%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET706+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n003.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 00:21:31 EDT 2022 % Result : Theorem 4.34s 1.74s % Output : Proof 7.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET706+4 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n003.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jul 11 06:50:00 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.59 ____ _ % 0.19/0.59 ___ / __ \_____(_)___ ________ __________ % 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic % 0.19/0.59 (ePrincess v.1.0) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2015 % 0.19/0.59 (c) Peter Backeman, 2014-2015 % 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.59 Bug reports to peter@backeman.se % 0.19/0.59 % 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.53/0.93 Prover 0: Preprocessing ... % 1.91/1.14 Prover 0: Warning: ignoring some quantifiers % 1.91/1.16 Prover 0: Constructing countermodel ... % 3.00/1.40 Prover 0: gave up % 3.00/1.40 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.00/1.43 Prover 1: Preprocessing ... % 3.47/1.53 Prover 1: Constructing countermodel ... % 4.34/1.74 Prover 1: proved (341ms) % 4.34/1.74 % 4.34/1.74 No countermodel exists, formula is valid % 4.34/1.74 % SZS status Theorem for theBenchmark % 4.34/1.74 % 4.34/1.74 Generating proof ... found it (size 160) % 6.62/2.27 % 6.62/2.27 % SZS output start Proof for theBenchmark % 6.62/2.27 Assumed formulas after preprocessing and simplification: % 6.62/2.28 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & difference(v1, v2) = v4 & difference(v0, v2) = v3 & difference(v0, v1) = v5 & union(v4, v5) = v6 & equal_set(v3, v6) = v7 & subset(v2, v1) = 0 & subset(v1, v0) = 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 = 0 | ~ (sum(v9) = v10) | ~ (member(v8, v12) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = v13)) & ! [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 | ~ (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] : ( ~ (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 | ~ (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] : ( ~ (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)) % 6.96/2.31 | 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: % 6.96/2.31 | (1) ~ (all_0_0_0 = 0) & difference(all_0_6_6, all_0_5_5) = all_0_3_3 & difference(all_0_7_7, all_0_5_5) = all_0_4_4 & difference(all_0_7_7, all_0_6_6) = all_0_2_2 & union(all_0_3_3, all_0_2_2) = all_0_1_1 & equal_set(all_0_4_4, all_0_1_1) = all_0_0_0 & subset(all_0_5_5, all_0_6_6) = 0 & subset(all_0_6_6, all_0_7_7) = 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 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [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 | ~ (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] : ( ~ (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 | ~ (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] : ( ~ (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) % 6.96/2.33 | % 6.96/2.33 | Applying alpha-rule on (1) yields: % 6.96/2.33 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 6.96/2.33 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 6.96/2.33 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 6.96/2.33 | (5) ! [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))) % 6.96/2.33 | (6) ! [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)) % 6.96/2.33 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 6.96/2.33 | (8) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 6.96/2.33 | (9) union(all_0_3_3, all_0_2_2) = all_0_1_1 % 6.96/2.33 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 6.96/2.33 | (11) difference(all_0_7_7, all_0_6_6) = all_0_2_2 % 6.96/2.33 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 6.96/2.33 | (13) ! [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)) % 6.96/2.33 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 6.96/2.33 | (15) ! [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)) % 6.96/2.33 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 6.96/2.33 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 6.96/2.33 | (18) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 6.96/2.33 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 6.96/2.33 