%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET706+4 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.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 15:26:04 EDT 2023 % Result : Theorem 7.54s 1.85s % Output : Proof 10.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET706+4 : TPTP v8.1.2. Released v2.2.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n007.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 : Sat Aug 26 15:38:41 EDT 2023 % 0.12/0.34 % CPUTime : % 0.18/0.61 ________ _____ % 0.18/0.61 ___ __ \_________(_)________________________________ % 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.61 % 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.61 (2023-06-19) % 0.18/0.61 % 0.18/0.61 (c) Philipp Rümmer, 2009-2023 % 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.61 Amanda Stjerna. % 0.18/0.61 Free software under BSD-3-Clause. % 0.18/0.61 % 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.61 % 0.18/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.65 Running up to 7 provers in parallel. % 0.18/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.12/1.07 Prover 1: Preprocessing ... % 2.12/1.07 Prover 4: Preprocessing ... % 2.83/1.10 Prover 5: Preprocessing ... % 2.83/1.10 Prover 0: Preprocessing ... % 2.83/1.10 Prover 6: Preprocessing ... % 2.83/1.10 Prover 3: Preprocessing ... % 2.83/1.10 Prover 2: Preprocessing ... % 5.21/1.46 Prover 1: Constructing countermodel ... % 5.21/1.48 Prover 5: Proving ... % 5.21/1.48 Prover 6: Proving ... % 5.21/1.48 Prover 3: Constructing countermodel ... % 5.21/1.48 Prover 2: Proving ... % 5.80/1.53 Prover 4: Constructing countermodel ... % 5.80/1.55 Prover 0: Proving ... % 7.54/1.85 Prover 3: proved (1183ms) % 7.54/1.85 % 7.54/1.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.54/1.85 % 7.54/1.85 Prover 5: stopped % 7.54/1.85 Prover 2: stopped % 7.54/1.85 Prover 6: stopped % 7.54/1.86 Prover 0: stopped % 7.54/1.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.54/1.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.54/1.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.54/1.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.54/1.86 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.38/1.90 Prover 10: Preprocessing ... % 8.38/1.91 Prover 11: Preprocessing ... % 8.38/1.91 Prover 13: Preprocessing ... % 8.38/1.91 Prover 7: Preprocessing ... % 8.38/1.93 Prover 8: Preprocessing ... % 8.84/1.97 Prover 10: Warning: ignoring some quantifiers % 8.84/1.97 Prover 7: Warning: ignoring some quantifiers % 8.84/1.98 Prover 10: Constructing countermodel ... % 8.84/1.98 Prover 7: Constructing countermodel ... % 9.20/2.02 Prover 10: gave up % 9.20/2.04 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.48/2.06 Prover 16: Preprocessing ... % 9.48/2.06 Prover 1: Found proof (size 111) % 9.48/2.06 Prover 1: proved (1409ms) % 9.48/2.07 Prover 4: stopped % 9.48/2.07 Prover 7: stopped % 9.48/2.08 Prover 16: stopped % 9.48/2.09 Prover 13: Warning: ignoring some quantifiers % 9.48/2.10 Prover 8: Warning: ignoring some quantifiers % 9.48/2.10 Prover 13: Constructing countermodel ... % 9.48/2.10 Prover 11: Constructing countermodel ... % 9.48/2.11 Prover 8: Constructing countermodel ... % 9.48/2.11 Prover 13: stopped % 9.48/2.11 Prover 11: stopped % 9.48/2.12 Prover 8: stopped % 9.48/2.12 % 9.48/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.48/2.12 % 9.48/2.13 % SZS output start Proof for theBenchmark % 10.08/2.14 Assumptions after simplification: % 10.08/2.14 --------------------------------- % 10.08/2.14 % 10.08/2.14 (difference) % 10.08/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.08/2.18 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 10.08/2.18 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 & % 10.08/2.18 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 10.08/2.18 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, % 10.08/2.18 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 10.08/2.18 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 10.08/2.18 % 10.08/2.18 (equal_set) % 10.08/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 10.08/2.18 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 10.08/2.18 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 10.08/2.18 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 10.08/2.18 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 10.08/2.18 % 10.08/2.18 (subset) % 