%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET352+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 : n019.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 15:24:42 EDT 2023 % Result : Theorem 10.44s 2.35s % Output : Proof 13.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET352+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n019.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Sat Aug 26 08:41:13 EDT 2023 % 0.11/0.32 % CPUTime : % 0.17/0.62 ________ _____ % 0.17/0.62 ___ __ \_________(_)________________________________ % 0.17/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.62 % 0.17/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.62 (2023-06-19) % 0.17/0.62 % 0.17/0.62 (c) Philipp Rümmer, 2009-2023 % 0.17/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.62 Amanda Stjerna. % 0.17/0.62 Free software under BSD-3-Clause. % 0.17/0.62 % 0.17/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.62 % 0.17/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.63 Running up to 7 provers in parallel. % 0.17/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.19/1.15 Prover 4: Preprocessing ... % 2.19/1.16 Prover 1: Preprocessing ... % 3.00/1.20 Prover 6: Preprocessing ... % 3.00/1.20 Prover 0: Preprocessing ... % 3.00/1.20 Prover 5: Preprocessing ... % 3.00/1.20 Prover 3: Preprocessing ... % 3.00/1.20 Prover 2: Preprocessing ... % 6.21/1.70 Prover 6: Proving ... % 6.50/1.72 Prover 1: Constructing countermodel ... % 6.62/1.76 Prover 5: Proving ... % 6.62/1.78 Prover 4: Constructing countermodel ... % 6.62/1.78 Prover 2: Proving ... % 6.62/1.81 Prover 3: Constructing countermodel ... % 7.24/1.88 Prover 0: Proving ... % 10.44/2.35 Prover 3: proved (1685ms) % 10.44/2.35 % 10.44/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.44/2.35 % 10.44/2.35 Prover 2: stopped % 10.44/2.35 Prover 0: stopped % 10.44/2.36 Prover 6: stopped % 10.44/2.36 Prover 5: stopped % 10.44/2.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.44/2.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.44/2.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.44/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.44/2.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.13/2.41 Prover 11: Preprocessing ... % 11.13/2.43 Prover 13: Preprocessing ... % 11.13/2.43 Prover 10: Preprocessing ... % 11.13/2.44 Prover 8: Preprocessing ... % 11.13/2.44 Prover 1: Found proof (size 69) % 11.13/2.44 Prover 1: proved (1787ms) % 11.13/2.44 Prover 7: Preprocessing ... % 11.13/2.44 Prover 4: stopped % 11.13/2.48 Prover 7: stopped % 11.79/2.49 Prover 10: stopped % 11.79/2.49 Prover 13: stopped % 11.79/2.50 Prover 11: stopped % 11.99/2.57 Prover 8: Warning: ignoring some quantifiers % 11.99/2.58 Prover 8: Constructing countermodel ... % 11.99/2.59 Prover 8: stopped % 11.99/2.59 % 11.99/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.99/2.59 % 11.99/2.61 % SZS output start Proof for theBenchmark % 11.99/2.61 Assumptions after simplification: % 11.99/2.61 --------------------------------- % 11.99/2.61 % 11.99/2.61 (equal_set) % 12.46/2.65 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 12.46/2.65 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 12.46/2.65 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 12.46/2.65 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 12.46/2.65 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 12.46/2.65 % 12.46/2.65 (subset) % 12.46/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 12.46/2.66 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 12.46/2.66 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 12.46/2.66 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 12.46/2.66 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 12.46/2.66 % 12.46/2.66 (sum) % 12.46/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (sum(v1) % 12.46/2.66 = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ! [v4: $i] : ( % 12.46/2.66 ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 12.46/2.66 member(v4, v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 12.46/2.66 (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 12.46/2.66 $i] : (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3))) % 12.46/2.66 % 12.46/2.67 (thI40) % 12.46/2.