%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET807+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n012.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 17.46s 6.26s % Output : Proof 19.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET807+4 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n012.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Mon Jul 11 10:49:58 EDT 2022 % 0.13/0.35 % CPUTime : % 0.44/0.60 ____ _ % 0.44/0.60 ___ / __ \_____(_)___ ________ __________ % 0.44/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.44/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.44/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.44/0.60 % 0.44/0.60 A Theorem Prover for First-Order Logic % 0.44/0.60 (ePrincess v.1.0) % 0.44/0.60 % 0.44/0.60 (c) Philipp Rümmer, 2009-2015 % 0.44/0.60 (c) Peter Backeman, 2014-2015 % 0.44/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.44/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.44/0.60 Bug reports to peter@backeman.se % 0.44/0.60 % 0.44/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.44/0.60 % 0.44/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.65/0.97 Prover 0: Preprocessing ... % 2.41/1.23 Prover 0: Warning: ignoring some quantifiers % 2.41/1.26 Prover 0: Constructing countermodel ... % 16.09/5.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 16.32/6.00 Prover 1: Preprocessing ... % 17.00/6.18 Prover 1: Constructing countermodel ... % 17.46/6.26 Prover 1: proved (308ms) % 17.46/6.26 Prover 0: stopped % 17.46/6.26 % 17.46/6.26 No countermodel exists, formula is valid % 17.46/6.26 % SZS status Theorem for theBenchmark % 17.46/6.26 % 17.46/6.26 Generating proof ... found it (size 44) % 18.81/6.56 % 18.81/6.56 % SZS output start Proof for theBenchmark % 18.81/6.56 Assumed formulas after preprocessing and simplification: % 18.81/6.56 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & pre_order(subset_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(subset_predicate, v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(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(subset_predicate, v3, v4) = 0) | subset(v3, v4) = 0) & ! [v3] : ! [v4] : ( ~ (equal_set(v3, v4) = 0) | (subset(v4, v3) = 0 & subset(v3, v4) = 0)) & ! [v3] : ~ (member(v3, empty_set) = 0)) % 19.15/6.62 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields: % 19.15/6.62 | (1) ~ (all_0_0_0 = 0) & pre_order(subset_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(subset_predicate, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(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(subset_predicate, v0, v1) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) % 19.15/6.63 | % 19.15/6.63 | Applying alpha-rule on (1) yields: % 19.15/6.63 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 19.15/6.63 | (3) ! [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)) % 19.15/6.63 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 19.15/6.63 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) % 19.15/6.64 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 19.15/6.64 | (7) ! [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)))) % 19.15/6.64 | (8) ! [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)))) % 19.15/6.64 | (9) ! [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))) % 19.15/6.64 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 19.15/6.64 | (11) ! [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)))) % 19.15/6.64 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 19.15/6.64 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 19.15/6.64 | (14) ! [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))) % 19.15/6.64 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 19.15/6.64 | (16) ! [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)) % 19.15/6.64 | (17) power_set(all_0_2_2) = all_0_1_1 % 19.15/6.64 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 19.15/6.64 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 19.15/6.64 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) % 19.15/6.64 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 19.15/6.64 