%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET083+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 : n016.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 15:23:40 EDT 2023 % Result : Theorem 65.59s 9.42s % Output : Proof 70.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET083+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n016.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Aug 26 09:30:41 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 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.18/1.14 Prover 1: Preprocessing ... % 3.18/1.14 Prover 4: Preprocessing ... % 3.67/1.18 Prover 6: Preprocessing ... % 3.67/1.18 Prover 5: Preprocessing ... % 3.67/1.18 Prover 0: Preprocessing ... % 3.67/1.18 Prover 2: Preprocessing ... % 3.67/1.18 Prover 3: Preprocessing ... % 8.77/1.89 Prover 1: Warning: ignoring some quantifiers % 9.35/1.97 Prover 3: Warning: ignoring some quantifiers % 9.35/2.02 Prover 3: Constructing countermodel ... % 9.35/2.02 Prover 4: Warning: ignoring some quantifiers % 9.35/2.02 Prover 1: Constructing countermodel ... % 9.35/2.03 Prover 6: Proving ... % 10.03/2.04 Prover 5: Proving ... % 10.03/2.09 Prover 4: Constructing countermodel ... % 10.93/2.18 Prover 0: Proving ... % 10.93/2.18 Prover 2: Proving ... % 65.59/9.42 Prover 5: proved (8793ms) % 65.59/9.42 % 65.59/9.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 65.59/9.42 % 65.59/9.42 Prover 6: stopped % 65.59/9.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 65.59/9.43 Prover 2: stopped % 65.59/9.43 Prover 3: stopped % 65.59/9.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 65.59/9.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 65.59/9.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 65.59/9.48 Prover 0: stopped % 65.59/9.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 65.59/9.52 Prover 7: Preprocessing ... % 65.59/9.56 Prover 13: Preprocessing ... % 65.59/9.56 Prover 11: Preprocessing ... % 65.59/9.57 Prover 8: Preprocessing ... % 66.85/9.58 Prover 10: Preprocessing ... % 66.85/9.63 Prover 7: Warning: ignoring some quantifiers % 67.72/9.64 Prover 7: Constructing countermodel ... % 68.42/9.73 Prover 8: Warning: ignoring some quantifiers % 68.42/9.73 Prover 10: Warning: ignoring some quantifiers % 68.42/9.74 Prover 8: Constructing countermodel ... % 68.42/9.74 Prover 10: Constructing countermodel ... % 68.42/9.76 Prover 13: Warning: ignoring some quantifiers % 68.92/9.81 Prover 13: Constructing countermodel ... % 68.92/9.86 Prover 11: Warning: ignoring some quantifiers % 69.49/9.87 Prover 11: Constructing countermodel ... % 69.84/9.91 Prover 7: Found proof (size 74) % 69.84/9.91 Prover 7: proved (487ms) % 69.84/9.91 Prover 11: stopped % 69.84/9.91 Prover 10: stopped % 69.84/9.91 Prover 13: stopped % 69.84/9.92 Prover 4: stopped % 69.84/9.92 Prover 8: stopped % 69.84/9.92 Prover 1: stopped % 69.84/9.92 % 69.84/9.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 69.84/9.92 % 70.00/9.94 % SZS output start Proof for theBenchmark % 70.00/9.94 Assumptions after simplification: % 70.00/9.94 --------------------------------- % 70.00/9.94 % 70.00/9.94 (compose_defn1) % 70.00/9.96 $i(universal_class) & ? [v0: $i] : (cross_product(universal_class, % 70.00/9.97 universal_class) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 70.00/9.97 ( ~ (compose(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | subclass(v3, v0))) % 70.00/9.97 % 70.00/9.97 (element_relation) % 70.00/9.97 $i(element_relation) & $i(universal_class) & ? [v0: $i] : % 70.00/9.97 (cross_product(universal_class, universal_class) = v0 & $i(v0) & % 70.00/9.97 subclass(element_relation, v0)) % 70.00/9.97 % 70.00/9.97 (flip) % 70.00/9.97 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : (cross_product(v0, % 70.00/9.97 universal_class) = v1 & cross_product(universal_class, universal_class) = % 70.00/9.97 v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (flip(v2) = v3) | ~ % 70.00/9.97 $i(v2) | subclass(v3, v1))) % 70.00/9.97 % 70.00/9.97 (flip_defn) % 70.00/9.98 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : (cross_product(v0, % 70.00/9.98 universal_class) = v1 & cross_product(universal_class, universal_class) = % 70.00/9.98 v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 70.00/9.98 : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (flip(v5) = v8) | ~ % 70.00/9.98 (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v2) = v6) | ~ $i(v5) | % 70.00/9.98 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ member(v7, v5) | ? [v9: $i] : ? % 70.00/9.98 [v10: $i] : (ordered_pair(v9, v4) = v10 & ordered_pair(v2, v3) = v9 & % 70.00/9.98 $i(v10) & $i(v9) & ( ~ member(v10, v1) | member(v10, v8)))) & ! [v2: % 70.00/9.98 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] % 70.00/9.98 : ! [v8: $i] : ( ~ (flip(v5) = v8) | ~ (ordered_pair(v6, v4) = v7) | ~ % 70.00/9.98 (ordered_pair(v2, v3) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 70.00/9.98 $i(v2) | ~ member(v7, v8) | member(v7, v1)) & ! [v2: $i] : ! [v3: $i] : % 70.00/9.98 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 70.00/9.98 (flip(v5) = v8) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v2, % 70.00/9.98 v3) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 70.00/9.98 member(v7, v8) | ? [v9: $i] : ? [v10: $i] : (ordered_pair(v9, v4) = v10 % 70.00/9.98 & ordered_pair(v3, v2) = v9 & $i(v10) & $i(v9) & member(v10, v5))) & ! % 70.00/9.98 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 70.00/9.98 $i] : ! [v8: $i] : ( ~ (flip(v5) = v8) | ~ (ordered_pair(v6, v4) = v7) | % 70.00/9.98 ~ (ordered_pair(v2, v3) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 70.00/9.98 $i(v2) | ~ member(v7, v1) | member(v7, v8) | ? [v9: $i] : ? [v10: $i] : % 70.00/9.98 (ordered_pair(v9, v4) = v10 & ordered_pair(v3, v2) = v9 & $i(v10) & $i(v9) % 70.00/9.98 & ~ member(v10, v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 70.00/9.98 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (flip(v5) = v6) | % 70.00/9.98 ~ (ordered_pair(v7, v4) = v8) | ~ (ordered_pair(v3, v2) = v7) | ~ $i(v5) % 70.00/9.98 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: $i] : ? [v10: $i] : % 70.00/9.98 (ordered_pair(v9, v4) = v10 & ordered_pair(v2, v3) = v9 & $i(v10) & $i(v9) % 70.00/9.98 & ( ~ member(v10, v6) | (member(v10, v1) & member(v8, v5)))))) % 70.00/9.98 % 70.00/9.98 (function_defn) % 70.00/9.98 $i(identity_relation) & $i(universal_class) & ? [v0: $i] : % 70.00/9.98 (cross_product(universal_class, universal_class) = v0 & $i(v0) & ! [v1: $i] : % 70.00/9.98 ! [v2: $i] : ( ~ (inverse(v1) = v2) | ~ $i(v1) | ~ function(v1) | % 70.00/9.98 subclass(v1, v0)) & ! [v1: $i] : ! [v2: $i] : ( ~ (inverse(v1) = v2) | % 70.00/9.98 ~ $i(v1) | ~ function(v1) | ? [v3: $i] : (compose(v1, v2) = v3 & $i(v3) % 70.00/9.98 & subclass(v3, identity_relation))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 70.00/9.98 (inverse(v1) = v2) | ~ $i(v1) | ~ subclass(v1, v0) | function(v1) | ? % 70.00/9.98 [v3: $i] : (compose(v1, v2) = v3 & $i(v3) & ~ subclass(v3, % 70.00/9.98 identity_relation)))) % 70.00/9.98 % 70.00/9.98 (rotate) % 70.00/9.98 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : (cross_product(v0, % 70.00/9.98 universal_class) = v1 & cross_product(universal_class, universal_class) = % 70.00/9.98 v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (rotate(v2) = v3) | % 70.00/9.98 ~ $i(v2) | subclass(v3, v1))) % 70.00/9.98 % 70.00/9.98 (rotate_defn) % 70.00/9.99 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : (cross_product(v0, % 70.00/9.99 universal_class) = v1 & cross_product(universal_class, universal_class) = % 70.00/9.99 v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 70.00/9.99 : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (rotate(v2) = v8) | ~ % 70.00/9.99 (ordered_pair(v6, v5) = v7) | ~ (ordered_pair(v3, v4) = v6) | ~ $i(v5) | % 70.00/9.99 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ member(v7, v8) | member(v7, v1)) & % 70.00/9.99 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: % 70.00/9.99 $i] : ! [v8: $i] : ( ~ (rotate(v2) = v8) | ~ (ordered_pair(v6, v5) = v7) % 70.00/9.99 | ~ (ordered_pair(v3, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 70.00/9.99 $i(v2) | ~ member(v7, v8) | ? [v9: $i] : ? [v10: $i] : % 70.00/9.99 (ordered_pair(v9, v3) = v10 & ordered_pair(v4, v5) = v9 & $i(v10) & $i(v9) % 70.00/9.99 & member(v10, v2))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 70.00/9.99 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (rotate(v2) = v8) | ~ % 70.00/9.99 (ordered_pair(v6, v5) = v7) | ~ (ordered_pair(v3, v4) = v6) | ~ $i(v5) | % 70.00/9.99 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ member(v7, v1) | member(v7, v8) | % 70.00/9.99 ? [v9: $i] : ? [v10: $i] : (ordered_pair(v9, v3) = v10 & ordered_pair(v4, % 70.00/9.99 v5) = v9 & $i(v10) & $i(v9) & ~ member(v10, v2))) & ! [v2: $i] : ! % 70.00/9.99 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 70.00/9.99 $i] : ( ~ (rotate(v2) = v8) | ~ (ordered_pair(v6, v3) = v7) | ~ % 70.00/9.99 (ordered_pair(v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ % 70.00/9.99 $i(v2) | ~ member(v7, v2) | ? [v9: $i] : ? [v10: $i] : % 70.00/9.99 (ordered_pair(v9, v5) = v10 & ordered_pair(v3, v4) = v9 & $i(v10) & $i(v9) % 70.00/9.99 & ( ~ member(v10, v1) | member(v10, v8)))) & ! [v2: $i] : ! [v3: $i] : % 70.00/9.99 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 70.00/9.99 (rotate(v2) = v6) | ~ (ordered_pair(v7, v3) = v8) | ~ (ordered_pair(v4, % 70.00/9.99 v5) = v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v9: % 70.00/9.99 $i] : ? [v10: $i] : (ordered_pair(v9, v5) = v10 & ordered_pair(v3, v4) % 