%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET806+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%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 : 600s % DateTime : Tue Jul 19 00:22:12 EDT 2022 % Result : Theorem 18.67s 6.24s % Output : Proof 21.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SET806+4 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n005.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jul 9 16:31:07 EDT 2022 % 0.12/0.33 % CPUTime : % 0.17/0.58 ____ _ % 0.17/0.58 ___ / __ \_____(_)___ ________ __________ % 0.17/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.17/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.17/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.17/0.58 % 0.17/0.58 A Theorem Prover for First-Order Logic % 0.17/0.58 (ePrincess v.1.0) % 0.17/0.58 % 0.17/0.58 (c) Philipp Rümmer, 2009-2015 % 0.17/0.58 (c) Peter Backeman, 2014-2015 % 0.17/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.17/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.17/0.58 Bug reports to peter@backeman.se % 0.17/0.58 % 0.17/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.17/0.58 % 0.17/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.68/0.92 Prover 0: Preprocessing ... % 2.29/1.16 Prover 0: Warning: ignoring some quantifiers % 2.64/1.19 Prover 0: Constructing countermodel ... % 17.36/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 17.36/5.97 Prover 1: Preprocessing ... % 18.29/6.13 Prover 1: Constructing countermodel ... % 18.67/6.24 Prover 1: proved (316ms) % 18.67/6.24 Prover 0: stopped % 18.67/6.24 % 18.67/6.24 No countermodel exists, formula is valid % 18.67/6.24 % SZS status Theorem for theBenchmark % 18.67/6.24 % 18.67/6.24 Generating proof ... found it (size 111) % 21.03/6.74 % 21.03/6.74 % SZS output start Proof for theBenchmark % 21.03/6.74 Assumed formulas after preprocessing and simplification: % 21.03/6.74 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & equivalence(equal_set_predicate, v1) = v2 & power_set(v0) = v1 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (pre_order(v3, v4) = 0) | ~ (apply(v3, v5, v7) = v8) | ~ (apply(v3, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (apply(v3, v6, v7) = v12 & member(v7, v4) = v11 & member(v6, v4) = v10 & member(v5, v4) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equivalence_class(v5, v4, v3) = v7) | ~ (member(v6, v7) = v8) | ? [v9] : ? [v10] : (apply(v3, v5, v6) = v10 & member(v6, v4) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equivalence(v4, v3) = 0) | ~ (apply(v4, v5, v7) = v8) | ~ (apply(v4, v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (apply(v4, v6, v7) = v12 & member(v7, v3) = v11 & member(v6, v3) = v10 & member(v5, v3) = v9 & ( ~ (v12 = 0) | ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (product(v4) = v5) | ~ (member(v3, v6) = v7) | ~ (member(v3, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (difference(v5, v4) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : (member(v3, v5) = v8 & member(v3, v4) = v9 & ( ~ (v8 = 0) | v9 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (union(v4, v5) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & member(v3, v5) = v9 & member(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (intersection(v4, v5) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : (member(v3, v5) = v9 & member(v3, v4) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (partition(v3, v4) = 0) | ~ (member(v7, v5) = 0) | ~ (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v7, v6) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (sum(v4) = v5) | ~ (member(v3, v7) = 0) | ~ (member(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & member(v7, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = v3 | ~ (equivalence_class(v7, v6, v5) = v4) | ~ (equivalence_class(v7, v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = v3 | ~ (apply(v7, v6, v5) = v4) | ~ (apply(v7, v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (equivalence_class(v5, v4, v3) = v7) | ~ (member(v6, v7) = 0) | (apply(v3, v5, v6) = 0 & member(v6, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (pre_order(v3, v4) = 0) | ~ (apply(v3, v5, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & member(v5, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equivalence(v4, v3) = 0) | ~ (apply(v4, v5, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & member(v5, v3) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (partition(v3, v4) = 0) | ~ (subset(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & member(v5, v3) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (product(v4) = v5) | ~ (member(v3, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v4) = 0 & member(v3, v7) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unordered_pair(v4, v3) = v5) | ~ (member(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unordered_pair(v3, v4) = v5) | ~ (member(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (power_set(v4) = v5) | ~ (member(v3, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & subset(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v3 | v4 = v3 | ~ (unordered_pair(v4, v5) = v6) | ~ (member(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (pre_order(v6, v5) = v4) | ~ (pre_order(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (equivalence(v6, v5) = v4) | ~ (equivalence(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (partition(v6, v5) = v4) | ~ (partition(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (disjoint(v6, v5) = v4) | ~ (disjoint(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (unordered_pair(v6, v5) = v4) | ~ (unordered_pair(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (difference(v6, v5) = v4) | ~ (difference(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (union(v6, v5) = v4) | ~ (union(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (intersection(v6, v5) = v4) | ~ (intersection(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (equal_set(v6, v5) = v4) | ~ (equal_set(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (subset(v6, v5) = v4) | ~ (subset(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (member(v6, v5) = v4) | ~ (member(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (equivalence(v4, v3) = 0) | ~ (apply(v4, v5, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : (apply(v4, v6, v5) = v9 & member(v6, v3) = v8 & member(v5, v3) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | v9 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (difference(v5, v4) = v6) | ~ (member(v3, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & member(v3, v5) = 0 & member(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | ~ (member(v3, v6) = 0) | ? [v7] : ? [v8] : (member(v3, v5) = v8 & member(v3, v4) = v7 & (v8 = 0 | v7 = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v4, v5) = v6) | ~ (member(v3, v6) = 0) | (member(v3, v5) = 0 & member(v3, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = 0) & apply(v3, v7, v8) = 0 & apply(v3, v6, v8) = v14 & apply(v3, v6, v7) = 0 & member(v8, v4) = 0 & member(v7, v4) = 0 & member(v6, v4) = 0) | (v7 = 0 & ~ (v8 = 0) & apply(v3, v6, v6) = v8 & member(v6, v4) = 0))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v4, v3) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = 0) & apply(v4, v7, v8) = 0 & apply(v4, v6, v8) = v14 & apply(v4, v6, v7) = 0 & member(v8, v3) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0) | (v10 = 0 & v9 = 0 & v8 = 0 & ~ (v11 = 0) & apply(v4, v7, v6) = v11 & apply(v4, v6, v7) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0) | (v7 = 0 & ~ (v8 = 0) & apply(v4, v6, v6) = v8 & member(v6, v3) = 0))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apply(equal_set_predicate, v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & equal_set(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (partition(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v9 = 0 & v8 = 0 & ~ (v7 = v6) & member(v10, v7) = 0 & member(v10, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0) | (v7 = 0 & ~ (v8 = 0) & subset(v6, v4) = v8 & member(v6, v3) = 0) | (v7 = 0 & member(v6, v4) = 0 & ! [v13] : ( ~ (member(v6, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & member(v13, v3) = v14))))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (disjoint(v3, v4) = v5) | ? [v6] : (member(v6, v4) = 0 & member(v6, v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (singleton(v3) = v4) | ~ (member(v3, v4) = v5)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equal_set(v3, v4) = v5) | ? [v6] : ? [v7] : (subset(v4, v3) = v7 & subset(v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & member(v6, v4) = v7 & member(v6, v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (product(v5) = v4) | ~ (product(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (sum(v5) = v4) | ~ (sum(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (singleton(v5) = v4) | ~ (singleton(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (singleton(v4) = v5) | ~ (member(v3, v5) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (power_set(v5) = v4) | ~ (power_set(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (partition(v3, v4) = 0) | ~ (member(v5, v4) = 0) | ? [v6] : (member(v6, v3) = 0 & member(v5, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (disjoint(v3, v4) = 0) | ~ (member(v5, v3) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v5, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sum(v4) = v5) | ~ (member(v3, v5) = 0) | ? [v6] : (member(v6, v4) = 0 & member(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (power_set(v4) = v5) | ~ (member(v3, v5) = 0) | subset(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset(v3, v4) = 0) | ~ (member(v5, v3) = 0) | member(v5, v4) = 0) & ! [v3] : ! [v4] : ( ~ (apply(equal_set_predicate, v3, v4) = 0) | equal_set(v3, v4) = 0) & ! [v3] : ! [v4] : ( ~ (equal_set(v3, v4) = 0) | (subset(v4, v3) = 0 & subset(v3, v4) = 0)) & ! [v3] : ~ (member(v3, empty_set) = 0)) % 21.03/6.78 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 21.03/6.78 | (1) ~ (all_0_0_0 = 0) & equivalence(equal_set_predicate, all_0_1_1) = all_0_0_0 & power_set(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : ? [v7] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v1, v3, v4) = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v1, v3, v2) = v6 & member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pre_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equivalence(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apply(equal_set_predicate, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & equal_set(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (partition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 & ! [v10] : ( ~ (member(v3, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ( ~ (apply(equal_set_predicate, v0, v1) = 0) | equal_set(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) % 21.45/6.80 | % 21.45/6.80 | Applying alpha-rule on (1) yields: % 21.45/6.80 | (2) ~ (all_0_0_0 = 0) % 21.45/6.80 | (3) power_set(all_0_2_2) = all_0_1_1 % 21.45/6.80 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 21.45/6.80 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 21.45/6.80 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0)) % 21.45/6.80 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 21.45/6.80 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 21.45/6.80 | (9) equivalence(equal_set_predicate, all_0_1_1) = all_0_0_0 % 21.45/6.80 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 21.45/6.80 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (partition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & v6 = 0 & v5 = 0 & ~ (v4 = v3) & member(v7, v4) = 0 & member(v7, v3) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & subset(v3, v1) = v5 & member(v3, v0) = 0) | (v4 = 0 & member(v3, v1) = 0 & ! [v10] : ( ~ (member(v3, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v0) = v11))))) % 21.45/6.80 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 21.45/6.80 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 21.45/6.80 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 21.45/6.80 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 21.45/6.80 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 21.45/6.80 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 21.45/6.80 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 21.45/6.80 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apply(equal_set_predicate, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & equal_set(v0, v1) = v3)) % 21.45/6.80 | (20) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 21.45/6.80 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0)) % 21.45/6.80 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 21.45/6.80 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 21.45/6.80 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 21.45/6.80 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 21.45/6.80 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 21.45/6.81 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 21.45/6.81 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) % 21.45/6.81 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v1, v3, v4) = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 21.45/6.81 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 21.45/6.81 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 21.45/6.81 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 21.45/6.81 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (apply(v1, v3, v2) = v6 & member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) % 21.45/6.81 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equivalence(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v11 & apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v7 = 0 & v6 = 0 & v5 = 0 & ~ (v8 = 0) & apply(v1, v4, v3) = v8 & apply(v1, v3, v4) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v1, v3, v3) = v5 & member(v3, v0) = 0))) % 21.45/6.81 | (35) ! [v0] : ~ (member(v0, empty_set) = 0) % 21.45/6.81 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0)) % 21.45/6.81 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (apply(v0, v3, v4) = v9 & member(v4, v1) = v8 & member(v3, v1) = v7 & member(v2, v1) = v6 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 21.45/6.81 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) % 21.45/6.81 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) % 21.45/6.81 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 21.45/6.81 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 21.45/6.81 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (partition(v0, v1) = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v4, v3) = v5)) % 21.45/6.81 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 21.45/6.81 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) % 21.45/6.81 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (pre_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v4 = 0 & ~ (v5 = 0) & apply(v0, v3, v3) = v5 & member(v3, v1) = 0))) % 21.45/6.81 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) % 21.45/6.81 | (47) ! [v0] : ! [v1] : ( ~ (apply(equal_set_predicate, v0, v1) = 0) | equal_set(v0, v1) = 0) % 