%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET693+4 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 15:26:01 EDT 2023 % Result : Theorem 8.77s 1.90s % Output : Proof 12.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET693+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n004.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 15:33:52 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.05/1.00 Prover 1: Preprocessing ... % 2.05/1.00 Prover 4: Preprocessing ... % 2.67/1.04 Prover 5: Preprocessing ... % 2.67/1.04 Prover 6: Preprocessing ... % 2.67/1.04 Prover 2: Preprocessing ... % 2.67/1.04 Prover 0: Preprocessing ... % 2.67/1.04 Prover 3: Preprocessing ... % 4.19/1.42 Prover 5: Proving ... % 4.19/1.43 Prover 1: Constructing countermodel ... % 5.04/1.44 Prover 4: Constructing countermodel ... % 5.04/1.45 Prover 6: Proving ... % 5.04/1.46 Prover 2: Proving ... % 5.04/1.47 Prover 3: Constructing countermodel ... % 5.04/1.49 Prover 0: Proving ... % 6.82/1.62 Prover 3: gave up % 7.03/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.03/1.65 Prover 7: Preprocessing ... % 7.03/1.66 Prover 1: gave up % 7.03/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.03/1.71 Prover 8: Preprocessing ... % 7.03/1.71 Prover 7: Warning: ignoring some quantifiers % 7.75/1.73 Prover 7: Constructing countermodel ... % 8.24/1.81 Prover 7: gave up % 8.24/1.83 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.24/1.85 Prover 8: Warning: ignoring some quantifiers % 8.73/1.87 Prover 9: Preprocessing ... % 8.77/1.87 Prover 8: Constructing countermodel ... % 8.77/1.89 Prover 6: proved (1257ms) % 8.77/1.90 % 8.77/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.77/1.90 % 8.77/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.77/1.90 Prover 5: stopped % 8.77/1.90 Prover 0: stopped % 8.77/1.90 Prover 2: stopped % 8.77/1.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.77/1.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.02/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.02/1.92 Prover 16: Preprocessing ... % 9.02/1.93 Prover 10: Preprocessing ... % 9.02/1.96 Prover 13: Preprocessing ... % 9.02/1.96 Prover 11: Preprocessing ... % 9.29/2.03 Prover 10: Warning: ignoring some quantifiers % 9.29/2.04 Prover 16: Warning: ignoring some quantifiers % 9.29/2.06 Prover 10: Constructing countermodel ... % 9.29/2.07 Prover 16: Constructing countermodel ... % 9.29/2.11 Prover 13: Warning: ignoring some quantifiers % 10.38/2.12 Prover 9: Constructing countermodel ... % 10.38/2.13 Prover 9: stopped % 10.38/2.13 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.38/2.13 Prover 13: Constructing countermodel ... % 10.38/2.14 Prover 19: Preprocessing ... % 10.38/2.15 Prover 11: Constructing countermodel ... % 10.38/2.15 Prover 10: gave up % 10.85/2.19 Prover 8: gave up % 10.85/2.25 Prover 19: Warning: ignoring some quantifiers % 11.36/2.27 Prover 19: Constructing countermodel ... % 11.47/2.30 Prover 4: Found proof (size 119) % 11.47/2.30 Prover 4: proved (1667ms) % 11.47/2.30 Prover 11: stopped % 11.47/2.30 Prover 19: stopped % 11.47/2.30 Prover 13: stopped % 11.47/2.31 Prover 16: stopped % 11.47/2.31 % 11.47/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.47/2.31 % 11.70/2.32 % SZS output start Proof for theBenchmark % 11.70/2.33 Assumptions after simplification: % 11.70/2.33 --------------------------------- % 11.70/2.33 % 11.70/2.33 (equal_set) % 11.79/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 11.79/2.36 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 11.79/2.36 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 11.79/2.36 $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | ~ $i(v1) | % 11.79/2.36 ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & % 11.79/2.36 subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : % 11.79/2.36 ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 11.79/2.36 | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = % 11.79/2.36 v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 11.79/2.36 (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v0) = 0 & % 11.79/2.36 subset(v0, v1) = 0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) = % 11.79/2.36 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, % 11.79/2.36 v1) = v3 & subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] % 