%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET201+3 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 15:24:17 EDT 2023 % Result : Theorem 6.10s 1.62s % Output : Proof 7.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET201+3 : TPTP v8.1.2. Released v2.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 08:43:38 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.66 ________ _____ % 0.20/0.66 ___ __ \_________(_)________________________________ % 0.20/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.66 % 0.20/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.66 (2023-06-19) % 0.20/0.66 % 0.20/0.66 (c) Philipp Rümmer, 2009-2023 % 0.20/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.66 Amanda Stjerna. % 0.20/0.66 Free software under BSD-3-Clause. % 0.20/0.66 % 0.20/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.66 % 0.20/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.68 Running up to 7 provers in parallel. % 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.98/1.07 Prover 1: Preprocessing ... % 1.98/1.07 Prover 4: Preprocessing ... % 2.65/1.12 Prover 5: Preprocessing ... % 2.65/1.12 Prover 0: Preprocessing ... % 2.65/1.12 Prover 6: Preprocessing ... % 2.65/1.12 Prover 3: Preprocessing ... % 2.65/1.12 Prover 2: Preprocessing ... % 4.06/1.37 Prover 5: Proving ... % 4.06/1.37 Prover 3: Warning: ignoring some quantifiers % 4.06/1.37 Prover 2: Proving ... % 4.06/1.38 Prover 1: Warning: ignoring some quantifiers % 4.06/1.39 Prover 3: Constructing countermodel ... % 4.06/1.39 Prover 1: Constructing countermodel ... % 4.75/1.40 Prover 4: Warning: ignoring some quantifiers % 4.75/1.41 Prover 0: Proving ... % 4.75/1.42 Prover 6: Proving ... % 4.75/1.42 Prover 4: Constructing countermodel ... % 6.10/1.61 Prover 3: proved (925ms) % 6.10/1.62 % 6.10/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.10/1.62 % 6.10/1.62 Prover 0: proved (935ms) % 6.10/1.62 % 6.10/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.10/1.62 % 6.10/1.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.10/1.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.10/1.62 Prover 5: stopped % 6.10/1.63 Prover 2: stopped % 6.10/1.63 Prover 6: stopped % 6.10/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.10/1.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.10/1.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.10/1.66 Prover 7: Preprocessing ... % 6.10/1.66 Prover 8: Preprocessing ... % 6.10/1.66 Prover 13: Preprocessing ... % 6.10/1.67 Prover 11: Preprocessing ... % 6.10/1.67 Prover 10: Preprocessing ... % 6.10/1.71 Prover 10: Warning: ignoring some quantifiers % 6.10/1.71 Prover 10: Constructing countermodel ... % 6.10/1.73 Prover 7: Warning: ignoring some quantifiers % 6.10/1.73 Prover 7: Constructing countermodel ... % 6.10/1.75 Prover 1: Found proof (size 44) % 6.10/1.75 Prover 1: proved (1064ms) % 6.10/1.75 Prover 10: stopped % 6.10/1.75 Prover 7: stopped % 6.10/1.75 Prover 4: stopped % 6.10/1.75 Prover 13: Warning: ignoring some quantifiers % 6.10/1.76 Prover 13: Constructing countermodel ... % 6.10/1.76 Prover 13: stopped % 6.10/1.77 Prover 8: Warning: ignoring some quantifiers % 