%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET159+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 00:18:01 EDT 2022 % Result : Theorem 4.01s 1.62s % Output : Proof 6.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET159+4 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n004.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 : Mon Jul 11 05:07:37 EDT 2022 % 0.13/0.34 % CPUTime : % 0.52/0.59 ____ _ % 0.52/0.59 ___ / __ \_____(_)___ ________ __________ % 0.52/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.59 % 0.52/0.59 A Theorem Prover for First-Order Logic % 0.52/0.59 (ePrincess v.1.0) % 0.52/0.59 % 0.52/0.59 (c) Philipp Rümmer, 2009-2015 % 0.52/0.59 (c) Peter Backeman, 2014-2015 % 0.52/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.59 Bug reports to peter@backeman.se % 0.52/0.59 % 0.52/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.59 % 0.52/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.91 Prover 0: Preprocessing ... % 2.08/1.09 Prover 0: Warning: ignoring some quantifiers % 2.08/1.12 Prover 0: Constructing countermodel ... % 2.69/1.29 Prover 0: gave up % 2.69/1.29 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.69/1.31 Prover 1: Preprocessing ... % 3.13/1.42 Prover 1: Constructing countermodel ... % 4.01/1.62 Prover 1: proved (331ms) % 4.01/1.62 % 4.01/1.62 No countermodel exists, formula is valid % 4.01/1.62 % SZS status Theorem for theBenchmark % 4.01/1.62 % 4.01/1.62 Generating proof ... found it (size 94) % 6.31/2.11 % 6.31/2.11 % SZS output start Proof for theBenchmark % 6.31/2.11 Assumed formulas after preprocessing and simplification: % 6.31/2.11 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & union(v3, v2) = v4 & union(v1, v2) = v5 & union(v0, v5) = v6 & union(v0, v1) = v3 & 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)) % 6.49/2.15 | 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: % 6.49/2.15 | (1) ~ (all_0_0_0 = 0) & union(all_0_4_4, all_0_5_5) = all_0_3_3 & union(all_0_6_6, all_0_5_5) = all_0_2_2 & union(all_0_7_7, all_0_2_2) = all_0_1_1 & union(all_0_7_7, all_0_6_6) = all_0_4_4 & 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) % 6.68/2.16 | % 6.68/2.16 | Applying alpha-rule on (1) yields: % 6.68/2.16 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 6.68/2.16 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 6.68/2.16 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 6.68/2.16 | (5) union(all_0_6_6, all_0_5_5) = all_0_2_2 % 6.68/2.16 | (6) ! [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))) % 6.68/2.16 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 6.68/2.16 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 6.68/2.16 | (9) ! [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)) % 6.68/2.16 | (10) ! [v0] : ~ (member(v0, empty_set) = 0) % 6.68/2.16 | (11) ! [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)) % 6.68/2.16 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 6.68/2.16 | (13) ~ (all_0_0_0 = 0) % 6.68/2.16 | (14) ! [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)))) % 6.68/2.16 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 