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 6.96/2.33 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 6.96/2.33 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 6.96/2.33 | (23) ! [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)))) % 6.96/2.33 | (24) ~ (all_0_0_0 = 0) % 6.96/2.33 | (25) ! [v0] : ~ (member(v0, empty_set) = 0) % 6.96/2.33 | (26) subset(all_0_5_5, all_0_6_6) = 0 % 6.96/2.33 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 6.96/2.33 | (28) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 6.96/2.34 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 6.96/2.34 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 6.96/2.34 | (31) ! [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)) % 6.96/2.34 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 6.96/2.34 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 6.96/2.34 | (34) subset(all_0_6_6, all_0_7_7) = 0 % 6.96/2.34 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 6.96/2.34 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 6.96/2.34 | (37) ! [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))) % 6.96/2.34 | (38) difference(all_0_6_6, all_0_5_5) = all_0_3_3 % 6.96/2.34 | (39) equal_set(all_0_4_4, all_0_1_1) = all_0_0_0 % 6.96/2.34 | (40) difference(all_0_7_7, all_0_5_5) = all_0_4_4 % 6.96/2.34 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 6.96/2.34 | (42) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 6.96/2.34 | % 6.96/2.34 | Instantiating formula (18) with all_0_0_0, all_0_1_1, all_0_4_4 and discharging atoms equal_set(all_0_4_4, all_0_1_1) = all_0_0_0, yields: % 6.96/2.34 | (43) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v1 & subset(all_0_4_4, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.96/2.34 | % 6.96/2.34 +-Applying beta-rule and splitting (43), into two cases. % 6.96/2.34 |-Branch one: % 6.96/2.34 | (44) all_0_0_0 = 0 % 6.96/2.34 | % 6.96/2.34 | Equations (44) can reduce 24 to: % 6.96/2.34 | (45) $false % 6.96/2.34 | % 6.96/2.34 |-The branch is then unsatisfiable % 6.96/2.34 |-Branch two: % 6.96/2.34 | (24) ~ (all_0_0_0 = 0) % 6.96/2.34 | (47) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_4_4) = v1 & subset(all_0_4_4, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 6.96/2.34 | % 6.96/2.34 | Instantiating (47) with all_14_0_8, all_14_1_9 yields: % 6.96/2.34 | (48) subset(all_0_1_1, all_0_4_4) = all_14_0_8 & subset(all_0_4_4, all_0_1_1) = all_14_1_9 & ( ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0)) % 6.96/2.34 | % 6.96/2.34 | Applying alpha-rule on (48) yields: % 6.96/2.34 | (49) subset(all_0_1_1, all_0_4_4) = all_14_0_8 % 6.96/2.34 | (50) subset(all_0_4_4, all_0_1_1) = all_14_1_9 % 6.96/2.34 | (51) ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0) % 6.96/2.34 | % 6.96/2.34 | Instantiating formula (29) with all_14_0_8, all_0_4_4, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_4_4) = all_14_0_8, yields: % 6.96/2.34 | (52) all_14_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1) % 6.96/2.34 | % 6.96/2.34 | Instantiating formula (29) with all_14_1_9, all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = all_14_1_9, yields: % 6.96/2.34 | (53) all_14_1_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0) % 6.96/2.35 | % 6.96/2.35 +-Applying beta-rule and splitting (51), into two cases. % 6.96/2.35 |-Branch one: % 6.96/2.35 | (54) ~ (all_14_0_8 = 0) % 6.96/2.35 | % 6.96/2.35 +-Applying beta-rule and splitting (52), into two cases. % 6.96/2.35 |-Branch one: % 6.96/2.35 | (55) all_14_0_8 = 0 % 6.96/2.35 | % 6.96/2.35 | Equations (55) can reduce 54 to: % 6.96/2.35 | (45) $false % 6.96/2.35 | % 6.96/2.35 |-The branch is then unsatisfiable % 6.96/2.35 |-Branch two: % 6.96/2.35 | (54) ~ (all_14_0_8 = 0) % 6.96/2.35 | (58) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_4_4) = v1) % 6.96/2.35 | % 6.96/2.35 | Instantiating (58) with all_42_0_10, all_42_1_11 yields: % 6.96/2.35 | (59) ~ (all_42_0_10 = 0) & member(all_42_1_11, all_0_1_1) = 0 & member(all_42_1_11, all_0_4_4) = all_42_0_10 % 6.96/2.35 | % 6.96/2.35 | Applying alpha-rule on (59) yields: % 6.96/2.35 | (60) ~ (all_42_0_10 = 0) % 6.96/2.35 | (61) member(all_42_1_11, all_0_1_1) = 0 % 6.96/2.35 | (62) member(all_42_1_11, all_0_4_4) = all_42_0_10 % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (35) with