%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET358+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 00:19:12 EDT 2022 % Result : Theorem 4.59s 1.77s % Output : Proof 7.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET358+4 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jul 10 00:46:36 EDT 2022 % 0.13/0.34 % CPUTime : % 0.64/0.63 ____ _ % 0.64/0.63 ___ / __ \_____(_)___ ________ __________ % 0.64/0.63 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.64/0.63 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.64/0.63 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.64/0.63 % 0.64/0.63 A Theorem Prover for First-Order Logic % 0.64/0.63 (ePrincess v.1.0) % 0.64/0.63 % 0.64/0.63 (c) Philipp Rümmer, 2009-2015 % 0.64/0.63 (c) Peter Backeman, 2014-2015 % 0.64/0.63 (contributions by Angelo Brillout, Peter Baumgartner) % 0.64/0.63 Free software under GNU Lesser General Public License (LGPL). % 0.64/0.63 Bug reports to peter@backeman.se % 0.64/0.63 % 0.64/0.63 For more information, visit http://user.uu.se/~petba168/breu/ % 0.64/0.63 % 0.64/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.80/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.66/0.98 Prover 0: Preprocessing ... % 2.11/1.17 Prover 0: Warning: ignoring some quantifiers % 2.11/1.19 Prover 0: Constructing countermodel ... % 2.79/1.34 Prover 0: gave up % 2.79/1.34 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.79/1.37 Prover 1: Preprocessing ... % 3.27/1.47 Prover 1: Constructing countermodel ... % 4.59/1.77 Prover 1: proved (427ms) % 4.59/1.77 % 4.59/1.77 No countermodel exists, formula is valid % 4.59/1.77 % SZS status Theorem for theBenchmark % 4.59/1.77 % 4.59/1.77 Generating proof ... found it (size 133) % 6.95/2.30 % 6.95/2.30 % SZS output start Proof for theBenchmark % 6.95/2.30 Assumed formulas after preprocessing and simplification: % 6.95/2.30 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & sum(v5) = v6 & sum(v1) = v3 & sum(v0) = v2 & union(v2, v3) = v4 & union(v0, v1) = v5 & equal_set(v4, v6) = v7 & ! [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)) % 6.95/2.34 | 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: % 6.95/2.34 | (1) ~ (all_0_0_0 = 0) & sum(all_0_2_2) = all_0_1_1 & sum(all_0_6_6) = all_0_4_4 & sum(all_0_7_7) = all_0_5_5 & union(all_0_5_5, all_0_4_4) = all_0_3_3 & union(all_0_7_7, all_0_6_6) = all_0_2_2 & equal_set(all_0_3_3, all_0_1_1) = all_0_0_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) % 7.15/2.35 | % 7.15/2.35 | Applying alpha-rule on (1) yields: % 7.15/2.35 | (2) union(all_0_5_5, all_0_4_4) = all_0_3_3 % 7.15/2.35 | (3) ! [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))) % 7.15/2.35 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 7.15/2.35 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 7.15/2.35 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 7.15/2.35 | (7) ! [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)) % 7.15/2.35 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 7.15/2.35 | (9) sum(all_0_7_7) = all_0_5_5 % 7.15/2.35 | (10) ! [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)) % 7.15/2.35 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 7.15/2.35 | (12) ! [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)))) % 7.15/2.35 | (13) union(all_0_7_7, all_0_6_6) = all_0_2_2 % 7.15/2.35 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 7.15/2.35 | (15) ! [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)) % 7.15/2.35 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 7.15/2.35 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 7.15/2.35 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 7.15/2.35 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 7.15/2.36 | (20) ~ (all_0_0_0 = 0) % 7.15/2.36 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 7.15/2.36 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 7.15/2.36 | (23) sum(all_0_6_6) = all_0_4_4 % 7.15/2.36 | (24) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 7.15/2.36 | (25) ! [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)) % 7.15/2.36 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 7.15/2.36 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 7.15/2.36 | (28) ! [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))) % 7.15/2.36 | (29) sum(all_0_2_2) = all_0_1_1 % 7.15/2.36 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 7.15/2.36 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 7.15/2.36 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 7.15/2.36 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 7.15/2.36 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 7.15/2.36 | (35) ! [v0] : ~ (member(v0, empty_set) = 0) % 7.15/2.36 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 7.15/2.36 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 7.15/2.36 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 7.15/2.36 | (39) equal_set(all_0_3_3, all_0_1_1) = all_0_0_0 % 7.15/2.36 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 7.15/2.36 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 7.15/2.36 | % 7.15/2.36 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 7.15/2.36 | (42) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v1 & subset(all_0_3_3, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 7.15/2.36 | % 7.15/2.36 +-Applying beta-rule and splitting (42), into two cases. % 7.15/2.36 |-Branch one: % 7.15/2.36 | (43) all_0_0_0 = 0 % 7.15/2.36 | % 7.15/2.36 | Equations (43) can reduce 20 to: % 7.15/2.36 | (44) $false % 7.15/2.36 | % 7.15/2.36 |-The branch is then unsatisfiable % 7.15/2.36 |-Branch two: % 7.15/2.36 | (20) ~ (all_0_0_0 = 0) % 7.15/2.36 | (46) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v1 & subset(all_0_3_3, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 7.15/2.37 | % 7.15/2.37 | Instantiating (46) with all_14_0_8, all_14_1_9 yields: % 7.15/2.37 | (47) subset(all_0_1_1, all_0_3_3) = all_14_0_8 & subset(all_0_3_3, all_0_1_1) = all_14_1_9 & ( ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0)) % 7.15/2.37 | % 7.15/2.37 | Applying alpha-rule on (47) yields: % 7.15/2.37 | (48) subset(all_0_1_1, all_0_3_3) = all_14_0_8 % 7.15/2.37 | (49) subset(all_0_3_3, all_0_1_1) = all_14_1_9 % 7.15/2.37 | (50) ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0) % 7.15/2.37 | % 7.15/2.37 | Instantiating formula (19) with all_14_0_8, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_14_0_8, yields: % 7.15/2.37 | (51) all_14_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 7.15/2.37 | % 7.15/2.37 | Instantiating formula (19) with all_14_1_9, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_14_1_9, yields: % 7.15/2.37 | (52) all_14_1_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 7.15/2.37 | % 7.15/2.37 +-Applying beta-rule and splitting (50), into two cases. % 7.15/2.37 |-Branch one: % 7.15/2.37 | (53) ~ (all_14_0_8 = 0) % 7.15/2.37 | % 7.15/2.37 +-Applying beta-rule and splitting (51), into two cases. % 7.15/2.37 |-Branch one: % 7.15/2.37 | (54) all_14_0_8 = 0 % 7.15/2.37 | % 7.15/2.37 | Equations (54) can reduce 53 to: % 7.15/2.37 | (44) $false % 7.15/2.37 | % 7.15/2.37 |-The branch is then unsatisfiable % 7.15/2.37 |-Branch two: % 7.15/2.37 | (53) ~ (all_14_0_8 = 0) % 7.15/2.37 | (57) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 7.15/2.37 | % 7.15/2.37 | Instantiating (57) with all_53_0_10, all_53_1_11 yields: % 7.15/2.37 | (58) ~ (all_53_0_10 = 0) & member(all_53_1_11, all_0_1_1) = 0 & member(all_53_1_11, all_0_3_3) = all_53_0_10 % 7.15/2.37 | % 7.15/2.37 | Applying alpha-rule on (58) yields: % 7.15/2.37 | (59) ~ (all_53_0_10 = 0) % 7.15/2.37 | (60) member(all_53_1_11, all_0_1_1) = 0 % 7.15/2.37 | (61) member(all_53_1_11, all_0_3_3) = all_53_0_10 % 7.15/2.37 | % 7.15/2.37 | Instantiating formula (32) with all_0_1_1, all_0_2_2, all_53_1_11 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_11, all_0_1_1) = 0, yields: % 7.15/2.37 | (62) ? [v0] : (member(v0, all_0_2_2) = 0 & member(all_53_1_11, v0) = 0) % 7.15/2.37 | % 7.15/2.37 | Instantiating formula (10) with all_53_0_10, all_0_3_3, all_0_4_4, all_0_5_5, all_53_1_11 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_53_1_11, all_0_3_3) = all_53_0_10, yields: % 7.15/2.37 | (63) all_53_0_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_11, all_0_4_4) = v1 & member(all_53_1_11, all_0_5_5) = v0) % 7.15/2.37 | % 7.15/2.37 | Instantiating (62) with all_68_0_12 yields: % 7.15/2.37 | (64) member(all_68_0_12, all_0_2_2) = 0 & member(all_53_1_11, all_68_0_12) = 0 % 7.15/2.37 | % 7.15/2.37 | Applying alpha-rule on (64) yields: % 7.15/2.37 | (65) member(all_68_0_12, all_0_2_2) = 0 % 7.15/2.37 | (66) member(all_53_1_11, all_68_0_12) = 0 % 7.15/2.37 | % 7.15/2.37 +-Applying beta-rule and splitting (63), into two cases. % 7.15/2.37 |-Branch one: % 7.15/2.37 | (67) all_53_0_10 = 0 % 7.15/2.37 | % 7.15/2.37 | Equations (67) can reduce 59 to: % 7.15/2.37 | (44) $false % 7.15/2.37 | % 7.15/2.37 |-The branch is then unsatisfiable % 7.15/2.37 |-Branch two: % 7.15/2.37 | (59) ~ (all_53_0_10 = 0) % 7.15/2.37 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_53_1_11, all_0_4_4) = v1 & member(all_53_1_11, all_0_5_5) = v0) % 7.15/2.37 | % 7.15/2.37 | Instantiating (70) with all_74_0_13, all_74_1_14 yields: % 7.15/2.37 | (71) ~ (all_74_0_13 = 0) & ~ (all_74_1_14 = 0) & member(all_53_1_11, all_0_4_4) = all_74_0_13 & member(all_53_1_11, all_0_5_5) = all_74_1_14 % 7.15/2.37 | % 7.15/2.37 | Applying alpha-rule on (71) yields: % 7.15/2.37 | (72) ~ (all_74_0_13 = 0) % 7.15/2.37 | (73) ~ (all_74_1_14 = 0) % 7.15/2.37 | (74) member(all_53_1_11, all_0_4_4) = all_74_0_13 % 7.15/2.37 | (75) member(all_53_1_11, all_0_5_5) = all_74_1_14 % 7.15/2.37 | % 7.15/2.37 | Instantiating formula (3) with all_0_2_2, all_0_6_6, all_0_7_7, all_68_0_12 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_68_0_12, all_0_2_2) = 0, yields: % 7.15/2.37 | (76) ? [v0] : ? [v1] : (member(all_68_0_12, all_0_6_6) = v1 & member(all_68_0_12, all_0_7_7) = v0 & (v1 = 0 | v0 = 0)) % 7.15/2.37 | % 7.15/2.37 | Instantiating formula (25) with all_0_1_1, all_74_0_13, all_0_4_4, all_0_6_6, all_53_1_11 and discharging atoms sum(all_0_6_6) = all_0_4_4, member(all_53_1_11, all_0_1_1) = 0, member(all_53_1_11, all_0_4_4) = all_74_0_13, yields: % 7.15/2.37 | (77) all_74_0_13 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_6_6) = v0) % 7.15/2.37 | % 7.15/2.37 | Instantiating formula (25) with all_68_0_12, all_74_0_13, all_0_4_4, all_0_6_6, all_53_1_11 and discharging atoms sum(all_0_6_6) = all_0_4_4, member(all_53_1_11, all_68_0_12) = 0, member(all_53_1_11, all_0_4_4) = all_74_0_13, yields: % 7.15/2.37 | (78) all_74_0_13 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_68_0_12, all_0_6_6) = v0) % 7.15/2.37 | % 7.15/2.37 | Instantiating formula (25) with all_68_0_12, all_74_1_14, all_0_5_5, all_0_7_7, all_53_1_11 and discharging atoms sum(all_0_7_7) = all_0_5_5, member(all_53_1_11, all_68_0_12) = 0, member(all_53_1_11, all_0_5_5) = all_74_1_14, yields: % 7.15/2.37 | (79) all_74_1_14 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_68_0_12, all_0_7_7) = v0) % 7.15/2.37 | % 7.15/2.37 | Instantiating (76) with all_89_0_15, all_89_1_16 yields: % 7.15/2.37 | (80) member(all_68_0_12, all_0_6_6) = all_89_0_15 & member(all_68_0_12, all_0_7_7) = all_89_1_16 & (all_89_0_15 = 0 | all_89_1_16 = 0) % 7.15/2.38 | % 7.15/2.38 | Applying alpha-rule on (80) yields: % 7.15/2.38 | (81) member(all_68_0_12, all_0_6_6) = all_89_0_15 % 7.15/2.38 | (82) member(all_68_0_12, all_0_7_7) = all_89_1_16 % 7.15/2.38 | (83) all_89_0_15 = 0 | all_89_1_16 = 0 % 7.15/2.38 | % 7.15/2.38 +-Applying beta-rule and splitting (79), into two cases. % 7.15/2.38 |-Branch one: % 7.15/2.38 | (84) all_74_1_14 = 0 % 7.15/2.38 | % 7.15/2.38 | Equations (84) can reduce 73 to: % 7.15/2.38 | (44) $false % 7.15/2.38 | % 7.15/2.38 |-The branch is then unsatisfiable % 7.15/2.38 |-Branch two: % 7.15/2.38 | (73) ~ (all_74_1_14 = 0) % 7.15/2.38 | (87) ? [v0] : ( ~ (v0 = 0) & member(all_68_0_12, all_0_7_7) = v0) % 7.15/2.38 | % 7.15/2.38 | Instantiating (87) with all_95_0_17 yields: % 7.15/2.38 | (88) ~ (all_95_0_17 = 0) & member(all_68_0_12, all_0_7_7) = all_95_0_17 % 7.15/2.38 | % 7.15/2.38 | Applying alpha-rule on (88) yields: % 7.15/2.38 | (89) ~ (all_95_0_17 = 0) % 7.15/2.38 | (90) member(all_68_0_12, all_0_7_7) = all_95_0_17 % 7.15/2.38 | % 7.15/2.38 +-Applying beta-rule and splitting (77), into two cases. % 7.15/2.38 |-Branch one: % 7.15/2.38 | (91) all_74_0_13 = 0 % 7.15/2.38 | % 7.15/2.38 | Equations (91) can reduce 72 to: % 7.15/2.38 | (44) $false % 7.15/2.38 | % 7.15/2.38 |-The branch is then unsatisfiable % 7.15/2.38 |-Branch two: % 7.15/2.38 | (72) ~ (all_74_0_13 = 0) % 7.15/2.38 | (94) ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_6_6) = v0) % 7.15/2.38 | % 7.15/2.38 +-Applying beta-rule and splitting (78), into two cases. % 7.15/2.38 |-Branch one: % 7.15/2.38 | (91) all_74_0_13 = 0 % 7.15/2.38 | % 7.15/2.38 | Equations (91) can reduce 72 to: % 7.15/2.38 | (44) $false % 7.15/2.38 | % 7.15/2.38 |-The branch is then unsatisfiable % 7.15/2.38 |-Branch two: % 7.15/2.38 | (72) ~ (all_74_0_13 = 0) % 7.15/2.38 | (98) ? [v0] : ( ~ (v0 = 0) & member(all_68_0_12, all_0_6_6) = v0) % 7.15/2.38 | % 7.15/2.38 | Instantiating (98) with all_110_0_19 yields: % 7.15/2.38 | (99) ~ (all_110_0_19 = 0) & member(all_68_0_12, all_0_6_6) = all_110_0_19 % 7.15/2.38 | % 7.15/2.38 | Applying alpha-rule on (99) yields: % 7.15/2.38 | (100) ~ (all_110_0_19 = 0) % 7.15/2.38 | (101) member(all_68_0_12, all_0_6_6) = all_110_0_19 % 7.15/2.38 | % 7.15/2.38 | Instantiating formula (37) with all_68_0_12, all_0_6_6, all_89_0_15, all_110_0_19 and discharging atoms member(all_68_0_12, all_0_6_6) = all_110_0_19, member(all_68_0_12, all_0_6_6) = all_89_0_15, yields: % 7.15/2.38 | (102) all_110_0_19 = all_89_0_15 % 7.15/2.38 | % 7.15/2.38 | Instantiating formula (37) with all_68_0_12, all_0_7_7, all_89_1_16, all_95_0_17 and discharging atoms member(all_68_0_12, all_0_7_7) = all_95_0_17, member(all_68_0_12, all_0_7_7) = all_89_1_16, yields: % 7.15/2.38 | (103) all_95_0_17 = all_89_1_16 % 7.15/2.38 | % 7.15/2.38 | Equations (102) can reduce 100 to: % 7.15/2.38 | (104) ~ (all_89_0_15 = 0) % 7.15/2.38 | % 7.15/2.38 | Equations (103) can reduce 89 to: % 7.15/2.38 | (105) ~ (all_89_1_16 = 0) % 7.15/2.38 | % 7.15/2.38 +-Applying beta-rule and splitting (83), into two cases. % 7.15/2.38 |-Branch one: % 7.15/2.38 | (106) all_89_0_15 = 0 % 7.15/2.38 | % 7.15/2.38 | Equations (106) can reduce 104 to: % 7.15/2.38 | (44) $false % 7.15/2.38 | % 7.15/2.38 |-The branch is then unsatisfiable % 7.15/2.38 |-Branch two: % 7.15/2.38 | (104) ~ (all_89_0_15 = 0) % 7.15/2.38 | (109) all_89_1_16 = 0 % 7.15/2.38 | % 7.15/2.38 | Equations (109) can reduce 105 to: % 7.15/2.38 | (44) $false % 7.15/2.38 | % 7.15/2.38 |-The branch is then unsatisfiable % 7.15/2.38 |-Branch two: % 7.15/2.38 | (54) all_14_0_8 = 0 % 7.15/2.38 | (112) ~ (all_14_1_9 = 0) % 7.15/2.38 | % 7.15/2.38 +-Applying beta-rule and splitting (52), into two