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 19.15/6.64 | (23) pre_order(subset_predicate, all_0_1_1) = all_0_0_0 % 19.15/6.64 | (24) ~ (all_0_0_0 = 0) % 19.15/6.64 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 19.15/6.64 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 19.15/6.64 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 19.15/6.64 | (28) ! [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)) % 19.15/6.64 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apply(subset_predicate, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 19.15/6.64 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) % 19.15/6.64 | (31) ! [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))) % 19.15/6.65 | (32) ! [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))) % 19.15/6.65 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 19.15/6.65 | (34) ! [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)))) % 19.15/6.65 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) % 19.15/6.65 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 19.15/6.65 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 19.15/6.65 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 19.15/6.65 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 19.15/6.65 | (40) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 19.15/6.65 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 19.15/6.65 | (42) ! [v0] : ~ (member(v0, empty_set) = 0) % 19.15/6.65 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0)) % 19.15/6.65 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 19.15/6.65 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 19.15/6.65 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 19.15/6.65 | (47) ! [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)) % 19.15/6.65 | (48) ! [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)) % 19.15/6.65 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 19.15/6.65 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 19.15/6.65 | (51) ! [v0] : ! [v1] : ( ~ (apply(subset_predicate, v0, v1) = 0) | subset(v0, v1) = 0) % 19.15/6.65 | (52) ! [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))) % 19.15/6.65 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) % 19.15/6.65 | (54) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 19.15/6.65 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0)) % 19.15/6.65 | (56) ! [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))))) % 19.15/6.65 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 19.15/6.65 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 19.15/6.65 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) % 19.15/6.65 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0)) % 19.15/6.65 | % 19.15/6.65 | Instantiating formula (52) with all_0_0_0, all_0_1_1, subset_predicate and discharging atoms pre_order(subset_predicate, all_0_1_1) = all_0_0_0, yields: % 19.15/6.65 | (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(subset_predicate, v1, v2) = 0 & apply(subset_predicate, v0, v2) = v8 & apply(subset_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) | (v1 = 0 & ~ (v2 = 0) & apply(subset_predicate, v0, v0) = v2 & member(v0, all_0_1_1) = 0)) % 19.15/6.65 | % 19.15/6.65 +-Applying beta-rule and splitting (61), into two cases. % 19.15/6.65 |-Branch one: % 19.15/6.65 | (62) all_0_0_0 = 0 % 19.15/6.65 | % 19.15/6.65 | Equations (62) can reduce 24 to: % 19.15/6.65 | (63) $false % 19.15/6.65 | % 19.15/6.65 |-The branch is then unsatisfiable % 19.15/6.65 |-Branch two: % 19.15/6.65 | (24) ~ (all_0_0_0 = 0) % 19.15/6.65 | (65) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) & apply(subset_predicate, v1, v2) = 0 & apply(subset_predicate, v0, v2) = v8 & apply(subset_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) | (v1 = 0 & ~ (v2 = 0) & apply(subset_predicate, v0, v0) = v2 & member(v0, all_0_1_1) = 0)) % 19.15/6.66 | % 19.15/6.66 | 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: % 19.15/6.66 | (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(subset_predicate, all_10_7_10, all_10_6_9) = 0 & apply(subset_predicate, all_10_8_11, all_10_6_9) = all_10_0_3 & apply(subset_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_7_10 = 0 & ~ (all_10_6_9 = 0) & apply(subset_predicate, all_10_8_11, all_10_8_11) = all_10_6_9 & member(all_10_8_11, all_0_1_1) = 0) % 19.15/6.66 | % 19.15/6.66 +-Applying beta-rule and splitting (66), into two cases. % 19.15/6.66 |-Branch one: % 19.15/6.66 | (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(subset_predicate, all_10_7_10, all_10_6_9) = 0 & apply(subset_predicate, all_10_8_11, all_10_6_9) = all_10_0_3 & apply(subset_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 % 19.15/6.66 | % 19.15/6.66 | Applying alpha-rule on (67) yields: % 19.15/6.66 | (68) all_10_1_4 = 0 % 19.15/6.66 | (69) member(all_10_6_9, all_0_1_1) = 0 % 19.15/6.66 | (70) apply(subset_predicate, all_10_8_11, all_10_7_10) = 0 % 19.15/6.66 | (71) member(all_10_8_11, all_0_1_1) = 0 % 19.15/6.66 | (72) all_10_5_8 = 0 % 19.15/6.66 | (73) all_10_4_7 = 0 % 19.15/6.66 | (74) all_10_3_6 = 0 % 19.15/6.66 | (75) apply(subset_predicate, all_10_8_11, all_10_6_9) = all_10_0_3 % 19.15/6.66 | (76) ~ (all_10_0_3 = 0) % 19.15/6.66 | (77) all_10_2_5 = 0 % 19.15/6.66 | (78) apply(subset_predicate, all_10_7_10, all_10_6_9) = 0 % 19.15/6.66 | (79) member(all_10_7_10, all_0_1_1) = 0 % 19.15/6.66 | % 19.15/6.66 | Instantiating formula (51) with all_10_6_9, all_10_7_10 and discharging atoms apply(subset_predicate, all_10_7_10, all_10_6_9) = 0, yields: % 19.15/6.66 | (80) subset(all_10_7_10, all_10_6_9) = 0 % 19.15/6.66 | % 19.15/6.66 | Instantiating formula (29) with all_10_0_3, all_10_6_9, all_10_8_11 and discharging atoms apply(subset_predicate, all_10_8_11, all_10_6_9) = all_10_0_3, yields: % 19.15/6.66 | (81) all_10_0_3 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_10_8_11, all_10_6_9) = v0) % 19.15/6.66 | % 19.15/6.66 | Instantiating formula (51) with all_10_7_10, all_10_8_11 and discharging atoms apply(subset_predicate, all_10_8_11, all_10_7_10) = 0, yields: % 19.15/6.66 | (82) subset(all_10_8_11, all_10_7_10) = 0 % 19.15/6.66 | % 19.15/6.66 +-Applying beta-rule and splitting (81), into two cases. % 19.15/6.66 |-Branch one: % 19.15/6.66 | (83) all_10_0_3 = 0 % 19.15/6.66 | % 19.15/6.66 | Equations (83) can reduce 76 to: % 19.15/6.66 | (63) $false % 19.15/6.66 | % 19.15/6.66 |-The branch is then unsatisfiable % 19.15/6.66 |-Branch two: % 19.15/6.66 | (76) ~ (all_10_0_3 = 0) % 19.15/6.66 | (86) ? [v0] : ( ~ (v0 = 0) & subset(all_10_8_11, all_10_6_9) = v0) % 19.15/6.66 | % 19.15/6.66 | Instantiating (86) with all_36_0_12 yields: % 19.15/6.66 | (87) ~ (all_36_0_12 = 0) & subset(all_10_8_11, all_10_6_9) = all_36_0_12 % 19.15/6.66 | % 19.15/6.66 | Applying alpha-rule on (87) yields: % 19.15/6.66 | (88) ~ (all_36_0_12 = 0) % 19.15/6.66 | (89) subset(all_10_8_11, all_10_6_9) = all_36_0_12 % 19.15/6.66 | % 19.15/6.66 | Instantiating formula (10) with all_36_0_12, all_10_6_9, all_10_8_11 and discharging atoms subset(all_10_8_11, all_10_6_9) = all_36_0_12, yields: % 19.15/6.66 | (90) all_36_0_12 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_6_9) = v1 & member(v0, all_10_8_11) = 0) % 19.15/6.66 | % 19.15/6.66 +-Applying beta-rule and splitting (90), into two cases. % 19.15/6.66 |-Branch one: % 19.15/6.66 | (91) all_36_0_12 = 0 % 19.15/6.66 | % 19.15/6.66 | Equations (91) can reduce 88 to: % 19.15/6.66 | (63) $false % 19.15/6.66 | % 19.15/6.66 |-The branch is then unsatisfiable % 19.15/6.66 |-Branch two: % 19.15/6.66 | (88) ~ (all_36_0_12 = 0) % 19.15/6.66 | (94) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_6_9) = v1 & member(v0, all_10_8_11) = 0) % 19.15/6.66 | % 19.15/6.66 | Instantiating (94) with all_49_0_13, all_49_1_14 yields: % 19.15/6.66 | (95) ~ (all_49_0_13 = 0) & member(all_49_1_14, all_10_6_9) = all_49_0_13 & member(all_49_1_14, all_10_8_11) = 0 % 19.15/6.66 | % 19.15/6.66 | Applying alpha-rule on (95) yields: % 19.15/6.66 | (96) ~ (all_49_0_13 = 0) % 19.15/6.66 | (97) member(all_49_1_14, all_10_6_9) = all_49_0_13 % 19.15/6.66 | (98) member(all_49_1_14, all_10_8_11) = 0 % 19.15/6.66 | % 19.15/6.66 | Instantiating formula (45) with all_49_1_14, all_10_7_10, all_10_8_11 and discharging atoms subset(all_10_8_11, all_10_7_10) = 