%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET358+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 : n011.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 15:24:44 EDT 2023 % Result : Theorem 8.39s 1.91s % Output : Proof 10.85s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET358+4 : TPTP v8.1.2. Released v2.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n011.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 09:58:39 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.44/1.05 Prover 4: Preprocessing ... % 2.44/1.05 Prover 1: Preprocessing ... % 2.63/1.11 Prover 3: Preprocessing ... % 2.63/1.11 Prover 5: Preprocessing ... % 2.63/1.11 Prover 2: Preprocessing ... % 2.63/1.11 Prover 0: Preprocessing ... % 2.63/1.11 Prover 6: Preprocessing ... % 5.34/1.47 Prover 1: Constructing countermodel ... % 5.34/1.48 Prover 3: Constructing countermodel ... % 5.34/1.49 Prover 6: Proving ... % 5.34/1.49 Prover 5: Proving ... % 5.34/1.50 Prover 2: Proving ... % 5.34/1.51 Prover 0: Proving ... % 5.87/1.56 Prover 4: Constructing countermodel ... % 8.39/1.91 Prover 0: proved (1275ms) % 8.39/1.91 % 8.39/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.39/1.91 % 8.39/1.91 Prover 3: stopped % 8.39/1.92 Prover 2: stopped % 8.39/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.39/1.92 Prover 6: stopped % 8.39/1.92 Prover 5: stopped % 8.39/1.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.39/1.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.39/1.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.39/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.39/1.95 Prover 11: Preprocessing ... % 8.39/1.96 Prover 7: Preprocessing ... % 8.39/1.96 Prover 8: Preprocessing ... % 8.39/1.97 Prover 10: Preprocessing ... % 8.39/1.97 Prover 13: Preprocessing ... % 9.12/2.04 Prover 10: Warning: ignoring some quantifiers % 9.62/2.06 Prover 7: Warning: ignoring some quantifiers % 9.62/2.06 Prover 10: Constructing countermodel ... % 9.62/2.06 Prover 13: Warning: ignoring some quantifiers % 9.62/2.07 Prover 7: Constructing countermodel ... % 9.99/2.10 Prover 10: gave up % 9.99/2.11 Prover 13: Constructing countermodel ... % 9.99/2.11 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.99/2.12 Prover 8: Warning: ignoring some quantifiers % 9.99/2.12 Prover 16: Preprocessing ... % 9.99/2.13 Prover 1: Found proof (size 107) % 9.99/2.13 Prover 1: proved (1496ms) % 9.99/2.13 Prover 7: stopped % 9.99/2.13 Prover 4: stopped % 9.99/2.13 Prover 13: stopped % 9.99/2.13 Prover 8: Constructing countermodel ... % 9.99/2.14 Prover 11: Constructing countermodel ... % 9.99/2.14 Prover 8: stopped % 9.99/2.14 Prover 16: stopped % 9.99/2.14 Prover 11: stopped % 9.99/2.14 % 9.99/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.99/2.14 % 10.35/2.16 % SZS output start Proof for theBenchmark % 10.35/2.16 Assumptions after simplification: % 10.35/2.16 --------------------------------- % 10.35/2.16 % 10.35/2.16 (equal_set) % 10.35/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 10.35/2.19 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 10.35/2.19 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 10.35/2.19 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 10.35/2.19 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 10.35/2.19 % 10.35/2.19 (subset) % 10.35/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 10.35/2.19 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 10.35/2.19 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 10.35/2.19 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 10.35/2.19 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 10.35/2.19 % 10.35/2.19 (sum) % 10.35/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (sum(v1) % 10.35/2.19 = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ! [v4: $i] : ( % 10.35/2.19 ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 10.35/2.19 member(v4, v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.35/2.19 (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 10.35/2.19 $i] : (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3))) % 10.35/2.19 % 10.35/2.19 (thI37) % 10.35/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 10.35/2.19 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & sum(v5) = v6 & sum(v1) = % 10.35/2.20 v3 & sum(v0) = v2 & union(v2, v3) = v4 & union(v0, v1) = v5 & equal_set(v4, % 10.35/2.20 v6) = v7 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.35/2.20 % 10.35/2.20 (union) % 10.35/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.35/2.20 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 10.35/2.20 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 10.35/2.20 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 10.35/2.20 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 10.35/2.20 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 10.35/2.20 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 10.35/2.20 % 10.35/2.20 (function-axioms) % 10.35/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.35/2.20 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 10.35/2.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.35/2.20 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 10.35/2.20 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 10.35/2.20 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 10.35/2.20 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 10.35/2.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.35/2.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 10.35/2.20 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.35/2.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 10.35/2.20 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.35/2.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.35/2.20 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 10.35/2.20 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 10.35/2.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 10.35/2.20 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 10.35/2.20 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 10.35/2.20 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 10.35/2.20 (power_set(v2) = v0)) % 10.35/2.20 % 10.35/2.20 Further assumptions not needed in the proof: % 10.35/2.20 -------------------------------------------- % 10.35/2.20 difference, empty_set, intersection, power_set, product, singleton, % 10.35/2.20 unordered_pair % 10.35/2.20 % 10.35/2.20 Those formulas are unsatisfiable: % 10.35/2.20 --------------------------------- % 10.35/2.20 % 10.35/2.20 Begin of proof % 10.35/2.20 | % 10.35/2.20 | ALPHA: (subset) implies: % 10.35/2.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 10.35/2.21 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 10.35/2.21 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 10.35/2.21 | % 10.35/2.21 | ALPHA: (equal_set) implies: % 10.35/2.21 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 10.35/2.21 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.35/2.21 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 10.35/2.21 | 0)))) % 10.35/2.21 | % 10.35/2.21 | ALPHA: (union) implies: % 10.35/2.21 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 10.35/2.21 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 10.35/2.21 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 10.35/2.21 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 10.35/2.21 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 10.35/2.21 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 10.35/2.21 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 10.35/2.21 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 10.35/2.21 | v5)) % 10.35/2.21 | % 10.35/2.21 | ALPHA: (sum) implies: % 10.35/2.21 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1) = v2) | ~ % 10.35/2.21 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 10.35/2.21 | (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3))) % 10.35/2.21 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.35/2.21 | (sum(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 10.35/2.21 | ! [v4: $i] : ( ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( % 10.35/2.21 | ~ (v5 = 0) & member(v4, v1) = v5))) % 10.35/2.21 | % 10.35/2.21 | ALPHA: (function-axioms) implies: % 10.35/2.21 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.35/2.21 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 10.35/2.21 | = v0)) % 10.35/2.21 | % 10.35/2.21 | DELTA: instantiating (thI37) with fresh symbols