%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET082+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 : 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 15:23:40 EDT 2023 % Result : Theorem 19.41s 3.37s % Output : Proof 65.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n004.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 09:21:37 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 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 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 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 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 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 % 3.23/1.14 Prover 4: Preprocessing ... % 3.23/1.15 Prover 1: Preprocessing ... % 3.70/1.18 Prover 0: Preprocessing ... % 3.70/1.18 Prover 5: Preprocessing ... % 3.70/1.18 Prover 6: Preprocessing ... % 3.70/1.18 Prover 2: Preprocessing ... % 3.70/1.18 Prover 3: Preprocessing ... % 8.86/1.93 Prover 1: Warning: ignoring some quantifiers % 9.51/1.97 Prover 5: Proving ... % 9.51/1.97 Prover 6: Proving ... % 9.51/1.98 Prover 3: Warning: ignoring some quantifiers % 9.60/2.00 Prover 4: Warning: ignoring some quantifiers % 9.60/2.01 Prover 1: Constructing countermodel ... % 9.60/2.03 Prover 3: Constructing countermodel ... % 9.60/2.06 Prover 4: Constructing countermodel ... % 9.60/2.08 Prover 2: Proving ... % 9.60/2.09 Prover 0: Proving ... % 19.41/3.37 Prover 0: proved (2754ms) % 19.41/3.37 % 19.41/3.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.41/3.37 % 19.41/3.37 Prover 2: stopped % 19.41/3.37 Prover 6: stopped % 19.41/3.38 Prover 5: stopped % 19.41/3.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 19.41/3.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 19.41/3.38 Prover 3: stopped % 19.41/3.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.41/3.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 19.41/3.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 19.41/3.43 Prover 8: Preprocessing ... % 19.41/3.47 Prover 10: Preprocessing ... % 19.41/3.47 Prover 7: Preprocessing ... % 20.62/3.48 Prover 11: Preprocessing ... % 20.80/3.49 Prover 13: Preprocessing ... % 21.07/3.58 Prover 8: Warning: ignoring some quantifiers % 21.07/3.59 Prover 8: Constructing countermodel ... % 21.76/3.61 Prover 10: Warning: ignoring some quantifiers % 21.76/3.62 Prover 10: Constructing countermodel ... % 21.76/3.63 Prover 7: Warning: ignoring some quantifiers % 21.76/3.64 Prover 7: Constructing countermodel ... % 22.46/3.71 Prover 13: Warning: ignoring some quantifiers % 22.46/3.74 Prover 13: Constructing countermodel ... % 22.46/3.78 Prover 11: Warning: ignoring some quantifiers % 22.46/3.79 Prover 11: Constructing countermodel ... % 23.33/3.96 Prover 10: gave up % 23.33/3.98 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 24.53/4.02 Prover 16: Preprocessing ... % 26.25/4.21 Prover 16: Warning: ignoring some quantifiers % 26.46/4.23 Prover 16: Constructing countermodel ... % 64.17/9.14 Prover 13: stopped % 64.43/9.16 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 64.43/9.17 Prover 11: Found proof (size 159) % 64.43/9.17 Prover 11: proved (5790ms) % 64.43/9.17 Prover 7: stopped % 64.43/9.17 Prover 1: stopped % 64.43/9.17 Prover 4: stopped % 64.43/9.18 Prover 16: stopped % 64.43/9.18 Prover 8: stopped % 64.43/9.19 Prover 19: Preprocessing ... % 65.19/9.29 Prover 19: Warning: ignoring some quantifiers % 65.19/9.29 Prover 19: Constructing countermodel ... % 65.19/9.30 Prover 19: stopped % 65.19/9.30 % 65.19/9.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 65.19/9.30 % 65.19/9.31 % SZS output start Proof for theBenchmark % 65.19/9.31 Assumptions after simplification: % 65.19/9.31 --------------------------------- % 65.19/9.31 % 65.19/9.31 (choice) % 65.19/9.34 $i(null_class) & $i(universal_class) & ? [v0: $i] : (function(v0) = 0 & % 65.19/9.34 $i(v0) & ! [v1: $i] : ! [v2: $i] : (v1 = null_class | ~ (apply(v0, v1) = % 65.19/9.34 v2) | ~ $i(v1) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & member(v2, % 65.19/9.34 v1) = 0) | ( ~ (v3 = 0) & member(v1, universal_class) = v3))) & ! % 65.19/9.34 [v1: $i] : (v1 = null_class | ~ (member(v1, universal_class) = 0) | ~ % 65.19/9.34 $i(v1) | ? [v2: $i] : (apply(v0, v1) = v2 & member(v2, v1) = 0 & % 65.19/9.34 $i(v2)))) % 65.19/9.34 % 65.19/9.34 (complement) % 65.19/9.35 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 65.19/9.35 (v3 = 0 | ~ (complement(v0) = v2) | ~ (member(v1, v2) = v3) | ~ $i(v1) | ~ % 65.19/9.35 $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 = 0 & member(v1, v0) = 0) | ( ~ % 65.19/9.35 (v4 = 0) & member(v1, universal_class) = v4))) & ! [v0: $i] : ! [v1: % 65.19/9.35 $i] : ! [v2: int] : (v2 = 0 | ~ (member(v1, v0) = v2) | ~ $i(v1) | ~ % 65.19/9.35 $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ((v5 = 0 & % 65.19/9.35 complement(v0) = v4 & member(v1, v4) = 0 & $i(v4)) | ( ~ (v3 = 0) & % 65.19/9.35 member(v1, universal_class) = v3))) & ! [v0: $i] : ! [v1: $i] : ! % 65.19/9.35 [v2: $i] : ( ~ (complement(v0) = v2) | ~ (member(v1, v2) = 0) | ~ $i(v1) | % 65.19/9.35 ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, % 65.19/9.35 universal_class) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 65.19/9.35 (member(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 65.19/9.35 ? [v5: int] : ((v5 = 0 & ~ (v2 = 0) & member(v1, universal_class) = 0) | ( % 65.19/9.35 ~ (v4 = 0) & complement(v0) = v3 & member(v1, v3) = v4 & $i(v3)))) % 65.19/9.35 % 65.19/9.35 (element_relation_defn) % 65.19/9.35 $i(element_relation) & $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! % 65.19/9.35 [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 65.19/9.35 int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & v4 = 0 & member(v1, % 65.19/9.35 universal_class) = 0 & member(v0, v1) = 0) | ( ~ (v3 = 0) & member(v2, % 65.19/9.35 element_relation) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 65.19/9.35 ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? % 65.19/9.35 [v4: int] : ? [v5: int] : ((v5 = 0 & member(v2, element_relation) = 0) | ( % 65.19/9.35 ~ (v4 = 0) & member(v0, v1) = v4) | ( ~ (v3 = 0) & member(v1, % 65.19/9.35 universal_class) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : % 65.19/9.35 ( ~ (member(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] % 65.19/9.35 : ? [v5: int] : ((v5 = 0 & v2 = 0 & member(v1, universal_class) = 0) | ( ~ % 65.19/9.35 (v4 = 0) & ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4 % 65.19/9.35 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, v1) = 0) | ~ % 65.19/9.35 $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 & % 65.19/9.35 ordered_pair(v0, v1) = v3 & member(v3, element_relation) = 0 & $i(v3)) | % 65.19/9.35 ( ~ (v2 = 0) & member(v1, universal_class) = v2))) % 65.19/9.35 % 65.19/9.35 (extensionality) % 65.50/9.35 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v1, v0) = 