%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET593+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 : n009.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 15:25:28 EDT 2023 % Result : Theorem 6.08s 1.53s % Output : Proof 7.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET593+3 : TPTP v8.1.2. Released v2.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n009.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sat Aug 26 12:01:35 EDT 2023 % 0.14/0.34 % CPUTime : % 0.61/0.61 ________ _____ % 0.61/0.61 ___ __ \_________(_)________________________________ % 0.61/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.61 % 0.61/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.61 (2023-06-19) % 0.61/0.61 % 0.61/0.61 (c) Philipp Rümmer, 2009-2023 % 0.61/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.61 Amanda Stjerna. % 0.61/0.61 Free software under BSD-3-Clause. % 0.61/0.61 % 0.61/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.61 % 0.61/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.66/0.62 Running up to 7 provers in parallel. % 0.66/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.66/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.66/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.66/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.66/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.66/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.66/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.31/1.03 Prover 1: Preprocessing ... % 2.31/1.03 Prover 4: Preprocessing ... % 2.31/1.07 Prover 0: Preprocessing ... % 2.31/1.07 Prover 2: Preprocessing ... % 2.31/1.07 Prover 5: Preprocessing ... % 2.31/1.08 Prover 6: Preprocessing ... % 2.31/1.08 Prover 3: Preprocessing ... % 3.84/1.27 Prover 5: Proving ... % 3.84/1.27 Prover 3: Warning: ignoring some quantifiers % 3.84/1.29 Prover 3: Constructing countermodel ... % 3.84/1.30 Prover 2: Proving ... % 3.84/1.30 Prover 1: Warning: ignoring some quantifiers % 4.33/1.30 Prover 6: Proving ... % 4.33/1.31 Prover 0: Proving ... % 4.33/1.31 Prover 4: Warning: ignoring some quantifiers % 4.33/1.31 Prover 1: Constructing countermodel ... % 4.33/1.32 Prover 4: Constructing countermodel ... % 6.04/1.53 Prover 0: proved (903ms) % 6.04/1.53 % 6.08/1.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.08/1.53 % 6.08/1.54 Prover 3: stopped % 6.08/1.55 Prover 2: stopped % 6.08/1.55 Prover 5: stopped % 6.08/1.55 Prover 6: stopped % 6.08/1.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.08/1.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.08/1.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.08/1.55 Prover 7: Preprocessing ... % 6.08/1.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.08/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.08/1.57 Prover 10: Preprocessing ... % 6.08/1.58 Prover 8: Preprocessing ... % 6.08/1.58 Prover 11: Preprocessing ... % 6.08/1.59 Prover 13: Preprocessing ... % 6.08/1.59 Prover 7: Warning: ignoring some quantifiers % 6.08/1.60 Prover 7: Constructing countermodel ... % 6.57/1.64 Prover 10: Warning: ignoring some quantifiers % 6.57/1.64 Prover 1: Found proof (size 63) % 6.57/1.64 Prover 1: proved (1006ms) % 6.57/1.64 Prover 4: stopped % 6.57/1.64 Prover 7: stopped % 6.57/1.64 Prover 13: Warning: ignoring some quantifiers % 6.57/1.64 Prover 10: Constructing countermodel ... % 