%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU451+1 : TPTP v8.1.2. Released v3.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n001.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 17:44:57 EDT 2023 % Result : Theorem 21.16s 3.59s % Output : Proof 21.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU451+1 : TPTP v8.1.2. Released v3.4.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n001.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 17:44:39 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.34/1.08 Prover 1: Preprocessing ... % 2.34/1.08 Prover 4: Preprocessing ... % 3.24/1.12 Prover 2: Preprocessing ... % 3.24/1.12 Prover 3: Preprocessing ... % 3.24/1.12 Prover 0: Preprocessing ... % 3.24/1.12 Prover 6: Preprocessing ... % 3.24/1.12 Prover 5: Preprocessing ... % 6.81/1.65 Prover 1: Warning: ignoring some quantifiers % 6.81/1.71 Prover 5: Proving ... % 6.81/1.72 Prover 1: Constructing countermodel ... % 7.56/1.73 Prover 4: Warning: ignoring some quantifiers % 7.56/1.74 Prover 6: Proving ... % 7.56/1.77 Prover 3: Warning: ignoring some quantifiers % 8.04/1.80 Prover 2: Proving ... % 8.04/1.81 Prover 4: Constructing countermodel ... % 8.04/1.84 Prover 3: Constructing countermodel ... % 8.60/1.88 Prover 0: Proving ... % 10.45/2.14 Prover 3: gave up % 10.45/2.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.45/2.19 Prover 1: gave up % 10.45/2.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.00/2.23 Prover 7: Preprocessing ... % 11.00/2.23 Prover 8: Preprocessing ... % 11.54/2.35 Prover 7: Warning: ignoring some quantifiers % 11.54/2.37 Prover 7: Constructing countermodel ... % 12.89/2.47 Prover 8: Warning: ignoring some quantifiers % 12.89/2.50 Prover 8: Constructing countermodel ... % 15.18/2.79 Prover 8: gave up % 15.18/2.80 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 15.96/2.89 Prover 9: Preprocessing ... % 15.96/2.97 Prover 7: gave up % 15.96/2.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.96/3.06 Prover 10: Preprocessing ... % 16.96/3.15 Prover 9: Warning: ignoring some quantifiers % 16.96/3.16 Prover 10: Warning: ignoring some quantifiers % 16.96/3.17 Prover 9: Constructing countermodel ... % 18.28/3.18 Prover 10: Constructing countermodel ... % 21.16/3.59 Prover 4: Found proof (size 188) % 21.16/3.59 Prover 4: proved (2972ms) % 21.16/3.59 Prover 9: stopped % 21.16/3.59 Prover 10: stopped % 21.16/3.59 Prover 6: stopped % 21.16/3.59 Prover 2: stopped % 21.16/3.59 Prover 0: stopped % 21.16/3.59 Prover 5: stopped % 21.16/3.59 % 21.16/3.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.16/3.59 % 21.51/3.65 % SZS output start Proof for theBenchmark % 21.51/3.65 Assumptions after simplification: % 21.51/3.65 --------------------------------- % 21.51/3.65 % 21.51/3.65 (dt_k6_partfun1) % 21.51/3.68 ! [v0: $i] : ! [v1: $i] : ( ~ (k6_partfun1(v0) = v1) | ~ $i(v0) | % 21.51/3.68 m2_relset_1(v1, v0, v0) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.51/3.68 (k6_partfun1(v0) = v1) | ~ $i(v0) | v1_partfun1(v1, v0, v0) = 0) % 21.51/3.68 % 21.51/3.68 (dt_k7_relset_1) % 21.51/3.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.51/3.68 $i] : ! [v6: $i] : ( ~ (k7_relset_1(v0, v1, v2, v3, v4, v5) = v6) | ~ % 21.51/3.68 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: % 21.51/3.68 any] : ? [v8: any] : ? [v9: any] : (m1_relset_1(v5, v2, v3) = v8 & % 21.51/3.68 m1_relset_1(v4, v0, v1) = v7 & m2_relset_1(v6, v0, v3) = v9 & ( ~ (v8 = 0) % 21.51/3.68 | ~ (v7 = 0) | v9 = 0))) % 21.51/3.68 % 21.51/3.68 (dt_k9_relset_2) % 21.51/3.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.51/3.68 $i] : ( ~ (k9_relset_2(v0, v1, v2, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | % 21.51/3.68 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: any] % 21.51/3.68 : ? [v9: $i] : ? [v10: $i] : ? [v11: any] : ? [v12: any] : % 21.51/3.68 (m2_relset_1(v5, v0, v2) = v12 & k2_zfmisc_1(v1, v2) = v9 & k2_zfmisc_1(v0, % 21.51/3.68 v1) = v6 & k1_zfmisc_1(v9) = v10 & k1_zfmisc_1(v6) = v7 & % 21.51/3.68 m1_subset_1(v4, v10) = v11 & m1_subset_1(v3, v7) = v8 & $i(v10) & $i(v9) & % 21.51/3.68 $i(v7) & $i(v6) & ( ~ (v11 = 0) | ~ (v8 = 0) | v12 = 0))) % 21.51/3.68 % 21.51/3.69 (dt_m2_relset_1) % 21.51/3.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.51/3.69 int] : (v5 = 0 | ~ (k2_zfmisc_1(v0, v1) = v3) | ~ (k1_zfmisc_1(v3) = v4) | % 21.51/3.69 ~ (m1_subset_1(v2, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 21.51/3.69 int] : ( ~ (v6 = 0) & m2_relset_1(v2, v0, v1) = v6)) & ! [v0: $i] : ! % 21.51/3.69 [v1: $i] : ! [v2: $i] : ( ~ (m2_relset_1(v2, v0, v1) = 0) | ~ $i(v2) | ~ % 21.51/3.69 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (k2_zfmisc_1(v0, v1) = v3 & % 21.51/3.69 k1_zfmisc_1(v3) = v4 & m1_subset_1(v2, v4) = 0 & $i(v4) & $i(v3))) % 21.51/3.69 % 21.51/3.69 (redefinition_k6_partfun1) % 21.51/3.69 ! [v0: $i] : ! [v1: $i] : ( ~ (k6_relat_1(v0) = v1) | ~ $i(v0) | % 21.51/3.69 (k6_partfun1(v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 21.51/3.69 (k6_partfun1(v0) = v1) | ~ $i(v0) | (k6_relat_1(v0) = v1 & $i(v1))) % 21.51/3.69 % 21.51/3.69 (redefinition_k7_relset_1) % 21.51/3.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.51/3.69 $i] : ! [v6: $i] : ( ~ (k7_relset_1(v0, v1, v2, v3, v4, v5) = v6) | ~ % 21.51/3.69 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: % 21.51/3.69 any] : ? [v8: any] : ? [v9: $i] : (m1_relset_1(v5, v2, v3) = v8 & % 21.51/3.69 m1_relset_1(v4, v0, v1) = v7 & k5_relat_1(v4, v5) = v9 & $i(v9) & ( ~ (v8 % 21.51/3.69 = 0) | ~ (v7 = 0) | v9 = v6))) % 21.51/3.69 % 21.51/3.69 (redefinition_k9_relset_2) % 21.51/3.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.51/3.69 $i] : ( ~ (k9_relset_2(v0, v1, v2, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | % 21.51/3.69 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: any] % 21.51/3.69 : ? [v9: $i] : ? [v10: $i] : ? [v11: any] : ? [v12: $i] : % 21.51/3.69 (k5_relat_1(v3, v4) = v12 & k2_zfmisc_1(v1, v2) = v9 & k2_zfmisc_1(v0, v1) = % 21.51/3.69 v6 & k1_zfmisc_1(v9) = v10 & k1_zfmisc_1(v6) = v7 & m1_subset_1(v4, v10) = % 21.51/3.69 v11 & m1_subset_1(v3, v7) = v8 & $i(v12) & $i(v10) & $i(v9) & $i(v7) & % 21.51/3.69 $i(v6) & ( ~ (v11 = 0) | ~ (v8 = 0) | v12 = v5))) % 21.51/3.69 % 21.51/3.69 (redefinition_m2_relset_1) % 21.51/3.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 21.51/3.70 (m1_relset_1(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 21.51/3.70 int] : ( ~ (v4 = 0) & m2_relset_1(v2, v0, v1) = v4)) & ! [v0: $i] : ! % 21.51/3.70 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (m2_relset_1(v2, v0, v1) % 21.51/3.70 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 21.51/3.70 m1_relset_1(v2, v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 21.51/3.70 ( ~ (m1_relset_1(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.51/3.70 m2_relset_1(v2, v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.51/3.70 (m2_relset_1(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 21.51/3.70 m1_relset_1(v2, v0, v1) = 0) % 21.51/3.70 % 21.51/3.70 (t23_funct_2) % 21.51/3.