0) | ~ $i(v1) | % 65.50/9.35 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v0, v1) = v2)) & ! [v0: % 65.50/9.35 $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ~ $i(v1) | ~ % 65.50/9.35 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v1, v0) = v2)) & ! [v0: $i] % 65.50/9.35 : ! [v1: int] : (v1 = 0 | ~ (subclass(v0, v0) = v1) | ~ $i(v0)) % 65.50/9.35 % 65.50/9.35 (inductive_defn) % 65.50/9.36 $i(successor_relation) & $i(null_class) & ! [v0: $i] : ! [v1: int] : (v1 = 0 % 65.50/9.36 | ~ (inductive(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: % 65.50/9.36 int] : (( ~ (v4 = 0) & image(successor_relation, v0) = v3 & subclass(v3, % 65.50/9.36 v0) = v4 & $i(v3)) | ( ~ (v2 = 0) & member(null_class, v0) = v2))) & % 65.50/9.36 ! [v0: $i] : ! [v1: $i] : ( ~ (image(successor_relation, v0) = v1) | ~ % 65.50/9.36 $i(v0) | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & % 65.50/9.36 subclass(v1, v0) = 0 & member(null_class, v0) = 0) | ( ~ (v2 = 0) & % 65.50/9.36 inductive(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 65.50/9.36 (image(successor_relation, v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: % 65.50/9.36 int] : ? [v4: int] : ((v4 = 0 & inductive(v0) = 0) | ( ~ (v3 = 0) & % 65.50/9.36 subclass(v1, v0) = v3) | ( ~ (v2 = 0) & member(null_class, v0) = v2))) & % 65.50/9.36 ! [v0: $i] : ! [v1: any] : ( ~ (member(null_class, v0) = v1) | ~ $i(v0) | % 65.50/9.36 ? [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 & v1 = 0 & % 65.50/9.36 image(successor_relation, v0) = v3 & subclass(v3, v0) = 0 & $i(v3)) | ( % 65.50/9.36 ~ (v2 = 0) & inductive(v0) = v2))) & ! [v0: $i] : ( ~ (inductive(v0) = % 65.50/9.36 0) | ~ $i(v0) | ? [v1: $i] : (image(successor_relation, v0) = v1 & % 65.50/9.36 subclass(v1, v0) = 0 & member(null_class, v0) = 0 & $i(v1))) & ! [v0: $i] % 65.50/9.36 : ( ~ (member(null_class, v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: int] : % 65.50/9.36 ? [v3: int] : ((v3 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & % 65.50/9.36 image(successor_relation, v0) = v1 & subclass(v1, v0) = v2 & $i(v1)))) % 65.50/9.36 % 65.50/9.36 (infinity) % 65.50/9.36 $i(universal_class) & ? [v0: $i] : (inductive(v0) = 0 & member(v0, % 65.50/9.36 universal_class) = 0 & $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 65.50/9.36 (subclass(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 65.50/9.36 inductive(v1) = v3)) & ! [v1: $i] : ( ~ (inductive(v1) = 0) | ~ $i(v1) % 65.50/9.36 | subclass(v0, v1) = 0)) % 65.50/9.36 % 65.50/9.36 (ordered_pair_defn) % 65.50/9.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (singleton(v1) = % 65.50/9.36 v2) | ~ (unordered_pair(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 65.50/9.36 $i] : ? [v5: $i] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 & % 65.50/9.36 unordered_pair(v5, v3) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: % 65.50/9.36 $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 65.50/9.36 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (singleton(v1) = v4 & % 65.50/9.36 singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4) % 65.50/9.36 = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 65.50/9.36 % 65.50/9.36 (power_class) % 65.56/9.36 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ( ~ (power_class(v0) = v1) | % 65.56/9.36 ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & member(v1, % 65.56/9.36 universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = % 65.56/9.36 v2))) & ! [v0: $i] : ( ~ (member(v0, universal_class) = 0) | ~ $i(v0) % 65.56/9.36 | ? [v1: $i] : (power_class(v0) = v1 & member(v1, universal_class) = 0 & % 65.56/9.36 $i(v1))) % 65.56/9.36 % 65.56/9.36 (power_class_defn) % 65.56/9.37 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 65.56/9.37 (v3 = 0 | ~ (power_class(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | % 65.56/9.37 ~ $i(v0) | ? [v4: int] : ? [v5: int] : (( ~ (v5 = 0) & subclass(v0, v1) = % 65.56/9.37 v5) | ( ~ (v4 = 0) & member(v0, universal_class) = v4))) & ! [v0: $i] : % 65.56/9.37 ! [v1: $i] : ! [v2: $i] : ( ~ (power_class(v1) = v2) | ~ (member(v0, v2) = % 65.56/9.37 0) | ~ $i(v1) | ~ $i(v0) | (subclass(v0, v1) = 0 & member(v0, % 65.56/9.37 universal_class) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 65.56/9.37 (subclass(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] % 65.56/9.37 : ? [v5: int] : ((v5 = 0 & v2 = 0 & member(v0, universal_class) = 0) | ( ~ % 65.56/9.37 (v4 = 0) & power_class(v1) = v3 & member(v0, v3) = v4 & $i(v3)))) & ! % 65.56/9.37 [v0: $i] : ! [v1: $i] : ( ~ (subclass(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 65.56/9.37 ? [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 & power_class(v1) = v3 & % 65.56/9.37 member(v0, v3) = 0 & $i(v3)) | ( ~ (v2 = 0) & member(v0, % 65.56/9.37 universal_class) = v2))) % 65.56/9.37 % 65.56/9.37 (singleton_is_null_class) % 65.56/9.37 $i(null_class) & $i(universal_class) & ? [v0: $i] : ? [v1: int] : ? [v2: % 65.56/9.37 $i] : ( ~ (v2 = null_class) & ~ (v1 = 0) & singleton(v0) = v2 & member(v0, % 65.56/9.37 universal_class) = v1 & $i(v2) & $i(v0)) % 65.56/9.37 % 65.56/9.37 (singleton_set_defn) % 65.56/9.37 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 65.56/9.37 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 65.56/9.37 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1))) % 65.56/9.37 % 65.56/9.37 (unordered_pair) % 65.56/9.37 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 65.56/9.37 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | member(v2, % 65.56/9.37 universal_class) = 0) % 65.56/9.37 % 65.56/9.37 (unordered_pair_defn) % 65.56/9.37 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : % 65.56/9.37 (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ~ % 65.56/9.37 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, % 65.56/9.37 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 65.56/9.37 [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = % 65.56/9.37 v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, % 65.56/9.37 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 65.56/9.37 [v3: $i] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ % 65.56/9.37 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 65.56/9.37 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ % 65.56/9.37 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v0, % 65.56/9.37 universal_class) = 0) % 65.56/9.37 % 65.56/9.37 (function-axioms) % 65.56/9.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 65.56/9.38 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0: % 65.56/9.38 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) % 65.56/9.38 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 65.56/9.38 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 65.56/9.38 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 65.56/9.38 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ % 65.56/9.38 (compose(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 65.56/9.38 $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & ! % 65.56/9.