%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET143+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 : n022.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 15:24:00 EDT 2023 % Result : Theorem 7.05s 1.72s % Output : Proof 8.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET143+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.35 % Computer : n022.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Sat Aug 26 09:20:10 EDT 2023 % 0.16/0.36 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.97/1.02 Prover 4: Preprocessing ... % 1.97/1.03 Prover 1: Preprocessing ... % 2.59/1.07 Prover 3: Preprocessing ... % 2.59/1.07 Prover 5: Preprocessing ... % 2.59/1.07 Prover 2: Preprocessing ... % 2.59/1.07 Prover 6: Preprocessing ... % 2.59/1.07 Prover 0: Preprocessing ... % 5.16/1.41 Prover 6: Proving ... % 5.16/1.43 Prover 5: Proving ... % 5.16/1.45 Prover 4: Constructing countermodel ... % 5.16/1.48 Prover 2: Proving ... % 5.16/1.48 Prover 1: Constructing countermodel ... % 5.16/1.49 Prover 3: Constructing countermodel ... % 5.16/1.52 Prover 0: Proving ... % 7.05/1.71 Prover 3: proved (1067ms) % 7.05/1.72 % 7.05/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.05/1.72 % 7.05/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.05/1.72 Prover 6: stopped % 7.05/1.72 Prover 2: stopped % 7.05/1.73 Prover 0: stopped % 7.69/1.75 Prover 5: stopped % 7.69/1.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.69/1.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.69/1.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.69/1.76 Prover 7: Preprocessing ... % 7.69/1.76 Prover 8: Preprocessing ... % 7.69/1.76 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.69/1.78 Prover 11: Preprocessing ... % 7.69/1.79 Prover 13: Preprocessing ... % 7.69/1.79 Prover 10: Preprocessing ... % 8.08/1.81 Prover 1: Found proof (size 79) % 8.08/1.81 Prover 1: proved (1161ms) % 8.08/1.81 Prover 4: stopped % 8.08/1.82 Prover 10: stopped % 8.08/1.82 Prover 7: Warning: ignoring some quantifiers % 8.08/1.82 Prover 11: stopped % 8.08/1.83 Prover 7: Constructing countermodel ... % 8.08/1.83 Prover 7: stopped % 8.08/1.83 Prover 13: stopped % 8.49/1.85 Prover 8: Warning: ignoring some quantifiers % 8.52/1.86 Prover 8: Constructing countermodel ... % 8.52/1.86 Prover 8: stopped % 8.52/1.86 % 8.52/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.52/1.86 % 8.52/1.87 % SZS output start Proof for theBenchmark % 8.52/1.88 Assumptions after simplification: % 8.52/1.88 --------------------------------- % 8.52/1.88 % 8.52/1.88 (equal_set) % 8.52/1.90 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 8.52/1.90 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 8.52/1.90 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 8.52/1.90 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 8.52/1.90 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.52/1.90 % 8.52/1.90 (intersection) % 8.76/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.76/1.91 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 8.76/1.91 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 8.76/1.91 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 8.76/1.91 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 8.76/1.91 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 8.76/1.91 0 & member(v0, v1) = 0)) % 8.76/1.91 % 8.76/1.91 (subset) % 8.76/1.91 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.76/1.91 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.76/1.91 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.76/1.91 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.76/1.91 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.76/1.91 % 8.76/1.91 (thI08) % 8.76/1.91 