6.57/1.65 Prover 13: Constructing countermodel ... % 6.57/1.65 Prover 10: stopped % 6.57/1.65 Prover 11: Warning: ignoring some quantifiers % 6.57/1.65 Prover 13: stopped % 6.57/1.65 Prover 11: Constructing countermodel ... % 6.57/1.65 Prover 8: Warning: ignoring some quantifiers % 6.57/1.66 Prover 11: stopped % 6.57/1.66 Prover 8: Constructing countermodel ... % 6.57/1.67 Prover 8: stopped % 6.57/1.67 % 6.57/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.57/1.67 % 7.04/1.68 % SZS output start Proof for theBenchmark % 7.04/1.68 Assumptions after simplification: % 7.04/1.68 --------------------------------- % 7.04/1.68 % 7.04/1.68 (commutativity_of_union) % 7.04/1.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) % 7.04/1.71 | ~ $i(v0) | (union(v1, v0) = v2 & $i(v2))) % 7.04/1.71 % 7.04/1.71 (difference_defn) % 7.04/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 7.04/1.72 | ~ (difference(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 7.04/1.72 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 & % 7.04/1.72 member(v2, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 7.04/1.72 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v0, v1) = v3) | ~ (member(v2, % 7.04/1.72 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 7.04/1.72 0) & member(v2, v1) = v4 & member(v2, v0) = 0)) % 7.04/1.72 % 7.04/1.72 (prove_th52) % 7.04/1.72 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 7.04/1.72 any] : ? [v6: $i] : ? [v7: any] : (subset(v6, v1) = v7 & subset(v4, v2) = % 7.04/1.72 v5 & subset(v0, v3) = 0 & difference(v0, v2) = v6 & difference(v0, v1) = v4 % 7.04/1.72 & union(v1, v2) = v3 & $i(v6) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 7.04/1.72 ( ~ (v7 = 0) | ~ (v5 = 0))) % 7.04/1.72 % 7.04/1.72 (subset_defn) % 7.04/1.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 7.04/1.72 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 7.04/1.72 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 7.04/1.72 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 7.04/1.72 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 7.04/1.72 % 7.04/1.72 (union_defn) % 7.04/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 7.04/1.73 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 7.04/1.73 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 7.04/1.73 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : % 7.04/1.73 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) % 7.04/1.73 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 7.04/1.73 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 7.04/1.73 % 7.04/1.73 (function-axioms) % 7.04/1.73 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 7.04/1.73 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 7.04/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 7.04/1.73 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 7.04/1.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 7.04/1.73 (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 7.04/1.