%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU263+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:43:44 EDT 2023 % Result : Theorem 6.62s 1.67s % Output : Proof 9.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU263+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n004.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Aug 23 18:27:53 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.78/0.97 Prover 4: Preprocessing ... % 1.78/0.97 Prover 1: Preprocessing ... % 2.71/1.03 Prover 3: Preprocessing ... % 2.71/1.03 Prover 2: Preprocessing ... % 2.71/1.03 Prover 5: Preprocessing ... % 2.71/1.03 Prover 6: Preprocessing ... % 2.71/1.03 Prover 0: Preprocessing ... % 4.34/1.28 Prover 1: Warning: ignoring some quantifiers % 4.41/1.30 Prover 5: Proving ... % 4.41/1.30 Prover 2: Proving ... % 4.41/1.30 Prover 6: Proving ... % 4.41/1.33 Prover 3: Warning: ignoring some quantifiers % 4.41/1.33 Prover 1: Constructing countermodel ... % 4.41/1.34 Prover 3: Constructing countermodel ... % 4.41/1.34 Prover 4: Warning: ignoring some quantifiers % 4.41/1.37 Prover 0: Proving ... % 4.41/1.38 Prover 4: Constructing countermodel ... % 5.81/1.50 Prover 3: gave up % 5.81/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.81/1.52 Prover 1: gave up % 5.81/1.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.81/1.57 Prover 7: Preprocessing ... % 5.81/1.57 Prover 8: Preprocessing ... % 6.62/1.62 Prover 7: Warning: ignoring some quantifiers % 6.62/1.66 Prover 7: Constructing countermodel ... % 6.62/1.67 Prover 0: proved (1053ms) % 6.62/1.67 % 6.62/1.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.62/1.67 % 6.62/1.67 Prover 2: stopped % 6.62/1.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.62/1.68 Prover 8: Warning: ignoring some quantifiers % 6.62/1.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.62/1.69 Prover 6: stopped % 6.62/1.69 Prover 5: stopped % 6.62/1.69 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.62/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.62/1.69 Prover 8: Constructing countermodel ... % 7.30/1.70 Prover 11: Preprocessing ... % 7.30/1.71 Prover 10: Preprocessing ... % 7.30/1.72 Prover 13: Preprocessing ... % 7.30/1.72 Prover 16: Preprocessing ... % 7.30/1.75 Prover 10: Warning: ignoring some quantifiers % 7.30/1.75 Prover 16: Warning: ignoring some quantifiers % 7.30/1.76 Prover 10: Constructing countermodel ... % 7.30/1.76 Prover 16: Constructing countermodel ... % 8.00/1.79 Prover 10: gave up % 8.00/1.80 Prover 8: gave up % 8.00/1.80 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.00/1.80 Prover 13: Warning: ignoring some quantifiers % 8.00/1.81 Prover 13: Constructing countermodel ... % 8.00/1.82 Prover 19: Preprocessing ... % 8.00/1.82 Prover 4: Found proof (size 76) % 8.00/1.82 Prover 4: proved (1197ms) % 8.00/1.82 Prover 7: stopped % 8.00/1.82 Prover 16: stopped % 8.00/1.82 Prover 13: stopped % 8.00/1.82 Prover 11: Warning: ignoring some quantifiers % 8.00/1.83 Prover 11: Constructing countermodel ... % 8.00/1.84 Prover 11: stopped % 8.00/1.87 Prover 19: Warning: ignoring some quantifiers % 8.00/1.88 Prover 19: Constructing countermodel ... % 8.57/1.89 Prover 19: stopped % 8.57/1.89 % 8.57/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.57/1.89 % 8.59/1.91 % SZS output start Proof for theBenchmark % 8.59/1.91 Assumptions after simplification: % 8.59/1.91 --------------------------------- % 8.59/1.91 % 8.59/1.91 (cc1_relset_1) % 8.59/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 8.59/1.94 (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2, % 8.59/1.94 v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation(v2) = 0) % 8.59/1.94 % 8.59/1.94 (d1_relset_1) % 8.59/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.59/1.94 | ~ (subset(v2, v3) = v4) | ~ (cartesian_product2(v0, v1) = v3) | ~ % 8.59/1.