%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV373+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 : n031.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 22:56:04 EDT 2023 % Result : Theorem 10.24s 2.13s % Output : Proof 13.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SWV373+1 : TPTP v8.1.2. Released v3.3.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n031.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 07:13:11 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.19/1.18 Prover 1: Preprocessing ... % 3.41/1.19 Prover 4: Preprocessing ... % 3.71/1.23 Prover 5: Preprocessing ... % 3.71/1.23 Prover 2: Preprocessing ... % 3.71/1.23 Prover 0: Preprocessing ... % 3.71/1.23 Prover 3: Preprocessing ... % 3.71/1.24 Prover 6: Preprocessing ... % 7.53/1.77 Prover 1: Warning: ignoring some quantifiers % 7.89/1.84 Prover 3: Warning: ignoring some quantifiers % 8.29/1.86 Prover 1: Constructing countermodel ... % 8.29/1.87 Prover 3: Constructing countermodel ... % 8.29/1.88 Prover 6: Proving ... % 8.29/1.89 Prover 4: Constructing countermodel ... % 8.29/1.94 Prover 5: Proving ... % 9.36/2.00 Prover 0: Proving ... % 9.36/2.10 Prover 2: Proving ... % 10.24/2.13 Prover 0: proved (1490ms) % 10.24/2.13 % 10.24/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.24/2.13 % 10.24/2.13 Prover 2: stopped % 10.24/2.13 Prover 6: stopped % 10.24/2.13 Prover 3: stopped % 10.24/2.13 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.24/2.13 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.24/2.13 Prover 5: stopped % 10.24/2.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.24/2.14 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.24/2.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.24/2.18 Prover 10: Preprocessing ... % 10.24/2.19 Prover 13: Preprocessing ... % 10.24/2.19 Prover 11: Preprocessing ... % 10.24/2.19 Prover 7: Preprocessing ... % 10.24/2.20 Prover 8: Preprocessing ... % 11.37/2.32 Prover 4: Found proof (size 83) % 11.37/2.32 Prover 4: proved (1677ms) % 11.37/2.32 Prover 1: stopped % 11.91/2.35 Prover 7: Warning: ignoring some quantifiers % 11.91/2.37 Prover 10: Warning: ignoring some quantifiers % 12.07/2.37 Prover 7: Constructing countermodel ... % 12.07/2.39 Prover 10: Constructing countermodel ... % 12.07/2.39 Prover 7: stopped % 12.07/2.40 Prover 10: stopped % 12.07/2.40 Prover 8: Warning: ignoring some quantifiers % 12.40/2.42 Prover 8: Constructing countermodel ... % 12.40/2.44 Prover 8: stopped % 12.57/2.45 Prover 11: Constructing countermodel ... % 12.57/2.45 Prover 13: Warning: ignoring some quantifiers % 12.57/2.47 Prover 11: stopped % 12.57/2.47 Prover 13: Constructing countermodel ... % 12.57/2.48 Prover 13: stopped % 12.57/2.48 % 12.57/2.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.57/2.49 % 12.57/2.50 % SZS output start Proof for theBenchmark % 12.57/2.50 Assumptions after simplification: % 12.57/2.50 --------------------------------- % 12.57/2.50 % 12.57/2.50 (ax39) % 12.96/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 12.96/2.53 int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = % 12.96/2.53 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ % 12.96/2.53 (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0: $i] : ! [v1: $i] : ! % 12.96/2.53 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (contains_cpq(v4, v3) = 0) | ~ % 12.96/2.53 (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 12.96/2.53 contains_slb(v1, v3) = 0) % 12.96/2.53 % 12.96/2.53 (ax47) % 12.96/2.53 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.96/2.53 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 12.96/2.53 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 12.96/2.53 : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 & % 12.96/2.53 triple(v0, v7, bad) = v8 & update_slb(v1, v5) = v7 & contains_slb(v1, v5) % 12.96/2.53 = v6 & $i(v8) & $i(v7) & $i(v5) & (v8 = v4 | v6 = 0))) % 12.96/2.53 % 12.96/2.54 (ax48) % 12.96/2.54 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 12.96/2.54 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 12.96/2.54 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 12.96/2.54 : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : % 12.96/2.54 (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & update_slb(v1, v5) = % 12.96/2.54 v9 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = v6 & % 12.96/2.54 strictly_less_than(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ % 12.96/2.54 (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 12.96/2.54 % 12.96/2.54 (ax49) % 12.96/2.54 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 12.96/2.54 [v4: $i] : ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ % 12.96/2.54 (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) | ~ % 12.96/2.54 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] % 12.96/2.54 : ? [v10: $i] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & % 12.96/2.54 lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = % 12.96/2.54 v8 & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) % 12.96/2.54 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 12.96/2.54 create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | % 12.96/2.54 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] % 12.96/2.54 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : (findmin_pqp_res(v0) = v5 & % 12.96/2.54 triple(v0, v9, v2) = v10 & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = % 12.96/2.54 v7 & contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & $i(v9) % 12.96/2.54 & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 12.96/2.54 % 12.96/2.54 (ax51) % 12.96/2.55 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 12.96/2.55 [v4: $i] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, % 12.96/2.55 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (findmin_pqp_res(v0) % 12.96/2.55 = v4 & $i(v4))) % 12.96/2.55 % 12.96/2.55 (ax52) % 12.96/2.55 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ? % 12.96/2.55 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = % 12.96/2.55 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: % 12.96/2.55 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 12.96/2.55 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & % 12.96/2.55 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : ! % 12.96/2.55 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 12.96/2.55 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & % 12.96/2.55 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2))) % 12.96/2.55 % 12.96/2.55 (l9_co) % 12.96/2.55 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 12.96/2.55 int] : ? [v6: $i] : ( ~ (v5 = 0) & findmin_cpq_res(v3) = v4 & ok(v6) = 0 & % 12.96/2.55 contains_cpq(v3, v4) = v5 & triple(v0, v1, v2) = v3 & findmin_cpq_eff(v3) = % 12.96/2.55 v6 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.96/2.55 % 12.96/2.55 (l9_l10) % 12.96/2.55 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 12.96/2.55 (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] % 12.96/2.55 : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: any] : % 12.96/2.55 (findmin_pqp_res(v0) = v6 & ok(v4) = v5 & findmin_cpq_eff(v3) = v4 & % 12.96/2.55 lookup_slb(v1, v6) = v8 & contains_slb(v1, v6) = v7 & less_than(v8, v6) = % 12.96/2.55 v9 & $i(v8) & $i(v6) & $i(v4) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0 & ~ (v1 = % 12.96/2.55 create_slb))))) % 12.96/2.55 % 12.96/2.55 (function-axioms) % 12.96/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 12.96/2.56 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 12.96/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.96/2.56 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 12.96/2.56 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 12.96/2.56 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 12.96/2.56 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 12.96/2.56 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 12.96/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.96/2.56 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 12.96/2.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.96/2.56 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 12.96/2.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 12.96/2.56 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.96/2.