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 12.46/2.67 int] : ( ~ (v5 = 0) & sum(v2) = v3 & unordered_pair(v0, v1) = v2 & union(v0, % 12.46/2.67 v1) = v4 & equal_set(v3, v4) = v5 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 12.46/2.67 $i(v0)) % 12.46/2.67 % 12.46/2.67 (union) % 12.46/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.46/2.67 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 12.46/2.67 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 12.46/2.67 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 12.46/2.67 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 12.46/2.67 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 12.46/2.67 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 12.46/2.67 % 12.46/2.67 (unordered_pair) % 12.46/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.46/2.68 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | % 12.46/2.68 ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0))) & ! [v0: $i] : ! % 12.46/2.68 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 | ~ % 12.46/2.68 (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ % 12.46/2.68 $i(v1) | ~ $i(v0)) % 12.46/2.68 % 12.46/2.68 (function-axioms) % 12.46/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.46/2.69 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 12.46/2.69 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.46/2.69 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 12.46/2.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 12.46/2.69 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.46/2.69 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 12.46/2.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 12.46/2.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 12.46/2.69 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.46/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 12.46/2.69 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 12.46/2.69 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.46/2.69 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 12.46/2.69 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 12.46/2.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 12.46/2.69 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 12.46/2.69 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 12.46/2.69 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 12.46/2.69 (power_set(v2) = v0)) % 12.46/2.69 % 12.46/2.69 Further assumptions not needed in the proof: % 12.46/2.69 -------------------------------------------- % 12.46/2.69 difference, empty_set, intersection, power_set, product, singleton % 12.46/2.69 % 12.46/2.69 Those formulas are unsatisfiable: % 12.46/2.69 --------------------------------- % 12.46/2.69 % 12.46/2.69 Begin of proof % 12.46/2.69 | % 12.46/2.69 | ALPHA: (subset) implies: % 12.46/2.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 12.46/2.69 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 12.46/2.69 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 12.88/2.69 | % 12.88/2.69 | ALPHA: (equal_set) implies: % 12.88/2.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 12.88/2.70 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 12.88/2.70 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 12.88/2.70 | 0)))) % 12.88/2.70 | % 12.88/2.70 | ALPHA: (union) implies: % 12.88/2.70 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 12.88/2.70 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 12.88/2.70 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 12.88/2.70 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 12.88/2.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.88/2.70 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 12.88/2.70 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 12.88/2.70 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 12.88/2.70 | v5)) % 12.88/2.70 | % 12.88/2.70 | ALPHA: (unordered_pair) implies: % 12.88/2.