%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET171+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 : n021.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 15:24:09 EDT 2023 % Result : Theorem 7.40s 1.73s % Output : Proof 9.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET171+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n021.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sat Aug 26 11:04:26 EDT 2023 % 0.14/0.36 % CPUTime : % 0.22/0.62 ________ _____ % 0.22/0.62 ___ __ \_________(_)________________________________ % 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.62 % 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.62 (2023-06-19) % 0.22/0.62 % 0.22/0.62 (c) Philipp Rümmer, 2009-2023 % 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.62 Amanda Stjerna. % 0.22/0.62 Free software under BSD-3-Clause. % 0.22/0.62 % 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.62 % 0.22/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.63 Running up to 7 provers in parallel. % 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.36/1.02 Prover 1: Preprocessing ... % 2.36/1.02 Prover 4: Preprocessing ... % 2.80/1.06 Prover 6: Preprocessing ... % 2.80/1.06 Prover 3: Preprocessing ... % 2.80/1.06 Prover 5: Preprocessing ... % 2.80/1.06 Prover 2: Preprocessing ... % 2.80/1.06 Prover 0: Preprocessing ... % 4.97/1.40 Prover 3: Constructing countermodel ... % 4.97/1.41 Prover 1: Constructing countermodel ... % 4.97/1.42 Prover 5: Proving ... % 4.97/1.42 Prover 6: Proving ... % 4.97/1.45 Prover 2: Proving ... % 5.11/1.47 Prover 0: Proving ... % 5.11/1.48 Prover 4: Constructing countermodel ... % 7.40/1.72 Prover 3: proved (1082ms) % 7.40/1.72 % 7.40/1.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.40/1.73 % 7.40/1.73 Prover 2: stopped % 7.40/1.73 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.40/1.73 Prover 6: stopped % 7.81/1.74 Prover 5: stopped % 7.81/1.74 Prover 0: stopped % 7.89/1.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.89/1.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.89/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.89/1.76 Prover 7: Preprocessing ... % 7.89/1.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.89/1.77 Prover 8: Preprocessing ... % 7.89/1.79 Prover 10: Preprocessing ... % 7.89/1.79 Prover 13: Preprocessing ... % 7.89/1.80 Prover 11: Preprocessing ... % 8.32/1.84 Prover 7: Warning: ignoring some quantifiers % 8.32/1.84 Prover 10: Warning: ignoring some quantifiers % 8.32/1.85 Prover 7: Constructing countermodel ... % 8.67/1.86 Prover 10: Constructing countermodel ... % 8.67/1.87 Prover 13: Warning: ignoring some quantifiers % 8.67/1.88 Prover 8: Warning: ignoring some quantifiers % 8.67/1.89 Prover 13: Constructing countermodel ... % 8.67/1.89 Prover 8: Constructing countermodel ... % 8.67/1.91 Prover 1: Found proof (size 121) % 8.67/1.91 Prover 1: proved (1269ms) % 8.67/1.91 Prover 4: stopped % 8.67/1.91 Prover 13: stopped % 8.67/1.91 Prover 10: gave up % 8.67/1.92 Prover 7: stopped % 8.67/1.92 Prover 8: stopped % 8.67/1.94 Prover 11: Constructing countermodel ... % 9.26/1.94 Prover 11: stopped % 9.26/1.94 % 9.26/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.26/1.94 % 9.26/1.96 % SZS output start Proof for theBenchmark % 9.26/1.96 Assumptions after simplification: % 9.26/1.96 --------------------------------- % 9.26/1.96 % 9.26/1.96 (equal_set) % 9.46/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 9.46/1.99 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 9.46/1.99 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 9.46/1.99 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 9.46/1.99 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 9.46/1.99 % 9.46/1.99 (intersection) % 9.46/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 9.46/1.99 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 9.46/1.99 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 9.46/1.99 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 9.46/1.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 9.46/1.99 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 9.46/1.99 0 & member(v0, v1) = 0)) % 9.46/1.99 % 9.46/1.99 (subset) % 9.46/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 9.46/1.99 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 9.46/1.99 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 9.46/2.00 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 9.46/2.00 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 9.46/2.00 % 9.46/2.00 (thI11) % 9.46/2.00 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 9.46/2.00 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & union(v0, % 9.46/2.00 v3) = v4 & union(v0, v2) = v6 & union(v0, v1) = v5 & intersection(v5, v6) % 9.46/2.00 = v7 & intersection(v1, v2) = v3 & equal_set(v4, v7) = v8 & $i(v7) & $i(v6) % 9.46/2.00 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 9.46/2.00 % 9.46/2.00 (union) % 9.46/2.