10.08/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 10.08/2.19 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 10.08/2.19 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 10.08/2.19 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 10.08/2.19 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 10.08/2.19 % 10.08/2.19 (thI49) % 10.08/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 10.08/2.19 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & difference(v1, v2) = v4 & % 10.08/2.19 difference(v0, v2) = v3 & difference(v0, v1) = v5 & union(v4, v5) = v6 & % 10.08/2.19 equal_set(v3, v6) = v7 & subset(v2, v1) = 0 & subset(v1, v0) = 0 & $i(v6) & % 10.08/2.19 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.08/2.19 % 10.08/2.19 (union) % 10.33/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.33/2.19 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 10.33/2.19 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 10.33/2.19 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 10.33/2.19 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 10.33/2.19 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 10.33/2.19 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 10.33/2.19 % 10.33/2.19 (function-axioms) % 10.33/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.33/2.20 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 10.33/2.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.33/2.20 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 10.33/2.20 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 10.33/2.20 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 10.33/2.20 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 10.33/2.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.33/2.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 10.33/2.20 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.33/2.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 10.33/2.20 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.33/2.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.33/2.20 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 10.33/2.20 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 10.33/2.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 10.33/2.20 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 10.33/2.20 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 10.33/2.20 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 10.33/2.20 (power_set(v2) = v0)) % 10.33/2.20 % 10.33/2.20 Further assumptions not needed in the proof: % 10.33/2.20 -------------------------------------------- % 10.33/2.20 empty_set, intersection, power_set, product, singleton, sum, unordered_pair % 10.33/2.20 % 10.33/2.20 Those formulas are unsatisfiable: % 10.33/2.20 --------------------------------- % 10.33/2.20 % 10.33/2.20 Begin of proof % 10.33/2.20 | % 10.33/2.20 | ALPHA: (subset) implies: % 10.33/2.20 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 10.33/2.20 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 10.33/2.20 | member(v2, v1) = 0)) % 10.33/2.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 10.33/2.20 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 10.33/2.20 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 10.33/2.20 | % 10.33/2.20 | ALPHA: (equal_set) implies: % 10.33/2.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 10.33/2.20 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.33/2.20 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 10.33/2.20 | 0)))) % 10.33/2.20 | % 10.33/2.20 | ALPHA: (union) implies: % 10.33/2.20 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 10.33/2.20 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 10.33/2.20 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 10.33/2.20 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 10.33/2.20 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 10.33/2.20 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 10.33/2.20 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 10.33/2.20 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 10.33/2.20 | v5)) % 10.33/2.20 | % 10.33/2.20 | ALPHA: (difference) implies: % 10.33/2.21 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.33/2.21 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ % 10.33/2.21 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0 % 10.33/2.21 | & member(v0, v1) = v4)) % 10.33/2.21 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 