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.76/1.91 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & intersection(v3, v2) = v4 % 8.76/1.91 & intersection(v1, v2) = v5 & intersection(v0, v5) = v6 & intersection(v0, % 8.76/1.91 v1) = v3 & equal_set(v4, v6) = v7 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 8.76/1.91 $i(v2) & $i(v1) & $i(v0)) % 8.76/1.91 % 8.76/1.91 (function-axioms) % 8.76/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.76/1.92 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.76/1.92 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.76/1.92 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.76/1.92 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.76/1.92 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.76/1.92 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.76/1.92 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.76/1.92 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.76/1.92 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.76/1.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.76/1.92 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.76/1.92 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.76/1.92 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.76/1.92 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.76/1.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.76/1.92 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.76/1.92 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.76/1.92 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.76/1.92 (power_set(v2) = v0)) % 8.76/1.92 % 8.76/1.92 Further assumptions not needed in the proof: % 8.76/1.92 -------------------------------------------- % 8.76/1.92 difference, empty_set, power_set, product, singleton, sum, union, unordered_pair % 8.76/1.92 % 8.76/1.92 Those formulas are unsatisfiable: % 8.76/1.92 --------------------------------- % 8.76/1.92 % 8.76/1.92 Begin of proof % 8.76/1.92 | % 8.76/1.92 | ALPHA: (subset) implies: % 8.76/1.93 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.76/1.93 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.76/1.93 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.76/1.93 | % 8.76/1.93 | ALPHA: (equal_set) implies: % 8.76/1.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 8.76/1.93 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 8.76/1.93 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 8.76/1.93 | 0)))) % 8.76/1.93 | % 8.76/1.93 | ALPHA: (intersection) implies: % 8.76/1.93 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.76/1.93 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 8.76/1.93 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 8.76/1.93 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 8.76/1.93 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 8.76/1.93 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 8.76/1.93 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 8.76/1.93 | 0)))) % 8.76/1.93 | % 8.76/1.93 | ALPHA: (function-axioms) implies: % 8.76/1.93 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.76/1.93 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 8.76/1.93 | = v0)) % 8.76/1.93 | % 8.76/1.93 | DELTA: instantiating (thI08) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.76/1.93 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives: % 8.76/1.93 | (6) ~ (all_15_0 = 0) & intersection(all_15_4, all_15_5) = all_15_3 & % 8.76/1.93 | intersection(all_15_6, all_15_5) = all_15_2 & intersection(all_15_7, % 8.76/1.93 | all_15_2) = all_15_1 & intersection(all_15_7, all_15_6) = all_15_4 & % 8.76/1.93 | equal_set(all_15_3, all_15_1) = all_15_0 & $i(all_15_1) & $i(all_15_2) % 8.76/1.93 | & $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & % 8.76/1.93 | $i(all_15_7) % 8.76/1.93 | % 8.76/1.93 | ALPHA: (6) implies: % 8.76/1.93 | (7) ~ (all_15_0 = 0) % 8.76/1.93 | (8) $i(all_15_7) % 8.76/1.93 | (9) $i(all_15_6) % 8.76/1.93 | (10) $i(all_15_5) % 8.76/1.93 | (11) $i(all_15_4) % 8.76/1.93 | (12) $i(all_15_3) % 8.76/1.93 | (13) $i(all_15_2) % 8.76/1.93 | (14) $i(all_15_1) % 8.76/1.93 | (15) equal_set(all_15_3, all_15_1) = all_15_0 % 8.76/1.93 | (16) intersection(all_15_7, all_15_6) = all_15_4 % 8.76/1.93 | (17) intersection(all_15_7, all_15_2) = all_15_1 % 8.76/1.93 | (18) intersection(all_15_6, all_15_5) = all_15_2 % 8.76/1.94 | (19) intersection(all_15_4, all_15_5) = all_15_3 % 8.76/1.94 | % 8.76/1.94 | GROUND_INST: instantiating (2) with all_15_3, all_15_1, all_15_0, simplifying % 8.76/1.94 | with (12), (14), (15) gives: % 8.76/1.94 | (20) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 8.76/1.94 | all_15_3) = v1 & subset(all_15_3, all_15_1) = v0 & ( ~ (v1 = 0) | % 8.76/1.94 | ~ (v0 = 0))) % 8.76/1.94 | % 8.76/1.94 | BETA: splitting (20) gives: % 8.76/1.94 | % 8.76/1.94 | Case 1: % 8.76/1.94 | | % 8.76/1.94 | | (21) all_15_0 = 0 % 8.76/1.94 | | % 8.76/1.94 | | REDUCE: (7), (21) imply: % 8.76/1.94 | | (22) $false % 8.76/1.94 | | % 8.76/1.94 | | CLOSE: (22) is inconsistent. % 8.76/1.94 | | % 8.76/1.94 | Case 2: % 8.76/1.94 | | % 8.76/1.94 | | (23) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_3) = v1 & % 8.76/1.94 | | subset(all_15_3, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.76/1.94 | | % 8.76/1.94 | | DELTA: instantiating (23) with fresh symbols all_24_0, all_24_1 gives: % 8.76/1.94 | | (24) subset(all_15_1, all_15_3) = all_24_0 & subset(all_15_3, all_15_1) = % 8.76/1.94 | | all_24_1 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0)) % 8.76/1.94 | | % 8.76/1.94 | | ALPHA: (24) implies: % 8.76/1.94 | | (25) subset(all_15_3, all_15_1) = all_24_1 % 8.76/1.94 | | (26) subset(all_15_1, all_15_3) = all_24_0 % 8.76/1.94 | | (27) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 8.76/1.94 | | % 8.76/1.94 | | GROUND_INST: instantiating (1) with all_15_3, all_15_1, all_24_1, % 8.76/1.94 | | simplifying with (12), (14), (25) gives: % 8.76/1.94 | | (28) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.76/1.94 | | member(v0, all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 8.76/1.94 | | % 8.76/1.94 | | GROUND_INST: instantiating (1) with all_15_1, all_15_3, all_24_0, % 8.76/1.94 | | simplifying with (12), (14), (26) gives: % 8.76/1.94 | | (29) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.76/1.94 | | member(v0, all_15_1) = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 8.76/1.94 | | % 8.76/1.94 | | BETA: splitting (27) gives: % 8.76/1.94 | | % 8.76/1.94 | | Case 1: % 8.76/1.94 | | | % 8.76/1.94 | | | (30) ~ (all_24_0 = 0) % 8.76/1.94 | | | % 8.76/1.94 | | | BETA: splitting (29) gives: % 8.76/1.94 | | | % 8.76/1.94 | | | Case 1: % 8.76/1.94 | | | | % 8.76/1.94 | | | | (31) all_24_0 = 0 % 8.76/1.94 | | | | % 8.76/1.94 | | | | REDUCE: (30), (31) imply: % 8.76/1.94 | | | | (32) $false % 8.76/1.94 | | | | % 8.76/1.94 | | | | CLOSE: (32) is inconsistent. % 8.76/1.94 | | | | % 8.76/1.94 | | | Case 2: % 8.76/1.94 | | | | % 8.76/1.94 | | | | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 8.76/1.94 | | | | = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 8.76/1.94 | | | | % 8.76/1.94 | | | | DELTA: instantiating (33) with fresh symbols all_37_0, all_37_1 gives: % 8.76/1.94 | | | | (34) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 & % 8.76/1.94 | | | | member(all_37_1, all_15_3) = all_37_0 & $i(all_37_1) % 8.76/1.94 | | | | % 8.76/1.94 | | | | ALPHA: (34) implies: % 8.76/1.95 | | | | (35) ~ (all_37_0 = 0) % 8.96/1.95 | | | | (36) $i(all_37_1) % 