%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET086+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 : n025.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 15:23:41 EDT 2023 % Result : Theorem 13.43s 2.61s % Output : Proof 17.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET086+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n025.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 12:10:22 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 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 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 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 % 3.05/1.13 Prover 1: Preprocessing ... % 3.05/1.13 Prover 4: Preprocessing ... % 3.60/1.17 Prover 0: Preprocessing ... % 3.60/1.17 Prover 5: Preprocessing ... % 3.60/1.17 Prover 2: Preprocessing ... % 3.60/1.17 Prover 6: Preprocessing ... % 3.60/1.17 Prover 3: Preprocessing ... % 9.57/2.19 Prover 1: Warning: ignoring some quantifiers % 9.57/2.23 Prover 3: Warning: ignoring some quantifiers % 10.26/2.24 Prover 6: Proving ... % 10.26/2.24 Prover 5: Proving ... % 10.26/2.27 Prover 1: Constructing countermodel ... % 10.26/2.29 Prover 3: Constructing countermodel ... % 11.83/2.35 Prover 4: Warning: ignoring some quantifiers % 11.83/2.41 Prover 2: Proving ... % 12.67/2.48 Prover 4: Constructing countermodel ... % 13.43/2.58 Prover 0: Proving ... % 13.43/2.61 Prover 3: proved (1978ms) % 13.43/2.61 % 13.43/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.43/2.61 % 13.72/2.63 Prover 5: stopped % 13.72/2.63 Prover 0: stopped % 13.72/2.63 Prover 6: stopped % 13.72/2.63 Prover 2: stopped % 13.85/2.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.85/2.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.85/2.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.85/2.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.85/2.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.39/2.74 Prover 8: Preprocessing ... % 14.39/2.75 Prover 7: Preprocessing ... % 14.39/2.75 Prover 10: Preprocessing ... % 14.39/2.76 Prover 11: Preprocessing ... % 14.39/2.76 Prover 13: Preprocessing ... % 15.79/3.02 Prover 10: Warning: ignoring some quantifiers % 16.63/3.06 Prover 7: Warning: ignoring some quantifiers % 16.63/3.07 Prover 1: Found proof (size 12) % 16.63/3.07 Prover 1: proved (2448ms) % 16.63/3.07 Prover 4: Found proof (size 19) % 16.63/3.07 Prover 4: proved (2449ms) % 16.89/3.09 Prover 10: Constructing countermodel ... % 16.89/3.09 Prover 13: Warning: ignoring some quantifiers % 16.89/3.09 Prover 7: Constructing countermodel ... % 16.89/3.10 Prover 8: Warning: ignoring some quantifiers % 16.89/3.11 Prover 10: stopped % 16.89/3.12 Prover 7: stopped % 16.89/3.13 Prover 11: Warning: ignoring some quantifiers % 16.89/3.13 Prover 13: Constructing countermodel ... % 16.89/3.13 Prover 8: Constructing countermodel ... % 16.89/3.14 Prover 13: stopped % 17.34/3.14 Prover 11: Constructing countermodel ... % 17.34/3.14 Prover 8: stopped % 17.42/3.17 Prover 11: stopped % 17.42/3.17 % 17.42/3.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.42/3.17 % 17.42/3.17 % SZS output start Proof for theBenchmark % 17.42/3.18 Assumptions after simplification: % 17.42/3.18 --------------------------------- % 17.42/3.18 % 17.42/3.18 (member_of_substitution) % 17.42/3.21 $i(universal_class) & ? [v0: $i] : ($i(v0) & ! [v1: $i] : ( ~ (member(v1, % 17.42/3.21 universal_class) = 0) | ~ $i(v1) | ? [v2: $i] : ( ~ (v2 = v0) & % 17.42/3.21 singleton(v1) = v2 & $i(v2))) & ? [v1: $i] : (singleton(v1) = v0 & % 17.42/3.21 member(v1, universal_class) = 0 & $i(v1))) % 17.42/3.21 % 17.42/3.21 (function-axioms) % 17.69/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 17.69/3.23 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0: % 17.69/3.23 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) % 17.69/3.23 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.69/3.23 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 17.69/3.23 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.69/3.23 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ % 17.69/3.23 (compose(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 17.69/3.23 $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & ! % 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, % 17.69/3.23 v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.69/3.23 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ % 17.69/3.23 (intersection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.69/3.23 [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, % 17.69/3.23 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.69/3.23 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! % 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.69/3.23 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 17.69/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.69/3.23 : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & ! % 17.69/3.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.69/3.23 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! % 17.69/3.