%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET691+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 : n007.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 6.66s 1.65s % Output : Proof 8.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET691+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n007.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sat Aug 26 10:54:11 EDT 2023 % 0.14/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.63/1.07 Prover 4: Preprocessing ... % 2.63/1.07 Prover 1: Preprocessing ... % 2.63/1.10 Prover 3: Preprocessing ... % 2.63/1.10 Prover 5: Preprocessing ... % 2.63/1.10 Prover 6: Preprocessing ... % 2.63/1.10 Prover 2: Preprocessing ... % 2.63/1.10 Prover 0: Preprocessing ... % 5.42/1.47 Prover 3: Constructing countermodel ... % 5.42/1.48 Prover 6: Proving ... % 5.42/1.50 Prover 1: Constructing countermodel ... % 5.42/1.50 Prover 5: Proving ... % 5.42/1.52 Prover 0: Proving ... % 5.42/1.53 Prover 4: Constructing countermodel ... % 5.42/1.55 Prover 2: Proving ... % 6.66/1.65 Prover 3: proved (1016ms) % 6.66/1.65 % 6.66/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.66/1.65 % 6.66/1.66 Prover 2: stopped % 6.66/1.68 Prover 5: stopped % 6.66/1.68 Prover 0: stopped % 6.66/1.69 Prover 6: stopped % 6.66/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.66/1.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.66/1.69 Prover 7: Preprocessing ... % 6.66/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.66/1.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.66/1.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.66/1.70 Prover 8: Preprocessing ... % 6.66/1.71 Prover 1: Found proof (size 36) % 6.66/1.71 Prover 1: proved (1084ms) % 6.66/1.71 Prover 4: stopped % 6.66/1.72 Prover 7: stopped % 6.66/1.72 Prover 13: Preprocessing ... % 6.66/1.72 Prover 10: Preprocessing ... % 6.66/1.73 Prover 11: Preprocessing ... % 7.37/1.74 Prover 10: stopped % 7.37/1.75 Prover 13: stopped % 7.37/1.76 Prover 11: stopped % 7.76/1.80 Prover 8: Warning: ignoring some quantifiers % 7.76/1.81 Prover 8: Constructing countermodel ... % 7.76/1.82 Prover 8: stopped % 7.76/1.82 % 7.76/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.76/1.82 % 7.76/1.83 % SZS output start Proof for theBenchmark % 7.76/1.83 Assumptions after simplification: % 7.76/1.83 --------------------------------- % 7.76/1.83 % 7.76/1.83 (empty_set) % 7.76/1.85 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0)) % 7.76/1.85 % 7.76/1.85 (equal_set) % 7.76/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 7.76/1.86 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 7.76/1.86 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 7.76/1.86 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 7.76/1.86 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 7.76/1.86 % 7.76/1.86 (subset) % 7.76/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 7.76/1.86 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 7.76/1.86 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 7.76/1.86 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 7.76/1.86 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 7.76/1.86 % 7.76/1.86 (thI16) % 8.08/1.86 $i(empty_set) & ? [v0: $i] : ? [v1: any] : ? [v2: any] : (equal_set(v0, % 8.08/1.86 empty_set) = v2 & subset(v0, empty_set) = v1 & $i(v0) & ((v2 = 0 & ~ (v1 % 8.08/1.86 = 0)) | (v1 = 0 & ~ (v2 = 0)))) % 8.08/1.86 % 8.08/1.86 (function-axioms) % 8.08/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.08/1.87 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.08/1.87 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.08/1.87 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.08/1.87 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.08/1.87 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.08/1.87 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.08/1.87 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.08/1.87 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.08/1.87 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.08/1.87 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.08/1.87 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.08/1.87 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.08/1.87 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.08/1.87 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.08/1.