%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET351+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 : n002.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 15:24:42 EDT 2023 % Result : Theorem 7.59s 1.98s % Output : Proof 11.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET351+4 : TPTP v8.1.2. Released v2.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n002.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 15:36:33 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.66/1.09 Prover 4: Preprocessing ... % 2.66/1.10 Prover 1: Preprocessing ... % 2.89/1.13 Prover 5: Preprocessing ... % 2.89/1.13 Prover 6: Preprocessing ... % 2.89/1.13 Prover 3: Preprocessing ... % 2.89/1.13 Prover 0: Preprocessing ... % 2.89/1.15 Prover 2: Preprocessing ... % 6.23/1.68 Prover 3: Constructing countermodel ... % 6.23/1.69 Prover 1: Constructing countermodel ... % 6.79/1.69 Prover 6: Proving ... % 6.79/1.70 Prover 5: Proving ... % 6.79/1.70 Prover 2: Proving ... % 6.79/1.70 Prover 4: Constructing countermodel ... % 6.79/1.70 Prover 0: Proving ... % 7.59/1.98 Prover 3: proved (1340ms) % 7.59/1.98 % 7.59/1.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.59/1.98 % 7.59/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.59/1.98 Prover 2: stopped % 7.59/1.98 Prover 6: stopped % 7.59/2.01 Prover 5: stopped % 7.59/2.01 Prover 0: stopped % 7.59/2.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.59/2.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.59/2.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.59/2.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.55/2.05 Prover 8: Preprocessing ... % 8.55/2.05 Prover 7: Preprocessing ... % 8.55/2.07 Prover 11: Preprocessing ... % 8.55/2.07 Prover 10: Preprocessing ... % 8.55/2.11 Prover 13: Preprocessing ... % 9.83/2.14 Prover 1: Found proof (size 45) % 9.83/2.14 Prover 1: proved (1504ms) % 9.83/2.14 Prover 4: stopped % 9.83/2.14 Prover 11: stopped % 9.83/2.15 Prover 13: stopped % 9.83/2.16 Prover 7: Warning: ignoring some quantifiers % 9.83/2.17 Prover 7: Constructing countermodel ... % 9.83/2.18 Prover 10: Warning: ignoring some quantifiers % 9.83/2.19 Prover 7: stopped % 9.83/2.19 Prover 10: Constructing countermodel ... % 9.83/2.20 Prover 8: Warning: ignoring some quantifiers % 9.83/2.21 Prover 8: Constructing countermodel ... % 9.83/2.21 Prover 10: stopped % 9.83/2.22 Prover 8: stopped % 9.83/2.22 % 9.83/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.83/2.22 % 10.42/2.23 % SZS output start Proof for theBenchmark % 10.42/2.24 Assumptions after simplification: % 10.42/2.24 --------------------------------- % 10.42/2.24 % 10.42/2.24 (equal_set) % 10.42/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 10.42/2.29 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 10.42/2.29 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 10.42/2.29 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 10.42/2.29 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 10.42/2.29 % 10.42/2.29 (singleton) % 10.42/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | % 10.42/2.29 ~ (member(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.42/2.29 $i] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0) | ~ % 10.42/2.29 $i(v1) | ~ $i(v0)) % 10.72/2.29 % 10.72/2.29 (subset) % 10.72/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 10.72/2.30 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 10.72/2.30 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 10.72/2.30 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 10.72/2.30 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 10.72/2.30 % 10.72/2.30 (sum) % 10.72/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (sum(v1) % 10.72/2.31 = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ! [v4: $i] : ( % 10.72/2.31 ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & % 10.72/2.31 member(v4, v1) = v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.72/2.31 (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 10.72/2.31 $i] : (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3))) % 10.72/2.31 % 10.72/2.31 (thI39) % 10.72/2.31 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 