%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET812+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 : n005.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 15:26:32 EDT 2023 % Result : Theorem 12.77s 2.40s % Output : Proof 16.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET812+4 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 11:14:53 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.08/1.09 Prover 4: Preprocessing ... % 3.08/1.11 Prover 1: Preprocessing ... % 3.08/1.13 Prover 6: Preprocessing ... % 3.08/1.13 Prover 3: Preprocessing ... % 3.08/1.13 Prover 0: Preprocessing ... % 3.08/1.13 Prover 2: Preprocessing ... % 3.08/1.13 Prover 5: Preprocessing ... % 7.21/1.66 Prover 5: Proving ... % 7.21/1.67 Prover 6: Proving ... % 7.51/1.70 Prover 2: Proving ... % 7.51/1.72 Prover 1: Constructing countermodel ... % 7.93/1.74 Prover 3: Constructing countermodel ... % 8.77/1.88 Prover 4: Constructing countermodel ... % 8.77/1.93 Prover 0: Proving ... % 9.43/1.99 Prover 3: gave up % 9.43/1.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.03/2.07 Prover 7: Preprocessing ... % 10.03/2.07 Prover 6: gave up % 10.03/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.03/2.09 Prover 1: gave up % 10.03/2.09 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 10.03/2.10 Prover 8: Preprocessing ... % 10.64/2.12 Prover 9: Preprocessing ... % 10.76/2.15 Prover 7: Warning: ignoring some quantifiers % 10.76/2.17 Prover 7: Constructing countermodel ... % 11.42/2.26 Prover 8: Warning: ignoring some quantifiers % 11.42/2.27 Prover 8: Constructing countermodel ... % 12.66/2.37 Prover 9: Constructing countermodel ... % 12.77/2.40 Prover 0: proved (1775ms) % 12.77/2.40 % 12.77/2.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.77/2.40 % 12.77/2.41 Prover 9: stopped % 12.77/2.41 Prover 5: stopped % 12.96/2.42 Prover 2: stopped % 13.07/2.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.07/2.43 Prover 7: gave up % 13.07/2.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.07/2.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.07/2.43 Prover 8: gave up % 13.07/2.44 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.07/2.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 13.07/2.47 Prover 10: Preprocessing ... % 13.07/2.48 Prover 16: Preprocessing ... % 13.07/2.48 Prover 11: Preprocessing ... % 13.07/2.49 Prover 13: Preprocessing ... % 13.07/2.51 Prover 19: Preprocessing ... % 13.74/2.53 Prover 10: Warning: ignoring some quantifiers % 13.74/2.54 Prover 10: Constructing countermodel ... % 13.74/2.56 Prover 13: Warning: ignoring some quantifiers % 13.74/2.58 Prover 16: Warning: ignoring some quantifiers % 14.30/2.60 Prover 16: Constructing countermodel ... % 14.30/2.60 Prover 13: Constructing countermodel ... % 14.30/2.60 Prover 10: gave up % 14.30/2.67 Prover 19: Warning: ignoring some quantifiers % 14.30/2.69 Prover 19: Constructing countermodel ... % 15.48/2.76 Prover 4: Found proof (size 102) % 15.48/2.76 Prover 4: proved (2131ms) % 15.48/2.76 Prover 16: stopped % 15.48/2.76 Prover 13: stopped % 15.48/2.76 Prover 19: stopped % 15.48/2.77 Prover 11: Constructing countermodel ... % 15.48/2.78 Prover 11: stopped % 15.63/2.78 % 15.63/2.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.63/2.78 % 15.63/2.80 % SZS output start Proof for theBenchmark % 15.63/2.80 Assumptions after simplification: % 15.63/2.80 --------------------------------- % 15.63/2.80 % 15.63/2.80 (equal_set) % 15.89/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 15.89/2.84 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 15.89/2.84 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 15.89/2.84 $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | ~ $i(v1) | % 15.89/2.84 ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & % 15.89/2.84 subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : % 15.89/2.84 ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 15.89/2.84 | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = % 15.89/2.84 v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.89/2.84 (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v0) = 0 & % 15.89/2.84 subset(v0, v1) = 0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) = % 15.89/2.84 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, % 15.89/2.84 v1) = v3 & subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] % 15.89/2.84 : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 15.89/2.85 any] : ? [v3: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = v2 & ( ~ % 15.89/2.85 (v2 = 0) | v3 = 0))) % 15.89/2.85 % 15.89/2.85 (intersection) % 15.89/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 15.89/2.85 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 15.89/2.85 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 15.89/2.85 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 15.89/2.