%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET094+1 : TPTP v8.1.2. Bugfixed v7.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 15:23:45 EDT 2023 % Result : Theorem 13.04s 2.50s % Output : Proof 16.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET094+1 : TPTP v8.1.2. Bugfixed v7.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n004.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 15:22:53 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.26/1.16 Prover 4: Preprocessing ... % 3.26/1.16 Prover 1: Preprocessing ... % 3.26/1.20 Prover 2: Preprocessing ... % 3.26/1.20 Prover 6: Preprocessing ... % 3.26/1.20 Prover 3: Preprocessing ... % 3.26/1.20 Prover 5: Preprocessing ... % 3.26/1.20 Prover 0: Preprocessing ... % 8.90/1.98 Prover 3: Warning: ignoring some quantifiers % 8.90/1.98 Prover 1: Warning: ignoring some quantifiers % 9.45/1.99 Prover 5: Proving ... % 9.45/2.00 Prover 3: Constructing countermodel ... % 9.45/2.00 Prover 6: Proving ... % 9.45/2.03 Prover 1: Constructing countermodel ... % 9.45/2.03 Prover 4: Warning: ignoring some quantifiers % 9.45/2.06 Prover 2: Proving ... % 9.45/2.08 Prover 4: Constructing countermodel ... % 10.68/2.20 Prover 0: Proving ... % 13.04/2.49 Prover 0: proved (1870ms) % 13.04/2.50 % 13.04/2.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.04/2.50 % 13.04/2.51 Prover 3: stopped % 13.31/2.51 Prover 6: stopped % 13.31/2.51 Prover 2: stopped % 13.31/2.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.31/2.52 Prover 5: stopped % 13.31/2.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.31/2.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.31/2.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.31/2.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.50/2.58 Prover 7: Preprocessing ... % 13.50/2.59 Prover 8: Preprocessing ... % 13.50/2.61 Prover 10: Preprocessing ... % 13.50/2.61 Prover 11: Preprocessing ... % 13.50/2.62 Prover 13: Preprocessing ... % 14.65/2.74 Prover 7: Warning: ignoring some quantifiers % 14.65/2.75 Prover 10: Warning: ignoring some quantifiers % 14.65/2.77 Prover 7: Constructing countermodel ... % 14.65/2.79 Prover 10: Constructing countermodel ... % 14.65/2.80 Prover 13: Warning: ignoring some quantifiers % 14.65/2.80 Prover 8: Warning: ignoring some quantifiers % 14.65/2.83 Prover 8: Constructing countermodel ... % 14.65/2.83 Prover 13: Constructing countermodel ... % 16.09/2.89 Prover 11: Warning: ignoring some quantifiers % 16.09/2.90 Prover 11: Constructing countermodel ... % 16.46/2.95 Prover 4: Found proof (size 22) % 16.46/2.95 Prover 4: proved (2317ms) % 16.46/2.96 Prover 1: stopped % 16.46/2.96 Prover 10: stopped % 16.46/2.96 Prover 13: stopped % 16.46/2.96 Prover 8: stopped % 16.46/2.96 Prover 11: stopped % 16.46/2.96 Prover 7: stopped % 16.46/2.96 % 16.46/2.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.46/2.96 % 16.46/2.96 % SZS output start Proof for theBenchmark % 16.46/2.97 Assumptions after simplification: % 16.46/2.97 --------------------------------- % 16.46/2.97 % 16.46/2.97 (member_singleton_singleton) % 16.46/2.99 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 16.46/2.99 ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : (member_of(v1) = v3 & % 16.46/2.99 singleton(v3) = v4 & member(v0, universal_class) = v2 & $i(v4) & $i(v3) & % 16.46/2.99 ( ~ (v2 = 0) | v4 = v1))) & ! [v0: $i] : ( ~ (member(v0, universal_class) % 16.46/2.99 = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (member_of(v1) = v2 & % 16.46/2.99 singleton(v2) = v1 & singleton(v0) = v1 & $i(v2) & $i(v1))) % 16.46/2.99 % 16.46/2.99 (member_singleton_universal) % 16.46/2.99 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 16.46/2.99 ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] : (member_of(v1) = v3 & % 16.46/2.99 member(v3, universal_class) = v4 & member(v0, universal_class) = v2 & % 16.46/2.99 $i(v3) & ( ~ (v2 = 0) | v4 = 0))) & ! [v0: $i] : ( ~ (member(v0, % 16.46/2.99 universal_class) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 16.46/2.99 (member_of(v1) = v2 & singleton(v0) = v1 & member(v2, universal_class) = 0 & % 16.46/2.99 $i(v2) & $i(v1))) % 16.46/2.99 % 16.46/2.99 (property_of_singletons1_1) % 16.46/3.00 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & member_of(v0) = v2 & % 16.46/3.00 singleton(v2) = v0 & member(v1, v0) = 0 & $i(v2) & $i(v1) & $i(v0)) % 16.46/3.00 % 16.46/3.00 (singleton_set_defn) % 16.46/3.00 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 16.46/3.00 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 16.46/3.00 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1))) % 16.46/3.00 % 16.46/3.00 (unordered_pair_defn) % 16.46/3.00 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 16.46/3.00 (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ~ % 16.46/3.00 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, % 16.46/3.00 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.46/3.00 [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = % 16.46/3.00 v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, % 16.46/3.00 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.46/3.00 [v3: $i] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ % 16.46/3.00 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 16.46/3.