%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET081+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 : n027.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 15:23:39 EDT 2023 % Result : Theorem 13.06s 2.53s % Output : Proof 17.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET081+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.14/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n027.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sat Aug 26 16:04:50 EDT 2023 % 0.14/0.36 % CPUTime : % 0.22/0.62 ________ _____ % 0.22/0.62 ___ __ \_________(_)________________________________ % 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.62 % 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.62 (2023-06-19) % 0.22/0.62 % 0.22/0.62 (c) Philipp Rümmer, 2009-2023 % 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.62 Amanda Stjerna. % 0.22/0.62 Free software under BSD-3-Clause. % 0.22/0.62 % 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.62 % 0.22/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.43/1.21 Prover 4: Preprocessing ... % 3.43/1.21 Prover 1: Preprocessing ... % 3.81/1.25 Prover 3: Preprocessing ... % 3.81/1.25 Prover 6: Preprocessing ... % 3.81/1.25 Prover 0: Preprocessing ... % 3.81/1.25 Prover 5: Preprocessing ... % 3.81/1.25 Prover 2: Preprocessing ... % 8.96/2.01 Prover 1: Warning: ignoring some quantifiers % 8.96/2.01 Prover 5: Proving ... % 8.96/2.03 Prover 6: Proving ... % 8.96/2.04 Prover 3: Warning: ignoring some quantifiers % 8.96/2.04 Prover 1: Constructing countermodel ... % 9.57/2.07 Prover 3: Constructing countermodel ... % 9.82/2.08 Prover 4: Warning: ignoring some quantifiers % 9.82/2.13 Prover 2: Proving ... % 9.82/2.13 Prover 4: Constructing countermodel ... % 9.82/2.21 Prover 0: Proving ... % 13.06/2.53 Prover 5: proved (1879ms) % 13.06/2.53 Prover 0: proved (1886ms) % 13.06/2.53 % 13.06/2.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.06/2.53 % 13.06/2.53 % 13.06/2.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.06/2.53 % 13.06/2.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.06/2.54 Prover 3: stopped % 13.06/2.56 Prover 6: stopped % 13.06/2.57 Prover 2: stopped % 13.06/2.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.06/2.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.06/2.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.06/2.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.46/2.60 Prover 7: Preprocessing ... % 13.46/2.61 Prover 8: Preprocessing ... % 13.46/2.62 Prover 10: Preprocessing ... % 14.00/2.65 Prover 13: Preprocessing ... % 14.06/2.68 Prover 11: Preprocessing ... % 14.34/2.79 Prover 7: Warning: ignoring some quantifiers % 14.34/2.85 Prover 10: Warning: ignoring some quantifiers % 14.34/2.85 Prover 7: Constructing countermodel ... % 14.34/2.86 Prover 10: Constructing countermodel ... % 15.22/2.90 Prover 8: Warning: ignoring some quantifiers % 15.22/2.93 Prover 8: Constructing countermodel ... % 15.22/2.97 Prover 13: Warning: ignoring some quantifiers % 16.28/3.00 Prover 13: Constructing countermodel ... % 16.28/3.02 Prover 11: Warning: ignoring some quantifiers % 16.73/3.05 Prover 11: Constructing countermodel ... % 17.25/3.15 Prover 4: Found proof (size 9) % 17.25/3.15 Prover 4: proved (2496ms) % 17.25/3.15 Prover 11: stopped % 17.25/3.15 Prover 13: stopped % 17.25/3.15 Prover 10: stopped % 17.25/3.15 Prover 1: stopped % 17.25/3.15 Prover 7: stopped % 17.25/3.15 Prover 8: stopped % 17.25/3.15 % 17.25/3.