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 17.69/3.23 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: $i] : ! [v1: % 17.69/3.23 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ % 17.69/3.23 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 17.69/3.23 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0: % 17.69/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 17.69/3.23 ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0)) & ! [v0: $i] : ! [v1: % 17.69/3.23 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = % 17.69/3.23 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.69/3.23 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.69/3.23 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & ! % 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~ % 17.69/3.23 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.69/3.23 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.69/3.23 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & ! % 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) | % 17.69/3.23 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 17.69/3.23 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 17.69/3.23 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & ! % 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 17.69/3.23 (singleton(v2) = v0)) % 17.69/3.23 % 17.69/3.23 Further assumptions not needed in the proof: % 17.69/3.23 -------------------------------------------- % 17.69/3.23 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 17.69/3.23 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 17.69/3.23 element_relation, element_relation_defn, extensionality, first_second, flip, % 17.69/3.23 flip_defn, function_defn, identity_relation, image_defn, inductive_defn, % 17.69/3.23 infinity, intersection, inverse_defn, null_class_defn, ordered_pair_defn, % 17.69/3.23 power_class, power_class_defn, range_of_defn, regularity, replacement, % 17.69/3.23 restrict_defn, rotate, rotate_defn, singleton_set_defn, subclass_defn, % 17.69/3.23 successor_defn, successor_relation_defn1, successor_relation_defn2, sum_class, % 17.69/3.23 sum_class_defn, union_defn, unordered_pair, unordered_pair_defn % 17.69/3.23 % 17.69/3.23 Those formulas are unsatisfiable: % 17.69/3.23 --------------------------------- % 17.69/3.23 % 17.69/3.23 Begin of proof % 17.69/3.23 | % 17.69/3.23 | ALPHA: (member_of_substitution) implies: % 17.69/3.24 | (1) ? [v0: $i] : ($i(v0) & ! [v1: $i] : ( ~ (member(v1, universal_class) % 17.69/3.24 | = 0) | ~ $i(v1) | ? [v2: $i] : ( ~ (v2 = v0) & singleton(v1) = % 17.69/3.24 | v2 & $i(v2))) & ? [v1: $i] : (singleton(v1) = v0 & member(v1, % 17.69/3.24 | universal_class) = 0 & $i(v1))) % 17.69/3.24 | % 17.69/3.24 | ALPHA: (function-axioms) implies: % 17.69/3.24 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 17.69/3.24 | = v1) | ~ (singleton(v2) = v0)) % 17.69/3.24 | % 17.69/3.24 | DELTA: instantiating (1) with fresh symbol all_56_0 gives: % 17.69/3.24 | (3) $i(all_56_0) & ! [v0: $i] : ( ~ (member(v0, universal_class) = 0) | ~ % 17.69/3.24 | $i(v0) | ? [v1: any] : ( ~ (v1 = all_56_0) & singleton(v0) = v1 & % 17.69/3.24 | $i(v1))) & ? [v0: $i] : (singleton(v0) = all_56_0 & member(v0, % 17.69/3.24 | universal_class) = 0 & $i(v0)) % 17.69/3.24 | % 17.69/3.24 | ALPHA: (3) implies: % 17.69/3.24 | (4) ! [v0: $i] : ( ~ (member(v0, universal_class) = 0) | ~ $i(v0) | ? % 17.69/3.24 | [v1: any] : ( ~ (v1 = all_56_0) & singleton(v0) = v1 & $i(v1))) % 17.69/3.24 | (5) ? [v0: $i] : (singleton(v0) = all_56_0 & member(v0, universal_class) = % 17.69/3.24 | 0 & $i(v0)) % 17.69/3.24 | % 17.69/3.24 | DELTA: instantiating (5) with fresh symbol all_68_0 gives: % 17.69/3.24 | (6) singleton(all_68_0) = all_56_0 & member(all_68_0, universal_class) = 0 % 17.69/3.24 | & $i(all_68_0) % 17.69/3.24 | % 17.69/3.24 | ALPHA: (6) implies: % 17.69/3.25 | (7) $i(all_68_0) % 17.69/3.25 | (8) member(all_68_0, universal_class) = 0 % 17.69/3.25 | (9) singleton(all_68_0) = all_56_0 % 17.69/3.25 | % 17.69/3.25 | GROUND_INST: instantiating (4) with all_68_0, simplifying with (7), (8) gives: % 17.69/3.25 | (10) ? [v0: any] : ( ~ (v0 = all_56_0) & singleton(all_68_0) = v0 & % 17.69/3.25 | $i(v0)) % 17.69/3.25 | % 17.69/3.25 | DELTA: instantiating (10) with fresh symbol all_90_0 gives: % 17.69/3.25 | (11) ~ (all_90_0 = all_56_0) & singleton(all_68_0) = all_90_0 & % 17.69/3.25 | $i(all_90_0) % 17.69/3.25 | % 17.69/3.25 | ALPHA: (11) implies: % 17.69/3.25 | (12) ~ (all_90_0 = all_56_0) % 17.87/3.25 | (13) singleton(all_68_0) = all_90_0 % 17.87/3.25 | % 17.87/3.25 | GROUND_INST: instantiating (2) with all_56_0, all_90_0, all_68_0, simplifying % 17.87/3.25 | with (9), (13) gives: % 17.87/3.25 | (14) all_90_0 = all_56_0 % 17.87/3.25 | % 17.87/3.25 | REDUCE: (12), (14) imply: % 17.87/3.25 | (15) $false % 17.87/3.25 | % 17.87/3.25 | CLOSE: (15) is inconsistent. % 17.87/3.25 | % 17.87/3.25 End of proof % 17.87/3.25 % SZS output end Proof for theBenchmark % 17.87/3.25 % 17.87/3.25 2646ms %------------------------------------------------------------------------------