%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV391+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 : n012.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 22:56:08 EDT 2023 % Result : Theorem 16.56s 3.09s % Output : Proof 29.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SWV391+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.31 % Computer : n012.cluster.edu % 0.09/0.31 % Model : x86_64 x86_64 % 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.31 % Memory : 8042.1875MB % 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.31 % CPULimit : 300 % 0.09/0.31 % WCLimit : 300 % 0.09/0.31 % DateTime : Tue Aug 29 08:09:39 EDT 2023 % 0.09/0.31 % CPUTime : % 0.15/0.59 ________ _____ % 0.15/0.59 ___ __ \_________(_)________________________________ % 0.15/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.59 % 0.15/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.59 (2023-06-19) % 0.15/0.59 % 0.15/0.59 (c) Philipp Rümmer, 2009-2023 % 0.15/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.59 Amanda Stjerna. % 0.15/0.59 Free software under BSD-3-Clause. % 0.15/0.59 % 0.15/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.59 % 0.15/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.15/0.61 Running up to 7 provers in parallel. % 0.15/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.15/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.72/1.28 Prover 4: Preprocessing ... % 3.72/1.28 Prover 1: Preprocessing ... % 4.19/1.33 Prover 0: Preprocessing ... % 4.19/1.33 Prover 5: Preprocessing ... % 4.19/1.33 Prover 6: Preprocessing ... % 4.19/1.33 Prover 2: Preprocessing ... % 4.19/1.33 Prover 3: Preprocessing ... % 9.31/2.15 Prover 1: Warning: ignoring some quantifiers % 9.31/2.29 Prover 3: Warning: ignoring some quantifiers % 11.13/2.35 Prover 1: Constructing countermodel ... % 11.13/2.37 Prover 4: Constructing countermodel ... % 11.13/2.37 Prover 3: Constructing countermodel ... % 11.13/2.38 Prover 5: Proving ... % 11.13/2.38 Prover 6: Proving ... % 12.50/2.58 Prover 0: Proving ... % 12.50/2.62 Prover 2: Proving ... % 15.76/3.08 Prover 0: proved (2462ms) % 16.56/3.09 % 16.56/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.56/3.09 % 16.56/3.10 Prover 3: stopped % 16.56/3.10 Prover 5: stopped % 16.56/3.10 Prover 6: stopped % 16.56/3.11 Prover 2: stopped % 16.56/3.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.56/3.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.56/3.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.56/3.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.56/3.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.73/3.17 Prover 8: Preprocessing ... % 16.73/3.19 Prover 10: Preprocessing ... % 17.40/3.20 Prover 13: Preprocessing ... % 17.40/3.22 Prover 7: Preprocessing ... % 17.40/3.25 Prover 11: Preprocessing ... % 18.98/3.43 Prover 7: Warning: ignoring some quantifiers % 18.98/3.47 Prover 8: Warning: ignoring some quantifiers % 18.98/3.48 Prover 7: Constructing countermodel ... % 18.98/3.50 Prover 10: Warning: ignoring some quantifiers % 18.98/3.51 Prover 8: Constructing countermodel ... % 18.98/3.57 Prover 10: Constructing countermodel ... % 18.98/3.61 Prover 13: Warning: ignoring some quantifiers % 19.27/3.65 Prover 13: Constructing countermodel ... % 21.08/3.76 Prover 11: Constructing countermodel ... % 23.36/4.05 Prover 7: gave up % 23.36/4.06 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 24.57/4.20 Prover 16: Preprocessing ... % 25.34/4.38 Prover 10: gave up % 25.34/4.39 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 25.34/4.51 Prover 19: Preprocessing ... % 27.13/4.54 Prover 16: Warning: ignoring some quantifiers % 27.16/4.57 Prover 16: Constructing countermodel ... % 27.16/4.58 Prover 11: Found proof (size 134) % 27.16/4.58 Prover 11: proved (1474ms) % 27.16/4.58 Prover 13: stopped % 27.16/4.58 Prover 4: stopped % 27.16/4.58 Prover 1: stopped % 27.16/4.59 Prover 16: stopped % 27.16/4.59 Prover 8: stopped % 28.29/4.76 Prover 19: Warning: ignoring some quantifiers % 28.29/4.78 Prover 19: Constructing countermodel ... % 28.48/4.81 Prover 19: stopped % 28.48/4.81 % 28.48/4.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 28.48/4.81 % 28.48/4.82 % SZS output start Proof for theBenchmark % 28.48/4.83 Assumptions after simplification: % 28.48/4.83 --------------------------------- % 28.48/4.83 % 28.48/4.83 (ax40) % 28.69/4.87 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 28.69/4.87 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) = v3)) % 28.69/4.87 % 28.69/4.87 (ax44) % 28.69/4.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 28.69/4.88 $i] : ! [v6: $i] : ( ~ (remove_pqp(v0, v3) = v4) | ~ (triple(v4, v5, v2) = % 28.69/4.88 v6) | ~ (remove_slb(v1, v3) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 28.69/4.88 ~ $i(v0) | ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? % 28.69/4.88 [v11: $i] : ((v11 = v6 & triple(v0, v1, v2) = v10 & remove_cpq(v10, v3) = v6 % 28.69/4.88 & $i(v10) & $i(v6)) | ( ~ (v9 = 0) & lookup_slb(v1, v3) = v8 & % 28.69/4.88 less_than(v8, v3) = v9 & $i(v8)) | ( ~ (v7 = 0) & contains_slb(v1, v3) = % 28.69/4.88 v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 28.69/4.88 $i] : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = % 28.69/4.88 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? % 28.69/4.88 [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ((v11 % 28.69/4.88 = v5 & remove_pqp(v0, v3) = v9 & triple(v9, v10, v2) = v5 & % 28.69/4.88 remove_slb(v1, v3) = v10 & $i(v10) & $i(v9) & $i(v5)) | ( ~ (v8 = 0) & % 28.69/4.88 lookup_slb(v1, v3) = v7 & less_than(v7, v3) = v8 & $i(v7)) | ( ~ (v6 = % 28.69/4.88 0) & contains_slb(v1, v3) = v6))) % 28.69/4.88 % 28.69/4.88 (ax45) % 28.69/4.88 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 28.69/4.88 : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | % 28.69/4.88 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: $i] : % 28.69/4.88 ? [v8: int] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ((v11 = v5 & % 28.69/4.88 remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = v5 & remove_slb(v1, v3) % 28.69/4.88 = v10 & $i(v10) & $i(v9) & $i(v5)) | ( ~ (v8 = 0) & lookup_slb(v1, v3) = % 28.69/4.88 v7 & strictly_less_than(v3, v7) = v8 & $i(v7)) | ( ~ (v6 = 0) & % 28.69/4.88 contains_slb(v1, v3) = v6))) % 28.69/4.88 % 28.69/4.88 (l27_co) % 28.69/4.88 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 28.69/4.88 $i] : ? [v6: int] : ( ~ (v6 = 0) & ok(v5) = 0 & triple(v0, v1, v2) = v4 & % 28.69/4.88 check_cpq(v5) = 0 & check_cpq(v4) = v6 & remove_cpq(v4, v3) = v5 & $i(v5) & % 28.69/4.89 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 28.69/4.89 % 28.69/4.89 (l27_l30) % 28.69/4.