cases. % 7.15/2.38 |-Branch one: % 7.15/2.38 | (113) all_14_1_9 = 0 % 7.15/2.38 | % 7.15/2.38 | Equations (113) can reduce 112 to: % 7.15/2.38 | (44) $false % 7.15/2.38 | % 7.15/2.38 |-The branch is then unsatisfiable % 7.15/2.38 |-Branch two: % 7.15/2.38 | (112) ~ (all_14_1_9 = 0) % 7.15/2.38 | (116) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 7.15/2.38 | % 7.15/2.38 | Instantiating (116) with all_53_0_21, all_53_1_22 yields: % 7.15/2.38 | (117) ~ (all_53_0_21 = 0) & member(all_53_1_22, all_0_1_1) = all_53_0_21 & member(all_53_1_22, all_0_3_3) = 0 % 7.15/2.38 | % 7.15/2.38 | Applying alpha-rule on (117) yields: % 7.15/2.38 | (118) ~ (all_53_0_21 = 0) % 7.15/2.38 | (119) member(all_53_1_22, all_0_1_1) = all_53_0_21 % 7.15/2.38 | (120) member(all_53_1_22, all_0_3_3) = 0 % 7.15/2.38 | % 7.15/2.38 | Instantiating formula (25) with all_0_3_3, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_0_1_1) = all_53_0_21, member(all_53_1_22, all_0_3_3) = 0, yields: % 7.15/2.39 | (121) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_2_2) = v0) % 7.15/2.39 | % 7.15/2.39 | Instantiating formula (32) with all_0_4_4, all_0_6_6, all_53_1_22 and discharging atoms sum(all_0_6_6) = all_0_4_4, yields: % 7.15/2.39 | (122) ~ (member(all_53_1_22, all_0_4_4) = 0) | ? [v0] : (member(v0, all_0_6_6) = 0 & member(all_53_1_22, v0) = 0) % 7.15/2.39 | % 7.15/2.39 | Instantiating formula (32) with all_0_5_5, all_0_7_7, all_53_1_22 and discharging atoms sum(all_0_7_7) = all_0_5_5, yields: % 7.15/2.39 | (123) ~ (member(all_53_1_22, all_0_5_5) = 0) | ? [v0] : (member(v0, all_0_7_7) = 0 & member(all_53_1_22, v0) = 0) % 7.15/2.39 | % 7.15/2.39 | Instantiating formula (3) with all_0_3_3, all_0_4_4, all_0_5_5, all_53_1_22 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_53_1_22, all_0_3_3) = 0, yields: % 7.15/2.39 | (124) ? [v0] : ? [v1] : (member(all_53_1_22, all_0_4_4) = v1 & member(all_53_1_22, all_0_5_5) = v0 & (v1 = 0 | v0 = 0)) % 7.15/2.39 | % 7.15/2.39 | Instantiating (124) with all_68_0_23, all_68_1_24 yields: % 7.15/2.39 | (125) member(all_53_1_22, all_0_4_4) = all_68_0_23 & member(all_53_1_22, all_0_5_5) = all_68_1_24 & (all_68_0_23 = 0 | all_68_1_24 = 0) % 7.15/2.39 | % 7.15/2.39 | Applying alpha-rule on (125) yields: % 7.15/2.39 | (126) member(all_53_1_22, all_0_4_4) = all_68_0_23 % 7.15/2.39 | (127) member(all_53_1_22, all_0_5_5) = all_68_1_24 % 7.15/2.39 | (128) all_68_0_23 = 0 | all_68_1_24 = 0 % 7.15/2.39 | % 7.15/2.39 +-Applying beta-rule and splitting (121), into two cases. % 7.15/2.39 |-Branch one: % 7.15/2.39 | (129) all_53_0_21 = 0 % 7.15/2.39 | % 7.15/2.39 | Equations (129) can reduce 118 to: % 7.15/2.39 | (44) $false % 7.15/2.39 | % 7.15/2.39 |-The branch is then unsatisfiable % 7.15/2.39 |-Branch two: % 7.15/2.39 | (118) ~ (all_53_0_21 = 0) % 7.15/2.39 | (132) ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_2_2) = v0) % 7.15/2.39 | % 7.15/2.39 | Instantiating formula (37) with all_53_1_22, all_0_5_5, all_68_1_24, 0 and discharging atoms member(all_53_1_22, all_0_5_5) = all_68_1_24, yields: % 7.15/2.39 | (133) all_68_1_24 = 0 | ~ (member(all_53_1_22, all_0_5_5) = 0) % 7.15/2.39 | % 7.15/2.39 | Instantiating formula (25) with all_0_4_4, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_0_1_1) = all_53_0_21, yields: % 7.15/2.39 | (134) all_53_0_21 = 0 | ~ (member(all_53_1_22, all_0_4_4) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_2_2) = v0) % 7.15/2.39 | % 7.15/2.39 | Instantiating formula (25) with all_0_4_4, all_68_1_24, all_0_5_5, all_0_7_7, all_53_1_22 and discharging atoms sum(all_0_7_7) = all_0_5_5, member(all_53_1_22, all_0_5_5) = all_68_1_24, yields: % 7.15/2.39 | (135) all_68_1_24 = 0 | ~ (member(all_53_1_22, all_0_4_4) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_7_7) = v0) % 