6.68/2.16 | (16) ! [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)) % 6.68/2.16 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 6.68/2.16 | (18) ! [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)) % 6.68/2.17 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 6.68/2.17 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 6.68/2.17 | (21) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 6.68/2.17 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 6.68/2.17 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 6.68/2.17 | (24) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 6.68/2.17 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 6.68/2.17 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 6.68/2.17 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 6.68/2.17 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 6.68/2.17 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 6.68/2.17 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 6.68/2.17 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 6.68/2.17 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 6.68/2.17 | (33) union(all_0_4_4, all_0_5_5) = all_0_3_3 % 6.68/2.17 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 6.68/2.17 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 6.68/2.17 | (36) equal_set(all_0_3_3, all_0_1_1) = all_0_0_0 % 6.68/2.17 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 6.68/2.17 | (38) union(all_0_7_7, all_0_2_2) = all_0_1_1 % 6.68/2.17 | (39) union(all_0_7_7, all_0_6_6) = all_0_4_4 % 6.68/2.17 | (40) ! [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))) % 6.68/2.17 | % 6.68/2.17 | Instantiating formula (20) 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: % 6.68/2.17 | (41) 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))) % 6.68/2.17 | % 6.68/2.17 +-Applying beta-rule and splitting (41), into two cases. % 6.68/2.17 |-Branch one: % 6.68/2.17 | (42) all_0_0_0 = 0 % 6.68/2.17 | % 6.68/2.17 | Equations (42) can reduce 13 to: % 6.68/2.17 | (43) $false % 6.68/2.17 | % 6.68/2.17 |-The branch is then unsatisfiable % 6.68/2.17 |-Branch two: % 6.68/2.17 | (13) ~ (all_0_0_0 = 0) % 6.68/2.17 | (45) ? [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))) % 6.68/2.17 | % 6.68/2.17 | Instantiating (45) with all_14_0_8, all_14_1_9 yields: % 6.68/2.17 | (46) 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)) % 6.68/2.17 | % 6.68/2.17 | Applying alpha-rule on (46) yields: % 6.68/2.18 | (47) subset(all_0_1_1, all_0_3_3) = all_14_0_8 % 6.68/2.18 | (48) subset(all_0_3_3, all_0_1_1) = all_14_1_9 % 6.68/2.18 | (49) ~ (all_14_0_8 = 0) | ~ (all_14_1_9 = 0) % 6.68/2.18 | % 6.68/2.18 | Instantiating formula (37) 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: % 6.68/2.18 | (50) all_14_0_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 6.68/2.18 | % 6.68/2.18 | Instantiating formula (37) 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: % 6.68/2.18 | (51) all_14_1_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 6.68/2.18 | % 6.68/2.18 +-Applying beta-rule and splitting (49), into two