%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET024+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 : n024.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 15:23:13 EDT 2023 % Result : Theorem 13.56s 2.67s % Output : Proof 19.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET024+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n024.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 11:33:54 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.03/1.23 Prover 1: Preprocessing ... % 3.03/1.23 Prover 4: Preprocessing ... % 3.63/1.27 Prover 2: Preprocessing ... % 3.63/1.27 Prover 6: Preprocessing ... % 3.63/1.27 Prover 3: Preprocessing ... % 3.63/1.27 Prover 0: Preprocessing ... % 3.63/1.27 Prover 5: Preprocessing ... % 8.17/1.96 Prover 1: Warning: ignoring some quantifiers % 9.65/2.06 Prover 3: Warning: ignoring some quantifiers % 9.65/2.09 Prover 3: Constructing countermodel ... % 9.65/2.09 Prover 5: Proving ... % 9.65/2.09 Prover 1: Constructing countermodel ... % 9.65/2.10 Prover 6: Proving ... % 10.10/2.13 Prover 4: Warning: ignoring some quantifiers % 10.35/2.18 Prover 4: Constructing countermodel ... % 10.35/2.20 Prover 2: Proving ... % 10.89/2.27 Prover 0: Proving ... % 13.56/2.66 Prover 0: proved (2021ms) % 13.56/2.66 % 13.56/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.56/2.67 % 13.56/2.67 Prover 3: stopped % 13.56/2.68 Prover 2: stopped % 13.56/2.69 Prover 5: stopped % 13.56/2.70 Prover 6: stopped % 14.44/2.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.44/2.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.44/2.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.44/2.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.44/2.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.61/2.73 Prover 10: Preprocessing ... % 14.61/2.74 Prover 7: Preprocessing ... % 14.61/2.74 Prover 8: Preprocessing ... % 14.61/2.77 Prover 11: Preprocessing ... % 14.61/2.80 Prover 13: Preprocessing ... % 15.73/2.89 Prover 10: Warning: ignoring some quantifiers % 15.73/2.93 Prover 10: Constructing countermodel ... % 15.73/2.93 Prover 7: Warning: ignoring some quantifiers % 16.34/2.98 Prover 7: Constructing countermodel ... % 16.86/3.03 Prover 11: Warning: ignoring some quantifiers % 16.86/3.05 Prover 8: Warning: ignoring some quantifiers % 16.86/3.05 Prover 11: Constructing countermodel ... % 16.86/3.07 Prover 8: Constructing countermodel ... % 16.86/3.08 Prover 13: Warning: ignoring some quantifiers % 16.86/3.11 Prover 13: Constructing countermodel ... % 18.00/3.29 Prover 7: Found proof (size 10) % 18.00/3.29 Prover 7: proved (621ms) % 18.00/3.29 Prover 10: gave up % 18.00/3.29 Prover 11: stopped % 18.00/3.29 Prover 13: stopped % 18.00/3.29 Prover 8: stopped % 18.00/3.29 Prover 4: stopped % 18.00/3.29 Prover 1: stopped % 18.00/3.29 % 18.00/3.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.00/3.29 % 18.00/3.29 % SZS output start Proof for theBenchmark % 18.00/3.30 Assumptions after simplification: % 18.00/3.30 --------------------------------- % 18.00/3.30 % 18.00/3.30 (set_in_its_singleton) % 18.71/3.32 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : (singleton(v0) = v1 & $i(v1) % 18.71/3.32 & $i(v0) & member(v0, universal_class) & ~ member(v0, v1)) % 18.71/3.32 % 18.71/3.32 (singleton_set_defn) % 18.71/3.32 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 18.71/3.33 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 18.71/3.33 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1))) % 18.71/3.33 % 18.71/3.33 (unordered_pair_defn) % 18.71/3.33 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 18.71/3.33 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 18.71/3.33 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 18.71/3.33 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.71/3.33 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : ! % 18.71/3.33 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ % 18.71/3.33 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : ! % 18.71/3.33 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 18.71/3.33 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) % 18.71/3.33 % 18.71/3.33 Further assumptions not needed in the proof: % 18.71/3.33 -------------------------------------------- % 18.71/3.33 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 18.71/3.33 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 18.71/3.33 element_relation, element_relation_defn, extensionality, first_second, flip, % 18.71/3.33 flip_defn, function_defn, identity_relation, image_defn, inductive_defn, % 18.71/3.33 infinity, intersection, inverse_defn, null_class_defn, ordered_pair_defn, % 18.71/3.33 power_class, power_class_defn, range_of_defn, regularity, replacement, % 18.71/3.33 restrict_defn, rotate, rotate_defn, subclass_defn, successor_defn, % 18.71/3.33 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn, % 18.71/3.33 union_defn, unordered_pair % 18.71/3.33 % 18.71/3.33 Those formulas are unsatisfiable: % 18.71/3.33 --------------------------------- % 18.71/3.33 % 18.71/3.33 Begin of proof % 18.71/3.33 | % 18.71/3.33 | ALPHA: (unordered_pair_defn) implies: % 18.71/3.33 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 18.71/3.33 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) | % 18.71/3.33 | member(v0, v2)) % 18.71/3.33 | % 18.71/3.33 | ALPHA: (singleton_set_defn) implies: % 18.71/3.33 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 18.71/3.33 | (unordered_pair(v0, v0) = v1 & $i(v1))) % 18.71/3.33 | % 18.71/3.33 | ALPHA: (set_in_its_singleton) implies: % 18.71/3.33 | (3) ? [v0: $i] : ? [v1: $i] : (singleton(v0) = v1 & $i(v1) & $i(v0) & % 18.71/3.33 | member(v0, universal_class) & ~ member(v0, v1)) % 18.71/3.33 | % 18.71/3.34 | DELTA: instantiating (3) with fresh symbols all_41_0, all_41_1 gives: % 18.71/3.34 | (4) singleton(all_41_1) = all_41_0 & $i(all_41_0) & $i(all_41_1) & % 18.71/3.34 | member(all_41_1, universal_class) & ~ member(all_41_1, all_41_0) % 18.71/3.34 | % 18.71/3.34 | ALPHA: (4) implies: % 18.71/3.34 | (5) ~ member(all_41_1, all_41_0) % 18.71/3.34 | (6) member(all_41_1, universal_class) % 18.71/3.34 | (7) $i(all_41_1) % 18.71/3.34 | (8) singleton(all_41_1) = all_41_0 % 18.71/3.34 | % 18.71/3.34 | GROUND_INST: instantiating (2) with all_41_1, all_41_0, simplifying with (7), % 18.71/3.34 | (8) gives: % 18.71/3.34 | (9) unordered_pair(all_41_1, all_41_1) = all_41_0 & $i(all_41_0) % 18.71/3.34 | % 18.71/3.34 | ALPHA: (9) implies: % 18.71/3.34 | (10) unordered_pair(all_41_1, all_41_1) = all_41_0 % 18.71/3.34 | % 18.71/3.34 | GROUND_INST: instantiating (1) with all_41_1, all_41_1, all_41_0, simplifying % 18.71/3.34 | with (5), (6), (7), (10) gives: % 18.71/3.34 | (11) $false % 18.71/3.34 | % 18.71/3.34 | CLOSE: (11) is inconsistent. % 18.71/3.34 | % 18.71/3.34 End of proof % 19.08/3.34 % SZS output end Proof for theBenchmark % 19.08/3.34 % 19.08/3.34 2721ms %------------------------------------------------------------------------------