%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET807+4 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n025.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 15:26:31 EDT 2023 % Result : Theorem 9.45s 1.99s % Output : Proof 11.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET807+4 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n025.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 16:50:53 EDT 2023 % 0.14/0.34 % 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 ... % 0.20/0.62 Running up to 7 provers in parallel. % 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 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 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 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 % 2.58/1.08 Prover 1: Preprocessing ... % 2.58/1.08 Prover 4: Preprocessing ... % 3.17/1.12 Prover 5: Preprocessing ... % 3.17/1.12 Prover 2: Preprocessing ... % 3.17/1.12 Prover 3: Preprocessing ... % 3.17/1.12 Prover 0: Preprocessing ... % 3.17/1.12 Prover 6: Preprocessing ... % 6.70/1.61 Prover 5: Proving ... % 6.70/1.66 Prover 2: Proving ... % 6.70/1.67 Prover 6: Proving ... % 6.70/1.67 Prover 1: Constructing countermodel ... % 6.70/1.67 Prover 3: Constructing countermodel ... % 7.62/1.79 Prover 4: Constructing countermodel ... % 8.31/1.82 Prover 0: Proving ... % 9.45/1.99 Prover 3: proved (1356ms) % 9.45/1.99 % 9.45/1.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.45/1.99 % 9.45/2.00 Prover 5: stopped % 9.45/2.00 Prover 6: stopped % 9.67/2.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.67/2.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.67/2.01 Prover 2: stopped % 9.67/2.02 Prover 0: stopped % 9.67/2.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.67/2.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.67/2.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.67/2.04 Prover 8: Preprocessing ... % 9.67/2.04 Prover 7: Preprocessing ... % 9.67/2.07 Prover 11: Preprocessing ... % 9.67/2.07 Prover 1: Found proof (size 52) % 9.67/2.07 Prover 1: proved (1443ms) % 9.67/2.08 Prover 4: stopped % 9.67/2.08 Prover 13: Preprocessing ... % 9.67/2.09 Prover 10: Preprocessing ... % 9.67/2.09 Prover 7: stopped % 9.67/2.12 Prover 10: stopped % 9.67/2.12 Prover 13: stopped % 9.67/2.13 Prover 11: stopped % 10.49/2.20 Prover 8: Warning: ignoring some quantifiers % 10.49/2.21 Prover 8: Constructing countermodel ... % 10.49/2.22 Prover 8: stopped % 10.49/2.22 % 10.49/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.49/2.22 % 10.49/2.23 % SZS output start Proof for theBenchmark % 11.03/2.23 Assumptions after simplification: % 11.03/2.23 --------------------------------- % 11.03/2.23 % 11.03/2.23 (pre_order) % 11.03/2.27 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pre_order(v0, v1) = % 11.03/2.27 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? % 11.03/2.27 [v6: int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v6 & % 11.03/2.27 apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & % 11.03/2.27 member(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: % 11.03/2.27 int] : ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 & % 11.03/2.27 $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (pre_order(v0, v1) = 0) | ~ % 11.03/2.27 $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] % 11.03/2.27 : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~ % 11.03/2.27 $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] : ? [v8: % 11.03/2.27 any] : ? [v9: any] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & % 11.03/2.27 