%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET025+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 : 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 15:23:14 EDT 2023 % Result : Theorem 13.26s 2.58s % Output : Proof 18.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET025+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 : n015.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 16:36:23 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.18/1.18 Prover 1: Preprocessing ... % 3.18/1.18 Prover 4: Preprocessing ... % 3.64/1.22 Prover 0: Preprocessing ... % 3.64/1.22 Prover 2: Preprocessing ... % 3.64/1.22 Prover 6: Preprocessing ... % 3.64/1.22 Prover 5: Preprocessing ... % 3.64/1.22 Prover 3: Preprocessing ... % 8.90/1.99 Prover 1: Warning: ignoring some quantifiers % 8.90/2.03 Prover 3: Warning: ignoring some quantifiers % 8.90/2.06 Prover 3: Constructing countermodel ... % 8.90/2.08 Prover 6: Proving ... % 8.90/2.08 Prover 5: Proving ... % 8.90/2.09 Prover 1: Constructing countermodel ... % 8.90/2.14 Prover 4: Warning: ignoring some quantifiers % 10.43/2.19 Prover 4: Constructing countermodel ... % 10.43/2.22 Prover 2: Proving ... % 11.55/2.33 Prover 0: Proving ... % 13.26/2.58 Prover 5: proved (1947ms) % 13.26/2.58 % 13.26/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.26/2.58 % 13.26/2.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.26/2.58 Prover 3: stopped % 13.26/2.59 Prover 6: stopped % 13.26/2.59 Prover 2: stopped % 13.26/2.59 Prover 0: stopped % 13.26/2.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.26/2.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.26/2.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.26/2.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.39/2.68 Prover 11: Preprocessing ... % 14.39/2.68 Prover 7: Preprocessing ... % 14.39/2.71 Prover 8: Preprocessing ... % 14.39/2.71 Prover 13: Preprocessing ... % 14.39/2.71 Prover 10: Preprocessing ... % 15.09/2.87 Prover 7: Warning: ignoring some quantifiers % 15.09/2.88 Prover 10: Warning: ignoring some quantifiers % 15.09/2.90 Prover 7: Constructing countermodel ... % 15.09/2.91 Prover 10: Constructing countermodel ... % 16.44/2.96 Prover 8: Warning: ignoring some quantifiers % 16.44/2.96 Prover 13: Warning: ignoring some quantifiers % 16.56/2.97 Prover 8: Constructing countermodel ... % 16.56/2.98 Prover 13: Constructing countermodel ... % 17.08/3.05 Prover 11: Warning: ignoring some quantifiers % 17.08/3.07 Prover 11: Constructing countermodel ... % 18.17/3.20 Prover 7: Found proof (size 11) % 18.17/3.20 Prover 7: proved (614ms) % 18.17/3.20 Prover 10: stopped % 18.17/3.20 Prover 13: stopped % 18.17/3.20 Prover 11: stopped % 18.17/3.20 Prover 8: stopped % 18.17/3.21 Prover 4: stopped % 18.17/3.21 Prover 1: stopped % 18.17/3.21 % 18.17/3.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.17/3.21 % 18.17/3.21 % SZS output start Proof for theBenchmark % 18.17/3.22 Assumptions after simplification: % 18.17/3.22 --------------------------------- % 18.17/3.22 % 18.17/3.22 (ordered_pair_defn) % 18.17/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (singleton(v1) = % 18.17/3.24 v2) | ~ (unordered_pair(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 18.17/3.24 $i] : ? [v5: $i] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 & % 18.17/3.24 unordered_pair(v5, v3) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: % 18.17/3.24 $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 18.17/3.24 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (singleton(v1) = v4 & % 18.17/3.24 singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4) % 18.17/3.24 = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 18.17/3.24 % 18.17/3.24 (ordered_pair_is_set) % 18.17/3.24 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 18.17/3.24 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ~ member(v2, % 18.17/3.24 universal_class)) % 