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, % 65.56/9.38 v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 65.56/9.38 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ % 65.56/9.38 (intersection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 65.56/9.38 [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, % 65.56/9.38 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 65.56/9.38 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! % 65.56/9.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 65.56/9.38 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 65.56/9.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 65.56/9.38 : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & ! % 65.56/9.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 65.56/9.38 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! % 65.56/9.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 65.56/9.38 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: $i] : ! [v1: % 65.56/9.38 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ % 65.56/9.38 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 65.56/9.38 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0: % 65.56/9.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 65.56/9.38 ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0)) & ! [v0: $i] : ! [v1: % 65.56/9.38 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = % 65.56/9.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 65.56/9.38 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 65.56/9.38 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & ! % 65.56/9.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~ % 65.56/9.38 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 65.56/9.38 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 65.56/9.38 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & ! % 65.56/9.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) | % 65.56/9.38 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 65.56/9.38 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 65.56/9.38 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & ! % 65.56/9.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 65.56/9.38 (singleton(v2) = v0)) % 65.56/9.38 % 65.56/9.38 Further assumptions not needed in the proof: % 65.56/9.38 -------------------------------------------- % 65.56/9.38 apply_defn, class_elements_are_sets, compose_defn1, compose_defn2, % 65.56/9.38 cross_product, cross_product_defn, disjoint_defn, domain_of, element_relation, % 65.56/9.38 first_second, flip, flip_defn, function_defn, identity_relation, image_defn, % 65.56/9.38 intersection, inverse_defn, null_class_defn, range_of_defn, regularity, % 65.56/9.38 replacement, restrict_defn, rotate, rotate_defn, subclass_defn, successor_defn, % 65.56/9.38 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn, % 65.56/9.38 union_defn % 65.56/9.38 % 65.56/9.38 Those formulas are unsatisfiable: % 65.56/9.38 --------------------------------- % 65.56/9.38 % 65.56/9.38 Begin of proof % 65.56/9.38 | % 65.56/9.38 | ALPHA: (extensionality) implies: % 65.56/9.38 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v1, v0) = 0) | ~ % 65.56/9.38 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v0, v1) = % 65.56/9.38 | v2)) % 65.56/9.38 | % 65.56/9.38 | ALPHA: (unordered_pair_defn) implies: % 65.56/9.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 65.56/9.38 | (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 65.56/9.38 | ~ $i(v1) | ~ $i(v0) | member(v0, universal_class) = 0) % 65.56/9.39 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = % 65.56/9.39 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ % 65.56/9.39 | $i(v2) | ~ $i(v1) | ~ $i(v0)) % 65.56/9.39 | % 65.56/9.39 | ALPHA: (unordered_pair) implies: % 65.56/9.39 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 65.56/9.39 | v2) | ~ $i(v1) | ~ $i(v0) | member(v2, universal_class) = 0) % 65.56/9.39 | % 65.56/9.39 | ALPHA: (singleton_set_defn) implies: % 65.56/9.39 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 65.56/9.39 | (unordered_pair(v0, v0) = v1 & $i(v1))) % 65.56/9.39 | % 65.56/9.39 | ALPHA: (ordered_pair_defn) implies: % 65.56/9.39 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 65.56/9.39 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 65.56/9.39 | $i] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3, % 65.56/9.39 | v5) = v2 & unordered_pair(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3) % 65.56/9.39 | & $i(v2))) % 65.56/9.39 | % 65.56/9.39 | ALPHA: (element_relation_defn) implies: % 65.56/9.39 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (member(v0, v1) = v2) | % 65.56/9.39 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] : % 65.56/9.39 | ((v5 = 0 & v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v4 = 0) & % 65.56/9.39 | ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4 & % 65.56/9.39 | $i(v3)))) % 65.56/9.39 | % 65.56/9.39 | ALPHA: (complement) implies: % 65.56/9.39 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (member(v1, v0) = v2) | % 65.56/9.39 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] : % 65.56/9.39 | ((v5 = 0 & ~ (v2 = 0) & member(v1, universal_class) = 0) | ( ~ (v4 = % 65.56/9.39 | 0) & complement(v0) = v3 & member(v1, v3) = v4 & $i(v3)))) % 65.56/9.39 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (member(v1, v0) % 65.56/9.39 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? % 65.56/9.39 | [v5: int] : ((v5 = 0 & complement(v0) = v4 & member(v1, v4) = 0 & % 65.56/9.39 | $i(v4)) | ( ~ (v3 = 0) & member(v1, universal_class) = v3))) % 65.56/9.39 | % 65.56/9.39 | ALPHA: (inductive_defn) implies: % 65.56/9.39 | (10) ! [v0: $i] : ( ~ (inductive(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 65.56/9.39 | (image(successor_relation, v0) = v1 & subclass(v1, v0) = 0 & % 65.56/9.39 | member(null_class, v0) = 0 & $i(v1))) % 65.56/9.39 | % 65.56/9.39 | ALPHA: (infinity) implies: % 65.56/9.39 | (11) ? [v0: $i] : (inductive(v0) = 0 & member(v0, universal_class) = 0 & % 65.56/9.39 | $i(v0) & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, v1) % 65.56/9.39 | = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & inductive(v1) % 65.56/9.39 | = v3)) & ! [v1: $i] : ( ~ (inductive(v1) = 0) | ~ $i(v1) | % 65.56/9.39 | subclass(v0, v1) = 0)) % 65.56/9.39 | % 65.56/9.39 | ALPHA: (power_class_defn) implies: % 65.56/9.39 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (subclass(v0, v1) = 0) | ~ $i(v1) | % 65.56/9.39 | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 & % 65.56/9.39 | power_class(v1) = v3 & member(v0, v3) = 0 & $i(v3)) | ( ~ (v2 = % 65.56/9.39 | 0) & member(v0, universal_class) = v2))) % 65.56/9.40 