%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET692+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 : n014.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 15:26:01 EDT 2023 % Result : Theorem 8.93s 2.04s % Output : Proof 11.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.17 % Problem : SET692+4 : TPTP v8.1.2. Released v2.2.0. % 0.12/0.17 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.37 % Computer : n014.cluster.edu % 0.13/0.37 % Model : x86_64 x86_64 % 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.37 % Memory : 8042.1875MB % 0.13/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.37 % CPULimit : 300 % 0.13/0.37 % WCLimit : 300 % 0.13/0.37 % DateTime : Sat Aug 26 11:30:02 EDT 2023 % 0.13/0.37 % 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/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 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 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 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 % 2.17/1.11 Prover 4: Preprocessing ... % 2.17/1.11 Prover 1: Preprocessing ... % 2.86/1.16 Prover 0: Preprocessing ... % 2.86/1.16 Prover 5: Preprocessing ... % 2.86/1.16 Prover 2: Preprocessing ... % 2.86/1.16 Prover 6: Preprocessing ... % 2.86/1.16 Prover 3: Preprocessing ... % 6.12/1.68 Prover 6: Proving ... % 6.43/1.69 Prover 5: Proving ... % 6.43/1.71 Prover 1: Constructing countermodel ... % 6.43/1.71 Prover 3: Constructing countermodel ... % 6.43/1.72 Prover 4: Constructing countermodel ... % 6.43/1.73 Prover 0: Proving ... % 6.83/1.75 Prover 2: Proving ... % 8.53/2.03 Prover 3: proved (1406ms) % 8.93/2.04 % 8.93/2.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.93/2.04 % 8.93/2.04 Prover 0: stopped % 8.93/2.04 Prover 5: stopped % 8.93/2.04 Prover 6: stopped % 8.93/2.04 Prover 2: stopped % 8.93/2.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.93/2.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.93/2.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.93/2.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.93/2.05 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.02/2.12 Prover 7: Preprocessing ... % 9.02/2.13 Prover 8: Preprocessing ... % 9.02/2.14 Prover 11: Preprocessing ... % 9.02/2.14 Prover 13: Preprocessing ... % 9.02/2.14 Prover 10: Preprocessing ... % 9.02/2.20 Prover 1: Found proof (size 65) % 9.02/2.20 Prover 1: proved (1579ms) % 9.02/2.20 Prover 4: stopped % 9.02/2.22 Prover 13: stopped % 9.02/2.23 Prover 11: stopped % 9.02/2.24 Prover 7: Warning: ignoring some quantifiers % 9.02/2.24 Prover 10: Warning: ignoring some quantifiers % 9.02/2.25 Prover 7: Constructing countermodel ... % 10.21/2.26 Prover 10: Constructing countermodel ... % 10.21/2.26 Prover 7: stopped % 10.21/2.27 Prover 10: stopped % 10.51/2.30 Prover 8: Warning: ignoring some quantifiers % 10.51/2.31 Prover 8: Constructing countermodel ... % 10.51/2.32 Prover 8: stopped % 10.51/2.32 % 10.51/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.51/2.32 % 10.51/2.34 % SZS output start Proof for theBenchmark % 10.51/2.34 Assumptions after simplification: % 10.51/2.34 --------------------------------- % 10.51/2.34 % 10.51/2.34 (equal_set) % 10.93/2.38 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 10.93/2.38 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 10.93/2.38 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 10.93/2.38 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 10.93/2.38 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 10.93/2.38 % 10.93/2.38 (intersection) % 10.93/2.