all_15_0, all_15_1, all_15_2, % 10.35/2.21 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives: % 10.35/2.21 | (8) ~ (all_15_0 = 0) & sum(all_15_2) = all_15_1 & sum(all_15_6) = all_15_4 % 10.35/2.21 | & sum(all_15_7) = all_15_5 & union(all_15_5, all_15_4) = all_15_3 & % 10.35/2.21 | union(all_15_7, all_15_6) = all_15_2 & equal_set(all_15_3, all_15_1) = % 10.35/2.21 | all_15_0 & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & % 10.35/2.21 | $i(all_15_5) & $i(all_15_6) & $i(all_15_7) % 10.35/2.21 | % 10.35/2.21 | ALPHA: (8) implies: % 10.35/2.21 | (9) ~ (all_15_0 = 0) % 10.35/2.21 | (10) $i(all_15_7) % 10.35/2.21 | (11) $i(all_15_6) % 10.35/2.22 | (12) $i(all_15_5) % 10.35/2.22 | (13) $i(all_15_4) % 10.35/2.22 | (14) $i(all_15_3) % 10.35/2.22 | (15) $i(all_15_2) % 10.35/2.22 | (16) $i(all_15_1) % 10.35/2.22 | (17) equal_set(all_15_3, all_15_1) = all_15_0 % 10.35/2.22 | (18) union(all_15_7, all_15_6) = all_15_2 % 10.35/2.22 | (19) union(all_15_5, all_15_4) = all_15_3 % 10.35/2.22 | (20) sum(all_15_7) = all_15_5 % 10.35/2.22 | (21) sum(all_15_6) = all_15_4 % 10.35/2.22 | (22) sum(all_15_2) = all_15_1 % 10.35/2.22 | % 10.35/2.22 | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_15_0, simplifying % 10.35/2.22 | with (14), (16), (17) gives: % 10.35/2.22 | (23) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 10.35/2.22 | all_15_3) = v1 & subset(all_15_3, all_15_1) = v0 & ( ~ (v1 = 0) | % 10.35/2.22 | ~ (v0 = 0))) % 10.35/2.22 | % 10.35/2.22 | BETA: splitting (23) gives: % 10.35/2.22 | % 10.35/2.22 | Case 1: % 10.35/2.22 | | % 10.35/2.22 | | (24) all_15_0 = 0 % 10.35/2.22 | | % 10.35/2.22 | | REDUCE: (9), (24) imply: % 10.35/2.22 | | (25) $false % 10.35/2.22 | | % 10.35/2.22 | | CLOSE: (25) is inconsistent. % 10.35/2.22 | | % 10.35/2.22 | Case 2: % 10.35/2.22 | | % 10.35/2.22 | | (26) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_3) = v1 & % 10.35/2.22 | | subset(all_15_3, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.35/2.22 | | % 10.35/2.22 | | DELTA: instantiating (26) with fresh symbols all_24_0, all_24_1 gives: % 10.35/2.22 | | (27) subset(all_15_1, all_15_3) = all_24_0 & subset(all_15_3, all_15_1) = % 10.35/2.22 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0)) % 10.35/2.22 | | % 10.35/2.22 | | ALPHA: (27) implies: % 10.35/2.22 | | (28) subset(all_15_3, all_15_1) = all_24_1 % 10.35/2.22 | | (29) subset(all_15_1, all_15_3) = all_24_0 % 10.35/2.22 | | (30) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 10.35/2.22 | | % 10.35/2.22 | | GROUND_INST: instantiating (1) with all_15_3, all_15_1, all_24_1, % 10.35/2.22 | | simplifying with (14), (16), (28) gives: % 10.35/2.22 | | (31) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.35/2.22 | | member(v0, all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 10.35/2.22 | | % 10.35/2.22 | | GROUND_INST: instantiating (1) with all_15_1, all_15_3, all_24_0, % 10.35/2.22 | | simplifying with (14), (16), (29) gives: % 10.35/2.22 | | (32) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.35/2.22 | | member(v0, all_15_1) = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 10.35/2.22 | | % 10.35/2.22 | | BETA: splitting (30) gives: % 10.35/2.22 | | % 10.35/2.22 | | Case 1: % 10.35/2.22 | | | % 10.35/2.22 | | | (33) ~ (all_24_0 = 0) % 10.35/2.22 | | | % 10.35/2.22 | | | BETA: splitting (32) gives: % 10.35/2.22 | | | % 10.35/2.22 | | | Case 1: % 10.35/2.22 | | | | % 10.35/2.22 | | | | (34) all_24_0 = 0 % 10.35/2.22 | | | | % 10.35/2.22 | | | | REDUCE: (33), (34) imply: % 10.35/2.22 | | | | (35) $false % 10.35/2.22 | | | | % 10.35/2.22 | | | | CLOSE: (35) is inconsistent. % 10.35/2.22 | | | | % 10.35/2.22 | | | Case 2: % 10.35/2.22 | | | | % 10.35/2.22 | | | | (36) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 10.35/2.22 | | | | = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 10.35/2.22 | | | | % 10.35/2.22 | | | | DELTA: instantiating (36) with fresh symbols all_37_0, all_37_1 gives: % 10.35/2.22 | | | | (37) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 & % 10.35/2.22 | | | | member(all_37_1, all_15_3) = all_37_0 & $i(all_37_1) % 10.35/2.22 | | | | % 10.35/2.22 | | | | ALPHA: (37) implies: % 10.35/2.22 | | | | (38) ~ (all_37_0 = 0) % 10.35/2.23 | | | | (39) $i(all_37_1) % 10.35/2.23 | | | | (40) member(all_37_1, all_15_3) = all_37_0 % 10.35/2.23 | | | | (41) member(all_37_1, all_15_1) = 0 % 10.35/2.23 | | | | % 10.35/2.23 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_5, all_15_4, % 10.35/2.23 | | | | all_15_3, all_37_0, simplifying with (12), (13), (19), % 10.35/2.23 | | | | (39), (40) gives: % 10.35/2.23 | | | | (42) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 10.35/2.23 | | | | (v0 = 0) & member(all_37_1, all_15_4) = v1 & member(all_37_1, % 10.35/2.23 | | | | all_15_5) = v0) % 10.35/2.23 | | | | % 10.35/2.23 | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_2, all_15_1, % 10.35/2.23 | | | | simplifying with (15), (22), (39), (41) gives: % 10.35/2.23 | | | | (43) ? [v0: $i] : (member(v0, all_15_2) = 0 & member(all_37_1, v0) = % 10.35/2.23 | | | | 0 & $i(v0)) % 10.35/2.23 | | | | % 10.35/2.23 | | | | DELTA: instantiating (43) with fresh symbol all_44_0 gives: % 10.35/2.23 | | | | (44) member(all_44_0, all_15_2) = 0 & member(all_37_1, all_44_0) = 0 % 10.35/2.23 | | | | & $i(all_44_0) % 10.35/2.23 | | | | % 10.35/2.23 | | | | ALPHA: (44) implies: % 10.35/2.23 | | | | (45) $i(all_44_0) % 10.35/2.23 | | | | (46) member(all_37_1, all_44_0) = 0 % 10.35/2.23 | | | | (47) member(all_44_0, all_15_2) = 0 % 10.35/2.23 | | | | % 10.35/2.23 | | | | BETA: splitting (42) gives: % 10.35/2.23 | | | | % 10.35/2.23 | | | | Case 1: % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | (48) all_37_0 = 0 % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | REDUCE: (38), (48) imply: % 10.35/2.23 | | | | | (49) $false % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | CLOSE: (49) is inconsistent. % 10.35/2.23 | | | | | % 10.35/2.23 | | | | Case 2: % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | (50) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 10.35/2.23 | | | | | member(all_37_1, all_15_4) = v1 & member(all_37_1, all_15_5) % 10.35/2.23 | | | | | = v0) % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | DELTA: instantiating (50) with fresh symbols all_50_0, all_50_1 gives: % 10.35/2.23 | | | | | (51) ~ (all_50_0 = 0) & ~ (all_50_1 = 0) & member(all_37_1, % 10.35/2.23 | | | | | all_15_4) = all_50_0 & member(all_37_1, all_15_5) = all_50_1 % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | ALPHA: (51) implies: % 10.35/2.23 | | | | | (52) ~ (all_50_1 = 0) % 10.35/2.23 | | | | | (53) ~ (all_50_0 = 0) % 10.35/2.23 | | | | | (54) member(all_37_1, all_15_5) = all_50_1 % 10.35/2.23 | | | | | (55) member(all_37_1, all_15_4) = all_50_0 % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_7, all_15_5, % 10.35/2.23 | | | | | all_50_1, simplifying with (10), (20), (39), (54) gives: % 10.35/2.23 | | | | | (56) all_50_1 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | % 10.35/2.23 | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 10.35/2.23 | | | | | all_15_7) = v1)) % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_6, all_15_4, % 10.35/2.23 | | | | | all_50_0, simplifying with (11), (21), (39), (55) gives: % 10.35/2.23 | | | | | (57) all_50_0 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | % 10.35/2.23 | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 10.35/2.23 | | | | | all_15_6) = v1)) % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | GROUND_INST: instantiating (3) with all_44_0, all_15_7, all_15_6, % 10.35/2.23 | | | | | all_15_2, simplifying with (10), (11), (18), (45), (47) % 10.35/2.23 | | | | | gives: % 10.35/2.23 | | | | | (58) ? [v0: any] : ? [v1: any] : (member(all_44_0, all_15_6) = v1 % 10.35/2.23 | | | | | & member(all_44_0, all_15_7) = v0 & (v1 = 0 | v0 = 0)) % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | DELTA: instantiating (58) with fresh symbols all_57_0, all_57_1 gives: % 10.35/2.23 | | | | | (59) member(all_44_0, all_15_6) = all_57_0 & member(all_44_0, % 10.35/2.23 | | | | | all_15_7) = all_57_1 & (all_57_0 = 0 | all_57_1 = 0) % 10.35/2.23 | | | | | % 10.35/2.23 | | | | | ALPHA: (59) implies: % 10.35/2.24 | | | | | (60) member(all_44_0, all_15_7) = all_57_1 % 10.35/2.24 | | | | | (61) member(all_44_0, all_15_6) = all_57_0 % 10.35/2.24 | | | | | (62) all_57_0 = 0 | all_57_1 = 0 % 10.35/2.24 | | | | | % 10.35/2.24 | | | | | BETA: splitting (56) gives: % 10.35/2.24 | | | | | % 10.35/2.24 | | | | | Case 1: % 10.35/2.24 | | | | | | % 10.35/2.24 | | | | | | (63) all_50_1 = 0 % 10.35/2.24 | | | | | | % 10.35/2.24 | | | | | | REDUCE: (52), (63) imply: % 10.35/2.24 | | | | | | (64) $false % 10.35/2.24 | | | | | | % 10.35/2.24 | | | | | | CLOSE: (64) is inconsistent. % 10.35/2.24 | | | | | | % 10.35/2.24 | | | | | Case 2: % 10.35/2.24 | | | | | | % 10.35/2.24 | | | | | | (65) ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ $i(v0) | % 10.35/2.24 | | | | | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_7) = v1)) % 10.35/2.24 | | | | | | % 10.35/2.24 | | | | | | GROUND_INST: instantiating (65) with all_44_0, simplifying with % 10.35/2.24 | | | | | | (45), (46) gives: % 10.35/2.24 | | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & member(all_44_0, all_15_7) = % 10.35/2.24 | | | | | | v0) % 10.35/2.24 | | | | | | % 10.35/2.24 | | | | | | BETA: splitting (57) gives: % 10.35/2.24 | | | | | | % 10.35/2.24 | | | | | | Case 1: % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | (67) all_50_0 = 0 % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | REDUCE: (53), (67) imply: % 10.35/2.24 | | | | | | | (68) $false % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | CLOSE: (68) is inconsistent. % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | Case 2: % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | (69) ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ $i(v0) | % 10.35/2.24 | | | | | | | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_6) = % 10.35/2.24 | | | | | | | v1)) % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | GROUND_INST: instantiating (69) with all_44_0, simplifying with % 10.35/2.24 | | | | | | | (45), (46) gives: % 10.35/2.24 | | | | | | | (70) ? [v0: int] : ( ~ (v0 = 0) & member(all_44_0, all_15_6) = % 10.35/2.24 | | | | | | | v0) % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | DELTA: instantiating (66) with fresh symbol all_68_0 gives: % 10.35/2.24 | | | | | | | (71) ~ (all_68_0 = 0) & member(all_44_0, all_15_7) = all_68_0 % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | ALPHA: (71) implies: % 10.35/2.24 | | | | | | | (72) ~ (all_68_0 = 0) % 10.35/2.24 | | | | | | | (73) member(all_44_0, all_15_7) = all_68_0 % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | DELTA: instantiating (70) with fresh symbol all_72_0 gives: % 10.35/2.24 | | | | | | | (74) ~ (all_72_0 = 0) & member(all_44_0, all_15_6) = all_72_0 % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | ALPHA: (74) implies: % 10.35/2.24 | | | | | | | (75) ~ (all_72_0 = 0) % 10.35/2.24 | | | | | | | (76) member(all_44_0, all_15_6) = all_72_0 % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | GROUND_INST: instantiating (7) with all_57_1, all_68_0, all_15_7, % 10.35/2.24 | | | | | | | all_44_0, simplifying with (60), (73) gives: % 10.35/2.24 | | | | | | | (77) all_68_0 = all_57_1 % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | GROUND_INST: instantiating (7) with all_57_0, all_72_0, all_15_6, % 10.35/2.24 | | | | | | | all_44_0, simplifying with (61), (76) gives: % 10.35/2.24 | | | | | | | (78) all_72_0 = all_57_0 % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | REDUCE: (75), (78) imply: % 10.35/2.24 | | | | | | | (79) ~ (all_57_0 = 0) % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | REDUCE: (72), (77) imply: % 10.35/2.24 | | | | | | | (80) ~ (all_57_1 = 0) % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | BETA: splitting (62) gives: % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | | Case 1: % 10.35/2.24 | | | | | | | | % 10.35/2.24 | | | | | | | | (81) all_57_0 = 0 % 10.35/2.24 | | | | | | | | % 10.35/2.24 | | | | | | | | REDUCE: (79), (81) imply: % 10.35/2.24 | | | | | | | | (82) $false % 10.35/2.24 | | | | | | | | % 10.35/2.24 | | | | | | | | CLOSE: (82) is inconsistent. % 10.35/2.24 | | | | | | | | % 10.35/2.24 | | | | | | | Case 2: % 10.35/2.24 | | | | | | | | % 10.35/2.24 | | | | | | | | (83) all_57_1 = 0 % 10.35/2.24 | | | | | | | | % 10.35/2.24 | | | | | | | | REDUCE: (80), (83) imply: % 10.35/2.24 | | | | | | | | (84) $false % 10.35/2.24 | | | | | | | | % 10.35/2.24 | | | | | | | | CLOSE: (84) is inconsistent. % 10.35/2.24 | | | | | | | | % 10.35/2.24 | | | | | | | End of split % 10.35/2.24 | | | | | | | % 10.35/2.24 | | | | | | End of split % 