%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV407+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 : n023.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 22:56:12 EDT 2023 % Result : Theorem 22.71s 3.66s % Output : Proof 23.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SWV407+1 : TPTP v8.1.2. Released v3.3.0. % 0.03/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n023.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Tue Aug 29 06:14:40 EDT 2023 % 0.12/0.33 % CPUTime : % 0.57/0.59 ________ _____ % 0.57/0.59 ___ __ \_________(_)________________________________ % 0.57/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.57/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.57/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.57/0.59 % 0.57/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.57/0.59 (2023-06-19) % 0.57/0.59 % 0.57/0.59 (c) Philipp Rümmer, 2009-2023 % 0.57/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.57/0.59 Amanda Stjerna. % 0.57/0.59 Free software under BSD-3-Clause. % 0.57/0.59 % 0.57/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.57/0.59 % 0.57/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.57/0.60 Running up to 7 provers in parallel. % 0.57/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.57/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.57/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.57/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.57/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.57/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.57/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.35/1.12 Prover 4: Preprocessing ... % 3.35/1.12 Prover 1: Preprocessing ... % 3.85/1.17 Prover 5: Preprocessing ... % 3.85/1.17 Prover 0: Preprocessing ... % 3.85/1.17 Prover 3: Preprocessing ... % 3.85/1.17 Prover 2: Preprocessing ... % 4.10/1.18 Prover 6: Preprocessing ... % 8.51/1.79 Prover 1: Warning: ignoring some quantifiers % 8.87/1.83 Prover 3: Warning: ignoring some quantifiers % 9.03/1.86 Prover 1: Constructing countermodel ... % 9.03/1.86 Prover 3: Constructing countermodel ... % 9.03/1.86 Prover 5: Proving ... % 9.03/1.86 Prover 6: Proving ... % 9.03/1.86 Prover 4: Constructing countermodel ... % 9.03/1.88 Prover 0: Proving ... % 9.55/1.95 Prover 2: Proving ... % 13.58/2.50 Prover 3: gave up % 13.58/2.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.63/2.59 Prover 7: Preprocessing ... % 15.73/2.75 Prover 7: Warning: ignoring some quantifiers % 16.00/2.77 Prover 7: Constructing countermodel ... % 20.70/3.40 Prover 1: gave up % 20.70/3.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.53/3.47 Prover 8: Preprocessing ... % 22.20/3.62 Prover 8: Warning: ignoring some quantifiers % 22.71/3.64 Prover 4: Found proof (size 371) % 22.71/3.64 Prover 4: proved (3036ms) % 22.71/3.65 Prover 8: Constructing countermodel ... % 22.71/3.65 Prover 5: stopped % 22.71/3.65 Prover 0: stopped % 22.71/3.65 Prover 2: stopped % 22.71/3.65 Prover 7: stopped % 22.71/3.65 Prover 6: stopped % 22.71/3.66 Prover 8: stopped % 22.71/3.66 % 22.71/3.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.71/3.66 % 23.00/3.68 % SZS output start Proof for theBenchmark % 23.00/3.69 Assumptions after simplification: % 23.00/3.69 --------------------------------- % 23.00/3.69 % 23.00/3.69 (ax20) % 23.00/3.71 $i(create_slb) & ! [v0: $i] : ( ~ (contains_slb(create_slb, v0) = 0) | ~ % 23.00/3.71 $i(v0)) % 23.00/3.71 % 23.00/3.71 (ax39) % 23.00/3.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 23.00/3.71 int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) = % 23.00/3.71 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ % 23.00/3.71 (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0: $i] : ! [v1: $i] : ! % 23.00/3.71 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (contains_cpq(v4, v3) = 0) | ~ % 23.00/3.71 (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 23.00/3.71 contains_slb(v1, v3) = 0) % 23.00/3.71 % 23.00/3.71 (ax47) % 23.00/3.71 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.00/3.71 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.00/3.71 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 23.00/3.71 : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 & % 23.00/3.71 triple(v0, v7, bad) = v8 & update_slb(v1, v5) = v7 & contains_slb(v1, v5) % 23.00/3.71 = v6 & $i(v8) & $i(v7) & $i(v5) & (v8 = v4 | v6 = 0))) % 23.00/3.71 % 23.00/3.71 (ax48) % 23.00/3.72 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.00/3.72 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.00/3.72 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 23.00/3.72 : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : % 23.00/3.72 (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & update_slb(v1, v5) = % 23.00/3.72 v9 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = v6 & % 23.00/3.72 strictly_less_than(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ % 23.00/3.72 (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 23.00/3.72 % 23.00/3.72 (ax49) % 23.00/3.72 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 23.00/3.72 [v4: $i] : ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ % 23.00/3.72 (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) | ~ % 23.00/3.72 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] % 23.00/3.72 : ? [v10: $i] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & % 23.00/3.72 lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = % 23.00/3.72 v8 & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) % 23.00/3.72 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 23.00/3.72 create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | % 23.00/3.72 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] % 23.00/3.72 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : (findmin_pqp_res(v0) = v5 & % 23.00/3.72 triple(v0, v9, v2) = v10 & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = % 23.00/3.72 v7 & contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & $i(v9) % 23.00/3.72 & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 23.00/3.72 % 23.00/3.72 (ax51) % 23.00/3.72 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 23.00/3.72 [v4: $i] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, % 23.00/3.72 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (findmin_pqp_res(v0) % 23.00/3.72 = v4 & $i(v4))) % 23.00/3.72 % 23.00/3.72 (ax52) % 23.00/3.72 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ? % 23.00/3.72 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = % 23.00/3.72 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: % 23.00/3.72 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 23.00/3.72 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & % 23.00/3.72 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : ! % 23.00/3.72 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 23.00/3.72 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & % 23.00/3.72 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2))) % 23.00/3.72 % 23.00/3.72 (l43_co) % 23.00/3.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 23.00/3.73 $i] : ? [v6: $i] : (findmin_cpq_res(v3) = v4 & contains_cpq(v3, v6) = 0 & % 23.00/3.73 triple(v0, v1, v2) = v3 & check_cpq(v5) = 0 & findmin_cpq_eff(v3) = v5 & % 23.00/3.73 strictly_less_than(v6, v4) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) % 23.00/3.73 & $i(v1) & $i(v0)) % 23.00/3.73 % 23.00/3.73 (l43_l44) % 23.00/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 23.00/3.73 $i] : ( ~ (findmin_cpq_res(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~ % 23.00/3.73 (strictly_less_than(v3, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.00/3.73 $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : ? [v10: % 23.00/3.73 $i] : ? [v11: int] : ? [v12: int] : (findmin_pqp_res(v0) = v7 & % 23.00/3.73 update_slb(v1, v7) = v8 & pair_in_list(v8, v3, v7) = v9 & contains_slb(v1, % 23.00/3.73 v3) = v6 & $i(v10) & $i(v8) & $i(v7) & ( ~ (v6 = 0) | v9 = 0 | (v12 = 0 % 23.00/3.73 & v11 = 0 & pair_in_list(v8, v3, v10) = 0 & less_than(v7, v10) = 0)))) % 23.00/3.73 % 23.00/3.73 (l43_li4142) % 23.00/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 23.00/3.73 $i] : ! [v6: int] : (v6 = 0 | ~ (triple(v0, v1, v2) = v3) | ~ % 23.00/3.73 (less_than(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | % 23.00/3.73 ~ $i(v0) | ? [v7: int] : (( ~ (v7 = 0) & check_cpq(v3) = v7) | ( ~ (v7 = 0) % 23.00/3.73 & pair_in_list(v1, v4, v5) = v7))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.00/3.73 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (triple(v0, v1, v2) = % 23.00/3.73 v3) | ~ (pair_in_list(v1, v4, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 23.00/3.73 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ((v6 = 0 & less_than(v5, v4) % 23.00/3.73 = 0) | ( ~ (v6 = 0) & check_cpq(v3) = v6))) & ! [v0: $i] : ! [v1: $i] % 23.00/3.73 : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 23.00/3.73 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] % 23.00/3.73 : ? [v8: int] : ($i(v6) & $i(v5) & ((v7 = 0 & ~ (v8 = 0) & % 23.00/3.73 pair_in_list(v1, v5, v6) = 0 & less_than(v6, v5) = v8) | (v4 = 0 & % 23.00/3.73 check_cpq(v3) = 0)))) % 23.00/3.73 % 23.00/3.73 (stricly_smaller_definition) % 23.00/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 23.00/3.73 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 23.00/3.73 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 23.00/3.73 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 23.00/3.73 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 23.00/3.73 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 % 23.00/3.73 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 23.00/3.73 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 23.00/3.73 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 % 23.00/3.73 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.00/3.73 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 23.00/3.73 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( % 23.00/3.73 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 23.00/3.73 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( % 23.00/3.73 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0: % 23.00/3.73 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 23.00/3.73 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, % 23.00/3.73 v0) = v2 & (v3 = 0 | v2 = 0))) % 23.00/3.73 % 23.00/3.73 (totality) % 23.00/3.73 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) = % 23.00/3.73 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : ! % 23.00/3.73 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) | % 23.00/3.73 ~ $i(v0) | less_than(v1, v0) = 0) % 23.00/3.73 % 23.00/3.73 (transitivity) % 23.00/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.00/3.74 (less_than(v1, v2) = 0) | ~ (less_than(v0, v2) = v3) | ~ $i(v2) | ~ % 23.00/3.74 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v0, v1) = v4)) % 23.00/3.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.00/3.74 (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ~ $i(v2) | ~ % 23.00/3.74 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v1, v2) = v4)) % 23.00/3.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (less_than(v1, v2) = 0) | ~ % 23.00/3.74 (less_than(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, % 23.00/3.74 v2) = 0) % 23.00/3.74 % 23.00/3.74 (function-axioms) % 23.33/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 23.33/3.74 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 23.33/3.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.33/3.74 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 23.33/3.74 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.33/3.74 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 23.33/3.74 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 23.33/3.74 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 23.33/3.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.33/3.74 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 23.33/3.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.33/3.74 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 23.33/3.74 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 23.33/3.74 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 23.33/3.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 23.33/3.74 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.33/3.74 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 23.33/3.74 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 23.33/3.74 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 23.33/3.74 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.33/3.74 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 23.33/3.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.33/3.74 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 23.33/3.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.33/3.74 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 23.33/3.74 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 23.33/3.74 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 23.33/3.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.33/3.74 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 23.33/3.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 23.33/3.74 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 23.33/3.