%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET770+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 00:21:57 EDT 2022 % Result : Theorem 20.05s 6.27s % Output : Proof 22.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET770+4 : TPTP v8.1.0. Released v2.2.0. % 0.08/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.35 % Computer : n017.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sun Jul 10 18:59:18 EDT 2022 % 0.14/0.35 % CPUTime : % 0.47/0.60 ____ _ % 0.47/0.60 ___ / __ \_____(_)___ ________ __________ % 0.47/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.47/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.47/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.47/0.60 % 0.47/0.60 A Theorem Prover for First-Order Logic % 0.47/0.60 (ePrincess v.1.0) % 0.47/0.60 % 0.47/0.60 (c) Philipp Rümmer, 2009-2015 % 0.47/0.60 (c) Peter Backeman, 2014-2015 % 0.47/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.47/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.47/0.60 Bug reports to peter@backeman.se % 0.47/0.60 % 0.47/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.47/0.60 % 0.47/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.74/0.95 Prover 0: Preprocessing ... % 2.46/1.21 Prover 0: Warning: ignoring some quantifiers % 2.74/1.24 Prover 0: Constructing countermodel ... % 18.55/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 18.60/5.99 Prover 1: Preprocessing ... % 19.58/6.17 Prover 1: Constructing countermodel ... % 20.05/6.26 Prover 1: proved (320ms) % 20.05/6.27 Prover 0: stopped % 20.05/6.27 % 20.05/6.27 No countermodel exists, formula is valid % 20.05/6.27 % SZS status Theorem for theBenchmark % 20.05/6.27 % 20.05/6.27 Generating proof ... found it (size 190) % 22.25/6.77 % 22.25/6.77 % SZS output start Proof for theBenchmark % 22.25/6.77 Assumed formulas after preprocessing and simplification: % 22.25/6.77 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & ~ (v6 = 0) & equivalence_class(v3, v0, v1) = v5 & equivalence_class(v2, v0, v1) = v4 & equivalence(v1, v0) = 0 & disjoint(v4, v5) = v7 & equal_set(v4, v5) = v6 & member(v3, v0) = 0 & member(v2, v0) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (pre_order(v8, v9) = 0) | ~ (apply(v8, v10, v12) = v13) | ~ (apply(v8, v10, v11) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (apply(v8, v11, v12) = v17 & member(v12, v9) = v16 & member(v11, v9) = v15 & member(v10, v9) = v14 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (equivalence_class(v10, v9, v8) = v12) | ~ (member(v11, v12) = v13) | ? [v14] : ? [v15] : (apply(v8, v10, v11) = v15 & member(v11, v9) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (equivalence(v9, v8) = 0) | ~ (apply(v9, v10, v12) = v13) | ~ (apply(v9, v10, v11) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (apply(v9, v11, v12) = v17 & member(v12, v8) = v16 & member(v11, v8) = v15 & member(v10, v8) = v14 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v11) = v12) | ~ (member(v8, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v11, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v13 & member(v8, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & member(v8, v10) = v14 & member(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : (member(v8, v10) = v14 & member(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (partition(v8, v9) = 0) | ~ (member(v12, v10) = 0) | ~ (member(v11, v8) = 0) | ~ (member(v10, v8) = 0) | ? [v13] : ( ~ (v13 = 0) & member(v12, v11) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum(v9) = v10) | ~ (member(v8, v12) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (equivalence_class(v12, v11, v10) = v9) | ~ (equivalence_class(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (apply(v12, v11, v10) = v9) | ~ (apply(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (equivalence_class(v10, v9, v8) = v12) | ~ (member(v11, v12) = 0) | (apply(v8, v10, v11) = 0 & member(v11, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (pre_order(v8, v9) = 0) | ~ (apply(v8, v10, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (equivalence(v9, v8) = 0) | ~ (apply(v9, v10, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (partition(v8, v9) = 0) | ~ (subset(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = 0 & member(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v9, v8) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (power_set(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v8 | v9 = v8 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (pre_order(v11, v10) = v9) | ~ (pre_order(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equivalence(v11, v10) = v9) | ~ (equivalence(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (partition(v11, v10) = v9) | ~ (partition(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (disjoint(v11, v10) = v9) | ~ (disjoint(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (difference(v11, v10) = v9) | ~ (difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection(v11, v10) = v9) | ~ (intersection(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_set(v11, v10) = v9) | ~ (equal_set(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (member(v11, v10) = v9) | ~ (member(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (equivalence(v9, v8) = 0) | ~ (apply(v9, v10, v11) = 0) | ? [v12] : ? [v13] : ? [v14] : (apply(v9, v11, v10) = v14 & member(v11, v8) = v13 & member(v10, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (difference(v10, v9) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v8, v10) = 0 & member(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9, v10) = v11) | ~ (member(v8, v11) = 0) | ? [v12] : ? [v13] : (member(v8, v10) = v13 & member(v8, v9) = v12 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v9, v10) = v11) | ~ (member(v8, v11) = 0) | (member(v8, v10) = 0 & member(v8, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (pre_order(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v19 = 0) & apply(v8, v12, v13) = 0 & apply(v8, v11, v13) = v19 & apply(v8, v11, v12) = 0 & member(v13, v9) = 0 & member(v12, v9) = 0 & member(v11, v9) = 0) | (v12 = 0 & ~ (v13 = 0) & apply(v8, v11, v11) = v13 & member(v11, v9) = 0))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equivalence(v9, v8) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v18 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & ~ (v19 = 0) & apply(v9, v12, v13) = 0 & apply(v9, v11, v13) = v19 & apply(v9, v11, v12) = 0 & member(v13, v8) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0) | (v15 = 0 & v14 = 0 & v13 = 0 & ~ (v16 = 0) & apply(v9, v12, v11) = v16 & apply(v9, v11, v12) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0) | (v12 = 0 & ~ (v13 = 0) & apply(v9, v11, v11) = v13 & member(v11, v8) = 0))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (partition(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & v16 = 0 & v14 = 0 & v13 = 0 & ~ (v12 = v11) & member(v15, v12) = 0 & member(v15, v11) = 0 & member(v12, v8) = 0 & member(v11, v8) = 0) | (v12 = 0 & ~ (v13 = 0) & subset(v11, v9) = v13 & member(v11, v8) = 0) | (v12 = 0 & member(v11, v9) = 0 & ! [v18] : ( ~ (member(v11, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & member(v18, v8) = v19))))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : (member(v11, v9) = 0 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (member(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_set(v8, v9) = v10) | ? [v11] : ? [v12] : (subset(v9, v8) = v12 & subset(v8, v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v9) = v12 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (product(v10) = v9) | ~ (product(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sum(v10) = v9) | ~ (sum(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v9) = v10) | ~ (member(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (power_set(v10) = v9) | ~ (power_set(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (partition(v8, v9) = 0) | ~ (member(v10, v9) = 0) | ? [v11] : (member(v11, v8) = 0 & member(v10, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v8, v9) = 0) | ~ (member(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum(v9) = v10) | ~ (member(v8, v10) = 0) | ? [v11] : (member(v11, v9) = 0 & member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_set(v9) = v10) | ~ (member(v8, v10) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (member(v10, v8) = 0) | member(v10, v9) = 0) & ! [v8] : ! [v9] : ( ~ (equal_set(v8, v9) = 0) | (subset(v9, v8) = 0 & subset(v8, v9) = 0)) & ! [v8] : ~ (member(v8, empty_set) = 0)) % 22.25/6.81 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields: % 22.25/6.81 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & equivalence_class(all_0_4_4, all_0_7_7, all_0_6_6) = all_0_2_2 & equivalence_class(all_0_5_5, all_0_7_7, all_0_6_6) = all_0_3_3 & equivalence(all_0_6_6, all_0_7_7) = 0 & disjoint(all_0_3_3, all_0_2_2) = all_0_0_0 & equal_set(all_0_3_3, all_0_2_2) = all_0_1_1 & member(all_0_4_4, all_0_7_7) = 0 & member(all_0_5_5, all_0_7_7) = 0 & ! [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 | ~ (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] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) % 22.25/6.83 | % 22.25/6.83 | Applying alpha-rule on (1) yields: % 22.25/6.83 | (2) ! [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))) % 22.25/6.83 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 22.25/6.83 | (4) member(all_0_4_4, all_0_7_7) = 0 % 22.25/6.83 | (5) equivalence(all_0_6_6, all_0_7_7) = 0 % 22.25/6.83 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 22.25/6.83 | (7) ! [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)))) % 22.25/6.83 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | (apply(v0, v2, v3) = 0 & member(v3, v1) = 0)) % 22.25/6.83 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (partition(v0, v1) = 0) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 22.25/6.83 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 22.25/6.83 | (11) equivalence_class(all_0_5_5, all_0_7_7, all_0_6_6) = all_0_3_3 % 22.25/6.83 | (12) ~ (all_0_0_0 = 0) % 22.25/6.83 | (13) ! [v0] : ~ (member(v0, empty_set) = 0) % 22.25/6.83 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 22.25/6.83 | (15) ! [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)) % 22.25/6.83 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 22.25/6.83 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 22.25/6.83 | (18) ! [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))))) % 22.25/6.83 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 22.25/6.83 | (20) ! [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))) % 22.25/6.83 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 22.25/6.83 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 22.25/6.83 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 22.25/6.83 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 22.25/6.83 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0)) % 22.25/6.83 | (26) ! [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)) % 22.25/6.83 | (27) equal_set(all_0_3_3, all_0_2_2) = all_0_1_1 % 22.25/6.83 | (28) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 22.25/6.83 | (29) ! [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)) % 22.74/6.83 | (30) ! [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)) % 22.74/6.83 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 22.74/6.83 | (32) equivalence_class(all_0_4_4, all_0_7_7, all_0_6_6) = all_0_2_2 % 22.74/6.83 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) % 22.74/6.84 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 22.74/6.84 | (35) ! [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)))) % 22.74/6.84 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 22.74/6.84 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (partition(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : (member(v3, v0) = 0 & member(v2, v3) = 0)) % 22.74/6.84 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 22.74/6.84 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 22.74/6.84 | (40) member(all_0_5_5, all_0_7_7) = 0 % 22.74/6.84 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) % 22.74/6.84 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) % 22.74/6.84 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 22.74/6.84 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) % 22.74/6.84 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 22.74/6.84 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 22.74/6.84 | (47) ! [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))) % 22.74/6.84 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (pre_order(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v1) = v4)) % 22.74/6.84 | (49) ! [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)))) % 22.74/6.84 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 22.74/6.84 | (51) ! [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)))) % 22.74/6.84 | (52) ! [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))) % 22.74/6.84 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 22.74/6.84 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0)) % 22.74/6.84 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3, v2) = v0)) % 22.74/6.84 | (56) ! [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)) % 