%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET595+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 15:25:29 EDT 2023 % Result : Theorem 9.16s 2.18s % Output : Proof 11.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET595+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n019.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 11:51:43 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.65 Running up to 7 provers in parallel. % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.66/1.18 Prover 1: Preprocessing ... % 2.66/1.18 Prover 4: Preprocessing ... % 2.66/1.23 Prover 3: Preprocessing ... % 2.66/1.23 Prover 6: Preprocessing ... % 2.66/1.23 Prover 0: Preprocessing ... % 2.66/1.23 Prover 2: Preprocessing ... % 2.66/1.23 Prover 5: Preprocessing ... % 6.27/1.75 Prover 6: Proving ... % 6.59/1.77 Prover 5: Proving ... % 6.59/1.80 Prover 1: Constructing countermodel ... % 6.59/1.81 Prover 3: Constructing countermodel ... % 6.59/1.84 Prover 2: Proving ... % 6.59/1.84 Prover 4: Constructing countermodel ... % 7.08/1.85 Prover 0: Proving ... % 9.16/2.18 Prover 3: proved (1523ms) % 9.16/2.18 % 9.16/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.16/2.18 % 9.16/2.19 Prover 5: stopped % 9.16/2.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.16/2.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.16/2.20 Prover 2: stopped % 9.16/2.20 Prover 0: stopped % 9.16/2.21 Prover 6: stopped % 9.16/2.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.16/2.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.16/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.16/2.23 Prover 7: Preprocessing ... % 9.16/2.23 Prover 8: Preprocessing ... % 9.16/2.25 Prover 10: Preprocessing ... % 9.16/2.28 Prover 11: Preprocessing ... % 9.16/2.28 Prover 13: Preprocessing ... % 9.16/2.29 Prover 1: Found proof (size 64) % 9.16/2.29 Prover 1: proved (1638ms) % 9.16/2.29 Prover 4: stopped % 9.16/2.31 Prover 7: Warning: ignoring some quantifiers % 9.16/2.32 Prover 7: Constructing countermodel ... % 9.16/2.33 Prover 10: Warning: ignoring some quantifiers % 9.16/2.34 Prover 7: stopped % 9.16/2.34 Prover 10: Constructing countermodel ... % 9.16/2.35 Prover 11: stopped % 9.16/2.35 Prover 13: stopped % 9.16/2.36 Prover 10: stopped % 9.49/2.39 Prover 8: Warning: ignoring some quantifiers % 9.49/2.40 Prover 8: Constructing countermodel ... % 9.49/2.41 Prover 8: stopped % 9.49/2.41 % 9.49/2.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.49/2.41 % 10.89/2.42 % SZS output start Proof for theBenchmark % 10.89/2.43 Assumptions after simplification: % 10.89/2.43 --------------------------------- % 10.89/2.43 % 10.89/2.43 (difference) % 11.02/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 11.02/2.48 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 11.02/2.48 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 & % 11.02/2.48 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 11.02/2.48 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, % 11.02/2.48 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 11.02/2.48 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 11.02/2.48 % 11.02/2.48 (equal_set) % 11.02/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 11.02/2.48 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 11.02/2.48 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 11.02/2.48 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 11.02/2.48 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 11.02/2.48 % 11.02/2.48 (subset) % 11.02/2.49 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 11.02/2.49 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 11.02/2.49 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 11.02/2.49 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 11.02/2.49 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 11.02/2.49 % 11.02/2.49 (thI27) % 11.02/2.49 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 11.02/2.49 = 0) & difference(v1, v0) = v2 & union(v2, v0) = v3 & equal_set(v3, v1) = % 11.02/2.49 v4 & subset(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.02/2.49 % 11.02/2.49 (union) % 11.02/2.