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 8.59/1.94 relation_of2(v2, v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 8.59/1.94 : ! [v3: int] : (v3 = 0 | ~ (relation_of2(v2, v0, v1) = v3) | ~ $i(v2) | ~ % 8.59/1.94 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & subset(v2, % 8.59/1.94 v4) = v5 & cartesian_product2(v0, v1) = v4 & $i(v4))) & ! [v0: $i] : ! % 8.59/1.94 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (subset(v2, v3) = 0) | ~ % 8.59/1.94 (cartesian_product2(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 8.59/1.94 relation_of2(v2, v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( % 8.59/1.94 ~ (relation_of2(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 8.59/1.95 [v3: $i] : (subset(v2, v3) = 0 & cartesian_product2(v0, v1) = v3 & $i(v3))) % 8.59/1.95 % 8.59/1.95 (dt_m2_relset_1) % 8.59/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.59/1.95 int] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = % 8.59/1.95 v4) | ~ (element(v2, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 8.59/1.95 [v6: int] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & ! % 8.59/1.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, v1) % 8.59/1.95 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 8.59/1.95 (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0 & % 8.59/1.95 $i(v4) & $i(v3))) % 8.59/1.95 % 8.59/1.95 (redefinition_m2_relset_1) % 8.59/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.59/1.95 (relation_of2_as_subset(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.59/1.95 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & ! % 8.59/1.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.59/1.95 (relation_of2(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 8.59/1.95 [v4: int] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & ! % 8.59/1.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, v1) % 8.59/1.95 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2(v2, v0, v1) = 0) & % 8.59/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1) = 0) | % 8.59/1.95 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2_as_subset(v2, v0, v1) = 0) % 8.59/1.95 % 8.59/1.95 (t119_zfmisc_1) % 8.59/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 8.59/1.96 $i] : ! [v6: int] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ~ % 8.59/1.96 (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | % 8.59/1.96 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : % 8.59/1.96 (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) % 8.59/1.96 % 8.59/1.96 (t12_relset_1) % 8.59/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, % 8.59/1.96 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] % 8.59/1.96 : (relation_dom(v2) = v3 & relation_rng(v2) = v4 & subset(v4, v1) = 0 & % 8.59/1.96 subset(v3, v0) = 0 & $i(v4) & $i(v3))) % 8.59/1.96 % 8.59/1.96 (t14_relset_1) % 8.59/1.96 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.59/1.96 int] : ( ~ (v5 = 0) & relation_rng(v3) = v4 & relation_of2_as_subset(v3, v2, % 8.59/1.96 v1) = v5 & relation_of2_as_subset(v3, v2, v0) = 0 & subset(v4, v1) = 0 & % 8.59/1.96 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.59/1.96 % 8.59/1.96 (t1_xboole_1) % 8.59/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.59/1.96 (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.59/1.96 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : % 8.59/1.96 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v0, v2) = v3) % 8.59/1.96 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] % 8.59/1.96 : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 8.59/1.96 $i] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ % 8.59/1.96 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0) % 8.59/1.96 % 8.59/1.96 (t21_relat_1) % 8.59/1.97 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 8.59/1.97 any] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : (relation_rng(v0) = v3 & % 8.59/1.97 subset(v0, v4) = v5 & cartesian_product2(v1, v3) = v4 & relation(v0) = v2 % 8.59/1.97 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : % 8.59/1.97 ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: % 8.59/1.97 $i] : ? [v5: any] : (relation_dom(v0) = v3 & subset(v0, v4) = v5 & % 8.59/1.97 cartesian_product2(v3, v1) = v4 & relation(v0) = v2 & $i(v4) & $i(v3) & ( % 8.59/1.97 ~ (v2 = 0) | v5 = 0))) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ % 8.59/1.97 $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (relation_dom(v0) = v1 & % 8.59/1.97 relation_rng(v0) = v2 & subset(v0, v3) = 0 & cartesian_product2(v1, v2) = % 8.59/1.97 v3 & $i(v3) & $i(v2) & $i(v1))) % 8.59/1.97 % 8.59/1.97 (function-axioms) % 8.59/1.97 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.59/1.97 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = % 8.59/1.97 v1) | ~ (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0: % 8.59/1.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.59/1.97 : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~ % 8.59/1.97 (relation_of2(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.59/1.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.59/1.97 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 8.59/1.97 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ % 8.59/1.97 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.59/1.97 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, % 8.59/1.97 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 8.59/1.97 [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 8.59/1.97 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = % 8.59/1.97 v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 8.59/1.97 $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: % 8.59/1.97 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.59/1.97 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 8.59/1.97 % 8.59/1.97 Further assumptions not needed in the proof: % 8.59/1.97 -------------------------------------------- % 8.59/1.97 dt_k1_relat_1, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_zfmisc_1, dt_m1_relset_1, % 8.59/1.97 dt_m1_subset_1, existence_m1_relset_1, existence_m1_subset_1, % 8.59/1.97 existence_m2_relset_1, reflexivity_r1_tarski, t3_subset % 8.59/1.97 % 8.59/1.97 Those formulas are unsatisfiable: % 8.59/1.97 --------------------------------- % 8.59/1.97 % 8.59/1.97 Begin of proof % 8.59/1.97 | % 8.59/1.98 | ALPHA: (d1_relset_1) implies: % 8.59/1.98 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.59/1.98 | (relation_of2(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 8.59/1.98 | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & subset(v2, v4) = v5 & % 8.59/1.98 | cartesian_product2(v0, v1) = v4 & $i(v4))) % 8.59/1.98 | % 8.59/1.98 | ALPHA: (dt_m2_relset_1) implies: % 8.59/1.98 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 8.59/1.98 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 8.59/1.98 | $i(v0) | ? [v3: $i] : ? [v4: $i] : (cartesian_product2(v0, v1) = v3 % 8.59/1.98 | & powerset(v3) = v4 & element(v2, v4) = 0 & $i(v4) & $i(v3))) % 8.59/1.98 | % 8.59/1.98 | ALPHA: (redefinition_m2_relset_1) implies: % 8.59/1.98 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.59/1.98 | (relation_of2_as_subset(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 8.59/1.98 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = % 8.59/1.98 | v4)) % 8.59/1.98 | % 8.59/1.98 | ALPHA: (t1_xboole_1) implies: % 8.59/1.98 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.59/1.98 | (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ % 8.59/1.98 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v1, v2) = % 8.59/1.98 | v4)) % 8.59/1.98 | % 8.59/1.98 | ALPHA: (t21_relat_1) implies: % 8.89/1.98 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 8.89/1.98 | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 8.89/1.98 | (relation_dom(v0) = v3 & subset(v0, v4) = v5 & cartesian_product2(v3, % 8.89/1.98 | v1) = v4 & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | % 8.89/1.98 | v5 = 0))) % 8.89/1.98 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 8.89/1.98 | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : % 8.89/1.98 | (relation_rng(v0) = v3 & subset(v0, v4) = v5 & cartesian_product2(v1, % 8.89/1.98 | v3) = v4 & relation(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | % 8.89/1.98 | v5 = 0))) % 8.89/1.98 | % 8.89/1.98 | ALPHA: (function-axioms) implies: % 8.89/1.99 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.89/1.99 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 8.89/1.99 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 8.89/1.99 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 8.89/1.99 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 8.89/1.99 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 9.02/1.99 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.02/1.99 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = % 9.02/1.99 | v0)) % 9.02/1.99 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 9.02/1.99 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 9.02/1.99 | v2) = v0)) % 9.02/1.99 | % 9.02/1.99 | DELTA: instantiating (t14_relset_1) with fresh symbols all_16_0, all_16_1, % 9.02/1.99 | all_16_2, all_16_3, all_16_4, all_16_5 gives: % 9.02/1.99 | (12) ~ (all_16_0 = 0) & relation_rng(all_16_2) = all_16_1 & % 9.02/1.99 | relation_of2_as_subset(all_16_2, all_16_3, all_16_4) = all_16_0 & % 9.02/1.99 | relation_of2_as_subset(all_16_2, all_16_3, all_16_5) = 0 & % 9.02/1.99 | subset(all_16_1, all_16_4) = 0 & $i(all_16_1) & $i(all_16_2) & % 9.02/1.99 | $i(all_16_3) & $i(all_16_4) & $i(all_16_5) % 9.02/1.99 | % 9.02/1.99 | ALPHA: (12) implies: % 9.02/1.99 | (13) ~ (all_16_0 = 0) % 9.02/1.99 | (14) $i(all_16_5) % 9.02/1.99 | (15) $i(all_16_4) % 9.02/1.99 | (16) $i(all_16_3) % 9.02/1.99 | (17) $i(all_16_2) % 9.02/1.99 | (18) subset(all_16_1, all_16_4) = 0 % 9.02/1.99 | (19) relation_of2_as_subset(all_16_2, all_16_3, all_16_5) = 0 % 9.02/1.99 | (20) relation_of2_as_subset(all_16_2, all_16_3, all_16_4) = all_16_0 % 9.02/1.99 | (21) relation_rng(all_16_2) = all_16_1 % 9.02/1.99 | % 9.02/1.99 | GROUND_INST: instantiating (t12_relset_1) with all_16_3, all_16_5, all_16_2, % 9.02/1.99 | simplifying with (14), (16), (17), (19) gives: % 9.02/1.99 | (22) ? [v0: $i] : ? [v1: $i] : (relation_dom(all_16_2) = v0 & % 9.02/1.99 | relation_rng(all_16_2) = v1 & subset(v1, all_16_5) = 0 & subset(v0, % 9.02/1.99 | all_16_3) = 0 & $i(v1) & $i(v0)) % 9.02/1.99 | % 9.02/1.99 | GROUND_INST: instantiating (2) with all_16_3, all_16_5, all_16_2, simplifying % 9.02/1.99 | with (14), (16), (17), (19) gives: % 9.02/2.00 | (23) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_16_3, all_16_5) = % 9.02/2.00 | v0 & powerset(v0) = v1 & element(all_16_2, v1) = 0 & $i(v1) & % 9.02/2.00 | $i(v0)) % 9.02/2.00 | % 9.02/2.00 | GROUND_INST: instantiating (3) with all_16_3, all_16_4, all_16_2, all_16_0, % 9.02/2.00 | simplifying with (15), (16), (17), (20) gives: % 9.02/2.00 | (24) all_16_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & relation_of2(all_16_2, % 9.02/2.00 | all_16_3, all_16_4) = v0) % 9.02/2.00 | % 9.02/2.00 | GROUND_INST: instantiating (5) with all_16_2, all_16_1, simplifying with (17), % 9.02/2.00 | (21) gives: % 9.02/2.00 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 9.02/2.00 | (relation_dom(all_16_2) = v1 & subset(all_16_2, v2) = v3 & % 9.02/2.00 | cartesian_product2(v1, all_16_1) = v2 & relation(all_16_2) = v0 & % 9.02/2.00 | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = 0)) % 9.02/2.00 | % 9.02/2.00 | DELTA: instantiating (23) with fresh symbols all_26_0, all_26_1 gives: % 9.02/2.00 | (26) cartesian_product2(all_16_3, all_16_5) = all_26_1 & powerset(all_26_1) % 9.02/2.00 | = all_26_0 & element(all_16_2, all_26_0) = 0 & $i(all_26_0) & % 9.02/2.00 | $i(all_26_1) % 9.02/2.00 | % 9.02/2.00 | ALPHA: (26) implies: % 9.02/2.00 | (27) element(all_16_2, all_26_0) = 0 % 9.02/2.00 | (28) powerset(all_26_1) = all_26_0 % 9.02/2.00 | (29) cartesian_product2(all_16_3, all_16_5) = all_26_1 % 9.02/2.00 | % 9.02/2.00 | DELTA: instantiating (22) with fresh symbols all_28_0, all_28_1 gives: % 9.02/2.00 | (30) relation_dom(all_16_2) = all_28_1 & relation_rng(all_16_2) = all_28_0 % 9.02/2.00 | & subset(all_28_0, all_16_5) = 0 & subset(all_28_1, all_16_3) = 0 & % 9.02/2.00 | $i(all_28_0) & $i(all_28_1) % 9.02/2.00 | % 9.02/2.00 | ALPHA: (30) implies: % 9.02/2.00 | (31) subset(all_28_1, all_16_3) = 0 % 9.02/2.00 | (32) relation_rng(all_16_2) = all_28_0 % 9.02/2.00 | (33) relation_dom(all_16_2) = all_28_1 % 9.02/2.00 | % 9.02/2.00 | DELTA: instantiating (25) with fresh symbols all_30_0, all_30_1, all_30_2, % 9.02/2.00 | all_30_3 gives: % 9.02/2.00 | (34) relation_dom(all_16_2) = all_30_2 & subset(all_16_2, all_30_1) = % 9.02/2.00 | all_30_0 & cartesian_product2(all_30_2, all_16_1) = all_30_1 & % 9.02/2.00 | relation(all_16_2) = all_30_3 & $i(all_30_1) & $i(all_30_2) & ( ~ % 9.02/2.00 | (all_30_3 = 0) | all_30_0 = 0) % 9.02/2.00 | % 9.02/2.00 | ALPHA: (34) implies: % 9.02/2.00 | (35) $i(all_30_2) % 9.02/2.00 | (36) relation(all_16_2) = all_30_3 % 9.02/2.00 | (37) cartesian_product2(all_30_2, all_16_1) = all_30_1 % 9.02/2.00 | (38) relation_dom(all_16_2) = all_30_2 % 9.02/2.00 | % 9.02/2.00 | BETA: splitting (24) gives: % 9.02/2.00 | % 9.02/2.00 | Case 1: % 9.02/2.00 | | % 9.02/2.00 | | (39) all_16_0 = 0 % 9.02/2.00 | | % 9.02/2.00 | | REDUCE: (13), (39) imply: % 9.02/2.00 | | (40) $false % 9.02/2.00 | | % 9.02/2.00 | | CLOSE: (40) is inconsistent. % 9.02/2.00 | | % 9.02/2.01 | Case 2: % 9.02/2.01 | | % 9.02/2.01 | | (41) ? [v0: int] : ( ~ (v0 = 0) & relation_of2(all_16_2, all_16_3, % 9.02/2.01 | | all_16_4) = v0) % 9.02/2.01 | | % 9.02/2.01 | | DELTA: instantiating (41) with fresh symbol all_36_0 gives: % 