%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV380+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 : n018.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 22:56:05 EDT 2023 % Result : Theorem 11.84s 2.37s % Output : Proof 15.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWV380+1 : TPTP v8.1.2. Released v3.3.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n018.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 11:03:17 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.08/1.14 Prover 1: Preprocessing ... % 3.08/1.15 Prover 4: Preprocessing ... % 3.44/1.19 Prover 2: Preprocessing ... % 3.44/1.19 Prover 6: Preprocessing ... % 3.44/1.19 Prover 5: Preprocessing ... % 3.44/1.19 Prover 3: Preprocessing ... % 3.44/1.19 Prover 0: Preprocessing ... % 7.25/1.75 Prover 1: Warning: ignoring some quantifiers % 7.25/1.78 Prover 3: Warning: ignoring some quantifiers % 7.94/1.82 Prover 1: Constructing countermodel ... % 7.94/1.82 Prover 3: Constructing countermodel ... % 7.94/1.87 Prover 6: Proving ... % 7.94/1.88 Prover 5: Proving ... % 7.94/1.95 Prover 4: Constructing countermodel ... % 8.88/1.96 Prover 0: Proving ... % 8.88/2.01 Prover 2: Proving ... % 10.30/2.16 Prover 3: gave up % 10.30/2.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.30/2.21 Prover 7: Preprocessing ... % 11.84/2.37 Prover 0: proved (1747ms) % 11.84/2.37 % 11.84/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.84/2.37 % 11.84/2.39 Prover 5: stopped % 11.84/2.39 Prover 2: stopped % 11.84/2.40 Prover 6: stopped % 11.84/2.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.20/2.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.20/2.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.20/2.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.20/2.43 Prover 8: Preprocessing ... % 12.20/2.44 Prover 7: Warning: ignoring some quantifiers % 12.51/2.45 Prover 11: Preprocessing ... % 12.51/2.45 Prover 10: Preprocessing ... % 12.51/2.46 Prover 13: Preprocessing ... % 12.51/2.47 Prover 7: Constructing countermodel ... % 12.51/2.58 Prover 8: Warning: ignoring some quantifiers % 12.51/2.60 Prover 10: Warning: ignoring some quantifiers % 13.66/2.61 Prover 8: Constructing countermodel ... % 13.66/2.62 Prover 10: Constructing countermodel ... % 14.55/2.73 Prover 13: Warning: ignoring some quantifiers % 14.55/2.74 Prover 11: Constructing countermodel ... % 14.55/2.75 Prover 4: Found proof (size 221) % 14.55/2.75 Prover 4: proved (2121ms) % 14.55/2.75 Prover 7: stopped % 14.55/2.75 Prover 10: stopped % 14.55/2.75 Prover 1: stopped % 14.55/2.75 Prover 8: stopped % 14.83/2.76 Prover 13: Constructing countermodel ... % 14.83/2.76 Prover 11: stopped % 14.83/2.79 Prover 13: stopped % 14.83/2.79 % 14.83/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.83/2.79 % 14.83/2.81 % SZS output start Proof for theBenchmark % 14.83/2.82 Assumptions after simplification: % 14.83/2.82 --------------------------------- % 14.83/2.82 % 14.83/2.82 (ax40) % 15.21/2.84 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 15.21/2.84 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) = v3)) % 15.21/2.84 % 15.21/2.84 (ax41) % 15.21/2.84 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | % 15.21/2.84 ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) = % 15.21/2.84 0) % 15.21/2.84 % 15.21/2.84 (ax46) % 15.21/2.84 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.21/2.84 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 15.21/2.84 (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3 & $i(v3))) % 15.21/2.84 % 15.21/2.84 (ax47) % 15.21/2.85 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.21/2.85 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 15.21/2.85 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 15.21/2.85 : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 & % 15.21/2.85 triple(v0, v7, bad) = v8 & update_slb(v1, v5) = v7 & contains_slb(v1, v5) % 15.21/2.85 = v6 & $i(v8) & $i(v7) & $i(v5) & (v8 = v4 | v6 = 0))) % 15.21/2.85 % 15.21/2.85 (ax48) % 15.21/2.85 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.21/2.85 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 15.21/2.85 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 15.21/2.85 : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : % 15.21/2.85 (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & update_slb(v1, v5) = % 15.21/2.85 v9 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = v6 & % 15.21/2.85 strictly_less_than(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ % 15.21/2.85 (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 15.21/2.85 % 15.21/2.85 (ax49) % 15.21/2.86 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 15.21/2.86 [v4: $i] : ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ % 15.21/2.86 (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) | ~ % 15.21/2.86 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] % 15.21/2.86 : ? [v10: $i] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 & % 15.21/2.86 lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) = % 15.21/2.86 v8 & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v5))) % 15.21/2.86 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 15.21/2.86 create_slb | ~ (triple(v0, v1, v2) = v3) | ~ (findmin_cpq_eff(v3) = v4) | % 15.21/2.86 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: any] : ? [v7: $i] % 15.21/2.86 : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : (findmin_pqp_res(v0) = v5 & % 15.21/2.86 triple(v0, v9, v2) = v10 & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = % 15.21/2.86 v7 & contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & $i(v9) % 15.21/2.86 & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = v4))) % 15.21/2.86 % 15.21/2.86 (ax50) % 15.21/2.86 $i(create_slb) & $i(bottom) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.21/2.86 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 15.21/2.86 findmin_cpq_res(v2) = bottom) % 15.21/2.86 % 15.21/2.86 (ax51) % 15.21/2.86 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 15.21/2.86 [v4: $i] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, % 15.21/2.86 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (findmin_pqp_res(v0) % 15.21/2.86 = v4 & $i(v4))) % 15.21/2.86 % 15.21/2.86 (ax52) % 15.21/2.87 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ? % 15.21/2.87 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = % 15.21/2.87 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: % 15.21/2.87 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 15.21/2.87 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & % 15.21/2.87 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : ! % 15.21/2.87 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 15.21/2.87 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & % 15.21/2.87 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2))) % 15.21/2.87 % 15.21/2.87 (ax53) % 15.21/2.87 ! [v0: $i] : ! [v1: $i] : ( ~ (removemin_cpq_res(v0) = v1) | ~ $i(v0) | % 15.21/2.87 (findmin_cpq_res(v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.21/2.87 (findmin_cpq_res(v0) = v1) | ~ $i(v0) | (removemin_cpq_res(v0) = v1 & % 15.21/2.87 $i(v1))) % 15.21/2.87 % 15.21/2.87 (l16_co) % 15.21/2.