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3, % 7.04/1.73 v2) = v1) | ~ (member(v3, v2) = v0)) % 7.04/1.73 % 7.04/1.73 Further assumptions not needed in the proof: % 7.04/1.73 -------------------------------------------- % 7.04/1.73 equal_member_defn, reflexivity_of_subset % 7.04/1.73 % 7.04/1.73 Those formulas are unsatisfiable: % 7.04/1.73 --------------------------------- % 7.04/1.73 % 7.04/1.73 Begin of proof % 7.04/1.73 | % 7.04/1.73 | ALPHA: (union_defn) implies: % 7.04/1.74 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, % 7.04/1.74 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 7.04/1.74 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v2, v1) = v5 & % 7.04/1.74 | member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 7.04/1.74 | % 7.04/1.74 | ALPHA: (difference_defn) implies: % 7.04/1.74 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 7.04/1.74 | (difference(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ % 7.04/1.74 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = % 7.04/1.74 | v4 & member(v2, v0) = 0)) % 7.04/1.74 | % 7.04/1.74 | ALPHA: (subset_defn) implies: % 7.04/1.74 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 7.04/1.74 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 7.04/1.74 | member(v2, v1) = 0)) % 7.04/1.74 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 7.04/1.74 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 7.04/1.74 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 7.04/1.74 | % 7.04/1.74 | ALPHA: (function-axioms) implies: % 7.04/1.74 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 7.04/1.74 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 7.04/1.74 | = v0)) % 7.04/1.74 | % 7.04/1.74 | DELTA: instantiating (prove_th52) with fresh symbols all_9_0, all_9_1, % 7.04/1.74 | all_9_2, all_9_3, all_9_4, all_9_5, all_9_6, all_9_7 gives: % 7.04/1.74 | (6) subset(all_9_1, all_9_6) = all_9_0 & subset(all_9_3, all_9_5) = all_9_2 % 7.04/1.74 | & subset(all_9_7, all_9_4) = 0 & difference(all_9_7, all_9_5) = all_9_1 % 7.04/1.74 | & difference(all_9_7, all_9_6) = all_9_3 & union(all_9_6, all_9_5) = % 7.04/1.74 | all_9_4 & $i(all_9_1) & $i(all_9_3) & $i(all_9_4) & $i(all_9_5) & % 7.04/1.74 | $i(all_9_6) & $i(all_9_7) & ( ~ (all_9_0 = 0) | ~ (all_9_2 = 0)) % 7.04/1.74 | % 7.04/1.74 | ALPHA: (6) implies: % 7.04/1.75 | (7) $i(all_9_7) % 7.04/1.75 | (8) $i(all_9_6) % 7.04/1.75 | (9) $i(all_9_5) % 7.04/1.75 | (10) $i(all_9_3) % 7.04/1.75 | (11) $i(all_9_1) % 7.04/1.75 | (12) union(all_9_6, all_9_5) = all_9_4 % 7.04/1.75 | (13) difference(all_9_7, all_9_6) = all_9_3 % 7.04/1.75 | (14) difference(all_9_7, all_9_5) = all_9_1 % 7.04/1.75 | (15) subset(all_9_7, all_9_4) = 0 % 7.04/1.75 | (16) subset(all_9_3, all_9_5) = all_9_2 % 7.04/1.75 | (17) subset(all_9_1, all_9_6) = all_9_0 % 7.04/1.75 | (18) ~ (all_9_0 = 0) | ~ (all_9_2 = 0) % 7.04/1.75 | % 7.04/1.75 | GROUND_INST: instantiating (commutativity_of_union) with all_9_6, all_9_5, % 7.04/1.75 | all_9_4, simplifying with (8), (9), (12) gives: % 7.04/1.75 | (19) union(all_9_5, all_9_6) = all_9_4 & $i(all_9_4) % 7.04/1.75 | % 7.04/1.75 | ALPHA: (19) implies: % 7.04/1.75 | (20) $i(all_9_4) % 7.04/1.75 | (21) union(all_9_5, all_9_6) = all_9_4 % 7.04/1.75 | % 7.04/1.75 | GROUND_INST: instantiating (3) with all_9_7, all_9_4, simplifying with (7), % 7.04/1.75 | (15), (20) gives: % 7.04/1.75 | (22) ! [v0: $i] : ( ~ (member(v0, all_9_7) = 0) | ~ $i(v0) | member(v0, % 7.04/1.75 | all_9_4) = 0) % 7.04/1.75 | % 7.04/1.75 | GROUND_INST: instantiating (4) with all_9_3, all_9_5, all_9_2, simplifying % 7.04/1.75 | with (9), (10), (16) gives: % 7.04/1.75 | (23) all_9_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 7.04/1.75 | all_9_3) = 0 & member(v0, all_9_5) = v1 & $i(v0)) % 7.04/1.75 | % 7.04/1.75 | GROUND_INST: instantiating (4) with all_9_1, all_9_6, all_9_0, simplifying % 7.04/1.75 | with (8), (11), (17) gives: % 7.04/1.75 | (24) all_9_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 7.04/1.75 | all_9_1) = 0 & member(v0, all_9_6) = v1 & $i(v0)) % 7.04/1.75 | % 7.04/1.75 | BETA: splitting (18) gives: % 7.04/1.75 | % 7.04/1.75 | Case 1: % 7.04/1.75 | | % 7.04/1.75 | | (25) ~ (all_9_0 = 0) % 7.04/1.75 | | % 7.04/1.75 | | BETA: splitting (24) gives: % 7.04/1.75 | | % 7.04/1.75 | | Case 1: % 7.04/1.75 | | | % 7.04/1.75 | | | (26) all_9_0 = 0 % 7.04/1.75 | | | % 7.04/1.75 | | | REDUCE: (25), (26) imply: % 7.04/1.76 | | | (27) $false % 7.04/1.76 | | | % 7.04/1.76 | | | CLOSE: (27) is inconsistent. % 7.04/1.76 | | | % 7.04/1.76 | | Case 2: % 7.04/1.76 | | | % 7.04/1.76 | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_9_1) = % 7.04/1.76 | | | 0 & member(v0, all_9_6) = v1 & $i(v0)) % 7.04/1.76 | | | % 7.04/1.76 | | | DELTA: instantiating (28) with fresh symbols all_36_0, all_36_1 gives: % 7.04/1.76 | | | (29) ~ (all_36_0 = 0) & member(all_36_1, all_9_1) = 0 & % 7.04/1.76 | | | member(all_36_1, all_9_6) = all_36_0 & $i(all_36_1) % 7.04/1.76 | | | % 7.04/1.76 | | | ALPHA: (29) implies: % 7.04/1.76 | | | (30) ~ (all_36_0 = 0) % 7.04/1.76 | | | (31) $i(all_36_1) % 7.04/1.76 | | | (32) member(all_36_1, all_9_6) = all_36_0 % 7.04/1.76 | | | (33) member(all_36_1, all_9_1) = 0 % 7.04/1.76 | | | % 7.04/1.76 | | | GROUND_INST: instantiating (2) with all_9_7, all_9_5, all_36_1, all_9_1, % 7.04/1.76 | | | simplifying with (7), (9), (14), (31), (33) gives: % 7.04/1.76 | | | (34) ? [v0: int] : ( ~ (v0 = 0) & member(all_36_1, all_9_5) = v0 & % 7.04/1.76 | | | member(all_36_1, all_9_7) = 0) % 7.04/1.76 | | | % 7.04/1.76 | | | DELTA: instantiating (34) with fresh symbol all_43_0 gives: % 7.04/1.76 | | | (35) ~ (all_43_0 = 0) & member(all_36_1, all_9_5) = all_43_0 & % 7.04/1.76 | | | member(all_36_1, all_9_7) = 0 % 7.04/1.76 | | | % 7.04/1.76 | | | ALPHA: (35) implies: % 7.04/1.76 | | | (36) ~ (all_43_0 = 0) % 7.04/1.76 | | | (37) member(all_36_1, all_9_7) = 0 % 7.04/1.76 | | | (38) member(all_36_1, all_9_5) = all_43_0 % 7.04/1.76 | | | % 7.04/1.76 | | | GROUND_INST: instantiating (22) with all_36_1, simplifying with (31), (37) % 7.04/1.76 | | | gives: % 7.04/1.76 | | | (39) member(all_36_1, all_9_4) = 0 % 7.04/1.76 | | | % 7.04/1.76 | | | GROUND_INST: instantiating (1) with all_9_5, all_9_6, all_36_1, all_9_4, % 7.04/1.76 | | | simplifying with (8), (9), (21), (31), (39) gives: % 7.04/1.76 | | | (40) ? [v0: any] : ? [v1: any] : (member(all_36_1, all_9_5) = v0 & % 7.04/1.76 | | | member(all_36_1, all_9_6) = v1 & (v1 = 0 | v0 = 0)) % 7.04/1.76 | | | % 7.04/1.76 | | | GROUND_INST: instantiating (1) with all_9_6, all_9_5, all_36_1, all_9_4, % 7.04/1.76 | | | simplifying with (8), (9), (12), (31), (39) gives: % 7.04/1.76 | | | (41) ? [v0: any] : ? [v1: any] : (member(all_36_1, all_9_5) = v1 & % 7.04/1.76 | | | member(all_36_1, all_9_6) = v0 & (v1 = 0 | v0 = 0)) % 7.04/1.76 | | | % 7.04/1.76 | | | DELTA: instantiating (41) with fresh symbols all_56_0, all_56_1 gives: % 7.04/1.76 | | | (42) member(all_36_1, all_9_5) = all_56_0 & member(all_36_1, all_9_6) = % 7.04/1.76 | | | all_56_1 & (all_56_0 = 0 | all_56_1 = 0) % 7.04/1.76 | | | % 7.04/1.76 | | | ALPHA: (42) implies: % 7.04/1.77 | | | (43) member(all_36_1, all_9_6) = all_56_1 % 7.04/1.77 | | | % 7.04/1.77 | | | DELTA: instantiating (40) with fresh symbols all_58_0, all_58_1 gives: % 7.04/1.77 | | | (44) member(all_36_1, all_9_5) = all_58_1 & member(all_36_1, all_9_6) = % 7.04/1.77 | | | all_58_0 & (all_58_0 = 0 | all_58_1 = 0) % 7.04/1.77 | | | % 7.04/1.77 | | | ALPHA: (44) implies: % 7.04/1.77 | | | (45) member(all_36_1, all_9_6) = all_58_0 % 7.04/1.77 | | | (46) member(all_36_1, all_9_5) = all_58_1 % 7.04/1.77 | | | (47) all_58_0 = 0 | all_58_1 = 0 % 7.04/1.77 | | | % 7.04/1.77 | | | GROUND_INST: instantiating (5) with all_36_0, all_58_0, all_9_6, all_36_1, % 7.04/1.77 | | | simplifying with (32), (45) gives: % 7.04/1.77 | | | (48) all_58_0 = all_36_0 % 7.04/1.77 | | | % 7.04/1.77 | | | GROUND_INST: instantiating (5) with all_56_1, all_58_0, all_9_6, all_36_1, % 7.04/1.77 | | | simplifying with (43), (45) gives: % 7.04/1.77 | | | (49) all_58_0 = all_56_1 % 7.04/1.77 | | | % 7.04/1.77 | | | GROUND_INST: instantiating (5) with all_43_0, all_58_1, all_9_5, all_36_1, % 7.04/1.77 | | | simplifying with (38), (46) gives: % 7.04/1.77 | | | (50) all_58_1 = all_43_0 % 7.04/1.77 | | | % 7.04/1.77 | | | COMBINE_EQS: (48), (49) imply: % 7.04/1.77 | | | (51) all_56_1 = all_36_0 % 7.04/1.77 | | | % 7.04/1.77 | | | BETA: splitting (47) gives: % 7.04/1.77 | | | % 7.04/1.77 | | | Case 1: % 7.04/1.77 | | | | % 7.04/1.77 | | | | (52) all_58_0 = 0 % 7.04/1.77 | | | | % 7.04/1.77 | | | | COMBINE_EQS: (48), (52) imply: % 7.04/1.77 | | | | (53) all_36_0 = 0 % 7.04/1.77 | | | | % 7.04/1.77 | | | | REDUCE: (30), (53) imply: % 7.04/1.77 | | | | (54) $false % 7.04/1.77 | | | | % 7.04/1.77 | | | | CLOSE: (54) is inconsistent. % 7.04/1.77 | | | | % 7.04/1.77 | | | Case 2: % 7.04/1.77 | | | | % 7.04/1.77 | | | | (55) all_58_1 = 0 % 7.04/1.77 | | | | % 7.04/1.77 | | | | COMBINE_EQS: (50), (55) imply: % 7.53/1.77 | | | | (56) all_43_0 = 0 % 7.53/1.77 | | | | % 7.53/1.77 | | | | SIMP: (56) implies: % 7.53/1.77 | | | | (57) all_43_0 = 0 % 7.53/1.77 | | | | % 7.53/1.77 | | | | REDUCE: (36), (57) imply: % 7.53/1.77 | | | | (58) $false % 7.53/1.77 | | | | % 7.53/1.77 | | | | CLOSE: (58) is inconsistent. % 7.53/1.77 | | | | % 7.53/1.77 | | | End of split % 7.53/1.77 | | | % 7.53/1.77 | | End of split % 7.53/1.77 | | % 7.53/1.77 | Case 2: % 7.53/1.77 | | % 7.53/1.77 | | (59) ~ (all_9_2 = 0) % 7.53/1.77 | | % 7.53/1.77 | | BETA: splitting (23) gives: % 7.53/1.77 | | % 7.53/1.77 | | Case 1: % 7.53/1.77 | | | % 7.53/1.77 | | | (60) all_9_2 = 0 % 7.53/1.77 | | | % 7.53/1.77 | | | REDUCE: (59), (60) imply: % 7.53/1.77 | | | (61) $false % 7.53/1.77 | | | % 7.53/1.77 | | | CLOSE: (61) is inconsistent. % 7.53/1.77 | | | % 7.53/1.77 | | Case 2: % 7.53/1.77 | | | % 7.53/1.77 | | | (62) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_9_3) = % 7.53/1.77 | | | 0 & member(v0, all_9_5) = v1 & $i(v0)) % 7.53/1.77 | | | % 7.53/1.77 | | | DELTA: instantiating (62) with fresh symbols all_36_0, all_36_1 gives: % 7.53/1.77 | | | (63) ~ (all_36_0 = 0) & member(all_36_1, all_9_3) = 0 & % 7.53/1.77 | | | member(all_36_1, all_9_5) = all_36_0 & $i(all_36_1) % 7.53/1.77 | | | % 7.53/1.77 | | | ALPHA: (63) implies: % 7.53/1.77 | | | (64) ~ (all_36_0 = 0) % 7.53/1.77 | | | (65) $i(all_36_1) % 7.53/1.77 | | | (66) member(all_36_1, all_9_5) = all_36_0 % 7.53/1.77 | | | (67) member(all_36_1, all_9_3) = 0 % 7.53/1.77 | | | % 7.53/1.77 | | | GROUND_INST: instantiating (2) with all_9_7, all_9_6, all_36_1, all_9_3, % 7.53/1.77 | | | simplifying with (7), (8), (13), (65), (67) gives: % 7.53/1.78 | | | (68) ? [v0: int] : ( ~ (v0 = 0) & member(all_36_1, all_9_6) = v0 & % 7.53/1.78 | | | member(all_36_1, all_9_7) = 0) % 7.53/1.78 | | | % 7.53/1.78 | | | DELTA: instantiating (68) with fresh symbol all_44_0 gives: % 7.53/1.78 | | | (69) ~ (all_44_0 = 0) & member(all_36_1, all_9_6) = all_44_0 & % 7.53/1.78 | | | member(all_36_1, all_9_7) = 0 % 7.53/1.78 | | | % 7.53/1.78 | | | ALPHA: (69) implies: % 7.53/1.78 | | | (70) ~ (all_44_0 = 0) % 7.53/1.78 | | | (71) member(all_36_1, all_9_7) = 0 % 7.53/1.78 | | | (72) member(all_36_1, all_9_6) = all_44_0 % 7.53/1.78 | | | % 7.53/1.78 | | | GROUND_INST: instantiating (22) with all_36_1, simplifying with (65), (71) % 7.53/1.78 | | | gives: % 7.53/1.78 | | | (73) member(all_36_1, all_9_4) = 0 % 7.53/1.78 | | | % 7.53/1.78 | | | GROUND_INST: instantiating (1) with all_9_5, all_9_6, all_36_1, all_9_4, % 7.53/1.78 | | | simplifying with (8), (9), (21), (65), (73) gives: % 7.53/1.78 | | | (74) ? [v0: any] : ? [v1: any] : (member(all_36_1, all_9_5) = v0 & % 7.53/1.78 | | | member(all_36_1, all_9_6) = v1 & (v1 = 0 | v0 = 0)) % 7.53/1.78 | | | % 7.53/1.78 | | | DELTA: instantiating (74) with fresh symbols all_59_0, all_59_1 gives: % 7.53/1.78 | | | (75) member(all_36_1, all_9_5) = all_59_1 & member(all_36_1, all_9_6) = % 7.53/1.78 | | | all_59_0 & (all_59_0 = 0 | all_59_1 = 0) % 7.53/1.78 | | | % 7.53/1.78 | | | ALPHA: (75) implies: % 7.53/1.78 | | | (76) member(all_36_1, all_9_6) = all_59_0 % 7.53/1.78 | | | (77) member(all_36_1, all_9_5) = all_59_1 % 7.53/1.78 | | | (78) all_59_0 = 0 | all_59_1 = 0 % 7.53/1.78 | | | % 7.53/1.78 | | | GROUND_INST: instantiating (5) with all_44_0, all_59_0, all_9_6, all_36_1, % 7.53/1.78 | | | simplifying with (72), (76) gives: % 7.53/1.78 | | | (79) all_59_0 = all_44_0 % 7.53/1.78 | | | % 7.53/1.78 | | | GROUND_INST: instantiating (5) with all_36_0, all_59_1, all_9_5, all_36_1, % 7.53/1.78 | | | simplifying with (66), (77) gives: % 7.53/1.78 | | | (80) all_59_1 = all_36_0 % 7.53/1.78 | | | % 7.53/1.78 | | | BETA: splitting (78) gives: % 7.53/1.78 | | | % 7.53/1.78 | | | Case 1: % 7.53/1.78 | | | | % 7.53/1.78 | | | | (81) all_59_0 = 0 % 7.53/1.78 | | | | % 7.53/1.78 | | | | COMBINE_EQS: (79), (81) imply: % 7.53/1.78 | | | | (82) all_44_0 = 0 % 7.53/1.78 | | | | % 7.53/1.78 | | | | REDUCE: (70), (82) imply: % 7.53/1.78 | | | | (83) $false % 7.53/1.78 | | | | % 7.53/1.78 | | | | CLOSE: (83) is inconsistent. % 7.53/1.78 | | | | % 7.53/1.78 | | | Case 2: % 7.53/1.78 | | | | % 7.53/1.78 | | | | (84) all_59_1 = 0 % 7.53/1.78 | | | | % 7.53/1.78 | | | | COMBINE_EQS: (80), (84) imply: % 7.53/1.78 | | | | (85) all_36_0 = 0 % 7.53/1.78 | | | | % 7.53/1.78 | | | | SIMP: (85) implies: % 7.53/1.78 | | | | (86) all_36_0 = 0 % 7.53/1.78 | | | | % 7.53/1.78 | | | | REDUCE: (64), (86) imply: % 7.53/1.78 | | | | (87) $false % 7.53/1.78 | | | | % 7.53/1.78 | | | | CLOSE: (87) is inconsistent. % 7.53/1.78 | | | | % 7.53/1.78 | | | End of split % 7.53/1.78 | | | % 7.53/1.78 | | End of split % 7.53/1.78 | | % 7.53/1.78 | End of split % 7.53/1.78 | % 7.53/1.78 End of proof % 7.53/1.78 % SZS output end Proof for theBenchmark % 7.53/1.78 % 7.53/1.78 1172ms %------------------------------------------------------------------------------