%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET199+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 : n026.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 15:24:16 EDT 2023 % Result : Theorem 7.16s 1.76s % Output : Proof 8.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET199+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n026.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Sat Aug 26 10:28:33 EDT 2023 % 0.14/0.35 % 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 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.34/1.08 Prover 4: Preprocessing ... % 2.34/1.08 Prover 1: Preprocessing ... % 2.76/1.12 Prover 5: Preprocessing ... % 2.76/1.12 Prover 2: Preprocessing ... % 2.76/1.12 Prover 3: Preprocessing ... % 2.76/1.12 Prover 6: Preprocessing ... % 2.76/1.12 Prover 0: Preprocessing ... % 5.12/1.52 Prover 6: Proving ... % 5.12/1.53 Prover 3: Constructing countermodel ... % 5.12/1.53 Prover 5: Proving ... % 5.12/1.53 Prover 1: Constructing countermodel ... % 5.12/1.54 Prover 2: Proving ... % 5.12/1.56 Prover 4: Constructing countermodel ... % 5.12/1.56 Prover 0: Proving ... % 7.16/1.76 Prover 3: proved (1117ms) % 7.16/1.76 % 7.16/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.16/1.76 % 7.16/1.76 Prover 6: stopped % 7.16/1.76 Prover 5: stopped % 7.16/1.76 Prover 0: stopped % 7.41/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.41/1.77 Prover 2: stopped % 7.41/1.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.41/1.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.41/1.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.41/1.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.41/1.81 Prover 13: Preprocessing ... % 7.41/1.82 Prover 10: Preprocessing ... % 7.41/1.82 Prover 11: Preprocessing ... % 7.41/1.82 Prover 7: Preprocessing ... % 7.41/1.83 Prover 8: Preprocessing ... % 7.90/1.83 Prover 1: Found proof (size 60) % 7.90/1.83 Prover 1: proved (1196ms) % 7.90/1.83 Prover 4: stopped % 7.90/1.83 Prover 10: stopped % 7.90/1.84 Prover 7: stopped % 7.90/1.86 Prover 11: stopped % 7.90/1.86 Prover 13: stopped % 8.10/1.90 Prover 8: Warning: ignoring some quantifiers % 8.10/1.91 Prover 8: Constructing countermodel ... % 8.10/1.92 Prover 8: stopped % 8.10/1.92 % 8.10/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.10/1.92 % 8.43/1.93 % SZS output start Proof for theBenchmark % 8.43/1.93 Assumptions after simplification: % 8.43/1.93 --------------------------------- % 8.43/1.93 % 8.43/1.93 (intersection) % 8.59/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.59/1.97 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 8.59/1.97 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 8.59/1.97 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 8.59/1.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 8.59/1.97 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 8.59/1.97 0 & member(v0, v1) = 0)) % 8.59/1.97 % 8.59/1.97 (subset) % 8.59/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.59/1.97 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.59/1.97 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.59/1.97 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.59/1.97 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.59/1.97 % 8.59/1.97 (thI46) % 8.59/1.