all_0_3_3, all_0_6_6, all_0_5_5, all_42_1_11 and discharging atoms difference(all_0_6_6, all_0_5_5) = all_0_3_3, yields: % 6.96/2.35 | (63) ~ (member(all_42_1_11, all_0_3_3) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_42_1_11, all_0_5_5) = v0 & member(all_42_1_11, all_0_6_6) = 0) % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (35) with all_0_2_2, all_0_7_7, all_0_6_6, all_42_1_11 and discharging atoms difference(all_0_7_7, all_0_6_6) = all_0_2_2, yields: % 6.96/2.35 | (64) ~ (member(all_42_1_11, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_42_1_11, all_0_6_6) = v0 & member(all_42_1_11, all_0_7_7) = 0) % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (5) with all_0_1_1, all_0_2_2, all_0_3_3, all_42_1_11 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_42_1_11, all_0_1_1) = 0, yields: % 6.96/2.35 | (65) ? [v0] : ? [v1] : (member(all_42_1_11, all_0_2_2) = v1 & member(all_42_1_11, all_0_3_3) = v0 & (v1 = 0 | v0 = 0)) % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (27) with all_42_1_11, all_0_6_6, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_6_6) = 0, yields: % 6.96/2.35 | (66) ~ (member(all_42_1_11, all_0_5_5) = 0) | member(all_42_1_11, all_0_6_6) = 0 % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (27) with all_42_1_11, all_0_7_7, all_0_6_6 and discharging atoms subset(all_0_6_6, all_0_7_7) = 0, yields: % 6.96/2.35 | (67) ~ (member(all_42_1_11, all_0_6_6) = 0) | member(all_42_1_11, all_0_7_7) = 0 % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (37) with all_42_0_10, all_0_4_4, all_0_7_7, all_0_5_5, all_42_1_11 and discharging atoms difference(all_0_7_7, all_0_5_5) = all_0_4_4, member(all_42_1_11, all_0_4_4) = all_42_0_10, yields: % 6.96/2.35 | (68) all_42_0_10 = 0 | ? [v0] : ? [v1] : (member(all_42_1_11, all_0_5_5) = v1 & member(all_42_1_11, all_0_7_7) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 6.96/2.35 | % 6.96/2.35 | Instantiating (65) with all_57_0_12, all_57_1_13 yields: % 6.96/2.35 | (69) member(all_42_1_11, all_0_2_2) = all_57_0_12 & member(all_42_1_11, all_0_3_3) = all_57_1_13 & (all_57_0_12 = 0 | all_57_1_13 = 0) % 6.96/2.35 | % 6.96/2.35 | Applying alpha-rule on (69) yields: % 6.96/2.35 | (70) member(all_42_1_11, all_0_2_2) = all_57_0_12 % 6.96/2.35 | (71) member(all_42_1_11, all_0_3_3) = all_57_1_13 % 6.96/2.35 | (72) all_57_0_12 = 0 | all_57_1_13 = 0 % 6.96/2.35 | % 6.96/2.35 +-Applying beta-rule and splitting (68), into two cases. % 6.96/2.35 |-Branch one: % 6.96/2.35 | (73) all_42_0_10 = 0 % 6.96/2.35 | % 6.96/2.35 | Equations (73) can reduce 60 to: % 6.96/2.35 | (45) $false % 6.96/2.35 | % 6.96/2.35 |-The branch is then unsatisfiable % 6.96/2.35 |-Branch two: % 6.96/2.35 | (60) ~ (all_42_0_10 = 0) % 6.96/2.35 | (76) ? [v0] : ? [v1] : (member(all_42_1_11, all_0_5_5) = v1 & member(all_42_1_11, all_0_7_7) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 6.96/2.35 | % 6.96/2.35 | Instantiating (76) with all_63_0_14, all_63_1_15 yields: % 6.96/2.35 | (77) member(all_42_1_11, all_0_5_5) = all_63_0_14 & member(all_42_1_11, all_0_7_7) = all_63_1_15 & ( ~ (all_63_1_15 = 0) | all_63_0_14 = 0) % 6.96/2.35 | % 6.96/2.35 | Applying alpha-rule on (77) yields: % 6.96/2.35 | (78) member(all_42_1_11, all_0_5_5) = all_63_0_14 % 6.96/2.35 | (79) member(all_42_1_11, all_0_7_7) = all_63_1_15 % 6.96/2.35 | (80) ~ (all_63_1_15 = 0) | all_63_0_14 = 0 % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (30) with all_42_1_11, all_0_2_2, all_57_0_12, 0 and discharging atoms member(all_42_1_11, all_0_2_2) = all_57_0_12, yields: % 6.96/2.35 | (81) all_57_0_12 = 0 | ~ (member(all_42_1_11, all_0_2_2) = 0) % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (30) with all_42_1_11, all_0_5_5, all_63_0_14, 0 and discharging atoms member(all_42_1_11, all_0_5_5) = all_63_0_14, yields: % 6.96/2.35 | (82) all_63_0_14 = 0 | ~ (member(all_42_1_11, all_0_5_5) = 0) % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (30) with all_42_1_11, all_0_7_7, all_63_1_15, 0 and discharging atoms member(all_42_1_11, all_0_7_7) = all_63_1_15, yields: % 6.96/2.35 | (83) all_63_1_15 = 0 | ~ (member(all_42_1_11, all_0_7_7) = 0) % 6.96/2.35 | % 6.96/2.35 | Instantiating formula (30) with all_42_1_11, all_0_7_7, all_63_1_15, all_57_0_12 and discharging atoms member(all_42_1_11, all_0_7_7) = all_63_1_15, yields: % 6.96/2.36 | (84) all_63_1_15 = all_57_0_12 | ~ (member(all_42_1_11, all_0_7_7) = all_57_0_12) % 6.96/2.36 | % 6.96/2.36 | Instantiating formula (30) with all_42_1_11, all_0_7_7, all_63_1_15, all_57_1_13 and discharging atoms member(all_42_1_11, all_0_7_7) = all_63_1_15, yields: % 6.96/2.36 | (85) all_63_1_15 = all_57_1_13 | ~ (member(all_42_1_11, all_0_7_7) = all_57_1_13) % 6.96/2.36 | % 6.96/2.36 | Instantiating formula (37) with all_57_1_13, all_0_3_3, all_0_6_6, all_0_5_5, all_42_1_11 and discharging atoms difference(all_0_6_6, all_0_5_5) = all_0_3_3, member(all_42_1_11, all_0_3_3) = all_57_1_13, yields: % 6.96/2.36 | (86) all_57_1_13 = 0 | ? [v0] : ? [v1] : (member(all_42_1_11, all_0_5_5) = v1 & member(all_42_1_11, all_0_6_6) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 6.96/2.36 | % 6.96/2.36 +-Applying beta-rule and splitting (66), into two cases. % 6.96/2.36 |-Branch one: % 6.96/2.36 | (87) ~ (member(all_42_1_11, all_0_5_5) = 0) % 6.96/2.36 | % 6.96/2.36 | Using (78) and (87) yields: % 6.96/2.36 | (88) ~ (all_63_0_14 = 0) % 6.96/2.36 | % 6.96/2.36 +-Applying beta-rule and splitting (80), into two cases. % 6.96/2.36 |-Branch one: % 6.96/2.36 | (89) ~ (all_63_1_15 = 0) % 6.96/2.36 | % 6.96/2.36 +-Applying beta-rule and splitting (67), into two cases. % 6.96/2.36 |-Branch one: % 6.96/2.36 | (90) ~ (member(all_42_1_11, all_0_6_6) = 0) % 6.96/2.36 | % 6.96/2.36 +-Applying beta-rule and splitting (63), into two cases. % 6.96/2.36 |-Branch one: % 6.96/2.36 | (91) ~ (member(all_42_1_11, all_0_3_3) = 0) % 6.96/2.36 | % 6.96/2.36 +-Applying beta-rule and splitting (64), into two cases. % 6.96/2.36 |-Branch one: % 6.96/2.36 | (92) ~ (member(all_42_1_11, all_0_2_2) = 0) % 6.96/2.36 | % 6.96/2.36 | Using (70) and (92) yields: % 6.96/2.36 | (93) ~ (all_57_0_12 = 0) % 6.96/2.36 | % 6.96/2.36 | Using (71) and (91) yields: % 6.96/2.36 | (94) ~ (all_57_1_13 = 0) % 6.96/2.36 | % 6.96/2.36 +-Applying beta-rule and splitting (72), into two cases. % 6.96/2.36 |-Branch one: % 6.96/2.36 | (95) all_57_0_12 = 0 % 6.96/2.36 | % 6.96/2.36 | Equations (95) can reduce 93 to: % 6.96/2.36 | (45) $false % 6.96/2.36 | % 6.96/2.36 |-The branch is then unsatisfiable % 6.96/2.36 |-Branch two: % 6.96/2.36 | (93) ~ (all_57_0_12 = 0) % 6.96/2.36 | (98) all_57_1_13 = 0 % 6.96/2.36 | % 6.96/2.36 | Equations (98) can reduce 94 to: % 6.96/2.36 | (45) $false % 6.96/2.36 | % 6.96/2.36 |-The branch is then unsatisfiable % 6.96/2.36 |-Branch two: % 6.96/2.36 | (100) member(all_42_1_11, all_0_2_2) = 0 % 6.96/2.36 | (101) ? [v0] : ( ~ (v0 = 0) & member(all_42_1_11, all_0_6_6) = v0 & member(all_42_1_11, all_0_7_7) = 0) % 6.96/2.36 | % 6.96/2.36 | Instantiating (101) with all_110_0_16 yields: % 6.96/2.36 | (102) ~ (all_110_0_16 = 0) & member(all_42_1_11, all_0_6_6) = all_110_0_16 & member(all_42_1_11, all_0_7_7) = 0 % 6.96/2.36 | % 6.96/2.36 | Applying alpha-rule on (102) yields: % 6.96/2.36 | (103) ~ (all_110_0_16 = 0) % 6.96/2.36 | (104) member(all_42_1_11, all_0_6_6) = all_110_0_16 % 6.96/2.36 | (105) member(all_42_1_11, all_0_7_7) = 0 % 6.96/2.36 | % 6.96/2.36 +-Applying beta-rule and splitting (81), into two cases. % 6.96/2.36 |-Branch one: % 6.96/2.36 | (92) ~ (member(all_42_1_11, all_0_2_2) = 0) % 6.96/2.36 | % 6.96/2.36 | Using (100) and (92) yields: % 6.96/2.36 | (107) $false % 6.96/2.36 | % 6.96/2.36 |-The branch is then unsatisfiable % 6.96/2.36 |-Branch two: % 6.96/2.36 | (100) member(all_42_1_11, all_0_2_2) = 0 % 6.96/2.36 | (95) all_57_0_12 = 0 % 6.96/2.36 | % 6.96/2.36 +-Applying beta-rule and splitting (84), into two cases. % 6.96/2.36 |-Branch one: % 6.96/2.36 | (110) ~ (member(all_42_1_11, all_0_7_7) = all_57_0_12) % 6.96/2.36 | % 6.96/2.36 | From (95) and (110) follows: % 6.96/2.36 | (111) ~ (member(all_42_1_11, all_0_7_7) = 0) % 6.96/2.36 | % 6.96/2.36 | Using (105) and (111) yields: % 6.96/2.36 | (107) $false % 6.96/2.36 | % 6.96/2.36 |-The branch is then unsatisfiable % 6.96/2.36 |-Branch two: % 6.96/2.36 | (113) member(all_42_1_11, all_0_7_7) = all_57_0_12 % 6.96/2.36 | (114) all_63_1_15 = all_57_0_12 % 6.96/2.36 | % 6.96/2.36 | Combining equations (95,114) yields a new equation: % 6.96/2.36 | (115) all_63_1_15 = 0 % 6.96/2.36 | % 6.96/2.36 | Equations (115) can reduce 89 to: % 6.96/2.36 | (45) $false % 6.96/2.36 | % 6.96/2.36 |-The branch is then unsatisfiable % 6.96/2.36 |-Branch two: % 6.96/2.36 | (117) member(all_42_1_11, all_0_3_3) = 