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 15.89/2.85 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 15.89/2.85 0 & member(v0, v1) = 0)) % 15.89/2.85 % 15.89/2.85 (ordinal_number) % 15.89/2.85 $i(member_predicate) & $i(on) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 % 15.89/2.85 = 0 | ~ (subset(v1, v0) = v2) | ~ (member(v0, on) = 0) | ~ $i(v1) | ~ % 15.89/2.85 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & member(v1, v0) = v3)) & ! [v0: $i] : % 15.89/2.85 ! [v1: int] : (v1 = 0 | ~ (member(v0, on) = v1) | ~ $i(v0) | ? [v2: any] : % 15.89/2.85 ? [v3: any] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ($i(v4) & ((v5 = % 15.89/2.85 0 & ~ (v6 = 0) & subset(v4, v0) = v6 & member(v4, v0) = 0) | % 15.89/2.85 (strict_well_order(member_predicate, v0) = v3 & set(v0) = v2 & ( ~ (v3 = % 15.89/2.85 0) | ~ (v2 = 0)))))) & ! [v0: $i] : ! [v1: any] : ( ~ % 15.89/2.85 (strict_well_order(member_predicate, v0) = v1) | ~ $i(v0) | ? [v2: any] : % 15.89/2.85 ? [v3: any] : (set(v0) = v3 & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 & % 15.89/2.85 v1 = 0 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) = % 15.89/2.85 v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) = % 15.89/2.85 v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4) | % 15.89/2.85 subset(v4, v0) = 0))))) & ! [v0: $i] : ! [v1: any] : ( ~ (set(v0) % 15.89/2.85 = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 15.89/2.85 (strict_well_order(member_predicate, v0) = v3 & member(v0, on) = v2 & ( ~ % 15.89/2.85 (v2 = 0) | (v3 = 0 & v1 = 0 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ % 15.89/2.85 (subset(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & % 15.89/2.85 member(v4, v0) = v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | % 15.89/2.85 ~ $i(v4) | subset(v4, v0) = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.89/2.85 (member(v1, v0) = 0) | ~ (member(v0, on) = 0) | ~ $i(v1) | ~ $i(v0) | % 15.89/2.85 subset(v1, v0) = 0) & ! [v0: $i] : ( ~ (strict_well_order(member_predicate, % 15.89/2.85 v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? % 15.89/2.85 [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & subset(v3, v0) % 15.89/2.85 = v5 & member(v3, v0) = 0) | (set(v0) = v1 & member(v0, on) = v2 & ( ~ % 15.89/2.85 (v1 = 0) | v2 = 0))))) & ! [v0: $i] : ( ~ (set(v0) = 0) | ~ $i(v0) % 15.89/2.85 | ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : % 15.89/2.85 ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & subset(v3, v0) = v5 & member(v3, v0) = 0) % 15.89/2.85 | (strict_well_order(member_predicate, v0) = v1 & member(v0, on) = v2 & % 15.89/2.85 ( ~ (v1 = 0) | v2 = 0))))) & ! [v0: $i] : ( ~ (member(v0, on) = 0) | % 15.89/2.85 ~ $i(v0) | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0)) % 15.89/2.85 % 15.89/2.85 (power_set) % 15.89/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.89/2.86 (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 15.89/2.86 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] % 15.89/2.86 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 15.89/2.86 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, % 15.89/2.86 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.89/2.86 (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 15.89/2.86 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | % 15.89/2.86 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (power_set(v1) = v2 & member(v0, v2) = % 15.89/2.86 0 & $i(v2))) % 15.89/2.86 % 15.89/2.86 (subset) % 15.89/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.89/2.86 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.89/2.86 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 15.89/2.86 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 15.89/2.86 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 15.89/2.86 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.89/2.86 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 15.89/2.86 ~ $i(v0) | member(v2, v1) = 0) % 15.89/2.86 % 15.89/2.86 (thV10) % 15.89/2.86 $i(on) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 15.89/2.86 & intersection(v0, v1) = v2 & power_set(v0) = v1 & equal_set(v0, v2) = v3 & % 15.89/2.86 member(v0, on) = 0 & $i(v2) & $i(v1) & $i(v0)) % 15.89/2.86 % 15.89/2.86 (function-axioms) % 15.89/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 15.89/2.86 | ~ (initial_segment(v4, v3, v2) = v1) | ~ (initial_segment(v4, v3, v2) = % 15.89/2.86 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.89/2.86 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 15.89/2.86 ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.89/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.89/2.86 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0: % 15.89/2.