%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET814+4 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.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 15:26:33 EDT 2023 % Result : Theorem 14.49s 3.07s % Output : Proof 22.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET814+4 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n020.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sat Aug 26 12:37:45 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.67 ________ _____ % 0.21/0.67 ___ __ \_________(_)________________________________ % 0.21/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.67 % 0.21/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.67 (2023-06-19) % 0.21/0.67 % 0.21/0.67 (c) Philipp Rümmer, 2009-2023 % 0.21/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.67 Amanda Stjerna. % 0.21/0.67 Free software under BSD-3-Clause. % 0.21/0.67 % 0.21/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.67 % 0.21/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.69 Running up to 7 provers in parallel. % 0.21/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.12/1.29 Prover 4: Preprocessing ... % 3.12/1.29 Prover 1: Preprocessing ... % 3.75/1.35 Prover 2: Preprocessing ... % 3.75/1.35 Prover 0: Preprocessing ... % 3.75/1.35 Prover 3: Preprocessing ... % 3.75/1.35 Prover 6: Preprocessing ... % 3.75/1.37 Prover 5: Preprocessing ... % 9.38/2.17 Prover 2: Proving ... % 9.38/2.17 Prover 5: Proving ... % 9.38/2.17 Prover 6: Proving ... % 9.38/2.18 Prover 3: Constructing countermodel ... % 9.38/2.18 Prover 1: Constructing countermodel ... % 9.38/2.24 Prover 4: Constructing countermodel ... % 10.13/2.40 Prover 0: Proving ... % 11.28/2.48 Prover 3: gave up % 11.28/2.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.28/2.49 Prover 1: gave up % 11.28/2.51 Prover 6: gave up % 11.81/2.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.81/2.55 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 12.21/2.65 Prover 7: Preprocessing ... % 12.21/2.65 Prover 9: Preprocessing ... % 12.21/2.65 Prover 8: Preprocessing ... % 13.28/2.81 Prover 7: Warning: ignoring some quantifiers % 13.97/2.84 Prover 7: Constructing countermodel ... % 14.49/2.97 Prover 8: Warning: ignoring some quantifiers % 14.49/2.99 Prover 8: Constructing countermodel ... % 14.49/3.07 Prover 0: proved (2368ms) % 14.49/3.07 % 14.49/3.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.49/3.07 % 14.49/3.08 Prover 2: stopped % 14.49/3.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.49/3.09 Prover 5: stopped % 14.49/3.09 Prover 9: Constructing countermodel ... % 14.49/3.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.49/3.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.49/3.11 Prover 9: stopped % 14.49/3.13 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.59/3.15 Prover 10: Preprocessing ... % 16.53/3.18 Prover 11: Preprocessing ... % 16.53/3.19 Prover 16: Preprocessing ... % 16.53/3.19 Prover 13: Preprocessing ... % 16.91/3.23 Prover 8: gave up % 16.91/3.24 Prover 7: gave up % 17.06/3.25 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 17.06/3.30 Prover 10: Warning: ignoring some quantifiers % 17.06/3.31 Prover 16: Warning: ignoring some quantifiers % 17.06/3.31 Prover 19: Preprocessing ... % 17.56/3.33 Prover 16: Constructing countermodel ... % 17.56/3.33 Prover 10: Constructing countermodel ... % 17.56/3.35 Prover 13: Warning: ignoring some quantifiers % 17.92/3.37 Prover 13: Constructing countermodel ... % 17.92/3.44 Prover 10: gave up % 19.26/3.55 Prover 19: Warning: ignoring some quantifiers % 19.26/3.57 Prover 11: Constructing countermodel ... % 19.26/3.57 Prover 19: Constructing countermodel ... % 19.26/3.81 Prover 4: Found proof (size 114) % 19.26/3.81 Prover 4: proved (3112ms) % 19.26/3.82 Prover 11: stopped % 19.26/3.82 Prover 19: stopped % 19.26/3.82 Prover 16: stopped % 19.26/3.82 Prover 13: stopped % 19.26/3.82 % 19.26/3.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.26/3.82 % 19.26/3.84 % SZS output start Proof for theBenchmark % 20.67/3.84 Assumptions after simplification: % 20.67/3.84 --------------------------------- % 20.67/3.84 % 20.67/3.84 (ordinal_number) % 21.62/3.90 $i(member_predicate) & $i(on) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 % 21.62/3.90 = 0 | ~ (subset(v1, v0) = v2) | ~ (member(v0, on) = 0) | ~ $i(v1) | ~ % 21.62/3.90 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & member(v1, v0) = v3)) & ! [v0: $i] : % 21.62/3.90 ! [v1: int] : (v1 = 0 | ~ (member(v0, on) = v1) | ~ $i(v0) | ? [v2: any] : % 21.62/3.91 ? [v3: any] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ($i(v4) & ((v5 = % 21.62/3.91 0 & ~ (v6 = 0) & subset(v4, v0) = v6 & member(v4, v0) = 0) | % 21.62/3.91 (strict_well_order(member_predicate, v0) = v3 & set(v0) = v2 & ( ~ (v3 = % 21.62/3.91 0) | ~ (v2 = 0)))))) & ! [v0: $i] : ! [v1: any] : ( ~ % 21.62/3.91 (strict_well_order(member_predicate, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 21.62/3.91 ? [v3: any] : (set(v0) = v3 & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 & % 21.62/3.91 v1 = 0 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) = % 21.62/3.91 v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) = % 21.62/3.91 v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4) | % 21.62/3.91 subset(v4, v0) = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ (set(v0) % 21.62/3.91 = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 21.62/3.91 (strict_well_order(member_predicate, v0) = v3 & member(v0, on) = v2 & ( ~ % 21.62/3.91 (v2 = 0) | (v3 = 0 & v1 = 0 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 21.62/3.91 (subset(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & % 21.62/3.91 member(v4, v0) = v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | % 21.62/3.91 ~ $i(v4) | subset(v4, v0) = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.62/3.91 (member(v1, v0) = 0) | ~ (member(v0, on) = 0) | ~ $i(v1) | ~ $i(v0) | % 21.62/3.91 subset(v1, v0) = 0) & ! [v0: $i] : ( ~ (strict_well_order(member_predicate, % 21.62/3.91 v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? % 21.62/3.91 [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & subset(v3, v0) % 21.62/3.91 = v5 & member(v3, v0) = 0) | (set(v0) = v1 & member(v0, on) = v2 & ( ~ % 21.62/3.91 (v1 = 0) | v2 = 0))))) & ! [v0: $i] : ( ~ (set(v0) = 0) | ~ $i(v0) % 21.62/3.91 | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : % 21.62/3.91 ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & subset(v3, v0) = v5 & member(v3, v0) = 0) % 21.62/3.91 | (strict_well_order(member_predicate, v0) = v1 & member(v0, on) = v2 & % 21.62/3.91 ( ~ (v1 = 0) | v2 = 0))))) & ! [v0: $i] : ( ~ (member(v0, on) = 0) | % 21.62/3.91 ~ $i(v0) | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0)) % 21.62/3.91 % 21.62/3.91 (power_set) % 21.62/3.