%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET702+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 15:26:03 EDT 2023 % Result : Theorem 6.62s 1.66s % Output : Proof 8.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET702+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n026.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 08:33:18 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 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 % 2.65/1.08 Prover 1: Preprocessing ... % 2.65/1.08 Prover 4: Preprocessing ... % 2.65/1.12 Prover 3: Preprocessing ... % 2.65/1.12 Prover 0: Preprocessing ... % 2.65/1.12 Prover 6: Preprocessing ... % 2.65/1.12 Prover 2: Preprocessing ... % 2.65/1.12 Prover 5: Preprocessing ... % 4.74/1.45 Prover 6: Proving ... % 4.74/1.45 Prover 5: Proving ... % 4.74/1.47 Prover 1: Constructing countermodel ... % 4.74/1.48 Prover 3: Constructing countermodel ... % 4.74/1.49 Prover 4: Constructing countermodel ... % 4.74/1.50 Prover 2: Proving ... % 4.74/1.51 Prover 0: Proving ... % 6.62/1.66 Prover 3: proved (1016ms) % 6.62/1.66 % 6.62/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.62/1.66 % 6.62/1.66 Prover 5: stopped % 6.62/1.66 Prover 6: stopped % 6.62/1.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.62/1.67 Prover 0: stopped % 6.62/1.67 Prover 2: stopped % 6.62/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.62/1.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.62/1.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.62/1.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.62/1.70 Prover 7: Preprocessing ... % 6.62/1.71 Prover 13: Preprocessing ... % 6.62/1.71 Prover 11: Preprocessing ... % 6.62/1.72 Prover 10: Preprocessing ... % 6.62/1.72 Prover 8: Preprocessing ... % 7.22/1.75 Prover 1: Found proof (size 33) % 7.22/1.75 Prover 1: proved (1107ms) % 7.22/1.75 Prover 4: stopped % 7.22/1.75 Prover 13: stopped % 7.22/1.76 Prover 11: stopped % 7.22/1.76 Prover 7: Warning: ignoring some quantifiers % 7.22/1.77 Prover 7: Constructing countermodel ... % 7.22/1.77 Prover 10: Warning: ignoring some quantifiers % 7.63/1.78 Prover 7: stopped % 7.63/1.78 Prover 10: Constructing countermodel ... % 7.63/1.79 Prover 10: stopped % 7.63/1.81 Prover 8: Warning: ignoring some quantifiers % 7.63/1.82 Prover 8: Constructing countermodel ... % 7.63/1.82 Prover 8: stopped % 7.63/1.82 % 7.63/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.63/1.82 % 7.63/1.83 % SZS output start Proof for theBenchmark % 7.63/1.83 Assumptions after simplification: % 7.63/1.83 --------------------------------- % 7.63/1.83 % 7.63/1.83 (intersection) % 8.01/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.01/1.86 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 8.01/1.86 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 8.01/1.86 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 8.01/1.86 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 8.01/1.86 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 8.01/1.86 0 & member(v0, v1) = 0)) % 8.01/1.86 % 8.01/1.86 (product) % 8.01/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.01/1.87 (product(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 8.01/1.87 [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) % 8.01/1.87 = v5 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 8.01/1.87 (product(v1) = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ! % 8.01/1.87 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (member(v0, v3) = v4) | ~ $i(v3) | % 8.01/1.87 ? [v5: int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 8.01/1.87 % 8.01/1.87 (subset) % 8.01/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 8.01/1.87 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 8.01/1.87 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 8.01/1.87 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 8.01/1.87 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 8.01/1.87 % 8.01/1.87 (thI36) % 8.01/1.