%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET101+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 : n031.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 15:23:48 EDT 2023 % Result : Theorem 14.93s 2.72s % Output : Proof 22.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET101+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n031.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 16:18:38 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.54 ________ _____ % 0.20/0.54 ___ __ \_________(_)________________________________ % 0.20/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.54 % 0.20/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.54 (2023-06-19) % 0.20/0.54 % 0.20/0.54 (c) Philipp Rümmer, 2009-2023 % 0.20/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.54 Amanda Stjerna. % 0.20/0.54 Free software under BSD-3-Clause. % 0.20/0.54 % 0.20/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.54 % 0.20/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.55 Running up to 7 provers in parallel. % 0.20/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.91/1.06 Prover 4: Preprocessing ... % 2.91/1.07 Prover 1: Preprocessing ... % 3.56/1.10 Prover 3: Preprocessing ... % 3.56/1.10 Prover 6: Preprocessing ... % 3.56/1.10 Prover 2: Preprocessing ... % 3.56/1.10 Prover 0: Preprocessing ... % 3.60/1.10 Prover 5: Preprocessing ... % 9.41/1.99 Prover 1: Warning: ignoring some quantifiers % 9.41/2.01 Prover 3: Warning: ignoring some quantifiers % 9.41/2.08 Prover 3: Constructing countermodel ... % 9.41/2.08 Prover 5: Proving ... % 9.41/2.08 Prover 1: Constructing countermodel ... % 9.41/2.09 Prover 6: Proving ... % 9.41/2.09 Prover 4: Warning: ignoring some quantifiers % 10.09/2.17 Prover 2: Proving ... % 10.09/2.17 Prover 4: Constructing countermodel ... % 11.54/2.24 Prover 0: Proving ... % 14.93/2.71 Prover 0: proved (2155ms) % 14.93/2.71 % 14.93/2.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.93/2.72 % 14.93/2.72 Prover 3: stopped % 14.93/2.72 Prover 6: stopped % 14.93/2.74 Prover 5: stopped % 14.93/2.75 Prover 2: stopped % 14.93/2.76 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.93/2.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.93/2.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.93/2.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.93/2.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.68/2.90 Prover 10: Preprocessing ... % 15.68/2.90 Prover 7: Preprocessing ... % 15.68/2.91 Prover 13: Preprocessing ... % 16.52/2.91 Prover 8: Preprocessing ... % 16.52/2.92 Prover 11: Preprocessing ... % 17.71/3.12 Prover 7: Warning: ignoring some quantifiers % 17.71/3.13 Prover 10: Warning: ignoring some quantifiers % 17.71/3.16 Prover 10: Constructing countermodel ... % 18.34/3.16 Prover 7: Constructing countermodel ... % 18.48/3.19 Prover 8: Warning: ignoring some quantifiers % 18.48/3.20 Prover 8: Constructing countermodel ... % 18.91/3.27 Prover 13: Warning: ignoring some quantifiers % 18.91/3.29 Prover 11: Warning: ignoring some quantifiers % 18.91/3.31 Prover 11: Constructing countermodel ... % 18.91/3.31 Prover 13: Constructing countermodel ... % 20.75/3.60 Prover 10: gave up % 21.67/3.64 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 21.93/3.68 Prover 16: Preprocessing ... % 21.93/3.73 Prover 7: Found proof (size 19) % 21.93/3.73 Prover 7: proved (1009ms) % 21.93/3.73 Prover 8: stopped % 21.93/3.73 Prover 11: stopped % 21.93/3.73 Prover 13: stopped % 21.93/3.73 Prover 4: stopped % 21.93/3.73 Prover 1: stopped % 22.63/3.75 Prover 16: stopped % 22.63/3.75 % 22.63/3.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 22.63/3.75 % 22.63/3.76 % SZS output start Proof for theBenchmark % 22.63/3.76 Assumptions after simplification: % 22.63/3.76 --------------------------------- % 22.63/3.76 % 22.63/3.76 (ordered_pair_defn) % 22.87/3.