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = % 12.88/2.70 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ % 12.88/2.70 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 12.88/2.70 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.88/2.70 | (v4 = 0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 12.88/2.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ~ (v2 = v0) & ~ (v1 = v0))) % 12.88/2.70 | % 12.88/2.70 | ALPHA: (sum) implies: % 12.88/2.70 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1) = v2) | ~ % 12.88/2.70 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 12.88/2.70 | (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3))) % 12.88/2.71 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.88/2.71 | (sum(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 12.88/2.71 | ! [v4: $i] : ( ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( % 12.88/2.71 | ~ (v5 = 0) & member(v4, v1) = v5))) % 12.88/2.71 | % 12.88/2.71 | ALPHA: (function-axioms) implies: % 12.88/2.71 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.88/2.71 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 12.88/2.71 | = v0)) % 12.88/2.71 | % 12.88/2.71 | DELTA: instantiating (thI40) with fresh symbols all_15_0, all_15_1, all_15_2, % 12.88/2.71 | all_15_3, all_15_4, all_15_5 gives: % 12.88/2.71 | (10) ~ (all_15_0 = 0) & sum(all_15_3) = all_15_2 & % 12.88/2.71 | unordered_pair(all_15_5, all_15_4) = all_15_3 & union(all_15_5, % 12.88/2.71 | all_15_4) = all_15_1 & equal_set(all_15_2, all_15_1) = all_15_0 & % 12.88/2.71 | $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & % 12.88/2.71 | $i(all_15_5) % 12.88/2.71 | % 12.88/2.71 | ALPHA: (10) implies: % 12.88/2.71 | (11) ~ (all_15_0 = 0) % 12.88/2.71 | (12) $i(all_15_5) % 12.88/2.71 | (13) $i(all_15_4) % 12.88/2.71 | (14) $i(all_15_3) % 12.88/2.71 | (15) $i(all_15_2) % 12.88/2.71 | (16) $i(all_15_1) % 12.88/2.71 | (17) equal_set(all_15_2, all_15_1) = all_15_0 % 12.88/2.71 | (18) union(all_15_5, all_15_4) = all_15_1 % 12.88/2.71 | (19) unordered_pair(all_15_5, all_15_4) = all_15_3 % 12.88/2.71 | (20) sum(all_15_3) = all_15_2 % 12.88/2.71 | % 12.88/2.71 | GROUND_INST: instantiating (2) with all_15_2, all_15_1, all_15_0, simplifying % 12.88/2.71 | with (15), (16), (17) gives: % 12.88/2.71 | (21) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 12.88/2.71 | all_15_2) = v1 & subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | % 12.88/2.71 | ~ (v0 = 0))) % 12.88/2.72 | % 12.88/2.72 | BETA: splitting (21) gives: % 12.88/2.72 | % 12.88/2.72 | Case 1: % 12.88/2.72 | | % 12.88/2.72 | | (22) all_15_0 = 0 % 12.88/2.72 | | % 12.88/2.72 | | REDUCE: (11), (22) imply: % 12.88/2.72 | | (23) $false % 12.88/2.72 | | % 12.88/2.72 | | CLOSE: (23) is inconsistent. % 12.88/2.72 | | % 12.88/2.72 | Case 2: % 12.88/2.72 | | % 12.88/2.72 | | (24) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_2) = v1 & % 12.88/2.72 | | subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 12.88/2.72 | | % 12.88/2.72 | | DELTA: instantiating (24) with fresh symbols all_24_0, all_24_1 gives: % 12.88/2.72 | | (25) subset(all_15_1, all_15_2) = all_24_0 & subset(all_15_2, all_15_1) = % 12.88/2.72 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0)) % 12.88/2.72 | | % 12.88/2.72 | | ALPHA: (25) implies: % 12.88/2.72 | | (26) subset(all_15_2, all_15_1) = all_24_1 % 12.88/2.72 | | (27) subset(all_15_1, all_15_2) = all_24_0 % 12.88/2.72 | | (28) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 12.88/2.72 | | % 12.88/2.72 | | GROUND_INST: instantiating (1) with all_15_2, all_15_1, all_24_1, % 12.88/2.72 | | simplifying with (15), (16), (26) gives: % 12.88/2.72 | | (29) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.88/2.72 | | member(v0, all_15_1) = v1 & member(v0, all_15_2) = 0 & $i(v0)) % 12.88/2.72 | | % 12.88/2.72 | | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_24_0, % 12.88/2.72 | | simplifying with (15), (16), (27) gives: % 12.88/2.72 | | (30) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 12.88/2.72 | | member(v0, all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 12.88/2.72 | | % 12.88/2.72 | | BETA: splitting (28) gives: % 12.88/2.72 | | % 12.88/2.72 | | Case 1: % 12.88/2.72 | | | % 12.88/2.72 | | | (31) ~ (all_24_0 = 0) % 12.88/2.72 | | | % 12.88/2.72 | | | BETA: splitting (30) gives: % 12.88/2.72 | | | % 12.88/2.72 | | | Case 1: % 12.88/2.72 | | | | % 12.88/2.73 | | | | (32) all_24_0 = 0 % 12.88/2.73 | | | | % 12.88/2.73 | | | | REDUCE: (31), (32) imply: % 12.88/2.73 | | | | (33) $false % 12.88/2.73 | | | | % 12.88/2.73 | | | | CLOSE: (33) is inconsistent. % 12.88/2.73 | | | | % 12.88/2.73 | | | Case 2: % 12.88/2.73 | | | | % 12.88/2.73 | | | | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 12.88/2.73 | | | | = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 12.88/2.73 | | | | % 12.88/2.73 | | | | DELTA: instantiating (34) with fresh symbols all_37_0, all_37_1 gives: % 12.88/2.73 | | | | (35) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 & % 12.88/2.73 | | | | member(all_37_1, all_15_2) = all_37_0 & $i(all_37_1) % 12.88/2.73 | | | | % 12.88/2.73 | | | | ALPHA: (35) implies: % 12.88/2.73 | | | | (36) ~ (all_37_0 = 0) % 12.88/2.73 | | | | (37) $i(all_37_1) % 12.88/2.73 | | | | (38) member(all_37_1, all_15_2) = all_37_0 % 12.88/2.73 | | | | (39) member(all_37_1, all_15_1) = 0 % 12.88/2.73 | | | | % 12.88/2.73 | | | | GROUND_INST: instantiating (8) with all_37_1, all_15_3, all_15_2, % 12.88/2.73 | | | | all_37_0, simplifying with (14), (20), (37), (38) gives: % 12.88/2.73 | | | | (40) all_37_0 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ % 12.88/2.73 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_3) = % 12.88/2.73 | | | | v1)) % 12.88/2.73 | | | | % 12.88/2.73 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_5, all_15_4, % 12.88/2.73 | | | | all_15_1, simplifying with (12), (13), (18), (37), (39) % 12.88/2.73 | | | | gives: % 12.88/2.73 | | | | (41) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_4) = v1 & % 12.88/2.73 | | | | member(all_37_1, all_15_5) = v0 & (v1 = 0 | v0 = 0)) % 12.88/2.73 | | | | % 12.88/2.73 | | | | DELTA: instantiating (41) with fresh symbols all_44_0, all_44_1 gives: % 12.88/2.73 | | | | (42) member(all_37_1, all_15_4) = all_44_0 & member(all_37_1, % 12.88/2.73 | | | | all_15_5) = all_44_1 & (all_44_0 = 0 | all_44_1 = 0) % 12.88/2.73 | | | | % 12.88/2.73 | | | | ALPHA: (42) implies: % 12.88/2.73 | | | | (43) member(all_37_1, all_15_5) = all_44_1 % 12.88/2.73 | | | | (44) member(all_37_1, all_15_4) = all_44_0 % 12.88/2.73 | | | | (45) all_44_0 = 0 | all_44_1 = 0 % 12.88/2.73 | | | | % 12.88/2.73 | | | | BETA: splitting (40) gives: % 12.88/2.73 | | | | % 12.88/2.73 | | | | Case 1: % 12.88/2.73 | | | | | % 12.88/2.73 | | | | | (46) all_37_0 = 0 % 12.88/2.73 | | | | | % 12.88/2.73 | | | | | REDUCE: (36), (46) imply: % 12.88/2.73 | | | | | (47) $false % 12.88/2.73 | | | | | % 12.88/2.73 | | | | | CLOSE: (47) is inconsistent. % 12.88/2.73 | | | | | % 12.88/2.74 | | | | Case 2: % 12.88/2.74 | | | | | % 12.88/2.74 | | | | | (48) ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ $i(v0) | ? % 12.88/2.74 | | | | | [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_3) = v1)) % 12.88/2.74 | | | | | % 12.88/2.74 | | | | | BETA: splitting (45) gives: % 12.88/2.74 | | | | | % 12.88/2.74 | | | | | Case 1: % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | (49) all_44_0 = 0 % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | REDUCE: (44), (49) imply: % 12.88/2.74 | | | | | | (50) member(all_37_1, all_15_4) = 0 % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | GROUND_INST: instantiating (48) with all_15_4, simplifying with % 12.88/2.74 | | | | | | (13), (50) gives: % 12.88/2.74 | | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_4, all_15_3) = % 12.88/2.74 | | | | | | v0) % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | DELTA: instantiating (51) with fresh symbol all_91_0 