10.35/2.24 | | | | | | % 10.35/2.24 | | | | | End of split % 10.35/2.24 | | | | | % 10.35/2.24 | | | | End of split % 10.35/2.24 | | | | % 10.35/2.24 | | | End of split % 10.35/2.24 | | | % 10.35/2.24 | | Case 2: % 10.35/2.24 | | | % 10.35/2.24 | | | (85) ~ (all_24_1 = 0) % 10.35/2.24 | | | % 10.35/2.24 | | | BETA: splitting (31) gives: % 10.35/2.24 | | | % 10.35/2.24 | | | Case 1: % 10.35/2.24 | | | | % 10.35/2.24 | | | | (86) all_24_1 = 0 % 10.35/2.24 | | | | % 10.35/2.24 | | | | REDUCE: (85), (86) imply: % 10.35/2.24 | | | | (87) $false % 10.35/2.24 | | | | % 10.35/2.24 | | | | CLOSE: (87) is inconsistent. % 10.35/2.24 | | | | % 10.35/2.24 | | | Case 2: % 10.35/2.24 | | | | % 10.35/2.24 | | | | (88) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 10.35/2.24 | | | | = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 10.35/2.24 | | | | % 10.35/2.24 | | | | DELTA: instantiating (88) with fresh symbols all_37_0, all_37_1 gives: % 10.35/2.25 | | | | (89) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 & % 10.35/2.25 | | | | member(all_37_1, all_15_3) = 0 & $i(all_37_1) % 10.35/2.25 | | | | % 10.35/2.25 | | | | ALPHA: (89) implies: % 10.35/2.25 | | | | (90) ~ (all_37_0 = 0) % 10.35/2.25 | | | | (91) $i(all_37_1) % 10.35/2.25 | | | | (92) member(all_37_1, all_15_3) = 0 % 10.35/2.25 | | | | (93) member(all_37_1, all_15_1) = all_37_0 % 10.35/2.25 | | | | % 10.35/2.25 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_5, all_15_4, % 10.35/2.25 | | | | all_15_3, simplifying with (12), (13), (19), (91), (92) % 10.35/2.25 | | | | gives: % 10.35/2.25 | | | | (94) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_4) = v1 & % 10.35/2.25 | | | | member(all_37_1, all_15_5) = v0 & (v1 = 0 | v0 = 0)) % 10.35/2.25 | | | | % 10.35/2.25 | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_2, all_15_1, % 10.35/2.25 | | | | all_37_0, simplifying with (15), (22), (91), (93) gives: % 10.35/2.25 | | | | (95) all_37_0 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ % 10.35/2.25 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) = % 10.35/2.25 | | | | v1)) % 10.35/2.25 | | | | % 10.35/2.25 | | | | DELTA: instantiating (94) with fresh symbols all_45_0, all_45_1 gives: % 10.35/2.25 | | | | (96) member(all_37_1, all_15_4) = all_45_0 & member(all_37_1, % 10.35/2.25 | | | | all_15_5) = all_45_1 & (all_45_0 = 0 | all_45_1 = 0) % 10.35/2.25 | | | | % 10.35/2.25 | | | | ALPHA: (96) implies: % 10.35/2.25 | | | | (97) member(all_37_1, all_15_5) = all_45_1 % 10.35/2.25 | | | | (98) member(all_37_1, all_15_4) = all_45_0 % 10.85/2.25 | | | | (99) all_45_0 = 0 | all_45_1 = 0 % 10.85/2.25 | | | | % 10.85/2.25 | | | | BETA: splitting (95) gives: % 10.85/2.25 | | | | % 10.85/2.25 | | | | Case 1: % 10.85/2.25 | | | | | % 10.85/2.25 | | | | | (100) all_37_0 = 0 % 10.85/2.25 | | | | | % 10.85/2.25 | | | | | REDUCE: (90), (100) imply: % 10.85/2.25 | | | | | (101) $false % 10.85/2.25 | | | | | % 10.85/2.25 | | | | | CLOSE: (101) is inconsistent. % 10.85/2.25 | | | | | % 10.85/2.25 | | | | Case 2: % 10.85/2.25 | | | | | % 10.85/2.25 | | | | | (102) ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ $i(v0) | ? % 10.85/2.25 | | | | | [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) = v1)) % 10.85/2.25 | | | | | % 10.85/2.25 | | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_6, all_15_4, % 10.85/2.25 | | | | | all_45_0, simplifying with (11), (21), (91), (98) gives: % 10.85/2.25 | | | | | (103) all_45_0 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | % 10.85/2.25 | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 10.85/2.25 | | | | | all_15_6) = v1)) % 10.85/2.25 | | | | | % 10.85/2.25 | | | | | BETA: splitting (99) gives: % 10.85/2.25 | | | | | % 10.85/2.25 | | | | | Case 1: % 10.85/2.25 | | | | | | % 10.85/2.25 | | | | | | (104) all_45_0 = 0 % 10.85/2.25 | | | | | | % 10.85/2.25 | | | | | | REDUCE: (98), (104) imply: % 10.85/2.25 | | | | | | (105) member(all_37_1, all_15_4) = 0 % 10.85/2.25 | | | | | | % 10.85/2.25 | | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_6, all_15_4, % 10.85/2.25 | | | | | | simplifying with (11), (21), (91), (105) gives: % 10.85/2.25 | | | | | | (106) ? [v0: $i] : (member(v0, all_15_6) = 0 & member(all_37_1, % 10.85/2.25 | | | | | | v0) = 0 & $i(v0)) % 10.85/2.25 | | | | | | % 10.85/2.25 | | | | | | DELTA: instantiating (106) with fresh symbol all_74_0 gives: % 10.85/2.25 | | | | | | (107) member(all_74_0, all_15_6) = 0 & member(all_37_1, all_74_0) % 10.85/2.25 | | | | | | = 0 & $i(all_74_0) % 10.85/2.25 | | | | | | % 10.85/2.25 | | | | | | ALPHA: (107) implies: % 10.85/2.25 | | | | | | (108) $i(all_74_0) % 10.85/2.25 | | | | | | (109) member(all_37_1, all_74_0) = 0 % 10.85/2.25 | | | | | | (110) member(all_74_0, all_15_6) = 0 % 10.85/2.25 | | | | | | % 10.85/2.25 | | | | | | GROUND_INST: instantiating (102) with all_74_0, simplifying with % 10.85/2.25 | | | | | | (108), (109) gives: % 10.85/2.25 | | | | | | (111) ? [v0: int] : ( ~ (v0 = 0) & member(all_74_0, all_15_2) = % 10.85/2.25 | | | | | | v0) % 10.85/2.25 | | | | | | % 10.85/2.25 | | | | | | DELTA: instantiating (111) with fresh symbol all_81_0 gives: % 10.85/2.25 | | | | | | (112) ~ (all_81_0 = 0) & member(all_74_0, all_15_2) = all_81_0 % 10.85/2.25 | | | | | | % 10.85/2.25 | | | | | | ALPHA: (112) implies: % 10.85/2.25 | | | | | | (113) ~ (all_81_0 = 0) % 10.85/2.25 | | | | | | (114) member(all_74_0, all_15_2) = all_81_0 % 10.85/2.25 | | | | | | % 10.85/2.26 | | | | | | GROUND_INST: instantiating (4) with all_74_0, all_15_7, all_15_6, % 10.85/2.26 | | | | | | all_15_2, all_81_0, simplifying with (10), (11), (18), % 10.85/2.26 | | | | | | (108), (114) gives: % 10.85/2.26 | | | | | | (115) all_81_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 10.85/2.26 | | | | | | ~ (v0 = 0) & member(all_74_0, all_15_6) = v1 & % 10.85/2.26 | | | | | | member(all_74_0, all_15_7) = v0) % 10.85/2.26 | | | | | | % 10.85/2.26 | | | | | | BETA: splitting (115) gives: % 10.85/2.26 | | | | | | % 10.85/2.26 | | | | | | Case 1: % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | (116) all_81_0 = 0 % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | REDUCE: (113), (116) imply: % 10.85/2.26 | | | | | | | (117) $false % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | CLOSE: (117) is inconsistent. % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | Case 2: % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | (118) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 10.85/2.26 | | | | | | | & member(all_74_0, all_15_6) = v1 & member(all_74_0, % 10.85/2.26 | | | | | | | all_15_7) = v0) % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | DELTA: instantiating (118) with fresh symbols all_100_0, all_100_1 % 10.85/2.26 | | | | | | | gives: % 10.85/2.26 | | | | | | | (119) ~ (all_100_0 = 0) & ~ (all_100_1 = 0) & % 10.85/2.26 | | | | | | | member(all_74_0, all_15_6) = all_100_0 & member(all_74_0, % 10.85/2.26 | | | | | | | all_15_7) = all_100_1 % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | ALPHA: (119) implies: % 10.85/2.26 | | | | | | | (120) ~ (all_100_0 = 0) % 10.85/2.26 | | | | | | | (121) member(all_74_0, all_15_6) = all_100_0 % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | GROUND_INST: instantiating (7) with 0, all_100_0, all_15_6, % 10.85/2.26 | | | | | | | all_74_0, simplifying with (110), (121) gives: % 10.85/2.26 | | | | | | | (122) all_100_0 = 0 % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | REDUCE: (120), (122) imply: % 10.85/2.26 | | | | | | | (123) $false % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | CLOSE: (123) is inconsistent. % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | End of split % 10.85/2.26 | | | | | | % 10.85/2.26 | | | | | Case 2: % 10.85/2.26 | | | | | | % 10.85/2.26 | | | | | | (124) all_45_1 = 0 % 10.85/2.26 | | | | | | (125) ~ (all_45_0 = 0) % 10.85/2.26 | | | | | | % 10.85/2.26 | | | | | | REDUCE: (97), (124) imply: % 10.85/2.26 | | | | | | (126) member(all_37_1, all_15_5) = 0 % 10.85/2.26 | | | | | | % 10.85/2.26 | | | | | | BETA: splitting (103) gives: % 10.85/2.26 | | | | | | % 10.85/2.26 | | | | | | Case 1: % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | (127) all_45_0 = 0 % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | REDUCE: (125), (127) imply: % 10.85/2.26 | | | | | | | (128) $false % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | CLOSE: (128) is inconsistent. % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | Case 2: % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_7, all_15_5, % 