7.15/2.39 | % 7.15/2.39 | Instantiating formula (25) with all_0_5_5, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_0_1_1) = all_53_0_21, yields: % 7.15/2.39 | (136) all_53_0_21 = 0 | ~ (member(all_53_1_22, all_0_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_0_5_5, all_0_2_2) = v0) % 7.15/2.39 | % 7.15/2.39 +-Applying beta-rule and splitting (123), into two cases. % 7.15/2.39 |-Branch one: % 7.15/2.39 | (137) ~ (member(all_53_1_22, all_0_5_5) = 0) % 7.15/2.39 | % 7.15/2.39 | Using (127) and (137) yields: % 7.15/2.39 | (138) ~ (all_68_1_24 = 0) % 7.15/2.39 | % 7.15/2.39 +-Applying beta-rule and splitting (128), into two cases. % 7.15/2.39 |-Branch one: % 7.15/2.39 | (139) all_68_0_23 = 0 % 7.15/2.39 | % 7.15/2.39 | From (139) and (126) follows: % 7.15/2.39 | (140) member(all_53_1_22, all_0_4_4) = 0 % 7.15/2.40 | % 7.15/2.40 +-Applying beta-rule and splitting (122), into two cases. % 7.15/2.40 |-Branch one: % 7.15/2.40 | (141) ~ (member(all_53_1_22, all_0_4_4) = 0) % 7.15/2.40 | % 7.15/2.40 | Using (140) and (141) yields: % 7.15/2.40 | (142) $false % 7.15/2.40 | % 7.15/2.40 |-The branch is then unsatisfiable % 7.15/2.40 |-Branch two: % 7.15/2.40 | (140) member(all_53_1_22, all_0_4_4) = 0 % 7.15/2.40 | (144) ? [v0] : (member(v0, all_0_6_6) = 0 & member(all_53_1_22, v0) = 0) % 7.15/2.40 | % 7.15/2.40 | Instantiating (144) with all_112_0_28 yields: % 7.15/2.40 | (145) member(all_112_0_28, all_0_6_6) = 0 & member(all_53_1_22, all_112_0_28) = 0 % 7.15/2.40 | % 7.15/2.40 | Applying alpha-rule on (145) yields: % 7.15/2.40 | (146) member(all_112_0_28, all_0_6_6) = 0 % 7.15/2.40 | (147) member(all_53_1_22, all_112_0_28) = 0 % 7.15/2.40 | % 7.15/2.40 +-Applying beta-rule and splitting (135), into two cases. % 7.15/2.40 |-Branch one: % 7.15/2.40 | (141) ~ (member(all_53_1_22, all_0_4_4) = 0) % 7.15/2.40 | % 7.15/2.40 | Using (140) and (141) yields: % 7.15/2.40 | (142) $false % 7.15/2.40 | % 7.15/2.40 |-The branch is then unsatisfiable % 7.15/2.40 |-Branch two: % 7.15/2.40 | (140) member(all_53_1_22, all_0_4_4) = 0 % 7.15/2.40 | (151) all_68_1_24 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_7_7) = v0) % 7.15/2.40 | % 7.15/2.40 +-Applying beta-rule and splitting (134), into two cases. % 7.15/2.40 |-Branch one: % 7.15/2.40 | (141) ~ (member(all_53_1_22, all_0_4_4) = 0) % 7.15/2.40 | % 7.15/2.40 | Using (140) and (141) yields: % 7.15/2.40 | (142) $false % 7.15/2.40 | % 7.15/2.40 |-The branch is then unsatisfiable % 7.15/2.40 |-Branch two: % 7.15/2.40 | (140) member(all_53_1_22, all_0_4_4) = 0 % 7.15/2.40 | (155) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_2_2) = v0) % 7.15/2.40 | % 7.15/2.40 +-Applying beta-rule and splitting (155), into two cases. % 7.15/2.40 |-Branch one: % 7.15/2.40 | (129) all_53_0_21 = 0 % 7.15/2.40 | % 7.15/2.40 | Equations (129) can reduce 118 to: % 7.15/2.40 | (44) $false % 7.15/2.40 | % 7.15/2.40 |-The branch is then unsatisfiable % 7.15/2.40 |-Branch two: % 7.15/2.40 | (118) ~ (all_53_0_21 = 0) % 7.15/2.40 | (159) ? [v0] : ( ~ (v0 = 0) & member(all_0_4_4, all_0_2_2) = v0) % 7.15/2.40 | % 7.15/2.40 | Instantiating formula (25) with all_112_0_28, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_112_0_28) = 0, member(all_53_1_22, all_0_1_1) = all_53_0_21, yields: % 7.15/2.40 | (160) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_112_0_28, all_0_2_2) = v0) % 7.15/2.40 | % 7.15/2.40 +-Applying beta-rule and splitting (160), into two cases. % 7.15/2.40 |-Branch one: % 7.15/2.40 | (129) all_53_0_21 = 0 % 7.15/2.40 | % 7.15/2.40 | Equations (129) can reduce 118 to: % 7.15/2.40 | (44) $false % 7.15/2.40 | % 7.15/2.40 |-The branch is then unsatisfiable % 7.15/2.40 |-Branch two: % 7.15/2.40 | (118) ~ (all_53_0_21 = 0) % 7.15/2.40 | (164) ? [v0] : ( ~ (v0 = 