%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET688+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 : n031.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 15:26:00 EDT 2023 % Result : Theorem 6.58s 1.70s % Output : Proof 8.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET688+4 : TPTP v8.1.2. Released v2.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n031.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 14:23:08 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 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 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 % 2.46/1.03 Prover 4: Preprocessing ... % 2.46/1.04 Prover 1: Preprocessing ... % 2.46/1.08 Prover 5: Preprocessing ... % 2.46/1.08 Prover 6: Preprocessing ... % 2.46/1.08 Prover 0: Preprocessing ... % 2.46/1.08 Prover 2: Preprocessing ... % 2.46/1.08 Prover 3: Preprocessing ... % 5.34/1.46 Prover 6: Proving ... % 5.34/1.48 Prover 3: Constructing countermodel ... % 5.34/1.49 Prover 5: Proving ... % 5.34/1.50 Prover 1: Constructing countermodel ... % 5.34/1.51 Prover 4: Constructing countermodel ... % 5.34/1.52 Prover 0: Proving ... % 5.34/1.52 Prover 2: Proving ... % 6.58/1.70 Prover 3: proved (1072ms) % 6.58/1.70 % 6.58/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.58/1.70 % 6.58/1.70 Prover 0: stopped % 6.58/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.58/1.70 Prover 2: stopped % 6.58/1.70 Prover 6: stopped % 7.06/1.73 Prover 5: stopped % 7.06/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.06/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.06/1.73 Prover 7: Preprocessing ... % 7.06/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.06/1.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.06/1.75 Prover 10: Preprocessing ... % 7.43/1.76 Prover 8: Preprocessing ... % 7.43/1.77 Prover 11: Preprocessing ... % 7.43/1.78 Prover 1: Found proof (size 36) % 7.43/1.78 Prover 1: proved (1161ms) % 7.43/1.78 Prover 4: stopped % 7.43/1.78 Prover 10: stopped % 7.43/1.79 Prover 13: Preprocessing ... % 7.43/1.80 Prover 7: Warning: ignoring some quantifiers % 7.43/1.81 Prover 7: Constructing countermodel ... % 7.43/1.81 Prover 11: stopped % 7.43/1.82 Prover 7: stopped % 7.43/1.83 Prover 13: stopped % 8.06/1.86 Prover 8: Warning: ignoring some quantifiers % 8.06/1.87 Prover 8: Constructing countermodel ... % 8.06/1.88 Prover 8: stopped % 8.06/1.88 % 8.06/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.06/1.88 % 8.06/1.88 % SZS output start Proof for theBenchmark % 8.06/1.89 Assumptions after simplification: % 8.06/1.89 --------------------------------- % 8.06/1.89 % 8.06/1.89 (equal_set) % 8.24/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 8.24/1.92 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 8.24/1.92 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 8.24/1.92 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 8.24/1.92 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.24/1.92 % 8.24/1.92 (subset) % 8.24/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.24/1.92 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.24/1.92 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.24/1.92 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.24/1.92 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.24/1.92 % 8.24/1.92 (thI04) % 8.24/1.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 8.24/1.92 (v4 = 0) & ~ (v3 = 0) & equal_set(v1, v2) = v4 & equal_set(v0, v2) = 0 & % 8.24/1.92 equal_set(v0, v1) = v3 & subset(v1, v2) = 0 & subset(v0, v1) = 0 & $i(v2) & % 8.24/1.92 $i(v1) & $i(v0)) % 8.24/1.92 % 8.24/1.92 (function-axioms) % 8.24/1.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.24/1.93 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.24/1.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.24/1.93 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.24/1.