%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET584+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 : n011.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 15:25:24 EDT 2023 % Result : Theorem 4.54s 1.38s % Output : Proof 6.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SET584+3 : TPTP v8.1.2. Released v2.2.0. % 0.11/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.35 % Computer : n011.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 300 % 0.15/0.35 % DateTime : Sat Aug 26 10:24:24 EDT 2023 % 0.15/0.36 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.08/0.99 Prover 4: Preprocessing ... % 2.08/0.99 Prover 1: Preprocessing ... % 2.08/1.03 Prover 3: Preprocessing ... % 2.08/1.03 Prover 6: Preprocessing ... % 2.08/1.03 Prover 2: Preprocessing ... % 2.08/1.03 Prover 0: Preprocessing ... % 2.08/1.03 Prover 5: Preprocessing ... % 3.37/1.18 Prover 3: Warning: ignoring some quantifiers % 3.37/1.19 Prover 5: Proving ... % 3.37/1.19 Prover 2: Proving ... % 3.37/1.19 Prover 3: Constructing countermodel ... % 3.37/1.20 Prover 6: Proving ... % 3.37/1.21 Prover 4: Warning: ignoring some quantifiers % 3.37/1.21 Prover 1: Warning: ignoring some quantifiers % 3.37/1.21 Prover 0: Proving ... % 3.37/1.22 Prover 1: Constructing countermodel ... % 3.83/1.22 Prover 4: Constructing countermodel ... % 4.54/1.38 Prover 0: proved (729ms) % 4.54/1.38 % 4.54/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.54/1.38 % 4.54/1.38 Prover 3: stopped % 4.54/1.39 Prover 6: stopped % 4.54/1.39 Prover 2: stopped % 4.54/1.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.54/1.40 Prover 5: stopped % 4.54/1.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.54/1.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.54/1.40 Prover 7: Preprocessing ... % 4.54/1.40 Prover 8: Preprocessing ... % 4.54/1.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.54/1.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.54/1.42 Prover 13: Preprocessing ... % 4.54/1.42 Prover 10: Preprocessing ... % 5.25/1.42 Prover 11: Preprocessing ... % 5.25/1.43 Prover 7: Warning: ignoring some quantifiers % 5.25/1.43 Prover 7: Constructing countermodel ... % 5.25/1.45 Prover 10: Warning: ignoring some quantifiers % 5.25/1.45 Prover 10: Constructing countermodel ... % 5.25/1.45 Prover 13: Warning: ignoring some quantifiers % 5.49/1.46 Prover 13: Constructing countermodel ... % 5.49/1.48 Prover 1: Found proof (size 57) % 5.49/1.48 Prover 1: proved (831ms) % 5.49/1.49 Prover 4: stopped % 5.49/1.49 Prover 7: stopped % 5.49/1.49 Prover 13: stopped % 5.49/1.49 Prover 10: stopped % 5.49/1.49 Prover 11: Warning: ignoring some quantifiers % 5.49/1.49 Prover 8: Warning: ignoring some quantifiers % 5.49/1.49 Prover 11: Constructing countermodel ... % 5.49/1.49 Prover 8: Constructing countermodel ... % 5.49/1.50 Prover 11: stopped % 5.49/1.50 Prover 8: stopped % 5.49/1.50 % 5.49/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.49/1.50 % 5.49/1.51 % SZS output start Proof for theBenchmark % 5.49/1.51 Assumptions after simplification: % 5.49/1.51 --------------------------------- % 5.49/1.51 % 5.49/1.51 (commutativity_of_union) % 5.94/1.