8.96/1.95 | | | | (37) member(all_37_1, all_15_3) = all_37_0 % 8.96/1.95 | | | | (38) member(all_37_1, all_15_1) = 0 % 8.96/1.95 | | | | % 8.96/1.95 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_4, all_15_5, % 8.96/1.95 | | | | all_15_3, all_37_0, simplifying with (10), (11), (19), % 8.96/1.95 | | | | (36), (37) gives: % 8.96/1.95 | | | | (39) all_37_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1, % 8.96/1.95 | | | | all_15_4) = v0 & member(all_37_1, all_15_5) = v1 & ( ~ (v1 = % 8.96/1.95 | | | | 0) | ~ (v0 = 0))) % 8.96/1.95 | | | | % 8.96/1.95 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_7, all_15_2, % 8.96/1.95 | | | | all_15_1, simplifying with (8), (13), (17), (36), (38) % 8.96/1.95 | | | | gives: % 8.96/1.95 | | | | (40) member(all_37_1, all_15_2) = 0 & member(all_37_1, all_15_7) = 0 % 8.96/1.95 | | | | % 8.96/1.95 | | | | ALPHA: (40) implies: % 8.96/1.95 | | | | (41) member(all_37_1, all_15_7) = 0 % 8.96/1.95 | | | | (42) member(all_37_1, all_15_2) = 0 % 8.96/1.95 | | | | % 8.96/1.95 | | | | BETA: splitting (39) gives: % 8.96/1.95 | | | | % 8.96/1.95 | | | | Case 1: % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | (43) all_37_0 = 0 % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | REDUCE: (35), (43) imply: % 8.96/1.95 | | | | | (44) $false % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | CLOSE: (44) is inconsistent. % 8.96/1.95 | | | | | % 8.96/1.95 | | | | Case 2: % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | (45) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_4) = v0 % 8.96/1.95 | | | | | & member(all_37_1, all_15_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 8.96/1.95 | | | | | 0))) % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | DELTA: instantiating (45) with fresh symbols all_49_0, all_49_1 gives: % 8.96/1.95 | | | | | (46) member(all_37_1, all_15_4) = all_49_1 & member(all_37_1, % 8.96/1.95 | | | | | all_15_5) = all_49_0 & ( ~ (all_49_0 = 0) | ~ (all_49_1 = % 8.96/1.95 | | | | | 0)) % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | ALPHA: (46) implies: % 8.96/1.95 | | | | | (47) member(all_37_1, all_15_5) = all_49_0 % 8.96/1.95 | | | | | (48) member(all_37_1, all_15_4) = all_49_1 % 8.96/1.95 | | | | | (49) ~ (all_49_0 = 0) | ~ (all_49_1 = 0) % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_7, all_15_6, % 8.96/1.95 | | | | | all_15_4, all_49_1, simplifying with (8), (9), (16), % 8.96/1.95 | | | | | (36), (48) gives: % 8.96/1.95 | | | | | (50) all_49_1 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1, % 8.96/1.95 | | | | | all_15_6) = v1 & member(all_37_1, all_15_7) = v0 & ( ~ (v1 % 8.96/1.95 | | | | | = 0) | ~ (v0 = 0))) % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_6, all_15_5, % 8.96/1.95 | | | | | all_15_2, simplifying with (9), (10), (18), (36), (42) % 8.96/1.95 | | | | | gives: % 8.96/1.95 | | | | | (51) member(all_37_1, all_15_5) = 0 & member(all_37_1, all_15_6) = % 8.96/1.95 | | | | | 0 % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | ALPHA: (51) implies: % 8.96/1.95 | | | | | (52) member(all_37_1, all_15_6) = 0 % 8.96/1.95 | | | | | (53) member(all_37_1, all_15_5) = 0 % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | BETA: splitting (50) gives: % 8.96/1.95 | | | | | % 8.96/1.95 | | | | | Case 1: % 8.96/1.95 | | | | | | % 8.96/1.95 | | | | | | (54) all_49_1 = 0 % 8.96/1.95 | | | | | | % 8.96/1.95 | | | | | | BETA: splitting (49) gives: % 8.96/1.95 | | | | | | % 8.96/1.95 | | | | | | Case 1: % 8.96/1.95 | | | | | | | % 8.96/1.95 | | | | | | | (55) ~ (all_49_0 = 0) % 8.96/1.95 | | | | | | | % 8.96/1.95 | | | | | | | GROUND_INST: instantiating (5) with all_49_0, 0, all_15_5, % 8.96/1.96 | | | | | | | all_37_1, simplifying with (47), (53) gives: % 