%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET093+1 : TPTP v8.1.2. Bugfixed v7.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n015.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 15:23:44 EDT 2023 % Result : Theorem 12.81s 2.49s % Output : Proof 18.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET093+1 : TPTP v8.1.2. Bugfixed v7.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n015.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 10:21:38 EDT 2023 % 0.20/0.35 % 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 ... % 0.20/0.64 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 3.63/1.25 Prover 4: Preprocessing ... % 3.63/1.26 Prover 1: Preprocessing ... % 3.63/1.30 Prover 2: Preprocessing ... % 3.63/1.30 Prover 5: Preprocessing ... % 3.63/1.30 Prover 3: Preprocessing ... % 3.63/1.30 Prover 6: Preprocessing ... % 3.63/1.30 Prover 0: Preprocessing ... % 8.47/1.95 Prover 1: Warning: ignoring some quantifiers % 9.06/1.99 Prover 1: Constructing countermodel ... % 9.06/1.99 Prover 6: Proving ... % 9.06/1.99 Prover 3: Warning: ignoring some quantifiers % 9.06/1.99 Prover 5: Proving ... % 9.06/2.00 Prover 4: Warning: ignoring some quantifiers % 9.06/2.02 Prover 3: Constructing countermodel ... % 9.06/2.04 Prover 2: Proving ... % 9.06/2.05 Prover 4: Constructing countermodel ... % 9.06/2.07 Prover 0: Proving ... % 12.45/2.49 Prover 0: proved (1839ms) % 12.81/2.49 % 12.81/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.81/2.49 % 12.81/2.49 Prover 6: stopped % 12.81/2.49 Prover 5: stopped % 12.81/2.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.81/2.49 Prover 2: stopped % 12.81/2.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.81/2.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.81/2.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.81/2.50 Prover 3: stopped % 12.81/2.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.25/2.60 Prover 11: Preprocessing ... % 13.64/2.61 Prover 13: Preprocessing ... % 13.64/2.62 Prover 10: Preprocessing ... % 13.64/2.65 Prover 7: Preprocessing ... % 14.00/2.67 Prover 8: Preprocessing ... % 14.00/2.75 Prover 10: Warning: ignoring some quantifiers % 14.00/2.77 Prover 10: Constructing countermodel ... % 14.00/2.84 Prover 7: Warning: ignoring some quantifiers % 14.00/2.86 Prover 7: Constructing countermodel ... % 14.00/2.87 Prover 13: Warning: ignoring some quantifiers % 14.00/2.87 Prover 8: Warning: ignoring some quantifiers % 15.12/2.89 Prover 8: Constructing countermodel ... % 15.12/2.89 Prover 13: Constructing countermodel ... % 15.12/2.91 Prover 11: Warning: ignoring some quantifiers % 16.07/2.93 Prover 11: Constructing countermodel ... % 17.45/3.12 Prover 10: gave up % 17.45/3.14 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 17.68/3.18 Prover 16: Preprocessing ... % 17.68/3.20 Prover 7: Found proof (size 10) % 17.68/3.20 Prover 7: proved (702ms) % 17.68/3.20 Prover 8: stopped % 17.68/3.20 Prover 4: stopped % 17.68/3.20 Prover 11: stopped % 17.68/3.20 Prover 1: stopped % 17.68/3.20 Prover 13: stopped % 18.23/3.23 Prover 16: stopped % 18.23/3.23 % 18.23/3.