10.33/2.21 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ % 10.33/2.21 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 10.33/2.21 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 10.33/2.21 | % 10.33/2.21 | ALPHA: (function-axioms) implies: % 10.33/2.21 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.33/2.21 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 10.33/2.21 | = v0)) % 10.33/2.21 | % 10.33/2.21 | DELTA: instantiating (thI49) with fresh symbols all_15_0, all_15_1, all_15_2, % 10.33/2.21 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives: % 10.33/2.21 | (9) ~ (all_15_0 = 0) & difference(all_15_6, all_15_5) = all_15_3 & % 10.33/2.21 | difference(all_15_7, all_15_5) = all_15_4 & difference(all_15_7, % 10.33/2.21 | all_15_6) = all_15_2 & union(all_15_3, all_15_2) = all_15_1 & % 10.33/2.21 | equal_set(all_15_4, all_15_1) = all_15_0 & subset(all_15_5, all_15_6) = % 10.33/2.21 | 0 & subset(all_15_6, all_15_7) = 0 & $i(all_15_1) & $i(all_15_2) & % 10.33/2.21 | $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & % 10.33/2.21 | $i(all_15_7) % 10.33/2.21 | % 10.33/2.21 | ALPHA: (9) implies: % 10.33/2.21 | (10) ~ (all_15_0 = 0) % 10.33/2.21 | (11) $i(all_15_7) % 10.33/2.21 | (12) $i(all_15_6) % 10.33/2.21 | (13) $i(all_15_5) % 10.33/2.21 | (14) $i(all_15_4) % 10.33/2.21 | (15) $i(all_15_3) % 10.33/2.21 | (16) $i(all_15_2) % 10.33/2.21 | (17) $i(all_15_1) % 10.33/2.21 | (18) subset(all_15_6, all_15_7) = 0 % 10.33/2.21 | (19) subset(all_15_5, all_15_6) = 0 % 10.33/2.21 | (20) equal_set(all_15_4, all_15_1) = all_15_0 % 10.33/2.21 | (21) union(all_15_3, all_15_2) = all_15_1 % 10.33/2.21 | (22) difference(all_15_7, all_15_6) = all_15_2 % 10.33/2.21 | (23) difference(all_15_7, all_15_5) = all_15_4 % 10.33/2.21 | (24) difference(all_15_6, all_15_5) = all_15_3 % 10.33/2.21 | % 10.33/2.21 | GROUND_INST: instantiating (1) with all_15_6, all_15_7, simplifying with (11), % 10.33/2.21 | (12), (18) gives: % 10.33/2.21 | (25) ! [v0: $i] : ( ~ (member(v0, all_15_6) = 0) | ~ $i(v0) | member(v0, % 10.33/2.21 | all_15_7) = 0) % 10.33/2.21 | % 10.33/2.21 | GROUND_INST: instantiating (1) with all_15_5, all_15_6, simplifying with (12), % 10.33/2.21 | (13), (19) gives: % 10.33/2.21 | (26) ! [v0: $i] : ( ~ (member(v0, all_15_5) = 0) | ~ $i(v0) | member(v0, % 10.33/2.21 | all_15_6) = 0) % 10.33/2.21 | % 10.33/2.21 | GROUND_INST: instantiating (3) with all_15_4, all_15_1, all_15_0, simplifying % 10.33/2.21 | with (14), (17), (20) gives: % 10.33/2.21 | (27) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 10.33/2.21 | all_15_4) = v1 & subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | % 10.33/2.21 | ~ (v0 = 0))) % 10.33/2.21 | % 10.33/2.21 | BETA: splitting (27) gives: % 10.33/2.21 | % 10.33/2.21 | Case 1: % 10.33/2.22 | | % 10.33/2.22 | | (28) all_15_0 = 0 % 10.33/2.22 | | % 10.33/2.22 | | REDUCE: (10), (28) imply: % 10.33/2.22 | | (29) $false % 10.33/2.22 | | % 10.33/2.22 | | CLOSE: (29) is inconsistent. % 10.33/2.22 | | % 10.33/2.22 | Case 2: % 10.33/2.22 | | % 10.33/2.22 | | (30) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_4) = v1 & % 10.33/2.22 | | subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.33/2.22 | | % 10.33/2.22 | | DELTA: instantiating (30) with fresh symbols all_27_0, all_27_1 gives: % 10.33/2.22 | | (31) subset(all_15_1, all_15_4) = all_27_0 & subset(all_15_4, all_15_1) = % 10.33/2.22 | | all_27_1 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0)) % 10.33/2.22 | | % 10.33/2.22 | | ALPHA: (31) implies: % 10.33/2.22 | | (32) subset(all_15_4, all_15_1) = all_27_1 % 10.33/2.22 | | (33) subset(all_15_1, all_15_4) = all_27_0 % 10.33/2.22 | | (34) ~ (all_27_0 = 0) | ~ (all_27_1 = 0) % 10.33/2.22 | | % 10.33/2.22 | | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_27_1, % 10.33/2.22 | | simplifying with (14), (17), (32) gives: % 10.33/2.22 | | (35) all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.33/2.22 | | member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 10.33/2.22 | | % 10.33/2.22 | | GROUND_INST: instantiating (2) with all_15_1, all_15_4, all_27_0, % 10.33/2.22 | | simplifying with (14), (17), (33) gives: % 10.33/2.22 | | (36) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.33/2.22 | | member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 10.33/2.22 | | % 10.33/2.22 | | BETA: splitting (34) gives: % 10.33/2.22 | | % 10.33/2.22 | | Case 1: % 10.33/2.22 | | | % 10.33/2.22 | | | (37) ~ (all_27_0 = 0) % 10.33/2.22 | | | % 10.33/2.22 | | | BETA: splitting (36) gives: % 10.33/2.22 | | | % 10.33/2.22 | | | Case 1: % 10.33/2.22 | | | | % 10.33/2.22 | | | | (38) all_27_0 = 0 % 10.33/2.22 | | | | % 10.33/2.22 | | | | REDUCE: (37), (38) imply: % 10.33/2.22 | | | | (39) $false % 10.33/2.22 | | | | % 10.33/2.22 | | | | CLOSE: (39) is inconsistent. % 10.33/2.22 | | | | % 10.33/2.22 | | | Case 2: % 10.33/2.22 | | | | % 10.33/2.22 | | | | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 10.33/2.22 | | | | = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 10.33/2.22 | | | | % 10.33/2.22 | | | | DELTA: instantiating (40) with fresh symbols all_40_0, all_40_1 gives: % 10.33/2.22 | | | | (41) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = 0 & % 10.33/2.22 | | | | member(all_40_1, all_15_4) = all_40_0 & $i(all_40_1) % 10.33/2.22 | | | | % 10.33/2.22 | | | | ALPHA: (41) implies: % 10.33/2.22 | | | | (42) ~ (all_40_0 = 0) % 10.33/2.22 | | | | (43) $i(all_40_1) % 10.33/2.22 | | | | (44) member(all_40_1, all_15_4) = all_40_0 % 10.33/2.22 | | | | (45) member(all_40_1, all_15_1) = 0 % 10.33/2.22 | | | | % 10.33/2.22 | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_5, all_15_7, % 10.33/2.22 | | | | all_15_4, all_40_0, simplifying with (11), (13), (23), % 10.33/2.22 | | | | (43), (44) gives: % 10.33/2.22 | | | | (46) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1, % 10.33/2.22 | | | | all_15_5) = v1 & member(all_40_1, all_15_7) = v0 & ( ~ (v0 = % 10.33/2.22 | | | | 0) | v1 = 0)) % 10.33/2.22 | | | | % 10.33/2.22 | | | | GROUND_INST: instantiating (4) with all_40_1, all_15_3, all_15_2, % 10.33/2.22 | | | | all_15_1, simplifying with (15), (16), (21), (43), (45) % 10.33/2.22 | | | | gives: % 10.33/2.22 | | | | (47) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_2) = v1 & % 10.33/2.22 | | | | member(all_40_1, all_15_3) = v0 & (v1 = 0 | v0 = 0)) % 10.33/2.22 | | | | % 10.33/2.22 | | | | DELTA: instantiating (47) with fresh symbols all_47_0, all_47_1 gives: % 10.33/2.22 | | | | (48) member(all_40_1, all_15_2) = all_47_0 & member(all_40_1, % 10.33/2.23 | | | | all_15_3) = all_47_1 & (all_47_0 = 0 | all_47_1 = 0) % 10.33/2.23 | | | | % 10.33/2.23 | | | | ALPHA: (48) implies: % 10.33/2.23 | | | | (49) member(all_40_1, all_15_3) = all_47_1 % 10.33/2.23 | | | | (50) member(all_40_1, all_15_2) = all_47_0 % 10.33/2.23 | | | | (51) all_47_0 = 0 | all_47_1 = 0 % 10.33/2.23 | | | | % 10.33/2.23 | | | | BETA: splitting (46) gives: % 10.33/2.23 | | | | % 10.33/2.23 | | | | Case 1: % 10.33/2.23 | | | | | % 10.33/2.23 | | | | | (52) all_40_0 = 0 % 10.33/2.23 | | | | | % 10.33/2.23 | | | | | REDUCE: (42), (52) imply: % 10.33/2.23 | | | | | (53) $false % 10.33/2.23 | | | | | % 10.33/2.23 | | | | | CLOSE: (53) is inconsistent. % 10.33/2.23 | | | | | % 10.33/2.23 | | | | Case 2: % 10.33/2.23 | | | | | % 10.33/2.23 | | | | | (54) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_5) = v1 % 10.33/2.23 | | | | | & member(all_40_1, all_15_7) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 10.33/2.23 | | | | | % 10.33/2.23 | | | | | DELTA: instantiating (54) with fresh symbols all_53_0, all_53_1 gives: % 10.33/2.23 | | | | | (55) member(all_40_1, all_15_5) = all_53_0 & member(all_40_1, % 10.33/2.23 | | | | | all_15_7) = all_53_1 & ( ~ (all_53_1 = 0) | all_53_0 = 0) % 10.33/2.23 | | | | | % 10.33/2.23 | | | | | ALPHA: (55) implies: % 10.33/2.23 | | | | | (56) member(all_40_1, all_15_7) = all_53_1 % 10.33/2.23 | | | | | (57) member(all_40_1, all_15_5) = all_53_0 % 10.33/2.23 | | | | | (58) ~ (all_53_1 = 0) | all_53_0 = 0 % 10.33/2.23 | | | | | % 10.33/2.23 | | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_6, all_15_7, % 10.33/2.23 | | | | | all_15_2, all_47_0, simplifying with (11), (12), (22), % 10.33/2.23 | | | | | (43), (50) gives: % 10.33/2.23 | | | | | (59) all_47_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1, % 10.33/2.23 | | | | | all_15_6) = v1 & member(all_40_1, all_15_7) = v0 & ( ~ (v0 % 10.33/2.23 | | | | | = 0) | v1 = 0)) % 10.33/2.23 | | | | | % 10.33/2.23 | | | | | BETA: splitting (51) gives: % 10.33/2.23 | | | | | % 10.33/2.23 | | | | | Case 1: % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | (60) all_47_0 = 0 % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | REDUCE: (50), (60) imply: % 10.33/2.23 | | | | | | (61) member(all_40_1, all_15_2) = 0 % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | GROUND_INST: instantiating (6) with