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.89/2.86 : (v1 = v0 | ~ (strict_order(v3, v2) = v1) | ~ (strict_order(v3, v2) = v0)) % 15.89/2.86 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.89/2.86 [v3: $i] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~ % 15.89/2.86 (strict_well_order(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 15.89/2.86 : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ % 15.89/2.86 (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.89/2.86 ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) % 15.89/2.86 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 15.89/2.86 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 15.89/2.86 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) % 15.89/2.86 | ~ (intersection(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.89/2.86 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.89/2.86 (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0: % 15.89/2.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.89/2.86 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 15.89/2.86 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.89/2.86 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: % 15.89/2.86 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (suc(v2) = v1) | ~ (suc(v2) % 15.89/2.86 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.89/2.86 $i] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0)) & ! [v0: $i] : ! % 15.89/2.86 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 15.89/2.86 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 15.89/2.86 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 15.89/2.86 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 15.89/2.86 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 15.89/2.86 (power_set(v2) = v0)) % 15.89/2.86 % 15.89/2.86 Further assumptions not needed in the proof: % 15.89/2.86 -------------------------------------------- % 15.89/2.86 difference, empty_set, initial_segment, least, product, rel_member, set_member, % 15.89/2.86 singleton, strict_order, strict_well_order, successor, sum, union, % 15.89/2.86 unordered_pair % 15.89/2.86 % 15.89/2.86 Those formulas are unsatisfiable: % 15.89/2.86 --------------------------------- % 15.89/2.86 % 15.89/2.86 Begin of proof % 15.89/2.86 | % 15.89/2.86 | ALPHA: (subset) implies: % 15.89/2.87 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 15.89/2.87 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 15.89/2.87 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (equal_set) implies: % 15.89/2.87 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | % 15.89/2.87 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, % 15.89/2.87 | v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = % 15.89/2.87 | 0)))) % 15.89/2.87 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 15.89/2.87 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 15.89/2.87 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 15.89/2.87 | 0)))) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (power_set) implies: % 15.89/2.87 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 15.89/2.87 | $i(v0) | ? [v2: $i] : (power_set(v1) = v2 & member(v0, v2) = 0 & % 15.89/2.87 | $i(v2))) % 15.89/2.87 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 15.89/2.87 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 15.89/2.87 | (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4 & $i(v3))) % 15.89/2.87 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.89/2.87 | (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ % 15.89/2.87 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (intersection) implies: % 15.89/2.87 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.89/2.87 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 15.89/2.87 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 15.89/2.87 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 15.89/2.87 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 15.89/2.87 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 15.89/2.87 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 15.89/2.87 | 0)))) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (ordinal_number) implies: % 15.89/2.87 | (9) ! [v0: $i] : ( ~ (member(v0, on) = 0) | ~ $i(v0) | % 15.89/2.87 | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0)) % 15.89/2.87 | (10) ! [v0: $i] : ! [v1: any] : ( ~ (set(v0) = v1) | ~ $i(v0) | ? [v2: % 15.89/2.87 | any] : ? [v3: any] : (strict_well_order(member_predicate, v0) = % 15.89/2.87 | v3 & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0 & ! % 15.89/2.87 | [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) = v5) | % 