cases. % 6.68/2.18 |-Branch one: % 6.68/2.18 | (52) ~ (all_14_0_8 = 0) % 6.68/2.18 | % 6.68/2.18 +-Applying beta-rule and splitting (50), into two cases. % 6.68/2.18 |-Branch one: % 6.68/2.18 | (53) all_14_0_8 = 0 % 6.68/2.18 | % 6.68/2.18 | Equations (53) can reduce 52 to: % 6.68/2.18 | (43) $false % 6.68/2.18 | % 6.68/2.18 |-The branch is then unsatisfiable % 6.68/2.18 |-Branch two: % 6.68/2.18 | (52) ~ (all_14_0_8 = 0) % 6.68/2.18 | (56) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 6.68/2.18 | % 6.68/2.18 | Instantiating (56) with all_42_0_10, all_42_1_11 yields: % 6.68/2.18 | (57) ~ (all_42_0_10 = 0) & member(all_42_1_11, all_0_1_1) = 0 & member(all_42_1_11, all_0_3_3) = all_42_0_10 % 6.68/2.18 | % 6.68/2.18 | Applying alpha-rule on (57) yields: % 6.68/2.18 | (58) ~ (all_42_0_10 = 0) % 6.68/2.18 | (59) member(all_42_1_11, all_0_1_1) = 0 % 6.68/2.18 | (60) member(all_42_1_11, all_0_3_3) = all_42_0_10 % 6.68/2.18 | % 6.68/2.18 | Instantiating formula (6) with all_0_2_2, all_0_5_5, all_0_6_6, all_42_1_11 and discharging atoms union(all_0_6_6, all_0_5_5) = all_0_2_2, yields: % 6.68/2.18 | (61) ~ (member(all_42_1_11, all_0_2_2) = 0) | ? [v0] : ? [v1] : (member(all_42_1_11, all_0_5_5) = v1 & member(all_42_1_11, all_0_6_6) = v0 & (v1 = 0 | v0 = 0)) % 6.68/2.18 | % 6.68/2.18 | Instantiating formula (6) with all_0_1_1, all_0_2_2, all_0_7_7, all_42_1_11 and discharging atoms union(all_0_7_7, all_0_2_2) = all_0_1_1, member(all_42_1_11, all_0_1_1) = 0, yields: % 6.68/2.18 | (62) ? [v0] : ? [v1] : (member(all_42_1_11, all_0_2_2) = v1 & member(all_42_1_11, all_0_7_7) = v0 & (v1 = 0 | v0 = 0)) % 6.68/2.18 | % 6.68/2.18 | Instantiating formula (16) with all_42_0_10, all_0_3_3, all_0_5_5, all_0_4_4, all_42_1_11 and discharging atoms union(all_0_4_4, all_0_5_5) = all_0_3_3, member(all_42_1_11, all_0_3_3) = all_42_0_10, yields: % 6.68/2.18 | (63) all_42_0_10 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_11, all_0_4_4) = v0 & member(all_42_1_11, all_0_5_5) = v1) % 6.68/2.18 | % 6.68/2.18 | Instantiating (62) with all_57_0_12, all_57_1_13 yields: % 6.68/2.18 | (64) member(all_42_1_11, all_0_2_2) = all_57_0_12 & member(all_42_1_11, all_0_7_7) = all_57_1_13 & (all_57_0_12 = 0 | all_57_1_13 = 0) % 6.68/2.18 | % 6.68/2.18 | Applying alpha-rule on (64) yields: % 6.68/2.18 | (65) member(all_42_1_11, all_0_2_2) = all_57_0_12 % 6.68/2.18 | (66) member(all_42_1_11, all_0_7_7) = all_57_1_13 % 6.68/2.18 | (67) all_57_0_12 = 0 | all_57_1_13 = 0 % 6.68/2.18 | % 6.68/2.18 +-Applying beta-rule and splitting (63), into two cases. % 6.68/2.18 |-Branch one: % 6.68/2.18 | (68) all_42_0_10 = 0 % 6.68/2.18 | % 6.68/2.18 | Equations (68) can reduce 58 to: % 6.68/2.18 | (43) $false % 6.68/2.18 | % 6.68/2.18 |-The branch is then unsatisfiable % 6.68/2.18 |-Branch two: % 6.68/2.18 | (58) ~ (all_42_0_10 = 0) % 6.68/2.18 | (71) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_11, all_0_4_4) = v0 & member(all_42_1_11, all_0_5_5) = v1) % 6.68/2.18 | % 6.68/2.18 | Instantiating (71) with all_63_0_14, all_63_1_15 yields: % 6.68/2.18 | (72) ~ (all_63_0_14 = 0) & ~ (all_63_1_15 = 0) & member(all_42_1_11, all_0_4_4) = all_63_1_15 & member(all_42_1_11, all_0_5_5) = all_63_0_14 % 6.68/2.18 | % 6.68/2.18 | Applying alpha-rule on (72) yields: % 6.68/2.18 | (73) ~ (all_63_0_14 = 0) % 6.68/2.18 | (74) ~ (all_63_1_15 = 0) % 6.68/2.18 | (75) member(all_42_1_11, all_0_4_4) = all_63_1_15 % 6.68/2.18 | (76) member(all_42_1_11, all_0_5_5) = all_63_0_14 % 6.68/2.18 | % 6.68/2.18 | Instantiating formula (16) with all_63_1_15, all_0_4_4, all_0_6_6, all_0_7_7, all_42_1_11 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_4_4, member(all_42_1_11, all_0_4_4) = all_63_1_15, yields: % 6.68/2.18 | (77) all_63_1_15 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_11, all_0_6_6) = v1 & member(all_42_1_11, all_0_7_7) = v0) % 6.68/2.18 | % 6.68/2.18 +-Applying beta-rule and splitting (77), into two cases. % 6.68/2.18 |-Branch one: % 6.68/2.18 | (78) all_63_1_15 = 0 % 6.68/2.18 | % 6.68/2.18 | Equations (78) can reduce 74 to: % 6.68/2.18 | (43) $false % 6.68/2.18 | % 6.68/2.18 |-The branch is then unsatisfiable % 6.68/2.18 |-Branch two: % 6.68/2.18 | (74) ~ (all_63_1_15 = 0) % 6.68/2.18 | (81) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_11, all_0_6_6) = v1 & member(all_42_1_11, all_0_7_7) = v0) % 6.68/2.18 | % 6.68/2.18 | Instantiating (81) with all_76_0_16, all_76_1_17 yields: % 6.68/2.18 | (82) ~ (all_76_0_16 = 0) & ~ (all_76_1_17 = 0) & member(all_42_1_11, all_0_6_6) = all_76_0_16 & member(all_42_1_11, all_0_7_7) = all_76_1_17 % 6.68/2.18 | % 6.68/2.18 | Applying alpha-rule on (82) yields: % 6.68/2.18 | (83) ~ (all_76_0_16 = 0) % 6.68/2.18 | (84) ~ (all_76_1_17 = 0) % 6.68/2.18 | (85) member(all_42_1_11, all_0_6_6) = all_76_0_16 % 6.68/2.18 | (86) member(all_42_1_11, all_0_7_7) = all_76_1_17 % 6.68/2.18 | % 6.68/2.18 +-Applying beta-rule and splitting (61), into two cases. % 6.68/2.18 |-Branch one: % 6.68/2.18 | (87) ~ (member(all_42_1_11, all_0_2_2) = 0) % 6.68/2.18 | % 6.68/2.18 | Instantiating formula (3) with all_42_1_11, all_0_7_7, all_76_1_17, all_57_1_13 and discharging atoms member(all_42_1_11, all_0_7_7) = all_76_1_17, member(all_42_1_11, all_0_7_7) = all_57_1_13, yields: % 6.68/2.18 | (88) all_76_1_17 = all_57_1_13 % 6.68/2.19 | % 6.68/2.19 | Using (65) and (87) yields: % 6.68/2.19 | (89) ~ (all_57_0_12 = 0) % 6.68/2.19 | % 6.68/2.19 | Equations (88) can reduce 84 to: % 6.68/2.19 | (90) ~ (all_57_1_13 = 0) % 6.68/2.19 | % 6.68/2.19 +-Applying beta-rule and splitting (67), into two cases. % 6.68/2.19 |-Branch one: % 6.68/2.19 | (91) all_57_0_12 = 0 % 6.68/2.19 | % 6.68/2.19 | Equations (91) can reduce 89 to: % 6.68/2.19 | (43) $false % 6.68/2.19 | % 6.68/2.19 |-The branch is then unsatisfiable % 6.68/2.19 |-Branch two: % 6.68/2.19 | (89) ~ (all_57_0_12 = 0) % 6.68/2.19 | (94) all_57_1_13 = 0 % 6.68/2.19 | % 6.68/2.19 | Equations (94) can reduce 90 to: % 6.68/2.19 | (43) $false % 6.68/2.19 | % 6.68/2.19 |-The branch is then unsatisfiable % 6.68/2.19 |-Branch two: % 6.68/2.19 | (96) member(all_42_1_11, all_0_2_2) = 0 % 6.68/2.19 | (97) ? [v0] : ? [v1] : (member(all_42_1_11, all_0_5_5) = v1 & member(all_42_1_11, all_0_6_6) = v0 & (v1 = 0 | v0 = 0)) % 6.68/2.19 | % 6.68/2.19 | Instantiating (97) with all_82_0_18, all_82_1_19 yields: % 6.68/2.19 | (98) member(all_42_1_11, all_0_5_5) = all_82_0_18 & member(all_42_1_11, all_0_6_6) = all_82_1_19 & (all_82_0_18 = 0 | all_82_1_19 = 0) % 6.68/2.19 | % 6.68/2.19 | Applying alpha-rule on (98) yields: % 6.68/2.19 | (99) member(all_42_1_11, all_0_5_5) = all_82_0_18 % 6.68/2.19 | (100) member(all_42_1_11, all_0_6_6) = all_82_1_19 % 6.68/2.19 | (101) all_82_0_18 = 0 | all_82_1_19 = 0 % 6.68/2.19 | % 6.68/2.19 | Instantiating formula (3) with all_42_1_11, all_0_5_5, all_82_0_18, all_63_0_14 and discharging atoms member(all_42_1_11, all_0_5_5) = all_82_0_18, member(all_42_1_11, all_0_5_5) = all_63_0_14, yields: % 6.68/2.19 | (102) all_82_0_18 = all_63_0_14 % 6.68/2.19 | % 6.68/2.19 | Instantiating formula (3) with all_42_1_11, all_0_6_6, all_76_0_16, all_82_1_19 and discharging atoms member(all_42_1_11, all_0_6_6) = all_82_1_19, member(all_42_1_11, all_0_6_6) = all_76_0_16, yields: % 6.68/2.19 | (103) all_82_1_19 = all_76_0_16 % 6.68/2.19 | % 6.68/2.19 +-Applying beta-rule and splitting (101), into two cases. % 6.68/2.19 |-Branch one: % 6.68/2.19 | (104) all_82_0_18 = 0 % 6.68/2.19 | % 6.68/2.19 | Combining equations (104,102) yields a new equation: % 6.68/2.19 | (105) all_63_0_14 = 0 % 6.68/2.19 | % 6.68/2.19 | Equations (105) can reduce 73 to: % 6.68/2.19 | (43) $false % 6.68/2.19 | % 6.68/2.19 |-The branch is then unsatisfiable % 6.68/2.19 |-Branch two: % 6.68/2.19 | (107) ~ (all_82_0_18 = 0) % 6.68/2.19 | (108) all_82_1_19 = 0 % 6.68/2.19 | % 6.68/2.19 | Combining equations (108,103) yields a new equation: % 6.68/2.19 | (109) all_76_0_16 = 0 % 6.68/2.19 | % 6.68/2.19 | Equations (109) can reduce 83 to: % 6.68/2.19 | (43) $false % 6.68/2.19 | % 6.68/2.19 |-The branch is then unsatisfiable % 6.68/2.19 |-Branch two: % 6.68/2.19 | (53) all_14_0_8 = 0 % 6.68/2.19 | (112) ~ (all_14_1_9 = 0) % 6.68/2.19 | % 6.68/2.19 +-Applying beta-rule and splitting (51), into two cases. % 6.68/2.19 |-Branch one: % 6.68/2.19 | (113) all_14_1_9 = 0 % 6.68/2.19 | % 6.68/2.19 | Equations (113) can reduce 112 to: % 6.68/2.19 | (43) $false % 6.68/2.19 | % 6.68/2.19 |-The branch is then unsatisfiable % 6.68/2.19 |-Branch two: % 6.68/2.19 | (112) ~ (all_14_1_9 = 0) % 6.68/2.19 | (116) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 6.68/2.19 | % 6.68/2.19 | Instantiating (116) with all_42_0_20, all_42_1_21 yields: % 6.68/2.19 | (117) ~ (all_42_0_20 = 0) & member(all_42_1_21, all_0_1_1) = all_42_0_20 & member(all_42_1_21, all_0_3_3) = 0 % 6.68/2.19 | % 6.68/2.19 | Applying alpha-rule on (117) yields: % 6.68/2.19 | (118) ~ (all_42_0_20 = 0) % 6.68/2.19 | (119) member(all_42_1_21, all_0_1_1) = all_42_0_20 % 6.68/2.19 | (120) member(all_42_1_21, all_0_3_3) = 0 % 6.68/2.19 | % 6.68/2.19 | Instantiating formula (16) with all_42_0_20, all_0_1_1, all_0_2_2, all_0_7_7, all_42_1_21 and discharging atoms union(all_0_7_7, all_0_2_2) = all_0_1_1, member(all_42_1_21, all_0_1_1) = all_42_0_20, yields: % 6.68/2.19 | (121) all_42_0_20 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_21, all_0_2_2) = v1 & member(all_42_1_21, all_0_7_7) = v0) % 