%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET013+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 : n013.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 15:23:05 EDT 2023 % Result : Theorem 6.89s 1.60s % Output : Proof 8.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET013+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n013.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 10:18:17 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.17/0.98 Prover 4: Preprocessing ... % 2.17/0.98 Prover 1: Preprocessing ... % 2.17/1.02 Prover 3: Preprocessing ... % 2.17/1.02 Prover 2: Preprocessing ... % 2.17/1.02 Prover 0: Preprocessing ... % 2.17/1.02 Prover 6: Preprocessing ... % 2.17/1.02 Prover 5: Preprocessing ... % 5.05/1.38 Prover 5: Proving ... % 5.05/1.39 Prover 2: Proving ... % 5.05/1.39 Prover 6: Proving ... % 5.05/1.39 Prover 1: Constructing countermodel ... % 5.05/1.41 Prover 4: Constructing countermodel ... % 5.05/1.41 Prover 3: Constructing countermodel ... % 5.05/1.42 Prover 0: Proving ... % 6.89/1.60 Prover 3: proved (973ms) % 6.89/1.60 % 6.89/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.89/1.60 % 6.89/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.89/1.61 Prover 5: stopped % 6.89/1.61 Prover 0: stopped % 6.89/1.61 Prover 2: stopped % 6.89/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.89/1.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.89/1.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.89/1.61 Prover 6: proved (985ms) % 6.89/1.61 % 6.89/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.89/1.61 % 6.89/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.89/1.64 Prover 10: Preprocessing ... % 7.18/1.64 Prover 11: Preprocessing ... % 7.18/1.65 Prover 7: Preprocessing ... % 7.18/1.66 Prover 13: Preprocessing ... % 7.18/1.67 Prover 8: Preprocessing ... % 7.18/1.70 Prover 1: Found proof (size 55) % 7.18/1.70 Prover 1: proved (1078ms) % 7.18/1.70 Prover 4: stopped % 7.18/1.71 Prover 13: stopped % 7.18/1.71 Prover 11: stopped % 7.18/1.72 Prover 10: Warning: ignoring some quantifiers % 7.18/1.72 Prover 7: Warning: ignoring some quantifiers % 7.18/1.74 Prover 7: Constructing countermodel ... % 7.18/1.74 Prover 10: Constructing countermodel ... % 7.91/1.74 Prover 7: stopped % 7.91/1.74 Prover 10: stopped % 7.91/1.76 Prover 8: Warning: ignoring some quantifiers % 7.91/1.77 Prover 8: Constructing countermodel ... % 7.91/1.78 Prover 8: stopped % 7.91/1.78 % 7.91/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.91/1.78 % 7.91/1.78 % SZS output start Proof for theBenchmark % 7.91/1.79 Assumptions after simplification: % 7.91/1.79 --------------------------------- % 7.91/1.79 % 7.91/1.79 (equal_set) % 8.20/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 8.20/1.82 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 8.20/1.82 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 8.20/1.82 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 8.20/1.82 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.20/1.82 % 8.20/1.82 (intersection) % 8.20/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.20/1.82 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 8.20/1.82 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 8.20/1.82 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 8.20/1.82 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 8.20/1.82 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 8.20/1.82 0 & member(v0, v1) = 0)) % 8.20/1.82 % 8.20/1.82 (subset) % 8.20/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.20/1.82 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.20/1.82 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.20/1.82 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.20/1.82 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.20/1.82 % 8.20/1.82 (thI06) % 8.20/1.82 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 8.20/1.82 = 0) & intersection(v1, v0) = v3 & intersection(v0, v1) = v2 & % 8.20/1.82 equal_set(v2, v3) = v4 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.20/1.82 % 8.20/1.82 (function-axioms) % 8.20/1.