gives: % 12.88/2.74 | | | | | | (52) ~ (all_91_0 = 0) & member(all_15_4, all_15_3) = all_91_0 % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | ALPHA: (52) implies: % 12.88/2.74 | | | | | | (53) ~ (all_91_0 = 0) % 12.88/2.74 | | | | | | (54) member(all_15_4, all_15_3) = all_91_0 % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | GROUND_INST: instantiating (6) with all_15_4, all_15_5, all_15_4, % 12.88/2.74 | | | | | | all_15_3, all_91_0, simplifying with (12), (13), (19), % 12.88/2.74 | | | | | | (54) gives: % 12.88/2.74 | | | | | | (55) all_91_0 = 0 % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | REDUCE: (53), (55) imply: % 12.88/2.74 | | | | | | (56) $false % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | CLOSE: (56) is inconsistent. % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | Case 2: % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | (57) all_44_1 = 0 % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | REDUCE: (43), (57) imply: % 12.88/2.74 | | | | | | (58) member(all_37_1, all_15_5) = 0 % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | GROUND_INST: instantiating (48) with all_15_5, simplifying with % 12.88/2.74 | | | | | | (12), (58) gives: % 12.88/2.74 | | | | | | (59) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_5, all_15_3) = % 12.88/2.74 | | | | | | v0) % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | DELTA: instantiating (59) with fresh symbol all_91_0 gives: % 12.88/2.74 | | | | | | (60) ~ (all_91_0 = 0) & member(all_15_5, all_15_3) = all_91_0 % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | ALPHA: (60) implies: % 12.88/2.74 | | | | | | (61) ~ (all_91_0 = 0) % 12.88/2.74 | | | | | | (62) member(all_15_5, all_15_3) = all_91_0 % 12.88/2.74 | | | | | | % 12.88/2.74 | | | | | | GROUND_INST: instantiating (6) with all_15_5, all_15_5, all_15_4, % 12.88/2.74 | | | | | | all_15_3, all_91_0, simplifying with (12), (13), (19), % 12.88/2.74 | | | | | | (62) gives: % 12.88/2.74 | | | | | | (63) all_91_0 = 0 % 12.88/2.74 | | | | | | % 12.88/2.75 | | | | | | REDUCE: (61), (63) imply: % 12.88/2.75 | | | | | | (64) $false % 12.88/2.75 | | | | | | % 12.88/2.75 | | | | | | CLOSE: (64) is inconsistent. % 12.88/2.75 | | | | | | % 12.88/2.75 | | | | | End of split % 12.88/2.75 | | | | | % 12.88/2.75 | | | | End of split % 12.88/2.75 | | | | % 12.88/2.75 | | | End of split % 12.88/2.75 | | | % 12.88/2.75 | | Case 2: % 12.88/2.75 | | | % 12.88/2.75 | | | (65) ~ (all_24_1 = 0) % 12.88/2.75 | | | % 12.88/2.75 | | | BETA: splitting (29) gives: % 12.88/2.75 | | | % 12.88/2.75 | | | Case 1: % 12.88/2.75 | | | | % 12.88/2.75 | | | | (66) all_24_1 = 0 % 12.88/2.75 | | | | % 12.88/2.75 | | | | REDUCE: (65), (66) imply: % 12.88/2.75 | | | | (67) $false % 12.88/2.75 | | | | % 12.88/2.75 | | | | CLOSE: (67) is inconsistent. % 12.88/2.75 | | | | % 12.88/2.75 | | | Case 2: % 12.88/2.75 | | | | % 12.88/2.75 | | | | (68) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 12.88/2.75 | | | | = v1 & member(v0, all_15_2) = 0 & $i(v0)) % 12.88/2.75 | | | | % 12.88/2.75 | | | | DELTA: instantiating (68) with fresh symbols all_37_0, all_37_1 gives: % 12.88/2.75 | | | | (69) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 & % 12.88/2.75 | | | | member(all_37_1, all_15_2) = 0 & $i(all_37_1) % 12.88/2.75 | | | | % 12.88/2.75 | | | | ALPHA: (69) implies: % 12.88/2.75 | | | | (70) ~ (all_37_0 = 0) % 12.88/2.75 | | | | (71) $i(all_37_1) % 12.88/2.75 | | | | (72) member(all_37_1, all_15_2) = 0 % 12.88/2.75 | | | | (73) member(all_37_1, all_15_1) = all_37_0 % 12.88/2.75 | | | | % 12.88/2.75 | | | | GROUND_INST: instantiating (7) with all_37_1, all_15_3, all_15_2, % 12.88/2.75 | | | | simplifying with (14), (20), (71), (72) gives: % 12.88/2.75 | | | | (74) ? [v0: $i] : (member(v0, all_15_3) = 0 & member(all_37_1, v0) = % 12.88/2.75 | | | | 0 & $i(v0)) % 12.88/2.75 | | | | % 12.88/2.75 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_5, all_15_4, % 12.88/2.75 | | | | all_15_1, all_37_0, simplifying with (12), (13), (18), % 12.88/2.75 | | | | (71), (73) gives: % 12.88/2.75 | | | | (75) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 12.88/2.75 | | | | (v0 = 0) & member(all_37_1, all_15_4) = v1 & member(all_37_1, % 12.88/2.75 | | | | all_15_5) = v0) % 12.88/2.75 | | | | % 12.88/2.75 | | | | DELTA: instantiating (74) with fresh symbol all_45_0 gives: % 12.88/2.75 | | | | (76) member(all_45_0, all_15_3) = 0 & member(all_37_1, all_45_0) = 0 % 12.88/2.75 | | | | & $i(all_45_0) % 12.88/2.75 | | | | % 12.88/2.75 | | | | ALPHA: (76) implies: % 12.88/2.77 | | | | (77) $i(all_45_0) % 12.88/2.77 | | | | (78) member(all_37_1, all_45_0) = 0 % 12.88/2.77 | | | | (79) member(all_45_0, all_15_3) = 0 % 12.88/2.77 | | | | % 12.88/2.77 | | | | BETA: splitting (75) gives: % 12.88/2.77 | | | | % 12.88/2.77 | | | | Case 1: % 12.88/2.77 | | | | | % 12.88/2.77 | | | | | (80) all_37_0 = 0 % 12.88/2.77 | | | | | % 12.88/2.77 | | | | | REDUCE: (70), (80) imply: % 12.88/2.77 | | | | | (81) $false % 12.88/2.77 | | | | | % 12.88/2.77 | | | | | CLOSE: (81) is inconsistent. % 12.88/2.77 | | | | | % 12.88/2.77 | | | | Case 2: % 12.88/2.77 | | | | | % 12.88/2.77 | | | | | (82) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 12.88/2.77 | | | | | member(all_37_1, all_15_4) = v1 & member(all_37_1, all_15_5) % 12.88/2.77 | | | | | = v0) % 12.88/2.77 | | | | | % 12.88/2.77 | | | | | DELTA: instantiating (82) with fresh symbols all_51_0, all_51_1 gives: % 12.88/2.78 | | | | | (83) ~ (all_51_0 = 0) & ~ (all_51_1 = 0) & member(all_37_1, % 12.88/2.78 | | | | | all_15_4) = all_51_0 & member(all_37_1, all_15_5) = all_51_1 % 12.88/2.78 | | | | | % 12.88/2.78 | | | | | ALPHA: (83) implies: % 12.88/2.78 | | | | | (84) ~ (all_51_1 = 0) % 12.88/2.78 | | | | | (85) ~ (all_51_0 = 0) % 12.88/2.78 | | | | | (86) member(all_37_1, all_15_5) = all_51_1 % 12.88/2.78 | | | | | (87) member(all_37_1, all_15_4) = all_51_0 % 12.88/2.78 | | | | | % 12.88/2.78 | | | | | GROUND_INST: instantiating (5) with all_45_0, all_15_5, all_15_4, % 12.88/2.78 | | | | | all_15_3, simplifying with (12), (13), (19), (77), (79) % 12.88/2.78 | | | | | gives: % 12.88/2.78 | | | | | (88) all_45_0 = all_15_4 | all_45_0 = all_15_5 % 12.88/2.78 | | | | | % 12.88/2.78 | | | | | BETA: splitting (88) gives: % 12.88/2.78 | | | | | % 12.88/2.78 | | | | | Case 1: % 12.88/2.78 | | | | | | % 12.88/2.78 | | | | | | (89) all_45_0 = all_15_4 % 13.28/2.78 | | | | | | % 13.28/2.78 | | | | | | REDUCE: (78), (89) imply: % 13.28/2.78 | | | | | | (90) member(all_37_1, all_15_4) = 0 % 13.28/2.78 | | | | | | % 13.28/2.78 | | | | | | GROUND_INST: instantiating (9) with all_51_0, 0, all_15_4, all_37_1, % 13.28/2.78 | | | | | | simplifying with (87), (90) gives: % 13.28/2.78 | | | | | | (91) all_51_0 = 0 % 13.28/2.78 | | | | | | % 13.28/2.78 | | | | | | REDUCE: (85), (91) imply: % 13.28/2.78 | | | | | | (92) $false % 13.28/2.78 | | | | | | % 13.28/2.78 | | | | | | CLOSE: (92) is inconsistent. % 13.28/2.78 | | | | | | % 13.28/2.78 | | | | | Case 2: % 13.28/2.78 | | | | | | % 13.28/2.78 | | | | | | (93) all_45_0 = all_15_5 % 13.28/2.78 | | | | | | % 13.28/2.78 | | | | | | REDUCE: (78), (93) imply: % 13.28/2.78 | | | | | | (94) member(all_37_1, all_15_5) = 0 % 13.28/2.78 | | | | | | % 13.28/2.78 | | | | | | GROUND_INST: instantiating (9) with all_51_1, 0, all_15_5, all_37_1, % 13.28/2.78 | | | | | | simplifying with (86), (94) gives: % 13.28/2.78 | | | | | | (95) all_51_1 = 0 % 13.28/2.78 | | | | | | % 13.30/2.78 | | | | | | REDUCE: (84), (95) imply: % 13.30/2.78 | | | | | | (96) $false % 13.30/2.78 | | | | | | % 13.30/2.78 | | | | | | CLOSE: (96) is inconsistent. % 13.30/2.78 | | | | | | % 13.30/2.78 | | | | | End of split % 13.30/2.78 | | | | | % 13.30/2.78 | | | | End of split % 13.30/2.78 | | | | % 13.30/2.78 | | | End of split % 13.30/2.78 | | | % 13.30/2.78 | | End of split % 13.30/2.78 | | % 13.30/2.78 | End of split % 13.30/2.78 | % 13.30/2.78 End of proof % 13.30/2.78 % SZS output end Proof for theBenchmark % 13.30/2.78 % 13.30/2.78 2163ms %------------------------------------------------------------------------------