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.08/1.87 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.08/1.87 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.08/1.87 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.08/1.87 (power_set(v2) = v0)) % 8.08/1.87 % 8.08/1.87 Further assumptions not needed in the proof: % 8.08/1.87 -------------------------------------------- % 8.08/1.87 difference, intersection, power_set, product, singleton, sum, union, % 8.08/1.87 unordered_pair % 8.08/1.87 % 8.08/1.87 Those formulas are unsatisfiable: % 8.08/1.87 --------------------------------- % 8.08/1.87 % 8.08/1.87 Begin of proof % 8.08/1.87 | % 8.08/1.87 | ALPHA: (subset) implies: % 8.08/1.87 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.08/1.87 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.08/1.87 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.08/1.87 | % 8.08/1.87 | ALPHA: (equal_set) implies: % 8.08/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | % 8.08/1.88 | ~ $i(v0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.08/1.88 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 8.08/1.88 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 8.08/1.88 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 8.08/1.88 | 0)))) % 8.08/1.88 | % 8.08/1.88 | ALPHA: (empty_set) implies: % 8.08/1.88 | (4) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0)) % 8.08/1.88 | % 8.08/1.88 | ALPHA: (thI16) implies: % 8.08/1.88 | (5) $i(empty_set) % 8.08/1.88 | (6) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (equal_set(v0, empty_set) = % 8.08/1.88 | v2 & subset(v0, empty_set) = v1 & $i(v0) & ((v2 = 0 & ~ (v1 = 0)) | % 8.08/1.88 | (v1 = 0 & ~ (v2 = 0)))) % 8.08/1.88 | % 8.08/1.88 | ALPHA: (function-axioms) implies: % 8.08/1.88 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.08/1.88 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 8.08/1.88 | = v0)) % 8.08/1.88 | % 8.08/1.88 | DELTA: instantiating (6) with fresh symbols all_15_0, all_15_1, all_15_2 % 8.08/1.88 | gives: % 8.08/1.88 | (8) equal_set(all_15_2, empty_set) = all_15_0 & subset(all_15_2, empty_set) % 8.08/1.88 | = all_15_1 & $i(all_15_2) & ((all_15_0 = 0 & ~ (all_15_1 = 0)) | % 8.08/1.88 | (all_15_1 = 0 & ~ (all_15_0 = 0))) % 8.08/1.88 | % 8.08/1.88 | ALPHA: (8) implies: % 8.08/1.88 | (9) $i(all_15_2) % 8.08/1.88 | (10) subset(all_15_2, empty_set) = all_15_1 % 8.08/1.88 | (11) equal_set(all_15_2, empty_set) = all_15_0 % 8.08/1.88 | (12) (all_15_0 = 0 & ~ (all_15_1 = 0)) | (all_15_1 = 0 & ~ (all_15_0 = % 8.08/1.88 | 0)) % 8.08/1.88 | % 8.08/1.88 | GROUND_INST: instantiating (3) with all_15_2, empty_set, all_15_0, simplifying % 8.08/1.88 | with (5), (9), (11) gives: % 8.08/1.88 | (13) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_2, % 8.08/1.88 | empty_set) = v0 & subset(empty_set, all_15_2) = v1 & ( ~ (v1 = 0) % 8.08/1.88 | | ~ (v0 = 0))) % 8.08/1.88 | % 8.08/1.88 | BETA: splitting (12) gives: % 8.08/1.88 | % 8.08/1.88 | Case 1: % 8.08/1.88 | | % 8.08/1.88 | | (14) all_15_0 = 0 & ~ (all_15_1 = 0) % 8.08/1.88 | | % 8.08/1.89 | | ALPHA: (14) implies: % 8.08/1.89 | | (15) all_15_0 = 0 % 8.08/1.89 | | (16) ~ (all_15_1 = 0) % 8.08/1.89 | | % 8.08/1.89 | | REDUCE: (11), (15) imply: % 8.08/1.89 | | (17) equal_set(all_15_2, empty_set) = 0 % 8.08/1.89 | | % 8.08/1.89 | | GROUND_INST: instantiating (2) with all_15_2, empty_set, simplifying with % 8.08/1.89 | | (5), (9), (17) gives: % 8.08/1.89 | | (18) subset(all_15_2, empty_set) = 0 & subset(empty_set, all_15_2) = 0 % 8.08/1.89 | | % 8.08/1.89 | | ALPHA: (18) implies: % 8.08/1.89 | | (19) subset(all_15_2, empty_set) = 0 % 8.08/1.89 | | % 8.08/1.89 | | GROUND_INST: instantiating (7) with all_15_1, 0, empty_set, all_15_2, % 8.08/1.89 | | simplifying with (10), (19) gives: % 8.08/1.89 | | (20) all_15_1 = 0 % 8.08/1.89 | | % 8.08/1.89 | | REDUCE: (16), (20) imply: % 