0 % 6.96/2.36 | (118) ? [v0] : ( ~ (v0 = 0) & member(all_42_1_11, all_0_5_5) = v0 & member(all_42_1_11, all_0_6_6) = 0) % 6.96/2.37 | % 6.96/2.37 | Instantiating (118) with all_106_0_17 yields: % 6.96/2.37 | (119) ~ (all_106_0_17 = 0) & member(all_42_1_11, all_0_5_5) = all_106_0_17 & member(all_42_1_11, all_0_6_6) = 0 % 6.96/2.37 | % 6.96/2.37 | Applying alpha-rule on (119) yields: % 6.96/2.37 | (120) ~ (all_106_0_17 = 0) % 6.96/2.37 | (121) member(all_42_1_11, all_0_5_5) = all_106_0_17 % 6.96/2.37 | (122) member(all_42_1_11, all_0_6_6) = 0 % 6.96/2.37 | % 6.96/2.37 | Using (122) and (90) yields: % 6.96/2.37 | (107) $false % 6.96/2.37 | % 6.96/2.37 |-The branch is then unsatisfiable % 6.96/2.37 |-Branch two: % 6.96/2.37 | (122) member(all_42_1_11, all_0_6_6) = 0 % 6.96/2.37 | (105) member(all_42_1_11, all_0_7_7) = 0 % 6.96/2.37 | % 6.96/2.37 +-Applying beta-rule and splitting (86), into two cases. % 6.96/2.37 |-Branch one: % 6.96/2.37 | (98) all_57_1_13 = 0 % 6.96/2.37 | % 6.96/2.37 +-Applying beta-rule and splitting (85), into two cases. % 6.96/2.37 |-Branch one: % 6.96/2.37 | (127) ~ (member(all_42_1_11, all_0_7_7) = all_57_1_13) % 6.96/2.37 | % 6.96/2.37 | From (98) and (127) follows: % 6.96/2.37 | (111) ~ (member(all_42_1_11, all_0_7_7) = 0) % 6.96/2.37 | % 6.96/2.37 | Using (105) and (111) yields: % 6.96/2.37 | (107) $false % 6.96/2.37 | % 6.96/2.37 |-The branch is then unsatisfiable % 6.96/2.37 |-Branch two: % 6.96/2.37 | (130) member(all_42_1_11, all_0_7_7) = all_57_1_13 % 6.96/2.37 | (131) all_63_1_15 = all_57_1_13 % 6.96/2.37 | % 6.96/2.37 | Combining equations (98,131) yields a new equation: % 6.96/2.37 | (115) all_63_1_15 = 0 % 6.96/2.37 | % 6.96/2.37 | Equations (115) can reduce 89 to: % 6.96/2.37 | (45) $false % 6.96/2.37 | % 6.96/2.37 |-The branch is then unsatisfiable % 6.96/2.37 |-Branch two: % 6.96/2.37 | (94) ~ (all_57_1_13 = 0) % 6.96/2.37 | (135) ? [v0] : ? [v1] : (member(all_42_1_11, all_0_5_5) = v1 & member(all_42_1_11, all_0_6_6) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 6.96/2.37 | % 6.96/2.37 +-Applying beta-rule and splitting (72), into two cases. % 6.96/2.37 |-Branch one: % 6.96/2.37 | (95) all_57_0_12 = 0 % 6.96/2.37 | % 6.96/2.37 | From (95) and (70) follows: % 6.96/2.37 | (100) member(all_42_1_11, all_0_2_2) = 0 % 6.96/2.37 | % 6.96/2.37 +-Applying beta-rule and splitting (64), into two cases. % 6.96/2.37 |-Branch one: % 6.96/2.37 | (92) ~ (member(all_42_1_11, all_0_2_2) = 0) % 6.96/2.37 | % 6.96/2.37 | Using (100) and (92) yields: % 6.96/2.37 | (107) $false % 6.96/2.37 | % 6.96/2.37 |-The branch is then unsatisfiable % 6.96/2.37 |-Branch two: % 6.96/2.37 | (100) member(all_42_1_11, all_0_2_2) = 0 % 6.96/2.37 | (101) ? [v0] : ( ~ (v0 = 0) & member(all_42_1_11, all_0_6_6) = v0 & member(all_42_1_11, all_0_7_7) = 0) % 6.96/2.37 | % 6.96/2.37 | Instantiating (101) with all_120_0_20 yields: % 6.96/2.37 | (142) ~ (all_120_0_20 = 0) & member(all_42_1_11, all_0_6_6) = all_120_0_20 & member(all_42_1_11, all_0_7_7) = 0 % 6.96/2.37 | % 6.96/2.37 | Applying alpha-rule on (142) yields: % 6.96/2.37 | (143) ~ (all_120_0_20 = 0) % 6.96/2.37 | (144) member(all_42_1_11, all_0_6_6) = all_120_0_20 % 6.96/2.37 | (105) member(all_42_1_11, all_0_7_7) = 0 % 7.34/2.37 | % 7.34/2.37 +-Applying beta-rule and splitting (83), into two cases. % 7.34/2.37 |-Branch one: % 7.34/2.37 | (111) ~ (member(all_42_1_11, all_0_7_7) = 0) % 7.34/2.37 | % 7.34/2.37 | Using (105) and (111) yields: % 7.34/2.37 | (107) $false % 7.34/2.37 | % 7.34/2.37 |-The branch is then unsatisfiable % 7.34/2.37 |-Branch two: % 7.34/2.37 | (105) member(all_42_1_11, all_0_7_7) = 0 % 7.34/2.37 | (115) all_63_1_15 = 0 % 7.34/2.37 | % 7.34/2.37 | Equations (115) can reduce 89 to: % 7.34/2.37 | (45) $false % 7.34/2.37 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (93) ~ (all_57_0_12 = 0) % 7.34/2.38 | (98) all_57_1_13 = 0 % 7.34/2.38 | % 7.34/2.38 | Equations (98) can reduce 94 to: % 7.34/2.38 | (45) $false % 7.34/2.38 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (115) all_63_1_15 = 0 % 7.34/2.38 | (155) all_63_0_14 = 0 % 7.34/2.38 | % 7.34/2.38 | Equations (155) can reduce 88 to: % 7.34/2.38 | (45) $false % 7.34/2.38 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (157) member(all_42_1_11, all_0_5_5) = 0 % 7.34/2.38 | (122) member(all_42_1_11, all_0_6_6) = 0 % 7.34/2.38 | % 