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (singleton(v1) = % 22.87/3.80 v2) | ~ (unordered_pair(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 22.87/3.80 $i] : ? [v5: $i] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 & % 22.87/3.80 unordered_pair(v5, v3) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: % 22.87/3.80 $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 22.87/3.80 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (singleton(v1) = v4 & % 22.87/3.80 singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4) % 22.87/3.80 = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 22.87/3.80 % 22.87/3.80 (singleton_member_of_ordered_pair) % 22.87/3.80 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ordered_pair(v0, v1) % 22.87/3.80 = v3 & singleton(v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ~ % 22.87/3.80 member(v2, v3)) % 22.87/3.80 % 22.87/3.80 (singleton_set_defn) % 22.87/3.80 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 22.87/3.80 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 22.87/3.80 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1))) % 22.87/3.80 % 22.87/3.81 (unordered_pair) % 22.87/3.81 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 22.87/3.81 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | member(v2, % 22.87/3.81 universal_class)) % 22.87/3.81 % 22.87/3.81 (unordered_pair_defn) % 22.87/3.81 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 22.87/3.81 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 22.87/3.81 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 22.87/3.81 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 22.87/3.81 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : ! % 22.87/3.81 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ % 22.87/3.81 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : ! % 22.87/3.81 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 22.87/3.81 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) % 22.87/3.81 % 22.87/3.81 (function-axioms) % 22.87/3.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 22.87/3.82 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0: % 22.87/3.82 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) % 22.87/3.82 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 22.87/3.82 : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = % 22.87/3.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 22.87/3.82 ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 22.87/3.82 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 22.87/3.82 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 22.87/3.82 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 22.87/3.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 22.87/3.82 ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0: % 22.87/3.82 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.87/3.82 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 22.87/3.82 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, % 22.87/3.82 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 22.87/3.82 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ % 22.87/3.82 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 22.87/3.82 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0: $i] : ! [v1: % 22.87/3.82 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = % 22.87/3.82 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.87/3.82 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 22.87/3.82 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & ! % 22.87/3.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~ % 22.87/3.82 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.87/3.82 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 22.87/3.82 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & ! % 22.87/3.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) | % 22.87/3.82 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 22.87/3.82 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 22.87/3.82 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & ! % 22.87/3.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 22.87/3.82 (singleton(v2) = v0)) % 22.87/3.82 % 22.87/3.82 Further assumptions not needed in the proof: % 22.87/3.82 -------------------------------------------- % 22.87/3.82 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 22.87/3.82 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 22.87/3.82 element_relation, element_relation_defn, extensionality, first_second, flip, % 22.87/3.82 flip_defn, function_defn, identity_relation, image_defn, inductive_defn, % 22.87/3.82 infinity, intersection, inverse_defn, null_class_defn, power_class, % 22.87/3.82 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate, % 22.87/3.82 rotate_defn, subclass_defn, successor_defn, successor_relation_defn1, % 22.87/3.82 successor_relation_defn2, sum_class, sum_class_defn, union_defn % 22.87/3.82 % 22.87/3.82 