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subclass(v0, v1) = v2) % 65.56/9.40 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] % 65.56/9.40 | : ((v5 = 0 & v2 = 0 & member(v0, universal_class) = 0) | ( ~ (v4 = % 65.56/9.40 | 0) & power_class(v1) = v3 & member(v0, v3) = v4 & $i(v3)))) % 65.56/9.40 | % 65.56/9.40 | ALPHA: (power_class) implies: % 65.56/9.40 | (14) ! [v0: $i] : ( ~ (member(v0, universal_class) = 0) | ~ $i(v0) | ? % 65.56/9.40 | [v1: $i] : (power_class(v0) = v1 & member(v1, universal_class) = 0 & % 65.56/9.40 | $i(v1))) % 65.56/9.40 | % 65.56/9.40 | ALPHA: (choice) implies: % 65.56/9.40 | (15) ? [v0: $i] : (function(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 65.56/9.40 | (v1 = null_class | ~ (apply(v0, v1) = v2) | ~ $i(v1) | ? [v3: % 65.56/9.40 | int] : ? [v4: int] : ((v4 = 0 & member(v2, v1) = 0) | ( ~ (v3 = % 65.56/9.40 | 0) & member(v1, universal_class) = v3))) & ! [v1: $i] : (v1 % 65.56/9.40 | = null_class | ~ (member(v1, universal_class) = 0) | ~ $i(v1) | % 65.56/9.40 | ? [v2: $i] : (apply(v0, v1) = v2 & member(v2, v1) = 0 & $i(v2)))) % 65.56/9.40 | % 65.56/9.40 | ALPHA: (singleton_is_null_class) implies: % 65.56/9.40 | (16) $i(universal_class) % 65.56/9.40 | (17) ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ( ~ (v2 = null_class) & ~ % 65.56/9.40 | (v1 = 0) & singleton(v0) = v2 & member(v0, universal_class) = v1 & % 65.56/9.40 | $i(v2) & $i(v0)) % 65.56/9.40 | % 65.56/9.40 | ALPHA: (function-axioms) implies: % 65.56/9.40 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 65.56/9.40 | = v1) | ~ (singleton(v2) = v0)) % 65.56/9.40 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 65.56/9.40 | (complement(v2) = v1) | ~ (complement(v2) = v0)) % 65.56/9.40 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 65.56/9.40 | (power_class(v2) = v1) | ~ (power_class(v2) = v0)) % 65.56/9.40 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 65.56/9.40 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 65.56/9.40 | v2) = v0)) % 65.56/9.40 | % 65.56/9.40 | DELTA: instantiating (17) with fresh symbols all_40_0, all_40_1, all_40_2 % 65.56/9.40 | gives: % 65.56/9.40 | (22) ~ (all_40_0 = null_class) & ~ (all_40_1 = 0) & singleton(all_40_2) = % 65.56/9.40 | all_40_0 & member(all_40_2, universal_class) = all_40_1 & $i(all_40_0) % 65.56/9.40 | & $i(all_40_2) % 65.56/9.40 | % 65.56/9.40 | ALPHA: (22) implies: % 65.56/9.40 | (23) ~ (all_40_1 = 0) % 65.56/9.40 | (24) ~ (all_40_0 = null_class) % 65.56/9.40 | (25) $i(all_40_2) % 65.56/9.40 | (26) member(all_40_2, universal_class) = all_40_1 % 65.56/9.40 | (27) singleton(all_40_2) = all_40_0 % 65.56/9.40 | % 65.56/9.40 | DELTA: instantiating (11) with fresh symbol all_52_0 gives: % 65.56/9.40 | (28) inductive(all_52_0) = 0 & member(all_52_0, universal_class) = 0 & % 65.56/9.40 | $i(all_52_0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 65.56/9.40 | (subclass(all_52_0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 65.56/9.40 | 0) & inductive(v0) = v2)) & ! [v0: $i] : ( ~ (inductive(v0) = % 65.56/9.40 | 0) | ~ $i(v0) | subclass(all_52_0, v0) = 0) % 65.56/9.40 | % 65.56/9.40 | ALPHA: (28) implies: % 65.56/9.40 | (29) $i(all_52_0) % 65.56/9.40 | (30) member(all_52_0, universal_class) = 0 % 65.56/9.40 | (31) inductive(all_52_0) = 0 % 65.56/9.40 | (32) ! [v0: $i] : ( ~ (inductive(v0) = 0) | ~ $i(v0) | subclass(all_52_0, % 65.56/9.40 | v0) = 0) % 65.56/9.40 | % 65.56/9.40 | DELTA: instantiating (15) with fresh symbol all_55_0 gives: % 65.56/9.41 | (33) function(all_55_0) = 0 & $i(all_55_0) & ! [v0: $i] : ! [v1: $i] : % 65.56/9.41 | (v0 = null_class | ~ (apply(all_55_0, v0) = v1) | ~ $i(v0) | ? [v2: % 65.56/9.41 | int] : ? [v3: int] : ((v3 = 0 & member(v1, v0) = 0) | ( ~ (v2 = % 65.56/9.41 | 0) & member(v0, universal_class) = v2))) & ! [v0: $i] : (v0 = % 65.56/9.41 | null_class | ~ (member(v0, universal_class) = 0) | ~ $i(v0) | ? % 65.56/9.41 | [v1: $i] : (apply(all_55_0, v0) = v1 & member(v1, v0) = 0 & $i(v1))) % 65.56/9.41 | % 65.56/9.41 | ALPHA: (33) implies: % 65.56/9.41 | (34) ! [v0: $i] : (v0 = null_class | ~ (member(v0, universal_class) = 0) % 65.56/9.41 | | ~ $i(v0) | ? [v1: $i] : (apply(all_55_0, v0) = v1 & member(v1, % 65.56/9.41 | v0) = 0 & $i(v1))) % 65.56/9.41 | % 65.56/9.41 | GROUND_INST: instantiating (8) with universal_class, all_40_2, all_40_1, % 65.56/9.41 | simplifying with (16), (25), (26) gives: % 65.78/9.41 | (35) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & ~ (all_40_1 = % 65.78/9.41 | 0) & member(all_40_2, universal_class) = 0) | ( ~ (v1 = 0) & % 65.78/9.41 | complement(universal_class) = v0 & member(all_40_2, v0) = v1 & % 65.78/9.41 | $i(v0))) % 65.78/9.41 | % 65.78/9.41 | GROUND_INST: instantiating (7) with all_40_2, universal_class, all_40_1, % 65.78/9.41 | simplifying with (16), (25), (26) gives: % 65.78/9.41 | (36) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & all_40_1 = 0 & % 65.78/9.41 | member(universal_class, universal_class) = 0) | ( ~ (v1 = 0) & % 65.78/9.41 | ordered_pair(all_40_2, universal_class) = v0 & member(v0, % 65.78/9.41 | element_relation) = v1 & $i(v0))) % 65.78/9.41 | % 65.78/9.41 | GROUND_INST: instantiating (14) with all_52_0, simplifying with (29), (30) % 65.78/9.41 | gives: % 65.78/9.41 | (37) ? [v0: $i] : (power_class(all_52_0) = v0 & member(v0, % 65.78/9.41 | universal_class) = 0 & $i(v0)) % 65.78/9.41 | % 65.78/9.41 | GROUND_INST: instantiating (8) with universal_class, all_52_0, 0, simplifying % 65.78/9.41 | with (16), (29), (30) gives: % 65.78/9.41 | (38) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 65.78/9.41 | complement(universal_class) = v0 & member(all_52_0, v0) = v1 & % 65.78/9.41 | $i(v0)) % 65.78/9.41 | % 65.78/9.41 | GROUND_INST: instantiating (5) with all_40_2, all_40_0, simplifying with (25), % 65.78/9.41 | (27) gives: % 65.78/9.41 | (39) unordered_pair(all_40_2, all_40_2) = all_40_0 & $i(all_40_0) % 65.78/9.41 | % 65.78/9.41 | ALPHA: (39) implies: % 65.78/9.41 | (40) unordered_pair(all_40_2, all_40_2) = all_40_0 % 65.78/9.41 | % 65.78/9.41 | GROUND_INST: instantiating (32) with all_52_0, simplifying with (29), (31) % 65.78/9.41 | gives: % 65.78/9.41 | (41) subclass(all_52_0, all_52_0) = 0 % 65.78/9.41 | % 65.78/9.41 | GROUND_INST: instantiating (10) with all_52_0, simplifying with (29), (31) % 65.78/9.41 | gives: % 65.78/9.41 | (42) ? [v0: $i] : (image(successor_relation, all_52_0) = v0 & subclass(v0, % 65.78/9.41 | all_52_0) = 0 & member(null_class, all_52_0) = 0 & $i(v0)) % 65.78/9.41 | % 65.78/9.41 | DELTA: instantiating (37) with fresh symbol all_83_0 gives: % 65.78/9.41 | (43) power_class(all_52_0) = all_83_0 & member(all_83_0, universal_class) = % 65.78/9.41 | 0 & $i(all_83_0) % 65.78/9.41 | % 65.78/9.41 | ALPHA: (43) implies: % 65.78/9.41 | (44) power_class(all_52_0) = all_83_0 % 65.78/9.41 | % 65.78/9.41 | DELTA: instantiating (38) with fresh symbols all_87_0, all_87_1 gives: % 65.78/9.41 | (45) ~ (all_87_0 = 0) & complement(universal_class) = all_87_1 & % 65.78/9.41 | member(all_52_0, all_87_1) = all_87_0 & $i(all_87_1) % 65.78/9.41 | % 65.78/9.41 | ALPHA: (45) implies: % 65.78/9.41 | (46) ~ (all_87_0 = 0) % 65.78/9.41 | (47) member(all_52_0, all_87_1) = all_87_0 % 65.78/9.41 | (48) complement(universal_class) = all_87_1 % 65.78/9.41 | % 65.78/9.41 | DELTA: instantiating (42) with fresh symbol all_89_0 gives: % 65.78/9.41 | (49) image(successor_relation, all_52_0) = all_89_0 & subclass(all_89_0, % 65.78/9.41 | all_52_0) = 0 & member(null_class, all_52_0) = 0 & $i(all_89_0) % 65.78/9.41 | % 65.78/9.41 | ALPHA: (49) implies: % 65.78/9.41 | (50) $i(all_89_0) % 65.78/9.41 | (51) subclass(all_89_0, all_52_0) = 0 % 65.78/9.41 | % 65.78/9.41 | DELTA: instantiating (36) with fresh symbols all_103_0, all_103_1, all_103_2 % 65.78/9.41 | gives: % 65.78/9.41 | (52) (all_103_0 = 0 & all_40_1 = 0 & member(universal_class, % 65.78/9.41 | universal_class) = 0) | ( ~ (all_103_1 = 0) & % 65.78/9.41 | ordered_pair(all_40_2, universal_class) = all_103_2 & % 65.78/9.41 | member(all_103_2, element_relation) = all_103_1 & $i(all_103_2)) % 65.78/9.41 | % 65.78/9.41 | DELTA: instantiating (35) with fresh symbols all_104_0, all_104_1, all_104_2 % 65.78/9.41 | gives: % 65.78/9.41 | (53) (all_104_0 = 0 & ~ (all_40_1 = 0) & member(all_40_2, universal_class) % 65.78/9.42 | = 0) | ( ~ (all_104_1 = 0) & complement(universal_class) = all_104_2 % 65.78/9.42 | & member(all_40_2, all_104_2) = all_104_1 & $i(all_104_2)) % 65.78/9.42 | % 65.78/9.42 | BETA: splitting (53) gives: % 65.78/9.42 | % 65.78/9.42 | Case 1: % 65.78/9.42 | | % 65.78/9.42 | | (54) all_104_0 = 0 & ~ (all_40_1 = 0) & member(all_40_2, % 65.78/9.42 | | universal_class) = 0 % 65.78/9.42 | | % 65.78/9.42 | | ALPHA: (54) implies: % 65.78/9.42 | | (55) member(all_40_2, universal_class) = 0 % 65.78/9.42 | | % 65.78/9.42 | | REF_CLOSE: (21), (23), (26), (55) are inconsistent by sub-proof #1. % 65.78/9.42 | | % 65.78/9.42 | Case 2: % 65.78/9.42 | | % 65.78/9.42 | | (56) ~ (all_104_1 = 0) & complement(universal_class) = all_104_2 & % 65.78/9.42 | | member(all_40_2, all_104_2) = all_104_1 & $i(all_104_2) % 65.78/9.42 | | % 65.78/9.42 | | ALPHA: (56) implies: % 65.78/9.42 | | (57) ~ (all_104_1 = 0) % 65.78/9.42 | | (58) $i(all_104_2) % 65.78/9.42 | | (59) member(all_40_2, all_104_2) = all_104_1 % 65.78/9.42 | | (60) complement(universal_class) = all_104_2 % 65.78/9.42 | | % 65.78/9.42 | | BETA: splitting (52) gives: % 65.78/9.42 | | % 65.78/9.42 | | Case 1: % 65.78/9.42 | | | % 65.78/9.42 | | | (61) all_103_0 = 0 & all_40_1 = 0 & member(universal_class, % 65.78/9.42 | | | universal_class) = 0 % 65.78/9.42 | | | % 65.78/9.42 | | | ALPHA: (61) implies: % 65.78/9.42 | | | (62) all_40_1 = 0 % 65.78/9.42 | | | % 65.78/9.42 | | | REDUCE: (23), (62) imply: % 65.78/9.42 | | | (63) $false % 65.78/9.42 | | | % 65.78/9.42 | | | CLOSE: (63) is inconsistent. % 65.78/9.42 | | | % 65.78/9.42 | | Case 2: % 65.78/9.42 | | | % 65.78/9.42 | | | (64) ~ (all_103_1 = 0) & ordered_pair(all_40_2, universal_class) = % 65.78/9.42 | | | all_103_2 & member(all_103_2, element_relation) = all_103_1 & % 65.78/9.42 | | | $i(all_103_2) % 65.78/9.42 | | | % 65.78/9.42 | | | ALPHA: (64) implies: % 65.78/9.42 | | | (65) ordered_pair(all_40_2, universal_class) = all_103_2 % 65.78/9.42 | | | % 65.78/9.42 | | | GROUND_INST: instantiating (19) with all_87_1, all_104_2, universal_class, % 65.78/9.42 | | | simplifying with (48), (60) gives: % 65.78/9.42 | | | (66) all_104_2 = all_87_1 % 65.78/9.42 | | | % 65.78/9.42 | | | REDUCE: (59), (66) imply: % 65.78/9.42 | | | (67) member(all_40_2, all_87_1) = all_104_1 % 65.78/9.42 | | | % 65.78/9.42 | | | REDUCE: (58), (66) imply: % 65.78/9.42 | | | (68) $i(all_87_1) % 65.78/9.42 | | | % 65.78/9.42 | | | GROUND_INST: instantiating (9) with all_87_1, all_40_2, all_104_1, % 65.78/9.42 | | | simplifying with (25), (67), (68) gives: % 65.78/9.42 | | | (69) all_104_1 = 0 | ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = % 65.78/9.42 | | | 0 & complement(all_87_1) = v1 & member(all_40_2, v1) = 0 & % 65.78/9.42 | | | $i(v1)) | ( ~ (v0 = 0) & member(all_40_2, universal_class) = % 65.78/9.42 | | | v0)) % 65.78/9.42 | | | % 65.78/9.42 | | | GROUND_INST: instantiating (8) with all_87_1, all_40_2, all_104_1, % 65.78/9.42 | | | simplifying with (25), (67), (68) gives: % 65.78/9.42 | | | (70) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & ~ % 65.78/9.42 | | | (all_104_1 = 0) & member(all_40_2, universal_class) = 0) | ( ~ % 65.78/9.42 | | | (v1 = 0) & complement(all_87_1) = v0 & member(all_40_2, v0) = % 65.78/9.42 | | | v1 & $i(v0))) % 65.78/9.42 | | | % 65.78/9.42 | | | GROUND_INST: instantiating (9) with all_87_1, all_52_0, all_87_0, % 65.78/9.42 | | | simplifying with (29), (47), (68) gives: % 65.78/9.42 | | | (71) all_87_0 = 0 | ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = % 65.78/9.42 | | | 0 & complement(all_87_1) = v1 & member(all_52_0, v1) = 0 & % 65.78/9.42 | | | $i(v1)) | ( ~ (v0 = 0) & member(all_52_0, universal_class) = % 65.78/9.42 | | | v0)) % 65.78/9.42 | | | % 65.78/9.42 | | | GROUND_INST: instantiating (12) with all_52_0, all_52_0, simplifying with % 65.78/9.42 | | | (29), (41) gives: % 65.78/9.42 | | | (72) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 & % 65.78/9.42 | | | power_class(all_52_0) = v1 & member(all_52_0, v1) = 0 & % 65.78/9.42 | | | $i(v1)) | ( ~ (v0 = 0) & member(all_52_0, universal_class) = % 65.78/9.42 | | | v0)) % 65.78/9.42 | | | % 65.78/9.42 | | | GROUND_INST: instantiating (1) with all_52_0, all_89_0, simplifying with % 65.78/9.42 | | | (29), (50), (51) gives: % 65.78/9.42 | | | (73) all_89_0 = all_52_0 | ? [v0: int] : ( ~ (v0 = 0) & % 65.78/9.42 | | | subclass(all_52_0, all_89_0) = v0) % 65.78/9.42 | | | % 65.78/9.42 | | | GROUND_INST: instantiating (12) with all_89_0, all_52_0, simplifying with % 65.78/9.42 | | | (29), (50), (51) gives: % 65.78/9.42 | | | (74) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 & % 65.78/9.42 | | | power_class(all_52_0) = v1 & member(all_89_0, v1) = 0 & % 65.78/9.42 | | | $i(v1)) | ( ~ (v0 = 0) & member(all_89_0, universal_class) = % 65.78/9.42 | | | v0)) % 65.78/9.42 | | | % 65.78/9.42 | | | GROUND_INST: instantiating (13) with all_89_0, all_52_0, 0, simplifying % 65.78/9.42 | | | with (29), (50), (51) gives: % 65.78/9.43 | | | (75) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 65.78/9.43 | | | member(all_89_0, universal_class) = 0) | ( ~ (v1 = 0) & % 65.78/9.43 | | | power_class(all_52_0) = v0 & member(all_89_0, v0) = v1 & % 65.78/9.43 | | | $i(v0))) % 65.78/9.43 | | | % 65.78/9.43 | | | GROUND_INST: instantiating (4) with all_40_2, all_40_2, all_40_0, % 65.78/9.43 | | | simplifying with (25), (40) gives: % 65.78/9.43 | | | (76) member(all_40_0, universal_class) = 0 % 65.78/9.43 | | | % 65.78/9.43 | | | GROUND_INST: instantiating (6) with all_40_2, universal_class, all_103_2, % 65.78/9.43 | | | simplifying