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 12.96/2.56 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 12.96/2.56 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 12.96/2.56 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 12.96/2.56 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 12.96/2.56 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 12.96/2.56 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 12.96/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 12.96/2.56 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 12.96/2.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.96/2.56 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 12.96/2.56 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 12.96/2.56 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 12.96/2.56 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.96/2.56 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 12.96/2.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.96/2.56 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 12.96/2.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 12.96/2.56 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: % 12.96/2.56 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | % 12.96/2.56 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 12.96/2.56 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! % 12.96/2.56 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 12.96/2.56 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 12.96/2.56 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | % 12.96/2.56 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 12.96/2.56 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! % 12.96/2.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = % 12.96/2.56 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 12.96/2.56 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = % 12.96/2.56 v1) | ~ (isnonempty_slb(v2) = v0)) % 12.96/2.56 % 12.96/2.56 Further assumptions not needed in the proof: % 12.96/2.56 -------------------------------------------- % 12.96/2.56 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 12.96/2.56 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax40, ax41, ax42, ax43, ax44, % 12.96/2.56 ax45, ax46, ax50, ax53, bottom_smallest, reflexivity, % 12.96/2.56 stricly_smaller_definition, totality, transitivity % 12.96/2.56 % 12.96/2.56 Those formulas are unsatisfiable: % 12.96/2.56 --------------------------------- % 12.96/2.56 % 12.96/2.56 Begin of proof % 12.96/2.56 | % 12.96/2.56 | ALPHA: (ax39) implies: % 12.96/2.56 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 12.96/2.56 | ! [v5: int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, % 12.96/2.56 | v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 12.96/2.56 | ? [v6: int] : ( ~ (v6 = 0) & contains_slb(v1, v3) = v6)) % 12.96/2.56 | % 12.96/2.56 | ALPHA: (ax47) implies: % 12.96/2.56 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 12.96/2.56 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 12.96/2.56 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 12.96/2.56 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 12.96/2.56 | (findmin_pqp_res(v0) = v5 & triple(v0, v7, bad) = v8 & update_slb(v1, % 12.96/2.56 | v5) = v7 & contains_slb(v1, v5) = v6 & $i(v8) & $i(v7) & $i(v5) & % 12.96/2.56 | (v8 = v4 | v6 = 0))) % 12.96/2.56 | % 12.96/2.56 | ALPHA: (ax48) implies: % 12.96/2.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 12.96/2.57 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 12.96/2.57 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 12.96/2.57 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 12.96/2.57 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & % 12.96/2.57 | update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 12.96/2.57 | contains_slb(v1, v5) = v6 & strictly_less_than(v5, v7) = v8 & % 12.96/2.57 | $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | % 12.96/2.57 | v10 = v4))) % 12.96/2.57 | % 12.96/2.57 | ALPHA: (ax49) implies: % 12.96/2.