21.45/6.81 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) % 21.45/6.81 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 21.45/6.81 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : ? [v7] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 21.45/6.81 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) % 21.45/6.81 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) % 21.45/6.81 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 21.45/6.81 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) % 21.45/6.81 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 21.45/6.82 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 21.45/6.82 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 21.45/6.82 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) % 21.45/6.82 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 21.45/6.82 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 21.45/6.82 | % 21.45/6.82 | Instantiating formula (34) with all_0_0_0, equal_set_predicate, all_0_1_1 and discharging atoms equivalence(equal_set_predicate, all_0_1_1) = all_0_0_0, yields: % 21.45/6.82 | (61) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(equal_set_predicate, v1, v2) = 0 & apply(equal_set_predicate, v0, v2) = v8 & apply(equal_set_predicate, v0, v1) = 0 & member(v2, all_0_1_1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(equal_set_predicate, v1, v0) = v5 & apply(equal_set_predicate, v0, v1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(equal_set_predicate, v0, v0) = v2 & member(v0, all_0_1_1) = 0)) % 21.45/6.82 | % 21.45/6.82 +-Applying beta-rule and splitting (61), into two cases. % 21.45/6.82 |-Branch one: % 21.45/6.82 | (62) all_0_0_0 = 0 % 21.45/6.82 | % 21.45/6.82 | Equations (62) can reduce 2 to: % 21.45/6.82 | (63) $false % 21.45/6.82 | % 21.45/6.82 |-The branch is then unsatisfiable % 21.45/6.82 |-Branch two: % 21.45/6.82 | (2) ~ (all_0_0_0 = 0) % 21.45/6.82 | (65) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(equal_set_predicate, v1, v2) = 0 & apply(equal_set_predicate, v0, v2) = v8 & apply(equal_set_predicate, v0, v1) = 0 & member(v2, all_0_1_1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v4 = 0 & v3 = 0 & v2 = 0 & ~ (v5 = 0) & apply(equal_set_predicate, v1, v0) = v5 & apply(equal_set_predicate, v0, v1) = 0 & member(v1, all_0_1_1) = 0 & member(v0, all_0_1_1) = 0) | (v1 = 0 & ~ (v2 = 0) & apply(equal_set_predicate, v0, v0) = v2 & member(v0, all_0_1_1) = 0)) % 21.45/6.82 | % 21.45/6.82 | Instantiating (65) with all_10_0_3, all_10_1_4, all_10_2_5, all_10_3_6, all_10_4_7, all_10_5_8, all_10_6_9, all_10_7_10, all_10_8_11 yields: % 21.45/6.82 | (66) (all_10_1_4 = 0 & all_10_2_5 = 0 & all_10_3_6 = 0 & all_10_4_7 = 0 & all_10_5_8 = 0 & ~ (all_10_0_3 = 0) & apply(equal_set_predicate, all_10_7_10, all_10_6_9) = 0 & apply(equal_set_predicate, all_10_8_11, all_10_6_9) = all_10_0_3 & apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0 & member(all_10_6_9, all_0_1_1) = 0 & member(all_10_7_10, all_0_1_1) = 0 & member(all_10_8_11, all_0_1_1) = 0) | (all_10_4_7 = 0 & all_10_5_8 = 0 & all_10_6_9 = 0 & ~ (all_10_3_6 = 0) & apply(equal_set_predicate, all_10_7_10, all_10_8_11) = all_10_3_6 & apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0 & member(all_10_7_10, all_0_1_1) = 0 & member(all_10_8_11, all_0_1_1) = 0) | (all_10_7_10 = 0 & ~ (all_10_6_9 = 0) & apply(equal_set_predicate, all_10_8_11, all_10_8_11) = all_10_6_9 & member(all_10_8_11, all_0_1_1) = 0) % 21.45/6.82 | % 21.45/6.82 +-Applying beta-rule and splitting (66), into two cases. % 21.45/6.82 |-Branch one: % 21.45/6.82 | (67) (all_10_1_4 = 0 & all_10_2_5 = 0 & all_10_3_6 = 0 & all_10_4_7 = 0 & all_10_5_8 = 0 & ~ (all_10_0_3 = 0) & apply(equal_set_predicate, all_10_7_10, all_10_6_9) = 0 & apply(equal_set_predicate, all_10_8_11, all_10_6_9) = all_10_0_3 & apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0 & member(all_10_6_9, all_0_1_1) = 0 & member(all_10_7_10, all_0_1_1) = 0 & member(all_10_8_11, all_0_1_1) = 0) | (all_10_4_7 = 0 & all_10_5_8 = 0 & all_10_6_9 = 0 & ~ (all_10_3_6 = 0) & apply(equal_set_predicate, all_10_7_10, all_10_8_11) = all_10_3_6 & apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0 & member(all_10_7_10, all_0_1_1) = 0 & member(all_10_8_11, all_0_1_1) = 0) % 21.45/6.82 | % 21.45/6.82 +-Applying beta-rule and splitting (67), into two cases. % 21.45/6.82 |-Branch one: % 21.45/6.82 | (68) all_10_1_4 = 0 & all_10_2_5 = 0 & all_10_3_6 = 0 & all_10_4_7 = 0 & all_10_5_8 = 0 & ~ (all_10_0_3 = 0) & apply(equal_set_predicate, all_10_7_10, all_10_6_9) = 0 & apply(equal_set_predicate, all_10_8_11, all_10_6_9) = all_10_0_3 & apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0 & member(all_10_6_9, all_0_1_1) = 0 & member(all_10_7_10, all_0_1_1) = 0 & member(all_10_8_11, all_0_1_1) = 0 % 21.45/6.82 | % 21.45/6.82 | Applying alpha-rule on (68) yields: % 21.45/6.82 | (69) member(all_10_7_10, all_0_1_1) = 0 % 21.45/6.82 | (70) all_10_5_8 = 0 % 21.45/6.82 | (71) all_10_4_7 = 0 % 21.45/6.82 | (72) member(all_10_8_11, all_0_1_1) = 0 % 21.45/6.82 | (73) apply(equal_set_predicate, all_10_8_11, all_10_6_9) = all_10_0_3 % 21.45/6.82 | (74) all_10_3_6 = 0 % 21.45/6.82 | (75) all_10_2_5 = 0 % 21.45/6.82 | (76) all_10_1_4 = 0 % 21.45/6.82 | (77) ~ (all_10_0_3 = 0) % 21.45/6.82 | (78) member(all_10_6_9, all_0_1_1) = 0 % 21.45/6.82 | (79) apply(equal_set_predicate, all_10_7_10, all_10_6_9) = 0 % 21.45/6.82 | (80) apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0 % 21.45/6.82 | % 21.45/6.82 | Instantiating formula (47) with all_10_6_9, all_10_7_10 and discharging atoms apply(equal_set_predicate, all_10_7_10, all_10_6_9) = 0, yields: % 21.45/6.82 | (81) equal_set(all_10_7_10, all_10_6_9) = 0 % 21.45/6.82 | % 21.45/6.82 | Instantiating formula (19) with all_10_0_3, all_10_6_9, all_10_8_11 and discharging atoms apply(equal_set_predicate, all_10_8_11, all_10_6_9) = all_10_0_3, yields: % 21.45/6.82 | (82) all_10_0_3 = 0 | ? [v0] : ( ~ (v0 = 0) & equal_set(all_10_8_11, all_10_6_9) = v0) % 21.45/6.82 | % 21.45/6.82 | Instantiating formula (47) with all_10_7_10, all_10_8_11 and discharging atoms apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0, yields: % 21.45/6.82 | (83) equal_set(all_10_8_11, all_10_7_10) = 0 % 21.45/6.82 | % 21.45/6.82 +-Applying beta-rule and splitting (82), into two cases. % 21.45/6.82 |-Branch one: % 21.45/6.82 | (84) all_10_0_3 = 0 % 21.45/6.82 | % 21.45/6.82 | Equations (84) can reduce 77 to: % 21.45/6.82 | (63) $false % 21.45/6.82 | % 21.45/6.82 |-The branch is then unsatisfiable % 21.45/6.82 |-Branch two: % 21.45/6.82 | (77) ~ (all_10_0_3 = 0) % 21.45/6.82 | (87) ? [v0] : ( ~ (v0 = 0) & equal_set(all_10_8_11, all_10_6_9) = v0) % 21.45/6.82 | % 21.45/6.82 | Instantiating (87) with all_36_0_12 yields: % 21.45/6.82 | (88) ~ (all_36_0_12 = 0) & equal_set(all_10_8_11, all_10_6_9) = all_36_0_12 % 21.45/6.82 | % 21.45/6.82 | Applying alpha-rule on (88) yields: % 21.45/6.82 | (89) ~ (all_36_0_12 = 0) % 21.45/6.82 | (90) equal_set(all_10_8_11, all_10_6_9) = all_36_0_12 % 21.45/6.82 | % 21.45/6.82 | Instantiating formula (20) with all_10_6_9, all_10_7_10 and discharging atoms equal_set(all_10_7_10, all_10_6_9) = 0, yields: % 21.45/6.82 | (91) subset(all_10_6_9, all_10_7_10) = 0 & subset(all_10_7_10, all_10_6_9) = 0 % 21.45/6.82 | % 21.45/6.82 | Applying alpha-rule on (91) yields: % 21.45/6.82 | (92) subset(all_10_6_9, all_10_7_10) = 0 % 21.45/6.82 | (93) subset(all_10_7_10, all_10_6_9) = 0 % 21.45/6.82 | % 21.45/6.82 | Instantiating formula (26) with all_36_0_12, all_10_6_9, all_10_8_11 and discharging atoms equal_set(all_10_8_11, all_10_6_9) = all_36_0_12, yields: % 21.45/6.82 | (94) all_36_0_12 = 0 | ? [v0] : ? [v1] : (subset(all_10_6_9, all_10_8_11) = v1 & subset(all_10_8_11, all_10_6_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.45/6.82 | % 21.45/6.82 | Instantiating formula (20) with all_10_7_10, all_10_8_11 and discharging atoms equal_set(all_10_8_11, all_10_7_10) = 0, yields: % 21.45/6.82 | (95) subset(all_10_7_10, all_10_8_11) = 0 & subset(all_10_8_11, all_10_7_10) = 0 % 21.45/6.82 | % 21.45/6.82 | Applying alpha-rule on (95) yields: % 21.45/6.82 | (96) subset(all_10_7_10, all_10_8_11) = 0 % 21.45/6.82 | (97) subset(all_10_8_11, all_10_7_10) = 0 % 21.45/6.82 | % 21.45/6.82 +-Applying beta-rule and splitting (94), into two cases. % 21.45/6.82 |-Branch one: % 21.45/6.82 | (98) all_36_0_12 = 0 % 21.45/6.82 | % 21.45/6.82 | Equations (98) can reduce 89 to: % 21.45/6.82 | (63) $false % 21.45/6.82 | % 21.45/6.82 |-The branch is then unsatisfiable % 21.45/6.82 |-Branch two: % 21.45/6.82 | (89) ~ (all_36_0_12 = 0) % 21.45/6.82 | (101) ? [v0] : ? [v1] : (subset(all_10_6_9, all_10_8_11) = v1 & subset(all_10_8_11, all_10_6_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.45/6.83 | % 21.45/6.83 | Instantiating (101) with all_48_0_13, all_48_1_14 yields: % 21.45/6.83 | (102) subset(all_10_6_9, all_10_8_11) = all_48_0_13 & subset(all_10_8_11, all_10_6_9) = all_48_1_14 & ( ~ (all_48_0_13 = 0) | ~ (all_48_1_14 = 0)) % 21.45/6.83 | % 21.45/6.83 | Applying alpha-rule on (102) yields: % 21.45/6.83 | (103) subset(all_10_6_9, all_10_8_11) = all_48_0_13 % 21.45/6.83 | (104) subset(all_10_8_11, all_10_6_9) = all_48_1_14 % 21.45/6.83 | (105) ~ (all_48_0_13 = 0) | ~ (all_48_1_14 = 0) % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (57) with all_10_7_10, all_10_8_11, 0, all_48_0_13 and discharging atoms subset(all_10_7_10, all_10_8_11) = 0, yields: % 21.45/6.83 | (106) all_48_0_13 = 0 | ~ (subset(all_10_7_10, all_10_8_11) = all_48_0_13) % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (17) with all_48_0_13, all_10_8_11, all_10_6_9 and discharging atoms subset(all_10_6_9, all_10_8_11) = all_48_0_13, yields: % 21.45/6.83 | (107) all_48_0_13 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_6_9) = 0 & member(v0, all_10_8_11) = v1) % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (17) with all_48_1_14, all_10_6_9, all_10_8_11 and discharging atoms subset(all_10_8_11, all_10_6_9) = all_48_1_14, yields: % 21.45/6.83 | (108) all_48_1_14 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_6_9) = v1 & member(v0, all_10_8_11) = 0) % 21.45/6.83 | % 21.45/6.83 +-Applying beta-rule and splitting (106), into