%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET012+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 : n005.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 15:23:04 EDT 2023 % Result : Theorem 7.03s 1.73s % Output : Proof 8.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET012+4 : TPTP v8.1.2. Released v2.2.0. % 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n005.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 08:47:38 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.08/1.06 Prover 1: Preprocessing ... % 2.08/1.06 Prover 4: Preprocessing ... % 2.86/1.11 Prover 6: Preprocessing ... % 2.86/1.11 Prover 3: Preprocessing ... % 2.86/1.11 Prover 0: Preprocessing ... % 2.86/1.11 Prover 2: Preprocessing ... % 2.86/1.11 Prover 5: Preprocessing ... % 4.95/1.47 Prover 6: Proving ... % 4.95/1.47 Prover 5: Proving ... % 5.54/1.47 Prover 1: Constructing countermodel ... % 5.54/1.48 Prover 3: Constructing countermodel ... % 5.54/1.49 Prover 2: Proving ... % 5.73/1.52 Prover 0: Proving ... % 5.95/1.53 Prover 4: Constructing countermodel ... % 7.03/1.73 Prover 3: proved (1116ms) % 7.03/1.73 % 7.03/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.03/1.73 % 7.03/1.73 Prover 2: stopped % 7.03/1.73 Prover 0: stopped % 7.03/1.73 Prover 5: stopped % 7.03/1.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.03/1.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.03/1.74 Prover 6: stopped % 7.03/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.03/1.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.03/1.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.76/1.77 Prover 7: Preprocessing ... % 7.76/1.77 Prover 13: Preprocessing ... % 7.76/1.79 Prover 8: Preprocessing ... % 7.76/1.79 Prover 11: Preprocessing ... % 7.76/1.79 Prover 10: Preprocessing ... % 8.11/1.82 Prover 1: Found proof (size 61) % 8.11/1.82 Prover 1: proved (1210ms) % 8.13/1.82 Prover 4: stopped % 8.13/1.83 Prover 7: stopped % 8.13/1.84 Prover 13: stopped % 8.13/1.85 Prover 10: Warning: ignoring some quantifiers % 8.13/1.85 Prover 11: stopped % 8.13/1.86 Prover 10: Constructing countermodel ... % 8.13/1.87 Prover 10: stopped % 8.13/1.88 Prover 8: Warning: ignoring some quantifiers % 8.13/1.89 Prover 8: Constructing countermodel ... % 8.13/1.90 Prover 8: stopped % 8.13/1.90 % 8.13/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.13/1.90 % 8.13/1.91 % SZS output start Proof for theBenchmark % 8.13/1.91 Assumptions after simplification: % 8.13/1.91 --------------------------------- % 8.13/1.91 % 8.13/1.91 (difference) % 8.13/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.13/1.94 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 8.13/1.94 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 & % 8.13/1.94 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 8.13/1.94 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, % 8.13/1.94 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 8.13/1.94 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 8.13/1.94 % 8.13/1.94 (equal_set) % 8.13/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 8.13/1.95 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 8.13/1.95 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 8.13/1.95 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 8.13/1.95 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.13/1.95 % 8.13/1.95 (subset) % 8.13/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.13/1.95 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.13/1.95 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.13/1.95 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.13/1.95 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.13/1.95 % 8.13/1.95 (thI23) % 8.13/1.