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.33/3.74 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: % 23.33/3.74 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | % 23.33/3.74 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.33/3.74 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! % 23.33/3.74 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 23.33/3.74 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 23.33/3.74 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | % 23.33/3.74 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 23.33/3.74 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! % 23.33/3.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = % 23.33/3.74 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 23.33/3.74 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = % 23.33/3.74 v1) | ~ (isnonempty_slb(v2) = v0)) % 23.33/3.74 % 23.33/3.74 Further assumptions not needed in the proof: % 23.33/3.74 -------------------------------------------- % 23.33/3.74 ax18, ax19, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, % 23.33/3.74 ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax40, ax41, ax42, ax43, ax44, ax45, % 23.33/3.74 ax46, ax50, ax53, bottom_smallest, reflexivity % 23.33/3.74 % 23.33/3.74 Those formulas are unsatisfiable: % 23.33/3.74 --------------------------------- % 23.33/3.74 % 23.33/3.74 Begin of proof % 23.33/3.74 | % 23.33/3.74 | ALPHA: (transitivity) implies: % 23.33/3.75 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.33/3.75 | (less_than(v0, v2) = v3) | ~ (less_than(v0, v1) = 0) | ~ $i(v2) | % 23.33/3.75 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & less_than(v1, % 23.33/3.75 | v2) = v4)) % 23.33/3.75 | % 23.33/3.75 | ALPHA: (totality) implies: % 23.33/3.75 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 23.33/3.75 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) % 23.33/3.75 | % 23.33/3.75 | ALPHA: (stricly_smaller_definition) implies: % 23.33/3.75 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (strictly_less_than(v0, v1) = 0) | ~ % 23.33/3.75 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & less_than(v1, v0) % 23.33/3.75 | = v2 & less_than(v0, v1) = 0)) % 23.33/3.75 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2) % 23.33/3.75 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 23.33/3.75 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 = % 23.33/3.75 | 0) | (v4 = 0 & ~ (v2 = 0))))) % 23.33/3.75 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 23.33/3.75 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 23.33/3.75 | (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 23.33/3.75 | 0) | v4 = 0))) % 23.33/3.75 | % 23.33/3.75 | ALPHA: (ax20) implies: % 23.33/3.75 | (6) ! [v0: $i] : ( ~ (contains_slb(create_slb, v0) = 0) | ~ $i(v0)) % 23.33/3.75 | % 23.33/3.75 | ALPHA: (ax39) implies: % 23.33/3.75 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 23.33/3.75 | ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | ~ % 23.33/3.75 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | contains_slb(v1, v3) = % 23.33/3.75 | 0) % 23.33/3.75 | % 23.33/3.75 | ALPHA: (ax47) implies: % 23.33/3.75 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.33/3.75 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.33/3.75 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 23.33/3.75 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 23.33/3.75 | (findmin_pqp_res(v0) = v5 & triple(v0, v7, bad) = v8 & update_slb(v1, % 23.33/3.75 | v5) = v7 & contains_slb(v1, v5) = v6 & $i(v8) & $i(v7) & $i(v5) & % 23.33/3.75 | (v8 = v4 | v6 = 0))) % 23.33/3.75 | % 23.33/3.75 | ALPHA: (ax48) implies: % 23.33/3.75 | (9) $i(bad) % 23.33/3.75 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.33/3.75 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.33/3.75 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 23.33/3.75 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 23.33/3.75 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 % 23.33/3.75 | & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 23.33/3.75 | contains_slb(v1, v5) = v6 & strictly_less_than(v5, v7) = v8 & % 23.33/3.75 | $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | % 23.33/3.75 | v10 = v4))) % 23.33/3.75 | % 23.33/3.75 | ALPHA: (ax49) implies: % 23.33/3.75 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.33/3.75 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.33/3.75 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 23.33/3.75 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 23.33/3.75 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, v2) = v10 % 23.33/3.75 | & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 23.33/3.75 | contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & % 23.33/3.75 | $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = % 23.33/3.75 | v4))) % 23.33/3.76 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.33/3.76 | ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ % 23.33/3.76 | (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) % 23.33/3.76 | | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] % 23.33/3.76 | : ? [v9: $i] : ? [v10: $i] : (triple(v0, v1, v2) = v9 & % 23.33/3.76 | findmin_cpq_eff(v9) = v10 & lookup_slb(v1, v3) = v7 & % 23.33/3.76 | contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & $i(v10) & % 23.33/3.76 | $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) % 23.33/3.76 | % 23.33/3.76 | ALPHA: (ax51) implies: % 23.33/3.76 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.33/3.76 | (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, % 23.33/3.76 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 23.33/3.76 | (findmin_pqp_res(v0) = v4 & $i(v4))) % 23.33/3.76 | % 23.33/3.76 | ALPHA: (ax52) implies: % 23.33/3.76 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) % 23.33/3.76 | | ? [v2: $i] : ? [v3: $i] : (findmin_cpq_res(v0) = v3 & % 23.33/3.76 | removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2 & $i(v3) & % 23.33/3.76 | $i(v2))) % 23.33/3.76 | % 23.33/3.76 | ALPHA: (l43_li4142) implies: % 23.33/3.76 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.33/3.76 | ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v3) | ~ (pair_in_list(v1, v4, % 23.33/3.76 | v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ % 23.33/3.76 | $i(v0) | ? [v6: int] : ((v6 = 0 & less_than(v5, v4) = 0) | ( ~ (v6 % 23.33/3.76 | = 0) & check_cpq(v3) = v6))) % 23.33/3.76 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.33/3.76 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (triple(v0, v1, v2) = v3) | % 23.33/3.76 | ~ (less_than(v5, v4) = v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ % 23.33/3.76 | $i(v1) | ~ $i(v0) | ? [v7: int] : (( ~ (v7 = 0) & check_cpq(v3) = % 23.33/3.76 | v7) | ( ~ (v7 = 0) & pair_in_list(v1, v4, v5) = v7))) % 23.33/3.76 | % 23.33/3.76 | ALPHA: (function-axioms) implies: % 23.33/3.76 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.33/3.76 | : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) % 23.33/3.76 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.33/3.76 | (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 23.33/3.76 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.33/3.76 | (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) % 23.33/3.76 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.33/3.76 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ % 23.33/3.76 | (less_than(v3, v2) = v0)) % 23.33/3.76 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.33/3.76 | : ! [v3: $i] : (v1 = v0 | ~ (strictly_less_than(v3, v2) = v1) | ~ % 23.33/3.76 | (strictly_less_than(v3, v2) = v0)) % 23.33/3.76 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.33/3.76 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 23.33/3.76 | (contains_slb(v3, v2) = v0)) % 23.33/3.76 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.33/3.76 | (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 23.33/3.76 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.33/3.76 | (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 23.33/3.76 | (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.33/3.76 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) % 23.33/3.76 | = v1) | ~ (pair_in_list(v4, v3, v2) = v0)) % 23.33/3.76 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.33/3.76 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = % 23.33/3.76 | v0)) % 23.33/3.76 | % 23.33/3.76 | DELTA: instantiating (l43_co) with fresh symbols all_48_0, all_48_1, all_48_2, % 23.33/3.76 | all_48_3, all_48_4, all_48_5, all_48_6 gives: % 23.33/3.77 | (27) findmin_cpq_res(all_48_3) = all_48_2 & contains_cpq(all_48_3, % 23.33/3.77 | all_48_0) = 0 & triple(all_48_6, all_48_5, all_48_4) = all_48_3 & % 23.33/3.77 | check_cpq(all_48_1) = 0 & findmin_cpq_eff(all_48_3) = all_48_1 & % 23.33/3.77 | strictly_less_than(all_48_0, all_48_2) = 0 & $i(all_48_0) & % 23.33/3.77 | $i(all_48_1) & $i(all_48_2) & $i(all_48_3) & $i(all_48_4) & % 23.33/3.77 | $i(all_48_5) & $i(all_48_6) % 23.33/3.77 | % 23.33/3.77 | ALPHA: (27) implies: % 23.33/3.77 | (28) $i(all_48_6) % 23.33/3.77 | (29) $i(all_48_5) % 23.33/3.77 | (30) $i(all_48_4) % 23.33/3.77 | (31) $i(all_48_3) % 23.33/3.77 | (32) $i(all_48_2) % 23.33/3.77 | (33) $i(all_48_0) % 23.33/3.77 | (34) strictly_less_than(all_48_0, all_48_2) = 0 % 23.33/3.77 | (35) findmin_cpq_eff(all_48_3) = all_48_1 % 23.33/3.77 | (36) check_cpq(all_48_1) = 0 % 23.33/3.77 | (37) triple(all_48_6, all_48_5, all_48_4) = all_48_3 % 23.33/3.77 | (38) contains_cpq(all_48_3, all_48_0) = 0 % 23.33/3.77 | (39) findmin_cpq_res(all_48_3) = all_48_2 % 23.33/3.77 | % 23.33/3.77 | GROUND_INST: instantiating (3) with all_48_0, all_48_2, simplifying with (32), % 23.33/3.77 | (33), (34) gives: % 23.33/3.77 | (40) ? [v0: int] : ( ~ (v0 = 0) & less_than(all_48_0, all_48_2) = 0 & % 23.33/3.77 | less_than(all_48_2, all_48_0) = v0) % 23.33/3.77 | % 23.33/3.77 | GROUND_INST: instantiating (14) with all_48_3, all_48_1, simplifying with % 23.33/3.77 | (31), (35) gives: % 23.33/3.77 | (41) ? [v0: $i] : ? [v1: $i] : (findmin_cpq_res(all_48_3) = v1 & % 23.33/3.77 | removemin_cpq_eff(all_48_3) = v0 & remove_cpq(all_48_1, v1) = v0 & % 23.33/3.77 | $i(v1) & $i(v0)) % 23.33/3.77 | % 23.33/3.77 | GROUND_INST: instantiating (11) with all_48_6, all_48_5, all_48_4, all_48_3, % 23.33/3.77 | all_48_1, simplifying with (28), (29), (30), (35), (37) gives: % 23.33/3.77 | (42) all_48_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 23.33/3.77 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_48_6) = % 23.33/3.77 | v0 & triple(all_48_6, v4, all_48_4) = v5 & update_slb(all_48_5, v0) % 23.33/3.77 | = v4 & lookup_slb(all_48_5, v0) = v2 & contains_slb(all_48_5, v0) = % 23.33/3.77 | v1 & less_than(v2, v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( % 23.33/3.77 | ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_48_1)) % 23.33/3.77 | % 23.33/3.77 | GROUND_INST: instantiating (10) with all_48_6, all_48_5, all_48_4, all_48_3, % 23.33/3.77 | all_48_1, simplifying with (28), (29), (30), (35), (37) gives: % 23.49/3.77 | (43) all_48_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 23.49/3.77 | [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_48_6) = % 23.49/3.77 | v0 & triple(all_48_6, v4, bad) = v5 & update_slb(all_48_5, v0) = v4 % 23.49/3.77 | & lookup_slb(all_48_5, v0) = v2 & contains_slb(all_48_5, v0) = v1 & % 23.49/3.77 | strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) % 23.49/3.77 | & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_48_1)) % 23.49/3.77 | % 23.49/3.77 | GROUND_INST: instantiating (8) with all_48_6, all_48_5, all_48_4, all_48_3, % 23.49/3.77 | all_48_1, simplifying with (28), (29), (30), (35), (37) gives: % 23.49/3.77 | (44) all_48_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? % 23.49/3.77 | [v3: $i] : (findmin_pqp_res(all_48_6) = v0 & triple(all_48_6, v2, bad) % 23.49/3.77 | = v3 & update_slb(all_48_5, v0) = v2 & contains_slb(all_48_5, v0) = % 23.49/3.77 | v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_48_1 | v1 = 0)) % 23.49/3.77 | % 23.49/3.77 | GROUND_INST: instantiating (7) with all_48_6, all_48_5, all_48_4, all_48_0, % 23.49/3.77 | all_48_3, simplifying with (28), (29), (30), (33), (37), (38) % 23.49/3.77 | gives: % 23.49/3.77 | (45) contains_slb(all_48_5, all_48_0) = 0 % 23.49/3.77 | % 23.49/3.77 | GROUND_INST: instantiating (l43_l44) with all_48_6, all_48_5, all_48_4, % 23.49/3.77 | all_48_0, all_48_3, all_48_2, simplifying with (28), (29), (30), % 23.49/3.77 | (33), (34), (37), (39) gives: % 23.49/3.77 | (46) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] % 23.49/3.77 | : ? [v5: int] : ? [v6: int] : (findmin_pqp_res(all_48_6) = v1 & % 23.49/3.77 | update_slb(all_48_5, v1) = v2 & pair_in_list(v2, all_48_0, v1) = v3 % 23.49/3.77 | & contains_slb(all_48_5, all_48_0) = v0 & $i(v4) & $i(v2) & $i(v1) & % 23.49/3.77 | ( ~ (v0 = 0) | v3 = 0 | (v6 = 0 & v5 = 0 & pair_in_list(v2, % 23.49/3.77 | all_48_0, v4) = 0 & less_than(v1, v4) = 0))) % 23.49/3.77 | % 23.49/3.78 | GROUND_INST: instantiating (13) with all_48_6, all_48_5, all_48_4, all_48_3, % 23.49/3.78 | all_48_2, simplifying with (28), (29), (30), (37), (39) gives: % 23.49/3.78 | (47) all_48_5 = create_slb | (findmin_pqp_res(all_48_6) = all_48_2 & % 23.49/3.78 | $i(all_48_2)) % 23.49/3.78 | % 23.49/3.78 | DELTA: instantiating (40) with fresh symbol all_56_0 gives: % 23.49/3.78 | (48) ~ (all_56_0 = 0) & less_than(all_48_0, all_48_2) = 0 & % 23.49/3.78 | less_than(all_48_2, all_48_0) = all_56_0 % 23.49/3.78 | % 23.49/3.78 | ALPHA: (48) implies: % 23.49/3.78 | (49) ~ (all_56_0 = 0) % 23.49/3.78 | (50) less_than(all_48_2, all_48_0) = all_56_0 % 23.49/3.78 | (51) less_than(all_48_0, all_48_2) = 0 % 23.49/3.78 | % 23.49/3.78 | DELTA: instantiating (41) with fresh symbols