15.89/2.87 | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) = % 15.89/2.87 | v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4) % 15.89/2.87 | | subset(v4, v0) = 0))))) % 15.89/2.87 | (11) ! [v0: $i] : ! [v1: any] : ( ~ (strict_well_order(member_predicate, % 15.89/2.87 | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (set(v0) = % 15.89/2.87 | v3 & member(v0, on) = v2 & ( ~ (v2 = 0) | (v3 = 0 & v1 = 0 & ! % 15.89/2.87 | [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (subset(v4, v0) = v5) | % 15.89/2.87 | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & member(v4, v0) = % 15.89/2.87 | v6)) & ! [v4: $i] : ( ~ (member(v4, v0) = 0) | ~ $i(v4) % 15.89/2.87 | | subset(v4, v0) = 0))))) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (thV10) implies: % 15.89/2.87 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) % 15.89/2.87 | & intersection(v0, v1) = v2 & power_set(v0) = v1 & equal_set(v0, v2) % 15.89/2.87 | = v3 & member(v0, on) = 0 & $i(v2) & $i(v1) & $i(v0)) % 15.89/2.87 | % 15.89/2.87 | ALPHA: (function-axioms) implies: % 15.89/2.87 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) % 15.89/2.87 | = v1) | ~ (power_set(v2) = v0)) % 15.89/2.88 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.89/2.88 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 15.89/2.88 | v2) = v0)) % 15.89/2.88 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.89/2.88 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 15.89/2.88 | v2) = v0)) % 15.89/2.88 | % 15.89/2.88 | DELTA: instantiating (12) with fresh symbols all_23_0, all_23_1, all_23_2, % 15.89/2.88 | all_23_3 gives: % 15.89/2.88 | (16) ~ (all_23_0 = 0) & intersection(all_23_3, all_23_2) = all_23_1 & % 15.89/2.88 | power_set(all_23_3) = all_23_2 & equal_set(all_23_3, all_23_1) = % 15.89/2.88 | all_23_0 & member(all_23_3, on) = 0 & $i(all_23_1) & $i(all_23_2) & % 15.89/2.88 | $i(all_23_3) % 15.89/2.88 | % 15.89/2.88 | ALPHA: (16) implies: % 15.89/2.88 | (17) ~ (all_23_0 = 0) % 15.89/2.88 | (18) $i(all_23_3) % 15.89/2.88 | (19) $i(all_23_2) % 15.89/2.88 | (20) $i(all_23_1) % 15.89/2.88 | (21) member(all_23_3, on) = 0 % 15.89/2.88 | (22) equal_set(all_23_3, all_23_1) = all_23_0 % 15.89/2.88 | (23) power_set(all_23_3) = all_23_2 % 15.89/2.88 | (24) intersection(all_23_3, all_23_2) = all_23_1 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (9) with all_23_3, simplifying with (18), (21) % 15.89/2.88 | gives: % 15.89/2.88 | (25) strict_well_order(member_predicate, all_23_3) = 0 & set(all_23_3) = 0 % 15.89/2.88 | % 15.89/2.88 | ALPHA: (25) implies: % 15.89/2.88 | (26) set(all_23_3) = 0 % 15.89/2.88 | (27) strict_well_order(member_predicate, all_23_3) = 0 % 15.89/2.88 | % 15.89/2.88 | GROUND_INST: instantiating (3) with all_23_3, all_23_1, all_23_0, simplifying % 15.89/2.88 | with (18), (20), (22) gives: % 15.89/2.88 | (28) all_23_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_23_1, % 15.89/2.88 | all_23_3) = v1 & subset(all_23_3, all_23_1) = v0 & ( ~ (v1 = 0) | % 15.89/2.88 | ~ (v0 = 0))) % 15.89/2.88 | % 15.89/2.88 | BETA: splitting (28) gives: % 15.89/2.88 | % 15.89/2.88 | Case 1: % 15.89/2.88 | | % 15.89/2.88 | | (29) all_23_0 = 0 % 15.89/2.88 | | % 15.89/2.88 | | REDUCE: (17), (29) imply: % 15.89/2.88 | | (30) $false % 15.89/2.88 | | % 15.89/2.88 | | CLOSE: (30) is inconsistent. % 15.89/2.88 | | % 15.89/2.88 | Case 2: % 15.89/2.88 | | % 15.89/2.88 | | (31) ? [v0: any] : ? [v1: any] : (subset(all_23_1, all_23_3) = v1 & % 15.89/2.88 | | subset(all_23_3, all_23_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 15.89/2.88 | | % 15.89/2.88 | | DELTA: instantiating (31) with fresh symbols all_35_0, all_35_1 gives: % 15.89/2.88 | | (32) subset(all_23_1, all_23_3) = all_35_0 & subset(all_23_3, all_23_1) = % 15.89/2.88 | | all_35_1 & ( ~ (all_35_0 = 0) | ~ (all_35_1 = 0)) % 15.89/2.88 | | % 15.89/2.88 | | ALPHA: (32) implies: % 15.89/2.88 | | (33) subset(all_23_3, all_23_1) = all_35_1 % 15.89/2.88 | | (34) subset(all_23_1, all_23_3) = all_35_0 % 15.89/2.88 | | (35) ~ (all_35_0 = 0) | ~ (all_35_1 = 0) % 15.89/2.88 | | % 15.89/2.88 | | GROUND_INST: instantiating (5) with all_23_3, all_23_1, all_35_1, % 15.89/2.88 | | simplifying with (18), (20), (33) gives: % 15.89/2.88 | | (36) all_35_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.89/2.88 | | power_set(all_23_1) = v0 & member(all_23_3, v0) = v1 & $i(v0)) % 15.89/2.88 | | % 15.89/2.88 | | GROUND_INST: instantiating (1) with all_23_3, all_23_1, all_35_1, % 15.89/2.88 | | simplifying with (18), (20), (33) gives: % 15.89/2.88 | | (37) all_35_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.89/2.88 | | member(v0, all_23_1) = v1 & member(v0, all_23_3) = 0 & $i(v0)) % 15.89/2.88 | | % 15.89/2.88 | | GROUND_INST: instantiating (2) with