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.25/3.15 % 17.25/3.15 % SZS output start Proof for theBenchmark % 17.56/3.16 Assumptions after simplification: % 17.56/3.16 --------------------------------- % 17.56/3.16 % 17.56/3.16 (only_member_in_singleton) % 17.56/3.18 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & singleton(v0) = v2 & % 17.56/3.18 member(v1, v2) = 0 & $i(v2) & $i(v1) & $i(v0)) % 17.56/3.18 % 17.56/3.18 (singleton_set_defn) % 17.56/3.18 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 17.56/3.18 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 17.56/3.18 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1))) % 17.56/3.18 % 17.56/3.18 (unordered_pair_defn) % 17.56/3.19 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 17.56/3.19 (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ~ % 17.56/3.19 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, % 17.56/3.19 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.56/3.19 [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = % 17.56/3.19 v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, % 17.56/3.19 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.56/3.19 [v3: $i] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ % 17.56/3.19 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 17.56/3.19 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ % 17.56/3.19 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v0, % 17.56/3.19 universal_class) = 0) % 17.56/3.19 % 17.56/3.19 Further assumptions not needed in the proof: % 17.56/3.19 -------------------------------------------- % 17.56/3.19 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 17.56/3.19 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 17.56/3.19 element_relation, element_relation_defn, extensionality, first_second, flip, % 17.56/3.19 flip_defn, function_defn, identity_relation, image_defn, inductive_defn, % 17.56/3.19 infinity, intersection, inverse_defn, null_class_defn, ordered_pair_defn, % 17.56/3.19 power_class, power_class_defn, range_of_defn, regularity, replacement, % 17.56/3.19 restrict_defn, rotate, rotate_defn, subclass_defn, successor_defn, % 17.56/3.19 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn, % 17.56/3.19 union_defn, unordered_pair % 17.56/3.19 % 17.56/3.19 Those formulas are unsatisfiable: % 17.56/3.19 --------------------------------- % 17.56/3.19 % 17.56/3.19 Begin of proof % 17.56/3.19 | % 17.56/3.19 | ALPHA: (unordered_pair_defn) implies: % 17.56/3.19 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = % 17.56/3.19 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ % 17.56/3.19 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 17.56/3.19 | % 17.56/3.19 | ALPHA: (singleton_set_defn) implies: % 17.56/3.20 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 17.56/3.20 | (unordered_pair(v0, v0) = v1 & $i(v1))) % 17.56/3.20 | % 17.56/3.20 | DELTA: instantiating (only_member_in_singleton) with fresh symbols all_40_0, % 17.56/3.20 | all_40_1, all_40_2 gives: % 17.56/3.20 | (3) ~ (all_40_1 = all_40_2) & singleton(all_40_2) = all_40_0 & % 17.56/3.20 | member(all_40_1, all_40_0) = 0 & $i(all_40_0) & $i(all_40_1) & % 17.56/3.20 | $i(all_40_2) % 17.56/3.20 | % 17.56/3.20 | ALPHA: (3) implies: % 17.56/3.20 | (4) ~ (all_40_1 = all_40_2) % 17.56/3.20 | (5) $i(all_40_2) % 17.56/3.20 | (6) $i(all_40_1) % 17.56/3.20 | (7) member(all_40_1, all_40_0) = 0 % 17.56/3.20 | (8) singleton(all_40_2) = all_40_0 % 17.56/3.20 | % 17.56/3.20 | GROUND_INST: instantiating (2) with all_40_2, all_40_0, simplifying with (5), % 17.56/3.20 | (8) gives: % 17.56/3.20 | (9) unordered_pair(all_40_2, all_40_2) = all_40_0 & $i(all_40_0) % 17.56/3.20 | % 17.56/3.20 | ALPHA: (9) implies: % 17.56/3.20 | (10) unordered_pair(all_40_2, all_40_2) = all_40_0 % 17.56/3.20 | % 17.56/3.20 | GROUND_INST: instantiating (1) with all_40_1, all_40_2, all_40_2, all_40_0, % 17.56/3.20 | simplifying with (5), (6), (7), (10) gives: % 17.56/3.20 | (11) all_40_1 = all_40_2 % 17.56/3.20 | % 17.56/3.20 | REDUCE: (4), (11) imply: % 17.56/3.20 | (12) $false % 17.56/3.20 | % 17.56/3.20 | CLOSE: (12) is inconsistent. % 17.56/3.20 | % 17.56/3.20 End of proof % 17.56/3.20 % SZS output end Proof for theBenchmark % 17.56/3.20 % 17.56/3.20 2579ms %------------------------------------------------------------------------------