Those formulas are unsatisfiable: % 22.87/3.82 --------------------------------- % 22.87/3.82 % 22.87/3.82 Begin of proof % 22.87/3.83 | % 22.87/3.83 | ALPHA: (unordered_pair_defn) implies: % 22.87/3.83 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 22.87/3.83 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) | % 22.87/3.83 | member(v0, v2)) % 22.87/3.83 | % 22.87/3.83 | ALPHA: (unordered_pair) implies: % 22.87/3.83 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 22.87/3.83 | v2) | ~ $i(v1) | ~ $i(v0) | member(v2, universal_class)) % 22.87/3.83 | % 22.87/3.83 | ALPHA: (singleton_set_defn) implies: % 22.87/3.83 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 22.87/3.83 | (unordered_pair(v0, v0) = v1 & $i(v1))) % 22.87/3.83 | % 22.87/3.83 | ALPHA: (ordered_pair_defn) implies: % 22.87/3.83 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 22.87/3.83 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 22.87/3.83 | $i] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3, % 22.87/3.83 | v5) = v2 & unordered_pair(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3) % 22.87/3.83 | & $i(v2))) % 22.87/3.83 | % 22.87/3.83 | ALPHA: (function-axioms) implies: % 22.87/3.83 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 22.87/3.83 | = v1) | ~ (singleton(v2) = v0)) % 22.87/3.83 | % 22.87/3.83 | DELTA: instantiating (singleton_member_of_ordered_pair) with fresh symbols % 22.87/3.83 | all_53_0, all_53_1, all_53_2, all_53_3 gives: % 22.87/3.83 | (6) ordered_pair(all_53_3, all_53_2) = all_53_0 & singleton(all_53_3) = % 22.87/3.83 | all_53_1 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3) & % 22.87/3.83 | ~ member(all_53_1, all_53_0) % 22.87/3.83 | % 22.87/3.83 | ALPHA: (6) implies: % 22.87/3.83 | (7) ~ member(all_53_1, all_53_0) % 22.87/3.83 | (8) $i(all_53_3) % 22.87/3.83 | (9) $i(all_53_2) % 22.87/3.83 | (10) singleton(all_53_3) = all_53_1 % 22.87/3.83 | (11) ordered_pair(all_53_3, all_53_2) = all_53_0 % 22.87/3.83 | % 22.87/3.84 | GROUND_INST: instantiating (3) with all_53_3, all_53_1, simplifying with (8), % 22.87/3.84 | (10) gives: % 22.87/3.84 | (12) unordered_pair(all_53_3, all_53_3) = all_53_1 & $i(all_53_1) % 22.87/3.84 | % 22.87/3.84 | ALPHA: (12) implies: % 22.87/3.84 | (13) unordered_pair(all_53_3, all_53_3) = all_53_1 % 22.87/3.84 | % 22.87/3.84 | GROUND_INST: instantiating (4) with all_53_3, all_53_2, all_53_0, simplifying % 22.87/3.84 | with (8), (9), (11) gives: % 22.87/3.84 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(all_53_2) = v1 & % 22.87/3.84 | singleton(all_53_3) = v0 & unordered_pair(v0, v2) = all_53_0 & % 22.87/3.84 | unordered_pair(all_53_3, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & % 22.87/3.84 | $i(all_53_0)) % 22.87/3.84 | % 22.87/3.84 | DELTA: instantiating (14) with fresh symbols all_98_0, all_98_1, all_98_2 % 22.87/3.84 | gives: % 22.87/3.84 | (15) singleton(all_53_2) = all_98_1 & singleton(all_53_3) = all_98_2 & % 22.87/3.84 | unordered_pair(all_98_2, all_98_0) = all_53_0 & % 22.87/3.84 | unordered_pair(all_53_3, all_98_1) = all_98_0 & $i(all_98_0) & % 22.87/3.84 | $i(all_98_1) & $i(all_98_2) & $i(all_53_0) % 22.87/3.84 | % 22.87/3.84 | ALPHA: (15) implies: % 22.87/3.84 | (16) $i(all_98_2) % 22.87/3.84 | (17) $i(all_98_0) % 22.87/3.84 | (18) unordered_pair(all_98_2, all_98_0) = all_53_0 % 22.87/3.84 | (19) singleton(all_53_3) = all_98_2 % 22.87/3.84 | % 22.87/3.84 | GROUND_INST: instantiating (5) with all_53_1, all_98_2, all_53_3, simplifying % 22.87/3.84 | with (10), (19) gives: % 22.87/3.84 | (20) all_98_2 = all_53_1 % 22.87/3.84 | % 22.87/3.84 | REDUCE: (18), (20) imply: % 22.87/3.84 | (21) unordered_pair(all_53_1, all_98_0) = all_53_0 % 22.87/3.84 | % 22.87/3.84 | REDUCE: (16), (20) imply: % 22.87/3.84 | (22) $i(all_53_1) % 22.87/3.84 | % 22.87/3.84 | GROUND_INST: instantiating (2) with all_53_3, all_53_3, all_53_1, simplifying % 22.87/3.84 | with (8), (13) gives: % 22.87/3.84 | (23) member(all_53_1, universal_class) % 22.87/3.84 | % 22.87/3.84 | GROUND_INST: instantiating (1) with all_53_1, all_98_0, all_53_0, simplifying % 22.87/3.84 | with (7), (17), (21), (22), (23) gives: % 22.87/3.84 | (24) $false % 22.87/3.84 | % 22.87/3.84 | CLOSE: (24) is inconsistent. % 22.87/3.84 | % 22.87/3.84 End of proof % 22.87/3.84 % SZS output end Proof for theBenchmark % 22.87/3.84 % 22.87/3.84 3305ms %------------------------------------------------------------------------------