8.96/1.96 | | | | | | | (56) all_49_0 = 0 % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | REDUCE: (55), (56) imply: % 8.96/1.96 | | | | | | | (57) $false % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | CLOSE: (57) is inconsistent. % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | Case 2: % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | (58) ~ (all_49_1 = 0) % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | REDUCE: (54), (58) imply: % 8.96/1.96 | | | | | | | (59) $false % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | CLOSE: (59) is inconsistent. % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | End of split % 8.96/1.96 | | | | | | % 8.96/1.96 | | | | | Case 2: % 8.96/1.96 | | | | | | % 8.96/1.96 | | | | | | (60) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_6) = % 8.96/1.96 | | | | | | v1 & member(all_37_1, all_15_7) = v0 & ( ~ (v1 = 0) | ~ % 8.96/1.96 | | | | | | (v0 = 0))) % 8.96/1.96 | | | | | | % 8.96/1.96 | | | | | | DELTA: instantiating (60) with fresh symbols all_61_0, all_61_1 % 8.96/1.96 | | | | | | gives: % 8.96/1.96 | | | | | | (61) member(all_37_1, all_15_6) = all_61_0 & member(all_37_1, % 8.96/1.96 | | | | | | all_15_7) = all_61_1 & ( ~ (all_61_0 = 0) | ~ (all_61_1 = % 8.96/1.96 | | | | | | 0)) % 8.96/1.96 | | | | | | % 8.96/1.96 | | | | | | ALPHA: (61) implies: % 8.96/1.96 | | | | | | (62) member(all_37_1, all_15_7) = all_61_1 % 8.96/1.96 | | | | | | (63) member(all_37_1, all_15_6) = all_61_0 % 8.96/1.96 | | | | | | (64) ~ (all_61_0 = 0) | ~ (all_61_1 = 0) % 8.96/1.96 | | | | | | % 8.96/1.96 | | | | | | GROUND_INST: instantiating (5) with 0, all_61_1, all_15_7, all_37_1, % 8.96/1.96 | | | | | | simplifying with (41), (62) gives: % 8.96/1.96 | | | | | | (65) all_61_1 = 0 % 8.96/1.96 | | | | | | % 8.96/1.96 | | | | | | GROUND_INST: instantiating (5) with 0, all_61_0, all_15_6, all_37_1, % 8.96/1.96 | | | | | | simplifying with (52), (63) gives: % 8.96/1.96 | | | | | | (66) all_61_0 = 0 % 8.96/1.96 | | | | | | % 8.96/1.96 | | | | | | BETA: splitting (64) gives: % 8.96/1.96 | | | | | | % 8.96/1.96 | | | | | | Case 1: % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | (67) ~ (all_61_0 = 0) % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | REDUCE: (66), (67) imply: % 8.96/1.96 | | | | | | | (68) $false % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | CLOSE: (68) is inconsistent. % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | Case 2: % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | (69) ~ (all_61_1 = 0) % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | REDUCE: (65), (69) imply: % 8.96/1.96 | | | | | | | (70) $false % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | | CLOSE: (70) is inconsistent. % 8.96/1.96 | | | | | | | % 8.96/1.96 | | | | | | End of split % 8.96/1.96 | | | | | | % 8.96/1.96 | | | | | End of split % 8.96/1.96 | | | | | % 8.96/1.96 | | | | End of split % 8.96/1.96 | | | | % 8.96/1.96 | | | End of split % 8.96/1.96 | | | % 8.96/1.96 | | Case 2: % 8.96/1.96 | | | % 8.96/1.96 | | | (71) ~ (all_24_1 = 0) % 8.96/1.96 | | | % 8.96/1.96 | | | BETA: splitting (28) gives: % 8.96/1.96 | | | % 8.96/1.96 | | | Case 1: % 8.96/1.96 | | | | % 8.96/1.96 | | | | (72) all_24_1 = 0 % 8.96/1.96 | | | | % 8.96/1.96 | | | | REDUCE: (71), (72) imply: % 8.96/1.96 | | | | (73) $false % 8.96/1.96 | | | | % 8.96/1.96 | | | | CLOSE: (73) is inconsistent. % 8.96/1.96 | | | | % 8.96/1.96 | | | Case 2: % 8.96/1.96 | | | | % 8.96/1.96 | | | | (74) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 8.96/1.96 | | | | = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 8.96/1.96 | | | | % 8.96/1.96 | | | | DELTA: instantiating (74) with fresh symbols all_37_0, all_37_1 gives: % 8.96/1.96 | | | | (75) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 & % 8.96/1.96 | | | | member(all_37_1, all_15_3) = 0 & $i(all_37_1) % 8.96/1.96 | | | | % 8.96/1.96 | | | | ALPHA: (75) implies: % 8.96/1.96 | | | | (76) ~ (all_37_0 = 0) % 8.96/1.96 | | | | (77) $i(all_37_1) % 8.96/1.96 | | | | (78) member(all_37_1, all_15_3) = 0 % 8.96/1.96 | | | | (79) member(all_37_1, all_15_1) = all_37_0 % 8.96/1.96 | | | | % 8.96/1.96 | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_4, all_15_5, % 8.96/1.96 | | | | all_15_3, simplifying with (10), (11), (19), (77), (78) % 8.96/1.96 | | | | gives: % 8.96/1.96 | | | | (80) member(all_37_1, all_15_4) = 0 & member(all_37_1, all_15_5) = 0 % 8.96/1.96 | | | | % 8.96/1.96 | | | | ALPHA: (80) implies: % 8.96/1.96 | | | | (81) member(all_37_1, all_15_5) = 0 % 8.96/1.96 | | | | (82) member(all_37_1, all_15_4) = 0 % 8.96/1.96 | | | | % 8.96/1.96 | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_7, all_15_2, % 8.96/1.96 | | | | all_15_1, all_37_0, simplifying with (8), (13), (17), (77), % 8.96/1.96 | | | | (79) gives: % 8.96/1.97 | | | | (83) all_37_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1, % 8.96/1.97 | | | | all_15_2) = v1 & member(all_37_1, all_15_7) = v0 & ( ~ (v1 = % 8.96/1.97 | | | | 0) | ~ (v0 = 0))) % 8.96/1.97 | | | | % 8.96/1.97 | | | | BETA: splitting (83) gives: % 8.96/1.97 | | | | % 8.96/1.97 | | | | Case 1: % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | (84) all_37_0 = 0 % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | REDUCE: (76), (84) imply: % 8.96/1.97 | | | | | (85) $false % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | CLOSE: (85) is inconsistent. % 8.96/1.97 | | | | | % 8.96/1.97 | | | | Case 2: % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | (86) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_2) = v1 % 8.96/1.97 | | | | | & member(all_37_1, all_15_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 8.96/1.97 | | | | | 0))) % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | DELTA: instantiating (86) with fresh symbols all_50_0, all_50_1 gives: % 8.96/1.97 | | | | | (87) member(all_37_1, all_15_2) = all_50_0 & member(all_37_1, % 8.96/1.97 | | | | | all_15_7) = all_50_1 & ( ~ (all_50_0 = 0) | ~ (all_50_1 = % 8.96/1.97 | | | | | 0)) % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | ALPHA: (87) implies: % 8.96/1.97 | | | | | (88) member(all_37_1, all_15_7) = all_50_1 % 8.96/1.97 | | | | | (89) member(all_37_1, all_15_2) = all_50_0 % 8.96/1.97 | | | | | (90) ~ (all_50_0 = 0) | ~ (all_50_1 = 0) % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | GROUND_INST: instantiating (3) with all_37_1, all_15_7, all_15_6, % 8.96/1.97 | | | | | all_15_4, simplifying with (8), (9), (16), (77), (82) % 8.96/1.97 | | | | | gives: % 8.96/1.97 | | | | | (91) member(all_37_1, all_15_6) = 0 & member(all_37_1, all_15_7) = % 8.96/1.97 | | | | | 0 % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | ALPHA: (91) implies: % 8.96/1.97 | | | | | (92) member(all_37_1, all_15_7) = 0 % 8.96/1.97 | | | | | (93) member(all_37_1, all_15_6) = 0 % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | GROUND_INST: instantiating (4) with all_37_1, all_15_6, all_15_5, % 8.96/1.97 | | | | | all_15_2, all_50_0, simplifying with (9), (10), (18), % 8.96/1.97 | | | | | (77), (89) gives: % 8.96/1.97 | | | | | (94) all_50_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_37_1, % 8.96/1.97 | | | | | all_15_5) = v1 & member(all_37_1, all_15_6) = v0 & ( ~ (v1 % 8.96/1.97 | | | | | = 0) | ~ (v0 = 0))) % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | BETA: splitting (94) gives: % 8.96/1.97 | | | | | % 8.96/1.97 | | | | | Case 1: % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | (95) all_50_0 = 