all_23_1, all_23_3, all_35_1, % 15.89/2.89 | | simplifying with (18), (20), (33) gives: % 15.89/2.89 | | (38) ? [v0: any] : ? [v1: any] : (equal_set(all_23_1, all_23_3) = v0 & % 15.89/2.89 | | subset(all_23_1, all_23_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 15.89/2.89 | | all_35_1 = 0))) % 15.89/2.89 | | % 15.89/2.89 | | GROUND_INST: instantiating (5) with all_23_1, all_23_3, all_35_0, % 15.89/2.89 | | simplifying with (18), (20), (34) gives: % 15.89/2.89 | | (39) all_35_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.89/2.89 | | power_set(all_23_3) = v0 & member(all_23_1, v0) = v1 & $i(v0)) % 15.89/2.89 | | % 15.89/2.89 | | GROUND_INST: instantiating (1) with all_23_1, all_23_3, all_35_0, % 15.89/2.89 | | simplifying with (18), (20), (34) gives: % 15.89/2.89 | | (40) all_35_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.89/2.89 | | member(v0, all_23_1) = 0 & member(v0, all_23_3) = v1 & $i(v0)) % 15.89/2.89 | | % 15.89/2.89 | | GROUND_INST: instantiating (10) with all_23_3, 0, simplifying with (18), % 15.89/2.89 | | (26) gives: % 15.89/2.89 | | (41) ? [v0: any] : ? [v1: any] : (strict_well_order(member_predicate, % 15.89/2.89 | | all_23_3) = v1 & member(all_23_3, on) = v0 & ( ~ (v0 = 0) | (v1 % 15.89/2.89 | | = 0 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v2, % 15.89/2.89 | | all_23_3) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 15.89/2.89 | | 0) & member(v2, all_23_3) = v4)) & ! [v2: $i] : ( ~ % 15.89/2.89 | | (member(v2, all_23_3) = 0) | ~ $i(v2) | subset(v2, % 15.89/2.89 | | all_23_3) = 0)))) % 15.89/2.89 | | % 15.89/2.89 | | GROUND_INST: instantiating (11) with all_23_3, 0, simplifying with (18), % 15.89/2.89 | | (27) gives: % 15.89/2.89 | | (42) ? [v0: any] : ? [v1: any] : (set(all_23_3) = v1 & member(all_23_3, % 15.89/2.89 | | on) = v0 & ( ~ (v0 = 0) | (v1 = 0 & ! [v2: $i] : ! [v3: int] : % 15.89/2.89 | | (v3 = 0 | ~ (subset(v2, all_23_3) = v3) | ~ $i(v2) | ? [v4: % 15.89/2.89 | | int] : ( ~ (v4 = 0) & member(v2, all_23_3) = v4)) & ! % 15.89/2.89 | | [v2: $i] : ( ~ (member(v2, all_23_3) = 0) | ~ $i(v2) | % 15.89/2.89 | | subset(v2, all_23_3) = 0)))) % 15.89/2.89 | | % 15.89/2.89 | | DELTA: instantiating (38) with fresh symbols all_45_0, all_45_1 gives: % 15.89/2.89 | | (43) equal_set(all_23_1, all_23_3) = all_45_1 & subset(all_23_1, % 15.89/2.89 | | all_23_3) = all_45_0 & ( ~ (all_45_1 = 0) | (all_45_0 = 0 & % 15.89/2.89 | | all_35_1 = 0)) % 15.89/2.89 | | % 15.89/2.89 | | ALPHA: (43) implies: % 15.89/2.89 | | (44) subset(all_23_1, all_23_3) = all_45_0 % 15.89/2.89 | | % 15.89/2.89 | | DELTA: instantiating (41) with fresh symbols all_51_0, all_51_1 gives: % 15.89/2.89 | | (45) strict_well_order(member_predicate, all_23_3) = all_51_0 & % 15.89/2.89 | | member(all_23_3, on) = all_51_1 & ( ~ (all_51_1 = 0) | (all_51_0 = 0 % 15.89/2.89 | | & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, % 15.89/2.89 | | all_23_3) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) % 15.89/2.89 | | & member(v0, all_23_3) = v2)) & ! [v0: $i] : ( ~ % 15.89/2.89 | | (member(v0, all_23_3) = 0) | ~ $i(v0) | subset(v0, all_23_3) % 15.89/2.89 | | = 0))) % 15.89/2.89 | | % 15.89/2.89 | | ALPHA: (45) implies: % 15.89/2.89 | | (46) member(all_23_3, on) = all_51_1 % 15.89/2.89 | | (47) ~ (all_51_1 = 0) | (all_51_0 = 0 & ! [v0: $i] : ! [v1: int] : (v1 % 15.89/2.89 | | = 0 | ~ (subset(v0, all_23_3) = v1) | ~ $i(v0) | ? [v2: int] % 15.89/2.89 | | : ( ~ (v2 = 0) & member(v0, all_23_3) = v2)) & ! [v0: $i] : ( ~ % 15.89/2.89 | | (member(v0, all_23_3) = 0) | ~ $i(v0) | subset(v0, all_23_3) = % 15.89/2.89 | | 0)) % 15.89/2.89 | | % 15.89/2.89 | | DELTA: instantiating (42) with fresh symbols all_53_0, all_53_1 gives: % 15.89/2.89 | | (48) set(all_23_3) = all_53_0 & member(all_23_3, on) = all_53_1 & ( ~ % 15.89/2.89 | | (all_53_1 = 0) | (all_53_0 = 0 & ! [v0: $i] : ! [v1: int] : (v1 % 15.89/2.89 | | = 0 | ~ (subset(v0, all_23_3) = v1) | ~ $i(v0) | ? [v2: % 15.89/2.89 | | int] : ( ~ (v2 = 0) & member(v0, all_23_3) = v2)) & ! [v0: % 15.89/2.89 | | $i] : ( ~ (member(v0, all_23_3) = 0) | ~ $i(v0) | subset(v0, % 15.89/2.89 | | all_23_3) = 0))) % 15.89/2.89 | | % 15.89/2.89 | | ALPHA: (48) implies: % 15.89/2.89 | | (49) member(all_23_3, on) = all_53_1 % 15.89/2.89 | | % 15.89/2.89 | | GROUND_INST: instantiating (14) with 0, all_53_1, on, all_23_3, simplifying % 15.89/2.89 | | with (21), (49) gives: % 15.89/2.89 | | (50) all_53_1 = 0 % 15.89/2.89 | | % 15.89/2.89 | | GROUND_INST: instantiating (14) with all_51_1, all_53_1, on, all_23_3, % 15.89/2.89 | | simplifying with (46), (49) gives: % 15.89/2.89 | | (51) all_53_1 = all_51_1 % 15.89/2.89 | | % 15.89/2.89 | | GROUND_INST: instantiating (15) with all_35_0, all_45_0, all_23_3, all_23_1, % 15.89/2.89 | | simplifying with (34), (44) gives: % 15.89/2.89 | | (52) all_45_0 = all_35_0 % 15.89/2.89 | | % 15.89/2.89 | | COMBINE_EQS: (50), (51) imply: % 15.89/2.89 | | (53) all_51_1 = 0 % 15.89/2.90 | | % 15.89/2.90 | | BETA: splitting (47) gives: % 15.89/2.90 | | % 15.89/2.90 | | Case 1: % 15.89/2.90 | | | % 15.89/2.90 | | | (54) ~ (all_51_1 = 0) % 15.89/2.90 | | | % 15.89/2.90 | | | REDUCE: (53), (54) imply: % 15.89/2.90 | | | (55) $false % 15.89/2.90 | | | % 15.89/2.90 | | | CLOSE: (55) is inconsistent. % 15.89/2.90 | | | % 15.89/2.90 | | Case 2: % 15.89/2.90 | | | % 15.89/2.90 | | | (56) all_51_0 = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 15.89/2.90 | | | (subset(v0, all_23_3) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 % 15.89/2.90 | | | = 0) & member(v0, all_23_3) = v2)) & ! [v0: $i] : ( ~ % 15.89/2.90 | | | (member(v0, all_23_3) = 0) | ~ $i(v0) | subset(v0, all_23_3) = % 15.89/2.90 | | | 0) % 15.89/2.90 | | | % 15.89/2.90 | | | ALPHA: (56) implies: % 15.89/2.90 | | | (57) ! [v0: $i] : ( ~ (member(v0, all_23_3) = 0) | ~ $i(v0) | % 15.89/2.90 | | | subset(v0, all_23_3) = 0) % 15.89/2.90 | | | (58) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, all_23_3) = % 15.89/2.90 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0, % 15.89/2.90 | | | all_23_3) = v2)) % 15.89/2.90 | | | % 15.89/2.90 | | | GROUND_INST: instantiating (58) with all_23_1, all_35_0, simplifying with % 15.89/2.90 | | | (20), (34) gives: % 15.89/2.90 | | | (59) all_35_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_23_1, % 15.89/2.90 | | | all_23_3) = v0) % 15.89/2.90 | | | % 15.89/2.90 | | | BETA: splitting (35) gives: % 15.89/2.90 | | | % 15.89/2.90 | | | Case 1: % 15.89/2.90 | | | | % 15.89/2.90 | | | | (60) ~ (all_35_0 = 0) % 15.89/2.90 | | | | % 15.89/2.90 | | | | BETA: splitting (40) gives: % 15.89/2.90 | | | | % 15.89/2.90 | | | | Case 1: % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | (61) all_35_0 = 0 % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | REDUCE: (60), (61) imply: % 15.89/2.90 | | | | | (62) $false % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | CLOSE: (62) is inconsistent. % 15.89/2.90 | | | | | % 15.89/2.90 | | | | Case 2: % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | (63) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 15.89/2.90 | | | | | all_23_1) = 0 & member(v0, all_23_3) = v1 & $i(v0)) % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | DELTA: instantiating (63) with fresh symbols all_97_0, all_97_1 gives: % 15.89/2.90 | | | | | (64) ~ (all_97_0 = 0) & member(all_97_1, all_23_1) = 0 & % 15.89/2.90 | | | | | member(all_97_1, all_23_3) = all_97_0 & $i(all_97_1) % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | ALPHA: (64) implies: % 15.89/2.90 | | | | | (65) ~ (all_97_0 = 0) % 15.89/2.90 | | | | | (66) $i(all_97_1) % 15.89/2.90 | | | | | (67) member(all_97_1, all_23_3) = all_97_0 % 15.89/2.90 | | | | | (68) member(all_97_1, all_23_1) = 0 % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | BETA: splitting (39) gives: % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | Case 1: % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | | (69) all_35_0 = 0 % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | | REDUCE: (60), (69) imply: % 15.89/2.90 | | | | | | (70) $false % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | | CLOSE: (70) is inconsistent. % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | Case 2: % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | | (71) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 15.89/2.90 | | | | | | power_set(all_23_3) = v0 & member(all_23_1, v0) = v1 & % 15.89/2.90 | | | | | | $i(v0)) % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | | DELTA: instantiating (71) with fresh symbols all_103_0, all_103_1 % 15.89/2.90 | | | | | | gives: % 15.89/2.90 | | | | | | (72) ~ (all_103_0 = 0) & power_set(all_23_3) = all_103_1 & % 15.89/2.90 | | | | | | member(all_23_1, all_103_1) = all_103_0 & $i(all_103_1) % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | | ALPHA: (72) implies: % 15.89/2.90 | | | | | | (73) $i(all_103_1) % 15.89/2.90 | | | | | | (74) power_set(all_23_3) = all_103_1 % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | | BETA: splitting (59) gives: % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | | Case 1: % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | (75) all_35_0 = 0 % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | REDUCE: (60), (75) imply: % 15.89/2.90 | | | | | | | (76) $false % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | CLOSE: (76) is inconsistent. % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | Case 2: % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | GROUND_INST: instantiating (13) with all_23_2, all_103_1, % 15.89/2.90 | | | | | | | all_23_3, simplifying with (23), (74) gives: % 15.89/2.90 | | | | | | | (77) all_103_1 = all_23_2 % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | GROUND_INST: instantiating (7) with all_97_1, all_23_3, all_23_2, % 15.89/2.90 | | | | | | | all_23_1, simplifying with (18), (19), (24), (66), % 15.89/2.90 | | | | | | | (68) gives: % 15.89/2.90 | | | | | | | (78) member(all_97_1, all_23_2) = 0 & member(all_97_1, % 15.89/2.90 | | | | | | | all_23_3) = 0 % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | ALPHA: (78) implies: % 15.89/2.90 | | | | | | | (79) member(all_97_1, all_23_3) = 0 % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | GROUND_INST: instantiating (14) with all_97_0, 0, all_23_3, % 15.89/2.90 | | | | | | | all_97_1, simplifying with (67), (79) gives: % 15.89/2.90 | | | | | | | (80) all_97_0 = 0 % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | REDUCE: (65), (80) imply: % 15.89/2.90 | | | | | | | (81) $false % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | | CLOSE: (81) is inconsistent. % 15.89/2.90 | | | | | | | % 15.89/2.90 | | | | | | End of split % 15.89/2.90 | | | | | | % 15.89/2.90 | | | | | End of split % 15.89/2.90 | | | | | % 15.89/2.90 | | | | End of split % 15.89/2.90 | | | | % 15.89/2.90 | | | Case 2: % 15.89/2.90 | | | | % 15.89/2.90 | | | | (82) all_35_0 = 0 % 15.89/2.90 | | | | (83) ~ (all_35_1 = 0) % 15.89/2.90 | | | | % 15.89/2.90 | | | | REDUCE: (34), (82) imply: % 15.89/2.90 | | | | (84) subset(all_23_1, all_23_3) = 0 % 15.89/2.90 | | | | % 15.89/2.90 | | | | BETA: splitting (37) gives: % 15.89/2.90 | | | | % 15.89/2.90 | | | | Case 1: % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | (85) all_35_1 = 0 % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | REDUCE: (83), (85) imply: % 15.89/2.90 | | | | | (86) $false % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | CLOSE: (86) is inconsistent. % 15.89/2.90 | | | | | % 15.89/2.90 | | | | Case 2: % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | (87) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 15.89/2.90 | | | | | all_23_1) = v1 & member(v0, all_23_3) = 0 & $i(v0)) % 15.89/2.90 | | | | | % 15.89/2.90 | | | | | DELTA: instantiating (87) with fresh symbols all_97_0, all_97_1 gives: % 15.89/2.91 | | | | | (88) ~ (all_97_0 = 0) & member(all_97_1, all_23_1) = all_97_0 & % 15.89/2.91 | | | | | member(all_97_1, all_23_3) = 0 & $i(all_97_1) % 15.89/2.91 | | | | | % 15.89/2.91 | | | | | ALPHA: (88) implies: % 15.89/2.91 | | | | | (89) ~ (all_97_0 = 0) % 15.89/2.91 | | | | | (90) $i(all_97_1) % 15.89/2.91 | | | | | (91) member(all_97_1, all_23_3) = 0 % 15.89/2.91 | | | | | (92) member(all_97_1, all_23_1) = all_97_0 % 15.89/2.91 | | | | | % 15.89/2.91 | | | | | BETA: splitting (36) gives: % 15.89/2.91 | | | | | % 15.89/2.91 | | | | | Case 1: % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | (93) all_35_1 = 0 % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | REDUCE: (83), (93) imply: % 15.89/2.91 | | | | | | (94) $false % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | CLOSE: (94) is inconsistent. % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | Case 2: % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | GROUND_INST: instantiating (57) with all_97_1, simplifying with % 15.89/2.91 | | | | | | (90), (91) gives: % 15.89/2.91 | | | | | | (95) subset(all_97_1, all_23_3) = 0 % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | GROUND_INST: instantiating (8) with all_97_1, all_23_3, all_23_2, % 15.89/2.91 | | | | | | all_23_1, all_97_0, simplifying with (18), (19), (24), % 15.89/2.91 | | | | | | (90), (92) gives: % 15.89/2.91 | | | | | | (96) all_97_0 = 0 | ? [v0: any] : ? [v1: any] : % 15.89/2.91 | | | | | | (member(all_97_1, all_23_2) = v1 & member(all_97_1, % 15.89/2.91 | | | | | | all_23_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | GROUND_INST: instantiating (4) with all_23_1, all_23_3, simplifying % 15.89/2.91 | | | | | | with (18), (20), (84) gives: % 15.89/2.91 | | | | | | (97) ? [v0: $i] : (power_set(all_23_3) = v0 & member(all_23_1, % 15.89/2.91 | | | | | | v0) = 0 & $i(v0)) % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | DELTA: instantiating (97) with fresh symbol all_110_0 gives: % 15.89/2.91 | | | | | | (98) power_set(all_23_3) = all_110_0 & member(all_23_1, % 15.89/2.91 | | | | | | all_110_0) = 0 & $i(all_110_0) % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | ALPHA: (98) implies: % 15.89/2.91 | | | | | | (99) power_set(all_23_3) = all_110_0 % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | BETA: splitting (96) gives: % 15.89/2.91 | | | | | | % 15.89/2.91 | | | | | | Case 1: % 15.89/2.91 | | | | | | | % 15.89/2.91 | | | | | | | (100) all_97_0 = 0 % 15.89/2.91 | | | | | | | % 15.89/2.91 | | | | | | | REDUCE: (89), (100) imply: % 15.89/2.91 | | | | | | | (101) $false % 15.89/2.91 | | | | | | | % 15.89/2.91 | | | | | | | CLOSE: (101) is inconsistent. % 15.89/2.91 | | | | | | | % 15.89/2.91 | | | | | | Case 2: % 15.89/2.91 | | | | | | | % 15.89/2.91 | | | | | | | (102) ? [v0: any] : ? [v1: any] : (member(all_97_1, all_23_2) % 15.89/2.91 | | | | | | | = v1 & member(all_97_1, all_23_3) = v0 & ( ~ (v1 = 0) | % 15.89/2.91 | | | | | | | ~ (v0 = 0))) % 15.89/2.91 | | | | | | | % 15.89/2.91 | | | | | | | DELTA: instantiating (102) with fresh symbols all_132_0, all_132_1 % 15.89/2.91 | | | | | | | gives: % 15.89/2.91 | | | | | | | (103) member(all_97_1, all_23_2) = all_132_0 & member(all_97_1, % 15.89/2.91 | | | | | | | all_23_3) = all_132_1 & ( ~ (all_132_0 = 0) | ~ % 15.89/2.91 | | | | | | | (all_132_1 = 0)) % 15.89/2.91 | | | | | | | % 15.89/2.91 | | | | | | | ALPHA: (103) implies: % 16.25/2.91 | | | | | | | (104) member(all_97_1, all_23_3) = all_132_1 % 16.25/2.91 | | | | | | | (105) member(all_97_1, all_23_2) = all_132_0 % 16.25/2.91 | | | | | | | (106) ~ (all_132_0 = 0) | ~ (all_132_1 = 0) % 16.25/2.91 | | | | | | | % 16.25/2.91 | | | | | | | GROUND_INST: instantiating (14) with 0, all_132_1, all_23_3, % 16.25/2.91 | | | | | | | all_97_1, simplifying with (91), (104) gives: % 16.25/2.91 | | | | | | | (107) all_132_1 = 0 % 16.25/2.91 | | | | | | | % 16.25/2.91 | | | | | | | GROUND_INST: instantiating (13) with all_23_2, all_110_0, % 16.25/2.91 | | | | | | | all_23_3, simplifying with (23), (99) gives: % 16.25/2.91 | | | | | | | (108) all_110_0 = all_23_2 % 16.25/2.91 | | | | | | | % 16.25/2.91 | | | | | | | BETA: splitting (106) gives: % 16.25/2.91 | | | | | | | % 16.25/2.91 | | | | | | | Case 1: % 16.25/2.91 | | | | | | | | % 16.25/2.91 | | | | | | | | (109) ~ (all_132_0 = 0) % 16.25/2.91 | | | | | | | | % 16.25/2.91 | | | | | | | | GROUND_INST: instantiating (6) with all_97_1, all_23_3, % 16.25/2.91 | | | | | | | | all_23_2, all_132_0, simplifying with (18), (23), % 16.25/2.91 | | | | | | | | (90), (105) gives: % 16.25/2.91 | | | | | | | | (110) all_132_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 16.25/2.91 | | | | | | | | subset(all_97_1, all_23_3) = v0) % 16.25/2.91 | | | | | | | | % 16.25/2.91 | | | | | | | | BETA: splitting (110) gives: % 16.25/2.91 | | | | | | | | % 16.25/2.91 | | | | | | | | Case 1: % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | | (111) all_132_0 = 0 % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | | REDUCE: (109), (111) imply: % 16.25/2.91 | | | | | | | | | (112) $false % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | | CLOSE: (112) is inconsistent. % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | Case 2: % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | | (113) ? [v0: int] : ( ~ (v0 = 0) & subset(all_97_1, % 16.25/2.91 | | | | | | | | | all_23_3) = v0) % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | | DELTA: instantiating (113) with fresh symbol all_176_0 gives: % 16.25/2.91 | | | | | | | | | (114) ~ (all_176_0 = 0) & subset(all_97_1, all_23_3) = % 16.25/2.91 | | | | | | | | | all_176_0 % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | | ALPHA: (114) implies: % 16.25/2.91 | | | | | | | | | (115) ~ (all_176_0 = 0) % 16.25/2.91 | | | | | | | | | (116) subset(all_97_1, all_23_3) = all_176_0 % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_176_0, all_23_3, % 16.25/2.91 | | | | | | | | | all_97_1, simplifying with (95), (116) gives: % 16.25/2.91 | | | | | | | | | (117) all_176_0 = 0 % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | | REDUCE: (115), (117) imply: % 16.25/2.91 | | | | | | | | | (118) $false % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | | CLOSE: (118) is inconsistent. % 16.25/2.91 | | | | | | | | | % 16.25/2.91 | | | | | | | | End of split % 16.25/2.91 | | | | | | | | % 16.25/2.91 | | | | | | | Case 2: % 16.25/2.91 | | | | | | | | % 16.25/2.91 | | | | | | | | (119) ~ (all_132_1 = 0) % 16.25/2.91 | | | | | | | | % 16.25/2.91 | | | | | | | | REDUCE: (107), (119) imply: % 16.25/2.91 | | | | | | | | (120) $false % 16.25/2.91 | | | | | | | | % 16.25/2.91 | | | | | | | | CLOSE: (120) is inconsistent. % 16.25/2.91 | | | | | | | | % 16.25/2.91 | | | | | | | End of split % 16.25/2.91 | | | | | | | % 16.25/2.91 | | | | | | End of split % 16.25/2.91 | | | | | | % 16.25/2.91 | | | | | End of split % 16.25/2.91 | | | | | % 16.25/2.91 | | | | End of split % 16.25/2.91 | | | | % 16.25/2.91 | | | End of split % 16.25/2.91 | | | % 16.25/2.91 | | End of split % 16.25/2.91 | | % 16.25/2.91 | End of split % 16.25/2.91 | % 16.25/2.91 End of proof % 16.25/2.91 % SZS output end Proof for theBenchmark % 16.25/2.91 % 16.25/2.91 2308ms %------------------------------------------------------------------------------