%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU183+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n019.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 17:43:07 EDT 2023 % Result : Theorem 26.43s 4.44s % Output : Proof 35.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU183+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.36 % Computer : n019.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Wed Aug 23 13:59:44 EDT 2023 % 0.13/0.36 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.79/1.49 Prover 4: Preprocessing ... % 4.79/1.50 Prover 1: Preprocessing ... % 4.79/1.53 Prover 6: Preprocessing ... % 4.79/1.53 Prover 2: Preprocessing ... % 4.79/1.53 Prover 3: Preprocessing ... % 4.79/1.53 Prover 5: Preprocessing ... % 4.79/1.53 Prover 0: Preprocessing ... % 15.19/2.94 Prover 1: Warning: ignoring some quantifiers % 15.19/3.00 Prover 3: Warning: ignoring some quantifiers % 15.19/3.01 Prover 5: Proving ... % 16.30/3.04 Prover 3: Constructing countermodel ... % 16.52/3.07 Prover 1: Constructing countermodel ... % 16.52/3.13 Prover 6: Proving ... % 17.34/3.24 Prover 4: Warning: ignoring some quantifiers % 18.68/3.37 Prover 4: Constructing countermodel ... % 18.68/3.39 Prover 2: Proving ... % 19.68/3.48 Prover 0: Proving ... % 26.43/4.44 Prover 3: proved (3783ms) % 26.43/4.44 % 26.43/4.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 26.43/4.44 % 26.43/4.44 Prover 0: stopped % 26.43/4.44 Prover 5: stopped % 26.43/4.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 26.43/4.46 Prover 6: stopped % 26.43/4.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 26.43/4.47 Prover 2: stopped % 26.43/4.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 26.43/4.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 26.43/4.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 28.14/4.61 Prover 7: Preprocessing ... % 28.14/4.64 Prover 11: Preprocessing ... % 28.76/4.71 Prover 8: Preprocessing ... % 28.76/4.77 Prover 10: Preprocessing ... % 29.67/4.81 Prover 13: Preprocessing ... % 29.67/4.95 Prover 7: Warning: ignoring some quantifiers % 30.54/4.98 Prover 7: Constructing countermodel ... % 31.56/5.10 Prover 10: Warning: ignoring some quantifiers % 31.56/5.13 Prover 10: Constructing countermodel ... % 32.47/5.20 Prover 8: Warning: ignoring some quantifiers % 32.47/5.22 Prover 13: Warning: ignoring some quantifiers % 32.89/5.24 Prover 8: Constructing countermodel ... % 33.01/5.27 Prover 13: Constructing countermodel ... % 33.88/5.43 Prover 1: Found proof (size 156) % 33.88/5.43 Prover 1: proved (4776ms) % 33.88/5.43 Prover 8: stopped % 33.88/5.43 Prover 13: stopped % 33.88/5.43 Prover 7: stopped % 33.88/5.44 Prover 10: stopped % 33.88/5.44 Prover 4: stopped % 34.51/5.46 Prover 11: Warning: ignoring some quantifiers % 34.67/5.50 Prover 11: Constructing countermodel ... % 34.95/5.54 Prover 11: stopped % 34.95/5.54 % 34.95/5.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 34.95/5.54 % 34.95/5.56 % SZS output start Proof for theBenchmark % 34.95/5.56 Assumptions after simplification: % 34.95/5.56 --------------------------------- % 34.95/5.57 % 34.95/5.57 (d3_tarski) % 34.95/5.59 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 34.95/5.59 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 34.95/5.59 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 34.95/5.59 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 34.95/5.59 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 34.95/5.59 % 34.95/5.59 (d4_relat_1) % 34.95/5.60 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 34.95/5.60 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 34.95/5.60 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 34.95/5.60 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = % 34.95/5.60 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 34.95/5.60 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6) % 34.95/5.60 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 34.95/5.60 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 34.95/5.60 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 34.95/5.60 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 34.95/5.60 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) & % 34.95/5.60 $i(v3))))))) % 34.95/5.60 % 34.95/5.60 (d5_relat_1) % 34.95/5.61 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 34.95/5.61 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~ % 34.95/5.61 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~ % 34.95/5.61 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = % 34.95/5.61 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i] % 34.95/5.61 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6) % 34.95/5.61 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 % 34.95/5.61 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~ % 34.95/5.61 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) & % 34.95/5.61 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 34.95/5.61 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) & % 34.95/5.61 $i(v3))))))) % 34.95/5.61 % 34.95/5.61 (d8_relat_1) % 34.95/5.61 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : % 34.95/5.61 ( ~ (relation_composition(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 % 34.95/5.61 = 0) & relation(v1) = v3) | ! [v3: $i] : ( ~ (relation(v3) = 0) | ~ % 34.95/5.61 $i(v3) | (( ~ (v3 = v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! % 34.95/5.61 [v7: int] : (v7 = 0 | ~ (ordered_pair(v4, v5) = v6) | ~ (in(v6, % 34.95/5.61 v2) = v7) | ~ $i(v5) | ~ $i(v4) | ! [v8: $i] : ! [v9: % 34.95/5.61 $i] : ( ~ (ordered_pair(v4, v8) = v9) | ~ (in(v9, v0) = 0) | % 34.95/5.62 ~ $i(v8) | ? [v10: $i] : ? [v11: int] : ( ~ (v11 = 0) & % 34.95/5.62 ordered_pair(v8, v5) = v10 & in(v10, v1) = v11 & $i(v10)))) % 34.95/5.62 & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4, % 34.95/5.62 v5) = v6) | ~ (in(v6, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ? % 34.95/5.62 [v7: $i] : ? [v8: $i] : ? [v9: $i] : (ordered_pair(v7, v5) = % 34.95/5.62 v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) = 0 & in(v8, v0) = % 34.95/5.62 0 & $i(v9) & $i(v8) & $i(v7))))) & (v3 = v2 | ? [v4: $i] : ? % 34.95/5.62 [v5: $i] : ? [v6: $i] : ? [v7: any] : (ordered_pair(v4, v5) = v6 & % 34.95/5.62 in(v6, v3) = v7 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v7 = 0) | ! % 34.95/5.62 [v8: $i] : ! [v9: $i] : ( ~ (ordered_pair(v4, v8) = v9) | ~ % 34.95/5.62 (in(v9, v0) = 0) | ~ $i(v8) | ? [v10: $i] : ? [v11: int] : % 34.95/5.62 ( ~ (v11 = 0) & ordered_pair(v8, v5) = v10 & in(v10, v1) = v11 % 34.95/5.62 & $i(v10)))) & (v7 = 0 | ? [v8: $i] : ? [v9: $i] : ? % 34.95/5.62 [v10: $i] : (ordered_pair(v8, v5) = v10 & ordered_pair(v4, v8) = % 34.95/5.62 v9 & in(v10, v1) = 0 & in(v9, v0) = 0 & $i(v10) & $i(v9) & % 34.95/5.62 $i(v8))))))))) % 34.95/5.62 % 34.95/5.62 (dt_k5_relat_1) % 34.95/5.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 34.95/5.62 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 34.95/5.62 (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | % 34.95/5.62 ~ (v3 = 0) | v5 = 0))) % 34.95/5.62 % 34.95/5.62 (t25_relat_1) % 34.95/5.62 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 34.95/5.62 any] : ? [v3: $i] : (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) & % 34.95/5.62 ( ~ (v2 = 0) | ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~ % 34.95/5.62 (relation_rng(v4) = v5) | ~ (subset(v1, v5) = v6) | ~ $i(v4) | ? % 34.95/5.62 [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: any] : % 34.95/5.62 (relation_dom(v4) = v9 & relation(v4) = v7 & subset(v3, v9) = v10 & % 34.95/5.62 subset(v0, v4) = v8 & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 % 34.95/5.62 & v6 = 0))))))) % 34.95/5.62 % 34.95/5.62 (t45_relat_1) % 34.95/5.62 ? [v0: $i] : (relation(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ? [v3: % 34.95/5.62 $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & relation_composition(v0, % 34.95/5.62 v1) = v2 & relation_rng(v2) = v3 & relation_rng(v1) = v4 & relation(v1) % 34.95/5.62 = 0 & subset(v3, v4) = v5 & $i(v4) & $i(v3) & $i(v2) & $i(v1))) % 34.95/5.62 % 34.95/5.62 (function-axioms) % 34.95/5.