0 % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | BETA: splitting (90) gives: % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | Case 1: % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | (96) ~ (all_50_0 = 0) % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | REDUCE: (95), (96) imply: % 8.96/1.97 | | | | | | | (97) $false % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | CLOSE: (97) is inconsistent. % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | Case 2: % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | (98) ~ (all_50_1 = 0) % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | GROUND_INST: instantiating (5) with all_50_1, 0, all_15_7, % 8.96/1.97 | | | | | | | all_37_1, simplifying with (88), (92) gives: % 8.96/1.97 | | | | | | | (99) all_50_1 = 0 % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | REDUCE: (98), (99) imply: % 8.96/1.97 | | | | | | | (100) $false % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | CLOSE: (100) is inconsistent. % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | End of split % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | Case 2: % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | (101) ? [v0: any] : ? [v1: any] : (member(all_37_1, all_15_5) = % 8.96/1.97 | | | | | | v1 & member(all_37_1, all_15_6) = v0 & ( ~ (v1 = 0) | ~ % 8.96/1.97 | | | | | | (v0 = 0))) % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | DELTA: instantiating (101) with fresh symbols all_62_0, all_62_1 % 8.96/1.97 | | | | | | gives: % 8.96/1.97 | | | | | | (102) member(all_37_1, all_15_5) = all_62_0 & member(all_37_1, % 8.96/1.97 | | | | | | all_15_6) = all_62_1 & ( ~ (all_62_0 = 0) | ~ (all_62_1 % 8.96/1.97 | | | | | | = 0)) % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | ALPHA: (102) implies: % 8.96/1.97 | | | | | | (103) member(all_37_1, all_15_6) = all_62_1 % 8.96/1.97 | | | | | | (104) member(all_37_1, all_15_5) = all_62_0 % 8.96/1.97 | | | | | | (105) ~ (all_62_0 = 0) | ~ (all_62_1 = 0) % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | GROUND_INST: instantiating (5) with 0, all_62_1, all_15_6, all_37_1, % 8.96/1.97 | | | | | | simplifying with (93), (103) gives: % 8.96/1.97 | | | | | | (106) all_62_1 = 0 % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | GROUND_INST: instantiating (5) with 0, all_62_0, all_15_5, all_37_1, % 8.96/1.97 | | | | | | simplifying with (81), (104) gives: % 8.96/1.97 | | | | | | (107) all_62_0 = 0 % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | BETA: splitting (105) gives: % 8.96/1.97 | | | | | | % 8.96/1.97 | | | | | | Case 1: % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | (108) ~ (all_62_0 = 0) % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | REDUCE: (107), (108) imply: % 8.96/1.97 | | | | | | | (109) $false % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | | CLOSE: (109) is inconsistent. % 8.96/1.97 | | | | | | | % 8.96/1.97 | | | | | | Case 2: % 8.96/1.97 | | | | | | | % 8.96/1.98 | | | | | | | (110) ~ (all_62_1 = 0) % 8.96/1.98 | | | | | | | % 8.96/1.98 | | | | | | | REDUCE: (106), (110) imply: % 8.96/1.98 | | | | | | | (111) $false % 8.96/1.98 | | | | | | | % 8.96/1.98 | | | | | | | CLOSE: (111) is inconsistent. % 8.96/1.98 | | | | | | | % 8.96/1.98 | | | | | | End of split % 8.96/1.98 | | | | | | % 8.96/1.98 | | | | | End of split % 8.96/1.98 | | | | | % 8.96/1.98 | | | | End of split % 8.96/1.98 | | | | % 8.96/1.98 | | | End of split % 8.96/1.98 | | | % 8.96/1.98 | | End of split % 8.96/1.98 | | % 8.96/1.98 | End of split % 8.96/1.98 | % 8.96/1.98 End of proof % 8.96/1.98 % SZS output end Proof for theBenchmark % 8.96/1.98 % 8.96/1.98 1347ms %------------------------------------------------------------------------------