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.20/1.83 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.20/1.83 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.20/1.83 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.20/1.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.20/1.83 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.20/1.83 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.20/1.83 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.20/1.83 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.20/1.83 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.20/1.83 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.20/1.83 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.20/1.83 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.20/1.83 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.20/1.83 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.20/1.83 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.20/1.83 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.20/1.83 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.20/1.83 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.20/1.83 (power_set(v2) = v0)) % 8.20/1.83 % 8.20/1.83 Further assumptions not needed in the proof: % 8.20/1.83 -------------------------------------------- % 8.20/1.83 difference, empty_set, power_set, product, singleton, sum, union, unordered_pair % 8.20/1.83 % 8.20/1.83 Those formulas are unsatisfiable: % 8.20/1.83 --------------------------------- % 8.20/1.83 % 8.20/1.83 Begin of proof % 8.20/1.83 | % 8.20/1.83 | ALPHA: (subset) implies: % 8.20/1.83 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.20/1.83 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.20/1.83 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.20/1.83 | % 8.20/1.83 | ALPHA: (equal_set) implies: % 8.20/1.83 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 8.20/1.83 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 8.20/1.83 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 8.20/1.83 | 0)))) % 8.20/1.83 | % 8.20/1.83 | ALPHA: (intersection) implies: % 8.20/1.84 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.20/1.84 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 8.20/1.84 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 8.20/1.84 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 8.20/1.84 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 8.20/1.84 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 8.20/1.84 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 8.20/1.84 | 0)))) % 8.20/1.84 | % 8.20/1.84 | ALPHA: (function-axioms) implies: % 8.20/1.84 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.20/1.84 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 8.20/1.84 | = v0)) % 8.20/1.84 | % 8.20/1.84 | DELTA: instantiating (thI06) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.20/1.84 | all_15_3, all_15_4 gives: % 8.20/1.84 | (6) ~ (all_15_0 = 0) & intersection(all_15_3, all_15_4) = all_15_1 & % 8.20/1.84 | intersection(all_15_4, all_15_3) = all_15_2 & equal_set(all_15_2, % 8.20/1.84 | all_15_1) = all_15_0 & $i(all_15_1) & $i(all_15_2) & $i(all_15_3) & % 8.20/1.84 | $i(all_15_4) % 8.20/1.84 | % 8.20/1.84 | ALPHA: (6) implies: % 8.20/1.84 | (7) ~ (all_15_0 = 0) % 8.20/1.84 | (8) $i(all_15_4) % 8.20/1.84 | (9) $i(all_15_3) % 8.20/1.84 | (10) $i(all_15_2) % 8.20/1.84 | (11) $i(all_15_1) % 8.20/1.84 | (12) equal_set(all_15_2, all_15_1) = all_15_0 % 8.20/1.84 | (13) intersection(all_15_4, all_15_3) = all_15_2 % 