0) & member(all_112_0_28, all_0_2_2) = v0) % 7.15/2.40 | % 7.15/2.40 | Instantiating (164) with all_160_0_34 yields: % 7.15/2.40 | (165) ~ (all_160_0_34 = 0) & member(all_112_0_28, all_0_2_2) = all_160_0_34 % 7.15/2.40 | % 7.15/2.40 | Applying alpha-rule on (165) yields: % 7.15/2.40 | (166) ~ (all_160_0_34 = 0) % 7.15/2.40 | (167) member(all_112_0_28, all_0_2_2) = all_160_0_34 % 7.15/2.40 | % 7.15/2.40 | Instantiating formula (10) with all_160_0_34, all_0_2_2, all_0_6_6, all_0_7_7, all_112_0_28 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_112_0_28, all_0_2_2) = all_160_0_34, yields: % 7.15/2.40 | (168) all_160_0_34 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_112_0_28, all_0_6_6) = v1 & member(all_112_0_28, all_0_7_7) = v0) % 7.15/2.40 | % 7.15/2.40 +-Applying beta-rule and splitting (168), into two cases. % 7.15/2.40 |-Branch one: % 7.15/2.40 | (169) all_160_0_34 = 0 % 7.15/2.40 | % 7.15/2.40 | Equations (169) can reduce 166 to: % 7.15/2.40 | (44) $false % 7.15/2.40 | % 7.15/2.40 |-The branch is then unsatisfiable % 7.15/2.40 |-Branch two: % 7.15/2.40 | (166) ~ (all_160_0_34 = 0) % 7.15/2.40 | (172) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_112_0_28, all_0_6_6) = v1 & member(all_112_0_28, all_0_7_7) = v0) % 7.15/2.40 | % 7.15/2.40 | Instantiating (172) with all_177_0_35, all_177_1_36 yields: % 7.15/2.40 | (173) ~ (all_177_0_35 = 0) & ~ (all_177_1_36 = 0) & member(all_112_0_28, all_0_6_6) = all_177_0_35 & member(all_112_0_28, all_0_7_7) = all_177_1_36 % 7.15/2.40 | % 7.15/2.40 | Applying alpha-rule on (173) yields: % 7.15/2.40 | (174) ~ (all_177_0_35 = 0) % 7.15/2.40 | (175) ~ (all_177_1_36 = 0) % 7.15/2.40 | (176) member(all_112_0_28, all_0_6_6) = all_177_0_35 % 7.15/2.40 | (177) member(all_112_0_28, all_0_7_7) = all_177_1_36 % 7.15/2.40 | % 7.15/2.40 | Instantiating formula (37) with all_112_0_28, all_0_6_6, all_177_0_35, 0 and discharging atoms member(all_112_0_28, all_0_6_6) = all_177_0_35, member(all_112_0_28, all_0_6_6) = 0, yields: % 7.15/2.40 | (178) all_177_0_35 = 0 % 7.15/2.40 | % 7.15/2.40 | Equations (178) can reduce 174 to: % 7.15/2.40 | (44) $false % 7.15/2.40 | % 7.15/2.40 |-The branch is then unsatisfiable % 7.15/2.41 |-Branch two: % 7.15/2.41 | (180) ~ (all_68_0_23 = 0) % 7.15/2.41 | (181) all_68_1_24 = 0 % 7.15/2.41 | % 7.15/2.41 | Equations (181) can reduce 138 to: % 7.15/2.41 | (44) $false % 7.15/2.41 | % 7.15/2.41 |-The branch is then unsatisfiable % 7.15/2.41 |-Branch two: % 7.15/2.41 | (183) member(all_53_1_22, all_0_5_5) = 0 % 7.15/2.41 | (184) ? [v0] : (member(v0, all_0_7_7) = 0 & member(all_53_1_22, v0) = 0) % 7.15/2.41 | % 7.15/2.41 | Instantiating (184) with all_100_0_37 yields: % 7.15/2.41 | (185) member(all_100_0_37, all_0_7_7) = 0 & member(all_53_1_22, all_100_0_37) = 0 % 7.15/2.41 | % 7.15/2.41 | Applying alpha-rule on (185) yields: % 7.15/2.41 | (186) member(all_100_0_37, all_0_7_7) = 0 % 7.15/2.41 | (187) member(all_53_1_22, all_100_0_37) = 0 % 7.15/2.41 | % 7.15/2.41 +-Applying beta-rule and splitting (133), into two cases. % 7.15/2.41 |-Branch one: % 7.15/2.41 | (137) ~ (member(all_53_1_22, all_0_5_5) = 0) % 7.15/2.41 | % 7.15/2.41 | Using (183) and (137) yields: % 7.15/2.41 | (142) $false % 7.15/2.41 | % 7.15/2.41 |-The branch is then unsatisfiable % 7.15/2.41 |-Branch two: % 7.15/2.41 | (183) member(all_53_1_22, all_0_5_5) = 0 % 7.15/2.41 | (181) all_68_1_24 = 0 % 7.15/2.41 | % 7.15/2.41 | From (181) and (127) follows: % 7.15/2.41 | (183) member(all_53_1_22, all_0_5_5) = 0 % 7.15/2.41 | % 7.15/2.41 +-Applying beta-rule and splitting (136), into two cases. % 7.15/2.41 |-Branch one: % 7.15/2.41 | (137) ~ (member(all_53_1_22, all_0_5_5) = 0) % 7.15/2.41 | % 7.15/2.41 | Using (183) and (137) yields: % 7.15/2.41 | (142) $false % 7.15/2.41 | % 7.15/2.41 |-The branch is then unsatisfiable % 7.15/2.41 |-Branch two: % 7.15/2.41 | (183) member(all_53_1_22, all_0_5_5) = 0 % 7.15/2.41 | (196) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_5_5, all_0_2_2) = v0) % 7.15/2.41 | % 7.15/2.41 +-Applying beta-rule and splitting (196), into two cases. % 7.15/2.41 |-Branch one: % 7.15/2.41 | (129) all_53_0_21 = 0 % 7.15/2.41 | % 7.15/2.41 | Equations (129) can reduce 118 to: % 7.15/2.41 | (44) $false % 7.15/2.41 | % 7.15/2.41 |-The branch is then unsatisfiable % 7.15/2.41 |-Branch two: % 7.15/2.41 | (118) ~ (all_53_0_21 = 0) % 7.15/2.41 | (200) ? [v0] : ( ~ (v0 = 0) & member(all_0_5_5, all_0_2_2) = v0) % 7.15/2.41 | % 7.15/2.41 | Instantiating formula (25) with all_100_0_37, all_53_0_21, all_0_1_1, all_0_2_2, all_53_1_22 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_53_1_22, all_100_0_37) = 0, member(all_53_1_22, all_0_1_1) = all_53_0_21, yields: % 7.15/2.41 | (201) all_53_0_21 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_100_0_37, all_0_2_2) = v0) % 7.15/2.41 | % 7.15/2.41 +-Applying beta-rule and splitting (201), into two cases. % 7.15/2.41 |-Branch one: % 7.15/2.41 | (129) all_53_0_21 = 0 % 7.15/2.41 | % 7.15/2.41 | Equations (129) can reduce 118 to: % 7.15/2.41 | (44) $false % 7.15/2.41 | % 7.15/2.41 |-The branch is then unsatisfiable % 7.15/2.41 |-Branch two: % 7.15/2.41 | (118) ~ (all_53_0_21 = 0) % 7.15/2.41 | (205) ? [v0] : ( ~ (v0 = 0) & member(all_100_0_37, all_0_2_2) = v0) % 7.15/2.41 | % 7.15/2.41 | Instantiating (205) with all_140_0_41 yields: % 7.15/2.41 | (206) ~ (all_140_0_41 = 0) & member(all_100_0_37, all_0_2_2) = all_140_0_41 % 7.15/2.41 | % 7.15/2.41 | Applying alpha-rule on (206) yields: % 7.15/2.41 | (207) ~ (all_140_0_41 = 0) % 7.15/2.41 | (208) member(all_100_0_37, all_0_2_2) = all_140_0_41 % 7.15/2.41 | % 7.15/2.41 | Instantiating formula (10) with all_140_0_41, all_0_2_2, all_0_6_6, all_0_7_7, all_100_0_37 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_100_0_37, all_0_2_2) = all_140_0_41, yields: % 7.15/2.41 | (209) all_140_0_41 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_100_0_37, all_0_6_6) = v1 & member(all_100_0_37, all_0_7_7) = v0) % 7.15/2.41 | % 7.15/2.41 +-Applying beta-rule and splitting (209), into two cases. % 7.15/2.41 |-Branch one: % 7.15/2.41 | (210) all_140_0_41 = 0 % 7.15/2.41 | % 7.15/2.41 | Equations (210) can reduce 207 to: % 7.15/2.41 | (44) $false % 7.15/2.41 | % 7.15/2.41 |-The branch is then unsatisfiable % 7.15/2.41 |-Branch two: % 7.15/2.41 | (207) ~ (all_140_0_41 = 0) % 7.15/2.41 | (213) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_100_0_37, all_0_6_6) = v1 & member(all_100_0_37, all_0_7_7) = v0) % 7.15/2.41 | % 7.15/2.41 | Instantiating (213) with all_157_0_42, all_157_1_43 yields: % 7.15/2.41 | (214) ~ (all_157_0_42 = 0) & ~ (all_157_1_43 = 0) & member(all_100_0_37, all_0_6_6) = all_157_0_42 & member(all_100_0_37, all_0_7_7) = all_157_1_43 % 7.15/2.41 | % 7.15/2.41 | Applying alpha-rule on (214) yields: % 7.15/2.41 | (215) ~ (all_157_0_42 = 0) % 7.15/2.41 | (216) ~ (all_157_1_43 = 0) % 7.15/2.41 | (217) member(all_100_0_37, all_0_6_6) = all_157_0_42 % 7.15/2.41 | (218) member(all_100_0_37, all_0_7_7) = all_157_1_43 % 7.15/2.41 | % 7.15/2.41 | Instantiating formula (37) with all_100_0_37, all_0_7_7, all_157_1_43, 0 and discharging atoms member(all_100_0_37, all_0_7_7) = all_157_1_43, member(all_100_0_37, all_0_7_7) = 0, yields: % 7.15/2.41 | (219) all_157_1_43 = 0 % 7.15/2.41 | % 7.15/2.41 | Equations (219) can reduce 216 to: % 7.15/2.41 | (44) $false % 7.15/2.41 | % 7.15/2.41 |-The branch is then unsatisfiable % 7.15/2.41 % SZS output end Proof for theBenchmark % 7.15/2.41 % 7.15/2.41 1768ms %------------------------------------------------------------------------------