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.93/2.39 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 10.93/2.39 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 10.93/2.39 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 10.93/2.39 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 10.93/2.39 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 10.93/2.39 0 & member(v0, v1) = 0)) % 10.93/2.39 % 10.93/2.39 (subset) % 10.93/2.39 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 10.93/2.39 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 10.93/2.39 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 10.93/2.39 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 10.93/2.39 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 10.93/2.39 % 10.93/2.40 (thI19) % 10.93/2.40 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 10.93/2.40 (intersection(v0, v1) = v2 & equal_set(v0, v2) = v3 & subset(v0, v1) = v4 & % 10.93/2.40 $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = % 11.02/2.40 0)))) % 11.02/2.40 % 11.02/2.40 (function-axioms) % 11.02/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.02/2.41 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 11.02/2.41 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.02/2.41 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 11.02/2.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 11.02/2.41 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.02/2.41 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 11.02/2.41 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.02/2.41 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 11.02/2.41 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.02/2.41 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 11.02/2.41 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.02/2.41 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.02/2.41 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 11.02/2.41 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 11.02/2.41 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 11.02/2.41 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 11.02/2.41 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 11.02/2.41 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 11.02/2.41 (power_set(v2) = v0)) % 11.02/2.41 % 11.02/2.41 Further assumptions not needed in the proof: % 11.02/2.41 -------------------------------------------- % 11.02/2.41 difference, empty_set, power_set, product, singleton, sum, union, unordered_pair % 11.02/2.41 % 11.02/2.41 Those formulas are unsatisfiable: % 11.02/2.41 --------------------------------- % 11.02/2.41 % 11.02/2.41 Begin of proof % 11.02/2.41 | % 11.10/2.42 | ALPHA: (subset) implies: % 11.10/2.42 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 11.10/2.42 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 11.10/2.42 | member(v2, v1) = 0)) % 11.10/2.42 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 11.10/2.42 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 11.10/2.42 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 11.10/2.42 | % 11.10/2.42 | ALPHA: (equal_set) implies: % 11.10/2.42 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | % 11.10/2.42 | ~ $i(v0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 11.10/2.42 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 11.10/2.42 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 11.10/2.42 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 11.10/2.42 | 0)))) % 11.10/2.42 | % 11.10/2.42 | ALPHA: (intersection) implies: % 11.10/2.43 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 11.10/2.43 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 11.10/2.43 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 