11.79/2.36 : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 11.79/2.36 any] : ? [v3: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = v2 & ( ~ % 11.79/2.36 (v2 = 0) | v3 = 0))) % 11.79/2.36 % 11.79/2.36 (subset) % 11.79/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.79/2.36 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 11.79/2.36 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 11.79/2.36 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 11.79/2.36 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 11.79/2.36 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 11.79/2.36 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 11.79/2.36 ~ $i(v0) | member(v2, v1) = 0) % 11.79/2.36 % 11.79/2.36 (thI20) % 11.79/2.37 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 11.79/2.37 (union(v0, v1) = v2 & equal_set(v0, v2) = v3 & subset(v1, v0) = v4 & $i(v2) & % 11.79/2.37 $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 11.79/2.37 % 11.79/2.37 (union) % 11.79/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 11.79/2.37 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 11.79/2.37 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 11.79/2.37 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 11.79/2.37 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 11.79/2.37 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 11.79/2.37 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 11.79/2.37 % 11.79/2.37 (function-axioms) % 11.79/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.79/2.37 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 11.79/2.37 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.79/2.37 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 11.79/2.37 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 11.79/2.37 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.79/2.37 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 11.79/2.37 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.79/2.37 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 11.79/2.37 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.79/2.37 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 11.79/2.37 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.79/2.38 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.79/2.38 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 11.79/2.38 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 11.79/2.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 11.79/2.38 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 11.79/2.38 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 11.79/2.38 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 11.79/2.38 (power_set(v2) = v0)) % 11.79/2.38 % 11.79/2.38 Further assumptions not needed in the proof: % 11.79/2.38 -------------------------------------------- % 11.79/2.38 difference, empty_set, intersection, power_set, product, singleton, sum, % 11.79/2.38 unordered_pair % 11.79/2.38 % 11.79/2.38 Those formulas are unsatisfiable: % 11.79/2.38 --------------------------------- % 11.79/2.38 % 11.79/2.38 Begin of proof % 11.79/2.38 | % 11.79/2.38 | ALPHA: (subset) implies: % 11.79/2.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 11.79/2.38 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 11.79/2.38 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 11.79/2.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.79/2.38 | (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ % 11.79/2.38 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = % 11.79/2.38 | v4)) % 11.79/2.38 | % 11.79/2.38 | ALPHA: (equal_set) implies: % 11.79/2.38 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 11.79/2.38 | $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, v1) = v3 & % 11.79/2.38 | subset(v1, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 11.79/2.38 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | % 11.79/2.38 | ~ $i(v0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 11.79/2.38 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | % 11.79/2.38 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, % 11.79/2.38 | v1) = v3 & subset(v1, v0) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = % 11.79/2.38 | 0)))) % 11.79/2.38 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | % 11.79/2.38 