%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET060+1 : TPTP v8.1.2. Bugfixed v5.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.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 15:23:28 EDT 2023 % Result : Theorem 13.92s 2.65s % Output : Proof 18.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET060+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n020.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Sat Aug 26 08:13:00 EDT 2023 % 0.15/0.35 % CPUTime : % 0.22/0.64 ________ _____ % 0.22/0.64 ___ __ \_________(_)________________________________ % 0.22/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.64 % 0.22/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.64 (2023-06-19) % 0.22/0.64 % 0.22/0.64 (c) Philipp Rümmer, 2009-2023 % 0.22/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.64 Amanda Stjerna. % 0.22/0.64 Free software under BSD-3-Clause. % 0.22/0.64 % 0.22/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.64 % 0.22/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.65 Running up to 7 provers in parallel. % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 3.54/1.19 Prover 1: Preprocessing ... % 3.54/1.19 Prover 4: Preprocessing ... % 4.04/1.27 Prover 3: Preprocessing ... % 4.04/1.27 Prover 5: Preprocessing ... % 4.04/1.27 Prover 6: Preprocessing ... % 4.04/1.27 Prover 2: Preprocessing ... % 4.04/1.27 Prover 0: Preprocessing ... % 8.13/2.00 Prover 1: Warning: ignoring some quantifiers % 9.14/2.11 Prover 3: Warning: ignoring some quantifiers % 9.14/2.11 Prover 1: Constructing countermodel ... % 9.14/2.13 Prover 6: Proving ... % 9.14/2.13 Prover 5: Proving ... % 9.14/2.13 Prover 3: Constructing countermodel ... % 10.20/2.15 Prover 4: Warning: ignoring some quantifiers % 10.20/2.20 Prover 4: Constructing countermodel ... % 11.08/2.28 Prover 2: Proving ... % 11.08/2.31 Prover 0: Proving ... % 13.92/2.65 Prover 3: proved (1982ms) % 13.92/2.65 % 13.92/2.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.92/2.65 % 13.92/2.66 Prover 0: stopped % 13.92/2.66 Prover 2: stopped % 13.92/2.67 Prover 5: stopped % 13.92/2.67 Prover 6: stopped % 13.92/2.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.92/2.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.92/2.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.92/2.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.92/2.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.92/2.77 Prover 13: Preprocessing ... % 13.92/2.77 Prover 7: Preprocessing ... % 13.92/2.77 Prover 10: Preprocessing ... % 13.92/2.78 Prover 8: Preprocessing ... % 14.41/2.79 Prover 11: Preprocessing ... % 15.83/2.95 Prover 7: Warning: ignoring some quantifiers % 15.83/2.95 Prover 10: Warning: ignoring some quantifiers % 16.20/2.97 Prover 8: Warning: ignoring some quantifiers % 16.20/2.98 Prover 10: Constructing countermodel ... % 16.20/2.99 Prover 7: Constructing countermodel ... % 16.20/3.01 Prover 8: Constructing countermodel ... % 16.85/3.07 Prover 13: Warning: ignoring some quantifiers % 17.15/3.11 Prover 11: Warning: ignoring some quantifiers % 17.15/3.12 Prover 11: Constructing countermodel ... % 17.15/3.13 Prover 13: Constructing countermodel ... % 17.70/3.19 Prover 10: Found proof (size 8) % 17.70/3.19 Prover 10: proved (522ms) % 17.70/3.20 Prover 11: stopped % 17.70/3.20 Prover 1: stopped % 17.70/3.20 Prover 4: stopped % 17.70/3.20 Prover 8: stopped % 17.70/3.20 Prover 13: stopped % 17.70/3.21 Prover 7: stopped % 17.70/3.21 % 17.70/3.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.70/3.21 % 17.70/3.21 % SZS output start Proof for theBenchmark % 17.70/3.21 Assumptions after simplification: % 17.70/3.21 --------------------------------- % 17.70/3.21 % 17.70/3.21 (complement) % 18.09/3.24 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 18.09/3.24 (complement(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v1, v2) | ~ % 18.09/3.24 member(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 18.09/3.24 (complement(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v1, v2) | % 18.09/3.24 member(v1, universal_class)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 18.09/3.24 (complement(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v1, % 18.09/3.24 universal_class) | member(v1, v2) | member(v1, v0)) % 18.09/3.24 % 18.09/3.24 (intersection) % 18.09/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, % 18.09/3.24 v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v2, v3) | % 18.09/3.24 member(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 18.09/3.24 ~ (intersection(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 18.09/3.24 member(v2, v3) | member(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.09/3.24 ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.09/3.24 $i(v0) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) % 18.09/3.24 % 18.09/3.24 (special_classes_lemma) % 18.09/3.24 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (complement(v0) = v2 & % 18.09/3.24 intersection(v2, v0) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & member(v1, % 18.09/3.24 v3)) % 18.09/3.24 % 18.09/3.24 Further assumptions not needed in the proof: % 18.09/3.24 -------------------------------------------- % 18.09/3.25 apply_defn, choice, class_elements_are_sets, compose_defn1, compose_defn2, % 18.09/3.25 cross_product, cross_product_defn, disjoint_defn, domain_of, element_relation, % 18.09/3.25 element_relation_defn, extensionality, first_second, flip, flip_defn, % 18.09/3.25 function_defn, identity_relation, image_defn, inductive_defn, infinity, % 18.09/3.25 inverse_defn, null_class_defn, ordered_pair_defn, power_class, power_class_defn, % 18.09/3.25 range_of_defn, regularity, replacement, restrict_defn, rotate, rotate_defn, % 18.09/3.25 singleton_set_defn, subclass_defn, successor_defn, successor_relation_defn1, % 18.09/3.25 successor_relation_defn2, sum_class, sum_class_defn, union_defn, unordered_pair, % 18.09/3.25 unordered_pair_defn % 18.09/3.25 % 18.09/3.25 Those formulas are unsatisfiable: % 18.09/3.25 --------------------------------- % 18.09/3.25 % 18.09/3.25 Begin of proof % 18.09/3.25 | % 18.09/3.25 | ALPHA: (intersection) implies: % 18.09/3.25 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.09/3.25 | (intersection(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 18.09/3.25 | member(v2, v3) | member(v2, v0)) % 18.09/3.25 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.09/3.25 | (intersection(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 18.09/3.25 | member(v2, v3) | member(v2, v1)) % 18.09/3.25 | % 18.09/3.25 | ALPHA: (complement) implies: % 18.09/3.25 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (complement(v0) = v2) | % 18.09/3.25 | ~ $i(v1) | ~ $i(v0) | ~ member(v1, v2) | ~ member(v1, v0)) % 18.09/3.25 | % 18.09/3.25 | DELTA: instantiating (special_classes_lemma) with fresh symbols all_53_0, % 18.09/3.25 | all_53_1, all_53_2, all_53_3 gives: % 18.09/3.25 | (4) complement(all_53_3) = all_53_1 & intersection(all_53_1, all_53_3) = % 18.09/3.25 | all_53_0 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) & % 18.09/3.25 | member(all_53_2, all_53_0) % 18.09/3.25 | % 18.09/3.25 | ALPHA: (4) implies: % 18.09/3.25 | (5) member(all_53_2, all_53_0) % 18.09/3.25 | (6) $i(all_53_3) % 18.09/3.25 | (7) $i(all_53_2) % 18.09/3.25 | (8) $i(all_53_1) % 18.09/3.25 | (9) intersection(all_53_1, all_53_3) = all_53_0 % 18.09/3.25 | (10) complement(all_53_3) = all_53_1 % 18.09/3.25 | % 18.09/3.26 | GROUND_INST: instantiating (2) with all_53_1, all_53_3, all_53_2, all_53_0, % 18.09/3.26 | simplifying with (5), (6), (7), (8), (9) gives: % 18.09/3.26 | (11) member(all_53_2, all_53_3) % 18.09/3.26 | % 18.09/3.26 | GROUND_INST: instantiating (1) with all_53_1, all_53_3, all_53_2, all_53_0, % 18.09/3.26 | simplifying with (5), (6), (7), (8), (9) gives: % 18.09/3.26 | (12) member(all_53_2, all_53_1) % 18.09/3.26 | % 18.09/3.26 | GROUND_INST: instantiating (3) with all_53_3, all_53_2, all_53_1, simplifying % 18.09/3.26 | with (6), (7), (10), (11), (12) gives: % 18.09/3.26 | (13) $false % 18.09/3.26 | % 18.09/3.26 | CLOSE: (13) is inconsistent. % 18.09/3.26 | % 18.09/3.26 End of proof % 18.09/3.26 % SZS output end Proof for theBenchmark % 18.09/3.26 % 18.09/3.26 2620ms %------------------------------------------------------------------------------