7.22/1.78 Prover 8: Constructing countermodel ... % 7.22/1.78 Prover 8: stopped % 7.22/1.79 Prover 11: Warning: ignoring some quantifiers % 7.22/1.80 Prover 11: Constructing countermodel ... % 7.22/1.80 Prover 11: stopped % 7.22/1.80 % 7.22/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.22/1.80 % 7.22/1.81 % SZS output start Proof for theBenchmark % 7.22/1.82 Assumptions after simplification: % 7.22/1.82 --------------------------------- % 7.22/1.82 % 7.22/1.82 (commutativity_of_intersection) % 7.22/1.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ % 7.22/1.86 $i(v1) | ~ $i(v0) | (intersection(v1, v0) = v2 & $i(v2))) % 7.22/1.86 % 7.22/1.86 (intersection_defn) % 7.22/1.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 7.22/1.87 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 7.22/1.87 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 & % 7.22/1.87 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 7.22/1.87 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~ % 7.22/1.87 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = % 7.22/1.87 0 & member(v2, v0) = 0)) % 7.22/1.87 % 7.22/1.87 (prove_th41) % 7.22/1.87 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 7.22/1.87 $i] : ? [v6: int] : ( ~ (v6 = 0) & subset(v4, v5) = v6 & subset(v2, v3) = 0 % 7.74/1.87 & subset(v0, v1) = 0 & intersection(v1, v3) = v5 & intersection(v0, v2) = v4 % 7.74/1.87 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 7.74/1.87 % 7.74/1.87 (subset_defn) % 7.74/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 7.74/1.88 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 7.74/1.88 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 7.74/1.88 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 7.74/1.88 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 7.74/1.88 % 7.74/1.88 (function-axioms) % 7.74/1.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.74/1.88 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 7.74/1.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.74/1.88 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: % 7.74/1.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 7.74/1.88 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 7.74/1.88 % 7.74/1.88 Further assumptions not needed in the proof: % 7.74/1.88 -------------------------------------------- % 7.74/1.88 equal_member_defn, reflexivity_of_subset % 7.74/1.88 % 7.74/1.88 Those formulas are unsatisfiable: % 7.74/1.88 --------------------------------- % 7.74/1.88 % 7.74/1.88 Begin of proof % 7.74/1.88 | % 7.74/1.88 | ALPHA: (intersection_defn) implies: % 7.74/1.89 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.74/1.89 | (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | % 7.74/1.89 | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 7.74/1.89 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 7.74/1.89 | (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | % 7.74/1.89 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 7.74/1.89 | (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 7.74/1.89 | 0)))) % 7.74/1.89 | % 7.74/1.89 | ALPHA: (subset_defn) implies: % 7.74/1.89 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 