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: % 15.21/2.87 $i] : ( ~ (v4 = 0) & ok(v5) = 0 & ok(v3) = v4 & triple(v0, v1, v2) = v3 & % 15.21/2.87 removemin_cpq_eff(v3) = v5 & $i(v5) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.21/2.87 % 15.21/2.87 (l16_l14) % 15.21/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 15.21/2.87 $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) | ~ % 15.21/2.87 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 15.21/2.87 (ok(v5) = v7 & ok(v4) = v6 & ( ~ (v7 = 0) | v6 = 0))) % 15.21/2.87 % 15.21/2.87 (stricly_smaller_definition) % 15.41/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 15.41/2.88 (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 15.41/2.88 ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 15.41/2.88 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | % 15.41/2.88 ~ (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 15.41/2.88 any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 % 15.41/2.88 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ % 15.41/2.88 (less_than(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 15.41/2.88 any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 % 15.41/2.88 = 0) | (v4 = 0 & ~ (v2 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.41/2.88 any] : ( ~ (less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : % 15.41/2.88 ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( % 15.41/2.88 ~ (v3 = 0) | (v2 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.41/2.88 (strictly_less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( % 15.41/2.88 ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) & ! [v0: % 15.41/2.88 $i] : ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 15.41/2.88 [v2: any] : ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, % 15.41/2.88 v0) = v2 & (v3 = 0 | v2 = 0))) % 15.41/2.88 % 15.41/2.88 (totality) % 15.41/2.88 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, v0) = % 15.41/2.88 v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) & ! [v0: $i] : ! % 15.41/2.88 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v0, v1) = v2) | ~ $i(v1) | % 15.41/2.88 ~ $i(v0) | less_than(v1, v0) = 0) % 15.41/2.88 % 15.41/2.88 (function-axioms) % 15.41/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 15.41/2.89 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: % 15.41/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.41/2.89 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~ % 15.41/2.89 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.41/2.89 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) % 15.41/2.89 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 15.41/2.89 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: % 15.41/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.41/2.89 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) % 15.41/2.89 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.41/2.89 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! % 15.41/2.89 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) % 15.41/2.89 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.41/2.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3, % 15.41/2.89 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.41/2.89 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~ % 15.41/2.89 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 15.41/2.89 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = % 15.41/2.89 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 15.41/2.89 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0: % 15.41/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.41/2.89 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0)) % 15.41/2.89 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.41/2.89 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 15.41/2.89 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 15.41/2.89 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.41/2.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.41/2.89 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) & % 15.41/2.89 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.41/2.89 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0)) % 15.41/2.89 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.41/2.89 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: % 15.41/2.89 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | % 15.41/2.89 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.41/2.89 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! % 15.41/2.89 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 15.41/2.89 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.41/2.89 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | % 15.41/2.89 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 % 15.41/2.89 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! % 15.41/2.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = % 15.41/2.89 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.41/2.89 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = % 15.41/2.89 v1) | ~ (isnonempty_slb(v2) = v0)) % 15.41/2.89 % 15.41/2.89 Further assumptions not needed in the proof: % 15.41/2.89 -------------------------------------------- % 15.41/2.89 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, % 15.41/2.89 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax42, ax43, ax44, ax45, % 15.41/2.89 bottom_smallest, reflexivity, transitivity % 15.41/2.89 % 15.41/2.89 Those formulas are unsatisfiable: % 15.41/2.89 --------------------------------- % 15.41/2.89 % 15.41/2.89 Begin of proof % 15.41/2.89 | % 15.41/2.89 | ALPHA: (totality) implies: % 15.41/2.89 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 15.41/2.89 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | less_than(v0, v1) = 0) % 15.41/2.89 | % 15.41/2.89 | ALPHA: (stricly_smaller_definition) implies: % 15.41/2.89 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v0, v1) = v2) % 15.41/2.89 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 15.41/2.89 | (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 = % 15.41/2.89 | 0) | (v2 = 0 & ~ (v4 = 0))))) % 15.41/2.89 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (less_than(v1, v0) = v2) % 15.41/2.89 | | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 15.41/2.89 | (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 = % 15.41/2.89 | 0) | (v4 = 0 & ~ (v2 = 0))))) % 15.41/2.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (less_than(v1, % 15.41/2.89 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 15.41/2.89 | (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 = % 15.41/2.89 | 0) | v4 = 0))) % 15.41/2.90 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 15.41/2.90 | (strictly_less_than(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 15.41/2.90 | any] : ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = % 15.41/2.90 | v3 & ( ~ (v3 = 0) | v4 = 0))) % 15.41/2.90 | % 15.41/2.90 | ALPHA: (ax40) implies: % 15.41/2.90 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 15.41/2.90 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & ok(v2) % 15.41/2.90 | = v3)) % 15.41/2.90 | % 15.41/2.90 | ALPHA: (ax41) implies: % 15.41/2.90 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | ~ % 15.41/2.90 | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 15.41/2.90 | ok(v3) = 0) % 15.41/2.90 | % 15.41/2.90 | ALPHA: (ax46) implies: % 15.41/2.90 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb, % 15.41/2.90 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (triple(v0, % 15.41/2.90 | create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3 & $i(v3))) % 15.41/2.90 | % 15.41/2.90 | ALPHA: (ax47) implies: % 15.41/2.90 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.41/2.90 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 15.41/2.90 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 15.41/2.90 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 15.41/2.90 | (findmin_pqp_res(v0) = v5 & triple(v0, v7, bad) = v8 & update_slb(v1, % 15.41/2.90 | v5) = v7 & contains_slb(v1, v5) = v6 & $i(v8) & $i(v7) & $i(v5) & % 15.41/2.90 | (v8 = v4 | v6 = 0))) % 15.41/2.90 | % 15.41/2.90 | ALPHA: (ax48) implies: % 15.41/2.90 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.41/2.90 