70.00/9.99 = v9 & $i(v10) & $i(v9) & ( ~ member(v10, v6) | (member(v10, v1) & % 70.00/9.99 member(v8, v2)))))) % 70.00/9.99 % 70.00/9.99 (singleton_identified_by_element1) % 70.00/9.99 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) % 70.00/9.99 & singleton(v1) = v2 & singleton(v0) = v2 & $i(v2) & $i(v1) & $i(v0) & % 70.00/9.99 member(v0, universal_class)) % 70.00/9.99 % 70.00/9.99 (singleton_set_defn) % 70.00/9.99 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 70.00/9.99 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 70.00/9.99 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1))) % 70.00/9.99 % 70.00/9.99 (successor_relation_defn1) % 70.00/9.99 $i(successor_relation) & $i(universal_class) & ? [v0: $i] : % 70.00/9.99 (cross_product(universal_class, universal_class) = v0 & $i(v0) & % 70.00/9.99 subclass(successor_relation, v0)) % 70.00/9.99 % 70.00/9.99 (unordered_pair_defn) % 70.00/9.99 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 70.00/9.99 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 70.00/9.99 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 70.00/9.99 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.00/9.99 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : ! % 70.00/9.99 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ % 70.00/9.99 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : ! % 70.00/9.99 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ % 70.00/9.99 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) % 70.00/9.99 % 70.00/9.99 (function-axioms) % 70.00/10.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 70.00/10.00 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0: % 70.00/10.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) % 70.00/10.00 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 70.00/10.00 : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = % 70.00/10.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 70.00/10.00 ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 70.00/10.00 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 70.00/10.00 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 70.00/10.00 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 70.00/10.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 70.00/10.00 ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0: % 70.00/10.00 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 70.00/10.00 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i] % 70.00/10.00 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, % 70.00/10.00 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 70.00/10.00 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ % 70.00/10.00 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 70.00/10.00 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0: $i] : ! [v1: % 70.00/10.00 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = % 70.00/10.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 70.00/10.00 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 70.00/10.00 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & ! % 70.00/10.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~ % 70.00/10.00 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 70.00/10.00 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 70.00/10.00 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & ! % 70.00/10.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) | % 70.00/10.00 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 70.00/10.00 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 70.00/10.00 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & ! % 70.00/10.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 70.00/10.00 (singleton(v2) = v0)) % 70.00/10.00 % 70.00/10.00 Further assumptions not needed in the proof: % 70.00/10.00 -------------------------------------------- % 70.00/10.00 apply_defn, choice, class_elements_are_sets, complement, compose_defn2, % 70.00/10.00 cross_product, cross_product_defn, disjoint_defn, domain_of, % 70.00/10.00 element_relation_defn, extensionality, first_second, identity_relation, % 70.00/10.00 image_defn, inductive_defn, infinity, intersection, inverse_defn, % 70.00/10.00 null_class_defn, ordered_pair_defn, power_class, power_class_defn, % 70.00/10.00 range_of_defn, regularity, replacement, restrict_defn, subclass_defn, % 70.00/10.00 successor_defn, successor_relation_defn2, sum_class, sum_class_defn, union_defn, % 70.00/10.00 unordered_pair % 70.00/10.00 % 70.00/10.00 Those formulas are unsatisfiable: % 70.00/10.00 --------------------------------- % 70.00/10.00 % 70.00/10.00 Begin of proof % 70.00/10.00 | % 70.00/10.00 | ALPHA: (unordered_pair_defn) implies: % 70.00/10.