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.62/3.91 (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 21.62/3.91 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 21.62/3.91 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 21.62/3.91 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, % 21.62/3.91 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.62/3.91 (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 21.62/3.91 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | % 21.62/3.91 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (power_set(v1) = v2 & member(v0, v2) = % 21.62/3.91 0 & $i(v2))) % 21.62/3.91 % 21.62/3.91 (rel_member) % 21.62/3.92 $i(member_predicate) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 21.62/3.92 (apply(member_predicate, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 21.62/3.92 int] : ( ~ (v3 = 0) & member(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : % 21.62/3.92 ! [v2: int] : (v2 = 0 | ~ (member(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 21.62/3.92 [v3: int] : ( ~ (v3 = 0) & apply(member_predicate, v0, v1) = v3)) & ! [v0: % 21.62/3.92 $i] : ! [v1: $i] : ( ~ (apply(member_predicate, v0, v1) = 0) | ~ $i(v1) | % 21.62/3.92 ~ $i(v0) | member(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, % 21.62/3.92 v1) = 0) | ~ $i(v1) | ~ $i(v0) | apply(member_predicate, v0, v1) = 0) % 21.62/3.92 % 21.62/3.92 (strict_order) % 21.62/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.62/3.94 int] : (v5 = 0 | ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v4) = v5) | % 21.62/3.94 ~ (strict_order(v0, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 21.62/3.94 | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : % 21.62/3.94 (apply(v0, v2, v3) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & % 21.62/3.94 member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 21.62/3.94 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 21.62/3.94 [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ % 21.62/3.94 (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ~ $i(v4) | ~ % 21.62/3.94 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 21.62/3.94 ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & % 21.62/3.94 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | % 21.62/3.94 ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.62/3.94 ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (apply(v0, v2, v4) = % 21.62/3.94 v5) | ~ (strict_order(v0, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v4) % 21.62/3.94 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 21.62/3.94 any] : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & apply(v0, % 21.62/3.94 v2, v3) = v8 & member(v4, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) % 21.62/3.94 | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] % 21.62/3.94 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v3, v4) = 0) | ~ % 21.62/3.94 (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ~ $i(v4) | ~ % 21.62/3.94 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 21.62/3.94 ? [v7: any] : ? [v8: any] : (apply(v0, v2, v4) = v8 & member(v4, v1) = v7 & % 21.62/3.94 member(v3, v1) = v6 & member(v2, v1) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | % 21.62/3.94 ~ (v5 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 21.62/3.94 [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v3, v4) = 0) | ~ (strict_order(v0, % 21.62/3.94 v1) = 0) | ~ (member(v2, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | % 21.62/3.94 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 21.62/3.94 any] : (apply(v0, v2, v4) = v8 & apply(v0, v2, v3) = v7 & member(v4, v1) = % 21.62/3.94 v6 & member(v3, v1) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v8 = % 21.62/3.94 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 21.62/3.94 $i] : ( ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ~ % 21.62/3.94 (member(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.62/3.94 $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 21.62/3.94 (apply(v0, v3, v4) = v7 & apply(v0, v2, v4) = v8 & member(v3, v1) = v6 & % 21.62/3.94 member(v2, v1) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v8 = 0))) % 21.62/3.94 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 21.62/3.94 (strict_order(v0, v1) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = % 21.62/3.94 0) | ~ (member(v2, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 21.62/3.94 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : (apply(v0, % 21.62/3.94 v3, v4) = v6 & apply(v0, v2, v4) = v7 & apply(v0, v2, v3) = v5 & ( ~ (v6 % 21.62/3.94 = 0) | ~ (v5 = 0) | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.62/3.94 $i] : ! [v3: $i] : ( ~ (apply(v0, v3, v2) = 0) | ~ (strict_order(v0, v1) = % 21.62/3.94 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 21.62/3.94 [v5: any] : ? [v6: any] : (apply(v0, v2, v3) = v6 & member(v3, v1) = v5 & % 21.62/3.94 member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) & ! % 21.62/3.94 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v0, v2, v3) = % 21.62/3.94 0) | ~ (strict_order(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 21.62/3.94 ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : (apply(v0, v3, v2) = % 21.62/3.94 v6 & member(v3, v1) = v5 & member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = % 21.62/3.94 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = % 21.62/3.94 0 | ~ (strict_order(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 21.62/3.94 ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 21.62/3.94 [v9: int] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13: $i] : ? % 21.62/3.94 [v14: int] : ? [v15: int] : ? [v16: int] : ? [v17: int] : ($i(v13) & % 21.62/3.94 $i(v12) & $i(v5) & $i(v4) & $i(v3) & ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = % 21.62/3.94 0 & apply(v0, v13, v12) = 0 & apply(v0, v12, v13) = 0 & member(v13, % 21.62/3.94 v1) = 0 & member(v12, v1) = 0) | (v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 % 21.62/3.94 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = % 21.62/3.94 v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 % 21.62/3.94 & member(v3, v1) = 0)))) % 21.62/3.94 % 21.62/3.94 (strict_well_order) % 21.62/3.95 ! [v0: $i] : ! [v1: $i] : ! [v2: MultipleValueBool] : ! [v3: $i] : ! [v4: % 21.62/3.95 $i] : ( ~ (strict_order(v0, v1) = v2) | ~ (subset(v3, v1) = 0) | ~ % 21.62/3.95 (member(v4, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? % 21.62/3.95 [v5: int] : ? [v6: $i] : ? [v7: int] : ($i(v6) & ((v7 = 0 & least(v6, v0, % 21.62/3.95 v3) = 0) | ( ~ (v5 = 0) & strict_well_order(v0, v1) = v5)))) & ! % 21.62/3.