09/4.48 | | | | | | | | (178) all_115_1 = all_115_2 | ? [v0: any] : ? [v1: any] : % 27.09/4.48 | | | | | | | | (apply(all_32_5, all_115_1, all_127_0) = v1 & % 27.09/4.48 | | | | | | | | apply(all_32_5, all_115_2, all_127_0) = v0 & ( ~ (v1 % 27.09/4.48 | | | | | | | | = 0) | ~ (v0 = 0))) % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | GROUND_INST: instantiating (10) with all_32_5, all_32_3, % 27.09/4.48 | | | | | | | | all_32_2, all_115_1, all_115_2, all_127_0, % 27.09/4.48 | | | | | | | | simplifying with (24), (26), (27), (31), (125), % 27.09/4.48 | | | | | | | | (126), (129), (143), (145) gives: % 27.09/4.48 | | | | | | | | (179) all_115_1 = all_115_2 | ? [v0: any] : ? [v1: any] : % 27.09/4.48 | | | | | | | | ? [v2: any] : (apply(all_32_5, all_115_1, all_127_0) = % 27.09/4.48 | | | | | | | | v2 & member(all_127_0, all_32_2) = v1 & % 27.09/4.48 | | | | | | | | member(all_115_2, all_32_3) = v0 & ( ~ (v2 = 0) | ~ % 27.09/4.48 | | | | | | | | (v1 = 0) | ~ (v0 = 0))) % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | BETA: splitting (175) gives: % 27.09/4.48 | | | | | | | | % 27.09/4.48 | | | | | | | | Case 1: % 27.09/4.48 | | | | | | | | | % 27.09/4.48 | | | | | | | | | (180) all_125_0 = all_115_0 % 27.09/4.48 | | | | | | | | | % 27.09/4.48 | | | | | | | | | BETA: splitting (176) gives: % 27.09/4.48 | | | | | | | | | % 27.09/4.48 | | | | | | | | | Case 1: % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | (181) all_115_1 = all_115_2 % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | REDUCE: (124), (181) imply: % 27.09/4.48 | | | | | | | | | | (182) $false % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | CLOSE: (182) is inconsistent. % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | Case 2: % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | (183) ? [v0: any] : ? [v1: any] : (apply(all_32_5, % 27.09/4.48 | | | | | | | | | | all_115_1, all_125_0) = v1 & apply(all_32_5, % 27.09/4.48 | | | | | | | | | | all_115_2, all_125_0) = v0 & ( ~ (v1 = 0) | ~ % 27.09/4.48 | | | | | | | | | | (v0 = 0))) % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | DELTA: instantiating (183) with fresh symbols all_186_0, % 27.09/4.48 | | | | | | | | | | all_186_1 gives: % 27.09/4.48 | | | | | | | | | | (184) apply(all_32_5, all_115_1, all_125_0) = all_186_0 & % 27.09/4.48 | | | | | | | | | | apply(all_32_5, all_115_2, all_125_0) = all_186_1 & % 27.09/4.48 | | | | | | | | | | ( ~ (all_186_0 = 0) | ~ (all_186_1 = 0)) % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | ALPHA: (184) implies: % 27.09/4.48 | | | | | | | | | | (185) apply(all_32_5, all_115_1, all_125_0) = all_186_0 % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | REDUCE: (180), (185) imply: % 27.09/4.48 | | | | | | | | | | (186) apply(all_32_5, all_115_1, all_115_0) = all_186_0 % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | BETA: splitting (177) gives: % 27.09/4.48 | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | Case 1: % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | (187) all_115_1 = all_115_2 % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | REDUCE: (124), (187) imply: % 27.09/4.48 | | | | | | | | | | | (188) $false % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | CLOSE: (188) is inconsistent. % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | Case 2: % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | (189) ? [v0: any] : ? [v1: any] : (apply(all_32_5, % 27.09/4.48 | | | | | | | | | | | all_115_1, all_125_0) = v0 & apply(all_32_5, % 27.09/4.48 | | | | | | | | | | | all_115_2, all_125_0) = v1 & ( ~ (v1 = 0) | ~ % 27.09/4.48 | | | | | | | | | | | (v0 = 0))) % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | DELTA: instantiating (189) with fresh symbols all_191_0, % 27.09/4.48 | | | | | | | | | | | all_191_1 