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.23/3.23 % 18.23/3.23 % SZS output start Proof for theBenchmark % 18.23/3.24 Assumptions after simplification: % 18.23/3.24 --------------------------------- % 18.23/3.24 % 18.23/3.24 (corollary_2_to_singletons_are_sets) % 18.23/3.26 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : (member_of(v0) = v1 & % 18.23/3.26 singleton(v1) = v0 & $i(v1) & $i(v0) & ~ member(v0, universal_class)) % 18.23/3.26 % 18.23/3.26 (singleton_set_defn) % 18.23/3.26 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 18.23/3.26 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 18.23/3.26 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1))) % 18.23/3.26 % 18.23/3.26 (unordered_pair) % 18.23/3.26 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 18.23/3.26 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | member(v2, % 18.23/3.26 universal_class)) % 18.23/3.26 % 18.23/3.26 Further assumptions not needed in the proof: % 18.23/3.26 -------------------------------------------- % 18.23/3.26 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 18.23/3.26 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 18.23/3.26 element_relation, element_relation_defn, extensionality, first_second, flip, % 18.23/3.26 flip_defn, function_defn, identity_relation, image_defn, inductive_defn, % 18.23/3.26 infinity, intersection, inverse_defn, member_singleton_singleton, % 18.23/3.26 member_singleton_universal, member_universal_self, null_class_defn, % 18.23/3.26 ordered_pair_defn, power_class, power_class_defn, range_of_defn, regularity, % 18.23/3.26 replacement, restrict_defn, rotate, rotate_defn, singleton_self, subclass_defn, % 18.23/3.26 successor_defn, successor_relation_defn1, successor_relation_defn2, sum_class, % 18.23/3.26 sum_class_defn, union_defn, unordered_pair_defn % 18.23/3.26 % 18.23/3.26 Those formulas are unsatisfiable: % 18.23/3.26 --------------------------------- % 18.23/3.26 % 18.23/3.26 Begin of proof % 18.23/3.26 | % 18.23/3.26 | ALPHA: (unordered_pair) implies: % 18.23/3.27 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 18.23/3.27 | v2) | ~ $i(v1) | ~ $i(v0) | member(v2, universal_class)) % 18.23/3.27 | % 18.23/3.27 | ALPHA: (singleton_set_defn) implies: % 18.23/3.27 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 18.23/3.27 | (unordered_pair(v0, v0) = v1 & $i(v1))) % 18.23/3.27 | % 18.23/3.27 | ALPHA: (corollary_2_to_singletons_are_sets) implies: % 18.23/3.27 | (3) ? [v0: $i] : ? [v1: $i] : (member_of(v0) = v1 & singleton(v1) = v0 & % 18.23/3.27 | $i(v1) & $i(v0) & ~ member(v0, universal_class)) % 18.23/3.27 | % 18.23/3.27 | DELTA: instantiating (3) with fresh symbols all_45_0, all_45_1 gives: % 18.23/3.27 | (4) member_of(all_45_1) = all_45_0 & singleton(all_45_0) = all_45_1 & % 18.23/3.27 | $i(all_45_0) & $i(all_45_1) & ~ member(all_45_1, universal_class) % 18.23/3.27 | % 18.23/3.27 | ALPHA: (4) implies: % 18.23/3.27 | (5) ~ member(all_45_1, universal_class) % 18.23/3.27 | (6) $i(all_45_0) % 18.23/3.27 | (7) singleton(all_45_0) = all_45_1 % 18.23/3.27 | % 18.23/3.27 | GROUND_INST: instantiating (2) with all_45_0, all_45_1, simplifying with (6), % 18.23/3.27 | (7) gives: % 18.23/3.27 | (8) unordered_pair(all_45_0, all_45_0) = all_45_1 & $i(all_45_1) % 18.23/3.27 | % 18.23/3.27 | ALPHA: (8) implies: % 18.23/3.27 | (9) unordered_pair(all_45_0, all_45_0) = all_45_1 % 18.23/3.27 | % 18.23/3.27 | GROUND_INST: instantiating (1) with all_45_0, all_45_0, all_45_1, simplifying % 18.23/3.27 | with (5), (6), (9) gives: % 18.23/3.27 | (10) $false % 18.23/3.27 | % 18.23/3.27 | CLOSE: (10) is inconsistent. % 18.23/3.27 | % 18.23/3.27 End of proof % 18.23/3.27 % SZS output end Proof for theBenchmark % 18.23/3.27 % 18.23/3.27 2642ms %------------------------------------------------------------------------------