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0, v1) = v2) | ~ $i(v1) % 5.94/1.54 | ~ $i(v0) | (union(v1, v0) = v2 & $i(v2))) % 5.94/1.54 % 5.94/1.54 (prove_th33) % 5.94/1.54 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 5.94/1.54 int] : ( ~ (v5 = 0) & subset(v3, v4) = v5 & subset(v0, v1) = 0 & union(v1, % 5.94/1.54 v2) = v4 & union(v0, v2) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 5.94/1.54 $i(v0)) % 5.94/1.54 % 5.94/1.54 (subset_defn) % 5.94/1.55 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 5.94/1.55 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 5.94/1.55 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 5.94/1.55 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 5.94/1.55 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 5.94/1.55 % 5.94/1.55 (union_defn) % 5.94/1.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 5.94/1.55 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 5.94/1.55 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 5.94/1.55 member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : % 5.94/1.55 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) % 5.94/1.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 5.94/1.55 (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 5.94/1.55 % 5.94/1.55 (function-axioms) % 5.94/1.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.94/1.56 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 5.94/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.94/1.56 (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 5.94/1.56 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 5.94/1.56 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.94/1.56 % 5.94/1.56 Further assumptions not needed in the proof: % 5.94/1.56 -------------------------------------------- % 5.94/1.56 equal_member_defn, reflexivity_of_subset % 5.94/1.56 % 5.94/1.56 Those formulas are unsatisfiable: % 5.94/1.56 --------------------------------- % 5.94/1.56 % 5.94/1.56 Begin of proof % 5.94/1.56 | % 5.94/1.56 | ALPHA: (union_defn) implies: % 5.94/1.56 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v0, % 5.94/1.56 | v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 5.94/1.56 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v2, v1) = v5 & % 5.94/1.56 | member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) % 5.94/1.56 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 5.94/1.56 | (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ % 5.94/1.56 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 5.94/1.56 | (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = % 5.94/1.56 | v5)) % 5.94/1.56 | % 5.94/1.56 | ALPHA: (subset_defn) implies: % 5.94/1.57 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 5.94/1.57 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 5.94/1.57 | member(v2, v1) = 0)) % 5.94/1.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 5.94/1.57 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 5.94/1.57 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 5.94/1.57 | % 5.94/1.57 | ALPHA: (function-axioms) implies: % 5.94/1.57 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.94/1.57 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 5.94/1.57 | = v0)) % 5.94/1.57 | % 5.94/1.57 | DELTA: instantiating (prove_th33) with fresh symbols all_8_0, all_8_1, % 5.94/1.57 | all_8_2, all_8_3, all_8_4, all_8_5 gives: % 6.15/1.57 | (6) ~ (all_8_0 = 0) & subset(all_8_2, all_8_1) = all_8_0 & subset(all_8_5, % 6.15/1.57 | all_8_4) = 0 & union(all_8_4, all_8_3) = all_8_1 & union(all_8_5, % 6.15/1.57 | all_8_3) = all_8_2 & $i(all_8_1) & $i(all_8_2) & $i(all_8_3) & % 6.15/1.57 | $i(all_8_4) & $i(all_8_5) % 6.15/1.57 | % 6.15/1.57 | ALPHA: (6) implies: % 6.15/1.57 | (7) ~ (all_8_0 = 0) % 6.15/1.57 | (8) $i(all_8_5) % 