18.17/3.24 % 18.17/3.24 (unordered_pair) % 18.17/3.24 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 18.17/3.24 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | member(v2, % 18.17/3.24 universal_class)) % 18.17/3.24 % 18.17/3.24 Further assumptions not needed in the proof: % 18.17/3.24 -------------------------------------------- % 18.17/3.25 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 18.17/3.25 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 18.17/3.25 element_relation, element_relation_defn, extensionality, first_second, flip, % 18.17/3.25 flip_defn, function_defn, identity_relation, image_defn, inductive_defn, % 18.17/3.25 infinity, intersection, inverse_defn, null_class_defn, power_class, % 18.17/3.25 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate, % 18.17/3.25 rotate_defn, singleton_set_defn, subclass_defn, successor_defn, % 18.17/3.25 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn, % 18.17/3.25 union_defn, unordered_pair_defn % 18.17/3.25 % 18.17/3.25 Those formulas are unsatisfiable: % 18.17/3.25 --------------------------------- % 18.17/3.25 % 18.17/3.25 Begin of proof % 18.17/3.25 | % 18.17/3.25 | ALPHA: (unordered_pair) implies: % 18.17/3.25 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 18.17/3.25 | v2) | ~ $i(v1) | ~ $i(v0) | member(v2, universal_class)) % 18.17/3.25 | % 18.17/3.25 | ALPHA: (ordered_pair_defn) implies: % 18.17/3.25 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 18.17/3.25 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 18.17/3.25 | $i] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3, % 18.17/3.25 | v5) = v2 & unordered_pair(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3) % 18.17/3.25 | & $i(v2))) % 18.17/3.25 | % 18.17/3.25 | ALPHA: (ordered_pair_is_set) implies: % 18.17/3.25 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & % 18.17/3.25 | $i(v2) & $i(v1) & $i(v0) & ~ member(v2, universal_class)) % 18.17/3.25 | % 18.17/3.25 | DELTA: instantiating (3) with fresh symbols all_41_0, all_41_1, all_41_2 % 18.17/3.25 | gives: % 18.17/3.25 | (4) ordered_pair(all_41_2, all_41_1) = all_41_0 & $i(all_41_0) & % 18.17/3.25 | $i(all_41_1) & $i(all_41_2) & ~ member(all_41_0, universal_class) % 18.17/3.25 | % 18.17/3.25 | ALPHA: (4) implies: % 18.17/3.25 | (5) ~ member(all_41_0, universal_class) % 18.17/3.25 | (6) $i(all_41_2) % 18.17/3.25 | (7) $i(all_41_1) % 18.17/3.25 | (8) ordered_pair(all_41_2, all_41_1) = all_41_0 % 18.17/3.25 | % 18.17/3.25 | GROUND_INST: instantiating (2) with all_41_2, all_41_1, all_41_0, simplifying % 18.17/3.25 | with (6), (7), (8) gives: % 18.17/3.26 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(all_41_1) = v1 & % 18.17/3.26 | singleton(all_41_2) = v0 & unordered_pair(v0, v2) = all_41_0 & % 18.17/3.26 | unordered_pair(all_41_2, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & % 18.17/3.26 | $i(all_41_0)) % 18.17/3.26 | % 18.55/3.26 | DELTA: instantiating (9) with fresh symbols all_96_0, all_96_1, all_96_2 % 18.55/3.26 | gives: % 18.55/3.26 | (10) singleton(all_41_1) = all_96_1 & singleton(all_41_2) = all_96_2 & % 18.55/3.26 | unordered_pair(all_96_2, all_96_0) = all_41_0 & % 18.55/3.26 | unordered_pair(all_41_2, all_96_1) = all_96_0 & $i(all_96_0) & % 18.55/3.26 | $i(all_96_1) & $i(all_96_2) & $i(all_41_0) % 18.55/3.26 | % 18.55/3.26 | ALPHA: (10) implies: % 18.55/3.26 | (11) $i(all_96_2) % 18.55/3.26 | (12) $i(all_96_0) % 18.55/3.26 | (13) unordered_pair(all_96_2, all_96_0) = all_41_0 % 18.55/3.26 | % 18.55/3.26 | GROUND_INST: instantiating (1) with all_96_2, all_96_0, all_41_0, simplifying % 18.55/3.26 | with (5), (11), (12), (13) gives: % 18.55/3.26 | (14) $false % 18.55/3.26 | % 18.55/3.26 | CLOSE: (14) is inconsistent. % 18.55/3.26 | % 18.55/3.26 End of proof % 18.55/3.26 % SZS output end Proof for theBenchmark % 18.55/3.26 % 18.55/3.26 2655ms %------------------------------------------------------------------------------