%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM858+1 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.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 11:50:28 EDT 2023 % Result : Theorem 71.23s 10.53s % Output : Proof 73.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM858+1 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n008.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 : Fri Aug 25 12:50:47 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.62 ________ _____ % 0.18/0.62 ___ __ \_________(_)________________________________ % 0.18/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.62 % 0.18/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.62 (2023-06-19) % 0.18/0.62 % 0.18/0.62 (c) Philipp Rümmer, 2009-2023 % 0.18/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.62 Amanda Stjerna. % 0.18/0.62 Free software under BSD-3-Clause. % 0.18/0.62 % 0.18/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.62 % 0.18/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.64 Running up to 7 provers in parallel. % 0.18/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.21/1.14 Prover 4: Preprocessing ... % 2.21/1.15 Prover 1: Preprocessing ... % 2.72/1.20 Prover 3: Preprocessing ... % 2.72/1.20 Prover 2: Preprocessing ... % 2.72/1.20 Prover 0: Preprocessing ... % 2.72/1.20 Prover 6: Preprocessing ... % 2.72/1.20 Prover 5: Preprocessing ... % 6.03/1.69 Prover 2: Proving ... % 6.03/1.69 Prover 5: Proving ... % 6.03/1.69 Prover 6: Proving ... % 6.03/1.69 Prover 1: Constructing countermodel ... % 6.03/1.70 Prover 3: Constructing countermodel ... % 7.16/1.88 Prover 0: Proving ... % 7.16/1.89 Prover 4: Constructing countermodel ... % 8.54/2.04 Prover 3: gave up % 8.54/2.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.61/2.09 Prover 7: Preprocessing ... % 8.61/2.14 Prover 1: gave up % 8.61/2.17 Prover 7: Warning: ignoring some quantifiers % 8.61/2.17 Prover 7: Constructing countermodel ... % 8.61/2.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.61/2.23 Prover 8: Preprocessing ... % 10.43/2.34 Prover 7: gave up % 10.43/2.37 Prover 8: Warning: ignoring some quantifiers % 10.43/2.37 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 10.43/2.38 Prover 8: Constructing countermodel ... % 11.04/2.46 Prover 9: Preprocessing ... % 13.22/2.75 Prover 8: gave up % 13.22/2.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.71/2.79 Prover 9: Constructing countermodel ... % 13.71/2.80 Prover 10: Preprocessing ... % 14.31/2.90 Prover 10: Warning: ignoring some quantifiers % 14.31/2.91 Prover 10: Constructing countermodel ... % 59.45/8.91 Prover 2: stopped % 59.45/8.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 59.45/8.97 Prover 11: Preprocessing ... % 60.94/9.17 Prover 11: Constructing countermodel ... % 71.23/10.52 Prover 4: Found proof (size 757) % 71.23/10.52 Prover 4: proved (9871ms) % 71.23/10.52 Prover 6: stopped % 71.23/10.52 Prover 11: stopped % 71.23/10.52 Prover 10: stopped % 71.23/10.53 Prover 5: stopped % 71.23/10.53 Prover 0: stopped % 71.23/10.53 Prover 9: stopped % 71.23/10.53 % 71.23/10.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 71.23/10.53 % 71.98/10.61 % SZS output start Proof for theBenchmark % 71.98/10.62 Assumptions after simplification: % 71.98/10.62 --------------------------------- % 71.98/10.62 % 71.98/10.62 (lesseq_ref) % 72.28/10.66 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (lesseq(v0, v0) = v1) | ~ $i(v0)) % 72.28/10.66 % 72.28/10.66 (lesseq_total) % 72.28/10.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (lesseq(v1, v0) = v2) % 72.28/10.66 | ~ $i(v1) | ~ $i(v0) | lesseq(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : % 72.28/10.66 ! [v2: int] : (v2 = 0 | ~ (lesseq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 72.28/10.66 lesseq(v1, v0) = 0) % 72.28/10.66 % 72.28/10.66 (max_1) % 72.28/10.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (max(v0, v1) = v2) | % 72.28/10.67 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & lesseq(v1, v0) = v3)) & % 72.28/10.67 ! [v0: $i] : ! [v1: $i] : ( ~ (lesseq(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 72.28/10.67 max(v0, v1) = v0) % 72.28/10.67 % 72.28/10.67 (max_2) % 72.28/10.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (max(v0, v1) = v2) | % 72.28/10.67 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & lesseq(v0, v1) = v3)) & % 72.28/10.67 ! [v0: $i] : ! [v1: $i] : ( ~ (lesseq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 72.28/10.67 max(v0, v1) = v1) % 72.28/10.67 % 72.28/10.67 (max_is_ub_1) % 72.28/10.67 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 72.28/10.67 (minsol_model_ub(v0, v1, v2) = v3 & minsol_model_max(v0, v1, v2) = v4 & $i(v2) % 72.28/10.67 & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 72.28/10.67 % 72.28/10.67 (minsol_model_max) % 72.28/10.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: MultipleValueBool] : ! [v4: % 72.28/10.69 $i] : ! [v5: int] : (v5 = 0 | ~ (model_max(v0, v1, v2) = v3) | ~ % 72.28/10.69 (lesseq(v2, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 72.28/10.69 [v6: int] : (( ~ (v6 = 0) & minsol_model_max(v0, v1, v2) = v6) | ( ~ (v6 = % 72.28/10.69 0) & model_max(v0, v1, v4) = v6))) & ! [v0: $i] : ! [v1: $i] : ! % 72.28/10.69 [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (minsol_model_max(v0, v1, % 72.28/10.69 v2) = 0) | ~ (lesseq(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 72.28/10.69 | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & model_max(v0, v1, v3) = v5)) & % 72.28/10.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: MultipleValueBool] : ! [v4: % 72.28/10.69 $i] : ( ~ (model_max(v0, v1, v4) = 0) | ~ (model_max(v0, v1, v2) = v3) | ~ % 72.28/10.69 $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ((v5 = 0 & % 72.28/10.69 lesseq(v2, v4) = 0) | ( ~ (v5 = 0) & minsol_model_max(v0, v1, v2) = % 72.28/10.69 v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 % 72.28/10.69 | ~ (minsol_model_max(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 72.28/10.69 | ? [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ($i(v5) & ((v6 % 72.28/10.69 = 0 & ~ (v7 = 0) & model_max(v0, v1, v5) = 0 & lesseq(v2, v5) = v7) | % 72.28/10.69 ( ~ (v4 = 0) & model_max(v0, v1, v2) = v4)))) & ! [v0: $i] : ! [v1: % 72.28/10.69 $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (model_max(v0, v1, v2) = v3) % 72.28/10.69 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 72.28/10.69 minsol_model_max(v0, v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 72.28/10.69 $i] : ! [v3: $i] : ( ~ (minsol_model_max(v0, v1, v2) = 0) | ~ % 72.28/10.69 (model_max(v0, v1, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 72.28/10.69 | lesseq(v2, v3) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 72.28/10.69 (minsol_model_max(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 72.28/10.69 model_max(v0, v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 72.28/10.69 (model_max(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 72.28/10.69 int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ($i(v4) & ((v5 = 0 & ~ % 72.28/10.69 (v6 = 0) & model_max(v0, v1, v4) = 0 & lesseq(v2, v4) = v6) | (v3 = 0 % 72.28/10.69 & minsol_model_max(v0, v1, v2) = 0)))) % 72.28/10.69 % 72.28/10.69 (minsol_model_ub) % 72.28/10.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: MultipleValueBool] : ! [v4: % 72.28/10.70 $i] : ! [v5: int] : (v5 = 0 | ~ (model_ub(v0, v1, v2) = v3) | ~ % 72.28/10.70 (lesseq(v2, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 72.28/10.70 [v6: int] : (( ~ (v6 = 0) & minsol_model_ub(v0, v1, v2) = v6) | ( ~ (v6 = 0) % 72.28/10.70 & model_ub(v0, v1, v4) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 72.28/10.70 : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (minsol_model_ub(v0, v1, v2) = 0) % 72.28/10.70 | ~ (lesseq(v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 72.28/10.70 ? [v5: int] : ( ~ (v5 = 0) & model_ub(v0, v1, v3) = v5)) & ! [v0: $i] : ! % 72.28/10.70 [v1: $i] : ! [v2: $i] : ! [v3: MultipleValueBool] : ! [v4: $i] : ( ~ % 72.28/10.70 (model_ub(v0, v1, v4) = 0) | ~ (model_ub(v0, v1, v2) = v3) | ~ $i(v4) | ~ % 72.28/10.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ((v5 = 0 & lesseq(v2, v4) = % 72.28/10.70 0) | ( ~ (v5 = 0) & minsol_model_ub(v0, v1, v2) = v5))) & ! [v0: $i] : % 72.28/10.70 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (minsol_model_ub(v0, % 72.28/10.70 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? % 72.28/10.70 [v5: $i] : ? [v6: int] : ? [v7: int] : ($i(v5) & ((v6 = 0 & ~ (v7 = 0) & % 72.28/10.70 model_ub(v0, v1, v5) = 0 & lesseq(v2, v5) = v7) | ( ~ (v4 = 0) & % 72.28/10.70 model_ub(v0, v1, v2) = v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 72.28/10.70 $i] : ! [v3: int] : (v3 = 0 | ~ (model_ub(v0, v1, v2) = v3) | ~ $i(v2) | % 72.28/10.70 ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & minsol_model_ub(v0, v1, % 72.28/10.70 v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 72.28/10.70 (minsol_model_ub(v0, v1, v2) = 0) | ~ (model_ub(v0, v1, v3) = 0) | ~ % 72.28/10.70 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | lesseq(v2, v3) = 0) & ! [v0: % 72.28/10.70 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (minsol_model_ub(v0, v1, v2) = 0) | ~ % 72.28/10.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | model_ub(v0, v1, v2) = 0) & ! [v0: $i] : % 72.28/10.70 ! [v1: $i] : ! [v2: $i] : ( ~ (model_ub(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 72.28/10.70 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: % 72.28/10.70 int] : ($i(v4) & ((v5 = 0 & ~ (v6 = 0) & model_ub(v0, v1, v4) = 0 & % 72.28/10.70 lesseq(v2, v4) = v6) | (v3 = 0 & minsol_model_ub(v0, v1, v2) = 0)))) % 72.28/10.70 % 72.28/10.70 (model_max_1) % 72.28/10.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 72.28/10.70 (model_max(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 72.28/10.70 $i] : ( ~ (v4 = v2) & max(v0, v1) = v4 & $i(v4))) & ! [v0: $i] : ! [v1: % 72.28/10.70 $i] : ! [v2: $i] : ( ~ (model_max(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) % 72.28/10.70 | ~ $i(v0) | max(v0, v1) = v2) % 72.28/10.70 % 72.28/10.70 (model_ub_1) % 72.28/10.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 72.28/10.71 (model_ub(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 72.28/10.71 int] : ( ~ (v4 = 0) & ub(v0, v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : % 72.28/10.71 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (ub(v0, v1, v2) = v3) | ~ $i(v2) | % 72.28/10.71 ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & model_ub(v0, v1, v2) = % 72.28/10.71 v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (model_ub(v0, v1, v2) % 72.28/10.71 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ub(v0, v1, v2) = 0) & ! [v0: % 72.28/10.71 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ub(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 72.28/10.71 $i(v1) | ~ $i(v0) | model_ub(v0, v1, v2) = 0) % 72.28/10.71 % 72.28/10.71 (summation_monotone) % 72.28/10.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 72.28/10.71 | ~ (summation(v1) = v3) | ~ (summation(v0) = v2) | ~ (lesseq(v2, v3) = % 72.28/10.71 v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & lesseq(v0, v1) % 72.28/10.71 = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 72.28/10.71 (summation(v1) = v3) | ~ (summation(v0) = v2) | ~ (lesseq(v2, v3) = 0) | % 72.28/10.71 ~ $i(v1) | ~ $i(v0) | lesseq(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! % 72.28/10.71 [v2: int] : (v2 = 0 | ~ (lesseq(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 72.28/10.71 [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & summation(v1) = v4 & % 72.28/10.71 summation(v0) = v3 & lesseq(v3, v4) = v5 & $i(v4) & $i(v3))) & ! [v0: $i] % 72.28/10.71 : ! [v1: $i] : ( ~ (lesseq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] % 72.28/10.71 : ? [v3: $i] : (summation(v1) = v3 & summation(v0) = v2 & lesseq(v2, v3) = % 72.58/10.71 0 & $i(v3) & $i(v2))) % 72.58/10.71 % 72.58/10.71 (ub) % 72.58/10.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (ub(v0, % 72.58/10.71 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 72.58/10.71 [v5: any] : (lesseq(v1, v2) = v5 & lesseq(v0, v2) = v4 & ( ~ (v5 = 0) | ~ % 72.58/10.71 (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ub(v0, v1, % 72.58/10.71 v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (lesseq(v1, v2) = 0 & % 72.58/10.71 lesseq(v0, v2) = 0)) % 72.58/10.71 % 72.58/10.71 (function-axioms) % 72.58/10.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 72.58/10.71 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (minsol_model_ub(v4, v3, v2) = v1) | ~ % 72.58/10.71 (minsol_model_ub(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 72.58/10.71 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 72.58/10.71 (minsol_model_max(v4, v3, v2) = v1) | ~ (minsol_model_max(v4, v3, v2) = % 72.58/10.71 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 72.58/10.71 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (model_ub(v4, v3, v2) = v1) % 72.58/10.71 | ~ (model_ub(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 72.58/10.71 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 72.58/10.71 (model_max(v4, v3, v2) = v1) | ~ (model_max(v4, v3, v2) = v0)) & ! [v0: % 72.58/10.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 72.58/10.71 : ! [v4: $i] : (v1 = v0 | ~ (ub(v4, v3, v2) = v1) | ~ (ub(v4, v3, v2) = % 72.58/10.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 72.58/10.71 ~ (max(v3, v2) = v1) | ~ (max(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 72.58/10.71 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sum(v3, v2) = v1) | ~ (sum(v3, v2) % 72.58/10.71 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 72.58/10.71 $i] : ! [v3: $i] : (v1 = v0 | ~ (lesseq(v3, v2) = v1) | ~ (lesseq(v3, v2) % 72.58/10.71 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 72.58/10.71 (summation(v2) = v1) | ~ (summation(v2) = v0)) % 72.58/10.71 % 72.58/10.71 Further assumptions not needed in the proof: % 72.58/10.71 -------------------------------------------- % 72.58/10.72 lesseq_antisymmetric, lesseq_trans, sum_monotone_1 % 72.58/10.72 % 72.58/10.72 Those formulas are unsatisfiable: % 72.58/10.72 --------------------------------- % 72.58/10.72 % 72.58/10.72 Begin of proof % 72.58/10.72 | % 72.58/10.72 | ALPHA: (lesseq_total) implies: % 72.58/10.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (lesseq(v1, v0) % 72.58/10.72 | = v2) | ~ $i(v1) | ~ $i(v0) | lesseq(v0, v1) = 0) % 72.58/10.72 | % 72.58/10.72 | ALPHA: (summation_monotone) implies: % 72.58/10.72 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (lesseq(v0, v1) = 0) | ~ $i(v1) | ~ % 72.58/10.72 | $i(v0) | ? [v2: $i] : ? [v3: $i] : (summation(v1) = v3 & % 72.58/10.72 | summation(v0) = v2 & lesseq(v2, v3) = 0 & $i(v3) & $i(v2))) % 72.58/10.72 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (lesseq(v0, v1) % 72.58/10.72 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: % 72.58/10.72 | int] : ( ~ (v5 = 0) & summation(v1) = v4 & summation(v0) = v3 & % 72.58/10.72 | lesseq(v3, v4) = v5 & $i(v4) & $i(v3))) % 72.58/10.72 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 72.58/10.72 | (summation(v1) = v3) | ~ (summation(v0) = v2) | ~ (lesseq(v2, v3) = % 72.58/10.72 | 0) | ~ $i(v1) | ~ $i(v0) | lesseq(v0, v1) = 0) % 72.58/10.72 | % 72.58/10.72 | ALPHA: (max_1) implies: % 72.58/10.72 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (lesseq(v1, v0) = 0) | ~ $i(v1) | ~ % 72.58/10.72 | $i(v0) | max(v0, v1) = v0) % 72.58/10.72 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (max(v0, v1) = % 72.58/10.72 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 72.58/10.72 | lesseq(v1, v0) = v3)) % 72.58/10.72 | % 72.58/10.72 | ALPHA: (max_2) implies: % 72.58/10.72 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (lesseq(v0, v1) = 0) | ~ $i(v1) | ~ % 72.58/10.72 | $i(v0) | max(v0, v1) = v1) % 72.58/10.72 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (max(v0, v1) = % 72.58/10.72 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 72.58/10.72 | lesseq(v0, v1) = v3)) % 72.58/10.72 | % 72.58/10.72 | ALPHA: (ub) implies: % 72.58/10.72 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ub(v0, v1, v2) = 0) | ~ % 72.58/10.72 | $i(v2) | ~ $i(v1) | ~ $i(v0) | (lesseq(v1, v2) = 0 & lesseq(v0, v2) % 72.58/10.72 | = 0)) % 72.58/10.72 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 72.58/10.72 | (ub(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 72.58/10.72 | any] : ? [v5: any] : (lesseq(v1, v2) = v5 & lesseq(v0, v2) = v4 & % 72.58/10.72 | ( ~ (v5 = 0) | ~ (v4 = 0)))) % 72.58/10.72 | % 72.58/10.72 | ALPHA: (model_max_1) implies: % 72.58/10.73 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (model_max(v0, v1, v2) = % 72.58/10.73 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | max(v0, v1) = v2) % 72.58/10.73 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 72.58/10.73 | (model_max(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 72.58/10.73 | ? [v4: $i] : ( ~ (v4 = v2) & max(v0, v1) = v4 & $i(v4))) % 72.58/10.73 | % 72.58/10.73 | ALPHA: (model_ub_1) implies: % 72.58/10.73 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (model_ub(v0, v1, v2) = % 72.58/10.73 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ub(v0, v1, v2) = 0) % 72.58/10.73 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 72.58/10.73 | (model_ub(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 72.58/10.73 | [v4: int] : ( ~ (v4 = 0) & ub(v0, v1, v2) = v4)) % 72.58/10.73 | % 72.58/10.73 | ALPHA: (minsol_model_max) implies: % 72.58/10.73 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (model_max(v0, v1, v2) = % 72.58/10.73 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 72.58/10.73 | $i] : ? [v5: int] : ? [v6: int] : ($i(v4) & ((v5 = 0 & ~ (v6 = % 72.58/10.73 | 0) & model_max(v0, v1, v4) = 0 & lesseq(v2, v4) = v6) | (v3 % 72.58/10.73 | = 0 & minsol_model_max(v0, v1, v2) = 0)))) % 72.58/10.73 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (minsol_model_max(v0, % 72.58/10.73 | v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | model_max(v0, % 72.58/10.73 | v1, v2) = 0) % 72.58/10.73 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 72.58/10.73 | (minsol_model_max(v0, v1, v2) = 0) | ~ (model_max(v0, v1, v3) = 0) % 72.58/10.73 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | lesseq(v2, v3) = % 72.58/10.73 | 0) % 72.58/10.73 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 72.58/10.73 | (minsol_model_max(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 72.58/10.73 | $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : % 72.58/10.73 | ($i(v5) & ((v6 = 0 & ~ (v7 = 0) & model_max(v0, v1, v5) = 0 & % 72.58/10.73 | lesseq(v2, v5) = v7) | ( ~ (v4 = 0) & model_max(v0, v1, v2) = % 72.58/10.73 | v4)))) % 72.58/10.73 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: MultipleValueBool] : % 72.58/10.73 | ! [v4: $i] : ( ~ (model_max(v0, v1, v4) = 0) | ~ (model_max(v0, v1, % 72.58/10.73 | v2) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 72.58/10.73 | [v5: int] : ((v5 = 0 & lesseq(v2, v4) = 0) | ( ~ (v5 = 0) & % 72.58/10.73 | minsol_model_max(v0, v1, v2) = v5))) % 72.58/10.73 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: MultipleValueBool] : % 72.58/10.73 | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (model_max(v0, v1, v2) = v3) % 72.58/10.73 | | ~ (lesseq(v2, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ % 72.58/10.73 | $i(v0) | ? [v6: int] : (( ~ (v6 = 0) & minsol_model_max(v0, v1, v2) % 72.58/10.73 | = v6) | ( ~ (v6 = 0) & model_max(v0, v1, v4) = v6))) % 72.58/10.73 | % 72.58/10.73 | ALPHA: (minsol_model_ub) implies: % 72.58/10.73 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (model_ub(v0, v1, v2) = % 72.58/10.73 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 72.58/10.73 | $i] : ? [v5: int] : ? [v6: int] : ($i(v4) & ((v5 = 0 & ~ (v6 = % 72.58/10.73 | 0) & model_ub(v0, v1, v4) = 0 & lesseq(v2, v4) = v6) | (v3 = % 72.58/10.73 | 0 & minsol_model_ub(v0, v1, v2) = 0)))) % 72.58/10.74 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (minsol_model_ub(v0, v1, % 72.58/10.74 | v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | model_ub(v0, v1, % 72.58/10.74 | v2) = 0) % 72.58/10.74 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 72.58/10.74 | (minsol_model_ub(v0, v1, v2) = 0) | ~ (model_ub(v0, v1, v3) = 0) | % 72.58/10.74 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | lesseq(v2, v3) = 0) % 72.58/10.74 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 72.58/10.74 | (minsol_model_ub(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 72.58/10.74 | $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : % 72.58/10.74 | ($i(v5) & ((v6 = 0 & ~ (v7 = 0) & model_ub(v0, v1, v5) = 0 & % 72.58/10.74 | lesseq(v2, v5) = v7) | ( ~ (v4 = 0) & model_ub(v0, v1, v2) = % 72.58/10.74 | v4)))) % 72.58/10.74 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 72.58/10.74 | (v4 = 0 | ~ (minsol_model_ub(v0, v1, v2) = 0) | ~ (lesseq(v2, v3) = % 72.58/10.74 | v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] % 72.58/10.74 | : ( ~ (v5 = 0) & model_ub(v0, v1, v3) = v5)) % 72.58/10.74 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: MultipleValueBool] : % 72.58/10.74 | ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (model_ub(v0, v1, v2) = v3) % 72.58/10.74 | | ~ (lesseq(v2, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ % 72.58/10.74 | $i(v0) | ? [v6: int] : (( ~ (v6 = 0) & minsol_model_ub(v0, v1, v2) % 72.58/10.74 | = v6) | ( ~ (v6 = 0) & model_ub(v0, v1, v4) = v6))) % 72.58/10.74 | % 72.58/10.74 | ALPHA: (function-axioms) implies: % 72.58/10.74 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (summation(v2) % 72.58/10.74 | = v1) | ~ (summation(v2) = v0)) % 72.58/10.74 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 72.58/10.74 | : ! [v3: $i] : (v1 = v0 | ~ (lesseq(v3, v2) = v1) | ~ (lesseq(v3, % 72.58/10.74 | v2) = v0)) % 72.58/10.74 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 72.58/10.74 | (max(v3, v2) = v1) | ~ (max(v3, v2) = v0)) % 72.58/10.74 | (30) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 72.58/10.74 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (ub(v4, v3, v2) = v1) | ~ % 72.58/10.74 | (ub(v4, v3, v2) = v0)) % 72.58/10.74 | (31) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 72.58/10.74 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (model_ub(v4, v3, v2) = % 72.58/10.74 | v1) | ~ (model_ub(v4, v3, v2) = v0)) % 72.58/10.74 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 72.58/10.74 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (minsol_model_max(v4, v3, % 72.58/10.74 | v2) = v1) | ~ (minsol_model_max(v4, v3, v2) = v0)) % 72.58/10.74 | (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 72.58/10.74 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (minsol_model_ub(v4, v3, % 72.58/10.74 | v2) = v1) | ~ (minsol_model_ub(v4, v3, v2) = v0)) % 72.58/10.74 | % 72.58/10.74 | DELTA: instantiating (max_is_ub_1) with fresh symbols all_16_0, all_16_1, % 72.58/10.74 | all_16_2, all_16_3, all_16_4 gives: % 72.58/10.74 | (34) minsol_model_ub(all_16_4, all_16_3, all_16_2) = all_16_1 & % 72.58/10.74 | minsol_model_max(all_16_4, all_16_3, all_16_2) = all_16_0 & % 72.58/10.74 | $i(all_16_2) & $i(all_16_3) & $i(all_16_4) & ((all_16_0 = 0 & ~ % 72.58/10.74 | (all_16_1 = 0)) | (all_16_1 = 0 & ~ (all_16_0 = 0))) % 72.58/10.75 | % 72.58/10.75 | ALPHA: (34) implies: % 72.58/10.75 | (35) $i(all_16_4) % 72.58/10.75 | (36) $i(all_16_3) % 72.58/10.75 | (37) $i(all_16_2) % 72.58/10.75 | (38) minsol_model_max(all_16_4, all_16_3, all_16_2) = all_16_0 % 72.58/10.75 | (39) minsol_model_ub(all_16_4, all_16_3, all_16_2) = all_16_1 % 72.58/10.75 | (40) (all_16_0 = 0 & ~ (all_16_1 = 0)) | (all_16_1 = 0 & ~ (all_16_0 = % 72.58/10.75 | 0)) % 72.58/10.75 | % 72.58/10.75 | GROUND_INST: instantiating (18) with all_16_4, all_16_3, all_16_2, all_16_0, % 72.58/10.75 | simplifying with (35), (36), (37), (38) gives: % 72.58/10.75 | (41) all_16_0 = 0 | ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: % 72.58/10.75 | int] : ($i(v1) & ((v2 = 0 & ~ (v3 = 0) & model_max(all_16_4, % 72.58/10.75 | all_16_3, v1) = 0 & lesseq(all_16_2, v1) = v3) | ( ~ (v0 = 0) % 72.58/10.75 | & model_max(all_16_4, all_16_3, all_16_2) = v0))) % 72.58/10.75 | % 72.58/10.75 | GROUND_INST: instantiating (24) with all_16_4, all_16_3, all_16_2, all_16_1, % 72.58/10.75 | simplifying with (35), (36), (37), (39) gives: % 72.58/10.75 | (42) all_16_1 = 0 | ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: % 72.58/10.75 | int] : ($i(v1) & ((v2 = 0 & ~ (v3 = 0) & model_ub(all_16_4, % 72.58/10.75 | all_16_3, v1) = 0 & lesseq(all_16_2, v1) = v3) | ( ~ (v0 = 0) % 72.58/10.75 | & model_ub(all_16_4, all_16_3, all_16_2) = v0))) % 72.58/10.75 | % 72.58/10.75 | BETA: splitting (40) gives: % 72.58/10.75 | % 72.58/10.75 | Case 1: % 72.58/10.75 | | % 72.58/10.75 | | (43) all_16_0 = 0 & ~ (all_16_1 = 0) % 72.58/10.75 | | % 72.58/10.75 | | ALPHA: (43) implies: % 72.58/10.75 | | (44) all_16_0 = 0 % 72.58/10.75 | | (45) ~ (all_16_1 = 0) % 72.58/10.75 | | % 72.58/10.75 | | REDUCE: (38), (44) imply: % 72.58/10.75 | | (46) minsol_model_max(all_16_4, all_16_3, all_16_2) = 0 % 72.58/10.75 | | % 72.58/10.75 | | BETA: splitting (42) gives: % 72.58/10.75 | | % 72.58/10.75 | | Case 1: % 72.58/10.75 | | | % 72.58/10.75 | | | (47) all_16_1 = 0 % 72.58/10.75 | | | % 72.58/10.75 | | | REDUCE: (45), (47) imply: % 72.58/10.75 | | | (48) $false % 72.58/10.75 | | | % 72.58/10.75 | | | CLOSE: (48) is inconsistent. % 72.58/10.75 | | | % 72.58/10.75 | | Case 2: % 72.58/10.75 | | | % 72.58/10.75 | | | (49) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ($i(v1) % 72.58/10.75 | | | & ((v2 = 0 & ~ (v3 = 0) & model_ub(all_16_4, all_16_3, v1) = 0 % 72.58/10.75 | | | & lesseq(all_16_2, v1) = v3) | ( ~ (v0 = 0) & % 72.58/10.75 | | | model_ub(all_16_4, all_16_3, all_16_2) = v0))) % 72.58/10.75 | | | % 72.58/10.75 | | | DELTA: instantiating (49) with fresh symbols all_29_0, all_29_1, all_29_2, % 72.58/10.75 | | | all_29_3 gives: % 72.58/10.76 | | | (50) $i(all_29_2) & ((all_29_1 = 0 & ~ (all_29_0 = 0) & % 72.58/10.76 | | | model_ub(all_16_4, all_16_3, all_29_2) = 0 & lesseq(all_16_2, % 72.58/10.76 | | | all_29_2) = all_29_0) | ( ~ (all_29_3 = 0) & % 72.58/10.76 | | | model_ub(all_16_4, all_16_3, all_16_2) = all_29_3)) % 72.58/10.76 | | | % 72.58/10.76 | | | ALPHA: (50) implies: % 72.58/10.76 | | | (51) $i(all_29_2) % 72.58/10.76 | | | (52) (all_29_1 = 0 & ~ (all_29_0 = 0) & model_ub(all_16_4, all_16_3, % 72.58/10.76 | | | all_29_2) = 0 & lesseq(all_16_2, all_29_2) = all_29_0) | ( ~ % 72.58/10.76 | | | (all_29_3 = 0) & model_ub(all_16_4, all_16_3, all_16_2) = % 72.58/10.76 | | | all_29_3) % 72.58/10.76 | | | % 72.58/10.76 | | | GROUND_INST: instantiating (16) with all_16_4, all_16_3, all_16_2, % 72.58/10.76 | | | simplifying with (35), (36), (37), (46) gives: % 72.58/10.76 | | | (53) model_max(all_16_4, all_16_3, all_16_2) = 0 % 72.58/10.76 | | | % 72.58/10.76 | | | GROUND_INST: instantiating (17) with all_16_4, all_16_3, all_16_2, % 72.58/10.76 | | | all_16_2, simplifying with (35), (36), (37), (46), (53) % 72.58/10.76 | | | gives: % 72.58/10.76 | | | (54) lesseq(all_16_2, all_16_2) = 0 % 72.58/10.76 | | | % 72.81/10.76 | | | GROUND_INST: instantiating (11) with all_16_4, all_16_3, all_16_2, % 72.81/10.76 | | | simplifying with (35), (36), (37), (53) gives: % 72.81/10.76 | | | (55) max(all_16_4, all_16_3) = all_16_2 % 72.81/10.76 | | | % 72.81/10.76 | | | GROUND_INST: instantiating (8) with all_16_4, all_16_3, all_16_2, % 72.81/10.76 | | | simplifying with (35), (36), (55) gives: % 72.81/10.76 | | | (56) all_16_2 = all_16_3 | ? [v0: int] : ( ~ (v0 = 0) & % 72.81/10.76 | | | lesseq(all_16_4, all_16_3) = v0) % 72.81/10.76 | | | % 72.81/10.76 | | | GROUND_INST: instantiating (6) with all_16_4, all_16_3, all_16_2, % 72.81/10.76 | | | simplifying with (35), (36), (55) gives: % 72.81/10.76 | | | (57) all_16_2 = all_16_4 | ? [v0: int] : ( ~ (v0 = 0) & % 72.81/10.76 | | | lesseq(all_16_3, all_16_4) = v0) % 72.81/10.76 | | | % 72.81/10.76 | | | BETA: splitting (52) gives: % 72.81/10.76 | | | % 72.81/10.76 | | | Case 1: % 72.81/10.76 | | | | % 72.81/10.76 | | | | (58) all_29_1 = 0 & ~ (all_29_0 = 0) & model_ub(all_16_4, all_16_3, % 72.81/10.76 | | | | all_29_2) = 0 & lesseq(all_16_2, all_29_2) = all_29_0 % 72.81/10.76 | | | | % 72.81/10.76 | | | | ALPHA: (58) implies: % 72.81/10.76 | | | | (59) ~ (all_29_0 = 0) % 72.81/10.76 | | | | (60) lesseq(all_16_2, all_29_2) = all_29_0 % 72.81/10.76 | | | | (61) model_ub(all_16_4, all_16_3, all_29_2) = 0 % 72.81/10.76 | | | | % 72.81/10.76 | | | | GROUND_INST: instantiating (20) with all_16_4, all_16_3, all_16_2, 0, % 72.81/10.76 | | | | all_29_2, all_29_0, simplifying with (35), (36), (37), % 72.81/10.76 | | | | (51), (53), (60) gives: % 72.81/10.77 | | | | (62) all_29_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & % 72.81/10.77 | | | | minsol_model_max(all_16_4, all_16_3, all_16_2) = v0) | ( ~ % 72.81/10.77 | | | | (v0 = 0) & model_max(all_16_4, all_16_3, all_29_2) = v0)) % 72.81/10.77 | | | | % 72.81/10.77 | | | | GROUND_INST: instantiating (13) with all_16_4, all_16_3, all_29_2, % 72.81/10.77 | | | | simplifying with (35), (36), (51), (61) gives: % 72.81/10.77 | | | | (63) ub(all_16_4, all_16_3, all_29_2) = 0 % 72.81/10.77 | | | | % 72.81/10.77 | | | | BETA: splitting (62) gives: % 72.81/10.77 | | | | % 72.81/10.77 | | | | Case 1: % 72.81/10.77 | | | | | % 72.81/10.77 | | | | | (64) all_29_0 = 0 % 72.81/10.77 | | | | | % 72.81/10.77 | | | | | REDUCE: (59), (64) imply: % 72.81/10.77 | | | | | (65) $false % 72.81/10.77 | | | | | % 72.81/10.77 | | | | | CLOSE: (65) is inconsistent. % 72.81/10.77 | | | | | % 72.81/10.77 | | | | Case 2: % 72.81/10.77 | | | | | % 72.81/10.77 | | | | | % 72.81/10.77 | | | | | GROUND_INST: instantiating (9) with all_16_4, all_16_3, all_29_2, % 72.81/10.77 | | | | | simplifying with (35), (36), (51), (63) gives: % 72.81/10.77 | | | | | (66) lesseq(all_16_3, all_29_2) = 0 & lesseq(all_16_4, all_29_2) = % 72.81/10.77 | | | | | 0 % 72.81/10.77 | | | | | % 72.81/10.77 | | | | | ALPHA: (66) implies: % 72.81/10.77 | | | | | (67) lesseq(all_16_4, all_29_2) = 0 % 72.81/10.77 | | | | | (68) lesseq(all_16_3, all_29_2) = 0 % 72.81/10.77 | | | | | % 72.81/10.77 | | | | | BETA: splitting (57) gives: % 72.81/10.77 | | | | | % 72.81/10.77 | | | | | Case 1: % 72.81/10.77 | | | | | | % 72.81/10.77 | | | | | | (69) all_16_2 = all_16_4 % 72.81/10.77 | | | | | | % 72.81/10.77 | | | | | | REDUCE: (60), (69) imply: % 72.81/10.77 | | | | | | (70) lesseq(all_16_4, all_29_2) = all_29_0 % 72.81/10.77 | | | | | | % 72.81/10.77 | | | | | | GROUND_INST: instantiating (28) with 0, all_29_0, all_29_2, % 72.81/10.77 | | | | | | all_16_4, simplifying with (67), (70) gives: % 72.81/10.77 | | | | | | (71) all_29_0 = 0 % 72.81/10.77 | | | | | | % 72.81/10.77 | | | | | | REDUCE: (59), (71) imply: % 72.81/10.77 | | | | | | (72) $false % 72.81/10.77 | | | | | | % 72.81/10.77 | | | | | | CLOSE: (72) is inconsistent. % 72.81/10.77 | | | | | | % 72.81/10.77 | | | | | Case 2: % 72.81/10.77 | | | | | | % 72.81/10.77 | | | | | | (73) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_3, all_16_4) = % 72.81/10.77 | | | | | | v0) % 72.81/10.77 | | | | | | % 72.81/10.77 | | | | | | DELTA: instantiating (73) with fresh symbol all_237_0 gives: % 72.81/10.77 | | | | | | (74) ~ (all_237_0 = 0) & lesseq(all_16_3, all_16_4) = all_237_0 % 72.81/10.77 | | | | | | % 72.81/10.77 | | | | | | ALPHA: (74) implies: % 72.81/10.78 | | | | | | (75) ~ (all_237_0 = 0) % 72.81/10.78 | | | | | | (76) lesseq(all_16_3, all_16_4) = all_237_0 % 72.81/10.78 | | | | | | % 72.81/10.78 | | | | | | BETA: splitting (56) gives: % 72.81/10.78 | | | | | | % 72.81/10.78 | | | | | | Case 1: % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | (77) all_16_2 = all_16_3 % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | REDUCE: (60), (77) imply: % 72.81/10.78 | | | | | | | (78) lesseq(all_16_3, all_29_2) = all_29_0 % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | GROUND_INST: instantiating (28) with 0, all_29_0, all_29_2, % 72.81/10.78 | | | | | | | all_16_3, simplifying with (68), (78) gives: % 72.81/10.78 | | | | | | | (79) all_29_0 = 0 % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | REDUCE: (59), (79) imply: % 72.81/10.78 | | | | | | | (80) $false % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | CLOSE: (80) is inconsistent. % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | Case 2: % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | (81) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_4, all_16_3) = % 72.81/10.78 | | | | | | | v0) % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | DELTA: instantiating (81) with fresh symbol all_245_0 gives: % 72.81/10.78 | | | | | | | (82) ~ (all_245_0 = 0) & lesseq(all_16_4, all_16_3) = % 72.81/10.78 | | | | | | | all_245_0 % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | ALPHA: (82) implies: % 72.81/10.78 | | | | | | | (83) ~ (all_245_0 = 0) % 72.81/10.78 | | | | | | | (84) lesseq(all_16_4, all_16_3) = all_245_0 % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | GROUND_INST: instantiating (1) with all_16_3, all_16_4, all_245_0, % 72.81/10.78 | | | | | | | simplifying with (35), (36), (84) gives: % 72.81/10.78 | | | | | | | (85) all_245_0 = 0 | lesseq(all_16_3, all_16_4) = 0 % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | BETA: splitting (85) gives: % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | | Case 1: % 72.81/10.78 | | | | | | | | % 72.81/10.78 | | | | | | | | (86) lesseq(all_16_3, all_16_4) = 0 % 72.81/10.78 | | | | | | | | % 72.81/10.78 | | | | | | | | GROUND_INST: instantiating (28) with all_237_0, 0, all_16_4, % 72.81/10.78 | | | | | | | | all_16_3, simplifying with (76), (86) gives: % 72.81/10.78 | | | | | | | | (87) all_237_0 = 0 % 72.81/10.78 | | | | | | | | % 72.81/10.78 | | | | | | | | REDUCE: (75), (87) imply: % 72.81/10.78 | | | | | | | | (88) $false % 72.81/10.78 | | | | | | | | % 72.81/10.78 | | | | | | | | CLOSE: (88) is inconsistent. % 72.81/10.78 | | | | | | | | % 72.81/10.78 | | | | | | | Case 2: % 72.81/10.78 | | | | | | | | % 72.81/10.78 | | | | | | | | (89) all_245_0 = 0 % 72.81/10.78 | | | | | | | | % 72.81/10.78 | | | | | | | | REDUCE: (83), (89) imply: % 72.81/10.78 | | | | | | | | (90) $false % 72.81/10.78 | | | | | | | | % 72.81/10.78 | | | | | | | | CLOSE: (90) is inconsistent. % 72.81/10.78 | | | | | | | | % 72.81/10.78 | | | | | | | End of split % 72.81/10.78 | | | | | | | % 72.81/10.78 | | | | | | End of split % 72.81/10.78 | | | | | | % 72.81/10.78 | | | | | End of split % 72.81/10.78 | | | | | % 72.81/10.78 | | | | End of split % 72.81/10.78 | | | | % 72.81/10.78 | | | Case 2: % 72.81/10.78 | | | | % 72.81/10.78 | | | | (91) ~ (all_29_3 = 0) & model_ub(all_16_4, all_16_3, all_16_2) = % 72.81/10.78 | | | | all_29_3 % 72.81/10.78 | | | | % 72.81/10.78 | | | | ALPHA: (91) implies: % 72.81/10.78 | | | | (92) ~ (all_29_3 = 0) % 72.81/10.78 | | | | (93) model_ub(all_16_4, all_16_3, all_16_2) = all_29_3 % 72.81/10.78 | | | | % 72.81/10.79 | | | | GROUND_INST: instantiating (14) with all_16_4, all_16_3, all_16_2, % 72.81/10.79 | | | | all_29_3, simplifying with (35), (36), (37), (93) gives: % 72.81/10.79 | | | | (94) all_29_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & ub(all_16_4, % 72.81/10.79 | | | | all_16_3, all_16_2) = v0) % 72.81/10.79 | | | | % 72.81/10.79 | | | | BETA: splitting (94) gives: % 72.81/10.79 | | | | % 72.81/10.79 | | | | Case 1: % 72.81/10.79 | | | | | % 72.81/10.79 | | | | | (95) all_29_3 = 0 % 72.81/10.79 | | | | | % 72.81/10.79 | | | | | REDUCE: (92), (95) imply: % 72.81/10.79 | | | | | (96) $false % 72.81/10.79 | | | | | % 72.81/10.79 | | | | | CLOSE: (96) is inconsistent. % 72.81/10.79 | | | | | % 72.81/10.79 | | | | Case 2: % 72.81/10.79 | | | | | % 72.81/10.79 | | | | | (97) ? [v0: int] : ( ~ (v0 = 0) & ub(all_16_4, all_16_3, all_16_2) % 72.81/10.79 | | | | | = v0) % 72.81/10.79 | | | | | % 72.81/10.79 | | | | | DELTA: instantiating (97) with fresh symbol all_164_0 gives: % 72.81/10.79 | | | | | (98) ~ (all_164_0 = 0) & ub(all_16_4, all_16_3, all_16_2) = % 72.81/10.79 | | | | | all_164_0 % 72.81/10.79 | | | | | % 72.81/10.79 | | | | | ALPHA: (98) implies: % 72.81/10.79 | | | | | (99) ~ (all_164_0 = 0) % 72.81/10.79 | | | | | (100) ub(all_16_4, all_16_3, all_16_2) = all_164_0 % 72.81/10.79 | | | | | % 72.81/10.79 | | | | | GROUND_INST: instantiating (10) with all_16_4, all_16_3, all_16_2, % 72.81/10.79 | | | | | all_164_0, simplifying with (35), (36), (37), (100) % 72.81/10.79 | | | | | gives: % 72.81/10.79 | | | | | (101) all_164_0 = 0 | ? [v0: any] : ? [v1: any] : % 72.81/10.79 | | | | | (lesseq(all_16_3, all_16_2) = v1 & lesseq(all_16_4, all_16_2) % 72.81/10.79 | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 72.81/10.79 | | | | | % 72.81/10.79 | | | | | BETA: splitting (101) gives: % 72.81/10.79 | | | | | % 72.81/10.79 | | | | | Case 1: % 72.81/10.79 | | | | | | % 72.81/10.79 | | | | | | (102) all_164_0 = 0 % 72.81/10.79 | | | | | | % 72.81/10.79 | | | | | | REDUCE: (99), (102) imply: % 72.81/10.79 | | | | | | (103) $false % 72.81/10.79 | | | | | | % 72.81/10.79 | | | | | | CLOSE: (103) is inconsistent. % 72.81/10.79 | | | | | | % 72.81/10.79 | | | | | Case 2: % 72.81/10.79 | | | | | | % 72.81/10.79 | | | | | | (104) ? [v0: any] : ? [v1: any] : (lesseq(all_16_3, all_16_2) = % 72.81/10.79 | | | | | | v1 & lesseq(all_16_4, all_16_2) = v0 & ( ~ (v1 = 0) | ~ % 72.81/10.79 | | | | | | (v0 = 0))) % 72.81/10.79 | | | | | | % 72.81/10.79 | | | | | | DELTA: instantiating (104) with fresh symbols all_188_0, all_188_1 % 72.81/10.79 | | | | | | gives: % 72.81/10.79 | | | | | | (105) lesseq(all_16_3, all_16_2) = all_188_0 & lesseq(all_16_4, % 72.81/10.79 | | | | | | all_16_2) = all_188_1 & ( ~ (all_188_0 = 0) | ~ % 72.81/10.79 | | | | | | (all_188_1 = 0)) % 72.81/10.79 | | | | | | % 72.81/10.79 | | | | | | ALPHA: (105) implies: % 72.81/10.79 | | | | | | (106) lesseq(all_16_4, all_16_2) = all_188_1 % 72.81/10.79 | | | | | | (107) lesseq(all_16_3, all_16_2) = all_188_0 % 72.81/10.79 | | | | | | (108) ~ (all_188_0 = 0) | ~ (all_188_1 = 0) % 72.81/10.79 | | | | | | % 72.81/10.79 | | | | | | BETA: splitting (57) gives: % 72.81/10.79 | | | | | | % 72.81/10.79 | | | | | | Case 1: % 72.81/10.79 | | | | | | | % 72.81/10.79 | | | | | | | (109) all_16_2 = all_16_4 % 72.81/10.79 | | | | | | | % 72.81/10.79 | | | | | | | REDUCE: (54), (109) imply: % 72.81/10.79 | | | | | | | (110) lesseq(all_16_4, all_16_4) = 0 % 72.81/10.79 | | | | | | | % 72.81/10.79 | | | | | | | REDUCE: (107), (109) imply: % 72.81/10.79 | | | | | | | (111) lesseq(all_16_3, all_16_4) = all_188_0 % 72.81/10.79 | | | | | | | % 72.81/10.79 | | | | | | | REDUCE: (106), (109) imply: % 72.81/10.79 | | | | | | | (112) lesseq(all_16_4, all_16_4) = all_188_1 % 72.81/10.79 | | | | | | | % 72.81/10.79 | | | | | | | GROUND_INST: instantiating (28) with 0, all_188_1, all_16_4, % 72.81/10.80 | | | | | | | all_16_4, simplifying with (110), (112) gives: % 72.81/10.80 | | | | | | | (113) all_188_1 = 0 % 72.81/10.80 | | | | | | | % 72.81/10.80 | | | | | | | BETA: splitting (108) gives: % 72.81/10.80 | | | | | | | % 72.81/10.80 | | | | | | | Case 1: % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | (114) ~ (all_188_0 = 0) % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | BETA: splitting (56) gives: % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | Case 1: % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | (115) all_16_2 = all_16_3 % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | COMBINE_EQS: (109), (115) imply: % 72.81/10.80 | | | | | | | | | (116) all_16_3 = all_16_4 % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | SIMP: (116) implies: % 72.81/10.80 | | | | | | | | | (117) all_16_3 = all_16_4 % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | REDUCE: (111), (117) imply: % 72.81/10.80 | | | | | | | | | (118) lesseq(all_16_4, all_16_4) = all_188_0 % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_188_0, all_16_4, % 72.81/10.80 | | | | | | | | | all_16_4, simplifying with (110), (118) gives: % 72.81/10.80 | | | | | | | | | (119) all_188_0 = 0 % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | REDUCE: (114), (119) imply: % 72.81/10.80 | | | | | | | | | (120) $false % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | CLOSE: (120) is inconsistent. % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | Case 2: % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | (121) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_4, % 72.81/10.80 | | | | | | | | | all_16_3) = v0) % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | DELTA: instantiating (121) with fresh symbol all_214_0 gives: % 72.81/10.80 | | | | | | | | | (122) ~ (all_214_0 = 0) & lesseq(all_16_4, all_16_3) = % 72.81/10.80 | | | | | | | | | all_214_0 % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | ALPHA: (122) implies: % 72.81/10.80 | | | | | | | | | (123) ~ (all_214_0 = 0) % 72.81/10.80 | | | | | | | | | (124) lesseq(all_16_4, all_16_3) = all_214_0 % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | GROUND_INST: instantiating (1) with all_16_3, all_16_4, % 72.81/10.80 | | | | | | | | | all_214_0, simplifying with (35), (36), (124) % 72.81/10.80 | | | | | | | | | gives: % 72.81/10.80 | | | | | | | | | (125) all_214_0 = 0 | lesseq(all_16_3, all_16_4) = 0 % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | BETA: splitting (125) gives: % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | Case 1: % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | (126) lesseq(all_16_3, all_16_4) = 0 % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | GROUND_INST: instantiating (28) with all_188_0, 0, all_16_4, % 72.81/10.80 | | | | | | | | | | all_16_3, simplifying with (111), (126) gives: % 72.81/10.80 | | | | | | | | | | (127) all_188_0 = 0 % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | REDUCE: (114), (127) imply: % 72.81/10.80 | | | | | | | | | | (128) $false % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | CLOSE: (128) is inconsistent. % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | Case 2: % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | (129) all_214_0 = 0 % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | REDUCE: (123), (129) imply: % 72.81/10.80 | | | | | | | | | | (130) $false % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | CLOSE: (130) is inconsistent. % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | End of split % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | End of split % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | Case 2: % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | (131) ~ (all_188_1 = 0) % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | REDUCE: (113), (131) imply: % 72.81/10.80 | | | | | | | | (132) $false % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | CLOSE: (132) is inconsistent. % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | End of split % 72.81/10.80 | | | | | | | % 72.81/10.80 | | | | | | Case 2: % 72.81/10.80 | | | | | | | % 72.81/10.80 | | | | | | | (133) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_3, all_16_4) % 72.81/10.80 | | | | | | | = v0) % 72.81/10.80 | | | | | | | % 72.81/10.80 | | | | | | | DELTA: instantiating (133) with fresh symbol all_200_0 gives: % 72.81/10.80 | | | | | | | (134) ~ (all_200_0 = 0) & lesseq(all_16_3, all_16_4) = % 72.81/10.80 | | | | | | | all_200_0 % 72.81/10.80 | | | | | | | % 72.81/10.80 | | | | | | | ALPHA: (134) implies: % 72.81/10.80 | | | | | | | (135) ~ (all_200_0 = 0) % 72.81/10.80 | | | | | | | (136) lesseq(all_16_3, all_16_4) = all_200_0 % 72.81/10.80 | | | | | | | % 72.81/10.80 | | | | | | | BETA: splitting (56) gives: % 72.81/10.80 | | | | | | | % 72.81/10.80 | | | | | | | Case 1: % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | (137) all_16_2 = all_16_3 % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | REDUCE: (54), (137) imply: % 72.81/10.80 | | | | | | | | (138) lesseq(all_16_3, all_16_3) = 0 % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | REDUCE: (107), (137) imply: % 72.81/10.80 | | | | | | | | (139) lesseq(all_16_3, all_16_3) = all_188_0 % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | REDUCE: (106), (137) imply: % 72.81/10.80 | | | | | | | | (140) lesseq(all_16_4, all_16_3) = all_188_1 % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | GROUND_INST: instantiating (28) with 0, all_188_0, all_16_3, % 72.81/10.80 | | | | | | | | all_16_3, simplifying with (138), (139) gives: % 72.81/10.80 | | | | | | | | (141) all_188_0 = 0 % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | BETA: splitting (108) gives: % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | | Case 1: % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | (142) ~ (all_188_0 = 0) % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | REDUCE: (141), (142) imply: % 72.81/10.80 | | | | | | | | | (143) $false % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | CLOSE: (143) is inconsistent. % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | Case 2: % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | (144) ~ (all_188_1 = 0) % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | GROUND_INST: instantiating (1) with all_16_3, all_16_4, % 72.81/10.80 | | | | | | | | | all_188_1, simplifying with (35), (36), (140) % 72.81/10.80 | | | | | | | | | gives: % 72.81/10.80 | | | | | | | | | (145) all_188_1 = 0 | lesseq(all_16_3, all_16_4) = 0 % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | BETA: splitting (145) gives: % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | | Case 1: % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | (146) lesseq(all_16_3, all_16_4) = 0 % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | REF_CLOSE: (28), (135), (136), (146) are inconsistent by % 72.81/10.80 | | | | | | | | | | sub-proof #2. % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | Case 2: % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | (147) all_188_1 = 0 % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | REDUCE: (144), (147) imply: % 72.81/10.80 | | | | | | | | | | (148) $false % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | | CLOSE: (148) is inconsistent. % 72.81/10.80 | | | | | | | | | | % 72.81/10.80 | | | | | | | | | End of split % 72.81/10.80 | | | | | | | | | % 72.81/10.80 | | | | | | | | End of split % 72.81/10.80 | | | | | | | | % 72.81/10.80 | | | | | | | Case 2: % 72.81/10.80 | | | | | | | | % 72.81/10.81 | | | | | | | | (149) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_4, % 72.81/10.81 | | | | | | | | all_16_3) = v0) % 72.81/10.81 | | | | | | | | % 72.81/10.81 | | | | | | | | DELTA: instantiating (149) with fresh symbol all_208_0 gives: % 72.81/10.81 | | | | | | | | (150) ~ (all_208_0 = 0) & lesseq(all_16_4, all_16_3) = % 72.81/10.81 | | | | | | | | all_208_0 % 72.81/10.81 | | | | | | | | % 72.81/10.81 | | | | | | | | ALPHA: (150) implies: % 72.81/10.81 | | | | | | | | (151) ~ (all_208_0 = 0) % 72.81/10.81 | | | | | | | | (152) lesseq(all_16_4, all_16_3) = all_208_0 % 72.81/10.81 | | | | | | | | % 72.81/10.81 | | | | | | | | GROUND_INST: instantiating (1) with all_16_3, all_16_4, % 72.81/10.81 | | | | | | | | all_208_0, simplifying with (35), (36), (152) % 72.81/10.81 | | | | | | | | gives: % 72.81/10.81 | | | | | | | | (153) all_208_0 = 0 | lesseq(all_16_3, all_16_4) = 0 % 72.81/10.81 | | | | | | | | % 72.81/10.81 | | | | | | | | BETA: splitting (153) gives: % 72.81/10.81 | | | | | | | | % 72.81/10.81 | | | | | | | | Case 1: % 72.81/10.81 | | | | | | | | | % 72.81/10.81 | | | | | | | | | (154) lesseq(all_16_3, all_16_4) = 0 % 72.81/10.81 | | | | | | | | | % 72.81/10.81 | | | | | | | | | REF_CLOSE: (28), (135), (136), (154) are inconsistent by % 72.81/10.81 | | | | | | | | | sub-proof #2. % 72.81/10.81 | | | | | | | | | % 72.81/10.81 | | | | | | | | Case 2: % 72.81/10.81 | | | | | | | | | % 72.81/10.81 | | | | | | | | | (155) all_208_0 = 0 % 72.81/10.81 | | | | | | | | | % 72.81/10.81 | | | | | | | | | REDUCE: (151), (155) imply: % 72.81/10.81 | | | | | | | | | (156) $false % 72.81/10.81 | | | | | | | | | % 72.81/10.81 | | | | | | | | | CLOSE: (156) is inconsistent. % 72.81/10.81 | | | | | | | | | % 72.81/10.81 | | | | | | | | End of split % 72.81/10.81 | | | | | | | | % 72.81/10.81 | | | | | | | End of split % 72.81/10.81 | | | | | | | % 72.81/10.81 | | | | | | End of split % 72.81/10.81 | | | | | | % 72.81/10.81 | | | | | End of split % 72.81/10.81 | | | | | % 72.81/10.81 | | | | End of split % 72.81/10.81 | | | | % 72.81/10.81 | | | End of split % 72.81/10.81 | | | % 72.81/10.81 | | End of split % 72.81/10.81 | | % 72.81/10.81 | Case 2: % 72.81/10.81 | | % 72.81/10.81 | | (157) all_16_1 = 0 & ~ (all_16_0 = 0) % 72.81/10.81 | | % 72.81/10.81 | | ALPHA: (157) implies: % 72.81/10.81 | | (158) all_16_1 = 0 % 72.81/10.81 | | (159) ~ (all_16_0 = 0) % 72.81/10.81 | | % 72.81/10.81 | | REDUCE: (39), (158) imply: % 72.81/10.81 | | (160) minsol_model_ub(all_16_4, all_16_3, all_16_2) = 0 % 72.81/10.81 | | % 72.81/10.81 | | BETA: splitting (41) gives: % 72.81/10.81 | | % 72.81/10.81 | | Case 1: % 72.81/10.81 | | | % 72.81/10.81 | | | (161) all_16_0 = 0 % 72.81/10.81 | | | % 72.81/10.81 | | | REDUCE: (159), (161) imply: % 72.81/10.81 | | | (162) $false % 72.81/10.81 | | | % 72.81/10.81 | | | CLOSE: (162) is inconsistent. % 72.81/10.81 | | | % 72.81/10.81 | | Case 2: % 72.81/10.81 | | | % 72.81/10.81 | | | (163) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : % 72.81/10.81 | | | ($i(v1) & ((v2 = 0 & ~ (v3 = 0) & model_max(all_16_4, all_16_3, % 72.81/10.81 | | | v1) = 0 & lesseq(all_16_2, v1) = v3) | ( ~ (v0 = 0) & % 72.81/10.81 | | | model_max(all_16_4, all_16_3, all_16_2) = v0))) % 72.81/10.81 | | | % 72.81/10.81 | | | DELTA: instantiating (163) with fresh symbols all_29_0, all_29_1, % 72.81/10.81 | | | all_29_2, all_29_3 gives: % 72.81/10.81 | | | (164) $i(all_29_2) & ((all_29_1 = 0 & ~ (all_29_0 = 0) & % 72.81/10.81 | | | model_max(all_16_4, all_16_3, all_29_2) = 0 & % 72.81/10.81 | | | lesseq(all_16_2, all_29_2) = all_29_0) | ( ~ (all_29_3 = 0) & % 72.81/10.81 | | | model_max(all_16_4, all_16_3, all_16_2) = all_29_3)) % 72.81/10.81 | | | % 72.81/10.81 | | | ALPHA: (164) implies: % 72.81/10.81 | | | (165) $i(all_29_2) % 72.81/10.81 | | | (166) (all_29_1 = 0 & ~ (all_29_0 = 0) & model_max(all_16_4, all_16_3, % 72.81/10.81 | | | all_29_2) = 0 & lesseq(all_16_2, all_29_2) = all_29_0) | ( ~ % 72.81/10.81 | | | (all_29_3 = 0) & model_max(all_16_4, all_16_3, all_16_2) = % 72.81/10.81 | | | all_29_3) % 72.81/10.81 | | | % 72.81/10.81 | | | GROUND_INST: instantiating (22) with all_16_4, all_16_3, all_16_2, % 72.81/10.81 | | | simplifying with (35), (36), (37), (160) gives: % 72.81/10.81 | | | (167) model_ub(all_16_4, all_16_3, all_16_2) = 0 % 72.81/10.81 | | | % 72.81/10.81 | | | GROUND_INST: instantiating (23) with all_16_4, all_16_3, all_16_2, % 72.81/10.81 | | | all_16_2, simplifying with (35), (36), (37), (160), (167) % 72.81/10.81 | | | gives: % 72.81/10.81 | | | (168) lesseq(all_16_2, all_16_2) = 0 % 72.81/10.81 | | | % 72.81/10.81 | | | GROUND_INST: instantiating (13) with all_16_4, all_16_3, all_16_2, % 72.81/10.81 | | | simplifying with (35), (36), (37), (167) gives: % 72.81/10.81 | | | (169) ub(all_16_4, all_16_3, all_16_2) = 0 % 72.81/10.81 | | | % 72.81/10.81 | | | GROUND_INST: instantiating (21) with all_16_4, all_16_3, all_16_2, % 72.81/10.81 | | | simplifying with (35), (36), (37), (167) gives: % 72.81/10.81 | | | (170) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : % 72.81/10.81 | | | ($i(v1) & ((v2 = 0 & ~ (v3 = 0) & model_ub(all_16_4, all_16_3, % 72.81/10.81 | | | v1) = 0 & lesseq(all_16_2, v1) = v3) | (v0 = 0 & % 72.81/10.81 | | | minsol_model_ub(all_16_4, all_16_3, all_16_2) = 0))) % 72.81/10.81 | | | % 72.81/10.81 | | | DELTA: instantiating (170) with fresh symbols all_44_0, all_44_1, % 72.81/10.81 | | | all_44_2, all_44_3 gives: % 72.81/10.81 | | | (171) $i(all_44_2) & ((all_44_1 = 0 & ~ (all_44_0 = 0) & % 72.81/10.81 | | | model_ub(all_16_4, all_16_3, all_44_2) = 0 & lesseq(all_16_2, % 72.81/10.81 | | | all_44_2) = all_44_0) | (all_44_3 = 0 & % 72.81/10.81 | | | minsol_model_ub(all_16_4, all_16_3, all_16_2) = 0)) % 72.81/10.81 | | | % 72.81/10.81 | | | ALPHA: (171) implies: % 72.81/10.81 | | | (172) $i(all_44_2) % 72.81/10.81 | | | (173) (all_44_1 = 0 & ~ (all_44_0 = 0) & model_ub(all_16_4, all_16_3, % 72.81/10.81 | | | all_44_2) = 0 & lesseq(all_16_2, all_44_2) = all_44_0) | % 72.81/10.81 | | | (all_44_3 = 0 & minsol_model_ub(all_16_4, all_16_3, all_16_2) = % 72.81/10.81 | | | 0) % 72.81/10.81 | | | % 72.81/10.81 | | | GROUND_INST: instantiating (2) with all_16_2, all_16_2, simplifying with % 72.81/10.81 | | | (37), (168) gives: % 72.81/10.81 | | | (174) ? [v0: $i] : ? [v1: $i] : (summation(all_16_2) = v1 & % 72.81/10.81 | | | summation(all_16_2) = v0 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.82 | | | $i(v0)) % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (9) with all_16_4, all_16_3, all_16_2, % 72.81/10.82 | | | simplifying with (35), (36), (37), (169) gives: % 72.81/10.82 | | | (175) lesseq(all_16_3, all_16_2) = 0 & lesseq(all_16_4, all_16_2) = 0 % 72.81/10.82 | | | % 72.81/10.82 | | | ALPHA: (175) implies: % 72.81/10.82 | | | (176) lesseq(all_16_4, all_16_2) = 0 % 72.81/10.82 | | | (177) lesseq(all_16_3, all_16_2) = 0 % 72.81/10.82 | | | % 72.81/10.82 | | | DELTA: instantiating (174) with fresh symbols all_56_0, all_56_1 gives: % 72.81/10.82 | | | (178) summation(all_16_2) = all_56_0 & summation(all_16_2) = all_56_1 & % 72.81/10.82 | | | lesseq(all_56_1, all_56_0) = 0 & $i(all_56_0) & $i(all_56_1) % 72.81/10.82 | | | % 72.81/10.82 | | | ALPHA: (178) implies: % 72.81/10.82 | | | (179) $i(all_56_0) % 72.81/10.82 | | | (180) lesseq(all_56_1, all_56_0) = 0 % 72.81/10.82 | | | (181) summation(all_16_2) = all_56_1 % 72.81/10.82 | | | (182) summation(all_16_2) = all_56_0 % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (27) with all_56_1, all_56_0, all_16_2, % 72.81/10.82 | | | simplifying with (181), (182) gives: % 72.81/10.82 | | | (183) all_56_0 = all_56_1 % 72.81/10.82 | | | % 72.81/10.82 | | | REDUCE: (180), (183) imply: % 72.81/10.82 | | | (184) lesseq(all_56_1, all_56_1) = 0 % 72.81/10.82 | | | % 72.81/10.82 | | | REDUCE: (179), (183) imply: % 72.81/10.82 | | | (185) $i(all_56_1) % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (5) with all_16_2, all_16_4, simplifying with % 72.81/10.82 | | | (35), (37), (176) gives: % 72.81/10.82 | | | (186) max(all_16_2, all_16_4) = all_16_2 % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (7) with all_16_4, all_16_2, simplifying with % 72.81/10.82 | | | (35), (37), (176) gives: % 72.81/10.82 | | | (187) max(all_16_4, all_16_2) = all_16_2 % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (2) with all_16_4, all_16_2, simplifying with % 72.81/10.82 | | | (35), (37), (176) gives: % 72.81/10.82 | | | (188) ? [v0: $i] : ? [v1: $i] : (summation(all_16_2) = v1 & % 72.81/10.82 | | | summation(all_16_4) = v0 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.82 | | | $i(v0)) % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (5) with all_16_2, all_16_3, simplifying with % 72.81/10.82 | | | (36), (37), (177) gives: % 72.81/10.82 | | | (189) max(all_16_2, all_16_3) = all_16_2 % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (2) with all_16_3, all_16_2, simplifying with % 72.81/10.82 | | | (36), (37), (177) gives: % 72.81/10.82 | | | (190) ? [v0: $i] : ? [v1: $i] : (summation(all_16_2) = v1 & % 72.81/10.82 | | | summation(all_16_3) = v0 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.82 | | | $i(v0)) % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (2) with all_56_1, all_56_1, simplifying with % 72.81/10.82 | | | (184), (185) gives: % 72.81/10.82 | | | (191) ? [v0: $i] : ? [v1: $i] : (summation(all_56_1) = v1 & % 72.81/10.82 | | | summation(all_56_1) = v0 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.82 | | | $i(v0)) % 72.81/10.82 | | | % 72.81/10.82 | | | DELTA: instantiating (188) with fresh symbols all_68_0, all_68_1 gives: % 72.81/10.82 | | | (192) summation(all_16_2) = all_68_0 & summation(all_16_4) = all_68_1 & % 72.81/10.82 | | | lesseq(all_68_1, all_68_0) = 0 & $i(all_68_0) & $i(all_68_1) % 72.81/10.82 | | | % 72.81/10.82 | | | ALPHA: (192) implies: % 72.81/10.82 | | | (193) $i(all_68_1) % 72.81/10.82 | | | (194) $i(all_68_0) % 72.81/10.82 | | | (195) lesseq(all_68_1, all_68_0) = 0 % 72.81/10.82 | | | (196) summation(all_16_4) = all_68_1 % 72.81/10.82 | | | (197) summation(all_16_2) = all_68_0 % 72.81/10.82 | | | % 72.81/10.82 | | | DELTA: instantiating (191) with fresh symbols all_70_0, all_70_1 gives: % 72.81/10.82 | | | (198) summation(all_56_1) = all_70_0 & summation(all_56_1) = all_70_1 & % 72.81/10.82 | | | lesseq(all_70_1, all_70_0) = 0 & $i(all_70_0) & $i(all_70_1) % 72.81/10.82 | | | % 72.81/10.82 | | | ALPHA: (198) implies: % 72.81/10.82 | | | (199) $i(all_70_0) % 72.81/10.82 | | | (200) lesseq(all_70_1, all_70_0) = 0 % 72.81/10.82 | | | (201) summation(all_56_1) = all_70_1 % 72.81/10.82 | | | (202) summation(all_56_1) = all_70_0 % 72.81/10.82 | | | % 72.81/10.82 | | | DELTA: instantiating (190) with fresh symbols all_72_0, all_72_1 gives: % 72.81/10.82 | | | (203) summation(all_16_2) = all_72_0 & summation(all_16_3) = all_72_1 & % 72.81/10.82 | | | lesseq(all_72_1, all_72_0) = 0 & $i(all_72_0) & $i(all_72_1) % 72.81/10.82 | | | % 72.81/10.82 | | | ALPHA: (203) implies: % 72.81/10.82 | | | (204) $i(all_72_1) % 72.81/10.82 | | | (205) lesseq(all_72_1, all_72_0) = 0 % 72.81/10.82 | | | (206) summation(all_16_3) = all_72_1 % 72.81/10.82 | | | (207) summation(all_16_2) = all_72_0 % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (27) with all_56_1, all_72_0, all_16_2, % 72.81/10.82 | | | simplifying with (181), (207) gives: % 72.81/10.82 | | | (208) all_72_0 = all_56_1 % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (27) with all_68_0, all_72_0, all_16_2, % 72.81/10.82 | | | simplifying with (197), (207) gives: % 72.81/10.82 | | | (209) all_72_0 = all_68_0 % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (27) with all_70_1, all_70_0, all_56_1, % 72.81/10.82 | | | simplifying with (201), (202) gives: % 72.81/10.82 | | | (210) all_70_0 = all_70_1 % 72.81/10.82 | | | % 72.81/10.82 | | | COMBINE_EQS: (208), (209) imply: % 72.81/10.82 | | | (211) all_68_0 = all_56_1 % 72.81/10.82 | | | % 72.81/10.82 | | | REDUCE: (205), (208) imply: % 72.81/10.82 | | | (212) lesseq(all_72_1, all_56_1) = 0 % 72.81/10.82 | | | % 72.81/10.82 | | | REDUCE: (200), (210) imply: % 72.81/10.82 | | | (213) lesseq(all_70_1, all_70_1) = 0 % 72.81/10.82 | | | % 72.81/10.82 | | | REDUCE: (195), (211) imply: % 72.81/10.82 | | | (214) lesseq(all_68_1, all_56_1) = 0 % 72.81/10.82 | | | % 72.81/10.82 | | | REDUCE: (199), (210) imply: % 72.81/10.82 | | | (215) $i(all_70_1) % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (7) with all_68_1, all_56_1, simplifying with % 72.81/10.82 | | | (185), (193), (214) gives: % 72.81/10.82 | | | (216) max(all_68_1, all_56_1) = all_56_1 % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (2) with all_68_1, all_56_1, simplifying with % 72.81/10.82 | | | (185), (193), (214) gives: % 72.81/10.82 | | | (217) ? [v0: $i] : ? [v1: $i] : (summation(all_68_1) = v0 & % 72.81/10.82 | | | summation(all_56_1) = v1 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.82 | | | $i(v0)) % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (2) with all_70_1, all_70_1, simplifying with % 72.81/10.82 | | | (213), (215) gives: % 72.81/10.82 | | | (218) ? [v0: $i] : ? [v1: $i] : (summation(all_70_1) = v1 & % 72.81/10.82 | | | summation(all_70_1) = v0 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.82 | | | $i(v0)) % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (7) with all_72_1, all_56_1, simplifying with % 72.81/10.82 | | | (185), (204), (212) gives: % 72.81/10.82 | | | (219) max(all_72_1, all_56_1) = all_56_1 % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (2) with all_72_1, all_56_1, simplifying with % 72.81/10.82 | | | (185), (204), (212) gives: % 72.81/10.82 | | | (220) ? [v0: $i] : ? [v1: $i] : (summation(all_72_1) = v0 & % 72.81/10.82 | | | summation(all_56_1) = v1 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.82 | | | $i(v0)) % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (8) with all_16_2, all_16_4, all_16_2, % 72.81/10.82 | | | simplifying with (35), (37), (186) gives: % 72.81/10.82 | | | (221) all_16_2 = all_16_4 | ? [v0: int] : ( ~ (v0 = 0) & % 72.81/10.82 | | | lesseq(all_16_2, all_16_4) = v0) % 72.81/10.82 | | | % 72.81/10.82 | | | GROUND_INST: instantiating (8) with all_16_2, all_16_3, all_16_2, % 72.81/10.82 | | | simplifying with (36), (37), (189) gives: % 72.81/10.82 | | | (222) all_16_2 = all_16_3 | ? [v0: int] : ( ~ (v0 = 0) & % 72.81/10.82 | | | lesseq(all_16_2, all_16_3) = v0) % 72.81/10.82 | | | % 72.81/10.83 | | | DELTA: instantiating (217) with fresh symbols all_84_0, all_84_1 gives: % 72.81/10.83 | | | (223) summation(all_68_1) = all_84_1 & summation(all_56_1) = all_84_0 & % 72.81/10.83 | | | lesseq(all_84_1, all_84_0) = 0 & $i(all_84_0) & $i(all_84_1) % 72.81/10.83 | | | % 72.81/10.83 | | | ALPHA: (223) implies: % 72.81/10.83 | | | (224) $i(all_84_1) % 72.81/10.83 | | | (225) $i(all_84_0) % 72.81/10.83 | | | (226) lesseq(all_84_1, all_84_0) = 0 % 72.81/10.83 | | | (227) summation(all_56_1) = all_84_0 % 72.81/10.83 | | | % 72.81/10.83 | | | DELTA: instantiating (220) with fresh symbols all_86_0, all_86_1 gives: % 72.81/10.83 | | | (228) summation(all_72_1) = all_86_1 & summation(all_56_1) = all_86_0 & % 72.81/10.83 | | | lesseq(all_86_1, all_86_0) = 0 & $i(all_86_0) & $i(all_86_1) % 72.81/10.83 | | | % 72.81/10.83 | | | ALPHA: (228) implies: % 72.81/10.83 | | | (229) $i(all_86_1) % 72.81/10.83 | | | (230) lesseq(all_86_1, all_86_0) = 0 % 72.81/10.83 | | | (231) summation(all_56_1) = all_86_0 % 72.81/10.83 | | | (232) summation(all_72_1) = all_86_1 % 72.81/10.83 | | | % 72.81/10.83 | | | DELTA: instantiating (218) with fresh symbols all_88_0, all_88_1 gives: % 72.81/10.83 | | | (233) summation(all_70_1) = all_88_0 & summation(all_70_1) = all_88_1 & % 72.81/10.83 | | | lesseq(all_88_1, all_88_0) = 0 & $i(all_88_0) & $i(all_88_1) % 72.81/10.83 | | | % 72.81/10.83 | | | ALPHA: (233) implies: % 72.81/10.83 | | | (234) $i(all_88_0) % 72.81/10.83 | | | (235) lesseq(all_88_1, all_88_0) = 0 % 72.81/10.83 | | | (236) summation(all_70_1) = all_88_1 % 72.81/10.83 | | | (237) summation(all_70_1) = all_88_0 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (27) with all_70_1, all_86_0, all_56_1, % 72.81/10.83 | | | simplifying with (201), (231) gives: % 72.81/10.83 | | | (238) all_86_0 = all_70_1 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (27) with all_84_0, all_86_0, all_56_1, % 72.81/10.83 | | | simplifying with (227), (231) gives: % 72.81/10.83 | | | (239) all_86_0 = all_84_0 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (27) with all_88_1, all_88_0, all_70_1, % 72.81/10.83 | | | simplifying with (236), (237) gives: % 72.81/10.83 | | | (240) all_88_0 = all_88_1 % 72.81/10.83 | | | % 72.81/10.83 | | | COMBINE_EQS: (238), (239) imply: % 72.81/10.83 | | | (241) all_84_0 = all_70_1 % 72.81/10.83 | | | % 72.81/10.83 | | | REDUCE: (235), (240) imply: % 72.81/10.83 | | | (242) lesseq(all_88_1, all_88_1) = 0 % 72.81/10.83 | | | % 72.81/10.83 | | | REDUCE: (230), (238) imply: % 72.81/10.83 | | | (243) lesseq(all_86_1, all_70_1) = 0 % 72.81/10.83 | | | % 72.81/10.83 | | | REDUCE: (226), (241) imply: % 72.81/10.83 | | | (244) lesseq(all_84_1, all_70_1) = 0 % 72.81/10.83 | | | % 72.81/10.83 | | | REDUCE: (234), (240) imply: % 72.81/10.83 | | | (245) $i(all_88_1) % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (2) with all_84_1, all_70_1, simplifying with % 72.81/10.83 | | | (215), (224), (244) gives: % 72.81/10.83 | | | (246) ? [v0: $i] : ? [v1: $i] : (summation(all_84_1) = v0 & % 72.81/10.83 | | | summation(all_70_1) = v1 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.83 | | | $i(v0)) % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (2) with all_86_1, all_70_1, simplifying with % 72.81/10.83 | | | (215), (229), (243) gives: % 72.81/10.83 | | | (247) ? [v0: $i] : ? [v1: $i] : (summation(all_86_1) = v0 & % 72.81/10.83 | | | summation(all_70_1) = v1 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.83 | | | $i(v0)) % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (2) with all_88_1, all_88_1, simplifying with % 72.81/10.83 | | | (242), (245) gives: % 72.81/10.83 | | | (248) ? [v0: $i] : ? [v1: $i] : (summation(all_88_1) = v1 & % 72.81/10.83 | | | summation(all_88_1) = v0 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.83 | | | $i(v0)) % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (6) with all_68_1, all_56_1, all_56_1, % 72.81/10.83 | | | simplifying with (185), (193), (216) gives: % 72.81/10.83 | | | (249) all_68_1 = all_56_1 | ? [v0: int] : ( ~ (v0 = 0) & % 72.81/10.83 | | | lesseq(all_56_1, all_68_1) = v0) % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (6) with all_72_1, all_56_1, all_56_1, % 72.81/10.83 | | | simplifying with (185), (204), (219) gives: % 72.81/10.83 | | | (250) all_72_1 = all_56_1 | ? [v0: int] : ( ~ (v0 = 0) & % 72.81/10.83 | | | lesseq(all_56_1, all_72_1) = v0) % 72.81/10.83 | | | % 72.81/10.83 | | | DELTA: instantiating (248) with fresh symbols all_100_0, all_100_1 gives: % 72.81/10.83 | | | (251) summation(all_88_1) = all_100_0 & summation(all_88_1) = all_100_1 % 72.81/10.83 | | | & lesseq(all_100_1, all_100_0) = 0 & $i(all_100_0) & % 72.81/10.83 | | | $i(all_100_1) % 72.81/10.83 | | | % 72.81/10.83 | | | ALPHA: (251) implies: % 72.81/10.83 | | | (252) summation(all_88_1) = all_100_1 % 72.81/10.83 | | | (253) summation(all_88_1) = all_100_0 % 72.81/10.83 | | | % 72.81/10.83 | | | DELTA: instantiating (247) with fresh symbols all_102_0, all_102_1 gives: % 72.81/10.83 | | | (254) summation(all_86_1) = all_102_1 & summation(all_70_1) = all_102_0 % 72.81/10.83 | | | & lesseq(all_102_1, all_102_0) = 0 & $i(all_102_0) & % 72.81/10.83 | | | $i(all_102_1) % 72.81/10.83 | | | % 72.81/10.83 | | | ALPHA: (254) implies: % 72.81/10.83 | | | (255) $i(all_102_1) % 72.81/10.83 | | | (256) $i(all_102_0) % 72.81/10.83 | | | (257) lesseq(all_102_1, all_102_0) = 0 % 72.81/10.83 | | | (258) summation(all_70_1) = all_102_0 % 72.81/10.83 | | | (259) summation(all_86_1) = all_102_1 % 72.81/10.83 | | | % 72.81/10.83 | | | DELTA: instantiating (246) with fresh symbols all_104_0, all_104_1 gives: % 72.81/10.83 | | | (260) summation(all_84_1) = all_104_1 & summation(all_70_1) = all_104_0 % 72.81/10.83 | | | & lesseq(all_104_1, all_104_0) = 0 & $i(all_104_0) & % 72.81/10.83 | | | $i(all_104_1) % 72.81/10.83 | | | % 72.81/10.83 | | | ALPHA: (260) implies: % 72.81/10.83 | | | (261) $i(all_104_1) % 72.81/10.83 | | | (262) lesseq(all_104_1, all_104_0) = 0 % 72.81/10.83 | | | (263) summation(all_70_1) = all_104_0 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (27) with all_88_1, all_104_0, all_70_1, % 72.81/10.83 | | | simplifying with (236), (263) gives: % 72.81/10.83 | | | (264) all_104_0 = all_88_1 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (27) with all_102_0, all_104_0, all_70_1, % 72.81/10.83 | | | simplifying with (258), (263) gives: % 72.81/10.83 | | | (265) all_104_0 = all_102_0 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (27) with all_100_1, all_100_0, all_88_1, % 72.81/10.83 | | | simplifying with (252), (253) gives: % 72.81/10.83 | | | (266) all_100_0 = all_100_1 % 72.81/10.83 | | | % 72.81/10.83 | | | COMBINE_EQS: (264), (265) imply: % 72.81/10.83 | | | (267) all_102_0 = all_88_1 % 72.81/10.83 | | | % 72.81/10.83 | | | REDUCE: (262), (264) imply: % 72.81/10.83 | | | (268) lesseq(all_104_1, all_88_1) = 0 % 72.81/10.83 | | | % 72.81/10.83 | | | REDUCE: (257), (267) imply: % 72.81/10.83 | | | (269) lesseq(all_102_1, all_88_1) = 0 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (7) with all_102_1, all_88_1, simplifying with % 72.81/10.83 | | | (245), (255), (269) gives: % 72.81/10.83 | | | (270) max(all_102_1, all_88_1) = all_88_1 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (2) with all_102_1, all_88_1, simplifying with % 72.81/10.83 | | | (245), (255), (269) gives: % 72.81/10.83 | | | (271) ? [v0: $i] : ? [v1: $i] : (summation(all_102_1) = v0 & % 72.81/10.83 | | | summation(all_88_1) = v1 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.83 | | | $i(v0)) % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (2) with all_104_1, all_88_1, simplifying with % 72.81/10.83 | | | (245), (261), (268) gives: % 72.81/10.83 | | | (272) ? [v0: $i] : ? [v1: $i] : (summation(all_104_1) = v0 & % 72.81/10.83 | | | summation(all_88_1) = v1 & lesseq(v0, v1) = 0 & $i(v1) & % 72.81/10.83 | | | $i(v0)) % 72.81/10.83 | | | % 72.81/10.83 | | | DELTA: instantiating (272) with fresh symbols all_116_0, all_116_1 gives: % 72.81/10.83 | | | (273) summation(all_104_1) = all_116_1 & summation(all_88_1) = % 72.81/10.83 | | | all_116_0 & lesseq(all_116_1, all_116_0) = 0 & $i(all_116_0) & % 72.81/10.83 | | | $i(all_116_1) % 72.81/10.83 | | | % 72.81/10.83 | | | ALPHA: (273) implies: % 72.81/10.83 | | | (274) $i(all_116_0) % 72.81/10.83 | | | (275) summation(all_88_1) = all_116_0 % 72.81/10.83 | | | % 72.81/10.83 | | | DELTA: instantiating (271) with fresh symbols all_118_0, all_118_1 gives: % 72.81/10.83 | | | (276) summation(all_102_1) = all_118_1 & summation(all_88_1) = % 72.81/10.83 | | | all_118_0 & lesseq(all_118_1, all_118_0) = 0 & $i(all_118_0) & % 72.81/10.83 | | | $i(all_118_1) % 72.81/10.83 | | | % 72.81/10.83 | | | ALPHA: (276) implies: % 72.81/10.83 | | | (277) $i(all_118_1) % 72.81/10.83 | | | (278) lesseq(all_118_1, all_118_0) = 0 % 72.81/10.83 | | | (279) summation(all_88_1) = all_118_0 % 72.81/10.83 | | | (280) summation(all_102_1) = all_118_1 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (27) with all_100_1, all_118_0, all_88_1, % 72.81/10.83 | | | simplifying with (252), (279) gives: % 72.81/10.83 | | | (281) all_118_0 = all_100_1 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (27) with all_116_0, all_118_0, all_88_1, % 72.81/10.83 | | | simplifying with (275), (279) gives: % 72.81/10.83 | | | (282) all_118_0 = all_116_0 % 72.81/10.83 | | | % 72.81/10.83 | | | COMBINE_EQS: (281), (282) imply: % 72.81/10.83 | | | (283) all_116_0 = all_100_1 % 72.81/10.83 | | | % 72.81/10.83 | | | REDUCE: (278), (281) imply: % 72.81/10.83 | | | (284) lesseq(all_118_1, all_100_1) = 0 % 72.81/10.83 | | | % 72.81/10.83 | | | REDUCE: (274), (283) imply: % 72.81/10.83 | | | (285) $i(all_100_1) % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (7) with all_118_1, all_100_1, simplifying with % 72.81/10.83 | | | (277), (284), (285) gives: % 72.81/10.83 | | | (286) max(all_118_1, all_100_1) = all_100_1 % 72.81/10.83 | | | % 72.81/10.83 | | | GROUND_INST: instantiating (6) with all_102_1, all_88_1, all_88_1, % 72.81/10.83 | | | simplifying with (245), (255), (270) gives: % 72.81/10.83 | | | (287) all_102_1 = all_88_1 | ? [v0: int] : ( ~ (v0 = 0) & % 72.81/10.83 | | | lesseq(all_88_1, all_102_1) = v0) % 72.81/10.83 | | | % 72.81/10.84 | | | GROUND_INST: instantiating (6) with all_118_1, all_100_1, all_100_1, % 72.81/10.84 | | | simplifying with (277), (285), (286) gives: % 72.81/10.84 | | | (288) all_118_1 = all_100_1 | ? [v0: int] : ( ~ (v0 = 0) & % 72.81/10.84 | | | lesseq(all_100_1, all_118_1) = v0) % 72.81/10.84 | | | % 72.81/10.84 | | | BETA: splitting (166) gives: % 72.81/10.84 | | | % 72.81/10.84 | | | Case 1: % 72.81/10.84 | | | | % 72.81/10.84 | | | | (289) all_29_1 = 0 & ~ (all_29_0 = 0) & model_max(all_16_4, % 72.81/10.84 | | | | all_16_3, all_29_2) = 0 & lesseq(all_16_2, all_29_2) = % 72.81/10.84 | | | | all_29_0 % 72.81/10.84 | | | | % 72.81/10.84 | | | | ALPHA: (289) implies: % 72.81/10.84 | | | | (290) ~ (all_29_0 = 0) % 72.81/10.84 | | | | (291) lesseq(all_16_2, all_29_2) = all_29_0 % 72.81/10.84 | | | | (292) model_max(all_16_4, all_16_3, all_29_2) = 0 % 72.81/10.84 | | | | % 72.81/10.84 | | | | GROUND_INST: instantiating (26) with all_16_4, all_16_3, all_16_2, 0, % 72.81/10.84 | | | | all_29_2, all_29_0, simplifying with (35), (36), (37), % 72.81/10.84 | | | | (165), (167), (291) gives: % 72.81/10.84 | | | | (293) all_29_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & % 72.81/10.84 | | | | minsol_model_ub(all_16_4, all_16_3, all_16_2) = v0) | ( ~ % 72.81/10.84 | | | | (v0 = 0) & model_ub(all_16_4, all_16_3, all_29_2) = v0)) % 72.81/10.84 | | | | % 72.81/10.84 | | | | GROUND_INST: instantiating (25) with all_16_4, all_16_3, all_16_2, % 72.81/10.84 | | | | all_29_2, all_29_0, simplifying with (35), (36), (37), % 72.81/10.84 | | | | (160), (165), (291) gives: % 72.81/10.84 | | | | (294) all_29_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & model_ub(all_16_4, % 72.81/10.84 | | | | all_16_3, all_29_2) = v0) % 72.81/10.84 | | | | % 72.81/10.84 | | | | GROUND_INST: instantiating (1) with all_29_2, all_16_2, all_29_0, % 72.81/10.84 | | | | simplifying with (37), (165), (291) gives: % 72.81/10.84 | | | | (295) all_29_0 = 0 | lesseq(all_29_2, all_16_2) = 0 % 72.81/10.84 | | | | % 72.81/10.84 | | | | GROUND_INST: instantiating (3) with all_16_2, all_29_2, all_29_0, % 72.81/10.84 | | | | simplifying with (37), (165), (291) gives: % 72.81/10.84 | | | | (296) all_29_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ % 72.81/10.84 | | | | (v2 = 0) & summation(all_29_2) = v1 & summation(all_16_2) = % 72.81/10.84 | | | | v0 & lesseq(v0, v1) = v2 & $i(v1) & $i(v0)) % 72.81/10.84 | | | | % 72.81/10.84 | | | | GROUND_INST: instantiating (19) with all_16_4, all_16_3, all_29_2, 0, % 72.81/10.84 | | | | all_29_2, simplifying with (35), (36), (165), (292) gives: % 72.81/10.84 | | | | (297) ? [v0: int] : ((v0 = 0 & lesseq(all_29_2, all_29_2) = 0) | ( ~ % 72.81/10.84 | | | | (v0 = 0) & minsol_model_max(all_16_4, all_16_3, all_29_2) = % 72.81/10.84 | | | | v0)) % 72.81/10.84 | | | | % 72.81/10.84 | | | | GROUND_INST: instantiating (11) with all_16_4, all_16_3, all_29_2, % 72.81/10.84 | | | | simplifying with (35), (36), (165), (292) gives: % 72.81/10.84 | | | | (298) max(all_16_4, all_16_3) = all_29_2 % 72.81/10.84 | | | | % 72.81/10.84 | | | | GROUND_INST: instantiating (15) with all_16_4, all_16_3, all_29_2, % 72.81/10.84 | | | | simplifying with (35), (36), (165), (292) gives: % 72.81/10.84 | | | | (299) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : % 72.81/10.84 | | | | ($i(v1) & ((v2 = 0 & ~ (v3 = 0) & model_max(all_16_4, % 72.81/10.84 | | | | all_16_3, v1) = 0 & lesseq(all_29_2, v1) = v3) | (v0 = % 72.81/10.84 | | | | 0 & minsol_model_max(all_16_4, all_16_3, all_29_2) = 0))) % 72.81/10.84 | | | | % 72.81/10.84 | | | | DELTA: instantiating (297) with fresh symbol all_170_0 gives: % 72.81/10.84 | | | | (300) (all_170_0 = 0 & lesseq(all_29_2, all_29_2) = 0) | ( ~ % 72.81/10.84 | | | | (all_170_0 = 0) & minsol_model_max(all_16_4, all_16_3, % 72.81/10.84 | | | | all_29_2) = all_170_0) % 72.81/10.84 | | | | % 72.81/10.84 | | | | DELTA: instantiating (299) with fresh symbols all_177_0, all_177_1, % 72.81/10.84 | | | | all_177_2, all_177_3 gives: % 72.81/10.84 | | | | (301) $i(all_177_2) & ((all_177_1 = 0 & ~ (all_177_0 = 0) & % 72.81/10.84 | | | | model_max(all_16_4, all_16_3, all_177_2) = 0 & % 72.81/10.84 | | | | lesseq(all_29_2, all_177_2) = all_177_0) | (all_177_3 = 0 & % 72.81/10.84 | | | | minsol_model_max(all_16_4, all_16_3, all_29_2) = 0)) % 72.81/10.84 | | | | % 72.81/10.84 | | | | ALPHA: (301) implies: % 72.81/10.84 | | | | (302) $i(all_177_2) % 72.81/10.84 | | | | (303) (all_177_1 = 0 & ~ (all_177_0 = 0) & model_max(all_16_4, % 72.81/10.84 | | | | all_16_3, all_177_2) = 0 & lesseq(all_29_2, all_177_2) = % 72.81/10.84 | | | | all_177_0) | (all_177_3 = 0 & minsol_model_max(all_16_4, % 72.81/10.84 | | | | all_16_3, all_29_2) = 0) % 72.81/10.84 | | | | % 72.81/10.84 | | | | BETA: splitting (295) gives: % 72.81/10.84 | | | | % 72.81/10.84 | | | | Case 1: % 72.81/10.84 | | | | | % 72.81/10.84 | | | | | (304) lesseq(all_29_2, all_16_2) = 0 % 72.81/10.84 | | | | | % 72.81/10.84 | | | | | BETA: splitting (296) gives: % 72.81/10.84 | | | | | % 72.81/10.84 | | | | | Case 1: % 72.81/10.84 | | | | | | % 72.81/10.84 | | | | | | (305) all_29_0 = 0 % 72.81/10.84 | | | | | | % 72.81/10.84 | | | | | | REDUCE: (290), (305) imply: % 72.81/10.84 | | | | | | (306) $false % 72.81/10.84 | | | | | | % 72.81/10.84 | | | | | | CLOSE: (306) is inconsistent. % 72.81/10.84 | | | | | | % 72.81/10.84 | | | | | Case 2: % 72.81/10.84 | | | | | | % 72.81/10.84 | | | | | | (307) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 72.81/10.84 | | | | | | summation(all_29_2) = v1 & summation(all_16_2) = v0 & % 72.81/10.84 | | | | | | lesseq(v0, v1) = v2 & $i(v1) & $i(v0)) % 72.81/10.84 | | | | | | % 72.81/10.84 | | | | | | DELTA: instantiating (307) with fresh symbols all_186_0, all_186_1, % 72.81/10.84 | | | | | | all_186_2 gives: % 72.81/10.84 | | | | | | (308) ~ (all_186_0 = 0) & summation(all_29_2) = all_186_1 & % 72.81/10.84 | | | | | | summation(all_16_2) = all_186_2 & lesseq(all_186_2, % 72.81/10.84 | | | | | | all_186_1) = all_186_0 & $i(all_186_1) & $i(all_186_2) % 72.81/10.84 | | | | | | % 72.81/10.84 | | | | | | ALPHA: (308) implies: % 72.81/10.84 | | | | | | (309) summation(all_16_2) = all_186_2 % 72.81/10.84 | | | | | | % 72.81/10.84 | | | | | | BETA: splitting (294) gives: % 72.81/10.84 | | | | | | % 72.81/10.84 | | | | | | Case 1: % 72.81/10.84 | | | | | | | % 72.81/10.84 | | | | | | | (310) all_29_0 = 0 % 72.81/10.84 | | | | | | | % 72.81/10.84 | | | | | | | REDUCE: (290), (310) imply: % 72.81/10.84 | | | | | | | (311) $false % 72.81/10.84 | | | | | | | % 72.81/10.84 | | | | | | | CLOSE: (311) is inconsistent. % 72.81/10.84 | | | | | | | % 72.81/10.84 | | | | | | Case 2: % 72.81/10.84 | | | | | | | % 72.81/10.84 | | | | | | | (312) ? [v0: int] : ( ~ (v0 = 0) & model_ub(all_16_4, % 72.81/10.84 | | | | | | | all_16_3, all_29_2) = v0) % 72.81/10.84 | | | | | | | % 72.81/10.84 | | | | | | | DELTA: instantiating (312) with fresh symbol all_191_0 gives: % 72.81/10.84 | | | | | | | (313) ~ (all_191_0 = 0) & model_ub(all_16_4, all_16_3, % 72.81/10.84 | | | | | | | all_29_2) = all_191_0 % 72.81/10.84 | | | | | | | % 72.81/10.84 | | | | | | | ALPHA: (313) implies: % 72.81/10.84 | | | | | | | (314) model_ub(all_16_4, all_16_3, all_29_2) = all_191_0 % 72.81/10.84 | | | | | | | % 72.81/10.84 | | | | | | | BETA: splitting (293) gives: % 72.81/10.84 | | | | | | | % 72.81/10.84 | | | | | | | Case 1: % 72.81/10.84 | | | | | | | | % 72.81/10.84 | | | | | | | | (315) all_29_0 = 0 % 72.81/10.84 | | | | | | | | % 72.81/10.84 | | | | | | | | REDUCE: (290), (315) imply: % 72.81/10.84 | | | | | | | | (316) $false % 72.81/10.84 | | | | | | | | % 72.81/10.84 | | | | | | | | CLOSE: (316) is inconsistent. % 72.81/10.84 | | | | | | | | % 72.81/10.84 | | | | | | | Case 2: % 72.81/10.84 | | | | | | | | % 72.81/10.84 | | | | | | | | (317) ? [v0: int] : (( ~ (v0 = 0) & % 72.81/10.84 | | | | | | | | minsol_model_ub(all_16_4, all_16_3, all_16_2) = v0) % 72.81/10.84 | | | | | | | | | ( ~ (v0 = 0) & model_ub(all_16_4, all_16_3, % 72.81/10.84 | | | | | | | | all_29_2) = v0)) % 72.81/10.84 | | | | | | | | % 72.81/10.84 | | | | | | | | DELTA: instantiating (317) with fresh symbol all_196_0 gives: % 72.81/10.84 | | | | | | | | (318) ( ~ (all_196_0 = 0) & minsol_model_ub(all_16_4, % 72.81/10.84 | | | | | | | | all_16_3, all_16_2) = all_196_0) | ( ~ (all_196_0 = % 72.81/10.84 | | | | | | | | 0) & model_ub(all_16_4, all_16_3, all_29_2) = % 72.81/10.84 | | | | | | | | all_196_0) % 72.81/10.84 | | | | | | | | % 72.81/10.84 | | | | | | | | BETA: splitting (318) gives: % 72.81/10.84 | | | | | | | | % 72.81/10.84 | | | | | | | | Case 1: % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | (319) ~ (all_196_0 = 0) & minsol_model_ub(all_16_4, % 72.81/10.84 | | | | | | | | | all_16_3, all_16_2) = all_196_0 % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | ALPHA: (319) implies: % 72.81/10.84 | | | | | | | | | (320) ~ (all_196_0 = 0) % 72.81/10.84 | | | | | | | | | (321) minsol_model_ub(all_16_4, all_16_3, all_16_2) = % 72.81/10.84 | | | | | | | | | all_196_0 % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_196_0, all_16_2, % 72.81/10.84 | | | | | | | | | all_16_3, all_16_4, simplifying with (160), (321) % 72.81/10.84 | | | | | | | | | gives: % 72.81/10.84 | | | | | | | | | (322) all_196_0 = 0 % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | REDUCE: (320), (322) imply: % 72.81/10.84 | | | | | | | | | (323) $false % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | CLOSE: (323) is inconsistent. % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | Case 2: % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | (324) ~ (all_196_0 = 0) & model_ub(all_16_4, all_16_3, % 72.81/10.84 | | | | | | | | | all_29_2) = all_196_0 % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | ALPHA: (324) implies: % 72.81/10.84 | | | | | | | | | (325) ~ (all_196_0 = 0) % 72.81/10.84 | | | | | | | | | (326) model_ub(all_16_4, all_16_3, all_29_2) = all_196_0 % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | GROUND_INST: instantiating (27) with all_56_1, all_186_2, % 72.81/10.84 | | | | | | | | | all_16_2, simplifying with (181), (309) gives: % 72.81/10.84 | | | | | | | | | (327) all_186_2 = all_56_1 % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | GROUND_INST: instantiating (31) with all_191_0, all_196_0, % 72.81/10.84 | | | | | | | | | all_29_2, all_16_3, all_16_4, simplifying with % 72.81/10.84 | | | | | | | | | (314), (326) gives: % 72.81/10.84 | | | | | | | | | (328) all_196_0 = all_191_0 % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | REDUCE: (325), (328) imply: % 72.81/10.84 | | | | | | | | | (329) ~ (all_191_0 = 0) % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | BETA: splitting (173) gives: % 72.81/10.84 | | | | | | | | | % 72.81/10.84 | | | | | | | | | Case 1: % 72.81/10.84 | | | | | | | | | | % 72.81/10.84 | | | | | | | | | | (330) all_44_1 = 0 & ~ (all_44_0 = 0) & % 72.81/10.84 | | | | | | | | | | model_ub(all_16_4, all_16_3, all_44_2) = 0 & % 72.81/10.84 | | | | | | | | | | lesseq(all_16_2, all_44_2) = all_44_0 % 72.81/10.84 | | | | | | | | | | % 72.81/10.84 | | | | | | | | | | ALPHA: (330) implies: % 72.81/10.84 | | | | | | | | | | (331) ~ (all_44_0 = 0) % 72.81/10.84 | | | | | | | | | | (332) lesseq(all_16_2, all_44_2) = all_44_0 % 72.81/10.84 | | | | | | | | | | (333) model_ub(all_16_4, all_16_3, all_44_2) = 0 % 72.81/10.84 | | | | | | | | | | % 72.81/10.84 | | | | | | | | | | GROUND_INST: instantiating (23) with all_16_4, all_16_3, % 72.81/10.84 | | | | | | | | | | all_16_2, all_44_2, simplifying with (35), (36), % 72.81/10.84 | | | | | | | | | | (37), (160), (172), (333) gives: % 72.81/10.84 | | | | | | | | | | (334) lesseq(all_16_2, all_44_2) = 0 % 72.81/10.84 | | | | | | | | | | % 72.81/10.84 | | | | | | | | | | GROUND_INST: instantiating (28) with all_44_0, 0, all_44_2, % 72.81/10.84 | | | | | | | | | | all_16_2, simplifying with (332), (334) gives: % 72.81/10.84 | | | | | | | | | | (335) all_44_0 = 0 % 73.22/10.84 | | | | | | | | | | % 73.22/10.84 | | | | | | | | | | REDUCE: (331), (335) imply: % 73.22/10.84 | | | | | | | | | | (336) $false % 73.22/10.84 | | | | | | | | | | % 73.22/10.84 | | | | | | | | | | CLOSE: (336) is inconsistent. % 73.22/10.84 | | | | | | | | | | % 73.22/10.84 | | | | | | | | | Case 2: % 73.22/10.84 | | | | | | | | | | % 73.22/10.84 | | | | | | | | | | (337) all_44_3 = 0 & minsol_model_ub(all_16_4, all_16_3, % 73.22/10.84 | | | | | | | | | | all_16_2) = 0 % 73.22/10.84 | | | | | | | | | | % 73.22/10.84 | | | | | | | | | | GROUND_INST: instantiating (2) with all_29_2, all_16_2, % 73.22/10.84 | | | | | | | | | | simplifying with (37), (165), (304) gives: % 73.22/10.84 | | | | | | | | | | (338) ? [v0: $i] : ? [v1: $i] : (summation(all_29_2) = % 73.22/10.84 | | | | | | | | | | v0 & summation(all_16_2) = v1 & lesseq(v0, v1) = % 73.22/10.84 | | | | | | | | | | 0 & $i(v1) & $i(v0)) % 73.22/10.84 | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | GROUND_INST: instantiating (8) with all_16_4, all_16_3, % 73.22/10.85 | | | | | | | | | | all_29_2, simplifying with (35), (36), (298) % 73.22/10.85 | | | | | | | | | | gives: % 73.22/10.85 | | | | | | | | | | (339) all_29_2 = all_16_3 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.85 | | | | | | | | | | lesseq(all_16_4, all_16_3) = v0) % 73.22/10.85 | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | GROUND_INST: instantiating (6) with all_16_4, all_16_3, % 73.22/10.85 | | | | | | | | | | all_29_2, simplifying with (35), (36), (298) % 73.22/10.85 | | | | | | | | | | gives: % 73.22/10.85 | | | | | | | | | | (340) all_29_2 = all_16_4 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.85 | | | | | | | | | | lesseq(all_16_3, all_16_4) = v0) % 73.22/10.85 | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | GROUND_INST: instantiating (14) with all_16_4, all_16_3, % 73.22/10.85 | | | | | | | | | | all_29_2, all_191_0, simplifying with (35), (36), % 73.22/10.85 | | | | | | | | | | (165), (314) gives: % 73.22/10.85 | | | | | | | | | | (341) all_191_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.85 | | | | | | | | | | ub(all_16_4, all_16_3, all_29_2) = v0) % 73.22/10.85 | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | DELTA: instantiating (338) with fresh symbols all_220_0, % 73.22/10.85 | | | | | | | | | | all_220_1 gives: % 73.22/10.85 | | | | | | | | | | (342) summation(all_29_2) = all_220_1 & % 73.22/10.85 | | | | | | | | | | summation(all_16_2) = all_220_0 & lesseq(all_220_1, % 73.22/10.85 | | | | | | | | | | all_220_0) = 0 & $i(all_220_0) & $i(all_220_1) % 73.22/10.85 | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | ALPHA: (342) implies: % 73.22/10.85 | | | | | | | | | | (343) summation(all_16_2) = all_220_0 % 73.22/10.85 | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | BETA: splitting (341) gives: % 73.22/10.85 | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | Case 1: % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | (344) all_191_0 = 0 % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | REDUCE: (329), (344) imply: % 73.22/10.85 | | | | | | | | | | | (345) $false % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | CLOSE: (345) is inconsistent. % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | Case 2: % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | (346) ? [v0: int] : ( ~ (v0 = 0) & ub(all_16_4, % 73.22/10.85 | | | | | | | | | | | all_16_3, all_29_2) = v0) % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | DELTA: instantiating (346) with fresh symbol all_238_0 % 73.22/10.85 | | | | | | | | | | | gives: % 73.22/10.85 | | | | | | | | | | | (347) ~ (all_238_0 = 0) & ub(all_16_4, all_16_3, % 73.22/10.85 | | | | | | | | | | | all_29_2) = all_238_0 % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | ALPHA: (347) implies: % 73.22/10.85 | | | | | | | | | | | (348) ~ (all_238_0 = 0) % 73.22/10.85 | | | | | | | | | | | (349) ub(all_16_4, all_16_3, all_29_2) = all_238_0 % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | GROUND_INST: instantiating (27) with all_56_1, all_220_0, % 73.22/10.85 | | | | | | | | | | | all_16_2, simplifying with (181), (343) gives: % 73.22/10.85 | | | | | | | | | | | (350) all_220_0 = all_56_1 % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | BETA: splitting (222) gives: % 73.22/10.85 | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | Case 1: % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | (351) all_16_2 = all_16_3 % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | REDUCE: (187), (351) imply: % 73.22/10.85 | | | | | | | | | | | | (352) max(all_16_4, all_16_3) = all_16_3 % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | REDUCE: (304), (351) imply: % 73.22/10.85 | | | | | | | | | | | | (353) lesseq(all_29_2, all_16_3) = 0 % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | REDUCE: (291), (351) imply: % 73.22/10.85 | | | | | | | | | | | | (354) lesseq(all_16_3, all_29_2) = all_29_0 % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | BETA: splitting (339) gives: % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | Case 1: % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | (355) all_29_2 = all_16_3 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | REDUCE: (353), (355) imply: % 73.22/10.85 | | | | | | | | | | | | | (356) lesseq(all_16_3, all_16_3) = 0 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | REDUCE: (354), (355) imply: % 73.22/10.85 | | | | | | | | | | | | | (357) lesseq(all_16_3, all_16_3) = all_29_0 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_29_0, all_16_3, % 73.22/10.85 | | | | | | | | | | | | | all_16_3, simplifying with (356), (357) gives: % 73.22/10.85 | | | | | | | | | | | | | (358) all_29_0 = 0 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | REDUCE: (290), (358) imply: % 73.22/10.85 | | | | | | | | | | | | | (359) $false % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | CLOSE: (359) is inconsistent. % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | Case 2: % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | (360) ~ (all_29_2 = all_16_3) % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_29_2, all_16_3, % 73.22/10.85 | | | | | | | | | | | | | all_16_3, all_16_4, simplifying with (298), (352) % 73.22/10.85 | | | | | | | | | | | | | gives: % 73.22/10.85 | | | | | | | | | | | | | (361) all_29_2 = all_16_3 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | REDUCE: (360), (361) imply: % 73.22/10.85 | | | | | | | | | | | | | (362) $false % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | CLOSE: (362) is inconsistent. % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | End of split % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | Case 2: % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | (363) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_2, % 73.22/10.85 | | | | | | | | | | | | all_16_3) = v0) % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | DELTA: instantiating (363) with fresh symbol all_255_0 % 73.22/10.85 | | | | | | | | | | | | gives: % 73.22/10.85 | | | | | | | | | | | | (364) ~ (all_255_0 = 0) & lesseq(all_16_2, all_16_3) = % 73.22/10.85 | | | | | | | | | | | | all_255_0 % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | ALPHA: (364) implies: % 73.22/10.85 | | | | | | | | | | | | (365) ~ (all_255_0 = 0) % 73.22/10.85 | | | | | | | | | | | | (366) lesseq(all_16_2, all_16_3) = all_255_0 % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | BETA: splitting (221) gives: % 73.22/10.85 | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | Case 1: % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | (367) all_16_2 = all_16_4 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | REDUCE: (189), (367) imply: % 73.22/10.85 | | | | | | | | | | | | | (368) max(all_16_4, all_16_3) = all_16_4 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | REDUCE: (304), (367) imply: % 73.22/10.85 | | | | | | | | | | | | | (369) lesseq(all_29_2, all_16_4) = 0 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | REDUCE: (291), (367) imply: % 73.22/10.85 | | | | | | | | | | | | | (370) lesseq(all_16_4, all_29_2) = all_29_0 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | BETA: splitting (340) gives: % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | Case 1: % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | (371) all_29_2 = all_16_4 % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | REDUCE: (369), (371) imply: % 73.22/10.85 | | | | | | | | | | | | | | (372) lesseq(all_16_4, all_16_4) = 0 % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | REDUCE: (370), (371) imply: % 73.22/10.85 | | | | | | | | | | | | | | (373) lesseq(all_16_4, all_16_4) = all_29_0 % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_29_0, all_16_4, % 73.22/10.85 | | | | | | | | | | | | | | all_16_4, simplifying with (372), (373) gives: % 73.22/10.85 | | | | | | | | | | | | | | (374) all_29_0 = 0 % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | REDUCE: (290), (374) imply: % 73.22/10.85 | | | | | | | | | | | | | | (375) $false % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | CLOSE: (375) is inconsistent. % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | Case 2: % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | (376) ~ (all_29_2 = all_16_4) % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_29_2, all_16_4, % 73.22/10.85 | | | | | | | | | | | | | | all_16_3, all_16_4, simplifying with (298), (368) % 73.22/10.85 | | | | | | | | | | | | | | gives: % 73.22/10.85 | | | | | | | | | | | | | | (377) all_29_2 = all_16_4 % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | REDUCE: (376), (377) imply: % 73.22/10.85 | | | | | | | | | | | | | | (378) $false % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | CLOSE: (378) is inconsistent. % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | End of split % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | Case 2: % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | (379) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_2, % 73.22/10.85 | | | | | | | | | | | | | all_16_4) = v0) % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | DELTA: instantiating (379) with fresh symbol all_263_0 % 73.22/10.85 | | | | | | | | | | | | | gives: % 73.22/10.85 | | | | | | | | | | | | | (380) ~ (all_263_0 = 0) & lesseq(all_16_2, all_16_4) = % 73.22/10.85 | | | | | | | | | | | | | all_263_0 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | ALPHA: (380) implies: % 73.22/10.85 | | | | | | | | | | | | | (381) ~ (all_263_0 = 0) % 73.22/10.85 | | | | | | | | | | | | | (382) lesseq(all_16_2, all_16_4) = all_263_0 % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | BETA: splitting (249) gives: % 73.22/10.85 | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | Case 1: % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | (383) all_68_1 = all_56_1 % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | REDUCE: (196), (383) imply: % 73.22/10.85 | | | | | | | | | | | | | | (384) summation(all_16_4) = all_56_1 % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_16_2, all_16_4, % 73.22/10.85 | | | | | | | | | | | | | | all_56_1, all_56_1, simplifying with (35), (37), % 73.22/10.85 | | | | | | | | | | | | | | (181), (184), (384) gives: % 73.22/10.85 | | | | | | | | | | | | | | (385) lesseq(all_16_2, all_16_4) = 0 % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_263_0, 0, all_16_4, % 73.22/10.85 | | | | | | | | | | | | | | all_16_2, simplifying with (382), (385) gives: % 73.22/10.85 | | | | | | | | | | | | | | (386) all_263_0 = 0 % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | REDUCE: (381), (386) imply: % 73.22/10.85 | | | | | | | | | | | | | | (387) $false % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | CLOSE: (387) is inconsistent. % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | Case 2: % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_16_4, all_16_3, % 73.22/10.85 | | | | | | | | | | | | | | all_16_2, all_16_4, all_263_0, simplifying with % 73.22/10.85 | | | | | | | | | | | | | | (35), (36), (37), (160), (382) gives: % 73.22/10.85 | | | | | | | | | | | | | | (388) all_263_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.85 | | | | | | | | | | | | | | model_ub(all_16_4, all_16_3, all_16_4) = v0) % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_16_4, all_16_3, % 73.22/10.85 | | | | | | | | | | | | | | all_16_2, all_16_3, all_255_0, simplifying with % 73.22/10.85 | | | | | | | | | | | | | | (35), (36), (37), (160), (366) gives: % 73.22/10.85 | | | | | | | | | | | | | | (389) all_255_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.85 | | | | | | | | | | | | | | model_ub(all_16_4, all_16_3, all_16_3) = v0) % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_16_4, all_16_3, % 73.22/10.85 | | | | | | | | | | | | | | all_29_2, all_238_0, simplifying with (35), (36), % 73.22/10.85 | | | | | | | | | | | | | | (165), (349) gives: % 73.22/10.85 | | | | | | | | | | | | | | (390) all_238_0 = 0 | ? [v0: any] : ? [v1: any] : % 73.22/10.85 | | | | | | | | | | | | | | (lesseq(all_16_3, all_29_2) = v1 & % 73.22/10.85 | | | | | | | | | | | | | | lesseq(all_16_4, all_29_2) = v0 & ( ~ (v1 = 0) | % 73.22/10.85 | | | | | | | | | | | | | | ~ (v0 = 0))) % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | BETA: splitting (389) gives: % 73.22/10.85 | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | Case 1: % 73.22/10.85 | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | (391) all_255_0 = 0 % 73.22/10.85 | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | REDUCE: (365), (391) imply: % 73.22/10.85 | | | | | | | | | | | | | | | (392) $false % 73.22/10.85 | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | CLOSE: (392) is inconsistent. % 73.22/10.85 | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | Case 2: % 73.22/10.85 | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | (393) ? [v0: int] : ( ~ (v0 = 0) & model_ub(all_16_4, % 73.22/10.85 | | | | | | | | | | | | | | | all_16_3, all_16_3) = v0) % 73.22/10.85 | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | DELTA: instantiating (393) with fresh symbol all_339_0 % 73.22/10.85 | | | | | | | | | | | | | | | gives: % 73.22/10.85 | | | | | | | | | | | | | | | (394) ~ (all_339_0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.85 | | | | | | | | | | | | | | | all_16_3) = all_339_0 % 73.22/10.85 | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | ALPHA: (394) implies: % 73.22/10.85 | | | | | | | | | | | | | | | (395) ~ (all_339_0 = 0) % 73.22/10.85 | | | | | | | | | | | | | | | (396) model_ub(all_16_4, all_16_3, all_16_3) = all_339_0 % 73.22/10.85 | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | BETA: splitting (388) gives: % 73.22/10.85 | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | Case 1: % 73.22/10.85 | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | | (397) all_263_0 = 0 % 73.22/10.85 | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | | REDUCE: (381), (397) imply: % 73.22/10.85 | | | | | | | | | | | | | | | | (398) $false % 73.22/10.85 | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | | CLOSE: (398) is inconsistent. % 73.22/10.85 | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | Case 2: % 73.22/10.85 | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | | (399) ? [v0: int] : ( ~ (v0 = 0) & model_ub(all_16_4, % 73.22/10.85 | | | | | | | | | | | | | | | | all_16_3, all_16_4) = v0) % 73.22/10.85 | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | | DELTA: instantiating (399) with fresh symbol all_344_0 % 73.22/10.85 | | | | | | | | | | | | | | | | gives: % 73.22/10.85 | | | | | | | | | | | | | | | | (400) ~ (all_344_0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.85 | | | | | | | | | | | | | | | | all_16_4) = all_344_0 % 73.22/10.85 | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | | ALPHA: (400) implies: % 73.22/10.85 | | | | | | | | | | | | | | | | (401) ~ (all_344_0 = 0) % 73.22/10.85 | | | | | | | | | | | | | | | | (402) model_ub(all_16_4, all_16_3, all_16_4) = all_344_0 % 73.22/10.85 | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | | BETA: splitting (390) gives: % 73.22/10.85 | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | | Case 1: % 73.22/10.85 | | | | | | | | | | | | | | | | | % 73.22/10.85 | | | | | | | | | | | | | | | | | (403) all_238_0 = 0 % 73.22/10.85 | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | REDUCE: (348), (403) imply: % 73.22/10.86 | | | | | | | | | | | | | | | | | (404) $false % 73.22/10.86 | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | CLOSE: (404) is inconsistent. % 73.22/10.86 | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | Case 2: % 73.22/10.86 | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | (405) ? [v0: any] : ? [v1: any] : (lesseq(all_16_3, % 73.22/10.86 | | | | | | | | | | | | | | | | | all_29_2) = v1 & lesseq(all_16_4, all_29_2) = % 73.22/10.86 | | | | | | | | | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 73.22/10.86 | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | DELTA: instantiating (405) with fresh symbols all_357_0, % 73.22/10.86 | | | | | | | | | | | | | | | | | all_357_1 gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | (406) lesseq(all_16_3, all_29_2) = all_357_0 & % 73.22/10.86 | | | | | | | | | | | | | | | | | lesseq(all_16_4, all_29_2) = all_357_1 & ( ~ % 73.22/10.86 | | | | | | | | | | | | | | | | | (all_357_0 = 0) | ~ (all_357_1 = 0)) % 73.22/10.86 | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | ALPHA: (406) implies: % 73.22/10.86 | | | | | | | | | | | | | | | | | (407) lesseq(all_16_4, all_29_2) = all_357_1 % 73.22/10.86 | | | | | | | | | | | | | | | | | (408) lesseq(all_16_3, all_29_2) = all_357_0 % 73.22/10.86 | | | | | | | | | | | | | | | | | (409) ~ (all_357_0 = 0) | ~ (all_357_1 = 0) % 73.22/10.86 | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | BETA: splitting (300) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | Case 1: % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | (410) all_170_0 = 0 & lesseq(all_29_2, all_29_2) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | ALPHA: (410) implies: % 73.22/10.86 | | | | | | | | | | | | | | | | | | (411) lesseq(all_29_2, all_29_2) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_29_2, all_16_4, % 73.22/10.86 | | | | | | | | | | | | | | | | | | all_357_1, simplifying with (35), (165), (407) % 73.22/10.86 | | | | | | | | | | | | | | | | | | gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | (412) all_357_1 = 0 | lesseq(all_29_2, all_16_4) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_29_2, all_16_3, % 73.22/10.86 | | | | | | | | | | | | | | | | | | all_357_0, simplifying with (36), (165), (408) % 73.22/10.86 | | | | | | | | | | | | | | | | | | gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | (413) all_357_0 = 0 | lesseq(all_29_2, all_16_3) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_16_4, all_16_3, % 73.22/10.86 | | | | | | | | | | | | | | | | | | all_16_3, all_339_0, simplifying with (35), (36), % 73.22/10.86 | | | | | | | | | | | | | | | | | | (396) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | (414) all_339_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.86 | | | | | | | | | | | | | | | | | | ub(all_16_4, all_16_3, all_16_3) = v0) % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | Case 1: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (415) all_339_0 = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | REDUCE: (395), (415) imply: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (416) $false % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | CLOSE: (416) is inconsistent. % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | Case 2: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (417) ? [v0: int] : ( ~ (v0 = 0) & ub(all_16_4, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_16_3, all_16_3) = v0) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (417) with fresh symbol all_487_0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (418) ~ (all_487_0 = 0) & ub(all_16_4, all_16_3, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_16_3) = all_487_0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (10), (28), (35), (36), (339), (340), (407), % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (408), (409), (411), (412), (413), (418) are % 73.22/10.86 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | Case 2: % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | (419) ~ (all_170_0 = 0) & minsol_model_max(all_16_4, % 73.22/10.86 | | | | | | | | | | | | | | | | | | all_16_3, all_29_2) = all_170_0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | ALPHA: (419) implies: % 73.22/10.86 | | | | | | | | | | | | | | | | | | (420) ~ (all_170_0 = 0) % 73.22/10.86 | | | | | | | | | | | | | | | | | | (421) minsol_model_max(all_16_4, all_16_3, all_29_2) = % 73.22/10.86 | | | | | | | | | | | | | | | | | | all_170_0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | Case 1: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (422) all_177_1 = 0 & ~ (all_177_0 = 0) & % 73.22/10.86 | | | | | | | | | | | | | | | | | | | model_max(all_16_4, all_16_3, all_177_2) = 0 & % 73.22/10.86 | | | | | | | | | | | | | | | | | | | lesseq(all_29_2, all_177_2) = all_177_0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (423) ~ (all_177_0 = 0) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (424) lesseq(all_29_2, all_177_2) = all_177_0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (425) model_max(all_16_4, all_16_3, all_177_2) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_29_2, all_16_4, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_357_1, simplifying with (35), (165), (407) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (426) all_357_1 = 0 | lesseq(all_29_2, all_16_4) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_29_2, all_16_3, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_357_0, simplifying with (36), (165), (408) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (427) all_357_0 = 0 | lesseq(all_29_2, all_16_3) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_177_2, all_29_2, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_177_0, simplifying with (165), (302), (424) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (428) all_177_0 = 0 | lesseq(all_177_2, all_29_2) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_16_4, all_16_3, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_177_2, simplifying with (35), (36), (302), % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (425) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (429) max(all_16_4, all_16_3) = all_177_2 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_16_4, all_16_3, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_16_4, all_344_0, simplifying with (35), (36), % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (402) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (430) all_344_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.86 | | | | | | | | | | | | | | | | | | | ub(all_16_4, all_16_3, all_16_4) = v0) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_16_4, all_16_3, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_16_3, all_339_0, simplifying with (35), (36), % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (396) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (431) all_339_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.86 | | | | | | | | | | | | | | | | | | | ub(all_16_4, all_16_3, all_16_3) = v0) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (428) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | Case 1: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | (432) lesseq(all_177_2, all_29_2) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (431) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | Case 1: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | (433) all_339_0 = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (433) imply: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | (434) $false % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | CLOSE: (434) is inconsistent. % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | Case 2: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | (435) ? [v0: int] : ( ~ (v0 = 0) & ub(all_16_4, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | all_16_3, all_16_3) = v0) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | (436) all_344_0 = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (401), (436) imply: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | (437) $false % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (437) is inconsistent. % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_29_2, all_177_2, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | all_16_3, all_16_4, simplifying with (298), (429) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | (438) all_177_2 = all_29_2 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (432), (438) imply: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | (439) lesseq(all_29_2, all_29_2) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (435) with fresh symbol all_487_0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | (440) ~ (all_487_0 = 0) & ub(all_16_4, all_16_3, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | all_16_3) = all_487_0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (10), (28), (35), (36), (339), (340), (407), % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | (408), (409), (426), (427), (439), (440) are % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | Case 2: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | (441) all_177_0 = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (441) imply: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | (442) $false % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | CLOSE: (442) is inconsistent. % 73.22/10.86 | | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | Case 2: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (443) all_177_3 = 0 & minsol_model_max(all_16_4, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_16_3, all_29_2) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | ALPHA: (443) implies: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (444) minsol_model_max(all_16_4, all_16_3, all_29_2) = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_170_0, all_29_2, % 73.22/10.86 | | | | | | | | | | | | | | | | | | | all_16_3, all_16_4, simplifying with (421), (444) % 73.22/10.86 | | | | | | | | | | | | | | | | | | | gives: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (445) all_170_0 = 0 % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | REDUCE: (420), (445) imply: % 73.22/10.86 | | | | | | | | | | | | | | | | | | | (446) $false % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | | CLOSE: (446) is inconsistent. % 73.22/10.86 | | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | | % 73.22/10.86 | | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | | % 73.22/10.86 | | | | | | | | | End of split % 73.22/10.86 | | | | | | | | | % 73.22/10.86 | | | | | | | | End of split % 73.22/10.86 | | | | | | | | % 73.22/10.86 | | | | | | | End of split % 73.22/10.86 | | | | | | | % 73.22/10.86 | | | | | | End of split % 73.22/10.86 | | | | | | % 73.22/10.86 | | | | | End of split % 73.22/10.86 | | | | | % 73.22/10.86 | | | | Case 2: % 73.22/10.86 | | | | | % 73.22/10.86 | | | | | (447) all_29_0 = 0 % 73.22/10.86 | | | | | % 73.22/10.86 | | | | | REDUCE: (290), (447) imply: % 73.22/10.86 | | | | | (448) $false % 73.22/10.86 | | | | | % 73.22/10.86 | | | | | CLOSE: (448) is inconsistent. % 73.22/10.86 | | | | | % 73.22/10.86 | | | | End of split % 73.22/10.86 | | | | % 73.22/10.86 | | | Case 2: % 73.22/10.86 | | | | % 73.22/10.86 | | | | (449) ~ (all_29_3 = 0) & model_max(all_16_4, all_16_3, all_16_2) = % 73.22/10.86 | | | | all_29_3 % 73.22/10.86 | | | | % 73.22/10.86 | | | | ALPHA: (449) implies: % 73.22/10.86 | | | | (450) ~ (all_29_3 = 0) % 73.22/10.86 | | | | (451) model_max(all_16_4, all_16_3, all_16_2) = all_29_3 % 73.22/10.86 | | | | % 73.22/10.86 | | | | GROUND_INST: instantiating (12) with all_16_4, all_16_3, all_16_2, % 73.22/10.86 | | | | all_29_3, simplifying with (35), (36), (37), (451) gives: % 73.22/10.86 | | | | (452) all_29_3 = 0 | ? [v0: any] : ( ~ (v0 = all_16_2) & % 73.22/10.86 | | | | max(all_16_4, all_16_3) = v0 & $i(v0)) % 73.22/10.86 | | | | % 73.22/10.86 | | | | BETA: splitting (452) gives: % 73.22/10.86 | | | | % 73.22/10.86 | | | | Case 1: % 73.22/10.86 | | | | | % 73.22/10.86 | | | | | (453) all_29_3 = 0 % 73.22/10.86 | | | | | % 73.22/10.86 | | | | | REDUCE: (450), (453) imply: % 73.22/10.86 | | | | | (454) $false % 73.22/10.86 | | | | | % 73.22/10.86 | | | | | CLOSE: (454) is inconsistent. % 73.22/10.86 | | | | | % 73.22/10.86 | | | | Case 2: % 73.22/10.86 | | | | | % 73.22/10.86 | | | | | (455) ? [v0: any] : ( ~ (v0 = all_16_2) & max(all_16_4, all_16_3) % 73.22/10.86 | | | | | = v0 & $i(v0)) % 73.22/10.86 | | | | | % 73.22/10.86 | | | | | DELTA: instantiating (455) with fresh symbol all_180_0 gives: % 73.22/10.86 | | | | | (456) ~ (all_180_0 = all_16_2) & max(all_16_4, all_16_3) = % 73.22/10.86 | | | | | all_180_0 & $i(all_180_0) % 73.22/10.86 | | | | | % 73.22/10.86 | | | | | ALPHA: (456) implies: % 73.22/10.86 | | | | | (457) ~ (all_180_0 = all_16_2) % 73.22/10.86 | | | | | (458) $i(all_180_0) % 73.22/10.87 | | | | | (459) max(all_16_4, all_16_3) = all_180_0 % 73.22/10.87 | | | | | % 73.22/10.87 | | | | | GROUND_INST: instantiating (8) with all_16_4, all_16_3, all_180_0, % 73.22/10.87 | | | | | simplifying with (35), (36), (459) gives: % 73.22/10.87 | | | | | (460) all_180_0 = all_16_3 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.87 | | | | | lesseq(all_16_4, all_16_3) = v0) % 73.22/10.87 | | | | | % 73.22/10.87 | | | | | GROUND_INST: instantiating (6) with all_16_4, all_16_3, all_180_0, % 73.22/10.87 | | | | | simplifying with (35), (36), (459) gives: % 73.22/10.87 | | | | | (461) all_180_0 = all_16_4 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.87 | | | | | lesseq(all_16_3, all_16_4) = v0) % 73.22/10.87 | | | | | % 73.22/10.87 | | | | | BETA: splitting (222) gives: % 73.22/10.87 | | | | | % 73.22/10.87 | | | | | Case 1: % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | (462) all_16_2 = all_16_3 % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | REDUCE: (457), (462) imply: % 73.22/10.87 | | | | | | (463) ~ (all_180_0 = all_16_3) % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | REDUCE: (187), (462) imply: % 73.22/10.87 | | | | | | (464) max(all_16_4, all_16_3) = all_16_3 % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | GROUND_INST: instantiating (29) with all_180_0, all_16_3, all_16_3, % 73.22/10.87 | | | | | | all_16_4, simplifying with (459), (464) gives: % 73.22/10.87 | | | | | | (465) all_180_0 = all_16_3 % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | REDUCE: (463), (465) imply: % 73.22/10.87 | | | | | | (466) $false % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | CLOSE: (466) is inconsistent. % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | Case 2: % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | (467) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_2, all_16_3) = % 73.22/10.87 | | | | | | v0) % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | DELTA: instantiating (467) with fresh symbol all_214_0 gives: % 73.22/10.87 | | | | | | (468) ~ (all_214_0 = 0) & lesseq(all_16_2, all_16_3) = all_214_0 % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | ALPHA: (468) implies: % 73.22/10.87 | | | | | | (469) ~ (all_214_0 = 0) % 73.22/10.87 | | | | | | (470) lesseq(all_16_2, all_16_3) = all_214_0 % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | BETA: splitting (221) gives: % 73.22/10.87 | | | | | | % 73.22/10.87 | | | | | | Case 1: % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | (471) all_16_2 = all_16_4 % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | REDUCE: (457), (471) imply: % 73.22/10.87 | | | | | | | (472) ~ (all_180_0 = all_16_4) % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | REDUCE: (189), (471) imply: % 73.22/10.87 | | | | | | | (473) max(all_16_4, all_16_3) = all_16_4 % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | GROUND_INST: instantiating (29) with all_180_0, all_16_4, % 73.22/10.87 | | | | | | | all_16_3, all_16_4, simplifying with (459), (473) % 73.22/10.87 | | | | | | | gives: % 73.22/10.87 | | | | | | | (474) all_180_0 = all_16_4 % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | REDUCE: (472), (474) imply: % 73.22/10.87 | | | | | | | (475) $false % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | CLOSE: (475) is inconsistent. % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | Case 2: % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | (476) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_2, all_16_4) % 73.22/10.87 | | | | | | | = v0) % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | DELTA: instantiating (476) with fresh symbol all_222_0 gives: % 73.22/10.87 | | | | | | | (477) ~ (all_222_0 = 0) & lesseq(all_16_2, all_16_4) = % 73.22/10.87 | | | | | | | all_222_0 % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | ALPHA: (477) implies: % 73.22/10.87 | | | | | | | (478) ~ (all_222_0 = 0) % 73.22/10.87 | | | | | | | (479) lesseq(all_16_2, all_16_4) = all_222_0 % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | BETA: splitting (249) gives: % 73.22/10.87 | | | | | | | % 73.22/10.87 | | | | | | | Case 1: % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | (480) all_68_1 = all_56_1 % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | REDUCE: (196), (480) imply: % 73.22/10.87 | | | | | | | | (481) summation(all_16_4) = all_56_1 % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | GROUND_INST: instantiating (4) with all_16_2, all_16_4, % 73.22/10.87 | | | | | | | | all_56_1, all_56_1, simplifying with (35), (37), % 73.22/10.87 | | | | | | | | (181), (184), (481) gives: % 73.22/10.87 | | | | | | | | (482) lesseq(all_16_2, all_16_4) = 0 % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | GROUND_INST: instantiating (28) with all_222_0, 0, all_16_4, % 73.22/10.87 | | | | | | | | all_16_2, simplifying with (479), (482) gives: % 73.22/10.87 | | | | | | | | (483) all_222_0 = 0 % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | REDUCE: (478), (483) imply: % 73.22/10.87 | | | | | | | | (484) $false % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | CLOSE: (484) is inconsistent. % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | Case 2: % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | (485) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_56_1, % 73.22/10.87 | | | | | | | | all_68_1) = v0) % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | DELTA: instantiating (485) with fresh symbol all_230_0 gives: % 73.22/10.87 | | | | | | | | (486) ~ (all_230_0 = 0) & lesseq(all_56_1, all_68_1) = % 73.22/10.87 | | | | | | | | all_230_0 % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | ALPHA: (486) implies: % 73.22/10.87 | | | | | | | | (487) ~ (all_230_0 = 0) % 73.22/10.87 | | | | | | | | (488) lesseq(all_56_1, all_68_1) = all_230_0 % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | BETA: splitting (250) gives: % 73.22/10.87 | | | | | | | | % 73.22/10.87 | | | | | | | | Case 1: % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | (489) all_72_1 = all_56_1 % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | REDUCE: (206), (489) imply: % 73.22/10.87 | | | | | | | | | (490) summation(all_16_3) = all_56_1 % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | GROUND_INST: instantiating (4) with all_16_2, all_16_3, % 73.22/10.87 | | | | | | | | | all_56_1, all_56_1, simplifying with (36), (37), % 73.22/10.87 | | | | | | | | | (181), (184), (490) gives: % 73.22/10.87 | | | | | | | | | (491) lesseq(all_16_2, all_16_3) = 0 % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | GROUND_INST: instantiating (28) with all_214_0, 0, all_16_3, % 73.22/10.87 | | | | | | | | | all_16_2, simplifying with (470), (491) gives: % 73.22/10.87 | | | | | | | | | (492) all_214_0 = 0 % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | REDUCE: (469), (492) imply: % 73.22/10.87 | | | | | | | | | (493) $false % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | CLOSE: (493) is inconsistent. % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | Case 2: % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | (494) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_56_1, % 73.22/10.87 | | | | | | | | | all_72_1) = v0) % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | DELTA: instantiating (494) with fresh symbol all_238_0 gives: % 73.22/10.87 | | | | | | | | | (495) ~ (all_238_0 = 0) & lesseq(all_56_1, all_72_1) = % 73.22/10.87 | | | | | | | | | all_238_0 % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | ALPHA: (495) implies: % 73.22/10.87 | | | | | | | | | (496) ~ (all_238_0 = 0) % 73.22/10.87 | | | | | | | | | (497) lesseq(all_56_1, all_72_1) = all_238_0 % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | GROUND_INST: instantiating (26) with all_16_4, all_16_3, % 73.22/10.87 | | | | | | | | | all_16_2, 0, all_16_4, all_222_0, simplifying with % 73.22/10.87 | | | | | | | | | (35), (36), (37), (167), (479) gives: % 73.22/10.87 | | | | | | | | | (498) all_222_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & % 73.22/10.87 | | | | | | | | | minsol_model_ub(all_16_4, all_16_3, all_16_2) = % 73.22/10.87 | | | | | | | | | v0) | ( ~ (v0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.87 | | | | | | | | | all_16_4) = v0)) % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | GROUND_INST: instantiating (25) with all_16_4, all_16_3, % 73.22/10.87 | | | | | | | | | all_16_2, all_16_4, all_222_0, simplifying with % 73.22/10.87 | | | | | | | | | (35), (36), (37), (160), (479) gives: % 73.22/10.87 | | | | | | | | | (499) all_222_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.87 | | | | | | | | | model_ub(all_16_4, all_16_3, all_16_4) = v0) % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | GROUND_INST: instantiating (26) with all_16_4, all_16_3, % 73.22/10.87 | | | | | | | | | all_16_2, 0, all_16_3, all_214_0, simplifying with % 73.22/10.87 | | | | | | | | | (35), (36), (37), (167), (470) gives: % 73.22/10.87 | | | | | | | | | (500) all_214_0 = 0 | ? [v0: int] : (( ~ (v0 = 0) & % 73.22/10.87 | | | | | | | | | minsol_model_ub(all_16_4, all_16_3, all_16_2) = % 73.22/10.87 | | | | | | | | | v0) | ( ~ (v0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.87 | | | | | | | | | all_16_3) = v0)) % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | GROUND_INST: instantiating (25) with all_16_4, all_16_3, % 73.22/10.87 | | | | | | | | | all_16_2, all_16_3, all_214_0, simplifying with % 73.22/10.87 | | | | | | | | | (35), (36), (37), (160), (470) gives: % 73.22/10.87 | | | | | | | | | (501) all_214_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.22/10.87 | | | | | | | | | model_ub(all_16_4, all_16_3, all_16_3) = v0) % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, all_68_1, % 73.22/10.87 | | | | | | | | | all_230_0, simplifying with (185), (193), (488) % 73.22/10.87 | | | | | | | | | gives: % 73.22/10.87 | | | | | | | | | (502) all_230_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: % 73.22/10.87 | | | | | | | | | int] : ( ~ (v2 = 0) & summation(all_68_1) = v1 & % 73.22/10.87 | | | | | | | | | summation(all_56_1) = v0 & lesseq(v0, v1) = v2 & % 73.22/10.87 | | | | | | | | | $i(v1) & $i(v0)) % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | GROUND_INST: instantiating (3) with all_56_1, all_72_1, % 73.22/10.87 | | | | | | | | | all_238_0, simplifying with (185), (204), (497) % 73.22/10.87 | | | | | | | | | gives: % 73.22/10.87 | | | | | | | | | (503) all_238_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: % 73.22/10.87 | | | | | | | | | int] : ( ~ (v2 = 0) & summation(all_72_1) = v1 & % 73.22/10.87 | | | | | | | | | summation(all_56_1) = v0 & lesseq(v0, v1) = v2 & % 73.22/10.87 | | | | | | | | | $i(v1) & $i(v0)) % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | BETA: splitting (503) gives: % 73.22/10.87 | | | | | | | | | % 73.22/10.87 | | | | | | | | | Case 1: % 73.22/10.87 | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | (504) all_238_0 = 0 % 73.22/10.87 | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | REDUCE: (496), (504) imply: % 73.22/10.87 | | | | | | | | | | (505) $false % 73.22/10.87 | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | CLOSE: (505) is inconsistent. % 73.22/10.87 | | | | | | | | | | % 73.22/10.87 | | | | | | | | | Case 2: % 73.22/10.87 | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | (506) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 % 73.22/10.87 | | | | | | | | | | = 0) & summation(all_72_1) = v1 & % 73.22/10.87 | | | | | | | | | | summation(all_56_1) = v0 & lesseq(v0, v1) = v2 & % 73.22/10.87 | | | | | | | | | | $i(v1) & $i(v0)) % 73.22/10.87 | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | DELTA: instantiating (506) with fresh symbols all_256_0, % 73.22/10.87 | | | | | | | | | | all_256_1, all_256_2 gives: % 73.22/10.87 | | | | | | | | | | (507) ~ (all_256_0 = 0) & summation(all_72_1) = % 73.22/10.87 | | | | | | | | | | all_256_1 & summation(all_56_1) = all_256_2 & % 73.22/10.87 | | | | | | | | | | lesseq(all_256_2, all_256_1) = all_256_0 & % 73.22/10.87 | | | | | | | | | | $i(all_256_1) & $i(all_256_2) % 73.22/10.87 | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | ALPHA: (507) implies: % 73.22/10.87 | | | | | | | | | | (508) ~ (all_256_0 = 0) % 73.22/10.87 | | | | | | | | | | (509) $i(all_256_2) % 73.22/10.87 | | | | | | | | | | (510) $i(all_256_1) % 73.22/10.87 | | | | | | | | | | (511) lesseq(all_256_2, all_256_1) = all_256_0 % 73.22/10.87 | | | | | | | | | | (512) summation(all_56_1) = all_256_2 % 73.22/10.87 | | | | | | | | | | (513) summation(all_72_1) = all_256_1 % 73.22/10.87 | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | BETA: splitting (502) gives: % 73.22/10.87 | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | Case 1: % 73.22/10.87 | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | (514) all_230_0 = 0 % 73.22/10.87 | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | REDUCE: (487), (514) imply: % 73.22/10.87 | | | | | | | | | | | (515) $false % 73.22/10.87 | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | CLOSE: (515) is inconsistent. % 73.22/10.87 | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | Case 2: % 73.22/10.87 | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | (516) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 % 73.22/10.87 | | | | | | | | | | | = 0) & summation(all_68_1) = v1 & % 73.22/10.87 | | | | | | | | | | | summation(all_56_1) = v0 & lesseq(v0, v1) = v2 & % 73.22/10.87 | | | | | | | | | | | $i(v1) & $i(v0)) % 73.22/10.87 | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | DELTA: instantiating (516) with fresh symbols all_261_0, % 73.22/10.87 | | | | | | | | | | | all_261_1, all_261_2 gives: % 73.22/10.87 | | | | | | | | | | | (517) ~ (all_261_0 = 0) & summation(all_68_1) = % 73.22/10.87 | | | | | | | | | | | all_261_1 & summation(all_56_1) = all_261_2 & % 73.22/10.87 | | | | | | | | | | | lesseq(all_261_2, all_261_1) = all_261_0 & % 73.22/10.87 | | | | | | | | | | | $i(all_261_1) & $i(all_261_2) % 73.22/10.87 | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | ALPHA: (517) implies: % 73.22/10.87 | | | | | | | | | | | (518) summation(all_56_1) = all_261_2 % 73.22/10.87 | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | BETA: splitting (501) gives: % 73.22/10.87 | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | Case 1: % 73.22/10.87 | | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | | (519) all_214_0 = 0 % 73.22/10.87 | | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | | REDUCE: (469), (519) imply: % 73.22/10.87 | | | | | | | | | | | | (520) $false % 73.22/10.87 | | | | | | | | | | | | % 73.22/10.87 | | | | | | | | | | | | CLOSE: (520) is inconsistent. % 73.22/10.87 | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | Case 2: % 73.22/10.88 | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | (521) ? [v0: int] : ( ~ (v0 = 0) & model_ub(all_16_4, % 73.22/10.88 | | | | | | | | | | | | all_16_3, all_16_3) = v0) % 73.22/10.88 | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | DELTA: instantiating (521) with fresh symbol all_266_0 % 73.22/10.88 | | | | | | | | | | | | gives: % 73.22/10.88 | | | | | | | | | | | | (522) ~ (all_266_0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.88 | | | | | | | | | | | | all_16_3) = all_266_0 % 73.22/10.88 | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | ALPHA: (522) implies: % 73.22/10.88 | | | | | | | | | | | | (523) model_ub(all_16_4, all_16_3, all_16_3) = all_266_0 % 73.22/10.88 | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | BETA: splitting (500) gives: % 73.22/10.88 | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | Case 1: % 73.22/10.88 | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | (524) all_214_0 = 0 % 73.22/10.88 | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | REDUCE: (469), (524) imply: % 73.22/10.88 | | | | | | | | | | | | | (525) $false % 73.22/10.88 | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | CLOSE: (525) is inconsistent. % 73.22/10.88 | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | Case 2: % 73.22/10.88 | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | (526) ? [v0: int] : (( ~ (v0 = 0) & % 73.22/10.88 | | | | | | | | | | | | | minsol_model_ub(all_16_4, all_16_3, all_16_2) % 73.22/10.88 | | | | | | | | | | | | | = v0) | ( ~ (v0 = 0) & model_ub(all_16_4, % 73.22/10.88 | | | | | | | | | | | | | all_16_3, all_16_3) = v0)) % 73.22/10.88 | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | DELTA: instantiating (526) with fresh symbol all_271_0 % 73.22/10.88 | | | | | | | | | | | | | gives: % 73.22/10.88 | | | | | | | | | | | | | (527) ( ~ (all_271_0 = 0) & minsol_model_ub(all_16_4, % 73.22/10.88 | | | | | | | | | | | | | all_16_3, all_16_2) = all_271_0) | ( ~ % 73.22/10.88 | | | | | | | | | | | | | (all_271_0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.88 | | | | | | | | | | | | | all_16_3) = all_271_0) % 73.22/10.88 | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | BETA: splitting (498) gives: % 73.22/10.88 | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | Case 1: % 73.22/10.88 | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | (528) all_222_0 = 0 % 73.22/10.88 | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | REDUCE: (478), (528) imply: % 73.22/10.88 | | | | | | | | | | | | | | (529) $false % 73.22/10.88 | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | CLOSE: (529) is inconsistent. % 73.22/10.88 | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | Case 2: % 73.22/10.88 | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | (530) ? [v0: int] : (( ~ (v0 = 0) & % 73.22/10.88 | | | | | | | | | | | | | | minsol_model_ub(all_16_4, all_16_3, all_16_2) % 73.22/10.88 | | | | | | | | | | | | | | = v0) | ( ~ (v0 = 0) & model_ub(all_16_4, % 73.22/10.88 | | | | | | | | | | | | | | all_16_3, all_16_4) = v0)) % 73.22/10.88 | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | DELTA: instantiating (530) with fresh symbol all_275_0 % 73.22/10.88 | | | | | | | | | | | | | | gives: % 73.22/10.88 | | | | | | | | | | | | | | (531) ( ~ (all_275_0 = 0) & minsol_model_ub(all_16_4, % 73.22/10.88 | | | | | | | | | | | | | | all_16_3, all_16_2) = all_275_0) | ( ~ % 73.22/10.88 | | | | | | | | | | | | | | (all_275_0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.88 | | | | | | | | | | | | | | all_16_4) = all_275_0) % 73.22/10.88 | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | BETA: splitting (499) gives: % 73.22/10.88 | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | Case 1: % 73.22/10.88 | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | (532) all_222_0 = 0 % 73.22/10.88 | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | REDUCE: (478), (532) imply: % 73.22/10.88 | | | | | | | | | | | | | | | (533) $false % 73.22/10.88 | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | CLOSE: (533) is inconsistent. % 73.22/10.88 | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | Case 2: % 73.22/10.88 | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | (534) ? [v0: int] : ( ~ (v0 = 0) & model_ub(all_16_4, % 73.22/10.88 | | | | | | | | | | | | | | | all_16_3, all_16_4) = v0) % 73.22/10.88 | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | DELTA: instantiating (534) with fresh symbol all_279_0 % 73.22/10.88 | | | | | | | | | | | | | | | gives: % 73.22/10.88 | | | | | | | | | | | | | | | (535) ~ (all_279_0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.88 | | | | | | | | | | | | | | | all_16_4) = all_279_0 % 73.22/10.88 | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | ALPHA: (535) implies: % 73.22/10.88 | | | | | | | | | | | | | | | (536) ~ (all_279_0 = 0) % 73.22/10.88 | | | | | | | | | | | | | | | (537) model_ub(all_16_4, all_16_3, all_16_4) = all_279_0 % 73.22/10.88 | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | BETA: splitting (527) gives: % 73.22/10.88 | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | Case 1: % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | (538) ~ (all_271_0 = 0) & minsol_model_ub(all_16_4, % 73.22/10.88 | | | | | | | | | | | | | | | | all_16_3, all_16_2) = all_271_0 % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | ALPHA: (538) implies: % 73.22/10.88 | | | | | | | | | | | | | | | | (539) ~ (all_271_0 = 0) % 73.22/10.88 | | | | | | | | | | | | | | | | (540) minsol_model_ub(all_16_4, all_16_3, all_16_2) = % 73.22/10.88 | | | | | | | | | | | | | | | | all_271_0 % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_271_0, all_16_2, % 73.22/10.88 | | | | | | | | | | | | | | | | all_16_3, all_16_4, simplifying with (160), (540) % 73.22/10.88 | | | | | | | | | | | | | | | | gives: % 73.22/10.88 | | | | | | | | | | | | | | | | (541) all_271_0 = 0 % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | REDUCE: (539), (541) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | (542) $false % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | CLOSE: (542) is inconsistent. % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | Case 2: % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | (543) ~ (all_271_0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.88 | | | | | | | | | | | | | | | | all_16_3) = all_271_0 % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | ALPHA: (543) implies: % 73.22/10.88 | | | | | | | | | | | | | | | | (544) ~ (all_271_0 = 0) % 73.22/10.88 | | | | | | | | | | | | | | | | (545) model_ub(all_16_4, all_16_3, all_16_3) = all_271_0 % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | BETA: splitting (531) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | Case 1: % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | (546) ~ (all_275_0 = 0) & minsol_model_ub(all_16_4, % 73.22/10.88 | | | | | | | | | | | | | | | | | all_16_3, all_16_2) = all_275_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | ALPHA: (546) implies: % 73.22/10.88 | | | | | | | | | | | | | | | | | (547) ~ (all_275_0 = 0) % 73.22/10.88 | | | | | | | | | | | | | | | | | (548) minsol_model_ub(all_16_4, all_16_3, all_16_2) = % 73.22/10.88 | | | | | | | | | | | | | | | | | all_275_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_275_0, all_16_2, % 73.22/10.88 | | | | | | | | | | | | | | | | | all_16_3, all_16_4, simplifying with (160), (548) % 73.22/10.88 | | | | | | | | | | | | | | | | | gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | (549) all_275_0 = 0 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | REDUCE: (547), (549) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | | (550) $false % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | CLOSE: (550) is inconsistent. % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | Case 2: % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | (551) ~ (all_275_0 = 0) & model_ub(all_16_4, all_16_3, % 73.22/10.88 | | | | | | | | | | | | | | | | | all_16_4) = all_275_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | ALPHA: (551) implies: % 73.22/10.88 | | | | | | | | | | | | | | | | | (552) model_ub(all_16_4, all_16_3, all_16_4) = all_275_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_70_1, all_261_2, % 73.22/10.88 | | | | | | | | | | | | | | | | | all_56_1, simplifying with (201), (518) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | (553) all_261_2 = all_70_1 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_256_2, all_261_2, % 73.22/10.88 | | | | | | | | | | | | | | | | | all_56_1, simplifying with (512), (518) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | (554) all_261_2 = all_256_2 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_86_1, all_256_1, % 73.22/10.88 | | | | | | | | | | | | | | | | | all_72_1, simplifying with (232), (513) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | (555) all_256_1 = all_86_1 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_275_0, all_279_0, % 73.22/10.88 | | | | | | | | | | | | | | | | | all_16_4, all_16_3, all_16_4, simplifying with % 73.22/10.88 | | | | | | | | | | | | | | | | | (537), (552) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | (556) all_279_0 = all_275_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_266_0, all_271_0, % 73.22/10.88 | | | | | | | | | | | | | | | | | all_16_3, all_16_3, all_16_4, simplifying with % 73.22/10.88 | | | | | | | | | | | | | | | | | (523), (545) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | (557) all_271_0 = all_266_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (554) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | | (558) all_256_2 = all_70_1 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | REDUCE: (536), (556) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | | (559) ~ (all_275_0 = 0) % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | REDUCE: (544), (557) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | | (560) ~ (all_266_0 = 0) % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | REDUCE: (511), (555), (558) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | | (561) lesseq(all_70_1, all_86_1) = all_256_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | Case 1: % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | (562) all_102_1 = all_88_1 % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | REDUCE: (259), (562) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | | | (563) summation(all_86_1) = all_88_1 % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_70_1, all_86_1, % 73.22/10.88 | | | | | | | | | | | | | | | | | | all_88_1, all_88_1, simplifying with (215), (229), % 73.22/10.88 | | | | | | | | | | | | | | | | | | (236), (242), (563) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | | (564) lesseq(all_70_1, all_86_1) = 0 % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_256_0, 0, all_86_1, % 73.22/10.88 | | | | | | | | | | | | | | | | | | all_70_1, simplifying with (561), (564) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | | (565) all_256_0 = 0 % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | REDUCE: (508), (565) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | | | (566) $false % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | CLOSE: (566) is inconsistent. % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | Case 2: % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | (567) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_88_1, % 73.22/10.88 | | | | | | | | | | | | | | | | | | all_102_1) = v0) % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | DELTA: instantiating (567) with fresh symbol all_315_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | | gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | | (568) ~ (all_315_0 = 0) & lesseq(all_88_1, all_102_1) = % 73.22/10.88 | | | | | | | | | | | | | | | | | | all_315_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | ALPHA: (568) implies: % 73.22/10.88 | | | | | | | | | | | | | | | | | | (569) ~ (all_315_0 = 0) % 73.22/10.88 | | | | | | | | | | | | | | | | | | (570) lesseq(all_88_1, all_102_1) = all_315_0 % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | Case 1: % 73.22/10.88 | | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | | (571) all_118_1 = all_100_1 % 73.22/10.88 | | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | | REDUCE: (280), (571) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | | | | (572) summation(all_102_1) = all_100_1 % 73.22/10.88 | | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | | REDUCE: (284), (571) imply: % 73.22/10.88 | | | | | | | | | | | | | | | | | | | (573) lesseq(all_100_1, all_100_1) = 0 % 73.22/10.88 | | | | | | | | | | | | | | | | | | | % 73.22/10.88 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_88_1, all_102_1, % 73.22/10.88 | | | | | | | | | | | | | | | | | | | all_100_1, all_100_1, simplifying with (245), % 73.22/10.88 | | | | | | | | | | | | | | | | | | | (252), (255), (572), (573) gives: % 73.22/10.88 | | | | | | | | | | | | | | | | | | | (574) lesseq(all_88_1, all_102_1) = 0 % 73.22/10.88 | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_315_0, 0, all_102_1, % 73.41/10.88 | | | | | | | | | | | | | | | | | | | all_88_1, simplifying with (570), (574) gives: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | (575) all_315_0 = 0 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | REDUCE: (569), (575) imply: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | (576) $false % 73.41/10.88 | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | CLOSE: (576) is inconsistent. % 73.41/10.88 | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_16_4, all_16_3, % 73.41/10.88 | | | | | | | | | | | | | | | | | | | all_16_4, all_275_0, simplifying with (35), (36), % 73.41/10.88 | | | | | | | | | | | | | | | | | | | (552) gives: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | (577) all_275_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.41/10.88 | | | | | | | | | | | | | | | | | | | ub(all_16_4, all_16_3, all_16_4) = v0) % 73.41/10.88 | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_16_4, all_16_3, % 73.41/10.88 | | | | | | | | | | | | | | | | | | | all_16_3, all_266_0, simplifying with (35), (36), % 73.41/10.88 | | | | | | | | | | | | | | | | | | | (523) gives: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | (578) all_266_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 73.41/10.88 | | | | | | | | | | | | | | | | | | | ub(all_16_4, all_16_3, all_16_3) = v0) % 73.41/10.88 | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | BETA: splitting (577) gives: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | (579) all_275_0 = 0 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (579) imply: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | (580) $false % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | CLOSE: (580) is inconsistent. % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | (581) ? [v0: int] : ( ~ (v0 = 0) & ub(all_16_4, % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | all_16_3, all_16_4) = v0) % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (581) with fresh symbol all_361_0 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | gives: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | (582) ~ (all_361_0 = 0) & ub(all_16_4, all_16_3, % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | all_16_4) = all_361_0 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | ALPHA: (582) implies: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | (583) ~ (all_361_0 = 0) % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | (584) ub(all_16_4, all_16_3, all_16_4) = all_361_0 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | BETA: splitting (578) gives: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | (585) all_266_0 = 0 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | REDUCE: (560), (585) imply: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | (586) $false % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | CLOSE: (586) is inconsistent. % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | (587) ? [v0: int] : ( ~ (v0 = 0) & ub(all_16_4, % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | all_16_3, all_16_3) = v0) % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (587) with fresh symbol all_366_0 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | gives: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | (588) ~ (all_366_0 = 0) & ub(all_16_4, all_16_3, % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | all_16_3) = all_366_0 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | ALPHA: (588) implies: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | (589) ~ (all_366_0 = 0) % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | (590) ub(all_16_4, all_16_3, all_16_3) = all_366_0 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | (591) all_180_0 = all_16_4 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (460) gives: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | | (592) all_180_0 = all_16_3 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (591), (592) imply: % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | | (593) all_16_3 = all_16_4 % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.88 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (593) implies: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (594) all_16_3 = all_16_4 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (594) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (595) ub(all_16_4, all_16_4, all_16_4) = all_366_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (594) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (596) ub(all_16_4, all_16_4, all_16_4) = all_361_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_361_0, all_366_0, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | all_16_4, all_16_4, all_16_4, simplifying with % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (595), (596) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (597) all_366_0 = all_361_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_16_4, all_16_4, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | all_16_4, all_361_0, simplifying with (35), (596) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (598) all_361_0 = 0 | ? [v0: any] : ? [v1: any] : % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (lesseq(all_16_4, all_16_4) = v1 & % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | lesseq(all_16_4, all_16_4) = v0 & ( ~ (v1 = 0) | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = 0))) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (598) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (599) all_361_0 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (599) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (600) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (600) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (601) ? [v0: any] : ? [v1: any] : (lesseq(all_16_4, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | all_16_4) = v1 & lesseq(all_16_4, all_16_4) = % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (601) with fresh symbols all_490_0, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | all_490_1 gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (602) lesseq(all_16_4, all_16_4) = all_490_0 & % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | lesseq(all_16_4, all_16_4) = all_490_1 & ( ~ % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (all_490_0 = 0) | ~ (all_490_1 = 0)) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (602) implies: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (603) lesseq(all_16_4, all_16_4) = all_490_1 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (604) lesseq(all_16_4, all_16_4) = all_490_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (605) ~ (all_490_0 = 0) | ~ (all_490_1 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_490_1, all_490_0, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | all_16_4, all_16_4, simplifying with (603), (604) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (606) all_490_0 = all_490_1 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (605) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (607) ~ (all_490_0 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (606), (607) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (608) ~ (all_490_1 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (lesseq_ref) with all_16_4, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_490_1, simplifying with (35), (603) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_490_1 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (608), (609) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (610) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (610) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (611) ~ (all_490_1 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (lesseq_ref) with all_16_4, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_490_1, simplifying with (35), (603) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_490_1 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (611), (612) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (613) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (613) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (614) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_4, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | all_16_3) = v0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (614) with fresh symbol all_426_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (615) ~ (all_426_0 = 0) & lesseq(all_16_4, all_16_3) = % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | all_426_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (615) implies: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (616) ~ (all_426_0 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (617) lesseq(all_16_4, all_16_3) = all_426_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_16_3, all_16_4, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | all_426_0, simplifying with (35), (36), (617) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (618) all_426_0 = 0 | lesseq(all_16_3, all_16_4) = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_16_4, all_16_3, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | all_16_4, all_361_0, simplifying with (35), (36), % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (584) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (619) all_361_0 = 0 | ? [v0: any] : ? [v1: any] : % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (lesseq(all_16_3, all_16_4) = v1 & % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | lesseq(all_16_4, all_16_4) = v0 & ( ~ (v1 = 0) | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = 0))) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (618) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (620) lesseq(all_16_3, all_16_4) = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (619) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (621) all_361_0 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (621) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (622) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (622) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (623) ? [v0: any] : ? [v1: any] : (lesseq(all_16_3, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_16_4) = v1 & lesseq(all_16_4, all_16_4) = % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (623) with fresh symbols all_473_0, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_473_1 gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (624) lesseq(all_16_3, all_16_4) = all_473_0 & % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | lesseq(all_16_4, all_16_4) = all_473_1 & ( ~ % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (all_473_0 = 0) | ~ (all_473_1 = 0)) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (624) implies: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (625) lesseq(all_16_4, all_16_4) = all_473_1 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (626) lesseq(all_16_3, all_16_4) = all_473_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (627) ~ (all_473_0 = 0) | ~ (all_473_1 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_473_0, all_16_4, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_16_3, simplifying with (620), (626) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_473_0 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (627) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (629) ~ (all_473_0 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (628), (629) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (630) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (630) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (631) ~ (all_473_1 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (lesseq_ref) with all_16_4, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | all_473_1, simplifying with (35), (625) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (632) all_473_1 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (631), (632) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (633) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (633) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (634) all_426_0 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (616), (634) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (635) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (635) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | (636) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_3, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | all_16_4) = v0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (636) with fresh symbol all_404_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | (637) ~ (all_404_0 = 0) & lesseq(all_16_3, all_16_4) = % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | all_404_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (637) implies: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | (638) ~ (all_404_0 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | (639) lesseq(all_16_3, all_16_4) = all_404_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_16_4, all_16_3, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | all_404_0, simplifying with (35), (36), (639) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | (640) all_404_0 = 0 | lesseq(all_16_4, all_16_3) = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_16_4, all_16_3, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | all_16_3, all_366_0, simplifying with (35), (36), % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | (590) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | (641) all_366_0 = 0 | ? [v0: any] : ? [v1: any] : % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | (lesseq(all_16_3, all_16_3) = v1 & % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | lesseq(all_16_4, all_16_3) = v0 & ( ~ (v1 = 0) | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = 0))) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (640) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (642) lesseq(all_16_4, all_16_3) = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (641) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (643) all_366_0 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (643) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (644) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (644) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (645) ? [v0: any] : ? [v1: any] : (lesseq(all_16_3, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | all_16_3) = v1 & lesseq(all_16_4, all_16_3) = % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (645) with fresh symbols all_478_0, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | all_478_1 gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (646) lesseq(all_16_3, all_16_3) = all_478_0 & % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | lesseq(all_16_4, all_16_3) = all_478_1 & ( ~ % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (all_478_0 = 0) | ~ (all_478_1 = 0)) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (646) implies: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (647) lesseq(all_16_4, all_16_3) = all_478_1 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (648) lesseq(all_16_3, all_16_3) = all_478_0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (649) ~ (all_478_0 = 0) | ~ (all_478_1 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_478_1, all_16_3, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | all_16_4, simplifying with (642), (647) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | (650) all_478_1 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (649) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (651) ~ (all_478_0 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (lesseq_ref) with all_16_3, % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | all_478_0, simplifying with (36), (648) gives: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (652) all_478_0 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (651), (652) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (653) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (653) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (654) ~ (all_478_1 = 0) % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (654) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | (655) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (655) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (656) all_404_0 = 0 % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (638), (656) imply: % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | (657) $false % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (657) is inconsistent. % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | | % 73.41/10.89 | | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | | % 73.41/10.89 | | | | | | | | | End of split % 73.41/10.89 | | | | | | | | | % 73.41/10.89 | | | | | | | | End of split % 73.41/10.89 | | | | | | | | % 73.41/10.89 | | | | | | | End of split % 73.41/10.89 | | | | | | | % 73.41/10.89 | | | | | | End of split % 73.41/10.89 | | | | | | % 73.41/10.89 | | | | | End of split % 73.41/10.89 | | | | | % 73.41/10.89 | | | | End of split % 73.41/10.89 | | | | % 73.41/10.89 | | | End of split % 73.41/10.89 | | | % 73.41/10.90 | | End of split % 73.41/10.90 | | % 73.41/10.90 | End of split % 73.41/10.90 | % 73.41/10.90 End of proof % 73.41/10.90 % 73.41/10.90 Sub-proof #1 shows that the following formulas are inconsistent: % 73.41/10.90 ---------------------------------------------------------------- % 73.41/10.90 (1) all_29_2 = all_16_3 | ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_4, % 73.41/10.90 all_16_3) = v0) % 73.41/10.90 (2) lesseq(all_29_2, all_29_2) = 0 % 73.41/10.90 (3) ~ (all_357_0 = 0) | ~ (all_357_1 = 0) % 73.41/10.90 (4) lesseq(all_16_3, all_29_2) = all_357_0 % 73.41/10.90 (5) ~ (all_487_0 = 0) & ub(all_16_4, all_16_3, all_16_3) = all_487_0 % 73.41/10.90 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (lesseq(v1, v0) = % 73.41/10.90 v2) | ~ $i(v1) | ~ $i(v0) | lesseq(v0, v1) = 0) % 73.41/10.90 (7) $i(all_16_3) % 73.41/10.90 (8) lesseq(all_16_4, all_29_2) = all_357_1 % 73.41/10.90 (9) all_357_0 = 0 | lesseq(all_29_2, all_16_3) = 0 % 73.41/10.90 (10) $i(all_16_4) % 73.41/10.90 (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 73.41/10.90 ! [v3: $i] : (v1 = v0 | ~ (lesseq(v3, v2) = v1) | ~ (lesseq(v3, v2) = % 73.41/10.90 v0)) % 73.41/10.90 (12) all_29_2 = all_16_4 | ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_3, % 73.41/10.90 all_16_4) = v0) % 73.41/10.90 (13) all_357_1 = 0 | lesseq(all_29_2, all_16_4) = 0 % 73.41/10.90 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 73.41/10.90 (ub(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 73.41/10.90 any] : ? [v5: any] : (lesseq(v1, v2) = v5 & lesseq(v0, v2) = v4 & ( % 73.41/10.90 ~ (v5 = 0) | ~ (v4 = 0)))) % 73.41/10.90 % 73.41/10.90 Begin of proof % 73.41/10.90 | % 73.41/10.90 | ALPHA: (5) implies: % 73.41/10.90 | (15) ~ (all_487_0 = 0) % 73.41/10.90 | (16) ub(all_16_4, all_16_3, all_16_3) = all_487_0 % 73.41/10.90 | % 73.41/10.90 | BETA: splitting (1) gives: % 73.41/10.90 | % 73.41/10.90 | Case 1: % 73.41/10.90 | | % 73.41/10.90 | | (17) all_29_2 = all_16_3 % 73.41/10.90 | | % 73.41/10.90 | | REDUCE: (2), (17) imply: % 73.41/10.90 | | (18) lesseq(all_16_3, all_16_3) = 0 % 73.41/10.90 | | % 73.41/10.90 | | REDUCE: (4), (17) imply: % 73.41/10.90 | | (19) lesseq(all_16_3, all_16_3) = all_357_0 % 73.41/10.90 | | % 73.41/10.90 | | REDUCE: (8), (17) imply: % 73.41/10.90 | | (20) lesseq(all_16_4, all_16_3) = all_357_1 % 73.41/10.90 | | % 73.41/10.90 | | GROUND_INST: instantiating (11) with 0, all_357_0, all_16_3, all_16_3, % 73.41/10.90 | | simplifying with (18), (19) gives: % 73.41/10.90 | | (21) all_357_0 = 0 % 73.41/10.90 | | % 73.41/10.90 | | BETA: splitting (3) gives: % 73.41/10.90 | | % 73.41/10.90 | | Case 1: % 73.41/10.90 | | | % 73.41/10.90 | | | (22) ~ (all_357_0 = 0) % 73.41/10.90 | | | % 73.41/10.90 | | | REDUCE: (21), (22) imply: % 73.41/10.90 | | | (23) $false % 73.41/10.90 | | | % 73.41/10.90 | | | CLOSE: (23) is inconsistent. % 73.41/10.90 | | | % 73.41/10.90 | | Case 2: % 73.41/10.90 | | | % 73.41/10.90 | | | (24) ~ (all_357_1 = 0) % 73.41/10.90 | | | % 73.41/10.90 | | | BETA: splitting (13) gives: % 73.41/10.90 | | | % 73.41/10.90 | | | Case 1: % 73.41/10.90 | | | | % 73.41/10.90 | | | | (25) lesseq(all_29_2, all_16_4) = 0 % 73.41/10.90 | | | | % 73.41/10.90 | | | | REDUCE: (17), (25) imply: % 73.41/10.90 | | | | (26) lesseq(all_16_3, all_16_4) = 0 % 73.41/10.90 | | | | % 73.41/10.90 | | | | BETA: splitting (12) gives: % 73.41/10.90 | | | | % 73.41/10.90 | | | | Case 1: % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | (27) all_29_2 = all_16_4 % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | COMBINE_EQS: (17), (27) imply: % 73.41/10.90 | | | | | (28) all_16_3 = all_16_4 % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | SIMP: (28) implies: % 73.41/10.90 | | | | | (29) all_16_3 = all_16_4 % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | REDUCE: (26), (29) imply: % 73.41/10.90 | | | | | (30) lesseq(all_16_4, all_16_4) = 0 % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | REDUCE: (20), (29) imply: % 73.41/10.90 | | | | | (31) lesseq(all_16_4, all_16_4) = all_357_1 % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | GROUND_INST: instantiating (11) with 0, all_357_1, all_16_4, all_16_4, % 73.41/10.90 | | | | | simplifying with (30), (31) gives: % 73.41/10.90 | | | | | (32) all_357_1 = 0 % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | REDUCE: (24), (32) imply: % 73.41/10.90 | | | | | (33) $false % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | CLOSE: (33) is inconsistent. % 73.41/10.90 | | | | | % 73.41/10.90 | | | | Case 2: % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | (34) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_3, all_16_4) = v0) % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | DELTA: instantiating (34) with fresh symbol all_515_0 gives: % 73.41/10.90 | | | | | (35) ~ (all_515_0 = 0) & lesseq(all_16_3, all_16_4) = all_515_0 % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | ALPHA: (35) implies: % 73.41/10.90 | | | | | (36) ~ (all_515_0 = 0) % 73.41/10.90 | | | | | (37) lesseq(all_16_3, all_16_4) = all_515_0 % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | GROUND_INST: instantiating (11) with 0, all_515_0, all_16_4, all_16_3, % 73.41/10.90 | | | | | simplifying with (26), (37) gives: % 73.41/10.90 | | | | | (38) all_515_0 = 0 % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | REDUCE: (36), (38) imply: % 73.41/10.90 | | | | | (39) $false % 73.41/10.90 | | | | | % 73.41/10.90 | | | | | CLOSE: (39) is inconsistent. % 73.41/10.90 | | | | | % 73.41/10.90 | | | | End of split % 73.41/10.90 | | | | % 73.41/10.90 | | | Case 2: % 73.41/10.90 | | | | % 73.41/10.90 | | | | (40) all_357_1 = 0 % 73.41/10.90 | | | | % 73.41/10.90 | | | | REDUCE: (24), (40) imply: % 73.41/10.90 | | | | (41) $false % 73.41/10.90 | | | | % 73.41/10.90 | | | | CLOSE: (41) is inconsistent. % 73.41/10.90 | | | | % 73.41/10.90 | | | End of split % 73.41/10.90 | | | % 73.41/10.90 | | End of split % 73.41/10.90 | | % 73.41/10.90 | Case 2: % 73.41/10.90 | | % 73.41/10.90 | | (42) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_4, all_16_3) = v0) % 73.41/10.90 | | % 73.41/10.90 | | DELTA: instantiating (42) with fresh symbol all_499_0 gives: % 73.41/10.90 | | (43) ~ (all_499_0 = 0) & lesseq(all_16_4, all_16_3) = all_499_0 % 73.41/10.90 | | % 73.41/10.90 | | ALPHA: (43) implies: % 73.41/10.90 | | (44) ~ (all_499_0 = 0) % 73.41/10.90 | | (45) lesseq(all_16_4, all_16_3) = all_499_0 % 73.41/10.90 | | % 73.41/10.90 | | BETA: splitting (12) gives: % 73.41/10.90 | | % 73.41/10.90 | | Case 1: % 73.41/10.90 | | | % 73.41/10.90 | | | (46) all_29_2 = all_16_4 % 73.41/10.90 | | | % 73.41/10.90 | | | REDUCE: (2), (46) imply: % 73.41/10.90 | | | (47) lesseq(all_16_4, all_16_4) = 0 % 73.41/10.90 | | | % 73.41/10.90 | | | REDUCE: (8), (46) imply: % 73.41/10.90 | | | (48) lesseq(all_16_4, all_16_4) = all_357_1 % 73.41/10.90 | | | % 73.41/10.90 | | | BETA: splitting (9) gives: % 73.41/10.90 | | | % 73.41/10.90 | | | Case 1: % 73.41/10.90 | | | | % 73.41/10.90 | | | | (49) lesseq(all_29_2, all_16_3) = 0 % 73.41/10.90 | | | | % 73.41/10.90 | | | | REDUCE: (46), (49) imply: % 73.41/10.90 | | | | (50) lesseq(all_16_4, all_16_3) = 0 % 73.41/10.90 | | | | % 73.41/10.90 | | | | GROUND_INST: instantiating (11) with all_499_0, 0, all_16_3, all_16_4, % 73.41/10.90 | | | | simplifying with (45), (50) gives: % 73.41/10.90 | | | | (51) all_499_0 = 0 % 73.41/10.90 | | | | % 73.41/10.91 | | | | REDUCE: (44), (51) imply: % 73.41/10.91 | | | | (52) $false % 73.41/10.91 | | | | % 73.41/10.91 | | | | CLOSE: (52) is inconsistent. % 73.41/10.91 | | | | % 73.41/10.91 | | | Case 2: % 73.41/10.91 | | | | % 73.41/10.91 | | | | (53) all_357_0 = 0 % 73.41/10.91 | | | | % 73.41/10.91 | | | | BETA: splitting (3) gives: % 73.41/10.91 | | | | % 73.41/10.91 | | | | Case 1: % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | (54) ~ (all_357_0 = 0) % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | REDUCE: (53), (54) imply: % 73.41/10.91 | | | | | (55) $false % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | CLOSE: (55) is inconsistent. % 73.41/10.91 | | | | | % 73.41/10.91 | | | | Case 2: % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | (56) ~ (all_357_1 = 0) % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | GROUND_INST: instantiating (11) with 0, all_357_1, all_16_4, all_16_4, % 73.41/10.91 | | | | | simplifying with (47), (48) gives: % 73.41/10.91 | | | | | (57) all_357_1 = 0 % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | REDUCE: (56), (57) imply: % 73.41/10.91 | | | | | (58) $false % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | CLOSE: (58) is inconsistent. % 73.41/10.91 | | | | | % 73.41/10.91 | | | | End of split % 73.41/10.91 | | | | % 73.41/10.91 | | | End of split % 73.41/10.91 | | | % 73.41/10.91 | | Case 2: % 73.41/10.91 | | | % 73.41/10.91 | | | (59) ? [v0: int] : ( ~ (v0 = 0) & lesseq(all_16_3, all_16_4) = v0) % 73.41/10.91 | | | % 73.41/10.91 | | | DELTA: instantiating (59) with fresh symbol all_507_0 gives: % 73.41/10.91 | | | (60) ~ (all_507_0 = 0) & lesseq(all_16_3, all_16_4) = all_507_0 % 73.41/10.91 | | | % 73.41/10.91 | | | ALPHA: (60) implies: % 73.41/10.91 | | | (61) ~ (all_507_0 = 0) % 73.41/10.91 | | | (62) lesseq(all_16_3, all_16_4) = all_507_0 % 73.41/10.91 | | | % 73.41/10.91 | | | GROUND_INST: instantiating (6) with all_16_4, all_16_3, all_507_0, % 73.41/10.91 | | | simplifying with (7), (10), (62) gives: % 73.41/10.91 | | | (63) all_507_0 = 0 | lesseq(all_16_4, all_16_3) = 0 % 73.41/10.91 | | | % 73.41/10.91 | | | GROUND_INST: instantiating (14) with all_16_4, all_16_3, all_16_3, % 73.41/10.91 | | | all_487_0, simplifying with (7), (10), (16) gives: % 73.41/10.91 | | | (64) all_487_0 = 0 | ? [v0: any] : ? [v1: any] : (lesseq(all_16_3, % 73.41/10.91 | | | all_16_3) = v1 & lesseq(all_16_4, all_16_3) = v0 & ( ~ (v1 = % 73.41/10.91 | | | 0) | ~ (v0 = 0))) % 73.41/10.91 | | | % 73.41/10.91 | | | BETA: splitting (63) gives: % 73.41/10.91 | | | % 73.41/10.91 | | | Case 1: % 73.41/10.91 | | | | % 73.41/10.91 | | | | (65) lesseq(all_16_4, all_16_3) = 0 % 73.41/10.91 | | | | % 73.41/10.91 | | | | BETA: splitting (64) gives: % 73.41/10.91 | | | | % 73.41/10.91 | | | | Case 1: % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | (66) all_487_0 = 0 % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | REDUCE: (15), (66) imply: % 73.41/10.91 | | | | | (67) $false % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | CLOSE: (67) is inconsistent. % 73.41/10.91 | | | | | % 73.41/10.91 | | | | Case 2: % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | (68) ? [v0: any] : ? [v1: any] : (lesseq(all_16_3, all_16_3) = v1 % 73.41/10.91 | | | | | & lesseq(all_16_4, all_16_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 73.41/10.91 | | | | | 0))) % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | DELTA: instantiating (68) with fresh symbols all_597_0, all_597_1 % 73.41/10.91 | | | | | gives: % 73.41/10.91 | | | | | (69) lesseq(all_16_3, all_16_3) = all_597_0 & lesseq(all_16_4, % 73.41/10.91 | | | | | all_16_3) = all_597_1 & ( ~ (all_597_0 = 0) | ~ (all_597_1 % 73.41/10.91 | | | | | = 0)) % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | ALPHA: (69) implies: % 73.41/10.91 | | | | | (70) lesseq(all_16_4, all_16_3) = all_597_1 % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | GROUND_INST: instantiating (11) with all_499_0, all_597_1, all_16_3, % 73.41/10.91 | | | | | all_16_4, simplifying with (45), (70) gives: % 73.41/10.91 | | | | | (71) all_597_1 = all_499_0 % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | GROUND_INST: instantiating (11) with 0, all_597_1, all_16_3, all_16_4, % 73.41/10.91 | | | | | simplifying with (65), (70) gives: % 73.41/10.91 | | | | | (72) all_597_1 = 0 % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | COMBINE_EQS: (71), (72) imply: % 73.41/10.91 | | | | | (73) all_499_0 = 0 % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | SIMP: (73) implies: % 73.41/10.91 | | | | | (74) all_499_0 = 0 % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | REDUCE: (44), (74) imply: % 73.41/10.91 | | | | | (75) $false % 73.41/10.91 | | | | | % 73.41/10.91 | | | | | CLOSE: (75) is inconsistent. % 73.41/10.91 | | | | | % 73.41/10.91 | | | | End of split % 73.41/10.91 | | | | % 73.41/10.91 | | | Case 2: % 73.41/10.91 | | | | % 73.41/10.91 | | | | (76) all_507_0 = 0 % 73.41/10.91 | | | | % 73.41/10.91 | | | | REDUCE: (61), (76) imply: % 73.41/10.91 | | | | (77) $false % 73.41/10.91 | | | | % 73.41/10.91 | | | | CLOSE: (77) is inconsistent. % 73.41/10.91 | | | | % 73.41/10.91 | | | End of split % 73.41/10.91 | | | % 73.41/10.91 | | End of split % 73.41/10.91 | | % 73.41/10.91 | End of split % 73.41/10.91 | % 73.41/10.91 End of proof % 73.41/10.91 % 73.41/10.91 Sub-proof #2 shows that the following formulas are inconsistent: % 73.41/10.91 ---------------------------------------------------------------- % 73.41/10.91 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 73.41/10.91 ! [v3: $i] : (v1 = v0 | ~ (lesseq(v3, v2) = v1) | ~ (lesseq(v3, v2) = % 73.41/10.91 v0)) % 73.41/10.91 (2) lesseq(all_16_3, all_16_4) = all_200_0 % 73.41/10.91 (3) lesseq(all_16_3, all_16_4) = 0 % 73.41/10.91 (4) ~ (all_200_0 = 0) % 73.41/10.91 % 73.41/10.91 Begin of proof % 73.41/10.91 | % 73.41/10.91 | GROUND_INST: instantiating (1) with all_200_0, 0, all_16_4, all_16_3, % 73.41/10.91 | simplifying with (2), (3) gives: % 73.41/10.91 | (5) all_200_0 = 0 % 73.41/10.91 | % 73.41/10.91 | REDUCE: (4), (5) imply: % 73.41/10.91 | (6) $false % 73.41/10.91 | % 73.41/10.91 | CLOSE: (6) is inconsistent. % 73.41/10.91 | % 73.41/10.91 End of proof % 73.41/10.91 % SZS output end Proof for theBenchmark % 73.41/10.91 % 73.41/10.91 10289ms %------------------------------------------------------------------------------