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 12.96/2.57 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 12.96/2.57 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 12.96/2.57 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 12.96/2.57 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, v2) = v10 & % 12.96/2.57 | update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 12.96/2.57 | contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & % 12.96/2.57 | $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 12.96/2.57 | % 12.96/2.57 | ALPHA: (ax51) implies: % 12.96/2.57 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 12.96/2.57 | (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, % 12.96/2.57 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 12.96/2.57 | (findmin_pqp_res(v0) = v4 & $i(v4))) % 12.96/2.57 | % 12.96/2.57 | ALPHA: (ax52) implies: % 12.96/2.57 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) % 12.96/2.57 | | ? [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & % 12.96/2.57 | findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2 & $i(v3) & % 12.96/2.57 | $i(v2))) % 12.96/2.57 | % 12.96/2.57 | ALPHA: (l9_l10) implies: % 12.96/2.57 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, % 12.96/2.57 | v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 12.96/2.57 | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: % 12.96/2.57 | any] : (findmin_pqp_res(v0) = v6 & ok(v4) = v5 & % 12.96/2.57 | findmin_cpq_eff(v3) = v4 & lookup_slb(v1, v6) = v8 & % 12.96/2.57 | contains_slb(v1, v6) = v7 & less_than(v8, v6) = v9 & $i(v8) & % 12.96/2.57 | $i(v6) & $i(v4) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0 & ~ (v1 = % 12.96/2.57 | create_slb))))) % 12.96/2.57 | % 12.96/2.57 | ALPHA: (function-axioms) implies: % 12.96/2.57 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 12.96/2.57 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 12.96/2.57 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 12.96/2.57 | (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 13.21/2.57 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 13.21/2.57 | (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 13.21/2.57 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 13.21/2.57 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 13.21/2.57 | (contains_slb(v3, v2) = v0)) % 13.21/2.57 | % 13.21/2.57 | DELTA: instantiating (l9_co) with fresh symbols all_47_0, all_47_1, all_47_2, % 13.21/2.57 | all_47_3, all_47_4, all_47_5, all_47_6 gives: % 13.21/2.57 | (12) ~ (all_47_1 = 0) & findmin_cpq_res(all_47_3) = all_47_2 & % 13.21/2.58 | ok(all_47_0) = 0 & contains_cpq(all_47_3, all_47_2) = all_47_1 & % 13.21/2.58 | triple(all_47_6, all_47_5, all_47_4) = all_47_3 & % 13.21/2.58 | findmin_cpq_eff(all_47_3) = all_47_0 & $i(all_47_0) & $i(all_47_2) & % 13.21/2.58 | $i(all_47_3) & $i(all_47_4) & $i(all_47_5) & $i(all_47_6) % 13.21/2.58 | % 13.21/2.58 | ALPHA: (12) implies: % 13.21/2.58 | (13) ~ (all_47_1 = 0) % 13.21/2.58 | (14) $i(all_47_6) % 13.21/2.58 | (15) $i(all_47_5) % 13.21/2.58 | (16) $i(all_47_4) % 13.21/2.58 | (17) $i(all_47_3) % 13.21/2.58 | (18) $i(all_47_2) % 13.21/2.58 | (19) findmin_cpq_eff(all_47_3) = all_47_0 % 13.21/2.58 | (20) triple(all_47_6, all_47_5, all_47_4) = all_47_3 % 13.21/2.58 | (21) contains_cpq(all_47_3, all_47_2) = all_47_1 % 13.21/2.58 | (22) ok(all_47_0) = 0 % 13.21/2.58 | (23) findmin_cpq_res(all_47_3) = all_47_2 % 13.21/2.58 | % 13.21/2.58 | GROUND_INST: instantiating (4) with all_47_6, all_47_5, all_47_4, all_47_3, % 13.21/2.58 | all_47_0, simplifying with (14), (15), (16), (19), (20) gives: % 13.21/2.58 | (24) all_47_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 13.21/2.58 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_6) = % 13.21/2.58 | v0 & triple(all_47_6, v4, all_47_4) = v5 & update_slb(all_47_5, v0) % 13.21/2.58 | = v4 & lookup_slb(all_47_5, v0) = v2 & contains_slb(all_47_5, v0) = % 13.21/2.58 | v1 & less_than(v2, v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( % 13.21/2.58 | ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_47_0)) % 13.21/2.58 | % 13.21/2.58 | GROUND_INST: instantiating (3) with all_47_6, all_47_5, all_47_4, all_47_3, % 13.21/2.58 | all_47_0, simplifying with (14), (15), (16), (19), (20) gives: % 13.21/2.58 | (25) all_47_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 13.21/2.58 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_6) = % 13.21/2.58 | v0 & triple(all_47_6, v4, bad) = v5 & update_slb(all_47_5, v0) = v4 % 13.21/2.58 | & lookup_slb(all_47_5, v0) = v2 & contains_slb(all_47_5, v0) = v1 & % 13.21/2.58 | strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) % 13.21/2.58 | & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_47_0)) % 13.21/2.58 | % 13.21/2.58 | GROUND_INST: instantiating (2) with all_47_6, all_47_5, all_47_4, all_47_3, % 13.21/2.58 | all_47_0, simplifying with (14), (15), (16), (19), (20) gives: % 13.21/2.58 | (26) all_47_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 13.21/2.58 | [v3: $i] : (findmin_pqp_res(all_47_6) = v0 & triple(all_47_6, v2, bad) % 13.21/2.58 | = v3 & update_slb(all_47_5, v0) = v2 & contains_slb(all_47_5, v0) = % 13.21/2.58 | v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_47_0 | v1 = 0)) % 13.21/2.58 | % 13.21/2.58 | GROUND_INST: instantiating (7) with all_47_6, all_47_5, all_47_4, all_47_3, % 13.21/2.58 | simplifying with (14), (15), (16), (20) gives: % 13.21/2.58 | (27) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] % 13.21/2.58 | : ? [v5: any] : (findmin_pqp_res(all_47_6) = v2 & ok(v0) = v1 & % 13.21/2.58 | findmin_cpq_eff(all_47_3) = v0 & lookup_slb(all_47_5, v2) = v4 & % 13.21/2.58 | contains_slb(all_47_5, v2) = v3 & less_than(v4, v2) = v5 & $i(v4) & % 13.21/2.58 | $i(v2) & $i(v0) & ( ~ (v1 = 0) | (v5 = 0 & v3 = 0 & ~ (all_47_5 = % 13.21/2.58 | create_slb)))) % 13.21/2.58 | % 13.21/2.59 | GROUND_INST: instantiating (1) with all_47_6, all_47_5, all_47_4, all_47_2, % 13.21/2.59 | all_47_3, all_47_1, simplifying with (14), (15), (16), (18), % 13.21/2.59 | (20), (21) gives: % 13.21/2.59 | (28) all_47_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_47_5, % 13.21/2.59 | all_47_2) = v0) % 13.21/2.59 | % 13.21/2.59 | GROUND_INST: instantiating (5) with all_47_6, all_47_5, all_47_4, all_47_3, % 13.21/2.59 | all_47_2, simplifying with (14), (15), (16), (20), (23) gives: % 13.21/2.59 | (29) all_47_5 = create_slb | (findmin_pqp_res(all_47_6) = all_47_2 & % 13.21/2.59 | $i(all_47_2)) % 13.21/2.59 | % 13.21/2.59 | GROUND_INST: instantiating (6) with all_47_3, all_47_2, simplifying with (17), % 13.21/2.59 | (23) gives: % 13.21/2.59 | (30) ? [v0: $i] : ? [v1: $i] : (removemin_cpq_eff(all_47_3) = v0 & % 13.21/2.59 | findmin_cpq_eff(all_47_3) = v1 & remove_cpq(v1, all_47_2) = v0 & % 13.21/2.59 | $i(v1) & $i(v0)) % 13.21/2.59 | % 13.21/2.59 | DELTA: instantiating (30) with fresh symbols all_57_0, all_57_1 gives: % 13.21/2.59 | (31) removemin_cpq_eff(all_47_3) = all_57_1 & findmin_cpq_eff(all_47_3) = % 13.21/2.59 | all_57_0 & remove_cpq(all_57_0, all_47_2) = all_57_1 & $i(all_57_0) & % 13.21/2.59 | $i(all_57_1) % 13.21/2.59 | % 13.21/2.59 | ALPHA: (31) implies: % 13.21/2.59 | (32) findmin_cpq_eff(all_47_3) = all_57_0 % 13.21/2.59 | % 13.21/2.59 | DELTA: instantiating (27) with fresh symbols all_59_0, all_59_1, all_59_2, % 13.21/2.59 | all_59_3, all_59_4, all_59_5 gives: % 13.21/2.59 | (33) findmin_pqp_res(all_47_6) = all_59_3 & ok(all_59_5) = all_59_4 & % 13.21/2.59 | findmin_cpq_eff(all_47_3) = all_59_5 & lookup_slb(all_47_5, all_59_3) % 13.21/2.59 | = all_59_1 & contains_slb(all_47_5, all_59_3) = all_59_2 & % 13.21/2.59 | less_than(all_59_1, all_59_3) = all_59_0 & $i(all_59_1) & $i(all_59_3) % 13.21/2.59 | & $i(all_59_5) & ( ~ (all_59_4 = 0) | (all_59_0 = 0 & all_59_2 = 0 & % 13.21/2.59 | ~ (all_47_5 = create_slb))) % 13.21/2.59 | % 13.21/2.59 | ALPHA: (33) implies: % 13.21/2.59 | (34) contains_slb(all_47_5, all_59_3) = all_59_2 % 13.21/2.59 | (35) findmin_cpq_eff(all_47_3) = all_59_5 % 13.21/2.59 | (36) ok(all_59_5) = all_59_4 % 13.21/2.59 | (37) findmin_pqp_res(all_47_6) = all_59_3 % 13.21/2.59 | (38) ~ (all_59_4 = 0) | (all_59_0 = 0 & all_59_2 = 0 & ~ (all_47_5 = % 13.21/2.59 | create_slb)) % 13.21/2.59 | % 13.21/2.59 | BETA: splitting (28) gives: % 13.21/2.59 | % 13.21/2.59 | Case 1: % 13.21/2.59 | | % 13.21/2.59 | | (39) all_47_1 = 0 % 13.21/2.59 | | % 13.21/2.59 | | REDUCE: (13), (39) imply: % 13.21/2.59 | | (40) $false % 13.21/2.59 | | % 13.21/2.59 | | CLOSE: (40) is inconsistent. % 13.21/2.59 | | % 13.21/2.59 | Case 2: % 13.21/2.59 | | % 13.21/2.59 | | (41) ? [v0: int] : ( ~ (v0 = 0) & contains_slb(all_47_5, all_47_2) = v0) % 13.21/2.59 | | % 13.21/2.59 | | DELTA: instantiating (41) with fresh symbol all_65_0 gives: % 13.21/2.59 | | (42) ~ (all_65_0 = 