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ % 16.46/3.00 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v0, % 16.46/3.00 universal_class) = 0) % 16.46/3.00 % 16.46/3.00 (function-axioms) % 16.88/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 16.88/3.01 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0: % 16.88/3.01 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) % 16.88/3.01 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.88/3.01 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 16.88/3.01 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 16.88/3.01 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ % 16.88/3.01 (compose(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 16.88/3.01 $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & ! % 16.88/3.01 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, % 16.88/3.01 v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 16.88/3.01 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ % 16.88/3.01 (intersection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 16.88/3.01 [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, % 16.88/3.01 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 16.88/3.01 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! % 16.88/3.01 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.88/3.01 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 16.88/3.01 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.88/3.01 : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & ! % 16.88/3.01 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.88/3.01 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! % 16.88/3.01 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (member_of(v2) = v1) | ~ % 16.88/3.01 (member_of(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.88/3.01 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~ % 16.88/3.01 (function(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.88/3.01 ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0)) & ! [v0: $i] : ! % 16.88/3.01 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ % 16.88/3.01 (sum_class(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.88/3.01 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (inductive(v2) = v1) | ~ % 16.88/3.01 (inductive(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.88/3.01 ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 16.88/3.01 : ! [v2: $i] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! % 16.88/3.01 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ % 16.88/3.01 (successor(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.88/3.01 ~ (flip(v2) = v1) | ~ (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 16.88/3.01 [v2: $i] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: % 16.88/3.01 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ % 16.88/3.01 (domain_of(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.88/3.01 ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: % 16.88/3.01 $i] : ! [v2: $i] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & % 16.88/3.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ % 16.88/3.01 (second(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.88/3.01 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 16.88/3.01 % 16.88/3.01 Further assumptions not needed in the proof: % 16.88/3.01 -------------------------------------------- % 16.88/3.01 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 16.88/3.01 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 16.88/3.01 element_relation, element_relation_defn, extensionality, first_second, flip, % 16.88/3.01 flip_defn, function_defn, identity_relation, image_defn, inductive_defn, % 16.88/3.01 infinity, intersection, inverse_defn, member_universal_self, null_class_defn, % 16.88/3.01 ordered_pair_defn, power_class, power_class_defn, range_of_defn, regularity, % 16.88/3.01 replacement, restrict_defn, rotate, rotate_defn, singleton_self, subclass_defn, % 16.88/3.01 successor_defn, successor_relation_defn1, successor_relation_defn2, sum_class, % 16.88/3.01 sum_class_defn, union_defn, unordered_pair % 16.88/3.01 % 16.88/3.01 Those formulas are unsatisfiable: % 16.88/3.01 --------------------------------- % 16.88/3.01 % 16.88/3.01 Begin of proof % 16.88/3.01 | % 16.88/3.01 | ALPHA: (unordered_pair_defn) implies: % 16.88/3.