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 11.02/2.50 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 11.02/2.50 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 11.02/2.50 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 11.02/2.50 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 11.02/2.50 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 11.02/2.50 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 11.02/2.50 % 11.02/2.50 (function-axioms) % 11.02/2.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.02/2.51 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 11.02/2.51 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.02/2.51 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 11.02/2.51 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 11.02/2.51 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.02/2.51 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 11.02/2.51 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.02/2.51 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 11.02/2.51 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.02/2.51 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 11.02/2.51 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.02/2.51 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.02/2.51 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 11.02/2.51 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 11.02/2.51 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 11.02/2.51 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 11.02/2.51 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 11.02/2.51 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 11.02/2.51 (power_set(v2) = v0)) % 11.02/2.51 % 11.02/2.51 Further assumptions not needed in the proof: % 11.02/2.51 -------------------------------------------- % 11.02/2.51 empty_set, intersection, power_set, product, singleton, sum, unordered_pair % 11.02/2.51 % 11.02/2.51 Those formulas are unsatisfiable: % 11.02/2.51 --------------------------------- % 11.02/2.51 % 11.02/2.51 Begin of proof % 11.02/2.51 | % 11.02/2.51 | ALPHA: (subset) implies: % 11.02/2.51 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 11.02/2.51 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 11.02/2.51 | member(v2, v1) = 0)) % 11.02/2.52 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 11.02/2.52 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 11.02/2.52 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 11.02/2.52 | % 11.02/2.52 | ALPHA: (equal_set) implies: % 11.02/2.52 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 11.02/2.52 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 11.02/2.52 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 11.02/2.52 | 0)))) % 11.02/2.52 | % 11.02/2.52 | ALPHA: (union) implies: % 11.02/2.52 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 11.02/2.52 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 11.02/2.52 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 11.02/2.52 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 11.02/2.52 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 11.02/2.52 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 11.02/2.52 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 11.02/2.52 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 11.02/2.52 | v5)) % 11.02/2.52 | % 11.02/2.52 | ALPHA: (difference) implies: % 11.42/2.53 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 11.42/2.53 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ % 11.42/2.53 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0 % 11.42/2.53 | & member(v0, v1) = v4)) % 11.42/2.53 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 11.42/2.53 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ % 11.42/2.53 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 11.42/2.53 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 11.42/2.53 | % 11.42/2.53 | ALPHA: (function-axioms) implies: % 11.42/2.53 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.42/2.53 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 11.42/2.53 | = v0)) % 11.42/2.53 | % 11.42/2.53 | DELTA: instantiating (thI27) with fresh symbols all_15_0, all_15_1, all_15_2, % 11.42/2.53 | all_15_3, all_15_4 gives: % 11.42/2.53 | (9) ~ (all_15_0 = 0) & difference(all_15_3, all_15_4) = all_15_2 & % 11.42/2.53 | union(all_15_2, all_15_4) = all_15_1 & equal_set(all_15_1, all_15_3) = % 11.42/2.53 | all_15_0 & subset(all_15_4, all_15_3) = 0 & $i(all_15_1) & $i(all_15_2) % 11.42/2.53 | & $i(all_15_3) & $i(all_15_4) % 11.42/2.53 | % 11.42/2.53 | ALPHA: (9) implies: % 11.42/2.53 | (10) ~ (all_15_0 = 0) % 11.42/2.53 | (11) $i(all_15_4) % 11.42/2.53 | (12) $i(all_15_3) % 11.42/2.53 | (13) $i(all_15_2) % 11.42/2.54 | (14) $i(all_15_1) % 11.42/2.54 | (15) subset(all_15_4, all_15_3) = 0 % 11.42/2.54 | (16) equal_set(all_15_1, all_15_3) = all_15_0 % 11.42/2.54 | (17) union(all_15_2, all_15_4) = all_15_1 % 11.42/2.54 | (18) difference(all_15_3, all_15_4) = all_15_2 % 11.42/2.54 | % 11.42/2.54 | GROUND_INST: instantiating (1) with all_15_4, all_15_3, simplifying with (11), % 11.42/2.54 | (12), (15) gives: % 11.42/2.54 | (19) ! [v0: $i] : ( ~ (member(v0, all_15_4) = 0) | ~ $i(v0) | member(v0, % 11.42/2.54 | all_15_3) = 0) % 11.42/2.54 | % 11.42/2.54 | GROUND_INST: instantiating (3) with all_15_1, all_15_3, all_15_0, simplifying % 11.42/2.54 | with (12), (14), (16) gives: % 11.42/2.54 | (20) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 11.42/2.54 | all_15_3) = v0 & subset(all_15_3, all_15_1) = v1 & ( ~ (v1 = 0) | % 11.42/2.54 | ~ (v0 = 0))) % 11.42/2.54 | % 11.42/2.54 | BETA: splitting (20) gives: % 11.42/2.54 | % 11.42/2.54 | Case 1: % 11.42/2.54 | | % 11.42/2.54 | | (21) all_15_0 = 0 % 11.42/2.54 | | % 11.42/2.54 | | REDUCE: (10), (21) imply: % 11.42/2.54 | | (22) $false % 11.42/2.54 | | % 11.42/2.54 | | CLOSE: (22) is inconsistent. % 11.42/2.54 | | % 11.42/2.54 | Case 2: % 11.42/2.54 | | % 11.42/2.55 | | (23) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_3) = v0 & % 11.42/2.55 | | subset(all_15_3, all_15_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 11.42/2.55 | | % 11.42/2.55 | | DELTA: instantiating (23) with fresh symbols all_27_0, all_27_1 gives: % 11.42/2.55 | | (24) subset(all_15_1, all_15_3) = all_27_1 & subset(all_15_3, all_15_1) = % 11.42/2.55 | | all_27_0 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0)) % 11.42/2.55 | | % 11.42/2.55 | | ALPHA: (24) implies: % 11.42/2.55 | | (25) subset(all_15_3, all_15_1) = all_27_0 % 11.42/2.55 | | (26) subset(all_15_1, all_15_3) = all_27_1 % 11.42/2.55 | | (27) ~ (all_27_0 = 0) | ~ (all_27_1 = 0) % 11.42/2.55 | | % 11.42/2.55 | | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_27_0, % 11.42/2.55 | | simplifying with (12), (14), (25) gives: % 11.42/2.55 | | (28) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 11.42/2.55 | | member(v0, all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 11.42/2.55 | | % 11.42/2.55 | | GROUND_INST: instantiating (2) with all_15_1, all_15_3, all_27_1, % 11.42/2.55 | | simplifying with (12), (14), (26) gives: % 11.42/2.55 | | (29) all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 11.42/2.55 | | member(v0, all_15_1) = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 11.42/2.55 | | % 11.42/2.55 | | BETA: splitting (27) gives: % 11.42/2.55 | | % 11.42/2.55 | | Case 1: % 11.42/2.55 | | | % 11.42/2.55 | | | (30) ~ (all_27_0 = 0) % 11.42/2.55 | | | % 11.42/2.55 | | | BETA: splitting (28) gives: % 11.42/2.55 | | | % 11.42/2.55 | | | Case 1: % 11.42/2.55 | | | | % 11.42/2.55 | | | | (31) all_27_0 = 0 % 11.42/2.55 | | | | % 11.42/2.55 | | | | REDUCE: (30), (31) imply: % 11.42/2.55 | | | | (32) $false % 11.42/2.55 | | | | % 11.42/2.55 | | | | CLOSE: (32) is inconsistent. % 11.42/2.55 | | | | % 11.42/2.55 | | | Case 2: % 11.42/2.55 | | | | % 11.42/2.55 | | | | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 11.42/2.55 | | | | = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 11.42/2.55 | | | | % 11.42/2.55 | | | | DELTA: instantiating (33) with fresh symbols all_40_0, all_40_1 gives: % 11.42/2.55 | | | | (34) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = all_40_0 & % 11.42/2.55 | | | | member(all_40_1, all_15_3) = 0 & $i(all_40_1) % 11.42/2.55 | | | | % 11.42/2.55 | | | | ALPHA: (34) implies: % 11.42/2.55 | | | | (35) ~ (all_40_0 = 0) % 11.42/2.56 | | | | (36) $i(all_40_1) % 11.42/2.56 | | | | (37) member(all_40_1, all_15_3) = 0 % 11.42/2.56 | | | | (38) member(all_40_1, all_15_1) = all_40_0 % 11.42/2.56 | | | | % 11.42/2.56 | | | | GROUND_INST: instantiating (5) with all_40_1, all_15_2, all_15_4, % 11.42/2.56 | | | | all_15_1, all_40_0, simplifying with (11), (13), (17), % 11.42/2.56 | | | | (36), (38) gives: % 11.42/2.56 | | | | (39) all_40_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 11.42/2.56 | | | | (v0 = 0) & member(all_40_1, all_15_2) = v0 & member(all_40_1, % 11.42/2.56 | | | | all_15_4) = v1) % 11.42/2.56 | | | | % 11.42/2.56 | | | | BETA: splitting (39) gives: % 11.42/2.56 | | | | % 11.42/2.56 | | | | Case 1: % 11.42/2.56 | | | | | % 11.42/2.56 | | | | | (40) all_40_0 = 0 % 11.42/2.56 | | | | | % 11.42/2.56 | | | | | REDUCE: (35), (40) imply: % 11.42/2.56 | | | | | (41) $false % 11.42/2.56 | | | | | % 11.42/2.56 | | | | | CLOSE: (41) is inconsistent. % 11.42/2.56 | | | | | % 11.42/2.56 | | | | Case 2: % 11.42/2.56 | | | | | % 11.42/2.56 | | | | | (42) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 11.42/2.56 | | | | | member(all_40_1, all_15_2) = v0 & member(all_40_1, all_15_4) % 11.42/2.56 | | | | | = v1) % 11.42/2.56 | | | | | % 11.42/2.56 | | | | | DELTA: instantiating (42) with fresh symbols all_55_0, all_55_1 gives: % 11.42/2.56 | | | | | (43) ~ (all_55_0 = 0) & ~ (all_55_1 = 0) & member(all_40_1, % 11.42/2.56 | | | | | all_15_2) = all_55_1 & member(all_40_1, all_15_4) = all_55_0 % 11.42/2.56 | | | | | % 11.42/2.56 | | | | | ALPHA: (43) implies: % 11.42/2.56 | | | | | (44) ~ (all_55_1 = 0) % 11.42/2.56 | | | | | (45) ~ (all_55_0 = 0) % 11.42/2.56 | | | | | (46) member(all_40_1, all_15_4) = all_55_0 % 11.42/2.56 | | | | | (47) member(all_40_1, all_15_2) = all_55_1 % 11.42/2.56 | | | | | % 11.42/2.56 | | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_4, all_15_3, % 11.42/2.56 | | | | | all_15_2, all_55_1, simplifying with (11), (12), (18), % 11.42/2.56 | | | | | (36), (47) gives: % 11.42/2.56 | | | | | (48) all_55_1 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1, % 11.42/2.56 | | | | | all_15_3) = v0 & member(all_40_1, all_15_4) = v1 & ( ~ (v0 % 11.42/2.56 | | | | | = 0) | v1 = 0)) % 11.42/2.56 | | | | | % 11.42/2.57 | | | | | BETA: splitting (48) gives: % 11.42/2.57 | | | | | % 11.42/2.57 | | | | | Case 1: % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | (49) all_55_1 = 0 % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | REDUCE: (44), (49) imply: % 11.42/2.57 | | | | | | (50) $false % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | CLOSE: (50) is inconsistent. % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | Case 2: % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | (51) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_3) = % 11.42/2.57 | | | | | | v0 & member(all_40_1, all_15_4) = v1 & ( ~ (v0 = 0) | v1 = % 11.42/2.57 | | | | | | 0)) % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | DELTA: instantiating (51) with fresh symbols all_68_0, all_68_1 % 11.42/2.57 | | | | | | gives: % 11.42/2.57 | | | | | | (52) member(all_40_1, all_15_3) = all_68_1 & member(all_40_1, % 11.42/2.57 | | | | | | all_15_4) = all_68_0 & ( ~ (all_68_1 = 0) | all_68_0 = 0) % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | ALPHA: (52) implies: % 11.42/2.57 | | | | | | (53) member(all_40_1, all_15_4) = all_68_0 % 11.42/2.57 | | | | | | (54) member(all_40_1, all_15_3) = all_68_1 % 11.42/2.57 | | | | | | (55) ~ (all_68_1 = 0) | all_68_0 = 0 % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | GROUND_INST: instantiating (8) with all_55_0, all_68_0, all_15_4, % 11.42/2.57 | | | | | | all_40_1, simplifying with (46), (53) gives: % 11.42/2.57 | | | | | | (56) all_68_0 = all_55_0 % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | GROUND_INST: instantiating (8) with 0, all_68_1, all_15_3, all_40_1, % 11.42/2.57 | | | | | | simplifying with (37), (54) gives: % 11.42/2.57 | | | | | | (57) all_68_1 = 0 % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | BETA: splitting (55) gives: % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | | Case 1: % 11.42/2.57 | | | | | | | % 11.42/2.57 | | | | | | | (58) ~ (all_68_1 = 0) % 11.42/2.57 | | | | | | | % 11.42/2.57 | | | | | | | REDUCE: (57), (58) imply: % 11.42/2.57 | | | | | | | (59) $false % 11.42/2.57 | | | | | | | % 11.42/2.57 | | | | | | | CLOSE: (59) is inconsistent. % 11.42/2.57 | | | | | | | % 11.42/2.57 | | | | | | Case 2: % 11.42/2.57 | | | | | | | % 11.42/2.57 | | | | | | | (60) all_68_0 = 0 % 11.42/2.57 | | | | | | | % 11.42/2.57 | | | | | | | COMBINE_EQS: (56), (60) imply: % 11.42/2.57 | | | | | | | (61) all_55_0 = 0 % 11.42/2.57 | | | | | | | % 11.42/2.57 | | | | | | | REDUCE: (45), (61) imply: % 11.42/2.57 | | | | | | | (62) $false % 11.42/2.57 | | | | | | | % 11.42/2.57 | | | | | | | CLOSE: (62) is inconsistent. % 11.42/2.57 | | | | | | | % 11.42/2.57 | | | | | | End of split % 11.42/2.57 | | | | | | % 11.42/2.57 | | | | | End of split % 11.42/2.57 | | | | | % 11.42/2.57 | | | | End of split % 11.42/2.57 | | | | % 11.42/2.57 | | | End of split % 11.42/2.57 | | | % 11.42/2.57 | | Case 2: % 11.42/2.57 | | | % 11.42/2.57 | | | (63) ~ (all_27_1 = 0) % 11.42/2.57 | | | % 11.42/2.57 | | | BETA: splitting (29) gives: % 11.42/2.57 | | | % 11.42/2.57 | | | Case 1: % 11.42/2.57 | | | | % 11.42/2.57 | | | | (64) all_27_1 = 0 % 11.42/2.57 | | | | % 11.42/2.57 | | | | REDUCE: (63), (64) imply: % 11.42/2.57 | | | | (65) $false % 11.42/2.57 | | | | % 11.42/2.57 | | | | CLOSE: (65) is inconsistent. % 11.42/2.57 | | | | % 11.42/2.57 | | | Case 2: % 11.42/2.57 | | | | % 11.42/2.58 | | | | (66) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 11.42/2.58 | | | | = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 11.42/2.58 | | | | % 11.42/2.58 | | | | DELTA: instantiating (66) with fresh symbols all_40_0, all_40_1 gives: % 11.42/2.58 | | | | (67) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = 0 & % 11.42/2.58 | | | | member(all_40_1, all_15_3) = all_40_0 & $i(all_40_1) % 11.42/2.58 | | | | % 11.42/2.58 | | | | ALPHA: (67) implies: % 11.67/2.58 | | | | (68) ~ (all_40_0 = 0) % 11.67/2.58 | | | | (69) $i(all_40_1) % 11.67/2.58 | | | | (70) member(all_40_1, all_15_3) = all_40_0 % 11.67/2.58 | | | | (71) member(all_40_1, all_15_1) = 0 % 11.67/2.58 | | | | % 11.67/2.58 | | | | GROUND_INST: instantiating (4) with all_40_1, all_15_2, all_15_4, % 11.67/2.58 | | | | all_15_1, simplifying with (11), (13), (17), (69), (71) % 11.67/2.58 | | | | gives: % 11.67/2.58 | | | | (72) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_2) = v0 & % 11.67/2.58 | | | | member(all_40_1, all_15_4) = v1 & (v1 = 0 | v0 = 0)) % 11.67/2.58 | | | | % 11.67/2.58 | | | | DELTA: instantiating (72) with fresh symbols all_48_0, all_48_1 gives: % 11.67/2.58 | | | | (73) member(all_40_1, all_15_2) = all_48_1 & member(all_40_1, % 11.67/2.58 | | | | all_15_4) = all_48_0 & (all_48_0 = 0 | all_48_1 = 0) % 11.67/2.58 | | | | % 11.67/2.58 | | | | ALPHA: (73) implies: % 11.67/2.58 | | | | (74) member(all_40_1, all_15_4) = all_48_0 % 11.67/2.58 | | | | (75) member(all_40_1, all_15_2) = all_48_1 % 11.67/2.59 | | | | (76) all_48_0 = 0 | all_48_1 = 0 % 11.67/2.59 | | | | % 11.67/2.59 | | | | BETA: splitting (76) gives: % 11.67/2.59 | | | | % 11.67/2.59 | | | | Case 1: % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | (77) all_48_0 = 0 % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | REDUCE: (74), (77) imply: % 11.67/2.59 | | | | | (78) member(all_40_1, all_15_4) = 0 % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | GROUND_INST: instantiating (19) with all_40_1, simplifying with (69), % 11.67/2.59 | | | | | (78) gives: % 11.67/2.59 | | | | | (79) member(all_40_1, all_15_3) = 0 % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | GROUND_INST: instantiating (8) with all_40_0, 0, all_15_3, all_40_1, % 11.67/2.59 | | | | | simplifying with (70), (79) gives: % 11.67/2.59 | | | | | (80) all_40_0 = 0 % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | REDUCE: (68), (80) imply: % 11.67/2.59 | | | | | (81) $false % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | CLOSE: (81) is inconsistent. % 11.67/2.59 | | | | | % 11.67/2.59 | | | | Case 2: % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | (82) all_48_1 = 0 % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | REDUCE: (75), (82) imply: % 11.67/2.59 | | | | | (83) member(all_40_1, all_15_2) = 0 % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | GROUND_INST: instantiating (6) with all_40_1, all_15_4, all_15_3, % 11.67/2.59 | | | | | all_15_2, simplifying with (11), (12), (18), (69), (83) % 11.67/2.59 | | | | | gives: % 11.67/2.59 | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_3) = 0 & % 11.67/2.59 | | | | | member(all_40_1, all_15_4) = v0) % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | DELTA: instantiating (84) with fresh symbol all_62_0 gives: % 11.67/2.59 | | | | | (85) ~ (all_62_0 = 0) & member(all_40_1, all_15_3) = 0 & % 11.67/2.59 | | | | | member(all_40_1, all_15_4) = all_62_0 % 11.67/2.59 | | | | | % 11.67/2.59 | | | | | ALPHA: (85) implies: % 11.67/2.60 | | | | | (86) member(all_40_1, all_15_3) = 0 % 11.67/2.60 | | | | | % 11.67/2.60 | | | | | GROUND_INST: instantiating (8) with all_40_0, 0, all_15_3, all_40_1, % 11.67/2.60 | | | | | simplifying with (70), (86) gives: % 11.67/2.60 | | | | | (87) all_40_0 = 0 % 11.67/2.60 | | | | | % 11.67/2.60 | | | | | REDUCE: (68), (87) imply: % 11.67/2.60 | | | | | (88) $false % 11.67/2.60 | | | | | % 11.67/2.60 | | | | | CLOSE: (88) is inconsistent. % 11.67/2.60 | | | | | % 11.67/2.60 | | | | End of split % 11.67/2.60 | | | | % 11.67/2.60 | | | End of split % 11.67/2.60 | | | % 11.67/2.60 | | End of split % 11.67/2.60 | | % 11.67/2.60 | End of split % 11.67/2.60 | % 11.67/2.60 End of proof % 11.67/2.60 % SZS output end Proof for theBenchmark % 11.67/2.60 % 11.67/2.60 1965ms %------------------------------------------------------------------------------