6.15/1.57 | (9) $i(all_8_4) % 6.15/1.57 | (10) $i(all_8_3) % 6.15/1.57 | (11) union(all_8_5, all_8_3) = all_8_2 % 6.15/1.58 | (12) union(all_8_4, all_8_3) = all_8_1 % 6.15/1.58 | (13) subset(all_8_5, all_8_4) = 0 % 6.15/1.58 | (14) subset(all_8_2, all_8_1) = all_8_0 % 6.15/1.58 | % 6.15/1.58 | GROUND_INST: instantiating (commutativity_of_union) with all_8_5, all_8_3, % 6.15/1.58 | all_8_2, simplifying with (8), (10), (11) gives: % 6.15/1.58 | (15) union(all_8_3, all_8_5) = all_8_2 & $i(all_8_2) % 6.15/1.58 | % 6.15/1.58 | ALPHA: (15) implies: % 6.15/1.58 | (16) $i(all_8_2) % 6.15/1.58 | (17) union(all_8_3, all_8_5) = all_8_2 % 6.15/1.58 | % 6.15/1.58 | GROUND_INST: instantiating (commutativity_of_union) with all_8_4, all_8_3, % 6.15/1.58 | all_8_1, simplifying with (9), (10), (12) gives: % 6.15/1.58 | (18) union(all_8_3, all_8_4) = all_8_1 & $i(all_8_1) % 6.15/1.58 | % 6.15/1.58 | ALPHA: (18) implies: % 6.15/1.58 | (19) $i(all_8_1) % 6.15/1.58 | (20) union(all_8_3, all_8_4) = all_8_1 % 6.15/1.58 | % 6.15/1.58 | GROUND_INST: instantiating (3) with all_8_5, all_8_4, simplifying with (8), % 6.15/1.58 | (9), (13) gives: % 6.15/1.58 | (21) ! [v0: $i] : ( ~ (member(v0, all_8_5) = 0) | ~ $i(v0) | member(v0, % 6.15/1.58 | all_8_4) = 0) % 6.15/1.58 | % 6.15/1.58 | GROUND_INST: instantiating (4) with all_8_2, all_8_1, all_8_0, simplifying % 6.15/1.58 | with (14), (16), (19) gives: % 6.15/1.58 | (22) all_8_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 6.15/1.58 | all_8_1) = v1 & member(v0, all_8_2) = 0 & $i(v0)) % 6.15/1.58 | % 6.15/1.58 | BETA: splitting (22) gives: % 6.15/1.58 | % 6.15/1.58 | Case 1: % 6.15/1.58 | | % 6.15/1.58 | | (23) all_8_0 = 0 % 6.15/1.58 | | % 6.15/1.58 | | REDUCE: (7), (23) imply: % 6.15/1.58 | | (24) $false % 6.15/1.58 | | % 6.15/1.58 | | CLOSE: (24) is inconsistent. % 6.15/1.58 | | % 6.15/1.58 | Case 2: % 6.15/1.58 | | % 6.15/1.58 | | (25) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_8_1) = v1 % 6.15/1.59 | | & member(v0, all_8_2) = 0 & $i(v0)) % 6.15/1.59 | | % 6.15/1.59 | | DELTA: instantiating (25) with fresh symbols all_21_0, all_21_1 gives: % 6.15/1.59 | | (26) ~ (all_21_0 = 0) & member(all_21_1, all_8_1) = all_21_0 & % 6.15/1.59 | | member(all_21_1, all_8_2) = 0 & $i(all_21_1) % 6.15/1.59 | | % 6.15/1.59 | | ALPHA: (26) implies: % 6.15/1.59 | | (27) ~ (all_21_0 = 0) % 6.15/1.59 | | (28) $i(all_21_1) % 6.15/1.59 | | (29) member(all_21_1, all_8_2) = 0 % 6.15/1.59 | | (30) member(all_21_1, all_8_1) = all_21_0 % 6.15/1.59 | | % 6.15/1.59 | | GROUND_INST: instantiating (1) with all_8_5, all_8_3, all_21_1, all_8_2, % 6.15/1.59 | | simplifying with (8), (10), (11), (28), (29) gives: % 6.15/1.59 | | (31) ? [v0: any] : ? [v1: any] : (member(all_21_1, all_8_3) = v1 & % 6.15/1.59 | | member(all_21_1, all_8_5) = v0 & (v1 = 0 | v0 = 0)) % 6.15/1.59 | | % 6.15/1.59 | | GROUND_INST: instantiating (2) with all_8_4, all_8_3, all_21_1, all_8_1, % 6.15/1.59 | | all_21_0, simplifying with (9), (10), (12), (28), (30) gives: % 6.15/1.59 | | (32) all_21_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 6.15/1.59 | | 0) & member(all_21_1, all_8_3) = v1 & member(all_21_1, all_8_4) % 6.15/1.59 | | = v0) % 6.15/1.59 | | % 6.15/1.59 | | GROUND_INST: instantiating (1) with all_8_3, all_8_5, all_21_1, all_8_2, % 6.15/1.59 | | simplifying with (8), (10), (17), (28), (29) gives: % 6.15/1.59 | | (33) ? [v0: any] : ? [v1: any] : (member(all_21_1, all_8_3) = v0 & % 6.15/1.59 | | member(all_21_1, all_8_5) = v1 & (v1 = 0 | v0 = 0)) % 