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 8.13/1.95 = 0) & difference(v1, v2) = v3 & difference(v1, v0) = v2 & equal_set(v3, % 8.13/1.95 v0) = v4 & subset(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.13/1.95 % 8.13/1.95 (function-axioms) % 8.13/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.13/1.96 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.13/1.96 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.13/1.96 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.13/1.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.13/1.96 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.13/1.96 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.13/1.96 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.13/1.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.13/1.96 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.13/1.96 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.13/1.96 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.13/1.96 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.13/1.96 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.13/1.96 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.13/1.96 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.13/1.96 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.13/1.96 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.13/1.96 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.13/1.96 (power_set(v2) = v0)) % 8.13/1.96 % 8.13/1.96 Further assumptions not needed in the proof: % 8.13/1.96 -------------------------------------------- % 8.13/1.96 empty_set, intersection, power_set, product, singleton, sum, union, % 8.13/1.96 unordered_pair % 8.13/1.96 % 8.13/1.96 Those formulas are unsatisfiable: % 8.13/1.96 --------------------------------- % 8.13/1.96 % 8.13/1.96 Begin of proof % 8.13/1.96 | % 8.13/1.96 | ALPHA: (subset) implies: % 8.13/1.97 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 8.13/1.97 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 8.13/1.97 | member(v2, v1) = 0)) % 8.13/1.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.13/1.97 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.13/1.97 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.13/1.97 | % 8.13/1.97 | ALPHA: (equal_set) implies: % 8.66/1.97 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 8.66/1.97 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 8.66/1.97 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 8.66/1.97 | 0)))) % 8.66/1.97 | % 8.66/1.97 | ALPHA: (difference) implies: % 8.66/1.97 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.66/1.97 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ % 8.66/1.97 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0 % 8.66/1.97 | & member(v0, v1) = v4)) % 8.66/1.97 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 8.66/1.97 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ % 8.66/1.97 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 8.66/1.97 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 8.66/1.97 | % 8.66/1.97 | ALPHA: (function-axioms) implies: % 8.66/1.97 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.66/1.97 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 8.66/1.97 | = v0)) % 8.66/1.97 | % 8.66/1.97 | DELTA: instantiating (thI23) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.66/1.97 | all_15_3, all_15_4 gives: % 8.66/1.97 | (7) ~ (all_15_0 = 0) & difference(all_15_3, all_15_2) = all_15_1 & % 8.66/1.97 | difference(all_15_3, all_15_4) = all_15_2 & equal_set(all_15_1, % 8.66/1.97 | all_15_4) = all_15_0 & subset(all_15_4, all_15_3) = 0 & $i(all_15_1) % 8.66/1.97 | & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) % 8.66/1.97 | % 8.66/1.97 | ALPHA: (7) implies: % 8.66/1.97 | (8) ~ (all_15_0 = 0) % 8.66/1.97 | (9) $i(all_15_4) % 8.66/1.97 | (10) $i(all_15_3) % 8.66/1.98 | (11) $i(all_15_2) % 8.66/1.98 | (12) $i(all_15_1) % 8.66/1.98 | (13) subset(all_15_4, all_15_3) = 0 % 8.66/1.98 | (14) equal_set(all_15_1, all_15_4) = all_15_0 % 8.66/1.98 | (15) difference(all_15_3, all_15_4) = all_15_2 % 8.66/1.98 | (16) difference(all_15_3, all_15_2) = all_15_1 % 8.66/1.98 | % 8.66/1.98 | GROUND_INST: instantiating (1) with all_15_4, all_15_3, simplifying with (9), % 8.66/1.98 | (10), (13) gives: % 8.66/1.98 | (17) ! [v0: $i] : ( ~ (member(v0, all_15_4) = 0) | ~ $i(v0) | member(v0, % 8.66/1.98 | all_15_3) = 0) % 8.66/1.98 | % 8.66/1.98 | GROUND_INST: instantiating (3) with all_15_1, all_15_4, all_15_0, simplifying % 8.66/1.98 | with (9), (12), (14) gives: % 8.66/1.98 | (18) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 8.66/1.98 | all_15_4) = v0 & subset(all_15_4, all_15_1) = v1 & ( ~ (v1 = 0) | % 8.66/1.98 | ~ (v0 = 0))) % 8.66/1.98 | % 8.66/1.98 | BETA: splitting (18) gives: % 8.66/1.98 | % 8.66/1.98 | Case 1: % 8.66/1.98 | | % 8.66/1.98 | | (19) all_15_0 = 0 % 8.66/1.98 | | % 8.66/1.98 | | REDUCE: (8), (19) imply: % 8.66/1.98 | | (20) $false % 8.66/1.98 | | % 8.66/1.98 | | CLOSE: (20) is inconsistent. % 8.66/1.98 | | % 8.66/1.98 | Case 2: % 8.66/1.98 | | % 8.66/1.98 | | (21) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_4) = v0 & % 8.66/1.98 | | subset(all_15_4, all_15_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.66/1.98 | | % 8.66/1.98 | | DELTA: instantiating (21) with fresh symbols all_27_0, all_27_1 gives: % 8.66/1.98 | | (22) subset(all_15_1, all_15_4) = all_27_1 & subset(all_15_4, all_15_1) = % 8.66/1.98 | | all_27_0 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0)) % 8.66/1.98 | | % 8.66/1.98 | | ALPHA: (22) implies: % 8.66/1.98 | | (23) subset(all_15_4, all_15_1) = all_27_0 % 8.66/1.98 | | (24) subset(all_15_1, all_15_4) = all_27_1 % 8.66/1.98 | | (25) ~ (all_27_0 = 0) | ~ (all_27_1 = 0) % 8.66/1.98 | | % 8.66/1.98 | | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_27_0, % 8.66/1.98 | | simplifying with (9), (12), (23) gives: % 8.66/1.98 | | (26) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.66/1.98 | | member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 8.66/1.98 | | % 8.66/1.98 | | GROUND_INST: instantiating (2) with all_15_1, all_15_4, all_27_1, % 8.66/1.98 | | simplifying with (9), (12), (24) gives: % 8.66/1.98 | | (27) all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.66/1.98 | | member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 8.66/1.98 | | % 8.66/1.98 | | BETA: splitting (25) gives: % 8.66/1.98 | | % 8.66/1.98 | | Case 1: % 8.66/1.98 | | | % 8.66/1.99 | | | (28) ~ (all_27_0 = 0) % 8.66/1.99 | | | % 