0) & contains_slb(all_47_5, all_47_2) = all_65_0 % 13.21/2.59 | | % 13.21/2.59 | | ALPHA: (42) implies: % 13.21/2.59 | | (43) ~ (all_65_0 = 0) % 13.21/2.59 | | (44) contains_slb(all_47_5, all_47_2) = all_65_0 % 13.21/2.59 | | % 13.21/2.59 | | GROUND_INST: instantiating (8) with all_47_0, all_59_5, all_47_3, % 13.21/2.59 | | simplifying with (19), (35) gives: % 13.21/2.59 | | (45) all_59_5 = all_47_0 % 13.21/2.59 | | % 13.21/2.59 | | GROUND_INST: instantiating (8) with all_57_0, all_59_5, all_47_3, % 13.21/2.59 | | simplifying with (32), (35) gives: % 13.21/2.59 | | (46) all_59_5 = all_57_0 % 13.21/2.59 | | % 13.21/2.59 | | COMBINE_EQS: (45), (46) imply: % 13.21/2.60 | | (47) all_57_0 = all_47_0 % 13.21/2.60 | | % 13.21/2.60 | | REDUCE: (36), (45) imply: % 13.21/2.60 | | (48) ok(all_47_0) = all_59_4 % 13.21/2.60 | | % 13.21/2.60 | | GROUND_INST: instantiating (9) with 0, all_59_4, all_47_0, simplifying with % 13.21/2.60 | | (22), (48) gives: % 13.21/2.60 | | (49) all_59_4 = 0 % 13.21/2.60 | | % 13.21/2.60 | | BETA: splitting (38) gives: % 13.21/2.60 | | % 13.21/2.60 | | Case 1: % 13.21/2.60 | | | % 13.21/2.60 | | | (50) ~ (all_59_4 = 0) % 13.21/2.60 | | | % 13.21/2.60 | | | REDUCE: (49), (50) imply: % 13.21/2.60 | | | (51) $false % 13.21/2.60 | | | % 13.21/2.60 | | | CLOSE: (51) is inconsistent. % 13.21/2.60 | | | % 13.21/2.60 | | Case 2: % 13.21/2.60 | | | % 13.21/2.60 | | | (52) all_59_0 = 0 & all_59_2 = 0 & ~ (all_47_5 = create_slb) % 13.21/2.60 | | | % 13.21/2.60 | | | ALPHA: (52) implies: % 13.21/2.60 | | | (53) all_59_2 = 0 % 13.21/2.60 | | | (54) ~ (all_47_5 = create_slb) % 13.21/2.60 | | | % 13.21/2.60 | | | REDUCE: (34), (53) imply: % 13.21/2.60 | | | (55) contains_slb(all_47_5, all_59_3) = 0 % 13.21/2.60 | | | % 13.21/2.60 | | | BETA: splitting (29) gives: % 13.21/2.60 | | | % 13.21/2.60 | | | Case 1: % 13.21/2.60 | | | | % 13.21/2.60 | | | | (56) all_47_5 = create_slb % 13.21/2.60 | | | | % 13.21/2.60 | | | | REDUCE: (54), (56) imply: % 13.21/2.60 | | | | (57) $false % 13.21/2.60 | | | | % 13.21/2.60 | | | | CLOSE: (57) is inconsistent. % 13.21/2.60 | | | | % 13.21/2.60 | | | Case 2: % 13.21/2.60 | | | | % 13.21/2.60 | | | | (58) findmin_pqp_res(all_47_6) = all_47_2 & $i(all_47_2) % 13.21/2.60 | | | | % 13.21/2.60 | | | | ALPHA: (58) implies: % 13.21/2.60 | | | | (59) findmin_pqp_res(all_47_6) = all_47_2 % 13.21/2.60 | | | | % 13.21/2.60 | | | | BETA: splitting (26) gives: % 13.21/2.60 | | | | % 13.21/2.60 | | | | Case 1: % 13.21/2.60 | | | | | % 13.21/2.60 | | | | | (60) all_47_5 = create_slb % 13.21/2.60 | | | | | % 13.21/2.60 | | | | | REDUCE: (54), (60) imply: % 13.21/2.60 | | | | | (61) $false % 13.21/2.60 | | | | | % 13.21/2.60 | | | | | CLOSE: (61) is inconsistent. % 13.21/2.60 | | | | | % 13.21/2.60 | | | | Case 2: % 13.21/2.60 | | | | | % 13.21/2.60 | | | | | (62) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 13.21/2.60 | | | | | (findmin_pqp_res(all_47_6) = v0 & triple(all_47_6, v2, bad) = % 13.21/2.60 | | | | | v3 & update_slb(all_47_5, v0) = v2 & contains_slb(all_47_5, % 13.21/2.60 | | | | | v0) = v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_47_0 | v1 % 13.21/2.60 | | | | | = 0)) % 13.21/2.60 | | | | | % 13.21/2.60 | | | | | DELTA: instantiating (62) with fresh symbols all_86_0, all_86_1, % 13.21/2.60 | | | | | all_86_2, all_86_3 gives: % 13.21/2.60 | | | | | (63) findmin_pqp_res(all_47_6) = all_86_3 & triple(all_47_6, % 13.21/2.60 | | | | | all_86_1, bad) = all_86_0 & update_slb(all_47_5, all_86_3) = % 13.21/2.60 | | | | | all_86_1 & contains_slb(all_47_5, all_86_3) = all_86_2 & % 13.21/2.60 | | | | | $i(all_86_0) & $i(all_86_1) & $i(all_86_3) & (all_86_0 = % 13.21/2.60 | | | | | all_47_0 | all_86_2 = 0) % 13.21/2.60 | | | | | % 13.21/2.60 | | | | | ALPHA: (63) implies: % 13.21/2.60 | | | | | (64) contains_slb(all_47_5, all_86_3) = all_86_2 % 13.21/2.60 | | | | | (65) findmin_pqp_res(all_47_6) = all_86_3 % 13.21/2.60 | | | | | % 13.21/2.60 | | | | | BETA: splitting (25) gives: % 13.21/2.60 | | | | | % 13.21/2.60 | | | | | Case 1: % 13.21/2.60 | | | | | | % 13.21/2.60 | | | | | | (66) all_47_5 = create_slb % 13.21/2.60 | | | | | | % 13.21/2.60 | | | | | | REDUCE: (54), (66) imply: % 13.21/2.60 | | | | | | (67) $false % 13.21/2.60 | | | | | | % 13.21/2.60 | | | | | | CLOSE: (67) is inconsistent. % 13.21/2.60 | | | | | | % 13.21/2.60 | | | | | Case 2: % 13.21/2.60 | | | | | | % 13.21/2.60 | | | | | | (68) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? % 13.21/2.60 | | | | | | [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_6) = v0 & % 13.21/2.60 | | | | | | triple(all_47_6, v4, bad) = v5 & update_slb(all_47_5, v0) % 13.21/2.60 | | | | | | = v4 & lookup_slb(all_47_5, v0) = v2 & % 13.21/2.60 | | | | | | contains_slb(all_47_5, v0) = v1 & strictly_less_than(v0, % 13.21/2.60 | | | | | | v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = % 13.21/2.60 | | | | | | 0) | ~ (v1 = 0) | v5 = all_47_0)) % 13.21/2.60 | | | | | | % 13.21/2.60 | | | | | | DELTA: instantiating (68) with fresh symbols all_91_0, all_91_1, % 13.21/2.60 | | | | | | all_91_2, all_91_3, all_91_4, all_91_5 gives: % 13.21/2.60 | | | | | | (69) findmin_pqp_res(all_47_6) = all_91_5 & triple(all_47_6, % 13.21/2.60 | | | | | | all_91_1, bad) = all_91_0 & update_slb(all_47_5, all_91_5) % 13.21/2.60 | | | | | | = all_91_1 & lookup_slb(all_47_5, all_91_5) = all_91_3 & % 13.21/2.60 | | | | | | contains_slb(all_47_5, all_91_5) = all_91_4 & % 13.21/2.60 | | | | | | strictly_less_than(all_91_5, all_91_3) = all_91_2 & % 13.21/2.60 | | | | | | $i(all_91_0) & $i(all_91_1) & $i(all_91_3) & $i(all_91_5) & % 13.21/2.60 | | | | | | ( ~ (all_91_2 = 0) | ~ (all_91_4 = 0) | all_91_0 = % 13.21/2.60 | | | | | | all_47_0) % 13.21/2.60 | | | | | | % 13.21/2.60 | | | | | | ALPHA: (69) implies: % 13.21/2.60 | | | | | | (70) contains_slb(all_47_5, all_91_5) = all_91_4 % 13.21/2.60 | | | | | | (71) findmin_pqp_res(all_47_6) = all_91_5 % 13.21/2.60 | | | | | | % 13.21/2.60 | | | | | | BETA: splitting (24) gives: % 13.21/2.60 | | | | | | % 13.21/2.60 | | | | | | Case 1: % 13.21/2.60 | | | | | | | % 13.21/2.60 | | | | | | | (72) all_47_5 = create_slb % 13.21/2.60 | | | | | | | % 13.21/2.60 | | | | | | | REDUCE: (54), (72) imply: % 13.21/2.60 | | | | | | | (73) $false % 13.21/2.60 | | | | | | | % 13.21/2.60 | | | | | | | CLOSE: (73) is inconsistent. % 13.21/2.60 | | | | | | | % 13.21/2.60 | | | | | | Case 2: % 13.21/2.60 | | | | | | | % 13.21/2.61 | | | | | | | (74) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 13.21/2.61 | | | | | | | ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_6) = v0 % 13.21/2.61 | | | | | | | & triple(all_47_6, v4, all_47_4) = v5 & % 13.21/2.61 | | | | | | | update_slb(all_47_5, v0) = v4 & lookup_slb(all_47_5, v0) % 13.21/2.61 | | | | | | | = v2 & contains_slb(all_47_5, v0) = v1 & less_than(v2, % 13.21/2.61 | | | | | | | v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 % 13.21/2.61 | | | | | | | = 0) | ~ (v1 = 0) | v5 = all_47_0)) % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | DELTA: instantiating (74) with fresh symbols all_97_0, all_97_1, % 13.21/2.61 | | | | | | | all_97_2, all_97_3, all_97_4, all_97_5 gives: % 13.21/2.61 | | | | | | | (75) findmin_pqp_res(all_47_6) = all_97_5 & triple(all_47_6, % 13.21/2.61 | | | | | | | all_97_1, all_47_4) = all_97_0 & update_slb(all_47_5, % 13.21/2.61 | | | | | | | all_97_5) = all_97_1 & lookup_slb(all_47_5, all_97_5) = % 13.21/2.61 | | | | | | | all_97_3 & contains_slb(all_47_5, all_97_5) = all_97_4 & % 13.21/2.61 | | | | | | | less_than(all_97_3, all_97_5) = all_97_2 & $i(all_97_0) & % 13.21/2.61 | | | | | | | $i(all_97_1) & $i(all_97_3) & $i(all_97_5) & ( ~ (all_97_2 % 13.21/2.61 | | | | | | | = 0) | ~ (all_97_4 = 0) | all_97_0 = all_47_0) % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | ALPHA: (75) implies: % 13.21/2.61 | | | | | | | (76) contains_slb(all_47_5, all_97_5) = all_97_4 % 13.21/2.61 | | | | | | | (77) findmin_pqp_res(all_47_6) = all_97_5 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | GROUND_INST: instantiating (10) with all_59_3, all_91_5, all_47_6, % 13.21/2.61 | | | | | | | simplifying with (37), (71) gives: % 13.21/2.61 | | | | | | | (78) all_91_5 = all_59_3 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | GROUND_INST: instantiating (10) with all_86_3, all_91_5, all_47_6, % 13.21/2.61 | | | | | | | simplifying with (65), (71) gives: % 13.21/2.61 | | | | | | | (79) all_91_5 = all_86_3 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | GROUND_INST: instantiating (10) with