all_58_0, all_58_1 gives: % 23.49/3.78 | (52) findmin_cpq_res(all_48_3) = all_58_0 & removemin_cpq_eff(all_48_3) = % 23.49/3.78 | all_58_1 & remove_cpq(all_48_1, all_58_0) = all_58_1 & $i(all_58_0) & % 23.49/3.78 | $i(all_58_1) % 23.49/3.78 | % 23.49/3.78 | ALPHA: (52) implies: % 23.49/3.78 | (53) $i(all_58_0) % 23.49/3.78 | (54) findmin_cpq_res(all_48_3) = all_58_0 % 23.49/3.78 | % 23.49/3.78 | DELTA: instantiating (46) with fresh symbols all_64_0, all_64_1, all_64_2, % 23.49/3.78 | all_64_3, all_64_4, all_64_5, all_64_6 gives: % 23.49/3.78 | (55) findmin_pqp_res(all_48_6) = all_64_5 & update_slb(all_48_5, all_64_5) % 23.49/3.78 | = all_64_4 & pair_in_list(all_64_4, all_48_0, all_64_5) = all_64_3 & % 23.49/3.78 | contains_slb(all_48_5, all_48_0) = all_64_6 & $i(all_64_2) & % 23.49/3.78 | $i(all_64_4) & $i(all_64_5) & ( ~ (all_64_6 = 0) | all_64_3 = 0 | % 23.49/3.78 | (all_64_0 = 0 & all_64_1 = 0 & pair_in_list(all_64_4, all_48_0, % 23.49/3.78 | all_64_2) = 0 & less_than(all_64_5, all_64_2) = 0)) % 23.49/3.78 | % 23.49/3.78 | ALPHA: (55) implies: % 23.49/3.78 | (56) $i(all_64_5) % 23.49/3.78 | (57) $i(all_64_2) % 23.49/3.78 | (58) contains_slb(all_48_5, all_48_0) = all_64_6 % 23.49/3.78 | (59) pair_in_list(all_64_4, all_48_0, all_64_5) = all_64_3 % 23.49/3.78 | (60) update_slb(all_48_5, all_64_5) = all_64_4 % 23.49/3.78 | (61) findmin_pqp_res(all_48_6) = all_64_5 % 23.49/3.78 | (62) ~ (all_64_6 = 0) | all_64_3 = 0 | (all_64_0 = 0 & all_64_1 = 0 & % 23.49/3.78 | pair_in_list(all_64_4, all_48_0, all_64_2) = 0 & less_than(all_64_5, % 23.49/3.78 | all_64_2) = 0) % 23.49/3.78 | % 23.49/3.78 | GROUND_INST: instantiating (22) with 0, all_64_6, all_48_0, all_48_5, % 23.49/3.78 | simplifying with (45), (58) gives: % 23.49/3.78 | (63) all_64_6 = 0 % 23.49/3.78 | % 23.49/3.78 | GROUND_INST: instantiating (19) with all_48_2, all_58_0, all_48_3, simplifying % 23.49/3.78 | with (39), (54) gives: % 23.49/3.78 | (64) all_58_0 = all_48_2 % 23.49/3.78 | % 23.49/3.78 | GROUND_INST: instantiating (4) with all_48_2, all_48_0, 0, simplifying with % 23.49/3.78 | (32), (33), (51) gives: % 23.49/3.78 | (65) ? [v0: int] : ? [v1: MultipleValueBool] : ( ~ (v0 = 0) & % 23.49/3.78 | strictly_less_than(all_48_2, all_48_0) = v0 & less_than(all_48_2, % 23.49/3.78 | all_48_0) = v1) % 23.49/3.78 | % 23.49/3.78 | DELTA: instantiating (65) with fresh symbols all_75_0, all_75_1 gives: % 23.49/3.78 | (66) ~ (all_75_1 = 0) & strictly_less_than(all_48_2, all_48_0) = all_75_1 % 23.49/3.78 | & less_than(all_48_2, all_48_0) = all_75_0 % 23.49/3.78 | % 23.49/3.78 | ALPHA: (66) implies: % 23.49/3.78 | (67) less_than(all_48_2, all_48_0) = all_75_0 % 23.49/3.78 | % 23.49/3.78 | GROUND_INST: instantiating (20) with all_56_0, all_75_0, all_48_0, all_48_2, % 23.49/3.78 | simplifying with (50), (67) gives: % 23.49/3.78 | (68) all_75_0 = all_56_0 % 23.49/3.78 | % 23.49/3.78 | BETA: splitting (47) gives: % 23.49/3.78 | % 23.49/3.78 | Case 1: % 23.49/3.78 | | % 23.49/3.78 | | (69) all_48_5 = create_slb % 23.49/3.78 | | % 23.49/3.78 | | REDUCE: (45), (69) imply: % 23.49/3.78 | | (70) contains_slb(create_slb, all_48_0) = 0 % 23.49/3.78 | | % 23.49/3.78 | | GROUND_INST: instantiating (6) with all_48_0, simplifying with (33), (70) % 23.49/3.78 | | gives: % 23.49/3.78 | | (71) $false % 23.49/3.78 | | % 23.49/3.78 | | CLOSE: (71) is inconsistent. % 23.49/3.78 | | % 23.49/3.78 | Case 2: % 23.49/3.78 | | % 23.49/3.78 | | (72) ~ (all_48_5 = create_slb) % 23.49/3.78 | | (73) findmin_pqp_res(all_48_6) = all_48_2 & $i(all_48_2) % 23.49/3.78 | | % 23.49/3.78 | | ALPHA: (73) implies: % 23.49/3.78 | | (74) findmin_pqp_res(all_48_6) = all_48_2 % 23.49/3.78 | | % 23.49/3.78 | | BETA: splitting (44) gives: % 23.49/3.78 | | % 23.49/3.78 | | Case 1: % 23.49/3.78 | | | % 23.49/3.78 | | | (75) all_48_5 = create_slb % 23.49/3.78 | | | % 23.49/3.78 | | | REDUCE: (72), (75) imply: % 23.49/3.78 | | | (76) $false % 23.49/3.78 | | | % 23.49/3.78 | | | CLOSE: (76) is inconsistent. % 23.49/3.78 | | | % 23.49/3.78 | | Case 2: % 23.49/3.78 | | | % 23.49/3.78 | | | (77) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 23.49/3.78 | | | (findmin_pqp_res(all_48_6) = v0 & triple(all_48_6, v2, bad) = v3 & % 23.49/3.78 | | | update_slb(all_48_5, v0) = v2 & contains_slb(all_48_5, v0) = v1 % 23.49/3.78 | | | & $i(v3) & $i(v2) & $i(v0) & (v3 = all_48_1 | v1 = 0)) % 23.49/3.78 | | | % 23.49/3.78 | | | DELTA: instantiating (77) with fresh symbols all_102_0, all_102_1, % 23.49/3.78 | | | all_102_2, all_102_3 gives: % 23.49/3.78 | | | (78) findmin_pqp_res(all_48_6) = all_102_3 & triple(all_48_6, % 23.49/3.78 | | | all_102_1, bad) = all_102_0 & update_slb(all_48_5, all_102_3) = % 23.49/3.78 | | | all_102_1 & contains_slb(all_48_5, all_102_3) = all_102_2 & % 23.49/3.78 | | | $i(all_102_0) & $i(all_102_1) & $i(all_102_3) & (all_102_0 = % 23.49/3.78 | | | all_48_1 | all_102_2 = 0) % 23.49/3.78 | | | % 23.49/3.78 | | | ALPHA: (78) implies: % 23.49/3.79 | | | (79) $i(all_102_1) % 23.49/3.79 | | | (80) contains_slb(all_48_5, all_102_3) = all_102_2 % 23.49/3.79 | | | (81) update_slb(all_48_5, all_102_3) = all_102_1 % 23.49/3.79 | | | (82) triple(all_48_6, all_102_1, bad) = all_102_0 % 23.49/3.79 | | | (83) findmin_pqp_res(all_48_6) = all_102_3 % 23.49/3.79 | | | (84) all_102_0 = all_48_1 | all_102_2 = 0 % 23.49/3.79 | | | % 23.49/3.79 | | | BETA: splitting (43) gives: % 23.49/3.79 | | | % 23.49/3.79 | | | Case 1: % 23.49/3.79 | | | | % 23.49/3.79 | | | | (85) all_48_5 = create_slb % 23.49/3.79 | | | | % 23.49/3.79 | | | | REDUCE: (72), (85) imply: % 23.49/3.79 | | | | (86) $false % 23.49/3.79 | | | | % 23.49/3.79 | | | | CLOSE: (86) is inconsistent. % 23.49/3.79 | | | | % 23.49/3.79 | | | Case 2: % 23.49/3.79 | | | | % 23.49/3.79 | | | | (87) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? % 23.49/3.79 | | | | [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_48_6) = v0 & % 23.49/3.79 | | | | triple(all_48_6, v4, bad) = v5 & update_slb(all_48_5, v0) = v4 % 23.49/3.79 | | | | & lookup_slb(all_48_5, v0) = v2 & contains_slb(all_48_5, v0) = % 23.49/3.79 | | | | v1 & strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & % 23.49/3.79 | | | | $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_48_1)) % 23.49/3.79 | | | | % 23.49/3.79 | | | | DELTA: instantiating (87) with fresh symbols all_107_0, all_107_1, % 23.49/3.79 | | | | all_107_2, all_107_3, all_107_4, all_107_5 gives: % 23.49/3.79 | | | | (88) findmin_pqp_res(all_48_6) = all_107_5 & triple(all_48_6, % 23.49/3.79 | | | | all_107_1, bad) = all_107_0 & update_slb(all_48_5, all_107_5) % 23.49/3.79 | | | | = all_107_1 & lookup_slb(all_48_5, all_107_5) = all_107_3 & % 23.49/3.79 | | | | contains_slb(all_48_5, all_107_5) = all_107_4 & % 23.49/3.79 | | | | strictly_less_than(all_107_5, all_107_3) = all_107_2 & % 23.49/3.79 | | | | $i(all_107_0) & $i(all_107_1) & $i(all_107_3) & $i(all_107_5) & % 23.49/3.79 | | | | ( ~ (all_107_2 = 0) | ~ (all_107_4 = 0) | all_107_0 = all_48_1) % 23.49/3.79 | | | | % 23.49/3.79 | | | | ALPHA: (88) implies: % 23.49/3.79 | | | | (89) strictly_less_than(all_107_5, all_107_3) = all_107_2 % 23.49/3.79 | | | | (90) contains_slb(all_48_5, all_107_5) = all_107_4 % 23.49/3.79 | | | | (91) lookup_slb(all_48_5, all_107_5) = all_107_3 % 23.49/3.79 | | | | (92) update_slb(all_48_5, all_107_5) = all_107_1 % 23.49/3.79 | | | | (93) triple(all_48_6, all_107_1, bad) = all_107_0 % 23.49/3.79 | | | | (94) findmin_pqp_res(all_48_6) = all_107_5 % 23.49/3.79 | | | | (95) ~ (all_107_2 = 0) | ~ (all_107_4 = 0) | all_107_0 = all_48_1 % 23.49/3.79 | | | | % 23.49/3.79 | | | | BETA: splitting (42) gives: % 23.49/3.79 | | | | % 23.49/3.79 | | | | Case 1: % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | (96) all_48_5 = create_slb % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (72), (96) imply: % 23.49/3.79 | | | | | (97) $false % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | CLOSE: (97) is inconsistent. % 23.49/3.79 | | | | | % 23.49/3.79 | | | | Case 2: % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | (98) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? % 23.49/3.79 | | | | | [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_48_6) = v0 & % 23.49/3.79 | | | | | triple(all_48_6, v4, all_48_4) = v5 & update_slb(all_48_5, % 23.49/3.79 | | | | | v0) = v4 & lookup_slb(all_48_5, v0) = v2 & % 23.49/3.79 | | | | | contains_slb(all_48_5, v0) = v1 & less_than(v2, v0) = v3 & % 23.49/3.79 | | | | | $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = % 23.49/3.79 | | | | | 0) | v5 = all_48_1)) % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | DELTA: instantiating (98) with fresh symbols all_112_0, all_112_1, % 23.49/3.79 | | | | | all_112_2, all_112_3, all_112_4, all_112_5 gives: % 23.49/3.79 | | | | | (99) findmin_pqp_res(all_48_6) = all_112_5 & triple(all_48_6, % 23.49/3.79 | | | | | all_112_1, all_48_4) = all_112_0 & update_slb(all_48_5, % 23.49/3.79 | | | | | all_112_5) = all_112_1 & lookup_slb(all_48_5, all_112_5) = % 23.49/3.79 | | | | | all_112_3 & contains_slb(all_48_5, all_112_5) = all_112_4 & % 23.49/3.79 | | | | | less_than(all_112_3, all_112_5) = all_112_2 & $i(all_112_0) & % 23.49/3.79 | | | | | $i(all_112_1) & $i(all_112_3) & $i(all_112_5) & ( ~ (all_112_2 % 23.49/3.79 | | | | | = 0) | ~ (all_112_4 = 0) | all_112_0 = all_48_1) % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | ALPHA: (99) implies: % 23.49/3.79 | | | | | (100) $i(all_112_3) % 23.49/3.79 | | | | | (101) less_than(all_112_3, all_112_5) = all_112_2 % 23.49/3.79 | | | | | (102) contains_slb(all_48_5, all_112_5) = all_112_4 % 23.49/3.79 | | | | | (103) lookup_slb(all_48_5, all_112_5) = all_112_3 % 23.49/3.79 | | | | | (104) update_slb(all_48_5, all_112_5) = all_112_1 % 23.49/3.79 | | | | | (105) triple(all_48_6, all_112_1, all_48_4) = all_112_0 % 23.49/3.79 | | | | | (106) findmin_pqp_res(all_48_6) = all_112_5 % 23.49/3.79 | | | | | (107) ~ (all_112_2 = 0) | ~ (all_112_4 = 0) | all_112_0 = % 23.49/3.79 | | | | | all_48_1 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | GROUND_INST: instantiating (18) with all_64_5, all_107_5, all_48_6, % 23.49/3.79 | | | | | simplifying with (61), (94) gives: % 23.49/3.79 | | | | | (108) all_107_5 = all_64_5 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | GROUND_INST: instantiating (18) with all_102_3, all_107_5, all_48_6, % 23.49/3.79 | | | | | simplifying with (83), (94) gives: % 23.49/3.79 | | | | | (109) all_107_5 = all_102_3 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | GROUND_INST: instantiating (18) with all_107_5, all_112_5, all_48_6, % 23.49/3.79 | | | | | simplifying with (94), (106) gives: % 23.49/3.79 | | | | | (110) all_112_5 = all_107_5 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | GROUND_INST: instantiating (18) with all_48_2, all_112_5, all_48_6, % 23.49/3.79 | | | | | simplifying with (74), (106) gives: % 23.49/3.79 | | | | | (111) all_112_5 = all_48_2 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | COMBINE_EQS: (110), (111) imply: % 23.49/3.79 | | | | | (112) all_107_5 = all_48_2 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | SIMP: (112) implies: % 23.49/3.79 | | | | | (113) all_107_5 = all_48_2 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | COMBINE_EQS: (109), (113) imply: % 23.49/3.79 | | | | | (114) all_102_3 = all_48_2 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | COMBINE_EQS: (108), (109) imply: % 23.49/3.79 | | | | | (115) all_102_3 = all_64_5 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | COMBINE_EQS: (114), (115) imply: % 23.49/3.79 | | | | | (116) all_64_5 = all_48_2 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (104), (111) imply: % 23.49/3.79 | | | | | (117) update_slb(all_48_5, all_48_2) = all_112_1 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (92), (113) imply: % 23.49/3.79 | | | | | (118) update_slb(all_48_5, all_48_2) = all_107_1 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (81), (114) imply: % 23.49/3.79 | | | | | (119) update_slb(all_48_5, all_48_2) = all_102_1 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (60), (116) imply: % 23.49/3.79 | | | | | (120) update_slb(all_48_5, all_48_2) = all_64_4 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (103), (111) imply: % 23.49/3.79 | | | | | (121) lookup_slb(all_48_5, all_48_2) = all_112_3 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (91), (113) imply: % 23.49/3.79 | | | | | (122) lookup_slb(all_48_5, all_48_2) = all_107_3 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (59), (116) imply: % 23.49/3.79 | | | | | (123) pair_in_list(all_64_4, all_48_0, all_48_2) = all_64_3 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (102), (111) imply: % 23.49/3.79 | | | | | (124) contains_slb(all_48_5, all_48_2) = all_112_4 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (90), (113) imply: % 23.49/3.79 | | | | | (125) contains_slb(all_48_5, all_48_2) = all_107_4 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (80), (114) imply: % 23.49/3.79 | | | | | (126) contains_slb(all_48_5, all_48_2) = all_102_2 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (89), (113) imply: % 23.49/3.79 | | | | | (127) strictly_less_than(all_48_2, all_107_3) = all_107_2 % 23.49/3.79 | | | | | % 23.49/3.79 | | | | | REDUCE: (101), (111) imply: % 23.49/3.80 | | | | | (128) less_than(all_112_3, all_48_2) = all_112_2 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (22) with all_107_4, all_112_4, all_48_2, % 23.49/3.80 | | | | | all_48_5, simplifying with (124), (125) gives: % 23.49/3.80 | | | | | (129) all_112_4 = all_107_4 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (22) with all_102_2, all_112_4, all_48_2, % 