8.08/1.89 | | (21) $false % 8.08/1.89 | | % 8.08/1.89 | | CLOSE: (21) is inconsistent. % 8.08/1.89 | | % 8.08/1.89 | Case 2: % 8.08/1.89 | | % 8.08/1.89 | | (22) all_15_1 = 0 & ~ (all_15_0 = 0) % 8.08/1.89 | | % 8.08/1.89 | | ALPHA: (22) implies: % 8.08/1.89 | | (23) all_15_1 = 0 % 8.08/1.89 | | (24) ~ (all_15_0 = 0) % 8.08/1.89 | | % 8.08/1.89 | | REDUCE: (10), (23) imply: % 8.08/1.89 | | (25) subset(all_15_2, empty_set) = 0 % 8.08/1.89 | | % 8.08/1.89 | | BETA: splitting (13) gives: % 8.08/1.89 | | % 8.08/1.89 | | Case 1: % 8.08/1.89 | | | % 8.08/1.89 | | | (26) all_15_0 = 0 % 8.08/1.89 | | | % 8.08/1.89 | | | REDUCE: (24), (26) imply: % 8.08/1.89 | | | (27) $false % 8.08/1.89 | | | % 8.08/1.89 | | | CLOSE: (27) is inconsistent. % 8.08/1.89 | | | % 8.08/1.89 | | Case 2: % 8.08/1.89 | | | % 8.08/1.89 | | | (28) ? [v0: any] : ? [v1: any] : (subset(all_15_2, empty_set) = v0 & % 8.08/1.89 | | | subset(empty_set, all_15_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.08/1.89 | | | % 8.08/1.89 | | | DELTA: instantiating (28) with fresh symbols all_28_0, all_28_1 gives: % 8.08/1.89 | | | (29) subset(all_15_2, empty_set) = all_28_1 & subset(empty_set, % 8.08/1.89 | | | all_15_2) = all_28_0 & ( ~ (all_28_0 = 0) | ~ (all_28_1 = 0)) % 8.08/1.89 | | | % 8.08/1.89 | | | ALPHA: (29) implies: % 8.08/1.89 | | | (30) subset(empty_set, all_15_2) = all_28_0 % 8.08/1.89 | | | (31) subset(all_15_2, empty_set) = all_28_1 % 8.08/1.89 | | | (32) ~ (all_28_0 = 0) | ~ (all_28_1 = 0) % 8.08/1.89 | | | % 8.08/1.89 | | | GROUND_INST: instantiating (7) with 0, all_28_1, empty_set, all_15_2, % 8.08/1.89 | | | simplifying with (25), (31) gives: % 8.08/1.89 | | | (33) all_28_1 = 0 % 8.08/1.89 | | | % 8.08/1.89 | | | BETA: splitting (32) gives: % 8.08/1.89 | | | % 8.08/1.89 | | | Case 1: % 8.08/1.89 | | | | % 8.08/1.89 | | | | (34) ~ (all_28_0 = 0) % 8.08/1.89 | | | | % 8.08/1.89 | | | | GROUND_INST: instantiating (1) with empty_set, all_15_2, all_28_0, % 8.08/1.89 | | | | simplifying with (5), (9), (30) gives: % 8.08/1.89 | | | | (35) all_28_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.08/1.89 | | | | member(v0, all_15_2) = v1 & member(v0, empty_set) = 0 & % 8.08/1.89 | | | | $i(v0)) % 8.08/1.89 | | | | % 8.08/1.89 | | | | BETA: splitting (35) gives: % 8.08/1.89 | | | | % 8.08/1.89 | | | | Case 1: % 8.08/1.89 | | | | | % 8.08/1.89 | | | | | (36) all_28_0 = 0 % 8.08/1.89 | | | | | % 8.08/1.89 | | | | | REDUCE: (34), (36) imply: % 8.08/1.89 | | | | | (37) $false % 8.08/1.89 | | | | | % 8.08/1.89 | | | | | CLOSE: (37) is inconsistent. % 8.08/1.89 | | | | | % 8.08/1.89 | | | | Case 2: % 8.08/1.89 | | | | | % 8.08/1.89 | | | | | (38) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.08/1.89 | | | | | all_15_2) = v1 & member(v0, empty_set) = 0 & $i(v0)) % 8.08/1.89 | | | | | % 8.08/1.89 | | | | | DELTA: instantiating (38) with fresh symbols all_48_0, all_48_1 gives: % 8.08/1.89 | | | | | (39) ~ (all_48_0 = 0) & member(all_48_1, all_15_2) = all_48_0 & % 8.08/1.89 | | | | | member(all_48_1, empty_set) = 0 & $i(all_48_1) % 8.08/1.89 | | | | | % 8.08/1.89 | | | | | ALPHA: (39) implies: % 8.08/1.89 | | | | | (40) $i(all_48_1) % 8.08/1.90 | | | | | (41) member(all_48_1, empty_set) = 0 % 8.08/1.90 | | | | | % 8.08/1.90 | | | | | GROUND_INST: instantiating (4) with all_48_1, simplifying with (40), % 8.08/1.90 | | | | | (41) gives: % 8.08/1.90 | | | | | (42) $false % 8.08/1.90 | | | | | % 8.08/1.90 | | | | | CLOSE: (42) is inconsistent. % 8.08/1.90 | | | | | % 8.08/1.90 | | | | End of split % 8.08/1.90 | | | | % 8.08/1.90 | | | Case 2: % 8.08/1.90 | | | | % 8.08/1.90 | | | | (43) ~ (all_28_1 = 0) % 8.08/1.90 | | | | % 8.08/1.90 | | | | REDUCE: (33), (43) imply: % 8.08/1.90 | | | | (44) $false % 8.08/1.90 | | | | % 8.08/1.90 | | | | CLOSE: (44) is inconsistent. % 8.08/1.90 | | | | % 8.08/1.90 | | | End of split % 8.08/1.90 | | | % 8.08/1.90 | | End of split % 8.08/1.90 | | % 8.08/1.90 | End of split % 8.08/1.90 | % 8.08/1.90 End of proof % 8.08/1.90 % SZS output end Proof for theBenchmark % 8.08/1.90 % 8.08/1.90 1288ms %------------------------------------------------------------------------------