all_40_1, all_15_6, all_15_7, % 10.33/2.23 | | | | | | all_15_2, simplifying with (11), (12), (22), (43), (61) % 10.33/2.23 | | | | | | gives: % 10.33/2.23 | | | | | | (62) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_6) = % 10.33/2.23 | | | | | | v0 & member(all_40_1, all_15_7) = 0) % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | DELTA: instantiating (62) with fresh symbol all_77_0 gives: % 10.33/2.23 | | | | | | (63) ~ (all_77_0 = 0) & member(all_40_1, all_15_6) = all_77_0 & % 10.33/2.23 | | | | | | member(all_40_1, all_15_7) = 0 % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | ALPHA: (63) implies: % 10.33/2.23 | | | | | | (64) ~ (all_77_0 = 0) % 10.33/2.23 | | | | | | (65) member(all_40_1, all_15_7) = 0 % 10.33/2.23 | | | | | | (66) member(all_40_1, all_15_6) = all_77_0 % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | GROUND_INST: instantiating (8) with all_53_1, 0, all_15_7, all_40_1, % 10.33/2.23 | | | | | | simplifying with (56), (65) gives: % 10.33/2.23 | | | | | | (67) all_53_1 = 0 % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | BETA: splitting (58) gives: % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | Case 1: % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | | (68) ~ (all_53_1 = 0) % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | | REDUCE: (67), (68) imply: % 10.33/2.23 | | | | | | | (69) $false % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | | CLOSE: (69) is inconsistent. % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | Case 2: % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | | (70) all_53_0 = 0 % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | | REDUCE: (57), (70) imply: % 10.33/2.23 | | | | | | | (71) member(all_40_1, all_15_5) = 0 % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | | GROUND_INST: instantiating (26) with all_40_1, simplifying with % 10.33/2.23 | | | | | | | (43), (71) gives: % 10.33/2.23 | | | | | | | (72) member(all_40_1, all_15_6) = 0 % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | | GROUND_INST: instantiating (8) with all_77_0, 0, all_15_6, % 10.33/2.23 | | | | | | | all_40_1, simplifying with (66), (72) gives: % 10.33/2.23 | | | | | | | (73) all_77_0 = 0 % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | | REDUCE: (64), (73) imply: % 10.33/2.23 | | | | | | | (74) $false % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | | CLOSE: (74) is inconsistent. % 10.33/2.23 | | | | | | | % 10.33/2.23 | | | | | | End of split % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | Case 2: % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | (75) all_47_1 = 0 % 10.33/2.23 | | | | | | (76) ~ (all_47_0 = 0) % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | REDUCE: (49), (75) imply: % 10.33/2.23 | | | | | | (77) member(all_40_1, all_15_3) = 0 % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | BETA: splitting (59) gives: % 10.33/2.23 | | | | | | % 10.33/2.23 | | | | | | Case 1: % 10.33/2.23 | | | | | | | % 10.33/2.24 | | | | | | | (78) all_47_0 = 0 % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | REDUCE: (76), (78) imply: % 10.33/2.24 | | | | | | | (79) $false % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | CLOSE: (79) is inconsistent. % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | Case 2: % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | (80) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_6) % 10.33/2.24 | | | | | | | = v1 & member(all_40_1, all_15_7) = v0 & ( ~ (v0 = 0) | % 10.33/2.24 | | | | | | | v1 = 0)) % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | DELTA: instantiating (80) with fresh symbols all_76_0, all_76_1 % 10.33/2.24 | | | | | | | gives: % 10.33/2.24 | | | | | | | (81) member(all_40_1, all_15_6) = all_76_0 & member(all_40_1, % 10.33/2.24 | | | | | | | all_15_7) = all_76_1 & ( ~ (all_76_1 = 0) | all_76_0 = % 10.33/2.24 | | | | | | | 0) % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | ALPHA: (81) implies: % 10.33/2.24 | | | | | | | (82) member(all_40_1, all_15_7) = all_76_1 % 10.33/2.24 | | | | | | | (83) member(all_40_1, all_15_6) = all_76_0 % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | GROUND_INST: instantiating (8) with all_53_1, all_76_1, all_15_7, % 10.33/2.24 | | | | | | | all_40_1, simplifying with (56), (82) gives: % 10.33/2.24 | | | | | | | (84) all_76_1 = all_53_1 % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | GROUND_INST: instantiating (6) with all_40_1, all_15_5, all_15_6, % 