7.34/2.38 +-Applying beta-rule and splitting (67), into two cases. % 7.34/2.38 |-Branch one: % 7.34/2.38 | (90) ~ (member(all_42_1_11, all_0_6_6) = 0) % 7.34/2.38 | % 7.34/2.38 | Using (122) and (90) yields: % 7.34/2.38 | (107) $false % 7.34/2.38 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (122) member(all_42_1_11, all_0_6_6) = 0 % 7.34/2.38 | (105) member(all_42_1_11, all_0_7_7) = 0 % 7.34/2.38 | % 7.34/2.38 +-Applying beta-rule and splitting (64), into two cases. % 7.34/2.38 |-Branch one: % 7.34/2.38 | (92) ~ (member(all_42_1_11, all_0_2_2) = 0) % 7.34/2.38 | % 7.34/2.38 +-Applying beta-rule and splitting (82), into two cases. % 7.34/2.38 |-Branch one: % 7.34/2.38 | (87) ~ (member(all_42_1_11, all_0_5_5) = 0) % 7.34/2.38 | % 7.34/2.38 | Using (157) and (87) yields: % 7.34/2.38 | (107) $false % 7.34/2.38 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (157) member(all_42_1_11, all_0_5_5) = 0 % 7.34/2.38 | (155) all_63_0_14 = 0 % 7.34/2.38 | % 7.34/2.38 | From (155) and (78) follows: % 7.34/2.38 | (157) member(all_42_1_11, all_0_5_5) = 0 % 7.34/2.38 | % 7.34/2.38 +-Applying beta-rule and splitting (63), into two cases. % 7.34/2.38 |-Branch one: % 7.34/2.38 | (91) ~ (member(all_42_1_11, all_0_3_3) = 0) % 7.34/2.38 | % 7.34/2.38 | Using (70) and (92) yields: % 7.34/2.38 | (93) ~ (all_57_0_12 = 0) % 7.34/2.38 | % 7.34/2.38 | Using (71) and (91) yields: % 7.34/2.38 | (94) ~ (all_57_1_13 = 0) % 7.34/2.38 | % 7.34/2.38 +-Applying beta-rule and splitting (72), into two cases. % 7.34/2.38 |-Branch one: % 7.34/2.38 | (95) all_57_0_12 = 0 % 7.34/2.38 | % 7.34/2.38 | Equations (95) can reduce 93 to: % 7.34/2.38 | (45) $false % 7.34/2.38 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (93) ~ (all_57_0_12 = 0) % 7.34/2.38 | (98) all_57_1_13 = 0 % 7.34/2.38 | % 7.34/2.38 | Equations (98) can reduce 94 to: % 7.34/2.38 | (45) $false % 7.34/2.38 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (117) member(all_42_1_11, all_0_3_3) = 0 % 7.34/2.38 | (118) ? [v0] : ( ~ (v0 = 0) & member(all_42_1_11, all_0_5_5) = v0 & member(all_42_1_11, all_0_6_6) = 0) % 7.34/2.38 | % 7.34/2.38 | Instantiating (118) with all_110_0_21 yields: % 7.34/2.38 | (179) ~ (all_110_0_21 = 0) & member(all_42_1_11, all_0_5_5) = all_110_0_21 & member(all_42_1_11, all_0_6_6) = 0 % 7.34/2.38 | % 7.34/2.38 | Applying alpha-rule on (179) yields: % 7.34/2.38 | (180) ~ (all_110_0_21 = 0) % 7.34/2.38 | (181) member(all_42_1_11, all_0_5_5) = all_110_0_21 % 7.34/2.38 | (122) member(all_42_1_11, all_0_6_6) = 0 % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (30) with all_42_1_11, all_0_5_5, all_110_0_21, 0 and discharging atoms member(all_42_1_11, all_0_5_5) = all_110_0_21, member(all_42_1_11, all_0_5_5) = 0, yields: % 7.34/2.38 | (183) all_110_0_21 = 0 % 7.34/2.38 | % 7.34/2.38 | Equations (183) can reduce 180 to: % 7.34/2.38 | (45) $false % 7.34/2.38 | % 7.34/2.38 |-The branch is then unsatisfiable % 7.34/2.38 |-Branch two: % 7.34/2.38 | (100) member(all_42_1_11, all_0_2_2) = 0 % 7.34/2.38 | (101) ? [v0] : ( ~ (v0 = 0) & member(all_42_1_11, all_0_6_6) = v0 & member(all_42_1_11, all_0_7_7) = 0) % 7.34/2.38 | % 7.34/2.38 | Instantiating (101) with all_98_0_22 yields: % 7.34/2.38 | (187) ~ (all_98_0_22 = 0) & member(all_42_1_11, all_0_6_6) = all_98_0_22 & member(all_42_1_11, all_0_7_7) = 0 % 7.34/2.38 | % 7.34/2.38 | Applying alpha-rule on (187) yields: % 7.34/2.38 | (188) ~ (all_98_0_22 = 0) % 7.34/2.38 | (189) member(all_42_1_11, all_0_6_6) = all_98_0_22 % 7.34/2.38 | (105) member(all_42_1_11, all_0_7_7) = 0 % 7.34/2.38 | % 7.34/2.38 | Instantiating formula (30) with all_42_1_11, all_0_6_6, all_98_0_22, 0 and discharging atoms member(all_42_1_11, all_0_6_6) = all_98_0_22, member(all_42_1_11, all_0_6_6) = 0, yields: % 7.34/2.39 | (191) all_98_0_22 = 0 % 7.34/2.39 | % 7.34/2.39 | Equations (191) can reduce 188 to: % 7.34/2.39 | (45) $false % 7.34/2.39 | % 7.34/2.39 |-The branch is then unsatisfiable % 7.34/2.39 |-Branch two: % 7.34/2.39 | (55) all_14_0_8 = 0 % 7.34/2.39 | (194) ~ (all_14_1_9 = 0) % 7.34/2.39 | % 7.34/2.39 +-Applying beta-rule and splitting (53), into two cases. % 7.34/2.39 |-Branch one: % 7.34/2.39 | (195) all_14_1_9 = 0 % 7.34/2.39 | % 7.34/2.39 | Equations (195) can reduce 194 to: % 7.34/2.39 | (45) $false % 7.34/2.39 | % 7.34/2.39 |-The branch is then unsatisfiable % 7.34/2.39 |-Branch