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 28.69/4.89 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (triple(v0, v1, v2) = v4) | % 28.69/4.89 ~ (remove_cpq(v4, v3) = v5) | ~ (less_than(v6, v3) = v7) | ~ $i(v6) | ~ % 28.69/4.89 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v8: int] : ? [v9: int] : % 28.69/4.89 (( ~ (v9 = 0) & ok(v5) = v9) | ( ~ (v8 = 0) & check_cpq(v5) = v8) | ( ~ (v8 % 28.69/4.89 = 0) & pair_in_list(v1, v3, v6) = v8))) & ! [v0: $i] : ! [v1: $i] : % 28.69/4.89 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 28.69/4.89 (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ % 28.69/4.89 (pair_in_list(v1, v3, v6) = 0) | ~ $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ % 28.69/4.89 $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ((v7 = 0 & less_than(v6, % 28.69/4.89 v3) = 0) | ( ~ (v8 = 0) & ok(v5) = v8) | ( ~ (v7 = 0) & check_cpq(v5) % 28.69/4.89 = v7))) % 28.69/4.89 % 28.69/4.89 (l27_l33) % 28.69/4.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 28.69/4.89 $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ % 28.69/4.89 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 28.69/4.89 ((v7 = 0 & contains_slb(v1, v3) = 0) | ( ~ (v6 = 0) & ok(v5) = v6))) % 28.69/4.89 % 28.69/4.89 (l27_li2829) % 28.69/4.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v1 % 28.69/4.89 | ~ (remove_slb(v0, v3) = v4) | ~ (pair_in_list(v0, v1, v2) = 0) | ~ % 28.69/4.89 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : % 28.69/4.89 ((v6 = 0 & pair_in_list(v4, v1, v2) = 0) | ( ~ (v5 = 0) & contains_slb(v0, % 28.69/4.89 v3) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 28.69/4.89 (v3 = v1 | ~ (pair_in_list(v0, v1, v2) = 0) | ~ (contains_slb(v0, v3) = 0) | % 28.69/4.89 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 28.69/4.89 (remove_slb(v0, v3) = v4 & pair_in_list(v4, v1, v2) = 0 & $i(v4))) % 28.69/4.89 % 28.69/4.90 (l27_li4142) % 28.97/4.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 28.97/4.90 $i] : ! [v6: int] : (v6 = 0 | ~ (triple(v0, v1, v2) = v3) | ~ % 28.97/4.90 (less_than(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | % 28.97/4.90 ~ $i(v0) | ? [v7: int] : (( ~ (v7 = 0) & check_cpq(v3) = v7) | ( ~ (v7 = 0) % 28.97/4.90 & pair_in_list(v1, v4, v5) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.97/4.90 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = % 28.97/4.90 v3) | ~ (pair_in_list(v1, v4, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 28.97/4.90 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ((v6 = 0 & less_than(v5, v4) % 28.97/4.90 = 0) | ( ~ (v6 = 0) & check_cpq(v3) = v6))) & ! [v0: $i] : ! [v1: $i] % 28.97/4.90 : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 28.97/4.90 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] % 28.97/4.90 : ? [v8: int] : ($i(v6) & $i(v5) & ((v7 = 0 & ~ (v8 = 0) & % 28.97/4.90 pair_in_list(v1, v5, v6) = 0 & less_than(v6, v5) = v8) | (v4 = 0 & % 28.97/4.90 check_cpq(v3) = 0)))) % 28.97/4.90 % 28.97/4.90 (stricly_smaller_definition) % 28.97/4.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 28.97/4.91 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 28.97/4.91 ? [v4: int] : ((v4 = 0 & less_than(v1, v0) = 0) | ( ~ (v3 = 0) & % 28.97/4.91 less_than(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : % 28.97/4.91 (v2 = 0 | ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 28.97/4.91 ? [v4: int] : ((v4 = 0 & strictly_less_than(v0, v1) = 0) | ( ~ (v3 = 0) & % 28.97/4.91 less_than(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( % 28.97/4.91 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 28.97/4.91 int] : ((v4 = 0 & ~ (v2 = 0) & less_than(v0, v1) = 0) | ( ~ (v3 = 0) & % 28.97/4.91 strictly_less_than(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 28.97/4.91 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : % 28.97/4.91 ? [v4: int] : ((v2 = 0 & ~ (v4 = 0) & less_than(v1, v0) = v4) | ( ~ (v3 = % 28.97/4.91 0) & strictly_less_than(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : % 28.97/4.91 ( ~ (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : % 28.97/4.91 ( ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0: % 28.97/4.91 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 28.97/4.91 [v2: int] : ? [v3: int] : ((v3 = 0 & strictly_less_than(v0, v1) = 0) | (v2 % 28.97/4.91 = 0 & less_than(v1, v0) = 0))) % 28.97/4.91 % 28.97/4.91 (totality) % 28.97/4.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) = % 28.97/4.91 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : ! % 28.97/4.91 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) | % 28.97/4.91 ~ $i(v0) | less_than(v1, v0) = 0) % 28.97/4.91 % 28.97/4.91 (function-axioms) % 28.97/4.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 28.97/4.92 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 28.97/4.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.97/4.92 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 28.97/4.92 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 28.97/4.92 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 28.97/4.92 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 28.97/4.92 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 28.97/4.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.97/4.92 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 28.97/4.92 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.97/4.92 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 28.97/4.92 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 28.97/4.92 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.97/4.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 28.97/4.92 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 28.97/4.92 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 28.97/4.92 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 28.97/4.92 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 28.97/4.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 28.97/4.92 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 28.97/4.