%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET696+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 : n003.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 15:26:02 EDT 2023 % Result : Theorem 7.20s 1.73s % Output : Proof 9.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.32 % Computer : n003.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 300 % 0.12/0.32 % DateTime : Sat Aug 26 09:18:24 EDT 2023 % 0.12/0.32 % CPUTime : % 0.17/0.57 ________ _____ % 0.17/0.57 ___ __ \_________(_)________________________________ % 0.17/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.57 % 0.17/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.57 (2023-06-19) % 0.17/0.57 % 0.17/0.57 (c) Philipp Rümmer, 2009-2023 % 0.17/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.57 Amanda Stjerna. % 0.17/0.57 Free software under BSD-3-Clause. % 0.17/0.57 % 0.17/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.57 % 0.17/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.59 Running up to 7 provers in parallel. % 0.17/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.17/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.37/0.99 Prover 4: Preprocessing ... % 2.37/0.99 Prover 1: Preprocessing ... % 2.37/1.02 Prover 6: Preprocessing ... % 2.37/1.02 Prover 3: Preprocessing ... % 2.37/1.02 Prover 2: Preprocessing ... % 2.37/1.02 Prover 0: Preprocessing ... % 2.37/1.03 Prover 5: Preprocessing ... % 5.89/1.49 Prover 5: Proving ... % 5.89/1.51 Prover 3: Constructing countermodel ... % 5.89/1.51 Prover 1: Constructing countermodel ... % 5.89/1.51 Prover 2: Proving ... % 6.12/1.52 Prover 6: Proving ... % 6.12/1.52 Prover 4: Constructing countermodel ... % 6.20/1.53 Prover 0: Proving ... % 7.20/1.73 Prover 3: proved (1133ms) % 7.20/1.73 % 7.20/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.20/1.73 % 7.20/1.74 Prover 5: stopped % 7.20/1.76 Prover 2: stopped % 7.83/1.77 Prover 0: stopped % 7.95/1.78 Prover 6: stopped % 7.95/1.79 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.95/1.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.95/1.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.95/1.79 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.95/1.79 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.95/1.80 Prover 7: Preprocessing ... % 7.95/1.81 Prover 8: Preprocessing ... % 8.19/1.83 Prover 13: Preprocessing ... % 8.26/1.83 Prover 11: Preprocessing ... % 8.26/1.84 Prover 1: Found proof (size 38) % 8.26/1.84 Prover 1: proved (1238ms) % 8.26/1.85 Prover 7: stopped % 8.26/1.85 Prover 4: stopped % 8.26/1.85 Prover 10: Preprocessing ... % 8.26/1.87 Prover 13: stopped % 8.26/1.88 Prover 10: stopped % 8.26/1.88 Prover 11: stopped % 8.71/1.93 Prover 8: Warning: ignoring some quantifiers % 8.71/1.94 Prover 8: Constructing countermodel ... % 8.71/1.95 Prover 8: stopped % 8.71/1.95 % 8.71/1.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.71/1.95 % 8.71/1.96 % SZS output start Proof for theBenchmark % 8.71/1.96 Assumptions after simplification: % 8.71/1.96 --------------------------------- % 8.71/1.96 % 8.71/1.96 (difference) % 8.71/2.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.71/2.00 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 8.71/2.00 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 & % 8.71/2.00 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 8.71/2.00 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, % 8.71/2.00 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 8.71/2.00 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 8.71/2.00 % 8.71/2.00 (empty_set) % 8.71/2.00 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0)) % 8.71/2.00 % 8.71/2.00 (equal_set) % 8.71/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 8.71/2.01 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 8.71/2.01 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 8.71/2.01 