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 21.62/3.95 (strict_well_order(v0, v1) = 0) | ~ (subset(v2, v1) = 0) | ~ (member(v3, % 21.62/3.95 v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 21.62/3.95 (least(v4, v0, v2) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] % 21.62/3.95 : (v2 = 0 | ~ (strict_order(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 21.62/3.95 int] : ( ~ (v3 = 0) & strict_well_order(v0, v1) = v3)) & ! [v0: $i] : ! % 21.62/3.95 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (strict_well_order(v0, v1) = v2) | ~ % 21.62/3.95 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] % 21.62/3.95 : ? [v7: int] : ($i(v6) & $i(v4) & ((v7 = 0 & v5 = 0 & subset(v4, v1) = 0 & % 21.62/3.95 member(v6, v4) = 0 & ! [v8: $i] : ( ~ (least(v8, v0, v4) = 0) | ~ % 21.62/3.95 $i(v8))) | ( ~ (v3 = 0) & strict_order(v0, v1) = v3)))) & ! [v0: % 21.62/3.95 $i] : ! [v1: $i] : ( ~ (strict_order(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 21.62/3.95 ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: int] : % 21.62/3.95 ($i(v5) & $i(v3) & ((v6 = 0 & v4 = 0 & subset(v3, v1) = 0 & member(v5, v3) = % 21.62/3.95 0 & ! [v7: $i] : ( ~ (least(v7, v0, v3) = 0) | ~ $i(v7))) | (v2 = 0 % 21.62/3.95 & strict_well_order(v0, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.62/3.95 (strict_well_order(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | strict_order(v0, % 21.62/3.95 v1) = 0) % 21.62/3.95 % 21.62/3.95 (subset) % 21.62/3.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.62/3.95 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.62/3.95 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 21.62/3.95 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 21.62/3.95 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 21.62/3.95 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.62/3.95 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 21.62/3.95 ~ $i(v0) | member(v2, v1) = 0) % 21.62/3.95 % 21.62/3.95 (sum) % 21.62/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 % 21.62/3.96 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | % 21.62/3.96 ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & member(v0, % 21.62/3.96 v4) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! % 21.62/3.96 [v4: $i] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ % 21.62/3.96 (member(v0, v2) = v3) | ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( % 21.62/3.96 ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 21.62/3.96 $i] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 21.62/3.96 ? [v3: $i] : (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3))) % 21.62/3.96 % 21.62/3.96 (thV14) % 21.62/3.96 $i(on) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & sum(v0) = % 21.62/3.96 v1 & subset(v1, v0) = v2 & member(v0, on) = 0 & $i(v1) & $i(v0)) % 21.62/3.96 % 21.62/3.96 (function-axioms) % 21.62/3.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 21.62/3.97 | ~ (initial_segment(v4, v3, v2) = v1) | ~ (initial_segment(v4, v3, v2) = % 21.62/3.97 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.62/3.97 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 21.62/3.97 ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.62/3.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 21.62/3.97 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0: % 21.62/3.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.62/3.97 : (v1 = v0 | ~ (strict_order(v3, v2) = v1) | ~ (strict_order(v3, v2) = v0)) % 21.62/3.97 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 21.62/3.97 [v3: $i] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~ % 21.62/3.97 (strict_well_order(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 21.62/3.97 : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 21.62/3.97 (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.62/3.97 ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) % 21.62/3.97 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 21.62/3.97 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 21.62/3.97 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) % 21.62/3.97 | ~ (intersection(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.62/3.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.62/3.97 (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0: % 21.62/3.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.62/3.97 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 21.62/3.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.62/3.97 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: % 21.62/3.97 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (suc(v2) = v1) | ~ (suc(v2) % 21.62/3.97 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 21.62/3.97 $i] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0)) & ! [v0: $i] : ! % 21.62/3.97 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 21.62/3.97 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 21.62/3.97 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 21.62/3.97 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 21.62/3.97 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 21.62/3.97 (power_set(v2) = v0)) % 21.62/3.97 % 21.62/3.97 Further assumptions not needed in the proof: % 21.62/3.97 -------------------------------------------- % 22.03/3.97 difference, empty_set, equal_set, initial_segment, intersection, least, product, % 22.03/3.97 set_member, singleton, successor, thI3, union, unordered_pair % 22.03/3.97 % 22.03/3.97 Those formulas are unsatisfiable: % 22.03/3.97 --------------------------------- % 22.03/3.97 % 22.03/3.97 Begin of proof % 22.03/3.97 | % 22.03/3.97 | ALPHA: (subset) implies: % 22.03/3.98 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 22.03/3.98 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2, % 22.03/3.98 | v1) = 0) % 22.03/3.98 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 22.03/3.98 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 22.03/3.98 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 22.03/3.98 | % 22.03/3.98 | ALPHA: (power_set) implies: % 22.06/3.98 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 22.06/3.98 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 