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : ? % 8.59/1.98 [v5: $i] : ? [v6: any] : (intersection(v1, v2) = v5 & subset(v0, v5) = v6 & % 8.59/1.98 subset(v0, v2) = v4 & subset(v0, v1) = v3 & $i(v5) & $i(v2) & $i(v1) & % 8.59/1.98 $i(v0) & ((v6 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (v4 = 0 & v3 = 0 & ~ (v6 % 8.59/1.98 = 0)))) % 8.59/1.98 % 8.59/1.98 (function-axioms) % 8.59/1.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.59/1.99 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.59/1.99 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.59/1.99 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.59/1.99 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.59/1.99 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.59/1.99 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.59/1.99 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.59/1.99 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.59/1.99 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.59/1.99 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.59/1.99 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.59/1.99 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.59/1.99 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.59/1.99 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.59/1.99 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.59/1.99 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.59/1.99 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.59/1.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.59/1.99 (power_set(v2) = v0)) % 8.59/1.99 % 8.59/1.99 Further assumptions not needed in the proof: % 8.59/1.99 -------------------------------------------- % 8.59/1.99 difference, empty_set, equal_set, power_set, product, singleton, sum, union, % 8.59/1.99 unordered_pair % 8.59/1.99 % 8.59/1.99 Those formulas are unsatisfiable: % 8.59/1.99 --------------------------------- % 8.59/1.99 % 8.59/1.99 Begin of proof % 8.59/1.99 | % 8.59/1.99 | ALPHA: (subset) implies: % 8.59/1.99 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 8.59/1.99 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 8.59/1.99 | member(v2, v1) = 0)) % 8.59/2.00 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.59/2.00 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.59/2.00 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.59/2.00 | % 8.59/2.00 | ALPHA: (intersection) implies: % 8.59/2.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.59/2.00 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 8.59/2.00 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 8.59/2.00 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 8.59/2.00 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 8.59/2.00 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 8.59/2.00 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 8.59/2.00 | 0)))) % 8.59/2.00 | % 8.59/2.00 | ALPHA: (function-axioms) implies: % 8.59/2.00 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.59/2.00 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 