two: % 7.34/2.39 | (194) ~ (all_14_1_9 = 0) % 7.34/2.39 | (198) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_4_4) = 0) % 7.34/2.39 | % 7.34/2.39 | Instantiating (198) with all_42_0_23, all_42_1_24 yields: % 7.34/2.39 | (199) ~ (all_42_0_23 = 0) & member(all_42_1_24, all_0_1_1) = all_42_0_23 & member(all_42_1_24, all_0_4_4) = 0 % 7.34/2.39 | % 7.34/2.39 | Applying alpha-rule on (199) yields: % 7.34/2.39 | (200) ~ (all_42_0_23 = 0) % 7.34/2.39 | (201) member(all_42_1_24, all_0_1_1) = all_42_0_23 % 7.34/2.39 | (202) member(all_42_1_24, all_0_4_4) = 0 % 7.34/2.39 | % 7.34/2.39 | Instantiating formula (15) with all_42_0_23, all_0_1_1, all_0_2_2, all_0_3_3, all_42_1_24 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_42_1_24, all_0_1_1) = all_42_0_23, yields: % 7.34/2.39 | (203) all_42_0_23 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_24, all_0_2_2) = v1 & member(all_42_1_24, all_0_3_3) = v0) % 7.34/2.39 | % 7.34/2.39 | Instantiating formula (35) with all_0_4_4, all_0_7_7, all_0_5_5, all_42_1_24 and discharging atoms difference(all_0_7_7, all_0_5_5) = all_0_4_4, member(all_42_1_24, all_0_4_4) = 0, yields: % 7.34/2.39 | (204) ? [v0] : ( ~ (v0 = 0) & member(all_42_1_24, all_0_5_5) = v0 & member(all_42_1_24, all_0_7_7) = 0) % 7.34/2.39 | % 7.34/2.39 | Instantiating (204) with all_57_0_25 yields: % 7.34/2.39 | (205) ~ (all_57_0_25 = 0) & member(all_42_1_24, all_0_5_5) = all_57_0_25 & member(all_42_1_24, all_0_7_7) = 0 % 7.34/2.39 | % 7.34/2.39 | Applying alpha-rule on (205) yields: % 7.34/2.39 | (206) ~ (all_57_0_25 = 0) % 7.34/2.39 | (207) member(all_42_1_24, all_0_5_5) = all_57_0_25 % 7.34/2.39 | (208) member(all_42_1_24, all_0_7_7) = 0 % 7.34/2.39 | % 7.34/2.39 +-Applying beta-rule and splitting (203), into two cases. % 7.34/2.39 |-Branch one: % 7.34/2.39 | (209) all_42_0_23 = 0 % 7.34/2.39 | % 7.34/2.39 | Equations (209) can reduce 200 to: % 7.34/2.39 | (45) $false % 7.34/2.39 | % 7.34/2.39 |-The branch is then unsatisfiable % 7.34/2.39 |-Branch two: % 7.34/2.39 | (200) ~ (all_42_0_23 = 0) % 7.34/2.39 | (212) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_24, all_0_2_2) = v1 & member(all_42_1_24, all_0_3_3) = v0) % 7.42/2.39 | % 7.42/2.39 | Instantiating (212) with all_63_0_26, all_63_1_27 yields: % 7.42/2.39 | (213) ~ (all_63_0_26 = 0) & ~ (all_63_1_27 = 0) & member(all_42_1_24, all_0_2_2) = all_63_0_26 & member(all_42_1_24, all_0_3_3) = all_63_1_27 % 7.42/2.39 | % 7.42/2.39 | Applying alpha-rule on (213) yields: % 7.42/2.39 | (214) ~ (all_63_0_26 = 0) % 7.42/2.39 | (215) ~ (all_63_1_27 = 0) % 7.42/2.39 | (216) member(all_42_1_24, all_0_2_2) = all_63_0_26 % 7.42/2.39 | (217) member(all_42_1_24, all_0_3_3) = all_63_1_27 % 7.42/2.39 | % 7.42/2.39 | Instantiating formula (30) with all_42_1_24, all_0_7_7, 0, all_57_0_25 and discharging atoms member(all_42_1_24, all_0_7_7) = 0, yields: % 7.42/2.39 | (218) all_57_0_25 = 0 | ~ (member(all_42_1_24, all_0_7_7) = all_57_0_25) % 7.42/2.39 | % 7.42/2.39 | Instantiating formula (37) with all_63_0_26, all_0_2_2, all_0_7_7, all_0_6_6, all_42_1_24 and discharging atoms difference(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_42_1_24, all_0_2_2) = all_63_0_26, yields: % 7.42/2.39 | (219) all_63_0_26 = 0 | ? [v0] : ? [v1] : (member(all_42_1_24, all_0_6_6) = v1 & member(all_42_1_24, all_0_7_7) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 7.42/2.39 | % 7.42/2.39 | Instantiating formula (37) with all_63_1_27, all_0_3_3, all_0_6_6, all_0_5_5, all_42_1_24 and discharging atoms difference(all_0_6_6, all_0_5_5) = all_0_3_3, member(all_42_1_24, all_0_3_3) = all_63_1_27, yields: % 7.42/2.39 | (220) all_63_1_27 = 0 | ? [v0] : ? [v1] : (member(all_42_1_24, all_0_5_5) = v1 & member(all_42_1_24, all_0_6_6) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 7.42/2.39 | % 7.42/2.39 +-Applying beta-rule and splitting (219), into two cases. % 7.42/2.39 |-Branch one: % 7.42/2.39 | (221) all_63_0_26 = 0 % 7.42/2.39 | % 7.42/2.39 | Equations (221) can reduce 214 to: % 7.42/2.39 | (45) $false % 7.42/2.39 | % 7.42/2.39 |-The branch is then unsatisfiable % 7.42/2.39 |-Branch two: % 7.42/2.39 | (214) ~ (all_63_0_26 = 0) % 7.42/2.39 | (224) ? [v0] : ? [v1] : (member(all_42_1_24, all_0_6_6) = v1 & member(all_42_1_24, all_0_7_7) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 7.42/2.39 | % 7.42/2.39 | Instantiating (224) with