22.74/6.84 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (equivalence(v1, v0) = 0) | ~ (apply(v1, v2, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) % 22.74/6.84 | (58) disjoint(all_0_3_3, all_0_2_2) = all_0_0_0 % 22.74/6.84 | (59) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 22.74/6.84 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 22.74/6.84 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 22.74/6.84 | (62) ~ (all_0_1_1 = 0) % 22.74/6.84 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 22.74/6.84 | (64) ! [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))) % 22.74/6.84 | % 22.74/6.84 | Instantiating formula (54) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms disjoint(all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 22.74/6.84 | (65) all_0_0_0 = 0 | ? [v0] : (member(v0, all_0_2_2) = 0 & member(v0, all_0_3_3) = 0) % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (59) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 22.74/6.85 | (66) all_0_1_1 = 0 | ? [v0] : ? [v1] : (subset(all_0_2_2, all_0_3_3) = v1 & subset(all_0_3_3, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.85 | % 22.74/6.85 +-Applying beta-rule and splitting (65), into two cases. % 22.74/6.85 |-Branch one: % 22.74/6.85 | (67) all_0_0_0 = 0 % 22.74/6.85 | % 22.74/6.85 | Equations (67) can reduce 12 to: % 22.74/6.85 | (68) $false % 22.74/6.85 | % 22.74/6.85 |-The branch is then unsatisfiable % 22.74/6.85 |-Branch two: % 22.74/6.85 | (12) ~ (all_0_0_0 = 0) % 22.74/6.85 | (70) ? [v0] : (member(v0, all_0_2_2) = 0 & member(v0, all_0_3_3) = 0) % 22.74/6.85 | % 22.74/6.85 | Instantiating (70) with all_22_0_8 yields: % 22.74/6.85 | (71) member(all_22_0_8, all_0_2_2) = 0 & member(all_22_0_8, all_0_3_3) = 0 % 22.74/6.85 | % 22.74/6.85 | Applying alpha-rule on (71) yields: % 22.74/6.85 | (72) member(all_22_0_8, all_0_2_2) = 0 % 22.74/6.85 | (73) member(all_22_0_8, all_0_3_3) = 0 % 22.74/6.85 | % 22.74/6.85 +-Applying beta-rule and splitting (66), into two cases. % 22.74/6.85 |-Branch one: % 22.74/6.85 | (74) all_0_1_1 = 0 % 22.74/6.85 | % 22.74/6.85 | Equations (74) can reduce 62 to: % 22.74/6.85 | (68) $false % 22.74/6.85 | % 22.74/6.85 |-The branch is then unsatisfiable % 22.74/6.85 |-Branch two: % 22.74/6.85 | (62) ~ (all_0_1_1 = 0) % 22.74/6.85 | (77) ? [v0] : ? [v1] : (subset(all_0_2_2, all_0_3_3) = v1 & subset(all_0_3_3, all_0_2_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.85 | % 22.74/6.85 | Instantiating (77) with all_27_0_9, all_27_1_10 yields: % 22.74/6.85 | (78) subset(all_0_2_2, all_0_3_3) = all_27_0_9 & subset(all_0_3_3, all_0_2_2) = all_27_1_10 & ( ~ (all_27_0_9 = 0) | ~ (all_27_1_10 = 0)) % 22.74/6.85 | % 22.74/6.85 | Applying alpha-rule on (78) yields: % 22.74/6.85 | (79) subset(all_0_2_2, all_0_3_3) = all_27_0_9 % 22.74/6.85 | (80) subset(all_0_3_3, all_0_2_2) = all_27_1_10 % 22.74/6.85 | (81) ~ (all_27_0_9 = 0) | ~ (all_27_1_10 = 0) % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (6) with all_27_0_9, all_0_3_3, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_3_3) = all_27_0_9, yields: % 22.74/6.85 | (82) all_27_0_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(v0, all_0_3_3) = v1) % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (6) with all_27_1_10, all_0_2_2, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_2_2) = all_27_1_10, yields: % 22.74/6.85 | (83) all_27_1_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, all_0_3_3) = 0) % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (8) with all_0_2_2, all_22_0_8, all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms equivalence_class(all_0_4_4, all_0_7_7, all_0_6_6) = all_0_2_2, member(all_22_0_8, all_0_2_2) = 0, yields: % 22.74/6.85 | (84) apply(all_0_6_6, all_0_4_4, all_22_0_8) = 0 & member(all_22_0_8, all_0_7_7) = 0 % 22.74/6.85 | % 22.74/6.85 | Applying alpha-rule on (84) yields: % 22.74/6.85 | (85) apply(all_0_6_6, all_0_4_4, all_22_0_8) = 0 % 22.74/6.85 | (86) member(all_22_0_8, all_0_7_7) = 0 % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (8) with all_0_3_3, all_22_0_8, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms equivalence_class(all_0_5_5, all_0_7_7, all_0_6_6) = all_0_3_3, member(all_22_0_8, all_0_3_3) = 0, yields: % 22.74/6.85 | (87) apply(all_0_6_6, all_0_5_5, all_22_0_8) = 0 & member(all_22_0_8, all_0_7_7) = 0 % 22.74/6.85 | % 22.74/6.85 | Applying alpha-rule on (87) yields: % 22.74/6.85 | (88) apply(all_0_6_6, all_0_5_5, all_22_0_8) = 0 % 22.74/6.85 | (86) member(all_22_0_8, all_0_7_7) = 0 % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (20) with all_22_0_8, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms equivalence(all_0_6_6, all_0_7_7) = 0, apply(all_0_6_6, all_0_4_4, all_22_0_8) = 0, yields: % 22.74/6.85 | (90) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_6_6, all_22_0_8, all_0_4_4) = v2 & member(all_22_0_8, all_0_7_7) = v1 & member(all_0_4_4, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (20) with all_22_0_8, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms equivalence(all_0_6_6, all_0_7_7) = 0, apply(all_0_6_6, all_0_5_5, all_22_0_8) = 0, yields: % 22.74/6.85 | (91) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_6_6, all_22_0_8, all_0_5_5) = v2 & member(all_22_0_8, all_0_7_7) = v1 & member(all_0_5_5, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.74/6.85 | % 22.74/6.85 | Instantiating (91) with all_48_0_11, all_48_1_12, all_48_2_13 yields: % 22.74/6.85 | (92) apply(all_0_6_6, all_22_0_8, all_0_5_5) = all_48_0_11 & member(all_22_0_8, all_0_7_7) = all_48_1_12 & member(all_0_5_5, all_0_7_7) = all_48_2_13 & ( ~ (all_48_1_12 = 0) | ~ (all_48_2_13 = 0) | all_48_0_11 = 0) % 22.74/6.85 | % 22.74/6.85 | Applying alpha-rule on (92) yields: % 22.74/6.85 | (93) apply(all_0_6_6, all_22_0_8, all_0_5_5) = all_48_0_11 % 22.74/6.85 | (94) member(all_22_0_8, all_0_7_7) = all_48_1_12 % 22.74/6.85 | (95) member(all_0_5_5, all_0_7_7) = all_48_2_13 % 22.74/6.85 | (96) ~ (all_48_1_12 = 0) | ~ (all_48_2_13 = 0) | all_48_0_11 = 0 % 22.74/6.85 | % 22.74/6.85 | Instantiating (90) with all_50_0_14, all_50_1_15, all_50_2_16 yields: % 22.74/6.85 | (97) apply(all_0_6_6, all_22_0_8, all_0_4_4) = all_50_0_14 & member(all_22_0_8, all_0_7_7) = all_50_1_15 & member(all_0_4_4, all_0_7_7) = all_50_2_16 & ( ~ (all_50_1_15 = 0) | ~ (all_50_2_16 = 0) | all_50_0_14 = 0) % 22.74/6.85 | % 22.74/6.85 | Applying alpha-rule on (97) yields: % 22.74/6.85 | (98) apply(all_0_6_6, all_22_0_8, all_0_4_4) = all_50_0_14 % 22.74/6.85 | (99) member(all_22_0_8, all_0_7_7) = all_50_1_15 % 22.74/6.85 | (100) member(all_0_4_4, all_0_7_7) = all_50_2_16 % 22.74/6.85 | (101) ~ (all_50_1_15 = 0) | ~ (all_50_2_16 = 0) | all_50_0_14 = 0 % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (38) with all_22_0_8, all_0_7_7, all_50_1_15, 0 and discharging atoms member(all_22_0_8, all_0_7_7) = all_50_1_15, member(all_22_0_8, all_0_7_7) = 0, yields: % 22.74/6.85 | (102) all_50_1_15 = 0 % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (38) with all_0_5_5, all_0_7_7, all_48_1_12, 0 and discharging atoms member(all_0_5_5, all_0_7_7) = 0, yields: % 22.74/6.85 | (103) all_48_1_12 = 0 | ~ (member(all_0_5_5, all_0_7_7) = all_48_1_12) % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (38) with all_22_0_8, all_0_7_7, all_48_1_12, all_50_1_15 and discharging atoms member(all_22_0_8, all_0_7_7) = all_50_1_15, member(all_22_0_8, all_0_7_7) = all_48_1_12, yields: % 22.74/6.85 | (104) all_50_1_15 = all_48_1_12 % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (38) with all_0_4_4, all_0_7_7, all_50_2_16, 0 and discharging atoms member(all_0_4_4, all_0_7_7) = all_50_2_16, member(all_0_4_4, all_0_7_7) = 0, yields: % 22.74/6.85 | (105) all_50_2_16 = 0 % 22.74/6.85 | % 22.74/6.85 | Instantiating formula (38) with all_0_5_5, all_0_7_7, all_48_2_13, 0 and discharging atoms member(all_0_5_5, all_0_7_7) = all_48_2_13, member(all_0_5_5, all_0_7_7) = 0, yields: % 22.74/6.85 | (106) all_48_2_13 = 0 % 22.74/6.85 | % 22.74/6.85 | Combining equations (102,104) yields a new equation: % 22.74/6.85 | (107) all_48_1_12 = 0 % 22.74/6.85 | % 22.74/6.85 | Combining equations (107,104) yields a new equation: % 22.74/6.85 | (102) all_50_1_15 = 0 % 22.74/6.85 | % 22.74/6.85 | From (107) and (94) follows: % 22.74/6.85 | (86) member(all_22_0_8, all_0_7_7) = 0 % 22.74/6.85 | % 22.74/6.85 | From (105) and (100) follows: % 22.74/6.85 | (4) member(all_0_4_4, all_0_7_7) = 0 % 22.74/6.85 | % 22.74/6.85 | From (106) and (95) follows: % 22.74/6.85 | (40) member(all_0_5_5, all_0_7_7) = 0 % 22.74/6.85 | % 22.74/6.85 +-Applying beta-rule and splitting (101), into two cases. % 22.74/6.85 |-Branch one: % 22.74/6.85 | (112) ~ (all_50_1_15 = 0) % 22.74/6.85 | % 22.74/6.85 | Equations (102) can reduce 112 to: % 22.74/6.85 | (68) $false % 22.74/6.85 | % 22.74/6.85 |-The branch is then unsatisfiable % 22.74/6.85 |-Branch two: % 22.74/6.85 | (102) all_50_1_15 = 0 % 22.74/6.85 | (115) ~ (all_50_2_16 = 0) | all_50_0_14 = 0 % 22.74/6.85 | % 22.74/6.85 +-Applying beta-rule and splitting (115), into two cases. % 22.74/6.85 |-Branch one: % 22.74/6.85 | (116) ~ (all_50_2_16 = 0) % 22.74/6.85 | % 22.74/6.85 | Equations (105) can reduce 116 to: % 22.74/6.85 | (68) $false % 22.74/6.85 | % 22.74/6.85 |-The branch is then unsatisfiable % 22.74/6.85 |-Branch two: % 22.74/6.85 | (105) all_50_2_16 = 0 % 22.74/6.85 | (119) all_50_0_14 = 0 % 22.74/6.85 | % 22.74/6.85 | From (119) and (98) follows: % 22.74/6.85 | (120) apply(all_0_6_6, all_22_0_8, all_0_4_4) = 0 % 22.74/6.85 | % 22.74/6.85 +-Applying beta-rule and splitting (96), into two cases. % 22.74/6.85 |-Branch one: % 22.74/6.85 | (121) ~ (all_48_1_12 = 0) % 22.74/6.86 | % 22.74/6.86 | Equations (107) can reduce 121 to: % 22.74/6.86 | (68) $false % 22.74/6.86 | % 22.74/6.86 |-The branch is then unsatisfiable % 22.74/6.86 |-Branch two: % 22.74/6.86 | (107) all_48_1_12 = 0 % 22.74/6.86 | (124) ~ (all_48_2_13 = 0) | all_48_0_11 = 0 % 22.74/6.86 | % 22.74/6.86 +-Applying beta-rule and splitting (124), into two cases. % 22.74/6.86 |-Branch one: % 22.74/6.86 | (125) ~ (all_48_2_13 = 0) % 22.74/6.86 | % 22.74/6.86 | Equations (106) can reduce 125 to: % 22.74/6.86 | (68) $false % 22.74/6.86 | % 22.74/6.86 |-The branch is then unsatisfiable % 22.74/6.86 |-Branch two: % 22.74/6.86 | (106) all_48_2_13 = 0 % 22.74/6.86 | (128) all_48_0_11 = 0 % 22.74/6.86 | % 22.74/6.86 | From (128) and (93) follows: % 22.74/6.86 | (129) apply(all_0_6_6, all_22_0_8, all_0_5_5) = 0 % 22.74/6.86 | % 22.74/6.86 +-Applying beta-rule and splitting (81), into two cases. % 22.74/6.86 |-Branch one: % 22.74/6.86 | (130) ~ (all_27_0_9 = 0) % 22.74/6.86 | % 22.74/6.86 +-Applying beta-rule and splitting (82), into two cases. % 22.74/6.86 |-Branch one: % 22.74/6.86 | (131) all_27_0_9 = 0 % 22.74/6.86 | % 22.74/6.86 | Equations (131) can reduce 130 to: % 22.74/6.86 | (68) $false % 22.74/6.86 | % 22.74/6.86 |-The branch is then unsatisfiable % 22.74/6.86 |-Branch two: % 22.74/6.86 | (130) ~ (all_27_0_9 = 0) % 22.74/6.86 | (134) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(v0, all_0_3_3) = v1) % 22.74/6.86 | % 22.74/6.86 | Instantiating (134) with all_105_0_17, all_105_1_18 yields: % 22.74/6.86 | (135) ~ (all_105_0_17 = 0) & member(all_105_1_18, all_0_2_2) = 0 & member(all_105_1_18, all_0_3_3) = all_105_0_17 % 22.74/6.86 | % 22.74/6.86 | Applying alpha-rule on (135) yields: % 22.74/6.86 | (136) ~ (all_105_0_17 = 0) % 22.74/6.86 | (137) member(all_105_1_18, all_0_2_2) = 0 % 22.74/6.86 | (138) member(all_105_1_18, all_0_3_3) = all_105_0_17 % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (8) with all_0_2_2, all_105_1_18, all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms equivalence_class(all_0_4_4, all_0_7_7, all_0_6_6) = all_0_2_2, member(all_105_1_18, all_0_2_2) = 0, yields: % 22.74/6.86 | (139) apply(all_0_6_6, all_0_4_4, all_105_1_18) = 0 & member(all_105_1_18, all_0_7_7) = 0 % 22.74/6.86 | % 22.74/6.86 | Applying alpha-rule on (139) yields: % 22.74/6.86 | (140) apply(all_0_6_6, all_0_4_4, all_105_1_18) = 0 % 22.74/6.86 | (141) member(all_105_1_18, all_0_7_7) = 0 % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (51) with all_105_0_17, all_0_3_3, all_105_1_18, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms equivalence_class(all_0_5_5, all_0_7_7, all_0_6_6) = all_0_3_3, member(all_105_1_18, all_0_3_3) = all_105_0_17, yields: % 22.74/6.86 | (142) all_105_0_17 = 0 | ? [v0] : ? [v1] : (apply(all_0_6_6, all_0_5_5, all_105_1_18) = v1 & member(all_105_1_18, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.86 | % 22.74/6.86 +-Applying beta-rule and splitting (142), into two cases. % 22.74/6.86 |-Branch one: % 22.74/6.86 | (143) all_105_0_17 = 0 % 22.74/6.86 | % 22.74/6.86 | Equations (143) can reduce 136 to: % 22.74/6.86 | (68) $false % 22.74/6.86 | % 22.74/6.86 |-The branch is then unsatisfiable % 22.74/6.86 |-Branch two: % 22.74/6.86 | (136) ~ (all_105_0_17 = 0) % 22.74/6.86 | (146) ? [v0] : ? [v1] : (apply(all_0_6_6, all_0_5_5, all_105_1_18) = v1 & member(all_105_1_18, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.86 | % 22.74/6.86 | Instantiating (146) with all_117_0_19, all_117_1_20 yields: % 22.74/6.86 | (147) apply(all_0_6_6, all_0_5_5, all_105_1_18) = all_117_0_19 & member(all_105_1_18, all_0_7_7) = all_117_1_20 & ( ~ (all_117_0_19 = 0) | ~ (all_117_1_20 = 0)) % 22.74/6.86 | % 22.74/6.86 | Applying alpha-rule on (147) yields: % 22.74/6.86 | (148) apply(all_0_6_6, all_0_5_5, all_105_1_18) = all_117_0_19 % 22.74/6.86 | (149) member(all_105_1_18, all_0_7_7) = all_117_1_20 % 22.74/6.86 | (150) ~ (all_117_0_19 = 0) | ~ (all_117_1_20 = 0) % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (38) with all_105_1_18, all_0_7_7, 0, all_117_1_20 and discharging atoms member(all_105_1_18, all_0_7_7) = all_117_1_20, member(all_105_1_18, all_0_7_7) = 0, yields: % 22.74/6.86 | (151) all_117_1_20 = 0 % 22.74/6.86 | % 22.74/6.86 | From (151) and (149) follows: % 22.74/6.86 | (141) member(all_105_1_18, all_0_7_7) = 0 % 22.74/6.86 | % 22.74/6.86 +-Applying beta-rule and splitting (150), into two cases. % 22.74/6.86 |-Branch one: % 22.74/6.86 | (153) ~ (all_117_0_19 = 0) % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (20) with all_105_1_18, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms equivalence(all_0_6_6, all_0_7_7) = 0, apply(all_0_6_6, all_0_4_4, all_105_1_18) = 0, yields: % 22.74/6.86 | (154) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_6_6, all_105_1_18, all_0_4_4) = v2 & member(all_105_1_18, all_0_7_7) = v1 & member(all_0_4_4, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (35) with all_117_0_19, all_105_1_18, all_22_0_8, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms equivalence(all_0_6_6, all_0_7_7) = 0, apply(all_0_6_6, all_0_5_5, all_105_1_18) = all_117_0_19, apply(all_0_6_6, all_0_5_5, all_22_0_8) = 0, yields: % 22.74/6.86 | (155) all_117_0_19 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_6_6, all_22_0_8, all_105_1_18) = v3 & member(all_105_1_18, all_0_7_7) = v2 & member(all_22_0_8, all_0_7_7) = v1 & member(all_0_5_5, all_0_7_7) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.86 | % 22.74/6.86 | Instantiating (154) with all_132_0_21, all_132_1_22, all_132_2_23 yields: % 22.74/6.86 | (156) apply(all_0_6_6, all_105_1_18, all_0_4_4) = all_132_0_21 & member(all_105_1_18, all_0_7_7) = all_132_1_22 & member(all_0_4_4, all_0_7_7) = all_132_2_23 & ( ~ (all_132_1_22 = 0) | ~ (all_132_2_23 = 0) | all_132_0_21 = 0) % 22.74/6.86 | % 22.74/6.86 | Applying alpha-rule on (156) yields: % 22.74/6.86 | (157) apply(all_0_6_6, all_105_1_18, all_0_4_4) = all_132_0_21 % 22.74/6.86 | (158) member(all_105_1_18, all_0_7_7) = all_132_1_22 % 22.74/6.86 | (159) member(all_0_4_4, all_0_7_7) = all_132_2_23 % 22.74/6.86 | (160) ~ (all_132_1_22 = 0) | ~ (all_132_2_23 = 0) | all_132_0_21 = 0 % 22.74/6.86 | % 22.74/6.86 +-Applying beta-rule and splitting (155), into two cases. % 22.74/6.86 |-Branch one: % 22.74/6.86 | (161) all_117_0_19 = 0 % 22.74/6.86 | % 22.74/6.86 | Equations (161) can reduce 153 to: % 22.74/6.86 | (68) $false % 22.74/6.86 | % 22.74/6.86 |-The branch is then unsatisfiable % 22.74/6.86 |-Branch two: % 22.74/6.86 | (153) ~ (all_117_0_19 = 0) % 22.74/6.86 | (164) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_6_6, all_22_0_8, all_105_1_18) = v3 & member(all_105_1_18, all_0_7_7) = v2 & member(all_22_0_8, all_0_7_7) = v1 & member(all_0_5_5, all_0_7_7) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.86 | % 22.74/6.86 | Instantiating (164) with all_141_0_24, all_141_1_25, all_141_2_26, all_141_3_27 yields: % 22.74/6.86 | (165) apply(all_0_6_6, all_22_0_8, all_105_1_18) = all_141_0_24 & member(all_105_1_18, all_0_7_7) = all_141_1_25 & member(all_22_0_8, all_0_7_7) = all_141_2_26 & member(all_0_5_5, all_0_7_7) = all_141_3_27 & ( ~ (all_141_0_24 = 0) | ~ (all_141_1_25 = 0) | ~ (all_141_2_26 = 0) | ~ (all_141_3_27 = 0)) % 22.74/6.86 | % 22.74/6.86 | Applying alpha-rule on (165) yields: % 22.74/6.86 | (166) member(all_0_5_5, all_0_7_7) = all_141_3_27 % 22.74/6.86 | (167) member(all_22_0_8, all_0_7_7) = all_141_2_26 % 22.74/6.86 | (168) apply(all_0_6_6, all_22_0_8, all_105_1_18) = all_141_0_24 % 22.74/6.86 | (169) member(all_105_1_18, all_0_7_7) = all_141_1_25 % 22.74/6.86 | (170) ~ (all_141_0_24 = 0) | ~ (all_141_1_25 = 0) | ~ (all_141_2_26 = 0) | ~ (all_141_3_27 = 0) % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (38) with all_105_1_18, all_0_7_7, all_141_1_25, 0 and discharging atoms member(all_105_1_18, all_0_7_7) = all_141_1_25, member(all_105_1_18, all_0_7_7) = 0, yields: % 22.74/6.86 | (171) all_141_1_25 = 0 % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (38) with all_105_1_18, all_0_7_7, all_132_1_22, all_141_1_25 and discharging atoms member(all_105_1_18, all_0_7_7) = all_141_1_25, member(all_105_1_18, all_0_7_7) = all_132_1_22, yields: % 22.74/6.86 | (172) all_141_1_25 = all_132_1_22 % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (38) with all_22_0_8, all_0_7_7, all_141_2_26, 0 and discharging atoms member(all_22_0_8, all_0_7_7) = all_141_2_26, member(all_22_0_8, all_0_7_7) = 0, yields: % 22.74/6.86 | (173) all_141_2_26 = 0 % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (38) with all_0_4_4, all_0_7_7, all_132_2_23, 0 and discharging atoms member(all_0_4_4, all_0_7_7) = all_132_2_23, member(all_0_4_4, all_0_7_7) = 0, yields: % 22.74/6.86 | (174) all_132_2_23 = 0 % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (38) with all_0_5_5, all_0_7_7, all_141_3_27, 0 and discharging atoms member(all_0_5_5, all_0_7_7) = all_141_3_27, member(all_0_5_5, all_0_7_7) = 0, yields: % 22.74/6.86 | (175) all_141_3_27 = 0 % 22.74/6.86 | % 22.74/6.86 | Combining equations (171,172) yields a new equation: % 22.74/6.86 | (176) all_132_1_22 = 0 % 22.74/6.86 | % 22.74/6.86 | Combining equations (176,172) yields a new equation: % 22.74/6.86 | (171) all_141_1_25 = 0 % 22.74/6.86 | % 22.74/6.86 | From (176) and (158) follows: % 22.74/6.86 | (141) member(all_105_1_18, all_0_7_7) = 0 % 22.74/6.86 | % 22.74/6.86 | From (173) and (167) follows: % 22.74/6.86 | (86) member(all_22_0_8, all_0_7_7) = 0 % 22.74/6.86 | % 22.74/6.86 | From (174) and (159) follows: % 22.74/6.86 | (4) member(all_0_4_4, all_0_7_7) = 0 % 22.74/6.86 | % 22.74/6.86 +-Applying beta-rule and splitting (170), into two cases. % 22.74/6.86 |-Branch one: % 22.74/6.86 | (181) ~ (all_141_0_24 = 0) % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (35) with all_141_0_24, all_105_1_18, all_0_4_4, all_22_0_8, all_0_6_6, all_0_7_7 and discharging atoms equivalence(all_0_6_6, all_0_7_7) = 0, apply(all_0_6_6, all_22_0_8, all_105_1_18) = all_141_0_24, apply(all_0_6_6, all_22_0_8, all_0_4_4) = 0, yields: % 22.74/6.86 | (182) all_141_0_24 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_6_6, all_0_4_4, all_105_1_18) = v3 & member(all_105_1_18, all_0_7_7) = v2 & member(all_22_0_8, all_0_7_7) = v0 & member(all_0_4_4, all_0_7_7) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.86 | % 22.74/6.86 +-Applying beta-rule and splitting (182), into two cases. % 22.74/6.86 |-Branch one: % 22.74/6.86 | (183) all_141_0_24 = 0 % 22.74/6.86 | % 22.74/6.86 | Equations (183) can reduce 181 to: % 22.74/6.86 | (68) $false % 22.74/6.86 | % 22.74/6.86 |-The branch is then unsatisfiable % 22.74/6.86 |-Branch two: % 22.74/6.86 | (181) ~ (all_141_0_24 = 0) % 22.74/6.86 | (186) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_6_6, all_0_4_4, all_105_1_18) = v3 & member(all_105_1_18, all_0_7_7) = v2 & member(all_22_0_8, all_0_7_7) = v0 & member(all_0_4_4, all_0_7_7) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.86 | % 22.74/6.86 | Instantiating (186) with all_178_0_28, all_178_1_29, all_178_2_30, all_178_3_31 yields: % 22.74/6.86 | (187) apply(all_0_6_6, all_0_4_4, all_105_1_18) = all_178_0_28 & member(all_105_1_18, all_0_7_7) = all_178_1_29 & member(all_22_0_8, all_0_7_7) = all_178_3_31 & member(all_0_4_4, all_0_7_7) = all_178_2_30 & ( ~ (all_178_0_28 = 0) | ~ (all_178_1_29 = 0) | ~ (all_178_2_30 = 0) | ~ (all_178_3_31 = 0)) % 22.74/6.86 | % 22.74/6.86 | Applying alpha-rule on (187) yields: % 22.74/6.86 | (188) member(all_22_0_8, all_0_7_7) = all_178_3_31 % 22.74/6.86 | (189) apply(all_0_6_6, all_0_4_4, all_105_1_18) = all_178_0_28 % 22.74/6.86 | (190) member(all_0_4_4, all_0_7_7) = all_178_2_30 % 22.74/6.86 | (191) member(all_105_1_18, all_0_7_7) = all_178_1_29 % 22.74/6.86 | (192) ~ (all_178_0_28 = 0) | ~ (all_178_1_29 = 0) | ~ (all_178_2_30 = 0) | ~ (all_178_3_31 = 0) % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (41) with all_0_6_6, all_0_4_4, all_105_1_18, all_178_0_28, 0 and discharging atoms apply(all_0_6_6, all_0_4_4, all_105_1_18) = all_178_0_28, apply(all_0_6_6, all_0_4_4, all_105_1_18) = 0, yields: % 22.74/6.86 | (193) all_178_0_28 = 0 % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (38) with all_105_1_18, all_0_7_7, all_178_1_29, 0 and discharging atoms member(all_105_1_18, all_0_7_7) = all_178_1_29, member(all_105_1_18, all_0_7_7) = 0, yields: % 22.74/6.86 | (194) all_178_1_29 = 0 % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (38) with all_22_0_8, all_0_7_7, all_178_3_31, 0 and discharging atoms member(all_22_0_8, all_0_7_7) = all_178_3_31, member(all_22_0_8, all_0_7_7) = 0, yields: % 22.74/6.86 | (195) all_178_3_31 = 0 % 22.74/6.86 | % 22.74/6.86 | Instantiating formula (38) with all_0_4_4, all_0_7_7, all_178_2_30, 0 and discharging atoms member(all_0_4_4, all_0_7_7) = all_178_2_30, member(all_0_4_4, all_0_7_7) = 0, yields: % 22.74/6.86 | (196) all_178_2_30 = 0 % 22.74/6.86 | % 22.74/6.86 +-Applying beta-rule and splitting (192), into two cases. % 22.74/6.86 |-Branch one: % 22.74/6.86 | (197) ~ (all_178_0_28 = 0) % 22.74/6.86 | % 22.74/6.86 | Equations (193) can reduce 197 to: % 22.74/6.86 | (68) $false % 22.74/6.86 | % 22.74/6.86 |-The branch is then unsatisfiable % 22.74/6.86 |-Branch two: % 22.74/6.86 | (193) all_178_0_28 = 0 % 22.74/6.87 | (200) ~ (all_178_1_29 = 0) | ~ (all_178_2_30 = 0) | ~ (all_178_3_31 = 0) % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (200), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (201) ~ (all_178_1_29 = 0) % 22.74/6.87 | % 22.74/6.87 | Equations (194) can reduce 201 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (194) all_178_1_29 = 0 % 22.74/6.87 | (204) ~ (all_178_2_30 = 0) | ~ (all_178_3_31 = 0) % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (204), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (205) ~ (all_178_2_30 = 0) % 22.74/6.87 | % 22.74/6.87 | Equations (196) can reduce 205 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (196) all_178_2_30 = 0 % 22.74/6.87 | (208) ~ (all_178_3_31 = 0) % 22.74/6.87 | % 22.74/6.87 | Equations (195) can reduce 208 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (183) all_141_0_24 = 0 % 22.74/6.87 | (211) ~ (all_141_1_25 = 0) | ~ (all_141_2_26 = 0) | ~ (all_141_3_27 = 0) % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (211), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (212) ~ (all_141_1_25 = 0) % 22.74/6.87 | % 22.74/6.87 | Equations (171) can reduce 212 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (171) all_141_1_25 = 0 % 22.74/6.87 | (215) ~ (all_141_2_26 = 0) | ~ (all_141_3_27 = 0) % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (215), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (216) ~ (all_141_2_26 = 0) % 22.74/6.87 | % 22.74/6.87 | Equations (173) can reduce 216 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (173) all_141_2_26 = 0 % 22.74/6.87 | (219) ~ (all_141_3_27 = 0) % 22.74/6.87 | % 22.74/6.87 | Equations (175) can reduce 219 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (161) all_117_0_19 = 0 % 22.74/6.87 | (222) ~ (all_117_1_20 = 0) % 22.74/6.87 | % 22.74/6.87 | Equations (151) can reduce 222 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (131) all_27_0_9 = 0 % 22.74/6.87 | (225) ~ (all_27_1_10 = 0) % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (83), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (226) all_27_1_10 = 0 % 22.74/6.87 | % 22.74/6.87 | Equations (226) can reduce 225 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (225) ~ (all_27_1_10 = 0) % 22.74/6.87 | (229) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, all_0_3_3) = 0) % 22.74/6.87 | % 22.74/6.87 | Instantiating (229) with all_105_0_32, all_105_1_33 yields: % 22.74/6.87 | (230) ~ (all_105_0_32 = 0) & member(all_105_1_33, all_0_2_2) = all_105_0_32 & member(all_105_1_33, all_0_3_3) = 0 % 22.74/6.87 | % 22.74/6.87 | Applying alpha-rule on (230) yields: % 22.74/6.87 | (231) ~ (all_105_0_32 = 0) % 22.74/6.87 | (232) member(all_105_1_33, all_0_2_2) = all_105_0_32 % 22.74/6.87 | (233) member(all_105_1_33, all_0_3_3) = 0 % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (51) with all_105_0_32, all_0_2_2, all_105_1_33, all_0_4_4, all_0_7_7, all_0_6_6 and discharging atoms equivalence_class(all_0_4_4, all_0_7_7, all_0_6_6) = all_0_2_2, member(all_105_1_33, all_0_2_2) = all_105_0_32, yields: % 22.74/6.87 | (234) all_105_0_32 = 0 | ? [v0] : ? [v1] : (apply(all_0_6_6, all_0_4_4, all_105_1_33) = v1 & member(all_105_1_33, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (8) with all_0_3_3, all_105_1_33, all_0_5_5, all_0_7_7, all_0_6_6 and discharging atoms equivalence_class(all_0_5_5, all_0_7_7, all_0_6_6) = all_0_3_3, member(all_105_1_33, all_0_3_3) = 0, yields: % 22.74/6.87 | (235) apply(all_0_6_6, all_0_5_5, all_105_1_33) = 0 & member(all_105_1_33, all_0_7_7) = 0 % 22.74/6.87 | % 22.74/6.87 | Applying alpha-rule on (235) yields: % 22.74/6.87 | (236) apply(all_0_6_6, all_0_5_5, all_105_1_33) = 0 % 22.74/6.87 | (237) member(all_105_1_33, all_0_7_7) = 0 % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (234), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (238) all_105_0_32 = 0 % 22.74/6.87 | % 22.74/6.87 | Equations (238) can reduce 231 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (231) ~ (all_105_0_32 = 0) % 22.74/6.87 | (241) ? [v0] : ? [v1] : (apply(all_0_6_6, all_0_4_4, all_105_1_33) = v1 & member(all_105_1_33, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.87 | % 22.74/6.87 | Instantiating (241) with all_117_0_34, all_117_1_35 yields: % 22.74/6.87 | (242) apply(all_0_6_6, all_0_4_4, all_105_1_33) = all_117_0_34 & member(all_105_1_33, all_0_7_7) = all_117_1_35 & ( ~ (all_117_0_34 = 0) | ~ (all_117_1_35 = 0)) % 22.74/6.87 | % 22.74/6.87 | Applying alpha-rule on (242) yields: % 22.74/6.87 | (243) apply(all_0_6_6, all_0_4_4, all_105_1_33) = all_117_0_34 % 22.74/6.87 | (244) member(all_105_1_33, all_0_7_7) = all_117_1_35 % 22.74/6.87 | (245) ~ (all_117_0_34 = 0) | ~ (all_117_1_35 = 0) % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (38) with all_105_1_33, all_0_7_7, 0, all_117_1_35 and discharging atoms member(all_105_1_33, all_0_7_7) = all_117_1_35, member(all_105_1_33, all_0_7_7) = 0, yields: % 22.74/6.87 | (246) all_117_1_35 = 0 % 22.74/6.87 | % 22.74/6.87 | From (246) and (244) follows: % 22.74/6.87 | (237) member(all_105_1_33, all_0_7_7) = 0 % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (245), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (248) ~ (all_117_0_34 = 0) % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (35) with all_117_0_34, all_105_1_33, all_22_0_8, all_0_4_4, all_0_6_6, all_0_7_7 and discharging atoms equivalence(all_0_6_6, all_0_7_7) = 0, apply(all_0_6_6, all_0_4_4, all_105_1_33) = all_117_0_34, apply(all_0_6_6, all_0_4_4, all_22_0_8) = 0, yields: % 22.74/6.87 | (249) all_117_0_34 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_6_6, all_22_0_8, all_105_1_33) = v3 & member(all_105_1_33, all_0_7_7) = v2 & member(all_22_0_8, all_0_7_7) = v1 & member(all_0_4_4, all_0_7_7) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (20) with all_105_1_33, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms equivalence(all_0_6_6, all_0_7_7) = 0, apply(all_0_6_6, all_0_5_5, all_105_1_33) = 0, yields: % 22.74/6.87 | (250) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_6_6, all_105_1_33, all_0_5_5) = v2 & member(all_105_1_33, all_0_7_7) = v1 & member(all_0_5_5, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.74/6.87 | % 22.74/6.87 | Instantiating (250) with all_132_0_36, all_132_1_37, all_132_2_38 yields: % 22.74/6.87 | (251) apply(all_0_6_6, all_105_1_33, all_0_5_5) = all_132_0_36 & member(all_105_1_33, all_0_7_7) = all_132_1_37 & member(all_0_5_5, all_0_7_7) = all_132_2_38 & ( ~ (all_132_1_37 = 0) | ~ (all_132_2_38 = 0) | all_132_0_36 = 0) % 22.74/6.87 | % 22.74/6.87 | Applying alpha-rule on (251) yields: % 22.74/6.87 | (252) apply(all_0_6_6, all_105_1_33, all_0_5_5) = all_132_0_36 % 22.74/6.87 | (253) member(all_105_1_33, all_0_7_7) = all_132_1_37 % 22.74/6.87 | (254) member(all_0_5_5, all_0_7_7) = all_132_2_38 % 22.74/6.87 | (255) ~ (all_132_1_37 = 0) | ~ (all_132_2_38 = 0) | all_132_0_36 = 0 % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (249), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (256) all_117_0_34 = 0 % 22.74/6.87 | % 22.74/6.87 | Equations (256) can reduce 248 to: % 22.74/6.87 | (68) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (248) ~ (all_117_0_34 = 0) % 22.74/6.87 | (259) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_6_6, all_22_0_8, all_105_1_33) = v3 & member(all_105_1_33, all_0_7_7) = v2 & member(all_22_0_8, all_0_7_7) = v1 & member(all_0_4_4, all_0_7_7) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.87 | % 22.74/6.87 | Instantiating (259) with all_141_0_39, all_141_1_40, all_141_2_41, all_141_3_42 yields: % 22.74/6.87 | (260) apply(all_0_6_6, all_22_0_8, all_105_1_33) = all_141_0_39 & member(all_105_1_33, all_0_7_7) = all_141_1_40 & member(all_22_0_8, all_0_7_7) = all_141_2_41 & member(all_0_4_4, all_0_7_7) = all_141_3_42 & ( ~ (all_141_0_39 = 0) | ~ (all_141_1_40 = 0) | ~ (all_141_2_41 = 0) | ~ (all_141_3_42 = 0)) % 22.74/6.87 | % 22.74/6.87 | Applying alpha-rule on (260) yields: % 22.74/6.87 | (261) member(all_0_4_4, all_0_7_7) = all_141_3_42 % 22.74/6.87 | (262) member(all_105_1_33, all_0_7_7) = all_141_1_40 % 22.74/6.87 | (263) ~ (all_141_0_39 = 0) | ~ (all_141_1_40 = 0) | ~ (all_141_2_41 = 0) | ~ (all_141_3_42 = 0) % 22.74/6.87 | (264) member(all_22_0_8, all_0_7_7) = all_141_2_41 % 22.74/6.87 | (265) apply(all_0_6_6, all_22_0_8, all_105_1_33) = all_141_0_39 % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (38) with all_105_1_33, all_0_7_7, all_141_1_40, 0 and discharging atoms member(all_105_1_33, all_0_7_7) = all_141_1_40, member(all_105_1_33, all_0_7_7) = 0, yields: % 22.74/6.87 | (266) all_141_1_40 = 0 % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (38) with all_105_1_33, all_0_7_7, all_132_1_37, all_141_1_40 and discharging atoms member(all_105_1_33, all_0_7_7) = all_141_1_40, member(all_105_1_33, all_0_7_7) = all_132_1_37, yields: % 22.74/6.87 | (267) all_141_1_40 = all_132_1_37 % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (38) with all_22_0_8, all_0_7_7, all_141_2_41, 0 and discharging atoms member(all_22_0_8, all_0_7_7) = all_141_2_41, member(all_22_0_8, all_0_7_7) = 0, yields: % 22.74/6.87 | (268) all_141_2_41 = 0 % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (38) with all_0_4_4, all_0_7_7, all_141_3_42, 0 and discharging atoms member(all_0_4_4, all_0_7_7) = all_141_3_42, member(all_0_4_4, all_0_7_7) = 0, yields: % 22.74/6.87 | (269) all_141_3_42 = 0 % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (38) with all_0_5_5, all_0_7_7, all_132_2_38, 0 and discharging atoms member(all_0_5_5, all_0_7_7) = all_132_2_38, member(all_0_5_5, all_0_7_7) = 0, yields: % 22.74/6.87 | (270) all_132_2_38 = 0 % 22.74/6.87 | % 22.74/6.87 | Combining equations (266,267) yields a new equation: % 22.74/6.87 | (271) all_132_1_37 = 0 % 22.74/6.87 | % 22.74/6.87 | Combining equations (271,267) yields a new equation: % 22.74/6.87 | (266) all_141_1_40 = 0 % 22.74/6.87 | % 22.74/6.87 | From (271) and (253) follows: % 22.74/6.87 | (237) member(all_105_1_33, all_0_7_7) = 0 % 22.74/6.87 | % 22.74/6.87 | From (268) and (264) follows: % 22.74/6.87 | (86) member(all_22_0_8, all_0_7_7) = 0 % 22.74/6.87 | % 22.74/6.87 | From (270) and (254) follows: % 22.74/6.87 | (40) member(all_0_5_5, all_0_7_7) = 0 % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (263), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (276) ~ (all_141_0_39 = 0) % 22.74/6.87 | % 22.74/6.87 | Instantiating formula (35) with all_141_0_39, all_105_1_33, all_0_5_5, all_22_0_8, all_0_6_6, all_0_7_7 and discharging