member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) % 11.03/2.27 | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: int] : (v3 = % 11.03/2.27 0 | ~ (apply(v0, v2, v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = % 11.03/2.28 0) & member(v2, v1) = v4)))) % 11.03/2.28 % 11.03/2.28 (rel_subset) % 11.03/2.28 $i(subset_predicate) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 11.03/2.28 (apply(subset_predicate, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 11.03/2.28 int] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : % 11.03/2.28 ( ~ (apply(subset_predicate, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v0, % 11.03/2.28 v1) = 0) % 11.03/2.28 % 11.03/2.28 (subset) % 11.03/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 11.03/2.28 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 11.03/2.28 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 11.03/2.28 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 11.03/2.28 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 11.03/2.28 % 11.03/2.28 (thIV18a) % 11.03/2.28 $i(subset_predicate) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 11.03/2.28 & pre_order(subset_predicate, v1) = v2 & power_set(v0) = v1 & $i(v1) & % 11.03/2.28 $i(v0)) % 11.03/2.28 % 11.03/2.28 (function-axioms) % 11.03/2.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 11.03/2.29 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, % 11.03/2.29 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 11.03/2.29 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = % 11.03/2.29 v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.03/2.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.29 (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0: % 11.03/2.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.03/2.29 : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) & % 11.03/2.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 11.03/2.29 $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) % 11.03/2.29 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.03/2.29 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 11.03/2.29 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.29 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 11.03/2.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.29 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 11.03/2.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 11.03/2.29 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.03/2.29 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 11.03/2.29 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.03/2.29 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 11.03/2.29 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.03/2.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 11.03/2.29 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.03/2.29 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.29 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 11.03/2.29 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 11.03/2.29 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 11.03/2.29 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 11.03/2.29 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 11.03/2.29 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 11.03/2.29 (power_set(v2) = v0)) % 11.03/2.29 % 11.03/2.29 Further assumptions not needed in the proof: % 11.03/2.29 -------------------------------------------- % 11.03/2.29 difference, disjoint, empty_set, equal_set, equivalence, equivalence_class, % 11.03/2.29 