with (16), (25), (65) gives: % 65.78/9.43 | | | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(all_40_2) = % 65.78/9.43 | | | v0 & singleton(universal_class) = v1 & unordered_pair(v0, v2) = % 65.78/9.43 | | | all_103_2 & unordered_pair(all_40_2, v1) = v2 & $i(v2) & $i(v1) % 65.78/9.43 | | | & $i(v0) & $i(all_103_2)) % 65.78/9.43 | | | % 65.78/9.43 | | | DELTA: instantiating (75) with fresh symbols all_151_0, all_151_1, % 65.78/9.43 | | | all_151_2 gives: % 65.78/9.43 | | | (78) (all_151_0 = 0 & member(all_89_0, universal_class) = 0) | ( ~ % 65.78/9.43 | | | (all_151_1 = 0) & power_class(all_52_0) = all_151_2 & % 65.78/9.43 | | | member(all_89_0, all_151_2) = all_151_1 & $i(all_151_2)) % 65.78/9.43 | | | % 65.78/9.43 | | | DELTA: instantiating (74) with fresh symbols all_153_0, all_153_1, % 65.78/9.43 | | | all_153_2 gives: % 65.78/9.43 | | | (79) (all_153_0 = 0 & power_class(all_52_0) = all_153_1 & % 65.78/9.43 | | | member(all_89_0, all_153_1) = 0 & $i(all_153_1)) | ( ~ % 65.78/9.43 | | | (all_153_2 = 0) & member(all_89_0, universal_class) = all_153_2) % 65.78/9.43 | | | % 65.78/9.43 | | | DELTA: instantiating (72) with fresh symbols all_162_0, all_162_1, % 65.78/9.43 | | | all_162_2 gives: % 65.78/9.43 | | | (80) (all_162_0 = 0 & power_class(all_52_0) = all_162_1 & % 65.78/9.43 | | | member(all_52_0, all_162_1) = 0 & $i(all_162_1)) | ( ~ % 65.78/9.43 | | | (all_162_2 = 0) & member(all_52_0, universal_class) = all_162_2) % 65.78/9.43 | | | % 65.78/9.43 | | | DELTA: instantiating (70) with fresh symbols all_167_0, all_167_1, % 65.78/9.43 | | | all_167_2 gives: % 65.78/9.43 | | | (81) (all_167_0 = 0 & ~ (all_104_1 = 0) & member(all_40_2, % 65.78/9.43 | | | universal_class) = 0) | ( ~ (all_167_1 = 0) & % 65.78/9.43 | | | complement(all_87_1) = all_167_2 & member(all_40_2, all_167_2) = % 65.78/9.43 | | | all_167_1 & $i(all_167_2)) % 65.78/9.43 | | | % 65.78/9.43 | | | DELTA: instantiating (77) with fresh symbols all_171_0, all_171_1, % 65.78/9.43 | | | all_171_2 gives: % 65.78/9.43 | | | (82) singleton(all_40_2) = all_171_2 & singleton(universal_class) = % 65.78/9.43 | | | all_171_1 & unordered_pair(all_171_2, all_171_0) = all_103_2 & % 65.78/9.43 | | | unordered_pair(all_40_2, all_171_1) = all_171_0 & $i(all_171_0) & % 65.78/9.43 | | | $i(all_171_1) & $i(all_171_2) & $i(all_103_2) % 65.78/9.43 | | | % 65.78/9.43 | | | ALPHA: (82) implies: % 65.78/9.43 | | | (83) $i(all_171_2) % 65.78/9.43 | | | (84) singleton(all_40_2) = all_171_2 % 65.78/9.43 | | | % 65.78/9.43 | | | BETA: splitting (71) gives: % 65.78/9.43 | | | % 65.78/9.43 | | | Case 1: % 65.78/9.43 | | | | % 65.78/9.43 | | | | (85) all_87_0 = 0 % 65.78/9.43 | | | | % 65.78/9.43 | | | | REDUCE: (46), (85) imply: % 65.78/9.43 | | | | (86) $false % 65.78/9.43 | | | | % 65.78/9.43 | | | | CLOSE: (86) is inconsistent. % 65.78/9.43 | | | | % 65.78/9.43 | | | Case 2: % 65.78/9.43 | | | | % 65.78/9.43 | | | | (87) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 & % 65.78/9.43 | | | | complement(all_87_1) = v1 & member(all_52_0, v1) = 0 & % 65.78/9.43 | | | | $i(v1)) | ( ~ (v0 = 0) & member(all_52_0, universal_class) = % 65.78/9.43 | | | | v0)) % 65.78/9.43 | | | | % 65.78/9.43 | | | | DELTA: instantiating (87) with fresh symbols all_185_0, all_185_1, % 65.78/9.43 | | | | all_185_2 gives: % 65.78/9.43 | | | | (88) (all_185_0 = 0 & complement(all_87_1) = all_185_1 & % 65.78/9.43 | | | | member(all_52_0, all_185_1) = 0 & $i(all_185_1)) | ( ~ % 65.78/9.43 | | | | (all_185_2 = 0) & member(all_52_0, universal_class) = % 65.78/9.43 | | | | all_185_2) % 65.78/9.43 | | | | % 65.78/9.43 | | | | BETA: splitting (88) gives: % 65.78/9.43 | | | | % 65.78/9.43 | | | | Case 1: % 65.78/9.43 | | | | | % 65.78/9.43 | | | | | (89) all_185_0 = 0 & complement(all_87_1) = all_185_1 & % 65.78/9.43 | | | | | member(all_52_0, all_185_1) = 0 & $i(all_185_1) % 65.78/9.43 | | | | | % 65.78/9.43 | | | | | ALPHA: (89) implies: % 65.78/9.43 | | | | | (90) complement(all_87_1) = all_185_1 % 65.78/9.43 | | | | | % 65.78/9.43 | | | | | BETA: splitting (80) gives: % 65.78/9.43 | | | | | % 65.78/9.43 | | | | | Case 1: % 65.78/9.43 | | | | | | % 65.78/9.43 | | | | | | (91) all_162_0 = 0 & power_class(all_52_0) = all_162_1 & % 65.78/9.43 | | | | | | member(all_52_0, all_162_1) = 0 & $i(all_162_1) % 65.78/9.43 | | | | | | % 65.78/9.43 | | | | | | ALPHA: (91) implies: % 65.78/9.43 | | | | | | (92) power_class(all_52_0) = all_162_1 % 65.78/9.43 | | | | | | % 65.78/9.43 | | | | | | BETA: splitting (69) gives: % 65.78/9.43 | | | | | | % 65.78/9.43 | | | | | | Case 1: % 65.78/9.43 | | | | | | | % 65.78/9.43 | | | | | | | (93) all_104_1 = 0 % 65.78/9.43 | | | | | | | % 65.78/9.43 | | | | | | | REDUCE: (57), (93) imply: % 65.78/9.43 | | | | | | | (94) $false % 65.78/9.43 | | | | | | | % 65.78/9.43 | | | | | | | CLOSE: (94) is inconsistent. % 65.78/9.43 | | | | | | | % 65.78/9.43 | | | | | | Case 2: % 65.78/9.43 | | | | | | | % 65.78/9.43 | | | | | | | (95) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 & % 65.78/9.43 | | | | | | | complement(all_87_1) = v1 & member(all_40_2, v1) = 0 & % 65.78/9.43 | | | | | | | $i(v1)) | ( ~ (v0 = 0) & member(all_40_2, % 65.78/9.43 | | | | | | | universal_class) = v0)) % 65.78/9.43 | | | | | | | % 65.78/9.43 | | | | | | | DELTA: instantiating (95) with fresh symbols all_209_0, all_209_1, % 65.78/9.43 | | | | | | | all_209_2 gives: % 65.78/9.43 | | | | | | | (96) (all_209_0 = 0 & complement(all_87_1) = all_209_1 & % 65.78/9.43 | | | | | | | member(all_40_2, all_209_1) = 0 & $i(all_209_1)) | ( ~ % 65.78/9.43 | | | | | | | (all_209_2 = 0) & member(all_40_2, universal_class) = % 65.78/9.43 | | | | | | | all_209_2) % 65.78/9.43 | | | | | | | % 65.78/9.43 | | | | | | | BETA: splitting (81) gives: % 65.78/9.43 | | | | | | | % 65.78/9.43 | | | | | | | Case 1: % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | (97) all_167_0 = 0 & ~ (all_104_1 = 0) & member(all_40_2, % 65.78/9.43 | | | | | | | | universal_class) = 0 % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | ALPHA: (97) implies: % 65.78/9.43 | | | | | | | | (98) member(all_40_2, universal_class) = 0 % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | REF_CLOSE: (21), (23), (26), (98) are inconsistent by sub-proof % 65.78/9.43 | | | | | | | | #1. % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | Case 2: % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | (99) ~ (all_167_1 = 0) & complement(all_87_1) = all_167_2 & % 65.78/9.43 | | | | | | | | member(all_40_2, all_167_2) = all_167_1 & $i(all_167_2) % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | ALPHA: (99) implies: % 65.78/9.43 | | | | | | | | (100) ~ (all_167_1 = 0) % 65.78/9.43 | | | | | | | | (101) member(all_40_2, all_167_2) = all_167_1 % 65.78/9.43 | | | | | | | | (102) complement(all_87_1) = all_167_2 % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | GROUND_INST: instantiating (18) with all_40_0, all_171_2, % 