10.85/2.26 | | | | | | | simplifying with (10), (20), (91), (126) gives: % 10.85/2.26 | | | | | | | (129) ? [v0: $i] : (member(v0, all_15_7) = 0 & % 10.85/2.26 | | | | | | | member(all_37_1, v0) = 0 & $i(v0)) % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | DELTA: instantiating (129) with fresh symbol all_86_0 gives: % 10.85/2.26 | | | | | | | (130) member(all_86_0, all_15_7) = 0 & member(all_37_1, % 10.85/2.26 | | | | | | | all_86_0) = 0 & $i(all_86_0) % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | ALPHA: (130) implies: % 10.85/2.26 | | | | | | | (131) $i(all_86_0) % 10.85/2.26 | | | | | | | (132) member(all_37_1, all_86_0) = 0 % 10.85/2.26 | | | | | | | (133) member(all_86_0, all_15_7) = 0 % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | GROUND_INST: instantiating (102) with all_86_0, simplifying with % 10.85/2.26 | | | | | | | (131), (132) gives: % 10.85/2.26 | | | | | | | (134) ? [v0: int] : ( ~ (v0 = 0) & member(all_86_0, all_15_2) % 10.85/2.26 | | | | | | | = v0) % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | DELTA: instantiating (134) with fresh symbol all_95_0 gives: % 10.85/2.26 | | | | | | | (135) ~ (all_95_0 = 0) & member(all_86_0, all_15_2) = all_95_0 % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | ALPHA: (135) implies: % 10.85/2.26 | | | | | | | (136) ~ (all_95_0 = 0) % 10.85/2.26 | | | | | | | (137) member(all_86_0, all_15_2) = all_95_0 % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | GROUND_INST: instantiating (4) with all_86_0, all_15_7, all_15_6, % 10.85/2.26 | | | | | | | all_15_2, all_95_0, simplifying with (10), (11), % 10.85/2.26 | | | | | | | (18), (131), (137) gives: % 10.85/2.26 | | | | | | | (138) all_95_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) % 10.85/2.26 | | | | | | | & ~ (v0 = 0) & member(all_86_0, all_15_6) = v1 & % 10.85/2.26 | | | | | | | member(all_86_0, all_15_7) = v0) % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | BETA: splitting (138) gives: % 10.85/2.26 | | | | | | | % 10.85/2.26 | | | | | | | Case 1: % 10.85/2.26 | | | | | | | | % 10.85/2.26 | | | | | | | | (139) all_95_0 = 0 % 10.85/2.26 | | | | | | | | % 10.85/2.26 | | | | | | | | REDUCE: (136), (139) imply: % 10.85/2.26 | | | | | | | | (140) $false % 10.85/2.26 | | | | | | | | % 10.85/2.26 | | | | | | | | CLOSE: (140) is inconsistent. % 10.85/2.26 | | | | | | | | % 10.85/2.26 | | | | | | | Case 2: % 10.85/2.26 | | | | | | | | % 10.85/2.26 | | | | | | | | (141) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 10.85/2.26 | | | | | | | | 0) & member(all_86_0, all_15_6) = v1 & % 10.85/2.26 | | | | | | | | member(all_86_0, all_15_7) = v0) % 10.85/2.26 | | | | | | | | % 10.85/2.26 | | | | | | | | DELTA: instantiating (141) with fresh symbols all_114_0, % 10.85/2.26 | | | | | | | | all_114_1 gives: % 10.85/2.26 | | | | | | | | (142) ~ (all_114_0 = 0) & ~ (all_114_1 = 0) & % 10.85/2.26 | | | | | | | | member(all_86_0, all_15_6) = all_114_0 & % 10.85/2.26 | | | | | | | | member(all_86_0, all_15_7) = all_114_1 % 10.85/2.26 | | | | | | | | % 10.85/2.26 | | | | | | | | ALPHA: (142) implies: % 10.85/2.26 | | | | | | | | (143) ~ (all_114_1 = 0) % 10.85/2.26 | | | | | | | | (144) member(all_86_0, all_15_7) = all_114_1 % 10.85/2.26 | | | | | | | | % 10.85/2.27 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_114_1, all_15_7, % 10.85/2.27 | | | | | | | | all_86_0, simplifying with (133), (144) gives: % 10.85/2.27 | | | | | | | | (145) all_114_1 = 0 % 10.85/2.27 | | | | | | | | % 10.85/2.27 | | | | | | | | REDUCE: (143), (145) imply: % 10.85/2.27 | | | | | | | | (146) $false % 10.85/2.27 | | | | | | | | % 10.85/2.27 | | | | | | | | CLOSE: (146) is inconsistent. % 10.85/2.27 | | | | | | | | % 10.85/2.27 | | | | | | | End of split % 10.85/2.27 | | | | | | | % 10.85/2.27 | | | | | | End of split % 10.85/2.27 | | | | | | % 10.85/2.27 | | | | | End of split % 10.85/2.27 | | | | | % 10.85/2.27 | | | | End of split % 10.85/2.27 | | | | % 10.85/2.27 | | | End of split % 10.85/2.27 | | | % 10.85/2.27 | | End of split % 10.85/2.27 | | % 10.85/2.27 | End of split % 10.85/2.27 | % 10.85/2.27 End of proof % 10.85/2.27 % SZS output end Proof for theBenchmark % 10.85/2.27 % 10.85/2.27 1654ms %------------------------------------------------------------------------------