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 15.41/2.90 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 15.41/2.90 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 15.41/2.90 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 % 15.41/2.90 | & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 15.41/2.90 | contains_slb(v1, v5) = v6 & strictly_less_than(v5, v7) = v8 & % 15.41/2.90 | $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | % 15.41/2.90 | v10 = v4))) % 15.41/2.90 | % 15.41/2.90 | ALPHA: (ax49) implies: % 15.41/2.90 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.41/2.90 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 15.41/2.90 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 15.41/2.90 | [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : % 15.41/2.90 | ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, v2) = v10 % 15.41/2.90 | & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 & % 15.41/2.90 | contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & % 15.41/2.90 | $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) | ~ (v6 = 0) | v10 = % 15.41/2.90 | v4))) % 15.41/2.90 | % 15.41/2.90 | ALPHA: (ax50) implies: % 15.41/2.90 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb, % 15.41/2.90 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | findmin_cpq_res(v2) = % 15.41/2.90 | bottom) % 15.41/2.90 | % 15.41/2.91 | ALPHA: (ax51) implies: % 15.41/2.91 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.41/2.91 | (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, % 15.41/2.91 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 15.41/2.91 | (findmin_pqp_res(v0) = v4 & $i(v4))) % 15.41/2.91 | % 15.41/2.91 | ALPHA: (ax52) implies: % 15.41/2.91 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ % 15.41/2.91 | $i(v0) | ? [v2: $i] : ? [v3: $i] : (findmin_cpq_res(v0) = v3 & % 15.41/2.91 | findmin_cpq_eff(v0) = v2 & remove_cpq(v2, v3) = v1 & $i(v3) & % 15.41/2.91 | $i(v2) & $i(v1))) % 15.41/2.91 | % 15.41/2.91 | ALPHA: (ax53) implies: % 15.41/2.91 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) % 15.41/2.91 | | (removemin_cpq_res(v0) = v1 & $i(v1))) % 15.41/2.91 | % 15.41/2.91 | ALPHA: (function-axioms) implies: % 15.41/2.91 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.41/2.91 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 15.41/2.91 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.41/2.91 | : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 15.41/2.91 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.41/2.91 | (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 15.41/2.91 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.41/2.91 | (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) % 15.41/2.91 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.41/2.91 | : ! [v3: $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ % 15.41/2.91 | (less_than(v3, v2) = v0)) % 15.41/2.91 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 15.41/2.91 | : ! [v3: $i] : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ % 15.41/2.91 | (contains_slb(v3, v2) = v0)) % 15.41/2.91 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.41/2.91 | (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) = v0)) % 15.41/2.91 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.41/2.91 | (update_slb(v3, v2) = v1) | ~ (update_slb(v3, v2) = v0)) % 15.41/2.91 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 15.41/2.91 | (v1 = v0 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = % 15.41/2.91 | v0)) % 15.41/2.91 | % 15.41/2.91 | DELTA: instantiating (l16_co) with fresh symbols all_47_0, all_47_1, all_47_2, % 15.41/2.91 | all_47_3, all_47_4, all_47_5 gives: % 15.41/2.91 | (25) ~ (all_47_1 = 0) & ok(all_47_0) = 0 & ok(all_47_2) = all_47_1 & % 15.41/2.91 | triple(all_47_5, all_47_4, all_47_3) = all_47_2 & % 15.41/2.91 | removemin_cpq_eff(all_47_2) = all_47_0 & $i(all_47_0) & $i(all_47_2) & % 15.41/2.91 | $i(all_47_3) & $i(all_47_4) & $i(all_47_5) % 15.41/2.91 | % 15.41/2.91 | ALPHA: (25) implies: % 15.41/2.91 | (26) ~ (all_47_1 = 0) % 15.41/2.92 | (27) $i(all_47_5) % 15.41/2.92 | (28) $i(all_47_4) % 15.41/2.92 | (29) $i(all_47_3) % 15.41/2.92 | (30) $i(all_47_2) % 15.41/2.92 | (31) removemin_cpq_eff(all_47_2) = all_47_0 % 15.41/2.92 | (32) triple(all_47_5, all_47_4, all_47_3) = all_47_2 % 15.41/2.92 | (33) ok(all_47_2) = all_47_1 % 15.41/2.92 | (34) ok(all_47_0) = 0 % 15.41/2.92 | % 15.41/2.92 | GROUND_INST: instantiating (14) with all_47_2, all_47_0, simplifying with % 15.41/2.92 | (30), (31) gives: % 15.41/2.92 | (35) ? [v0: $i] : ? [v1: $i] : (findmin_cpq_res(all_47_2) = v1 & % 15.41/2.92 | findmin_cpq_eff(all_47_2) = v0 & remove_cpq(v0, v1) = all_47_0 & % 15.41/2.92 | $i(v1) & $i(v0) & $i(all_47_0)) % 15.41/2.92 | % 15.41/2.92 | GROUND_INST: instantiating (7) with all_47_5, all_47_4, all_47_3, all_47_2, % 15.41/2.92 | simplifying with (27), (28), (29), (32) gives: % 15.41/2.92 | (36) all_47_3 = bad | ok(all_47_2) = 0 % 15.41/2.92 | % 15.41/2.92 | DELTA: instantiating (35) with fresh symbols all_54_0, all_54_1 gives: % 15.41/2.92 | (37) findmin_cpq_res(all_47_2) = all_54_0 & findmin_cpq_eff(all_47_2) = % 15.41/2.92 | all_54_1 & remove_cpq(all_54_1, all_54_0) = all_47_0 & $i(all_54_0) & % 15.41/2.92 | $i(all_54_1) & $i(all_47_0) % 15.41/2.92 | % 15.41/2.92 | ALPHA: (37) implies: % 15.41/2.92 | (38) remove_cpq(all_54_1, all_54_0) = all_47_0 % 15.41/2.92 | (39) findmin_cpq_eff(all_47_2) = all_54_1 % 15.41/2.92 | (40) findmin_cpq_res(all_47_2) = all_54_0 % 15.41/2.92 | % 15.41/2.92 | BETA: splitting (36) gives: % 15.41/2.92 | % 15.41/2.92 | Case 1: % 15.41/2.92 | | % 15.41/2.92 | | (41) ok(all_47_2) = 0 % 15.41/2.92 | | % 15.41/2.92 | | GROUND_INST: instantiating (17) with all_47_1, 0, all_47_2, simplifying with % 15.41/2.92 | | (33), (41) gives: % 15.41/2.92 | | (42) all_47_1 = 0 % 15.41/2.92 | | % 15.41/2.92 | | REDUCE: (26), (42) imply: % 15.41/2.92 | | (43) $false % 15.41/2.92 | | % 15.41/2.92 | | CLOSE: (43) is inconsistent. % 15.41/2.92 | | % 15.41/2.92 | Case 2: % 15.41/2.92 | | % 15.41/2.92 | | (44) all_47_3 = bad % 15.41/2.92 | | % 15.41/2.92 | | REDUCE: (32), (44) imply: % 15.41/2.92 | | (45) triple(all_47_5, all_47_4, bad) = all_47_2 % 15.41/2.92 | | % 15.41/2.92 | | REDUCE: (29), (44) imply: % 15.41/2.92 | | (46) $i(bad) % 15.41/2.92 | | % 15.41/2.92 | | GROUND_INST: instantiating (11) with all_47_5, all_47_4, bad, all_47_2, % 15.41/2.92 | | all_54_1, simplifying with (27), (28), (39), (45), (46) gives: % 15.41/2.93 | | (47) all_47_4 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : % 15.41/2.93 | | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_5) % 15.41/2.93 | | = v0 & triple(all_47_5, v4, bad) = v5 & update_slb(all_47_4, v0) = % 15.41/2.93 | | v4 & lookup_slb(all_47_4, v0) = v2 & contains_slb(all_47_4, v0) = % 15.41/2.93 | | v1 & less_than(v2, v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & % 15.41/2.93 | | ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_54_1)) % 15.41/2.93 | | % 15.41/2.93 | | GROUND_INST: instantiating (10) with all_47_5, all_47_4, bad, all_47_2, % 15.41/2.93 | | all_54_1, simplifying with (27), (28), (39), (45), (46) gives: % 15.41/2.93 | | (48) all_47_4 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : % 15.41/2.93 | | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_5) % 15.41/2.93 | | = v0 & triple(all_47_5, v4, bad) = v5 & update_slb(all_47_4, v0) = % 15.41/2.93 | | v4 & lookup_slb(all_47_4, v0) = v2 & contains_slb(all_47_4, v0) = % 15.41/2.93 | | v1 & strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v2) & % 15.41/2.93 | | $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = all_54_1)) % 15.41/2.93 | | % 15.41/2.93 | | GROUND_INST: instantiating (9) with all_47_5, all_47_4, bad, all_47_2, % 15.41/2.93 | | all_54_1, simplifying with (27), (28), (39), (45), (46) gives: % 15.41/2.93 | | (49) all_47_4 = create_slb | ? [v0: $i] : ? [v1: any] : ? [v2: $i] : % 15.41/2.93 | | ? [v3: $i] : (findmin_pqp_res(all_47_5) = v0 & triple(all_47_5, v2, % 15.41/2.93 | | bad) = v3 & update_slb(all_47_4, v0) = v2 & % 15.41/2.93 | | contains_slb(all_47_4, v0) = v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = % 15.41/2.93 | | all_54_1 | v1 = 0)) % 15.41/2.93 | | % 15.41/2.93 | | GROUND_INST: instantiating (13) with all_47_5, all_47_4, bad, all_47_2, % 15.41/2.93 | | all_54_0, simplifying with (27), (28), (40), (45), (46) gives: % 15.41/2.93 | | (50) all_47_4 = create_slb | (findmin_pqp_res(all_47_5) = all_54_0 & % 15.41/2.93 | | $i(all_54_0)) % 15.41/2.93 | | % 15.41/2.93 | | GROUND_INST: instantiating (15) with all_47_2, all_54_0, simplifying with % 15.41/2.93 | | (30), (40) gives: % 15.41/2.93 | | (51) removemin_cpq_res(all_47_2) = all_54_0 & $i(all_54_0) % 15.41/2.93 | | % 15.41/2.93 | | ALPHA: (51) implies: % 15.41/2.93 | | (52) $i(all_54_0) % 15.41/2.93 | | % 15.41/2.93 | | BETA: splitting (50) gives: % 15.41/2.93 | | % 15.41/2.93 | | Case 1: % 15.41/2.93 | | | % 15.41/2.93 | | | (53) all_47_4 = create_slb % 15.41/2.93 | | | % 15.41/2.93 | | | REDUCE: (45), (53) imply: % 15.41/2.93 | | | (54) triple(all_47_5, create_slb, bad) = all_47_2 % 15.41/2.93 | | | % 15.41/2.93 | | | REDUCE: (28), (53) imply: % 15.41/2.93 | | | (55) $i(create_slb) % 15.41/2.93 | | | % 15.41/2.93 | | | GROUND_INST: instantiating (12) with all_47_5, bad, all_47_2, simplifying % 15.41/2.93 | | | with (27), (46), (54) gives: % 15.41/2.93 | | | (56) findmin_cpq_res(all_47_2) = bottom % 15.41/2.93 | | | % 15.41/2.93 | | | GROUND_INST: instantiating (8) with all_47_5, bad, all_47_2, simplifying % 15.41/2.93 | | | with (27), (46), (54) gives: % 15.41/2.93 | | | (57) ? [v0: $i] : (triple(all_47_5, create_slb, bad) = v0 & % 15.41/2.93 | | | findmin_cpq_eff(all_47_2) = v0 & $i(v0)) % 15.41/2.93 | | | % 15.41/2.93 | | | DELTA: instantiating (57) with fresh symbol all_79_0 gives: % 15.41/2.93 | | | (58) triple(all_47_5, create_slb, bad) = all_79_0 & % 15.41/2.93 | | | findmin_cpq_eff(all_47_2) = all_79_0 & $i(all_79_0) % 15.41/2.93 | | | % 15.41/2.93 | | | ALPHA: (58) implies: % 15.41/2.93 | | | (59) findmin_cpq_eff(all_47_2) = all_79_0 % 15.41/2.93 | | | (60) triple(all_47_5, create_slb, bad) = all_79_0 % 15.41/2.93 | | | % 15.41/2.93 | | | GROUND_INST: instantiating (16) with all_54_1, all_79_0, all_47_2, % 15.41/2.94 | | | simplifying with (39), (59) gives: % 15.41/2.94 | | | (61) all_79_0 = all_54_1 % 15.41/2.94 | | | % 15.41/2.94 | | | GROUND_INST: instantiating (24) with all_47_2, all_79_0, bad, create_slb, % 15.41/2.94 | | | all_47_5, simplifying with (54), (60) gives: % 15.41/2.94 | | | (62) all_79_0 = all_47_2 % 15.41/2.94 | | | % 15.41/2.94 | | | GROUND_INST: instantiating (19) with all_54_0, bottom, all_47_2, % 15.41/2.94 | | | simplifying with (40), (56) gives: % 15.41/2.94 | | | (63) all_54_0 = bottom % 15.41/2.94 | | | % 15.71/2.94 | | | COMBINE_EQS: (61), (62) imply: % 15.71/2.94 | | | (64) all_54_1 = all_47_2 % 15.71/2.94 | | | % 15.71/2.94 | | | REDUCE: (38), (63), (64) imply: % 15.71/2.94 | | | (65) remove_cpq(all_47_2, bottom) = all_47_0 % 15.71/2.94 | | | % 15.71/2.94 | | | REDUCE: (52), (63) imply: % 15.71/2.94 | | | (66) $i(bottom) % 15.71/2.94 | | | % 15.71/2.94 | | | GROUND_INST: instantiating (l16_l14) with all_47_5, create_slb, bad, % 15.71/2.94 | | | bottom, all_47_2, all_47_0, simplifying with (27), (46), % 15.71/2.94 | | | (54), (55), (65), (66) gives: % 15.71/2.94 | | | (67) ? [v0: any] : ? [v1: any] : (ok(all_47_0) = v1 & ok(all_47_2) = % 15.71/2.94 | | | v0 & ( ~ (v1 = 0) | v0 = 0)) % 15.71/2.94 | | | % 15.71/2.94 | | | DELTA: instantiating (67) with fresh symbols all_90_0, all_90_1 gives: % 15.71/2.94 | | | (68) ok(all_47_0) = all_90_0 & ok(all_47_2) = all_90_1 & ( ~ (all_90_0 % 15.71/2.94 | | | = 0) | all_90_1 = 0) % 15.71/2.94 | | | % 15.71/2.94 | | | ALPHA: (68) implies: % 15.71/2.94 | | | (69) ok(all_47_2) = all_90_1 % 15.71/2.94 | | | (70) ok(all_47_0) = all_90_0 % 15.71/2.94 | | | (71) ~ (all_90_0 = 0) | all_90_1 = 0 % 15.71/2.94 | | | % 15.71/2.94 | | | GROUND_INST: instantiating (17) with all_47_1, all_90_1, all_47_2, % 15.71/2.94 | | | simplifying with (33), (69) gives: % 15.71/2.94 | | | (72) all_90_1 = all_47_1 % 15.71/2.94 | | | % 15.71/2.94 | | | GROUND_INST: instantiating (17) with 0, all_90_0, all_47_0, simplifying % 15.71/2.94 | | | with (34), (70) gives: % 15.71/2.94 | | | (73) all_90_0 = 0 % 15.71/2.94 | | | % 15.71/2.94 | | | BETA: splitting (71) gives: % 15.71/2.94 | | | % 15.71/2.94 | | | Case 1: % 15.71/2.94 | | | | % 15.71/2.94 | | | | (74) ~ (all_90_0 = 0) % 15.71/2.94 | | | | % 15.71/2.94 | | | | REDUCE: (73), (74) imply: % 15.71/2.94 | | | | (75) $false % 15.71/2.94 | | | | % 15.71/2.94 | | | | CLOSE: (75) is inconsistent. % 15.71/2.94 | | | | % 15.71/2.94 | | | Case 2: % 15.71/2.94 | | | | % 15.71/2.94 | | | | (76) all_90_1 = 0 % 15.71/2.94 | | | | % 15.71/2.94 | | | | COMBINE_EQS: (72), (76) imply: % 15.71/2.94 | | | | (77) all_47_1 = 0 % 15.71/2.94 | | | | % 15.71/2.94 | | | | SIMP: (77) implies: % 15.71/2.94 | | | | (78) all_47_1 = 0 % 15.71/2.94 | | | | % 15.71/2.94 | | | | REDUCE: (26), (78) imply: % 15.71/2.94 | | | | (79) $false % 15.71/2.94 | | | | % 15.71/2.94 | | | | CLOSE: (79) is inconsistent. % 15.71/2.94 | | | | % 15.71/2.94 | | | End of split % 15.71/2.94 | | | % 15.71/2.94 | | Case 2: % 15.71/2.94 | | | % 15.71/2.94 | | | (80) ~ (all_47_4 = create_slb) % 15.71/2.94 | | | (81) findmin_pqp_res(all_47_5) = all_54_0 & $i(all_54_0) % 15.71/2.94 | | | % 15.71/2.94 | | | ALPHA: (81) implies: % 15.71/2.94 | | | (82) findmin_pqp_res(all_47_5) = all_54_0 % 15.71/2.94 | | | % 15.71/2.94 | | | BETA: splitting (49) gives: % 15.71/2.94 | | | % 15.71/2.94 | | | Case 1: % 15.71/2.94 | | | | % 15.71/2.94 | | | | (83) all_47_4 = create_slb % 15.71/2.94 | | | | % 15.71/2.94 | | | | REDUCE: (80), (83) imply: % 15.71/2.94 | | | | (84) $false % 15.71/2.94 | | | | % 15.71/2.94 | | | | CLOSE: (84) is inconsistent. % 15.71/2.94 | | | | % 15.71/2.94 | | | Case 2: % 15.71/2.94 | | | | % 15.71/2.94 | | | | (85) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : % 15.71/2.94 | | | | (findmin_pqp_res(all_47_5) = v0 & triple(all_47_5, v2, bad) = v3 % 15.71/2.94 | | | | & update_slb(all_47_4, v0) = v2 & contains_slb(all_47_4, v0) = % 15.71/2.94 | | | | v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_54_1 | v1 = 0)) % 15.71/2.94 | | | | % 15.71/2.94 | | | | DELTA: instantiating (85) with fresh symbols all_77_0, all_77_1, % 15.71/2.94 | | | | all_77_2, all_77_3 gives: % 15.71/2.94 | | | | (86) findmin_pqp_res(all_47_5) = all_77_3 & triple(all_47_5, % 15.71/2.94 | | | | all_77_1, bad) = all_77_0 & update_slb(all_47_4, all_77_3) = % 15.71/2.94 | | | | all_77_1 & contains_slb(all_47_4, all_77_3) = all_77_2 & % 15.71/2.94 | | | | $i(all_77_0) & $i(all_77_1) & $i(all_77_3) & (all_77_0 = % 15.71/2.94 | | | | all_54_1 | all_77_2 = 0) % 15.71/2.94 | | | | % 15.71/2.94 | | | | ALPHA: (86) implies: % 15.71/2.94 | | | | (87) $i(all_77_3) % 15.71/2.94 | | | | (88) contains_slb(all_47_4, all_77_3) = all_77_2 % 15.71/2.94 | | | | (89) update_slb(all_47_4, all_77_3) = all_77_1 % 15.71/2.94 | | | | (90) triple(all_47_5, all_77_1, bad) = all_77_0 % 15.71/2.94 | | | | (91) findmin_pqp_res(all_47_5) = all_77_3 % 15.71/2.94 | | | | (92) all_77_0 = all_54_1 | all_77_2 = 0 % 15.71/2.94 | | | | % 15.71/2.94 | | | | BETA: splitting (47) gives: % 15.71/2.94 | | | | % 15.71/2.94 | | | | Case 1: % 15.71/2.94 | | | | | % 15.71/2.94 | | | | | (93) all_47_4 = create_slb % 15.71/2.94 | | | | | % 15.71/2.94 | | | | | REDUCE: (80), (93) imply: % 15.71/2.94 | | | | | (94) $false % 15.71/2.94 | | | | | % 15.71/2.94 | | | | | CLOSE: (94) is inconsistent. % 15.71/2.94 | | | | | % 15.71/2.94 | | | | Case 2: % 15.71/2.94 | | | | | % 15.71/2.95 | | | | | (95) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? % 15.71/2.95 | | | | | [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_5) = v0 & % 15.71/2.95 | | | | | triple(all_47_5, v4, bad) = v5 & update_slb(all_47_4, v0) = % 15.71/2.95 | | | | | v4 & lookup_slb(all_47_4, v0) = v2 & contains_slb(all_47_4, % 15.71/2.95 | | | | | v0) = v1 & less_than(v2, v0) = v3 & $i(v5) & $i(v4) & % 15.71/2.95 | | | | | $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0) | v5 = % 15.71/2.95 | | | | | all_54_1)) % 15.71/2.95 | | | | | % 15.71/2.95 | | | | | DELTA: instantiating (95) with fresh symbols all_82_0, all_82_1, % 15.71/2.95 | | | | | all_82_2, all_82_3, all_82_4, all_82_5 gives: % 15.71/2.95 | | | | | (96) findmin_pqp_res(all_47_5) = all_82_5 & triple(all_47_5, % 15.71/2.95 | | | | | all_82_1, bad) = all_82_0 & update_slb(all_47_4, all_82_5) = % 15.71/2.95 | | | | | all_82_1 & lookup_slb(all_47_4, all_82_5) = all_82_3 & % 15.71/2.95 | | | | | contains_slb(all_47_4, all_82_5) = all_82_4 & % 15.71/2.95 | | | | | less_than(all_82_3, all_82_5) = all_82_2 & $i(all_82_0) & % 15.71/2.95 | | | | | $i(all_82_1) & $i(all_82_3) & $i(all_82_5) & ( ~ (all_82_2 = % 15.71/2.95 | | | | | 0) | ~ (all_82_4 = 0) | all_82_0 = all_54_1) % 15.71/2.95 | | | | | % 15.71/2.95 | | | | | ALPHA: (96) implies: % 15.71/2.95 | | | | | (97) $i(all_82_1) % 15.71/2.95 | | | | | (98) less_than(all_82_3, all_82_5) = all_82_2 % 15.71/2.95 | | | | | (99) contains_slb(all_47_4, all_82_5) = all_82_4 % 15.71/2.95 | | | | | (100) lookup_slb(all_47_4, all_82_5) = all_82_3 % 15.71/2.95 | | | | | (101) update_slb(all_47_4, all_82_5) = all_82_1 % 15.71/2.95 | | | | | (102) triple(all_47_5, all_82_1, bad) = all_82_0 % 15.71/2.95 | | | | | (103) findmin_pqp_res(all_47_5) = all_82_5 % 15.71/2.95 | | | | | (104) ~ (all_82_2 = 0) | ~ (all_82_4 = 0) | all_82_0 = all_54_1 % 15.71/2.95 | | | | | % 15.71/2.95 | | | | | BETA: splitting (48) gives: % 15.71/2.95 | | | | | % 15.71/2.95 | | | | | Case 1: % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | (105) all_47_4 = create_slb % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (80), (105) imply: % 15.71/2.95 | | | | | | (106) $false % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | CLOSE: (106) is inconsistent. % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | Case 2: % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | (107) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 15.71/2.95 | | | | | | ? [v4: $i] : ? [v5: $i] : (findmin_pqp_res(all_47_5) = v0 % 15.71/2.95 | | | | | | & triple(all_47_5, v4, bad) = v5 & update_slb(all_47_4, % 15.71/2.95 | | | | | | v0) = v4 & lookup_slb(all_47_4, v0) = v2 & % 15.71/2.95 | | | | | | contains_slb(all_47_4, v0) = v1 & strictly_less_than(v0, % 15.71/2.95 | | | | | | v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 % 15.71/2.95 | | | | | | = 0) | ~ (v1 = 0) | v5 = all_54_1)) % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | DELTA: instantiating (107) with fresh symbols all_87_0, all_87_1, % 15.71/2.95 | | | | | | all_87_2, all_87_3, all_87_4, all_87_5 gives: % 15.71/2.95 | | | | | | (108) findmin_pqp_res(all_47_5) = all_87_5 & triple(all_47_5, % 15.71/2.95 | | | | | | all_87_1, bad) = all_87_0 & update_slb(all_47_4, % 15.71/2.95 | | | | | | all_87_5) = all_87_1 & lookup_slb(all_47_4, all_87_5) = % 15.71/2.95 | | | | | | all_87_3 & contains_slb(all_47_4, all_87_5) = all_87_4 & % 15.71/2.95 | | | | | | strictly_less_than(all_87_5, all_87_3) = all_87_2 & % 15.71/2.95 | | | | | | $i(all_87_0) & $i(all_87_1) & $i(all_87_3) & $i(all_87_5) & % 15.71/2.95 | | | | | | ( ~ (all_87_2 = 0) | ~ (all_87_4 = 0) | all_87_0 = % 15.71/2.95 | | | | | | all_54_1) % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | ALPHA: (108) implies: % 15.71/2.95 | | | | | | (109) $i(all_87_3) % 15.71/2.95 | | | | | | (110) strictly_less_than(all_87_5, all_87_3) = all_87_2 % 15.71/2.95 | | | | | | (111) contains_slb(all_47_4, all_87_5) = all_87_4 % 15.71/2.95 | | | | | | (112) lookup_slb(all_47_4, all_87_5) = all_87_3 % 15.71/2.95 | | | | | | (113) update_slb(all_47_4, all_87_5) = all_87_1 % 15.71/2.95 | | | | | | (114) triple(all_47_5, all_87_1, bad) = all_87_0 % 15.71/2.95 | | | | | | (115) findmin_pqp_res(all_47_5) = all_87_5 % 15.71/2.95 | | | | | | (116) ~ (all_87_2 = 0) | ~ (all_87_4 = 0) | all_87_0 = all_54_1 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | GROUND_INST: instantiating (18) with all_77_3, all_82_5, all_47_5, % 15.71/2.95 | | | | | | simplifying with (91), (103) gives: % 15.71/2.95 | | | | | | (117) all_82_5 = all_77_3 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | GROUND_INST: instantiating (18) with all_82_5, all_87_5, all_47_5, % 15.71/2.95 | | | | | | simplifying with (103), (115) gives: % 15.71/2.95 | | | | | | (118) all_87_5 = all_82_5 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | GROUND_INST: instantiating (18) with all_54_0, all_87_5, all_47_5, % 15.71/2.95 | | | | | | simplifying with (82), (115) gives: % 15.71/2.95 | | | | | | (119) all_87_5 = all_54_0 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | COMBINE_EQS: (118), (119) imply: % 15.71/2.95 | | | | | | (120) all_82_5 = all_54_0 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | SIMP: (120) implies: % 15.71/2.95 | | | | | | (121) all_82_5 = all_54_0 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | COMBINE_EQS: (117), (121) imply: % 15.71/2.95 | | | | | | (122) all_77_3 = all_54_0 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | SIMP: (122) implies: % 15.71/2.95 | | | | | | (123) all_77_3 = all_54_0 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (113), (119) imply: % 15.71/2.95 | | | | | | (124) update_slb(all_47_4, all_54_0) = all_87_1 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (101), (121) imply: % 15.71/2.95 | | | | | | (125) update_slb(all_47_4, all_54_0) = all_82_1 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (89), (123) imply: % 15.71/2.95 | | | | | | (126) update_slb(all_47_4, all_54_0) = all_77_1 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (112), (119) imply: % 15.71/2.95 | | | | | | (127) lookup_slb(all_47_4, all_54_0) = all_87_3 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (100), (121) imply: % 15.71/2.95 | | | | | | (128) lookup_slb(all_47_4, all_54_0) = all_82_3 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (111), (119) imply: % 15.71/2.95 | | | | | | (129) contains_slb(all_47_4, all_54_0) = all_87_4 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (99), (121) imply: % 15.71/2.95 | | | | | | (130) contains_slb(all_47_4, all_54_0) = all_82_4 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (88), (123) imply: % 15.71/2.95 | | | | | | (131) contains_slb(all_47_4, all_54_0) = all_77_2 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (110), (119) imply: % 15.71/2.95 | | | | | | (132) strictly_less_than(all_54_0, all_87_3) = all_87_2 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | REDUCE: (98), (121) imply: % 15.71/2.95 | | | | | | (133) less_than(all_82_3, all_54_0) = all_82_2 % 15.71/2.95 | | | | | | % 15.71/2.95 | | | | | | GROUND_INST: instantiating (21) with all_82_4, all_87_4, all_54_0, % 15.71/2.95 | | | | | | all_47_4, simplifying with (129), (130) gives: % 15.71/2.95 | | | | | | (134) all_87_4 = all_82_4 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | GROUND_INST: instantiating (21) with all_77_2, all_87_4, all_54_0, % 15.71/2.96 | | | | | | all_47_4, simplifying with (129), (131) gives: % 15.71/2.96 | | | | | | (135) all_87_4 = all_77_2 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | GROUND_INST: instantiating (22) with all_82_3, all_87_3, all_54_0, % 15.71/2.96 | | | | | | all_47_4, simplifying with (127), (128) gives: % 15.71/2.96 | | | | | | (136) all_87_3 = all_82_3 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | GROUND_INST: instantiating (23) with all_82_1, all_87_1, all_54_0, % 15.71/2.96 | | | | | | all_47_4, simplifying with (124), (125) gives: % 15.71/2.96 | | | | | | (137) all_87_1 = all_82_1 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | GROUND_INST: instantiating (23) with all_77_1, all_87_1, all_54_0, % 15.71/2.96 | | | | | | all_47_4, simplifying with (124), (126) gives: % 15.71/2.96 | | | | | | (138) all_87_1 = all_77_1 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | COMBINE_EQS: (137), (138) imply: % 15.71/2.96 | | | | | | (139) all_82_1 = all_77_1 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | SIMP: (139) implies: % 15.71/2.96 | | | | | | (140) all_82_1 = all_77_1 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | COMBINE_EQS: (134), (135) imply: % 15.71/2.96 | | | | | | (141) all_82_4 = all_77_2 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | SIMP: (141) implies: % 15.71/2.96 | | | | | | (142) all_82_4 = all_77_2 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | REDUCE: (114), (138) imply: % 15.71/2.96 | | | | | | (143) triple(all_47_5, all_77_1, bad) = all_87_0 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | REDUCE: (102), (140) imply: % 15.71/2.96 | | | | | | (144) triple(all_47_5, all_77_1, bad) = all_82_0 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | REDUCE: (132), (136) imply: % 15.71/2.96 | | | | | | (145) strictly_less_than(all_54_0, all_82_3) = all_87_2 % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | REDUCE: (109), (136) imply: % 15.71/2.96 | | | | | | (146) $i(all_82_3) % 15.71/2.96 | | | | | | % 15.71/2.96 | | | | | | REDUCE: (97), (140) imply: % 15.71/2.96 | | | | | | (147) $i(all_77_1) % 15.71/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (24) with all_77_0, all_87_0, bad, % 15.82/2.96 | | | | | | all_77_1, all_47_5, simplifying with (90), (143) gives: % 15.82/2.96 | | | | | | (148) all_87_0 = all_77_0 % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (24) with all_82_0, all_87_0, bad, % 15.82/2.96 | | | | | | all_77_1, all_47_5, simplifying with (143), (144) % 15.82/2.96 | | | | | | gives: % 15.82/2.96 | | | | | | (149) all_87_0 = all_82_0 % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | COMBINE_EQS: (148), (149) imply: % 15.82/2.96 | | | | | | (150) all_82_0 = all_77_0 % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (1) with all_54_0, all_82_3, all_82_2, % 15.82/2.96 | | | | | | simplifying with (52), (133), (146) gives: % 15.82/2.96 | | | | | | (151) all_82_2 = 0 | less_than(all_54_0, all_82_3) = 0 % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (4) with all_54_0, all_82_3, all_82_2, % 15.82/2.96 | | | | | | simplifying with (52), (133), (146) gives: % 15.82/2.96 | | | | | | (152) all_82_2 = 0 | ? [v0: any] : ? [v1: any] : % 15.82/2.96 | | | | | | (strictly_less_than(all_54_0, all_82_3) = v1 & % 15.82/2.96 | | | | | | less_than(all_54_0, all_82_3) = v0 & ( ~ (v0 = 0) | v1 = % 15.82/2.96 | | | | | | 0)) % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (3) with all_54_0, all_82_3, all_82_2, % 15.82/2.96 | | | | | | simplifying with (52), (133), (146) gives: % 15.82/2.96 | | | | | | (153) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_54_0, % 15.82/2.96 | | | | | | all_82_3) = v0 & less_than(all_54_0, all_82_3) = v1 & ( % 15.82/2.96 | | | | | | ~ (v0 = 0) | (v1 = 0 & ~ (all_82_2 = 0)))) % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (2) with all_82_3, all_54_0, all_82_2, % 15.82/2.96 | | | | | | simplifying with (52), (133), (146) gives: % 15.82/2.96 | | | | | | (154) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_82_3, % 15.82/2.96 | | | | | | all_54_0) = v0 & less_than(all_54_0, all_82_3) = v1 & ( % 15.82/2.96 | | | | | | ~ (v0 = 0) | (all_82_2 = 0 & ~ (v1 = 0)))) % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (5) with all_54_0, all_82_3, all_87_2, % 15.82/2.96 | | | | | | simplifying with (52), (145), (146) gives: % 15.82/2.96 | | | | | | (155) all_87_2 = 0 | ? [v0: any] : ? [v1: any] : % 15.82/2.96 | | | | | | (less_than(all_82_3, all_54_0) = v1 & less_than(all_54_0, % 15.82/2.96 | | | | | | all_82_3) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (6) with all_47_5, all_77_1, all_77_0, % 15.82/2.96 | | | | | | simplifying with (27), (90), (147) gives: % 15.82/2.96 | | | | | | (156) ? [v0: int] : ( ~ (v0 = 0) & ok(all_77_0) = v0) % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | DELTA: instantiating (156) with fresh symbol all_106_0 gives: % 15.82/2.96 | | | | | | (157) ~ (all_106_0 = 0) & ok(all_77_0) = all_106_0 % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | ALPHA: (157) implies: % 15.82/2.96 | | | | | | (158) ~ (all_106_0 = 0) % 15.82/2.96 | | | | | | (159) ok(all_77_0) = all_106_0 % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | DELTA: instantiating (154) with fresh symbols all_108_0, all_108_1 % 15.82/2.96 | | | | | | gives: % 15.82/2.96 | | | | | | (160) strictly_less_than(all_82_3, all_54_0) = all_108_1 & % 15.82/2.96 | | | | | | less_than(all_54_0, all_82_3) = all_108_0 & ( ~ (all_108_1 % 15.82/2.96 | | | | | | = 0) | (all_82_2 = 0 & ~ (all_108_0 = 0))) % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | ALPHA: (160) implies: % 15.82/2.96 | | | | | | (161) less_than(all_54_0, all_82_3) = all_108_0 % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | DELTA: instantiating (153) with fresh symbols all_110_0, all_110_1 % 15.82/2.96 | | | | | | gives: % 15.82/2.96 | | | | | | (162) strictly_less_than(all_54_0, all_82_3) = all_110_1 & % 15.82/2.96 | | | | | | less_than(all_54_0, all_82_3) = all_110_0 & ( ~ (all_110_1 % 15.82/2.96 | | | | | | = 0) | (all_110_0 = 0 & ~ (all_82_2 = 0))) % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | ALPHA: (162) implies: % 15.82/2.96 | | | | | | (163) less_than(all_54_0, all_82_3) = all_110_0 % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (20) with all_108_0, all_110_0, all_82_3, % 15.82/2.96 | | | | | | all_54_0, simplifying with (161), (163) gives: % 15.82/2.96 | | | | | | (164) all_110_0 = all_108_0 % 15.82/2.96 | | | | | | % 15.82/2.96 | | | | | | GROUND_INST: instantiating (3) with all_82_3, all_54_0, all_108_0, % 15.82/2.96 | | | | | | simplifying with (52), (146), (161) gives: % 15.82/2.97 | | | | | | (165) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_82_3, % 15.82/2.97 | | | | | | all_54_0) = v0 & less_than(all_82_3, all_54_0) = v1 & ( % 15.82/2.97 | | | | | | ~ (v0 = 0) | (v1 = 0 & ~ (all_108_0 = 0)))) % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | GROUND_INST: instantiating (2) with all_54_0, all_82_3, all_108_0, % 15.82/2.97 | | | | | | simplifying with (52), (146), (161) gives: % 15.82/2.97 | | | | | | (166) ? [v0: any] : ? [v1: any] : (strictly_less_than(all_54_0, % 15.82/2.97 | | | | | | all_82_3) = v0 & less_than(all_82_3, all_54_0) = v1 & ( % 15.82/2.97 | | | | | | ~ (v0 = 0) | (all_108_0 = 0 & ~ (v1 = 0)))) % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | DELTA: instantiating (166) with fresh symbols all_121_0, all_121_1 % 15.82/2.97 | | | | | | gives: % 15.82/2.97 | | | | | | (167) strictly_less_than(all_54_0, all_82_3) = all_121_1 & % 15.82/2.97 | | | | | | less_than(all_82_3, all_54_0) = all_121_0 & ( ~ (all_121_1 % 15.82/2.97 | | | | | | = 0) | (all_108_0 = 0 & ~ (all_121_0 = 0))) % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | ALPHA: (167) implies: % 15.82/2.97 | | | | | | (168) less_than(all_82_3, all_54_0) = all_121_0 % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | DELTA: instantiating (165) with fresh symbols all_123_0, all_123_1 % 15.82/2.97 | | | | | | gives: % 15.82/2.97 | | | | | | (169) strictly_less_than(all_82_3, all_54_0) = all_123_1 & % 15.82/2.97 | | | | | | less_than(all_82_3, all_54_0) = all_123_0 & ( ~ (all_123_1 % 15.82/2.97 | | | | | | = 0) | (all_123_0 = 0 & ~ (all_108_0 = 0))) % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | ALPHA: (169) implies: % 15.82/2.97 | | | | | | (170) less_than(all_82_3, all_54_0) = all_123_0 % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | GROUND_INST: instantiating (20) with all_82_2, all_123_0, all_54_0, % 15.82/2.97 | | | | | | all_82_3, simplifying with (133), (170) gives: % 15.82/2.97 | | | | | | (171) all_123_0 = all_82_2 % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | GROUND_INST: instantiating (20) with all_121_0, all_123_0, all_54_0, % 15.82/2.97 | | | | | | all_82_3, simplifying with (168), (170) gives: % 15.82/2.97 | | | | | | (172) all_123_0 = all_121_0 % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | COMBINE_EQS: (171), (172) imply: % 15.82/2.97 | | | | | | (173) all_121_0 = all_82_2 % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | BETA: splitting (92) gives: % 15.82/2.97 | | | | | | % 15.82/2.97 | | | | | | Case 1: % 15.82/2.97 | | | | | | | % 15.82/2.97 | | | | | | | (174) all_77_2 = 0 % 15.82/2.97 | | | | | | | % 15.82/2.97 | | | | | | | COMBINE_EQS: (142), (174) imply: % 15.82/2.97 | | | | | | | (175) all_82_4 = 0 % 15.82/2.97 | | | | | | | % 15.82/2.97 | | | | | | | COMBINE_EQS: (135), (174) imply: % 15.82/2.97 | | | | | | | (176) all_87_4 = 0 % 15.82/2.97 | | | | | | | % 15.82/2.97 | | | | | | | BETA: splitting (104) gives: % 15.82/2.97 | | | | | | | % 15.82/2.97 | | | | | | | Case 1: % 15.82/2.97 | | | | | | | | % 15.82/2.97 | | | | | | | | (177) ~ (all_82_2 = 0) % 15.82/2.97 | | | | | | | | % 15.82/2.97 | | | | | | | | BETA: splitting (151) gives: % 15.82/2.97 | | | | | | | | % 15.82/2.97 | | | | | | | | Case 1: % 15.82/2.97 | | | | | | | | | % 15.82/2.97 | | | | | | | | | (178) less_than(all_54_0, all_82_3) = 0 % 15.82/2.97 | | | | | | | | | % 15.82/2.97 | | | | | | | | | BETA: splitting (155) gives: % 15.82/2.97 | | | | | | | | | % 15.82/2.97 | | | | | | | | | Case 1: % 15.82/2.97 | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | (179) all_87_2 = 0 % 15.82/2.97 | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | BETA: splitting (116) gives: % 15.82/2.97 | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | Case 1: % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | (180) ~ (all_87_2 = 0) % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | REDUCE: (179), (180) imply: % 15.82/2.97 | | | | | | | | | | | (181) $false % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | CLOSE: (181) is inconsistent. % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | Case 2: % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | (182) ~ (all_87_4 = 0) | all_87_0 = all_54_1 % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | BETA: splitting (182) gives: % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | Case 1: % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | (183) ~ (all_87_4 = 0) % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | REDUCE: (176), (183) imply: % 15.82/2.97 | | | | | | | | | | | | (184) $false % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | CLOSE: (184) is inconsistent. % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | Case 2: % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | (185) all_87_0 = all_54_1 % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | COMBINE_EQS: (148), (185) imply: % 15.82/2.97 | | | | | | | | | | | | (186) all_77_0 = all_54_1 % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | SIMP: (186) implies: % 15.82/2.97 | | | | | | | | | | | | (187) all_77_0 = all_54_1 % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | REDUCE: (159), (187) imply: % 15.82/2.97 | | | | | | | | | | | | (188) ok(all_54_1) = all_106_0 % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | REDUCE: (90), (187) imply: % 15.82/2.97 | | | | | | | | | | | | (189) triple(all_47_5, all_77_1, bad) = all_54_1 % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | REF_CLOSE: (17), (27), (34), (38), (46), (52), (147), (158), % 15.82/2.97 | | | | | | | | | | | | (188), (189), (l16_l14) are inconsistent by % 15.82/2.97 | | | | | | | | | | | | sub-proof #1. % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | End of split % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | End of split % 15.82/2.97 | | | | | | | | | | % 15.82/2.97 | | | | | | | | | Case 2: % 15.82/2.97 | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | (190) ? [v0: any] : ? [v1: any] : (less_than(all_82_3, % 15.82/2.97 | | | | | | | | | | all_54_0) = v1 & less_than(all_54_0, all_82_3) % 15.82/2.97 | | | | | | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 15.82/2.97 | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | DELTA: instantiating (190) with fresh symbols all_159_0, % 15.82/2.97 | | | | | | | | | | all_159_1 gives: % 15.82/2.97 | | | | | | | | | | (191) less_than(all_82_3, all_54_0) = all_159_0 & % 15.82/2.97 | | | | | | | | | | less_than(all_54_0, all_82_3) = all_159_1 & ( ~ % 15.82/2.97 | | | | | | | | | | (all_159_1 = 0) | all_159_0 = 0) % 15.82/2.97 | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | ALPHA: (191) implies: % 15.82/2.97 | | | | | | | | | | (192) less_than(all_54_0, all_82_3) = all_159_1 % 15.82/2.97 | | | | | | | | | | (193) less_than(all_82_3, all_54_0) = all_159_0 % 15.82/2.97 | | | | | | | | | | (194) ~ (all_159_1 = 0) | all_159_0 = 0 % 15.82/2.97 | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | BETA: splitting (152) gives: % 15.82/2.97 | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | Case 1: % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | (195) all_82_2 = 0 % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | REDUCE: (177), (195) imply: % 15.82/2.97 | | | | | | | | | | | (196) $false % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | CLOSE: (196) is inconsistent. % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | Case 2: % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | (197) ? [v0: any] : ? [v1: any] : % 15.82/2.97 | | | | | | | | | | | (strictly_less_than(all_54_0, all_82_3) = v1 & % 15.82/2.97 | | | | | | | | | | | less_than(all_54_0, all_82_3) = v0 & ( ~ (v0 = % 15.82/2.97 | | | | | | | | | | | 0) | v1 = 0)) % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | DELTA: instantiating (197) with fresh symbols all_165_0, % 15.82/2.97 | | | | | | | | | | | all_165_1 gives: % 15.82/2.97 | | | | | | | | | | | (198) strictly_less_than(all_54_0, all_82_3) = all_165_0 % 15.82/2.97 | | | | | | | | | | | & less_than(all_54_0, all_82_3) = all_165_1 & ( ~ % 15.82/2.97 | | | | | | | | | | | (all_165_1 = 0) | all_165_0 = 0) % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | ALPHA: (198) implies: % 15.82/2.97 | | | | | | | | | | | (199) less_than(all_54_0, all_82_3) = all_165_1 % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_159_1, all_165_1, % 15.82/2.97 | | | | | | | | | | | all_82_3, all_54_0, simplifying with (192), (199) % 15.82/2.97 | | | | | | | | | | | gives: % 15.82/2.97 | | | | | | | | | | | (200) all_165_1 = all_159_1 % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_165_1, all_82_3, % 15.82/2.97 | | | | | | | | | | | all_54_0, simplifying with (178), (199) gives: % 15.82/2.97 | | | | | | | | | | | (201) all_165_1 = 0 % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_82_2, all_159_0, % 15.82/2.97 | | | | | | | | | | | all_54_0, all_82_3, simplifying with (133), (193) % 15.82/2.97 | | | | | | | | | | | gives: % 15.82/2.97 | | | | | | | | | | | (202) all_159_0 = all_82_2 % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | COMBINE_EQS: (200), (201) imply: % 15.82/2.97 | | | | | | | | | | | (203) all_159_1 = 0 % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | SIMP: (203) implies: % 15.82/2.97 | | | | | | | | | | | (204) all_159_1 = 0 % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | BETA: splitting (194) gives: % 15.82/2.97 | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | Case 1: % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | (205) ~ (all_159_1 = 0) % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | REDUCE: (204), (205) imply: % 15.82/2.97 | | | | | | | | | | | | (206) $false % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | CLOSE: (206) is inconsistent. % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | Case 2: % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.97 | | | | | | | | | | | | (207) all_159_0 = 0 % 15.82/2.97 | | | | | | | | | | | | % 15.82/2.98 | | | | | | | | | | | | COMBINE_EQS: (202), (207) imply: % 15.82/2.98 | | | | | | | | | | | | (208) all_82_2 = 0 % 15.82/2.98 | | | | | | | | | | | | % 15.82/2.98 | | | | | | | | | | | | SIMP: (208) implies: % 15.82/2.98 | | | | | | | | | | | | (209) all_82_2 = 0 % 15.82/2.98 | | | | | | | | | | | | % 15.82/2.98 | | | | | | | | | | | | REDUCE: (177), (209) imply: % 15.82/2.98 | | | | | | | | | | | | (210) $false % 15.82/2.98 | | | | | | | | | | | | % 15.82/2.98 | | | | | | | | | | | | CLOSE: (210) is inconsistent. % 15.82/2.98 | | | | | | | | | | | | % 15.82/2.98 | | | | | | | | | | | End of split % 15.82/2.98 | | | | | | | | | | | % 15.82/2.98 | | | | | | | | | | End of split % 15.82/2.98 | | | | | | | | | | % 15.82/2.98 | | | | | | | | | End of split % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | Case 2: % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | (211) all_82_2 = 0 % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | REDUCE: (177), (211) imply: % 15.82/2.98 | | | | | | | | | (212) $false % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | CLOSE: (212) is inconsistent. % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | End of split % 15.82/2.98 | | | | | | | | % 15.82/2.98 | | | | | | | Case 2: % 15.82/2.98 | | | | | | | | % 15.82/2.98 | | | | | | | | (213) ~ (all_82_4 = 0) | all_82_0 = all_54_1 % 15.82/2.98 | | | | | | | | % 15.82/2.98 | | | | | | | | BETA: splitting (213) gives: % 15.82/2.98 | | | | | | | | % 15.82/2.98 | | | | | | | | Case 1: % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | (214) ~ (all_82_4 = 0) % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | REDUCE: (175), (214) imply: % 15.82/2.98 | | | | | | | | | (215) $false % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | CLOSE: (215) is inconsistent. % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | Case 2: % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | (216) all_82_0 = all_54_1 % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | COMBINE_EQS: (150), (216) imply: % 15.82/2.98 | | | | | | | | | (217) all_77_0 = all_54_1 % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | SIMP: (217) implies: % 15.82/2.98 | | | | | | | | | (218) all_77_0 = all_54_1 % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | REDUCE: (159), (218) imply: % 15.82/2.98 | | | | | | | | | (219) ok(all_54_1) = all_106_0 % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | REDUCE: (90), (218) imply: % 15.82/2.98 | | | | | | | | | (220) triple(all_47_5, all_77_1, bad) = all_54_1 % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | | REF_CLOSE: (17), (27), (34), (38), (46), (52), (147), (158), % 15.82/2.98 | | | | | | | | | (219), (220), (l16_l14) are inconsistent by % 15.82/2.98 | | | | | | | | | sub-proof #1. % 15.82/2.98 | | | | | | | | | % 15.82/2.98 | | | | | | | | End of split % 15.82/2.98 | | | | | | | | % 15.82/2.98 | | | | | | | End of split % 15.82/2.98 | | | | | | | % 15.82/2.98 | | | | | | Case 2: % 15.82/2.98 | | | | | | | % 15.82/2.98 | | | | | | | (221) all_77_0 = all_54_1 % 15.82/2.98 | | | | | | | % 15.82/2.98 | | | | | | | REDUCE: (159), (221) imply: % 15.82/2.98 | | | | | | | (222) ok(all_54_1) = all_106_0 % 15.82/2.98 | | | | | | | % 15.82/2.98 | | | | | | | REDUCE: (90), (221) imply: % 15.82/2.98 | | | | | | | (223) triple(all_47_5, all_77_1, bad) = all_54_1 % 15.82/2.98 | | | | | | | % 15.82/2.98 | | | | | | | REF_CLOSE: (17), (27), (34), (38), (46), (52), (147), (158), % 15.82/2.98 | | | | | | | (222), (223), (l16_l14) are inconsistent by sub-proof % 15.82/2.98 | | | | | | | #1. % 15.82/2.98 | | | | | | | % 15.82/2.98 | | | | | | End of split % 15.82/2.98 | | | | | | % 15.82/2.98 | | | | | End of split % 15.82/2.98 | | | | | % 15.82/2.98 | | | | End of split % 15.82/2.98 | | | | % 15.82/2.98 | | | End of split % 15.82/2.98 | | | % 15.82/2.98 | | End of split % 15.82/2.98 | | % 15.82/2.98 | End of split % 15.82/2.98 | % 15.82/2.98 End of proof % 15.82/2.98 % 15.82/2.98 Sub-proof #1 shows that the following formulas are inconsistent: % 15.82/2.98 ---------------------------------------------------------------- % 15.82/2.98 (1) remove_cpq(all_54_1, all_54_0) = all_47_0 % 15.82/2.98 (2) triple(all_47_5, all_77_1, bad) = all_54_1 % 15.82/2.98 (3) $i(all_54_0) % 15.82/2.98 (4) ok(all_54_1) = all_106_0 % 15.82/2.98 (5) $i(all_47_5) % 15.82/2.98 (6) $i(bad) % 15.82/2.98 (7) $i(all_77_1) % 15.82/2.98 (8) ~ (all_106_0 = 0) % 15.82/2.98 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.82/2.98 (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) % 15.82/2.98 (10) ok(all_47_0) = 0 % 15.82/2.98 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 15.82/2.98 [v5: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ (remove_cpq(v4, v3) = v5) % 15.82/2.98 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 15.82/2.98 [v7: any] : (ok(v5) = v7 & ok(v4) = v6 & ( ~ (v7 = 0) | v6 = 0))) % 15.82/2.98 % 15.82/2.98 Begin of proof % 15.82/2.98 | % 15.82/2.98 | GROUND_INST: instantiating (11) with all_47_5, all_77_1, bad, all_54_0, % 15.82/2.98 | all_54_1, all_47_0, simplifying with (1), (2), (3), (5), (6), (7) % 15.82/2.98 | gives: % 15.82/2.98 | (12) ? [v0: any] : ? [v1: any] : (ok(all_54_1) = v0 & ok(all_47_0) = v1 & % 15.82/2.98 | ( ~ (v1 = 0) | v0 = 0)) % 15.82/2.98 | % 15.82/2.98 | DELTA: instantiating (12) with fresh symbols all_172_0, all_172_1 gives: % 15.82/2.98 | (13) ok(all_54_1) = all_172_1 & ok(all_47_0) = all_172_0 & ( ~ (all_172_0 = % 15.82/2.98 | 0) | all_172_1 = 0) % 15.82/2.98 | % 15.82/2.98 | ALPHA: (13) implies: % 15.82/2.98 | (14) ok(all_47_0) = all_172_0 % 15.82/2.98 | (15) ok(all_54_1) = all_172_1 % 15.82/2.98 | (16) ~ (all_172_0 = 0) | all_172_1 = 0 % 15.82/2.98 | % 15.82/2.98 | GROUND_INST: instantiating (9) with 0, all_172_0, all_47_0, simplifying with % 15.82/2.98 | (10), (14) gives: % 15.82/2.98 | (17) all_172_0 = 0 % 15.82/2.98 | % 15.82/2.98 | GROUND_INST: instantiating (9) with all_106_0, all_172_1, all_54_1, % 15.82/2.98 | simplifying with (4), (15) gives: % 15.82/2.98 | (18) all_172_1 = all_106_0 % 15.82/2.98 | % 15.82/2.98 | BETA: splitting (16) gives: % 15.82/2.98 | % 15.82/2.98 | Case 1: % 15.82/2.98 | | % 15.82/2.98 | | (19) ~ (all_172_0 = 0) % 15.82/2.98 | | % 15.82/2.98 | | REDUCE: (17), (19) imply: % 15.82/2.98 | | (20) $false % 15.82/2.98 | | % 15.82/2.98 | | CLOSE: (20) is inconsistent. % 15.82/2.98 | | % 15.82/2.98 | Case 2: % 15.82/2.98 | | % 15.82/2.98 | | (21) all_172_1 = 0 % 15.82/2.98 | | % 15.82/2.98 | | COMBINE_EQS: (18), (21) imply: % 15.82/2.98 | | (22) all_106_0 = 0 % 15.82/2.98 | | % 15.82/2.98 | | SIMP: (22) implies: % 15.82/2.98 | | (23) all_106_0 = 0 % 15.82/2.98 | | % 15.82/2.98 | | REDUCE: (8), (23) imply: % 15.82/2.98 | | (24) $false % 15.82/2.98 | | % 15.82/2.98 | | CLOSE: (24) is inconsistent. % 15.82/2.98 | | % 15.82/2.98 | End of split % 15.82/2.98 | % 15.82/2.98 End of proof % 15.82/2.98 % SZS output end Proof for theBenchmark % 15.82/2.98 % 15.82/2.98 2379ms %------------------------------------------------------------------------------