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = % 16.88/3.01 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ % 16.88/3.01 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 16.88/3.01 | % 16.88/3.01 | ALPHA: (singleton_set_defn) implies: % 16.88/3.01 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 16.88/3.01 | (unordered_pair(v0, v0) = v1 & $i(v1))) % 16.88/3.01 | % 16.88/3.01 | ALPHA: (member_singleton_universal) implies: % 16.88/3.02 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? % 16.88/3.02 | [v2: any] : ? [v3: $i] : ? [v4: any] : (member_of(v1) = v3 & % 16.88/3.02 | member(v3, universal_class) = v4 & member(v0, universal_class) = v2 % 16.88/3.02 | & $i(v3) & ( ~ (v2 = 0) | v4 = 0))) % 16.88/3.02 | % 16.88/3.02 | ALPHA: (member_singleton_singleton) implies: % 16.88/3.02 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? % 16.88/3.02 | [v2: any] : ? [v3: $i] : ? [v4: $i] : (member_of(v1) = v3 & % 16.88/3.02 | singleton(v3) = v4 & member(v0, universal_class) = v2 & $i(v4) & % 16.88/3.02 | $i(v3) & ( ~ (v2 = 0) | v4 = v1))) % 16.88/3.02 | % 16.88/3.02 | ALPHA: (function-axioms) implies: % 16.88/3.02 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (member_of(v2) % 16.88/3.02 | = v1) | ~ (member_of(v2) = v0)) % 16.88/3.02 | % 16.88/3.02 | DELTA: instantiating (property_of_singletons1_1) with fresh symbols all_51_0, % 16.88/3.02 | all_51_1, all_51_2 gives: % 16.88/3.02 | (6) ~ (all_51_0 = all_51_1) & member_of(all_51_2) = all_51_0 & % 16.88/3.02 | singleton(all_51_0) = all_51_2 & member(all_51_1, all_51_2) = 0 & % 16.88/3.02 | $i(all_51_0) & $i(all_51_1) & $i(all_51_2) % 16.88/3.02 | % 16.88/3.02 | ALPHA: (6) implies: % 16.88/3.02 | (7) ~ (all_51_0 = all_51_1) % 16.88/3.02 | (8) $i(all_51_1) % 16.88/3.02 | (9) $i(all_51_0) % 16.88/3.02 | (10) member(all_51_1, all_51_2) = 0 % 16.88/3.02 | (11) singleton(all_51_0) = all_51_2 % 16.88/3.02 | (12) member_of(all_51_2) = all_51_0 % 16.88/3.02 | % 16.88/3.02 | GROUND_INST: instantiating (4) with all_51_0, all_51_2, simplifying with (9), % 16.88/3.02 | (11) gives: % 16.88/3.02 | (13) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (member_of(all_51_2) = v1 & % 16.88/3.02 | singleton(v1) = v2 & member(all_51_0, universal_class) = v0 & $i(v2) % 16.88/3.02 | & $i(v1) & ( ~ (v0 = 0) | v2 = all_51_2)) % 16.88/3.02 | % 16.88/3.02 | GROUND_INST: instantiating (3) with all_51_0, all_51_2, simplifying with (9), % 16.88/3.02 | (11) gives: % 16.88/3.02 | (14) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (member_of(all_51_2) = v1 % 16.88/3.02 | & member(v1, universal_class) = v2 & member(all_51_0, % 16.88/3.02 | universal_class) = v0 & $i(v1) & ( ~ (v0 = 0) | v2 = 0)) % 16.88/3.02 | % 16.88/3.02 | GROUND_INST: instantiating (2) with all_51_0, all_51_2, simplifying with (9), % 16.88/3.02 | (11) gives: % 16.88/3.02 | (15) unordered_pair(all_51_0, all_51_0) = all_51_2 & $i(all_51_2) % 16.88/3.02 | % 16.88/3.02 | ALPHA: (15) implies: % 16.88/3.02 | (16) unordered_pair(all_51_0, all_51_0) = all_51_2 % 16.88/3.02 | % 16.88/3.02 | DELTA: instantiating (14) with fresh symbols all_119_0, all_119_1, all_119_2 % 16.88/3.02 | gives: % 16.88/3.02 | (17) member_of(all_51_2) = all_119_1 & member(all_119_1, universal_class) = % 16.88/3.02 | all_119_0 & member(all_51_0, universal_class) = all_119_2 & % 16.88/3.02 | $i(all_119_1) & ( ~ (all_119_2 = 0) | all_119_0 = 0) % 16.88/3.02 | % 16.88/3.02 | ALPHA: (17) implies: % 16.88/3.02 | (18) $i(all_119_1) % 16.88/3.02 | (19) member_of(all_51_2) = all_119_1 % 16.88/3.02 | % 16.88/3.02 | DELTA: instantiating (13) with fresh symbols all_125_0, all_125_1, all_125_2 % 16.88/3.02 | gives: % 16.88/3.02 | (20) member_of(all_51_2) = all_125_1 & singleton(all_125_1) = all_125_0 & % 16.88/3.02 | member(all_51_0, universal_class) = all_125_2 & $i(all_125_0) & % 16.88/3.02 | $i(all_125_1) & ( ~ (all_125_2 = 0) | all_125_0 = all_51_2) % 16.88/3.02 | % 16.88/3.02 | ALPHA: (20) implies: % 16.88/3.02 | (21) member_of(all_51_2) = all_125_1 % 16.88/3.02 | % 16.88/3.02 | GROUND_INST: instantiating (5) with all_51_0, all_125_1, all_51_2, simplifying % 16.88/3.02 | with (12), (21) gives: % 16.88/3.03 | (22) all_125_1 = all_51_0 % 16.88/3.03 | % 16.88/3.03 | GROUND_INST: instantiating (5) with all_119_1, all_125_1, all_51_2, % 16.88/3.03 | simplifying with (19), (21) gives: % 16.88/3.03 | (23) all_125_1 = all_119_1 % 16.88/3.03 | % 16.88/3.03 | COMBINE_EQS: (22), (23) imply: % 16.88/3.03 | (24) all_119_1 = all_51_0 % 16.88/3.03 | % 16.88/3.03 | GROUND_INST: instantiating (1) with all_51_1, all_51_0, all_51_0, all_51_2, % 16.88/3.03 | simplifying with (8), (9), (10), (16) gives: % 16.88/3.03 | (25) all_51_0 = all_51_1 % 16.88/3.03 | % 16.88/3.03 | REDUCE: (7), (25) imply: % 16.88/3.03 | (26) $false % 16.88/3.03 | % 16.88/3.03 | CLOSE: (26) is inconsistent. % 16.88/3.03 | % 16.88/3.03 End of proof % 16.88/3.03 % SZS output end Proof for theBenchmark % 16.88/3.03 % 16.88/3.03 2422ms %------------------------------------------------------------------------------