7.74/1.89 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 7.74/1.89 | member(v2, v1) = 0)) % 7.74/1.89 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 7.74/1.89 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 7.74/1.89 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 7.74/1.90 | % 7.74/1.90 | ALPHA: (function-axioms) implies: % 7.74/1.90 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.74/1.90 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 7.74/1.90 | = v0)) % 7.74/1.90 | % 7.74/1.90 | DELTA: instantiating (prove_th41) with fresh symbols all_8_0, all_8_1, % 7.74/1.90 | all_8_2, all_8_3, all_8_4, all_8_5, all_8_6 gives: % 7.74/1.90 | (6) ~ (all_8_0 = 0) & subset(all_8_2, all_8_1) = all_8_0 & subset(all_8_4, % 7.74/1.90 | all_8_3) = 0 & subset(all_8_6, all_8_5) = 0 & intersection(all_8_5, % 7.74/1.90 | all_8_3) = all_8_1 & intersection(all_8_6, all_8_4) = all_8_2 & % 7.74/1.90 | $i(all_8_1) & $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & % 7.74/1.90 | $i(all_8_6) % 7.74/1.90 | % 7.74/1.90 | ALPHA: (6) implies: % 7.74/1.90 | (7) ~ (all_8_0 = 0) % 7.74/1.90 | (8) $i(all_8_6) % 7.74/1.90 | (9) $i(all_8_5) % 7.74/1.90 | (10) $i(all_8_4) % 7.74/1.90 | (11) $i(all_8_3) % 7.74/1.90 | (12) intersection(all_8_6, all_8_4) = all_8_2 % 7.74/1.90 | (13) intersection(all_8_5, all_8_3) = all_8_1 % 7.74/1.90 | (14) subset(all_8_6, all_8_5) = 0 % 7.74/1.90 | (15) subset(all_8_4, all_8_3) = 0 % 7.74/1.90 | (16) subset(all_8_2, all_8_1) = all_8_0 % 7.74/1.90 | % 7.74/1.90 | GROUND_INST: instantiating (commutativity_of_intersection) with all_8_6, % 7.74/1.90 | all_8_4, all_8_2, simplifying with (8), (10), (12) gives: % 7.74/1.90 | (17) intersection(all_8_4, all_8_6) = all_8_2 & $i(all_8_2) % 7.74/1.90 | % 7.74/1.90 | ALPHA: (17) implies: % 7.74/1.91 | (18) $i(all_8_2) % 7.74/1.91 | (19) intersection(all_8_4, all_8_6) = all_8_2 % 7.74/1.91 | % 7.74/1.91 | GROUND_INST: instantiating (commutativity_of_intersection) with all_8_5, % 7.74/1.91 | all_8_3, all_8_1, simplifying with (9), (11), (13) gives: % 7.74/1.91 | (20) intersection(all_8_3, all_8_5) = all_8_1 & $i(all_8_1) % 7.74/1.91 | % 7.74/1.91 | ALPHA: (20) implies: % 7.74/1.91 | (21) $i(all_8_1) % 7.74/1.91 | (22) intersection(all_8_3, all_8_5) = all_8_1 % 7.74/1.91 | % 7.74/1.91 | GROUND_INST: instantiating (3) with all_8_6, all_8_5, simplifying with (8), % 7.74/1.91 | (9), (14) gives: % 7.74/1.91 | (23) ! [v0: $i] : ( ~ (member(v0, all_8_6) = 0) | ~ $i(v0) | member(v0, % 7.74/1.91 | all_8_5) = 0) % 7.74/1.91 | % 7.74/1.91 | GROUND_INST: instantiating (3) with all_8_4, all_8_3, simplifying with (10), % 7.74/1.91 | (11), (15) gives: % 7.74/1.91 | (24) ! [v0: $i] : ( ~ (member(v0, all_8_4) = 0) | ~ $i(v0) | member(v0, % 7.74/1.91 | all_8_3) = 0) % 7.74/1.91 | % 7.74/1.91 | GROUND_INST: instantiating (4) with all_8_2, all_8_1, all_8_0, simplifying % 7.74/1.91 | with (16), (18), (21) gives: % 7.74/1.91 | (25) all_8_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 7.74/1.91 | all_8_1) = v1 & member(v0, all_8_2) = 0 & $i(v0)) % 7.74/1.91 | % 7.74/1.91 | BETA: splitting (25) gives: % 7.74/1.91 | % 7.74/1.91 | Case 1: % 7.74/1.91 | | % 7.74/1.91 | | (26) all_8_0 = 0 % 7.74/1.91 | | % 7.74/1.91 | | REDUCE: (7), (26) imply: % 7.74/1.91 | | (27) $false % 7.74/1.91 | | % 7.74/1.91 | | CLOSE: (27) is inconsistent. % 7.74/1.91 | | % 7.74/1.91 | Case 2: % 7.74/1.91 | | % 7.74/1.91 | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_1) = v1 % 7.74/1.92 | | & member(v0, all_8_2) = 0 & $i(v0)) % 7.74/1.92 | | % 7.74/1.92 | | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1 gives: % 7.74/1.92 | | (29) ~ (all_22_0 = 0) & member(all_22_1, all_8_1) = all_22_0 & % 7.74/1.92 | | member(all_22_1, all_8_2) = 0 & $i(all_22_1) % 7.74/1.92 | | % 7.74/1.92 | | ALPHA: (29) implies: % 7.74/1.92 | | (30) ~ (all_22_0 = 0) % 7.74/1.92 | | (31) $i(all_22_1) % 7.74/1.92 | | (32) member(all_22_1, all_8_2) = 0 % 7.74/1.92 | | (33) member(all_22_1, all_8_1) = all_22_0 % 7.74/1.92 | | % 7.74/1.92 | | GROUND_INST: instantiating (2) with all_8_5, all_8_3, all_22_1, all_8_1, % 7.74/1.92 | | all_22_0, simplifying with (9), (11), (13), (31), (33) gives: % 7.74/1.92 | | (34) all_22_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_22_1, % 7.74/1.92 | | all_8_3) = v1 & member(all_22_1, all_8_5) = v0 & ( ~ (v1 = 0) | % 7.74/1.92 | | ~ (v0 = 0))) % 7.74/1.92 | | % 7.74/1.92 | | GROUND_INST: instantiating (1) with all_8_4, all_8_6, all_22_1, all_8_2, % 7.74/1.92 | | simplifying with (8), (10), (19), (31), (32) gives: % 7.74/1.92 | | (35) member(all_22_1, all_8_4) = 0 & member(all_22_1, all_8_6) = 0 % 7.74/1.92 | | % 7.74/1.92 | | ALPHA: (35) implies: % 7.74/1.92 | | (36) member(all_22_1, all_8_6) = 0 % 7.74/1.92 | | (37) member(all_22_1, all_8_4) = 0 % 7.74/1.92 | | % 7.74/1.92 | | GROUND_INST: instantiating (2) with all_8_3, all_8_5, all_22_1, all_8_1, % 7.74/1.92 | | all_22_0, simplifying with (9), (11), (22), (31), (33) gives: % 7.74/1.92 | | (38) all_22_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_22_1, % 7.74/1.92 | | all_8_3) = v0 & member(all_22_1, all_8_5) = v1 & ( ~ (v1 = 0) | % 7.74/1.92 | | ~ (v0 = 0))) % 7.74/1.92 | | % 7.74/1.92 | | BETA: splitting (38) gives: % 7.74/1.92 | | % 7.74/1.92 | | Case 1: % 7.74/1.92 | | | % 7.74/1.92 | | | (39) all_22_0 = 0 % 7.74/1.92 | | | % 7.74/1.92 | | | REDUCE: (30), (39) imply: % 7.74/1.92 | | | (40) $false % 7.74/1.92 | | | % 7.74/1.92 | | | CLOSE: (40) is inconsistent. % 7.74/1.92 | | | % 7.74/1.92 | | Case 2: % 7.74/1.92 | | | % 7.74/1.93 | | | (41) ? [v0: any] : ? [v1: any] : (member(all_22_1, all_8_3) = v0 & % 7.74/1.93 | | | member(all_22_1, all_8_5) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 7.74/1.93 | | | % 7.74/1.93 | | | DELTA: instantiating (41) with fresh symbols all_34_0, all_34_1 gives: % 7.74/1.93 | | | (42) member(all_22_1, all_8_3) = all_34_1 & member(all_22_1, all_8_5) = % 7.74/1.93 | | | all_34_0 & ( ~ (all_34_0 = 0) | ~ (all_34_1 = 0)) % 7.74/1.93 | | | % 7.74/1.93 | | | ALPHA: (42) implies: % 7.74/1.93 | | | (43) member(all_22_1, all_8_5) = all_34_0 % 7.74/1.93 | | | (44) member(all_22_1, all_8_3) = all_34_1 % 7.74/1.93 | | | (45) ~ (all_34_0 = 0) | ~ (all_34_1 = 0) % 7.74/1.93 | | | % 7.74/1.93 | | | BETA: splitting (34) gives: % 7.74/1.93 | | | % 7.74/1.93 | | | Case 1: % 7.74/1.93 | | | | % 