8.66/1.99 | | | BETA: splitting (26) gives: % 8.66/1.99 | | | % 8.66/1.99 | | | Case 1: % 8.66/1.99 | | | | % 8.66/1.99 | | | | (29) all_27_0 = 0 % 8.66/1.99 | | | | % 8.66/1.99 | | | | REDUCE: (28), (29) imply: % 8.66/1.99 | | | | (30) $false % 8.66/1.99 | | | | % 8.66/1.99 | | | | CLOSE: (30) is inconsistent. % 8.66/1.99 | | | | % 8.66/1.99 | | | Case 2: % 8.66/1.99 | | | | % 8.66/1.99 | | | | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 8.66/1.99 | | | | = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 8.66/1.99 | | | | % 8.66/1.99 | | | | DELTA: instantiating (31) with fresh symbols all_40_0, all_40_1 gives: % 8.66/1.99 | | | | (32) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = all_40_0 & % 8.66/1.99 | | | | member(all_40_1, all_15_4) = 0 & $i(all_40_1) % 8.66/1.99 | | | | % 8.66/1.99 | | | | ALPHA: (32) implies: % 8.66/1.99 | | | | (33) ~ (all_40_0 = 0) % 8.66/1.99 | | | | (34) $i(all_40_1) % 8.66/1.99 | | | | (35) member(all_40_1, all_15_4) = 0 % 8.66/1.99 | | | | (36) member(all_40_1, all_15_1) = all_40_0 % 8.66/1.99 | | | | % 8.66/1.99 | | | | GROUND_INST: instantiating (17) with all_40_1, simplifying with (34), % 8.66/1.99 | | | | (35) gives: % 8.66/1.99 | | | | (37) member(all_40_1, all_15_3) = 0 % 8.66/1.99 | | | | % 8.66/1.99 | | | | GROUND_INST: instantiating (5) with all_40_1, all_15_2, all_15_3, % 8.66/1.99 | | | | all_15_1, all_40_0, simplifying with (10), (11), (16), % 8.66/1.99 | | | | (34), (36) gives: % 8.66/1.99 | | | | (38) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1, % 8.66/1.99 | | | | all_15_2) = v1 & member(all_40_1, all_15_3) = v0 & ( ~ (v0 = % 8.66/1.99 | | | | 0) | v1 = 0)) % 8.66/1.99 | | | | % 8.66/1.99 | | | | BETA: splitting (38) gives: % 8.66/1.99 | | | | % 8.66/1.99 | | | | Case 1: % 8.66/1.99 | | | | | % 8.66/1.99 | | | | | (39) all_40_0 = 0 % 8.66/1.99 | | | | | % 8.66/1.99 | | | | | REDUCE: (33), (39) imply: % 8.66/1.99 | | | | | (40) $false % 8.66/1.99 | | | | | % 8.66/1.99 | | | | | CLOSE: (40) is inconsistent. % 8.66/1.99 | | | | | % 8.66/1.99 | | | | Case 2: % 8.66/1.99 | | | | | % 8.66/1.99 | | | | | (41) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_2) = v1 % 8.66/1.99 | | | | | & member(all_40_1, all_15_3) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 8.66/1.99 | | | | | % 8.66/1.99 | | | | | DELTA: instantiating (41) with fresh symbols all_52_0, all_52_1 gives: % 8.66/1.99 | | | | | (42) member(all_40_1, all_15_2) = all_52_0 & member(all_40_1, % 8.66/1.99 | | | | | all_15_3) = all_52_1 & ( ~ (all_52_1 = 0) | all_52_0 = 0) % 8.66/1.99 | | | | | % 8.66/1.99 | | | | | ALPHA: (42) implies: % 8.66/1.99 | | | | | (43) member(all_40_1, all_15_3) = all_52_1 % 8.66/1.99 | | | | | (44) member(all_40_1, all_15_2) = all_52_0 % 8.66/1.99 | | | | | (45) ~ (all_52_1 = 0) | all_52_0 = 0 % 8.66/1.99 | | | | | % 8.66/1.99 | | | | | GROUND_INST: instantiating (6) with 0, all_52_1, all_15_3, all_40_1, % 8.66/1.99 | | | | | simplifying with (37), (43) gives: % 8.66/1.99 | | | | | (46) all_52_1 = 0 % 8.66/1.99 | | | | | % 8.66/1.99 | | | | | BETA: splitting (45) gives: % 8.66/1.99 | | | | | % 8.66/1.99 | | | | | Case 1: % 8.66/1.99 | | | | | | % 8.66/1.99 | | | | | | (47) ~ (all_52_1 = 0) % 8.66/1.99 | | | | | | % 8.66/1.99 | | | | | | REDUCE: (46), (47) imply: % 8.66/1.99 | | | | | | (48) $false % 8.66/1.99 | | | | | | % 8.66/1.99 | | | | | | CLOSE: (48) is inconsistent. % 8.66/1.99 | | | | | | % 