10.33/2.24 | | | | | | | all_15_3, simplifying with (12), (13), (24), (43), % 10.33/2.24 | | | | | | | (77) gives: % 10.33/2.24 | | | | | | | (85) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_5) = % 10.33/2.24 | | | | | | | v0 & member(all_40_1, all_15_6) = 0) % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | DELTA: instantiating (85) with fresh symbol all_87_0 gives: % 10.33/2.24 | | | | | | | (86) ~ (all_87_0 = 0) & member(all_40_1, all_15_5) = all_87_0 % 10.33/2.24 | | | | | | | & member(all_40_1, all_15_6) = 0 % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | ALPHA: (86) implies: % 10.33/2.24 | | | | | | | (87) ~ (all_87_0 = 0) % 10.33/2.24 | | | | | | | (88) member(all_40_1, all_15_6) = 0 % 10.33/2.24 | | | | | | | (89) member(all_40_1, all_15_5) = all_87_0 % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | GROUND_INST: instantiating (8) with all_76_0, 0, all_15_6, % 10.33/2.24 | | | | | | | all_40_1, simplifying with (83), (88) gives: % 10.33/2.24 | | | | | | | (90) all_76_0 = 0 % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | GROUND_INST: instantiating (8) with all_53_0, all_87_0, all_15_5, % 10.33/2.24 | | | | | | | all_40_1, simplifying with (57), (89) gives: % 10.33/2.24 | | | | | | | (91) all_87_0 = all_53_0 % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | REDUCE: (87), (91) imply: % 10.33/2.24 | | | | | | | (92) ~ (all_53_0 = 0) % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | BETA: splitting (58) gives: % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | | Case 1: % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | | (93) ~ (all_53_1 = 0) % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | | GROUND_INST: instantiating (25) with all_40_1, simplifying with % 10.33/2.24 | | | | | | | | (43), (88) gives: % 10.33/2.24 | | | | | | | | (94) member(all_40_1, all_15_7) = 0 % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | | GROUND_INST: instantiating (8) with all_53_1, 0, all_15_7, % 10.33/2.24 | | | | | | | | all_40_1, simplifying with (56), (94) gives: % 10.33/2.24 | | | | | | | | (95) all_53_1 = 0 % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | | REDUCE: (93), (95) imply: % 10.33/2.24 | | | | | | | | (96) $false % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | | CLOSE: (96) is inconsistent. % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | Case 2: % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | | (97) all_53_0 = 0 % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | | REDUCE: (92), (97) imply: % 10.33/2.24 | | | | | | | | (98) $false % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | | CLOSE: (98) is inconsistent. % 10.33/2.24 | | | | | | | | % 10.33/2.24 | | | | | | | End of split % 10.33/2.24 | | | | | | | % 10.33/2.24 | | | | | | End of split % 10.33/2.24 | | | | | | % 10.33/2.24 | | | | | End of split % 10.33/2.24 | | | | | % 10.33/2.24 | | | | End of split % 10.33/2.24 | | | | % 10.33/2.24 | | | End of split % 10.33/2.24 | | | % 10.33/2.24 | | Case 2: % 10.33/2.24 | | | % 10.33/2.24 | | | (99) ~ (all_27_1 = 0) % 10.33/2.24 | | | % 10.33/2.24 | | | BETA: splitting (35) gives: % 10.33/2.24 | | | % 10.33/2.24 | | | Case 1: % 10.33/2.24 | | | | % 10.33/2.24 | | | | (100) all_27_1 = 0 % 10.33/2.24 | | | | % 10.33/2.24 | | | | REDUCE: (99), (100) imply: % 10.33/2.24 | | | | (101) $false % 10.33/2.24 | | | | % 10.33/2.24 | | | | CLOSE: (101) is inconsistent. % 10.33/2.24 | | | | % 10.33/2.24 | | | Case 2: % 10.33/2.24 | | | | % 10.33/2.24 | | | | (102) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 10.33/2.24 | | | | all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 10.33/2.24 | | | | % 10.33/2.24 | | | | DELTA: instantiating (102) with fresh symbols all_62_0, all_62_1 gives: % 10.33/2.24 | | | | (103) ~ (all_62_0 = 0) & member(all_62_1, all_15_1) = all_62_0 & % 10.33/2.24 | | | | member(all_62_1, all_15_4) = 0 & $i(all_62_1) % 10.33/2.24 | | | | % 10.33/2.24 | | | | ALPHA: (103) implies: % 10.33/2.25 | | | | (104) ~ (all_62_0 = 0) % 10.33/2.25 | | | | (105) $i(all_62_1) % 10.33/2.25 | | | | (106) member(all_62_1, all_15_4) = 0 % 10.33/2.25 | | | | (107) member(all_62_1, all_15_1) = all_62_0 % 10.33/2.25 | | | | % 10.33/2.25 | | | | GROUND_INST: instantiating (6) with all_62_1, all_15_5, all_15_7, % 10.33/2.25 | | | | all_15_4, simplifying with (11), (13), (23), (105), (106) % 10.33/2.25 | | | | gives: % 10.33/2.25 | | | | (108) ? [v0: int] : ( ~ (v0 = 