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 70.00/10.01 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) | % 70.00/10.01 | member(v0, v2)) % 70.00/10.01 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = % 70.00/10.01 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.00/10.01 | $i(v0) | ~ member(v0, v3)) % 70.00/10.01 | % 70.00/10.01 | ALPHA: (singleton_set_defn) implies: % 70.00/10.01 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 70.00/10.01 | (unordered_pair(v0, v0) = v1 & $i(v1))) % 70.00/10.01 | % 70.00/10.01 | ALPHA: (element_relation) implies: % 70.00/10.01 | (4) ? [v0: $i] : (cross_product(universal_class, universal_class) = v0 & % 70.00/10.01 | $i(v0) & subclass(element_relation, v0)) % 70.00/10.01 | % 70.00/10.01 | ALPHA: (rotate_defn) implies: % 70.00/10.01 | (5) ? [v0: $i] : ? [v1: $i] : (cross_product(v0, universal_class) = v1 & % 70.00/10.01 | cross_product(universal_class, universal_class) = v0 & $i(v1) & % 70.00/10.01 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 70.00/10.01 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (rotate(v2) = v8) | ~ % 70.00/10.01 | (ordered_pair(v6, v5) = v7) | ~ (ordered_pair(v3, v4) = v6) | ~ % 70.00/10.01 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ member(v7, v8) | % 70.00/10.01 | member(v7, v1)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 70.00/10.01 | $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (rotate(v2) = % 70.00/10.01 | v8) | ~ (ordered_pair(v6, v5) = v7) | ~ (ordered_pair(v3, v4) = % 70.00/10.01 | v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 70.00/10.01 | member(v7, v8) | ? [v9: $i] : ? [v10: $i] : (ordered_pair(v9, v3) % 70.00/10.01 | = v10 & ordered_pair(v4, v5) = v9 & $i(v10) & $i(v9) & % 70.00/10.01 | member(v10, v2))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 70.00/10.01 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (rotate(v2) % 70.00/10.01 | = v8) | ~ (ordered_pair(v6, v5) = v7) | ~ (ordered_pair(v3, v4) % 70.00/10.01 | = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 70.00/10.01 | member(v7, v1) | member(v7, v8) | ? [v9: $i] : ? [v10: $i] : % 70.00/10.01 | (ordered_pair(v9, v3) = v10 & ordered_pair(v4, v5) = v9 & $i(v10) & % 70.00/10.01 | $i(v9) & ~ member(v10, v2))) & ! [v2: $i] : ! [v3: $i] : ! % 70.00/10.01 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( % 70.00/10.01 | ~ (rotate(v2) = v8) | ~ (ordered_pair(v6, v3) = v7) | ~ % 70.00/10.01 | (ordered_pair(v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 70.00/10.01 | ~ $i(v2) | ~ member(v7, v2) | ? [v9: $i] : ? [v10: $i] : % 70.00/10.01 | (ordered_pair(v9, v5) = v10 & ordered_pair(v3, v4) = v9 & $i(v10) & % 70.00/10.01 | $i(v9) & ( ~ member(v10, v1) | member(v10, v8)))) & ! [v2: $i] : % 70.00/10.01 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : % 70.00/10.01 | ! [v8: $i] : ( ~ (rotate(v2) = v6) | ~ (ordered_pair(v7, v3) = v8) % 70.00/10.01 | | ~ (ordered_pair(v4, v5) = v7) | ~ $i(v5) | ~ $i(v4) | ~ % 70.00/10.01 | $i(v3) | ~ $i(v2) | ? [v9: $i] : ? [v10: $i] : (ordered_pair(v9, % 70.00/10.01 | v5) = v10 & ordered_pair(v3, v4) = v9 & $i(v10) & $i(v9) & ( ~ % 70.00/10.01 | member(v10, v6) | (member(v10, v1) & member(v8, v2)))))) % 70.00/10.01 | % 70.00/10.01 | ALPHA: (rotate) implies: % 70.00/10.01 | (6) ? [v0: $i] : ? [v1: $i] : (cross_product(v0, universal_class) = v1 & % 70.00/10.01 | cross_product(universal_class, universal_class) = v0 & $i(v1) & % 70.00/10.01 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (rotate(v2) = v3) | ~ % 70.00/10.01 | $i(v2) | subclass(v3, v1))) % 70.00/10.01 | % 70.00/10.01 | ALPHA: (flip_defn) implies: % 70.00/10.02 | (7) ? [v0: $i] : ? [v1: $i] : (cross_product(v0, universal_class) = v1 & % 70.00/10.02 | cross_product(universal_class, universal_class) = v0 & $i(v1) & % 70.00/10.02 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! % 70.00/10.02 | [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ (flip(v5) = v8) | ~ % 70.00/10.02 | (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v2) = v6) | ~ % 70.00/10.02 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ member(v7, v5) | ? % 70.00/10.02 | [v9: $i] : ? [v10: $i] : (ordered_pair(v9, v4) = v10 & % 70.00/10.02 | ordered_pair(v2, v3) = v9 & $i(v10) & $i(v9) & ( ~ member(v10, % 70.00/10.02 | v1) | member(v10, v8)))) & ! [v2: $i] : ! [v3: $i] : ! % 70.00/10.02 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( % 70.00/10.02 | ~ (flip(v5) = v8) | ~ (ordered_pair(v6, v4) = v7) | ~ % 70.00/10.02 | (ordered_pair(v2, v3) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 70.00/10.02 | ~ $i(v2) | ~ member(v7, v8) | member(v7, v1)) & ! [v2: $i] : ! % 70.00/10.02 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 70.00/10.02 | [v8: $i] : ( ~ (flip(v5) = v8) | ~ (ordered_pair(v6, v4) = v7) | ~ % 70.00/10.02 | (ordered_pair(v2, v3) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 70.00/10.02 | ~ $i(v2) | ~ member(v7, v8) | ? [v9: $i] : ? [v10: $i] : % 70.00/10.02 | (ordered_pair(v9, v4) = v10 & ordered_pair(v3, v2) = v9 & $i(v10) & % 70.00/10.02 | $i(v9) & member(v10, v5))) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 70.00/10.02 | $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ( ~ % 70.00/10.02 | (flip(v5) = v8) | ~ (ordered_pair(v6, v4) = v7) | ~ % 70.00/10.02 | (ordered_pair(v2, v3) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 70.00/10.02 | ~ $i(v2) | ~ member(v7, v1) | member(v7, v8) | ? [v9: $i] : ? % 70.00/10.02 | [v10: $i] : (ordered_pair(v9, v4) = v10 & ordered_pair(v3, v2) = v9 % 70.00/10.02 | & $i(v10) & $i(v9) & ~ member(v10, v5))) & ! [v2: $i] : ! [v3: % 70.00/10.02 | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! % 70.00/10.02 | [v8: $i] : ( ~ (flip(v5) = v6) | ~ (ordered_pair(v7, v4) = v8) | ~ % 70.00/10.02 | (ordered_pair(v3, v2) = v7) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | % 70.00/10.02 | ~ $i(v2) | ? [v9: $i] : ? [v10: $i] : (ordered_pair(v9, v4) = v10 % 70.00/10.02 | & ordered_pair(v2, v3) = v9 & $i(v10) & $i(v9) & ( ~ member(v10, % 70.00/10.02 | v6) | (member(v10, v1) & member(v8, v5)))))) % 70.00/10.02 | % 70.00/10.02 | ALPHA: (flip) implies: % 70.00/10.02 | (8) ? [v0: $i] : ? [v1: $i] : (cross_product(v0, universal_class) = v1 & % 70.00/10.02 | cross_product(universal_class, universal_class) = v0 & $i(v1) & % 70.00/10.02 | $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (flip(v2) = v3) | ~ $i(v2) % 70.00/10.02 | | subclass(v3, v1))) % 70.00/10.02 | % 70.00/10.02 | ALPHA: (successor_relation_defn1) implies: % 70.00/10.02 | (9) ? [v0: $i] : (cross_product(universal_class, universal_class) = v0 & % 70.00/10.02 | $i(v0) & subclass(successor_relation, v0)) % 70.00/10.02 | % 70.00/10.02 | ALPHA: (compose_defn1) implies: % 70.00/10.02 | (10) ? [v0: $i] : (cross_product(universal_class, universal_class) = v0 & % 70.00/10.02 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (compose(v2, % 70.44/10.02 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | subclass(v3, v0))) % 70.44/10.02 | % 70.44/10.02 | ALPHA: (function_defn) implies: % 70.44/10.02 | (11) ? [v0: $i] : (cross_product(universal_class, universal_class) = v0 & % 70.44/10.02 | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (inverse(v1) = v2) | ~ % 70.44/10.02 | $i(v1) | ~ function(v1) | subclass(v1, v0)) & ! [v1: $i] : ! % 70.44/10.02 | [v2: $i] : ( ~ (inverse(v1) = v2) | ~ $i(v1) | ~ function(v1) | ? % 70.44/10.02 | [v3: $i] : (compose(v1, v2) = v3 & $i(v3) & subclass(v3, % 70.44/10.02 | identity_relation))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 70.44/10.02 | (inverse(v1) = v2) | ~ $i(v1) | ~ subclass(v1, v0) | % 70.44/10.02 | function(v1) | ? [v3: $i] : (compose(v1, v2) = v3 & $i(v3) & ~ % 70.44/10.02 | subclass(v3, identity_relation)))) % 70.44/10.02 | % 70.44/10.02 | ALPHA: (singleton_identified_by_element1) implies: % 70.44/10.03 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & % 70.44/10.03 | singleton(v1) = v2 & singleton(v0) = v2 & $i(v2) & $i(v1) & $i(v0) & % 70.44/10.03 | member(v0, universal_class)) % 70.44/10.03 | % 70.44/10.03 | ALPHA: (function-axioms) implies: % 70.44/10.03 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 70.44/10.03 | (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) % 70.44/10.03 | % 70.44/10.03 | DELTA: instantiating (4) with fresh symbol all_37_0 gives: % 70.44/10.03 | (14) cross_product(universal_class, universal_class) = all_37_0 & % 70.44/10.03 | $i(all_37_0) & subclass(element_relation, all_37_0) % 70.44/10.03 | % 70.44/10.03 | ALPHA: (14) implies: % 70.44/10.03 | (15) cross_product(universal_class, universal_class) = all_37_0 % 70.44/10.03 | % 70.44/10.03 | DELTA: instantiating (9) with fresh symbol all_39_0 gives: % 70.44/10.03 | (16) cross_product(universal_class, universal_class) = all_39_0 & % 70.44/10.03 | $i(all_39_0) & subclass(successor_relation, all_39_0) % 70.44/10.03 | % 70.44/10.03 | ALPHA: (16) implies: % 70.44/10.03 | (17) cross_product(universal_class, universal_class) = all_39_0 % 70.44/10.03 | % 70.44/10.03 | DELTA: instantiating (10) with fresh symbol all_41_0 gives: % 70.44/10.03 | (18) cross_product(universal_class, universal_class) = all_41_0 & % 70.44/10.03 | $i(all_41_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 70.44/10.03 | (compose(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | subclass(v2, % 70.44/10.03 | all_41_0)) % 70.44/10.03 | % 70.44/10.03 | ALPHA: (18) implies: % 70.44/10.03 | (19) cross_product(universal_class, universal_class) = all_41_0 % 70.44/10.03 | % 70.44/10.03 | DELTA: instantiating (12) with fresh symbols all_53_0, all_53_1, all_53_2 % 70.44/10.03 | gives: % 70.44/10.03 | (20) ~ (all_53_1 = all_53_2) & singleton(all_53_1) = all_53_0 & % 70.44/10.03 | singleton(all_53_2) = all_53_0 & $i(all_53_0) & $i(all_53_1) & % 70.44/10.03 | $i(all_53_2) & member(all_53_2, universal_class) % 70.44/10.03 | % 70.44/10.03 | ALPHA: (20) implies: % 70.44/10.03 | (21) ~ (all_53_1 = all_53_2) % 70.44/10.03 | (22) member(all_53_2, universal_class) % 70.44/10.03 | (23) $i(all_53_2) % 70.44/10.03 | (24) $i(all_53_1) % 70.44/10.03 | (25) singleton(all_53_2) = all_53_0 % 70.44/10.03 | (26) singleton(all_53_1) = all_53_0 % 70.44/10.03 | % 70.44/10.03 | DELTA: instantiating (6) with fresh symbols all_55_0, all_55_1 gives: % 70.44/10.03 | (27) cross_product(all_55_1, universal_class) = all_55_0 & % 70.44/10.03 | cross_product(universal_class, universal_class) = all_55_1 & % 70.44/10.03 | $i(all_55_0) & $i(all_55_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 70.44/10.03 | (rotate(v0) = v1) | ~ $i(v0) | subclass(v1, all_55_0)) % 70.44/10.03 | % 70.44/10.03 | ALPHA: (27) implies: % 70.44/10.03 | (28) cross_product(universal_class, universal_class) = all_55_1 % 70.44/10.03 | (29) cross_product(all_55_1, universal_class) = all_55_0 % 70.44/10.03 | % 70.44/10.03 | DELTA: instantiating (8) with fresh symbols all_58_0, all_58_1 gives: % 70.44/10.03 | (30) cross_product(all_58_1, universal_class) = all_58_0 & % 70.44/10.03 | cross_product(universal_class, universal_class) = all_58_1 & % 70.44/10.03 | $i(all_58_0) & $i(all_58_1) & ! [v0: $i] : ! [v1: $i] : ( ~ % 70.44/10.03 | (flip(v0) = v1) | ~ $i(v0) | subclass(v1, all_58_0)) % 70.44/10.03 | % 70.44/10.03 | ALPHA: (30) implies: % 70.44/10.03 | (31) cross_product(universal_class, universal_class) = all_58_1 % 70.44/10.03 | % 70.44/10.03 | DELTA: instantiating (11) with fresh symbol all_61_0 gives: % 70.44/10.03 | (32) cross_product(universal_class, universal_class) = all_61_0 & % 70.44/10.03 | $i(all_61_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (inverse(v0) = v1) | ~ % 70.44/10.03 | $i(v0) | ~ function(v0) | subclass(v0, all_61_0)) & ! [v0: $i] : % 70.44/10.03 | ! [v1: $i] : ( ~ (inverse(v0) = v1) | ~ $i(v0) | ~ function(v0) | ? % 70.44/10.03 | [v2: $i] : (compose(v0, v1) = v2 & $i(v2) & subclass(v2, % 70.44/10.03 | identity_relation))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 70.44/10.03 | (inverse(v0) = v1) | ~ $i(v0) | ~ subclass(v0, all_61_0) | % 70.44/10.03 | function(v0) | ? [v2: $i] : (compose(v0, v1) = v2 & $i(v2) & ~ % 70.44/10.03 | subclass(v2, identity_relation))) % 70.44/10.03 | % 70.44/10.03 | ALPHA: (32) implies: % 70.44/10.03 | (33) cross_product(universal_class, universal_class) = all_61_0 % 70.44/10.03 | % 70.44/10.03 | DELTA: instantiating (7) with fresh symbols all_64_0, all_64_1 gives: % 70.44/10.04 | (34) cross_product(all_64_1, universal_class) = all_64_0 & % 70.44/10.04 | cross_product(universal_class, universal_class) = all_64_1 & % 70.44/10.04 | $i(all_64_0) & $i(all_64_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 70.44/10.04 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 70.44/10.04 | (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ % 70.44/10.04 | (ordered_pair(v1, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.44/10.04 | $i(v0) | ~ member(v5, v3) | ? [v7: $i] : ? [v8: $i] : % 70.44/10.04 | (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & $i(v8) & % 70.44/10.04 | $i(v7) & ( ~ member(v8, all_64_0) | member(v8, v6)))) & ! [v0: % 70.44/10.04 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 70.44/10.04 | [v5: $i] : ! [v6: $i] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, % 70.44/10.04 | v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ % 70.44/10.04 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v5, v6) | member(v5, % 70.44/10.04 | all_64_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 70.44/10.04 | : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (flip(v3) = v6) | ~ % 70.44/10.04 | (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ % 70.44/10.04 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v5, v6) | ? % 70.44/10.04 | [v7: $i] : ? [v8: $i] : (ordered_pair(v7, v2) = v8 & % 70.44/10.04 | ordered_pair(v1, v0) = v7 & $i(v8) & $i(v7) & member(v8, v3))) & % 70.44/10.04 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 70.44/10.04 | ! [v5: $i] : ! [v6: $i] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, % 70.44/10.04 | v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ $i(v3) | ~ % 70.44/10.04 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v5, all_64_0) | % 70.44/10.04 | member(v5, v6) | ? [v7: $i] : ? [v8: $i] : (ordered_pair(v7, v2) = % 70.44/10.04 | v8 & ordered_pair(v1, v0) = v7 & $i(v8) & $i(v7) & ~ member(v8, % 70.44/10.04 | v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 70.44/10.04 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (flip(v3) = v4) | ~ % 70.44/10.04 | (ordered_pair(v5, v2) = v6) | ~ (ordered_pair(v1, v0) = v5) | ~ % 70.44/10.04 