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 28.97/4.92 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 28.97/4.92 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.97/4.92 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 28.97/4.92 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 28.97/4.92 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 28.97/4.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.97/4.92 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 28.97/4.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 28.97/4.92 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 28.97/4.92 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 28.97/4.92 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: % 28.97/4.92 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | % 28.97/4.92 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 28.97/4.92 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! % 28.97/4.92 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 28.97/4.92 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 28.97/4.92 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | % 28.97/4.92 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 28.97/4.92 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! % 28.97/4.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = % 28.97/4.92 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 28.97/4.92 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = % 28.97/4.92 v1) | ~ (isnonempty_slb(v2) = v0)) % 28.97/4.92 % 28.97/4.92 Further assumptions not needed in the proof: % 28.97/4.92 -------------------------------------------- % 28.97/4.92 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 28.97/4.92 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax41, ax42, ax43, ax46, % 28.97/4.92 ax47, ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest, reflexivity, % 28.97/4.92 transitivity % 28.97/4.92 % 28.97/4.92 Those formulas are unsatisfiable: % 28.97/4.92 --------------------------------- % 28.97/4.92 % 28.97/4.92 Begin of proof % 28.97/4.92 | % 28.97/4.92 | ALPHA: (totality) implies: % 28.97/4.92 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 28.97/4.92 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) % 28.97/4.92 | % 28.97/4.92 | ALPHA: (stricly_smaller_definition) implies: % 28.97/4.92 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 28.97/4.92 | (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 28.97/4.92 | int] : ? [v4: int] : ((v4 = 0 & less_than(v1, v0) = 0) | ( ~ (v3 = % 28.97/4.92 | 0) & less_than(v0, v1) = v3))) % 28.97/4.92 | % 28.97/4.92 | ALPHA: (ax40) implies: % 28.97/4.92 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 28.97/4.92 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) % 28.97/4.92 | = v3)) % 28.97/4.92 | % 28.97/4.92 | ALPHA: (ax44) implies: % 28.97/4.93 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 28.97/4.93 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = % 28.97/4.93 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] % 28.97/4.93 | : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 28.97/4.93 | $i] : ((v11 = v5 & remove_pqp(v0, v3) = v9 & triple(v9, v10, v2) = % 28.97/4.93 | v5 & remove_slb(v1, v3) = v10 & $i(v10) & $i(v9) & $i(v5)) | ( ~ % 28.97/4.93 | (v8 = 0) & lookup_slb(v1, v3) = v7 & less_than(v7, v3) = v8 & % 28.97/4.93 | $i(v7)) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) % 28.97/4.93 | % 28.97/4.93 | ALPHA: (ax45) implies: % 28.97/4.93 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 28.97/4.93 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = % 28.97/4.93 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] % 28.97/4.93 | : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ? [v10: $i] : ? [v11: % 28.97/4.93 | $i] : ((v11 = v5 & remove_pqp(v0, v3) = v9 & triple(v9, v10, bad) = % 28.97/4.93 | v5 & remove_slb(v1, v3) = v10 & $i(v10) & $i(v9) & $i(v5)) | ( ~ % 28.97/4.93 | (v8 = 0) & lookup_slb(v1, v3) = v7 & strictly_less_than(v3, v7) = % 28.97/4.93 | v8 & $i(v7)) | ( ~ (v6 = 0) & contains_slb(v1, v3) = v6))) % 28.97/4.93 | % 28.97/4.93 | ALPHA: (l27_li4142) implies: % 28.97/4.93 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, % 28.97/4.93 | v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] % 28.97/4.93 | : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: int] : ($i(v6) & % 28.97/4.93 | $i(v5) & ((v7 = 0 & ~ (v8 = 0) & pair_in_list(v1, v5, v6) = 0 & % 28.97/4.93 | less_than(v6, v5) = v8) | (v4 = 0 & check_cpq(v3) = 0)))) % 28.97/4.93 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 28.97/4.93 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (triple(v0, v1, v2) = v3) | ~ % 28.97/4.93 | (less_than(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ % 28.97/4.93 | $i(v1) | ~ $i(v0) | ? [v7: int] : (( ~ (v7 = 0) & check_cpq(v3) = % 28.97/4.93 | v7) | ( ~ (v7 = 0) & pair_in_list(v1, v4, v5) = v7))) % 28.97/4.93 | % 28.97/4.93 | ALPHA: (l27_li2829) implies: % 28.97/4.94 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ % 28.97/4.94 | (pair_in_list(v0, v1, v2) = 0) | ~ (contains_slb(v0, v3) = 0) | ~ % 28.97/4.94 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 28.97/4.94 | (remove_slb(v0, v3) = v4 & pair_in_list(v4, v1, v2) = 0 & $i(v4))) % 28.97/4.94 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 28.97/4.94 | (v3 = v1 | ~ (remove_slb(v0, v3) = v4) | ~ (pair_in_list(v0, v1, v2) % 28.97/4.94 | = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] % 28.97/4.94 | : ? [v6: int] : ((v6 = 0 & pair_in_list(v4, v1, v2) = 0) | ( ~ (v5 = % 28.97/4.94 | 0) & contains_slb(v0, v3) = v5))) % 28.97/4.94 | % 28.97/4.94 | ALPHA: (l27_l30) implies: % 28.97/4.94 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 28.97/4.94 | ! [v5: $i] : ! [v6: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ % 28.97/4.94 | (remove_cpq(v4, v3) = v5) | ~ (pair_in_list(v1, v3, v6) = 0) | ~ % 28.97/4.94 | $i(v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: % 28.97/4.94 | int] : ? [v8: int] : ((v7 = 0 & less_than(v6, v3) = 0) | ( ~ (v8 % 28.97/4.94 | = 0) & ok(v5) = v8) | ( ~ (v7 = 0) & check_cpq(v5) = v7))) % 28.97/4.94 | % 28.97/4.94 | ALPHA: (function-axioms) implies: % 28.97/4.94 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.97/4.94 | : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) % 28.97/4.94 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.97/4.94 | : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 