%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET767+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 : n025.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 15:26:21 EDT 2023 % Result : Theorem 8.16s 1.85s % Output : Proof 9.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET767+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n025.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Aug 26 08:47:53 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.77/1.07 Prover 1: Preprocessing ... % 2.77/1.08 Prover 4: Preprocessing ... % 3.02/1.13 Prover 6: Preprocessing ... % 3.02/1.13 Prover 0: Preprocessing ... % 3.02/1.13 Prover 5: Preprocessing ... % 3.02/1.13 Prover 2: Preprocessing ... % 3.02/1.13 Prover 3: Preprocessing ... % 6.85/1.67 Prover 5: Proving ... % 6.85/1.68 Prover 2: Proving ... % 6.85/1.69 Prover 6: Proving ... % 6.85/1.73 Prover 3: Constructing countermodel ... % 6.85/1.74 Prover 1: Constructing countermodel ... % 8.16/1.85 Prover 3: proved (1219ms) % 8.16/1.85 % 8.16/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.16/1.85 % 8.16/1.86 Prover 2: stopped % 8.16/1.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.16/1.86 Prover 5: stopped % 8.16/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.16/1.87 Prover 6: stopped % 8.16/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.55/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.55/1.91 Prover 1: Found proof (size 16) % 8.55/1.91 Prover 1: proved (1286ms) % 8.55/1.91 Prover 8: Preprocessing ... % 8.55/1.94 Prover 7: Preprocessing ... % 8.55/1.94 Prover 11: Preprocessing ... % 8.55/1.95 Prover 10: Preprocessing ... % 8.95/1.98 Prover 7: stopped % 8.95/1.98 Prover 10: stopped % 8.95/1.99 Prover 0: Proving ... % 8.95/1.99 Prover 0: stopped % 8.95/1.99 Prover 4: Constructing countermodel ... % 8.95/2.01 Prover 4: stopped % 8.95/2.01 Prover 11: stopped % 8.95/2.07 Prover 8: Warning: ignoring some quantifiers % 8.95/2.08 Prover 8: Constructing countermodel ... % 8.95/2.09 Prover 8: stopped % 8.95/2.09 % 8.95/2.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.95/2.09 % 8.95/2.10 % SZS output start Proof for theBenchmark % 8.95/2.10 Assumptions after simplification: % 8.95/2.10 --------------------------------- % 8.95/2.10 % 8.95/2.10 (equivalence_class) % 8.95/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.95/2.13 int] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, % 8.95/2.13 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] % 8.95/2.13 : ? [v7: any] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 = % 8.95/2.13 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 8.95/2.13 [v3: $i] : ! [v4: $i] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ % 8.95/2.13 (member(v3, v4) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 8.95/2.13 (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) % 8.95/2.13 % 8.95/2.13 (subset) % 8.95/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.95/2.14 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.95/2.14 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.95/2.14 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.95/2.14 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.95/2.14 % 8.95/2.14 (thIII03) % 8.95/2.14 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 8.95/2.14 = 0) & equivalence_class(v2, v0, v1) = v3 & equivalence(v1, v0) = 0 & % 8.95/2.14 subset(v3, v0) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.95/2.14 % 8.95/2.14 (function-axioms) % 9.89/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 9.89/2.15 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, % 9.89/2.15 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 9.89/2.15 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = % 9.89/2.15 v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.89/2.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.89/2.15 (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0: % 9.89/2.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.89/2.15 : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) & % 9.89/2.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 9.89/2.15 $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) % 9.89/2.15 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.89/2.15 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 9.89/2.15 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.89/2.15 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 9.89/2.