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, % 11.79/2.38 | v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = % 11.79/2.38 | 0)))) % 11.79/2.38 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 11.79/2.38 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 11.79/2.38 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 11.79/2.38 | 0)))) % 11.79/2.38 | % 11.79/2.38 | ALPHA: (union) implies: % 11.79/2.39 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 11.79/2.39 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 11.79/2.39 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 11.79/2.39 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 11.79/2.39 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 11.79/2.39 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 11.79/2.39 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 11.79/2.39 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 11.79/2.39 | v5)) % 11.79/2.39 | % 11.79/2.39 | ALPHA: (function-axioms) implies: % 11.79/2.39 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 11.79/2.39 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 11.79/2.39 | v2) = v0)) % 11.79/2.39 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 11.79/2.39 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 11.79/2.39 | v2) = v0)) % 11.79/2.39 | % 11.79/2.39 | DELTA: instantiating (thI20) with fresh symbols all_15_0, all_15_1, all_15_2, % 11.79/2.39 | all_15_3, all_15_4 gives: % 11.79/2.39 | (12) union(all_15_4, all_15_3) = all_15_2 & equal_set(all_15_4, all_15_2) = % 11.79/2.39 | all_15_1 & subset(all_15_3, all_15_4) = all_15_0 & $i(all_15_2) & % 11.79/2.39 | $i(all_15_3) & $i(all_15_4) & ((all_15_0 = 0 & ~ (all_15_1 = 0)) | % 11.79/2.39 | (all_15_1 = 0 & ~ (all_15_0 = 0))) % 11.79/2.39 | % 11.79/2.39 | ALPHA: (12) implies: % 11.79/2.39 | (13) $i(all_15_4) % 11.79/2.39 | (14) $i(all_15_3) % 11.79/2.39 | (15) $i(all_15_2) % 11.79/2.39 | (16) subset(all_15_3, all_15_4) = all_15_0 % 11.79/2.39 | (17) equal_set(all_15_4, all_15_2) = all_15_1 % 11.79/2.39 | (18) union(all_15_4, all_15_3) = all_15_2 % 11.79/2.39 | (19) (all_15_0 = 0 & ~ (all_15_1 = 0)) | (all_15_1 = 0 & ~ (all_15_0 = % 11.79/2.39 | 0)) % 11.79/2.39 | % 11.79/2.39 | GROUND_INST: instantiating (1) with all_15_3, all_15_4, all_15_0, simplifying % 11.79/2.39 | with (13), (14), (16) gives: % 11.79/2.39 | (20) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.79/2.39 | all_15_3) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 11.79/2.39 | % 11.79/2.39 | GROUND_INST: instantiating (6) with all_15_4, all_15_3, all_15_0, simplifying % 11.79/2.39 | with (13), (14), (16) gives: % 11.79/2.39 | (21) ? [v0: any] : ? [v1: any] : (equal_set(all_15_4, all_15_3) = v0 & % 11.79/2.39 | subset(all_15_4, all_15_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_0 % 11.79/2.39 | = 0))) % 11.79/2.39 | % 11.79/2.39 | GROUND_INST: instantiating (5) with all_15_3, all_15_4, all_15_0, simplifying % 11.79/2.39 | with (13), (14), (16) gives: % 11.79/2.39 | (22) ? [v0: any] : ? [v1: any] : (equal_set(all_15_3, all_15_4) = v0 & % 11.79/2.39 | subset(all_15_4, all_15_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_0 % 11.79/2.39 | = 0))) % 11.79/2.39 | % 11.79/2.39 | GROUND_INST: instantiating (7) with all_15_4, all_15_2, all_15_1, simplifying % 11.79/2.39 | with (13), (15), (17) gives: % 11.79/2.40 | (23) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_2, % 11.79/2.40 | all_15_4) = v1 & subset(all_15_4, all_15_2) = v0 & ( ~ (v1 = 0) | % 11.79/2.40 | ~ (v0 = 0))) % 11.79/2.40 | % 11.79/2.40 | DELTA: instantiating (22) with fresh symbols all_22_0, all_22_1 gives: % 11.79/2.40 | (24) equal_set(all_15_3, all_15_4) = all_22_1 & subset(all_15_4, all_15_3) % 11.79/2.40 | = all_22_0 & ( ~ (all_22_1 = 0) | (all_22_0 = 0 & all_15_0 = 0)) % 11.79/2.40 | % 11.79/2.40 | ALPHA: (24) implies: % 11.79/2.40 | (25) subset(all_15_4, all_15_3) = all_22_0 % 11.79/2.40 | % 11.79/2.40 | DELTA: instantiating (21) with fresh symbols all_24_0, all_24_1 gives: % 11.79/2.40 | (26) equal_set(all_15_4, all_15_3) = all_24_1 & subset(all_15_4, all_15_3) % 11.79/2.40 | = all_24_0 & ( ~ (all_24_1 = 0) | (all_24_0 = 0 & all_15_0 = 0)) % 11.79/2.40 | % 11.79/2.40 | ALPHA: (26) implies: % 11.79/2.40 | (27) subset(all_15_4, all_15_3) = all_24_0 % 11.79/2.40 | % 11.79/2.40 | GROUND_INST: instantiating (11) with all_22_0, all_24_0, all_15_3, all_15_4, % 11.79/2.40 | simplifying with (25), (27) gives: % 11.79/2.40 | (28) all_24_0 = all_22_0 % 11.79/2.40 | % 11.79/2.40 | GROUND_INST: instantiating (6) with all_15_3, all_15_4, all_22_0, simplifying % 11.79/2.40 | with (13), (14), (25) gives: % 11.79/2.40 | (29) ? [v0: any] : ? [v1: any] : (equal_set(all_15_3, all_15_4) = v0 & % 11.79/2.40 | subset(all_15_3, all_15_4) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_22_0 % 11.79/2.40 | = 0))) % 11.79/2.40 | % 11.79/2.40 | GROUND_INST: instantiating (5) with all_15_4, all_15_3, all_22_0, simplifying % 11.79/2.40 | with (13), (14), (25) gives: % 11.79/2.40 | (30) ? [v0: any] : ? [v1: any] : (equal_set(all_15_4, all_15_3) = v0 & % 11.79/2.40 | subset(all_15_3, all_15_4) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_22_0 % 11.79/2.40 | = 0))) % 11.79/2.40 | % 11.79/2.40 | DELTA: instantiating (30) with fresh symbols all_35_0, all_35_1 gives: % 11.79/2.40 | (31) equal_set(all_15_4, all_15_3) = all_35_1 & subset(all_15_3, all_15_4) % 11.79/2.40 | = all_35_0 & ( ~ (all_35_1 = 0) | (all_35_0 = 0 & all_22_0 = 0)) % 11.79/2.40 | % 11.79/2.40 | ALPHA: (31) implies: % 11.79/2.40 | (32) subset(all_15_3, all_15_4) = all_35_0 % 11.79/2.40 | % 11.79/2.40 | DELTA: instantiating (29) with fresh symbols all_37_0, all_37_1 gives: % 11.79/2.40 | (33) equal_set(all_15_3, all_15_4) = all_37_1 & subset(all_15_3, all_15_4) % 11.79/2.40 | = all_37_0 & ( ~ (all_37_1 = 0) | (all_37_0 = 0 & all_22_0 = 0)) % 11.79/2.40 | % 11.79/2.40 | ALPHA: (33) implies: % 11.79/2.40 | (34) subset(all_15_3, all_15_4) = all_37_0 % 11.79/2.40 | % 11.79/2.40 | GROUND_INST: instantiating (11) with all_15_0, all_37_0, all_15_4, all_15_3, % 11.79/2.40 | simplifying with (16), (34) gives: % 11.79/2.40 | (35) all_37_0 = all_15_0 % 11.79/2.40 | % 11.79/2.40 | GROUND_INST: instantiating (11) with all_35_0, all_37_0, all_15_4, all_15_3, % 11.79/2.40 | simplifying with (32), (34) gives: % 11.79/2.40 | (36) all_37_0 = all_35_0 % 11.79/2.40 | % 11.79/2.40 | COMBINE_EQS: (35), (36) imply: % 11.79/2.40 | (37) all_35_0 = all_15_0 % 11.79/2.40 | % 11.79/2.40 | BETA: splitting (19) gives: % 11.79/2.40 | % 11.79/2.40 | Case 1: % 11.79/2.40 | | % 11.79/2.40 | | (38) all_15_0 = 0 & ~ (all_15_1 = 0) % 11.79/2.40 | | % 11.79/2.40 | | ALPHA: (38) implies: % 11.79/2.40 | | (39) all_15_0 = 0 % 11.79/2.40 | | (40) ~ (all_15_1 = 0) % 11.79/2.40 | | % 11.79/2.40 | | REDUCE: (16), (39) imply: % 11.79/2.40 | | (41) subset(all_15_3, all_15_4) = 0 % 11.79/2.40 | | % 11.79/2.40 | | BETA: splitting (23) gives: % 11.79/2.40 | | % 11.79/2.40 | | Case 1: % 11.79/2.40 | | | % 11.79/2.40 | | | (42) all_15_1 = 0 % 11.79/2.40 | | | % 11.79/2.40 | | | REDUCE: (40), (42) imply: % 11.79/2.40 | | | (43) $false % 11.79/2.40 | | | % 11.79/2.40 | | | CLOSE: (43) is inconsistent. % 11.79/2.40 | | | % 11.79/2.40 | | Case 2: % 11.79/2.40 | | | % 11.79/2.41 | | | (44) ? [v0: any] : ? [v1: any] : (subset(all_15_2, all_15_4) = v1 & % 11.79/2.41 | | | subset(all_15_4, all_15_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 11.79/2.41 | | | % 11.79/2.41 | | | DELTA: instantiating (44) with fresh symbols all_54_0, all_54_1 gives: % 11.79/2.41 | | | (45) subset(all_15_2, all_15_4) = all_54_0 & subset(all_15_4, all_15_2) % 11.79/2.41 | | | = all_54_1 & ( ~ (all_54_0 = 0) | ~ (all_54_1 = 0)) % 11.79/2.41 | | | % 11.79/2.41 | | | ALPHA: (45) implies: % 11.79/2.41 | | | (46) subset(all_15_4, all_15_2) = all_54_1 % 11.79/2.41 | | | (47) subset(all_15_2, all_15_4) = all_54_0 % 11.79/2.41 | | | (48) ~ (all_54_0 = 0) | ~ (all_54_1 = 0) % 11.79/2.41 | | | % 11.79/2.41 | | | GROUND_INST: instantiating (1) with all_15_4, all_15_2, all_54_1, % 11.79/2.41 | | | simplifying with (13), (15), (46) gives: % 11.79/2.41 | | | (49) all_54_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 11.79/2.41 | | | member(v0, all_15_2) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 11.79/2.41 | | | % 11.79/2.41 | | | GROUND_INST: instantiating (1) with all_15_2, all_15_4, all_54_0, % 11.79/2.41 | | | simplifying with (13), (15), (47) gives: % 11.79/2.41 | | | (50) all_54_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 11.79/2.41 | | | member(v0, all_15_2) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 11.79/2.41 | | | % 11.79/2.41 | | | BETA: splitting (48) gives: % 11.79/2.41 | | | % 11.79/2.41 | | | Case 1: % 11.79/2.41 | | | | % 11.79/2.41 | | | | (51) ~ (all_54_0 = 0) % 11.79/2.41 | | | | % 11.79/2.41 | | | | BETA: splitting (50) gives: % 11.79/2.41 | | | | % 11.79/2.41 | | | | Case 1: % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | (52) all_54_0 = 0 % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | REDUCE: (51), (52) imply: % 11.79/2.41 | | | | | (53) $false % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | CLOSE: (53) is inconsistent. % 11.79/2.41 | | | | | % 11.79/2.41 | | | | Case 2: % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | (54) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.79/2.41 | | | | | all_15_2) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | DELTA: instantiating (54) with fresh symbols all_125_0, all_125_1 % 11.79/2.41 | | | | | gives: % 11.79/2.41 | | | | | (55) ~ (all_125_0 = 0) & member(all_125_1, all_15_2) = 0 & % 11.79/2.41 | | | | | member(all_125_1, all_15_4) = all_125_0 & $i(all_125_1) % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | ALPHA: (55) implies: % 11.79/2.41 | | | | | (56) ~ (all_125_0 = 0) % 11.79/2.41 | | | | | (57) $i(all_125_1) % 11.79/2.41 | | | | | (58) member(all_125_1, all_15_4) = all_125_0 % 11.79/2.41 | | | | | (59) member(all_125_1, all_15_2) = 0 % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | GROUND_INST: instantiating (2) with all_15_3, all_15_4, all_125_1, % 11.79/2.41 | | | | | all_125_0, simplifying with (13), (14), (41), (57), (58) % 11.79/2.41 | | | | | gives: % 11.79/2.41 | | | | | (60) all_125_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 11.79/2.41 | | | | | member(all_125_1, all_15_3) = v0) % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | GROUND_INST: instantiating (8) with all_125_1, all_15_4, all_15_3, % 11.79/2.41 | | | | | all_15_2, simplifying with (13), (14), (18), (57), (59) % 11.79/2.41 | | | | | gives: % 11.79/2.41 | | | | | (61) ? [v0: any] : ? [v1: any] : (member(all_125_1, all_15_3) = % 11.79/2.41 | | | | | v1 & member(all_125_1, all_15_4) = v0 & (v1 = 0 | v0 = 0)) % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | DELTA: instantiating (61) with fresh symbols all_142_0, all_142_1 % 11.79/2.41 | | | | | gives: % 11.79/2.41 | | | | | (62) member(all_125_1, all_15_3) = all_142_0 & member(all_125_1, % 11.79/2.41 | | | | | all_15_4) = all_142_1 & (all_142_0 = 0 | all_142_1 = 0) % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | ALPHA: (62) implies: % 11.79/2.41 | | | | | (63) member(all_125_1, all_15_4) = all_142_1 % 11.79/2.41 | | | | | (64) member(all_125_1, all_15_3) = all_142_0 % 11.79/2.41 | | | | | (65) all_142_0 = 0 | all_142_1 = 0 % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | BETA: splitting (60) gives: % 11.79/2.41 | | | | | % 11.79/2.41 | | | | | Case 1: % 11.79/2.41 | | | | | | % 11.79/2.41 | | | | | | (66) all_125_0 = 0 % 11.79/2.41 | | | | | | % 11.79/2.41 | | | | | | REDUCE: (56), (66) imply: % 11.79/2.41 | | | | | | (67) $false % 12.22/2.41 | | | | | | % 12.22/2.41 | | | | | | CLOSE: (67) is inconsistent. % 12.22/2.41 | | | | | | % 12.22/2.41 | | | | | Case 2: % 12.22/2.41 | | | | | | % 12.22/2.42 | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & member(all_125_1, all_15_3) = % 12.22/2.42 | | | | | | v0) % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | DELTA: instantiating (68) with fresh symbol all_148_0 gives: % 12.22/2.42 | | | | | | (69) ~ (all_148_0 = 0) & member(all_125_1, all_15_3) = all_148_0 % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | ALPHA: (69) implies: % 12.22/2.42 | | | | | | (70) ~ (all_148_0 = 0) % 12.22/2.42 | | | | | | (71) member(all_125_1, all_15_3) = all_148_0 % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | GROUND_INST: instantiating (10) with all_125_0, all_142_1, all_15_4, % 12.22/2.42 | | | | | | all_125_1, simplifying with (58), (63) gives: % 12.22/2.42 | | | | | | (72) all_142_1 = all_125_0 % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | GROUND_INST: instantiating (10) with all_142_0, all_148_0, all_15_3, % 12.22/2.42 | | | | | | all_125_1, simplifying with (64), (71) gives: % 12.22/2.42 | | | | | | (73) all_148_0 = all_142_0 % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | REDUCE: (70), (73) imply: % 12.22/2.42 | | | | | | (74) ~ (all_142_0 = 0) % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | BETA: splitting (65) gives: % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | Case 1: % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | | (75) all_142_0 = 0 % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | | REDUCE: (74), (75) imply: % 12.22/2.42 | | | | | | | (76) $false % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | | CLOSE: (76) is inconsistent. % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | Case 2: % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | | (77) all_142_1 = 0 % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | | COMBINE_EQS: (72), (77) imply: % 12.22/2.42 | | | | | | | (78) all_125_0 = 0 % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | | SIMP: (78) implies: % 12.22/2.42 | | | | | | | (79) all_125_0 = 0 % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | | REDUCE: (56), (79) imply: % 12.22/2.42 | | | | | | | (80) $false % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | | CLOSE: (80) is inconsistent. % 12.22/2.42 | | | | | | | % 12.22/2.42 | | | | | | End of split % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | End of split % 12.22/2.42 | | | | | % 12.22/2.42 | | | | End of split % 12.22/2.42 | | | | % 12.22/2.42 | | | Case 2: % 12.22/2.42 | | | | % 12.22/2.42 | | | | (81) ~ (all_54_1 = 0) % 12.22/2.42 | | | | % 12.22/2.42 | | | | BETA: splitting (49) gives: % 12.22/2.42 | | | | % 12.22/2.42 | | | | Case 1: % 12.22/2.42 | | | | | % 12.22/2.42 | | | | | (82) all_54_1 = 0 % 12.22/2.42 | | | | | % 12.22/2.42 | | | | | REDUCE: (81), (82) imply: % 12.22/2.42 | | | | | (83) $false % 12.22/2.42 | | | | | % 12.22/2.42 | | | | | CLOSE: (83) is inconsistent. % 12.22/2.42 | | | | | % 12.22/2.42 | | | | Case 2: % 12.22/2.42 | | | | | % 12.22/2.42 | | | | | (84) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 12.22/2.42 | | | | | all_15_2) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 12.22/2.42 | | | | | % 12.22/2.42 | | | | | DELTA: instantiating (84) with fresh symbols all_125_0, all_125_1 % 12.22/2.42 | | | | | gives: % 12.22/2.42 | | | | | (85) ~ (all_125_0 = 0) & member(all_125_1, all_15_2) = all_125_0 & % 12.22/2.42 | | | | | member(all_125_1, all_15_4) = 0 & $i(all_125_1) % 12.22/2.42 | | | | | % 12.22/2.42 | | | | | ALPHA: (85) implies: % 12.22/2.42 | | | | | (86) ~ (all_125_0 = 0) % 12.22/2.42 | | | | | (87) $i(all_125_1) % 12.22/2.42 | | | | | (88) member(all_125_1, all_15_4) = 0 % 12.22/2.42 | | | | | (89) member(all_125_1, all_15_2) = all_125_0 % 12.22/2.42 | | | | | % 12.22/2.42 | | | | | GROUND_INST: instantiating (9) with all_125_1, all_15_4, all_15_3, % 12.22/2.42 | | | | | all_15_2, all_125_0, simplifying with (13), (14), (18), % 12.22/2.42 | | | | | (87), (89) gives: % 12.22/2.42 | | | | | (90) all_125_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 12.22/2.42 | | | | | ~ (v0 = 0) & member(all_125_1, all_15_3) = v1 & % 12.22/2.42 | | | | | member(all_125_1, all_15_4) = v0) % 12.22/2.42 | | | | | % 12.22/2.42 | | | | | BETA: splitting (90) gives: % 12.22/2.42 | | | | | % 12.22/2.42 | | | | | Case 1: % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | (91) all_125_0 = 0 % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | REDUCE: (86), (91) imply: % 12.22/2.42 | | | | | | (92) $false % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | CLOSE: (92) is inconsistent. % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | Case 2: % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | (93) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 12.22/2.42 | | | | | | member(all_125_1, all_15_3) = v1 & member(all_125_1, % 12.22/2.42 | | | | | | all_15_4) = v0) % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | DELTA: instantiating (93) with fresh symbols all_143_0, all_143_1 % 12.22/2.42 | | | | | | gives: % 12.22/2.42 | | | | | | (94) ~ (all_143_0 = 0) & ~ (all_143_1 = 0) & member(all_125_1, % 12.22/2.42 | | | | | | all_15_3) = all_143_0 & member(all_125_1, all_15_4) = % 12.22/2.42 | | | | | | all_143_1 % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | ALPHA: (94) implies: % 12.22/2.42 | | | | | | (95) ~ (all_143_1 = 0) % 12.22/2.42 | | | | | | (96) member(all_125_1, all_15_4) = all_143_1 % 12.22/2.42 | | | | | | % 12.22/2.42 | | | | | | GROUND_INST: instantiating (10) with 0, all_143_1, all_15_4, % 12.22/2.43 | | | | | | all_125_1, simplifying with (88), (96) gives: % 12.22/2.43 | | | | | | (97) all_143_1 = 0 % 12.22/2.43 | | | | | | % 12.22/2.43 | | | | | | REDUCE: (95), (97) imply: % 12.22/2.43 | | | | | | (98) $false % 12.22/2.43 | | | | | | % 12.22/2.43 | | | | | | CLOSE: (98) is inconsistent. % 12.22/2.43 | | | | | | % 12.22/2.43 | | | | | End of split % 12.22/2.43 | | | | | % 12.22/2.43 | | | | End of split % 12.22/2.43 | | | | % 12.22/2.43 | | | End of split % 12.22/2.43 | | | % 12.22/2.43 | | End of split % 12.22/2.43 | | % 12.22/2.43 | Case 2: % 12.22/2.43 | | % 12.22/2.43 | | (99) all_15_1 = 0 & ~ (all_15_0 = 0) % 12.22/2.43 | | % 12.22/2.43 | | ALPHA: (99) implies: % 12.22/2.43 | | (100) all_15_1 = 0 % 12.22/2.43 | | (101) ~ (all_15_0 = 0) % 12.22/2.43 | | % 12.22/2.43 | | REDUCE: (17), (100) imply: % 12.22/2.43 | | (102) equal_set(all_15_4, all_15_2) = 0 % 12.22/2.43 | | % 12.22/2.43 | | BETA: splitting (20) gives: % 12.22/2.43 | | % 12.22/2.43 | | Case 1: % 12.22/2.43 | | | % 12.22/2.43 | | | (103) all_15_0 = 0 % 12.22/2.43 | | | % 12.22/2.43 | | | REDUCE: (101), (103) imply: % 12.22/2.43 | | | (104) $false % 12.22/2.43 | | | % 12.22/2.43 | | | CLOSE: (104) is inconsistent. % 12.22/2.43 | | | % 12.22/2.43 | | Case 2: % 12.22/2.43 | | | % 12.22/2.43 | | | (105) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_3) % 12.22/2.43 | | | = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 12.22/2.43 | | | % 12.22/2.43 | | | DELTA: instantiating (105) with fresh symbols all_57_0, all_57_1 gives: % 12.22/2.43 | | | (106) ~ (all_57_0 = 0) & member(all_57_1, all_15_3) = 0 & % 12.22/2.43 | | | member(all_57_1, all_15_4) = all_57_0 & $i(all_57_1) % 12.22/2.43 | | | % 12.22/2.43 | | | ALPHA: (106) implies: % 12.22/2.43 | | | (107) ~ (all_57_0 = 0) % 12.22/2.43 | | | (108) $i(all_57_1) % 12.22/2.43 | | | (109) member(all_57_1, all_15_4) = all_57_0 % 12.22/2.43 | | | (110) member(all_57_1, all_15_3) = 0 % 12.22/2.43 | | | % 12.22/2.43 | | | GROUND_INST: instantiating (4) with all_15_4, all_15_2, simplifying with % 12.22/2.43 | | | (13), (15), (102) gives: % 12.22/2.43 | | | (111) subset(all_15_2, all_15_4) = 0 & subset(all_15_4, all_15_2) = 0 % 12.22/2.43 | | | % 12.22/2.43 | | | ALPHA: (111) implies: % 12.22/2.43 | | | (112) subset(all_15_4, all_15_2) = 0 % 12.22/2.43 | | | (113) subset(all_15_2, all_15_4) = 0 % 12.22/2.43 | | | % 12.22/2.43 | | | GROUND_INST: instantiating (2) with all_15_2, all_15_4, all_57_1, % 12.22/2.43 | | | all_57_0, simplifying with (13), (15), (108), (109), (113) % 12.22/2.43 | | | gives: % 12.22/2.43 | | | (114) all_57_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_57_1, % 12.22/2.43 | | | all_15_2) = v0) % 12.22/2.43 | | | % 12.22/2.43 | | | GROUND_INST: instantiating (3) with all_15_2, all_15_4, simplifying with % 12.22/2.43 | | | (13), (15), (113) gives: % 12.22/2.43 | | | (115) ? [v0: any] : ? [v1: any] : (equal_set(all_15_2, all_15_4) = v1 % 12.22/2.43 | | | & subset(all_15_4, all_15_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 12.22/2.43 | | | % 12.22/2.43 | | | GROUND_INST: instantiating (5) with all_15_2, all_15_4, 0, simplifying % 12.22/2.43 | | | with (13), (15), (113) gives: % 12.22/2.43 | | | (116) ? [v0: any] : ? [v1: any] : (equal_set(all_15_2, all_15_4) = v0 % 12.22/2.43 | | | & subset(all_15_4, all_15_2) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 12.22/2.43 | | | % 12.22/2.43 | | | DELTA: instantiating (115) with fresh symbols all_83_0, all_83_1 gives: % 12.22/2.43 | | | (117) equal_set(all_15_2, all_15_4) = all_83_0 & subset(all_15_4, % 12.22/2.43 | | | all_15_2) = all_83_1 & ( ~ (all_83_1 = 0) | all_83_0 = 0) % 12.22/2.43 | | | % 12.22/2.43 | | | ALPHA: (117) implies: % 12.22/2.43 | | | (118) subset(all_15_4, all_15_2) = all_83_1 % 12.22/2.43 | | | (119) ~ (all_83_1 = 0) | all_83_0 = 0 % 12.22/2.43 | | | % 12.22/2.43 | | | DELTA: instantiating (116) with fresh symbols all_87_0, all_87_1 gives: % 12.22/2.43 | | | (120) equal_set(all_15_2, all_15_4) = all_87_1 & subset(all_15_4, % 12.22/2.43 | | | all_15_2) = all_87_0 & ( ~ (all_87_1 = 0) | all_87_0 = 0) % 12.22/2.43 | | | % 12.22/2.43 | | | ALPHA: (120) implies: % 12.22/2.43 | | | (121) subset(all_15_4, all_15_2) = all_87_0 % 12.22/2.43 | | | % 12.22/2.43 | | | BETA: splitting (114) gives: % 12.22/2.43 | | | % 12.22/2.43 | | | Case 1: % 12.22/2.43 | | | | % 12.22/2.43 | | | | (122) all_57_0 = 0 % 12.22/2.43 | | | | % 12.22/2.43 | | | | REDUCE: (107), (122) imply: % 12.22/2.43 | | | | (123) $false % 12.22/2.43 | | | | % 12.22/2.43 | | | | CLOSE: (123) is inconsistent. % 12.22/2.43 | | | | % 12.22/2.43 | | | Case 2: % 12.22/2.43 | | | | % 12.22/2.44 | | | | (124) ? [v0: int] : ( ~ (v0 = 0) & member(all_57_1, all_15_2) = v0) % 12.22/2.44 | | | | % 12.22/2.44 | | | | DELTA: instantiating (124) with fresh symbol all_95_0 gives: % 12.22/2.44 | | | | (125) ~ (all_95_0 = 0) & member(all_57_1, all_15_2) = all_95_0 % 12.22/2.44 | | | | % 12.22/2.44 | | | | ALPHA: (125) implies: % 12.22/2.44 | | | | (126) ~ (all_95_0 = 0) % 12.22/2.44 | | | | (127) member(all_57_1, all_15_2) = all_95_0 % 12.22/2.44 | | | | % 12.22/2.44 | | | | GROUND_INST: instantiating (11) with 0, all_87_0, all_15_2, all_15_4, % 12.22/2.44 | | | | simplifying with (112), (121) gives: % 12.22/2.44 | | | | (128) all_87_0 = 0 % 12.22/2.44 | | | | % 12.22/2.44 | | | | GROUND_INST: instantiating (11) with all_83_1, all_87_0, all_15_2, % 12.22/2.44 | | | | all_15_4, simplifying with (118), (121) gives: % 12.22/2.44 | | | | (129) all_87_0 = all_83_1 % 12.22/2.44 | | | | % 12.22/2.44 | | | | COMBINE_EQS: (128), (129) imply: % 12.22/2.44 | | | | (130) all_83_1 = 0 % 12.22/2.44 | | | | % 12.22/2.44 | | | | BETA: splitting (119) gives: % 12.22/2.44 | | | | % 12.22/2.44 | | | | Case 1: % 12.22/2.44 | | | | | % 12.22/2.44 | | | | | (131) ~ (all_83_1 = 0) % 12.22/2.44 | | | | | % 12.22/2.44 | | | | | REDUCE: (130), (131) imply: % 12.22/2.44 | | | | | (132) $false % 12.22/2.44 | | | | | % 12.22/2.44 | | | | | CLOSE: (132) is inconsistent. % 12.22/2.44 | | | | | % 12.22/2.44 | | | | Case 2: % 12.22/2.44 | | | | | % 12.22/2.44 | | | | | % 12.22/2.44 | | | | | GROUND_INST: instantiating (9) with all_57_1, all_15_4, all_15_3, % 12.22/2.44 | | | | | all_15_2, all_95_0, simplifying with (13), (14), (18), % 12.22/2.44 | | | | | (108), (127) gives: % 12.22/2.44 | | | | | (133) all_95_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 12.22/2.44 | | | | | ~ (v0 = 0) & member(all_57_1, all_15_3) = v1 & % 12.22/2.44 | | | | | member(all_57_1, all_15_4) = v0) % 12.22/2.44 | | | | | % 12.22/2.44 | | | | | BETA: splitting (133) gives: % 12.22/2.44 | | | | | % 12.22/2.44 | | | | | Case 1: % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | | (134) all_95_0 = 0 % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | | REDUCE: (126), (134) imply: % 12.22/2.44 | | | | | | (135) $false % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | | CLOSE: (135) is inconsistent. % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | Case 2: % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | | (136) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 12.22/2.44 | | | | | | member(all_57_1, all_15_3) = v1 & member(all_57_1, % 12.22/2.44 | | | | | | all_15_4) = v0) % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | | DELTA: instantiating (136) with fresh symbols all_116_0, all_116_1 % 12.22/2.44 | | | | | | gives: % 12.22/2.44 | | | | | | (137) ~ (all_116_0 = 0) & ~ (all_116_1 = 0) & member(all_57_1, % 12.22/2.44 | | | | | | all_15_3) = all_116_0 & member(all_57_1, all_15_4) = % 12.22/2.44 | | | | | | all_116_1 % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | | ALPHA: (137) implies: % 12.22/2.44 | | | | | | (138) ~ (all_116_0 = 0) % 12.22/2.44 | | | | | | (139) member(all_57_1, all_15_3) = all_116_0 % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | | GROUND_INST: instantiating (10) with 0, all_116_0, all_15_3, % 12.22/2.44 | | | | | | all_57_1, simplifying with (110), (139) gives: % 12.22/2.44 | | | | | | (140) all_116_0 = 0 % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | | REDUCE: (138), (140) imply: % 12.22/2.44 | | | | | | (141) $false % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | | CLOSE: (141) is inconsistent. % 12.22/2.44 | | | | | | % 12.22/2.44 | | | | | End of split % 12.22/2.44 | | | | | % 12.22/2.44 | | | | End of split % 12.22/2.44 | | | | % 12.22/2.44 | | | End of split % 12.22/2.44 | | | % 12.22/2.44 | | End of split % 12.22/2.44 | | % 12.22/2.44 | End of split % 12.22/2.44 | % 12.22/2.44 End of proof % 12.22/2.44 % SZS output end Proof for theBenchmark % 12.22/2.44 % 12.22/2.44 1826ms %------------------------------------------------------------------------------