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 34.95/5.64 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, % 34.95/5.64 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 34.95/5.64 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ % 34.95/5.64 (are_equipotent(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.95/5.64 ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ % 34.95/5.64 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.95/5.64 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ % 34.95/5.64 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.95/5.64 ! [v3: $i] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ % 34.95/5.64 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 34.95/5.64 $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ % 34.95/5.64 (relation_composition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.95/5.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, % 34.95/5.64 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 34.95/5.64 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ % 34.95/5.64 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 34.95/5.64 : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ % 34.95/5.64 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 34.95/5.64 ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 34.95/5.64 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.95/5.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 34.95/5.64 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 34.95/5.64 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ % 34.95/5.64 (ordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.95/5.64 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 34.95/5.64 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 34.95/5.64 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ % 34.95/5.64 (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 34.95/5.64 : ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, % 34.95/5.64 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 34.95/5.64 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 34.95/5.64 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 34.95/5.64 [v3: $i] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, % 34.95/5.64 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 34.95/5.64 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 34.95/5.64 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.95/5.64 (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0: $i] % 34.95/5.64 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ % 34.95/5.64 (relation_field(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 34.95/5.64 v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] % 34.95/5.64 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = % 34.95/5.64 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.95/5.64 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : ! % 34.95/5.64 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 34.95/5.64 (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.95/5.64 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 34.95/5.64 (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.95/5.64 (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 34.95/5.64 ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & % 34.95/5.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (set_meet(v2) = v1) | % 34.95/5.64 ~ (set_meet(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 34.95/5.64 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ % 34.95/5.64 (relation(v2) = v0)) % 34.95/5.64 % 34.95/5.64 Further assumptions not needed in the proof: % 34.95/5.64 -------------------------------------------- % 34.95/5.64 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 34.95/5.64 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_relat_1, % 34.95/5.64 d1_setfam_1, d1_tarski, d1_xboole_0, d1_zfmisc_1, d2_subset_1, d2_tarski, % 34.95/5.64 d2_xboole_0, d2_zfmisc_1, d3_xboole_0, d4_subset_1, d4_tarski, d4_xboole_0, % 34.95/5.64 d5_subset_1, d5_tarski, d6_relat_1, d7_relat_1, d7_xboole_0, d8_setfam_1, % 34.95/5.64 d8_xboole_0, dt_k1_relat_1, dt_k1_setfam_1, dt_k1_tarski, dt_k1_xboole_0, % 34.95/5.64 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_subset_1, dt_k2_tarski, dt_k2_xboole_0, % 34.95/5.64 dt_k2_zfmisc_1, dt_k3_relat_1, dt_k3_subset_1, dt_k3_tarski, dt_k3_xboole_0, % 34.95/5.64 dt_k4_relat_1, dt_k4_tarski, dt_k4_xboole_0, dt_k5_setfam_1, dt_k6_setfam_1, % 34.95/5.64 dt_k6_subset_1, dt_k7_setfam_1, dt_m1_subset_1, existence_m1_subset_1, % 34.95/5.64 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_relat_1, fc2_subset_1, % 34.95/5.64 fc2_xboole_0, fc3_subset_1, fc3_xboole_0, fc4_subset_1, idempotence_k2_xboole_0, % 34.95/5.64 idempotence_k3_xboole_0, involutiveness_k3_subset_1, involutiveness_k4_relat_1, % 34.95/5.64 involutiveness_k7_setfam_1, irreflexivity_r2_xboole_0, l1_zfmisc_1, % 34.95/5.64 l23_zfmisc_1, l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, % 34.95/5.64 l3_subset_1, l3_zfmisc_1, l4_zfmisc_1, l50_zfmisc_1, l55_zfmisc_1, l71_subset_1, % 34.95/5.64 rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_subset_1, rc2_xboole_0, % 34.95/5.64 redefinition_k5_setfam_1, redefinition_k6_setfam_1, redefinition_k6_subset_1, % 34.95/5.64 reflexivity_r1_tarski, symmetry_r1_xboole_0, t106_zfmisc_1, t10_zfmisc_1, % 34.95/5.64 t118_zfmisc_1, t119_zfmisc_1, t12_xboole_1, t136_zfmisc_1, t17_xboole_1, % 34.95/5.64 t19_xboole_1, t1_boole, t1_subset, t1_xboole_1, t1_zfmisc_1, t20_relat_1, % 34.95/5.64 t21_relat_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_subset, t2_tarski, % 34.95/5.64 t2_xboole_1, t30_relat_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_relat_1, % 34.95/5.64 t37_xboole_1, t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, % 34.95/5.64 t3_subset, t3_xboole_0, t3_xboole_1, t40_xboole_1, t43_subset_1, t44_relat_1, % 34.95/5.64 t45_xboole_1, t46_setfam_1, t46_zfmisc_1, t47_setfam_1, t48_setfam_1, % 34.95/5.64 t48_xboole_1, t4_boole, t4_subset, t4_xboole_0, t50_subset_1, t54_subset_1, % 34.95/5.64 t5_subset, t60_xboole_1, t63_xboole_1, t65_zfmisc_1, t69_enumset1, t6_boole, % 34.95/5.64 t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1, % 34.95/5.64 t8_zfmisc_1, t92_zfmisc_1, t99_zfmisc_1, t9_tarski, t9_zfmisc_1 % 34.95/5.64 % 34.95/5.64 Those formulas are unsatisfiable: % 34.95/5.64 --------------------------------- % 34.95/5.64 % 34.95/5.64 Begin of proof % 34.95/5.64 | % 34.95/5.64 | ALPHA: (d3_tarski) implies: % 34.95/5.64 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 34.95/5.64 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 34.95/5.64 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 34.95/5.64 | % 34.95/5.64 | ALPHA: (function-axioms) implies: % 34.95/5.65 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 34.95/5.65 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 34.95/5.65 