10.72/2.31 sum(v1) = v2 & singleton(v0) = v1 & equal_set(v2, v0) = v3 & $i(v2) & $i(v1) % 10.72/2.31 & $i(v0)) % 10.72/2.31 % 10.72/2.31 (function-axioms) % 10.72/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.72/2.33 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 10.72/2.33 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.72/2.33 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 10.72/2.33 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 10.72/2.33 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 10.72/2.33 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 10.72/2.33 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.72/2.33 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 10.72/2.33 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.72/2.33 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 10.72/2.33 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.72/2.33 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.72/2.33 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 10.72/2.33 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 10.72/2.33 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 10.72/2.33 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 10.72/2.33 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 10.72/2.33 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 10.72/2.33 (power_set(v2) = v0)) % 10.72/2.33 % 10.72/2.33 Further assumptions not needed in the proof: % 10.72/2.33 -------------------------------------------- % 10.72/2.33 difference, empty_set, intersection, power_set, product, union, unordered_pair % 10.72/2.33 % 10.72/2.33 Those formulas are unsatisfiable: % 10.72/2.33 --------------------------------- % 10.72/2.33 % 10.72/2.33 Begin of proof % 10.72/2.33 | % 10.72/2.33 | ALPHA: (subset) implies: % 10.72/2.33 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 10.72/2.33 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 10.72/2.33 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 10.72/2.33 | % 10.72/2.33 | ALPHA: (equal_set) implies: % 10.72/2.34 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 10.72/2.34 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 10.72/2.34 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 10.72/2.34 | 0)))) % 10.72/2.34 | % 10.72/2.34 | ALPHA: (singleton) implies: % 10.72/2.34 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1) % 10.72/2.34 | = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 10.72/2.34 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) % 10.72/2.34 | = v1) | ~ (member(v0, v1) = v2) | ~ $i(v0)) % 10.72/2.34 | % 10.72/2.34 | ALPHA: (sum) implies: % 10.72/2.34 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sum(v1) = v2) | ~ % 10.72/2.34 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 10.72/2.34 | (member(v3, v1) = 0 & member(v0, v3) = 0 & $i(v3))) % 10.72/2.35 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.72/2.35 | (sum(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 10.72/2.35 | ! [v4: $i] : ( ~ (member(v0, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( % 10.72/2.35 | ~ (v5 = 0) & member(v4, v1) = v5))) % 10.72/2.35 | % 10.72/2.35 | ALPHA: (function-axioms) implies: % 10.72/2.35 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.72/2.35 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 10.72/2.35 | = v0)) % 10.72/2.35 | % 10.72/2.35 | DELTA: instantiating (thI39) with fresh symbols all_15_0, all_15_1, all_15_2, % 10.72/2.35 | all_15_3 gives: % 10.72/2.35 | (8) ~ (all_15_0 = 0) & sum(all_15_2) = all_15_1 & singleton(all_15_3) = % 10.72/2.35 | all_15_2 & equal_set(all_15_1, all_15_3) = all_15_0 & $i(all_15_1) & % 10.72/2.35 | $i(all_15_2) & $i(all_15_3) % 10.72/2.35 | % 10.72/2.35 | ALPHA: (8) implies: % 10.72/2.35 | (9) ~ (all_15_0 = 0) % 10.72/2.35 | (10) $i(all_15_3) % 10.72/2.35 | (11) $i(all_15_2) % 10.72/2.35 | (12) $i(all_15_1) % 10.72/2.35 | (13) equal_set(all_15_1, all_15_3) = all_15_0 % 10.72/2.35 | (14) singleton(all_15_3) = all_15_2 % 10.72/2.35 | (15) sum(all_15_2) = all_15_1 % 10.72/2.35 | % 10.72/2.36 | GROUND_INST: instantiating (2) with all_15_1, all_15_3, all_15_0, simplifying % 10.72/2.36 | with (10), (12), (13) gives: % 10.72/2.36 | (16) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 10.72/2.36 | all_15_3) = v0 & subset(all_15_3, all_15_1) = v1 & ( ~ (v1 = 0) | % 10.72/2.36 | ~ (v0 = 0))) % 10.72/2.36 | % 10.72/2.36 | BETA: splitting (16) gives: % 10.72/2.36 | % 10.72/2.36 | Case 1: % 10.72/2.36 | | % 10.72/2.36 | | (17) all_15_0 = 0 % 10.72/2.36 | | % 10.72/2.36 | | REDUCE: (9), (17) imply: % 10.72/2.36 | | (18) $false % 10.72/2.36 | | % 10.72/2.36 | | CLOSE: (18) is inconsistent. % 10.72/2.36 | | % 10.72/2.36 | Case 2: % 10.72/2.36 | | % 10.72/2.36 | | (19) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_3) = v0 & % 10.72/2.36 | | subset(all_15_3, all_15_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.72/2.36 | | % 10.72/2.36 | | DELTA: instantiating (19) with fresh symbols all_24_0, all_24_1 gives: % 10.72/2.36 | | (20) subset(all_15_1, all_15_3) = all_24_1 & subset(all_15_3, all_15_1) = % 10.72/2.36 | | all_24_0 & ( ~ (all_24_0 = 0) | ~ (all_24_1 = 0)) % 10.72/2.36 | | % 10.72/2.36 | | ALPHA: (20) implies: % 10.72/2.36 | | (21) subset(all_15_3, all_15_1) = all_24_0 % 10.72/2.36 | | (22) subset(all_15_1, all_15_3) = all_24_1 % 10.72/2.36 | | (23) ~ (all_24_0 = 0) | ~ (all_24_1 = 0) % 10.72/2.36 | | % 10.72/2.37 | | GROUND_INST: instantiating (1) with all_15_3, all_15_1, all_24_0, % 10.72/2.37 | | simplifying with (10), (12), (21) gives: % 10.72/2.37 | | (24) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.72/2.37 | | member(v0, all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 10.72/2.37 | | % 10.72/2.37 | | GROUND_INST: instantiating (1) with all_15_1, all_15_3, all_24_1, % 10.72/2.37 | | simplifying with (10), (12), (22) gives: % 10.72/2.37 | | (25) all_24_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.72/2.37 | | member(v0, all_15_1) = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 10.72/2.37 | | % 10.72/2.37 | | BETA: splitting (23) gives: % 10.72/2.37 | | % 10.72/2.37 | | Case 1: % 10.72/2.37 | | | % 11.09/2.37 | | | (26) ~ (all_24_0 = 0) % 11.09/2.37 | | | % 11.09/2.37 | | | BETA: splitting (24) gives: % 11.09/2.37 | | | % 11.09/2.37 | | | Case 1: % 11.09/2.37 | | | | % 11.09/2.37 | | | | (27) all_24_0 = 0 % 11.09/2.37 | | | | % 11.09/2.37 | | | | REDUCE: (26), (27) imply: % 11.09/2.37 | | | | (28) $false % 11.09/2.37 | | | | % 11.09/2.37 | | | | CLOSE: (28) is inconsistent. % 11.09/2.37 | | | | % 11.09/2.37 | | | Case 2: % 11.09/2.37 | | | | % 11.09/2.37 | | | | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 11.09/2.37 | | | | = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 11.09/2.37 | | | | % 11.09/2.37 | | | | DELTA: instantiating (29) with fresh symbols all_37_0, all_37_1 gives: % 11.10/2.37 | | | | (30) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = all_37_0 & % 11.10/2.37 | | | | member(all_37_1, all_15_3) = 0 & $i(all_37_1) % 11.10/2.37 | | | | % 11.10/2.37 | | | | ALPHA: (30) implies: % 11.10/2.37 | | | | (31) ~ (all_37_0 = 0) % 11.10/2.37 | | | | (32) $i(all_37_1) % 11.10/2.37 | | | | (33) member(all_37_1, all_15_3) = 0 % 11.10/2.37 | | | | (34) member(all_37_1, all_15_1) = all_37_0 % 11.10/2.37 | | | | % 11.10/2.37 | | | | GROUND_INST: instantiating (6) with all_37_1, all_15_2, all_15_1, % 11.10/2.37 | | | | all_37_0, simplifying with (11), (15), (32), (34) gives: % 11.10/2.38 | | | | (35) all_37_0 = 0 | ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ % 11.10/2.38 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) = % 11.10/2.38 | | | | v1)) % 11.10/2.38 | | | | % 11.10/2.38 | | | | BETA: splitting (35) gives: % 11.10/2.38 | | | | % 11.10/2.38 | | | | Case 1: % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | (36) all_37_0 = 0 % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | REDUCE: (31), (36) imply: % 11.10/2.38 | | | | | (37) $false % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | CLOSE: (37) is inconsistent. % 11.10/2.38 | | | | | % 11.10/2.38 | | | | Case 2: % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | (38) ! [v0: $i] : ( ~ (member(all_37_1, v0) = 0) | ~ $i(v0) | ? % 11.10/2.38 | | | | | [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) = v1)) % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | GROUND_INST: instantiating (38) with all_15_3, simplifying with (10), % 11.10/2.38 | | | | | (33) gives: % 11.10/2.38 | | | | | (39) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_3, all_15_2) = v0) % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | DELTA: instantiating (39) with fresh symbol all_53_0 gives: % 11.10/2.38 | | | | | (40) ~ (all_53_0 = 0) & member(all_15_3, all_15_2) = all_53_0 % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | ALPHA: (40) implies: % 11.10/2.38 | | | | | (41) ~ (all_53_0 = 0) % 11.10/2.38 | | | | | (42) member(all_15_3, all_15_2) = all_53_0 % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | GROUND_INST: instantiating (4) with all_15_3, all_15_2, all_53_0, % 11.10/2.38 | | | | | simplifying with (10), (14), (42) gives: % 11.10/2.38 | | | | | (43) all_53_0 = 0 % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | REDUCE: (41), (43) imply: % 11.10/2.38 | | | | | (44) $false % 11.10/2.38 | | | | | % 11.10/2.38 | | | | | CLOSE: (44) is inconsistent. % 11.10/2.38 | | | | | % 11.10/2.38 | | | | End of split % 11.10/2.38 | | | | % 11.10/2.38 | | | End of split % 11.10/2.38 | | | % 11.10/2.38 | | Case 2: % 11.10/2.38 | | | % 11.10/2.38 | | | (45) ~ (all_24_1 = 0) % 11.10/2.38 | | | % 11.10/2.38 | | | BETA: splitting (25) gives: % 11.10/2.38 | | | % 11.10/2.38 | | | Case 1: % 11.10/2.38 | | | | % 11.10/2.38 | | | | (46) all_24_1 = 0 % 11.10/2.38 | | | | % 11.10/2.38 | | | | REDUCE: (45), (46) imply: % 11.10/2.38 | | | | (47) $false % 11.10/2.38 | | | | % 11.10/2.38 | | | | CLOSE: (47) is inconsistent. % 11.10/2.38 | | | | % 11.10/2.38 | | | Case 2: % 11.10/2.38 | | | | % 11.10/2.39 | | | | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 11.10/2.39 | | | | = 0 & member(v0, all_15_3) = v1 & $i(v0)) % 11.10/2.39 | | | | % 11.10/2.39 | | | | DELTA: instantiating (48) with fresh symbols all_37_0, all_37_1 gives: % 11.10/2.39 | | | | (49) ~ (all_37_0 = 0) & member(all_37_1, all_15_1) = 0 & % 11.10/2.39 | | | | member(all_37_1, all_15_3) = all_37_0 & $i(all_37_1) % 11.10/2.39 | | | | % 11.10/2.39 | | | | ALPHA: (49) implies: % 11.10/2.39 | | | | (50) ~ (all_37_0 = 0) % 11.10/2.39 | | | | (51) $i(all_37_1) % 11.10/2.39 | | | | (52) member(all_37_1, all_15_3) = all_37_0 % 11.10/2.39 | | | | (53) member(all_37_1, all_15_1) = 0 % 11.10/2.39 | | | | % 11.10/2.39 | | | | GROUND_INST: instantiating (5) with all_37_1, all_15_2, all_15_1, % 11.10/2.39 | | | | simplifying with (11), (15), (51), (53) gives: % 11.10/2.39 | | | | (54) ? [v0: $i] : (member(v0, all_15_2) = 0 & member(all_37_1, v0) = % 11.10/2.39 | | | | 0 & $i(v0)) % 11.10/2.39 | | | | % 11.10/2.39 | | | | DELTA: instantiating (54) with fresh symbol all_45_0 gives: % 11.10/2.39 | | | | (55) member(all_45_0, all_15_2) = 0 & member(all_37_1, all_45_0) = 0 % 11.10/2.39 | | | | & $i(all_45_0) % 11.10/2.39 | | | | % 11.10/2.39 | | | | ALPHA: (55) implies: % 11.10/2.39 | | | | (56) $i(all_45_0) % 11.10/2.39 | | | | (57) member(all_37_1, all_45_0) = 0 % 11.10/2.39 | | | | (58) member(all_45_0, all_15_2) = 0 % 11.10/2.39 | | | | % 11.10/2.39 | | | | GROUND_INST: instantiating (3) with all_45_0, all_15_3, all_15_2, % 11.10/2.39 | | | | simplifying with (10), (14), (56), (58) gives: % 11.10/2.39 | | | | (59) all_45_0 = all_15_3 % 11.10/2.39 | | | | % 11.10/2.40 | | | | REDUCE: (57), (59) imply: % 11.10/2.40 | | | | (60) member(all_37_1, all_15_3) = 0 % 11.10/2.40 | | | | % 11.10/2.40 | | | | GROUND_INST: instantiating (7) with all_37_0, 0, all_15_3, all_37_1, % 11.10/2.40 | | | | simplifying with (52), (60) gives: % 11.10/2.40 | | | | (61) all_37_0 = 0 % 11.10/2.40 | | | | % 11.10/2.40 | | | | REDUCE: (50), (61) imply: % 11.10/2.40 | | | | (62) $false % 11.10/2.40 | | | | % 11.10/2.40 | | | | CLOSE: (62) is inconsistent. % 11.10/2.40 | | | | % 11.10/2.40 | | | End of split % 11.10/2.40 | | | % 11.10/2.40 | | End of split % 11.10/2.40 | | % 11.10/2.40 | End of split % 11.10/2.40 | % 11.10/2.40 End of proof % 11.10/2.40 % SZS output end Proof for theBenchmark % 11.10/2.40 % 11.10/2.40 1783ms %------------------------------------------------------------------------------