65.78/9.43 | | | | | | | | all_40_2, simplifying with (27), (84) gives: % 65.78/9.43 | | | | | | | | (103) all_171_2 = all_40_0 % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | GROUND_INST: instantiating (19) with all_167_2, all_185_1, % 65.78/9.43 | | | | | | | | all_87_1, simplifying with (90), (102) gives: % 65.78/9.43 | | | | | | | | (104) all_185_1 = all_167_2 % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | GROUND_INST: instantiating (20) with all_83_0, all_162_1, % 65.78/9.43 | | | | | | | | all_52_0, simplifying with (44), (92) gives: % 65.78/9.43 | | | | | | | | (105) all_162_1 = all_83_0 % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | REDUCE: (83), (103) imply: % 65.78/9.43 | | | | | | | | (106) $i(all_40_0) % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | BETA: splitting (96) gives: % 65.78/9.43 | | | | | | | | % 65.78/9.43 | | | | | | | | Case 1: % 65.78/9.43 | | | | | | | | | % 65.78/9.43 | | | | | | | | | (107) all_209_0 = 0 & complement(all_87_1) = all_209_1 & % 65.78/9.43 | | | | | | | | | member(all_40_2, all_209_1) = 0 & $i(all_209_1) % 65.78/9.43 | | | | | | | | | % 65.78/9.43 | | | | | | | | | ALPHA: (107) implies: % 65.78/9.43 | | | | | | | | | (108) member(all_40_2, all_209_1) = 0 % 65.78/9.43 | | | | | | | | | (109) complement(all_87_1) = all_209_1 % 65.78/9.43 | | | | | | | | | % 65.78/9.44 | | | | | | | | | GROUND_INST: instantiating (19) with all_167_2, all_209_1, % 65.78/9.44 | | | | | | | | | all_87_1, simplifying with (102), (109) gives: % 65.78/9.44 | | | | | | | | | (110) all_209_1 = all_167_2 % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | REDUCE: (108), (110) imply: % 65.78/9.44 | | | | | | | | | (111) member(all_40_2, all_167_2) = 0 % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | GROUND_INST: instantiating (21) with all_167_1, 0, all_167_2, % 65.78/9.44 | | | | | | | | | all_40_2, simplifying with (101), (111) gives: % 65.78/9.44 | | | | | | | | | (112) all_167_1 = 0 % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | REDUCE: (100), (112) imply: % 65.78/9.44 | | | | | | | | | (113) $false % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | CLOSE: (113) is inconsistent. % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | Case 2: % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | (114) ~ (all_209_2 = 0) & member(all_40_2, % 65.78/9.44 | | | | | | | | | universal_class) = all_209_2 % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | ALPHA: (114) implies: % 65.78/9.44 | | | | | | | | | (115) ~ (all_209_2 = 0) % 65.78/9.44 | | | | | | | | | (116) member(all_40_2, universal_class) = all_209_2 % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | GROUND_INST: instantiating (21) with all_40_1, all_209_2, % 65.78/9.44 | | | | | | | | | universal_class, all_40_2, simplifying with (26), % 65.78/9.44 | | | | | | | | | (116) gives: % 65.78/9.44 | | | | | | | | | (117) all_209_2 = all_40_1 % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | GROUND_INST: instantiating (34) with all_40_0, simplifying with % 65.78/9.44 | | | | | | | | | (76), (106) gives: % 65.78/9.44 | | | | | | | | | (118) all_40_0 = null_class | ? [v0: $i] : % 65.78/9.44 | | | | | | | | | (apply(all_55_0, all_40_0) = v0 & member(v0, % 65.78/9.44 | | | | | | | | | all_40_0) = 0 & $i(v0)) % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | BETA: splitting (118) gives: % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | | Case 1: % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | (119) all_40_0 = null_class % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | REDUCE: (24), (119) imply: % 65.78/9.44 | | | | | | | | | | (120) $false % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | CLOSE: (120) is inconsistent. % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | Case 2: % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | (121) ? [v0: $i] : (apply(all_55_0, all_40_0) = v0 & % 65.78/9.44 | | | | | | | | | | member(v0, all_40_0) = 0 & $i(v0)) % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | DELTA: instantiating (121) with fresh symbol all_413_0 % 65.78/9.44 | | | | | | | | | | gives: % 65.78/9.44 | | | | | | | | | | (122) apply(all_55_0, all_40_0) = all_413_0 & % 65.78/9.44 | | | | | | | | | | member(all_413_0, all_40_0) = 0 & $i(all_413_0) % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | ALPHA: (122) implies: % 65.78/9.44 | | | | | | | | | | (123) $i(all_413_0) % 65.78/9.44 | | | | | | | | | | (124) member(all_413_0, all_40_0) = 0 % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | BETA: splitting (73) gives: % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | Case 1: % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | (125) all_89_0 = all_52_0 % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | BETA: splitting (79) gives: % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | Case 1: % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | (126) all_153_0 = 0 & power_class(all_52_0) = all_153_1 % 65.78/9.44 | | | | | | | | | | | | & member(all_89_0, all_153_1) = 0 & $i(all_153_1) % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | ALPHA: (126) implies: % 65.78/9.44 | | | | | | | | | | | | (127) member(all_89_0, all_153_1) = 0 % 65.78/9.44 | | | | | | | | | | | | (128) power_class(all_52_0) = all_153_1 % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_83_0, all_153_1, % 65.78/9.44 | | | | | | | | | | | | all_52_0, simplifying with (44), (128) gives: % 65.78/9.44 | | | | | | | | | | | | (129) all_153_1 = all_83_0 % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | REDUCE: (127), (129) imply: % 65.78/9.44 | | | | | | | | | | | | (130) member(all_89_0, all_83_0) = 0 % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | BETA: splitting (78) gives: % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | Case 1: % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_413_0, all_40_2, % 65.78/9.44 | | | | | | | | | | | | | all_40_2, all_40_0, simplifying with (25), (40), % 65.78/9.44 | | | | | | | | | | | | | (123), (124) gives: % 65.78/9.44 | | | | | | | | | | | | | (131) all_413_0 = all_40_2 % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_413_0, all_40_2, % 65.78/9.44 | | | | | | | | | | | | | all_40_2, all_40_0, simplifying with (25), (40), % 65.78/9.44 | | | | | | | | | | | | | (123), (124) gives: % 65.78/9.44 | | | | | | | | | | | | | (132) member(all_413_0, universal_class) = 0 % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | REDUCE: (131), (132) imply: % 65.78/9.44 | | | | | | | | | | | | | (133) member(all_40_2, universal_class) = 0 % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | REF_CLOSE: (21), (23), (26), (133) are inconsistent by % 65.78/9.44 | | | | | | | | | | | | | sub-proof #1. % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | Case 2: % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | (134) ~ (all_151_1 = 0) & power_class(all_52_0) = % 