23.49/3.80 | | | | | all_48_5, simplifying with (124), (126) gives: % 23.49/3.80 | | | | | (130) all_112_4 = all_102_2 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (23) with all_107_3, all_112_3, all_48_2, % 23.49/3.80 | | | | | all_48_5, simplifying with (121), (122) gives: % 23.49/3.80 | | | | | (131) all_112_3 = all_107_3 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (24) with all_102_1, all_107_1, all_48_2, % 23.49/3.80 | | | | | all_48_5, simplifying with (118), (119) gives: % 23.49/3.80 | | | | | (132) all_107_1 = all_102_1 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (24) with all_107_1, all_112_1, all_48_2, % 23.49/3.80 | | | | | all_48_5, simplifying with (117), (118) gives: % 23.49/3.80 | | | | | (133) all_112_1 = all_107_1 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (24) with all_64_4, all_112_1, all_48_2, % 23.49/3.80 | | | | | all_48_5, simplifying with (117), (120) gives: % 23.49/3.80 | | | | | (134) all_112_1 = all_64_4 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | COMBINE_EQS: (133), (134) imply: % 23.49/3.80 | | | | | (135) all_107_1 = all_64_4 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | SIMP: (135) implies: % 23.49/3.80 | | | | | (136) all_107_1 = all_64_4 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | COMBINE_EQS: (129), (130) imply: % 23.49/3.80 | | | | | (137) all_107_4 = all_102_2 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | SIMP: (137) implies: % 23.49/3.80 | | | | | (138) all_107_4 = all_102_2 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | COMBINE_EQS: (132), (136) imply: % 23.49/3.80 | | | | | (139) all_102_1 = all_64_4 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | SIMP: (139) implies: % 23.49/3.80 | | | | | (140) all_102_1 = all_64_4 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | REDUCE: (105), (134) imply: % 23.49/3.80 | | | | | (141) triple(all_48_6, all_64_4, all_48_4) = all_112_0 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | REDUCE: (93), (136) imply: % 23.49/3.80 | | | | | (142) triple(all_48_6, all_64_4, bad) = all_107_0 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | REDUCE: (82), (140) imply: % 23.49/3.80 | | | | | (143) triple(all_48_6, all_64_4, bad) = all_102_0 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | REDUCE: (128), (131) imply: % 23.49/3.80 | | | | | (144) less_than(all_107_3, all_48_2) = all_112_2 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | REDUCE: (100), (131) imply: % 23.49/3.80 | | | | | (145) $i(all_107_3) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | REDUCE: (79), (140) imply: % 23.49/3.80 | | | | | (146) $i(all_64_4) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (26) with all_102_0, all_107_0, bad, % 23.49/3.80 | | | | | all_64_4, all_48_6, simplifying with (142), (143) gives: % 23.49/3.80 | | | | | (147) all_107_0 = all_102_0 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (2) with all_48_2, all_107_3, all_112_2, % 23.49/3.80 | | | | | simplifying with (32), (144), (145) gives: % 23.49/3.80 | | | | | (148) all_112_2 = 0 | less_than(all_48_2, all_107_3) = 0 % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (5) with all_48_2, all_107_3, all_112_2, % 23.49/3.80 | | | | | simplifying with (32), (144), (145) gives: % 23.49/3.80 | | | | | (149) all_112_2 = 0 | ? [v0: any] : ? [v1: any] : % 23.49/3.80 | | | | | (strictly_less_than(all_48_2, all_107_3) = v1 & % 23.49/3.80 | | | | | less_than(all_48_2, all_107_3) = v0 & ( ~ (v0 = 0) | v1 = % 23.49/3.80 | | | | | 0)) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (4) with all_48_2, all_107_3, all_112_2, % 23.49/3.80 | | | | | simplifying with (32), (144), (145) gives: % 23.49/3.80 | | | | | (150) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_48_2, % 23.49/3.80 | | | | | all_107_3) = v0 & less_than(all_48_2, all_107_3) = v1 & ( % 23.49/3.80 | | | | | ~ (v0 = 0) | (v1 = 0 & ~ (all_112_2 = 0)))) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (16) with all_48_6, all_64_4, bad, % 23.49/3.80 | | | | | all_102_0, all_48_0, all_48_2, all_56_0, simplifying with % 23.49/3.80 | | | | | (9), (28), (32), (33), (50), (143), (146) gives: % 23.49/3.80 | | | | | (151) all_56_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & % 23.49/3.80 | | | | | check_cpq(all_102_0) = v0) | ( ~ (v0 = 0) & % 23.49/3.80 | | | | | pair_in_list(all_64_4, all_48_0, all_48_2) = v0)) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (16) with all_48_6, all_64_4, bad, % 23.49/3.80 | | | | | all_102_0, all_48_2, all_107_3, all_112_2, simplifying % 23.49/3.80 | | | | | with (9), (28), (32), (143), (144), (145), (146) gives: % 23.49/3.80 | | | | | (152) all_112_2 = 0 | ? [v0: int] : (( ~ (v0 = 0) & % 23.49/3.80 | | | | | check_cpq(all_102_0) = v0) | ( ~ (v0 = 0) & % 23.49/3.80 | | | | | pair_in_list(all_64_4, all_48_2, all_107_3) = v0)) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (16) with all_48_6, all_64_4, all_48_4, % 23.49/3.80 | | | | | all_112_0, all_48_0, all_48_2, all_56_0, simplifying with % 23.49/3.80 | | | | | (28), (30), (32), (33), (50), (141), (146) gives: % 23.49/3.80 | | | | | (153) all_56_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & % 23.49/3.80 | | | | | check_cpq(all_112_0) = v0) | ( ~ (v0 = 0) & % 23.49/3.80 | | | | | pair_in_list(all_64_4, all_48_0, all_48_2) = v0)) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | GROUND_INST: instantiating (12) with all_48_6, all_48_5, bad, % 23.49/3.80 | | | | | all_48_2, all_64_4, all_102_0, simplifying with (9), % 23.49/3.80 | | | | | (28), (29), (74), (120), (143) gives: % 23.49/3.80 | | | | | (154) all_48_5 = create_slb | ? [v0: any] : ? [v1: $i] : ? [v2: % 23.49/3.80 | | | | | any] : ? [v3: $i] : ? [v4: $i] : (triple(all_48_6, % 23.49/3.80 | | | | | all_48_5, bad) = v3 & findmin_cpq_eff(v3) = v4 & % 23.49/3.80 | | | | | lookup_slb(all_48_5, all_48_2) = v1 & % 23.49/3.80 | | | | | contains_slb(all_48_5, all_48_2) = v0 & less_than(v1, % 23.49/3.80 | | | | | all_48_2) = v2 & $i(v4) & $i(v3) & $i(v1) & ( ~ (v2 = 0) % 23.49/3.80 | | | | | | ~ (v0 = 0) | v4 = all_102_0)) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | DELTA: instantiating (150) with fresh symbols all_135_0, all_135_1 % 23.49/3.80 | | | | | gives: % 23.49/3.80 | | | | | (155) strictly_less_than(all_48_2, all_107_3) = all_135_1 & % 23.49/3.80 | | | | | less_than(all_48_2, all_107_3) = all_135_0 & ( ~ (all_135_1 = % 23.49/3.80 | | | | | 0) | (all_135_0 = 0 & ~ (all_112_2 = 0))) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | ALPHA: (155) implies: % 23.49/3.80 | | | | | (156) strictly_less_than(all_48_2, all_107_3) = all_135_1 % 23.49/3.80 | | | | | (157) ~ (all_135_1 = 0) | (all_135_0 = 0 & ~ (all_112_2 = 0)) % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | BETA: splitting (154) gives: % 23.49/3.80 | | | | | % 23.49/3.80 | | | | | Case 1: % 23.49/3.80 | | | | | | % 23.49/3.80 | | | | | | (158) all_48_5 = create_slb % 23.49/3.80 | | | | | | % 23.49/3.80 | | | | | | REDUCE: (72), (158) imply: % 23.49/3.80 | | | | | | (159) $false % 23.49/3.80 | | | | | | % 23.49/3.80 | | | | | | CLOSE: (159) is inconsistent. % 23.49/3.80 | | | | | | % 23.49/3.80 | | | | | Case 2: % 23.49/3.80 | | | | | | % 23.49/3.80 | | | | | | (160) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : % 23.49/3.80 | | | | | | ? [v4: $i] : (triple(all_48_6, all_48_5, bad) = v3 & % 23.49/3.80 | | | | | | findmin_cpq_eff(v3) = v4 & lookup_slb(all_48_5, all_48_2) % 23.49/3.80 | | | | | | = v1 & contains_slb(all_48_5, all_48_2) = v0 & % 23.49/3.80 | | | | | | less_than(v1, all_48_2) = v2 & $i(v4) & $i(v3) & $i(v1) & % 23.49/3.80 | | | | | | ( ~ (v2 = 0) | ~ (v0 = 0) | v4 = all_102_0)) % 23.49/3.80 | | | | | | % 23.49/3.80 | | | | | | DELTA: instantiating (160) with fresh symbols all_145_0, all_145_1, % 23.49/3.80 | | | | | | all_145_2, all_145_3, all_145_4 gives: % 23.49/3.80 | | | | | | (161) triple(all_48_6, all_48_5, bad) = all_145_1 & % 23.49/3.80 | | | | | | findmin_cpq_eff(all_145_1) = all_145_0 & % 23.49/3.80 | | | | | | lookup_slb(all_48_5, all_48_2) = all_145_3 & % 23.49/3.80 | | | | | | contains_slb(all_48_5, all_48_2) = all_145_4 & % 23.49/3.80 | | | | | | less_than(all_145_3, all_48_2) = all_145_2 & $i(all_145_0) % 23.49/3.80 | | | | | | & $i(all_145_1) & $i(all_145_3) & ( ~ (all_145_2 = 0) | ~ % 23.49/3.80 | | | | | | (all_145_4 = 0) | all_145_0 = all_102_0) % 23.49/3.80 | | | | | | % 23.49/3.80 | | | | | | ALPHA: (161) implies: % 23.49/3.81 | | | | | | (162) $i(all_145_1) % 23.49/3.81 | | | | | | (163) contains_slb(all_48_5, all_48_2) = all_145_4 % 23.49/3.81 | | | | | | (164) lookup_slb(all_48_5, all_48_2) = all_145_3 % 23.49/3.81 | | | | | | (165) findmin_cpq_eff(all_145_1) = all_145_0 % 23.49/3.81 | | | | | | (166) triple(all_48_6, all_48_5, bad) = all_145_1 % 23.49/3.81 | | | | | | % 23.49/3.81 | | | | | | BETA: splitting (151) gives: % 23.49/3.81 | | | | | | % 23.49/3.81 | | | | | | Case 1: % 23.49/3.81 | | | | | | | % 23.49/3.81 | | | | | | | (167) all_56_0 = 0 % 23.49/3.81 | | | | | | | % 23.49/3.81 | | | | | | | REDUCE: (49), (167) imply: % 23.49/3.81 | | | | | | | (168) $false % 23.49/3.81 | | | | | | | % 23.49/3.81 | | | | | | | CLOSE: (168) is inconsistent. % 23.49/3.81 | | | | | | | % 23.49/3.81 | | | | | | Case 2: % 23.49/3.81 | | | | | | | % 23.49/3.81 | | | | | | | (169) ? [v0: int] : (( ~ (v0 = 0) & check_cpq(all_102_0) = v0) % 23.49/3.81 | | | | | | | | ( ~ (v0 = 0) & pair_in_list(all_64_4, all_48_0, % 23.49/3.81 | | | | | | | all_48_2) = v0)) % 23.49/3.81 | | | | | | | % 23.49/3.81 | | | | | | | DELTA: instantiating (169) with fresh symbol all_150_0 gives: % 23.49/3.81 | | | | | | | (170) ( ~ (all_150_0 = 0) & check_cpq(all_102_0) = all_150_0) | % 23.49/3.81 | | | | | | | ( ~ (all_150_0 = 0) & pair_in_list(all_64_4, all_48_0, % 23.49/3.81 | | | | | | | all_48_2) = all_150_0) % 23.49/3.81 | | | | | | | % 23.49/3.81 | | | | | | | BETA: splitting (153) gives: % 23.49/3.81 | | | | | | | % 23.49/3.81 | | | | | | | Case 1: % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | (171) all_56_0 = 0 % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | REDUCE: (49), (171) imply: % 23.49/3.81 | | | | | | | | (172) $false % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | CLOSE: (172) is inconsistent. % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | Case 2: % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | (173) ? [v0: int] : (( ~ (v0 = 0) & check_cpq(all_112_0) = % 23.49/3.81 | | | | | | | | v0) | ( ~ (v0 = 0) & pair_in_list(all_64_4, % 23.49/3.81 | | | | | | | | all_48_0, all_48_2) = v0)) % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | DELTA: instantiating (173) with fresh symbol all_154_0 gives: % 23.49/3.81 | | | | | | | | (174) ( ~ (all_154_0 = 0) & check_cpq(all_112_0) = all_154_0) % 23.49/3.81 | | | | | | | | | ( ~ (all_154_0 = 0) & pair_in_list(all_64_4, % 23.49/3.81 | | | | | | | | all_48_0, all_48_2) = all_154_0) % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | GROUND_INST: instantiating (21) with all_107_2, all_135_1, % 23.49/3.81 | | | | | | | | all_107_3, all_48_2, simplifying with (127), (156) % 23.49/3.81 | | | | | | | | gives: % 23.49/3.81 | | | | | | | | (175) all_135_1 = all_107_2 % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | GROUND_INST: instantiating (22) with all_102_2, all_145_4, % 23.49/3.81 | | | | | | | | all_48_2, all_48_5, simplifying with (126), (163) % 23.49/3.81 | | | | | | | | gives: % 23.49/3.81 | | | | | | | | (176) all_145_4 = all_102_2 % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | GROUND_INST: instantiating (23) with all_107_3, all_145_3, % 23.49/3.81 | | | | | | | | all_48_2, all_48_5, simplifying with (122), (164) % 23.49/3.81 | | | | | | | | gives: % 23.49/3.81 | | | | | | | | (177) all_145_3 = all_107_3 % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | GROUND_INST: instantiating (14) with all_145_1, all_145_0, % 23.49/3.81 | | | | | | | | simplifying with (162), (165) gives: % 23.49/3.81 | | | | | | | | (178) ? [v0: $i] : ? [v1: $i] : (findmin_cpq_res(all_145_1) % 23.49/3.81 | | | | | | | | = v1 & removemin_cpq_eff(all_145_1) = v0 & % 23.49/3.81 | | | | | | | | remove_cpq(all_145_0, v1) = v0 & $i(v1) & $i(v0)) % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | GROUND_INST: instantiating (11) with all_48_6, all_48_5, bad, % 23.49/3.81 | | | | | | | | all_145_1, all_145_0, simplifying with (9), (28), % 23.49/3.81 | | | | | | | | (29), (165), (166) gives: % 23.49/3.81 | | | | | | | | (179) all_48_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? % 23.49/3.81 | | | | | | | | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 23.49/3.81 | | | | | | | | (findmin_pqp_res(all_48_6) = v0 & triple(all_48_6, v4, % 23.49/3.81 | | | | | | | | bad) = v5 & update_slb(all_48_5, v0) = v4 & % 23.49/3.81 | | | | | | | | lookup_slb(all_48_5, v0) = v2 & % 23.49/3.81 | | | | | | | | contains_slb(all_48_5, v0) = v1 & less_than(v2, v0) = % 23.49/3.81 | | | | | | | | v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = 0) % 23.49/3.81 | | | | | | | | | ~ (v1 = 0) | v5 = all_145_0)) % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | GROUND_INST: instantiating (10) with all_48_6, all_48_5, bad, % 23.49/3.81 | | | | | | | | all_145_1, all_145_0, simplifying with (9), (28), % 23.49/3.81 | | | | | | | | (29), (165), (166) gives: % 23.49/3.81 | | | | | | | | (180) all_48_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? % 23.49/3.81 | | | | | | | | [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : % 23.49/3.81 | | | | | | | | (findmin_pqp_res(all_48_6) = v0 & triple(all_48_6, v4, % 23.49/3.81 | | | | | | | | bad) = v5 & update_slb(all_48_5, v0) = v4 & % 23.49/3.81 | | | | | | | | lookup_slb(all_48_5, v0) = v2 & % 23.49/3.81 | | | | | | | | contains_slb(all_48_5, v0) = v1 & % 23.49/3.81 | | | | | | | | strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & % 23.49/3.81 | | | | | | | | $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = % 23.49/3.81 | | | | | | | | all_145_0)) % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | GROUND_INST: instantiating (8) with all_48_6, all_48_5, bad, % 23.49/3.81 | | | | | | | | all_145_1, all_145_0, simplifying with (9), (28), % 23.49/3.81 | | | | | | | | (29), (165), (166) gives: % 23.49/3.81 | | | | | | | | (181) all_48_5 = create_slb | ? [v0: $i] : ? [v1: any] : ? % 23.49/3.81 | | | | | | | | [v2: $i] : ? [v3: $i] : (findmin_pqp_res(all_48_6) = % 23.49/3.81 | | | | | | | | v0 & triple(all_48_6, v2, bad) = v3 & % 23.49/3.81 | | | | | | | | update_slb(all_48_5, v0) = v2 & % 23.49/3.81 | | | | | | | | contains_slb(all_48_5, v0) = v1 & $i(v3) & $i(v2) & % 23.49/3.81 | | | | | | | | $i(v0) & (v3 = all_145_0 | v1 = 0)) % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | DELTA: instantiating (178) with fresh symbols all_172_0, % 23.49/3.81 | | | | | | | | all_172_1 gives: % 23.49/3.81 | | | | | | | | (182) findmin_cpq_res(all_145_1) = all_172_0 & % 23.49/3.81 | | | | | | | | removemin_cpq_eff(all_145_1) = all_172_1 & % 23.49/3.81 | | | | | | | | remove_cpq(all_145_0, all_172_0) = all_172_1 & % 23.49/3.81 | | | | | | | | $i(all_172_0) & $i(all_172_1) % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | ALPHA: (182) implies: % 23.49/3.81 | | | | | | | | (183) findmin_cpq_res(all_145_1) = all_172_0 % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | GROUND_INST: instantiating (13) with all_48_6, all_48_5, bad, % 23.49/3.81 | | | | | | | | all_145_1, all_172_0, simplifying with (9), (28), % 23.49/3.81 | | | | | | | | (29), (166), (183) gives: % 23.49/3.81 | | | | | | | | (184) all_48_5 = create_slb | (findmin_pqp_res(all_48_6) = % 23.49/3.81 | | | | | | | | all_172_0 & $i(all_172_0)) % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | BETA: splitting (184) gives: % 23.49/3.81 | | | | | | | | % 23.49/3.81 | | | | | | | | Case 1: % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | | (185) all_48_5 = create_slb % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | | REDUCE: (72), (185) imply: % 23.49/3.81 | | | | | | | | | (186) $false % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | | CLOSE: (186) is inconsistent. % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | Case 2: % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | | (187) findmin_pqp_res(all_48_6) = all_172_0 & $i(all_172_0) % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | | ALPHA: (187) implies: % 23.49/3.81 | | | | | | | | | (188) findmin_pqp_res(all_48_6) = all_172_0 % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | | GROUND_INST: instantiating (18) with all_48_2, all_172_0, % 23.49/3.81 | | | | | | | | | all_48_6, simplifying with (74), (188) gives: % 23.49/3.81 | | | | | | | | | (189) all_172_0 = all_48_2 % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | | REDUCE: (183), (189) imply: % 23.49/3.81 | | | | | | | | | (190) findmin_cpq_res(all_145_1) = all_48_2 % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | | BETA: splitting (62) gives: % 23.49/3.81 | | | | | | | | | % 23.49/3.81 | | | | | | | | | Case 1: % 23.49/3.81 | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | (191) ~ (all_64_6 = 0) % 23.49/3.81 | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | REDUCE: (63), (191) imply: % 23.49/3.81 | | | | | | | | | | (192) $false % 23.49/3.81 | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | CLOSE: (192) is inconsistent. % 23.49/3.81 | | | | | | | | | | % 23.49/3.81 | | | | | | | | | Case 2: % 23.49/3.81 | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | (193) all_64_3 = 0 | (all_64_0 = 0 & all_64_1 = 0 & % 23.49/3.81 | | | | | | | | | | pair_in_list(all_64_4, all_48_0, all_64_2) = 0 & % 23.49/3.81 | | | | | | | | | | less_than(all_64_5, all_64_2) = 0) % 23.49/3.81 | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | BETA: splitting (84) gives: % 23.49/3.81 | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | Case 1: % 23.49/3.81 | | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | | (194) all_102_2 = 0 % 23.49/3.81 | | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | | COMBINE_EQS: (138), (194) imply: % 23.49/3.81 | | | | | | | | | | | (195) all_107_4 = 0 % 23.49/3.81 | | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | | COMBINE_EQS: (130), (194) imply: % 23.49/3.81 | | | | | | | | | | | (196) all_112_4 = 0 % 23.49/3.81 | | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | | DELTA: instantiating (46) with fresh symbols all_234_0, % 23.49/3.81 | | | | | | | | | | | all_234_1, all_234_2, all_234_3, all_234_4, % 23.49/3.81 | | | | | | | | | | | all_234_5, all_234_6 gives: % 23.49/3.81 | | | | | | | | | | | (197) findmin_pqp_res(all_48_6) = all_234_5 & % 23.49/3.81 | | | | | | | | | | | update_slb(all_48_5, all_234_5) = all_234_4 & % 23.49/3.81 | | | | | | | | | | | pair_in_list(all_234_4, all_48_0, all_234_5) = % 23.49/3.81 | | | | | | | | | | | all_234_3 & contains_slb(all_48_5, all_48_0) = % 23.49/3.81 | | | | | | | | | | | all_234_6 & $i(all_234_2) & $i(all_234_4) & % 23.49/3.81 | | | | | | | | | | | $i(all_234_5) & ( ~ (all_234_6 = 0) | all_234_3 = % 23.49/3.81 | | | | | | | | | | | 0 | (all_234_0 = 0 & all_234_1 = 0 & % 23.49/3.81 | | | | | | | | | | | pair_in_list(all_234_4, all_48_0, all_234_2) = % 23.49/3.81 | | | | | | | | | | | 0 & less_than(all_234_5, all_234_2) = 0)) % 23.49/3.81 | | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | | ALPHA: (197) implies: % 23.49/3.81 | | | | | | | | | | | (198) pair_in_list(all_234_4, all_48_0, all_234_5) = % 23.49/3.81 | | | | | | | | | | | all_234_3 % 23.49/3.81 | | | | | | | | | | | (199) update_slb(all_48_5, all_234_5) = all_234_4 % 23.49/3.81 | | | | | | | | | | | (200) findmin_pqp_res(all_48_6) = all_234_5 % 23.49/3.81 | | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_48_2, all_234_5, % 23.49/3.81 | | | | | | | | | | | all_48_6, simplifying with (74), (200) gives: % 23.49/3.81 | | | | | | | | | | | (201) all_234_5 = all_48_2 % 23.49/3.81 | | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | | REDUCE: (199), (201) imply: % 23.49/3.81 | | | | | | | | | | | (202) update_slb(all_48_5, all_48_2) = all_234_4 % 23.49/3.81 | | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | | REDUCE: (198), (201) imply: % 23.49/3.81 | | | | | | | | | | | (203) pair_in_list(all_234_4, all_48_0, all_48_2) = % 23.49/3.81 | | | | | | | | | | | all_234_3 % 23.49/3.81 | | | | | | | | | | | % 23.49/3.81 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_64_4, all_234_4, % 23.49/3.81 | | | | | | | | | | | all_48_2, all_48_5, simplifying with (120), (202) % 23.49/3.81 | | | | | | | | | | | gives: % 23.49/3.82 | | | | | | | | | | | (204) all_234_4 = all_64_4 % 23.49/3.82 | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | REDUCE: (203), (204) imply: % 23.49/3.82 | | | | | | | | | | | (205) pair_in_list(all_64_4, all_48_0, all_48_2) = % 23.49/3.82 | | | | | | | | | | | all_234_3 % 23.49/3.82 | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | GROUND_INST: instantiating (25) with all_64_3, all_234_3, % 23.49/3.82 | | | | | | | | | | | all_48_2, all_48_0, all_64_4, simplifying with % 23.49/3.82 | | | | | | | | | | | (123), (205) gives: % 23.49/3.82 | | | | | | | | | | | (206) all_234_3 = all_64_3 % 23.49/3.82 | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | BETA: splitting (95) gives: % 23.49/3.82 | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | (207) ~ (all_107_2 = 0) % 23.49/3.82 | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | BETA: splitting (107) gives: % 23.49/3.82 | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | (208) ~ (all_112_2 = 0) % 23.49/3.82 | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | BETA: splitting (148) gives: % 23.49/3.82 | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | (209) less_than(all_48_2, all_107_3) = 0 % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | BETA: splitting (149) gives: % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | (210) all_112_2 = 0 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | REDUCE: (208), (210) imply: % 23.49/3.82 | | | | | | | | | | | | | | | (211) $false % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent. % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | Case 2: % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | (212) ? [v0: any] : ? [v1: any] : % 23.49/3.82 | | | | | | | | | | | | | | | (strictly_less_than(all_48_2, all_107_3) = v1 & % 23.49/3.82 | | | | | | | | | | | | | | | less_than(all_48_2, all_107_3) = v0 & ( ~ (v0 = % 23.49/3.82 | | | | | | | | | | | | | | | 0) | v1 = 0)) % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | DELTA: instantiating (212) with fresh symbols all_278_0, % 23.49/3.82 | | | | | | | | | | | | | | | all_278_1 gives: % 23.49/3.82 | | | | | | | | | | | | | | | (213) strictly_less_than(all_48_2, all_107_3) = % 23.49/3.82 | | | | | | | | | | | | | | | all_278_0 & less_than(all_48_2, all_107_3) = % 23.49/3.82 | | | | | | | | | | | | | | | all_278_1 & ( ~ (all_278_1 = 0) | all_278_0 = 0) % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | ALPHA: (213) implies: % 23.49/3.82 | | | | | | | | | | | | | | | (214) less_than(all_48_2, all_107_3) = all_278_1 % 23.49/3.82 | | | | | | | | | | | | | | | (215) strictly_less_than(all_48_2, all_107_3) = % 23.49/3.82 | | | | | | | | | | | | | | | all_278_0 % 23.49/3.82 | | | | | | | | | | | | | | | (216) ~ (all_278_1 = 0) | all_278_0 = 0 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_278_1, all_107_3, % 23.49/3.82 | | | | | | | | | | | | | | | all_48_2, simplifying with (209), (214) gives: % 23.49/3.82 | | | | | | | | | | | | | | | (217) all_278_1 = 0 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_107_2, all_278_0, % 23.49/3.82 | | | | | | | | | | | | | | | all_107_3, all_48_2, simplifying with (127), (215) % 23.49/3.82 | | | | | | | | | | | | | | | gives: % 23.49/3.82 | | | | | | | | | | | | | | | (218) all_278_0 = all_107_2 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | (219) ~ (all_278_1 = 0) % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | REDUCE: (217), (219) imply: % 23.49/3.82 | | | | | | | | | | | | | | | | (220) $false % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent. % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | Case 2: % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | (221) all_278_0 = 0 % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (221) imply: % 23.49/3.82 | | | | | | | | | | | | | | | | (222) all_107_2 = 0 % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | REDUCE: (207), (222) imply: % 23.49/3.82 | | | | | | | | | | | | | | | | (223) $false % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent. % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | End of split % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | End of split % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | Case 2: % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | (224) all_112_2 = 0 % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | REDUCE: (208), (224) imply: % 23.49/3.82 | | | | | | | | | | | | | | (225) $false % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | CLOSE: (225) is inconsistent. % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | End of split % 23.49/3.82 | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | Case 2: % 23.49/3.82 | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | (226) ~ (all_112_4 = 0) | all_112_0 = all_48_1 % 23.49/3.82 | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | BETA: splitting (226) gives: % 23.49/3.82 | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | (227) ~ (all_112_4 = 0) % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | REDUCE: (196), (227) imply: % 23.49/3.82 | | | | | | | | | | | | | | (228) $false % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | CLOSE: (228) is inconsistent. % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | Case 2: % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | (229) all_112_0 = all_48_1 % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | REDUCE: (141), (229) imply: % 23.49/3.82 | | | | | | | | | | | | | | (230) triple(all_48_6, all_64_4, all_48_4) = all_48_1 % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | BETA: splitting (174) gives: % 23.49/3.82 | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | (231) ~ (all_154_0 = 0) & check_cpq(all_112_0) = % 23.49/3.82 | | | | | | | | | | | | | | | all_154_0 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | ALPHA: (231) implies: % 23.49/3.82 | | | | | | | | | | | | | | | (232) ~ (all_154_0 = 0) % 23.49/3.82 | | | | | | | | | | | | | | | (233) check_cpq(all_112_0) = all_154_0 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | REDUCE: (229), (233) imply: % 23.49/3.82 | | | | | | | | | | | | | | | (234) check_cpq(all_48_1) = all_154_0 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_154_0, all_48_1, % 23.49/3.82 | | | | | | | | | | | | | | | simplifying with (36), (234) gives: % 23.49/3.82 | | | | | | | | | | | | | | | (235) all_154_0 = 0 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | REDUCE: (232), (235) imply: % 23.49/3.82 | | | | | | | | | | | | | | | (236) $false % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | Case 2: % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | (237) ~ (all_154_0 = 0) & pair_in_list(all_64_4, % 