0) & member(all_62_1, all_15_5) = v0 & % 10.33/2.25 | | | | member(all_62_1, all_15_7) = 0) % 10.33/2.25 | | | | % 10.33/2.25 | | | | GROUND_INST: instantiating (5) with all_62_1, all_15_3, all_15_2, % 10.33/2.25 | | | | all_15_1, all_62_0, simplifying with (15), (16), (21), % 10.33/2.25 | | | | (105), (107) gives: % 10.33/2.25 | | | | (109) all_62_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 10.33/2.25 | | | | (v0 = 0) & member(all_62_1, all_15_2) = v1 & member(all_62_1, % 10.33/2.25 | | | | all_15_3) = v0) % 10.33/2.25 | | | | % 10.33/2.25 | | | | DELTA: instantiating (108) with fresh symbol all_69_0 gives: % 10.33/2.25 | | | | (110) ~ (all_69_0 = 0) & member(all_62_1, all_15_5) = all_69_0 & % 10.33/2.25 | | | | member(all_62_1, all_15_7) = 0 % 10.33/2.25 | | | | % 10.33/2.25 | | | | ALPHA: (110) implies: % 10.33/2.25 | | | | (111) ~ (all_69_0 = 0) % 10.33/2.25 | | | | (112) member(all_62_1, all_15_7) = 0 % 10.33/2.25 | | | | (113) member(all_62_1, all_15_5) = all_69_0 % 10.33/2.25 | | | | % 10.33/2.25 | | | | BETA: splitting (109) gives: % 10.33/2.25 | | | | % 10.33/2.25 | | | | Case 1: % 10.33/2.25 | | | | | % 10.33/2.25 | | | | | (114) all_62_0 = 0 % 10.33/2.25 | | | | | % 10.33/2.25 | | | | | REDUCE: (104), (114) imply: % 10.33/2.25 | | | | | (115) $false % 10.33/2.25 | | | | | % 10.33/2.25 | | | | | CLOSE: (115) is inconsistent. % 10.33/2.25 | | | | | % 10.33/2.25 | | | | Case 2: % 10.33/2.25 | | | | | % 10.63/2.25 | | | | | (116) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 10.63/2.25 | | | | | member(all_62_1, all_15_2) = v1 & member(all_62_1, % 10.63/2.25 | | | | | all_15_3) = v0) % 10.63/2.25 | | | | | % 10.63/2.25 | | | | | DELTA: instantiating (116) with fresh symbols all_75_0, all_75_1 % 10.63/2.25 | | | | | gives: % 10.63/2.25 | | | | | (117) ~ (all_75_0 = 0) & ~ (all_75_1 = 0) & member(all_62_1, % 10.63/2.25 | | | | | all_15_2) = all_75_0 & member(all_62_1, all_15_3) = % 10.63/2.25 | | | | | all_75_1 % 10.63/2.25 | | | | | % 10.63/2.25 | | | | | ALPHA: (117) implies: % 10.63/2.25 | | | | | (118) ~ (all_75_1 = 0) % 10.63/2.25 | | | | | (119) ~ (all_75_0 = 0) % 10.63/2.25 | | | | | (120) member(all_62_1, all_15_3) = all_75_1 % 10.63/2.25 | | | | | (121) member(all_62_1, all_15_2) = all_75_0 % 10.63/2.25 | | | | | % 10.63/2.25 | | | | | GROUND_INST: instantiating (7) with all_62_1, all_15_5, all_15_6, % 10.63/2.25 | | | | | all_15_3, all_75_1, simplifying with (12), (13), (24), % 10.63/2.25 | | | | | (105), (120) gives: % 10.63/2.25 | | | | | (122) all_75_1 = 0 | ? [v0: any] : ? [v1: any] : % 10.63/2.25 | | | | | (member(all_62_1, all_15_5) = v1 & member(all_62_1, all_15_6) % 10.63/2.25 | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 10.63/2.25 | | | | | % 10.63/2.25 | | | | | GROUND_INST: instantiating (7) with all_62_1, all_15_6, all_15_7, % 10.63/2.25 | | | | | all_15_2, all_75_0, simplifying with (11), (12), (22), % 10.63/2.25 | | | | | (105), (121) gives: % 10.63/2.25 | | | | | (123) all_75_0 = 0 | ? [v0: any] : ? [v1: any] : % 10.63/2.25 | | | | | (member(all_62_1, all_15_6) = v1 & member(all_62_1, all_15_7) % 10.63/2.25 | | | | | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 10.63/2.25 | | | | | % 10.63/2.25 | | | | | BETA: splitting (123) gives: % 10.63/2.25 | | | | | % 10.63/2.25 | | | | | Case 1: % 10.63/2.25 | | | | | | % 10.63/2.25 | | | | | | (124) all_75_0 = 0 % 10.63/2.25 | | | | | | % 10.63/2.25 | | | | | | REDUCE: (119), (124) imply: % 10.63/2.25 | | | | | | (125) $false % 10.63/2.25 | | | | | | % 10.63/2.25 | | | | | | CLOSE: (125) is inconsistent. % 10.63/2.25 | | | | | | % 10.63/2.25 | | | | | Case 2: % 10.63/2.25 | | | | | | % 10.63/2.25 | | | | | | (126) ? [v0: any] : ? [v1: any] : (member(all_62_1, all_15_6) = % 10.63/2.25 | | | | | | v1 & member(all_62_1, all_15_7) = v0 & ( ~ (v0 = 0) | v1 % 10.63/2.25 | | | | | | = 0)) % 10.63/2.25 | | | | | | % 10.63/2.25 | | | | | | DELTA: instantiating (126) with fresh symbols all_88_0, all_88_1 % 10.63/2.25 | | | | | | gives: % 10.63/2.25 | | | | | | (127) member(all_62_1, all_15_6) = all_88_0 & member(all_62_1, % 10.63/2.25 | | | | | | all_15_7) = all_88_1 & ( ~ (all_88_1 = 0) | all_88_0 = 0) % 10.63/2.25 | | | | | | % 10.63/2.25 | | | | | | ALPHA: (127) implies: % 10.63/2.25 | | | | | | (128) member(all_62_1, all_15_7) = all_88_1 % 10.63/2.25 | | | | | | (129) member(all_62_1, all_15_6) = all_88_0 % 10.63/2.26 | | | | | | (130) ~ (all_88_1 = 0) | all_88_0 = 0 % 10.63/2.26 | | | | | | % 