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.89/2.15 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 9.89/2.15 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 9.89/2.15 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 9.89/2.15 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 9.89/2.15 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.89/2.15 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 9.89/2.15 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.89/2.15 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 9.89/2.15 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 9.89/2.15 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.89/2.15 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 9.89/2.15 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 9.89/2.15 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 9.89/2.15 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 9.89/2.15 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 9.89/2.15 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 9.89/2.15 (power_set(v2) = v0)) % 9.89/2.15 % 9.89/2.15 Further assumptions not needed in the proof: % 9.89/2.15 -------------------------------------------- % 9.89/2.15 difference, disjoint, empty_set, equal_set, equivalence, intersection, % 9.89/2.15 partition, power_set, pre_order, product, singleton, sum, union, unordered_pair % 9.89/2.15 % 9.89/2.15 Those formulas are unsatisfiable: % 9.89/2.15 --------------------------------- % 9.89/2.15 % 9.89/2.15 Begin of proof % 9.89/2.15 | % 9.89/2.15 | ALPHA: (subset) implies: % 9.89/2.15 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 9.89/2.15 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 9.89/2.15 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 9.89/2.15 | % 9.89/2.15 | ALPHA: (equivalence_class) implies: % 9.89/2.15 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 9.89/2.15 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | ~ % 9.89/2.15 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (apply(v0, v2, v3) = 0 & % 9.89/2.15 | member(v3, v1) = 0)) % 9.89/2.15 | % 9.89/2.15 | ALPHA: (function-axioms) implies: % 9.89/2.15 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.89/2.15 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 9.89/2.15 | = v0)) % 9.89/2.15 | % 9.89/2.15 | DELTA: instantiating (thIII03) with fresh symbols all_20_0, all_20_1, % 9.89/2.15 | all_20_2, all_20_3, all_20_4 gives: % 9.89/2.16 | (4) ~ (all_20_0 = 0) & equivalence_class(all_20_2, all_20_4, all_20_3) = % 9.89/2.16 | all_20_1 & equivalence(all_20_3, all_20_4) = 0 & subset(all_20_1, % 9.89/2.16 | all_20_4) = all_20_0 & $i(all_20_1) & $i(all_20_2) & $i(all_20_3) & % 9.89/2.16 | $i(all_20_4) % 9.89/2.16 | % 9.89/2.16 | ALPHA: (4) implies: % 9.89/2.16 | (5) ~ (all_20_0 = 0) % 9.89/2.16 | (6) $i(all_20_4) % 9.89/2.16 | (7) $i(all_20_3) % 9.89/2.16 | (8) $i(all_20_2) % 9.89/2.16 | (9) $i(all_20_1) % 9.89/2.16 | (10) subset(all_20_1, all_20_4) = all_20_0 % 9.89/2.16 | (11) equivalence_class(all_20_2, all_20_4, all_20_3) = all_20_1 % 9.89/2.16 | % 9.89/2.16 | GROUND_INST: instantiating (1) with all_20_1, all_20_4, all_20_0, simplifying % 9.89/2.16 | with (6), (9), (10) gives: % 9.89/2.16 | (12) all_20_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 9.89/2.16 | all_20_1) = 0 & member(v0, all_20_4) = v1 & $i(v0)) % 9.89/2.16 | % 9.89/2.16 | BETA: splitting (12) gives: % 9.89/2.16 | % 9.89/2.16 | Case 1: % 9.89/2.16 | | % 9.89/2.16 | | (13) all_20_0 = 0 % 9.89/2.16 | | % 9.89/2.16 | | REDUCE: (5), (13) imply: % 9.89/2.16 | | (14) $false % 9.89/2.16 | | % 9.89/2.16 | | CLOSE: (14) is inconsistent. % 9.89/2.16 | | % 9.89/2.16 | Case 2: % 9.89/2.16 | | % 9.89/2.16 | | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_20_1) = 0 % 9.89/2.16 | | & member(v0, all_20_4) = v1 & $i(v0)) % 9.89/2.16 | | % 9.89/2.16 | | DELTA: instantiating (15) with fresh symbols all_32_0, all_32_1 gives: % 9.89/2.16 | | (16) ~ (all_32_0 = 0) & member(all_32_1, all_20_1) = 0 & % 9.89/2.16 | | member(all_32_1, all_20_4) = all_32_0 & $i(all_32_1) % 9.89/2.16 | | % 9.89/2.16 | | ALPHA: (16) implies: % 9.89/2.16 | | (17) ~ (all_32_0 = 0) % 9.89/2.16 | | (18) $i(all_32_1) % 9.89/2.16 | | (19) member(all_32_1, all_20_4) = all_32_0 % 9.89/2.16 | | (20) member(all_32_1, all_20_1) = 0 % 9.89/2.16 | | % 9.89/2.16 | | GROUND_INST: instantiating (2) with all_20_3, all_20_4, all_20_2, all_32_1, % 9.89/2.16 | | all_20_1, simplifying with (6), (7), (8), (11), (18), (20) % 9.89/2.16 | | gives: % 9.89/2.16 | | (21) apply(all_20_3, all_20_2, all_32_1) = 0 & member(all_32_1, all_20_4) % 9.89/2.16 | | = 0 % 9.89/2.16 | | % 9.89/2.16 | | ALPHA: (21) implies: % 9.89/2.16 | | (22) member(all_32_1, all_20_4) = 0 % 9.89/2.16 | | % 9.89/2.16 | | GROUND_INST: instantiating (3) with all_32_0, 0, all_20_4, all_32_1, % 9.89/2.16 | | simplifying with (19), (22) gives: % 9.89/2.16 | | (23) all_32_0 = 0 % 9.89/2.16 | | % 9.89/2.17 | | REDUCE: (17), (23) imply: % 9.89/2.17 | | (24) $false % 9.89/2.17 | | % 9.89/2.17 | | CLOSE: (24) is inconsistent. % 9.89/2.17 | | % 9.89/2.17 | End of split % 9.89/2.17 | % 9.89/2.17 End of proof % 9.89/2.17 % SZS output end Proof for theBenchmark % 9.89/2.17 % 9.89/2.17 1561ms %------------------------------------------------------------------------------