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 8.01/1.87 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & product(v5) = v6 & % 8.01/1.87 product(v1) = v3 & product(v0) = v2 & intersection(v2, v3) = v4 & % 8.01/1.87 intersection(v0, v1) = v5 & subset(v4, v6) = v7 & $i(v6) & $i(v5) & $i(v4) & % 8.01/1.87 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.01/1.87 % 8.01/1.87 (function-axioms) % 8.12/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.12/1.88 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 8.12/1.88 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.12/1.88 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 8.12/1.88 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 8.12/1.88 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.12/1.88 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 8.12/1.88 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 8.12/1.88 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 8.12/1.88 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.12/1.88 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 8.12/1.88 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 8.12/1.88 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.12/1.88 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 8.12/1.88 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 8.12/1.88 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 8.12/1.88 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 8.12/1.88 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 8.12/1.88 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 8.12/1.88 (power_set(v2) = v0)) % 8.12/1.88 % 8.12/1.88 Further assumptions not needed in the proof: % 8.12/1.88 -------------------------------------------- % 8.12/1.88 difference, empty_set, equal_set, power_set, singleton, sum, union, % 8.12/1.88 unordered_pair % 8.12/1.88 % 8.12/1.88 Those formulas are unsatisfiable: % 8.12/1.88 --------------------------------- % 8.12/1.88 % 8.12/1.88 Begin of proof % 8.12/1.88 | % 8.12/1.88 | ALPHA: (subset) implies: % 8.12/1.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.12/1.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.12/1.88 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 8.12/1.88 | % 8.12/1.88 | ALPHA: (intersection) implies: % 8.12/1.88 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.12/1.88 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 8.12/1.88 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 8.12/1.88 | % 8.12/1.88 | ALPHA: (product) implies: % 8.12/1.89 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (product(v1) = v2) | ~ % 8.12/1.89 | (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: % 8.12/1.89 | int] : (v4 = 0 | ~ (member(v0, v3) = v4) | ~ $i(v3) | ? [v5: % 8.12/1.89 | int] : ( ~ (v5 = 0) & member(v3, v1) = v5))) % 8.12/1.