65.78/9.44 | | | | | | | | | | | | | all_151_2 & member(all_89_0, all_151_2) = % 65.78/9.44 | | | | | | | | | | | | | all_151_1 & $i(all_151_2) % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | ALPHA: (134) implies: % 65.78/9.44 | | | | | | | | | | | | | (135) ~ (all_151_1 = 0) % 65.78/9.44 | | | | | | | | | | | | | (136) member(all_89_0, all_151_2) = all_151_1 % 65.78/9.44 | | | | | | | | | | | | | (137) power_class(all_52_0) = all_151_2 % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_83_0, all_151_2, % 65.78/9.44 | | | | | | | | | | | | | all_52_0, simplifying with (44), (137) gives: % 65.78/9.44 | | | | | | | | | | | | | (138) all_151_2 = all_83_0 % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | REDUCE: (136), (138) imply: % 65.78/9.44 | | | | | | | | | | | | | (139) member(all_89_0, all_83_0) = all_151_1 % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_151_1, all_83_0, % 65.78/9.44 | | | | | | | | | | | | | all_89_0, simplifying with (130), (139) gives: % 65.78/9.44 | | | | | | | | | | | | | (140) all_151_1 = 0 % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | REDUCE: (135), (140) imply: % 65.78/9.44 | | | | | | | | | | | | | (141) $false % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | | CLOSE: (141) is inconsistent. % 65.78/9.44 | | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | End of split % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | Case 2: % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | (142) ~ (all_153_2 = 0) & member(all_89_0, % 65.78/9.44 | | | | | | | | | | | | universal_class) = all_153_2 % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | ALPHA: (142) implies: % 65.78/9.44 | | | | | | | | | | | | (143) ~ (all_153_2 = 0) % 65.78/9.44 | | | | | | | | | | | | (144) member(all_89_0, universal_class) = all_153_2 % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | REDUCE: (125), (144) imply: % 65.78/9.44 | | | | | | | | | | | | (145) member(all_52_0, universal_class) = all_153_2 % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_153_2, % 65.78/9.44 | | | | | | | | | | | | universal_class, all_52_0, simplifying with (30), % 65.78/9.44 | | | | | | | | | | | | (145) gives: % 65.78/9.44 | | | | | | | | | | | | (146) all_153_2 = 0 % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | REDUCE: (143), (146) imply: % 65.78/9.44 | | | | | | | | | | | | (147) $false % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | | CLOSE: (147) is inconsistent. % 65.78/9.44 | | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | End of split % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | Case 2: % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | GROUND_INST: instantiating (3) with all_413_0, all_40_2, % 65.78/9.44 | | | | | | | | | | | all_40_2, all_40_0, simplifying with (25), (40), % 65.78/9.44 | | | | | | | | | | | (123), (124) gives: % 65.78/9.44 | | | | | | | | | | | (148) all_413_0 = all_40_2 % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | GROUND_INST: instantiating (2) with all_413_0, all_40_2, % 65.78/9.44 | | | | | | | | | | | all_40_2, all_40_0, simplifying with (25), (40), % 65.78/9.44 | | | | | | | | | | | (123), (124) gives: % 65.78/9.44 | | | | | | | | | | | (149) member(all_413_0, universal_class) = 0 % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | REDUCE: (148), (149) imply: % 65.78/9.44 | | | | | | | | | | | (150) member(all_40_2, universal_class) = 0 % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | | REF_CLOSE: (21), (23), (26), (150) are inconsistent by % 65.78/9.44 | | | | | | | | | | | sub-proof #1. % 65.78/9.44 | | | | | | | | | | | % 65.78/9.44 | | | | | | | | | | End of split % 65.78/9.44 | | | | | | | | | | % 65.78/9.44 | | | | | | | | | End of split % 65.78/9.44 | | | | | | | | | % 65.78/9.44 | | | | | | | | End of split % 65.78/9.44 | | | | | | | | % 65.78/9.44 | | | | | | | End of split % 65.78/9.44 | | | | | | | % 65.78/9.44 | | | | | | End of split % 65.78/9.44 | | | | | | % 65.78/9.44 | | | | | Case 2: % 65.78/9.44 | | | | | | % 65.78/9.44 | | | | | | (151) ~ (all_162_2 = 0) & member(all_52_0, universal_class) = % 65.78/9.44 | | | | | | all_162_2 % 65.78/9.44 | | | | | | % 65.78/9.44 | | | | | | ALPHA: (151) implies: % 65.78/9.44 | | | | | | (152) ~ (all_162_2 = 0) % 65.78/9.44 | | | | | | (153) member(all_52_0, universal_class) = all_162_2 % 65.78/9.45 | | | | | | % 65.78/9.45 | | | | | | GROUND_INST: instantiating (21) with 0, all_162_2, universal_class, % 65.78/9.45 | | | | | | all_52_0, simplifying with (30), (153) gives: % 65.78/9.45 | | | | | | (154) all_162_2 = 0 % 65.78/9.45 | | | | | | % 65.78/9.45 | | | | | | REDUCE: (152), (154) imply: % 65.78/9.45 | | | | | | (155) $false % 65.78/9.45 | | | | | | % 65.78/9.45 | | | | | | CLOSE: (155) is inconsistent. % 65.78/9.45 | | | | | | % 65.78/9.45 | | | | | End of split % 65.78/9.45 | | | | | % 65.78/9.45 | | | | Case 2: % 65.78/9.45 | | | | | % 65.78/9.45 | | | | | (156) ~ (all_185_2 = 0) & member(all_52_0, universal_class) = % 65.78/9.45 | | | | | all_185_2 % 65.78/9.45 | | | | | % 65.78/9.45 | | | | | ALPHA: (156) implies: % 65.78/9.45 | | | | | (157) ~ (all_185_2 = 0) % 65.78/9.45 | | | | | (158) member(all_52_0, universal_class) = all_185_2 % 65.78/9.45 | | | | | % 65.78/9.45 | | | | | GROUND_INST: instantiating (21) with 0, all_185_2, universal_class, % 65.78/9.45 | | | | | all_52_0, simplifying with (30), (158) gives: % 65.78/9.45 | | | | | (159) all_185_2 = 0 % 65.78/9.45 | | | | | % 65.78/9.45 | | | | | REDUCE: (157), (159) imply: % 65.78/9.45 | | | | | (160) $false % 65.78/9.45 | | | | | % 65.78/9.45 | | | | | CLOSE: (160) is inconsistent. % 65.78/9.45 | | | | | % 65.78/9.45 | | | | End of split % 65.78/9.45 | | | | % 65.78/9.45 | | | End of split % 65.78/9.45 | | | % 65.78/9.45 | | End of split % 65.78/9.45 | | % 65.78/9.45 | End of split % 65.78/9.45 | % 65.78/9.45 End of proof % 65.78/9.45 % 65.78/9.45 Sub-proof #1 shows that the following formulas are inconsistent: % 65.78/9.45 ---------------------------------------------------------------- % 65.78/9.45 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 65.78/9.45 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 65.78/9.45 v0)) % 65.78/9.45 (2) member(all_40_2, universal_class) = all_40_1 % 65.78/9.45 (3) member(all_40_2, universal_class) = 0 % 65.78/9.45 (4) ~ (all_40_1 = 0) % 65.78/9.45 % 65.78/9.45 Begin of proof % 65.78/9.45 | % 65.78/9.45 | GROUND_INST: instantiating (1) with all_40_1, 0, universal_class, all_40_2, % 65.78/9.45 | simplifying with (2), (3) gives: % 65.78/9.45 | (5) all_40_1 = 0 % 65.78/9.45 | % 65.78/9.45 | REDUCE: (4), (5) imply: % 65.78/9.45 | (6) $false % 65.78/9.45 | % 65.78/9.45 | CLOSE: (6) is inconsistent. % 65.78/9.45 | % 65.78/9.45 End of proof % 65.78/9.45 % SZS output end Proof for theBenchmark % 65.78/9.45 % 65.78/9.45 8857ms %------------------------------------------------------------------------------