23.49/3.82 | | | | | | | | | | | | | | | all_48_0, all_48_2) = all_154_0 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | ALPHA: (237) implies: % 23.49/3.82 | | | | | | | | | | | | | | | (238) ~ (all_154_0 = 0) % 23.49/3.82 | | | | | | | | | | | | | | | (239) pair_in_list(all_64_4, all_48_0, all_48_2) = % 23.49/3.82 | | | | | | | | | | | | | | | all_154_0 % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 23.49/3.82 | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | (240) all_48_5 = create_slb % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | REDUCE: (72), (240) imply: % 23.49/3.82 | | | | | | | | | | | | | | | | (241) $false % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | CLOSE: (241) is inconsistent. % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | Case 2: % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | (242) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: % 23.49/3.82 | | | | | | | | | | | | | | | | any] : ? [v4: $i] : ? [v5: $i] : % 23.49/3.82 | | | | | | | | | | | | | | | | (findmin_pqp_res(all_48_6) = v0 & triple(all_48_6, % 23.49/3.82 | | | | | | | | | | | | | | | | v4, bad) = v5 & update_slb(all_48_5, v0) = v4 % 23.49/3.82 | | | | | | | | | | | | | | | | & lookup_slb(all_48_5, v0) = v2 & % 23.49/3.82 | | | | | | | | | | | | | | | | contains_slb(all_48_5, v0) = v1 & less_than(v2, % 23.49/3.82 | | | | | | | | | | | | | | | | v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & % 23.49/3.82 | | | | | | | | | | | | | | | | ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_145_0)) % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | DELTA: instantiating (242) with fresh symbols all_272_0, % 23.49/3.82 | | | | | | | | | | | | | | | | all_272_1, all_272_2, all_272_3, all_272_4, % 23.49/3.82 | | | | | | | | | | | | | | | | all_272_5 gives: % 23.49/3.82 | | | | | | | | | | | | | | | | (243) findmin_pqp_res(all_48_6) = all_272_5 & % 23.49/3.82 | | | | | | | | | | | | | | | | triple(all_48_6, all_272_1, bad) = all_272_0 & % 23.49/3.82 | | | | | | | | | | | | | | | | update_slb(all_48_5, all_272_5) = all_272_1 & % 23.49/3.82 | | | | | | | | | | | | | | | | lookup_slb(all_48_5, all_272_5) = all_272_3 & % 23.49/3.82 | | | | | | | | | | | | | | | | contains_slb(all_48_5, all_272_5) = all_272_4 & % 23.49/3.82 | | | | | | | | | | | | | | | | less_than(all_272_3, all_272_5) = all_272_2 & % 23.49/3.82 | | | | | | | | | | | | | | | | $i(all_272_0) & $i(all_272_1) & $i(all_272_3) & % 23.49/3.82 | | | | | | | | | | | | | | | | $i(all_272_5) & ( ~ (all_272_2 = 0) | ~ % 23.49/3.82 | | | | | | | | | | | | | | | | (all_272_4 = 0) | all_272_0 = all_145_0) % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | ALPHA: (243) implies: % 23.49/3.82 | | | | | | | | | | | | | | | | (244) $i(all_272_5) % 23.49/3.82 | | | | | | | | | | | | | | | | (245) $i(all_272_1) % 23.49/3.82 | | | | | | | | | | | | | | | | (246) update_slb(all_48_5, all_272_5) = all_272_1 % 23.49/3.82 | | | | | | | | | | | | | | | | (247) findmin_pqp_res(all_48_6) = all_272_5 % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_64_3, all_154_0, % 23.49/3.82 | | | | | | | | | | | | | | | | all_48_2, all_48_0, all_64_4, simplifying with % 23.49/3.82 | | | | | | | | | | | | | | | | (123), (239) gives: % 23.49/3.82 | | | | | | | | | | | | | | | | (248) all_154_0 = all_64_3 % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_48_2, all_272_5, % 23.49/3.82 | | | | | | | | | | | | | | | | all_48_6, simplifying with (74), (247) gives: % 23.49/3.82 | | | | | | | | | | | | | | | | (249) all_272_5 = all_48_2 % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | REDUCE: (238), (248) imply: % 23.49/3.82 | | | | | | | | | | | | | | | | (250) ~ (all_64_3 = 0) % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | REDUCE: (246), (249) imply: % 23.49/3.82 | | | | | | | | | | | | | | | | (251) update_slb(all_48_5, all_48_2) = all_272_1 % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 23.49/3.82 | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | (252) all_64_3 = 0 % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | REDUCE: (250), (252) imply: % 23.49/3.82 | | | | | | | | | | | | | | | | | (253) $false % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent. % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | Case 2: % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | (254) all_64_0 = 0 & all_64_1 = 0 & % 23.49/3.82 | | | | | | | | | | | | | | | | | pair_in_list(all_64_4, all_48_0, all_64_2) = 0 & % 23.49/3.82 | | | | | | | | | | | | | | | | | less_than(all_64_5, all_64_2) = 0 % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | ALPHA: (254) implies: % 23.49/3.82 | | | | | | | | | | | | | | | | | (255) less_than(all_64_5, all_64_2) = 0 % 23.49/3.82 | | | | | | | | | | | | | | | | | (256) pair_in_list(all_64_4, all_48_0, all_64_2) = 0 % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | REDUCE: (116), (255) imply: % 23.49/3.82 | | | | | | | | | | | | | | | | | (257) less_than(all_48_2, all_64_2) = 0 % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_64_4, all_272_1, % 23.49/3.82 | | | | | | | | | | | | | | | | | all_48_2, all_48_5, simplifying with (120), (251) % 23.49/3.82 | | | | | | | | | | | | | | | | | gives: % 23.49/3.82 | | | | | | | | | | | | | | | | | (258) all_272_1 = all_64_4 % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_48_2, all_64_2, % 23.49/3.82 | | | | | | | | | | | | | | | | | all_48_0, all_56_0, simplifying with (32), (33), % 23.49/3.82 | | | | | | | | | | | | | | | | | (50), (57), (257) gives: % 23.49/3.82 | | | | | | | | | | | | | | | | | (259) all_56_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 23.49/3.82 | | | | | | | | | | | | | | | | | less_than(all_64_2, all_48_0) = v0) % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_48_6, all_64_4, % 23.49/3.82 | | | | | | | | | | | | | | | | | all_48_4, all_48_1, all_48_0, all_64_2, % 23.49/3.82 | | | | | | | | | | | | | | | | | simplifying with (28), (30), (33), (57), (146), % 23.49/3.82 | | | | | | | | | | | | | | | | | (230), (256) gives: % 23.49/3.82 | | | | | | | | | | | | | | | | | (260) ? [v0: int] : ((v0 = 0 & less_than(all_64_2, % 23.49/3.82 | | | | | | | | | | | | | | | | | all_48_0) = 0) | ( ~ (v0 = 0) & % 23.49/3.82 | | | | | | | | | | | | | | | | | check_cpq(all_48_1) = v0)) % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | DELTA: instantiating (260) with fresh symbol all_324_0 % 23.49/3.82 | | | | | | | | | | | | | | | | | gives: % 23.49/3.82 | | | | | | | | | | | | | | | | | (261) (all_324_0 = 0 & less_than(all_64_2, all_48_0) = % 23.49/3.82 | | | | | | | | | | | | | | | | | 0) | ( ~ (all_324_0 = 0) & check_cpq(all_48_1) = % 23.49/3.82 | | | | | | | | | | | | | | | | | all_324_0) % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | BETA: splitting (261) gives: % 23.49/3.82 | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | Case 1: % 23.49/3.82 | | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | | (262) all_324_0 = 0 & less_than(all_64_2, all_48_0) = 0 % 23.49/3.82 | | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | | ALPHA: (262) implies: % 23.49/3.82 | | | | | | | | | | | | | | | | | | (263) less_than(all_64_2, all_48_0) = 0 % 23.49/3.82 | | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (49), (259), (263) are inconsistent by % 23.49/3.82 | | | | | | | | | | | | | | | | | | sub-proof #1. % 23.49/3.82 | | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | Case 2: % 23.49/3.82 | | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | | (264) ~ (all_324_0 = 0) & check_cpq(all_48_1) = % 23.49/3.82 | | | | | | | | | | | | | | | | | | all_324_0 % 23.49/3.82 | | | | | | | | | | | | | | | | | | % 23.49/3.82 | | | | | | | | | | | | | | | | | | ALPHA: (264) implies: % 23.49/3.82 | | | | | | | | | | | | | | | | | | (265) ~ (all_324_0 = 0) % 23.49/3.82 | | | | | | | | | | | | | | | | | | (266) check_cpq(all_48_1) = all_324_0 % 23.49/3.82 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_324_0, all_48_1, % 23.49/3.83 | | | | | | | | | | | | | | | | | | simplifying with (36), (266) gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (267) all_324_0 = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | REDUCE: (265), (267) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (268) $false % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent. % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | End of split % 23.49/3.83 | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | End of split % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | End of split % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | End of split % 23.49/3.83 | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | End of split % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | End of split % 23.49/3.83 | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | Case 2: % 23.49/3.83 | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | (269) all_107_2 = 0 % 23.49/3.83 | | | | | | | | | | | | (270) ~ (all_107_4 = 0) | all_107_0 = all_48_1 % 23.49/3.83 | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | COMBINE_EQS: (175), (269) imply: % 23.49/3.83 | | | | | | | | | | | | (271) all_135_1 = 0 % 23.49/3.83 | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | REDUCE: (127), (269) imply: % 23.49/3.83 | | | | | | | | | | | | (272) strictly_less_than(all_48_2, all_107_3) = 0 % 23.49/3.83 | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | BETA: splitting (270) gives: % 23.49/3.83 | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | Case 1: % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | (273) ~ (all_107_4 = 0) % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | REDUCE: (195), (273) imply: % 23.49/3.83 | | | | | | | | | | | | | (274) $false % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | CLOSE: (274) is inconsistent. % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | Case 2: % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | (275) all_107_0 = all_48_1 % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | COMBINE_EQS: (147), (275) imply: % 23.49/3.83 | | | | | | | | | | | | | (276) all_102_0 = all_48_1 % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | SIMP: (276) implies: % 23.49/3.83 | | | | | | | | | | | | | (277) all_102_0 = all_48_1 % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | REDUCE: (143), (277) imply: % 23.49/3.83 | | | | | | | | | | | | | (278) triple(all_48_6, all_64_4, bad) = all_48_1 % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | BETA: splitting (157) gives: % 23.49/3.83 | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | Case 1: % 23.49/3.83 | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | (279) ~ (all_135_1 = 0) % 23.49/3.83 | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | REDUCE: (271), (279) imply: % 23.49/3.83 | | | | | | | | | | | | | | (280) $false % 23.49/3.83 | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | CLOSE: (280) is inconsistent. % 23.49/3.83 | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | Case 2: % 23.49/3.83 | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | (281) all_135_0 = 0 & ~ (all_112_2 = 0) % 23.49/3.83 | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | ALPHA: (281) implies: % 23.49/3.83 | | | | | | | | | | | | | | (282) ~ (all_112_2 = 0) % 23.49/3.83 | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | BETA: splitting (180) gives: % 23.49/3.83 | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | Case 1: % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | (283) all_48_5 = create_slb % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | REDUCE: (72), (283) imply: % 23.49/3.83 | | | | | | | | | | | | | | | (284) $false % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | CLOSE: (284) is inconsistent. % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | Case 2: % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | (285) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: % 23.49/3.83 | | | | | | | | | | | | | | | any] : ? [v4: $i] : ? [v5: $i] : % 23.49/3.83 | | | | | | | | | | | | | | | (findmin_pqp_res(all_48_6) = v0 & triple(all_48_6, % 23.49/3.83 | | | | | | | | | | | | | | | v4, bad) = v5 & update_slb(all_48_5, v0) = v4 % 23.49/3.83 | | | | | | | | | | | | | | | & lookup_slb(all_48_5, v0) = v2 & % 23.49/3.83 | | | | | | | | | | | | | | | contains_slb(all_48_5, v0) = v1 & % 23.49/3.83 | | | | | | | | | | | | | | | strictly_less_than(v0, v2) = v3 & $i(v5) & % 23.49/3.83 | | | | | | | | | | | | | | | $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 % 23.49/3.83 | | | | | | | | | | | | | | | = 0) | v5 = all_145_0)) % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | DELTA: instantiating (285) with fresh symbols all_266_0, % 23.49/3.83 | | | | | | | | | | | | | | | all_266_1, all_266_2, all_266_3, all_266_4, % 23.49/3.83 | | | | | | | | | | | | | | | all_266_5 gives: % 23.49/3.83 | | | | | | | | | | | | | | | (286) findmin_pqp_res(all_48_6) = all_266_5 & % 23.49/3.83 | | | | | | | | | | | | | | | triple(all_48_6, all_266_1, bad) = all_266_0 & % 23.49/3.83 | | | | | | | | | | | | | | | update_slb(all_48_5, all_266_5) = all_266_1 & % 23.49/3.83 | | | | | | | | | | | | | | | lookup_slb(all_48_5, all_266_5) = all_266_3 & % 23.49/3.83 | | | | | | | | | | | | | | | contains_slb(all_48_5, all_266_5) = all_266_4 & % 23.49/3.83 | | | | | | | | | | | | | | | strictly_less_than(all_266_5, all_266_3) = % 23.49/3.83 | | | | | | | | | | | | | | | all_266_2 & $i(all_266_0) & $i(all_266_1) & % 23.49/3.83 | | | | | | | | | | | | | | | $i(all_266_3) & $i(all_266_5) & ( ~ (all_266_2 = % 23.49/3.83 | | | | | | | | | | | | | | | 