intersection, partition, power_set, product, singleton, sum, union, % 11.03/2.29 unordered_pair % 11.03/2.29 % 11.03/2.29 Those formulas are unsatisfiable: % 11.03/2.29 --------------------------------- % 11.03/2.29 % 11.03/2.29 Begin of proof % 11.03/2.29 | % 11.03/2.29 | ALPHA: (subset) implies: % 11.03/2.29 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 11.03/2.29 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | % 11.03/2.29 | member(v2, v1) = 0)) % 11.03/2.29 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 11.03/2.29 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 11.03/2.29 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 11.03/2.29 | % 11.03/2.29 | ALPHA: (pre_order) implies: % 11.03/2.30 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pre_order(v0, % 11.03/2.30 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 11.03/2.30 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & apply(v0, v4, v5) = 0 & % 11.03/2.30 | apply(v0, v3, v5) = v6 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 % 11.03/2.30 | & member(v4, v1) = 0 & member(v3, v1) = 0 & $i(v5) & $i(v4) & % 11.03/2.30 | $i(v3)) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v0, v3, % 11.03/2.30 | v3) = v4 & member(v3, v1) = 0 & $i(v3))) % 11.03/2.30 | % 11.03/2.30 | ALPHA: (rel_subset) implies: % 11.03/2.30 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(subset_predicate, v0, v1) = 0) | % 11.03/2.30 | ~ $i(v1) | ~ $i(v0) | subset(v0, v1) = 0) % 11.03/2.30 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 11.03/2.30 | (apply(subset_predicate, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.03/2.30 | [v3: int] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 11.03/2.30 | % 11.03/2.30 | ALPHA: (thIV18a) implies: % 11.03/2.30 | (6) $i(subset_predicate) % 11.03/2.30 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 11.03/2.30 | pre_order(subset_predicate, v1) = v2 & power_set(v0) = v1 & $i(v1) & % 11.03/2.30 | $i(v0)) % 11.03/2.30 | % 11.03/2.30 | ALPHA: (function-axioms) implies: % 11.03/2.30 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.03/2.30 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 11.03/2.30 | = v0)) % 11.03/2.30 | % 11.03/2.30 | DELTA: instantiating (7) with fresh symbols all_21_0, all_21_1, all_21_2 % 11.03/2.30 | gives: % 11.03/2.30 | (9) ~ (all_21_0 = 0) & pre_order(subset_predicate, all_21_1) = all_21_0 & % 11.03/2.30 | power_set(all_21_2) = all_21_1 & $i(all_21_1) & $i(all_21_2) % 11.03/2.30 | % 11.03/2.30 | ALPHA: (9) implies: % 11.03/2.30 | (10) ~ (all_21_0 = 0) % 11.03/2.30 | (11) $i(all_21_1) % 11.39/2.30 | (12) pre_order(subset_predicate, all_21_1) = all_21_0 % 11.39/2.30 | % 11.39/2.30 | GROUND_INST: instantiating (3) with subset_predicate, all_21_1, all_21_0, % 11.39/2.30 | simplifying with (6), (11), (12) gives: % 11.39/2.31 | (13) all_21_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] % 11.39/2.31 | : ( ~ (v3 = 0) & apply(subset_predicate, v1, v2) = 0 & % 11.39/2.31 | apply(subset_predicate, v0, v2) = v3 & apply(subset_predicate, v0, % 11.39/2.31 | v1) = 0 & member(v2, all_21_1) = 0 & member(v1, all_21_1) = 0 & % 11.39/2.31 | member(v0, all_21_1) = 0 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] : % 11.39/2.31 | ? [v1: int] : ( ~ (v1 = 0) & apply(subset_predicate, v0, v0) = v1 & % 11.39/2.31 | member(v0, all_21_1) = 0 & $i(v0)) % 11.39/2.31 | % 11.39/2.31 | BETA: splitting (13) gives: % 11.39/2.31 | % 11.39/2.31 | Case 1: % 11.39/2.31 | | % 11.39/2.31 | | (14) all_21_0 = 0 % 11.39/2.31 | | % 11.39/2.31 | | REDUCE: (10), (14) imply: % 11.39/2.31 | | (15) $false % 11.39/2.31 | | % 11.39/2.31 | | CLOSE: (15) is inconsistent. % 11.39/2.31 | | % 11.39/2.31 | Case 2: % 11.39/2.31 | | % 11.39/2.31 | | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 11.39/2.31 | | 0) & apply(subset_predicate, v1, v2) = 0 & % 11.39/2.31 | | apply(subset_predicate, v0, v2) = v3 & apply(subset_predicate, v0, % 11.39/2.31 | | v1) = 0 & member(v2, all_21_1) = 0 & member(v1, all_21_1) = 0 & % 11.39/2.31 | | member(v0, all_21_1) = 0 & $i(v2) & $i(v1) & $i(v0)) | ? [v0: $i] % 11.39/2.31 | | : ? [v1: int] : ( ~ (v1 = 0) & apply(subset_predicate, v0, v0) = v1 % 11.39/2.31 | | & member(v0, all_21_1) = 0 & $i(v0)) % 11.39/2.31 | | % 11.39/2.31 | | BETA: splitting (16) gives: % 11.39/2.31 | | % 11.39/2.31 | | Case 1: % 11.39/2.31 | | | % 11.39/2.31 | | | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = % 11.39/2.31 | | | 0) & apply(subset_predicate, v1, v2) = 0 & % 11.39/2.31 | | | apply(subset_predicate, v0, v2) = v3 & apply(subset_predicate, % 11.39/2.31 | | | v0, v1) = 0 & member(v2, all_21_1) = 0 & member(v1, all_21_1) % 11.39/2.31 | | | = 0 & member(v0, all_21_1) = 0 & $i(v2) & $i(v1) & $i(v0)) % 11.39/2.31 | | | % 11.39/2.31 | | | DELTA: instantiating (17) with fresh symbols all_36_0, all_36_1, all_36_2, % 11.39/2.31 | | | all_36_3 gives: % 11.39/2.31 | | | (18) ~ (all_36_0 = 0) & apply(subset_predicate, all_36_2, all_36_1) = % 11.39/2.31 | | | 0 & apply(subset_predicate, all_36_3, all_36_1) = all_36_0 & % 11.39/2.31 | | | apply(subset_predicate, all_36_3, all_36_2) = 0 & member(all_36_1, % 11.39/2.31 | | | all_21_1) = 0 & member(all_36_2, all_21_1) = 0 & % 11.39/2.31 | | | member(all_36_3, all_21_1) = 0 & $i(all_36_1) & $i(all_36_2) & % 11.39/2.31 | | | $i(all_36_3) % 11.39/2.31 | | | % 11.39/2.31 | | | ALPHA: (18) implies: % 11.39/2.31 | | | (19) ~ (all_36_0 = 0) % 11.39/2.31 | | | (20) $i(all_36_3) % 11.39/2.31 | | | (21) $i(all_36_2) % 11.39/2.31 | | | (22) $i(all_36_1) % 11.39/2.31 | | | (23) apply(subset_predicate, all_36_3, all_36_2) = 0 % 11.39/2.31 | | | (24) apply(subset_predicate, all_36_3, all_36_1) = all_36_0 % 11.39/2.31 | | | (25) apply(subset_predicate, all_36_2, all_36_1) = 0 % 11.39/2.31 | | | % 11.39/2.32 | | | GROUND_INST: instantiating (4) with all_36_3, all_36_2, simplifying with % 11.39/2.32 | | | (20), (21), (23) gives: % 11.39/2.32 | | | (26) subset(all_36_3, all_36_2) = 0 % 11.39/2.32 | | | % 11.39/2.32 | | | GROUND_INST: instantiating (5) with all_36_3, all_36_1, all_36_0, % 11.39/2.32 | | | simplifying with (20), (22), (24) gives: % 11.39/2.32 | | | (27) all_36_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_36_3, % 11.39/2.32 | | | all_36_1) = v0) % 11.39/2.32 | | | % 11.39/2.32 | | | GROUND_INST: instantiating (4) with all_36_2, all_36_1, simplifying with % 11.39/2.32 | | | (21), (22), (25) gives: % 11.39/2.32 | | | (28) subset(all_36_2, all_36_1) = 0 % 11.39/2.32 | | | % 11.39/2.32 | | | BETA: splitting (27) gives: % 11.39/2.32 | | | % 11.39/2.32 | | | Case 1: % 11.39/2.32 | | | | % 11.39/2.32 | | | | (29) all_36_0 = 0 % 11.39/2.32 | | | | % 11.39/2.32 | | | | REDUCE: (19), (29) imply: % 11.39/2.32 | | | | (30) $false % 11.39/2.32 | | | | % 11.39/2.32 | | | | CLOSE: (30) is inconsistent. % 11.39/2.32 | | | | % 11.39/2.32 | | | Case 2: % 11.39/2.32 | | | | % 11.39/2.32 | | | | (31) ? [v0: int] : ( ~ (v0 = 0) & subset(all_36_3, all_36_1) = v0) % 11.39/2.32 | | | | % 11.39/2.32 | | | | DELTA: instantiating (31) with fresh symbol all_48_0 gives: % 11.39/2.32 | | | | (32) ~ (all_48_0 = 0) & subset(all_36_3, all_36_1) = all_48_0 % 11.39/2.32 | | | | % 11.39/2.32 | | | | ALPHA: (32) implies: % 