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 9.46/2.00 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 9.46/2.00 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 9.46/2.00 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 9.46/2.00 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 9.46/2.00 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 9.46/2.00 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 9.46/2.00 % 9.46/2.00 (function-axioms) % 9.46/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.46/2.01 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 9.46/2.01 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.46/2.01 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 9.46/2.01 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 9.46/2.01 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 9.46/2.01 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 9.46/2.01 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.46/2.01 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 9.46/2.01 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.46/2.01 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 9.46/2.01 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 9.46/2.01 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.46/2.01 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 9.46/2.01 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 9.46/2.01 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 9.46/2.01 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 9.46/2.01 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 9.46/2.01 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 9.46/2.01 (power_set(v2) = v0)) % 9.46/2.01 % 9.46/2.01 Further assumptions not needed in the proof: % 9.46/2.01 -------------------------------------------- % 9.46/2.01 difference, empty_set, power_set, product, singleton, sum, unordered_pair % 9.46/2.01 % 9.46/2.01 Those formulas are unsatisfiable: % 9.46/2.01 --------------------------------- % 9.46/2.01 % 9.46/2.01 Begin of proof % 9.46/2.01 | % 9.46/2.01 | ALPHA: (subset) implies: % 9.46/2.01 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 9.46/2.01 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 9.46/2.01 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 9.46/2.01 | % 9.46/2.01 | ALPHA: (equal_set) implies: % 9.46/2.01 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 9.46/2.01 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 9.46/2.01 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 9.46/2.01 | 0)))) % 9.46/2.01 | % 9.46/2.01 | ALPHA: (intersection) implies: % 9.46/2.01 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.46/2.01 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 9.46/2.01 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 9.46/2.01 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.46/2.01 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 9.46/2.01 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 9.46/2.01 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 9.46/2.01 | 0)))) % 9.46/2.01 | % 9.46/2.01 | ALPHA: (union) implies: % 9.46/2.01 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 9.46/2.01 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 9.46/2.01 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 9.46/2.01 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 9.46/2.02 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.46/2.02 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 9.46/2.02 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 9.46/2.02 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 9.46/2.02 | v5)) % 9.46/2.02 | % 9.46/2.02 | ALPHA: (function-axioms) implies: % 9.46/2.02 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.46/2.02 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 9.46/2.02 | = v0)) % 9.46/2.02 | % 9.46/2.02 | DELTA: instantiating (thI11) with fresh symbols all_15_0, all_15_1, all_15_2, % 9.46/2.02 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7, all_15_8 gives: % 9.46/2.02 | (8) ~ (all_15_0 = 0) & union(all_15_8, all_15_5) = all_15_4 & % 9.46/2.02 | union(all_15_8, all_15_6) = all_15_2 & union(all_15_8, all_15_7) = % 9.46/2.02 | all_15_3 & intersection(all_15_3, all_15_2) = all_15_1 & % 9.46/2.02 | intersection(all_15_7, all_15_6) = all_15_5 & equal_set(all_15_4, % 9.46/2.02 | all_15_1) = all_15_0 & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & % 9.46/2.02 | $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & $i(all_15_7) & % 9.46/2.02 | $i(all_15_8) % 9.46/2.02 | % 9.46/2.02 | ALPHA: (8) implies: % 9.46/2.02 | (9) ~ (all_15_0 = 0) % 9.46/2.02 | (10) $i(all_15_8) % 9.46/2.02 | (11) $i(all_15_7) % 9.46/2.02 | (12) $i(all_15_6) % 9.46/2.02 | (13) $i(all_15_5) % 9.46/2.02 | (14) $i(all_15_4) % 9.46/2.02 | (15) $i(all_15_3) % 9.46/2.02 | (16) $i(all_15_2) % 9.46/2.02 | (17) $i(all_15_1) % 9.46/2.02 | (18) equal_set(all_15_4, all_15_1) = all_15_0 % 9.46/2.02 | (19) intersection(all_15_7, all_15_6) = all_15_5 % 9.46/2.02 | (20) intersection(all_15_3, all_15_2) = all_15_1 % 9.46/2.02 | (21) union(all_15_8, all_15_7) = all_15_3 % 9.46/2.02 | (22) union(all_15_8, all_15_6) = all_15_2 % 9.46/2.02 | (23) union(all_15_8, all_15_5) = all_15_4 % 9.46/2.02 | % 9.46/2.02 | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_15_0, simplifying % 9.46/2.02 | with (14), (17), (18) gives: % 9.46/2.02 | (24) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 9.46/2.02 | all_15_4) = v1 & subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | % 9.46/2.02 | ~ (v0 = 0))) % 9.46/2.02 | % 9.46/2.02 | BETA: splitting (24) gives: % 9.46/2.02 | % 9.46/2.02 | Case 1: % 9.46/2.02 | | % 9.46/2.02 | | (25) all_15_0 = 0 % 9.46/2.02 | | % 9.46/2.02 | | REDUCE: (9), (25) imply: % 9.46/2.02 | | (26) $false % 9.46/2.02 | | % 9.46/2.02 | | CLOSE: (26) is inconsistent. % 9.46/2.02 | | % 9.46/2.02 | Case 2: % 9.46/2.02 | | % 9.46/2.02 | | (27) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_4) = v1 & % 9.46/2.02 | | subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 9.46/2.02 | | % 9.46/2.02 | | DELTA: instantiating (27) with fresh symbols all_24_0, all_24_1 gives: % 9.46/2.02 | | (28) subset(all_15_1, all_15_4) = all_24_0 & subset(all_15_4, all_15_1) = % 9.46/2.02 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0)) % 9.46/2.02 | | % 9.46/2.02 | | ALPHA: (28) implies: % 9.46/2.03 | | (29) subset(all_15_4, all_15_1) = all_24_1 % 9.46/2.03 | | (30) subset(all_15_1, all_15_4) = all_24_0 % 9.46/2.03 | | (31) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 9.46/2.03 | | % 9.46/2.03 | | GROUND_INST: instantiating (1) with all_15_4, all_15_1, all_24_1, % 9.46/2.03 | | simplifying with (14), (17), (29) gives: % 9.46/2.03 | | (32) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 9.46/2.03 | | member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 9.46/2.03 | | % 9.46/2.03 | | GROUND_INST: instantiating (1) with all_15_1, all_15_4, all_24_0, % 9.46/2.03 | | simplifying with (14), (17), (30) gives: % 9.46/2.03 | | (33) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 9.46/2.03 | | member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 9.46/2.03 | | % 9.46/2.03 | | BETA: splitting (31) gives: % 9.46/2.03 | | % 9.46/2.03 | | Case 1: % 9.46/2.03 | | | % 9.46/2.03 | | | (34) ~ (all_24_0 = 0) % 9.46/2.03 | | | % 9.46/2.03 | | | BETA: splitting (33) gives: % 9.46/2.03 | | | % 9.46/2.03 | | | Case 1: % 9.46/2.03 | | | | % 9.46/2.03 | | | | (35) all_24_0 = 0 % 9.46/2.03 | | | | % 9.46/2.03 | | | | REDUCE: (34), (35) imply: % 9.46/2.03 | | | | (36) $false % 9.46/2.03 | | | | % 9.46/2.03 | | | | CLOSE: (36) is inconsistent. % 9.46/2.03 | | | | % 9.46/2.03 | | | Case 2: % 9.46/2.03 | | | | % 9.46/2.03 | | | | (37) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 9.46/2.03 | | | | = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 9.46/2.03 | | | | % 9.46/2.03 | | | | DELTA: instantiating (37) with fresh symbols all_37_0, all_37_1 gives: % 9.46/2.03 | | | | (38) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 & % 9.46/2.03 | | | | member(all_37_1, all_15_4) = all_37_0 & $i(all_37_1) % 9.46/2.03 | | | | % 9.46/2.03 | | | | ALPHA: (38) implies: % 9.46/2.03 | | | | (39) ~ (all_37_0 = 0) % 9.46/2.03 | | | | (40) $i(all_37_1) % 9.46/2.03 | | | | (41) member(all_37_1, all_15_4) = all_37_0 % 9.46/2.03 | | | | (42) member(all_37_1, all_15_1) = 0 % 9.46/2.03 | | | | % 9.46/2.03 | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_8, all_15_5, % 9.46/2.03 | | | | all_15_4, all_37_0, simplifying with (10), (13), (23), % 9.46/2.03 | | | | (40), (41) gives: % 9.46/2.03 | | | | (43) all_37_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 9.46/2.03 | | | | (v0 = 0) & member(all_37_1, all_15_5) = v1 & member(all_37_1, % 9.46/2.03 | | | | all_15_8) = v0) % 9.46/2.03 | | | | % 9.46/2.03 