%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV374+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 : n011.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 12.97s 2.31s % Output : Proof 17.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.07 % Problem : SWV374+1 : TPTP v8.1.2. Released v3.3.0. % 0.07/0.07 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.07/0.26 % Computer : n011.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Tue Aug 29 08:22:41 EDT 2023 % 0.07/0.26 % CPUTime : % 0.10/0.44 ________ _____ % 0.10/0.44 ___ __ \_________(_)________________________________ % 0.10/0.44 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.10/0.44 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.10/0.44 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.10/0.44 % 0.10/0.44 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.10/0.44 (2023-06-19) % 0.10/0.44 % 0.10/0.44 (c) Philipp Rümmer, 2009-2023 % 0.10/0.44 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.10/0.44 Amanda Stjerna. % 0.10/0.44 Free software under BSD-3-Clause. % 0.10/0.44 % 0.10/0.44 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.10/0.44 % 0.10/0.44 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.10/0.45 Running up to 7 provers in parallel. % 0.10/0.46 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.10/0.46 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.10/0.46 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.10/0.46 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.10/0.46 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.10/0.46 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.10/0.46 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.85/0.96 Prover 4: Preprocessing ... % 2.85/0.97 Prover 1: Preprocessing ... % 3.40/1.01 Prover 0: Preprocessing ... % 3.40/1.01 Prover 5: Preprocessing ... % 3.40/1.01 Prover 2: Preprocessing ... % 3.40/1.01 Prover 6: Preprocessing ... % 3.40/1.01 Prover 3: Preprocessing ... % 7.29/1.59 Prover 1: Warning: ignoring some quantifiers % 7.86/1.61 Prover 3: Warning: ignoring some quantifiers % 7.86/1.65 Prover 5: Proving ... % 7.86/1.66 Prover 6: Proving ... % 7.86/1.66 Prover 3: Constructing countermodel ... % 8.50/1.67 Prover 1: Constructing countermodel ... % 8.50/1.68 Prover 4: Constructing countermodel ... % 8.50/1.69 Prover 2: Proving ... % 8.70/1.76 Prover 0: Proving ... % 11.56/2.11 Prover 3: gave up % 11.56/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.82/2.16 Prover 7: Preprocessing ... % 12.97/2.31 Prover 0: proved (1851ms) % 12.97/2.31 % 12.97/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.97/2.31 % 12.97/2.32 Prover 2: stopped % 12.97/2.33 Prover 6: stopped % 12.97/2.34 Prover 5: stopped % 12.97/2.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.97/2.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.97/2.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.97/2.35 Prover 7: Warning: ignoring some quantifiers % 12.97/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.97/2.36 Prover 8: Preprocessing ... % 13.71/2.39 Prover 7: Constructing countermodel ... % 13.71/2.39 Prover 10: Preprocessing ... % 13.89/2.39 Prover 11: Preprocessing ... % 13.89/2.40 Prover 13: Preprocessing ... % 13.89/2.49 Prover 10: Warning: ignoring some quantifiers % 13.89/2.51 Prover 10: Constructing countermodel ... % 14.26/2.52 Prover 8: Warning: ignoring some quantifiers % 14.89/2.53 Prover 8: Constructing countermodel ... % 15.50/2.61 Prover 1: gave up % 15.50/2.62 Prover 13: Warning: ignoring some quantifiers % 15.50/2.62 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.50/2.65 Prover 13: Constructing countermodel ... % 15.50/2.66 Prover 11: Constructing countermodel ... % 15.50/2.66 Prover 16: Preprocessing ... % 16.00/2.67 Prover 8: gave up % 16.00/2.69 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 16.00/2.70 Prover 4: Found proof (size 240) % 16.00/2.70 Prover 4: proved (2236ms) % 16.00/2.70 Prover 11: stopped % 16.00/2.70 Prover 10: stopped % 16.00/2.70 Prover 13: stopped % 16.00/2.70 Prover 7: stopped % 16.00/2.71 Prover 16: stopped % 16.00/2.71 Prover 19: Preprocessing ... % 16.77/2.82 Prover 19: Warning: ignoring some quantifiers % 16.82/2.83 Prover 19: Constructing countermodel ... % 16.82/2.84 Prover 19: stopped % 16.82/2.84 % 16.82/2.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.82/2.84 % 16.82/2.87 % SZS output start Proof for theBenchmark % 16.82/2.87 Assumptions after simplification: % 16.82/2.87 --------------------------------- % 16.82/2.87 % 16.82/2.87 (ax40) % 16.82/2.89 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 16.82/2.89 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) = v3)) % 16.82/2.89 % 16.82/2.89 (ax46) % 16.82/2.90 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 16.82/2.90 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 16.82/2.90 (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3 & $i(v3))) % 16.82/2.90 % 16.82/2.90 (ax47) % 16.82/2.90 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 16.82/2.90 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 16.82/2.90 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 16.82/2.90 : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 & % 16.82/2.90 triple(v0, v7, bad) = v8 & update_slb(v1, v5) = v7 & contains_slb(v1, v5) % 16.82/2.90 = v6 & $i(v8) & $i(v7) & $i(v5) & (v8 = v4 | v6 = 0))) % 16.82/2.90 % 16.82/2.90 (ax48) % 16.82/2.90 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 16.82/2.90 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 16.82/2.90 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 16.82/2.90 : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : % 16.82/2.90 (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & update_slb(v1, v5) = % 16.82/2.90 v9 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = v6 & % 16.82/2.90 strictly_less_than(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ % 16.82/2.90 (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 16.82/2.90 % 16.82/2.90 (ax49) % 16.82/2.90 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 16.82/2.90 [v4: $i] : ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ % 16.82/2.90 (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) | ~ % 16.82/2.90 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] % 16.82/2.90 : ? [v10: $i] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & % 16.82/2.90 lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = % 16.82/2.90 v8 & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) % 16.82/2.90 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 16.82/2.90 create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | % 16.82/2.90 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] % 16.82/2.90 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : (findmin_pqp_res(v0) = v5 & % 16.82/2.90 triple(v0, v9, v2) = v10 & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = % 16.82/2.90 v7 & contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & $i(v9) % 16.82/2.90 & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 16.82/2.90 % 16.82/2.90 (ax51) % 16.82/2.91 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 16.82/2.91 [v4: $i] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, % 16.82/2.91 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (findmin_pqp_res(v0) % 16.82/2.91 = v4 & $i(v4))) % 16.82/2.91 % 16.82/2.91 (ax52) % 17.17/2.91 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ? % 17.17/2.91 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = % 17.17/2.91 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: % 17.17/2.91 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 17.17/2.91 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & % 17.17/2.91 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : ! % 17.17/2.91 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 17.17/2.91 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & % 17.17/2.91 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2))) % 17.17/2.91 % 17.17/2.91 (l10_co) % 17.17/2.91 $i(create_slb) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 17.17/2.91 [v4: $i] : ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 17.17/2.91 (findmin_pqp_res(v0) = v5 & ok(v4) = 0 & triple(v0, v1, v2) = v3 & % 17.17/2.91 findmin_cpq_eff(v3) = v4 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = % 17.17/2.91 v6 & less_than(v7, v5) = v8 & $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 17.17/2.91 $i(v1) & $i(v0) & ( ~ (v8 = 0) | ~ (v6 = 0) | v1 = create_slb)) % 17.17/2.91 % 17.17/2.91 (stricly_smaller_definition) % 17.17/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 17.17/2.91 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 17.17/2.91 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 17.17/2.91 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 17.17/2.91 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 17.17/2.91 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 % 17.17/2.91 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 17.17/2.91 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 17.17/2.91 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 % 17.17/2.91 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 17.17/2.91 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 17.17/2.91 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( % 17.17/2.91 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 17.17/2.91 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( % 17.17/2.91 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0: % 17.17/2.91 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 17.17/2.91 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, % 17.17/2.91 v0) = v2 & (v3 = 0 | v2 = 0))) % 17.17/2.91 % 17.17/2.91 (totality) % 17.17/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) = % 17.17/2.91 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : ! % 17.17/2.91 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) | % 17.17/2.91 ~ $i(v0) | less_than(v1, v0) = 0) % 17.17/2.91 % 17.17/2.91 (function-axioms) % 17.17/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 17.17/2.92 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 17.17/2.