11.10/2.43 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 11.10/2.43 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 11.10/2.43 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 11.10/2.43 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 11.10/2.43 | 0)))) % 11.10/2.43 | % 11.10/2.43 | ALPHA: (function-axioms) implies: % 11.10/2.43 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.10/2.43 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 11.10/2.43 | = v0)) % 11.10/2.43 | % 11.10/2.43 | DELTA: instantiating (thI19) with fresh symbols all_15_0, all_15_1, all_15_2, % 11.10/2.43 | all_15_3, all_15_4 gives: % 11.10/2.43 | (8) intersection(all_15_4, all_15_3) = all_15_2 & equal_set(all_15_4, % 11.10/2.43 | all_15_2) = all_15_1 & subset(all_15_4, all_15_3) = all_15_0 & % 11.10/2.43 | $i(all_15_2) & $i(all_15_3) & $i(all_15_4) & ((all_15_0 = 0 & ~ % 11.10/2.43 | (all_15_1 = 0)) | (all_15_1 = 0 & ~ (all_15_0 = 0))) % 11.10/2.43 | % 11.10/2.43 | ALPHA: (8) implies: % 11.10/2.43 | (9) $i(all_15_4) % 11.10/2.43 | (10) $i(all_15_3) % 11.10/2.43 | (11) $i(all_15_2) % 11.10/2.43 | (12) subset(all_15_4, all_15_3) = all_15_0 % 11.10/2.43 | (13) equal_set(all_15_4, all_15_2) = all_15_1 % 11.10/2.43 | (14) intersection(all_15_4, all_15_3) = all_15_2 % 11.10/2.43 | (15) (all_15_0 = 0 & ~ (all_15_1 = 0)) | (all_15_1 = 0 & ~ (all_15_0 = % 11.10/2.43 | 0)) % 11.10/2.43 | % 11.10/2.43 | GROUND_INST: instantiating (2) with all_15_4, all_15_3, all_15_0, simplifying % 11.10/2.44 | with (9), (10), (12) gives: % 11.10/2.44 | (16) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.10/2.44 | all_15_3) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 11.10/2.44 | % 11.10/2.44 | GROUND_INST: instantiating (4) with all_15_4, all_15_2, all_15_1, simplifying % 11.10/2.44 | with (9), (11), (13) gives: % 11.10/2.44 | (17) all_15_1 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_2, % 11.10/2.44 | all_15_4) = v1 & subset(all_15_4, all_15_2) = v0 & ( ~ (v1 = 0) | % 11.10/2.44 | ~ (v0 = 0))) % 11.10/2.44 | % 11.10/2.44 | BETA: splitting (15) gives: % 11.10/2.44 | % 11.10/2.44 | Case 1: % 11.10/2.44 | | % 11.10/2.44 | | (18) all_15_0 = 0 & ~ (all_15_1 = 0) % 11.10/2.44 | | % 11.10/2.44 | | ALPHA: (18) implies: % 11.10/2.44 | | (19) all_15_0 = 0 % 11.10/2.44 | | (20) ~ (all_15_1 = 0) % 11.10/2.44 | | % 11.10/2.44 | | REDUCE: (12), (19) imply: % 11.10/2.44 | | (21) subset(all_15_4, all_15_3) = 0 % 11.10/2.44 | | % 11.10/2.44 | | BETA: splitting (17) gives: % 11.10/2.44 | | % 11.10/2.44 | | Case 1: % 11.10/2.44 | | | % 11.10/2.44 | | | (22) all_15_1 = 0 % 11.10/2.44 | | | % 11.10/2.44 | | | REDUCE: (20), (22) imply: % 11.10/2.44 | | | (23) $false % 11.10/2.44 | | | % 11.10/2.44 | | | CLOSE: (23) is inconsistent. % 11.10/2.44 | | | % 11.10/2.44 | | Case 2: % 11.10/2.44 | | | % 11.10/2.44 | | | (24) ? [v0: any] : ? [v1: any] : (subset(all_15_2, all_15_4) = v1 & % 11.10/2.44 | | | subset(all_15_4, all_15_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 11.10/2.44 | | | % 11.10/2.44 | | | DELTA: instantiating (24) with fresh symbols all_28_0, all_28_1 gives: % 11.10/2.44 | | | (25) subset(all_15_2, all_15_4) = all_28_0 & subset(all_15_4, all_15_2) % 11.10/2.44 | | | = all_28_1 & ( ~ (all_28_0 = 0) | ~ (all_28_1 = 0)) % 11.10/2.44 | | | % 11.10/2.44 | | | ALPHA: (25) implies: % 11.10/2.45 | | | (26) subset(all_15_4, all_15_2) = all_28_1 % 11.10/2.45 | | | (27) subset(all_15_2, all_15_4) = all_28_0 % 11.10/2.45 | | | (28) ~ (all_28_0 = 0) | ~ (all_28_1 = 0) % 11.10/2.45 | | | % 11.10/2.45 | | | GROUND_INST: instantiating (1) with all_15_4, all_15_3, simplifying with % 11.10/2.45 | | | (9), (10), (21) gives: % 11.10/2.45 | | | (29) ! [v0: $i] : ( ~ (member(v0, all_15_4) = 0) | ~ $i(v0) | % 11.10/2.45 | | | member(v0, all_15_3) = 0) % 11.10/2.45 | | | % 11.10/2.45 | | | GROUND_INST: instantiating (2) with all_15_4, all_15_2, all_28_1, % 11.10/2.45 | | | simplifying with (9), (11), (26) gives: % 11.10/2.45 | | | (30) all_28_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 11.10/2.45 | | | member(v0, all_15_2) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 11.10/2.45 | | | % 11.10/2.45 | | | GROUND_INST: instantiating (2) with all_15_2, all_15_4, all_28_0, % 11.10/2.45 | | | simplifying with (9), (11), (27) gives: % 11.10/2.45 | | | (31) all_28_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 11.10/2.45 | | | member(v0, all_15_2) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 11.10/2.45 | | | % 11.10/2.45 | | | BETA: splitting (28) gives: % 11.10/2.45 | | | % 11.10/2.45 | | | Case 1: % 11.10/2.45 | | | | % 11.10/2.45 | | | | (32) ~ (all_28_0 = 0) % 11.10/2.45 | | | | % 11.10/2.45 | | | | BETA: splitting (31) gives: % 11.10/2.45 | | | | % 11.10/2.45 | | | | Case 1: % 11.10/2.45 | | | | | % 11.10/2.45 | | | | | (33) all_28_0 = 0 % 11.10/2.45 | | | | | % 11.10/2.45 | | | | | REDUCE: (32), (33) imply: % 11.10/2.45 | | | | | (34) $false % 11.10/2.45 | | | | | % 11.10/2.45 | | | | | CLOSE: (34) is inconsistent. % 11.10/2.45 | | | | | % 11.10/2.45 | | | | Case 2: % 11.10/2.45 | | | | | % 11.10/2.45 | | | | | (35) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.10/2.45 | | | | | all_15_2) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 11.10/2.45 | | | | | % 11.10/2.45 | | | | | DELTA: instantiating (35) with fresh symbols all_44_0, all_44_1 gives: % 11.10/2.45 | | | | | (36) ~ (all_44_0 = 0) & member(all_44_1, all_15_2) = 0 & % 11.10/2.45 | | | | | member(all_44_1, all_15_4) = all_44_0 & $i(all_44_1) % 11.10/2.45 | | | | | % 11.10/2.45 | | | | | ALPHA: (36) implies: % 11.10/2.45 | | | | | (37) ~ (all_44_0 = 0) % 11.10/2.45 | | | | | (38) $i(all_44_1) % 11.10/2.45 | | | | | (39) member(all_44_1, all_15_4) = all_44_0 % 11.10/2.45 | | | | | (40) member(all_44_1, all_15_2) = 0 % 11.10/2.45 | | | | | % 11.10/2.46 | | | | | GROUND_INST: instantiating (5) with all_44_1, all_15_4, all_15_3, % 11.10/2.46 | | | | | all_15_2, simplifying with (9), (10), (14), (38), (40) % 11.10/2.46 | | | | | gives: % 11.10/2.46 | | | | | (41) member(all_44_1, all_15_3) = 0 & member(all_44_1, all_15_4) = % 11.10/2.46 | | | | | 0 % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | ALPHA: (41) implies: % 11.10/2.46 | | | | | (42) member(all_44_1, all_15_4) = 0 % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | GROUND_INST: instantiating (7) with all_44_0, 0, all_15_4, all_44_1, % 11.10/2.46 | | | | | simplifying with (39), (42) gives: % 11.10/2.46 | | | | | (43) all_44_0 = 0 % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | REDUCE: (37), (43) imply: % 11.10/2.46 | | | | | (44) $false % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | CLOSE: (44) is inconsistent. % 11.10/2.46 | | | | | % 11.10/2.46 | | | | End of split % 11.10/2.46 | | | | % 11.10/2.46 | | | Case 2: % 11.10/2.46 | | | | % 11.10/2.46 | | | | (45) ~ (all_28_1 = 0) % 11.10/2.46 | | | | % 11.10/2.46 | | | | BETA: splitting (30) gives: % 11.10/2.46 | | | | % 11.10/2.46 | | | | Case 1: % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | (46) all_28_1 = 0 % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | REDUCE: (45), (46) imply: % 11.10/2.46 | | | | | (47) $false % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | CLOSE: (47) is inconsistent. % 11.10/2.46 | | | | | % 11.10/2.46 | | | | Case 2: % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.10/2.46 | | | | | all_15_2) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | DELTA: instantiating (48) with fresh symbols all_44_0, all_44_1 gives: % 11.10/2.46 | | | | | (49) ~ (all_44_0 = 0) & member(all_44_1, all_15_2) = all_44_0 & % 11.10/2.46 | | | | | member(all_44_1, all_15_4) = 0 & $i(all_44_1) % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | ALPHA: (49) implies: % 11.10/2.46 | | | | | (50) ~ (all_44_0 = 0) % 11.10/2.46 | | | | | (51) $i(all_44_1) % 11.10/2.46 | | | | | (52) member(all_44_1, all_15_4) = 0 % 11.10/2.46 | | | | | (53) member(all_44_1, all_15_2) = all_44_0 % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | GROUND_INST: instantiating (29) with all_44_1, simplifying with (51), % 11.10/2.46 | | | | | (52) gives: % 11.10/2.46 | | | | | (54) member(all_44_1, all_15_3) = 0 % 11.10/2.46 | | | | | % 11.10/2.46 | | | | | GROUND_INST: instantiating (6) with all_44_1, all_15_4, all_15_3, % 11.10/2.46 | | | | | all_15_2, all_44_0, simplifying with (9), (10), (14), % 11.10/2.46 | | | | | (51), (53) gives: % 11.10/2.47 | | | | | (55) all_44_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_44_1, % 11.10/2.47 | | | | | all_15_3) = v1 & member(all_44_1, all_15_4) = v0 & ( ~ (v1 % 11.10/2.47 | | | | | = 0) | ~ (v0 = 0))) % 11.10/2.47 | | | | | % 11.10/2.47 | | | | | BETA: splitting (55) gives: % 11.10/2.47 | | | | | % 11.10/2.47 | | | | | Case 1: % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | (56) all_44_0 = 0 % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | REDUCE: (50), (56) imply: % 11.10/2.47 | | | | | | (57) $false % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | CLOSE: (57) is inconsistent. % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | Case 2: % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | (58) ? [v0: any] : ? [v1: any] : (member(all_44_1, all_15_3) = % 11.10/2.47 | | | | | | v1 & member(all_44_1, all_15_4) = v0 & ( ~ (v1 = 0) | ~ % 11.10/2.47 | | | | | | (v0 = 0))) % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | DELTA: instantiating (58) with fresh symbols all_57_0, all_57_1 % 11.10/2.47 | | | | | | gives: % 11.10/2.47 | | | | | | (59) member(all_44_1, all_15_3) = all_57_0 & member(all_44_1, % 11.10/2.47 | | | | | | all_15_4) = all_57_1 & ( ~ (all_57_0 = 0) | ~ (all_57_1 = % 11.10/2.47 | | | | | | 0)) % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | ALPHA: (59) implies: % 11.10/2.47 | | | | | | (60) member(all_44_1, all_15_4) = all_57_1 % 11.10/2.47 | | | | | | (61) member(all_44_1, all_15_3) = all_57_0 % 11.10/2.47 | | | | | | (62) ~ (all_57_0 = 0) | ~ (all_57_1 = 0) % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | GROUND_INST: instantiating (7) with 0, all_57_1, all_15_4, all_44_1, % 11.10/2.47 | | | | | | simplifying with (52), (60) gives: % 11.10/2.47 | | | | | | (63) all_57_1 = 0 % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | GROUND_INST: instantiating (7) with 0, all_57_0, all_15_3, all_44_1, % 11.10/2.47 | | | | | | simplifying with (54), (61) gives: % 11.10/2.47 | | | | | | (64) all_57_0 = 0 % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | BETA: splitting (62) gives: % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | | Case 1: % 11.10/2.47 | | | | | | | % 11.10/2.47 | | | | | | | (65) ~ (all_57_0 = 0) % 11.10/2.47 | | | | | | | % 11.10/2.47 | | | | | | | REDUCE: (64), (65) imply: % 11.10/2.47 | | | | | | | (66) $false % 11.10/2.47 | | | | | | | % 11.10/2.47 | | | | | | | CLOSE: (66) is inconsistent. % 11.10/2.47 | | | | | | | % 11.10/2.47 | | | | | | Case 2: % 11.10/2.47 | | | | | | | % 11.10/2.47 | | | | | | | (67) ~ (all_57_1 = 0) % 11.10/2.47 | | | | | | | % 11.10/2.47 | | | | | | | REDUCE: (63), (67) imply: % 11.10/2.47 | | | | | | | (68) $false % 11.10/2.47 | | | | | | | % 11.10/2.47 | | | | | | | CLOSE: (68) is inconsistent. % 11.10/2.47 | | | | | | | % 11.10/2.47 | | | | | | End of split % 11.10/2.47 | | | | | | % 11.10/2.47 | | | | | End of split % 11.10/2.47 | | | | | % 11.10/2.47 | | | | End of split % 11.10/2.47 | | | | % 11.10/2.47 | | | End of split % 11.10/2.47 | | | % 11.10/2.47 | | End of split % 11.10/2.47 | | % 11.10/2.47 | Case 2: % 11.10/2.47 | | % 11.10/2.47 | | (69) all_15_1 = 0 & ~ (all_15_0 = 0) % 11.10/2.47 | | % 11.10/2.47 | | ALPHA: (69) implies: % 11.10/2.47 | | (70) all_15_1 = 0 % 11.10/2.47 | | (71) ~ (all_15_0 = 0) % 11.10/2.47 | | % 11.10/2.47 | | REDUCE: (13), (70) imply: % 11.10/2.48 | | (72) equal_set(all_15_4, all_15_2) = 0 % 11.10/2.48 | | % 11.10/2.48 | | BETA: splitting (16) gives: % 11.10/2.48 | | % 11.10/2.48 | | Case 1: % 11.10/2.48 | | | % 11.10/2.48 | | | (73) all_15_0 = 0 % 11.10/2.48 | | | % 11.10/2.48 | | | REDUCE: (71), (73) imply: % 11.10/2.48 | | | (74) $false % 11.10/2.48 | | | % 11.10/2.48 | | | CLOSE: (74) is inconsistent. % 11.10/2.48 | | | % 11.10/2.48 | | Case 2: % 11.10/2.48 | | | % 11.10/2.48 | | | (75) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_3) = % 11.10/2.48 | | | v1 & member(v0, all_15_4) = 0 & $i(v0)) % 11.10/2.48 | | | % 11.10/2.48 | | | DELTA: instantiating (75) with fresh symbols all_28_0, all_28_1 gives: % 11.10/2.48 | | | (76) ~ (all_28_0 = 0) & member(all_28_1, all_15_3) = all_28_0 & % 11.10/2.48 | | | member(all_28_1, all_15_4) = 0 & $i(all_28_1) % 11.10/2.48 | | | % 11.10/2.48 | | | ALPHA: (76) implies: % 11.10/2.48 | | | (77) ~ (all_28_0 = 0) % 11.10/2.48 | | | (78) $i(all_28_1) % 11.10/2.48 | | | (79) member(all_28_1, all_15_4) = 0 % 11.10/2.48 | | | (80) member(all_28_1, all_15_3) = all_28_0 % 11.10/2.48 | | | % 11.10/2.48 | | | GROUND_INST: instantiating (3) with all_15_4, all_15_2, simplifying with % 11.10/2.48 | | | (9), (11), (72) gives: % 11.10/2.48 | | | (81) subset(all_15_2, all_15_4) = 0 & subset(all_15_4, all_15_2) = 0 % 11.10/2.48 | | | % 11.10/2.48 | | | ALPHA: (81) implies: % 11.10/2.48 | | | (82) subset(all_15_4, all_15_2) = 0 % 11.10/2.48 | | | % 11.10/2.48 | | | GROUND_INST: instantiating (1) with all_15_4, all_15_2, simplifying with % 11.10/2.48 | | | (9), (11), (82) gives: % 11.10/2.48 | | | (83) ! [v0: $i] : ( ~ (member(v0, all_15_4) = 0) | ~ $i(v0) | % 11.10/2.48 | | | member(v0, all_15_2) = 0) % 11.10/2.48 | | | % 11.10/2.48 | | | GROUND_INST: instantiating (83) with all_28_1, simplifying with (78), (79) % 11.10/2.48 | | | gives: % 11.10/2.48 | | | (84) member(all_28_1, all_15_2) = 0 % 11.10/2.48 | | | % 11.10/2.48 | | | GROUND_INST: instantiating (5) with all_28_1, all_15_4, all_15_3, % 11.10/2.48 | | | all_15_2, simplifying with (9), (10), (14), (78), (84) gives: % 11.10/2.48 | | | (85) member(all_28_1, all_15_3) = 0 & member(all_28_1, all_15_4) = 0 % 11.10/2.48 | | | % 11.10/2.48 | | | ALPHA: (85) implies: % 11.10/2.48 | | | (86) member(all_28_1, all_15_3) = 0 % 11.10/2.48 | | | % 11.10/2.48 | | | GROUND_INST: instantiating (7) with all_28_0, 0, all_15_3, all_28_1, % 11.10/2.48 | | | simplifying with (80), (86) gives: % 11.10/2.49 | | | (87) all_28_0 = 0 % 11.10/2.49 | | | % 11.10/2.49 | | | REDUCE: (77), (87) imply: % 11.10/2.49 | | | (88) $false % 11.10/2.49 | | | % 11.10/2.49 | | | CLOSE: (88) is inconsistent. % 11.10/2.49 | | | % 11.10/2.49 | | End of split % 11.10/2.49 | | % 11.10/2.49 | End of split % 11.10/2.49 | % 11.10/2.49 End of proof % 11.10/2.49 % SZS output end Proof for theBenchmark % 11.10/2.49 % 11.10/2.49 1883ms %------------------------------------------------------------------------------