two cases. % 21.45/6.83 |-Branch one: % 21.45/6.83 | (109) ~ (subset(all_10_7_10, all_10_8_11) = all_48_0_13) % 21.45/6.83 | % 21.45/6.83 | Using (96) and (109) yields: % 21.45/6.83 | (110) ~ (all_48_0_13 = 0) % 21.45/6.83 | % 21.45/6.83 +-Applying beta-rule and splitting (107), into two cases. % 21.45/6.83 |-Branch one: % 21.45/6.83 | (111) all_48_0_13 = 0 % 21.45/6.83 | % 21.45/6.83 | Equations (111) can reduce 110 to: % 21.45/6.83 | (63) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (110) ~ (all_48_0_13 = 0) % 21.45/6.83 | (114) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_6_9) = 0 & member(v0, all_10_8_11) = v1) % 21.45/6.83 | % 21.45/6.83 | Instantiating (114) with all_195_0_15, all_195_1_16 yields: % 21.45/6.83 | (115) ~ (all_195_0_15 = 0) & member(all_195_1_16, all_10_6_9) = 0 & member(all_195_1_16, all_10_8_11) = all_195_0_15 % 21.45/6.83 | % 21.45/6.83 | Applying alpha-rule on (115) yields: % 21.45/6.83 | (116) ~ (all_195_0_15 = 0) % 21.45/6.83 | (117) member(all_195_1_16, all_10_6_9) = 0 % 21.45/6.83 | (118) member(all_195_1_16, all_10_8_11) = all_195_0_15 % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (41) with all_195_1_16, all_10_8_11, all_195_0_15, 0 and discharging atoms member(all_195_1_16, all_10_8_11) = all_195_0_15, yields: % 21.45/6.83 | (119) all_195_0_15 = 0 | ~ (member(all_195_1_16, all_10_8_11) = 0) % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (18) with all_195_1_16, all_10_7_10, all_10_6_9 and discharging atoms subset(all_10_6_9, all_10_7_10) = 0, member(all_195_1_16, all_10_6_9) = 0, yields: % 21.45/6.83 | (120) member(all_195_1_16, all_10_7_10) = 0 % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (18) with all_195_1_16, all_10_8_11, all_10_7_10 and discharging atoms subset(all_10_7_10, all_10_8_11) = 0, member(all_195_1_16, all_10_7_10) = 0, yields: % 21.45/6.83 | (121) member(all_195_1_16, all_10_8_11) = 0 % 21.45/6.83 | % 21.45/6.83 +-Applying beta-rule and splitting (119), into two cases. % 21.45/6.83 |-Branch one: % 21.45/6.83 | (122) ~ (member(all_195_1_16, all_10_8_11) = 0) % 21.45/6.83 | % 21.45/6.83 | Using (121) and (122) yields: % 21.45/6.83 | (123) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (121) member(all_195_1_16, all_10_8_11) = 0 % 21.45/6.83 | (125) all_195_0_15 = 0 % 21.45/6.83 | % 21.45/6.83 | Equations (125) can reduce 116 to: % 21.45/6.83 | (63) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (127) subset(all_10_7_10, all_10_8_11) = all_48_0_13 % 21.45/6.83 | (111) all_48_0_13 = 0 % 21.45/6.83 | % 21.45/6.83 +-Applying beta-rule and splitting (105), into two cases. % 21.45/6.83 |-Branch one: % 21.45/6.83 | (110) ~ (all_48_0_13 = 0) % 21.45/6.83 | % 21.45/6.83 | Equations (111) can reduce 110 to: % 21.45/6.83 | (63) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (111) all_48_0_13 = 0 % 21.45/6.83 | (132) ~ (all_48_1_14 = 0) % 21.45/6.83 | % 21.45/6.83 +-Applying beta-rule and splitting (108), into two cases. % 21.45/6.83 |-Branch one: % 21.45/6.83 | (133) all_48_1_14 = 0 % 21.45/6.83 | % 21.45/6.83 | Equations (133) can reduce 132 to: % 21.45/6.83 | (63) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (132) ~ (all_48_1_14 = 0) % 21.45/6.83 | (136) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_6_9) = v1 & member(v0, all_10_8_11) = 0) % 21.45/6.83 | % 21.45/6.83 | Instantiating (136) with all_195_0_19, all_195_1_20 yields: % 21.45/6.83 | (137) ~ (all_195_0_19 = 0) & member(all_195_1_20, all_10_6_9) = all_195_0_19 & member(all_195_1_20, all_10_8_11) = 0 % 21.45/6.83 | % 21.45/6.83 | Applying alpha-rule on (137) yields: % 21.45/6.83 | (138) ~ (all_195_0_19 = 0) % 21.45/6.83 | (139) member(all_195_1_20, all_10_6_9) = all_195_0_19 % 21.45/6.83 | (140) member(all_195_1_20, all_10_8_11) = 0 % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (18) with all_195_1_20, all_10_7_10, all_10_8_11 and discharging atoms subset(all_10_8_11, all_10_7_10) = 0, member(all_195_1_20, all_10_8_11) = 0, yields: % 21.45/6.83 | (141) member(all_195_1_20, all_10_7_10) = 0 % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (18) with all_195_1_20, all_10_6_9, all_10_7_10 and discharging atoms subset(all_10_7_10, all_10_6_9) = 0, member(all_195_1_20, all_10_7_10) = 0, yields: % 21.45/6.83 | (142) member(all_195_1_20, all_10_6_9) = 0 % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (41) with all_195_1_20, all_10_6_9, 0, all_195_0_19 and discharging atoms member(all_195_1_20, all_10_6_9) = all_195_0_19, member(all_195_1_20, all_10_6_9) = 0, yields: % 21.45/6.83 | (143) all_195_0_19 = 0 % 21.45/6.83 | % 21.45/6.83 | Equations (143) can reduce 138 to: % 21.45/6.83 | (63) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (145) all_10_4_7 = 0 & all_10_5_8 = 0 & all_10_6_9 = 0 & ~ (all_10_3_6 = 0) & apply(equal_set_predicate, all_10_7_10, all_10_8_11) = all_10_3_6 & apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0 & member(all_10_7_10, all_0_1_1) = 0 & member(all_10_8_11, all_0_1_1) = 0 % 21.45/6.83 | % 21.45/6.83 | Applying alpha-rule on (145) yields: % 21.45/6.83 | (69) member(all_10_7_10, all_0_1_1) = 0 % 21.45/6.83 | (70) all_10_5_8 = 0 % 21.45/6.83 | (71) all_10_4_7 = 0 % 21.45/6.83 | (72) member(all_10_8_11, all_0_1_1) = 0 % 21.45/6.83 | (150) ~ (all_10_3_6 = 0) % 21.45/6.83 | (151) apply(equal_set_predicate, all_10_7_10, all_10_8_11) = all_10_3_6 % 21.45/6.83 | (152) all_10_6_9 = 0 % 21.45/6.83 | (80) apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0 % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (19) with all_10_3_6, all_10_8_11, all_10_7_10 and discharging atoms apply(equal_set_predicate, all_10_7_10, all_10_8_11) = all_10_3_6, yields: % 21.45/6.83 | (154) all_10_3_6 = 0 | ? [v0] : ( ~ (v0 = 0) & equal_set(all_10_7_10, all_10_8_11) = v0) % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (47) with all_10_7_10, all_10_8_11 and discharging atoms apply(equal_set_predicate, all_10_8_11, all_10_7_10) = 0, yields: % 21.45/6.83 | (83) equal_set(all_10_8_11, all_10_7_10) = 0 % 21.45/6.83 | % 21.45/6.83 +-Applying beta-rule and splitting (154), into two cases. % 21.45/6.83 |-Branch one: % 21.45/6.83 | (74) all_10_3_6 = 0 % 21.45/6.83 | % 21.45/6.83 | Equations (74) can reduce 150 to: % 21.45/6.83 | (63) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (150) ~ (all_10_3_6 = 0) % 21.45/6.83 | (159) ? [v0] : ( ~ (v0 = 0) & equal_set(all_10_7_10, all_10_8_11) = v0) % 21.45/6.83 | % 21.45/6.83 | Instantiating (159) with all_36_0_21 yields: % 21.45/6.83 | (160) ~ (all_36_0_21 = 0) & equal_set(all_10_7_10, all_10_8_11) = all_36_0_21 % 21.45/6.83 | % 21.45/6.83 | Applying alpha-rule on (160) yields: % 21.45/6.83 | (161) ~ (all_36_0_21 = 0) % 21.45/6.83 | (162) equal_set(all_10_7_10, all_10_8_11) = all_36_0_21 % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (26) with all_36_0_21, all_10_8_11, all_10_7_10 and discharging atoms equal_set(all_10_7_10, all_10_8_11) = all_36_0_21, yields: % 21.45/6.83 | (163) all_36_0_21 = 0 | ? [v0] : ? [v1] : (subset(all_10_7_10, all_10_8_11) = v0 & subset(all_10_8_11, all_10_7_10) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (20) with all_10_7_10, all_10_8_11 and discharging atoms equal_set(all_10_8_11, all_10_7_10) = 0, yields: % 21.45/6.83 | (95) subset(all_10_7_10, all_10_8_11) = 0 & subset(all_10_8_11, all_10_7_10) = 0 % 21.45/6.83 | % 21.45/6.83 | Applying alpha-rule on (95) yields: % 21.45/6.83 | (96) subset(all_10_7_10, all_10_8_11) = 0 % 21.45/6.83 | (97) subset(all_10_8_11, all_10_7_10) = 0 % 21.45/6.83 | % 21.45/6.83 +-Applying beta-rule and splitting (163), into two cases. % 21.45/6.83 |-Branch one: % 21.45/6.83 | (167) all_36_0_21 = 0 % 21.45/6.83 | % 21.45/6.83 | Equations (167) can reduce 161 to: % 21.45/6.83 | (63) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (161) ~ (all_36_0_21 = 0) % 21.45/6.83 | (170) ? [v0] : ? [v1] : (subset(all_10_7_10, all_10_8_11) = v0 & subset(all_10_8_11, all_10_7_10) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.45/6.83 | % 21.45/6.83 | Instantiating (170) with all_48_0_22, all_48_1_23 yields: % 21.45/6.83 | (171) subset(all_10_7_10, all_10_8_11) = all_48_1_23 & subset(all_10_8_11, all_10_7_10) = all_48_0_22 & ( ~ (all_48_0_22 = 0) | ~ (all_48_1_23 = 0)) % 21.45/6.83 | % 21.45/6.83 | Applying alpha-rule on (171) yields: % 21.45/6.83 | (172) subset(all_10_7_10, all_10_8_11) = all_48_1_23 % 21.45/6.83 | (173) subset(all_10_8_11, all_10_7_10) = all_48_0_22 % 21.45/6.83 | (174) ~ (all_48_0_22 = 0) | ~ (all_48_1_23 = 0) % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (57) with all_10_7_10, all_10_8_11, 0, all_48_1_23 and discharging atoms subset(all_10_7_10, all_10_8_11) = all_48_1_23, subset(all_10_7_10, all_10_8_11) = 0, yields: % 21.45/6.83 | (175) all_48_1_23 = 0 % 21.45/6.83 | % 21.45/6.83 | Instantiating formula (57) with all_10_8_11, all_10_7_10, 0, all_48_0_22 and discharging atoms subset(all_10_8_11, all_10_7_10) = all_48_0_22, subset(all_10_8_11, all_10_7_10) = 0, yields: % 21.45/6.83 | (176) all_48_0_22 = 0 % 21.45/6.83 | % 21.45/6.83 +-Applying beta-rule and splitting (174), into two cases. % 21.45/6.83 |-Branch one: % 21.45/6.83 | (177) ~ (all_48_0_22 = 0) % 21.45/6.83 | % 21.45/6.83 | Equations (176) can reduce 177 to: % 21.45/6.83 | (63) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (176) all_48_0_22 = 0 % 21.45/6.83 | (180) ~ (all_48_1_23 = 0) % 21.45/6.83 | % 21.45/6.83 | Equations (175) can reduce 180 to: % 21.45/6.83 | (63) $false % 21.45/6.83 | % 21.45/6.83 |-The branch is then unsatisfiable % 21.45/6.83 |-Branch two: % 21.45/6.83 | (182) all_10_7_10 = 0 & ~ (all_10_6_9 = 0) & apply(equal_set_predicate, all_10_8_11, all_10_8_11) = all_10_6_9 & member(all_10_8_11, all_0_1_1) = 0 % 21.45/6.84 | % 21.45/6.84 | Applying alpha-rule on (182) yields: % 21.45/6.84 | (183) all_10_7_10 = 0 % 21.45/6.84 | (184) ~ (all_10_6_9 = 0) % 21.45/6.84 | (185) apply(equal_set_predicate, all_10_8_11, all_10_8_11) = all_10_6_9 % 21.45/6.84 | (72) member(all_10_8_11, all_0_1_1) = 0 % 21.45/6.84 | % 21.45/6.84 | Instantiating formula (19) with all_10_6_9, all_10_8_11, all_10_8_11 and discharging atoms apply(equal_set_predicate, all_10_8_11, all_10_8_11) = all_10_6_9, yields: % 21.45/6.84 | (187) all_10_6_9 = 0 | ? [v0] : ( ~ (v0 = 