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 34.95/5.65 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 34.95/5.65 | % 34.95/5.65 | DELTA: instantiating (t45_relat_1) with fresh symbol all_157_0 gives: % 34.95/5.65 | (4) relation(all_157_0) = 0 & $i(all_157_0) & ? [v0: $i] : ? [v1: $i] : % 34.95/5.65 | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 34.95/5.65 | relation_composition(all_157_0, v0) = v1 & relation_rng(v1) = v2 & % 34.95/5.65 | relation_rng(v0) = v3 & relation(v0) = 0 & subset(v2, v3) = v4 & % 34.95/5.65 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 34.95/5.65 | % 34.95/5.65 | ALPHA: (4) implies: % 34.95/5.65 | (5) $i(all_157_0) % 34.95/5.65 | (6) relation(all_157_0) = 0 % 34.95/5.65 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : % 34.95/5.65 | ( ~ (v4 = 0) & relation_composition(all_157_0, v0) = v1 & % 34.95/5.65 | relation_rng(v1) = v2 & relation_rng(v0) = v3 & relation(v0) = 0 & % 34.95/5.65 | subset(v2, v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 34.95/5.65 | % 34.95/5.65 | DELTA: instantiating (7) with fresh symbols all_175_0, all_175_1, all_175_2, % 34.95/5.65 | all_175_3, all_175_4 gives: % 34.95/5.65 | (8) ~ (all_175_0 = 0) & relation_composition(all_157_0, all_175_4) = % 34.95/5.65 | all_175_3 & relation_rng(all_175_3) = all_175_2 & % 34.95/5.65 | relation_rng(all_175_4) = all_175_1 & relation(all_175_4) = 0 & % 34.95/5.65 | subset(all_175_2, all_175_1) = all_175_0 & $i(all_175_1) & % 34.95/5.65 | $i(all_175_2) & $i(all_175_3) & $i(all_175_4) % 34.95/5.65 | % 34.95/5.65 | ALPHA: (8) implies: % 34.95/5.65 | (9) ~ (all_175_0 = 0) % 34.95/5.65 | (10) $i(all_175_4) % 34.95/5.65 | (11) $i(all_175_3) % 34.95/5.65 | (12) $i(all_175_2) % 34.95/5.65 | (13) $i(all_175_1) % 34.95/5.65 | (14) subset(all_175_2, all_175_1) = all_175_0 % 34.95/5.65 | (15) relation(all_175_4) = 0 % 34.95/5.65 | (16) relation_rng(all_175_4) = all_175_1 % 34.95/5.65 | (17) relation_rng(all_175_3) = all_175_2 % 34.95/5.65 | (18) relation_composition(all_157_0, all_175_4) = all_175_3 % 34.95/5.65 | % 34.95/5.65 | GROUND_INST: instantiating (1) with all_175_2, all_175_1, all_175_0, % 34.95/5.65 | simplifying with (12), (13), (14) gives: % 34.95/5.65 | (19) all_175_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 34.95/5.65 | all_175_1) = v1 & in(v0, all_175_2) = 0 & $i(v0)) % 34.95/5.65 | % 34.95/5.65 | GROUND_INST: instantiating (d8_relat_1) with all_157_0, simplifying with (5), % 34.95/5.65 | (6) gives: % 34.95/5.66 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_composition(all_157_0, v0) = % 34.95/5.66 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & relation(v0) = v2) % 34.95/5.66 | | ! [v2: $i] : ( ~ (relation(v2) = 0) | ~ $i(v2) | (( ~ (v2 = v1) % 34.95/5.66 | | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: int] : % 34.95/5.66 | (v6 = 0 | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v1) = % 34.95/5.66 | v6) | ~ $i(v4) | ~ $i(v3) | ! [v7: $i] : ! [v8: $i] % 34.95/5.66 | : ( ~ (ordered_pair(v3, v7) = v8) | ~ (in(v8, all_157_0) % 34.95/5.66 | = 0) | ~ $i(v7) | ? [v9: $i] : ? [v10: int] : ( ~ % 34.95/5.66 | (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v0) = % 34.95/5.66 | v10 & $i(v9)))) & ! [v3: $i] : ! [v4: $i] : ! [v5: % 34.95/5.66 | $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v1) = % 34.95/5.66 | 0) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] : ? [v7: $i] : % 34.95/5.66 | ? [v8: $i] : (ordered_pair(v6, v4) = v8 & % 34.95/5.66 | ordered_pair(v3, v6) = v7 & in(v8, v0) = 0 & in(v7, % 34.95/5.66 | all_157_0) = 0 & $i(v8) & $i(v7) & $i(v6))))) & (v2 = % 34.95/5.66 | v1 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : % 34.95/5.66 | (ordered_pair(v3, v4) = v5 & in(v5, v2) = v6 & $i(v5) & $i(v4) % 34.95/5.66 | & $i(v3) & ( ~ (v6 = 0) | ! [v7: $i] : ! [v8: $i] : ( ~ % 34.95/5.66 | (ordered_pair(v3, v7) = v8) | ~ (in(v8, all_157_0) = 0) % 34.95/5.66 | | ~ $i(v7) | ? [v9: $i] : ? [v10: int] : ( ~ (v10 = % 34.95/5.66 | 0) & ordered_pair(v7, v4) = v9 & in(v9, v0) = v10 & % 34.95/5.66 | $i(v9)))) & (v6 = 0 | ? [v7: $i] : ? [v8: $i] : ? % 34.95/5.66 | [v9: $i] : (ordered_pair(v7, v4) = v9 & ordered_pair(v3, % 34.95/5.66 | v7) = v8 & in(v9, v0) = 0 & in(v8, all_157_0) = 0 & % 34.95/5.66 | $i(v9) & $i(v8) & $i(v7)))))))) % 34.95/5.66 | % 34.95/5.66 | GROUND_INST: instantiating (t25_relat_1) with all_175_4, all_175_1, % 34.95/5.66 | simplifying with (10), (16) gives: % 34.95/5.66 | (21) ? [v0: any] : ? [v1: $i] : (relation_dom(all_175_4) = v1 & % 34.95/5.66 | relation(all_175_4) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 34.95/5.66 | [v3: $i] : ! [v4: any] : ( ~ (relation_rng(v2) = v3) | ~ % 34.95/5.66 | (subset(all_175_1, v3) = v4) | ~ $i(v2) | ? [v5: any] : ? % 34.95/5.66 | [v6: any] : ? [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 % 34.95/5.66 | & relation(v2) = v5 & subset(v1, v7) = v8 & subset(all_175_4, % 34.95/5.66 | v2) = v6 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & % 34.95/5.66 | v4 = 0)))))) % 34.95/5.66 | % 34.95/5.66 | GROUND_INST: instantiating (d5_relat_1) with all_175_4, all_175_1, simplifying % 34.95/5.66 | with (10), (16) gives: % 34.95/5.66 | (22) ? [v0: int] : ( ~ (v0 = 0) & relation(all_175_4) = v0) | ( ? [v0: % 34.95/5.66 | any] : (v0 = all_175_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : % 34.95/5.66 | (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: % 34.95/5.66 | $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, % 34.95/5.66 | all_175_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 34.95/5.66 | ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, all_175_4) = % 34.95/5.66 | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_175_1) | ( ! [v0: $i] : % 34.95/5.66 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_175_1) = v1) | ~ $i(v0) % 34.95/5.66 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) % 34.95/5.66 | | ~ (in(v3, all_175_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( % 34.95/5.66 | ~ (in(v0, all_175_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 34.95/5.66 | $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_175_4) = 0 & % 34.95/5.66 | $i(v2) & $i(v1)))))) % 34.95/5.66 | % 34.95/5.66 | GROUND_INST: instantiating (t25_relat_1) with all_175_3, all_175_2, % 34.95/5.66 | simplifying with (11), (17) gives: % 35.33/5.66 | (23) ? [v0: any] : ? [v1: $i] : (relation_dom(all_175_3) = v1 & % 35.33/5.66 | relation(all_175_3) = v0 & $i(v1) & ( ~ (v0 = 0) | ! [v2: $i] : ! % 35.33/5.66 | [v3: $i] : ! [v4: any] : ( ~ (relation_rng(v2) = v3) | ~ % 35.33/5.66 | (subset(all_175_2, v3) = v4) | ~ $i(v2) | ? [v5: any] : ? % 35.33/5.66 | [v6: any] : ? [v7: $i] : ? [v8: any] : (relation_dom(v2) = v7 % 35.33/5.66 | & relation(v2) = v5 & subset(v1, v7) = v8 & subset(all_175_3, % 35.33/5.66 | v2) = v6 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & % 35.33/5.66 | v4 = 0)))))) % 35.33/5.66 | % 35.33/5.66 | GROUND_INST: instantiating (d5_relat_1) with all_175_3, all_175_2, simplifying % 35.33/5.66 | with (11), (17) gives: % 35.33/5.67 | (24) ? [v0: int] : ( ~ (v0 = 0) & relation(all_175_3) = v0) | ( ? [v0: % 35.33/5.67 | any] : (v0 = all_175_2 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : % 35.33/5.67 | (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: % 35.33/5.67 | $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, % 35.33/5.67 | all_175_3) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : % 35.33/5.67 | ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, all_175_3) = % 35.33/5.67 | 