all_92_0_28, all_92_1_29 yields: % 7.42/2.39 | (225) member(all_42_1_24, all_0_6_6) = all_92_0_28 & member(all_42_1_24, all_0_7_7) = all_92_1_29 & ( ~ (all_92_1_29 = 0) | all_92_0_28 = 0) % 7.42/2.39 | % 7.42/2.39 | Applying alpha-rule on (225) yields: % 7.42/2.39 | (226) member(all_42_1_24, all_0_6_6) = all_92_0_28 % 7.42/2.39 | (227) member(all_42_1_24, all_0_7_7) = all_92_1_29 % 7.42/2.39 | (228) ~ (all_92_1_29 = 0) | all_92_0_28 = 0 % 7.42/2.39 | % 7.42/2.39 +-Applying beta-rule and splitting (220), into two cases. % 7.42/2.39 |-Branch one: % 7.42/2.39 | (229) all_63_1_27 = 0 % 7.42/2.39 | % 7.42/2.39 | Equations (229) can reduce 215 to: % 7.42/2.39 | (45) $false % 7.42/2.39 | % 7.42/2.39 |-The branch is then unsatisfiable % 7.42/2.39 |-Branch two: % 7.42/2.39 | (215) ~ (all_63_1_27 = 0) % 7.42/2.39 | (232) ? [v0] : ? [v1] : (member(all_42_1_24, all_0_5_5) = v1 & member(all_42_1_24, all_0_6_6) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 7.42/2.39 | % 7.42/2.39 | Instantiating (232) with all_97_0_30, all_97_1_31 yields: % 7.42/2.39 | (233) member(all_42_1_24, all_0_5_5) = all_97_0_30 & member(all_42_1_24, all_0_6_6) = all_97_1_31 & ( ~ (all_97_1_31 = 0) | all_97_0_30 = 0) % 7.42/2.39 | % 7.42/2.39 | Applying alpha-rule on (233) yields: % 7.42/2.39 | (234) member(all_42_1_24, all_0_5_5) = all_97_0_30 % 7.42/2.39 | (235) member(all_42_1_24, all_0_6_6) = all_97_1_31 % 7.42/2.39 | (236) ~ (all_97_1_31 = 0) | all_97_0_30 = 0 % 7.42/2.39 | % 7.42/2.39 +-Applying beta-rule and splitting (218), into two cases. % 7.42/2.39 |-Branch one: % 7.42/2.39 | (237) ~ (member(all_42_1_24, all_0_7_7) = all_57_0_25) % 7.42/2.39 | % 7.42/2.39 | Instantiating formula (30) with all_42_1_24, all_0_5_5, all_97_0_30, all_57_0_25 and discharging atoms member(all_42_1_24, all_0_5_5) = all_97_0_30, member(all_42_1_24, all_0_5_5) = all_57_0_25, yields: % 7.42/2.39 | (238) all_97_0_30 = all_57_0_25 % 7.42/2.39 | % 7.42/2.40 | Instantiating formula (30) with all_42_1_24, all_0_6_6, all_92_0_28, all_97_1_31 and discharging atoms member(all_42_1_24, all_0_6_6) = all_97_1_31, member(all_42_1_24, all_0_6_6) = all_92_0_28, yields: % 7.42/2.40 | (239) all_97_1_31 = all_92_0_28 % 7.42/2.40 | % 7.42/2.40 | Instantiating formula (30) with all_42_1_24, all_0_7_7, all_92_1_29, 0 and discharging atoms member(all_42_1_24, all_0_7_7) = all_92_1_29, member(all_42_1_24, all_0_7_7) = 0, yields: % 7.42/2.40 | (240) all_92_1_29 = 0 % 7.42/2.40 | % 7.42/2.40 | Using (227) and (237) yields: % 7.42/2.40 | (241) ~ (all_92_1_29 = all_57_0_25) % 7.42/2.40 | % 7.42/2.40 | Equations (240) can reduce 241 to: % 7.42/2.40 | (242) ~ (all_57_0_25 = 0) % 7.42/2.40 | % 7.42/2.40 | Simplifying 242 yields: % 7.42/2.40 | (206) ~ (all_57_0_25 = 0) % 7.42/2.40 | % 7.42/2.40 +-Applying beta-rule and splitting (228), into two cases. % 7.42/2.40 |-Branch one: % 7.42/2.40 | (244) ~ (all_92_1_29 = 0) % 7.42/2.40 | % 7.42/2.40 | Equations (240) can reduce 244 to: % 7.42/2.40 | (45) $false % 7.42/2.40 | % 7.42/2.40 |-The branch is then unsatisfiable % 7.42/2.40 |-Branch two: % 7.42/2.40 | (240) all_92_1_29 = 0 % 7.42/2.40 | (247) all_92_0_28 = 0 % 7.42/2.40 | % 7.42/2.40 | Combining equations (247,239) yields a new equation: % 7.42/2.40 | (248) all_97_1_31 = 0 % 7.42/2.40 | % 7.42/2.40 +-Applying beta-rule and splitting (236), into two cases. % 7.42/2.40 |-Branch one: % 7.42/2.40 | (249) ~ (all_97_1_31 = 0) % 7.42/2.40 | % 7.42/2.40 | Equations (248) can reduce 249 to: % 7.42/2.40 | (45) $false % 7.42/2.40 | % 7.42/2.40 |-The branch is then unsatisfiable % 7.42/2.40 |-Branch two: % 7.42/2.40 | (248) all_97_1_31 = 0 % 7.42/2.40 | (252) all_97_0_30 = 0 % 7.42/2.40 | % 7.42/2.40 | Combining equations (252,238) yields a new equation: % 7.42/2.40 | (253) all_57_0_25 = 0 % 7.42/2.40 | % 7.42/2.40 | Equations (253) can reduce 206 to: % 7.42/2.40 | (45) $false % 7.42/2.40 | % 7.42/2.40 |-The branch is then unsatisfiable % 7.42/2.40 |-Branch two: % 7.42/2.40 | (255) member(all_42_1_24, all_0_7_7) = all_57_0_25 % 7.42/2.40 | (253) all_57_0_25 = 0 % 7.42/2.40 | % 7.42/2.40 | Equations (253) can reduce 206 to: % 7.42/2.40 | (45) $false % 7.42/2.40 | % 7.42/2.40 |-The branch is then unsatisfiable % 7.42/2.40 % SZS output end Proof for theBenchmark % 7.42/2.40 % 7.42/2.40 1800ms %------------------------------------------------------------------------------