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 21.51/3.70 (k7_relset_1(v0, v1, v1, v1, v2, v3) = v4) | ~ (k6_partfun1(v1) = v3) | ~ % 21.51/3.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 21.51/3.70 (k7_relset_1(v0, v0, v0, v1, v6, v2) = v7 & m2_relset_1(v2, v0, v1) = v5 & % 21.51/3.70 k6_partfun1(v0) = v6 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | (v7 = v2 & v4 = % 21.51/3.70 v2)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 21.51/3.70 [v4: $i] : ( ~ (k7_relset_1(v0, v0, v0, v1, v3, v2) = v4) | ~ % 21.51/3.70 (k6_partfun1(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : % 21.51/3.70 ? [v6: $i] : ? [v7: $i] : (k7_relset_1(v0, v1, v1, v1, v2, v6) = v7 & % 21.51/3.70 m2_relset_1(v2, v0, v1) = v5 & k6_partfun1(v1) = v6 & $i(v7) & $i(v6) & ( % 21.51/3.70 ~ (v5 = 0) | (v7 = v2 & v4 = v2)))) & ! [v0: $i] : ! [v1: $i] : ! % 21.51/3.70 [v2: $i] : ( ~ (m2_relset_1(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 21.51/3.70 $i(v0) | ? [v3: $i] : ? [v4: $i] : (k7_relset_1(v0, v1, v1, v1, v2, v4) = % 21.51/3.70 v2 & k7_relset_1(v0, v0, v0, v1, v3, v2) = v2 & k6_partfun1(v1) = v4 & % 21.51/3.70 k6_partfun1(v0) = v3 & $i(v4) & $i(v3))) % 21.51/3.70 % 21.51/3.70 (t65_relset_2) % 21.51/3.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 21.51/3.70 $i] : ? [v6: $i] : ( ~ (v6 = v4) & k9_relset_2(v0, v1, v1, v2, v5) = v6 & % 21.51/3.70 k9_relset_2(v0, v0, v1, v3, v2) = v4 & m2_relset_1(v2, v0, v1) = 0 & % 21.51/3.70 k6_partfun1(v1) = v5 & k6_partfun1(v0) = v3 & $i(v6) & $i(v5) & $i(v4) & % 21.51/3.70 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 21.51/3.70 % 21.51/3.70 (function-axioms) % 21.51/3.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.51/3.71 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (k7_relset_1(v7, v6, v5, v4, % 21.51/3.71 v3, v2) = v1) | ~ (k7_relset_1(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 21.51/3.71 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 21.51/3.71 ! [v6: $i] : (v1 = v0 | ~ (k9_relset_2(v6, v5, v4, v3, v2) = v1) | ~ % 21.51/3.71 (k9_relset_2(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 21.51/3.71 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 21.51/3.71 ~ (m1_relset_1(v4, v3, v2) = v1) | ~ (m1_relset_1(v4, v3, v2) = v0)) & ! % 21.51/3.71 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 21.51/3.71 $i] : ! [v4: $i] : (v1 = v0 | ~ (m2_relset_1(v4, v3, v2) = v1) | ~ % 21.51/3.71 (m2_relset_1(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.51/3.71 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 21.51/3.71 (v1_partfun1(v4, v3, v2) = v1) | ~ (v1_partfun1(v4, v3, v2) = v0)) & ! % 21.51/3.71 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 21.51/3.71 $i] : (v1 = v0 | ~ (r1_tarski(v3, v2) = v1) | ~ (r1_tarski(v3, v2) = v0)) % 21.51/3.71 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.51/3.71 (k5_relat_1(v3, v2) = v1) | ~ (k5_relat_1(v3, v2) = v0)) & ! [v0: $i] : ! % 21.51/3.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = % 21.51/3.71 v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 21.51/3.71 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.51/3.71 (m1_subset_1(v3, v2) = v1) | ~ (m1_subset_1(v3, v2) = v0)) & ! [v0: % 21.51/3.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 21.51/3.71 : (v1 = v0 | ~ (r2_hidden(v3, v2) = v1) | ~ (r2_hidden(v3, v2) = v0)) & ! % 21.51/3.71 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 21.51/3.71 | ~ (v4_relat_2(v2) = v1) | ~ (v4_relat_2(v2) = v0)) & ! [v0: % 21.51/3.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 21.51/3.71 ~ (v1_funct_1(v2) = v1) | ~ (v1_funct_1(v2) = v0)) & ! [v0: % 21.51/3.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 21.51/3.71 ~ (v3_relat_1(v2) = v1) | ~ (v3_relat_1(v2) = v0)) & ! [v0: $i] : ! [v1: % 21.51/3.71 $i] : ! [v2: $i] : (v1 = v0 | ~ (k6_relat_1(v2) = v1) | ~ (k6_relat_1(v2) % 21.51/3.71 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 21.51/3.71 (k6_partfun1(v2) = v1) | ~ (k6_partfun1(v2) = v0)) & ! [v0: $i] : ! [v1: % 21.51/3.71 $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ % 21.51/3.71 (k1_zfmisc_1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.51/3.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_xboole_0(v2) = v1) | ~ % 21.51/3.71 (v1_xboole_0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.51/3.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_relat_2(v2) = v1) | ~ % 21.51/3.71 (v1_relat_2(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.51/3.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_relat_1(v2) = v1) | ~ % 21.51/3.71 (v1_relat_1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.51/3.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v3_relat_2(v2) = v1) | ~ % 21.51/3.71 (v3_relat_2(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 21.51/3.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v8_relat_2(v2) = v1) | ~ % 21.51/3.71 (v8_relat_2(v2) = v0)) % 21.51/3.71 % 21.51/3.71 Further assumptions not needed in the proof: % 21.51/3.71 -------------------------------------------- % 21.51/3.71 antisymmetry_r2_hidden, cc1_partfun1, cc1_relat_1, cc1_relset_1, dt_k1_xboole_0, % 21.51/3.71 dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k5_relat_1, dt_k6_relat_1, dt_m1_relset_1, % 21.51/3.71 dt_m1_subset_1, existence_m1_relset_1, existence_m1_subset_1, % 21.51/3.71 existence_m2_relset_1, fc10_relat_1, fc12_relat_1, fc1_subset_1, fc1_sysrel, % 21.51/3.71 fc2_partfun1, fc4_relat_1, fc4_subset_1, fc9_relat_1, rc1_relat_1, rc1_subset_1, % 21.51/3.71 rc2_partfun1, rc2_relat_1, rc2_subset_1, rc3_partfun1, rc3_relat_1, % 21.51/3.71 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, % 21.51/3.71 t6_boole, t7_boole, t8_boole % 21.51/3.71 % 21.51/3.71 Those formulas are unsatisfiable: % 21.51/3.71 --------------------------------- % 21.51/3.71 % 21.51/3.71 Begin of proof % 21.51/3.71 | % 21.51/3.71 | ALPHA: (dt_k6_partfun1) implies: % 21.51/3.71 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (k6_partfun1(v0) = v1) | ~ $i(v0) | % 21.51/3.71 | m2_relset_1(v1, v0, v0) = 0) % 21.51/3.71 | % 21.51/3.71 | ALPHA: (dt_m2_relset_1) implies: % 21.51/3.71 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m2_relset_1(v2, v0, v1) % 21.51/3.71 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 21.51/3.71 | $i] : (k2_zfmisc_1(v0, v1) = v3 & k1_zfmisc_1(v3) = v4 & % 21.51/3.71 | m1_subset_1(v2, v4) = 0 & $i(v4) & $i(v3))) % 21.51/3.71 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 21.51/3.71 | ! [v5: int] : (v5 = 0 | ~ (k2_zfmisc_1(v0, v1) = v3) | ~ % 21.51/3.71 | (k1_zfmisc_1(v3) = v4) | ~ (m1_subset_1(v2, v4) = v5) | ~ $i(v2) | % 21.51/3.71 | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) & m2_relset_1(v2, % 21.51/3.72 | v0, v1) = v6)) % 21.51/3.72 | % 21.51/3.72 | ALPHA: (redefinition_k6_partfun1) implies: % 21.51/3.72 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (k6_partfun1(v0) = v1) | ~ $i(v0) | % 21.51/3.72 | (k6_relat_1(v0) = v1 & $i(v1))) % 21.51/3.72 | % 21.51/3.72 | ALPHA: (redefinition_m2_relset_1) implies: % 21.51/3.72 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m2_relset_1(v2, v0, v1) % 21.51/3.72 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | m1_relset_1(v2, v0, v1) % 21.51/3.72 | = 0) % 21.51/3.72 | % 21.51/3.72 | ALPHA: (t23_funct_2) implies: % 21.51/3.72 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m2_relset_1(v2, v0, v1) % 21.51/3.72 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 21.51/3.72 | $i] : (k7_relset_1(v0, v1, v1, v1, v2, v4) = v2 & k7_relset_1(v0, % 21.51/3.72 | v0, v0, v1, v3, v2) = v2 & k6_partfun1(v1) = v4 & k6_partfun1(v0) % 21.51/3.72 | = v3 & $i(v4) & $i(v3))) % 21.51/3.72 | % 21.51/3.72 | ALPHA: (function-axioms) implies: % 21.51/3.72 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 21.51/3.72 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) % 21.51/3.72 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 21.51/3.72 | (k6_partfun1(v2) = v1) | ~ (k6_partfun1(v2) = v0)) % 21.51/3.72 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 21.51/3.72 | ! [v3: $i] : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~ % 21.51/3.72 | (m1_subset_1(v3, v2) = v0)) % 21.51/3.72 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.51/3.72 | (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) % 21.51/3.72 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 21.51/3.72 | (k5_relat_1(v3, v2) = v1) | ~ (k5_relat_1(v3, v2) = v0)) % 21.51/3.72 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.51/3.72 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (m2_relset_1(v4, v3, v2) = % 21.51/3.72 | v1) | ~ (m2_relset_1(v4, v3, v2) = v0)) % 21.51/3.72 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 21.51/3.72 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (m1_relset_1(v4, v3, v2) = % 21.51/3.72 | v1) | ~ (m1_relset_1(v4, v3, v2) = v0)) % 21.51/3.72 | % 21.51/3.72 | DELTA: instantiating (t65_relset_2) with fresh symbols all_47_0, all_47_1, % 21.51/3.72 | all_47_2, all_47_3, all_47_4, all_47_5, all_47_6 gives: % 21.51/3.72 | (14) ~ (all_47_0 = all_47_2) & k9_relset_2(all_47_6, all_47_5, all_47_5, % 21.51/3.72 | all_47_4, all_47_1) = all_47_0 & k9_relset_2(all_47_6, all_47_6, % 21.51/3.72 | all_47_5, all_47_3, all_47_4) = all_47_2 & m2_relset_1(all_47_4, % 21.51/3.72 | all_47_6, all_47_5) = 0 & k6_partfun1(all_47_5) = all_47_1 & % 21.51/3.72 | k6_partfun1(all_47_6) = all_47_3 & $i(all_47_0) & $i(all_47_1) & % 21.51/3.72 | $i(all_47_2) & $i(all_47_3) & $i(all_47_4) & $i(all_47_5) & % 21.51/3.72 | $i(all_47_6) % 21.51/3.72 | % 21.51/3.72 | ALPHA: (14) implies: % 21.51/3.72 | (15) ~ (all_47_0 = all_47_2) % 21.51/3.72 | (16) $i(all_47_6) % 21.51/3.72 | (17) $i(all_47_5) % 21.51/3.72 | (18) $i(all_47_4) % 21.51/3.72 | (19) k6_partfun1(all_47_6) = all_47_3 % 21.51/3.72 | (20) k6_partfun1(all_47_5) = all_47_1 % 21.51/3.73 | (21) m2_relset_1(all_47_4, all_47_6, all_47_5) = 0 % 21.51/3.73 | (22) k9_relset_2(all_47_6, all_47_6, all_47_5, all_47_3, all_47_4) = % 21.51/3.73 | all_47_2 % 21.51/3.73 | (23) k9_relset_2(all_47_6, all_47_5, all_47_5, all_47_4, all_47_1) = % 21.51/3.73 | all_47_0 % 21.51/3.73 | % 21.51/3.73 | GROUND_INST: instantiating (1) with all_47_6, all_47_3, simplifying with (16), % 21.51/3.73 | (19) gives: % 21.51/3.73 | (24) m2_relset_1(all_47_3, all_47_6, all_47_6) = 0 % 21.51/3.73 | % 21.51/3.73 | GROUND_INST: instantiating (4) with all_47_6, all_47_3, simplifying with (16), % 21.51/3.73 | (19) gives: % 21.51/3.73 | (25) k6_relat_1(all_47_6) = all_47_3 & $i(all_47_3) % 21.51/3.73 | % 21.51/3.73 | ALPHA: (25) implies: % 21.51/3.73 | (26) $i(all_47_3) % 21.51/3.73 | % 21.51/3.73 | GROUND_INST: instantiating (1) with all_47_5, all_47_1, simplifying with (17), % 21.51/3.73 | (20) gives: % 21.51/3.73 | (27) m2_relset_1(all_47_1, all_47_5, all_47_5) = 0 % 21.51/3.73 | % 21.51/3.73 | GROUND_INST: instantiating (4) with all_47_5, all_47_1, simplifying with (17), % 21.51/3.73 | (20) gives: % 21.51/3.73 | (28) k6_relat_1(all_47_5) = all_47_1 & $i(all_47_1) % 21.51/3.73 | % 21.51/3.73 | ALPHA: (28) implies: % 21.51/3.73 | (29) $i(all_47_1) % 21.51/3.73 | % 21.51/3.73 | GROUND_INST: instantiating (5) with all_47_6, all_47_5, all_47_4, simplifying % 21.51/3.73 | with (16), (17), (18), (21) gives: % 21.51/3.73 | (30) m1_relset_1(all_47_4, all_47_6, all_47_5) = 0 % 21.51/3.73 | % 21.51/3.73 | GROUND_INST: instantiating (6) with all_47_6, all_47_5, all_47_4, simplifying % 21.51/3.73 | with (16), (17), (18), (21) gives: % 21.51/3.73 | (31) ? [v0: $i] : ? [v1: $i] : (k7_relset_1(all_47_6, all_47_5, all_47_5, % 21.51/3.73 | all_47_5, all_47_4, v1) = all_47_4 & k7_relset_1(all_47_6, % 21.51/3.73 | all_47_6, all_47_6, all_47_5, v0, all_47_4) = all_47_4 & % 21.51/3.73 | k6_partfun1(all_47_5) = v1 & k6_partfun1(all_47_6) = v0 & $i(v1) & % 21.51/3.73 | $i(v0)) % 21.51/3.73 | % 21.51/3.73 | GROUND_INST: instantiating (2) with all_47_6, all_47_5, all_47_4, simplifying % 21.51/3.73 | with (16), (17), (18), (21) gives: % 21.51/3.73 | (32) ? [v0: $i] : ? [v1: $i] : (k2_zfmisc_1(all_47_6, all_47_5) = v0 & % 21.51/3.73 | k1_zfmisc_1(v0) = v1 & m1_subset_1(all_47_4, v1) = 0 & $i(v1) & % 21.51/3.73 | $i(v0)) % 21.51/3.73 | % 21.51/3.73 | GROUND_INST: instantiating (dt_k9_relset_2) with all_47_6, all_47_6, all_47_5, % 21.51/3.73 | all_47_3, all_47_4, all_47_2, simplifying with (16), (17), (18), % 21.51/3.73 | (22), (26) gives: % 21.51/3.73 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 21.51/3.73 | ? [v5: any] : ? [v6: any] : (m2_relset_1(all_47_2, all_47_6, % 21.51/3.73 | all_47_5) = v6 & k2_zfmisc_1(all_47_6, all_47_5) = v3 & % 21.51/3.73 | k2_zfmisc_1(all_47_6, all_47_6) = v0 & k1_zfmisc_1(v3) = v4 & % 21.51/3.73 | k1_zfmisc_1(v0) = v1 & m1_subset_1(all_47_3, v1) = v2 & % 21.51/3.73 | m1_subset_1(all_47_4, v4) = v5 & $i(v4) & $i(v3) & $i(v1) & $i(v0) & % 21.51/3.73 | ( ~ (v5 = 0) | ~ (v2 = 0) | v6 = 0)) % 21.51/3.73 | % 21.51/3.74 | GROUND_INST: instantiating (redefinition_k9_relset_2) with all_47_6, all_47_6, % 21.51/3.74 | all_47_5, all_47_3, all_47_4, all_47_2, simplifying with (16), % 21.51/3.74 | (17), (18), (22), (26) gives: % 21.51/3.74 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 21.51/3.74 | ? [v5: any] : ? [v6: $i] : (k5_relat_1(all_47_3, all_47_4) = v6 & % 21.51/3.74 | k2_zfmisc_1(all_47_6, all_47_5) = v3 & k2_zfmisc_1(all_47_6, % 21.51/3.74 | all_47_6) = v0 & k1_zfmisc_1(v3) = v4 & k1_zfmisc_1(v0) = v1 & % 21.51/3.74 | m1_subset_1(all_47_3, v1) = v2 & m1_subset_1(all_47_4, v4) = v5 & % 21.51/3.74 | $i(v6) & $i(v4) & $i(v3) & $i(v1) & $i(v0) & ( ~ (v5 = 0) | ~ (v2 = % 21.51/3.74 | 0) | v6 = all_47_2)) % 21.51/3.74 | % 21.51/3.74 | GROUND_INST: instantiating (dt_k9_relset_2) with all_47_6, all_47_5, all_47_5, % 21.51/3.74 | all_47_4, all_47_1, all_47_0, simplifying with (16), (17), (18), % 21.51/3.74 | (23), (29) gives: % 21.51/3.74 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 21.51/3.74 | ? [v5: any] : ? [v6: any] : (m2_relset_1(all_47_0, all_47_6, % 21.51/3.74 | all_47_5) = v6 & k2_zfmisc_1(all_47_5, all_47_5) = v3 & % 21.51/3.74 | k2_zfmisc_1(all_47_6, all_47_5) = v0 & k1_zfmisc_1(v3) = v4 & % 21.51/3.74 | k1_zfmisc_1(v0) = v1 & m1_subset_1(all_47_1, v4) = v5 & % 21.51/3.74 | m1_subset_1(all_47_4, v1) = v2 & $i(v4) & $i(v3) & $i(v1) & $i(v0) & % 21.51/3.74 | ( ~ (v5 = 0) | ~ (v2 = 0) | v6 = 0)) % 21.51/3.74 | % 21.51/3.74 | GROUND_INST: instantiating (redefinition_k9_relset_2) with all_47_6, all_47_5, % 21.51/3.74 | all_47_5, all_47_4, all_47_1, all_47_0, simplifying with (16), % 21.51/3.74 | (17), (18), (23), (29) gives: % 21.51/3.74 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] : % 21.51/3.74 | ? [v5: any] : ? [v6: $i] : (k5_relat_1(all_47_4, all_47_1) = v6 & % 21.51/3.74 | k2_zfmisc_1(all_47_5, all_47_5) = v3 & k2_zfmisc_1(all_47_6, % 21.51/3.74 | all_47_5) = v0 & k1_zfmisc_1(v3) = v4 & k1_zfmisc_1(v0) = v1 & % 21.51/3.74 | m1_subset_1(all_47_1, v4) = v5 & m1_subset_1(all_47_4, v1) = v2 & % 21.51/3.74 | $i(v6) & $i(v4) & $i(v3) & $i(v1) & $i(v0) & ( ~ (v5 = 0) | ~ (v2 = % 21.51/3.74 | 0) | v6 = all_47_0)) % 21.51/3.74 | % 21.51/3.74 | DELTA: instantiating (32) with fresh symbols all_55_0, all_55_1 gives: % 21.51/3.74 | (37) k2_zfmisc_1(all_47_6, all_47_5) = all_55_1 & k1_zfmisc_1(all_55_1) = % 21.51/3.74 | all_55_0 & m1_subset_1(all_47_4, all_55_0) = 0 & $i(all_55_0) & % 21.51/3.74 | $i(all_55_1) % 21.51/3.74 | % 21.51/3.74 | ALPHA: (37) implies: % 21.51/3.74 | (38) m1_subset_1(all_47_4, all_55_0) = 0 % 21.51/3.74 | (39) k1_zfmisc_1(all_55_1) = all_55_0 % 21.51/3.74 | (40) k2_zfmisc_1(all_47_6, all_47_5) = all_55_1 % 21.51/3.74 | % 21.51/3.74 | DELTA: instantiating (31) with fresh symbols all_57_0, all_57_1 gives: % 21.51/3.74 | (41) k7_relset_1(all_47_6, all_47_5, all_47_5, all_47_5, all_47_4, % 21.51/3.74 | all_57_0) = all_47_4 & k7_relset_1(all_47_6, all_47_6, all_47_6, % 21.51/3.74 | all_47_5, all_57_1, all_47_4) = all_47_4 & k6_partfun1(all_47_5) = % 21.51/3.74 | all_57_0 & k6_partfun1(all_47_6) = all_57_1 & $i(all_57_0) & % 21.51/3.74 | $i(all_57_1) % 21.51/3.74 | % 21.51/3.74 | ALPHA: (41) implies: % 21.51/3.74 | (42) $i(all_57_1) % 21.51/3.74 | (43) $i(all_57_0) % 21.51/3.74 | (44) k6_partfun1(all_47_6) = all_57_1 % 21.51/3.74 | (45) k6_partfun1(all_47_5) = all_57_0 % 21.51/3.74 | (46) k7_relset_1(all_47_6, all_47_6, all_47_6, all_47_5, all_57_1, % 21.51/3.74 | all_47_4) = all_47_4 % 21.51/3.75 | (47) k7_relset_1(all_47_6, all_47_5, all_47_5, all_47_5, all_47_4, % 21.51/3.75 | all_57_0) = all_47_4 % 21.51/3.75 | % 21.51/3.75 | DELTA: instantiating (35) with fresh symbols all_67_0, all_67_1, all_67_2, % 21.51/3.75 | all_67_3, all_67_4, all_67_5, all_67_6 gives: % 21.51/3.75 | (48) m2_relset_1(all_47_0, all_47_6, all_47_5) = all_67_0 & % 21.51/3.75 | k2_zfmisc_1(all_47_5, all_47_5) = all_67_3 & k2_zfmisc_1(all_47_6, % 21.51/3.75 | all_47_5) = all_67_6 & k1_zfmisc_1(all_67_3) = all_67_2 & % 21.51/3.75 | k1_zfmisc_1(all_67_6) = all_67_5 & m1_subset_1(all_47_1, all_67_2) = % 21.51/3.75 | all_67_1 & m1_subset_1(all_47_4, all_67_5) = all_67_4 & $i(all_67_2) & % 21.51/3.75 | $i(all_67_3) & $i(all_67_5) & $i(all_67_6) & ( ~ (all_67_1 = 0) | ~ % 21.51/3.75 | (all_67_4 = 0) | all_67_0 = 0) % 21.51/3.75 | % 21.51/3.75 | ALPHA: (48) implies: % 21.51/3.75 | (49) m1_subset_1(all_47_4, all_67_5) = all_67_4 % 21.51/3.75 | (50) m1_subset_1(all_47_1, all_67_2) = all_67_1 % 21.51/3.75 | (51) k1_zfmisc_1(all_67_6) = all_67_5 % 21.51/3.75 | (52) k1_zfmisc_1(all_67_3) = all_67_2 % 21.51/3.75 | (53) k2_zfmisc_1(all_47_6, all_47_5) = all_67_6 % 21.51/3.75 | (54) k2_zfmisc_1(all_47_5, all_47_5) = all_67_3 % 21.51/3.75 | % 21.51/3.75 | DELTA: instantiating (33) with fresh symbols all_69_0, all_69_1, all_69_2, % 21.51/3.75 | all_69_3, all_69_4, all_69_5, all_69_6 gives: % 21.51/3.75 | (55) m2_relset_1(all_47_2, all_47_6, all_47_5) = all_69_0 & % 21.51/3.75 | k2_zfmisc_1(all_47_6, all_47_5) = all_69_3 & k2_zfmisc_1(all_47_6, % 21.51/3.75 | all_47_6) = all_69_6 & k1_zfmisc_1(all_69_3) = all_69_2 & % 21.51/3.75 | k1_zfmisc_1(all_69_6) = all_69_5 & m1_subset_1(all_47_3, all_69_5) = % 21.51/3.75 | all_69_4 & m1_subset_1(all_47_4, all_69_2) = all_69_1 & $i(all_69_2) & % 21.51/3.75 | $i(all_69_3) & $i(all_69_5) & $i(all_69_6) & ( ~ (all_69_1 = 0) | ~ % 21.51/3.75 | (all_69_4 = 0) | all_69_0 = 0) % 21.51/3.75 | % 21.51/3.75 | ALPHA: (55) implies: % 21.51/3.75 | (56) m1_subset_1(all_47_4, all_69_2) = all_69_1 % 21.51/3.75 | (57) m1_subset_1(all_47_3, all_69_5) = all_69_4 % 21.51/3.75 | (58) k1_zfmisc_1(all_69_6) = all_69_5 % 21.51/3.75 | (59) k1_zfmisc_1(all_69_3) = all_69_2 % 21.51/3.75 | (60) k2_zfmisc_1(all_47_6, all_47_6) = all_69_6 % 21.51/3.75 | (61) k2_zfmisc_1(all_47_6, all_47_5) = all_69_3 % 21.51/3.75 | % 21.51/3.75 | DELTA: instantiating (34) with fresh symbols all_71_0, all_71_1, all_71_2, % 21.51/3.75 | all_71_3, all_71_4, all_71_5, all_71_6 gives: % 21.51/3.75 | (62) k5_relat_1(all_47_3, all_47_4) = all_71_0 & k2_zfmisc_1(all_47_6, % 21.51/3.75 | all_47_5) = all_71_3 & k2_zfmisc_1(all_47_6, all_47_6) = all_71_6 & % 21.51/3.75 | k1_zfmisc_1(all_71_3) = all_71_2 & k1_zfmisc_1(all_71_6) = all_71_5 & % 21.51/3.75 | m1_subset_1(all_47_3, all_71_5) = all_71_4 & m1_subset_1(all_47_4, % 21.51/3.75 | all_71_2) = all_71_1 & $i(all_71_0) & $i(all_71_2) & $i(all_71_3) & % 21.51/3.75 | $i(all_71_5) & $i(all_71_6) & ( ~ (all_71_1 = 0) | ~ (all_71_4 = 0) | % 21.51/3.75 | all_71_0 = all_47_2) % 21.51/3.75 | % 21.51/3.75 | ALPHA: (62) implies: % 21.51/3.75 | (63) m1_subset_1(all_47_4, all_71_2) = all_71_1 % 21.51/3.75 | (64) m1_subset_1(all_47_3, all_71_5) = all_71_4 % 21.51/3.75 | (65) k1_zfmisc_1(all_71_6) = all_71_5 % 21.51/3.75 | (66) k1_zfmisc_1(all_71_3) = all_71_2 % 21.51/3.75 | (67) k2_zfmisc_1(all_47_6, all_47_6) = all_71_6 % 21.51/3.75 | (68) k2_zfmisc_1(all_47_6, all_47_5) = all_71_3 % 21.51/3.75 | (69) k5_relat_1(all_47_3, all_47_4) = all_71_0 % 21.51/3.75 | (70) ~ (all_71_1 = 0) | ~ (all_71_4 = 0) | all_71_0 = all_47_2 % 21.51/3.75 | % 21.51/3.75 | DELTA: instantiating (36) with fresh symbols all_73_0, all_73_1, all_73_2, % 21.51/3.75 | all_73_3, all_73_4, all_73_5, all_73_6 gives: % 21.51/3.75 | (71) k5_relat_1(all_47_4, all_47_1) = all_73_0 & k2_zfmisc_1(all_47_5, % 21.51/3.75 | all_47_5) = all_73_3 & k2_zfmisc_1(all_47_6, all_47_5) = all_73_6 & % 21.51/3.75 | k1_zfmisc_1(all_73_3) = all_73_2 & k1_zfmisc_1(all_73_6) = all_73_5 & % 21.51/3.75 | m1_subset_1(all_47_1, all_73_2) = all_73_1 & m1_subset_1(all_47_4, % 21.51/3.75 | all_73_5) = all_73_4 & $i(all_73_0) & $i(all_73_2) & $i(all_73_3) & % 21.51/3.76 | $i(all_73_5) & $i(all_73_6) & ( ~ (all_73_1 = 0) | ~ (all_73_4 = 0) | % 21.51/3.76 | all_73_0 = all_47_0) % 21.51/3.76 | % 21.51/3.76 | ALPHA: (71) implies: % 21.51/3.76 | (72) m1_subset_1(all_47_4, all_73_5) = all_73_4 % 21.51/3.76 | (73) m1_subset_1(all_47_1, all_73_2) = all_73_1 % 21.51/3.76 | (74) k1_zfmisc_1(all_73_6) = all_73_5 % 21.51/3.76 | (75) k1_zfmisc_1(all_73_3) = all_73_2 % 21.51/3.76 | (76) k2_zfmisc_1(all_47_6, all_47_5) = all_73_6 % 21.51/3.76 | (77) k2_zfmisc_1(all_47_5, all_47_5) = all_73_3 % 21.51/3.76 | (78) k5_relat_1(all_47_4, all_47_1) = all_73_0 % 21.51/3.76 | (79) ~ (all_73_1 = 0) | ~ (all_73_4 = 0) | all_73_0 = all_47_0 % 21.51/3.76 | % 21.51/3.76 | GROUND_INST: instantiating (10) with all_69_6, all_71_6, all_47_6, all_47_6, % 21.51/3.76 | simplifying with (60), (67) gives: % 21.51/3.76 | (80) all_71_6 = all_69_6 % 21.51/3.76 | % 21.51/3.76 | GROUND_INST: instantiating (10) with all_67_6, all_71_3, all_47_5, all_47_6, % 21.51/3.76 | simplifying with (53), (68) gives: % 21.51/3.76 | (81) all_71_3 = all_67_6 % 21.51/3.76 | % 21.51/3.76 | GROUND_INST: instantiating (10) with all_55_1, all_71_3, all_47_5, all_47_6, % 21.51/3.76 | simplifying with (40), (68) gives: % 21.51/3.76 | (82) all_71_3 = all_55_1 % 21.51/3.76 | % 21.51/3.76 | GROUND_INST: instantiating (10) with all_71_3, all_73_6, all_47_5, all_47_6, % 21.51/3.76 | simplifying with (68), (76) gives: % 21.51/3.76 | (83) all_73_6 = all_71_3 % 21.51/3.76 | % 21.51/3.76 | GROUND_INST: instantiating (10) with all_69_3, all_73_6, all_47_5, all_47_6, % 21.51/3.76 | simplifying with (61), (76) gives: % 21.51/3.76 | (84) all_73_6 = all_69_3 % 21.51/3.76 | % 21.51/3.76 | GROUND_INST: instantiating (10) with all_67_3, all_73_3, all_47_5, all_47_5, % 21.51/3.76 | simplifying with (54), (77) gives: % 21.51/3.76 | (85) all_73_3 = all_67_3 % 21.51/3.76 | % 21.51/3.76 | GROUND_INST: instantiating (8) with all_47_3, all_57_1, all_47_6, simplifying % 21.51/3.76 | with (19), (44) gives: % 21.51/3.76 | (86) all_57_1 = all_47_3 % 21.51/3.76 | % 21.51/3.76 | GROUND_INST: instantiating (8) with all_47_1, all_57_0, all_47_5, simplifying % 21.51/3.76 | with (20), (45) gives: % 21.51/3.76 | (87) all_57_0 = all_47_1 % 21.51/3.76 | % 21.51/3.76 | COMBINE_EQS: (83), (84) imply: % 21.51/3.76 | (88) all_71_3 = all_69_3 % 21.51/3.76 | % 21.51/3.76 | SIMP: (88) implies: % 21.51/3.76 | (89) all_71_3 = all_69_3 % 21.51/3.76 | % 21.51/3.76 | COMBINE_EQS: (82), (89) imply: % 21.51/3.76 | (90) all_69_3 = all_55_1 % 21.51/3.76 | % 21.51/3.76 | COMBINE_EQS: (81), (89) imply: % 21.51/3.76 | (91) all_69_3 = all_67_6 % 21.51/3.76 | % 21.51/3.76 | COMBINE_EQS: (90), (91) imply: % 21.51/3.76 | (92) all_67_6 = all_55_1 % 21.51/3.76 | % 21.51/3.76 | SIMP: (92) implies: % 21.51/3.76 | (93) all_67_6 = all_55_1 % 21.51/3.76 | % 21.51/3.76 | COMBINE_EQS: (84), (90) imply: % 21.51/3.76 | (94) all_73_6 = all_55_1 % 21.51/3.76 | % 21.51/3.76 | REDUCE: (47), (87) imply: % 21.51/3.76 | (95) k7_relset_1(all_47_6, all_47_5, all_47_5, all_47_5, all_47_4, % 21.51/3.76 | all_47_1) = all_47_4 % 21.51/3.76 | % 21.51/3.76 | REDUCE: (46), (86) imply: % 21.51/3.76 | (96) k7_relset_1(all_47_6, all_47_6, all_47_6, all_47_5, all_47_3, % 21.51/3.76 | all_47_4) = all_47_4 % 21.51/3.76 | % 21.51/3.76 | REDUCE: (75), (85) imply: % 21.51/3.77 | (97) k1_zfmisc_1(all_67_3) = all_73_2 % 21.51/3.77 | % 21.51/3.77 | REDUCE: (74), (94) imply: % 21.51/3.77 | (98) k1_zfmisc_1(all_55_1) = all_73_5 % 21.51/3.77 | % 21.51/3.77 | REDUCE: (66), (82) imply: % 21.85/3.77 | (99) k1_zfmisc_1(all_55_1) = all_71_2 % 21.85/3.77 | % 21.85/3.77 | REDUCE: (65), (80) imply: % 21.85/3.77 | (100) k1_zfmisc_1(all_69_6) = all_71_5 % 21.85/3.77 | % 21.85/3.77 | REDUCE: (59), (90) imply: % 21.85/3.77 | (101) k1_zfmisc_1(all_55_1) = all_69_2 % 21.85/3.77 | % 21.85/3.77 | REDUCE: (51), (93) imply: % 21.85/3.77 | (102) k1_zfmisc_1(all_55_1) = all_67_5 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (7) with all_55_0, all_73_5, all_55_1, simplifying % 21.85/3.77 | with (39), (98) gives: % 21.85/3.77 | (103) all_73_5 = all_55_0 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (7) with all_71_2, all_73_5, all_55_1, simplifying % 21.85/3.77 | with (98), (99) gives: % 21.85/3.77 | (104) all_73_5 = all_71_2 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (7) with all_69_2, all_73_5, all_55_1, simplifying % 21.85/3.77 | with (98), (101) gives: % 21.85/3.77 | (105) all_73_5 = all_69_2 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (7) with all_67_5, all_73_5, all_55_1, simplifying % 21.85/3.77 | with (98), (102) gives: % 21.85/3.77 | (106) all_73_5 = all_67_5 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (7) with all_67_2, all_73_2, all_67_3, simplifying % 21.85/3.77 | with (52), (97) gives: % 21.85/3.77 | (107) all_73_2 = all_67_2 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (7) with all_69_5, all_71_5, all_69_6, simplifying % 21.85/3.77 | with (58), (100) gives: % 21.85/3.77 | (108) all_71_5 = all_69_5 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (103), (104) imply: % 21.85/3.77 | (109) all_71_2 = all_55_0 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (104), (106) imply: % 21.85/3.77 | (110) all_71_2 = all_67_5 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (104), (105) imply: % 21.85/3.77 | (111) all_71_2 = all_69_2 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (109), (111) imply: % 21.85/3.77 | (112) all_69_2 = all_55_0 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (110), (111) imply: % 21.85/3.77 | (113) all_69_2 = all_67_5 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (112), (113) imply: % 21.85/3.77 | (114) all_67_5 = all_55_0 % 21.85/3.77 | % 21.85/3.77 | SIMP: (114) implies: % 21.85/3.77 | (115) all_67_5 = all_55_0 % 21.85/3.77 | % 21.85/3.77 | REDUCE: (73), (107) imply: % 21.85/3.77 | (116) m1_subset_1(all_47_1, all_67_2) = all_73_1 % 21.85/3.77 | % 21.85/3.77 | REDUCE: (64), (108) imply: % 21.85/3.77 | (117) m1_subset_1(all_47_3, all_69_5) = all_71_4 % 21.85/3.77 | % 21.85/3.77 | REDUCE: (72), (103) imply: % 21.85/3.77 | (118) m1_subset_1(all_47_4, all_55_0) = all_73_4 % 21.85/3.77 | % 21.85/3.77 | REDUCE: (63), (109) imply: % 21.85/3.77 | (119) m1_subset_1(all_47_4, all_55_0) = all_71_1 % 21.85/3.77 | % 21.85/3.77 | REDUCE: (56), (112) imply: % 21.85/3.77 | (120) m1_subset_1(all_47_4, all_55_0) = all_69_1 % 21.85/3.77 | % 21.85/3.77 | REDUCE: (49), (115) imply: % 21.85/3.77 | (121) m1_subset_1(all_47_4, all_55_0) = all_67_4 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (9) with 