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 8.71/2.01 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.71/2.01 % 8.71/2.01 (intersection) % 8.71/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.71/2.01 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 8.71/2.01 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 8.71/2.01 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 8.71/2.01 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 8.71/2.01 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 8.71/2.01 0 & member(v0, v1) = 0)) % 8.71/2.01 % 8.71/2.01 (subset) % 8.71/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.71/2.02 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.71/2.02 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.71/2.02 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.71/2.02 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.71/2.02 % 8.71/2.02 (thI28) % 8.71/2.02 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 8.71/2.02 [v4: int] : ( ~ (v4 = 0) & difference(v1, v0) = v2 & intersection(v2, v0) = v3 % 8.71/2.02 & equal_set(v3, empty_set) = v4 & subset(v0, v1) = 0 & $i(v3) & $i(v2) & % 8.71/2.02 $i(v1) & $i(v0)) % 8.71/2.02 % 8.71/2.02 (function-axioms) % 8.71/2.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.71/2.03 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.71/2.03 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.71/2.03 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.71/2.03 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.71/2.03 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.71/2.03 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.71/2.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.71/2.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.71/2.03 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.71/2.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.71/2.03 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.71/2.03 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.71/2.03 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.71/2.03 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.71/2.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.71/2.03 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.71/2.03 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.71/2.03 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.71/2.03 (power_set(v2) = v0)) % 8.71/2.03 % 8.71/2.03 Further assumptions not needed in the proof: % 8.71/2.03 -------------------------------------------- % 8.71/2.03 power_set, product, singleton, sum, union, unordered_pair % 8.71/2.03 % 8.71/2.03 Those formulas are unsatisfiable: % 8.71/2.03 --------------------------------- % 8.71/2.03 % 8.71/2.03 Begin of proof % 8.71/2.03 | % 8.71/2.03 | ALPHA: (subset) implies: % 8.71/2.03 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.71/2.03 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.71/2.03 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.71/2.03 | % 8.71/2.03 | ALPHA: (equal_set) implies: % 8.71/2.03 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 8.71/2.03 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 8.71/2.03 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 8.71/2.03 | 0)))) % 8.71/2.03 | % 8.71/2.03 | ALPHA: (intersection) implies: % 8.71/2.03 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.71/2.03 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 8.71/2.03 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 8.71/2.03 | % 8.71/2.03 | ALPHA: (empty_set) implies: % 8.71/2.04 | (4) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0)) % 8.71/2.04 | % 8.71/2.04 | ALPHA: (difference) implies: % 8.71/2.04 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.71/2.04 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ % 8.71/2.04 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0 % 8.71/2.04 | & member(v0, v1) = v4)) % 8.71/2.04 | % 8.71/2.04 | ALPHA: (thI28) implies: % 8.71/2.04 | (6) $i(empty_set) % 8.71/2.04 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : % 8.71/2.04 | ( ~ (v4 = 0) & difference(v1, v0) = v2 & intersection(v2, v0) = v3 & % 8.71/2.04 | equal_set(v3, empty_set) = v4 & subset(v0, v1) = 0 & $i(v3) & $i(v2) % 8.71/2.04 | & $i(v1) & $i(v0)) % 8.71/2.04 | % 8.71/2.04 | ALPHA: (function-axioms) implies: % 8.71/2.04 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.71/2.04 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 8.71/2.04 | = v0)) % 8.71/2.04 | % 8.71/2.04 | DELTA: instantiating (7) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.71/2.04 | all_15_3, all_15_4 gives: % 8.71/2.04 | (9) ~ (all_15_0 = 0) & difference(all_15_3, all_15_4) = all_15_2 & % 8.71/2.04 | intersection(all_15_2, all_15_4) = all_15_1 & equal_set(all_15_1, % 8.71/2.04 | empty_set) = all_15_0 & subset(all_15_4, all_15_3) = 0 & $i(all_15_1) % 8.71/2.04 | & $i(all_15_2) & $i(all_15_3) & $i(all_15_4) % 8.71/2.04 | % 8.71/2.04 | ALPHA: (9) implies: % 8.71/2.04 | (10) ~ (all_15_0 = 0) % 8.71/2.04 | (11) $i(all_15_4) % 8.71/2.04 | (12) $i(all_15_3) % 8.71/2.04 | (13) $i(all_15_2) % 8.71/2.04 | (14) $i(all_15_1) % 8.71/2.04 | (15) equal_set(all_15_1, empty_set) = all_15_0 % 8.71/2.04 | (16) intersection(all_15_2, all_15_4) = all_15_1 % 8.71/2.04 | (17) difference(all_15_3, all_15_4) = all_15_2 % 8.71/2.04 | % 8.71/2.05 | GROUND_INST: instantiating (2) with all_15_1, empty_set, all_15_0, simplifying % 8.71/2.05 | with (6), (14), (15) gives: % 8.71/2.05 | (18) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 8.71/2.05 | empty_set) = v0 & subset(empty_set, all_15_1) = v1 & ( ~ (v1 = 0) % 8.71/2.05 | | ~ (v0 = 0))) % 8.71/2.05 | % 8.71/2.05 | BETA: splitting (18) gives: % 8.71/2.05 | % 8.71/2.05 | Case 1: % 8.71/2.05 | | % 8.71/2.05 | | (19) all_15_0 = 0 % 8.71/2.05 | | % 8.71/2.05 | | REDUCE: (10), (19) imply: % 8.71/2.05 | | (20) $false % 8.71/2.05 | | % 8.71/2.05 | | CLOSE: (20) is inconsistent. % 8.71/2.05 | | % 8.71/2.05 | Case 2: % 8.71/2.05 | | % 8.71/2.05 | | (21) ? [v0: any] : ? [v1: any] : (subset(all_15_1, empty_set) = v0 & % 8.71/2.05 | | subset(empty_set, all_15_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.71/2.05 | | % 8.71/2.05 | | DELTA: instantiating (21) with fresh symbols all_27_0, all_27_1 gives: % 8.71/2.05 | | (22) subset(all_15_1, empty_set) = all_27_1 & subset(empty_set, all_15_1) % 8.71/2.05 | | = all_27_0 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0)) % 8.71/2.05 | | % 8.71/2.05 | | ALPHA: (22) implies: % 8.71/2.05 | | (23) subset(empty_set, all_15_1) = all_27_0 % 8.71/2.05 | | (24) subset(all_15_1, empty_set) = all_27_1 % 8.71/2.05 | | (25) ~ (all_27_0 = 0) | ~ (all_27_1 = 0) % 8.71/2.05 | | % 8.71/2.05 | | GROUND_INST: instantiating (1) with empty_set, all_15_1, all_27_0, % 8.71/2.05 | | simplifying with (6), (14), (23) gives: % 8.71/2.05 | | (26) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.71/2.05 | | member(v0, all_15_1) = v1 & member(v0, empty_set) = 0 & $i(v0)) % 8.71/2.05 | | % 8.71/2.05 | | GROUND_INST: instantiating (1) with all_15_1, empty_set, all_27_1, % 8.71/2.05 | | simplifying with (6), (14), (24) gives: % 8.71/2.06 | | (27) all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.71/2.06 | | member(v0, all_15_1) = 0 & member(v0, empty_set) = v1 & $i(v0)) % 8.71/2.06 | | % 8.71/2.06 | | BETA: splitting (25) gives: % 8.71/2.06 | | % 8.71/2.06 | | Case 1: % 8.71/2.06 | | | % 8.71/2.06 | | | (28) ~ (all_27_0 = 0) % 8.71/2.06 | | | % 8.71/2.06 | | | BETA: splitting (26) gives: % 8.71/2.06 | | | % 8.71/2.06 | | | Case 1: % 8.71/2.06 | | | | % 8.71/2.06 | | | | (29) all_27_0 = 0 % 8.71/2.06 | | | | % 8.71/2.06 | | | | REDUCE: (28), (29) imply: % 8.71/2.06 | | | | (30) $false % 8.71/2.06 | | | | % 8.71/2.06 | | | | CLOSE: (30) is