%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET062+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 : n022.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 15:23:29 EDT 2023 % Result : Theorem 11.82s 2.33s % Output : Proof 13.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET062+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n022.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 12:23:40 EDT 2023 % 0.13/0.35 % 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.30/1.14 Prover 4: Preprocessing ... % 3.30/1.14 Prover 1: Preprocessing ... % 3.30/1.18 Prover 6: Preprocessing ... % 3.30/1.18 Prover 5: Preprocessing ... % 3.30/1.18 Prover 2: Preprocessing ... % 3.30/1.18 Prover 3: Preprocessing ... % 3.30/1.18 Prover 0: Preprocessing ... % 8.42/1.90 Prover 3: Warning: ignoring some quantifiers % 8.91/1.91 Prover 1: Warning: ignoring some quantifiers % 8.91/1.91 Prover 5: Proving ... % 8.91/1.93 Prover 3: Constructing countermodel ... % 8.91/1.94 Prover 1: Constructing countermodel ... % 8.91/1.96 Prover 6: Proving ... % 9.36/1.99 Prover 4: Warning: ignoring some quantifiers % 9.36/2.04 Prover 2: Proving ... % 9.36/2.05 Prover 4: Constructing countermodel ... % 9.36/2.13 Prover 0: Proving ... % 11.82/2.33 Prover 6: proved (1694ms) % 11.82/2.33 % 11.82/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.82/2.33 % 11.82/2.33 Prover 3: stopped % 11.82/2.35 Prover 0: stopped % 11.82/2.35 Prover 5: stopped % 11.82/2.35 Prover 2: stopped % 12.24/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.24/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.24/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.24/2.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.24/2.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.24/2.39 Prover 7: Preprocessing ... % 12.24/2.41 Prover 8: Preprocessing ... % 12.24/2.41 Prover 11: Preprocessing ... % 12.24/2.42 Prover 10: Preprocessing ... % 12.24/2.43 Prover 13: Preprocessing ... % 12.24/2.44 Prover 1: Found proof (size 13) % 12.24/2.44 Prover 1: proved (1815ms) % 12.24/2.45 Prover 4: stopped % 12.97/2.47 Prover 10: stopped % 12.97/2.49 Prover 7: stopped % 12.97/2.49 Prover 11: stopped % 13.21/2.50 Prover 13: stopped % 13.46/2.57 Prover 8: Warning: ignoring some quantifiers % 13.46/2.59 Prover 8: Constructing countermodel ... % 13.46/2.59 Prover 8: stopped % 13.46/2.59 % 13.46/2.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.46/2.59 % 13.46/2.59 % SZS output start Proof for theBenchmark % 13.46/2.60 Assumptions after simplification: % 13.46/2.60 --------------------------------- % 13.46/2.60 % 13.46/2.60 (null_class_defn) % 13.74/2.62 $i(null_class) & ! [v0: $i] : ( ~ (member(v0, null_class) = 0) | ~ $i(v0)) % 13.74/2.62 % 13.74/2.62 (null_class_is_subclass) % 13.74/2.62 $i(null_class) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 13.74/2.62 subclass(null_class, v0) = v1 & $i(v0)) % 13.74/2.62 % 13.74/2.62 (subclass_defn) % 13.74/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, v1) = % 13.74/2.62 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 13.74/2.62 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 13.74/2.62 [v1: $i] : ( ~ (subclass(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : % 13.74/2.62 ( ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 13.74/2.63 % 13.74/2.63 Further assumptions not needed in the proof: % 13.74/2.63 -------------------------------------------- % 13.74/2.63 