0, all_71_1, all_55_0, all_47_4, % 21.85/3.77 | simplifying with (38), (119) gives: % 21.85/3.77 | (122) all_71_1 = 0 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (9) with all_69_1, all_71_1, all_55_0, all_47_4, % 21.85/3.77 | simplifying with (119), (120) gives: % 21.85/3.77 | (123) all_71_1 = all_69_1 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (9) with all_69_1, all_73_4, all_55_0, all_47_4, % 21.85/3.77 | simplifying with (118), (120) gives: % 21.85/3.77 | (124) all_73_4 = all_69_1 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (9) with all_67_4, all_73_4, all_55_0, all_47_4, % 21.85/3.77 | simplifying with (118), (121) gives: % 21.85/3.77 | (125) all_73_4 = all_67_4 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (9) with all_69_4, all_71_4, all_69_5, all_47_3, % 21.85/3.77 | simplifying with (57), (117) gives: % 21.85/3.77 | (126) all_71_4 = all_69_4 % 21.85/3.77 | % 21.85/3.77 | GROUND_INST: instantiating (9) with all_67_1, all_73_1, all_67_2, all_47_1, % 21.85/3.77 | simplifying with (50), (116) gives: % 21.85/3.77 | (127) all_73_1 = all_67_1 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (124), (125) imply: % 21.85/3.77 | (128) all_69_1 = all_67_4 % 21.85/3.77 | % 21.85/3.77 | SIMP: (128) implies: % 21.85/3.77 | (129) all_69_1 = all_67_4 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (122), (123) imply: % 21.85/3.77 | (130) all_69_1 = 0 % 21.85/3.77 | % 21.85/3.77 | SIMP: (130) implies: % 21.85/3.77 | (131) all_69_1 = 0 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (129), (131) imply: % 21.85/3.77 | (132) all_67_4 = 0 % 21.85/3.77 | % 21.85/3.77 | SIMP: (132) implies: % 21.85/3.77 | (133) all_67_4 = 0 % 21.85/3.77 | % 21.85/3.77 | COMBINE_EQS: (125), (133) imply: % 21.85/3.77 | (134) all_73_4 = 0 % 21.85/3.77 | % 21.85/3.78 | GROUND_INST: instantiating (3) with all_47_6, all_47_6, all_47_3, all_69_6, % 21.85/3.78 | all_69_5, all_69_4, simplifying with (16), (26), (57), (58), (60) % 21.85/3.78 | gives: % 21.85/3.78 | (135) all_69_4 = 0 | ? [v0: int] : ( ~ (v0 = 0) & m2_relset_1(all_47_3, % 21.85/3.78 | all_47_6, all_47_6) = v0) % 21.85/3.78 | % 21.85/3.78 | GROUND_INST: instantiating (3) with all_47_5, all_47_5, all_47_1, all_67_3, % 21.85/3.78 | all_67_2, all_67_1, simplifying with (17), (29), (50), (52), (54) % 21.85/3.78 | gives: % 21.85/3.78 | (136) all_67_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & m2_relset_1(all_47_1, % 21.85/3.78 | all_47_5, all_47_5) = v0) % 21.85/3.78 | % 21.85/3.78 | GROUND_INST: instantiating (5) with all_47_6, all_47_6, all_47_3, simplifying % 21.85/3.78 | with (16), (24), (26) gives: % 21.85/3.78 | (137) m1_relset_1(all_47_3, all_47_6, all_47_6) = 0 % 21.85/3.78 | % 21.85/3.78 | GROUND_INST: instantiating (5) with all_47_5, all_47_5, all_47_1, simplifying % 21.85/3.78 | with (17), (27), (29) gives: % 21.85/3.78 | (138) m1_relset_1(all_47_1, all_47_5, all_47_5) = 0 % 21.85/3.78 | % 21.85/3.78 | GROUND_INST: instantiating (dt_k7_relset_1) with all_47_6, all_47_6, all_47_6, % 21.85/3.78 | all_47_5, all_47_3, all_47_4, all_47_4, simplifying with (16), % 21.85/3.78 | (17), (18), (26), (96) gives: % 21.85/3.78 | (139) ? [v0: any] : ? [v1: any] : ? [v2: any] : (m1_relset_1(all_47_3, % 21.85/3.78 | all_47_6, all_47_6) = v0 & m1_relset_1(all_47_4, all_47_6, % 21.85/3.78 | all_47_5) = v1 & m2_relset_1(all_47_4, all_47_6, all_47_5) = v2 & % 21.85/3.78 | ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 21.85/3.78 | % 21.85/3.78 | GROUND_INST: instantiating (redefinition_k7_relset_1) with all_47_6, all_47_6, % 21.85/3.78 | all_47_6, all_47_5, all_47_3, all_47_4, all_47_4, simplifying % 21.85/3.78 | with (16), (17), (18), (26), (96) gives: % 21.85/3.78 | (140) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (m1_relset_1(all_47_3, % 21.85/3.78 | all_47_6, all_47_6) = v0 & m1_relset_1(all_47_4, all_47_6, % 21.85/3.78 | all_47_5) = v1 & k5_relat_1(all_47_3, all_47_4) = v2 & $i(v2) & ( % 21.85/3.78 | ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_47_4)) % 21.85/3.78 | % 21.85/3.78 | GROUND_INST: instantiating (dt_k7_relset_1) with all_47_6, all_47_5, all_47_5, % 21.85/3.78 | all_47_5, all_47_4, all_47_1, all_47_4, simplifying with (16), % 21.85/3.78 | (17), (18), (29), (95) gives: % 21.85/3.78 | (141) ? [v0: any] : ? [v1: any] : ? [v2: any] : (m1_relset_1(all_47_1, % 21.85/3.78 | all_47_5, all_47_5) = v1 & m1_relset_1(all_47_4, all_47_6, % 21.85/3.78 | all_47_5) = v0 & m2_relset_1(all_47_4, all_47_6, all_47_5) = v2 & % 21.85/3.78 | ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 21.85/3.78 | % 21.85/3.78 | GROUND_INST: instantiating (redefinition_k7_relset_1) with all_47_6, all_47_5, % 21.85/3.78 | all_47_5, all_47_5, all_47_4, all_47_1, all_47_4, simplifying % 21.85/3.78 | with (16), (17), (18), (29), (95) gives: % 21.85/3.78 | (142) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (m1_relset_1(all_47_1, % 21.85/3.78 | all_47_5, all_47_5) = v1 & m1_relset_1(all_47_4, all_47_6, % 21.85/3.78 | all_47_5) = v0 & k5_relat_1(all_47_4, all_47_1) = v2 & $i(v2) & ( % 21.85/3.78 | ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_47_4)) % 21.85/3.78 | % 21.85/3.78 | DELTA: instantiating (141) with fresh symbols all_125_0, all_125_1, all_125_2 % 21.85/3.78 | gives: % 21.85/3.78 | (143) m1_relset_1(all_47_1, all_47_5, all_47_5) = all_125_1 & % 21.85/3.78 | m1_relset_1(all_47_4, all_47_6, all_47_5) = all_125_2 & % 21.85/3.78 | m2_relset_1(all_47_4, all_47_6, all_47_5) = all_125_0 & ( ~ % 21.85/3.78 | (all_125_1 = 0) | ~ (all_125_2 = 0) | all_125_0 = 0) % 21.85/3.78 | % 21.85/3.78 | ALPHA: (143) implies: % 21.85/3.78 | (144) m1_relset_1(all_47_4, all_47_6, all_47_5) = all_125_2 % 21.85/3.78 | (145) m1_relset_1(all_47_1, all_47_5, all_47_5) = all_125_1 % 21.85/3.78 | % 21.85/3.78 | DELTA: instantiating (139) with fresh symbols all_127_0, all_127_1, all_127_2 % 21.85/3.78 | gives: % 21.85/3.78 | (146) m1_relset_1(all_47_3, all_47_6, all_47_6) = all_127_2 & % 21.85/3.78 | m1_relset_1(all_47_4, all_47_6, all_47_5) = all_127_1 & % 21.85/3.78 | m2_relset_1(all_47_4, all_47_6, all_47_5) = all_127_0 & ( ~ % 21.85/3.78 | (all_127_1 = 0) | ~ (all_127_2 = 0) | all_127_0 = 0) % 21.85/3.78 | % 21.85/3.78 | ALPHA: (146) implies: % 21.85/3.78 | (147) m1_relset_1(all_47_4, all_47_6, all_47_5) = all_127_1 % 21.85/3.78 | % 21.85/3.78 | DELTA: instantiating (140) with fresh symbols all_141_0, all_141_1, all_141_2 % 21.85/3.78 | gives: % 21.85/3.78 | (148) m1_relset_1(all_47_3, all_47_6, all_47_6) = all_141_2 & % 21.85/3.78 | m1_relset_1(all_47_4, all_47_6, all_47_5) = all_141_1 & % 21.85/3.78 | k5_relat_1(all_47_3, all_47_4) = all_141_0 & $i(all_141_0) & ( ~ % 21.85/3.78 | (all_141_1 = 0) | ~ (all_141_2 = 0) | all_141_0 = all_47_4) % 21.85/3.78 | % 21.85/3.78 | ALPHA: (148) implies: % 21.85/3.78 | (149) k5_relat_1(all_47_3, all_47_4) = all_141_0 % 21.85/3.78 | (150) m1_relset_1(all_47_4, all_47_6, all_47_5) = all_141_1 % 21.85/3.78 | (151) m1_relset_1(all_47_3, all_47_6, all_47_6) = all_141_2 % 21.85/3.78 | (152) ~ (all_141_1 = 0) | ~ (all_141_2 = 0) | all_141_0 = all_47_4 % 21.85/3.78 | % 21.85/3.78 | DELTA: instantiating (142) with fresh symbols all_155_0, all_155_1, all_155_2 % 21.85/3.79 | gives: % 21.85/3.79 | (153) m1_relset_1(all_47_1, all_47_5, all_47_5) = all_155_1 & % 21.85/3.79 | m1_relset_1(all_47_4, all_47_6, all_47_5) = all_155_2 & % 21.85/3.79 | k5_relat_1(all_47_4, all_47_1) = all_155_0 & $i(all_155_0) & ( ~ % 21.85/3.79 | (all_155_1 = 0) | ~ (all_155_2 = 0) | all_155_0 = all_47_4) % 21.85/3.79 | % 21.85/3.79 | ALPHA: (153) implies: % 21.85/3.79 | (154) k5_relat_1(all_47_4, all_47_1) = all_155_0 % 21.85/3.79 | (155) m1_relset_1(all_47_4, all_47_6, all_47_5) = all_155_2 % 21.85/3.79 | (156) m1_relset_1(all_47_1, all_47_5, all_47_5) = all_155_1 % 21.85/3.79 | (157) ~ (all_155_1 = 0) | ~ (all_155_2 = 0) | all_155_0 = all_47_4 % 21.85/3.79 | % 21.85/3.79 | BETA: splitting (136) gives: % 21.85/3.79 | % 21.85/3.79 | Case 1: % 21.85/3.79 | | % 21.85/3.79 | | (158) all_67_1 = 0 % 21.85/3.79 | | % 21.85/3.79 | | COMBINE_EQS: (127), (158) imply: % 21.85/3.79 | | (159) all_73_1 = 0 % 21.85/3.79 | | % 21.85/3.79 | | BETA: splitting (135) gives: % 21.85/3.79 | | % 21.85/3.79 | | Case 1: % 21.85/3.79 | | | % 21.85/3.79 | | | (160) all_69_4 = 0 % 21.85/3.79 | | | % 21.85/3.79 | | | COMBINE_EQS: (126), (160) imply: % 21.85/3.79 | | | (161) all_71_4 = 0 % 21.85/3.79 | | | % 21.85/3.79 | | | BETA: splitting (70) gives: % 21.85/3.79 | | | % 21.85/3.79 | | | Case 1: % 21.85/3.79 | | | | % 21.85/3.79 | | | | (162) ~ (all_71_1 = 0) % 21.85/3.79 | | | | % 21.85/3.79 | | | | REDUCE: (122), (162) imply: % 21.85/3.79 | | | | (163) $false % 21.85/3.79 | | | | % 21.85/3.79 | | | | CLOSE: (163) is inconsistent. % 21.85/3.79 | | | | % 21.85/3.79 | | | Case 2: % 21.85/3.79 | | | | % 21.85/3.79 | | | | (164) ~ (all_71_4 = 0) | all_71_0 = all_47_2 % 21.85/3.79 | | | | % 21.85/3.79 | | | | BETA: splitting (164) gives: % 21.85/3.79 | | | | % 21.85/3.79 | | | | Case 1: % 21.85/3.79 | | | | | % 21.85/3.79 | | | | | (165) ~ (all_71_4 = 0) % 21.85/3.79 | | | | | % 21.85/3.79 | | | | | REDUCE: (161), (165) imply: % 21.85/3.79 | | | | | (166) $false % 21.85/3.79 | | | | | % 21.85/3.79 | | | | | CLOSE: (166) is inconsistent. % 21.85/3.79 | | | | | % 21.85/3.79 | | | | Case 2: % 21.85/3.79 | | | | | % 21.85/3.79 | | | | | (167) all_71_0 = all_47_2 % 21.85/3.79 | | | | | % 21.85/3.79 | | | | | REDUCE: (69), (167) imply: % 21.85/3.79 | | | | | (168) k5_relat_1(all_47_3, all_47_4) = all_47_2 % 21.85/3.79 | | | | | % 21.85/3.79 | | | | | BETA: splitting (79) gives: % 21.85/3.79 | | | | | % 21.85/3.79 | | | | | Case 1: % 21.85/3.79 | | | | | | % 21.85/3.79 | | | | | | (169) ~ (all_73_1 = 0) % 21.85/3.79 | | | | | | % 21.85/3.79 | | | | | | REDUCE: (159), (169) imply: % 21.85/3.79 | | | | | | (170) $false % 21.85/3.79 | | | | | | % 21.85/3.79 | | | | | | CLOSE: (170) is inconsistent. % 21.85/3.79 | | | | | | % 21.85/3.79 | | | | | Case 2: % 21.85/3.79 | | | | | | % 21.85/3.79 | | | | | | (171) ~ (all_73_4 = 0) | all_73_0 = all_47_0 % 21.85/3.79 | | | | | | % 21.85/3.79 | | | | | | BETA: splitting (171) gives: % 21.85/3.79 | | | | | | % 21.85/3.79 | | | | | | Case 1: % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | (172) ~ (all_73_4 = 0) % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | REDUCE: (134), (172) imply: % 21.85/3.79 | | | | | | | (173) $false % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | CLOSE: (173) is inconsistent. % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | Case 2: % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | (174) all_73_0 = all_47_0 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | REDUCE: (78), (174) imply: % 21.85/3.79 | | | | | | | (175) k5_relat_1(all_47_4, all_47_1) = all_47_0 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | GROUND_INST: instantiating (11) with all_47_0, all_155_0, % 21.85/3.79 | | | | | | | all_47_1, all_47_4, simplifying with (154), (175) % 21.85/3.79 | | | | | | | gives: % 21.85/3.79 | | | | | | | (176) all_155_0 = all_47_0 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | GROUND_INST: instantiating (11) with all_47_2, all_141_0, % 21.85/3.79 | | | | | | | all_47_4, all_47_3, simplifying with (149), (168) % 21.85/3.79 | | | | | | | gives: % 21.85/3.79 | | | | | | | (177) all_141_0 = all_47_2 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | GROUND_INST: instantiating (13) with 0, all_127_1, all_47_5, % 21.85/3.79 | | | | | | | all_47_6, all_47_4, simplifying with (30), (147) % 21.85/3.79 | | | | | | | gives: % 21.85/3.79 | | | | | | | (178) all_127_1 = 0 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | GROUND_INST: instantiating (13) with all_127_1, all_141_1, % 21.85/3.79 | | | | | | | all_47_5, all_47_6, all_47_4, simplifying with (147), % 21.85/3.79 | | | | | | | (150) gives: % 21.85/3.79 | | | | | | | (179) all_141_1 = all_127_1 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | GROUND_INST: instantiating (13) with all_141_1, all_155_2, % 21.85/3.79 | | | | | | | all_47_5, all_47_6, all_47_4, simplifying with (150), % 21.85/3.79 | | | | | | | (155) gives: % 21.85/3.79 | | | | | | | (180) all_155_2 = all_141_1 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | GROUND_INST: instantiating (13) with all_125_2, all_155_2, % 21.85/3.79 | | | | | | | all_47_5, all_47_6, all_47_4, simplifying with (144), % 21.85/3.79 | | | | | | | (155) gives: % 21.85/3.79 | | | | | | | (181) all_155_2 = all_125_2 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | GROUND_INST: instantiating (13) with 0, all_141_2, all_47_6, % 21.85/3.79 | | | | | | | all_47_6, all_47_3, simplifying with (137), (151) % 21.85/3.79 | | | | | | | gives: % 21.85/3.79 | | | | | | | (182) all_141_2 = 0 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | GROUND_INST: instantiating (13) with all_125_1, all_155_1, % 21.85/3.79 | | | | | | | all_47_5, all_47_5, all_47_1, simplifying with (145), % 21.85/3.79 | | | | | | | (156) gives: % 21.85/3.79 | | | | | | | (183) all_155_1 = all_125_1 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | GROUND_INST: instantiating (13) with 0, all_155_1, all_47_5, % 21.85/3.79 | | | | | | | all_47_5, all_47_1, simplifying with (138), (156) % 21.85/3.79 | | | | | | | gives: % 21.85/3.79 | | | | | | | (184) all_155_1 = 0 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | COMBINE_EQS: (183), (184) imply: % 21.85/3.79 | | | | | | | (185) all_125_1 = 0 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | COMBINE_EQS: (180), (181) imply: % 21.85/3.79 | | | | | | | (186) all_141_1 = all_125_2 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | SIMP: (186) implies: % 