0, member(all_49_1_14, all_10_8_11) = 0, yields: % 19.15/6.66 | (99) member(all_49_1_14, all_10_7_10) = 0 % 19.15/6.66 | % 19.15/6.66 | Instantiating formula (45) with all_49_1_14, all_10_6_9, all_10_7_10 and discharging atoms subset(all_10_7_10, all_10_6_9) = 0, member(all_49_1_14, all_10_7_10) = 0, yields: % 19.15/6.66 | (100) member(all_49_1_14, all_10_6_9) = 0 % 19.15/6.66 | % 19.15/6.66 | Instantiating formula (12) with all_49_1_14, all_10_6_9, 0, all_49_0_13 and discharging atoms member(all_49_1_14, all_10_6_9) = all_49_0_13, member(all_49_1_14, all_10_6_9) = 0, yields: % 19.15/6.66 | (101) all_49_0_13 = 0 % 19.15/6.66 | % 19.15/6.66 | Equations (101) can reduce 96 to: % 19.15/6.66 | (63) $false % 19.15/6.66 | % 19.15/6.66 |-The branch is then unsatisfiable % 19.15/6.66 |-Branch two: % 19.15/6.66 | (103) all_10_7_10 = 0 & ~ (all_10_6_9 = 0) & apply(subset_predicate, all_10_8_11, all_10_8_11) = all_10_6_9 & member(all_10_8_11, all_0_1_1) = 0 % 19.15/6.66 | % 19.15/6.66 | Applying alpha-rule on (103) yields: % 19.15/6.66 | (104) all_10_7_10 = 0 % 19.15/6.66 | (105) ~ (all_10_6_9 = 0) % 19.15/6.66 | (106) apply(subset_predicate, all_10_8_11, all_10_8_11) = all_10_6_9 % 19.15/6.66 | (71) member(all_10_8_11, all_0_1_1) = 0 % 19.15/6.66 | % 19.15/6.66 | Instantiating formula (29) with all_10_6_9, all_10_8_11, all_10_8_11 and discharging atoms apply(subset_predicate, all_10_8_11, all_10_8_11) = all_10_6_9, yields: % 19.15/6.66 | (108) all_10_6_9 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_10_8_11, all_10_8_11) = v0) % 19.15/6.66 | % 19.15/6.66 +-Applying beta-rule and splitting (108), into two cases. % 19.15/6.66 |-Branch one: % 19.15/6.66 | (109) all_10_6_9 = 0 % 19.15/6.66 | % 19.15/6.66 | Equations (109) can reduce 105 to: % 19.15/6.66 | (63) $false % 19.15/6.66 | % 19.15/6.66 |-The branch is then unsatisfiable % 19.15/6.66 |-Branch two: % 19.15/6.66 | (105) ~ (all_10_6_9 = 0) % 19.15/6.66 | (112) ? [v0] : ( ~ (v0 = 0) & subset(all_10_8_11, all_10_8_11) = v0) % 19.15/6.66 | % 19.15/6.66 | Instantiating (112) with all_36_0_15 yields: % 19.15/6.66 | (113) ~ (all_36_0_15 = 0) & subset(all_10_8_11, all_10_8_11) = all_36_0_15 % 19.15/6.66 | % 19.15/6.66 | Applying alpha-rule on (113) yields: % 19.15/6.66 | (114) ~ (all_36_0_15 = 0) % 19.15/6.66 | (115) subset(all_10_8_11, all_10_8_11) = all_36_0_15 % 19.15/6.66 | % 19.15/6.66 | Instantiating formula (10) with all_36_0_15, all_10_8_11, all_10_8_11 and discharging atoms subset(all_10_8_11, all_10_8_11) = all_36_0_15, yields: % 19.15/6.66 | (116) all_36_0_15 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_8_11) = v1 & member(v0, all_10_8_11) = 0) % 19.15/6.66 | % 19.15/6.66 +-Applying beta-rule and splitting (116), into two cases. % 19.15/6.66 |-Branch one: % 19.15/6.66 | (117) all_36_0_15 = 0 % 19.15/6.66 | % 19.15/6.66 | Equations (117) can reduce 114 to: % 19.15/6.66 | (63) $false % 19.15/6.66 | % 19.15/6.66 |-The branch is then unsatisfiable % 19.15/6.66 |-Branch two: % 19.15/6.66 | (114) ~ (all_36_0_15 = 0) % 19.15/6.66 | (120) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_10_8_11) = v1 & member(v0, all_10_8_11) = 0) % 19.15/6.66 | % 19.15/6.66 | Instantiating (120) with all_49_0_16, all_49_1_17 yields: % 19.15/6.66 | (121) ~ (all_49_0_16 = 0) & member(all_49_1_17, all_10_8_11) = all_49_0_16 & member(all_49_1_17, all_10_8_11) = 0 % 19.15/6.66 | % 19.15/6.66 | Applying alpha-rule on (121) yields: % 19.15/6.66 | (122) ~ (all_49_0_16 = 0) % 19.15/6.66 | (123) member(all_49_1_17, all_10_8_11) = all_49_0_16 % 19.15/6.67 | (124) member(all_49_1_17, all_10_8_11) = 0 % 19.15/6.67 | % 19.15/6.67 | Instantiating formula (12) with all_49_1_17, all_10_8_11, 0, all_49_0_16 and discharging atoms member(all_49_1_17, all_10_8_11) = all_49_0_16, member(all_49_1_17, all_10_8_11) = 0, yields: % 19.15/6.67 | (125) all_49_0_16 = 0 % 19.15/6.67 | % 19.15/6.67 | Equations (125) can reduce 122 to: % 19.15/6.67 | (63) $false % 19.15/6.67 | % 19.15/6.67 |-The branch is then unsatisfiable % 19.15/6.67 % SZS output end Proof for theBenchmark % 19.15/6.67 % 19.15/6.67 6051ms %------------------------------------------------------------------------------