8.20/1.84 | (14) intersection(all_15_3, all_15_4) = all_15_1 % 8.20/1.84 | % 8.20/1.84 | GROUND_INST: instantiating (2) with all_15_2, all_15_1, all_15_0, simplifying % 8.20/1.84 | with (10), (11), (12) gives: % 8.20/1.84 | (15) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 8.20/1.84 | all_15_2) = v1 & subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | % 8.20/1.84 | ~ (v0 = 0))) % 8.20/1.84 | % 8.20/1.84 | BETA: splitting (15) gives: % 8.20/1.84 | % 8.20/1.84 | Case 1: % 8.20/1.84 | | % 8.20/1.84 | | (16) all_15_0 = 0 % 8.20/1.84 | | % 8.20/1.84 | | REDUCE: (7), (16) imply: % 8.20/1.84 | | (17) $false % 8.20/1.84 | | % 8.20/1.84 | | CLOSE: (17) is inconsistent. % 8.20/1.84 | | % 8.20/1.84 | Case 2: % 8.20/1.84 | | % 8.20/1.85 | | (18) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_2) = v1 & % 8.20/1.85 | | subset(all_15_2, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.20/1.85 | | % 8.20/1.85 | | DELTA: instantiating (18) with fresh symbols all_24_0, all_24_1 gives: % 8.20/1.85 | | (19) subset(all_15_1, all_15_2) = all_24_0 & subset(all_15_2, all_15_1) = % 8.20/1.85 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0)) % 8.20/1.85 | | % 8.20/1.85 | | ALPHA: (19) implies: % 8.20/1.85 | | (20) subset(all_15_2, all_15_1) = all_24_1 % 8.20/1.85 | | (21) subset(all_15_1, all_15_2) = all_24_0 % 8.20/1.85 | | (22) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 8.20/1.85 | | % 8.20/1.85 | | GROUND_INST: instantiating (1) with all_15_2, all_15_1, all_24_1, % 8.20/1.85 | | simplifying with (10), (11), (20) gives: % 8.20/1.85 | | (23) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.20/1.85 | | member(v0, all_15_1) = v1 & member(v0, all_15_2) = 0 & $i(v0)) % 8.20/1.85 | | % 8.20/1.85 | | GROUND_INST: instantiating (1) with all_15_1, all_15_2, all_24_0, % 8.20/1.85 | | simplifying with (10), (11), (21) gives: % 8.20/1.85 | | (24) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.20/1.85 | | member(v0, all_15_1) = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 8.20/1.85 | | % 8.20/1.85 | | BETA: splitting (22) gives: % 8.20/1.85 | | % 8.20/1.85 | | Case 1: % 8.20/1.85 | | | % 8.20/1.85 | | | (25) ~ (all_24_0 = 0) % 8.20/1.85 | | | % 8.20/1.85 | | | BETA: splitting (24) gives: % 8.20/1.85 | | | % 8.20/1.85 | | | Case 1: % 8.20/1.85 | | | | % 8.20/1.85 | | | | (26) all_24_0 = 0 % 8.20/1.85 | | | | % 8.20/1.85 | | | | REDUCE: (25), (26) imply: % 8.20/1.85 | | | | (27) $false % 8.20/1.85 | | | | % 8.20/1.85 | | | | CLOSE: (27) is inconsistent. % 8.20/1.85 | | | | % 8.20/1.85 | | | Case 2: % 8.20/1.85 | | | | % 8.20/1.85 | | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 8.20/1.85 | | | | = 0 & member(v0, all_15_2) = v1 & $i(v0)) % 8.20/1.85 | | | | % 8.20/1.85 | | | | DELTA: instantiating (28) with fresh symbols all_37_0, all_37_1 gives: % 8.20/1.85 | | | | (29) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 & % 8.20/1.85 | | | | member(all_37_1, all_15_2) = all_37_0 & $i(all_37_1) % 8.20/1.85 | | | | % 8.20/1.85 | | | | ALPHA: (29) implies: % 8.20/1.85 | | | | (30) ~ (all_37_0 = 0) % 8.20/1.85 | | | | (31) $i(all_37_1) % 8.20/1.85 | | | | (32) member(all_37_1, all_15_2) = all_37_0 % 8.20/1.85 | | | | (33) member(all_37_1, all_15_1) = 0 % 8.20/1.85 | | | | % 8.20/1.85 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_4, all_15_3, % 8.20/1.85 | | | | all_15_2, all_37_0, simplifying with (8), (9), (13), (31), % 8.20/1.85 | | | | (32) gives: % 8.20/1.85 | | | | (34) all_37_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1, % 8.20/1.85 | | | | all_15_3) = v1 & member(all_37_1, all_15_4) = v0 & ( ~ (v1 = % 8.20/1.85 | | | | 0) | ~ (v0 = 0))) % 8.20/1.85 | | | | % 8.20/1.85 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_3, all_15_4, % 8.20/1.85 | | | | all_15_1, simplifying with (8), (9), (14), (31), (33) % 8.20/1.85 | | | | gives: % 8.20/1.85 | | | | (35) member(all_37_1, all_15_3) = 0 & member(all_37_1, all_15_4) = 0 % 8.20/1.85 | | | | % 8.20/1.85 | | | | ALPHA: (35) implies: % 8.49/1.85 | | | | (36) member(all_37_1, all_15_4) = 0 % 8.49/1.85 | | | | (37) member(all_37_1, all_15_3) = 0 % 8.49/1.85 | | | | % 8.49/1.85 | | | | BETA: splitting (34) gives: % 8.49/1.85 | | | | % 8.49/1.85 | | | | Case 1: % 8.49/1.85 | | | | | % 8.49/1.85 | | | | | (38) all_37_0 = 0 % 8.49/1.85 | | | | | % 8.49/1.85 | | | | | REDUCE: (30), (38) imply: % 8.49/1.85 | | | | | (39) $false % 8.49/1.85 | | | | | % 8.49/1.85 | | | | | CLOSE: (39) is inconsistent. % 8.49/1.85 | | | | | % 8.49/1.85 | | | | Case 2: % 8.49/1.85 | | | | | % 8.49/1.85 | | | | | (40) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_3) = v1 % 8.49/1.85 | | | | | & member(all_37_1, all_15_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 8.49/1.85 | | | | | 0))) % 8.49/1.85 | | | | | % 8.49/1.85 | | | | | DELTA: instantiating (40) with fresh symbols all_49_0, all_49_1 gives: % 8.49/1.85 | | | | | (41) member(all_37_1, all_15_3) = all_49_0 & member(all_37_1, % 8.49/1.85 | | | | | all_15_4) = all_49_1 & ( ~ (all_49_0 = 0) | ~ (all_49_1 = % 8.49/1.86 | | | | | 0)) % 8.49/1.86 | | | | | % 8.49/1.86 | | | | | ALPHA: (41) implies: % 8.50/1.86 | | | | | (42) member(all_37_1, all_15_4) = all_49_1 % 8.50/1.86 | | | | | (43) member(all_37_1, all_15_3) = all_49_0 % 8.50/1.86 | | | | | (44) ~ (all_49_0 = 0) | ~ (all_49_1 = 0) % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | GROUND_INST: instantiating (5) with 0, all_49_1, all_15_4, all_37_1, % 8.50/1.86 | | | | | simplifying with (36), (42) gives: % 8.50/1.86 | | | | | (45) all_49_1 = 0 % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | GROUND_INST: instantiating (5) with 0, all_49_0, all_15_3, all_37_1, % 8.50/1.86 | | | | | simplifying with (37), (43) gives: % 8.50/1.86 | | | | | (46) all_49_0 = 0 % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | BETA: splitting (44) gives: % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | Case 1: % 8.50/1.86 | | | | | | % 8.50/1.86 | | | | | | (47) ~ (all_49_0 = 0) % 8.50/1.86 | | | | | | % 8.50/1.86 | | | | | | REDUCE: (46), (47) imply: % 8.50/1.86 | | | | | | (48) $false % 8.50/1.86 | | | | | | % 8.50/1.86 | | | | | | CLOSE: (48) is inconsistent. % 8.50/1.86 | | | | | | % 8.50/1.86 | | | | | Case 2: % 8.50/1.86 | | | | | | % 8.50/1.86 | | | | | | (49) ~ (all_49_1 = 0) % 8.50/1.86 | | | | | | % 8.50/1.86 | | | | | | REDUCE: (45), (49) imply: % 8.50/1.86 | | | | | | (50) $false % 8.50/1.86 | | | | | | % 8.50/1.86 | | | | | | CLOSE: (50) is inconsistent. % 8.50/1.86 | | | | | | % 8.50/1.86 | | | | | End of split % 8.50/1.86 | | | | | % 8.50/1.86 | | | | End of split % 8.50/1.86 | | | | % 8.50/1.86 | | | End of split % 8.50/1.86 | | | % 8.50/1.86 | | Case 2: % 8.50/1.86 | | | % 8.50/1.86 | | | (51) ~ (all_24_1 = 0) % 8.50/1.86 | | | % 8.50/1.86 | | | BETA: splitting (23) gives: % 8.50/1.86 | | | % 8.50/1.86 | | | Case 1: % 8.50/1.86 | | | | % 8.50/1.86 | | | | (52) all_24_1 = 0 % 8.50/1.86 | | | | % 8.50/1.86 | | | | REDUCE: (51), (52) imply: % 8.50/1.86 | | | | (53) $false % 8.50/1.86 | | | | % 8.50/1.86 | | | | CLOSE: (53) is inconsistent. % 8.50/1.86 | | | | % 8.50/1.86 | | | Case 2: % 8.50/1.86 | | | | % 8.50/1.86 | | | | (54) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 8.50/1.86 | | | | = v1 & member(v0, all_15_2) = 0 & $i(v0)) % 8.50/1.86 | | | | % 8.50/1.86 | | | | DELTA: instantiating (54) with fresh symbols all_37_0, all_37_1 gives: % 8.50/1.86 | | | | (55) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 & % 8.50/1.86 | | | | member(all_37_1, all_15_2) = 0 & $i(all_37_1) % 8.50/1.86 | | | | % 8.50/1.86 | | | | ALPHA: (55) implies: % 8.50/1.86 | | | | (56) ~ (all_37_0 = 0) % 8.50/1.86 | | | | (57) $i(all_37_1) % 