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: % 70.44/10.04 | $i] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & % 70.44/10.04 | $i(v8) & $i(v7) & ( ~ member(v8, v4) | (member(v8, all_64_0) & % 70.44/10.04 | member(v6, v3))))) % 70.44/10.04 | % 70.44/10.04 | ALPHA: (34) implies: % 70.44/10.04 | (35) cross_product(universal_class, universal_class) = all_64_1 % 70.44/10.04 | (36) cross_product(all_64_1, universal_class) = all_64_0 % 70.44/10.04 | % 70.44/10.04 | DELTA: instantiating (5) with fresh symbols all_67_0, all_67_1 gives: % 70.44/10.04 | (37) cross_product(all_67_1, universal_class) = all_67_0 & % 70.44/10.04 | cross_product(universal_class, universal_class) = all_67_1 & % 70.44/10.04 | $i(all_67_0) & $i(all_67_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 70.44/10.04 | : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 70.44/10.04 | (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ % 70.44/10.04 | (ordered_pair(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.44/10.04 | $i(v0) | ~ member(v5, v6) | member(v5, all_67_0)) & ! [v0: $i] : % 70.44/10.04 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 70.44/10.04 | ! [v6: $i] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | % 70.44/10.04 | ~ (ordered_pair(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 70.44/10.04 | ~ $i(v0) | ~ member(v5, v6) | ? [v7: $i] : ? [v8: $i] : % 70.44/10.04 | (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & $i(v8) & % 70.44/10.04 | $i(v7) & member(v8, v0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 70.44/10.04 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 70.44/10.04 | (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ % 70.44/10.04 | (ordered_pair(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.44/10.04 | $i(v0) | ~ member(v5, all_67_0) | member(v5, v6) | ? [v7: $i] : ? % 70.44/10.04 | [v8: $i] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & % 70.44/10.04 | $i(v8) & $i(v7) & ~ member(v8, v0))) & ! [v0: $i] : ! [v1: $i] % 70.44/10.04 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] % 70.44/10.04 | : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v1) = v5) | ~ % 70.44/10.04 | (ordered_pair(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.44/10.04 | $i(v0) | ~ member(v5, v0) | ? [v7: $i] : ? [v8: $i] : % 70.44/10.04 | (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & $i(v8) & % 70.44/10.04 | $i(v7) & ( ~ member(v8, all_67_0) | member(v8, v6)))) & ! [v0: % 70.44/10.04 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 70.44/10.04 | [v5: $i] : ! [v6: $i] : ( ~ (rotate(v0) = v4) | ~ (ordered_pair(v5, % 70.44/10.04 | v1) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ $i(v3) | ~ % 70.44/10.04 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: $i] : % 70.44/10.04 | (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & $i(v8) & % 70.44/10.04 | $i(v7) & ( ~ member(v8, v4) | (member(v8, all_67_0) & member(v6, % 70.44/10.04 | v0))))) % 70.44/10.04 | % 70.44/10.04 | ALPHA: (37) implies: % 70.44/10.04 | (38) cross_product(universal_class, universal_class) = all_67_1 % 70.44/10.04 | (39) cross_product(all_67_1, universal_class) = all_67_0 % 70.44/10.04 | % 70.44/10.04 | GROUND_INST: instantiating (13) with all_58_1, all_61_0, universal_class, % 70.44/10.04 | universal_class, simplifying with (31), (33) gives: % 70.44/10.05 | (40) all_61_0 = all_58_1 % 70.44/10.05 | % 70.44/10.05 | GROUND_INST: instantiating (13) with all_39_0, all_61_0, universal_class, % 70.44/10.05 | universal_class, simplifying with (17), (33) gives: % 70.44/10.05 | (41) all_61_0 = all_39_0 % 70.44/10.05 | % 70.44/10.05 | GROUND_INST: instantiating (13) with all_58_1, all_64_1, universal_class, % 70.44/10.05 | universal_class, simplifying with (31), (35) gives: % 70.44/10.05 | (42) all_64_1 = all_58_1 % 70.44/10.05 | % 70.44/10.05 | GROUND_INST: instantiating (13) with all_55_1, all_64_1, universal_class, % 70.44/10.05 | universal_class, simplifying with (28), (35) gives: % 70.44/10.05 | (43) all_64_1 = all_55_1 % 70.44/10.05 | % 70.44/10.05 | GROUND_INST: instantiating (13) with all_41_0, all_64_1, universal_class, % 70.44/10.05 | universal_class, simplifying with (19), (35) gives: % 70.44/10.05 | (44) all_64_1 = all_41_0 % 70.44/10.05 | % 70.44/10.05 | GROUND_INST: instantiating (13) with all_64_1, all_67_1, universal_class, % 70.44/10.05 | universal_class, simplifying with (35), (38) gives: % 70.44/10.05 | (45) all_67_1 = all_64_1 % 70.44/10.05 | % 70.44/10.05 | GROUND_INST: instantiating (13) with all_37_0, all_67_1, universal_class, % 70.44/10.05 | universal_class, simplifying with (15), (38) gives: % 70.44/10.05 | (46) all_67_1 = all_37_0 % 70.44/10.05 | % 70.44/10.05 | GROUND_INST: instantiating (13) with all_64_0, all_67_0, universal_class, % 70.44/10.05 | all_64_1, simplifying with (36) gives: % 70.44/10.05 | (47) all_67_0 = all_64_0 | ~ (cross_product(all_64_1, universal_class) = % 70.44/10.05 | all_67_0) % 70.44/10.05 | % 70.44/10.05 | GROUND_INST: instantiating (13) with all_55_0, all_67_0, universal_class, % 70.44/10.05 | all_55_1, simplifying with (29) gives: % 70.44/10.05 | (48) all_67_0 = all_55_0 | ~ (cross_product(all_55_1, universal_class) = % 70.44/10.05 | all_67_0) % 70.44/10.05 | % 70.44/10.05 | COMBINE_EQS: (45), (46) imply: % 70.44/10.05 | (49) all_64_1 = all_37_0 % 70.44/10.05 | % 70.44/10.05 | SIMP: (49) implies: % 70.44/10.05 | (50) all_64_1 = all_37_0 % 70.44/10.05 | % 70.44/10.05 | COMBINE_EQS: (43), (44) imply: % 70.44/10.05 | (51) all_55_1 = all_41_0 % 70.44/10.05 | % 70.44/10.05 | COMBINE_EQS: (43), (50) imply: % 70.44/10.05 | (52) all_55_1 = all_37_0 % 70.44/10.05 | % 70.44/10.05 | COMBINE_EQS: (42), (43) imply: % 70.44/10.05 | (53) all_58_1 = all_55_1 % 70.44/10.05 | % 70.44/10.05 | SIMP: (53) implies: % 70.44/10.05 | (54) all_58_1 = all_55_1 % 70.44/10.05 | % 70.44/10.05 | COMBINE_EQS: (40), (41) imply: % 70.44/10.05 | (55) all_58_1 = all_39_0 % 70.44/10.05 | % 70.44/10.05 | SIMP: (55) implies: % 70.44/10.05 | (56) all_58_1 = all_39_0 % 70.44/10.05 | % 70.44/10.05 | COMBINE_EQS: (54), (56) imply: % 70.44/10.05 | (57) all_55_1 = all_39_0 % 70.44/10.05 | % 70.44/10.05 | SIMP: (57) implies: % 70.44/10.05 | (58) all_55_1 = all_39_0 % 70.44/10.05 | % 70.44/10.05 | COMBINE_EQS: (51), (52) imply: % 70.44/10.05 | (59) all_41_0 = all_37_0 % 70.44/10.05 | % 70.44/10.05 | COMBINE_EQS: (51), (58) imply: % 70.44/10.05 | (60) all_41_0 = all_39_0 % 70.44/10.05 | % 70.44/10.05 | COMBINE_EQS: (59), (60) imply: % 70.44/10.05 | (61) all_39_0 = all_37_0 % 70.44/10.05 | % 70.44/10.05 | REDUCE: (39), (46) imply: % 70.44/10.05 | (62) cross_product(all_37_0, universal_class) = all_67_0 % 70.44/10.05 | % 70.44/10.05 | BETA: splitting (47) gives: % 70.44/10.05 | % 70.44/10.05 | Case 1: % 70.44/10.05 | | % 70.44/10.05 | | (63) ~ (cross_product(all_64_1, universal_class) = all_67_0) % 70.44/10.05 | | % 70.44/10.05 | | REDUCE: (50), (63) imply: % 70.44/10.05 | | (64) ~ (cross_product(all_37_0, universal_class) = all_67_0) % 70.44/10.05 | | % 70.44/10.05 | | PRED_UNIFY: (62), (64) imply: % 70.44/10.05 | | (65) $false % 70.44/10.05 | | % 70.44/10.05 | | CLOSE: (65) is inconsistent. % 70.44/10.05 | | % 70.44/10.05 | Case 2: % 70.44/10.05 | | % 70.44/10.05 | | (66) all_67_0 = all_64_0 % 70.44/10.05 | | % 70.44/10.05 | | REDUCE: (62), (66) imply: % 70.44/10.05 | | (67) cross_product(all_37_0, universal_class) = all_64_0 % 70.44/10.05 | | % 70.44/10.05 | | BETA: splitting (48) gives: % 70.44/10.05 | | % 70.44/10.05 | | Case 1: % 70.44/10.05 | | | % 70.44/10.05 | | | (68) ~ (cross_product(all_55_1, universal_class) = all_67_0) % 70.44/10.05 | | | % 70.44/10.05 | | | REDUCE: (52), (66), (68) imply: % 70.44/10.05 | | | (69) ~ (cross_product(all_37_0, universal_class) = all_64_0) % 70.44/10.05 | | | % 70.44/10.05 | | | PRED_UNIFY: (67), (69) imply: % 70.44/10.05 | | | (70) $false % 70.44/10.05 | | | % 70.44/10.05 | | | CLOSE: (70) is inconsistent. % 70.44/10.05 | | | % 70.44/10.05 | | Case 2: % 70.44/10.05 | | | % 70.44/10.05 | | | % 70.44/10.05 | | | GROUND_INST: instantiating (3) with all_53_2, all_53_0, simplifying with % 70.44/10.05 | | | (23), (25) gives: % 70.44/10.05 | | | (71) unordered_pair(all_53_2, all_53_2) = all_53_0 & $i(all_53_0) % 70.44/10.05 | | | % 70.44/10.05 | | | ALPHA: (71) implies: % 70.44/10.05 | | | (72) unordered_pair(all_53_2, all_53_2) = all_53_0 % 70.44/10.05 | | | % 70.44/10.05 | | | GROUND_INST: instantiating (3) with all_53_1, all_53_0, simplifying with % 70.44/10.05 | | | (24), (26) gives: % 70.44/10.05 | | | (73) unordered_pair(all_53_1, all_53_1) = all_53_0 & $i(all_53_0) % 70.44/10.05 | | | % 70.44/10.05 | | | ALPHA: (73) implies: % 70.44/10.05 | | | (74) unordered_pair(all_53_1, all_53_1) = all_53_0 % 70.44/10.05 | | | % 70.44/10.05 | | | GROUND_INST: instantiating (1) with all_53_2, all_53_2, all_53_0, % 70.44/10.05 | | | simplifying with (22), (23), (72) gives: % 70.44/10.05 | | | (75) member(all_53_2, all_53_0) % 70.44/10.05 | | | % 70.44/10.05 | | | GROUND_INST: instantiating (2) with all_53_2, all_53_1, all_53_1, % 70.44/10.05 | | | all_53_0, simplifying with (23), (24), (74), (75) gives: % 70.44/10.06 | | | (76) all_53_1 = all_53_2 % 70.44/10.06 | | | % 70.44/10.06 | | | REDUCE: (21), (76) imply: % 70.44/10.06 | | | (77) $false % 70.44/10.06 | | | % 70.44/10.06 | | | CLOSE: (77) is inconsistent. % 70.44/10.06 | | | % 70.44/10.06 | | End of split % 70.44/10.06 | | % 70.44/10.06 | End of split % 70.44/10.06 | % 70.44/10.06 End of proof % 70.44/10.06 % SZS output end Proof for theBenchmark % 70.44/10.06 % 70.44/10.06 9453ms %------------------------------------------------------------------------------