atoms equivalence(all_0_6_6, all_0_7_7) = 0, apply(all_0_6_6, all_22_0_8, all_105_1_33) = all_141_0_39, apply(all_0_6_6, all_22_0_8, all_0_5_5) = 0, yields: % 22.74/6.87 | (277) all_141_0_39 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_6_6, all_0_5_5, all_105_1_33) = v3 & member(all_105_1_33, all_0_7_7) = v2 & member(all_22_0_8, all_0_7_7) = v0 & member(all_0_5_5, all_0_7_7) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (103), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (278) ~ (member(all_0_5_5, all_0_7_7) = all_48_1_12) % 22.74/6.87 | % 22.74/6.87 | From (107) and (278) follows: % 22.74/6.87 | (279) ~ (member(all_0_5_5, all_0_7_7) = 0) % 22.74/6.87 | % 22.74/6.87 | Using (40) and (279) yields: % 22.74/6.87 | (280) $false % 22.74/6.87 | % 22.74/6.87 |-The branch is then unsatisfiable % 22.74/6.87 |-Branch two: % 22.74/6.87 | (281) member(all_0_5_5, all_0_7_7) = all_48_1_12 % 22.74/6.87 | (107) all_48_1_12 = 0 % 22.74/6.87 | % 22.74/6.87 | From (107) and (281) follows: % 22.74/6.87 | (40) member(all_0_5_5, all_0_7_7) = 0 % 22.74/6.87 | % 22.74/6.87 +-Applying beta-rule and splitting (277), into two cases. % 22.74/6.87 |-Branch one: % 22.74/6.87 | (284) all_141_0_39 = 0 % 22.74/6.88 | % 22.74/6.88 | Equations (284) can reduce 276 to: % 22.74/6.88 | (68) $false % 22.74/6.88 | % 22.74/6.88 |-The branch is then unsatisfiable % 22.74/6.88 |-Branch two: % 22.74/6.88 | (276) ~ (all_141_0_39 = 0) % 22.74/6.88 | (287) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (apply(all_0_6_6, all_0_5_5, all_105_1_33) = v3 & member(all_105_1_33, all_0_7_7) = v2 & member(all_22_0_8, all_0_7_7) = v0 & member(all_0_5_5, all_0_7_7) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.74/6.88 | % 22.74/6.88 | Instantiating (287) with all_178_0_43, all_178_1_44, all_178_2_45, all_178_3_46 yields: % 22.74/6.88 | (288) apply(all_0_6_6, all_0_5_5, all_105_1_33) = all_178_0_43 & member(all_105_1_33, all_0_7_7) = all_178_1_44 & member(all_22_0_8, all_0_7_7) = all_178_3_46 & member(all_0_5_5, all_0_7_7) = all_178_2_45 & ( ~ (all_178_0_43 = 0) | ~ (all_178_1_44 = 0) | ~ (all_178_2_45 = 0) | ~ (all_178_3_46 = 0)) % 22.74/6.88 | % 22.74/6.88 | Applying alpha-rule on (288) yields: % 22.74/6.88 | (289) ~ (all_178_0_43 = 0) | ~ (all_178_1_44 = 0) | ~ (all_178_2_45 = 0) | ~ (all_178_3_46 = 0) % 22.74/6.88 | (290) apply(all_0_6_6, all_0_5_5, all_105_1_33) = all_178_0_43 % 22.74/6.88 | (291) member(all_105_1_33, all_0_7_7) = all_178_1_44 % 22.74/6.88 | (292) member(all_22_0_8, all_0_7_7) = all_178_3_46 % 22.74/6.88 | (293) member(all_0_5_5, all_0_7_7) = all_178_2_45 % 22.74/6.88 | % 22.74/6.88 | Instantiating formula (41) with all_0_6_6, all_0_5_5, all_105_1_33, all_178_0_43, 0 and discharging atoms apply(all_0_6_6, all_0_5_5, all_105_1_33) = all_178_0_43, apply(all_0_6_6, all_0_5_5, all_105_1_33) = 0, yields: % 22.74/6.88 | (294) all_178_0_43 = 0 % 22.74/6.88 | % 22.74/6.88 | Instantiating formula (38) with all_105_1_33, all_0_7_7, all_178_1_44, 0 and discharging atoms member(all_105_1_33, all_0_7_7) = all_178_1_44, member(all_105_1_33, all_0_7_7) = 0, yields: % 22.74/6.88 | (295) all_178_1_44 = 0 % 22.74/6.88 | % 22.74/6.88 | Instantiating formula (38) with all_22_0_8, all_0_7_7, all_178_3_46, 0 and discharging atoms member(all_22_0_8, all_0_7_7) = all_178_3_46, member(all_22_0_8, all_0_7_7) = 0, yields: % 22.74/6.88 | (296) all_178_3_46 = 0 % 22.74/6.88 | % 22.74/6.88 | Instantiating formula (38) with all_0_5_5, all_0_7_7, all_178_2_45, 0 and discharging atoms member(all_0_5_5, all_0_7_7) = all_178_2_45, member(all_0_5_5, all_0_7_7) = 0, yields: % 22.74/6.88 | (297) all_178_2_45 = 0 % 22.74/6.88 | % 22.74/6.88 +-Applying beta-rule and splitting (289), into two cases. % 22.74/6.88 |-Branch one: % 22.74/6.88 | (298) ~ (all_178_0_43 = 0) % 22.74/6.88 | % 22.74/6.88 | Equations (294) can reduce 298 to: % 22.74/6.88 | (68) $false % 22.74/6.88 | % 22.74/6.88 |-The branch is then unsatisfiable % 22.74/6.88 |-Branch two: % 22.74/6.88 | (294) all_178_0_43 = 0 % 22.74/6.88 | (301) ~ (all_178_1_44 = 0) | ~ (all_178_2_45 = 0) | ~ (all_178_3_46 = 0) % 22.74/6.88 | % 22.74/6.88 +-Applying beta-rule and splitting (301), into two cases. % 22.74/6.88 |-Branch one: % 22.74/6.88 | (302) ~ (all_178_1_44 = 0) % 22.74/6.88 | % 22.74/6.88 | Equations (295) can reduce 302 to: % 22.74/6.88 | (68) $false % 22.74/6.88 | % 22.74/6.88 |-The branch is then unsatisfiable % 22.74/6.88 |-Branch two: % 22.74/6.88 | (295) all_178_1_44 = 0 % 22.74/6.88 | (305) ~ (all_178_2_45 = 0) | ~ (all_178_3_46 = 0) % 22.74/6.88 | % 22.74/6.88 +-Applying beta-rule and splitting (305), into two cases. % 22.74/6.88 |-Branch one: % 22.74/6.88 | (306) ~ (all_178_2_45 = 0) % 22.74/6.88 | % 22.74/6.88 | Equations (297) can reduce 306 to: % 22.74/6.88 | (68) $false % 22.74/6.88 | % 22.74/6.88 |-The branch is then unsatisfiable % 22.74/6.88 |-Branch two: % 22.74/6.88 | (297) all_178_2_45 = 0 % 22.74/6.88 | (309) ~ (all_178_3_46 = 0) % 22.74/6.88 | % 22.74/6.88 | Equations (296) can reduce 309 to: % 22.74/6.88 | (68) $false % 22.74/6.88 | % 22.74/6.88 |-The branch is then unsatisfiable % 22.74/6.88 |-Branch two: % 22.74/6.88 | (284) all_141_0_39 = 0 % 22.74/6.88 | (312) ~ (all_141_1_40 = 0) | ~ (all_141_2_41 = 0) | ~ (all_141_3_42 = 0) % 22.74/6.88 | % 22.74/6.88 +-Applying beta-rule and splitting (312), into two cases. % 22.74/6.88 |-Branch one: % 22.74/6.88 | (313) ~ (all_141_1_40 = 0) % 22.74/6.88 | % 22.74/6.88 | Equations (266) can reduce 313 to: % 22.74/6.88 | (68) $false % 22.74/6.88 | % 22.74/6.88 |-The branch is then unsatisfiable % 22.74/6.88 |-Branch two: % 22.74/6.88 | (266) all_141_1_40 = 0 % 22.74/6.88 | (316) ~ (all_141_2_41 = 0) | ~ (all_141_3_42 = 0) % 22.74/6.88 | % 22.74/6.88 +-Applying beta-rule and splitting (316), into two cases. % 22.74/6.88 |-Branch one: % 22.74/6.88 | (317) ~ (all_141_2_41 = 0) % 22.74/6.88 | % 22.74/6.88 | Equations (268) can reduce 317 to: % 22.74/6.88 | (68) $false % 22.74/6.88 | % 22.74/6.88 |-The branch is then unsatisfiable % 22.74/6.88 |-Branch two: % 22.74/6.88 | (268) all_141_2_41 = 0 % 22.74/6.88 | (320) ~ (all_141_3_42 = 0) % 22.74/6.88 | % 22.74/6.88 | Equations (269) can reduce 320 to: % 22.74/6.88 | (68) $false % 22.74/6.88 | % 22.74/6.88 |-The branch is then unsatisfiable % 22.74/6.88 |-Branch two: % 22.74/6.88 | (256) all_117_0_34 = 0 % 22.74/6.88 | (323) ~ (all_117_1_35 = 0) % 22.74/6.88 | % 22.74/6.88 | Equations (246) can reduce 323 to: % 22.74/6.88 | (68) $false % 22.74/6.88 | % 22.74/6.88 |-The branch is then unsatisfiable % 22.74/6.88 % SZS output end Proof for theBenchmark % 22.74/6.88 % 22.74/6.88 6266ms %------------------------------------------------------------------------------