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_3, all_15_2, % 9.46/2.03 | | | | all_15_1, simplifying with (15), (16), (20), (40), (42) % 9.46/2.03 | | | | gives: % 9.46/2.03 | | | | (44) member(all_37_1, all_15_2) = 0 & member(all_37_1, all_15_3) = 0 % 9.46/2.03 | | | | % 9.46/2.03 | | | | ALPHA: (44) implies: % 9.46/2.03 | | | | (45) member(all_37_1, all_15_3) = 0 % 9.46/2.03 | | | | (46) member(all_37_1, all_15_2) = 0 % 9.46/2.03 | | | | % 9.46/2.03 | | | | BETA: splitting (43) gives: % 9.46/2.03 | | | | % 9.46/2.03 | | | | Case 1: % 9.46/2.03 | | | | | % 9.46/2.03 | | | | | (47) all_37_0 = 0 % 9.46/2.03 | | | | | % 9.46/2.03 | | | | | REDUCE: (39), (47) imply: % 9.46/2.03 | | | | | (48) $false % 9.46/2.03 | | | | | % 9.46/2.03 | | | | | CLOSE: (48) is inconsistent. % 9.46/2.03 | | | | | % 9.46/2.03 | | | | Case 2: % 9.46/2.03 | | | | | % 9.46/2.03 | | | | | (49) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 9.46/2.03 | | | | | member(all_37_1, all_15_5) = v1 & member(all_37_1, all_15_8) % 9.46/2.03 | | | | | = v0) % 9.46/2.03 | | | | | % 9.46/2.03 | | | | | DELTA: instantiating (49) with fresh symbols all_49_0, all_49_1 gives: % 9.46/2.03 | | | | | (50) ~ (all_49_0 = 0) & ~ (all_49_1 = 0) & member(all_37_1, % 9.46/2.03 | | | | | all_15_5) = all_49_0 & member(all_37_1, all_15_8) = all_49_1 % 9.46/2.03 | | | | | % 9.46/2.03 | | | | | ALPHA: (50) implies: % 9.46/2.03 | | | | | (51) ~ (all_49_1 = 0) % 9.46/2.03 | | | | | (52) ~ (all_49_0 = 0) % 9.46/2.04 | | | | | (53) member(all_37_1, all_15_8) = all_49_1 % 9.46/2.04 | | | | | (54) member(all_37_1, all_15_5) = all_49_0 % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_7, all_15_6, % 9.46/2.04 | | | | | all_15_5, all_49_0, simplifying with (11), (12), (19), % 9.46/2.04 | | | | | (40), (54) gives: % 9.46/2.04 | | | | | (55) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1, % 9.46/2.04 | | | | | all_15_6) = v1 & member(all_37_1, all_15_7) = v0 & ( ~ (v1 % 9.46/2.04 | | | | | = 0) | ~ (v0 = 0))) % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_8, all_15_7, % 9.46/2.04 | | | | | all_15_3, simplifying with (10), (11), (21), (40), (45) % 9.46/2.04 | | | | | gives: % 9.46/2.04 | | | | | (56) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_7) = v1 % 9.46/2.04 | | | | | & member(all_37_1, all_15_8) = v0 & (v1 = 0 | v0 = 0)) % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_8, all_15_6, % 9.46/2.04 | | | | | all_15_2, simplifying with (10), (12), (22), (40), (46) % 9.46/2.04 | | | | | gives: % 9.46/2.04 | | | | | (57) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_6) = v1 % 9.46/2.04 | | | | | & member(all_37_1, all_15_8) = v0 & (v1 = 0 | v0 = 0)) % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | DELTA: instantiating (57) with fresh symbols all_56_0, all_56_1 gives: % 9.46/2.04 | | | | | (58) member(all_37_1, all_15_6) = all_56_0 & member(all_37_1, % 9.46/2.04 | | | | | all_15_8) = all_56_1 & (all_56_0 = 0 | all_56_1 = 0) % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | ALPHA: (58) implies: % 9.46/2.04 | | | | | (59) member(all_37_1, all_15_8) = all_56_1 % 9.46/2.04 | | | | | (60) member(all_37_1, all_15_6) = all_56_0 % 9.46/2.04 | | | | | (61) all_56_0 = 0 | all_56_1 = 0 % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | DELTA: instantiating (56) with fresh symbols all_58_0, all_58_1 gives: % 9.46/2.04 | | | | | (62) member(all_37_1, all_15_7) = all_58_0 & member(all_37_1, % 9.46/2.04 | | | | | all_15_8) = all_58_1 & (all_58_0 = 0 | all_58_1 = 0) % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | ALPHA: (62) implies: % 9.46/2.04 | | | | | (63) member(all_37_1, all_15_8) = all_58_1 % 9.46/2.04 | | | | | (64) member(all_37_1, all_15_7) = all_58_0 % 9.46/2.04 | | | | | (65) all_58_0 = 0 | all_58_1 = 0 % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | GROUND_INST: instantiating (7) with all_49_1, all_58_1, all_15_8, % 9.46/2.04 | | | | | all_37_1, simplifying with (53), (63) gives: % 9.46/2.04 | | | | | (66) all_58_1 = all_49_1 % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | GROUND_INST: instantiating (7) with all_56_1, all_58_1, all_15_8, % 9.46/2.04 | | | | | all_37_1, simplifying with (59), (63) gives: % 9.46/2.04 | | | | | (67) all_58_1 = all_56_1 % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | COMBINE_EQS: (66), (67) imply: % 9.46/2.04 | | | | | (68) all_56_1 = all_49_1 % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | BETA: splitting (61) gives: % 9.46/2.04 | | | | | % 9.46/2.04 | | | | | Case 1: % 9.46/2.04 | | | | | | % 9.46/2.04 | | | | | | (69) all_56_0 = 0 % 9.46/2.04 | | | | | | % 9.46/2.04 | | | | | | REDUCE: (60), (69) imply: % 9.46/2.04 | | | | | | (70) member(all_37_1, all_15_6) = 0 % 9.46/2.04 | | | | | | % 9.46/2.04 | | | | | | BETA: splitting (55) gives: % 9.46/2.04 | | | | | | % 9.46/2.04 | | | | | | Case 1: % 9.46/2.04 | | | | | | | % 9.46/2.04 | | | | | | | (71) all_49_0 = 0 % 9.46/2.04 | | | | | | | % 9.46/2.04 | | | | | | | REDUCE: (52), (71) imply: % 9.46/2.04 | | | | | | | (72) $false % 9.46/2.04 | | | | | | | % 9.46/2.04 | | | | | | | CLOSE: (72) is inconsistent. % 9.46/2.04 | | | | | | | % 9.46/2.04 | | | | | | Case 2: % 9.46/2.04 | | | | | | | % 9.46/2.04 | | | | | | | (73) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_6) % 9.46/2.04 | | | | | | | = v1 & member(all_37_1, all_15_7) = v0 & ( ~ (v1 = 0) | % 9.46/2.04 | | | | | | | ~ (v0 = 0))) % 9.46/2.04 | | | | | | | % 9.46/2.04 | | | | | | | DELTA: instantiating (73) with fresh symbols all_72_0, all_72_1 % 9.46/2.04 | | | | | | | gives: % 9.46/2.04 | | | | | | | (74) member(all_37_1, all_15_6) = all_72_0 & member(all_37_1, % 9.46/2.04 | | | | | | | all_15_7) = all_72_1 & ( ~ (all_72_0 = 0) | ~ (all_72_1 % 9.46/2.04 | | | | | | | = 0)) % 9.46/2.04 | | | | | | | % 9.46/2.05 | | | | | | | ALPHA: (74) implies: % 9.46/2.05 | | | | | | | (75) member(all_37_1, all_15_7) = all_72_1 % 9.46/2.05 | | | | | | | (76) member(all_37_1, all_15_6) = all_72_0 % 9.46/2.05 | | | | | | | (77) ~ (all_72_0 = 0) | ~ (all_72_1 = 0) % 9.46/2.05 | | | | | | | % 9.46/2.05 | | | | | | | BETA: splitting (65) gives: % 9.46/2.05 | | | | | | | % 9.46/2.05 | | | | | | | Case 1: % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | (78) all_58_0 = 0 % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | REDUCE: (64), (78) imply: % 9.46/2.05 | | | | | | | | (79) member(all_37_1, all_15_7) = 0 % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_72_1, all_15_7, % 9.46/2.05 | | | | | | | | all_37_1, simplifying with (75), (79) gives: % 9.46/2.05 | | | | | | | | (80) all_72_1 = 0 % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_72_0, all_15_6, % 9.46/2.05 | | | | | | | | all_37_1, simplifying with (70), (76) gives: % 9.46/2.05 | | | | | | | | (81) all_72_0 = 0 % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | BETA: splitting (77) gives: % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | Case 1: % 9.46/2.05 | | | | | | | | | % 9.46/2.05 | | | | | | | | | (82) ~ (all_72_0 = 0) % 9.46/2.05 | | | | | | | | | % 9.46/2.05 | | | | | | | | | REDUCE: (81), (82) imply: % 9.46/2.05 | | | | | | | | | (83) $false % 9.46/2.05 | | | | | | | | | % 9.46/2.05 | | | | | | | | | CLOSE: (83) is inconsistent. % 9.46/2.05 | | | | | | | | | % 9.46/2.05 | | | | | | | | Case 2: % 9.46/2.05 | | | | | | | | | % 9.46/2.05 | | | | | | | | | (84) ~ (all_72_1 = 0) % 9.46/2.05 | | | | | | | | | % 9.46/2.05 | | | | | | | | | REDUCE: (80), (84) imply: % 9.46/2.05 | | | | | | | | | (85) $false % 9.46/2.05 | | | | | | | | | % 9.46/2.05 | | | | | | | | | CLOSE: (85) is inconsistent. % 9.46/2.05 | | | | | | | | | % 9.46/2.05 | | | | | | | | End of split % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | Case 2: % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | (86) all_58_1 = 0 % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | COMBINE_EQS: (66), (86) imply: % 9.46/2.05 | | | | | | | | (87) all_49_1 = 0 % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | REDUCE: (51), (87) imply: % 9.46/2.05 | | | | | | | | (88) $false % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | | CLOSE: (88) is inconsistent. % 9.46/2.05 | | | | | | | | % 9.46/2.05 | | | | | | | End of split % 9.46/2.05 | | | | | | | % 9.46/2.05 | | | | | | End of split % 9.46/2.05 | | | | | | % 9.46/2.05 | | | | | Case 2: % 9.46/2.05 | | | | | | % 9.46/2.05 | | | | | | (89) all_56_1 = 0 % 9.46/2.05 | | | | | | % 9.46/2.05 | | | | | | COMBINE_EQS: (68), (89) imply: % 9.46/2.05 | | | | | | (90) all_49_1 = 0 % 9.46/2.05 | | | | | | % 9.46/2.05 | | | | | | SIMP: (90) implies: % 9.46/2.05 | | | | | | (91) all_49_1 = 0 % 9.46/2.05 | | | | | | % 9.46/2.05 | | | | | | REDUCE: (51), (91) imply: % 9.46/2.05 | | | | | | (92) $false % 9.46/2.05 | | | | | | % 9.46/2.05 | | | | | | CLOSE: (92) is inconsistent. % 9.46/2.05 | | | | | | % 9.46/2.05 | | | | | End of split % 9.46/2.05 | | | | | % 9.46/2.05 | | | | End of split % 9.46/2.05 | | | | % 9.46/2.05 | | | End of split % 9.46/2.05 | | | % 9.46/2.05 | | Case 2: % 9.46/2.05 | | | % 9.46/2.05 | | | (93) ~ (all_24_1 = 0) % 9.46/2.05 | | | % 9.46/2.05 | | | BETA: splitting (32) gives: % 9.46/2.05 | | | % 9.46/2.05 | | | Case 1: % 9.46/2.05 | | | | % 9.46/2.05 | | | | (94) all_24_1 = 0 % 9.46/2.05 | | | | % 9.46/2.05 | | | | REDUCE: (93), (94) imply: % 9.46/2.05 | | | | (95) $false % 9.46/2.05 | | | | % 9.46/2.05 | | | | CLOSE: (95) is inconsistent. % 9.46/2.05 | | | | % 9.46/2.05 | | | Case 2: % 9.46/2.05 | | | | % 9.46/2.05 | | | | (96) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 9.46/2.05 | | | | = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 9.46/2.05 | | | | % 9.46/2.05 | | | | DELTA: instantiating (96) with fresh symbols all_37_0, all_37_1 gives: % 9.46/2.05 | | | | (97) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 & % 9.46/2.05 | | | | member(all_37_1, all_15_4) = 0 & $i(all_37_1) % 9.46/2.05 | | | | % 9.46/2.05 | | | | ALPHA: (97) implies: % 9.46/2.05 | | | | (98) ~ (all_37_0 = 0) % 9.46/2.05 | | | | (99) $i(all_37_1) % 9.46/2.05 | | | | (100) member(all_37_1, all_15_4) = 0 % 9.46/2.05 | | | | (101) member(all_37_1, all_15_1) = all_37_0 % 9.46/2.05 | | | | % 9.46/2.05 | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_8, all_15_5, % 9.46/2.05 | | | | all_15_4, simplifying with (10), (13), (23), (99), (100) % 9.46/2.05 | | | | gives: % 9.46/2.06 | | | | (102) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_5) = v1 % 9.46/2.06 | | | | & member(all_37_1, all_15_8) = v0 & (v1 = 0 | v0 = 0)) % 9.46/2.06 | | | | % 9.46/2.06 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_3, all_15_2, % 9.46/2.06 | | | | all_15_1, all_37_0, simplifying with (15), (16), (20), % 9.46/2.06 | | | | (99), (101) gives: % 9.46/2.06 | | | | (103) all_37_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1, % 9.46/2.06 | | | | all_15_2) = v1 & member(all_37_1, all_15_3) = v0 & ( ~ (v1 % 9.46/2.06 | | | | = 0) | ~ (v0 = 0))) % 9.46/2.06 | | | | % 9.46/2.06 | | | | DELTA: instantiating (102) with fresh symbols all_45_0, all_45_1 gives: % 9.46/2.06 | | | | (104) member(all_37_1, all_15_5) = all_45_0 & member(all_37_1, % 9.46/2.06 | | | | all_15_8) = all_45_1 & (all_45_0 = 0 | all_45_1 = 0) % 9.46/2.06 | | | | % 9.46/2.06 | | | | ALPHA: (104) implies: % 9.46/2.06 | | | | (105) member(all_37_1, all_15_8) = all_45_1 % 9.46/2.06 | | | | (106) member(all_37_1, all_15_5) = all_45_0 % 9.46/2.06 | | | | (107) all_45_0 = 0 | all_45_1 = 0 % 9.46/2.06 | | | | % 9.46/2.06 | | | | BETA: splitting (103) gives: % 9.46/2.06 | | | | % 9.46/2.06 | | | | Case 1: % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | (108) all_37_0 = 0 % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | REDUCE: (98), (108) imply: % 9.46/2.06 | | | | | (109) $false % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | CLOSE: (109) is inconsistent. % 9.46/2.06 | | | | | % 9.46/2.06 | | | | Case 2: % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | (110) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_2) = % 9.46/2.06 | | | | | v1 & member(all_37_1, all_15_3) = v0 & ( ~ (v1 = 0) | ~ % 9.46/2.06 | | | | | (v0 = 0))) % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | DELTA: instantiating (110) with fresh symbols all_51_0, all_51_1 % 9.46/2.06 | | | | | gives: % 9.46/2.06 | | | | | (111) member(all_37_1, all_15_2) = all_51_0 & member(all_37_1, % 9.46/2.06 | | | | | all_15_3) = all_51_1 & ( ~ (all_51_0 = 0) | ~ (all_51_1 = % 9.46/2.06 | | | | | 0)) % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | ALPHA: (111) implies: % 9.46/2.06 | | | | | (112) member(all_37_1, all_15_3) = all_51_1 % 9.46/2.06 | | | | | (113) member(all_37_1, all_15_2) = all_51_0 % 9.46/2.06 | | | | | (114) ~ (all_51_0 = 0) | ~ (all_51_1 = 0) % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_8, all_15_7, % 9.46/2.06 | | | | | all_15_3, all_51_1, simplifying with (10), (11), (21), % 9.46/2.06 | | | | | (99), (112) gives: % 9.46/2.06 | | | | | (115) all_51_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 9.46/2.06 | | | | | ~ (v0 = 0) & member(all_37_1, all_15_7) = v1 & % 9.46/2.06 | | | | | member(all_37_1, all_15_8) = v0) % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_8, all_15_6, % 9.46/2.06 | | | | | all_15_2, all_51_0, simplifying with (10), (12), (22), % 9.46/2.06 | | | | | (99), (113) gives: % 9.46/2.06 | | | | | (116) all_51_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 9.46/2.06 | | | | | ~ (v0 = 0) & member(all_37_1, all_15_6) = v1 & % 9.46/2.06 | | | | | member(all_37_1, all_15_8) = v0) % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | BETA: splitting (107) gives: % 9.46/2.06 | | | | | % 9.46/2.06 | | | | | Case 1: % 9.46/2.06 | | | | | | % 9.46/2.06 | | | | | | (117) all_45_0 = 0 % 9.46/2.06 | | | | | | % 9.46/2.06 | | | | | | REDUCE: (106), (117) imply: % 9.46/2.06 | | | | | | (118) member(all_37_1, all_15_5) = 0 % 9.46/2.06 | | | | | | % 9.46/2.06 | | | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_7, all_15_6, % 9.46/2.06 | | | | | | all_15_5, simplifying with (11), (12), (19), (99), % 9.46/2.06 | | | | | | (118) gives: % 9.46/2.06 | | | | | | (119) member(all_37_1, all_15_6) = 0 & member(all_37_1, all_15_7) % 9.46/2.06 | | | | | | = 0 % 9.46/2.06 | | | | | | % 9.46/2.06 | | | | | | ALPHA: (119) implies: % 9.46/2.06 | | | | | | (120) member(all_37_1, all_15_7) = 0 % 9.46/2.06 | | | | | | (121) member(all_37_1, all_15_6) = 0 % 9.46/2.06 | | | | | | % 9.46/2.06 | | | | | | BETA: splitting (115) gives: % 9.46/2.06 | | | | | | % 9.46/2.06 | | | | | | Case 1: % 9.46/2.06 | | | | | | | % 9.46/2.06 | | | | | | | (122) all_51_1 = 0 % 9.46/2.06 | | | | | | | % 9.46/2.06 | | | | | | | BETA: splitting (114) gives: % 9.46/2.06 | | | | | | | % 9.46/2.06 | | | | | | | Case 1: % 9.46/2.06 | | | | | | | | % 9.46/2.06 | | | | | | | | (123) ~ (all_51_0 = 0) % 9.46/2.06 | | | | | | | | % 9.46/2.06 | | | | | | | | BETA: splitting (116) gives: % 9.46/2.06 | | | | | | | | % 9.46/2.06 | | | | | | | | Case 1: % 9.46/2.06 | | | | | | | | | % 9.46/2.06 | | | | | | | | | (124) all_51_0 = 0 % 9.46/2.06 | | | | | | | | | % 9.46/2.06 | | | | | | | | | REDUCE: (123), (124) imply: % 9.46/2.06 | | | | | | | | | (125) $false % 9.46/2.06 | | | | | | | | | % 9.46/2.06 | | | | | | | | | CLOSE: (125) is inconsistent. % 9.46/2.06 | | | | | | | | | % 9.46/2.06 | | | | | | | | Case 2: % 9.46/2.06 | | | | | | | | | % 9.46/2.06 | | | | | | | | | (126) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 9.46/2.06 | | | | | | | | | 0) & member(all_37_1, all_15_6) = v1 & % 9.46/2.06 | | | | | | | | | member(all_37_1, all_15_8) = v0) % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | DELTA: instantiating (126) with fresh symbols all_78_0, % 9.46/2.07 | | | | | | | | | all_78_1 gives: % 9.46/2.07 | | | | | | | | | (127) ~ (all_78_0 = 0) & ~ (all_78_1 = 0) & % 9.46/2.07 | | | | | | | | | member(all_37_1, all_15_6) = all_78_0 & % 9.46/2.07 | | | | | | | | | member(all_37_1, all_15_8) = all_78_1 % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | ALPHA: (127) implies: % 9.46/2.07 | | | | | | | | | (128) ~ (all_78_0 = 0) % 9.46/2.07 | | | | | | | | | (129) member(all_37_1, all_15_6) = all_78_0 % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_78_0, all_15_6, % 9.46/2.07 | | | | | | | | | all_37_1, simplifying with (121), (129) gives: % 9.46/2.07 | | | | | | | | | (130) all_78_0 = 0 % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | REDUCE: (128), (130) imply: % 9.46/2.07 | | | | | | | | | (131) $false % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | CLOSE: (131) is inconsistent. % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | End of split % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | Case 2: % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | | (132) ~ (all_51_1 = 0) % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | | REDUCE: (122), (132) imply: % 9.46/2.07 | | | | | | | | (133) $false % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | | CLOSE: (133) is inconsistent. % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | End of split % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | Case 2: % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | (134) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 9.46/2.07 | | | | | | | & member(all_37_1, all_15_7) = v1 & member(all_37_1, % 9.46/2.07 | | | | | | | all_15_8) = v0) % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | DELTA: instantiating (134) with fresh symbols all_70_0, all_70_1 % 9.46/2.07 | | | | | | | gives: % 9.46/2.07 | | | | | | | (135) ~ (all_70_0 = 0) & ~ (all_70_1 = 0) & member(all_37_1, % 9.46/2.07 | | | | | | | all_15_7) = all_70_0 & member(all_37_1, all_15_8) = % 9.46/2.07 | | | | | | | all_70_1 % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | ALPHA: (135) implies: % 9.46/2.07 | | | | | | | (136) ~ (all_70_0 = 0) % 9.46/2.07 | | | | | | | (137) member(all_37_1, all_15_7) = all_70_0 % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | GROUND_INST: instantiating (7) with 0, all_70_0, all_15_7, % 9.46/2.07 | | | | | | | all_37_1, simplifying with (120), (137) gives: % 9.46/2.07 | | | | | | | (138) all_70_0 = 0 % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | REDUCE: (136), (138) imply: % 9.46/2.07 | | | | | | | (139) $false % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | CLOSE: (139) is inconsistent. % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | End of split % 9.46/2.07 | | | | | | % 9.46/2.07 | | | | | Case 2: % 9.46/2.07 | | | | | | % 9.46/2.07 | | | | | | (140) all_45_1 = 0 % 9.46/2.07 | | | | | | % 9.46/2.07 | | | | | | REDUCE: (105), (140) imply: % 9.46/2.07 | | | | | | (141) member(all_37_1, all_15_8) = 0 % 9.46/2.07 | | | | | | % 9.46/2.07 | | | | | | BETA: splitting (115) gives: % 9.46/2.07 | | | | | | % 9.46/2.07 | | | | | | Case 1: % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | (142) all_51_1 = 0 % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | BETA: splitting (114) gives: % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | Case 1: % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | | (143) ~ (all_51_0 = 0) % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | | BETA: splitting (116) gives: % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | | Case 1: % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | (144) all_51_0 = 0 % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | REDUCE: (143), (144) imply: % 9.46/2.07 | | | | | | | | | (145) $false % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | CLOSE: (145) is inconsistent. % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | Case 2: % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | (146) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 9.46/2.07 | | | | | | | | | 0) & member(all_37_1, all_15_6) = v1 & % 9.46/2.07 | | | | | | | | | member(all_37_1, all_15_8) = v0) % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | DELTA: instantiating (146) with fresh symbols all_72_0, % 9.46/2.07 | | | | | | | | | all_72_1 gives: % 9.46/2.07 | | | | | | | | | (147) ~ (all_72_0 = 0) & ~ (all_72_1 = 0) & % 9.46/2.07 | | | | | | | | | member(all_37_1, all_15_6) = all_72_0 & % 9.46/2.07 | | | | | | | | | member(all_37_1, all_15_8) = all_72_1 % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | ALPHA: (147) implies: % 9.46/2.07 | | | | | | | | | (148) ~ (all_72_1 = 0) % 9.46/2.07 | | | | | | | | | (149) member(all_37_1, all_15_8) = all_72_1 % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_72_1, all_15_8, % 9.46/2.07 | | | | | | | | | all_37_1, simplifying with (141), (149) gives: % 9.46/2.07 | | | | | | | | | (150) all_72_1 = 0 % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | REDUCE: (148), (150) imply: % 9.46/2.07 | | | | | | | | | (151) $false % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | | CLOSE: (151) is inconsistent. % 9.46/2.07 | | | | | | | | | % 9.46/2.07 | | | | | | | | End of split % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | Case 2: % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | | (152) ~ (all_51_1 = 0) % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | | REDUCE: (142), (152) imply: % 9.46/2.07 | | | | | | | | (153) $false % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | | CLOSE: (153) is inconsistent. % 9.46/2.07 | | | | | | | | % 9.46/2.07 | | | | | | | End of split % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | Case 2: % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | (154) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) % 9.46/2.07 | | | | | | | & member(all_37_1, all_15_7) = v1 & member(all_37_1, % 9.46/2.07 | | | | | | | all_15_8) = v0) % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | DELTA: instantiating (154) with fresh symbols all_64_0, all_64_1 % 9.46/2.07 | | | | | | | gives: % 9.46/2.07 | | | | | | | (155) ~ (all_64_0 = 0) & ~ (all_64_1 = 0) & member(all_37_1, % 9.46/2.07 | | | | | | | all_15_7) = all_64_0 & member(all_37_1, all_15_8) = % 9.46/2.07 | | | | | | | all_64_1 % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | ALPHA: (155) implies: % 9.46/2.07 | | | | | | | (156) ~ (all_64_1 = 0) % 9.46/2.07 | | | | | | | (157) member(all_37_1, all_15_8) = all_64_1 % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | GROUND_INST: instantiating (7) with 0, all_64_1, all_15_8, % 9.46/2.07 | | | | | | | all_37_1, simplifying with (141), (157) gives: % 9.46/2.07 | | | | | | | (158) all_64_1 = 0 % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | REDUCE: (156), (158) imply: % 9.46/2.07 | | | | | | | (159) $false % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | | CLOSE: (159) is inconsistent. % 9.46/2.07 | | | | | | | % 9.46/2.07 | | | | | | End of split % 9.46/2.07 | | | | | | % 9.46/2.07 | | | | | End of split % 9.46/2.07 | | | | | % 9.46/2.07 | | | | End of split % 9.46/2.07 | | | | % 9.46/2.07 | | | End of split % 9.46/2.07 | | | % 9.46/2.07 | | End of split % 9.46/2.07 | | % 9.46/2.07 | End of split % 9.46/2.07 | % 9.46/2.07 End of proof % 9.46/2.07 % SZS output end Proof for theBenchmark % 9.46/2.07 % 9.46/2.07 1453ms %------------------------------------------------------------------------------