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_175_2) | ( ! [v0: $i] : % 35.33/5.67 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_175_2) = v1) | ~ $i(v0) % 35.33/5.67 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) % 35.33/5.67 | | ~ (in(v3, all_175_3) = 0) | ~ $i(v2))) & ! [v0: $i] : ( % 35.33/5.67 | ~ (in(v0, all_175_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 35.33/5.67 | $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_175_3) = 0 & % 35.33/5.67 | $i(v2) & $i(v1)))))) % 35.33/5.67 | % 35.33/5.67 | GROUND_INST: instantiating (dt_k5_relat_1) with all_157_0, all_175_4, % 35.33/5.67 | all_175_3, simplifying with (5), (10), (18) gives: % 35.33/5.67 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_175_3) = v2 % 35.33/5.67 | & relation(all_175_4) = v1 & relation(all_157_0) = v0 & ( ~ (v1 = 0) % 35.33/5.67 | | ~ (v0 = 0) | v2 = 0)) % 35.33/5.67 | % 35.33/5.67 | GROUND_INST: instantiating (20) with all_175_4, all_175_3, simplifying with % 35.33/5.67 | (10), (18) gives: % 35.33/5.67 | (26) ? [v0: int] : ( ~ (v0 = 0) & relation(all_175_4) = v0) | ! [v0: $i] % 35.33/5.67 | : ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0 = all_175_3) | ( ! % 35.33/5.67 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 35.33/5.67 | | ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_175_3) = % 35.33/5.67 | v4) | ~ $i(v2) | ~ $i(v1) | ! [v5: $i] : ! [v6: $i] : % 35.33/5.67 | ( ~ (ordered_pair(v1, v5) = v6) | ~ (in(v6, all_157_0) = 0) % 35.33/5.67 | | ~ $i(v5) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 35.33/5.67 | ordered_pair(v5, v2) = v7 & in(v7, all_175_4) = v8 & % 35.33/5.67 | $i(v7)))) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 35.33/5.67 | ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_175_3) = 0) | % 35.33/5.67 | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] : ? [v5: $i] : ? [v6: % 35.33/5.67 | $i] : (ordered_pair(v4, v2) = v6 & ordered_pair(v1, v4) = % 35.33/5.67 | v5 & in(v6, all_175_4) = 0 & in(v5, all_157_0) = 0 & % 35.33/5.67 | $i(v6) & $i(v5) & $i(v4))))) & (v0 = all_175_3 | ? [v1: % 35.33/5.67 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : % 35.33/5.67 | (ordered_pair(v1, v2) = v3 & in(v3, v0) = v4 & $i(v3) & $i(v2) & % 35.33/5.67 | $i(v1) & ( ~ (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ % 35.33/5.67 | (ordered_pair(v1, v5) = v6) | ~ (in(v6, all_157_0) = 0) | % 35.33/5.67 | ~ $i(v5) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 35.33/5.67 | ordered_pair(v5, v2) = v7 & in(v7, all_175_4) = v8 & % 35.33/5.67 | $i(v7)))) & (v4 = 0 | ? [v5: $i] : ? [v6: $i] : ? % 35.33/5.67 | [v7: $i] : (ordered_pair(v5, v2) = v7 & ordered_pair(v1, v5) % 35.33/5.67 | = v6 & in(v7, all_175_4) = 0 & in(v6, all_157_0) = 0 & % 35.33/5.67 | $i(v7) & $i(v6) & $i(v5))))))) % 35.33/5.67 | % 35.33/5.67 | DELTA: instantiating (25) with fresh symbols all_201_0, all_201_1, all_201_2 % 35.33/5.67 | gives: % 35.33/5.67 | (27) relation(all_175_3) = all_201_0 & relation(all_175_4) = all_201_1 & % 35.33/5.67 | relation(all_157_0) = all_201_2 & ( ~ (all_201_1 = 0) | ~ (all_201_2 % 35.33/5.67 | = 0) | all_201_0 = 0) % 35.33/5.67 | % 35.33/5.67 | ALPHA: (27) implies: % 35.33/5.67 | (28) relation(all_157_0) = all_201_2 % 35.33/5.67 | (29) relation(all_175_4) = all_201_1 % 35.33/5.67 | (30) relation(all_175_3) = all_201_0 % 35.33/5.67 | (31) ~ (all_201_1 = 0) | ~ (all_201_2 = 0) | all_201_0 = 0 % 35.33/5.67 | % 35.33/5.67 | DELTA: instantiating (21) with fresh symbols all_203_0, all_203_1 gives: % 35.33/5.67 | (32) relation_dom(all_175_4) = all_203_0 & relation(all_175_4) = all_203_1 % 35.33/5.67 | & $i(all_203_0) & ( ~ (all_203_1 = 0) | ! [v0: $i] : ! [v1: $i] : ! % 35.33/5.67 | [v2: any] : ( ~ (relation_rng(v0) = v1) | ~ (subset(all_175_1, v1) % 35.33/5.67 | = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 35.33/5.67 | ? [v6: any] : (relation_dom(v0) = v5 & relation(v0) = v3 & % 35.33/5.67 | subset(all_203_0, v5) = v6 & subset(all_175_4, v0) = v4 & $i(v5) % 35.33/5.67 | & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0))))) % 35.33/5.67 | % 35.33/5.67 | ALPHA: (32) implies: % 35.33/5.67 | (33) relation(all_175_4) = all_203_1 % 35.33/5.67 | (34) relation_dom(all_175_4) = all_203_0 % 35.33/5.67 | % 35.33/5.67 | DELTA: instantiating (23) with fresh symbols all_205_0, all_205_1 gives: % 35.33/5.68 | (35) relation_dom(all_175_3) = all_205_0 & relation(all_175_3) = all_205_1 % 35.33/5.68 | & $i(all_205_0) & ( ~ (all_205_1 = 0) | ! [v0: $i] : ! [v1: $i] : ! % 35.33/5.68 | [v2: any] : ( ~ (relation_rng(v0) = v1) | ~ (subset(all_175_2, v1) % 35.33/5.68 | = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 35.33/5.68 | ? [v6: any] : (relation_dom(v0) = v5 & relation(v0) = v3 & % 35.33/5.68 | subset(all_205_0, v5) = v6 & subset(all_175_3, v0) = v4 & $i(v5) % 35.33/5.68 | & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0))))) % 35.33/5.68 | % 35.33/5.68 | ALPHA: (35) implies: % 35.33/5.68 | (36) relation(all_175_3) = all_205_1 % 35.33/5.68 | (37) ~ (all_205_1 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 35.33/5.68 | (relation_rng(v0) = v1) | ~ (subset(all_175_2, v1) = v2) | ~ % 35.33/5.68 | $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 35.33/5.68 | (relation_dom(v0) = v5 & relation(v0) = v3 & subset(all_205_0, v5) = % 35.33/5.68 | v6 & subset(all_175_3, v0) = v4 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = % 35.33/5.68 | 0) | (v6 = 0 & v2 = 0)))) % 35.33/5.68 | % 35.33/5.68 | BETA: splitting (19) gives: % 35.33/5.68 | % 35.33/5.68 | Case 1: % 35.33/5.68 | | % 35.33/5.68 | | (38) all_175_0 = 0 % 35.33/5.68 | | % 35.33/5.68 | | REDUCE: (9), (38) imply: % 35.33/5.68 | | (39) $false % 35.33/5.68 | | % 35.33/5.68 | | CLOSE: (39) is inconsistent. % 35.33/5.68 | | % 35.33/5.68 | Case 2: % 35.33/5.68 | | % 35.33/5.68 | | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_175_1) = v1 & % 35.33/5.68 | | in(v0, all_175_2) = 0 & $i(v0)) % 35.33/5.68 | | % 35.33/5.68 | | DELTA: instantiating (40) with fresh symbols all_214_0, all_214_1 gives: % 35.33/5.68 | | (41) ~ (all_214_0 = 0) & in(all_214_1, all_175_1) = all_214_0 & % 35.33/5.68 | | in(all_214_1, all_175_2) = 0 & $i(all_214_1) % 35.33/5.68 | | % 35.33/5.68 | | ALPHA: (41) implies: % 35.33/5.68 | | (42) ~ (all_214_0 = 0) % 35.33/5.68 | | (43) $i(all_214_1) % 35.33/5.68 | | (44) in(all_214_1, all_175_2) = 0 % 35.33/5.68 | | (45) in(all_214_1, all_175_1) = all_214_0 % 35.33/5.68 | | % 35.33/5.68 | | GROUND_INST: instantiating (2) with 0, all_201_2, all_157_0, simplifying % 35.33/5.68 | | with (6), (28) gives: % 35.33/5.68 | | (46) all_201_2 = 0 % 35.33/5.68 | | % 35.33/5.68 | | GROUND_INST: instantiating (2) with 0, all_203_1, all_175_4, simplifying % 35.33/5.68 | | with (15), (33) gives: % 35.33/5.68 | | (47) all_203_1 = 0 % 35.33/5.68 | | % 35.33/5.68 | | GROUND_INST: instantiating (2) with all_201_1, all_203_1, all_175_4, % 35.33/5.68 | | simplifying with (29), (33) gives: % 35.33/5.68 | | (48) all_203_1 = all_201_1 % 35.33/5.68 | | % 35.33/5.68 | | GROUND_INST: instantiating (2) with all_201_0, all_205_1, all_175_3, % 35.33/5.68 | | simplifying with (30), (36) gives: % 35.33/5.68 | | (49) all_205_1 = all_201_0 % 35.33/5.68 | | % 35.33/5.68 | | COMBINE_EQS: (47), (48) imply: % 35.33/5.68 | | (50) all_201_1 = 0 % 35.33/5.68 | | % 35.33/5.68 | | SIMP: (50) implies: % 35.33/5.68 | | (51) all_201_1 = 0 % 35.33/5.68 | | % 35.33/5.68 | | BETA: splitting (31) gives: % 35.33/5.68 | | % 35.33/5.68 | | Case 1: % 35.33/5.68 | | | % 35.33/5.68 | | | (52) ~ (all_201_1 = 0) % 35.33/5.68 | | | % 35.33/5.68 | | | REDUCE: (51), (52) imply: % 35.33/5.68 | | | (53) $false % 35.33/5.68 | | | % 35.33/5.68 | | | CLOSE: (53) is inconsistent. % 35.33/5.68 | | | % 35.33/5.68 | | Case 2: % 35.33/5.68 | | | % 35.33/5.68 | | | (54) ~ (all_201_2 = 0) | all_201_0 = 0 % 35.33/5.68 | | | % 35.33/5.68 | | | BETA: splitting (22) gives: % 35.33/5.68 | | | % 35.33/5.68 | | | Case 1: % 35.33/5.68 | | | | % 35.33/5.68 | | | | (55) ? [v0: int] : ( ~ (v0 = 0) & relation(all_175_4) = v0) % 35.33/5.68 | | | | % 35.33/5.68 | | | | REF_CLOSE: (2), (10), (14), (15), (16), (37), (46), (49), (54), (55) are % 35.33/5.68 | | | | inconsistent by sub-proof #1. % 35.33/5.68 | | | | % 35.33/5.68 | | | Case 2: % 35.33/5.68 | | | | % 35.33/5.69 | | | | (56) ? [v0: any] : (v0 = all_175_1 | ~ $i(v0) | ? [v1: $i] : ? % 35.33/5.69 | | | | [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: % 35.33/5.69 | | | | $i] : ! [v4: $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ % 35.33/5.69 | | | | (in(v4, all_175_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? % 35.33/5.69 | | | | [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v1) = v4 & % 35.33/5.69 | | | | in(v4, all_175_4) = 0 & $i(v4) & $i(v3))))) & ( ~ % 35.33/5.69 | | | | $i(all_175_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 35.33/5.69 | | | | (in(v0, all_175_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! % 35.33/5.69 | | | | [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 35.33/5.69 | | | | all_175_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 35.33/5.69 | | | | (in(v0, all_175_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 35.33/5.69 | | | | [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_175_4) % 35.33/5.69 | | | | = 0 & $i(v2) & $i(v1))))) % 35.33/5.69 | | | | % 35.33/5.69 | | | | ALPHA: (56) implies: % 35.33/5.69 | | | | (57) ~ $i(all_175_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 35.33/5.69 | | | | (in(v0, all_175_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 35.33/5.69 | | | | $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 35.33/5.69 | | | | all_175_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 35.33/5.69 | | | | (in(v0, all_175_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 35.33/5.69 | | | | $i] : (ordered_pair(v1, v0) = v2 & in(v2, all_175_4) = 0 & % 35.33/5.69 | | | | $i(v2) & $i(v1)))) % 35.33/5.69 | | | | % 35.33/5.69 | | | | BETA: splitting (26) gives: % 35.33/5.69 | | | | % 35.33/5.69 | | | | Case 1: % 35.33/5.69 | | | | | % 35.33/5.69 | | | | | (58) ? [v0: int] : ( ~ (v0 = 0) & relation(all_175_4) = v0) % 35.33/5.69 | | | | | % 35.33/5.69 | | | | | REF_CLOSE: (2), (10), (14), (15), (16), (37), (46), (49), (54), (58) % 35.33/5.69 | | | | | are inconsistent by sub-proof #1. % 35.33/5.69 | | | | | % 35.33/5.69 | | | | Case 2: % 35.33/5.69 | | | | | % 35.33/5.69 | | | | | (59) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0 = % 35.33/5.69 | | | | | all_175_3) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 35.33/5.69 | | | | | : ! [v4: int] : (v4 = 0 | ~ (ordered_pair(v1, v2) = % 35.33/5.69 | | | | | v3) | ~ (in(v3, all_175_3) = v4) | ~ $i(v2) | ~ % 35.33/5.69 | | | | | $i(v1) | ! [v5: $i] : ! [v6: $i] : ( ~ % 35.33/5.69 | | | | | (ordered_pair(v1, v5) = v6) | ~ (in(v6, % 35.33/5.69 | | | | | all_157_0) = 0) | ~ $i(v5) | ? [v7: $i] : ? % 35.33/5.69 | | | | | [v8: int] : ( ~ (v8 = 0) & ordered_pair(v5, v2) = % 35.33/5.69 | | | | | v7 & in(v7, all_175_4) = v8 & $i(v7)))) & ! % 35.33/5.69 | | | | | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 35.33/5.69 | | | | | (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_175_3) % 35.33/5.69 | | | | | = 0) | ~ $i(v2) | ~ $i(v1) | ? [v4: $i] : ? % 35.33/5.69 | | | | | [v5: $i] : ? [v6: $i] : (ordered_pair(v4, v2) = v6 % 35.33/5.69 | | | | | & ordered_pair(v1, v4) = v5 & in(v6, all_175_4) = % 35.33/5.69 | | | | | 0 & in(v5, all_157_0) = 0 & $i(v6) & $i(v5) & % 35.33/5.69 | | | | | $i(v4))))) & (v0 = all_175_3 | ? [v1: $i] : ? % 35.33/5.69 | | | | | [v2: $i] : ? [v3: $i] : ? [v4: any] : % 35.33/5.69 | | | | | (ordered_pair(v1, v2) = v3 & in(v3, v0) = v4 & $i(v3) & % 35.33/5.69 | | | | | $i(v2) & $i(v1) & ( ~ (v4 = 0) | ! [v5: $i] : ! [v6: % 35.33/5.69 | | | | | $i] : ( ~ (ordered_pair(v1, v5) = v6) | ~ (in(v6, % 35.33/5.69 | | | | | all_157_0) = 0) | ~ $i(v5) | ? [v7: $i] : ? % 35.33/5.69 | | | | | [v8: int] : ( ~ (v8 = 0) & ordered_pair(v5, v2) = % 35.33/5.69 | | | | | v7 & in(v7, all_175_4) = v8 & $i(v7)))) & (v4 = % 35.33/5.69 | | | | | 0 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 35.33/5.69 | | | | | (ordered_pair(v5, v2) = v7 & ordered_pair(v1, v5) = % 35.33/5.69 | | | | | v6 & in(v7, all_175_4) = 0 & in(v6, all_157_0) = 0 % 35.33/5.69 | | | | | & $i(v7) & $i(v6) & $i(v5))))))) % 35.33/5.69 | | | | | % 35.33/5.69 | | | | | BETA: splitting (54) gives: % 35.33/5.69 | | | | | % 35.33/5.69 | | | | | Case 1: % 35.33/5.69 | | | | | | % 35.33/5.69 | | | | | | (60) ~ (all_201_2 = 0) % 35.33/5.69 | | | | | | % 35.33/5.69 | | | | | | REDUCE: (46), (60) imply: % 35.33/5.69 | | | | | | (61) $false % 35.33/5.69 | | | | | | % 35.33/5.69 | | | | | | CLOSE: (61) is inconsistent. % 35.33/5.69 | | | | | | % 35.33/5.69 | | | | | Case 2: % 35.33/5.69 | | | | | | % 35.33/5.69 | | | | | | (62) all_201_0 = 0 % 35.33/5.69 | | | | | | % 35.33/5.69 | | | | | | COMBINE_EQS: (49), (62) imply: % 35.33/5.69 | | | | | | (63) all_205_1 = 0 % 35.33/5.69 | | | | | | % 35.33/5.69 | | | | | | REDUCE: (30), (62) imply: % 35.33/5.69 | | | | | | (64) relation(all_175_3) = 0 % 35.33/5.69 | | | | | | % 35.33/5.69 | | | | | | BETA: splitting (57) gives: % 35.33/5.69 | | | | | | % 35.33/5.69 | | | | | | Case 1: % 35.33/5.69 | | | | | | | % 35.33/5.69 | | | | | | | (65) ~ $i(all_175_1) % 35.33/5.69 | | | | | | | % 35.33/5.69 | | | | | | | PRED_UNIFY: (13), (65) imply: % 35.33/5.69 | | | | | | | (66) $false % 35.33/5.69 | | | | | | | % 35.33/5.69 | | | | | | | CLOSE: (66) is inconsistent. % 35.33/5.69 | | | | | | | % 35.33/5.69 | | | | | | Case 2: % 35.33/5.69 | | | | | | | % 35.33/5.69 | | | | | | | (67) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 35.33/5.69 | | | | | | | all_175_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 35.33/5.69 | | | | | | | $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 35.33/5.69 | | | | | | | all_175_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ % 35.33/5.69 | | | | | | | (in(v0, all_175_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 35.33/5.69 | | | | | | | [v2: $i] : (ordered_pair(v1, v0) = v2 & in(v2, % 35.33/5.69 | | | | | | | all_175_4) = 0 & $i(v2) & $i(v1))) % 35.33/5.69 | | | | | | | % 35.33/5.69 | | | | | | | ALPHA: (67) implies: % 35.33/5.70 | | | | | | | (68) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 35.33/5.70 | | | | | | | all_175_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: % 35.33/5.70 | | | | | | | $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, % 35.33/5.70 | | | | | | | all_175_4) = 0) | ~ $i(v2))) % 35.33/5.70 | | | | | | | % 35.33/5.70 | | | | | | | BETA: splitting (24) gives: % 35.33/5.70 | | | | | | | % 35.33/5.70 | | | | | | | Case 1: % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | (69) ? [v0: int] : ( ~ (v0 = 0) & relation(all_175_3) = v0) % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | DELTA: instantiating (69) with fresh symbol all_261_0 gives: % 35.33/5.70 | | | | | | | | (70) ~ (all_261_0 = 0) & relation(all_175_3) = all_261_0 % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | ALPHA: (70) implies: % 35.33/5.70 | | | | | | | | (71) ~ (all_261_0 = 