0) | ~ (all_266_4 = 0) | all_266_0 = % 23.49/3.83 | | | | | | | | | | | | | | | all_145_0) % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | ALPHA: (286) implies: % 23.49/3.83 | | | | | | | | | | | | | | | (287) $i(all_266_5) % 23.49/3.83 | | | | | | | | | | | | | | | (288) $i(all_266_1) % 23.49/3.83 | | | | | | | | | | | | | | | (289) strictly_less_than(all_266_5, all_266_3) = % 23.49/3.83 | | | | | | | | | | | | | | | all_266_2 % 23.49/3.83 | | | | | | | | | | | | | | | (290) lookup_slb(all_48_5, all_266_5) = all_266_3 % 23.49/3.83 | | | | | | | | | | | | | | | (291) update_slb(all_48_5, all_266_5) = all_266_1 % 23.49/3.83 | | | | | | | | | | | | | | | (292) triple(all_48_6, all_266_1, bad) = all_266_0 % 23.49/3.83 | | | | | | | | | | | | | | | (293) findmin_pqp_res(all_48_6) = all_266_5 % 23.49/3.83 | | | | | | | | | | | | | | | (294) ~ (all_266_2 = 0) | ~ (all_266_4 = 0) | % 23.49/3.83 | | | | | | | | | | | | | | | all_266_0 = all_145_0 % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | BETA: splitting (170) gives: % 23.49/3.83 | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | Case 1: % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | (295) ~ (all_150_0 = 0) & check_cpq(all_102_0) = % 23.49/3.83 | | | | | | | | | | | | | | | | all_150_0 % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | ALPHA: (295) implies: % 23.49/3.83 | | | | | | | | | | | | | | | | (296) ~ (all_150_0 = 0) % 23.49/3.83 | | | | | | | | | | | | | | | | (297) check_cpq(all_102_0) = all_150_0 % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | REDUCE: (277), (297) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | (298) check_cpq(all_48_1) = all_150_0 % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_150_0, all_48_1, % 23.49/3.83 | | | | | | | | | | | | | | | | simplifying with (36), (298) gives: % 23.49/3.83 | | | | | | | | | | | | | | | | (299) all_150_0 = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | REDUCE: (296), (299) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | (300) $false % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | CLOSE: (300) is inconsistent. % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | Case 2: % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | (301) ~ (all_150_0 = 0) & pair_in_list(all_64_4, % 23.49/3.83 | | | | | | | | | | | | | | | | all_48_0, all_48_2) = all_150_0 % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | ALPHA: (301) implies: % 23.49/3.83 | | | | | | | | | | | | | | | | (302) ~ (all_150_0 = 0) % 23.49/3.83 | | | | | | | | | | | | | | | | (303) pair_in_list(all_64_4, all_48_0, all_48_2) = % 23.49/3.83 | | | | | | | | | | | | | | | | all_150_0 % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 23.49/3.83 | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | Case 1: % 23.49/3.83 | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | (304) all_112_2 = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | REDUCE: (282), (304) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | (305) $false % 23.49/3.83 | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent. % 23.49/3.83 | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | Case 2: % 23.49/3.83 | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | (306) ? [v0: int] : (( ~ (v0 = 0) & % 23.49/3.83 | | | | | | | | | | | | | | | | | check_cpq(all_102_0) = v0) | ( ~ (v0 = 0) & % 23.49/3.83 | | | | | | | | | | | | | | | | | pair_in_list(all_64_4, all_48_2, all_107_3) = % 23.49/3.83 | | | | | | | | | | | | | | | | | v0)) % 23.49/3.83 | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | DELTA: instantiating (306) with fresh symbol all_283_0 % 23.49/3.83 | | | | | | | | | | | | | | | | | gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | (307) ( ~ (all_283_0 = 0) & check_cpq(all_102_0) = % 23.49/3.83 | | | | | | | | | | | | | | | | | all_283_0) | ( ~ (all_283_0 = 0) & % 23.49/3.83 | | | | | | | | | | | | | | | | | pair_in_list(all_64_4, all_48_2, all_107_3) = % 23.49/3.83 | | | | | | | | | | | | | | | | | all_283_0) % 23.49/3.83 | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | BETA: splitting (307) gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | Case 1: % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | (308) ~ (all_283_0 = 0) & check_cpq(all_102_0) = % 23.49/3.83 | | | | | | | | | | | | | | | | | | all_283_0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | ALPHA: (308) implies: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (309) ~ (all_283_0 = 0) % 23.49/3.83 | | | | | | | | | | | | | | | | | | (310) check_cpq(all_102_0) = all_283_0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | REDUCE: (277), (310) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (311) check_cpq(all_48_1) = all_283_0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_283_0, all_48_1, % 23.49/3.83 | | | | | | | | | | | | | | | | | | simplifying with (36), (311) gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (312) all_283_0 = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | REDUCE: (309), (312) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (313) $false % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | CLOSE: (313) is inconsistent. % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | Case 2: % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_64_3, all_150_0, % 23.49/3.83 | | | | | | | | | | | | | | | | | | all_48_2, all_48_0, all_64_4, simplifying with % 23.49/3.83 | | | | | | | | | | | | | | | | | | (123), (303) gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (314) all_150_0 = all_64_3 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_48_2, all_266_5, % 23.49/3.83 | | | | | | | | | | | | | | | | | | all_48_6, simplifying with (74), (293) gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (315) all_266_5 = all_48_2 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | REDUCE: (302), (314) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (316) ~ (all_64_3 = 0) % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | REDUCE: (291), (315) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (317) update_slb(all_48_5, all_48_2) = all_266_1 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | REDUCE: (290), (315) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (318) lookup_slb(all_48_5, all_48_2) = all_266_3 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | REDUCE: (289), (315) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | (319) strictly_less_than(all_48_2, all_266_3) = % 23.49/3.83 | | | | | | | | | | | | | | | | | | all_266_2 % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | Case 1: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (320) all_64_3 = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | REDUCE: (316), (320) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (321) $false % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent. % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | Case 2: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (322) all_64_0 = 0 & all_64_1 = 0 & % 23.49/3.83 | | | | | | | | | | | | | | | | | | | pair_in_list(all_64_4, all_48_0, all_64_2) = 0 & % 23.49/3.83 | | | | | | | | | | | | | | | | | | | less_than(all_64_5, all_64_2) = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (323) less_than(all_64_5, all_64_2) = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (324) pair_in_list(all_64_4, all_48_0, all_64_2) = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | REDUCE: (116), (323) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (325) less_than(all_48_2, all_64_2) = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_107_3, all_266_3, % 23.49/3.83 | | | | | | | | | | | | | | | | | | | all_48_2, all_48_5, simplifying with (122), (318) % 23.49/3.83 | | | | | | | | | | | | | | | | | | | gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (326) all_266_3 = all_107_3 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_64_4, all_266_1, % 23.49/3.83 | | | | | | | | | | | | | | | | | | | all_48_2, all_48_5, simplifying with (120), (317) % 23.49/3.83 | | | | | | | | | | | | | | | | | | | gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (327) all_266_1 = all_64_4 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | REDUCE: (292), (327) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (328) triple(all_48_6, all_64_4, bad) = all_266_0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | REDUCE: (319), (326) imply: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (329) strictly_less_than(all_48_2, all_107_3) = % 23.49/3.83 | | | | | | | | | | | | | | | | | | | all_266_2 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_266_2, all_107_3, % 23.49/3.83 | | | | | | | | | | | | | | | | | | | all_48_2, simplifying with (272), (329) gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (330) all_266_2 = 0 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.83 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_48_1, all_266_0, bad, % 23.49/3.83 | | | | | | | | | | | | | | | | | | | all_64_4, all_48_6, simplifying with (278), (328) % 23.49/3.83 | | | | | | | | | | | | | | | | | | | gives: % 23.49/3.83 | | | | | | | | | | | | | | | | | | | (331) all_266_0 = all_48_1 % 23.49/3.83 | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | Case 1: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | (332) ~ (all_266_2 = 0) % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (332) imply: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | (333) $false % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | CLOSE: (333) is inconsistent. % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | Case 2: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_48_2, all_64_2, % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | all_48_0, all_56_0, simplifying with (32), (33), % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | (50), (57), (325) gives: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | (334) all_56_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | less_than(all_64_2, all_48_0) = v0) % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_48_6, all_64_4, bad, % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | all_48_1, all_48_0, all_64_2, simplifying with % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | (9), (28), (33), (57), (146), (278), (324) gives: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | (335) ? [v0: int] : ((v0 = 0 & less_than(all_64_2, % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | all_48_0) = 0) | ( ~ (v0 = 0) & % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | check_cpq(all_48_1) = v0)) % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (335) with fresh symbol all_365_0 % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | gives: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | (336) (all_365_0 = 0 & less_than(all_64_2, all_48_0) = % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | 0) | ( ~ (all_365_0 = 0) & check_cpq(all_48_1) = % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | all_365_0) % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | Case 1: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | (337) all_365_0 = 0 & less_than(all_64_2, all_48_0) = 0 % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | (338) less_than(all_64_2, all_48_0) = 0 % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (49), (334), (338) are inconsistent by % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | sub-proof #1. % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | Case 2: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | (339) ~ (all_365_0 = 0) & check_cpq(all_48_1) = % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | all_365_0 % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | (340) ~ (all_365_0 = 0) % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | (341) check_cpq(all_48_1) = all_365_0 % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_365_0, all_48_1, % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | simplifying with (36), (341) gives: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | (342) all_365_0 = 0 % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (340), (342) imply: % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | (343) $false % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | CLOSE: (343) is inconsistent. % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | End of split % 23.49/3.84 | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | Case 2: % 23.49/3.84 | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | (344) all_102_0 = all_48_1 % 23.49/3.84 | | | | | | | | | | | (345) ~ (all_102_2 = 0) % 23.49/3.84 | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | REDUCE: (143), (344) imply: % 23.49/3.84 | | | | | | | | | | | (346) triple(all_48_6, all_64_4, bad) = all_48_1 % 23.49/3.84 | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | BETA: splitting (181) gives: % 23.49/3.84 | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | Case 1: % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | (347) all_48_5 = create_slb % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | REDUCE: (72), (347) imply: % 23.49/3.84 | | | | | | | | | | | | (348) $false % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | CLOSE: (348) is inconsistent. % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | Case 2: % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | (349) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: % 23.49/3.84 | | | | | | | | | | | | $i] : (findmin_pqp_res(all_48_6) = v0 & % 23.49/3.84 | | | | | | | | | | | | triple(all_48_6, v2, bad) = v3 & % 23.49/3.84 | | | | | | | | | | | | update_slb(all_48_5, v0) = v2 & % 23.49/3.84 | | | | | | | | | | | | contains_slb(all_48_5, v0) = v1 & $i(v3) & % 23.49/3.84 | | | | | | | | | | | | $i(v2) & $i(v0) & (v3 = all_145_0 | v1 = 0)) % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | DELTA: instantiating (349) with fresh symbols all_233_0, % 23.49/3.84 | | | | | | | | | | | | all_233_1, all_233_2, all_233_3 gives: % 23.49/3.84 | | | | | | | | | | | | (350) findmin_pqp_res(all_48_6) = all_233_3 & % 23.49/3.84 | | | | | | | | | | | | triple(all_48_6, all_233_1, bad) = all_233_0 & % 23.49/3.84 | | | | | | | | | | | | update_slb(all_48_5, all_233_3) = all_233_1 & % 23.49/3.84 | | | | | | | | | | | | contains_slb(all_48_5, all_233_3) = all_233_2 & % 23.49/3.84 | | | | | | | | | | | | $i(all_233_0) & $i(all_233_1) & $i(all_233_3) & % 23.49/3.84 | | | | | | | | | | | | (all_233_0 = all_145_0 | all_233_2 = 0) % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | ALPHA: (350) implies: % 23.49/3.84 | | | | | | | | | | | | (351) $i(all_233_3) % 23.49/3.84 | | | | | | | | | | | | (352) $i(all_233_1) % 23.49/3.84 | | | | | | | | | | | | (353) contains_slb(all_48_5, all_233_3) = all_233_2 % 23.49/3.84 | | | | | | | | | | | | (354) update_slb(all_48_5, all_233_3) = all_233_1 % 23.49/3.84 | | | | | | | | | | | | (355) triple(all_48_6, all_233_1, bad) = all_233_0 % 23.49/3.84 | | | | | | | | | | | | (356) findmin_pqp_res(all_48_6) = all_233_3 % 23.49/3.84 | | | | | | | | | | | | (357) all_233_0 = all_145_0 | all_233_2 = 0 % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | BETA: splitting (170) gives: % 23.49/3.84 | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | Case 1: % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | (358) ~ (all_150_0 = 0) & check_cpq(all_102_0) = % 23.49/3.84 | | | | | | | | | | | | | all_150_0 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | ALPHA: (358) implies: % 23.49/3.84 | | | | | | | | | | | | | (359) ~ (all_150_0 = 0) % 23.49/3.84 | | | | | | | | | | | | | (360) check_cpq(all_102_0) = all_150_0 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | REDUCE: (344), (360) imply: % 23.49/3.84 | | | | | | | | | | | | | (361) check_cpq(all_48_1) = all_150_0 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_150_0, all_48_1, % 23.49/3.84 | | | | | | | | | | | | | simplifying with (36), (361) gives: % 23.49/3.84 | | | | | | | | | | | | | (362) all_150_0 = 0 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | REDUCE: (359), (362) imply: % 23.49/3.84 | | | | | | | | | | | | | (363) $false % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | CLOSE: (363) is inconsistent. % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | Case 2: % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | (364) ~ (all_150_0 = 0) & pair_in_list(all_64_4, % 23.49/3.84 | | | | | | | | | | | | | all_48_0, all_48_2) = all_150_0 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | ALPHA: (364) implies: % 23.49/3.84 | | | | | | | | | | | | | (365) ~ (all_150_0 = 0) % 23.49/3.84 | | | | | | | | | | | | | (366) pair_in_list(all_64_4, all_48_0, all_48_2) = % 23.49/3.84 | | | | | | | | | | | | | all_150_0 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_64_3, all_150_0, % 23.49/3.84 | | | | | | | | | | | | | all_48_2, all_48_0, all_64_4, simplifying with % 23.49/3.84 | | | | | | | | | | | | | (123), (366) gives: % 23.49/3.84 | | | | | | | | | | | | | (367) all_150_0 = all_64_3 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_48_2, all_233_3, % 23.49/3.84 | | | | | | | | | | | | | all_48_6, simplifying with (74), (356) gives: % 23.49/3.84 | | | | | | | | | | | | | (368) all_233_3 = all_48_2 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | REDUCE: (365), (367) imply: % 23.49/3.84 | | | | | | | | | | | | | (369) ~ (all_64_3 = 0) % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | REDUCE: (354), (368) imply: % 23.49/3.84 | | | | | | | | | | | | | (370) update_slb(all_48_5, all_48_2) = all_233_1 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | REDUCE: (353), (368) imply: % 23.49/3.84 | | | | | | | | | | | | | (371) contains_slb(all_48_5, all_48_2) = all_233_2 % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | BETA: splitting (193) gives: % 23.49/3.84 | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | Case 1: % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | (372) all_64_3 = 0 % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | REDUCE: (369), (372) imply: % 23.49/3.84 | | | | | | | | | | | | | | (373) $false % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | CLOSE: (373) is inconsistent. % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | Case 2: % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | (374) all_64_0 = 0 & all_64_1 = 0 & % 23.49/3.84 | | | | | | | | | | | | | | pair_in_list(all_64_4, all_48_0, all_64_2) = 0 & % 23.49/3.84 | | | | | | | | | | | | | | less_than(all_64_5, all_64_2) = 0 % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | ALPHA: (374) implies: % 23.49/3.84 | | | | | | | | | | | | | | (375) less_than(all_64_5, all_64_2) = 0 % 23.49/3.84 | | | | | | | | | | | | | | (376) pair_in_list(all_64_4, all_48_0, all_64_2) = 0 % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | REDUCE: (116), (375) imply: % 23.49/3.84 | | | | | | | | | | | | | | (377) less_than(all_48_2, all_64_2) = 0 % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_102_2, all_233_2, % 23.49/3.84 | | | | | | | | | | | | | | all_48_2, all_48_5, simplifying with (126), (371) % 23.49/3.84 | | | | | | | | | | | | | | gives: % 23.49/3.84 | | | | | | | | | | | | | | (378) all_233_2 = all_102_2 % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_64_4, all_233_1, % 23.49/3.84 | | | | | | | | | | | | | | all_48_2, all_48_5, simplifying with (120), (370) % 23.49/3.84 | | | | | | | | | | | | | | gives: % 23.49/3.84 | | | | | | | | | | | | | | (379) all_233_1 = all_64_4 % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | REDUCE: (355), (379) imply: % 23.49/3.84 | | | | | | | | | | | | | | (380) triple(all_48_6, all_64_4, bad) = all_233_0 % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | BETA: splitting (357) gives: % 23.49/3.84 | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | Case 1: % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | (381) all_233_2 = 0 % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | COMBINE_EQS: (378), (381) imply: % 23.49/3.84 | | | | | | | | | | | | | | | (382) all_102_2 = 0 % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | REDUCE: (345), (382) imply: % 23.49/3.84 | | | | | | | | | | | | | | | (383) $false % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | CLOSE: (383) is inconsistent. % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | Case 2: % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | (384) all_233_0 = all_145_0 % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | REDUCE: (380), (384) imply: % 23.49/3.84 | | | | | | | | | | | | | | | (385) triple(all_48_6, all_64_4, bad) = all_145_0 % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_48_1, all_145_0, bad, % 23.49/3.84 | | | | | | | | | | | | | | | all_64_4, all_48_6, simplifying with (346), (385) % 23.49/3.84 | | | | | | | | | | | | | | | gives: % 23.49/3.84 | | | | | | | | | | | | | | | (386) all_145_0 = all_48_1 % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.84 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_48_2, all_64_2, % 23.49/3.84 | | | | | | | | | | | | | | | all_48_0, all_56_0, simplifying with (32), (33), % 23.49/3.84 | | | | | | | | | | | | | | | (50), (57), (377) gives: % 23.49/3.84 | | | | | | | | | | | | | | | (387) all_56_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 23.49/3.84 | | | | | | | | | | | | | | | less_than(all_64_2, all_48_0) = v0) % 23.49/3.84 | | | | | | | | | | | | | | | % 23.49/3.85 | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_48_6, all_64_4, bad, % 23.49/3.85 | | | | | | | | | | | | | | | all_48_1, all_48_0, all_64_2, simplifying with % 23.49/3.85 | | | | | | | | | | | | | | | (9), (28), (33), (57), (146), (346), (376) gives: % 23.49/3.85 | | | | | | | | | | | | | | | (388) ? [v0: int] : ((v0 = 0 & less_than(all_64_2, % 23.49/3.85 | | | | | | | | | | | | | | | all_48_0) = 0) | ( ~ (v0 = 0) & % 23.49/3.85 | | | | | | | | | | | | | | | check_cpq(all_48_1) = v0)) % 23.49/3.85 | | | | | | | | | | | | | | | % 23.49/3.85 | | | | | | | | | | | | | | | DELTA: instantiating (388) with fresh symbol all_274_0 % 23.49/3.85 | | | | | | | | | | | | | | | gives: % 23.49/3.85 | | | | | | | | | | | | | | | (389) (all_274_0 = 0 & less_than(all_64_2, all_48_0) = % 23.49/3.85 | | | | | | | | | | | | | | | 0) | ( ~ (all_274_0 = 0) & check_cpq(all_48_1) = % 23.49/3.85 | | | | | | | | | | | | | | | all_274_0) % 23.49/3.85 | | | | | | | | | | | | | | | % 23.49/3.85 | | | | | | | | | | | | | | | BETA: splitting (389) gives: % 23.49/3.85 | | | | | | | | | | | | | | | % 23.49/3.85 | | | | | | | | | | | | | | | Case 1: % 23.49/3.85 | | | | | | | | | | | | | | | | % 23.49/3.85 | | | | | | | | | | | | | | | | (390) all_274_0 = 0 & less_than(all_64_2, all_48_0) = 0 % 23.49/3.85 | | | | | | | | | | | | | | | | % 23.49/3.85 | | | | | | | | | | | | | | | | ALPHA: (390) implies: % 23.49/3.85 | | | | | | | | | | | | | | | | (391) less_than(all_64_2, all_48_0) = 0 % 23.49/3.85 | | | | | | | | | | | | | | | | % 23.49/3.85 | | | | | | | | | | | | | | | | REF_CLOSE: (20), (49), (387), (391) are inconsistent by % 23.49/3.85 | | | | | | | | | | | | | | | | sub-proof #1. % 23.49/3.85 | | | | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | | | | Case 2: % 23.83/3.85 | | | | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | | | | | (392) ~ (all_274_0 = 0) & check_cpq(all_48_1) = % 23.83/3.85 | | | | | | | | | | | | | | | | all_274_0 % 23.83/3.85 | | | | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | | | | | ALPHA: (392) implies: % 23.83/3.85 | | | | | | | | | | | | | | | | (393) ~ (all_274_0 = 0) % 23.83/3.85 | | | | | | | | | | | | | | | | (394) check_cpq(all_48_1) = all_274_0 % 23.83/3.85 | | | | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_274_0, all_48_1, % 23.83/3.85 | | | | | | | | | | | | | | | | simplifying with (36), (394) gives: % 23.83/3.85 | | | | | | | | | | | | | | | | (395) all_274_0 = 0 % 23.83/3.85 | | | | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | | | | | REDUCE: (393), (395) imply: % 23.83/3.85 | | | | | | | | | | | | | | | | (396) $false % 23.83/3.85 | | | | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | | | | | CLOSE: (396) is inconsistent. % 23.83/3.85 | | | | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | | | | End of split % 23.83/3.85 | | | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | | | End of split % 23.83/3.85 | | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | | End of split % 23.83/3.85 | | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | | End of split % 23.83/3.85 | | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | | End of split % 23.83/3.85 | | | | | | | | | | | % 23.83/3.85 | | | | | | | | | | End of split % 23.83/3.85 | | | | | | | | | | % 23.83/3.85 | | | | | | | | | End of split % 23.83/3.85 | | | | | | | | | % 23.83/3.85 | | | | | | | | End of split % 23.83/3.85 | | | | | | | | % 23.83/3.85 | | | | | | | End of split % 23.83/3.85 | | | | | | | % 23.83/3.85 | | | | | | End of split % 23.83/3.85 | | | | | | % 23.83/3.85 | | | | | End of split % 23.83/3.85 | | | | | % 23.83/3.85 | | | | End of split % 23.83/3.85 | | | | % 23.83/3.85 | | | End of split % 23.83/3.85 | | | % 23.83/3.85 | | End of split % 23.83/3.85 | | % 23.83/3.85 | End of split % 23.83/3.85 | % 23.83/3.85 End of proof % 23.83/3.85 % 23.83/3.85 Sub-proof #1 shows that the following formulas are inconsistent: % 23.83/3.85 ---------------------------------------------------------------- % 23.83/3.85 (1) all_56_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & less_than(all_64_2, % 23.83/3.85 all_48_0) = v0) % 23.83/3.85 (2) ~ (all_56_0 = 0) % 23.83/3.85 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 23.83/3.85 ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, % 23.83/3.85 v2) = v0)) % 23.83/3.85 (4) less_than(all_64_2, all_48_0) = 0 % 23.83/3.85 % 23.83/3.85 Begin of proof % 23.83/3.85 | % 23.83/3.85 | BETA: splitting (1) gives: % 23.83/3.85 | % 23.83/3.85 | Case 1: % 23.83/3.85 | | % 23.83/3.85 | | (5) all_56_0 = 0 % 23.83/3.85 | | % 23.83/3.85 | | REDUCE: (2), (5) imply: % 23.83/3.85 | | (6) $false % 23.83/3.85 | | % 23.83/3.85 | | CLOSE: (6) is inconsistent. % 23.83/3.85 | | % 23.83/3.85 | Case 2: % 23.83/3.85 | | % 23.83/3.85 | | (7) ? [v0: int] : ( ~ (v0 = 0) & less_than(all_64_2, all_48_0) = v0) % 23.83/3.85 | | % 23.83/3.85 | | DELTA: instantiating (7) with fresh symbol all_293_0 gives: % 23.83/3.85 | | (8) ~ (all_293_0 = 0) & less_than(all_64_2, all_48_0) = all_293_0 % 23.83/3.85 | | % 23.83/3.85 | | ALPHA: (8) implies: % 23.83/3.85 | | (9) ~ (all_293_0 = 0) % 23.83/3.85 | | (10) less_than(all_64_2, all_48_0) = all_293_0 % 23.83/3.85 | | % 23.83/3.85 | | GROUND_INST: instantiating (3) with 0, all_293_0, all_48_0, all_64_2, % 23.83/3.85 | | simplifying with (4), (10) gives: % 23.83/3.85 | | (11) all_293_0 = 0 % 23.83/3.85 | | % 23.83/3.85 | | REDUCE: (9), (11) imply: % 23.83/3.85 | | (12) $false % 23.83/3.85 | | % 23.83/3.85 | | CLOSE: (12) is inconsistent. % 23.83/3.85 | | % 23.83/3.85 | End of split % 23.83/3.85 | % 23.83/3.85 End of proof % 23.83/3.85 % SZS output end Proof for theBenchmark % 23.83/3.85 % 23.83/3.85 3260ms %------------------------------------------------------------------------------