8.59/2.00 | = v0)) % 8.59/2.00 | % 8.59/2.00 | DELTA: instantiating (thI46) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.59/2.00 | all_15_3, all_15_4, all_15_5, all_15_6 gives: % 8.59/2.00 | (6) intersection(all_15_5, all_15_4) = all_15_1 & subset(all_15_6, % 8.59/2.00 | all_15_1) = all_15_0 & subset(all_15_6, all_15_4) = all_15_2 & % 8.59/2.00 | subset(all_15_6, all_15_5) = all_15_3 & $i(all_15_1) & $i(all_15_4) & % 8.59/2.00 | $i(all_15_5) & $i(all_15_6) & ((all_15_0 = 0 & ( ~ (all_15_2 = 0) | ~ % 8.59/2.00 | (all_15_3 = 0))) | (all_15_2 = 0 & all_15_3 = 0 & ~ (all_15_0 = % 8.59/2.00 | 0))) % 8.59/2.00 | % 8.59/2.00 | ALPHA: (6) implies: % 8.59/2.00 | (7) $i(all_15_6) % 8.59/2.00 | (8) $i(all_15_5) % 8.59/2.00 | (9) $i(all_15_4) % 8.59/2.00 | (10) $i(all_15_1) % 8.59/2.00 | (11) subset(all_15_6, all_15_5) = all_15_3 % 8.59/2.01 | (12) subset(all_15_6, all_15_4) = all_15_2 % 8.59/2.01 | (13) subset(all_15_6, all_15_1) = all_15_0 % 8.59/2.01 | (14) intersection(all_15_5, all_15_4) = all_15_1 % 8.59/2.01 | (15) (all_15_0 = 0 & ( ~ (all_15_2 = 0) | ~ (all_15_3 = 0))) | (all_15_2 = % 8.59/2.01 | 0 & all_15_3 = 0 & ~ (all_15_0 = 0)) % 8.59/2.01 | % 8.59/2.01 | GROUND_INST: instantiating (2) with all_15_6, all_15_5, all_15_3, simplifying % 8.59/2.01 | with (7), (8), (11) gives: % 8.59/2.01 | (16) all_15_3 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.59/2.01 | all_15_5) = v1 & member(v0, all_15_6) = 0 & $i(v0)) % 8.59/2.01 | % 8.59/2.01 | GROUND_INST: instantiating (2) with all_15_6, all_15_4, all_15_2, simplifying % 8.59/2.01 | with (7), (9), (12) gives: % 8.59/2.01 | (17) all_15_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.59/2.01 | all_15_4) = v1 & member(v0, all_15_6) = 0 & $i(v0)) % 8.59/2.01 | % 8.59/2.01 | GROUND_INST: instantiating (2) with all_15_6, all_15_1, all_15_0, simplifying % 8.59/2.01 | with (7), (10), (13) gives: % 8.59/2.01 | (18) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.59/2.01 | all_15_1) = v1 & member(v0, all_15_6) = 0 & $i(v0)) % 8.59/2.01 | % 8.59/2.01 | BETA: splitting (15) gives: % 8.59/2.01 | % 8.59/2.01 | Case 1: % 8.59/2.01 | | % 8.59/2.01 | | (19) all_15_0 = 0 & ( ~ (all_15_2 = 0) | ~ (all_15_3 = 0)) % 8.59/2.01 | | % 8.59/2.01 | | ALPHA: (19) implies: % 8.59/2.01 | | (20) all_15_0 = 0 % 8.59/2.01 | | (21) ~ (all_15_2 = 0) | ~ (all_15_3 = 0) % 8.59/2.01 | | % 8.59/2.01 | | REDUCE: (13), (20) imply: % 8.59/2.01 | | (22) subset(all_15_6, all_15_1) = 0 % 8.59/2.01 | | % 8.59/2.01 | | GROUND_INST: instantiating (1) with all_15_6, all_15_1, simplifying with % 8.59/2.01 | | (7), (10), (22) gives: % 8.59/2.01 | | (23) ! [v0: $i] : ( ~ (member(v0, all_15_6) = 0) | ~ $i(v0) | % 8.59/2.01 | | member(v0, all_15_1) = 0) % 8.59/2.01 | | % 8.59/2.01 | | BETA: splitting (17) gives: % 8.59/2.01 | | % 8.59/2.01 | | Case 1: % 8.59/2.01 | | | % 8.59/2.01 | | | (24) all_15_2 = 0 % 8.59/2.01 | | | % 8.59/2.01 | | | BETA: splitting (21) gives: % 8.59/2.01 | | | % 8.59/2.01 | | | Case 1: % 8.59/2.01 | | | | % 8.59/2.01 | | | | (25) ~ (all_15_2 = 0) % 8.59/2.01 | | | | % 8.59/2.01 | | | | REDUCE: (24), (25) imply: % 8.59/2.01 | | | | (26) $false % 8.59/2.02 | | | | % 8.59/2.02 | | | | CLOSE: (26) is