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.17/2.92 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 17.17/2.92 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.17/2.92 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 17.17/2.92 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 17.17/2.92 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 17.17/2.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.17/2.92 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 17.17/2.92 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.17/2.92 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 17.17/2.92 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 17.17/2.92 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.17/2.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 17.17/2.92 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 17.17/2.92 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 17.17/2.92 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.17/2.92 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 17.17/2.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 17.17/2.92 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 17.17/2.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.17/2.92 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 17.17/2.92 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.17/2.92 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 17.17/2.92 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 17.17/2.92 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.17/2.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.17/2.92 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 17.17/2.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.17/2.92 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 17.17/2.92 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.17/2.92 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: % 17.17/2.92 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | % 17.17/2.92 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.17/2.92 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! % 17.17/2.92 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 17.17/2.92 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 17.17/2.92 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | % 17.17/2.92 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 17.17/2.92 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! % 17.17/2.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = % 17.17/2.92 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 17.17/2.92 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = % 17.17/2.92 v1) | ~ (isnonempty_slb(v2) = v0)) % 17.17/2.92 % 17.17/2.92 Further assumptions not needed in the proof: % 17.17/2.92 -------------------------------------------- % 17.17/2.92 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 17.17/2.92 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax41, ax42, ax43, ax44, % 17.17/2.92 ax45, ax50, ax53, bottom_smallest, reflexivity, transitivity % 17.17/2.92 % 17.17/2.92 Those formulas are unsatisfiable: % 17.17/2.92 --------------------------------- % 17.17/2.92 % 17.17/2.92 Begin of proof % 17.17/2.92 | % 17.17/2.92 | ALPHA: (totality) implies: % 17.17/2.92 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 17.17/2.92 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) % 17.17/2.92 | % 17.17/2.92 | ALPHA: (stricly_smaller_definition) implies: % 17.17/2.92 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v0, v1) = v2) % 17.17/2.92 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 17.17/2.92 | (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 = % 17.17/2.92 | 0) | (v2 = 0 & ~ (v4 = 0))))) % 17.17/2.92 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2) % 17.17/2.92 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 17.17/2.92 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 = % 17.17/2.92 | 0) | (v4 = 0 & ~ (v2 = 0))))) % 17.17/2.93 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 17.17/2.93 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 17.17/2.93 | (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 17.17/2.93 | 0) | v4 = 0))) % 17.17/2.93 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 17.17/2.93 | (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 17.17/2.93 | any] : ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = % 17.17/2.93 | v3 & ( ~ (v3 = 0) | v4 = 0))) % 17.17/2.93 | % 17.17/2.93 | ALPHA: (ax40) implies: % 17.17/2.93 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 17.17/2.93 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) % 17.17/2.93 | = v3)) % 17.17/2.93 | % 17.17/2.93 | ALPHA: (ax46) implies: % 17.17/2.93 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb, % 17.17/2.93 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (triple(v0, % 17.17/2.93 | create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3 & $i(v3))) % 17.17/2.93 | % 17.17/2.93 | ALPHA: (ax47) implies: % 17.17/2.93 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.17/2.93 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 17.17/2.93 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.17/2.93 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 17.17/2.93 | (findmin_pqp_res(v0) = v5 & triple(v0, v7, bad) = v8 & update_slb(v1, % 17.17/2.93 | v5) = v7 & contains_slb(v1, v5) = v6 & $i(v8) & $i(v7) & $i(v5) & % 17.17/2.93 | (v8 = v4 | v6 = 0))) % 17.17/2.93 | % 17.17/2.93 | ALPHA: (ax48) implies: % 17.17/2.93 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.17/2.93 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 17.17/2.93 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.17/2.93 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 17.17/2.93 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & % 17.17/2.93 | update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 17.17/2.93 | contains_slb(v1, v5) = v6 & strictly_less_than(v5, v7) = v8 & % 17.17/2.93 | $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | % 17.17/2.93 | v10 = v4))) % 17.17/2.93 | % 17.17/2.93 | ALPHA: (ax49) implies: % 17.17/2.93 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.17/2.93 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 17.17/2.93 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 17.17/2.93 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 17.17/2.93 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, v2) = v10 % 17.17/2.93 | & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 17.17/2.93 | contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & % 17.17/2.93 | $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = % 17.17/2.93 | v4))) % 17.17/2.93 | % 17.17/2.93 | ALPHA: (ax51) implies: % 17.17/2.93 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.17/2.93 | (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, % 17.17/2.93 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.17/2.93 | (findmin_pqp_res(v0) = v4 & $i(v4))) % 17.17/2.93 | % 17.17/2.93 | ALPHA: (ax52) implies: % 17.17/2.93 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) % 17.17/2.93 | | ? [v2: $i] : ? [v3: $i] : (findmin_cpq_res(v0) = v3 & % 17.17/2.93 | removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2 & $i(v3) & % 17.17/2.93 | $i(v2))) % 17.17/2.93 | % 17.17/2.93 | ALPHA: (l10_co) implies: % 17.17/2.93 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 17.17/2.93 | ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : % 17.17/2.93 | (findmin_pqp_res(v0) = v5 & ok(v4) = 0 & triple(v0, v1, v2) = v3 & % 17.17/2.93 | findmin_cpq_eff(v3) = v4 & lookup_slb(v1, v5) = v7 & % 17.17/2.93 | contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v7) & $i(v5) % 17.17/2.93 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v8 = 0) | ~ (v6 % 17.17/2.94 | = 0) | v1 = create_slb)) % 17.17/2.94 | % 17.17/2.94 | ALPHA: (function-axioms) implies: % 17.17/2.94 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.17/2.94 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 17.17/2.94 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.17/2.94 | : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 17.17/2.94 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.17/2.94 | (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 17.17/2.94 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.17/2.94 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ % 17.17/2.94 | (less_than(v3, v2) = v0)) % 17.17/2.94 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.17/2.94 | : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ % 17.17/2.94 | (strictly_less_than(v3, v2) = v0)) % 17.17/2.94 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.17/2.94 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 17.17/2.94 | (contains_slb(v3, v2) = v0)) % 17.17/2.94 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.17/2.94 | (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 17.17/2.94 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.17/2.94 | (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 17.17/2.94 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 17.17/2.94 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = % 17.17/2.94 | v0)) % 17.17/2.94 | % 17.17/2.94 | DELTA: instantiating (13) with fresh symbols all_46_0, all_46_1, all_46_2, % 17.17/2.94 | all_46_3, all_46_4, all_46_5, all_46_6, all_46_7, all_46_8 gives: % 17.17/2.94 | (23) findmin_pqp_res(all_46_8) = all_46_3 & ok(all_46_4) = 0 & % 17.17/2.94 | triple(all_46_8, all_46_7, all_46_6) = all_46_5 & % 17.17/2.94 | findmin_cpq_eff(all_46_5) = all_46_4 & lookup_slb(all_46_7, all_46_3) % 17.17/2.94 | = all_46_1 & contains_slb(all_46_7, all_46_3) = all_46_2 & % 17.17/2.94 | less_than(all_46_1, all_46_3) = all_46_0 & $i(all_46_1) & $i(all_46_3) % 17.17/2.94 | & $i(all_46_4) & $i(all_46_5) & $i(all_46_6) & $i(all_46_7) & % 17.17/2.94 | $i(all_46_8) & ( ~ (all_46_0 = 0) | ~ (all_46_2 = 0) | all_46_7 = % 17.17/2.94 | create_slb) % 17.17/2.94 | % 17.17/2.94 | ALPHA: (23) implies: % 17.17/2.94 | (24) $i(all_46_8) % 17.17/2.94 | (25) $i(all_46_7) % 17.17/2.94 | (26) $i(all_46_6) % 17.17/2.94 | (27) $i(all_46_5) % 17.17/2.94 | (28) $i(all_46_3) % 17.17/2.94 | (29) $i(all_46_1) % 17.17/2.94 | (30) less_than(all_46_1, all_46_3) = all_46_0 % 17.17/2.94 | (31) contains_slb(all_46_7, all_46_3) = all_46_2 % 17.17/2.94 | (32) lookup_slb(all_46_7, all_46_3) = all_46_1 % 17.17/2.94 | (33) findmin_cpq_eff(all_46_5) = all_46_4 % 17.17/2.94 | (34) triple(all_46_8, all_46_7, all_46_6) = all_46_5 % 17.17/2.94 | (35) ok(all_46_4) = 0 % 17.17/2.94 | (36) findmin_pqp_res(all_46_8) = all_46_3 % 17.17/2.94 | (37) ~ (all_46_0 = 0) | ~ (all_46_2 = 0) | all_46_7 = create_slb % 17.17/2.94 | % 17.17/2.94 | GROUND_INST: instantiating (1) with all_46_3, all_46_1, all_46_0, simplifying % 17.17/2.94 | with (28), (29), (30) gives: % 17.17/2.94 | (38) all_46_0 = 0 | less_than(all_46_3, all_46_1) = 0 % 17.17/2.94 | % 17.17/2.94 | GROUND_INST: instantiating (4) with all_46_3, all_46_1, all_46_0, simplifying % 17.17/2.94 | with (28), (29), (30) gives: % 17.17/2.94 | (39) all_46_0 = 0 | ? [v0: any] : ? [v1: any] : % 17.17/2.94 | (strictly_less_than(all_46_3, all_46_1) = v1 & less_than(all_46_3, % 17.17/2.94 | all_46_1) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 17.17/2.95 | % 17.17/2.95 | GROUND_INST: instantiating (3) with all_46_3, all_46_1, all_46_0, simplifying % 17.17/2.95 | with (28), (29), (30) gives: % 17.17/2.95 | (40) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_3, all_46_1) % 17.17/2.95 | = v0 & less_than(all_46_3, all_46_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 17.17/2.95 | ~ (all_46_0 = 0)))) % 17.17/2.95 | % 17.17/2.95 | GROUND_INST: instantiating (2) with all_46_1, all_46_3, all_46_0, simplifying % 17.17/2.95 | with (28), (29), (30) gives: % 17.17/2.95 | (41) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_1, all_46_3) % 17.17/2.95 | = v0 & less_than(all_46_3, all_46_1) = v1 & ( ~ (v0 = 0) | (all_46_0 % 17.17/2.95 | = 0 & ~ (v1 = 0)))) % 17.17/2.95 | % 17.17/2.95 | GROUND_INST: instantiating (12) with all_46_5, all_46_4, simplifying with % 17.17/2.95 | (27), (33) gives: % 17.17/2.95 | (42) ? [v0: $i] : ? [v1: $i] : (findmin_cpq_res(all_46_5) = v1 & % 17.17/2.95 | removemin_cpq_eff(all_46_5) = v0 & remove_cpq(all_46_4, v1) = v0 & % 17.17/2.95 | $i(v1) & $i(v0)) % 17.17/2.95 | % 17.17/2.95 | GROUND_INST: instantiating (10) with all_46_8, all_46_7, all_46_6, all_46_5, % 17.17/2.95 | all_46_4, simplifying with (24), (25), (26), (33), (34) gives: % 17.17/2.95 | (43) all_46_7 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 17.17/2.95 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_46_8) = % 17.17/2.95 | v0 & triple(all_46_8, v4, all_46_6) = v5 & update_slb(all_46_7, v0) % 17.17/2.95 | = v4 & lookup_slb(all_46_7, v0) = v2 & contains_slb(all_46_7, v0) = % 17.17/2.95 | v1 & less_than(v2, v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( % 17.17/2.95 | ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_46_4)) % 17.17/2.95 | % 17.17/2.95 | GROUND_INST: instantiating (9) with all_46_8, all_46_7, all_46_6, all_46_5, % 17.17/2.95 | all_46_4, simplifying with (24), (25), (26), (33), (34) gives: % 17.17/2.95 | (44) all_46_7 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 17.17/2.95 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_46_8) = % 17.17/2.95 | v0 & triple(all_46_8, v4, bad) = v5 & update_slb(all_46_7, v0) = v4 % 17.17/2.95 | & lookup_slb(all_46_7, v0) = v2 & contains_slb(all_46_7, v0) = v1 & % 17.17/2.95 | strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) % 17.17/2.95 | & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_46_4)) % 17.17/2.95 | % 17.17/2.95 | GROUND_INST: instantiating (8) with all_46_8, all_46_7, all_46_6, all_46_5, % 17.17/2.95 | all_46_4, simplifying with (24), (25), (26), (33), (34) gives: % 17.17/2.95 | (45) all_46_7 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 17.17/2.95 | [v3: $i] : (findmin_pqp_res(all_46_8) = v0 & triple(all_46_8, v2, bad) % 17.17/2.95 | = v3 & update_slb(all_46_7, v0) = v2 & contains_slb(all_46_7, v0) = % 17.17/2.95 | v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_46_4 | v1 = 0)) % 17.17/2.95 | % 17.17/2.95 | DELTA: instantiating (42) with fresh symbols all_53_0, all_53_1 gives: % 17.17/2.95 | (46) findmin_cpq_res(all_46_5) = all_53_0 & removemin_cpq_eff(all_46_5) = % 17.17/2.95 | all_53_1 & remove_cpq(all_46_4, all_53_0) = all_53_1 & $i(all_53_0) & % 17.17/2.95 | $i(all_53_1) % 17.17/2.95 | % 17.17/2.95 | ALPHA: (46) implies: % 17.17/2.95 | (47) findmin_cpq_res(all_46_5) = all_53_0 % 17.17/2.95 | % 17.17/2.95 | DELTA: instantiating (41) with fresh symbols all_55_0, all_55_1 gives: % 17.17/2.95 | (48) strictly_less_than(all_46_1, all_46_3) = all_55_1 & % 17.17/2.95 | less_than(all_46_3, all_46_1) = all_55_0 & ( ~ (all_55_1 = 0) | % 17.17/2.95 | (all_46_0 = 0 & ~ (all_55_0 = 0))) % 17.17/2.95 | % 17.17/2.95 | ALPHA: (48) implies: % 17.17/2.95 | (49) less_than(all_46_3, all_46_1) = all_55_0 % 17.17/2.95 | % 17.17/2.95 | DELTA: instantiating (40) with fresh symbols all_57_0, all_57_1 gives: % 17.17/2.95 | (50) strictly_less_than(all_46_3, all_46_1) = all_57_1 & % 17.17/2.95 | less_than(all_46_3, all_46_1) = all_57_0 & ( ~ (all_57_1 = 0) | % 17.17/2.95 | (all_57_0 = 0 & ~ (all_46_0 = 0))) % 17.17/2.95 | % 17.17/2.95 | ALPHA: (50) implies: % 17.17/2.95 | (51) less_than(all_46_3, all_46_1) = all_57_0 % 17.17/2.95 | (52) strictly_less_than(all_46_3, all_46_1) = all_57_1 % 17.17/2.95 | % 17.17/2.95 | GROUND_INST: instantiating (17) with all_55_0, all_57_0, all_46_1, all_46_3, % 17.17/2.95 | simplifying with (49), (51) gives: % 17.17/2.95 | (53) all_57_0 = all_55_0 % 17.17/2.95 | % 17.17/2.95 | GROUND_INST: instantiating (3) with all_46_1, all_46_3, all_55_0, simplifying % 17.17/2.95 | with (28), (29), (49) gives: % 17.17/2.95 | (54) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_1, all_46_3) % 17.17/2.95 | = v0 & less_than(all_46_1, all_46_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 & % 17.17/2.95 | ~ (all_55_0 = 0)))) % 17.17/2.95 | % 17.17/2.95 | GROUND_INST: instantiating (2) with all_46_3, all_46_1, all_55_0, simplifying % 17.17/2.96 | with (28), (29), (49) gives: % 17.17/2.96 | (55) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_3, all_46_1) % 17.17/2.96 | = v0 & less_than(all_46_1, all_46_3) = v1 & ( ~ (v0 = 0) | (all_55_0 % 17.17/2.96 | = 0 & ~ (v1 = 0)))) % 17.17/2.96 | % 17.17/2.96 | GROUND_INST: instantiating (5) with all_46_3, all_46_1, all_57_1, simplifying % 17.17/2.96 | with (28), (29), (52) gives: % 17.17/2.96 | (56) all_57_1 = 0 | ? [v0: any] : ? [v1: any] : (less_than(all_46_1, % 17.17/2.96 | all_46_3) = v1 & less_than(all_46_3, all_46_1) = v0 & ( ~ (v0 = 0) % 17.17/2.96 | | v1 = 0)) % 17.17/2.96 | % 17.17/2.96 | GROUND_INST: instantiating (11) with all_46_8, all_46_7, all_46_6, all_46_5, % 17.17/2.96 | all_53_0, simplifying with (24), (25), (26), (34), (47) gives: % 17.17/2.96 | (57) all_46_7 = create_slb | (findmin_pqp_res(all_46_8) = all_53_0 & % 17.17/2.96 | $i(all_53_0)) % 17.17/2.96 | % 17.17/2.96 | DELTA: instantiating (55) with fresh symbols all_69_0, all_69_1 gives: % 17.17/2.96 | (58) strictly_less_than(all_46_3, all_46_1) = all_69_1 & % 17.17/2.96 | less_than(all_46_1, all_46_3) = all_69_0 & ( ~ (all_69_1 = 0) | % 17.17/2.96 | (all_55_0 = 0 & ~ (all_69_0 = 0))) % 17.17/2.96 | % 17.17/2.96 | ALPHA: (58) implies: % 17.17/2.96 | (59) less_than(all_46_1, all_46_3) = all_69_0 % 17.17/2.96 | (60) strictly_less_than(all_46_3, all_46_1) = all_69_1 % 17.17/2.96 | % 17.17/2.96 | DELTA: instantiating (54) with fresh symbols all_71_0, all_71_1 gives: % 17.17/2.96 | (61) strictly_less_than(all_46_1, all_46_3) = all_71_1 & % 17.17/2.96 | less_than(all_46_1, all_46_3) = all_71_0 & ( ~ (all_71_1 = 0) | % 17.17/2.96 | (all_71_0 = 0 & ~ (all_55_0 = 0))) % 17.17/2.96 | % 17.17/2.96 | ALPHA: (61) implies: % 17.17/2.96 | (62) less_than(all_46_1, all_46_3) = all_71_0 % 17.17/2.96 | % 17.17/2.96 | GROUND_INST: instantiating (17) with all_46_0, all_71_0, all_46_3, all_46_1, % 17.17/2.96 | simplifying with (30), (62) gives: % 17.17/2.96 | (63) all_71_0 = all_46_0 % 17.17/2.96 | % 17.17/2.96 | GROUND_INST: instantiating (17) with all_69_0, all_71_0, all_46_3, all_46_1, % 17.17/2.96 | simplifying with (59), (62) gives: % 17.17/2.96 | (64) all_71_0 = all_69_0 % 17.17/2.96 | % 17.17/2.96 | GROUND_INST: instantiating (18) with all_57_1, all_69_1, all_46_1, all_46_3, % 17.17/2.96 | simplifying with (52), (60) gives: % 17.17/2.96 | (65) all_69_1 = all_57_1 % 17.17/2.96 | % 17.17/2.96 | COMBINE_EQS: (63), (64) imply: % 17.17/2.96 | (66) all_69_0 = all_46_0 % 17.17/2.96 | % 17.17/2.96 | BETA: splitting (37) gives: % 17.17/2.96 | % 17.17/2.96 | Case 1: % 17.17/2.96 | | % 17.17/2.96 | | (67) ~ (all_46_0 = 0) % 17.17/2.96 | | % 17.17/2.96 | | BETA: splitting (38) gives: % 17.17/2.96 | | % 17.17/2.96 | | Case 1: % 17.17/2.96 | | | % 17.17/2.96 | | | (68) less_than(all_46_3, all_46_1) = 0 % 17.17/2.96 | | | % 17.17/2.96 | | | BETA: splitting (39) gives: % 17.17/2.96 | | | % 17.17/2.96 | | | Case 1: % 17.17/2.96 | | | | % 17.17/2.96 | | | | (69) all_46_0 = 0 % 17.17/2.96 | | | | % 17.17/2.96 | | | | REDUCE: (67), (69) imply: % 17.17/2.96 | | | | (70) $false % 17.17/2.96 | | | | % 17.17/2.96 | | | | CLOSE: (70) is inconsistent. % 17.17/2.96 | | | | % 17.17/2.96 | | | Case 2: % 17.17/2.96 | | | | % 17.17/2.96 | | | | (71) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_46_3, % 17.17/2.96 | | | | all_46_1) = v1 & less_than(all_46_3, all_46_1) = v0 & ( ~ % 17.17/2.96 | | | | (v0 = 0) | v1 = 0)) % 17.17/2.96 | | | | % 17.17/2.96 | | | | DELTA: instantiating (71) with fresh symbols all_96_0, all_96_1 gives: % 17.17/2.96 | | | | (72) strictly_less_than(all_46_3, all_46_1) = all_96_0 & % 17.17/2.96 | | | | less_than(all_46_3, all_46_1) = all_96_1 & ( ~ (all_96_1 = 0) | % 17.17/2.96 | | | | all_96_0 = 0) % 17.17/2.96 | | | | % 17.17/2.96 | | | | ALPHA: (72) implies: % 17.17/2.96 | | | | (73) strictly_less_than(all_46_3, all_46_1) = all_96_0 % 17.17/2.96 | | | | % 17.17/2.96 | | | | BETA: splitting (56) gives: % 17.17/2.96 | | | | % 17.17/2.96 | | | | Case 1: % 17.17/2.96 | | | | | % 17.17/2.96 | | | | | (74) all_57_1 = 0 % 17.17/2.96 | | | | | % 17.17/2.96 | | | | | REDUCE: (52), (74) imply: % 17.17/2.96 | | | | | (75) strictly_less_than(all_46_3, all_46_1) = 0 % 17.17/2.96 | | | | | % 17.17/2.96 | | | | | GROUND_INST: instantiating (18) with 0, all_96_0, all_46_1, all_46_3, % 17.17/2.96 | | | | | simplifying with (73), (75) gives: % 17.17/2.96 | | | | | (76) all_96_0 = 0 % 17.17/2.96 | | | | | % 17.17/2.96 | | | | | BETA: splitting (43) gives: % 17.17/2.96 | | | | | % 17.17/2.96 | | | | | Case 1: % 17.17/2.96 | | | | | | % 17.17/2.96 | | | | | | (77) all_46_7 = create_slb % 17.17/2.96 | | | | | | % 17.17/2.96 | | | | | | REDUCE: (34), (77) imply: % 17.17/2.96 | | | | | | (78) triple(all_46_8, create_slb, all_46_6) = all_46_5 % 17.17/2.96 | | | | | | % 17.17/2.96 | | | | | | REDUCE: (25), (77) imply: % 17.17/2.96 | | | | | | (79) $i(create_slb) % 17.17/2.96 | | | | | | % 17.17/2.96 | | | | | | REF_CLOSE: (6), (7), (14), (15), (24), (26), (33), (35), (78), (79) % 17.17/2.96 | | | | | | are inconsistent by sub-proof #2. % 17.17/2.96 | | | | | | % 17.17/2.96 | | | | | Case 2: % 17.17/2.96 | | | | | | % 17.17/2.96 | | | | | | (80) ~ (all_46_7 = create_slb) % 17.17/2.96 | | | | | | (81) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? % 17.17/2.96 | | | | | | [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_46_8) = v0 & % 17.17/2.96 | | | | | | triple(all_46_8, v4, all_46_6) = v5 & update_slb(all_46_7, % 17.17/2.96 | | | | | | v0) = v4 & lookup_slb(all_46_7, v0) = v2 & % 17.17/2.96 | | | | | | contains_slb(all_46_7, v0) = v1 & less_than(v2, v0) = v3 & % 17.17/2.96 | | | | | | $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 % 17.17/2.96 | | | | | | = 0) | v5 = all_46_4)) % 17.17/2.96 | | | | | | % 17.17/2.96 | | | | | | DELTA: instantiating (81) with fresh symbols all_113_0, all_113_1, % 17.17/2.96 | | | | | | all_113_2, all_113_3, all_113_4, all_113_5 gives: % 17.17/2.97 | | | | | | (82) findmin_pqp_res(all_46_8) = all_113_5 & triple(all_46_8, % 17.17/2.97 | | | | | | all_113_1, all_46_6) = all_113_0 & update_slb(all_46_7, % 17.17/2.97 | | | | | | all_113_5) = all_113_1 & lookup_slb(all_46_7, all_113_5) = % 17.17/2.97 | | | | | | all_113_3 & contains_slb(all_46_7, all_113_5) = all_113_4 & % 17.17/2.97 | | | | | | less_than(all_113_3, all_113_5) = all_113_2 & $i(all_113_0) % 17.17/2.97 | | | | | | & $i(all_113_1) & $i(all_113_3) & $i(all_113_5) & ( ~ % 17.17/2.97 | | | | | | (all_113_2 = 0) | ~ (all_113_4 = 0) | all_113_0 = % 17.17/2.97 | | | | | | all_46_4) % 17.17/2.97 | | | | | | % 17.17/2.97 | | | | | | ALPHA: (82) implies: % 17.17/2.97 | | | | | | (83) contains_slb(all_46_7, all_113_5) = all_113_4 % 17.17/2.97 | | | | | | (84) update_slb(all_46_7, all_113_5) = all_113_1 % 17.17/2.97 | | | | | | (85) findmin_pqp_res(all_46_8) = all_113_5 % 17.17/2.97 | | | | | | % 17.17/2.97 | | | | | | BETA: splitting (57) gives: % 17.17/2.97 | | | | | | % 17.17/2.97 | | | | | | Case 1: % 17.17/2.97 | | | | | | | % 17.17/2.97 | | | | | | | (86) all_46_7 = create_slb % 17.17/2.97 | | | | | | | % 17.17/2.97 | | | | | | | REDUCE: (80), (86) imply: % 17.17/2.97 | | | | | | | (87) $false % 17.17/2.97 | | | | | | | % 17.17/2.97 | | | | | | | CLOSE: (87) is inconsistent. % 17.17/2.97 | | | | | | | % 17.17/2.97 | | | | | | Case 2: % 17.17/2.97 | | | | | | | % 17.17/2.97 | | | | | | | (88) findmin_pqp_res(all_46_8) = all_53_0 & $i(all_53_0) % 17.17/2.97 | | | | | | | % 17.17/2.97 | | | | | | | ALPHA: (88) implies: % 17.17/2.97 | | | | | | | (89) findmin_pqp_res(all_46_8) = all_53_0 % 17.17/2.97 | | | | | | | % 17.17/2.97 | | | | | | | BETA: splitting (44) gives: % 17.17/2.97 | | | | | | | % 17.17/2.97 | | | | | | | Case 1: % 17.17/2.97 | | | | | | | | % 17.17/2.97 | | | | | | | | (90) all_46_7 = create_slb % 17.17/2.97 | | | | | | | | % 17.17/2.97 | | | | | | | | REDUCE: (80), (90) imply: % 17.17/2.97 | | | | | | | | (91) $false % 17.17/2.97 | | | | | | | | % 17.17/2.97 | | | | | | | | CLOSE: (91) is inconsistent. % 17.17/2.97 | | | | | | | | % 17.17/2.97 | | | | | | | Case 2: % 17.17/2.97 | | | | | | | | % 17.17/2.97 | | | | | | | | (92) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] % 17.17/2.97 | | | | | | | | : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_46_8) % 17.17/2.97 | | | | | | | | = v0 & triple(all_46_8, v4, bad) = v5 & % 17.17/2.97 | | | | | | | | update_slb(all_46_7, v0) = v4 & lookup_slb(all_46_7, % 17.17/2.97 | | | | | | | | v0) = v2 & contains_slb(all_46_7, v0) = v1 & % 17.17/2.97 | | | | | | | | strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & % 17.17/2.97 | | | | | | | | $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = % 17.17/2.97 | | | | | | | | all_46_4)) % 17.17/2.97 | | | | | | | | % 17.17/2.97 | | | | | | | | DELTA: instantiating (92) with fresh symbols all_122_0, % 17.17/2.97 | | | | | | | | all_122_1, all_122_2, all_122_3, all_122_4, all_122_5 % 17.17/2.97 | | | | | | | | gives: % 17.17/2.97 | | | | | | | | (93) findmin_pqp_res(all_46_8) = all_122_5 & triple(all_46_8, % 17.17/2.97 | | | | | | | | all_122_1, bad) = all_122_0 & update_slb(all_46_7, % 17.17/2.97 | | | | | | | | all_122_5) = all_122_1 & lookup_slb(all_46_7, % 17.17/2.97 | | | | | | | | all_122_5) = all_122_3 & contains_slb(all_46_7, % 17.17/2.97 | | | | | | | | all_122_5) = all_122_4 & strictly_less_than(all_122_5, % 17.17/2.97 | | | | | | | | all_122_3) = all_122_2 & $i(all_122_0) & $i(all_122_1) % 17.17/2.97 | | | | | | | | & $i(all_122_3) & $i(all_122_5) & ( ~ (all_122_2 = 0) | % 17.17/2.97 | | | | | | | | ~ (all_122_4 = 0) | all_122_0 = all_46_4) % 17.17/2.97 | | | | | | | | % 17.17/2.97 | | | | | | | | ALPHA: (93) implies: % 17.17/2.97 | | | | | | | | (94) $i(all_122_1) % 17.17/2.97 | | | | | | | | (95) strictly_less_than(all_122_5, all_122_3) = all_122_2 % 17.17/2.97 | | | | | | | | (96) contains_slb(all_46_7, all_122_5) = all_122_4 % 17.17/2.97 | | | | | | | | (97) lookup_slb(all_46_7, all_122_5) = all_122_3 % 17.17/2.97 | | | | | | | | (98) update_slb(all_46_7, all_122_5) = all_122_1 % 17.17/2.97 | | | | | | | | (99) triple(all_46_8, all_122_1, bad) = all_122_0 % 17.17/2.97 | | | | | | | | (100) findmin_pqp_res(all_46_8) = all_122_5 % 17.17/2.97 | | | | | | | | (101) ~ (all_122_2 = 0) | ~ (all_122_4 = 0) | all_122_0 = % 17.17/2.97 | | | | | | | | all_46_4 % 17.17/2.97 | | | | | | | | % 17.17/2.97 | | | | | | | | BETA: splitting (45) gives: % 17.17/2.97 | | | | | | | | % 17.17/2.97 | | | | | | | | Case 1: % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | (102) all_46_7 = create_slb % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | REDUCE: (80), (102) imply: % 17.17/2.97 | | | | | | | | | (103) $false % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | CLOSE: (103) is inconsistent. % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | Case 2: % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | (104) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: % 17.17/2.97 | | | | | | | | | $i] : (findmin_pqp_res(all_46_8) = v0 & % 17.17/2.97 | | | | | | | | | triple(all_46_8, v2, bad) = v3 & % 17.17/2.97 | | | | | | | | | update_slb(all_46_7, v0) = v2 & % 17.17/2.97 | | | | | | | | | contains_slb(all_46_7, v0) = v1 & $i(v3) & $i(v2) & % 17.17/2.97 | | | | | | | | | $i(v0) & (v3 = all_46_4 | v1 = 0)) % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | DELTA: instantiating (104) with fresh symbols all_127_0, % 17.17/2.97 | | | | | | | | | all_127_1, all_127_2, all_127_3 gives: % 17.17/2.97 | | | | | | | | | (105) findmin_pqp_res(all_46_8) = all_127_3 & % 17.17/2.97 | | | | | | | | | triple(all_46_8, all_127_1, bad) = all_127_0 & % 17.17/2.97 | | | | | | | | | update_slb(all_46_7, all_127_3) = all_127_1 & % 17.17/2.97 | | | | | | | | | contains_slb(all_46_7, all_127_3) = all_127_2 & % 17.17/2.97 | | | | | | | | | $i(all_127_0) & $i(all_127_1) & $i(all_127_3) & % 17.17/2.97 | | | | | | | | | (all_127_0 = all_46_4 | all_127_2 = 0) % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | ALPHA: (105) implies: % 17.17/2.97 | | | | | | | | | (106) contains_slb(all_46_7, all_127_3) = all_127_2 % 17.17/2.97 | | | | | | | | | (107) update_slb(all_46_7, all_127_3) = all_127_1 % 17.17/2.97 | | | | | | | | | (108) triple(all_46_8, all_127_1, bad) = all_127_0 % 17.17/2.97 | | | | | | | | | (109) findmin_pqp_res(all_46_8) = all_127_3 % 17.17/2.97 | | | | | | | | | (110) all_127_0 = all_46_4 | all_127_2 = 0 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | GROUND_INST: instantiating (16) with all_46_3, all_122_5, % 17.17/2.97 | | | | | | | | | all_46_8, simplifying with (36), (100) gives: % 17.17/2.97 | | | | | | | | | (111) all_122_5 = all_46_3 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | GROUND_INST: instantiating (16) with all_113_5, all_122_5, % 17.17/2.97 | | | | | | | | | all_46_8, simplifying with (85), (100) gives: % 17.17/2.97 | | | | | | | | | (112) all_122_5 = all_113_5 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | GROUND_INST: instantiating (16) with all_113_5, all_127_3, % 17.17/2.97 | | | | | | | | | all_46_8, simplifying with (85), (109) gives: % 17.17/2.97 | | | | | | | | | (113) all_127_3 = all_113_5 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | GROUND_INST: instantiating (16) with all_53_0, all_127_3, % 17.17/2.97 | | | | | | | | | all_46_8, simplifying with (89), (109) gives: % 17.17/2.97 | | | | | | | | | (114) all_127_3 = all_53_0 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | COMBINE_EQS: (113), (114) imply: % 17.17/2.97 | | | | | | | | | (115) all_113_5 = all_53_0 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | SIMP: (115) implies: % 17.17/2.97 | | | | | | | | | (116) all_113_5 = all_53_0 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | COMBINE_EQS: (111), (112) imply: % 17.17/2.97 | | | | | | | | | (117) all_113_5 = all_46_3 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | SIMP: (117) implies: % 17.17/2.97 | | | | | | | | | (118) all_113_5 = all_46_3 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | COMBINE_EQS: (116), (118) imply: % 17.17/2.97 | | | | | | | | | (119) all_53_0 = all_46_3 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | COMBINE_EQS: (114), (119) imply: % 17.17/2.97 | | | | | | | | | (120) all_127_3 = all_46_3 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | REDUCE: (107), (120) imply: % 17.17/2.97 | | | | | | | | | (121) update_slb(all_46_7, all_46_3) = all_127_1 % 17.17/2.97 | | | | | | | | | % 17.17/2.97 | | | | | | | | | REDUCE: (98), (111) imply: % 17.51/2.97 | | | | | | | | | (122) update_slb(all_46_7, all_46_3) = all_122_1 % 17.51/2.97 | | | | | | | | | % 17.51/2.97 | | | | | | | | | REDUCE: (84), (118) imply: % 17.51/2.97 | | | | | | | | | (123) update_slb(all_46_7, all_46_3) = all_113_1 % 17.51/2.97 | | | | | | | | | % 17.51/2.97 | | | | | | | | | REDUCE: (97), (111) imply: % 17.51/2.97 | | | | | | | | | (124) lookup_slb(all_46_7, all_46_3) = all_122_3 % 17.51/2.97 | | | | | | | | | % 17.51/2.97 | | | | | | | | | REDUCE: (106), (120) imply: % 17.51/2.97 | | | | | | | | | (125) contains_slb(all_46_7, all_46_3) = all_127_2 % 17.51/2.97 | | | | | | | | | % 17.51/2.97 | | | | | | | | | REDUCE: (96), (111) imply: % 17.51/2.97 | | | | | | | | | (126) contains_slb(all_46_7, all_46_3) = all_122_4 % 17.51/2.97 | | | | | | | | | % 17.51/2.97 | | | | | | | | | REDUCE: (83), (118) imply: % 17.51/2.97 | | | | | | | | | (127) contains_slb(all_46_7, all_46_3) = all_113_4 % 17.51/2.97 | | | | | | | | | % 17.51/2.97 | | | | | | | | | REDUCE: (95), (111) imply: % 17.51/2.97 | | | | | | | | | (128) strictly_less_than(all_46_3, all_122_3) = all_122_2 % 17.51/2.97 | | | | | | | | | % 17.51/2.97 | | | | | | | | | GROUND_INST: instantiating (19) with all_122_4, all_127_2, % 17.51/2.97 | | | | | | | | | all_46_3, all_46_7, simplifying with (125), (126) % 17.51/2.97 | | | | | | | | | gives: % 17.51/2.97 | | | | | | | | | (129) all_127_2 = all_122_4 % 17.51/2.97 | | | | | | | | | % 17.51/2.97 | | | | | | | | | GROUND_INST: instantiating (19) with all_113_4, all_127_2, % 17.51/2.97 | | | | | | | | | all_46_3, all_46_7, simplifying with (125), (127) % 17.51/2.97 | | | | | | | | | gives: % 17.51/2.98 | | | | | | | | | (130) all_127_2 = all_113_4 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | GROUND_INST: instantiating (20) with all_46_1, all_122_3, % 17.51/2.98 | | | | | | | | | all_46_3, all_46_7, simplifying with (32), (124) % 17.51/2.98 | | | | | | | | | gives: % 17.51/2.98 | | | | | | | | | (131) all_122_3 = all_46_1 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | GROUND_INST: instantiating (21) with all_122_1, all_127_1, % 17.51/2.98 | | | | | | | | | all_46_3, all_46_7, simplifying with (121), (122) % 17.51/2.98 | | | | | | | | | gives: % 17.51/2.98 | | | | | | | | | (132) all_127_1 = all_122_1 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | GROUND_INST: instantiating (21) with all_113_1, all_127_1, % 17.51/2.98 | | | | | | | | | all_46_3, all_46_7, simplifying with (121), (123) % 17.51/2.98 | | | | | | | | | gives: % 17.51/2.98 | | | | | | | | | (133) all_127_1 = all_113_1 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | COMBINE_EQS: (132), (133) imply: % 17.51/2.98 | | | | | | | | | (134) all_122_1 = all_113_1 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | SIMP: (134) implies: % 17.51/2.98 | | | | | | | | | (135) all_122_1 = all_113_1 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | COMBINE_EQS: (129), (130) imply: % 17.51/2.98 | | | | | | | | | (136) all_122_4 = all_113_4 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | SIMP: (136) implies: % 17.51/2.98 | | | | | | | | | (137) all_122_4 = all_113_4 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | REDUCE: (108), (133) imply: % 17.51/2.98 | | | | | | | | | (138) triple(all_46_8, all_113_1, bad) = all_127_0 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | REDUCE: (99), (135) imply: % 17.51/2.98 | | | | | | | | | (139) triple(all_46_8, all_113_1, bad) = all_122_0 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | REDUCE: (128), (131) imply: % 17.51/2.98 | | | | | | | | | (140) strictly_less_than(all_46_3, all_46_1) = all_122_2 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | REDUCE: (94), (135) imply: % 17.51/2.98 | | | | | | | | | (141) $i(all_113_1) % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_122_2, all_46_1, % 17.51/2.98 | | | | | | | | | all_46_3, simplifying with (75), (140) gives: % 17.51/2.98 | | | | | | | | | (142) all_122_2 = 0 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | GROUND_INST: instantiating (22) with all_122_0, all_127_0, bad, % 17.51/2.98 | | | | | | | | | all_113_1, all_46_8, simplifying with (138), (139) % 17.51/2.98 | | | | | | | | | gives: % 17.51/2.98 | | | | | | | | | (143) all_127_0 = all_122_0 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | GROUND_INST: instantiating (6) with all_46_8, all_113_1, % 17.51/2.98 | | | | | | | | | all_122_0, simplifying with (24), (139), (141) % 17.51/2.98 | | | | | | | | | gives: % 17.51/2.98 | | | | | | | | | (144) ? [v0: int] : ( ~ (v0 = 0) & ok(all_122_0) = v0) % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | DELTA: instantiating (144) with fresh symbol all_146_0 gives: % 17.51/2.98 | | | | | | | | | (145) ~ (all_146_0 = 0) & ok(all_122_0) = all_146_0 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | ALPHA: (145) implies: % 17.51/2.98 | | | | | | | | | (146) ~ (all_146_0 = 0) % 17.51/2.98 | | | | | | | | | (147) ok(all_122_0) = all_146_0 % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | BETA: splitting (101) gives: % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | | Case 1: % 17.51/2.98 | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | (148) ~ (all_122_2 = 0) % 17.51/2.98 | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | REDUCE: (142), (148) imply: % 17.51/2.98 | | | | | | | | | | (149) $false % 17.51/2.98 | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | CLOSE: (149) is inconsistent. % 17.51/2.98 | | | | | | | | | | % 17.51/2.98 | | | | | | | | | Case 2: % 17.51/2.98 | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | (150) ~ (all_122_4 = 0) | all_122_0 = all_46_4 % 17.51/2.98 | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | BETA: splitting (110) gives: % 17.51/2.98 | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | Case 1: % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | (151) all_127_2 = 0 % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | COMBINE_EQS: (130), (151) imply: % 17.51/2.98 | | | | | | | | | | | (152) all_113_4 = 0 % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | SIMP: (152) implies: % 17.51/2.98 | | | | | | | | | | | (153) all_113_4 = 0 % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | COMBINE_EQS: (137), (153) imply: % 17.51/2.98 | | | | | | | | | | | (154) all_122_4 = 0 % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | BETA: splitting (150) gives: % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | Case 1: % 17.51/2.98 | | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | | (155) ~ (all_122_4 = 0) % 17.51/2.98 | | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | | REDUCE: (154), (155) imply: % 17.51/2.98 | | | | | | | | | | | | (156) $false % 17.51/2.98 | | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | | CLOSE: (156) is inconsistent. % 17.51/2.98 | | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | Case 2: % 17.51/2.98 | | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | | (157) all_122_0 = all_46_4 % 17.51/2.98 | | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | | REDUCE: (147), (157) imply: % 17.51/2.98 | | | | | | | | | | | | (158) ok(all_46_4) = all_146_0 % 17.51/2.98 | | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | | REF_CLOSE: (15), (35), (146), (158) are inconsistent by % 17.51/2.98 | | | | | | | | | | | | sub-proof #1. % 17.51/2.98 | | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | End of split % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | Case 2: % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | (159) all_127_0 = all_46_4 % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | COMBINE_EQS: (143), (159) imply: % 17.51/2.98 | | | | | | | | | | | (160) all_122_0 = all_46_4 % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | REDUCE: (147), (160) imply: % 17.51/2.98 | | | | | | | | | | | (161) ok(all_46_4) = all_146_0 % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | | REF_CLOSE: (15), (35), (146), (161) are inconsistent by % 17.51/2.98 | | | | | | | | | | | sub-proof #1. % 17.51/2.98 | | | | | | | | | | | % 17.51/2.98 | | | | | | | | | | End of split % 17.51/2.98 | | | | | | | | | | % 17.51/2.98 | | | | | | | | | End of split % 17.51/2.98 | | | | | | | | | % 17.51/2.98 | | | | | | | | End of split % 17.51/2.98 | | | | | | | | % 17.51/2.98 | | | | | | | End of split % 17.51/2.98 | | | | | | | % 17.51/2.98 | | | | | | End of split % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | End of split % 17.51/2.98 | | | | | % 17.51/2.98 | | | | Case 2: % 17.51/2.98 | | | | | % 17.51/2.98 | | | | | (162) ? [v0: any] : ? [v1: any] : (less_than(all_46_1, all_46_3) % 17.51/2.98 | | | | | = v1 & less_than(all_46_3, all_46_1) = v0 & ( ~ (v0 = 0) | % 17.51/2.98 | | | | | v1 = 0)) % 17.51/2.98 | | | | | % 17.51/2.98 | | | | | DELTA: instantiating (162) with fresh symbols all_102_0, all_102_1 % 17.51/2.98 | | | | | gives: % 17.51/2.98 | | | | | (163) less_than(all_46_1, all_46_3) = all_102_0 & % 17.51/2.98 | | | | | less_than(all_46_3, all_46_1) = all_102_1 & ( ~ (all_102_1 = % 17.51/2.98 | | | | | 0) | all_102_0 = 0) % 17.51/2.98 | | | | | % 17.51/2.98 | | | | | ALPHA: (163) implies: % 17.51/2.98 | | | | | (164) less_than(all_46_3, all_46_1) = all_102_1 % 17.51/2.98 | | | | | (165) less_than(all_46_1, all_46_3) = all_102_0 % 17.51/2.98 | | | | | (166) ~ (all_102_1 = 0) | all_102_0 = 0 % 17.51/2.98 | | | | | % 17.51/2.98 | | | | | GROUND_INST: instantiating (17) with 0, all_102_1, all_46_1, all_46_3, % 17.51/2.98 | | | | | simplifying with (68), (164) gives: % 17.51/2.98 | | | | | (167) all_102_1 = 0 % 17.51/2.98 | | | | | % 17.51/2.98 | | | | | GROUND_INST: instantiating (17) with all_46_0, all_102_0, all_46_3, % 17.51/2.98 | | | | | all_46_1, simplifying with (30), (165) gives: % 17.51/2.98 | | | | | (168) all_102_0 = all_46_0 % 17.51/2.98 | | | | | % 17.51/2.98 | | | | | BETA: splitting (166) gives: % 17.51/2.98 | | | | | % 17.51/2.98 | | | | | Case 1: % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | | (169) ~ (all_102_1 = 0) % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | | REDUCE: (167), (169) imply: % 17.51/2.98 | | | | | | (170) $false % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | | CLOSE: (170) is inconsistent. % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | Case 2: % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | | (171) all_102_0 = 0 % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | | COMBINE_EQS: (168), (171) imply: % 17.51/2.98 | | | | | | (172) all_46_0 = 0 % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | | REDUCE: (67), (172) imply: % 17.51/2.98 | | | | | | (173) $false % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | | CLOSE: (173) is inconsistent. % 17.51/2.98 | | | | | | % 17.51/2.98 | | | | | End of split % 17.51/2.98 | | | | | % 17.51/2.98 | | | | End of split % 17.51/2.98 | | | | % 17.51/2.98 | | | End of split % 17.51/2.98 | | | % 17.51/2.98 | | Case 2: % 17.51/2.98 | | | % 17.51/2.98 | | | (174) all_46_0 = 0 % 17.51/2.98 | | | % 17.51/2.98 | | | REDUCE: (67), (174) imply: % 17.51/2.98 | | | (175) $false % 17.51/2.98 | | | % 17.51/2.98 | | | CLOSE: (175) is inconsistent. % 17.51/2.98 | | | % 17.51/2.98 | | End of split % 17.51/2.98 | | % 17.51/2.98 | Case 2: % 17.51/2.98 | | % 17.51/2.98 | | (176) ~ (all_46_2 = 0) | all_46_7 = create_slb % 17.51/2.98 | | % 17.51/2.98 | | BETA: splitting (44) gives: % 17.51/2.98 | | % 17.51/2.98 | | Case 1: % 17.51/2.98 | | | % 17.51/2.98 | | | (177) all_46_7 = create_slb % 17.51/2.98 | | | % 17.51/2.98 | | | REDUCE: (34), (177) imply: % 17.51/2.98 | | | (178) triple(all_46_8, create_slb, all_46_6) = all_46_5 % 17.51/2.98 | | | % 17.51/2.98 | | | REDUCE: (25), (177) imply: % 17.51/2.98 | | | (179) $i(create_slb) % 17.51/2.98 | | | % 17.51/2.98 | | | REF_CLOSE: (6), (7), (14), (15), (24), (26), (33), (35), (178), (179) are % 17.51/2.98 | | | inconsistent by sub-proof #2. % 17.51/2.98 | | | % 17.51/2.98 | | Case 2: % 17.51/2.98 | | | % 17.51/2.99 | | | (180) ~ (all_46_7 = create_slb) % 17.51/2.99 | | | (181) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4: % 17.51/2.99 | | | $i] : ? [v5: $i] : (findmin_pqp_res(all_46_8) = v0 & % 17.51/2.99 | | | triple(all_46_8, v4, bad) = v5 & update_slb(all_46_7, v0) = v4 % 17.51/2.99 | | | & lookup_slb(all_46_7, v0) = v2 & contains_slb(all_46_7, v0) = % 17.51/2.99 | | | v1 & strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v2) % 17.51/2.99 | | | & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_46_4)) % 17.51/2.99 | | | % 17.51/2.99 | | | DELTA: instantiating (181) with fresh symbols all_106_0, all_106_1, % 17.51/2.99 | | | all_106_2, all_106_3, all_106_4, all_106_5 gives: % 17.51/2.99 | | | (182) findmin_pqp_res(all_46_8) = all_106_5 & triple(all_46_8, % 17.51/2.99 | | | all_106_1, bad) = all_106_0 & update_slb(all_46_7, all_106_5) = % 17.51/2.99 | | | all_106_1 & lookup_slb(all_46_7, all_106_5) = all_106_3 & % 17.51/2.99 | | | contains_slb(all_46_7, all_106_5) = all_106_4 & % 17.51/2.99 | | | strictly_less_than(all_106_5, all_106_3) = all_106_2 & % 17.51/2.99 | | | $i(all_106_0) & $i(all_106_1) & $i(all_106_3) & $i(all_106_5) & ( % 17.51/2.99 | | | ~ (all_106_2 = 0) | ~ (all_106_4 = 0) | all_106_0 = all_46_4) % 17.51/2.99 | | | % 17.51/2.99 | | | ALPHA: (182) implies: % 17.51/2.99 | | | (183) contains_slb(all_46_7, all_106_5) = all_106_4 % 17.51/2.99 | | | (184) update_slb(all_46_7, all_106_5) = all_106_1 % 17.51/2.99 | | | (185) triple(all_46_8, all_106_1, bad) = all_106_0 % 17.51/2.99 | | | (186) findmin_pqp_res(all_46_8) = all_106_5 % 17.51/2.99 | | | % 17.51/2.99 | | | BETA: splitting (57) gives: % 17.51/2.99 | | | % 17.51/2.99 | | | Case 1: % 17.51/2.99 | | | | % 17.51/2.99 | | | | (187) all_46_7 = create_slb % 17.51/2.99 | | | | % 17.51/2.99 | | | | REDUCE: (180), (187) imply: % 17.51/2.99 | | | | (188) $false % 17.51/2.99 | | | | % 17.51/2.99 | | | | CLOSE: (188) is inconsistent. % 17.51/2.99 | | | | % 17.51/2.99 | | | Case 2: % 17.51/2.99 | | | | % 17.51/2.99 | | | | (189) findmin_pqp_res(all_46_8) = all_53_0 & $i(all_53_0) % 17.51/2.99 | | | | % 17.51/2.99 | | | | ALPHA: (189) implies: % 17.51/2.99 | | | | (190) findmin_pqp_res(all_46_8) = all_53_0 % 17.51/2.99 | | | | % 17.51/2.99 | | | | BETA: splitting (45) gives: % 17.51/2.99 | | | | % 17.51/2.99 | | | | Case 1: % 17.51/2.99 | | | | | % 17.51/2.99 | | | | | (191) all_46_7 = create_slb % 17.51/2.99 | | | | | % 17.51/2.99 | | | | | REDUCE: (180), (191) imply: % 17.51/2.99 | | | | | (192) $false % 17.51/2.99 | | | | | % 17.51/2.99 | | | | | CLOSE: (192) is inconsistent. % 17.51/2.99 | | | | | % 17.51/2.99 | | | | Case 2: % 17.51/2.99 | | | | | % 17.51/2.99 | | | | | (193) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 17.51/2.99 | | | | | (findmin_pqp_res(all_46_8) = v0 & triple(all_46_8, v2, bad) = % 17.51/2.99 | | | | | v3 & update_slb(all_46_7, v0) = v2 & contains_slb(all_46_7, % 17.51/2.99 | | | | | v0) = v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_46_4 | v1 % 17.51/2.99 | | | | | = 0)) % 17.51/2.99 | | | | | % 17.51/2.99 | | | | | DELTA: instantiating (193) with fresh symbols all_115_0, all_115_1, % 17.51/2.99 | | | | | all_115_2, all_115_3 gives: % 17.51/2.99 | | | | | (194) findmin_pqp_res(all_46_8) = all_115_3 & triple(all_46_8, % 17.51/2.99 | | | | | all_115_1, bad) = all_115_0 & update_slb(all_46_7, % 17.51/2.99 | | | | | all_115_3) = all_115_1 & contains_slb(all_46_7, all_115_3) % 17.51/2.99 | | | | | = all_115_2 & $i(all_115_0) & $i(all_115_1) & $i(all_115_3) & % 17.51/2.99 | | | | | (all_115_0 = all_46_4 | all_115_2 = 0) % 17.51/2.99 | | | | | % 17.51/2.99 | | | | | ALPHA: (194) implies: % 17.51/2.99 | | | | | (195) $i(all_115_1) % 17.51/2.99 | | | | | (196) contains_slb(all_46_7, all_115_3) = all_115_2 % 17.51/2.99 | | | | | (197) update_slb(all_46_7, all_115_3) = all_115_1 % 17.51/2.99 | | | | | (198) triple(all_46_8, all_115_1, bad) = all_115_0 % 17.51/2.99 | | | | | (199) findmin_pqp_res(all_46_8) = all_115_3 % 17.51/2.99 | | | | | (200) all_115_0 = all_46_4 | all_115_2 = 0 % 17.51/2.99 | | | | | % 17.51/2.99 | | | | | BETA: splitting (43) gives: % 17.51/2.99 | | | | | % 17.51/2.99 | | | | | Case 1: % 17.51/2.99 | | | | | | % 17.51/2.99 | | | | | | (201) all_46_7 = create_slb % 17.51/2.99 | | | | | | % 17.51/2.99 | | | | | | REDUCE: (180), (201) imply: % 17.51/2.99 | | | | | | (202) $false % 17.51/2.99 | | | | | | % 17.51/2.99 | | | | | | CLOSE: (202) is inconsistent. % 17.51/2.99 | | | | | | % 17.51/2.99 | | | | | Case 2: % 17.51/2.99 | | | | | | % 17.51/2.99 | | | | | | (203) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 17.51/2.99 | | | | | | ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_46_8) = v0 % 17.51/2.99 | | | | | | & triple(all_46_8, v4, all_46_6) = v5 & % 17.51/2.99 | | | | | | update_slb(all_46_7, v0) = v4 & lookup_slb(all_46_7, v0) % 17.51/2.99 | | | | | | = v2 & contains_slb(all_46_7, v0) = v1 & less_than(v2, % 17.51/2.99 | | | | | | v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 % 17.51/2.99 | | | | | | = 0) | ~ (v1 = 0) | v5 = all_46_4)) % 17.51/2.99 | | | | | | % 17.51/2.99 | | | | | | DELTA: instantiating (203) with fresh symbols all_120_0, all_120_1, % 17.51/2.99 | | | | | | all_120_2, all_120_3, all_120_4, all_120_5 gives: % 17.51/2.99 | | | | | | (204) findmin_pqp_res(all_46_8) = all_120_5 & triple(all_46_8, % 17.51/2.99 | | | | | | all_120_1, all_46_6) = all_120_0 & update_slb(all_46_7, % 17.51/2.99 | | | | | | all_120_5) = all_120_1 & lookup_slb(all_46_7, all_120_5) % 17.51/2.99 | | | | | | = all_120_3 & contains_slb(all_46_7, all_120_5) = all_120_4 % 17.51/2.99 | | | | | | & less_than(all_120_3, all_120_5) = all_120_2 & % 17.51/2.99 | | | | | | $i(all_120_0) & $i(all_120_1) & $i(all_120_3) & % 17.51/2.99 | | | | | | $i(all_120_5) & ( ~ (all_120_2 = 0) | ~ (all_120_4 = 0) | % 17.51/2.99 | | | | | | all_120_0 = all_46_4) % 17.51/2.99 | | | | | | % 17.51/2.99 | | | | | | ALPHA: (204) implies: % 17.51/2.99 | | | | | | (205) contains_slb(all_46_7, all_120_5) = all_120_4 % 17.51/2.99 | | | | | | (206) update_slb(all_46_7, all_120_5) = all_120_1 % 17.51/2.99 | | | | | | (207) findmin_pqp_res(all_46_8) = all_120_5 % 17.51/2.99 | | | | | | % 17.51/2.99 | | | | | | BETA: splitting (176) gives: % 17.51/2.99 | | | | | | % 17.51/2.99 | | | | | | Case 1: % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | (208) ~ (all_46_2 = 0) % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | GROUND_INST: instantiating (16) with all_46_3, all_115_3, % 17.51/2.99 | | | | | | | all_46_8, simplifying with (36), (199) gives: % 17.51/2.99 | | | | | | | (209) all_115_3 = all_46_3 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | GROUND_INST: instantiating (16) with all_106_5, all_115_3, % 17.51/2.99 | | | | | | | all_46_8, simplifying with (186), (199) gives: % 17.51/2.99 | | | | | | | (210) all_115_3 = all_106_5 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | GROUND_INST: instantiating (16) with all_115_3, all_120_5, % 17.51/2.99 | | | | | | | all_46_8, simplifying with (199), (207) gives: % 17.51/2.99 | | | | | | | (211) all_120_5 = all_115_3 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | GROUND_INST: instantiating (16) with all_53_0, all_120_5, % 17.51/2.99 | | | | | | | all_46_8, simplifying with (190), (207) gives: % 17.51/2.99 | | | | | | | (212) all_120_5 = all_53_0 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | COMBINE_EQS: (211), (212) imply: % 17.51/2.99 | | | | | | | (213) all_115_3 = all_53_0 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | SIMP: (213) implies: % 17.51/2.99 | | | | | | | (214) all_115_3 = all_53_0 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | COMBINE_EQS: (209), (210) imply: % 17.51/2.99 | | | | | | | (215) all_106_5 = all_46_3 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | COMBINE_EQS: (210), (214) imply: % 17.51/2.99 | | | | | | | (216) all_106_5 = all_53_0 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | COMBINE_EQS: (215), (216) imply: % 17.51/2.99 | | | | | | | (217) all_53_0 = all_46_3 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | SIMP: (217) implies: % 17.51/2.99 | | | | | | | (218) all_53_0 = all_46_3 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | COMBINE_EQS: (212), (218) imply: % 17.51/2.99 | | | | | | | (219) all_120_5 = all_46_3 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | REDUCE: (206), (219) imply: % 17.51/2.99 | | | | | | | (220) update_slb(all_46_7, all_46_3) = all_120_1 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | REDUCE: (197), (209) imply: % 17.51/2.99 | | | | | | | (221) update_slb(all_46_7, all_46_3) = all_115_1 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | REDUCE: (184), (215) imply: % 17.51/2.99 | | | | | | | (222) update_slb(all_46_7, all_46_3) = all_106_1 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | REDUCE: (205), (219) imply: % 17.51/2.99 | | | | | | | (223) contains_slb(all_46_7, all_46_3) = all_120_4 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | REDUCE: (196), (209) imply: % 17.51/2.99 | | | | | | | (224) contains_slb(all_46_7, all_46_3) = all_115_2 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | REDUCE: (183), (215) imply: % 17.51/2.99 | | | | | | | (225) contains_slb(all_46_7, all_46_3) = all_106_4 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | GROUND_INST: instantiating (19) with all_46_2, all_120_4, % 17.51/2.99 | | | | | | | all_46_3, all_46_7, simplifying with (31), (223) % 17.51/2.99 | | | | | | | gives: % 17.51/2.99 | | | | | | | (226) all_120_4 = all_46_2 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | GROUND_INST: instantiating (19) with all_115_2, all_120_4, % 17.51/2.99 | | | | | | | all_46_3, all_46_7, simplifying with (223), (224) % 17.51/2.99 | | | | | | | gives: % 17.51/2.99 | | | | | | | (227) all_120_4 = all_115_2 