0) % 35.33/5.70 | | | | | | | | (72) relation(all_175_3) = all_261_0 % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | GROUND_INST: instantiating (2) with 0, all_261_0, all_175_3, % 35.33/5.70 | | | | | | | | simplifying with (64), (72) gives: % 35.33/5.70 | | | | | | | | (73) all_261_0 = 0 % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | REDUCE: (71), (73) imply: % 35.33/5.70 | | | | | | | | (74) $false % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | CLOSE: (74) is inconsistent. % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | Case 2: % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | (75) ? [v0: any] : (v0 = all_175_2 | ~ $i(v0) | ? [v1: $i] % 35.33/5.70 | | | | | | | | : ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = % 35.33/5.70 | | | | | | | | 0) | ! [v3: $i] : ! [v4: $i] : ( ~ % 35.33/5.70 | | | | | | | | (ordered_pair(v3, v1) = v4) | ~ (in(v4, % 35.33/5.70 | | | | | | | | all_175_3) = 0) | ~ $i(v3))) & (v2 = 0 | ? % 35.33/5.70 | | | | | | | | [v3: $i] : ? [v4: $i] : (ordered_pair(v3, v1) = % 35.33/5.70 | | | | | | | | v4 & in(v4, all_175_3) = 0 & $i(v4) & $i(v3))))) % 35.33/5.70 | | | | | | | | & ( ~ $i(all_175_2) | ( ! [v0: $i] : ! [v1: int] : (v1 % 35.33/5.70 | | | | | | | | = 0 | ~ (in(v0, all_175_2) = v1) | ~ $i(v0) | ! % 35.33/5.70 | | | | | | | | [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) % 35.33/5.70 | | | | | | | | = v3) | ~ (in(v3, all_175_3) = 0) | ~ % 35.33/5.70 | | | | | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_175_2) % 35.33/5.70 | | | | | | | | = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 35.33/5.70 | | | | | | | | (ordered_pair(v1, v0) = v2 & in(v2, all_175_3) = 0 % 35.33/5.70 | | | | | | | | & $i(v2) & $i(v1))))) % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | ALPHA: (75) implies: % 35.33/5.70 | | | | | | | | (76) ~ $i(all_175_2) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 % 35.33/5.70 | | | | | | | | | ~ (in(v0, all_175_2) = v1) | ~ $i(v0) | ! [v2: % 35.33/5.70 | | | | | | | | $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = % 35.33/5.70 | | | | | | | | v3) | ~ (in(v3, all_175_3) = 0) | ~ $i(v2))) & % 35.33/5.70 | | | | | | | | ! [v0: $i] : ( ~ (in(v0, all_175_2) = 0) | ~ $i(v0) % 35.33/5.70 | | | | | | | | | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) % 35.33/5.70 | | | | | | | | = v2 & in(v2, all_175_3) = 0 & $i(v2) & $i(v1)))) % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | BETA: splitting (37) gives: % 35.33/5.70 | | | | | | | | % 35.33/5.70 | | | | | | | | Case 1: % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | | (77) ~ (all_205_1 = 0) % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | | REDUCE: (63), (77) imply: % 35.33/5.70 | | | | | | | | | (78) $false % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | | CLOSE: (78) is inconsistent. % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | Case 2: % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | | (79) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 35.33/5.70 | | | | | | | | | (relation_rng(v0) = v1) | ~ (subset(all_175_2, v1) % 35.33/5.70 | | | | | | | | | = v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 35.33/5.70 | | | | | | | | | ? [v5: $i] : ? [v6: any] : (relation_dom(v0) = v5 & % 35.33/5.70 | | | | | | | | | relation(v0) = v3 & subset(all_205_0, v5) = v6 & % 35.33/5.70 | | | | | | | | | subset(all_175_3, v0) = v4 & $i(v5) & ( ~ (v4 = 0) % 35.33/5.70 | | | | | | | | | | ~ (v3 = 0) | (v6 = 0 & v2 = 0)))) % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | | GROUND_INST: instantiating (79) with all_175_4, all_175_1, % 35.33/5.70 | | | | | | | | | all_175_0, simplifying with (10), (14), (16) % 35.33/5.70 | | | | | | | | | gives: % 35.33/5.70 | | | | | | | | | (80) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: % 35.33/5.70 | | | | | | | | | any] : (relation_dom(all_175_4) = v2 & % 35.33/5.70 | | | | | | | | | relation(all_175_4) = v0 & subset(all_205_0, v2) = % 35.33/5.70 | | | | | | | | | v3 & subset(all_175_3, all_175_4) = v1 & $i(v2) & ( % 35.33/5.70 | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & all_175_0 = % 35.33/5.70 | | | | | | | | | 0))) % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | | DELTA: instantiating (80) with fresh symbols all_261_0, % 35.33/5.70 | | | | | | | | | all_261_1, all_261_2, all_261_3 gives: % 35.33/5.70 | | | | | | | | | (81) relation_dom(all_175_4) = all_261_1 & % 35.33/5.70 | | | | | | | | | relation(all_175_4) = all_261_3 & subset(all_205_0, % 35.33/5.70 | | | | | | | | | all_261_1) = all_261_0 & subset(all_175_3, % 35.33/5.70 | | | | | | | | | all_175_4) = all_261_2 & $i(all_261_1) & ( ~ % 35.33/5.70 | | | | | | | | | (all_261_2 = 0) | ~ (all_261_3 = 0) | (all_261_0 = % 35.33/5.70 | | | | | | | | | 0 & all_175_0 = 0)) % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | | ALPHA: (81) implies: % 35.33/5.70 | | | | | | | | | (82) relation(all_175_4) = all_261_3 % 35.33/5.70 | | | | | | | | | (83) relation_dom(all_175_4) = all_261_1 % 35.33/5.70 | | | | | | | | | (84) ~ (all_261_2 = 0) | ~ (all_261_3 = 0) | (all_261_0 = % 35.33/5.70 | | | | | | | | | 0 & all_175_0 = 0) % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | | BETA: splitting (76) gives: % 35.33/5.70 | | | | | | | | | % 35.33/5.70 | | | | | | | | | Case 1: % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | (85) ~ $i(all_175_2) % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | PRED_UNIFY: (12), (85) imply: % 35.33/5.70 | | | | | | | | | | (86) $false % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | CLOSE: (86) is inconsistent. % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | Case 2: % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | (87) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, % 35.33/5.70 | | | | | | | | | | all_175_2) = v1) | ~ $i(v0) | ! [v2: $i] : % 35.33/5.70 | | | | | | | | | | ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ % 35.33/5.70 | | | | | | | | | | (in(v3, all_175_3) = 0) | ~ $i(v2))) & ! [v0: % 35.33/5.70 | | | | | | | | | | $i] : ( ~ (in(v0, all_175_2) = 0) | ~ $i(v0) | ? % 35.33/5.70 | | | | | | | | | | [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = % 35.33/5.70 | | | | | | | | | | v2 & in(v2, all_175_3) = 0 & $i(v2) & $i(v1))) % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | ALPHA: (87) implies: % 35.33/5.70 | | | | | | | | | | (88) ! [v0: $i] : ( ~ (in(v0, all_175_2) = 0) | ~ % 35.33/5.70 | | | | | | | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : % 35.33/5.70 | | | | | | | | | | (ordered_pair(v1, v0) = v2 & in(v2, all_175_3) = 0 % 35.33/5.70 | | | | | | | | | | & $i(v2) & $i(v1))) % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | GROUND_INST: instantiating (2) with 0, all_261_3, all_175_4, % 35.33/5.70 | | | | | | | | | | simplifying with (15), (82) gives: % 35.33/5.70 | | | | | | | | | | (89) all_261_3 = 0 % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | GROUND_INST: instantiating (3) with all_203_0, all_261_1, % 35.33/5.70 | | | | | | | | | | all_175_4, simplifying with (34), (83) gives: % 35.33/5.70 | | | | | | | | | | (90) all_261_1 = all_203_0 % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | BETA: splitting (84) gives: % 35.33/5.70 | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | Case 1: % 35.33/5.70 | | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | | GROUND_INST: instantiating (88) with all_214_1, simplifying % 35.33/5.70 | | | | | | | | | | | with (43), (44) gives: % 35.33/5.70 | | | | | | | | | | | (91) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, % 