9.02/2.01 | | (42) ~ (all_36_0 = 0) & relation_of2(all_16_2, all_16_3, all_16_4) = % 9.02/2.01 | | all_36_0 % 9.02/2.01 | | % 9.02/2.01 | | ALPHA: (42) implies: % 9.02/2.01 | | (43) ~ (all_36_0 = 0) % 9.02/2.01 | | (44) relation_of2(all_16_2, all_16_3, all_16_4) = all_36_0 % 9.02/2.01 | | % 9.02/2.01 | | GROUND_INST: instantiating (8) with all_16_1, all_28_0, all_16_2, % 9.02/2.01 | | simplifying with (21), (32) gives: % 9.02/2.01 | | (45) all_28_0 = all_16_1 % 9.02/2.01 | | % 9.02/2.01 | | GROUND_INST: instantiating (9) with all_28_1, all_30_2, all_16_2, % 9.02/2.01 | | simplifying with (33), (38) gives: % 9.02/2.01 | | (46) all_30_2 = all_28_1 % 9.02/2.01 | | % 9.02/2.01 | | REDUCE: (37), (46) imply: % 9.02/2.01 | | (47) cartesian_product2(all_28_1, all_16_1) = all_30_1 % 9.02/2.01 | | % 9.02/2.01 | | REDUCE: (35), (46) imply: % 9.02/2.01 | | (48) $i(all_28_1) % 9.02/2.01 | | % 9.02/2.01 | | GROUND_INST: instantiating (cc1_relset_1) with all_16_3, all_16_5, all_16_2, % 9.02/2.01 | | all_26_1, all_26_0, simplifying with (14), (16), (17), (27), % 9.02/2.01 | | (28), (29) gives: % 9.02/2.01 | | (49) relation(all_16_2) = 0 % 9.02/2.01 | | % 9.02/2.01 | | GROUND_INST: instantiating (1) with all_16_3, all_16_4, all_16_2, all_36_0, % 9.02/2.01 | | simplifying with (15), (16), (17), (44) gives: % 9.02/2.01 | | (50) all_36_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 9.02/2.01 | | subset(all_16_2, v0) = v1 & cartesian_product2(all_16_3, all_16_4) % 9.02/2.01 | | = v0 & $i(v0)) % 9.02/2.01 | | % 9.02/2.01 | | GROUND_INST: instantiating (6) with all_16_2, all_28_1, simplifying with % 9.02/2.01 | | (17), (33) gives: % 9.02/2.01 | | (51) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 9.02/2.01 | | (relation_rng(all_16_2) = v1 & subset(all_16_2, v2) = v3 & % 9.02/2.01 | | cartesian_product2(all_28_1, v1) = v2 & relation(all_16_2) = v0 & % 9.02/2.01 | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = 0)) % 9.02/2.01 | | % 9.02/2.01 | | DELTA: instantiating (51) with fresh symbols all_54_0, all_54_1, all_54_2, % 9.02/2.01 | | all_54_3 gives: % 9.02/2.01 | | (52) relation_rng(all_16_2) = all_54_2 & subset(all_16_2, all_54_1) = % 9.02/2.01 | | all_54_0 & cartesian_product2(all_28_1, all_54_2) = all_54_1 & % 9.02/2.01 | | relation(all_16_2) = all_54_3 & $i(all_54_1) & $i(all_54_2) & ( ~ % 9.02/2.01 | | (all_54_3 = 0) | all_54_0 = 0) % 9.02/2.01 | | % 9.02/2.01 | | ALPHA: (52) implies: % 9.02/2.01 | | (53) $i(all_54_2) % 9.02/2.01 | | (54) $i(all_54_1) % 9.02/2.01 | | (55) relation(all_16_2) = all_54_3 % 9.02/2.01 | | (56) cartesian_product2(all_28_1, all_54_2) = all_54_1 % 9.02/2.01 | | (57) subset(all_16_2, all_54_1) = all_54_0 % 9.02/2.01 | | (58) relation_rng(all_16_2) = all_54_2 % 9.02/2.01 | | (59) ~ (all_54_3 = 0) | all_54_0 = 0 % 9.02/2.01 | | % 9.02/2.01 | | BETA: splitting (50) gives: % 9.02/2.01 | | % 9.02/2.01 | | Case 1: % 9.02/2.01 | | | % 9.02/2.01 | | | (60) all_36_0 = 0 % 9.02/2.01 | | | % 9.02/2.01 | | | REDUCE: (43), (60) imply: % 9.02/2.01 | | | (61) $false % 9.02/2.01 | | | % 9.02/2.01 | | | CLOSE: (61) is inconsistent. % 9.02/2.01 | | | % 9.02/2.01 | | Case 2: % 9.02/2.01 | | | % 9.02/2.02 | | | (62) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(all_16_2, v0) = % 9.02/2.02 | | | v1 & cartesian_product2(all_16_3, all_16_4) = v0 & $i(v0)) % 9.02/2.02 | | | % 9.02/2.02 | | | DELTA: instantiating (62) with fresh symbols all_60_0, all_60_1 gives: % 9.02/2.02 | | | (63) ~ (all_60_0 = 0) & subset(all_16_2, all_60_1) = all_60_0 & % 9.02/2.02 | | | cartesian_product2(all_16_3, all_16_4) = all_60_1 & $i(all_60_1) % 9.02/2.02 | | | % 9.02/2.02 | | | ALPHA: (63) implies: % 9.02/2.02 | | | (64) ~ (all_60_0 = 0) % 9.02/2.02 | | | (65) $i(all_60_1) % 9.02/2.02 | | | (66) cartesian_product2(all_16_3, all_16_4) = all_60_1 % 9.02/2.02 | | | (67) subset(all_16_2, all_60_1) = all_60_0 % 9.02/2.02 | | | % 9.02/2.02 | | | GROUND_INST: instantiating (7) with all_30_3, all_54_3, all_16_2, % 9.02/2.02 | | | simplifying with (36), (55) gives: % 9.02/2.02 | | | (68) all_54_3 = all_30_3 % 9.02/2.02 | | | % 9.02/2.02 | | | GROUND_INST: instantiating (7) with 0, all_54_3, all_16_2, simplifying % 9.02/2.02 | | | with (49), (55) gives: % 9.02/2.02 | | | (69) all_54_3 = 0 % 9.02/2.02 | | | % 9.02/2.02 | | | GROUND_INST: instantiating (8) with all_16_1, all_54_2, all_16_2, % 9.02/2.02 | | | simplifying with (21), (58) gives: % 9.02/2.02 | | | (70) all_54_2 = all_16_1 % 9.02/2.02 | | | % 9.02/2.02 | | | COMBINE_EQS: (68), (69) imply: % 9.02/2.02 | | | (71) all_30_3 = 0 % 9.02/2.02 | | | % 9.02/2.02 | | | REDUCE: (56), (70) imply: % 9.02/2.02 | | | (72) cartesian_product2(all_28_1, all_16_1) = all_54_1 % 9.02/2.02 | | | % 9.02/2.02 | | | REDUCE: (53), (70) imply: % 9.02/2.02 | | | (73) $i(all_16_1) % 9.02/2.02 | | | % 9.02/2.02 | | | BETA: splitting (59) gives: % 9.02/2.02 | | | % 9.02/2.02 | | | Case 1: % 9.02/2.02 | | | | % 9.02/2.02 | | | | (74) ~ (all_54_3 = 0) % 9.02/2.02 | | | | % 9.02/2.02 | | | | REDUCE: (69), (74) imply: % 9.02/2.02 | | | | (75) $false % 9.02/2.02 | | | | % 9.02/2.02 | | | | CLOSE: (75) is inconsistent. % 9.02/2.02 | | | | % 9.02/2.02 | | | Case 2: % 9.02/2.02 | | | | % 9.02/2.02 | | | | (76) all_54_0 = 0 % 9.02/2.02 | | | | % 9.02/2.02 | | | | REDUCE: (57), (76) imply: % 9.02/2.02 | | | | (77) subset(all_16_2, all_54_1) = 0 % 9.02/2.02 | | | | % 9.02/2.02 | | | | GROUND_INST: instantiating (10) with all_30_1, all_54_1, all_16_1, % 9.02/2.02 | | | | all_28_1, simplifying with (47), (72) gives: % 9.02/2.02 | | | | (78) all_54_1 = all_30_1 % 9.02/2.02 | | | | % 9.02/2.02 | | | | REDUCE: (77), (78) imply: % 9.02/2.02 | | | | (79) subset(all_16_2, all_30_1) = 0 % 9.02/2.02 | | | | % 9.02/2.02 | | | | REDUCE: (54), (78) imply: % 9.02/2.02 | | | | (80) $i(all_30_1) % 9.02/2.02 | | | | % 9.02/2.02 | | | | GROUND_INST: instantiating (4) with all_16_2, all_30_1, all_60_1, % 9.02/2.02 | | | | all_60_0, simplifying with (17), (65), (67), (79), (80) % 9.02/2.02 | | | | gives: % 9.02/2.02 | | | | (81) all_60_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_30_1, % 9.02/2.02 | | | | all_60_1) = v0) % 9.02/2.02 | | | | % 9.02/2.02 | | | | BETA: splitting (81) gives: % 9.02/2.02 | | | | % 9.02/2.02 | | | | Case 1: % 9.02/2.02 | | | | | % 9.02/2.03 | | | | | (82) all_60_0 = 0 % 9.02/2.03 | | | | | % 9.02/2.03 | | | | | REDUCE: (64), (82) imply: % 9.02/2.03 | | | | | (83) $false % 9.02/2.03 | | | | | % 9.02/2.03 | | | | | CLOSE: (83) is inconsistent. % 9.02/2.03 | | | | | % 9.02/2.03 | | | | Case 2: % 9.02/2.03 | | | | | % 9.02/2.03 | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & subset(all_30_1, all_60_1) = v0) % 9.02/2.03 | | | | | % 9.02/2.03 | | | | | DELTA: instantiating (84) with fresh symbol all_100_0 gives: % 9.02/2.03 | | | | | (85) ~ (all_100_0 = 0) & subset(all_30_1, all_60_1) = all_100_0 % 9.02/2.03 | | | | | % 9.02/2.03 | | | | | ALPHA: (85) implies: % 9.02/2.03 | | | | | (86) ~ (all_100_0 = 0) % 9.02/2.03 | | | | | (87) subset(all_30_1, all_60_1) = all_100_0 % 9.02/2.03 | | | | | % 9.02/2.03 | | | | | GROUND_INST: instantiating (t119_zfmisc_1) with all_28_1, all_16_3, % 9.02/2.03 | | | | | all_16_1, all_16_4, all_30_1, all_60_1, all_100_0, % 9.02/2.03 | | | | | simplifying with (15), (16), (47), (48), (66), (73), (87) % 9.02/2.03 | | | | | gives: % 9.02/2.03 | | | | | (88) all_100_0 = 0 | ? [v0: any] : ? [v1: any] : % 9.02/2.03 | | | | | (subset(all_28_1, all_16_3) = v0 & subset(all_16_1, all_16_4) % 9.02/2.03 | | | | | = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 9.02/2.03 | | | | | % 9.02/2.03 | | | | | BETA: splitting (88) gives: % 9.02/2.03 | | | | | % 9.02/2.03 | | | | | Case 1: % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | (89) all_100_0 = 0 % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | REDUCE: (86), (89) imply: % 9.02/2.03 | | | | | | (90) $false % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | CLOSE: (90) is inconsistent. % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | Case 2: % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | (91) ? [v0: any] : ? [v1: any] : (subset(all_28_1, all_16_3) = % 9.02/2.03 | | | | | | v0 & subset(all_16_1, all_16_4) = v1 & ( ~ (v1 = 0) | ~ % 9.02/2.03 | | | | | | (v0 = 0))) % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | DELTA: instantiating (91) with fresh symbols all_112_0, all_112_1 % 9.02/2.03 | | | | | | gives: % 9.02/2.03 | | | | | | (92) subset(all_28_1, all_16_3) = all_112_1 & subset(all_16_1, % 9.02/2.03 | | | | | | all_16_4) = all_112_0 & ( ~ (all_112_0 = 0) | ~ % 9.02/2.03 | | | | | | (all_112_1 = 0)) % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | ALPHA: (92) implies: % 9.02/2.03 | | | | | | (93) subset(all_16_1, all_16_4) = all_112_0 % 9.02/2.03 | | | | | | (94) subset(all_28_1, all_16_3) = all_112_1 % 9.02/2.03 | | | | | | (95) ~ (all_112_0 = 0) | ~ (all_112_1 = 0) % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | GROUND_INST: instantiating (11) with 0, all_112_0, all_16_4, % 9.02/2.03 | | | | | | all_16_1, simplifying with (18), (93) gives: % 9.02/2.03 | | | | | | (96) all_112_0 = 0 % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | GROUND_INST: instantiating (11) with 0, all_112_1, all_16_3, % 9.02/2.03 | | | | | | all_28_1, simplifying with (31), (94) gives: % 9.02/2.03 | | | | | | (97) all_112_1 = 0 % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | BETA: splitting (95) gives: % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | | Case 1: % 9.02/2.03 | | | | | | | % 9.02/2.03 | | | | | | | (98) ~ (all_112_0 = 0) % 9.02/2.03 | | | | | | | % 9.02/2.03 | | | | | | | REDUCE: (96), (98) imply: % 9.02/2.03 | | | | | | | (99) $false % 9.02/2.03 | | | | | | | % 9.02/2.03 | | | | | | | CLOSE: (99) is inconsistent. % 9.02/2.03 | | | | | | | % 9.02/2.03 | | | | | | Case 2: % 9.02/2.03 | | | | | | | % 9.02/2.03 | | | | | | | (100) ~ (all_112_1 = 0) % 9.02/2.03 | | | | | | | % 9.02/2.03 | | | | | | | REDUCE: (97), (100) imply: % 9.02/2.03 | | | | | | | (101) $false % 9.02/2.03 | | | | | | | % 9.02/2.03 | | | | | | | CLOSE: (101) is inconsistent. % 9.02/2.03 | | | | | | | % 9.02/2.03 | | | | | | End of split % 9.02/2.03 | | | | | | % 9.02/2.03 | | | | | End of split % 9.02/2.03 | | | | | % 9.02/2.03 | | | | End of split % 9.02/2.03 | | | | % 9.02/2.03 | | | End of split % 9.02/2.03 | | | % 9.02/2.03 | | End of split % 9.02/2.03 | | % 9.02/2.04 | End of split % 9.02/2.04 | % 9.02/2.04 End of proof % 9.02/2.04 % SZS output end Proof for theBenchmark % 9.02/2.04 % 9.02/2.04 1435ms %------------------------------------------------------------------------------