28.97/4.94 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.97/4.94 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ % 28.97/4.94 | (less_than(v3, v2) = v0)) % 28.97/4.94 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.97/4.94 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 28.97/4.94 | (contains_slb(v3, v2) = v0)) % 28.97/4.94 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 28.97/4.94 | (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 28.97/4.94 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 28.97/4.94 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) % 28.97/4.94 | = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 28.97/4.94 | % 28.97/4.95 | DELTA: instantiating (l27_co) with fresh symbols all_50_0, all_50_1, all_50_2, % 28.97/4.95 | all_50_3, all_50_4, all_50_5, all_50_6 gives: % 28.97/4.95 | (17) ~ (all_50_0 = 0) & ok(all_50_1) = 0 & triple(all_50_6, all_50_5, % 28.97/4.95 | all_50_4) = all_50_2 & check_cpq(all_50_1) = 0 & check_cpq(all_50_2) % 28.97/4.95 | = all_50_0 & remove_cpq(all_50_2, all_50_3) = all_50_1 & $i(all_50_1) % 28.97/4.95 | & $i(all_50_2) & $i(all_50_3) & $i(all_50_4) & $i(all_50_5) & % 28.97/4.95 | $i(all_50_6) % 28.97/4.95 | % 28.97/4.95 | ALPHA: (17) implies: % 28.97/4.95 | (18) ~ (all_50_0 = 0) % 28.97/4.95 | (19) $i(all_50_6) % 28.97/4.95 | (20) $i(all_50_5) % 28.97/4.95 | (21) $i(all_50_4) % 28.97/4.95 | (22) $i(all_50_3) % 28.97/4.95 | (23) remove_cpq(all_50_2, all_50_3) = all_50_1 % 28.97/4.95 | (24) check_cpq(all_50_2) = all_50_0 % 28.97/4.95 | (25) check_cpq(all_50_1) = 0 % 28.97/4.95 | (26) triple(all_50_6, all_50_5, all_50_4) = all_50_2 % 28.97/4.95 | (27) ok(all_50_1) = 0 % 28.97/4.95 | % 28.97/4.95 | GROUND_INST: instantiating (4) with all_50_6, all_50_5, all_50_4, all_50_3, % 28.97/4.95 | all_50_2, all_50_1, simplifying with (19), (20), (21), (22), % 28.97/4.95 | (23), (26) gives: % 28.97/4.95 | (28) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] % 28.97/4.95 | : ? [v5: int] : ((v5 = all_50_1 & remove_pqp(all_50_6, all_50_3) = v3 % 28.97/4.95 | & triple(v3, v4, all_50_4) = all_50_1 & remove_slb(all_50_5, % 28.97/4.95 | all_50_3) = v4 & $i(v4) & $i(v3) & $i(all_50_1)) | ( ~ (v2 = 0) % 28.97/4.96 | & lookup_slb(all_50_5, all_50_3) = v1 & less_than(v1, all_50_3) = % 28.97/4.96 | v2 & $i(v1)) | ( ~ (v0 = 0) & contains_slb(all_50_5, all_50_3) = % 28.97/4.96 | v0)) % 28.97/4.96 | % 29.26/4.96 | GROUND_INST: instantiating (5) with all_50_6, all_50_5, all_50_4, all_50_3, % 29.26/4.96 | all_50_2, all_50_1, simplifying with (19), (20), (21), (22), % 29.26/4.96 | (23), (26) gives: % 29.26/4.96 | (29) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i] % 29.26/4.96 | : ? [v5: int] : ((v5 = all_50_1 & remove_pqp(all_50_6, all_50_3) = v3 % 29.26/4.96 | & triple(v3, v4, bad) = all_50_1 & remove_slb(all_50_5, all_50_3) % 29.26/4.96 | = v4 & $i(v4) & $i(v3) & $i(all_50_1)) | ( ~ (v2 = 0) & % 29.26/4.96 | lookup_slb(all_50_5, all_50_3) = v1 & strictly_less_than(all_50_3, % 29.26/4.96 | v1) = v2 & $i(v1)) | ( ~ (v0 = 0) & contains_slb(all_50_5, % 29.26/4.96 | all_50_3) = v0)) % 29.26/4.96 | % 29.26/4.96 | GROUND_INST: instantiating (l27_l33) with all_50_6, all_50_5, all_50_4, % 29.26/4.96 | all_50_3, all_50_2, all_50_1, simplifying with (19), (20), (21), % 29.26/4.96 | (22), (23), (26) gives: % 29.26/4.96 | (30) ? [v0: int] : ? [v1: int] : ((v1 = 0 & contains_slb(all_50_5, % 29.26/4.96 | all_50_3) = 0) | ( ~ (v0 = 0) & ok(all_50_1) = v0)) % 29.26/4.96 | % 29.26/4.96 | GROUND_INST: instantiating (6) with all_50_6, all_50_5, all_50_4, all_50_2, % 29.26/4.96 | simplifying with (19), (20), (21), (26) gives: % 29.26/4.96 | (31) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] % 29.26/4.96 | : ($i(v2) & $i(v1) & ((v3 = 0 & ~ (v4 = 0) & pair_in_list(all_50_5, % 29.26/4.96 | v1, v2) = 0 & less_than(v2, v1) = v4) | (v0 = 0 & % 29.26/4.96 | check_cpq(all_50_2) = 0))) % 29.26/4.96 | % 29.26/4.96 | DELTA: instantiating (30) with fresh symbols all_57_0, all_57_1 gives: % 29.26/4.96 | (32) (all_57_0 = 0 & contains_slb(all_50_5, all_50_3) = 0) | ( ~ (all_57_1 % 29.26/4.96 | = 0) & ok(all_50_1) = all_57_1) % 29.26/4.96 | % 29.26/4.96 | DELTA: instantiating (31) with fresh symbols all_59_0, all_59_1, all_59_2, % 29.26/4.96 | all_59_3, all_59_4 gives: % 29.26/4.96 | (33) $i(all_59_2) & $i(all_59_3) & ((all_59_1 = 0 & ~ (all_59_0 = 0) & % 29.26/4.96 | pair_in_list(all_50_5, all_59_3, all_59_2) = 0 & % 29.26/4.96 | less_than(all_59_2, all_59_3) = all_59_0) | (all_59_4 = 0 & % 29.26/4.96 | check_cpq(all_50_2) = 0)) % 29.26/4.96 | % 29.26/4.96 | ALPHA: (33) implies: % 29.26/4.96 | (34) $i(all_59_3) % 29.26/4.96 | (35) $i(all_59_2) % 29.26/4.96 | (36) (all_59_1 = 0 & ~ (all_59_0 = 0) & pair_in_list(all_50_5, all_59_3, % 29.26/4.96 | all_59_2) = 0 & less_than(all_59_2, all_59_3) = all_59_0) | % 29.26/4.96 | (all_59_4 = 0 & check_cpq(all_50_2) = 0) % 29.26/4.96 | % 29.26/4.96 | DELTA: instantiating (29) with fresh symbols all_61_0, all_61_1, all_61_2, % 29.26/4.96 | all_61_3, all_61_4, all_61_5 gives: % 29.26/4.96 | (37) (all_61_0 = all_50_1 & remove_pqp(all_50_6, all_50_3) = all_61_2 & % 29.26/4.96 | triple(all_61_2, all_61_1, bad) = all_50_1 & remove_slb(all_50_5, % 29.26/4.96 | all_50_3) = all_61_1 & $i(all_61_1) & $i(all_61_2) & $i(all_50_1)) % 29.26/4.96 | | ( ~ (all_61_3 = 0) & lookup_slb(all_50_5, all_50_3) = all_61_4 & % 29.26/4.96 | strictly_less_than(all_50_3, all_61_4) = all_61_3 & $i(all_61_4)) | % 29.26/4.96 | ( ~ (all_61_5 = 0) & contains_slb(all_50_5, all_50_3) = all_61_5) % 29.26/4.96 | % 29.26/4.96 | DELTA: instantiating (28) with fresh symbols all_62_0, all_62_1, all_62_2, % 29.26/4.96 | all_62_3, all_62_4, all_62_5 gives: % 29.26/4.97 | (38) (all_62_0 = all_50_1 & remove_pqp(all_50_6, all_50_3) = all_62_2 & % 29.26/4.97 | triple(all_62_2, all_62_1, all_50_4) = all_50_1 & % 29.26/4.97 | remove_slb(all_50_5, all_50_3) = all_62_1 & $i(all_62_1) & % 29.26/4.97 | $i(all_62_2) & $i(all_50_1)) | ( ~ (all_62_3 = 0) & % 29.26/4.97 | lookup_slb(all_50_5, all_50_3) = all_62_4 & less_than(all_62_4, % 29.26/4.97 | all_50_3) = all_62_3 & $i(all_62_4)) | ( ~ (all_62_5 = 0) & % 29.26/4.97 | contains_slb(all_50_5, all_50_3) = all_62_5) % 29.26/4.97 | % 29.26/4.97 | BETA: splitting (32) gives: % 29.26/4.97 | % 29.26/4.97 | Case 1: % 29.26/4.97 | | % 29.26/4.97 | | (39) all_57_0 = 0 & contains_slb(all_50_5, all_50_3) = 0 % 29.26/4.97 | | % 29.26/4.97 | | ALPHA: (39) implies: % 29.26/4.97 | | (40) contains_slb(all_50_5, all_50_3) = 0 % 29.26/4.97 | | % 29.26/4.97 | | BETA: splitting (36) gives: % 29.26/4.97 | | % 29.26/4.97 | | Case 1: % 29.26/4.97 | | | % 29.26/4.97 | | | (41) all_59_1 = 0 & ~ (all_59_0 = 0) & pair_in_list(all_50_5, % 29.26/4.97 | | | all_59_3, all_59_2) = 0 & less_than(all_59_2, all_59_3) = % 29.26/4.97 | | | all_59_0 % 29.26/4.97 | | | % 29.26/4.97 | | | ALPHA: (41) implies: % 29.26/4.97 | | | (42) ~ (all_59_0 = 0) % 29.26/4.97 | | | (43) less_than(all_59_2, all_59_3) = all_59_0 % 29.26/4.97 | | | (44) pair_in_list(all_50_5, all_59_3, all_59_2) = 0 % 29.26/4.97 | | | % 29.26/4.97 | | | GROUND_INST: instantiating (8) with all_50_5, all_59_3, all_59_2, % 29.26/4.97 | | | all_50_3, simplifying with (20), (22), (34), (35), (40), (44) % 29.26/4.97 | | | gives: % 29.26/4.97 | | | (45) all_59_3 = all_50_3 | ? [v0: $i] : (remove_slb(all_50_5, % 29.26/4.97 | | | all_50_3) = v0 & pair_in_list(v0, all_59_3, all_59_2) = 0 & % 29.26/4.97 | | | $i(v0)) % 29.26/4.97 | | | % 29.26/4.97 | | | BETA: splitting (37) gives: % 29.26/4.97 | | | % 29.26/4.97 | | | Case 1: % 29.26/4.97 | | | | % 29.26/4.97 | | | | (46) all_61_0 = all_50_1 & remove_pqp(all_50_6, all_50_3) = all_61_2 % 29.26/4.97 | | | | & triple(all_61_2, all_61_1, bad) = all_50_1 & % 29.26/4.97 | | | | remove_slb(all_50_5, all_50_3) = all_61_1 & $i(all_61_1) & % 29.26/4.97 | | | | $i(all_61_2) & $i(all_50_1) % 29.26/4.97 | | | | % 29.26/4.97 | | | | ALPHA: (46) implies: % 29.26/4.97 | | | | (47) $i(all_61_2) % 29.26/4.97 | | | | (48) $i(all_61_1) % 29.26/4.97 | | | | (49) triple(all_61_2, all_61_1, bad) = all_50_1 % 29.26/4.97 | | | | % 29.26/4.97 | | | | GROUND_INST: instantiating (3) with all_61_2, all_61_1, all_50_1, % 29.26/4.97 | | | | simplifying with (47), (48), (49) gives: % 29.26/4.97 | | | | (50) ? [v0: int] : ( ~ (v0 = 0) & ok(all_50_1) = v0) % 29.26/4.97 | | | | % 29.26/4.97 | | | | DELTA: instantiating (50) with fresh symbol all_125_0 gives: % 29.26/4.97 | | | | (51) ~ (all_125_0 = 0) & ok(all_50_1) = all_125_0 % 29.26/4.97 | | | | % 29.26/4.97 | | | | ALPHA: (51) implies: % 29.26/4.97 | | | | (52) ~ (all_125_0 = 0) % 29.26/4.97 | | | | (53) ok(all_50_1) = all_125_0 % 29.26/4.97 | | | | % 29.26/4.97 | | | | GROUND_INST: instantiating (12) with 0, all_125_0, all_50_1, simplifying % 29.26/4.97 | | | | with (27), (53) gives: % 29.26/4.97 | | | | (54) all_125_0 = 0 % 29.26/4.97 | | | | % 29.26/4.97 | | | | REDUCE: (52), (54) imply: % 29.26/4.98 | | | | (55) $false % 29.26/4.98 | | | | % 29.26/4.98 | | | | CLOSE: (55) is inconsistent. % 29.26/4.98 | | | | % 29.26/4.98 | | | Case 2: % 29.26/4.98 | | | | % 29.26/4.98 | | | | (56) ( ~ (all_61_3 = 0) & lookup_slb(all_50_5, all_50_3) = all_61_4 & % 29.26/4.98 | | | | strictly_less_than(all_50_3, all_61_4) = all_61_3 & % 29.26/4.98 | | | | $i(all_61_4)) | ( ~ (all_61_5 = 0) & contains_slb(all_50_5, % 29.26/4.98 | | | | all_50_3) = all_61_5) % 29.26/4.98 | | | | % 29.26/4.98 | | | | BETA: splitting (56) gives: % 29.26/4.98 | | | | % 29.26/4.98 | | | | Case 1: % 29.26/4.98 | | | | | % 29.26/4.98 | | | | | (57) ~ (all_61_3 = 0) & lookup_slb(all_50_5, all_50_3) = all_61_4 % 29.26/4.98 | | | | | & strictly_less_than(all_50_3, all_61_4) = all_61_3 & % 29.26/4.98 | | | | | $i(all_61_4) % 29.26/4.98 | | | | | % 29.26/4.98 | | | | | ALPHA: (57) implies: % 29.26/4.98 | | | | | (58) ~ (all_61_3 = 0) % 29.26/4.98 | | | | | (59) $i(all_61_4) % 29.26/4.98 | | | | | (60) strictly_less_than(all_50_3, all_61_4) = all_61_3 % 29.26/4.98 | | | | | (61) lookup_slb(all_50_5, all_50_3) = all_61_4 % 29.26/4.98 | | | | | % 29.26/4.98 | | | | | GROUND_INST: instantiating (2) with all_50_3, all_61_4, all_61_3, % 29.26/4.98 | | | | | simplifying with (22), (59), (60) gives: % 29.26/4.98 | | | | | (62) all_61_3 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 29.26/4.98 | | | | | less_than(all_61_4, all_50_3) = 0) | ( ~ (v0 = 0) & % 29.26/4.98 | | | | | less_than(all_50_3, all_61_4) = v0)) % 29.26/4.98 | | | | | % 29.26/4.98 | | | | | BETA: splitting (38) gives: % 29.26/4.98 | | | | | % 29.26/4.98 | | | | | Case 1: % 29.26/4.98 | | | | | | % 29.26/4.98 | | | | | | (63) all_62_0 = all_50_1 & remove_pqp(all_50_6, all_50_3) = % 29.26/4.98 | | | | | | all_62_2 & triple(all_62_2, all_62_1, all_50_4) = all_50_1 & % 29.26/4.98 | | | | | | remove_slb(all_50_5, all_50_3) = all_62_1 & $i(all_62_1) & % 29.26/4.98 | | | | | | $i(all_62_2) & $i(all_50_1) % 29.26/4.98 | | | | | | % 29.26/4.98 | | | | | | ALPHA: (63) implies: % 29.26/4.98 | | | | | | (64) $i(all_62_2) % 29.26/4.98 | | | | | | (65) $i(all_62_1) % 29.26/4.98 | | | | | | (66) remove_slb(all_50_5, all_50_3) = all_62_1 % 29.26/4.98 | | | | | | (67) triple(all_62_2, all_62_1, all_50_4) = all_50_1 % 29.26/4.98 | | | | | | % 29.26/4.98 | | | | | | GROUND_INST: instantiating (9) with all_50_5, all_59_3, all_59_2, % 29.26/4.98 | | | | | | all_50_3, all_62_1, simplifying with (20), (22), (34), % 29.26/4.98 | | | | | | (35), (44), (66) gives: % 29.26/4.98 | | | | | | (68) all_59_3 = all_50_3 | ? [v0: int] : ? [v1: int] : ((v1 = 0 % 29.26/4.98 | | | | | | & pair_in_list(all_62_1, all_59_3, all_59_2) = 0) | ( ~ % 29.26/4.98 | | | | | | (v0 = 0) & contains_slb(all_50_5, all_50_3) = v0)) % 29.26/4.98 | | | | | | % 29.26/4.98 | | | | | | GROUND_INST: instantiating (7) with all_62_2, all_62_1, all_50_4, % 29.26/4.98 | | | | | | all_50_1, all_59_3, all_59_2, all_59_0, simplifying % 29.26/4.98 | | | | | | with (21), (34), (35), (43), (64), (65), (67) gives: % 29.26/4.98 | | | | | | (69) all_59_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & % 29.26/4.98 | | | | | | check_cpq(all_50_1) = v0) | ( ~ (v0 = 0) & % 29.26/4.98 | | | | | | pair_in_list(all_62_1, all_59_3, all_59_2) = v0)) % 29.26/4.98 | | | | | | % 29.26/4.98 | | | | | | BETA: splitting (69) gives: % 29.26/4.98 | | | | | | % 29.26/4.98 | | | | | | Case 1: % 29.26/4.98 | | | | | | | % 29.26/4.98 | | | | | | | (70) all_59_0 = 0 % 29.26/4.98 | | | | | | | % 29.26/4.98 | | | | | | | REDUCE: (42), (70) imply: % 29.26/4.98 | | | | | | | (71) $false % 29.26/4.98 | | | | | | | % 29.26/4.98 | | | | | | | CLOSE: (71) is inconsistent. % 29.26/4.98 | | | | | | | % 29.26/4.98 | | | | | | Case 2: % 29.26/4.98 | | | | | | | % 29.26/4.98 | | | | | | | (72) ? [v0: int] : (( ~ (v0 = 0) & check_cpq(all_50_1) = v0) | % 29.26/4.98 | | | | | | | ( ~ (v0 = 0) & pair_in_list(all_62_1, all_59_3, % 