8.66/1.99 | | | | | Case 2: % 8.66/1.99 | | | | | | % 8.66/1.99 | | | | | | (49) all_52_0 = 0 % 8.66/1.99 | | | | | | % 8.66/1.99 | | | | | | REDUCE: (44), (49) imply: % 8.66/1.99 | | | | | | (50) member(all_40_1, all_15_2) = 0 % 8.66/1.99 | | | | | | % 8.66/1.99 | | | | | | GROUND_INST: instantiating (4) with all_40_1, all_15_4, all_15_3, % 8.66/1.99 | | | | | | all_15_2, simplifying with (9), (10), (15), (34), (50) % 8.66/1.99 | | | | | | gives: % 8.66/1.99 | | | | | | (51) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_3) = 0 % 8.66/1.99 | | | | | | & member(all_40_1, all_15_4) = v0) % 8.66/1.99 | | | | | | % 8.66/1.99 | | | | | | DELTA: instantiating (51) with fresh symbol all_67_0 gives: % 8.66/2.00 | | | | | | (52) ~ (all_67_0 = 0) & member(all_40_1, all_15_3) = 0 & % 8.66/2.00 | | | | | | member(all_40_1, all_15_4) = all_67_0 % 8.66/2.00 | | | | | | % 8.66/2.00 | | | | | | ALPHA: (52) implies: % 8.66/2.00 | | | | | | (53) ~ (all_67_0 = 0) % 8.66/2.00 | | | | | | (54) member(all_40_1, all_15_4) = all_67_0 % 8.66/2.00 | | | | | | % 8.66/2.00 | | | | | | GROUND_INST: instantiating (6) with 0, all_67_0, all_15_4, all_40_1, % 8.66/2.00 | | | | | | simplifying with (35), (54) gives: % 8.66/2.00 | | | | | | (55) all_67_0 = 0 % 8.66/2.00 | | | | | | % 8.66/2.00 | | | | | | REDUCE: (53), (55) imply: % 8.66/2.00 | | | | | | (56) $false % 8.66/2.00 | | | | | | % 8.66/2.00 | | | | | | CLOSE: (56) is inconsistent. % 8.66/2.00 | | | | | | % 8.66/2.00 | | | | | End of split % 8.66/2.00 | | | | | % 8.66/2.00 | | | | End of split % 8.66/2.00 | | | | % 8.66/2.00 | | | End of split % 8.66/2.00 | | | % 8.66/2.00 | | Case 2: % 8.66/2.00 | | | % 8.66/2.00 | | | (57) ~ (all_27_1 = 0) % 8.66/2.00 | | | % 8.66/2.00 | | | BETA: splitting (27) gives: % 8.66/2.00 | | | % 8.66/2.00 | | | Case 1: % 8.66/2.00 | | | | % 8.66/2.00 | | | | (58) all_27_1 = 0 % 8.66/2.00 | | | | % 8.66/2.00 | | | | REDUCE: (57), (58) imply: % 8.66/2.00 | | | | (59) $false % 8.66/2.00 | | | | % 8.66/2.00 | | | | CLOSE: (59) is inconsistent. % 8.66/2.00 | | | | % 8.66/2.00 | | | Case 2: % 8.66/2.00 | | | | % 8.66/2.00 | | | | (60) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 8.66/2.00 | | | | = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 8.66/2.00 | | | | % 8.66/2.00 | | | | DELTA: instantiating (60) with fresh symbols all_40_0, all_40_1 gives: % 8.66/2.00 | | | | (61) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = 0 & % 8.66/2.00 | | | | member(all_40_1, all_15_4) = all_40_0 & $i(all_40_1) % 8.66/2.00 | | | | % 8.66/2.00 | | | | ALPHA: (61) implies: % 8.66/2.00 | | | | (62) ~ (all_40_0 = 0) % 8.66/2.00 | | | | (63) $i(all_40_1) % 8.66/2.00 | | | | (64) member(all_40_1, all_15_4) = all_40_0 % 8.66/2.00 | | | | (65) member(all_40_1, all_15_1) = 0 % 8.66/2.00 | | | | % 8.66/2.00 | | | | GROUND_INST: instantiating (4) with all_40_1, all_15_2, all_15_3, % 8.66/2.00 | | | | all_15_1, simplifying with (10), (11), (16), (63), (65) % 8.66/2.00 | | | | gives: % 8.66/2.00 | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_2) = v0 & % 8.66/2.00 | | | | member(all_40_1, all_15_3) = 0) % 8.66/2.00 | | | | % 8.66/2.00 | | | | DELTA: instantiating (66) with fresh symbol all_48_0 gives: % 8.66/2.00 | | | | (67) ~ (all_48_0 = 0) & member(all_40_1, all_15_2) = all_48_0 & % 8.66/2.00 | | | | member(all_40_1, all_15_3) = 0 % 8.66/2.00 | | | | % 8.66/2.00 | | | | ALPHA: (67) implies: % 8.66/2.00 | | | | (68) ~ (all_48_0 = 0) % 8.66/2.00 | | | | (69) member(all_40_1, all_15_3) = 0 % 8.66/2.00 | | | | (70) member(all_40_1, all_15_2) = all_48_0 % 8.66/2.00 | | | | % 8.66/2.00 | | | | GROUND_INST: instantiating (5) with all_40_1, all_15_4, all_15_3, % 8.66/2.00 | | | | all_15_2, all_48_0, simplifying with (9), (10), (15), (63), % 8.66/2.00 | | | | (70) gives: % 8.66/2.00 | | | | (71) all_48_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1, % 8.66/2.00 | | | | all_15_3) = v0 & member(all_40_1, all_15_4) = v1 & ( ~ (v0 = % 8.66/2.00 | | | | 0) | v1 = 0)) % 8.66/2.00 | | | | % 8.66/2.00 | | | | BETA: splitting (71) gives: % 8.66/2.00 | | | | % 8.66/2.00 | | | | Case 1: % 8.66/2.00 | | | | | % 8.66/2.00 | | | | | (72) all_48_0 = 0 % 8.66/2.00 | | | | | % 8.66/2.00 | | | | | REDUCE: (68), (72) imply: % 8.66/2.00 | | | | | (73) $false % 8.66/2.00 | | | | | % 8.66/2.00 | | | | | CLOSE: (73) is inconsistent. % 8.66/2.00 | | | | | % 8.66/2.00 | | | | Case 2: % 8.66/2.00 | | | | | % 8.66/2.00 | | | | | (74) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_3) = v0 % 8.66/2.00 | | | | | & member(all_40_1, all_15_4) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 8.66/2.00 | | | | | % 8.66/2.00 | | | | | DELTA: instantiating (74) with fresh symbols all_57_0, all_57_1 gives: % 8.66/2.00 | | | | | (75) member(all_40_1, all_15_3) = all_57_1 & member(all_40_1, % 8.66/2.00 | | | | | all_15_4) = all_57_0 & ( ~ (all_57_1 = 0) | all_57_0 = 0) % 8.66/2.00 | | | | | % 8.66/2.00 | | | | | ALPHA: (75) implies: % 8.66/2.01 | | | | | (76) member(all_40_1, all_15_4) = all_57_0 % 8.66/2.01 | | | | | (77) member(all_40_1, all_15_3) = all_57_1 % 8.66/2.01 | | | | | (78) ~ (all_57_1 = 0) | all_57_0 = 0 % 8.66/2.01 | | | | | % 8.66/2.01 | | | | | GROUND_INST: instantiating (6) with all_40_0, all_57_0, all_15_4, % 8.66/2.01 | | | | | all_40_1, simplifying with (64), (76) gives: % 8.66/2.01 | | | | | (79) all_57_0 = all_40_0 % 8.66/2.01 | | | | | % 8.66/2.01 | | | | | GROUND_INST: instantiating (6) with 0, all_57_1, all_15_3, all_40_1, % 8.66/2.01 | | | | | simplifying with (69), (77) gives: % 8.66/2.01 | | | | | (80) all_57_1 = 0 % 8.66/2.01 | | | | | % 8.66/2.01 | | | | | BETA: splitting (78) gives: % 8.66/2.01 | | | | | % 8.66/2.01 | | | | | Case 1: % 8.66/2.01 | | | | | | % 8.66/2.01 | | | | | | (81) ~ (all_57_1 = 0) % 8.66/2.01 | | | | | | % 8.66/2.01 | | | | | | REDUCE: (80), (81) imply: % 8.66/2.01 | | | | | | (82) $false % 8.66/2.01 | | | | | | % 8.66/2.01 | | | | | | CLOSE: (82) is inconsistent. % 8.66/2.01 | | | | | | % 8.66/2.01 | | | | | Case 2: % 8.66/2.01 | | | | | | % 8.66/2.01 | | | | | | (83) all_57_0 = 0 % 8.66/2.01 | | | | | | % 8.66/2.01 | | | | | | COMBINE_EQS: (79), (83) imply: % 8.66/2.01 | | | | | | (84) all_40_0 = 0 % 8.66/2.01 | | | | | | % 8.66/2.01 | | | | | | REDUCE: (62), (84) imply: % 8.66/2.01 | | | | | | (85) $false % 8.66/2.01 | | | | | | % 8.66/2.01 | | | | | | CLOSE: (85) is inconsistent. % 8.66/2.01 | | | | | | % 8.66/2.01 | | | | | End of split % 8.66/2.01 | | | | | % 8.66/2.01 | | | | End of split % 8.66/2.01 | | | | % 8.66/2.01 | | | End of split % 8.66/2.01 | | | % 8.66/2.01 | | End of split % 8.66/2.01 | | % 8.66/2.01 | End of split % 8.66/2.01 | % 8.66/2.01 End of proof % 8.66/2.01 % SZS output end Proof for theBenchmark % 8.66/2.01 % 8.66/2.01 1417ms %------------------------------------------------------------------------------