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 13.74/2.63 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 13.74/2.63 element_relation, element_relation_defn, extensionality, first_second, flip, % 13.74/2.63 flip_defn, function_defn, identity_relation, image_defn, inductive_defn, % 13.74/2.63 infinity, intersection, inverse_defn, ordered_pair_defn, power_class, % 13.74/2.63 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate, % 13.74/2.63 rotate_defn, singleton_set_defn, successor_defn, successor_relation_defn1, % 13.74/2.63 successor_relation_defn2, sum_class, sum_class_defn, union_defn, unordered_pair, % 13.74/2.63 unordered_pair_defn % 13.74/2.63 % 13.74/2.63 Those formulas are unsatisfiable: % 13.74/2.63 --------------------------------- % 13.74/2.63 % 13.74/2.63 Begin of proof % 13.74/2.63 | % 13.74/2.63 | ALPHA: (subclass_defn) implies: % 13.74/2.63 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, % 13.74/2.63 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 13.74/2.63 | ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 13.74/2.63 | % 13.74/2.63 | ALPHA: (null_class_defn) implies: % 13.74/2.63 | (2) ! [v0: $i] : ( ~ (member(v0, null_class) = 0) | ~ $i(v0)) % 13.74/2.63 | % 13.74/2.63 | ALPHA: (null_class_is_subclass) implies: % 13.74/2.63 | (3) $i(null_class) % 13.74/2.63 | (4) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subclass(null_class, v0) = % 13.74/2.63 | v1 & $i(v0)) % 13.74/2.63 | % 13.74/2.63 | DELTA: instantiating (4) with fresh symbols all_38_0, all_38_1 gives: % 13.74/2.63 | (5) ~ (all_38_0 = 0) & subclass(null_class, all_38_1) = all_38_0 & % 13.74/2.63 | $i(all_38_1) % 13.74/2.63 | % 13.74/2.63 | ALPHA: (5) implies: % 13.74/2.63 | (6) ~ (all_38_0 = 0) % 13.74/2.63 | (7) $i(all_38_1) % 13.74/2.63 | (8) subclass(null_class, all_38_1) = all_38_0 % 13.74/2.63 | % 13.74/2.64 | GROUND_INST: instantiating (1) with null_class, all_38_1, all_38_0, % 13.74/2.64 | simplifying with (3), (7), (8) gives: % 13.74/2.64 | (9) all_38_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 13.74/2.64 | all_38_1) = v1 & member(v0, null_class) = 0 & $i(v0)) % 13.74/2.64 | % 13.74/2.64 | BETA: splitting (9) gives: % 13.74/2.64 | % 13.74/2.64 | Case 1: % 13.74/2.64 | | % 13.74/2.64 | | (10) all_38_0 = 0 % 13.74/2.64 | | % 13.74/2.64 | | REDUCE: (6), (10) imply: % 13.74/2.64 | | (11) $false % 13.74/2.64 | | % 13.74/2.64 | | CLOSE: (11) is inconsistent. % 13.74/2.64 | | % 13.74/2.64 | Case 2: % 13.74/2.64 | | % 13.74/2.64 | | (12) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_38_1) = % 13.74/2.64 | | v1 & member(v0, null_class) = 0 & $i(v0)) % 13.74/2.64 | | % 13.74/2.64 | | DELTA: instantiating (12) with fresh symbols all_103_0, all_103_1 gives: % 13.74/2.64 | | (13) ~ (all_103_0 = 0) & member(all_103_1, all_38_1) = all_103_0 & % 13.74/2.64 | | member(all_103_1, null_class) = 0 & $i(all_103_1) % 13.74/2.64 | | % 13.74/2.64 | | ALPHA: (13) implies: % 13.74/2.64 | | (14) $i(all_103_1) % 13.74/2.64 | | (15) member(all_103_1, null_class) = 0 % 13.74/2.64 | | % 13.74/2.64 | | GROUND_INST: instantiating (2) with all_103_1, simplifying with (14), (15) % 13.74/2.64 | | gives: % 13.74/2.64 | | (16) $false % 13.74/2.64 | | % 13.74/2.64 | | CLOSE: (16) is inconsistent. % 13.74/2.64 | | % 13.74/2.64 | End of split % 13.74/2.64 | % 13.74/2.64 End of proof % 13.74/2.64 % SZS output end Proof for theBenchmark % 13.74/2.64 % 13.74/2.64 2030ms %------------------------------------------------------------------------------