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | GROUND_INST: instantiating (19) with all_106_4, all_120_4, % 17.51/2.99 | | | | | | | all_46_3, all_46_7, simplifying with (223), (225) % 17.51/2.99 | | | | | | | gives: % 17.51/2.99 | | | | | | | (228) all_120_4 = all_106_4 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | GROUND_INST: instantiating (21) with all_115_1, all_120_1, % 17.51/2.99 | | | | | | | all_46_3, all_46_7, simplifying with (220), (221) % 17.51/2.99 | | | | | | | gives: % 17.51/2.99 | | | | | | | (229) all_120_1 = all_115_1 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | GROUND_INST: instantiating (21) with all_106_1, all_120_1, % 17.51/2.99 | | | | | | | all_46_3, all_46_7, simplifying with (220), (222) % 17.51/2.99 | | | | | | | gives: % 17.51/2.99 | | | | | | | (230) all_120_1 = all_106_1 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | COMBINE_EQS: (229), (230) imply: % 17.51/2.99 | | | | | | | (231) all_115_1 = all_106_1 % 17.51/2.99 | | | | | | | % 17.51/2.99 | | | | | | | SIMP: (231) implies: % 17.51/2.99 | | | | | | | (232) all_115_1 = all_106_1 % 17.51/2.99 | | | | | | | % 17.51/3.00 | | | | | | | COMBINE_EQS: (226), (227) imply: % 17.51/3.00 | | | | | | | (233) all_115_2 = all_46_2 % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | | COMBINE_EQS: (227), (228) imply: % 17.51/3.00 | | | | | | | (234) all_115_2 = all_106_4 % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | | COMBINE_EQS: (233), (234) imply: % 17.51/3.00 | | | | | | | (235) all_106_4 = all_46_2 % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | | REDUCE: (198), (232) imply: % 17.51/3.00 | | | | | | | (236) triple(all_46_8, all_106_1, bad) = all_115_0 % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | | REDUCE: (195), (232) imply: % 17.51/3.00 | | | | | | | (237) $i(all_106_1) % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | | BETA: splitting (200) gives: % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | | Case 1: % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | (238) all_115_2 = 0 % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | COMBINE_EQS: (233), (238) imply: % 17.51/3.00 | | | | | | | | (239) all_46_2 = 0 % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | SIMP: (239) implies: % 17.51/3.00 | | | | | | | | (240) all_46_2 = 0 % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | REDUCE: (208), (240) imply: % 17.51/3.00 | | | | | | | | (241) $false % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | CLOSE: (241) is inconsistent. % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | Case 2: % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | (242) all_115_0 = all_46_4 % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | REDUCE: (236), (242) imply: % 17.51/3.00 | | | | | | | | (243) triple(all_46_8, all_106_1, bad) = all_46_4 % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | GROUND_INST: instantiating (22) with all_106_0, all_46_4, bad, % 17.51/3.00 | | | | | | | | all_106_1, all_46_8, simplifying with (185), (243) % 17.51/3.00 | | | | | | | | gives: % 17.51/3.00 | | | | | | | | (244) all_106_0 = all_46_4 % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | GROUND_INST: instantiating (6) with all_46_8, all_106_1, % 17.51/3.00 | | | | | | | | all_46_4, simplifying with (24), (237), (243) % 17.51/3.00 | | | | | | | | gives: % 17.51/3.00 | | | | | | | | (245) ? [v0: int] : ( ~ (v0 = 0) & ok(all_46_4) = v0) % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | DELTA: instantiating (245) with fresh symbol all_147_0 gives: % 17.51/3.00 | | | | | | | | (246) ~ (all_147_0 = 0) & ok(all_46_4) = all_147_0 % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | ALPHA: (246) implies: % 17.51/3.00 | | | | | | | | (247) ~ (all_147_0 = 0) % 17.51/3.00 | | | | | | | | (248) ok(all_46_4) = all_147_0 % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | GROUND_INST: instantiating (15) with 0, all_147_0, all_46_4, % 17.51/3.00 | | | | | | | | simplifying with (35), (248) gives: % 17.51/3.00 | | | | | | | | (249) all_147_0 = 0 % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | REDUCE: (247), (249) imply: % 17.51/3.00 | | | | | | | | (250) $false % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | | CLOSE: (250) is inconsistent. % 17.51/3.00 | | | | | | | | % 17.51/3.00 | | | | | | | End of split % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | Case 2: % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | | (251) all_46_7 = create_slb % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | | REDUCE: (180), (251) imply: % 17.51/3.00 | | | | | | | (252) $false % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | | CLOSE: (252) is inconsistent. % 17.51/3.00 | | | | | | | % 17.51/3.00 | | | | | | End of split % 17.51/3.00 | | | | | | % 17.51/3.00 | | | | | End of split % 17.51/3.00 | | | | | % 17.51/3.00 | | | | End of split % 17.51/3.00 | | | | % 17.51/3.00 | | | End of split % 17.51/3.00 | | | % 17.51/3.00 | | End of split % 17.51/3.00 | | % 17.51/3.00 | End of split % 17.51/3.00 | % 17.51/3.00 End of proof % 17.51/3.00 % 17.51/3.00 Sub-proof #1 shows that the following formulas are inconsistent: % 17.51/3.00 ---------------------------------------------------------------- % 17.51/3.00 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.51/3.00 (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 17.51/3.00 (2) ok(all_46_4) = all_146_0 % 17.51/3.00 (3) ok(all_46_4) = 0 % 17.51/3.00 (4) ~ (all_146_0 = 0) % 17.51/3.00 % 17.51/3.00 Begin of proof % 17.51/3.00 | % 17.51/3.00 | GROUND_INST: instantiating (1) with 0, all_146_0, all_46_4, simplifying with % 17.51/3.00 | (2), (3) gives: % 17.51/3.00 | (5) all_146_0 = 0 % 17.51/3.00 | % 17.51/3.00 | REDUCE: (4), (5) imply: % 17.51/3.00 | (6) $false % 17.51/3.00 | % 17.51/3.00 | CLOSE: (6) is inconsistent. % 17.51/3.00 | % 17.51/3.00 End of proof % 17.51/3.00 % 17.51/3.00 Sub-proof #2 shows that the following formulas are inconsistent: % 17.51/3.00 ---------------------------------------------------------------- % 17.51/3.00 (1) $i(create_slb) % 17.51/3.00 (2) triple(all_46_8, create_slb, all_46_6) = all_46_5 % 17.51/3.00 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb, v1) % 17.51/3.00 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (triple(v0, create_slb, % 17.51/3.00 bad) = v3 & findmin_cpq_eff(v2) = v3 & $i(v3))) % 17.51/3.00 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = v2) % 17.51/3.00 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) = v3)) % 17.51/3.00 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.51/3.00 (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 17.51/3.00 (6) ok(all_46_4) = 0 % 17.51/3.00 (7) findmin_cpq_eff(all_46_5) = all_46_4 % 17.51/3.00 (8) $i(all_46_8) % 17.51/3.00 (9) $i(all_46_6) % 17.51/3.00 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 17.51/3.00 (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 17.51/3.00 % 17.51/3.00 Begin of proof % 17.51/3.00 | % 17.51/3.00 | GROUND_INST: instantiating (3) with all_46_8, all_46_6, all_46_5, simplifying % 17.51/3.00 | with (2), (8), (9) gives: % 17.51/3.00 | (11) ? [v0: $i] : (triple(all_46_8, create_slb, bad) = v0 & % 17.51/3.00 | findmin_cpq_eff(all_46_5) = v0 & $i(v0)) % 17.51/3.00 | % 17.51/3.00 | DELTA: instantiating (11) with fresh symbol all_112_0 gives: % 17.51/3.00 | (12) triple(all_46_8, create_slb, bad) = all_112_0 & % 17.51/3.00 | findmin_cpq_eff(all_46_5) = all_112_0 & $i(all_112_0) % 17.51/3.00 | % 17.51/3.00 | ALPHA: (12) implies: % 17.51/3.00 | (13) findmin_cpq_eff(all_46_5) = all_112_0 % 17.51/3.00 | (14) triple(all_46_8, create_slb, bad) = all_112_0 % 17.51/3.00 | % 17.51/3.00 | GROUND_INST: instantiating (10) with all_46_4, all_112_0, all_46_5, % 17.51/3.00 | simplifying with (7), (13) gives: % 17.51/3.00 | (15) all_112_0 = all_46_4 % 17.51/3.00 | % 17.51/3.00 | REDUCE: (14), (15) imply: % 17.51/3.00 | (16) triple(all_46_8, create_slb, bad) = all_46_4 % 17.51/3.00 | % 17.51/3.00 | GROUND_INST: instantiating (4) with all_46_8, create_slb, all_46_4, % 17.51/3.00 | simplifying with (1), (8), (16) gives: % 17.51/3.00 | (17) ? [v0: int] : ( ~ (v0 = 0) & ok(all_46_4) = v0) % 17.51/3.00 | % 17.51/3.00 | DELTA: instantiating (17) with fresh symbol all_124_0 gives: % 17.51/3.00 | (18) ~ (all_124_0 = 0) & ok(all_46_4) = all_124_0 % 17.51/3.00 | % 17.51/3.00 | ALPHA: (18) implies: % 17.51/3.00 | (19) ~ (all_124_0 = 0) % 17.51/3.00 | (20) ok(all_46_4) = all_124_0 % 17.51/3.00 | % 17.51/3.00 | GROUND_INST: instantiating (5) with 0, all_124_0, all_46_4, simplifying with % 17.51/3.00 | (6), (20) gives: % 17.51/3.00 | (21) all_124_0 = 0 % 17.51/3.00 | % 17.51/3.00 | REDUCE: (19), (21) imply: % 17.51/3.00 | (22) $false % 17.51/3.00 | % 17.51/3.00 | CLOSE: (22) is inconsistent. % 17.51/3.00 | % 17.51/3.00 End of proof % 17.51/3.00 % SZS output end Proof for theBenchmark % 17.51/3.00 % 17.51/3.00 2561ms %------------------------------------------------------------------------------