%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET073+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 : n002.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 15:23:36 EDT 2023 % Result : Theorem 15.87s 2.87s % Output : Proof 20.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET073+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n002.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sat Aug 26 16:38:03 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.23/1.13 Prover 1: Preprocessing ... % 3.23/1.13 Prover 4: Preprocessing ... % 3.48/1.17 Prover 5: Preprocessing ... % 3.48/1.17 Prover 6: Preprocessing ... % 3.48/1.17 Prover 0: Preprocessing ... % 3.48/1.17 Prover 2: Preprocessing ... % 3.48/1.17 Prover 3: Preprocessing ... % 8.50/1.91 Prover 1: Warning: ignoring some quantifiers % 8.50/1.95 Prover 3: Warning: ignoring some quantifiers % 8.50/1.96 Prover 6: Proving ... % 8.50/1.96 Prover 5: Proving ... % 8.50/1.96 Prover 1: Constructing countermodel ... % 9.32/2.01 Prover 3: Constructing countermodel ... % 9.32/2.02 Prover 4: Warning: ignoring some quantifiers % 9.92/2.07 Prover 4: Constructing countermodel ... % 9.92/2.09 Prover 2: Proving ... % 10.38/2.11 Prover 0: Proving ... % 15.87/2.87 Prover 5: proved (2232ms) % 15.87/2.87 % 15.87/2.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.87/2.87 % 15.87/2.89 Prover 2: stopped % 15.87/2.89 Prover 3: stopped % 15.87/2.89 Prover 6: stopped % 15.87/2.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.87/2.89 Prover 0: stopped % 15.87/2.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.87/2.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.87/2.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.87/2.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.88/2.99 Prover 10: Preprocessing ... % 16.88/2.99 Prover 11: Preprocessing ... % 16.88/2.99 Prover 8: Preprocessing ... % 16.88/3.00 Prover 7: Preprocessing ... % 16.88/3.00 Prover 13: Preprocessing ... % 18.12/3.16 Prover 10: Warning: ignoring some quantifiers % 18.12/3.16 Prover 7: Warning: ignoring some quantifiers % 18.12/3.19 Prover 10: Constructing countermodel ... % 18.12/3.19 Prover 13: Warning: ignoring some quantifiers % 18.12/3.24 Prover 7: Constructing countermodel ... % 18.12/3.25 Prover 8: Warning: ignoring some quantifiers % 18.12/3.25 Prover 13: Constructing countermodel ... % 18.12/3.28 Prover 8: Constructing countermodel ... % 18.96/3.32 Prover 11: Warning: ignoring some quantifiers % 19.70/3.36 Prover 11: Constructing countermodel ... % 19.70/3.42 Prover 10: Found proof (size 8) % 19.70/3.42 Prover 10: proved (533ms) % 19.70/3.42 Prover 8: stopped % 19.70/3.42 Prover 13: stopped % 19.70/3.42 Prover 4: stopped % 19.70/3.42 Prover 7: stopped % 20.19/3.42 Prover 11: stopped % 20.19/3.42 Prover 1: stopped % 20.19/3.42 % 20.19/3.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.19/3.42 % 20.19/3.43 % SZS output start Proof for theBenchmark % 20.19/3.43 Assumptions after simplification: % 20.19/3.43 --------------------------------- % 20.19/3.43 % 20.19/3.43 (corollary1_1) % 20.19/3.45 $i(null_class) & $i(universal_class) & ? [v0: $i] : ? [v1: $i] : % 20.19/3.45 (unordered_pair(v0, v1) = null_class & $i(v1) & $i(v0) & member(v0, % 20.19/3.45 universal_class)) % 20.19/3.45 % 20.19/3.45 (null_class_defn) % 20.19/3.45 $i(null_class) & ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, null_class)) % 20.19/3.45 % 20.19/3.45 (unordered_pair_defn) % 20.19/3.46 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 20.19/3.46 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 20.19/3.46 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.19/3.46 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 20.19/3.46 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : ! % 20.19/3.46 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ % 20.19/3.46 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : ! % 20.19/3.46 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 20.19/3.46 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) % 20.19/3.46 % 20.19/3.46 Further assumptions not needed in the proof: % 20.19/3.46 -------------------------------------------- % 20.19/3.46 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 20.19/3.46 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 20.19/3.46 element_relation, element_relation_defn, extensionality, first_second, flip, % 20.19/3.46 flip_defn, function_defn, identity_relation, image_defn, inductive_defn, % 20.19/3.46 infinity, intersection, inverse_defn, ordered_pair_defn, power_class, % 20.19/3.46 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate, % 20.19/3.46 rotate_defn, singleton_set_defn, subclass_defn, successor_defn, % 20.19/3.46 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn, % 20.35/3.46 union_defn, unordered_pair % 20.35/3.46 % 20.35/3.46 Those formulas are unsatisfiable: % 20.35/3.46 --------------------------------- % 20.35/3.46 % 20.35/3.46 Begin of proof % 20.35/3.46 | % 20.35/3.46 | ALPHA: (unordered_pair_defn) implies: % 20.35/3.46 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 20.35/3.46 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) | % 20.35/3.46 | member(v0, v2)) % 20.35/3.46 | % 20.35/3.46 | ALPHA: (null_class_defn) implies: % 20.35/3.46 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, null_class)) % 20.35/3.46 | % 20.35/3.46 | ALPHA: (corollary1_1) implies: % 20.35/3.46 | (3) ? [v0: $i] : ? [v1: $i] : (unordered_pair(v0, v1) = null_class & % 20.35/3.46 | $i(v1) & $i(v0) & member(v0, universal_class)) % 20.35/3.46 | % 20.35/3.46 | DELTA: instantiating (3) with fresh symbols all_41_0, all_41_1 gives: % 20.35/3.46 | (4) unordered_pair(all_41_1, all_41_0) = null_class & $i(all_41_0) & % 20.35/3.46 | $i(all_41_1) & member(all_41_1, universal_class) % 20.35/3.46 | % 20.35/3.46 | ALPHA: (4) implies: % 20.35/3.46 | (5) member(all_41_1, universal_class) % 20.35/3.46 | (6) $i(all_41_1) % 20.35/3.46 | (7) $i(all_41_0) % 20.35/3.46 | (8) unordered_pair(all_41_1, all_41_0) = null_class % 20.35/3.46 | % 20.35/3.47 | GROUND_INST: instantiating (1) with all_41_1, all_41_0, null_class, % 20.35/3.47 | simplifying with (5), (6), (7), (8) gives: % 20.35/3.47 | (9) member(all_41_1, null_class) % 20.35/3.47 | % 20.35/3.47 | GROUND_INST: instantiating (2) with all_41_1, simplifying with (6), (9) gives: % 20.35/3.47 | (10) $false % 20.35/3.47 | % 20.35/3.47 | CLOSE: (10) is inconsistent. % 20.35/3.47 | % 20.35/3.47 End of proof % 20.35/3.47 % SZS output end Proof for theBenchmark % 20.35/3.47 % 20.35/3.47 2860ms %------------------------------------------------------------------------------