21.85/3.79 | | | | | | | (187) all_141_1 = all_125_2 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | COMBINE_EQS: (179), (187) imply: % 21.85/3.79 | | | | | | | (188) all_127_1 = all_125_2 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | SIMP: (188) implies: % 21.85/3.79 | | | | | | | (189) all_127_1 = all_125_2 % 21.85/3.79 | | | | | | | % 21.85/3.79 | | | | | | | COMBINE_EQS: (178), (189) imply: % 21.85/3.80 | | | | | | | (190) all_125_2 = 0 % 21.85/3.80 | | | | | | | % 21.85/3.80 | | | | | | | COMBINE_EQS: (187), (190) imply: % 21.85/3.80 | | | | | | | (191) all_141_1 = 0 % 21.85/3.80 | | | | | | | % 21.85/3.80 | | | | | | | COMBINE_EQS: (181), (190) imply: % 21.85/3.80 | | | | | | | (192) all_155_2 = 0 % 21.85/3.80 | | | | | | | % 21.85/3.80 | | | | | | | BETA: splitting (157) gives: % 21.85/3.80 | | | | | | | % 21.85/3.80 | | | | | | | Case 1: % 21.85/3.80 | | | | | | | | % 21.85/3.80 | | | | | | | | (193) ~ (all_155_1 = 0) % 21.85/3.80 | | | | | | | | % 21.85/3.80 | | | | | | | | REDUCE: (184), (193) imply: % 21.85/3.80 | | | | | | | | (194) $false % 21.85/3.80 | | | | | | | | % 21.85/3.80 | | | | | | | | CLOSE: (194) is inconsistent. % 21.85/3.80 | | | | | | | | % 21.85/3.80 | | | | | | | Case 2: % 21.85/3.80 | | | | | | | | % 21.85/3.80 | | | | | | | | (195) ~ (all_155_2 = 0) | all_155_0 = all_47_4 % 21.85/3.80 | | | | | | | | % 21.85/3.80 | | | | | | | | BETA: splitting (152) gives: % 21.85/3.80 | | | | | | | | % 21.85/3.80 | | | | | | | | Case 1: % 21.85/3.80 | | | | | | | | | % 21.85/3.80 | | | | | | | | | (196) ~ (all_141_1 = 0) % 21.85/3.80 | | | | | | | | | % 21.85/3.80 | | | | | | | | | REDUCE: (191), (196) imply: % 21.85/3.80 | | | | | | | | | (197) $false % 21.85/3.80 | | | | | | | | | % 21.85/3.80 | | | | | | | | | CLOSE: (197) is inconsistent. % 21.85/3.80 | | | | | | | | | % 21.85/3.80 | | | | | | | | Case 2: % 21.85/3.80 | | | | | | | | | % 21.85/3.80 | | | | | | | | | (198) ~ (all_141_2 = 0) | all_141_0 = all_47_4 % 21.85/3.80 | | | | | | | | | % 21.85/3.80 | | | | | | | | | BETA: splitting (198) gives: % 21.85/3.80 | | | | | | | | | % 21.85/3.80 | | | | | | | | | Case 1: % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | (199) ~ (all_141_2 = 0) % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | REDUCE: (182), (199) imply: % 21.85/3.80 | | | | | | | | | | (200) $false % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | CLOSE: (200) is inconsistent. % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | Case 2: % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | (201) all_141_0 = all_47_4 % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | COMBINE_EQS: (177), (201) imply: % 21.85/3.80 | | | | | | | | | | (202) all_47_2 = all_47_4 % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | SIMP: (202) implies: % 21.85/3.80 | | | | | | | | | | (203) all_47_2 = all_47_4 % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | REDUCE: (15), (203) imply: % 21.85/3.80 | | | | | | | | | | (204) ~ (all_47_0 = all_47_4) % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | BETA: splitting (195) gives: % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | Case 1: % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | | (205) ~ (all_155_2 = 0) % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | | REDUCE: (192), (205) imply: % 21.85/3.80 | | | | | | | | | | | (206) $false % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | | CLOSE: (206) is inconsistent. % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | Case 2: % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | | (207) all_155_0 = all_47_4 % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | | COMBINE_EQS: (176), (207) imply: % 21.85/3.80 | | | | | | | | | | | (208) all_47_0 = all_47_4 % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | | SIMP: (208) implies: % 21.85/3.80 | | | | | | | | | | | (209) all_47_0 = all_47_4 % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | | REDUCE: (204), (209) imply: % 21.85/3.80 | | | | | | | | | | | (210) $false % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | | CLOSE: (210) is inconsistent. % 21.85/3.80 | | | | | | | | | | | % 21.85/3.80 | | | | | | | | | | End of split % 21.85/3.80 | | | | | | | | | | % 21.85/3.80 | | | | | | | | | End of split % 21.85/3.80 | | | | | | | | | % 21.85/3.80 | | | | | | | | End of split % 21.85/3.80 | | | | | | | | % 21.85/3.80 | | | | | | | End of split % 21.85/3.80 | | | | | | | % 21.85/3.80 | | | | | | End of split % 21.85/3.80 | | | | | | % 21.85/3.80 | | | | | End of split % 21.85/3.80 | | | | | % 21.85/3.80 | | | | End of split % 21.85/3.80 | | | | % 21.85/3.80 | | | End of split % 21.85/3.80 | | | % 21.85/3.80 | | Case 2: % 21.85/3.80 | | | % 21.85/3.80 | | | (211) ? [v0: int] : ( ~ (v0 = 0) & m2_relset_1(all_47_3, all_47_6, % 21.85/3.80 | | | all_47_6) = v0) % 21.85/3.80 | | | % 21.85/3.80 | | | DELTA: instantiating (211) with fresh symbol all_184_0 gives: % 21.85/3.80 | | | (212) ~ (all_184_0 = 0) & m2_relset_1(all_47_3, all_47_6, all_47_6) = % 21.85/3.80 | | | all_184_0 % 21.85/3.80 | | | % 21.85/3.80 | | | ALPHA: (212) implies: % 21.85/3.80 | | | (213) ~ (all_184_0 = 0) % 21.85/3.80 | | | (214) m2_relset_1(all_47_3, all_47_6, all_47_6) = all_184_0 % 21.85/3.80 | | | % 21.85/3.80 | | | GROUND_INST: instantiating (12) with 0, all_184_0, all_47_6, all_47_6, % 21.85/3.80 | | | all_47_3, simplifying with (24), (214) gives: % 21.85/3.80 | | | (215) all_184_0 = 0 % 21.85/3.80 | | | % 21.85/3.80 | | | REDUCE: (213), (215) imply: % 21.85/3.80 | | | (216) $false % 21.85/3.80 | | | % 21.85/3.80 | | | CLOSE: (216) is inconsistent. % 21.85/3.80 | | | % 21.85/3.80 | | End of split % 21.85/3.80 | | % 21.85/3.80 | Case 2: % 21.85/3.80 | | % 21.85/3.80 | | (217) ? [v0: int] : ( ~ (v0 = 0) & m2_relset_1(all_47_1, all_47_5, % 21.85/3.80 | | all_47_5) = v0) % 21.85/3.80 | | % 21.85/3.80 | | DELTA: instantiating (217) with fresh symbol all_171_0 gives: % 21.85/3.80 | | (218) ~ (all_171_0 = 0) & m2_relset_1(all_47_1, all_47_5, all_47_5) = % 21.85/3.80 | | all_171_0 % 21.85/3.80 | | % 21.85/3.80 | | ALPHA: (218) implies: % 21.85/3.80 | | (219) ~ (all_171_0 = 0) % 21.85/3.80 | | (220) m2_relset_1(all_47_1, all_47_5, all_47_5) = all_171_0 % 21.85/3.80 | | % 21.85/3.80 | | GROUND_INST: instantiating (12) with 0, all_171_0, all_47_5, all_47_5, % 21.85/3.80 | | all_47_1, simplifying with (27), (220) gives: % 21.85/3.80 | | (221) all_171_0 = 0 % 21.85/3.80 | | % 21.85/3.80 | | REDUCE: (219), (221) imply: % 21.85/3.80 | | (222) $false % 21.85/3.80 | | % 21.85/3.80 | | CLOSE: (222) is inconsistent. % 21.85/3.80 | | % 21.85/3.80 | End of split % 21.85/3.80 | % 21.85/3.80 End of proof % 21.85/3.80 % SZS output end Proof for theBenchmark % 21.85/3.80 % 21.85/3.80 3214ms %------------------------------------------------------------------------------