8.50/1.86 | | | | (58) member(all_37_1, all_15_2) = 0 % 8.50/1.86 | | | | (59) member(all_37_1, all_15_1) = all_37_0 % 8.50/1.86 | | | | % 8.50/1.86 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_4, all_15_3, % 8.50/1.86 | | | | all_15_2, simplifying with (8), (9), (13), (57), (58) % 8.50/1.86 | | | | gives: % 8.50/1.86 | | | | (60) member(all_37_1, all_15_3) = 0 & member(all_37_1, all_15_4) = 0 % 8.50/1.86 | | | | % 8.50/1.86 | | | | ALPHA: (60) implies: % 8.50/1.86 | | | | (61) member(all_37_1, all_15_4) = 0 % 8.50/1.86 | | | | (62) member(all_37_1, all_15_3) = 0 % 8.50/1.86 | | | | % 8.50/1.86 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_3, all_15_4, % 8.50/1.86 | | | | all_15_1, all_37_0, simplifying with (8), (9), (14), (57), % 8.50/1.86 | | | | (59) gives: % 8.50/1.86 | | | | (63) all_37_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1, % 8.50/1.86 | | | | all_15_3) = v0 & member(all_37_1, all_15_4) = v1 & ( ~ (v1 = % 8.50/1.86 | | | | 0) | ~ (v0 = 0))) % 8.50/1.86 | | | | % 8.50/1.86 | | | | BETA: splitting (63) gives: % 8.50/1.86 | | | | % 8.50/1.86 | | | | Case 1: % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | (64) all_37_0 = 0 % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | REDUCE: (56), (64) imply: % 8.50/1.86 | | | | | (65) $false % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | CLOSE: (65) is inconsistent. % 8.50/1.86 | | | | | % 8.50/1.86 | | | | Case 2: % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | (66) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_3) = v0 % 8.50/1.86 | | | | | & member(all_37_1, all_15_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 8.50/1.86 | | | | | 0))) % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | DELTA: instantiating (66) with fresh symbols all_50_0, all_50_1 gives: % 8.50/1.86 | | | | | (67) member(all_37_1, all_15_3) = all_50_1 & member(all_37_1, % 8.50/1.86 | | | | | all_15_4) = all_50_0 & ( ~ (all_50_0 = 0) | ~ (all_50_1 = % 8.50/1.86 | | | | | 0)) % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | ALPHA: (67) implies: % 8.50/1.86 | | | | | (68) member(all_37_1, all_15_4) = all_50_0 % 8.50/1.86 | | | | | (69) member(all_37_1, all_15_3) = all_50_1 % 8.50/1.86 | | | | | (70) ~ (all_50_0 = 0) | ~ (all_50_1 = 0) % 8.50/1.86 | | | | | % 8.50/1.86 | | | | | GROUND_INST: instantiating (5) with 0, all_50_0, all_15_4, all_37_1, % 8.50/1.86 | | | | | simplifying with (61), (68) gives: % 8.50/1.86 | | | | | (71) all_50_0 = 0 % 8.50/1.86 | | | | | % 8.50/1.87 | | | | | GROUND_INST: instantiating (5) with 0, all_50_1, all_15_3, all_37_1, % 8.50/1.87 | | | | | simplifying with (62), (69) gives: % 8.50/1.87 | | | | | (72) all_50_1 = 0 % 8.50/1.87 | | | | | % 8.50/1.87 | | | | | BETA: splitting (70) gives: % 8.50/1.87 | | | | | % 8.50/1.87 | | | | | Case 1: % 8.50/1.87 | | | | | | % 8.50/1.87 | | | | | | (73) ~ (all_50_0 = 0) % 8.50/1.87 | | | | | | % 8.50/1.87 | | | | | | REDUCE: (71), (73) imply: % 8.50/1.87 | | | | | | (74) $false % 8.50/1.87 | | | | | | % 8.50/1.87 | | | | | | CLOSE: (74) is inconsistent. % 8.50/1.87 | | | | | | % 8.50/1.87 | | | | | Case 2: % 8.50/1.87 | | | | | | % 8.50/1.87 | | | | | | (75) ~ (all_50_1 = 0) % 8.50/1.87 | | | | | | % 8.50/1.87 | | | | | | REDUCE: (72), (75) imply: % 8.50/1.87 | | | | | | (76) $false % 8.50/1.87 | | | | | | % 8.50/1.87 | | | | | | CLOSE: (76) is inconsistent. % 8.50/1.87 | | | | | | % 8.50/1.87 | | | | | End of split % 8.50/1.87 | | | | | % 8.50/1.87 | | | | End of split % 8.50/1.87 | | | | % 8.50/1.87 | | | End of split % 8.50/1.87 | | | % 8.50/1.87 | | End of split % 8.50/1.87 | | % 8.50/1.87 | End of split % 8.50/1.87 | % 8.50/1.87 End of proof % 8.50/1.87 % SZS output end Proof for theBenchmark % 8.50/1.87 % 8.50/1.87 1262ms %------------------------------------------------------------------------------