inconsistent. % 8.71/2.06 | | | | % 8.71/2.06 | | | Case 2: % 8.71/2.06 | | | | % 8.71/2.06 | | | | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 8.71/2.06 | | | | = v1 & member(v0, empty_set) = 0 & $i(v0)) % 8.71/2.06 | | | | % 8.71/2.06 | | | | DELTA: instantiating (31) with fresh symbols all_40_0, all_40_1 gives: % 8.71/2.06 | | | | (32) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = all_40_0 & % 8.71/2.06 | | | | member(all_40_1, empty_set) = 0 & $i(all_40_1) % 8.71/2.06 | | | | % 8.71/2.06 | | | | ALPHA: (32) implies: % 8.71/2.06 | | | | (33) $i(all_40_1) % 8.71/2.06 | | | | (34) member(all_40_1, empty_set) = 0 % 8.71/2.06 | | | | % 9.23/2.06 | | | | GROUND_INST: instantiating (4) with all_40_1, simplifying with (33), % 9.23/2.06 | | | | (34) gives: % 9.23/2.06 | | | | (35) $false % 9.23/2.06 | | | | % 9.23/2.06 | | | | CLOSE: (35) is inconsistent. % 9.23/2.06 | | | | % 9.23/2.06 | | | End of split % 9.23/2.06 | | | % 9.23/2.06 | | Case 2: % 9.23/2.06 | | | % 9.23/2.06 | | | (36) ~ (all_27_1 = 0) % 9.23/2.06 | | | % 9.23/2.06 | | | BETA: splitting (27) gives: % 9.23/2.06 | | | % 9.23/2.06 | | | Case 1: % 9.23/2.06 | | | | % 9.23/2.06 | | | | (37) all_27_1 = 0 % 9.23/2.06 | | | | % 9.23/2.06 | | | | REDUCE: (36), (37) imply: % 9.23/2.06 | | | | (38) $false % 9.23/2.06 | | | | % 9.23/2.06 | | | | CLOSE: (38) is inconsistent. % 9.23/2.06 | | | | % 9.23/2.06 | | | Case 2: % 9.23/2.06 | | | | % 9.23/2.06 | | | | (39) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 9.23/2.06 | | | | = 0 & member(v0, empty_set) = v1 & $i(v0)) % 9.23/2.06 | | | | % 9.23/2.06 | | | | DELTA: instantiating (39) with fresh symbols all_40_0, all_40_1 gives: % 9.23/2.06 | | | | (40) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = 0 & % 9.23/2.06 | | | | member(all_40_1, empty_set) = all_40_0 & $i(all_40_1) % 9.23/2.06 | | | | % 9.23/2.06 | | | | ALPHA: (40) implies: % 9.23/2.06 | | | | (41) $i(all_40_1) % 9.23/2.06 | | | | (42) member(all_40_1, all_15_1) = 0 % 9.23/2.06 | | | | % 9.23/2.06 | | | | GROUND_INST: instantiating (3) with all_40_1, all_15_2, all_15_4, % 9.23/2.06 | | | | all_15_1, simplifying with (11), (13), (16), (41), (42) % 9.23/2.06 | | | | gives: % 9.23/2.06 | | | | (43) member(all_40_1, all_15_2) = 0 & member(all_40_1, all_15_4) = 0 % 9.23/2.06 | | | | % 9.23/2.06 | | | | ALPHA: (43) implies: % 9.23/2.07 | | | | (44) member(all_40_1, all_15_4) = 0 % 9.23/2.07 | | | | (45) member(all_40_1, all_15_2) = 0 % 9.23/2.07 | | | | % 9.23/2.07 | | | | GROUND_INST: instantiating (5) with all_40_1, all_15_4, all_15_3, % 9.23/2.07 | | | | all_15_2, simplifying with (11), (12), (17), (41), (45) % 9.23/2.07 | | | | gives: % 9.23/2.07 | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_3) = 0 & % 9.23/2.07 | | | | member(all_40_1, all_15_4) = v0) % 9.23/2.07 | | | | % 9.23/2.07 | | | | DELTA: instantiating (46) with fresh symbol all_55_0 gives: % 9.23/2.07 | | | | (47) ~ (all_55_0 = 0) & member(all_40_1, all_15_3) = 0 & % 9.23/2.07 | | | | member(all_40_1, all_15_4) = all_55_0 % 9.23/2.07 | | | | % 9.23/2.07 | | | | ALPHA: (47) implies: % 9.23/2.07 | | | | (48) ~ (all_55_0 = 0) % 9.23/2.07 | | | | (49) member(all_40_1, all_15_4) = all_55_0 % 9.23/2.07 | | | | % 9.23/2.07 | | | | GROUND_INST: instantiating (8) with 0, all_55_0, all_15_4, all_40_1, % 9.23/2.07 | | | | simplifying with (44), (49) gives: % 9.23/2.07 | | | | (50) all_55_0 = 0 % 9.23/2.07 | | | | % 9.23/2.07 | | | | REDUCE: (48), (50) imply: % 9.23/2.07 | | | | (51) $false % 9.23/2.07 | | | | % 9.23/2.07 | | | | CLOSE: (51) is inconsistent. % 9.23/2.07 | | | | % 9.23/2.07 | | | End of split % 9.23/2.07 | | | % 9.23/2.07 | | End of split % 9.23/2.07 | | % 9.23/2.07 | End of split % 9.23/2.07 | % 9.23/2.07 End of proof % 9.23/2.07 % SZS output end Proof for theBenchmark % 9.23/2.07 % 9.23/2.07 1496ms %------------------------------------------------------------------------------