all_91_5, all_97_5, all_47_6, % 13.21/2.61 | | | | | | | simplifying with (71), (77) gives: % 13.21/2.61 | | | | | | | (80) all_97_5 = all_91_5 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | GROUND_INST: instantiating (10) with all_47_2, all_97_5, all_47_6, % 13.21/2.61 | | | | | | | simplifying with (59), (77) gives: % 13.21/2.61 | | | | | | | (81) all_97_5 = all_47_2 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | COMBINE_EQS: (80), (81) imply: % 13.21/2.61 | | | | | | | (82) all_91_5 = all_47_2 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | SIMP: (82) implies: % 13.21/2.61 | | | | | | | (83) all_91_5 = all_47_2 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | COMBINE_EQS: (78), (79) imply: % 13.21/2.61 | | | | | | | (84) all_86_3 = all_59_3 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | COMBINE_EQS: (79), (83) imply: % 13.21/2.61 | | | | | | | (85) all_86_3 = all_47_2 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | COMBINE_EQS: (84), (85) imply: % 13.21/2.61 | | | | | | | (86) all_59_3 = all_47_2 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | SIMP: (86) implies: % 13.21/2.61 | | | | | | | (87) all_59_3 = all_47_2 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | REDUCE: (76), (81) imply: % 13.21/2.61 | | | | | | | (88) contains_slb(all_47_5, all_47_2) = all_97_4 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | REDUCE: (70), (83) imply: % 13.21/2.61 | | | | | | | (89) contains_slb(all_47_5, all_47_2) = all_91_4 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | REDUCE: (64), (85) imply: % 13.21/2.61 | | | | | | | (90) contains_slb(all_47_5, all_47_2) = all_86_2 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | REDUCE: (55), (87) imply: % 13.21/2.61 | | | | | | | (91) contains_slb(all_47_5, all_47_2) = 0 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | GROUND_INST: instantiating (11) with all_65_0, all_86_2, all_47_2, % 13.21/2.61 | | | | | | | all_47_5, simplifying with (44), (90) gives: % 13.21/2.61 | | | | | | | (92) all_86_2 = all_65_0 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | GROUND_INST: instantiating (11) with all_86_2, all_91_4, all_47_2, % 13.21/2.61 | | | | | | | all_47_5, simplifying with (89), (90) gives: % 13.21/2.61 | | | | | | | (93) all_91_4 = all_86_2 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | GROUND_INST: instantiating (11) with all_91_4, all_97_4, all_47_2, % 13.21/2.61 | | | | | | | all_47_5, simplifying with (88), (89) gives: % 13.21/2.61 | | | | | | | (94) all_97_4 = all_91_4 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | GROUND_INST: instantiating (11) with 0, all_97_4, all_47_2, % 13.21/2.61 | | | | | | | all_47_5, simplifying with (88), (91) gives: % 13.21/2.61 | | | | | | | (95) all_97_4 = 0 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | COMBINE_EQS: (94), (95) imply: % 13.21/2.61 | | | | | | | (96) all_91_4 = 0 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | SIMP: (96) implies: % 13.21/2.61 | | | | | | | (97) all_91_4 = 0 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | COMBINE_EQS: (93), (97) imply: % 13.21/2.61 | | | | | | | (98) all_86_2 = 0 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | SIMP: (98) implies: % 13.21/2.61 | | | | | | | (99) all_86_2 = 0 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | COMBINE_EQS: (92), (99) imply: % 13.21/2.61 | | | | | | | (100) all_65_0 = 0 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | SIMP: (100) implies: % 13.21/2.61 | | | | | | | (101) all_65_0 = 0 % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | REDUCE: (43), (101) imply: % 13.21/2.61 | | | | | | | (102) $false % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | | CLOSE: (102) is inconsistent. % 13.21/2.61 | | | | | | | % 13.21/2.61 | | | | | | End of split % 13.21/2.61 | | | | | | % 13.21/2.61 | | | | | End of split % 13.21/2.61 | | | | | % 13.21/2.61 | | | | End of split % 13.21/2.61 | | | | % 13.21/2.61 | | | End of split % 13.21/2.61 | | | % 13.21/2.61 | | End of split % 13.21/2.61 | | % 13.21/2.61 | End of split % 13.21/2.61 | % 13.21/2.61 End of proof % 13.21/2.61 % SZS output end Proof for theBenchmark % 13.21/2.61 % 13.21/2.61 1994ms %------------------------------------------------------------------------------