7.74/1.93 | | | | (46) all_22_0 = 0 % 7.74/1.93 | | | | % 7.74/1.93 | | | | REDUCE: (30), (46) imply: % 7.74/1.93 | | | | (47) $false % 7.74/1.93 | | | | % 7.74/1.93 | | | | CLOSE: (47) is inconsistent. % 7.74/1.93 | | | | % 7.74/1.93 | | | Case 2: % 7.74/1.93 | | | | % 7.74/1.93 | | | | (48) ? [v0: any] : ? [v1: any] : (member(all_22_1, all_8_3) = v1 & % 7.74/1.93 | | | | member(all_22_1, all_8_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 7.74/1.93 | | | | % 7.74/1.93 | | | | DELTA: instantiating (48) with fresh symbols all_39_0, all_39_1 gives: % 7.74/1.93 | | | | (49) member(all_22_1, all_8_3) = all_39_0 & member(all_22_1, all_8_5) % 7.74/1.93 | | | | = all_39_1 & ( ~ (all_39_0 = 0) | ~ (all_39_1 = 0)) % 7.74/1.93 | | | | % 7.74/1.93 | | | | ALPHA: (49) implies: % 7.74/1.93 | | | | (50) member(all_22_1, all_8_5) = all_39_1 % 7.74/1.93 | | | | (51) member(all_22_1, all_8_3) = all_39_0 % 7.74/1.93 | | | | % 7.74/1.93 | | | | GROUND_INST: instantiating (5) with all_34_0, all_39_1, all_8_5, % 7.74/1.93 | | | | all_22_1, simplifying with (43), (50) gives: % 7.74/1.93 | | | | (52) all_39_1 = all_34_0 % 7.74/1.93 | | | | % 7.74/1.93 | | | | GROUND_INST: instantiating (5) with all_34_1, all_39_0, all_8_3, % 7.74/1.93 | | | | all_22_1, simplifying with (44), (51) gives: % 7.74/1.93 | | | | (53) all_39_0 = all_34_1 % 7.74/1.93 | | | | % 7.74/1.93 | | | | GROUND_INST: instantiating (23) with all_22_1, simplifying with (31), % 7.74/1.93 | | | | (36) gives: % 7.74/1.93 | | | | (54) member(all_22_1, all_8_5) = 0 % 7.74/1.93 | | | | % 7.74/1.93 | | | | GROUND_INST: instantiating (24) with all_22_1, simplifying with (31), % 7.74/1.93 | | | | (37) gives: % 7.74/1.93 | | | | (55) member(all_22_1, all_8_3) = 0 % 7.74/1.93 | | | | % 7.74/1.93 | | | | GROUND_INST: instantiating (5) with all_34_0, 0, all_8_5, all_22_1, % 7.74/1.93 | | | | simplifying with (43), (54) gives: % 7.74/1.94 | | | | (56) all_34_0 = 0 % 7.74/1.94 | | | | % 7.74/1.94 | | | | GROUND_INST: instantiating (5) with all_34_1, 0, all_8_3, all_22_1, % 7.74/1.94 | | | | simplifying with (44), (55) gives: % 7.74/1.94 | | | | (57) all_34_1 = 0 % 7.74/1.94 | | | | % 7.74/1.94 | | | | BETA: splitting (45) gives: % 7.74/1.94 | | | | % 7.74/1.94 | | | | Case 1: % 7.74/1.94 | | | | | % 7.74/1.94 | | | | | (58) ~ (all_34_0 = 0) % 7.74/1.94 | | | | | % 7.74/1.94 | | | | | REDUCE: (56), (58) imply: % 7.74/1.94 | | | | | (59) $false % 7.74/1.94 | | | | | % 7.74/1.94 | | | | | CLOSE: (59) is inconsistent. % 7.74/1.94 | | | | | % 7.74/1.94 | | | | Case 2: % 7.74/1.94 | | | | | % 7.74/1.94 | | | | | (60) ~ (all_34_1 = 0) % 7.74/1.94 | | | | | % 7.74/1.94 | | | | | REDUCE: (57), (60) imply: % 7.74/1.94 | | | | | (61) $false % 7.74/1.94 | | | | | % 7.74/1.94 | | | | | CLOSE: (61) is inconsistent. % 7.74/1.94 | | | | | % 7.74/1.94 | | | | End of split % 7.74/1.94 | | | | % 7.74/1.94 | | | End of split % 7.74/1.94 | | | % 7.74/1.94 | | End of split % 7.74/1.94 | | % 7.74/1.94 | End of split % 7.74/1.94 | % 7.74/1.94 End of proof % 7.74/1.94 % SZS output end Proof for theBenchmark % 7.74/1.94 % 7.74/1.94 1275ms %------------------------------------------------------------------------------