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.12/1.89 | (product(v1) = v2) | ~ (member(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) % 8.12/1.89 | | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & member(v4, v1) = 0 & % 8.12/1.89 | member(v0, v4) = v5 & $i(v4))) % 8.12/1.89 | % 8.12/1.89 | ALPHA: (function-axioms) implies: % 8.12/1.89 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.12/1.89 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 8.12/1.89 | = v0)) % 8.12/1.89 | % 8.12/1.89 | DELTA: instantiating (thI36) with fresh symbols all_15_0, all_15_1, all_15_2, % 8.12/1.89 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7 gives: % 8.12/1.89 | (6) ~ (all_15_0 = 0) & product(all_15_2) = all_15_1 & product(all_15_6) = % 8.12/1.89 | all_15_4 & product(all_15_7) = all_15_5 & intersection(all_15_5, % 8.12/1.89 | all_15_4) = all_15_3 & intersection(all_15_7, all_15_6) = all_15_2 & % 8.12/1.89 | subset(all_15_3, all_15_1) = all_15_0 & $i(all_15_1) & $i(all_15_2) & % 8.12/1.89 | $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & % 8.12/1.89 | $i(all_15_7) % 8.12/1.89 | % 8.12/1.89 | ALPHA: (6) implies: % 8.12/1.89 | (7) ~ (all_15_0 = 0) % 8.12/1.89 | (8) $i(all_15_7) % 8.12/1.89 | (9) $i(all_15_6) % 8.12/1.89 | (10) $i(all_15_5) % 8.12/1.89 | (11) $i(all_15_4) % 8.12/1.89 | (12) $i(all_15_3) % 8.12/1.89 | (13) $i(all_15_2) % 8.12/1.89 | (14) $i(all_15_1) % 8.12/1.89 | (15) subset(all_15_3, all_15_1) = all_15_0 % 8.12/1.89 | (16) intersection(all_15_7, all_15_6) = all_15_2 % 8.12/1.89 | (17) intersection(all_15_5, all_15_4) = all_15_3 % 8.12/1.89 | (18) product(all_15_7) = all_15_5 % 8.12/1.89 | (19) product(all_15_2) = all_15_1 % 8.12/1.89 | % 8.12/1.89 | GROUND_INST: instantiating (1) with all_15_3, all_15_1, all_15_0, simplifying % 8.12/1.89 | with (12), (14), (15) gives: % 8.12/1.89 | (20) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 8.12/1.89 | all_15_1) = v1 & member(v0, all_15_3) = 0 & $i(v0)) % 8.12/1.89 | % 8.12/1.89 | BETA: splitting (20) gives: % 8.12/1.89 | % 8.12/1.90 | Case 1: % 8.12/1.90 | | % 8.12/1.90 | | (21) all_15_0 = 0 % 8.12/1.90 | | % 8.12/1.90 | | REDUCE: (7), (21) imply: % 8.12/1.90 | | (22) $false % 8.12/1.90 | | % 8.12/1.90 | | CLOSE: (22) is inconsistent. % 8.12/1.90 | | % 8.12/1.90 | Case 2: % 8.12/1.90 | | % 8.12/1.90 | | (23) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) = % 8.12/1.90 | | v1 & member(v0, all_15_3) = 0 & $i(v0)) % 8.12/1.90 | | % 8.12/1.90 | | DELTA: instantiating (23) with fresh symbols all_24_0, all_24_1 gives: % 8.12/1.90 | | (24) ~ (all_24_0 = 0) & member(all_24_1, all_15_1) = all_24_0 & % 8.12/1.90 | | member(all_24_1, all_15_3) = 0 & $i(all_24_1) % 8.12/1.90 | | % 8.12/1.90 | | ALPHA: (24) implies: % 8.12/1.90 | | (25) ~ (all_24_0 = 0) % 8.12/1.90 | | (26) $i(all_24_1) % 8.12/1.90 | | (27) member(all_24_1, all_15_3) = 0 % 8.12/1.90 | | (28) member(all_24_1, all_15_1) = all_24_0 % 8.12/1.90 | | % 8.12/1.90 | | GROUND_INST: instantiating (2) with all_24_1, all_15_5, all_15_4, all_15_3, % 8.12/1.90 | | simplifying with (10), (11), (17), (26), (27) gives: % 8.12/1.90 | | (29) member(all_24_1, all_15_4) = 0 & member(all_24_1, all_15_5) = 0 % 8.12/1.90 | | % 8.12/1.90 | | ALPHA: (29) implies: % 8.12/1.90 | | (30) member(all_24_1, all_15_5) = 0 % 8.12/1.90 | | % 8.12/1.90 | | GROUND_INST: instantiating (4) with all_24_1, all_15_2, all_15_1, all_24_0, % 8.12/1.90 | | simplifying with (13), (19), (26), (28) gives: % 8.12/1.90 | | (31) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 8.12/1.90 | | member(v0, all_15_2) = 0 & member(all_24_1, v0) = v1 & $i(v0)) % 8.12/1.90 | | % 8.12/1.90 | | BETA: splitting (31) gives: % 8.12/1.90 | | % 8.12/1.90 | | Case 1: % 8.12/1.90 | | | % 8.12/1.90 | | | (32) all_24_0 = 0 % 8.12/1.90 | | | % 8.12/1.90 | | | REDUCE: (25), (32) imply: % 8.12/1.90 | | | (33) $false % 8.12/1.90 | | | % 8.12/1.90 | | | CLOSE: (33) is inconsistent. % 8.12/1.90 | | | % 8.12/1.90 | | Case 2: % 8.12/1.90 | | | % 8.12/1.90 | | | (34) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_2) = % 8.12/1.90 | | | 0 & member(all_24_1, v0) = v1 & $i(v0)) % 8.12/1.90 | | | % 8.12/1.90 | | | DELTA: instantiating (34) with fresh symbols all_36_0, all_36_1 gives: % 8.12/1.90 | | | (35) ~ (all_36_0 = 0) & member(all_36_1, all_15_2) = 0 & % 8.12/1.90 | | | member(all_24_1, all_36_1) = all_36_0 & $i(all_36_1) % 8.12/1.90 | | | % 8.12/1.90 | | | ALPHA: (35) implies: % 8.12/1.90 | | | (36) ~ (all_36_0 = 0) % 8.12/1.90 | | | (37) $i(all_36_1) % 8.12/1.90 | | | (38) member(all_24_1, all_36_1) = all_36_0 % 8.12/1.90 | | | (39) member(all_36_1, all_15_2) = 0 % 8.12/1.90 | | | % 8.12/1.90 | | | GROUND_INST: instantiating (3) with all_24_1, all_15_7, all_15_5, % 8.12/1.90 | | | simplifying with (8), (18), (26), (30) gives: % 8.12/1.91 | | | (40) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (member(all_24_1, v0) = % 8.12/1.91 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0, % 8.12/1.91 | | | all_15_7) = v2)) % 8.12/1.91 | | | % 8.12/1.91 | | | GROUND_INST: instantiating (2) with all_36_1, all_15_7, all_15_6, % 8.12/1.91 | | | all_15_2, simplifying with (8), (9), (16), (37), (39) gives: % 8.12/1.91 | | | (41) member(all_36_1, all_15_6) = 0 & member(all_36_1, all_15_7) = 0 % 8.12/1.91 | | | % 8.12/1.91 | | | ALPHA: (41) implies: % 8.12/1.91 | | | (42) member(all_36_1, all_15_7) = 0 % 8.12/1.91 | | | % 8.12/1.91 | | | GROUND_INST: instantiating (40) with all_36_1, all_36_0, simplifying with % 8.12/1.91 | | | (37), (38) gives: % 8.12/1.91 | | | (43) all_36_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_36_1, % 8.12/1.91 | | | all_15_7) = v0) % 8.12/1.91 | | | % 8.12/1.91 | | | BETA: splitting (43) gives: % 8.12/1.91 | | | % 8.12/1.91 | | | Case 1: % 8.12/1.91 | | | | % 8.12/1.91 | | | | (44) all_36_0 = 0 % 8.12/1.91 | | | | % 8.12/1.91 | | | | REDUCE: (36), (44) imply: % 8.12/1.91 | | | | (45) $false % 8.12/1.91 | | | | % 8.12/1.91 | | | | CLOSE: (45) is inconsistent. % 8.12/1.91 | | | | % 8.12/1.91 | | | Case 2: % 8.12/1.91 | | | | % 8.12/1.91 | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & member(all_36_1, all_15_7) = v0) % 8.12/1.91 | | | | % 8.12/1.91 | | | | DELTA: instantiating (46) with fresh symbol all_50_0 gives: % 8.12/1.91 | | | | (47) ~ (all_50_0 = 0) & member(all_36_1, all_15_7) = all_50_0 % 8.12/1.91 | | | | % 8.12/1.91 | | | | ALPHA: (47) implies: % 8.12/1.91 | | | | (48) ~ (all_50_0 = 0) % 8.12/1.91 | | | | (49) member(all_36_1, all_15_7) = all_50_0 % 8.12/1.91 | | | | % 8.12/1.91 | | | | GROUND_INST: instantiating (5) with 0, all_50_0, all_15_7, all_36_1, % 8.12/1.91 | | | | simplifying with (42), (49) gives: % 8.12/1.91 | | | | (50) all_50_0 = 0 % 8.12/1.91 | | | | % 8.12/1.91 | | | | REDUCE: (48), (50) imply: % 8.12/1.91 | | | | (51) $false % 8.12/1.91 | | | | % 8.12/1.91 | | | | CLOSE: (51) is inconsistent. % 8.12/1.91 | | | | % 8.12/1.91 | | | End of split % 8.12/1.91 | | | % 8.12/1.91 | | End of split % 8.12/1.91 | | % 8.12/1.91 | End of split % 8.12/1.91 | % 8.12/1.91 End of proof % 8.12/1.91 % SZS output end Proof for theBenchmark % 8.12/1.91 % 8.12/1.91 1289ms %------------------------------------------------------------------------------