22.06/3.98 | (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4 & $i(v3))) % 22.06/3.98 | % 22.06/3.98 | ALPHA: (sum) implies: % 22.06/3.98 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1) = v2) | ~ % 22.06/3.98 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 22.06/3.98 | (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3))) % 22.06/3.98 | % 22.06/3.98 | ALPHA: (ordinal_number) implies: % 22.06/3.98 | (5) ! [v0: $i] : ( ~ (member(v0, on) = 0) | ~ $i(v0) | % 22.06/3.98 | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0)) % 22.06/3.98 | (6) ! [v0: $i] : ! [v1: any] : ( ~ (set(v0) = v1) | ~ $i(v0) | ? [v2: % 22.06/3.98 | any] : ? [v3: any] : (strict_well_order(member_predicate, v0) = v3 % 22.06/3.98 | & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0 & ! [v4: % 22.06/3.98 | $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) = v5) | ~ % 22.06/3.98 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) = v6)) % 22.06/3.98 | & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4) | % 22.06/3.98 | subset(v4, v0) = 0))))) % 22.06/3.99 | (7) ! [v0: $i] : ! [v1: any] : ( ~ (strict_well_order(member_predicate, % 22.06/3.99 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (set(v0) = % 22.06/3.99 | v3 & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0 & ! % 22.06/3.99 | [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) = v5) | % 22.06/3.99 | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) = % 22.06/3.99 | v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4) | % 22.06/3.99 | subset(v4, v0) = 0))))) % 22.06/3.99 | % 22.06/3.99 | ALPHA: (strict_well_order) implies: % 22.06/3.99 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (strict_well_order(v0, v1) = 0) | ~ % 22.06/3.99 | $i(v1) | ~ $i(v0) | strict_order(v0, v1) = 0) % 22.06/3.99 | % 22.06/3.99 | ALPHA: (rel_member) implies: % 22.06/3.99 | (9) $i(member_predicate) % 22.06/3.99 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, v1) = 0) | ~ $i(v1) | ~ % 22.06/3.99 | $i(v0) | apply(member_predicate, v0, v1) = 0) % 22.06/3.99 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (member(v0, % 22.06/3.99 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) % 22.06/3.99 | & apply(member_predicate, v0, v1) = v3)) % 22.06/3.99 | % 22.06/3.99 | ALPHA: (strict_order) implies: % 22.06/3.99 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v0, % 22.06/3.99 | v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ~ $i(v3) | ~ % 22.06/3.99 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 22.06/3.99 | [v6: any] : (apply(v0, v3, v2) = v6 & member(v3, v1) = v5 & % 22.06/3.99 | member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) % 22.06/4.00 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v0, % 22.06/4.00 | v3, v2) = 0) | ~ (strict_order(v0, v1) = 0) | ~ $i(v3) | ~ % 22.06/4.00 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? % 22.06/4.00 | [v6: any] : (apply(v0, v2, v3) = v6 & member(v3, v1) = v5 & % 22.06/4.00 | member(v2, v1) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) % 22.06/4.00 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 22.06/4.00 | ( ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ~ % 22.06/4.00 | (member(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 22.06/4.00 | | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 22.06/4.00 | any] : (apply(v0, v3, v4) = v7 & apply(v0, v2, v4) = v8 & % 22.06/4.00 | member(v3, v1) = v6 & member(v2, v1) = v5 & ( ~ (v7 = 0) | ~ (v6 % 22.06/4.00 | = 0) | ~ (v5 = 0) | v8 = 0))) % 22.06/4.00 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 22.06/4.00 | ( ~ (apply(v0, v3, v4) = 0) | ~ (strict_order(v0, v1) = 0) | ~ % 22.06/4.00 | (member(v2, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 22.06/4.00 | | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 22.06/4.00 | any] : (apply(v0, v2, v4) = v8 & apply(v0, v2, v3) = v7 & % 22.06/4.00 | member(v4, v1) = v6 & member(v3, v1) = v5 & ( ~ (v7 = 0) | ~ (v6 % 22.06/4.00 | = 0) | ~ (v5 = 0) | v8 = 0))) % 22.06/4.00 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 22.19/4.00 | ! [v5: int] : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ % 22.19/4.00 | (strict_order(v0, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v4) | % 22.19/4.00 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 22.19/4.00 | [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & % 22.19/4.00 | apply(v0, v2, v3) = v8 & member(v4, v1) = v7 & member(v2, v1) = v6 % 22.19/4.00 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 22.19/4.00 | % 22.19/4.00 | ALPHA: (thV14) implies: % 22.19/4.01 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & sum(v0) = v1 % 22.19/4.01 | & subset(v1, v0) = v2 & member(v0, on) = 0 & $i(v1) & $i(v0)) % 22.19/4.01 | % 22.19/4.01 | ALPHA: (function-axioms) implies: % 22.19/4.01 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.19/4.01 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 22.19/4.01 | v2) = v0)) % 22.19/4.01 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.19/4.01 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 22.19/4.01 | ~ (apply(v4, v3, v2) = v0)) % 22.19/4.01 | % 22.19/4.01 | DELTA: instantiating (17) with fresh symbols all_24_0, all_24_1, all_24_2 % 22.19/4.01 | gives: % 22.19/4.01 | (20) ~ (all_24_0 = 0) & sum(all_24_2) = all_24_1 & subset(all_24_1, % 22.19/4.01 | all_24_2) = all_24_0 & member(all_24_2, on) = 0 & $i(all_24_1) & % 22.19/4.01 | $i(all_24_2) % 22.19/4.01 | % 22.19/4.01 | ALPHA: (20) implies: % 22.19/4.01 | (21) ~ (all_24_0 = 0) % 22.19/4.01 | (22) $i(all_24_2) % 22.19/4.01 | (23) $i(all_24_1) % 22.19/4.01 | (24) member(all_24_2, on) = 0 % 22.19/4.01 | (25) subset(all_24_1, all_24_2) = all_24_0 % 22.19/4.01 | (26) sum(all_24_2) = all_24_1 % 22.19/4.01 | % 22.19/4.01 | GROUND_INST: instantiating (5) with all_24_2, simplifying with (22), (24) % 22.19/4.01 | gives: % 22.19/4.01 | (27) strict_well_order(member_predicate, all_24_2) = 0 & set(all_24_2) = 0 % 22.19/4.01 | % 22.19/4.01 | ALPHA: (27) implies: % 22.19/4.01 | (28) set(all_24_2) = 0 % 22.19/4.01 | (29) strict_well_order(member_predicate, all_24_2) = 0 % 22.19/4.01 | % 22.19/4.01 | GROUND_INST: instantiating (3) with all_24_1, all_24_2, all_24_0, simplifying % 22.19/4.01 | with (22), (23), (25) gives: % 22.19/4.01 | (30) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 22.19/4.01 | power_set(all_24_2) = v0 & member(all_24_1, v0) = v1 & $i(v0)) % 22.19/4.01 | % 22.19/4.02 | GROUND_INST: instantiating (2) with all_24_1, all_24_2, all_24_0, simplifying % 22.19/4.02 | with (22), (23), (25) gives: % 22.19/4.02 | (31) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 22.19/4.02 | all_24_1) = 0 & member(v0, all_24_2) = v1 & $i(v0)) % 22.19/4.02 | % 22.19/4.02 | BETA: splitting (31) gives: % 22.19/4.02 | % 22.19/4.02 | Case 1: % 22.19/4.02 | | % 22.19/4.02 | | (32) all_24_0 = 0 % 22.19/4.02 | | % 22.19/4.02 | | REDUCE: (21), (32) imply: % 22.19/4.02 | | (33) $false % 22.19/4.02 | | % 22.19/4.02 | | CLOSE: (33) is inconsistent. % 22.19/4.02 | | % 22.19/4.02 | Case 2: % 22.19/4.02 | | % 22.19/4.02 | | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_24_1) = 0 % 22.19/4.02 | | & member(v0, all_24_2) = v1 & $i(v0)) % 22.19/4.02 | | % 22.19/4.02 | | DELTA: instantiating (34) with fresh symbols all_47_0, all_47_1 gives: % 22.19/4.02 | | (35) ~ (all_47_0 = 0) & member(all_47_1, all_24_1) = 0 & % 22.19/4.02 | | member(all_47_1, all_24_2) = all_47_0 & $i(all_47_1) % 22.19/4.02 | | % 22.19/4.02 | | ALPHA: (35) implies: % 22.19/4.02 | | (36) ~ (all_47_0 = 0) % 22.19/4.02 | | (37) $i(all_47_1) % 22.19/4.02 | | (38) member(all_47_1, all_24_2) = all_47_0 % 22.19/4.02 | | (39) member(all_47_1, all_24_1) = 0 % 22.19/4.02 | | % 22.19/4.02 | | BETA: splitting (30) gives: % 22.19/4.02 | | % 22.19/4.02 | | Case 1: % 22.19/4.02 | | | % 22.19/4.02 | | | (40) all_24_0 = 0 % 22.19/4.02 | | | % 22.19/4.02 | | | REDUCE: (21), (40) imply: % 22.19/4.02 | | | (41) $false % 22.19/4.02 | | | % 22.19/4.02 | | | CLOSE: (41) is inconsistent. % 22.19/4.02 | | | % 22.19/4.02 | | Case 2: % 22.19/4.02 | | | % 22.19/4.02 | | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & power_set(all_24_2) = % 22.19/4.02 | | | v0 & member(all_24_1, v0) = v1 & $i(v0)) % 22.19/4.02 | | | % 22.19/4.02 | | | DELTA: instantiating (42) with fresh symbols all_52_0, all_52_1 gives: % 22.28/4.02 | | | (43) ~ (all_52_0 = 0) & power_set(all_24_2) = all_52_1 & % 22.28/4.02 | | | member(all_24_1, all_52_1) = all_52_0 & $i(all_52_1) % 22.28/4.02 | | | % 22.28/4.02 | | | ALPHA: (43) implies: % 22.28/4.02 | | | (44) ~ (all_52_0 = 0) % 22.28/4.02 | | | (45) $i(all_52_1) % 22.28/4.02 | | | (46) member(all_24_1, all_52_1) = all_52_0 % 22.28/4.02 | | | % 22.28/4.02 | | | GROUND_INST: instantiating (11) with all_24_1, all_52_1, all_52_0, % 22.28/4.02 | | | simplifying with (23), (45), (46) gives: % 22.28/4.03 | | | (47) all_52_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 22.28/4.03 | | | apply(member_predicate, all_24_1, all_52_1) = v0) % 22.28/4.03 | | | % 22.28/4.03 | | | GROUND_INST: instantiating (4) with all_47_1, all_24_2, all_24_1, % 22.28/4.03 | | | simplifying with (22), (26), (37), (39) gives: % 22.28/4.03 | | | (48) ? [v0: $i] : (member(v0, all_24_2) = 0 & member(all_47_1, v0) = 0 % 22.28/4.03 | | | & $i(v0)) % 22.28/4.03 | | | % 22.28/4.03 | | | GROUND_INST: instantiating (10) with all_47_1, all_24_1, simplifying with % 22.28/4.03 | | | (23), (37), (39) gives: % 22.28/4.03 | | | (49) apply(member_predicate, all_47_1, all_24_1) = 0 % 22.28/4.03 | | | % 22.28/4.03 | | | GROUND_INST: instantiating (6) with all_24_2, 0, simplifying with (22), % 22.28/4.03 | | | (28) gives: % 22.28/4.03 | | | (50) ? [v0: any] : ? [v1: any] : (strict_well_order(member_predicate, % 22.28/4.03 | | | all_24_2) = v1 & member(all_24_2, on) = v0 & ( ~ (v0 = 0) | % 22.28/4.03 | | | (v1 = 0 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 22.28/4.03 | | | (subset(v2, all_24_2) = v3) | ~ $i(v2) | ? [v4: int] : ( % 22.28/4.03 | | | ~ (v4 = 0) & member(v2, all_24_2) = v4)) & ! [v2: $i] : % 22.28/4.03 | | | ( ~ (member(v2, all_24_2) = 0) | ~ $i(v2) | subset(v2, % 22.28/4.03 | | | all_24_2) = 0)))) % 22.28/4.03 | | | % 22.28/4.03 | | | GROUND_INST: instantiating (8) with member_predicate, all_24_2, % 22.28/4.03 | | | simplifying with (9), (22), (29) gives: % 22.28/4.03 | | | (51) strict_order(member_predicate, all_24_2) = 0 % 22.28/4.03 | | | % 22.28/4.03 | | | GROUND_INST: instantiating (7) with all_24_2, 0, simplifying with (22), % 22.28/4.03 | | | (29) gives: % 22.28/4.03 | | | (52) ? [v0: any] : ? [v1: any] : (set(all_24_2) = v1 & % 22.28/4.03 | | | member(all_24_2, on) = v0 & ( ~ (v0 = 0) | (v1 = 0 & ! [v2: $i] % 22.28/4.03 | | | : ! [v3: int] : (v3 = 0 | ~ (subset(v2, all_24_2) = v3) | % 22.28/4.03 | | | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, % 22.28/4.03 | | | all_24_2) = v4)) & ! [v2: $i] : ( ~ (member(v2, % 22.28/4.03 | | | all_24_2) = 0) | ~ $i(v2) | subset(v2, all_24_2) = % 22.28/4.03 | | | 0)))) % 22.28/4.03 | | | % 22.28/4.03 | | | DELTA: instantiating (48) with fresh symbol all_69_0 gives: % 22.28/4.03 | | | (53) member(all_69_0, all_24_2) = 0 & member(all_47_1, all_69_0) = 0 & % 22.28/4.03 | | | $i(all_69_0) % 22.28/4.03 | | | % 22.28/4.03 | | | ALPHA: (53) implies: % 22.28/4.03 | | | (54) $i(all_69_0) % 22.28/4.03 | | | (55) member(all_47_1, all_69_0) = 0 % 22.28/4.03 | | | (56) member(all_69_0, all_24_2) = 0 % 22.28/4.03 | | | % 22.28/4.03 | | | DELTA: instantiating (52) with fresh symbols all_75_0, all_75_1 gives: % 22.28/4.04 | | | (57) set(all_24_2) = all_75_0 & member(all_24_2, on) = all_75_1 & ( ~ % 22.28/4.04 | | | (all_75_1 = 0) | (all_75_0 = 0 & ! [v0: $i] : ! [v1: int] : % 22.28/4.04 | | | (v1 = 0 | ~ (subset(v0, all_24_2) = v1) | ~ $i(v0) | ? [v2: % 22.28/4.04 | | | int] : ( ~ (v2 = 0) & member(v0, all_24_2) = v2)) & ! % 22.28/4.04 | | | [v0: $i] : ( ~ (member(v0, all_24_2) = 0) | ~ $i(v0) | % 22.28/4.04 | | | subset(v0, all_24_2) = 0))) % 22.28/4.04 | | | % 22.28/4.04 | | | ALPHA: (57) implies: % 22.28/4.04 | | | (58) member(all_24_2, on) = all_75_1 % 22.28/4.04 | | | (59) ~ (all_75_1 = 0) | (all_75_0 = 0 & ! [v0: $i] : ! [v1: int] : % 22.28/4.04 | | | (v1 = 0 | ~ (subset(v0, all_24_2) = v1) | ~ $i(v0) | ? [v2: % 22.28/4.04 | | | int] : ( ~ (v2 = 0) & member(v0, all_24_2) = v2)) & ! [v0: % 22.28/4.04 | | | $i] : ( ~ (member(v0, all_24_2) = 0) | ~ $i(v0) | subset(v0, % 22.28/4.04 | | | all_24_2) = 0)) % 22.28/4.04 | | | % 22.28/4.04 | | | DELTA: instantiating (50) with fresh symbols all_77_0, all_77_1 gives: % 22.28/4.04 | | | (60) strict_well_order(member_predicate, all_24_2) = all_77_0 & % 22.28/4.04 | | | member(all_24_2, on) = all_77_1 & ( ~ (all_77_1 = 0) | (all_77_0 = % 22.28/4.04 | | | 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, % 22.28/4.04 | | | all_24_2) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 22.28/4.04 | | | 0) & member(v0, all_24_2) = v2)) & ! [v0: $i] : ( ~ % 22.28/4.04 | | | (member(v0, all_24_2) = 0) | ~ $i(v0) | subset(v0, % 22.28/4.04 | | | all_24_2) = 0))) % 22.28/4.04 | | | % 22.28/4.04 | | | ALPHA: (60) implies: % 22.28/4.04 | | | (61) member(all_24_2, on) = all_77_1 % 22.28/4.04 | | | % 22.28/4.04 | | | BETA: splitting (47) gives: % 22.28/4.04 | | | % 22.28/4.04 | | | Case 1: % 22.28/4.04 | | | | % 22.28/4.04 | | | | (62) all_52_0 = 0 % 22.28/4.04 | | | | % 22.28/4.04 | | | | REDUCE: (44), (62) imply: % 22.28/4.04 | | | | (63) $false % 22.28/4.04 | | | | % 22.28/4.04 | | | | CLOSE: (63) is inconsistent. % 22.28/4.04 | | | | % 22.28/4.04 | | | Case 2: % 22.28/4.04 | | | | % 22.28/4.04 | | | | (64) ? [v0: int] : ( ~ (v0 = 0) & apply(member_predicate, all_24_1, % 22.28/4.04 | | | | all_52_1) = v0) % 22.28/4.04 | | | | % 22.28/4.04 | | | | DELTA: instantiating (64) with fresh symbol all_88_0 gives: % 22.28/4.04 | | | | (65) ~ (all_88_0 = 0) & apply(member_predicate, all_24_1, all_52_1) % 22.28/4.04 | | | | = all_88_0 % 22.28/4.04 | | | | % 22.28/4.04 | | | | ALPHA: (65) implies: % 22.28/4.04 | | | | (66) ~ (all_88_0 = 0) % 22.28/4.04 | | | | (67) apply(member_predicate, all_24_1, all_52_1) = all_88_0 % 22.28/4.04 | | | | % 22.28/4.04 | | | | GROUND_INST: instantiating (18) with 0, all_77_1, on, all_24_2, % 22.28/4.04 | | | | simplifying with (24), (61) gives: % 22.28/4.04 | | | | (68) all_77_1 = 0 % 22.28/4.04 | | | | % 22.28/4.04 | | | | GROUND_INST: instantiating (18) with all_75_1, all_77_1, on, all_24_2, % 22.28/4.04 | | | | simplifying with (58), (61) gives: % 22.28/4.04 | | | | (69) all_77_1 = all_75_1 % 22.28/4.04 | | | | % 22.28/4.04 | | | | COMBINE_EQS: (68), (69) imply: % 22.28/4.04 | | | | (70) all_75_1 = 0 % 22.28/4.04 | | | | % 22.28/4.04 | | | | BETA: splitting (59) gives: % 22.28/4.04 | | | | % 22.28/4.04 | | | | Case 1: % 22.28/4.04 | | | | | % 22.28/4.04 | | | | | (71) ~ (all_75_1 = 0) % 22.28/4.04 | | | | | % 22.28/4.04 | | | | | REDUCE: (70), (71) imply: % 22.28/4.04 | | | | | (72) $false % 22.28/4.04 | | | | | % 22.28/4.04 | | | | | CLOSE: (72) is inconsistent. % 22.28/4.04 | | | | | % 22.28/4.04 | | | | Case 2: % 22.28/4.04 | | | | | % 22.28/4.04 | | | | | (73) all_75_0 = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 22.28/4.04 | | | | | (subset(v0, all_24_2) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ % 22.28/4.04 | | | | | (v2 = 0) & member(v0, all_24_2) = v2)) & ! [v0: $i] : ( ~ % 22.28/4.05 | | | | | (member(v0, all_24_2) = 0) | ~ $i(v0) | subset(v0, % 22.28/4.05 | | | | | all_24_2) = 0) % 22.28/4.05 | | | | | % 22.28/4.05 | | | | | ALPHA: (73) implies: % 22.28/4.05 | | | | | (74) ! [v0: $i] : ( ~ (member(v0, all_24_2) = 0) | ~ $i(v0) | % 22.28/4.05 | | | | | subset(v0, all_24_2) = 0) % 22.28/4.05 | | | | | % 22.28/4.05 | | | | | GROUND_INST: instantiating (10) with all_47_1, all_69_0, simplifying % 22.28/4.05 | | | | | with (37), (54), (55) gives: % 22.28/4.05 | | | | | (75) apply(member_predicate, all_47_1, all_69_0) = 0 % 22.28/4.05 | | | | | % 22.28/4.05 | | | | | GROUND_INST: instantiating (74) with all_69_0, simplifying with (54), % 22.28/4.05 | | | | | (56) gives: % 22.28/4.05 | | | | | (76) subset(all_69_0, all_24_2) = 0 % 22.28/4.05 | | | | | % 22.28/4.05 | | | | | GROUND_INST: instantiating (16) with member_predicate, all_24_2, % 22.28/4.05 | | | | | all_24_1, all_69_0, all_52_1, all_88_0, simplifying with % 22.28/4.05 | | | | | (9), (22), (23), (45), (51), (54), (56), (67) gives: % 22.28/4.05 | | | | | (77) all_88_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.28/4.05 | | | | | [v3: any] : (apply(member_predicate, all_69_0, all_52_1) = v3 % 22.28/4.05 | | | | | & apply(member_predicate, all_24_1, all_69_0) = v2 & % 22.28/4.05 | | | | | member(all_52_1, all_24_2) = v1 & member(all_24_1, all_24_2) % 22.28/4.05 | | | | | = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.28/4.05 | | | | | 0))) % 22.28/4.05 | | | | | % 22.28/4.05 | | | | | GROUND_INST: instantiating (15) with member_predicate, all_24_2, % 22.28/4.05 | | | | | all_69_0, all_47_1, all_24_1, simplifying with (9), (22), % 22.28/4.05 | | | | | (23), (37), (49), (51), (54), (56) gives: % 22.28/4.05 | | | | | (78) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.28/4.05 | | | | | (apply(member_predicate, all_69_0, all_47_1) = v2 & % 22.28/4.05 | | | | | apply(member_predicate, all_69_0, all_24_1) = v3 & % 22.28/4.05 | | | | | member(all_47_1, all_24_2) = v0 & member(all_24_1, all_24_2) % 22.28/4.05 | | | | | = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 22.28/4.05 | | | | | % 22.28/4.05 | | | | | GROUND_INST: instantiating (14) with member_predicate, all_24_2, % 22.28/4.05 | | | | | all_47_1, all_24_1, all_69_0, simplifying with (9), (22), % 22.28/4.05 | | | | | (23), (37), (49), (51), (54), (56) gives: % 22.28/4.05 | | | | | (79) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.28/4.05 | | | | | (apply(member_predicate, all_47_1, all_69_0) = v3 & % 22.28/4.05 | | | | | apply(member_predicate, all_24_1, all_69_0) = v2 & % 22.28/4.05 | | | | | member(all_47_1, all_24_2) = v0 & member(all_24_1, all_24_2) % 22.28/4.05 | | | | | = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 22.28/4.05 | | | | | % 22.28/4.05 | | | | | GROUND_INST: instantiating (13) with member_predicate, all_24_2, % 22.28/4.05 | | | | | all_24_1, all_47_1, simplifying with (9), (22), (23), % 22.28/4.05 | | | | | (37), (49), (51) gives: % 22.28/4.06 | | | | | (80) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.28/4.06 | | | | | (apply(member_predicate, all_24_1, all_47_1) = v2 & % 22.28/4.06 | | | | | member(all_47_1, all_24_2) = v1 & member(all_24_1, all_24_2) % 22.28/4.06 | | | | | = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | GROUND_INST: instantiating (12) with member_predicate, all_24_2, % 22.28/4.06 | | | | | all_47_1, all_24_1, simplifying with (9), (22), (23), % 22.28/4.06 | | | | | (37), (49), (51) gives: % 22.28/4.06 | | | | | (81) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.28/4.06 | | | | | (apply(member_predicate, all_24_1, all_47_1) = v2 & % 22.28/4.06 | | | | | member(all_47_1, all_24_2) = v0 & member(all_24_1, all_24_2) % 22.28/4.06 | | | | | = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | DELTA: instantiating (81) with fresh symbols all_124_0, all_124_1, % 22.28/4.06 | | | | | all_124_2 gives: % 22.28/4.06 | | | | | (82) apply(member_predicate, all_24_1, all_47_1) = all_124_0 & % 22.28/4.06 | | | | | member(all_47_1, all_24_2) = all_124_2 & member(all_24_1, % 22.28/4.06 | | | | | all_24_2) = all_124_1 & ( ~ (all_124_0 = 0) | ~ (all_124_1 % 22.28/4.06 | | | | | = 0) | ~ (all_124_2 = 0)) % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | ALPHA: (82) implies: % 22.28/4.06 | | | | | (83) member(all_47_1, all_24_2) = all_124_2 % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | DELTA: instantiating (80) with