gives: % 27.09/4.48 | | | | | | | | | | | (190) apply(all_32_5, all_115_1, all_125_0) = all_191_1 % 27.09/4.48 | | | | | | | | | | | & apply(all_32_5, all_115_2, all_125_0) = % 27.09/4.48 | | | | | | | | | | | all_191_0 & ( ~ (all_191_0 = 0) | ~ (all_191_1 = % 27.09/4.48 | | | | | | | | | | | 0)) % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | ALPHA: (190) implies: % 27.09/4.48 | | | | | | | | | | | (191) apply(all_32_5, all_115_2, all_125_0) = all_191_0 % 27.09/4.48 | | | | | | | | | | | (192) apply(all_32_5, all_115_1, all_125_0) = all_191_1 % 27.09/4.48 | | | | | | | | | | | (193) ~ (all_191_0 = 0) | ~ (all_191_1 = 0) % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | REDUCE: (180), (192) imply: % 27.09/4.48 | | | | | | | | | | | (194) apply(all_32_5, all_115_1, all_115_0) = all_191_1 % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | REDUCE: (180), (191) imply: % 27.09/4.48 | | | | | | | | | | | (195) apply(all_32_5, all_115_2, all_115_0) = all_191_0 % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | BETA: splitting (178) gives: % 27.09/4.48 | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | Case 1: % 27.09/4.48 | | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | | (196) all_115_1 = all_115_2 % 27.09/4.48 | | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | | REDUCE: (124), (196) imply: % 27.09/4.48 | | | | | | | | | | | | (197) $false % 27.09/4.48 | | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | | CLOSE: (197) is inconsistent. % 27.09/4.48 | | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | Case 2: % 27.09/4.48 | | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | | % 27.09/4.48 | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_191_0, all_115_0, % 27.09/4.48 | | | | | | | | | | | | all_115_2, all_32_5, simplifying with (167), (195) % 27.09/4.48 | | | | | | | | | | | | gives: % 27.09/4.49 | | | | | | | | | | | | (198) all_191_0 = 0 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_191_1, all_115_0, % 27.09/4.49 | | | | | | | | | | | | all_115_1, all_32_5, simplifying with (174), (194) % 27.09/4.49 | | | | | | | | | | | | gives: % 27.09/4.49 | | | | | | | | | | | | (199) all_191_1 = 0 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_186_0, all_191_1, % 27.09/4.49 | | | | | | | | | | | | all_115_0, all_115_1, all_32_5, simplifying with % 27.09/4.49 | | | | | | | | | | | | (186), (194) gives: % 27.09/4.49 | | | | | | | | | | | | (200) all_191_1 = all_186_0 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | COMBINE_EQS: (199), (200) imply: % 27.09/4.49 | | | | | | | | | | | | (201) all_186_0 = 0 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | BETA: splitting (193) gives: % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | Case 1: % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | (202) ~ (all_191_0 = 0) % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | REDUCE: (198), (202) imply: % 27.09/4.49 | | | | | | | | | | | | | (203) $false % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | CLOSE: (203) is inconsistent. % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | Case 2: % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | (204) ~ (all_191_1 = 0) % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | REDUCE: (199), (204) imply: % 27.09/4.49 | | | | | | | | | | | | | (205) $false % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | End of split % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | End of split % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | End of split % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | End of split % 27.09/4.49 | | | | | | | | | % 27.09/4.49 | | | | | | | | Case 2: % 27.09/4.49 | | | | | | | | | % 27.09/4.49 | | | | | | | | | (206) ? [v0: any] : ? [v1: any] : (apply(all_32_5, % 27.09/4.49 | | | | | | | | | all_115_1, all_125_0) = v0 & apply(all_32_5, % 27.09/4.49 | | | | | | | | | all_115_1, all_115_0) = v1 & ( ~ (v1 = 0) | ~ % 27.09/4.49 | | | | | | | | | (v0 = 0))) % 27.09/4.49 | | | | | | | | | % 27.09/4.49 | | | | | | | | | DELTA: instantiating (206) with fresh symbols all_183_0, % 27.09/4.49 | | | | | | | | | all_183_1 gives: % 27.09/4.49 | | | | | | | | | (207) apply(all_32_5, all_115_1, all_125_0) = all_183_1 & % 27.09/4.49 | | | | | | | | | apply(all_32_5, all_115_1, all_115_0) = all_183_0 & ( % 27.09/4.49 | | | | | | | | | ~ (all_183_0 = 0) | ~ (all_183_1 = 0)) % 27.09/4.49 | | | | | | | | | % 27.09/4.49 | | | | | | | | | ALPHA: (207) implies: % 27.09/4.49 | | | | | | | | | (208) apply(all_32_5, all_115_1, all_115_0) = all_183_0 % 27.09/4.49 | | | | | | | | | (209) apply(all_32_5, all_115_1, all_125_0) = all_183_1 % 27.09/4.49 | | | | | | | | | (210) ~ (all_183_0 = 0) | ~ (all_183_1 = 0) % 27.09/4.49 | | | | | | | | | % 27.09/4.49 | | | | | | | | | BETA: splitting (176) gives: % 27.09/4.49 | | | | | | | | | % 27.09/4.49 | | | | | | | | | Case 1: % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | (211) all_115_1 = all_115_2 % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | REDUCE: (124), (211) imply: % 27.09/4.49 | | | | | | | | | | (212) $false % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | CLOSE: (212) is inconsistent. % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | Case 2: % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | (213) ? [v0: any] : ? [v1: any] : (apply(all_32_5, % 27.09/4.49 | | | | | | | | | | all_115_1, all_125_0) = v1 & apply(all_32_5, % 27.09/4.49 | | | | | | | | | | all_115_2, all_125_0) = v0 & ( ~ (v1 = 0) | ~ % 27.09/4.49 | | | | | | | | | | (v0 = 0))) % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | DELTA: instantiating (213) with fresh symbols all_188_0, % 27.09/4.49 | | | | | | | | | | all_188_1 gives: % 27.09/4.49 | | | | | | | | | | (214) apply(all_32_5, all_115_1, all_125_0) = all_188_0 & % 27.09/4.49 | | | | | | | | | | apply(all_32_5, all_115_2, all_125_0) = all_188_1 & % 27.09/4.49 | | | | | | | | | | ( ~ (all_188_0 = 0) | ~ (all_188_1 = 0)) % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | ALPHA: (214) implies: % 27.09/4.49 | | | | | | | | | | (215) apply(all_32_5, all_115_1, all_125_0) = all_188_0 % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | BETA: splitting (177) gives: % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | Case 1: % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | (216) all_115_1 = all_115_2 % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | REDUCE: (124), (216) imply: % 27.09/4.49 | | | | | | | | | | | (217) $false % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | CLOSE: (217) is inconsistent. % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | Case 2: % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | (218) ? [v0: any] : ? [v1: any] : (apply(all_32_5, % 27.09/4.49 | | | | | | | | | | | all_115_1, all_125_0) = v0 & apply(all_32_5, % 27.09/4.49 | | | | | | | | | | | all_115_2, all_125_0) = v1 & ( ~ (v1 = 0) | ~ % 27.09/4.49 | | | | | | | | | | | (v0 = 0))) % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | DELTA: instantiating (218) with fresh symbols all_193_0, % 27.09/4.49 | | | | | | | | | | | all_193_1 gives: % 27.09/4.49 | | | | | | | | | | | (219) apply(all_32_5, all_115_1, all_125_0) = all_193_1 % 27.09/4.49 | | | | | | | | | | | & apply(all_32_5, all_115_2, all_125_0) = % 27.09/4.49 | | | | | | | | | | | all_193_0 & ( ~ (all_193_0 = 0) | ~ (all_193_1 = % 27.09/4.49 | | | | | | | | | | | 0)) % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | ALPHA: (219) implies: % 27.09/4.49 | | | | | | | | | | | (220) apply(all_32_5, all_115_1, all_125_0) = all_193_1 % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | BETA: splitting (179) gives: % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | Case 1: % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | (221) all_115_1 = all_115_2 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | REDUCE: (124), (221) imply: % 27.09/4.49 | | | | | | | | | | | | (222) $false % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | Case 2: % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_183_0, all_115_0, % 27.09/4.49 | | | | | | | | | | | | all_115_1, all_32_5, simplifying with (174), (208) % 27.09/4.49 | | | | | | | | | | | | gives: % 27.09/4.49 | | | | | | | | | | | | (223) all_183_0 = 0 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_188_0, all_125_0, % 27.09/4.49 | | | | | | | | | | | | all_115_1, all_32_5, simplifying with (141), (215) % 27.09/4.49 | | | | | | | | | | | | gives: % 27.09/4.49 | | | | | | | | | | | | (224) all_188_0 = 0 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_188_0, all_193_1, % 27.09/4.49 | | | | | | | | | | | | all_125_0, all_115_1, all_32_5, simplifying with % 27.09/4.49 | | | | | | | | | | | | (215), (220) gives: % 27.09/4.49 | | | | | | | | | | | | (225) all_193_1 = all_188_0 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_183_1, all_193_1, % 27.09/4.49 | | | | | | | | | | | | all_125_0, all_115_1, all_32_5, simplifying with % 27.09/4.49 | | | | | | | | | | | | (209), (220) gives: % 27.09/4.49 | | | | | | | | | | | | (226) all_193_1 = all_183_1 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | COMBINE_EQS: (225), (226) imply: % 27.09/4.49 | | | | | | | | | | | | (227) all_188_0 = all_183_1 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | SIMP: (227) implies: % 27.09/4.49 | | | | | | | | | | | | (228) all_188_0 = all_183_1 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | COMBINE_EQS: (224), (228) imply: % 27.09/4.49 | | | | | | | | | | | | (229) all_183_1 = 0 % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | BETA: splitting (210) gives: % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | Case 1: % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | (230) ~ (all_183_0 = 0) % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | REDUCE: (223), (230) imply: % 27.09/4.49 | | | | | | | | | | | | | (231) $false % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | CLOSE: (231) is inconsistent. % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | Case 2: % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | (232) ~ (all_183_1 = 0) % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | REDUCE: (229), (232) imply: % 27.09/4.49 | | | | | | | | | | | | | (233) $false % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | | CLOSE: (233) is inconsistent. % 27.09/4.49 | | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | | End of split % 27.09/4.49 | | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | | End of split % 27.09/4.49 | | | | | | | | | | | % 27.09/4.49 | | | | | | | | | | End of split % 27.09/4.49 | | | | | | | | | | % 27.09/4.49 | | | | | | | | | End of split % 27.09/4.49 | | | | | | | | | % 27.09/4.49 | | | | | | | | End of split % 27.09/4.49 | | | | | | | | % 27.09/4.49 | | | | | | | End of split % 27.09/4.49 | | | | | | | % 27.09/4.49 | | | | | | End of split % 27.09/4.49 | | | | | | % 27.09/4.49 | | | | | End of split % 27.09/4.49 | | | | | % 27.09/4.49 | | | | End of split % 27.09/4.49 | | | | % 27.09/4.49 | | | End of split % 27.09/4.49 | | | % 27.09/4.49 | | End of split % 27.09/4.49 | | % 27.09/4.49 | End of split % 27.09/4.49 | % 27.09/4.49 End of proof % 27.09/4.49 % SZS output end Proof for theBenchmark % 27.09/4.49 % 27.09/4.49 3893ms %------------------------------------------------------------------------------