11.39/2.32 | | | | (33) ~ (all_48_0 = 0) % 11.39/2.32 | | | | (34) subset(all_36_3, all_36_1) = all_48_0 % 11.39/2.32 | | | | % 11.39/2.32 | | | | GROUND_INST: instantiating (1) with all_36_3, all_36_2, simplifying with % 11.39/2.32 | | | | (20), (21), (26) gives: % 11.39/2.32 | | | | (35) ! [v0: $i] : ( ~ (member(v0, all_36_3) = 0) | ~ $i(v0) | % 11.39/2.32 | | | | member(v0, all_36_2) = 0) % 11.39/2.32 | | | | % 11.39/2.32 | | | | GROUND_INST: instantiating (2) with all_36_3, all_36_1, all_48_0, % 11.39/2.32 | | | | simplifying with (20), (22), (34) gives: % 11.39/2.32 | | | | (36) all_48_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 11.39/2.32 | | | | member(v0, all_36_1) = v1 & member(v0, all_36_3) = 0 & $i(v0)) % 11.39/2.32 | | | | % 11.39/2.32 | | | | GROUND_INST: instantiating (1) with all_36_2, all_36_1, simplifying with % 11.39/2.32 | | | | (21), (22), (28) gives: % 11.39/2.32 | | | | (37) ! [v0: $i] : ( ~ (member(v0, all_36_2) = 0) | ~ $i(v0) | % 11.39/2.32 | | | | member(v0, all_36_1) = 0) % 11.39/2.32 | | | | % 11.39/2.32 | | | | BETA: splitting (36) gives: % 11.39/2.32 | | | | % 11.39/2.32 | | | | Case 1: % 11.39/2.32 | | | | | % 11.39/2.32 | | | | | (38) all_48_0 = 0 % 11.39/2.32 | | | | | % 11.39/2.32 | | | | | REDUCE: (33), (38) imply: % 11.39/2.32 | | | | | (39) $false % 11.39/2.32 | | | | | % 11.39/2.32 | | | | | CLOSE: (39) is inconsistent. % 11.39/2.32 | | | | | % 11.39/2.32 | | | | Case 2: % 11.39/2.32 | | | | | % 11.39/2.33 | | | | | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.39/2.33 | | | | | all_36_1) = v1 & member(v0, all_36_3) = 0 & $i(v0)) % 11.39/2.33 | | | | | % 11.39/2.33 | | | | | DELTA: instantiating (40) with fresh symbols all_63_0, all_63_1 gives: % 11.39/2.33 | | | | | (41) ~ (all_63_0 = 0) & member(all_63_1, all_36_1) = all_63_0 & % 11.39/2.33 | | | | | member(all_63_1, all_36_3) = 0 & $i(all_63_1) % 11.39/2.33 | | | | | % 11.39/2.33 | | | | | ALPHA: (41) implies: % 11.39/2.33 | | | | | (42) ~ (all_63_0 = 0) % 11.39/2.33 | | | | | (43) $i(all_63_1) % 11.39/2.33 | | | | | (44) member(all_63_1, all_36_3) = 0 % 11.39/2.33 | | | | | (45) member(all_63_1, all_36_1) = all_63_0 % 11.39/2.33 | | | | | % 11.39/2.33 | | | | | GROUND_INST: instantiating (35) with all_63_1, simplifying with (43), % 11.39/2.33 | | | | | (44) gives: % 11.39/2.33 | | | | | (46) member(all_63_1, all_36_2) = 0 % 11.39/2.33 | | | | | % 11.39/2.33 | | | | | GROUND_INST: instantiating (37) with all_63_1, simplifying with (43), % 11.39/2.33 | | | | | (46) gives: % 11.39/2.33 | | | | | (47) member(all_63_1, all_36_1) = 0 % 11.39/2.33 | | | | | % 11.39/2.33 | | | | | GROUND_INST: instantiating (8) with all_63_0, 0, all_36_1, all_63_1, % 11.39/2.33 | | | | | simplifying with (45), (47) gives: % 11.39/2.33 | | | | | (48) all_63_0 = 0 % 11.39/2.33 | | | | | % 11.39/2.33 | | | | | REDUCE: (42), (48) imply: % 11.39/2.33 | | | | | (49) $false % 11.39/2.33 | | | | | % 11.39/2.33 | | | | | CLOSE: (49) is inconsistent. % 11.39/2.33 | | | | | % 11.39/2.33 | | | | End of split % 11.39/2.33 | | | | % 11.39/2.33 | | | End of split % 11.39/2.33 | | | % 11.39/2.33 | | Case 2: % 11.39/2.33 | | | % 11.39/2.33 | | | (50) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 11.39/2.33 | | | apply(subset_predicate, v0, v0) = v1 & member(v0, all_21_1) = 0 % 11.39/2.33 | | | & $i(v0)) % 11.39/2.33 | | | % 11.39/2.33 | | | DELTA: instantiating (50) with fresh symbols all_36_0, all_36_1 gives: % 11.39/2.33 | | | (51) ~ (all_36_0 = 0) & apply(subset_predicate, all_36_1, all_36_1) = % 11.39/2.33 | | | all_36_0 & member(all_36_1, all_21_1) = 0 & $i(all_36_1) % 11.39/2.33 | | | % 11.39/2.33 | | | ALPHA: (51) implies: % 11.39/2.33 | | | (52) ~ (all_36_0 = 0) % 11.39/2.33 | | | (53) $i(all_36_1) % 11.39/2.33 | | | (54) apply(subset_predicate, all_36_1, all_36_1) = all_36_0 % 11.39/2.33 | | | % 11.39/2.33 | | | GROUND_INST: instantiating (5) with all_36_1, all_36_1, all_36_0, % 11.39/2.33 | | | simplifying with (53), (54) gives: % 11.39/2.33 | | | (55) all_36_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_36_1, % 11.39/2.33 | | | all_36_1) = v0) % 11.39/2.33 | | | % 11.39/2.33 | | | BETA: splitting (55) gives: % 11.39/2.33 | | | % 11.39/2.33 | | | Case 1: % 11.39/2.33 | | | | % 11.39/2.33 | | | | (56) all_36_0 = 0 % 11.39/2.33 | | | | % 11.39/2.33 | | | | REDUCE: (52), (56) imply: % 11.39/2.33 | | | | (57) $false % 11.39/2.33 | | | | % 11.39/2.33 | | | | CLOSE: (57) is inconsistent. % 11.39/2.33 | | | | % 11.39/2.33 | | | Case 2: % 11.39/2.33 | | | | % 11.39/2.33 | | | | (58) ? [v0: int] : ( ~ (v0 = 0) & subset(all_36_1, all_36_1) = v0) % 11.39/2.33 | | | | % 11.39/2.33 | | | | DELTA: instantiating (58) with fresh symbol all_48_0 gives: % 11.39/2.33 | | | | (59) ~ (all_48_0 = 0) & subset(all_36_1, all_36_1) = all_48_0 % 11.39/2.33 | | | | % 11.39/2.34 | | | | ALPHA: (59) implies: % 11.39/2.34 | | | | (60) ~ (all_48_0 = 0) % 11.39/2.34 | | | | (61) subset(all_36_1, all_36_1) = all_48_0 % 11.39/2.34 | | | | % 11.39/2.34 | | | | GROUND_INST: instantiating (2) with all_36_1, all_36_1, all_48_0, % 11.39/2.34 | | | | simplifying with (53), (61) gives: % 11.39/2.34 | | | | (62) all_48_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 11.39/2.34 | | | | member(v0, all_36_1) = v1 & member(v0, all_36_1) = 0 & $i(v0)) % 11.39/2.34 | | | | % 11.39/2.34 | | | | BETA: splitting (62) gives: % 11.39/2.34 | | | | % 11.39/2.34 | | | | Case 1: % 11.39/2.34 | | | | | % 11.39/2.34 | | | | | (63) all_48_0 = 0 % 11.39/2.34 | | | | | % 11.39/2.34 | | | | | REDUCE: (60), (63) imply: % 11.39/2.34 | | | | | (64) $false % 11.39/2.34 | | | | | % 11.39/2.34 | | | | | CLOSE: (64) is inconsistent. % 11.39/2.34 | | | | | % 11.39/2.34 | | | | Case 2: % 11.39/2.34 | | | | | % 11.39/2.34 | | | | | (65) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.39/2.34 | | | | | all_36_1) = v1 & member(v0, all_36_1) = 0 & $i(v0)) % 11.39/2.34 | | | | | % 11.39/2.34 | | | | | DELTA: instantiating (65) with fresh symbols all_60_0, all_60_1 gives: % 11.39/2.34 | | | | | (66) ~ (all_60_0 = 0) & member(all_60_1, all_36_1) = all_60_0 & % 11.39/2.34 | | | | | member(all_60_1, all_36_1) = 0 & $i(all_60_1) % 11.39/2.34 | | | | | % 11.39/2.34 | | | | | ALPHA: (66) implies: % 11.39/2.34 | | | | | (67) ~ (all_60_0 = 0) % 11.39/2.34 | | | | | (68) member(all_60_1, all_36_1) = 0 % 11.39/2.34 | | | | | (69) member(all_60_1, all_36_1) = all_60_0 % 11.39/2.34 | | | | | % 11.39/2.34 | | | | | GROUND_INST: instantiating (8) with 0, all_60_0, all_36_1, all_60_1, % 11.39/2.34 | | | | | simplifying with (68), (69) gives: % 11.39/2.34 | | | | | (70) all_60_0 = 0 % 11.39/2.34 | | | | | % 11.39/2.34 | | | | | REDUCE: (67), (70) imply: % 11.39/2.34 | | | | | (71) $false % 11.39/2.34 | | | | | % 11.39/2.34 | | | | | CLOSE: (71) is inconsistent. % 11.39/2.34 | | | | | % 11.39/2.34 | | | | End of split % 11.39/2.34 | | | | % 11.39/2.34 | | | End of split % 11.39/2.34 | | | % 11.39/2.34 | | End of split % 11.39/2.34 | | % 11.39/2.34 | End of split % 11.39/2.34 | % 11.39/2.34 End of proof % 11.39/2.34 % SZS output end Proof for theBenchmark % 11.39/2.34 % 11.39/2.34 1730ms %------------------------------------------------------------------------------