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.24/1.93 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.24/1.93 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.24/1.93 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.24/1.93 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.24/1.93 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.24/1.93 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.24/1.93 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.24/1.93 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.24/1.93 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.24/1.93 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.24/1.93 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.24/1.93 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.24/1.93 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.24/1.93 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.24/1.93 (power_set(v2) = v0)) % 8.24/1.93 % 8.24/1.93 Further assumptions not needed in the proof: % 8.24/1.93 -------------------------------------------- % 8.24/1.93 difference, empty_set, intersection, power_set, product, singleton, sum, union, % 8.24/1.93 unordered_pair % 8.24/1.93 % 8.24/1.93 Those formulas are unsatisfiable: % 8.24/1.93 --------------------------------- % 8.24/1.93 % 8.24/1.93 Begin of proof % 8.24/1.93 | % 8.24/1.93 | ALPHA: (subset) implies: % 8.24/1.94 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 8.24/1.94 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 8.24/1.94 | member(v2, v1) = 0)) % 8.24/1.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.24/1.94 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.24/1.94 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.24/1.94 | % 8.24/1.94 | ALPHA: (equal_set) implies: % 8.24/1.94 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | % 8.24/1.94 | ~ $i(v0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.24/1.94 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 8.24/1.94 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 8.24/1.94 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 8.24/1.94 | 0)))) % 8.24/1.94 | % 8.24/1.94 | ALPHA: (function-axioms) implies: % 8.24/1.94 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.24/1.94 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 8.24/1.94 | = v0)) % 8.24/1.94 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.24/1.94 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 8.24/1.94 | = v0)) % 8.24/1.94 | % 8.24/1.94 | DELTA: instantiating (thI04) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.24/1.94 | all_15_3, all_15_4 gives: % 8.24/1.94 | (7) ~ (all_15_0 = 0) & ~ (all_15_1 = 0) & equal_set(all_15_3, all_15_2) = % 8.24/1.94 | all_15_0 & equal_set(all_15_4, all_15_2) = 0 & equal_set(all_15_4, % 8.24/1.94 | all_15_3) = all_15_1 & subset(all_15_3, all_15_2) = 0 & % 8.24/1.94 | subset(all_15_4, all_15_3) = 0 & $i(all_15_2) & $i(all_15_3) & % 8.24/1.94 | $i(all_15_4) % 8.24/1.94 | % 8.24/1.94 | ALPHA: (7) implies: % 8.24/1.94 | (8) ~ (all_15_1 = 0) % 8.24/1.94 | (9) ~ (all_15_0 = 0) % 8.24/1.94 | (10) $i(all_15_4) % 8.24/1.94 | (11) $i(all_15_3) % 8.24/1.94 | (12) $i(all_15_2) % 8.24/1.94 | (13) subset(all_15_4, all_15_3) = 0 % 8.24/1.94 | (14) subset(all_15_3, all_15_2) = 0 % 8.24/1.94 | (15) equal_set(all_15_4, all_15_3) = all_15_1 % 8.24/1.95 | (16) equal_set(all_15_4, all_15_2) = 0 % 8.24/1.95 | (17) equal_set(all_15_3, all_15_2) = all_15_0 % 8.24/1.95 | % 8.24/1.95 | GROUND_INST: instantiating (1) with all_15_4, all_15_3, simplifying with (10), % 8.24/1.95 | (11), (13) gives: % 8.24/1.95 | (18) ! [v0: $i] : ( ~ (member(v0, all_15_4) = 0) | ~ $i(v0) | member(v0, % 8.24/1.95 | all_15_3) = 0) % 8.24/1.95 | % 8.24/1.95 | GROUND_INST: instantiating (4) with all_15_4, all_15_3, all_15_1, simplifying % 8.24/1.95 | with (10), (11), (15) gives: % 8.24/1.95 | (19) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_3, % 8.24/1.95 | all_15_4) = v1 & subset(all_15_4, all_15_3) = v0 & ( ~ (v1 = 0) | % 8.24/1.95 | ~ (v0 = 0))) % 8.24/1.95 | % 8.24/1.95 | GROUND_INST: instantiating (3) with all_15_4, all_15_2, simplifying with (10), % 8.24/1.95 | (12), (16) gives: % 8.24/1.95 | (20) subset(all_15_2, all_15_4) = 0 & subset(all_15_4, all_15_2) = 0 % 8.24/1.95 | % 8.24/1.95 | ALPHA: (20) implies: % 8.24/1.95 | (21) subset(all_15_2, all_15_4) = 0 % 8.24/1.95 | % 8.24/1.95 | GROUND_INST: instantiating (4) with all_15_3, all_15_2, all_15_0, simplifying % 8.24/1.95 | with (11), (12), (17) gives: % 8.24/1.95 | (22) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_2, % 8.24/1.95 | all_15_3) = v1 & subset(all_15_3, all_15_2) = v0 & ( ~ (v1 = 0) | % 8.24/1.95 | ~ (v0 = 0))) % 8.24/1.95 | % 8.24/1.95 | BETA: splitting (22) gives: % 8.24/1.95 | % 8.24/1.95 | Case 1: % 8.24/1.95 | | % 8.24/1.95 | | (23) all_15_0 = 0 % 8.24/1.95 | | % 8.24/1.95 | | REDUCE: (9), (23) imply: % 8.24/1.95 | | (24) $false % 8.24/1.95 | | % 8.24/1.95 | | CLOSE: (24) is inconsistent. % 8.24/1.95 | | % 8.24/1.95 | Case 2: % 8.24/1.95 | | % 8.24/1.95 | | (25) ? [v0: any] : ? [v1: any] : (subset(all_15_2, all_15_3) = v1 & % 8.24/1.95 | | subset(all_15_3, all_15_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.24/1.95 | | % 8.24/1.95 | | DELTA: instantiating (25) with fresh symbols all_29_0, all_29_1 gives: % 8.24/1.95 | | (26) subset(all_15_2, all_15_3) = all_29_0 & subset(all_15_3, all_15_2) = % 8.24/1.95 | | all_29_1 & ( ~ (all_29_0 = 0) | ~ (all_29_1 = 0)) % 8.24/1.95 | | % 8.24/1.95 | | ALPHA: (26) implies: % 8.24/1.95 | | (27) subset(all_15_3, all_15_2) = all_29_1 % 8.24/1.96 | | (28) subset(all_15_2, all_15_3) = all_29_0 % 8.24/1.96 | | (29) ~ (all_29_0 = 0) | ~ (all_29_1 = 0) % 8.24/1.96 | | % 8.24/1.96 | | BETA: splitting (19) gives: % 8.24/1.96 | | % 8.24/1.96 | | Case 1: % 8.24/1.96 | | | % 8.24/1.96 | | | (30) all_15_1 = 0 % 8.24/1.96 | | | % 8.24/1.96 | | | REDUCE: (8), (30) imply: % 8.24/1.96 | | | (31) $false % 8.24/1.96 | | | % 8.24/1.96 | | | CLOSE: (31) is inconsistent. % 8.24/1.96 | | | % 8.24/1.96 | | Case 2: % 8.24/1.96 | | | % 8.24/1.96 | | | % 8.24/1.96 | | | GROUND_INST: instantiating (6) with 0, all_29_1, all_15_2, all_15_3, % 8.24/1.96 | | | simplifying with (14), (27) gives: % 8.24/1.96 | | | (32) all_29_1 = 0 % 8.24/1.96 | | | % 8.24/1.96 | | | BETA: splitting (29) gives: % 8.24/1.96 | | | % 8.24/1.96 | | | Case 1: % 8.24/1.96 | | | | % 8.24/1.96 | | | | (33) ~ (all_29_0 = 0) % 8.24/1.96 | | | | % 8.24/1.96 | | | | GROUND_INST: instantiating (1) with all_15_2, all_15_4, simplifying with % 8.24/1.96 | | | | (10), (12), (21) gives: % 8.24/1.96 | | | | (34) ! [v0: $i] : ( ~ (member(v0, all_15_2) = 0) | ~ $i(v0) | % 8.24/1.96 | | | | member(v0, all_15_4) = 0) % 8.24/1.96 | | | | % 8.24/1.96 | | | | GROUND_INST: instantiating (2) with all_15_2, all_15_3, all_29_0, % 8.24/1.96 | | | | simplifying with (11), (12), (28) gives: % 8.24/1.96 | | | | (35) all_29_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.24/1.96 | | | | member(v0, all_15_2) = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 8.24/1.96 | | | | % 8.24/1.96 | | | | BETA: splitting (35) gives: % 8.24/1.96 | | | | % 8.24/1.96 | | | | Case 1: % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | (36) all_29_0 = 0 % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | REDUCE: (33), (36) imply: % 8.24/1.96 | | | | | (37) $false % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | CLOSE: (37) is inconsistent. % 8.24/1.96 | | | | | % 8.24/1.96 | | | | Case 2: % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | (38) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.24/1.96 | | | | | all_15_2) = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | DELTA: instantiating (38) with fresh symbols all_58_0, all_58_1 gives: % 8.24/1.96 | | | | | (39) ~ (all_58_0 = 0) & member(all_58_1, all_15_2) = 0 & % 8.24/1.96 | | | | | member(all_58_1, all_15_3) = all_58_0 & $i(all_58_1) % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | ALPHA: (39) implies: % 8.24/1.96 | | | | | (40) ~ (all_58_0 = 0) % 8.24/1.96 | | | | | (41) $i(all_58_1) % 8.24/1.96 | | | | | (42) member(all_58_1, all_15_3) = all_58_0 % 8.24/1.96 | | | | | (43) member(all_58_1, all_15_2) = 0 % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | GROUND_INST: instantiating (34) with all_58_1, simplifying with (41), % 8.24/1.96 | | | | | (43) gives: % 8.24/1.96 | | | | | (44) member(all_58_1, all_15_4) = 0 % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | GROUND_INST: instantiating (18) with all_58_1, simplifying with (41), % 8.24/1.96 | | | | | (44) gives: % 8.24/1.96 | | | | | (45) member(all_58_1, all_15_3) = 0 % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | GROUND_INST: instantiating (5) with all_58_0, 0, all_15_3, all_58_1, % 8.24/1.96 | | | | | simplifying with (42), (45) gives: % 8.24/1.96 | | | | | (46) all_58_0 = 0 % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | REDUCE: (40), (46) imply: % 8.24/1.96 | | | | | (47) $false % 8.24/1.96 | | | | | % 8.24/1.96 | | | | | CLOSE: (47) is inconsistent. % 8.24/1.96 | | | | | % 8.24/1.96 | | | | End of split % 8.24/1.96 | | | | % 8.24/1.96 | | | Case 2: % 8.24/1.96 | | | | % 8.24/1.96 | | | | (48) ~ (all_29_1 = 0) % 8.24/1.96 | | | | % 8.24/1.96 | | | | REDUCE: (32), (48) imply: % 8.24/1.96 | | | | (49) $false % 8.24/1.96 | | | | % 8.24/1.96 | | | | CLOSE: (49) is inconsistent. % 8.24/1.96 | | | | % 8.24/1.96 | | | End of split % 8.24/1.96 | | | % 8.24/1.96 | | End of split % 8.24/1.96 | | % 8.24/1.96 | End of split % 8.24/1.96 | % 8.24/1.96 End of proof % 8.24/1.96 % SZS output end Proof for theBenchmark % 8.24/1.96 % 8.24/1.96 1361ms %------------------------------------------------------------------------------