35.33/5.70 | | | | | | | | | | | all_214_1) = v1 & in(v1, all_175_3) = 0 & % 35.33/5.70 | | | | | | | | | | | $i(v1) & $i(v0)) % 35.33/5.70 | | | | | | | | | | | % 35.33/5.70 | | | | | | | | | | | GROUND_INST: instantiating (68) with all_214_1, all_214_0, % 35.33/5.70 | | | | | | | | | | | simplifying with (43), (45) gives: % 35.33/5.70 | | | | | | | | | | | (92) all_214_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ % 35.33/5.70 | | | | | | | | | | | (ordered_pair(v0, all_214_1) = v1) | ~ (in(v1, % 35.33/5.70 | | | | | | | | | | | all_175_4) = 0) | ~ $i(v0)) % 35.33/5.70 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | GROUND_INST: instantiating (59) with all_175_3, simplifying % 35.33/5.71 | | | | | | | | | | | with (11), (64) gives: % 35.33/5.71 | | | | | | | | | | | (93) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 35.33/5.71 | | | | | | | | | | | int] : (v3 = 0 | ~ (ordered_pair(v0, v1) = v2) % 35.33/5.71 | | | | | | | | | | | | ~ (in(v2, all_175_3) = v3) | ~ $i(v1) | ~ % 35.33/5.71 | | | | | | | | | | | $i(v0) | ! [v4: $i] : ! [v5: $i] : ( ~ % 35.33/5.71 | | | | | | | | | | | (ordered_pair(v0, v4) = v5) | ~ (in(v5, % 35.33/5.71 | | | | | | | | | | | all_157_0) = 0) | ~ $i(v4) | ? [v6: $i] % 35.33/5.71 | | | | | | | | | | | : ? [v7: int] : ( ~ (v7 = 0) & % 35.33/5.71 | | | | | | | | | | | ordered_pair(v4, v1) = v6 & in(v6, % 35.33/5.71 | | | | | | | | | | | all_175_4) = v7 & $i(v6)))) & ! [v0: $i] % 35.33/5.71 | | | | | | | | | | | : ! [v1: $i] : ! [v2: $i] : ( ~ % 35.33/5.71 | | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, % 35.33/5.71 | | | | | | | | | | | all_175_3) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 35.33/5.71 | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 35.33/5.71 | | | | | | | | | | | (ordered_pair(v3, v1) = v5 & ordered_pair(v0, % 35.33/5.71 | | | | | | | | | | | v3) = v4 & in(v5, all_175_4) = 0 & in(v4, % 35.33/5.71 | | | | | | | | | | | all_157_0) = 0 & $i(v5) & $i(v4) & $i(v3))) % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | ALPHA: (93) implies: % 35.33/5.71 | | | | | | | | | | | (94) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 35.33/5.71 | | | | | | | | | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, % 35.33/5.71 | | | | | | | | | | | all_175_3) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 35.33/5.71 | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 35.33/5.71 | | | | | | | | | | | (ordered_pair(v3, v1) = v5 & ordered_pair(v0, % 35.33/5.71 | | | | | | | | | | | v3) = v4 & in(v5, all_175_4) = 0 & in(v4, % 35.33/5.71 | | | | | | | | | | | all_157_0) = 0 & $i(v5) & $i(v4) & $i(v3))) % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | GROUND_INST: instantiating (d4_relat_1) with all_175_4, % 35.33/5.71 | | | | | | | | | | | all_203_0, simplifying with (10), (34) gives: % 35.33/5.71 | | | | | | | | | | | (95) ? [v0: int] : ( ~ (v0 = 0) & relation(all_175_4) % 35.33/5.71 | | | | | | | | | | | = v0) | ( ? [v0: any] : (v0 = all_203_0 | ~ % 35.33/5.71 | | | | | | | | | | | $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1, % 35.33/5.71 | | | | | | | | | | | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: % 35.33/5.71 | | | | | | | | | | | $i] : ! [v4: $i] : ( ~ % 35.33/5.71 | | | | | | | | | | | (ordered_pair(v1, v3) = v4) | ~ (in(v4, % 35.33/5.71 | | | | | | | | | | | all_175_4) = 0) | ~ $i(v3))) & (v2 % 35.33/5.71 | | | | | | | | | | | = 0 | ? [v3: $i] : ? [v4: $i] : % 35.33/5.71 | | | | | | | | | | | (ordered_pair(v1, v3) = v4 & in(v4, % 35.33/5.71 | | | | | | | | | | | all_175_4) = 0 & $i(v4) & $i(v3))))) & % 35.33/5.71 | | | | | | | | | | | ( ~ $i(all_203_0) | ( ! [v0: $i] : ! [v1: int] % 35.33/5.71 | | | | | | | | | | | : (v1 = 0 | ~ (in(v0, all_203_0) = v1) | ~ % 35.33/5.71 | | | | | | | | | | | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ % 35.33/5.71 | | | | | | | | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, % 35.33/5.71 | | | | | | | | | | | all_175_4) = 0) | ~ $i(v2))) & ! % 35.33/5.71 | | | | | | | | | | | [v0: $i] : ( ~ (in(v0, all_203_0) = 0) | ~ % 35.33/5.71 | | | | | | | | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : % 35.33/5.71 | | | | | | | | | | | (ordered_pair(v0, v1) = v2 & in(v2, % 35.33/5.71 | | | | | | | | | | | all_175_4) = 0 & $i(v2) & $i(v1)))))) % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | DELTA: instantiating (91) with fresh symbols all_308_0, % 35.33/5.71 | | | | | | | | | | | all_308_1 gives: % 35.33/5.71 | | | | | | | | | | | (96) ordered_pair(all_308_1, all_214_1) = all_308_0 & % 35.33/5.71 | | | | | | | | | | | in(all_308_0, all_175_3) = 0 & $i(all_308_0) & % 35.33/5.71 | | | | | | | | | | | $i(all_308_1) % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | ALPHA: (96) implies: % 35.33/5.71 | | | | | | | | | | | (97) $i(all_308_1) % 35.33/5.71 | | | | | | | | | | | (98) in(all_308_0, all_175_3) = 0 % 35.33/5.71 | | | | | | | | | | | (99) ordered_pair(all_308_1, all_214_1) = all_308_0 % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | BETA: splitting (92) gives: % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | Case 1: % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | (100) all_214_0 = 0 % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | REDUCE: (42), (100) imply: % 35.33/5.71 | | | | | | | | | | | | (101) $false % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | CLOSE: (101) is inconsistent. % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | Case 2: % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | (102) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, % 35.33/5.71 | | | | | | | | | | | | all_214_1) = v1) | ~ (in(v1, all_175_4) = % 35.33/5.71 | | | | | | | | | | | | 0) | ~ $i(v0)) % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | BETA: splitting (95) gives: % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | Case 1: % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | | (103) ? [v0: int] : ( ~ (v0 = 0) & relation(all_175_4) % 35.33/5.71 | | | | | | | | | | | | | = v0) % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | | REF_CLOSE: (2), (10), (14), (15), (16), (37), (46), (49), % 35.33/5.71 | | | | | | | | | | | | | (54), (103) are inconsistent by sub-proof #1. % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | Case 2: % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | | GROUND_INST: instantiating (94) with all_308_1, all_214_1, % 35.33/5.71 | | | | | | | | | | | | | all_308_0, simplifying with (43), (97), (98), (99) % 35.33/5.71 | | | | | | | | | | | | | gives: % 35.33/5.71 | | | | | | | | | | | | | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 35.33/5.71 | | | | | | | | | | | | | (ordered_pair(v0, all_214_1) = v2 & % 35.33/5.71 | | | | | | | | | | | | | ordered_pair(all_308_1, v0) = v1 & in(v2, % 35.33/5.71 | | | | | | | | | | | | | all_175_4) = 0 & in(v1, all_157_0) = 0 & % 35.33/5.71 | | | | | | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | | DELTA: instantiating (104) with fresh symbols all_540_0, % 35.33/5.71 | | | | | | | | | | | | | all_540_1, all_540_2 gives: % 35.33/5.71 | | | | | | | | | | | | | (105) ordered_pair(all_540_2, all_214_1) = all_540_0 & % 35.33/5.71 | | | | | | | | | | | | | ordered_pair(all_308_1, all_540_2) = all_540_1 & % 35.33/5.71 | | | | | | | | | | | | | in(all_540_0, all_175_4) = 0 & in(all_540_1, % 35.33/5.71 | | | | | | | | | | | | | all_157_0) = 0 & $i(all_540_0) & $i(all_540_1) & % 35.33/5.71 | | | | | | | | | | | | | $i(all_540_2) % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | | ALPHA: (105) implies: % 35.33/5.71 | | | | | | | | | | | | | (106) $i(all_540_2) % 35.33/5.71 | | | | | | | | | | | | | (107) in(all_540_0, all_175_4) = 0 % 35.33/5.71 | | | | | | | | | | | | | (108) ordered_pair(all_540_2, all_214_1) = all_540_0 % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | | GROUND_INST: instantiating (102) with all_540_2, all_540_0, % 35.33/5.71 | | | | | | | | | | | | | simplifying with (106), (107), (108) gives: % 35.33/5.71 | | | | | | | | | | | | | (109) $false % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | | CLOSE: (109) is inconsistent. % 35.33/5.71 | | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | End of split % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | End of split % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | Case 2: % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | (110) ~ (all_261_3 = 0) | (all_261_0 = 0 & all_175_0 = % 35.33/5.71 | | | | | | | | | | | 0) % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | BETA: splitting (110) gives: % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | Case 1: % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | (111) ~ (all_261_3 = 0) % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | REDUCE: (89), (111) imply: % 35.33/5.71 | | | | | | | | | | | | (112) $false % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | CLOSE: (112) is inconsistent. % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | Case 2: % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | (113) all_261_0 = 0 & all_175_0 = 0 % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | ALPHA: (113) implies: % 35.33/5.71 | | | | | | | | | | | | (114) all_175_0 = 0 % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | REDUCE: (9), (114) imply: % 35.33/5.71 | | | | | | | | | | | | (115) $false % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | | CLOSE: (115) is inconsistent. % 35.33/5.71 | | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | | End of split % 35.33/5.71 | | | | | | | | | | | % 35.33/5.71 | | | | | | | | | | End of split % 35.33/5.71 | | | | | | | | | | % 35.33/5.71 | | | | | | | | | End of split % 35.33/5.71 | | | | | | | | | % 35.33/5.71 | | | | | | | | End of split % 35.33/5.71 | | | | | | | | % 35.33/5.71 | | | | | | | End of split % 35.33/5.71 | | | | | | | % 35.33/5.71 | | | | | | End of split % 35.33/5.71 | | | | | | % 35.33/5.71 | | | | | End of split % 35.33/5.71 | | | | | % 35.33/5.71 | | | | End of split % 35.33/5.71 | | | | % 35.33/5.71 | | | End of split % 35.33/5.71 | | | % 35.33/5.71 | | End of split % 35.33/5.71 | | % 35.33/5.71 | End of split % 35.33/5.71 | % 35.33/5.71 End of proof % 35.33/5.71 % 35.33/5.71 Sub-proof #1 shows that the following formulas are inconsistent: % 35.33/5.71 ---------------------------------------------------------------- % 35.33/5.71 (1) relation_rng(all_175_4) = all_175_1 % 35.33/5.71 (2) relation(all_175_4) = 0 % 35.33/5.71 (3) ~ (all_205_1 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 35.33/5.71 (relation_rng(v0) = v1) | ~ (subset(all_175_2, v1) = v2) | ~ $i(v0) | % 35.33/5.71 ? [v3: any] : ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 35.33/5.71 (relation_dom(v0) = v5 & relation(v0) = v3 & subset(all_205_0, v5) = v6 % 35.33/5.71 & subset(all_175_3, v0) = v4 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | % 35.33/5.71 (v6 = 0 & v2 = 0)))) % 35.33/5.71 (4) $i(all_175_4) % 35.33/5.71 (5) ? [v0: int] : ( ~ (v0 = 0) & relation(all_175_4) = v0) % 35.33/5.71 (6) subset(all_175_2, all_175_1) = all_175_0 % 35.33/5.71 (7) all_205_1 = all_201_0 % 35.33/5.72 (8) ~ (all_201_2 = 0) | all_201_0 = 0 % 35.33/5.72 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 35.33/5.72 (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 35.33/5.72 (10) all_201_2 = 0 % 35.33/5.72 % 35.33/5.72 Begin of proof % 35.33/5.72 | % 35.33/5.72 | DELTA: instantiating (5) with fresh symbol all_246_0 gives: % 35.33/5.72 | (11) ~ (all_246_0 = 0) & relation(all_175_4) = all_246_0 % 35.33/5.72 | % 35.33/5.72 | ALPHA: (11) implies: % 35.33/5.72 | (12) ~ (all_246_0 = 0) % 35.33/5.72 | (13) relation(all_175_4) = all_246_0 % 35.33/5.72 | % 35.33/5.72 | BETA: splitting (8) gives: % 35.33/5.72 | % 35.33/5.72 | Case 1: % 35.33/5.72 | | % 35.33/5.72 | | (14) ~ (all_201_2 = 0) % 35.33/5.72 | | % 35.33/5.72 | | REDUCE: (10), (14) imply: % 35.33/5.72 | | (15) $false % 35.33/5.72 | | % 35.33/5.72 | | CLOSE: (15) is inconsistent. % 35.33/5.72 | | % 35.33/5.72 | Case 2: % 35.33/5.72 | | % 35.33/5.72 | | (16) all_201_0 = 0 % 35.33/5.72 | | % 35.33/5.72 | | COMBINE_EQS: (7), (16) imply: % 35.33/5.72 | | (17) all_205_1 = 0 % 35.33/5.72 | | % 35.33/5.72 | | BETA: splitting (3) gives: % 35.33/5.72 | | % 35.33/5.72 | | Case 1: % 35.33/5.72 | | | % 35.33/5.72 | | | (18) ~ (all_205_1 = 0) % 35.33/5.72 | | | % 35.33/5.72 | | | REDUCE: (17), (18) imply: % 35.33/5.72 | | | (19) $false % 35.33/5.72 | | | % 35.33/5.72 | | | CLOSE: (19) is inconsistent. % 35.33/5.72 | | | % 35.33/5.72 | | Case 2: % 35.33/5.72 | | | % 35.33/5.72 | | | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (relation_rng(v0) = % 35.33/5.72 | | | v1) | ~ (subset(all_175_2, v1) = v2) | ~ $i(v0) | ? [v3: % 35.33/5.72 | | | any] : ? [v4: any] : ? [v5: $i] : ? [v6: any] : % 35.33/5.72 | | | (relation_dom(v0) = v5 & relation(v0) = v3 & subset(all_205_0, % 35.33/5.72 | | | v5) = v6 & subset(all_175_3, v0) = v4 & $i(v5) & ( ~ (v4 = % 35.33/5.72 | | | 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0)))) % 35.33/5.72 | | | % 35.33/5.72 | | | GROUND_INST: instantiating (20) with all_175_4, all_175_1, all_175_0, % 35.33/5.72 | | | simplifying with (1), (4), (6) gives: % 35.33/5.72 | | | (21) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 35.33/5.72 | | | (relation_dom(all_175_4) = v2 & relation(all_175_4) = v0 & % 35.33/5.72 | | | subset(all_205_0, v2) = v3 & subset(all_175_3, all_175_4) = v1 & % 35.33/5.72 | | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & all_175_0 = 0))) % 35.33/5.72 | | | % 35.33/5.72 | | | DELTA: instantiating (21) with fresh symbols all_260_0, all_260_1, % 35.33/5.72 | | | all_260_2, all_260_3 gives: % 35.33/5.72 | | | (22) relation_dom(all_175_4) = all_260_1 & relation(all_175_4) = % 35.33/5.72 | | | all_260_3 & subset(all_205_0, all_260_1) = all_260_0 & % 35.33/5.72 | | | subset(all_175_3, all_175_4) = all_260_2 & $i(all_260_1) & ( ~ % 35.33/5.72 | | | (all_260_2 = 0) | ~ (all_260_3 = 0) | (all_260_0 = 0 & % 35.33/5.72 | | | all_175_0 = 0)) % 35.33/5.72 | | | % 35.33/5.72 | | | ALPHA: (22) implies: % 35.33/5.72 | | | (23) relation(all_175_4) = all_260_3 % 35.33/5.72 | | | % 35.33/5.72 | | | GROUND_INST: instantiating (9) with 0, all_260_3, all_175_4, simplifying % 35.33/5.72 | | | with (2), (23) gives: % 35.33/5.72 | | | (24) all_260_3 = 0 % 35.33/5.72 | | | % 35.33/5.72 | | | GROUND_INST: instantiating (9) with all_246_0, all_260_3, all_175_4, % 35.33/5.72 | | | simplifying with (13), (23) gives: % 35.33/5.72 | | | (25) all_260_3 = all_246_0 % 35.33/5.72 | | | % 35.33/5.72 | | | COMBINE_EQS: (24), (25) imply: % 35.33/5.72 | | | (26) all_246_0 = 0 % 35.33/5.72 | | | % 35.33/5.72 | | | REDUCE: (12), (26) imply: % 35.33/5.72 | | | (27) $false % 35.33/5.72 | | | % 35.33/5.72 | | | CLOSE: (27) is inconsistent. % 35.33/5.72 | | | % 35.33/5.72 | | End of split % 35.33/5.72 | | % 35.33/5.72 | End of split % 35.33/5.72 | % 35.33/5.72 End of proof % 35.33/5.72 % SZS output end Proof for theBenchmark % 35.33/5.72 % 35.33/5.72 5086ms %------------------------------------------------------------------------------