inconsistent. % 8.59/2.02 | | | | % 8.59/2.02 | | | Case 2: % 8.59/2.02 | | | | % 8.59/2.02 | | | | (27) ~ (all_15_3 = 0) % 8.59/2.02 | | | | % 8.59/2.02 | | | | BETA: splitting (16) gives: % 8.59/2.02 | | | | % 8.59/2.02 | | | | Case 1: % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | (28) all_15_3 = 0 % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | REDUCE: (27), (28) imply: % 8.59/2.02 | | | | | (29) $false % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | CLOSE: (29) is inconsistent. % 8.59/2.02 | | | | | % 8.59/2.02 | | | | Case 2: % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | (30) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.59/2.02 | | | | | all_15_5) = v1 & member(v0, all_15_6) = 0 & $i(v0)) % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | DELTA: instantiating (30) with fresh symbols all_42_0, all_42_1 gives: % 8.59/2.02 | | | | | (31) ~ (all_42_0 = 0) & member(all_42_1, all_15_5) = all_42_0 & % 8.59/2.02 | | | | | member(all_42_1, all_15_6) = 0 & $i(all_42_1) % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | ALPHA: (31) implies: % 8.59/2.02 | | | | | (32) ~ (all_42_0 = 0) % 8.59/2.02 | | | | | (33) $i(all_42_1) % 8.59/2.02 | | | | | (34) member(all_42_1, all_15_6) = 0 % 8.59/2.02 | | | | | (35) member(all_42_1, all_15_5) = all_42_0 % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | GROUND_INST: instantiating (23) with all_42_1, simplifying with (33), % 8.59/2.02 | | | | | (34) gives: % 8.59/2.02 | | | | | (36) member(all_42_1, all_15_1) = 0 % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | GROUND_INST: instantiating (3) with all_42_1, all_15_5, all_15_4, % 8.59/2.02 | | | | | all_15_1, simplifying with (8), (9), (14), (33), (36) % 8.59/2.02 | | | | | gives: % 8.59/2.02 | | | | | (37) member(all_42_1, all_15_4) = 0 & member(all_42_1, all_15_5) = % 8.59/2.02 | | | | | 0 % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | ALPHA: (37) implies: % 8.59/2.02 | | | | | (38) member(all_42_1, all_15_5) = 0 % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | GROUND_INST: instantiating (5) with all_42_0, 0, all_15_5, all_42_1, % 8.59/2.02 | | | | | simplifying with (35), (38) gives: % 8.59/2.02 | | | | | (39) all_42_0 = 0 % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | REDUCE: (32), (39) imply: % 8.59/2.02 | | | | | (40) $false % 8.59/2.02 | | | | | % 8.59/2.02 | | | | | CLOSE: (40) is inconsistent. % 8.59/2.02 | | | | | % 8.59/2.02 | | | | End of split % 8.59/2.02 | | | | % 8.59/2.02 | | | End of split % 8.59/2.02 | | | % 8.59/2.02 | | Case 2: % 8.59/2.02 | | | % 8.59/2.02 | | | (41) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_4) = % 8.59/2.02 | | | v1 & member(v0, all_15_6) = 0 & $i(v0)) % 8.59/2.02 | | | % 8.59/2.02 | | | DELTA: instantiating (41) with fresh symbols all_34_0, all_34_1 gives: % 8.59/2.02 | | | (42) ~ (all_34_0 = 0) & member(all_34_1, all_15_4) = all_34_0 & % 8.59/2.02 | | | member(all_34_1, all_15_6) = 0 & $i(all_34_1) % 8.59/2.02 | | | % 8.59/2.02 | | | ALPHA: (42) implies: % 8.59/2.02 | | | (43) ~ (all_34_0 = 0) % 8.59/2.02 | | | (44) $i(all_34_1) % 8.59/2.03 | | | (45) member(all_34_1, all_15_6) = 0 % 8.59/2.03 | | | (46) member(all_34_1, all_15_4) = all_34_0 % 8.59/2.03 | | | % 8.59/2.03 | | | GROUND_INST: instantiating (23) with all_34_1, simplifying with (44), (45) % 8.59/2.03 | | | gives: % 8.59/2.03 | | | (47) member(all_34_1, all_15_1) = 0 % 8.59/2.03 | | | % 8.59/2.03 | | | GROUND_INST: instantiating (3) with all_34_1, all_15_5, all_15_4, % 8.59/2.03 | | | all_15_1, simplifying with (8), (9), (14), (44), (47) gives: % 8.59/2.03 | | | (48) member(all_34_1, all_15_4) = 0 & member(all_34_1, all_15_5) = 0 % 8.59/2.03 | | | % 8.59/2.03 | | | ALPHA: (48) implies: % 8.59/2.03 | | | (49) member(all_34_1, all_15_4) = 0 % 8.59/2.03 | | | % 8.59/2.03 | | | GROUND_INST: instantiating (5) with all_34_0, 0, all_15_4, all_34_1, % 8.59/2.03 | | | simplifying with (46), (49) gives: % 8.59/2.03 | | | (50) all_34_0 = 0 % 8.59/2.03 | | | % 8.59/2.03 | | | REDUCE: (43), (50) imply: % 8.59/2.03 | | | (51) $false % 8.59/2.03 | | | % 8.59/2.03 | | | CLOSE: (51) is inconsistent. % 8.59/2.03 | | | % 8.59/2.03 | | End of split % 8.59/2.03 | | % 8.59/2.03 | Case 2: % 8.59/2.03 | | % 8.59/2.03 | | (52) all_15_2 = 0 & all_15_3 = 0 & ~ (all_15_0 = 0) % 8.59/2.03 | | % 8.59/2.03 | | ALPHA: (52) implies: % 8.59/2.03 | | (53) all_15_3 = 0 % 8.59/2.03 | | (54) all_15_2 = 0 % 8.59/2.03 | | (55) ~ (all_15_0 = 0) % 8.59/2.03 | | % 8.59/2.03 | | REDUCE: (12), (54) imply: % 8.59/2.03 | | (56) subset(all_15_6, all_15_4) = 0 % 8.59/2.03 | | % 8.59/2.03 | | REDUCE: (11), (53) imply: % 8.59/2.03 | | (57) subset(all_15_6, all_15_5) = 0 % 8.59/2.03 | | % 8.59/2.03 | | BETA: splitting (18) gives: % 8.59/2.03 | | % 8.59/2.03 | | Case 1: % 8.94/2.03 | | | % 8.94/2.03 | | | (58) all_15_0 = 0 % 8.94/2.03 | | | % 8.94/2.03 | | | REDUCE: (55), (58) imply: % 8.94/2.03 | | | (59) $false % 8.94/2.03 | | | % 8.94/2.03 | | | CLOSE: (59) is inconsistent. % 8.94/2.03 | | | % 8.94/2.03 | | Case 2: % 8.94/2.03 | | | % 8.94/2.03 | | | (60) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) = % 8.94/2.03 | | | v1 & member(v0, all_15_6) = 0 & $i(v0)) % 8.94/2.03 | | | % 8.94/2.03 | | | DELTA: instantiating (60) with fresh symbols all_28_0, all_28_1 gives: % 8.94/2.03 | | | (61) ~ (all_28_0 = 0) & member(all_28_1, all_15_1) = all_28_0 & % 8.94/2.03 | | | member(all_28_1, all_15_6) = 0 & $i(all_28_1) % 8.94/2.03 | | | % 8.94/2.03 | | | ALPHA: (61) implies: % 8.94/2.03 | | | (62) ~ (all_28_0 = 0) % 8.94/2.03 | | | (63) $i(all_28_1) % 8.94/2.03 | | | (64) member(all_28_1, all_15_6) = 0 % 8.94/2.03 | | | (65) member(all_28_1, all_15_1) = all_28_0 % 8.94/2.03 | | | % 8.94/2.03 | | | GROUND_INST: instantiating (4) with all_28_1, all_15_5, all_15_4, % 8.94/2.03 | | | all_15_1, all_28_0, simplifying with (8), (9), (14), (63), % 8.94/2.03 | | | (65) gives: % 8.94/2.04 | | | (66) all_28_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_28_1, % 8.94/2.04 | | | all_15_4) = v1 & member(all_28_1, all_15_5) = v0 & ( ~ (v1 = % 8.94/2.04 | | | 0) | ~ (v0 = 0))) % 8.94/2.04 | | | % 8.94/2.04 | | | GROUND_INST: instantiating (1) with all_15_6, all_15_5, simplifying with % 8.94/2.04 | | | (7), (8), (57) gives: % 8.94/2.04 | | | (67) ! [v0: $i] : ( ~ (member(v0, all_15_6) = 0) | ~ $i(v0) | % 8.94/2.04 | | | member(v0, all_15_5) = 0) % 8.94/2.04 | | | % 8.94/2.04 | | | GROUND_INST: instantiating (1) with all_15_6, all_15_4, simplifying with % 8.94/2.04 | | | (7), (9), (56) gives: % 8.94/2.04 | | | (68) ! [v0: $i] : ( ~ (member(v0, all_15_6) = 0) | ~ $i(v0) | % 8.94/2.04 | | | member(v0, all_15_4) = 0) % 8.94/2.04 | | | % 8.94/2.04 | | | GROUND_INST: instantiating (68) with all_28_1, simplifying with (63), (64) % 8.94/2.04 | | | gives: % 8.94/2.04 | | | (69) member(all_28_1, all_15_4) = 0 % 8.94/2.04 | | | % 8.94/2.04 | | | GROUND_INST: instantiating (67) with all_28_1, simplifying with (63), (64) % 8.94/2.04 | | | gives: % 8.94/2.04 | | | (70) member(all_28_1, all_15_5) = 0 % 8.94/2.04 | | | % 8.94/2.04 | | | BETA: splitting (66) gives: % 8.94/2.04 | | | % 8.94/2.04 | | | Case 1: % 8.94/2.04 | | | | % 8.94/2.04 | | | | (71) all_28_0 = 0 % 8.94/2.04 | | | | % 8.94/2.04 | | | | REDUCE: (62), (71) imply: % 8.94/2.04 | | | | (72) $false % 8.94/2.04 | | | | % 8.94/2.04 | | | | CLOSE: (72) is inconsistent. % 8.94/2.04 | | | | % 8.94/2.04 | | | Case 2: % 8.94/2.04 | | | | % 8.94/2.04 | | | | (73) ? [v0: any] : ? [v1: any] : (member(all_28_1, all_15_4) = v1 & % 8.94/2.04 | | | | member(all_28_1, all_15_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 8.94/2.04 | | | | % 8.94/2.04 | | | | DELTA: instantiating (73) with fresh symbols all_43_0, all_43_1 gives: % 8.94/2.04 | | | | (74) member(all_28_1, all_15_4) = all_43_0 & member(all_28_1, % 8.94/2.04 | | | | all_15_5) = all_43_1 & ( ~ (all_43_0 = 0) | ~ (all_43_1 = 0)) % 8.94/2.04 | | | | % 8.94/2.04 | | | | ALPHA: (74) implies: % 8.94/2.04 | | | | (75) member(all_28_1, all_15_5) = all_43_1 % 8.94/2.04 | | | | (76) member(all_28_1, all_15_4) = all_43_0 % 8.94/2.04 | | | | (77) ~ (all_43_0 = 0) | ~ (all_43_1 = 0) % 8.94/2.04 | | | | % 8.94/2.04 | | | | GROUND_INST: instantiating (5) with 0, all_43_1, all_15_5, all_28_1, % 8.94/2.04 | | | | simplifying with (70), (75) gives: % 8.94/2.04 | | | | (78) all_43_1 = 0 % 8.94/2.04 | | | | % 8.94/2.04 | | | | GROUND_INST: instantiating (5) with 0, all_43_0, all_15_4, all_28_1, % 8.94/2.04 | | | | simplifying with (69), (76) gives: % 8.94/2.04 | | | | (79) all_43_0 = 0 % 8.94/2.04 | | | | % 8.94/2.04 | | | | BETA: splitting (77) gives: % 8.94/2.04 | | | | % 8.94/2.04 | | | | Case 1: % 8.94/2.04 | | | | | % 8.94/2.04 | | | | | (80) ~ (all_43_0 = 0) % 8.94/2.04 | | | | | % 8.94/2.04 | | | | | REDUCE: (79), (80) imply: % 8.94/2.04 | | | | | (81) $false % 8.94/2.04 | | | | | % 8.94/2.04 | | | | | CLOSE: (81) is inconsistent. % 8.94/2.04 | | | | | % 8.94/2.04 | | | | Case 2: % 8.94/2.04 | | | | | % 8.94/2.04 | | | | | (82) ~ (all_43_1 = 0) % 8.94/2.04 | | | | | % 8.94/2.04 | | | | | REDUCE: (78), (82) imply: % 8.94/2.04 | | | | | (83) $false % 8.94/2.04 | | | | | % 8.94/2.04 | | | | | CLOSE: (83) is inconsistent. % 8.94/2.04 | | | | | % 8.94/2.04 | | | | End of split % 8.94/2.04 | | | | % 8.94/2.04 | | | End of split % 8.94/2.05 | | | % 8.94/2.05 | | End of split % 8.94/2.05 | | % 8.94/2.05 | End of split % 8.94/2.05 | % 8.94/2.05 End of proof % 8.94/2.05 % SZS output end Proof for theBenchmark % 8.94/2.05 % 8.94/2.05 1431ms %------------------------------------------------------------------------------