6.15/1.59 | | % 6.15/1.59 | | GROUND_INST: instantiating (2) with all_8_3, all_8_4, all_21_1, all_8_1, % 6.15/1.59 | | all_21_0, simplifying with (9), (10), (20), (28), (30) gives: % 6.15/1.59 | | (34) all_21_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 6.15/1.59 | | 0) & member(all_21_1, all_8_3) = v0 & member(all_21_1, all_8_4) % 6.15/1.59 | | = v1) % 6.15/1.59 | | % 6.15/1.59 | | DELTA: instantiating (33) with fresh symbols all_28_0, all_28_1 gives: % 6.15/1.59 | | (35) member(all_21_1, all_8_3) = all_28_1 & member(all_21_1, all_8_5) = % 6.15/1.59 | | all_28_0 & (all_28_0 = 0 | all_28_1 = 0) % 6.15/1.59 | | % 6.15/1.59 | | ALPHA: (35) implies: % 6.15/1.59 | | (36) member(all_21_1, all_8_5) = all_28_0 % 6.15/1.59 | | (37) member(all_21_1, all_8_3) = all_28_1 % 6.15/1.59 | | % 6.15/1.59 | | DELTA: instantiating (31) with fresh symbols all_30_0, all_30_1 gives: % 6.15/1.60 | | (38) member(all_21_1, all_8_3) = all_30_0 & member(all_21_1, all_8_5) = % 6.15/1.60 | | all_30_1 & (all_30_0 = 0 | all_30_1 = 0) % 6.15/1.60 | | % 6.15/1.60 | | ALPHA: (38) implies: % 6.15/1.60 | | (39) member(all_21_1, all_8_5) = all_30_1 % 6.15/1.60 | | (40) member(all_21_1, all_8_3) = all_30_0 % 6.15/1.60 | | (41) all_30_0 = 0 | all_30_1 = 0 % 6.15/1.60 | | % 6.15/1.60 | | BETA: splitting (34) gives: % 6.15/1.60 | | % 6.15/1.60 | | Case 1: % 6.15/1.60 | | | % 6.15/1.60 | | | (42) all_21_0 = 0 % 6.15/1.60 | | | % 6.15/1.60 | | | REDUCE: (27), (42) imply: % 6.15/1.60 | | | (43) $false % 6.15/1.60 | | | % 6.15/1.60 | | | CLOSE: (43) is inconsistent. % 6.15/1.60 | | | % 6.15/1.60 | | Case 2: % 6.15/1.60 | | | % 6.15/1.60 | | | (44) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 6.15/1.60 | | | member(all_21_1, all_8_3) = v0 & member(all_21_1, all_8_4) = v1) % 6.15/1.60 | | | % 6.15/1.60 | | | DELTA: instantiating (44) with fresh symbols all_36_0, all_36_1 gives: % 6.15/1.60 | | | (45) ~ (all_36_0 = 0) & ~ (all_36_1 = 0) & member(all_21_1, all_8_3) % 6.15/1.60 | | | = all_36_1 & member(all_21_1, all_8_4) = all_36_0 % 6.15/1.60 | | | % 6.15/1.60 | | | ALPHA: (45) implies: % 6.15/1.60 | | | (46) ~ (all_36_1 = 0) % 6.15/1.60 | | | (47) member(all_21_1, all_8_4) = all_36_0 % 6.15/1.60 | | | (48) member(all_21_1, all_8_3) = all_36_1 % 6.15/1.60 | | | % 6.15/1.60 | | | BETA: splitting (32) gives: % 6.15/1.60 | | | % 6.15/1.60 | | | Case 1: % 6.15/1.60 | | | | % 6.15/1.60 | | | | (49) all_21_0 = 0 % 6.15/1.60 | | | | % 6.15/1.60 | | | | REDUCE: (27), (49) imply: % 6.15/1.60 | | | | (50) $false % 6.15/1.60 | | | | % 6.15/1.60 | | | | CLOSE: (50) is inconsistent. % 6.15/1.60 | | | | % 6.15/1.60 | | | Case 2: % 6.15/1.60 | | | | % 6.15/1.60 | | | | (51) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 6.15/1.60 | | | | member(all_21_1, all_8_3) = v1 & member(all_21_1, all_8_4) = % 6.15/1.60 | | | | v0) % 6.15/1.60 | | | | % 6.15/1.60 | | | | DELTA: instantiating (51) with fresh symbols all_41_0, all_41_1 gives: % 6.15/1.60 | | | | (52) ~ (all_41_0 = 0) & ~ (all_41_1 = 0) & member(all_21_1, % 6.15/1.60 | | | | all_8_3) = all_41_0 & member(all_21_1, all_8_4) = all_41_1 % 6.15/1.60 | | | | % 6.15/1.60 | | | | ALPHA: (52) implies: % 6.15/1.60 | | | | (53) ~ (all_41_1 = 0) % 6.15/1.60 | | | | (54) member(all_21_1, all_8_4) = all_41_1 % 6.15/1.60 | | | | (55) member(all_21_1, all_8_3) = all_41_0 % 6.15/1.60 | | | | % 6.15/1.60 | | | | GROUND_INST: instantiating (5) with all_28_0, all_30_1, all_8_5, % 6.15/1.60 | | | | all_21_1, simplifying with (36), (39) gives: % 6.15/1.60 | | | | (56) all_30_1 = all_28_0 % 6.15/1.60 | | | | % 6.15/1.60 | | | | GROUND_INST: instantiating (5) with all_36_0, all_41_1, all_8_4, % 6.15/1.60 | | | | all_21_1, simplifying with (47), (54) gives: % 6.15/1.60 | | | | (57) all_41_1 = all_36_0 % 6.15/1.60 | | | | % 6.15/1.60 | | | | GROUND_INST: instantiating (5) with all_30_0, all_36_1, all_8_3, % 6.15/1.60 | | | | all_21_1, simplifying with (40), (48) gives: % 6.15/1.60 | | | | (58) all_36_1 = all_30_0 % 6.15/1.60 | | | | % 6.15/1.60 | | | | GROUND_INST: instantiating (5) with all_36_1, all_41_0, all_8_3, % 6.15/1.60 | | | | all_21_1, simplifying with (48), (55) gives: % 6.15/1.60 | | | | (59) all_41_0 = all_36_1 % 6.15/1.60 | | | | % 6.15/1.60 | | | | GROUND_INST: instantiating (5) with all_28_1, all_41_0, all_8_3, % 6.15/1.60 | | | | all_21_1, simplifying with (37), (55) gives: % 6.15/1.61 | | | | (60) all_41_0 = all_28_1 % 6.15/1.61 | | | | % 6.15/1.61 | | | | COMBINE_EQS: (59), (60) imply: % 6.15/1.61 | | | | (61) all_36_1 = all_28_1 % 6.15/1.61 | | | | % 6.15/1.61 | | | | SIMP: (61) implies: % 6.15/1.61 | | | | (62) all_36_1 = all_28_1 % 6.15/1.61 | | | | % 6.15/1.61 | | | | COMBINE_EQS: (58), (62) imply: % 6.15/1.61 | | | | (63) all_30_0 = all_28_1 % 6.15/1.61 | | | | % 6.15/1.61 | | | | SIMP: (63) implies: % 6.15/1.61 | | | | (64) all_30_0 = all_28_1 % 6.15/1.61 | | | | % 6.15/1.61 | | | | REDUCE: (53), (57) imply: % 6.15/1.61 | | | | (65) ~ (all_36_0 = 0) % 6.15/1.61 | | | | % 6.15/1.61 | | | | REDUCE: (46), (62) imply: % 6.15/1.61 | | | | (66) ~ (all_28_1 = 0) % 6.15/1.61 | | | | % 6.15/1.61 | | | | BETA: splitting (41) gives: % 6.15/1.61 | | | | % 6.15/1.61 | | | | Case 1: % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | (67) all_30_0 = 0 % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | COMBINE_EQS: (64), (67) imply: % 6.15/1.61 | | | | | (68) all_28_1 = 0 % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | REDUCE: (66), (68) imply: % 6.15/1.61 | | | | | (69) $false % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | CLOSE: (69) is inconsistent. % 6.15/1.61 | | | | | % 6.15/1.61 | | | | Case 2: % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | (70) all_30_1 = 0 % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | COMBINE_EQS: (56), (70) imply: % 6.15/1.61 | | | | | (71) all_28_0 = 0 % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | REDUCE: (36), (71) imply: % 6.15/1.61 | | | | | (72) member(all_21_1, all_8_5) = 0 % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | GROUND_INST: instantiating (21) with all_21_1, simplifying with (28), % 6.15/1.61 | | | | | (72) gives: % 6.15/1.61 | | | | | (73) member(all_21_1, all_8_4) = 0 % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | GROUND_INST: instantiating (5) with all_36_0, 0, all_8_4, all_21_1, % 6.15/1.61 | | | | | simplifying with (47), (73) gives: % 6.15/1.61 | | | | | (74) all_36_0 = 0 % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | REDUCE: (65), (74) imply: % 6.15/1.61 | | | | | (75) $false % 6.15/1.61 | | | | | % 6.15/1.61 | | | | | CLOSE: (75) is inconsistent. % 6.15/1.61 | | | | | % 6.15/1.61 | | | | End of split % 6.15/1.61 | | | | % 6.15/1.61 | | | End of split % 6.15/1.61 | | | % 6.15/1.61 | | End of split % 6.15/1.61 | | % 6.15/1.61 | End of split % 6.15/1.61 | % 6.15/1.61 End of proof % 6.15/1.61 % SZS output end Proof for theBenchmark % 6.15/1.61 % 6.15/1.61 978ms %------------------------------------------------------------------------------