fresh symbols all_132_0, all_132_1, % 22.28/4.06 | | | | | all_132_2 gives: % 22.28/4.06 | | | | | (84) apply(member_predicate, all_24_1, all_47_1) = all_132_0 & % 22.28/4.06 | | | | | member(all_47_1, all_24_2) = all_132_1 & member(all_24_1, % 22.28/4.06 | | | | | all_24_2) = all_132_2 & ( ~ (all_132_0 = 0) | ~ (all_132_1 % 22.28/4.06 | | | | | = 0) | ~ (all_132_2 = 0)) % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | ALPHA: (84) implies: % 22.28/4.06 | | | | | (85) member(all_47_1, all_24_2) = all_132_1 % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | DELTA: instantiating (79) with fresh symbols all_134_0, all_134_1, % 22.28/4.06 | | | | | all_134_2, all_134_3 gives: % 22.28/4.06 | | | | | (86) apply(member_predicate, all_47_1, all_69_0) = all_134_0 & % 22.28/4.06 | | | | | apply(member_predicate, all_24_1, all_69_0) = all_134_1 & % 22.28/4.06 | | | | | member(all_47_1, all_24_2) = all_134_3 & member(all_24_1, % 22.28/4.06 | | | | | all_24_2) = all_134_2 & ( ~ (all_134_1 = 0) | ~ (all_134_2 % 22.28/4.06 | | | | | = 0) | ~ (all_134_3 = 0) | all_134_0 = 0) % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | ALPHA: (86) implies: % 22.28/4.06 | | | | | (87) member(all_47_1, all_24_2) = all_134_3 % 22.28/4.06 | | | | | (88) apply(member_predicate, all_47_1, all_69_0) = all_134_0 % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | DELTA: instantiating (78) with fresh symbols all_140_0, all_140_1, % 22.28/4.06 | | | | | all_140_2, all_140_3 gives: % 22.28/4.06 | | | | | (89) apply(member_predicate, all_69_0, all_47_1) = all_140_1 & % 22.28/4.06 | | | | | apply(member_predicate, all_69_0, all_24_1) = all_140_0 & % 22.28/4.06 | | | | | member(all_47_1, all_24_2) = all_140_3 & member(all_24_1, % 22.28/4.06 | | | | | all_24_2) = all_140_2 & ( ~ (all_140_1 = 0) | ~ (all_140_2 % 22.28/4.06 | | | | | = 0) | ~ (all_140_3 = 0) | all_140_0 = 0) % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | ALPHA: (89) implies: % 22.28/4.06 | | | | | (90) member(all_47_1, all_24_2) = all_140_3 % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | BETA: splitting (77) gives: % 22.28/4.06 | | | | | % 22.28/4.06 | | | | | Case 1: % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | (91) all_88_0 = 0 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | REDUCE: (66), (91) imply: % 22.28/4.06 | | | | | | (92) $false % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | CLOSE: (92) is inconsistent. % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | Case 2: % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | GROUND_INST: instantiating (18) with all_124_2, all_134_3, all_24_2, % 22.28/4.06 | | | | | | all_47_1, simplifying with (83), (87) gives: % 22.28/4.06 | | | | | | (93) all_134_3 = all_124_2 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | GROUND_INST: instantiating (18) with all_47_0, all_140_3, all_24_2, % 22.28/4.06 | | | | | | all_47_1, simplifying with (38), (90) gives: % 22.28/4.06 | | | | | | (94) all_140_3 = all_47_0 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | GROUND_INST: instantiating (18) with all_134_3, all_140_3, all_24_2, % 22.28/4.06 | | | | | | all_47_1, simplifying with (87), (90) gives: % 22.28/4.06 | | | | | | (95) all_140_3 = all_134_3 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | GROUND_INST: instantiating (18) with all_132_1, all_140_3, all_24_2, % 22.28/4.06 | | | | | | all_47_1, simplifying with (85), (90) gives: % 22.28/4.06 | | | | | | (96) all_140_3 = all_132_1 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | GROUND_INST: instantiating (19) with 0, all_134_0, all_69_0, % 22.28/4.06 | | | | | | all_47_1, member_predicate, simplifying with (75), (88) % 22.28/4.06 | | | | | | gives: % 22.28/4.06 | | | | | | (97) all_134_0 = 0 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | COMBINE_EQS: (94), (96) imply: % 22.28/4.06 | | | | | | (98) all_132_1 = all_47_0 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | COMBINE_EQS: (95), (96) imply: % 22.28/4.06 | | | | | | (99) all_134_3 = all_132_1 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | SIMP: (99) implies: % 22.28/4.06 | | | | | | (100) all_134_3 = all_132_1 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | COMBINE_EQS: (93), (100) imply: % 22.28/4.06 | | | | | | (101) all_132_1 = all_124_2 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | SIMP: (101) implies: % 22.28/4.06 | | | | | | (102) all_132_1 = all_124_2 % 22.28/4.06 | | | | | | % 22.28/4.06 | | | | | | COMBINE_EQS: (98), (102) imply: % 22.28/4.06 | | | | | | (103) all_124_2 = all_47_0 % 22.28/4.06 | | | | | | % 22.28/4.07 | | | | | | GROUND_INST: instantiating (1) with all_69_0, all_24_2, all_47_1, % 22.28/4.07 | | | | | | simplifying with (22), (37), (54), (55), (76) gives: % 22.28/4.07 | | | | | | (104) member(all_47_1, all_24_2) = 0 % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | GROUND_INST: instantiating (15) with member_predicate, all_24_2, % 22.28/4.07 | | | | | | all_69_0, all_47_1, all_69_0, simplifying with (9), % 22.28/4.07 | | | | | | (22), (37), (51), (54), (56), (75) gives: % 22.28/4.07 | | | | | | (105) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.28/4.07 | | | | | | (apply(member_predicate, all_69_0, all_69_0) = v3 & % 22.28/4.07 | | | | | | apply(member_predicate, all_69_0, all_47_1) = v2 & % 22.28/4.07 | | | | | | member(all_69_0, all_24_2) = v1 & member(all_47_1, % 22.28/4.07 | | | | | | all_24_2) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.28/4.07 | | | | | | 0) | v3 = 0)) % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | GROUND_INST: instantiating (14) with member_predicate, all_24_2, % 22.28/4.07 | | | | | | all_47_1, all_69_0, all_69_0, simplifying with (9), % 22.28/4.07 | | | | | | (22), (37), (51), (54), (56), (75) gives: % 22.28/4.07 | | | | | | (106) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 22.28/4.07 | | | | | | (apply(member_predicate, all_69_0, all_69_0) = v2 & % 22.28/4.07 | | | | | | apply(member_predicate, all_47_1, all_69_0) = v3 & % 22.28/4.07 | | | | | | member(all_69_0, all_24_2) = v1 & member(all_47_1, % 22.28/4.07 | | | | | | all_24_2) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.28/4.07 | | | | | | 0) | v3 = 0)) % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | GROUND_INST: instantiating (13) with member_predicate, all_24_2, % 22.28/4.07 | | | | | | all_69_0, all_47_1, simplifying with (9), (22), (37), % 22.28/4.07 | | | | | | (51), (54), (75) gives: % 22.28/4.07 | | | | | | (107) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.28/4.07 | | | | | | (apply(member_predicate, all_69_0, all_47_1) = v2 & % 22.28/4.07 | | | | | | member(all_69_0, all_24_2) = v0 & member(all_47_1, % 22.28/4.07 | | | | | | all_24_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.28/4.07 | | | | | | 0))) % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | GROUND_INST: instantiating (12) with member_predicate, all_24_2, % 22.28/4.07 | | | | | | all_47_1, all_69_0, simplifying with (9), (22), (37), % 22.28/4.07 | | | | | | (51), (54), (75) gives: % 22.28/4.07 | | | | | | (108) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.28/4.07 | | | | | | (apply(member_predicate, all_69_0, all_47_1) = v2 & % 22.28/4.07 | | | | | | member(all_69_0, all_24_2) = v1 & member(all_47_1, % 22.28/4.07 | | | | | | all_24_2) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.28/4.07 | | | | | | 0))) % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | DELTA: instantiating (108) with fresh symbols all_178_0, all_178_1, % 22.28/4.07 | | | | | | all_178_2 gives: % 22.28/4.07 | | | | | | (109) apply(member_predicate, all_69_0, all_47_1) = all_178_0 & % 22.28/4.07 | | | | | | member(all_69_0, all_24_2) = all_178_1 & member(all_47_1, % 22.28/4.07 | | | | | | all_24_2) = all_178_2 & ( ~ (all_178_0 = 0) | ~ % 22.28/4.07 | | | | | | (all_178_1 = 0) | ~ (all_178_2 = 0)) % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | ALPHA: (109) implies: % 22.28/4.07 | | | | | | (110) member(all_47_1, all_24_2) = all_178_2 % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | DELTA: instantiating (107) with fresh symbols all_180_0, all_180_1, % 22.28/4.07 | | | | | | all_180_2 gives: % 22.28/4.07 | | | | | | (111) apply(member_predicate, all_69_0, all_47_1) = all_180_0 & % 22.28/4.07 | | | | | | member(all_69_0, all_24_2) = all_180_2 & member(all_47_1, % 22.28/4.07 | | | | | | all_24_2) = all_180_1 & ( ~ (all_180_0 = 0) | ~ % 22.28/4.07 | | | | | | (all_180_1 = 0) | ~ (all_180_2 = 0)) % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | ALPHA: (111) implies: % 22.28/4.07 | | | | | | (112) member(all_47_1, all_24_2) = all_180_1 % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | DELTA: instantiating (105) with fresh symbols all_182_0, all_182_1, % 22.28/4.07 | | | | | | all_182_2, all_182_3 gives: % 22.28/4.07 | | | | | | (113) apply(member_predicate, all_69_0, all_69_0) = all_182_0 & % 22.28/4.07 | | | | | | apply(member_predicate, all_69_0, all_47_1) = all_182_1 & % 22.28/4.07 | | | | | | member(all_69_0, all_24_2) = all_182_2 & member(all_47_1, % 22.28/4.07 | | | | | | all_24_2) = all_182_3 & ( ~ (all_182_1 = 0) | ~ % 22.28/4.07 | | | | | | (all_182_2 = 0) | ~ (all_182_3 = 0) | all_182_0 = 0) % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | ALPHA: (113) implies: % 22.28/4.07 | | | | | | (114) member(all_47_1, all_24_2) = all_182_3 % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | DELTA: instantiating (106) with fresh symbols all_188_0, all_188_1, % 22.28/4.07 | | | | | | all_188_2, all_188_3 gives: % 22.28/4.07 | | | | | | (115) apply(member_predicate, all_69_0, all_69_0) = all_188_1 & % 22.28/4.07 | | | | | | apply(member_predicate, all_47_1, all_69_0) = all_188_0 & % 22.28/4.07 | | | | | | member(all_69_0, all_24_2) = all_188_2 & member(all_47_1, % 22.28/4.07 | | | | | | all_24_2) = all_188_3 & ( ~ (all_188_1 = 0) | ~ % 22.28/4.07 | | | | | | (all_188_2 = 0) | ~ (all_188_3 = 0) | all_188_0 = 0) % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | ALPHA: (115) implies: % 22.28/4.07 | | | | | | (116) member(all_47_1, all_24_2) = all_188_3 % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | GROUND_INST: instantiating (18) with all_47_0, all_182_3, all_24_2, % 22.28/4.07 | | | | | | all_47_1, simplifying with (38), (114) gives: % 22.28/4.07 | | | | | | (117) all_182_3 = all_47_0 % 22.28/4.07 | | | | | | % 22.28/4.07 | | | | | | GROUND_INST: instantiating (18) with all_178_2, all_182_3, all_24_2, % 22.28/4.07 | | | | | | all_47_1, simplifying with (110), (114) gives: % 22.28/4.08 | | | | | | (118) all_182_3 = all_178_2 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | GROUND_INST: instantiating (18) with 0, all_182_3, all_24_2, % 22.28/4.08 | | | | | | all_47_1, simplifying with (104), (114) gives: % 22.28/4.08 | | | | | | (119) all_182_3 = 0 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | GROUND_INST: instantiating (18) with all_182_3, all_188_3, all_24_2, % 22.28/4.08 | | | | | | all_47_1, simplifying with (114), (116) gives: % 22.28/4.08 | | | | | | (120) all_188_3 = all_182_3 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | GROUND_INST: instantiating (18) with all_180_1, all_188_3, all_24_2, % 22.28/4.08 | | | | | | all_47_1, simplifying with (112), (116) gives: % 22.28/4.08 | | | | | | (121) all_188_3 = all_180_1 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | COMBINE_EQS: (120), (121) imply: % 22.28/4.08 | | | | | | (122) all_182_3 = all_180_1 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | SIMP: (122) implies: % 22.28/4.08 | | | | | | (123) all_182_3 = all_180_1 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | COMBINE_EQS: (118), (123) imply: % 22.28/4.08 | | | | | | (124) all_180_1 = all_178_2 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | COMBINE_EQS: (119), (123) imply: % 22.28/4.08 | | | | | | (125) all_180_1 = 0 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | COMBINE_EQS: (117), (123) imply: % 22.28/4.08 | | | | | | (126) all_180_1 = all_47_0 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | COMBINE_EQS: (124), (125) imply: % 22.28/4.08 | | | | | | (127) all_178_2 = 0 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | COMBINE_EQS: (124), (126) imply: % 22.28/4.08 | | | | | | (128) all_178_2 = all_47_0 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | COMBINE_EQS: (127), (128) imply: % 22.28/4.08 | | | | | | (129) all_47_0 = 0 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | SIMP: (129) implies: % 22.28/4.08 | | | | | | (130) all_47_0 = 0 % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | REDUCE: (36), (130) imply: % 22.28/4.08 | | | | | | (131) $false % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | | CLOSE: (131) is inconsistent. % 22.28/4.08 | | | | | | % 22.28/4.08 | | | | | End of split % 22.28/4.08 | | | | | % 22.28/4.08 | | | | End of split % 22.28/4.08 | | | | % 22.28/4.08 | | | End of split % 22.28/4.08 | | | % 22.28/4.08 | | End of split % 22.28/4.08 | | % 22.28/4.08 | End of split % 22.28/4.08 | % 22.28/4.08 End of proof % 22.28/4.08 % SZS output end Proof for theBenchmark % 22.28/4.08 % 22.28/4.08 3406ms %------------------------------------------------------------------------------