29.26/4.98 | | | | | | | all_59_2) = v0)) % 29.26/4.98 | | | | | | | % 29.26/4.98 | | | | | | | DELTA: instantiating (72) with fresh symbol all_144_0 gives: % 29.26/4.98 | | | | | | | (73) ( ~ (all_144_0 = 0) & check_cpq(all_50_1) = all_144_0) | ( % 29.26/4.98 | | | | | | | ~ (all_144_0 = 0) & pair_in_list(all_62_1, all_59_3, % 29.26/4.99 | | | | | | | all_59_2) = all_144_0) % 29.26/4.99 | | | | | | | % 29.26/4.99 | | | | | | | BETA: splitting (73) gives: % 29.26/4.99 | | | | | | | % 29.26/4.99 | | | | | | | Case 1: % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | | (74) ~ (all_144_0 = 0) & check_cpq(all_50_1) = all_144_0 % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | | ALPHA: (74) implies: % 29.26/4.99 | | | | | | | | (75) ~ (all_144_0 = 0) % 29.26/4.99 | | | | | | | | (76) check_cpq(all_50_1) = all_144_0 % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | | GROUND_INST: instantiating (11) with 0, all_144_0, all_50_1, % 29.26/4.99 | | | | | | | | simplifying with (25), (76) gives: % 29.26/4.99 | | | | | | | | (77) all_144_0 = 0 % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | | REDUCE: (75), (77) imply: % 29.26/4.99 | | | | | | | | (78) $false % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | | CLOSE: (78) is inconsistent. % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | Case 2: % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | | (79) ~ (all_144_0 = 0) & pair_in_list(all_62_1, all_59_3, % 29.26/4.99 | | | | | | | | all_59_2) = all_144_0 % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | | ALPHA: (79) implies: % 29.26/4.99 | | | | | | | | (80) ~ (all_144_0 = 0) % 29.26/4.99 | | | | | | | | (81) pair_in_list(all_62_1, all_59_3, all_59_2) = all_144_0 % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | | BETA: splitting (45) gives: % 29.26/4.99 | | | | | | | | % 29.26/4.99 | | | | | | | | Case 1: % 29.26/4.99 | | | | | | | | | % 29.26/4.99 | | | | | | | | | (82) all_59_3 = all_50_3 % 29.26/4.99 | | | | | | | | | % 29.26/4.99 | | | | | | | | | REDUCE: (44), (82) imply: % 29.26/4.99 | | | | | | | | | (83) pair_in_list(all_50_5, all_50_3, all_59_2) = 0 % 29.26/4.99 | | | | | | | | | % 29.26/4.99 | | | | | | | | | REDUCE: (43), (82) imply: % 29.26/4.99 | | | | | | | | | (84) less_than(all_59_2, all_50_3) = all_59_0 % 29.26/4.99 | | | | | | | | | % 29.26/4.99 | | | | | | | | | GROUND_INST: instantiating (10) with all_50_6, all_50_5, % 29.26/4.99 | | | | | | | | | all_50_4, all_50_3, all_50_2, all_50_1, all_59_2, % 29.26/4.99 | | | | | | | | | simplifying with (19), (20), (21), (22), (23), % 29.26/4.99 | | | | | | | | | (26), (35), (83) gives: % 29.26/4.99 | | | | | | | | | (85) ? [v0: int] : ? [v1: int] : ((v0 = 0 & % 29.26/4.99 | | | | | | | | | less_than(all_59_2, all_50_3) = 0) | ( ~ (v1 = 0) % 29.26/4.99 | | | | | | | | | & ok(all_50_1) = v1) | ( ~ (v0 = 0) & % 29.26/4.99 | | | | | | | | | check_cpq(all_50_1) = v0)) % 29.26/4.99 | | | | | | | | | % 29.26/4.99 | | | | | | | | | DELTA: instantiating (85) with fresh symbols all_158_0, % 29.26/4.99 | | | | | | | | | all_158_1 gives: % 29.26/4.99 | | | | | | | | | (86) (all_158_1 = 0 & less_than(all_59_2, all_50_3) = 0) | % 29.26/4.99 | | | | | | | | | ( ~ (all_158_0 = 0) & ok(all_50_1) = all_158_0) | ( ~ % 29.26/4.99 | | | | | | | | | (all_158_1 = 0) & check_cpq(all_50_1) = all_158_1) % 29.26/4.99 | | | | | | | | | % 29.26/4.99 | | | | | | | | | BETA: splitting (86) gives: % 29.26/4.99 | | | | | | | | | % 29.26/4.99 | | | | | | | | | Case 1: % 29.26/4.99 | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | (87) all_158_1 = 0 & less_than(all_59_2, all_50_3) = 0 % 29.26/4.99 | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | ALPHA: (87) implies: % 29.26/4.99 | | | | | | | | | | (88) less_than(all_59_2, all_50_3) = 0 % 29.26/4.99 | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | GROUND_INST: instantiating (13) with all_59_0, 0, all_50_3, % 29.26/4.99 | | | | | | | | | | all_59_2, simplifying with (84), (88) gives: % 29.26/4.99 | | | | | | | | | | (89) all_59_0 = 0 % 29.26/4.99 | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | REDUCE: (42), (89) imply: % 29.26/4.99 | | | | | | | | | | (90) $false % 29.26/4.99 | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | CLOSE: (90) is inconsistent. % 29.26/4.99 | | | | | | | | | | % 29.26/4.99 | | | | | | | | | Case 2: % 29.26/4.99 | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | (91) ( ~ (all_158_0 = 0) & ok(all_50_1) = all_158_0) | ( % 29.26/4.99 | | | | | | | | | | ~ (all_158_1 = 0) & check_cpq(all_50_1) = % 29.26/4.99 | | | | | | | | | | all_158_1) % 29.26/4.99 | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | BETA: splitting (91) gives: % 29.26/4.99 | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | Case 1: % 29.26/4.99 | | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | | (92) ~ (all_158_0 = 0) & ok(all_50_1) = all_158_0 % 29.26/4.99 | | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | | ALPHA: (92) implies: % 29.26/4.99 | | | | | | | | | | | (93) ~ (all_158_0 = 0) % 29.26/4.99 | | | | | | | | | | | (94) ok(all_50_1) = all_158_0 % 29.26/4.99 | | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | | GROUND_INST: instantiating (12) with 0, all_158_0, all_50_1, % 29.26/4.99 | | | | | | | | | | | simplifying with (27), (94) gives: % 29.26/4.99 | | | | | | | | | | | (95) all_158_0 = 0 % 29.26/4.99 | | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | | REDUCE: (93), (95) imply: % 29.26/4.99 | | | | | | | | | | | (96) $false % 29.26/4.99 | | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | | CLOSE: (96) is inconsistent. % 29.26/4.99 | | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | Case 2: % 29.26/4.99 | | | | | | | | | | | % 29.26/4.99 | | | | | | | | | | | (97) ~ (all_158_1 = 0) & check_cpq(all_50_1) = % 29.26/4.99 | | | | | | | | | | | all_158_1 % 29.26/4.99 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | ALPHA: (97) implies: % 29.26/5.00 | | | | | | | | | | | (98) ~ (all_158_1 = 0) % 29.26/5.00 | | | | | | | | | | | (99) check_cpq(all_50_1) = all_158_1 % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | GROUND_INST: instantiating (11) with 0, all_158_1, all_50_1, % 29.26/5.00 | | | | | | | | | | | simplifying with (25), (99) gives: % 29.26/5.00 | | | | | | | | | | | (100) all_158_1 = 0 % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | REDUCE: (98), (100) imply: % 29.26/5.00 | | | | | | | | | | | (101) $false % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | CLOSE: (101) is inconsistent. % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | End of split % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | End of split % 29.26/5.00 | | | | | | | | | % 29.26/5.00 | | | | | | | | Case 2: % 29.26/5.00 | | | | | | | | | % 29.26/5.00 | | | | | | | | | (102) ~ (all_59_3 = all_50_3) % 29.26/5.00 | | | | | | | | | % 29.26/5.00 | | | | | | | | | BETA: splitting (68) gives: % 29.26/5.00 | | | | | | | | | % 29.26/5.00 | | | | | | | | | Case 1: % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | (103) all_59_3 = all_50_3 % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | REDUCE: (102), (103) imply: % 29.26/5.00 | | | | | | | | | | (104) $false % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | CLOSE: (104) is inconsistent. % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | Case 2: % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | (105) ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 29.26/5.00 | | | | | | | | | | pair_in_list(all_62_1, all_59_3, all_59_2) = 0) % 29.26/5.00 | | | | | | | | | | | ( ~ (v0 = 0) & contains_slb(all_50_5, all_50_3) % 29.26/5.00 | | | | | | | | | | = v0)) % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | DELTA: instantiating (105) with fresh symbols all_159_0, % 29.26/5.00 | | | | | | | | | | all_159_1 gives: % 29.26/5.00 | | | | | | | | | | (106) (all_159_0 = 0 & pair_in_list(all_62_1, all_59_3, % 29.26/5.00 | | | | | | | | | | all_59_2) = 0) | ( ~ (all_159_1 = 0) & % 29.26/5.00 | | | | | | | | | | contains_slb(all_50_5, all_50_3) = all_159_1) % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | BETA: splitting (106) gives: % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | Case 1: % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | (107) all_159_0 = 0 & pair_in_list(all_62_1, all_59_3, % 29.26/5.00 | | | | | | | | | | | all_59_2) = 0 % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | ALPHA: (107) implies: % 29.26/5.00 | | | | | | | | | | | (108) pair_in_list(all_62_1, all_59_3, all_59_2) = 0 % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_144_0, all_59_2, % 29.26/5.00 | | | | | | | | | | | all_59_3, all_62_1, simplifying with (81), (108) % 29.26/5.00 | | | | | | | | | | | gives: % 29.26/5.00 | | | | | | | | | | | (109) all_144_0 = 0 % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | REDUCE: (80), (109) imply: % 29.26/5.00 | | | | | | | | | | | (110) $false % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | CLOSE: (110) is inconsistent. % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | Case 2: % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | (111) ~ (all_159_1 = 0) & contains_slb(all_50_5, % 29.26/5.00 | | | | | | | | | | | all_50_3) = all_159_1 % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | ALPHA: (111) implies: % 29.26/5.00 | | | | | | | | | | | (112) ~ (all_159_1 = 0) % 29.26/5.00 | | | | | | | | | | | (113) contains_slb(all_50_5, all_50_3) = all_159_1 % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_159_1, all_50_3, % 29.26/5.00 | | | | | | | | | | | all_50_5, simplifying with (40), (113) gives: % 29.26/5.00 | | | | | | | | | | | (114) all_159_1 = 0 % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | REDUCE: (112), (114) imply: % 29.26/5.00 | | | | | | | | | | | (115) $false % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | | CLOSE: (115) is inconsistent. % 29.26/5.00 | | | | | | | | | | | % 29.26/5.00 | | | | | | | | | | End of split % 29.26/5.00 | | | | | | | | | | % 29.26/5.00 | | | | | | | | | End of split % 29.26/5.00 | | | | | | | | | % 29.26/5.00 | | | | | | | | End of split % 29.26/5.00 | | | | | | | | % 29.26/5.00 | | | | | | | End of split % 29.26/5.00 | | | | | | | % 29.26/5.00 | | | | | | End of split % 29.26/5.00 | | | | | | % 29.26/5.00 | | | | | Case 2: % 29.26/5.00 | | | | | | % 29.26/5.00 | | | | | | (116) ( ~ (all_62_3 = 0) & lookup_slb(all_50_5, all_50_3) = % 29.26/5.00 | | | | | | all_62_4 & less_than(all_62_4, all_50_3) = all_62_3 & % 29.26/5.00 | | | | | | $i(all_62_4)) | ( ~ (all_62_5 = 0) & % 29.26/5.00 | | | | | | contains_slb(all_50_5, all_50_3) = all_62_5) % 29.26/5.00 | | | | | | % 29.26/5.00 | | | | | | BETA: splitting (116) gives: % 29.26/5.00 | | | | | | % 29.26/5.00 | | | | | | Case 1: % 29.26/5.00 | | | | | | | % 29.26/5.01 | | | | | | | (117) ~ (all_62_3 = 0) & lookup_slb(all_50_5, all_50_3) = % 29.26/5.01 | | | | | | | all_62_4 & less_than(all_62_4, all_50_3) = all_62_3 & % 29.26/5.01 | | | | | | | $i(all_62_4) % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | | ALPHA: (117) implies: % 29.26/5.01 | | | | | | | (118) ~ (all_62_3 = 0) % 29.26/5.01 | | | | | | | (119) $i(all_62_4) % 29.26/5.01 | | | | | | | (120) less_than(all_62_4, all_50_3) = all_62_3 % 29.26/5.01 | | | | | | | (121) lookup_slb(all_50_5, all_50_3) = all_62_4 % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | | BETA: splitting (62) gives: % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | | Case 1: % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | | (122) all_61_3 = 0 % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | | REDUCE: (58), (122) imply: % 29.26/5.01 | | | | | | | | (123) $false % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | | CLOSE: (123) is inconsistent. % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | Case 2: % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | | (124) ? [v0: int] : ? [v1: int] : ((v1 = 0 & % 29.26/5.01 | | | | | | | | less_than(all_61_4, all_50_3) = 0) | ( ~ (v0 = 0) & % 29.26/5.01 | | | | | | | | less_than(all_50_3, all_61_4) = v0)) % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | | DELTA: instantiating (124) with fresh symbols all_138_0, % 29.26/5.01 | | | | | | | | all_138_1 gives: % 29.26/5.01 | | | | | | | | (125) (all_138_0 = 0 & less_than(all_61_4, all_50_3) = 0) | ( % 29.26/5.01 | | | | | | | | ~ (all_138_1 = 0) & less_than(all_50_3, all_61_4) = % 29.26/5.01 | | | | | | | | all_138_1) % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | | GROUND_INST: instantiating (15) with all_61_4, all_62_4, % 29.26/5.01 | | | | | | | | all_50_3, all_50_5, simplifying with (61), (121) % 29.26/5.01 | | | | | | | | gives: % 29.26/5.01 | | | | | | | | (126) all_62_4 = all_61_4 % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | | REDUCE: (120), (126) imply: % 29.26/5.01 | | | | | | | | (127) less_than(all_61_4, all_50_3) = all_62_3 % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | | BETA: splitting (125) gives: % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | | Case 1: % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | (128) all_138_0 = 0 & less_than(all_61_4, all_50_3) = 0 % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | ALPHA: (128) implies: % 29.26/5.01 | | | | | | | | | (129) less_than(all_61_4, all_50_3) = 0 % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | GROUND_INST: instantiating (13) with all_62_3, 0, all_50_3, % 29.26/5.01 | | | | | | | | | all_61_4, simplifying with (127), (129) gives: % 29.26/5.01 | | | | | | | | | (130) all_62_3 = 0 % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | REDUCE: (118), (130) imply: % 29.26/5.01 | | | | | | | | | (131) $false % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | CLOSE: (131) is inconsistent. % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | Case 2: % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | (132) ~ (all_138_1 = 0) & less_than(all_50_3, all_61_4) = % 29.26/5.01 | | | | | | | | | all_138_1 % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | ALPHA: (132) implies: % 29.26/5.01 | | | | | | | | | (133) ~ (all_138_1 = 0) % 29.26/5.01 | | | | | | | | | (134) less_than(all_50_3, all_61_4) = all_138_1 % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | GROUND_INST: instantiating (1) with all_61_4, all_50_3, % 29.26/5.01 | | | | | | | | | all_138_1, simplifying with (22), (59), (134) % 29.26/5.01 | | | | | | | | | gives: % 29.26/5.01 | | | | | | | | | (135) all_138_1 = 0 | less_than(all_61_4, all_50_3) = 0 % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | BETA: splitting (135) gives: % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | | Case 1: % 29.26/5.01 | | | | | | | | | | % 29.26/5.01 | | | | | | | | | | (136) less_than(all_61_4, all_50_3) = 0 % 29.26/5.01 | | | | | | | | | | % 29.26/5.01 | | | | | | | | | | GROUND_INST: instantiating (13) with all_62_3, 0, all_50_3, % 29.26/5.01 | | | | | | | | | | all_61_4, simplifying with (127), (136) gives: % 29.26/5.01 | | | | | | | | | | (137) all_62_3 = 0 % 29.26/5.01 | | | | | | | | | | % 29.26/5.01 | | | | | | | | | | REDUCE: (118), (137) imply: % 29.26/5.01 | | | | | | | | | | (138) $false % 29.26/5.01 | | | | | | | | | | % 29.26/5.01 | | | | | | | | | | CLOSE: (138) is inconsistent. % 29.26/5.01 | | | | | | | | | | % 29.26/5.01 | | | | | | | | | Case 2: % 29.26/5.01 | | | | | | | | | | % 29.26/5.01 | | | | | | | | | | (139) all_138_1 = 0 % 29.26/5.01 | | | | | | | | | | % 29.26/5.01 | | | | | | | | | | REDUCE: (133), (139) imply: % 29.26/5.01 | | | | | | | | | | (140) $false % 29.26/5.01 | | | | | | | | | | % 29.26/5.01 | | | | | | | | | | CLOSE: (140) is inconsistent. % 29.26/5.01 | | | | | | | | | | % 29.26/5.01 | | | | | | | | | End of split % 29.26/5.01 | | | | | | | | | % 29.26/5.01 | | | | | | | | End of split % 29.26/5.01 | | | | | | | | % 29.26/5.01 | | | | | | | End of split % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | Case 2: % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | | (141) ~ (all_62_5 = 0) & contains_slb(all_50_5, all_50_3) = % 29.26/5.01 | | | | | | | all_62_5 % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | | ALPHA: (141) implies: % 29.26/5.01 | | | | | | | (142) ~ (all_62_5 = 0) % 29.26/5.01 | | | | | | | (143) contains_slb(all_50_5, all_50_3) = all_62_5 % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | | GROUND_INST: instantiating (14) with 0, all_62_5, all_50_3, % 29.26/5.01 | | | | | | | all_50_5, simplifying with (40), (143) gives: % 29.26/5.01 | | | | | | | (144) all_62_5 = 0 % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | | REDUCE: (142), (144) imply: % 29.26/5.01 | | | | | | | (145) $false % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | | CLOSE: (145) is inconsistent. % 29.26/5.01 | | | | | | | % 29.26/5.01 | | | | | | End of split % 29.26/5.01 | | | | | | % 29.26/5.01 | | | | | End of split % 29.26/5.01 | | | | | % 29.26/5.01 | | | | Case 2: % 29.26/5.01 | | | | | % 29.26/5.01 | | | | | (146) ~ (all_61_5 = 0) & contains_slb(all_50_5, all_50_3) = % 29.26/5.01 | | | | | all_61_5 % 29.26/5.01 | | | | | % 29.26/5.01 | | | | | ALPHA: (146) implies: % 29.26/5.01 | | | | | (147) ~ (all_61_5 = 0) % 29.26/5.01 | | | | | (148) contains_slb(all_50_5, all_50_3) = all_61_5 % 29.26/5.01 | | | | | % 29.26/5.01 | | | | | GROUND_INST: instantiating (14) with 0, all_61_5, all_50_3, all_50_5, % 29.26/5.01 | | | | | simplifying with (40), (148) gives: % 29.26/5.01 | | | | | (149) all_61_5 = 0 % 29.26/5.01 | | | | | % 29.26/5.02 | | | | | REDUCE: (147), (149) imply: % 29.26/5.02 | | | | | (150) $false % 29.26/5.02 | | | | | % 29.26/5.02 | | | | | CLOSE: (150) is inconsistent. % 29.26/5.02 | | | | | % 29.26/5.02 | | | | End of split % 29.26/5.02 | | | | % 29.26/5.02 | | | End of split % 29.26/5.02 | | | % 29.26/5.02 | | Case 2: % 29.26/5.02 | | | % 29.26/5.02 | | | (151) all_59_4 = 0 & check_cpq(all_50_2) = 0 % 29.26/5.02 | | | % 29.26/5.02 | | | ALPHA: (151) implies: % 29.26/5.02 | | | (152) check_cpq(all_50_2) = 0 % 29.26/5.02 | | | % 29.26/5.02 | | | GROUND_INST: instantiating (11) with all_50_0, 0, all_50_2, simplifying % 29.26/5.02 | | | with (24), (152) gives: % 29.26/5.02 | | | (153) all_50_0 = 0 % 29.26/5.02 | | | % 29.26/5.02 | | | REDUCE: (18), (153) imply: % 29.26/5.02 | | | (154) $false % 29.26/5.02 | | | % 29.26/5.02 | | | CLOSE: (154) is inconsistent. % 29.26/5.02 | | | % 29.26/5.02 | | End of split % 29.26/5.02 | | % 29.26/5.02 | Case 2: % 29.26/5.02 | | % 29.26/5.02 | | (155) ~ (all_57_1 = 0) & ok(all_50_1) = all_57_1 % 29.26/5.02 | | % 29.26/5.02 | | ALPHA: (155) implies: % 29.26/5.02 | | (156) ~ (all_57_1 = 0) % 29.26/5.02 | | (157) ok(all_50_1) = all_57_1 % 29.26/5.02 | | % 29.26/5.02 | | GROUND_INST: instantiating (12) with 0, all_57_1, all_50_1, simplifying with % 29.26/5.02 | | (27), (157) gives: % 29.26/5.02 | | (158) all_57_1 = 0 % 29.26/5.02 | | % 29.26/5.02 | | REDUCE: (156), (158) imply: % 29.26/5.02 | | (159) $false % 29.26/5.02 | | % 29.26/5.02 | | CLOSE: (159) is inconsistent. % 29.26/5.02 | | % 29.26/5.02 | End of split % 29.26/5.02 | % 29.26/5.02 End of proof % 29.26/5.02 % SZS output end Proof for theBenchmark % 29.26/5.02 % 29.26/5.02 4425ms %------------------------------------------------------------------------------