0) & equal_set(all_10_8_11, all_10_8_11) = v0) % 21.45/6.84 | % 21.45/6.84 +-Applying beta-rule and splitting (187), into two cases. % 21.45/6.84 |-Branch one: % 21.45/6.84 | (152) all_10_6_9 = 0 % 21.45/6.84 | % 21.45/6.84 | Equations (152) can reduce 184 to: % 21.45/6.84 | (63) $false % 21.45/6.84 | % 21.45/6.84 |-The branch is then unsatisfiable % 21.45/6.84 |-Branch two: % 21.45/6.84 | (184) ~ (all_10_6_9 = 0) % 21.45/6.84 | (191) ? [v0] : ( ~ (v0 = 0) & equal_set(all_10_8_11, all_10_8_11) = v0) % 21.45/6.84 | % 21.45/6.84 | Instantiating (191) with all_36_0_24 yields: % 21.45/6.84 | (192) ~ (all_36_0_24 = 0) & equal_set(all_10_8_11, all_10_8_11) = all_36_0_24 % 21.45/6.84 | % 21.45/6.84 | Applying alpha-rule on (192) yields: % 21.45/6.84 | (193) ~ (all_36_0_24 = 0) % 21.45/6.84 | (194) equal_set(all_10_8_11, all_10_8_11) = all_36_0_24 % 21.45/6.84 | % 21.45/6.84 | Instantiating formula (26) with all_36_0_24, all_10_8_11, all_10_8_11 and discharging atoms equal_set(all_10_8_11, all_10_8_11) = all_36_0_24, yields: % 21.45/6.84 | (195) all_36_0_24 = 0 | ? [v0] : ? [v1] : (subset(all_10_8_11, all_10_8_11) = v1 & subset(all_10_8_11, all_10_8_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.45/6.84 | % 21.45/6.84 +-Applying beta-rule and splitting (195), into two cases. % 21.45/6.84 |-Branch one: % 21.45/6.84 | (196) all_36_0_24 = 0 % 21.45/6.84 | % 21.45/6.84 | Equations (196) can reduce 193 to: % 21.45/6.84 | (63) $false % 21.45/6.84 | % 21.45/6.84 |-The branch is then unsatisfiable % 21.45/6.84 |-Branch two: % 21.45/6.84 | (193) ~ (all_36_0_24 = 0) % 21.45/6.84 | (199) ? [v0] : ? [v1] : (subset(all_10_8_11, all_10_8_11) = v1 & subset(all_10_8_11, all_10_8_11) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 21.45/6.84 | % 21.45/6.84 | Instantiating (199) with all_49_0_25, all_49_1_26 yields: % 21.45/6.84 | (200) subset(all_10_8_11, all_10_8_11) = all_49_0_25 & subset(all_10_8_11, all_10_8_11) = all_49_1_26 & ( ~ (all_49_0_25 = 0) | ~ (all_49_1_26 = 0)) % 21.45/6.84 | % 21.45/6.84 | Applying alpha-rule on (200) yields: % 21.45/6.84 | (201) subset(all_10_8_11, all_10_8_11) = all_49_0_25 % 21.45/6.84 | (202) subset(all_10_8_11, all_10_8_11) = all_49_1_26 % 21.45/6.84 | (203) ~ (all_49_0_25 = 0) | ~ (all_49_1_26 = 0) % 21.45/6.84 | % 21.45/6.84 | Instantiating formula (57) with all_10_8_11, all_10_8_11, all_49_1_26, all_49_0_25 and discharging atoms subset(all_10_8_11, all_10_8_11) = all_49_0_25, subset(all_10_8_11, all_10_8_11) = all_49_1_26, yields: % 21.45/6.84 | (204) all_49_0_25 = all_49_1_26 % 21.45/6.84 | % 21.45/6.84 | From (204) and (201) follows: % 21.45/6.84 | (202) subset(all_10_8_11, all_10_8_11) = all_49_1_26 % 21.45/6.84 | % 21.45/6.84 +-Applying beta-rule and splitting (203), into two cases. % 21.45/6.84 |-Branch one: % 21.45/6.84 | (206) ~ (all_49_0_25 = 0) % 21.45/6.84 | % 21.45/6.84 | Equations (204) can reduce 206 to: % 21.45/6.84 | (207) ~ (all_49_1_26 = 0) % 21.45/6.84 | % 21.45/6.84 | Instantiating formula (17) with all_49_1_26, all_10_8_11, all_10_8_11 and discharging atoms subset(all_10_8_11, all_10_8_11) = all_49_1_26, yields: % 21.45/6.84 | (208) all_49_1_26 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_8_11) = v1 & member(v0, all_10_8_11) = 0) % 21.45/6.84 | % 21.45/6.84 +-Applying beta-rule and splitting (208), into two cases. % 21.45/6.84 |-Branch one: % 21.45/6.84 | (209) all_49_1_26 = 0 % 21.45/6.84 | % 21.45/6.84 | Equations (209) can reduce 207 to: % 21.45/6.84 | (63) $false % 21.45/6.84 | % 21.45/6.84 |-The branch is then unsatisfiable % 21.45/6.84 |-Branch two: % 21.45/6.84 | (207) ~ (all_49_1_26 = 0) % 21.45/6.84 | (212) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_8_11) = v1 & member(v0, all_10_8_11) = 0) % 21.45/6.84 | % 21.45/6.84 | Instantiating (212) with all_70_0_27, all_70_1_28 yields: % 21.45/6.84 | (213) ~ (all_70_0_27 = 0) & member(all_70_1_28, all_10_8_11) = all_70_0_27 & member(all_70_1_28, all_10_8_11) = 0 % 21.45/6.84 | % 21.45/6.84 | Applying alpha-rule on (213) yields: % 21.45/6.84 | (214) ~ (all_70_0_27 = 0) % 21.45/6.84 | (215) member(all_70_1_28, all_10_8_11) = all_70_0_27 % 21.45/6.84 | (216) member(all_70_1_28, all_10_8_11) = 0 % 21.45/6.84 | % 21.45/6.84 | Instantiating formula (41) with all_70_1_28, all_10_8_11, 0, all_70_0_27 and discharging atoms member(all_70_1_28, all_10_8_11) = all_70_0_27, member(all_70_1_28, all_10_8_11) = 0, yields: % 21.45/6.84 | (217) all_70_0_27 = 0 % 21.45/6.84 | % 21.45/6.84 | Equations (217) can reduce 214 to: % 21.45/6.84 | (63) $false % 21.45/6.84 | % 21.45/6.84 |-The branch is then unsatisfiable % 21.45/6.84 |-Branch two: % 21.45/6.84 | (219) all_49_0_25 = 0 % 21.45/6.84 | (207) ~ (all_49_1_26 = 0) % 21.45/6.84 | % 21.45/6.84 | Combining equations (219,204) yields a new equation: % 21.45/6.84 | (209) all_49_1_26 = 0 % 21.45/6.84 | % 21.45/6.84 | Equations (209) can reduce 207 to: % 21.45/6.84 | (63) $false % 21.45/6.84 | % 21.45/6.84 |-The branch is then unsatisfiable % 21.45/6.84 % SZS output end Proof for theBenchmark % 21.45/6.84 % 21.45/6.84 6251ms %------------------------------------------------------------------------------