10.63/2.26 | | | | | | BETA: splitting (122) gives: % 10.63/2.26 | | | | | | % 10.63/2.26 | | | | | | Case 1: % 10.63/2.26 | | | | | | | % 10.63/2.26 | | | | | | | (131) all_75_1 = 0 % 10.63/2.26 | | | | | | | % 10.63/2.26 | | | | | | | REDUCE: (118), (131) imply: % 10.63/2.26 | | | | | | | (132) $false % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | | CLOSE: (132) is inconsistent. % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | Case 2: % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | | (133) ? [v0: any] : ? [v1: any] : (member(all_62_1, all_15_5) % 10.66/2.26 | | | | | | | = v1 & member(all_62_1, all_15_6) = v0 & ( ~ (v0 = 0) | % 10.66/2.26 | | | | | | | v1 = 0)) % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | | DELTA: instantiating (133) with fresh symbols all_94_0, all_94_1 % 10.66/2.26 | | | | | | | gives: % 10.66/2.26 | | | | | | | (134) member(all_62_1, all_15_5) = all_94_0 & member(all_62_1, % 10.66/2.26 | | | | | | | all_15_6) = all_94_1 & ( ~ (all_94_1 = 0) | all_94_0 = % 10.66/2.26 | | | | | | | 0) % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | | ALPHA: (134) implies: % 10.66/2.26 | | | | | | | (135) member(all_62_1, all_15_6) = all_94_1 % 10.66/2.26 | | | | | | | (136) member(all_62_1, all_15_5) = all_94_0 % 10.66/2.26 | | | | | | | (137) ~ (all_94_1 = 0) | all_94_0 = 0 % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | | GROUND_INST: instantiating (8) with 0, all_88_1, all_15_7, % 10.66/2.26 | | | | | | | all_62_1, simplifying with (112), (128) gives: % 10.66/2.26 | | | | | | | (138) all_88_1 = 0 % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | | GROUND_INST: instantiating (8) with all_88_0, all_94_1, all_15_6, % 10.66/2.26 | | | | | | | all_62_1, simplifying with (129), (135) gives: % 10.66/2.26 | | | | | | | (139) all_94_1 = all_88_0 % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | | GROUND_INST: instantiating (8) with all_69_0, all_94_0, all_15_5, % 10.66/2.26 | | | | | | | all_62_1, simplifying with (113), (136) gives: % 10.66/2.26 | | | | | | | (140) all_94_0 = all_69_0 % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | | BETA: splitting (137) gives: % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | | Case 1: % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | | (141) ~ (all_94_1 = 0) % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | | REDUCE: (139), (141) imply: % 10.66/2.26 | | | | | | | | (142) ~ (all_88_0 = 0) % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | | BETA: splitting (130) gives: % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | | Case 1: % 10.66/2.26 | | | | | | | | | % 10.66/2.26 | | | | | | | | | (143) ~ (all_88_1 = 0) % 10.66/2.26 | | | | | | | | | % 10.66/2.26 | | | | | | | | | REDUCE: (138), (143) imply: % 10.66/2.26 | | | | | | | | | (144) $false % 10.66/2.26 | | | | | | | | | % 10.66/2.26 | | | | | | | | | CLOSE: (144) is inconsistent. % 10.66/2.26 | | | | | | | | | % 10.66/2.26 | | | | | | | | Case 2: % 10.66/2.26 | | | | | | | | | % 10.66/2.26 | | | | | | | | | (145) all_88_0 = 0 % 10.66/2.26 | | | | | | | | | % 10.66/2.26 | | | | | | | | | REDUCE: (142), (145) imply: % 10.66/2.26 | | | | | | | | | (146) $false % 10.66/2.26 | | | | | | | | | % 10.66/2.26 | | | | | | | | | CLOSE: (146) is inconsistent. % 10.66/2.26 | | | | | | | | | % 10.66/2.26 | | | | | | | | End of split % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | Case 2: % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | | (147) all_94_0 = 0 % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | | COMBINE_EQS: (140), (147) imply: % 10.66/2.26 | | | | | | | | (148) all_69_0 = 0 % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | | REDUCE: (111), (148) imply: % 10.66/2.26 | | | | | | | | (149) $false % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | | CLOSE: (149) is inconsistent. % 10.66/2.26 | | | | | | | | % 10.66/2.26 | | | | | | | End of split % 10.66/2.26 | | | | | | | % 10.66/2.26 | | | | | | End of split % 10.66/2.26 | | | | | | % 10.66/2.26 | | | | | End of split % 10.66/2.26 | | | | | % 10.66/2.26 | | | | End of split % 10.66/2.26 | | | | % 10.66/2.26 | | | End of split % 10.66/2.26 | | | % 10.66/2.26 | | End of split % 10.66/2.26 | | % 10.66/2.26 | End of split % 10.66/2.26 | % 10.66/2.26 End of proof % 10.66/2.26 % SZS output end Proof for theBenchmark % 10.66/2.26 % 10.66/2.26 1647ms %------------------------------------------------------------------------------