6.68/2.19 | % 6.68/2.19 | Instantiating formula (6) with all_0_3_3, all_0_5_5, all_0_4_4, all_42_1_21 and discharging atoms union(all_0_4_4, all_0_5_5) = all_0_3_3, member(all_42_1_21, all_0_3_3) = 0, yields: % 6.68/2.19 | (122) ? [v0] : ? [v1] : (member(all_42_1_21, all_0_4_4) = v0 & member(all_42_1_21, all_0_5_5) = v1 & (v1 = 0 | v0 = 0)) % 6.68/2.19 | % 6.68/2.19 | Instantiating formula (6) with all_0_4_4, all_0_6_6, all_0_7_7, all_42_1_21 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_4_4, yields: % 6.68/2.19 | (123) ~ (member(all_42_1_21, all_0_4_4) = 0) | ? [v0] : ? [v1] : (member(all_42_1_21, all_0_6_6) = v1 & member(all_42_1_21, all_0_7_7) = v0 & (v1 = 0 | v0 = 0)) % 6.68/2.19 | % 6.68/2.19 | Instantiating (122) with all_57_0_22, all_57_1_23 yields: % 6.68/2.20 | (124) member(all_42_1_21, all_0_4_4) = all_57_1_23 & member(all_42_1_21, all_0_5_5) = all_57_0_22 & (all_57_0_22 = 0 | all_57_1_23 = 0) % 6.68/2.20 | % 6.68/2.20 | Applying alpha-rule on (124) yields: % 6.68/2.20 | (125) member(all_42_1_21, all_0_4_4) = all_57_1_23 % 6.68/2.20 | (126) member(all_42_1_21, all_0_5_5) = all_57_0_22 % 6.68/2.20 | (127) all_57_0_22 = 0 | all_57_1_23 = 0 % 6.68/2.20 | % 6.68/2.20 +-Applying beta-rule and splitting (121), into two cases. % 6.68/2.20 |-Branch one: % 6.68/2.20 | (128) all_42_0_20 = 0 % 6.68/2.20 | % 6.68/2.20 | Equations (128) can reduce 118 to: % 6.68/2.20 | (43) $false % 6.68/2.20 | % 6.68/2.20 |-The branch is then unsatisfiable % 6.68/2.20 |-Branch two: % 6.68/2.20 | (118) ~ (all_42_0_20 = 0) % 6.68/2.20 | (131) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_21, all_0_2_2) = v1 & member(all_42_1_21, all_0_7_7) = v0) % 6.68/2.20 | % 6.68/2.20 | Instantiating (131) with all_63_0_24, all_63_1_25 yields: % 6.68/2.20 | (132) ~ (all_63_0_24 = 0) & ~ (all_63_1_25 = 0) & member(all_42_1_21, all_0_2_2) = all_63_0_24 & member(all_42_1_21, all_0_7_7) = all_63_1_25 % 6.68/2.20 | % 6.68/2.20 | Applying alpha-rule on (132) yields: % 6.68/2.20 | (133) ~ (all_63_0_24 = 0) % 6.68/2.20 | (134) ~ (all_63_1_25 = 0) % 6.68/2.20 | (135) member(all_42_1_21, all_0_2_2) = all_63_0_24 % 6.68/2.20 | (136) member(all_42_1_21, all_0_7_7) = all_63_1_25 % 6.68/2.20 | % 6.68/2.20 | Instantiating formula (16) with all_63_0_24, all_0_2_2, all_0_5_5, all_0_6_6, all_42_1_21 and discharging atoms union(all_0_6_6, all_0_5_5) = all_0_2_2, member(all_42_1_21, all_0_2_2) = all_63_0_24, yields: % 6.68/2.20 | (137) all_63_0_24 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_21, all_0_5_5) = v1 & member(all_42_1_21, all_0_6_6) = v0) % 6.68/2.20 | % 6.68/2.20 +-Applying beta-rule and splitting (137), into two cases. % 6.68/2.20 |-Branch one: % 6.68/2.20 | (138) all_63_0_24 = 0 % 6.68/2.20 | % 6.68/2.20 | Equations (138) can reduce 133 to: % 6.68/2.20 | (43) $false % 6.68/2.20 | % 6.68/2.20 |-The branch is then unsatisfiable % 6.68/2.20 |-Branch two: % 6.68/2.20 | (133) ~ (all_63_0_24 = 0) % 6.68/2.20 | (141) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_42_1_21, all_0_5_5) = v1 & member(all_42_1_21, all_0_6_6) = v0) % 6.68/2.20 | % 6.68/2.20 | Instantiating (141) with all_84_0_26, all_84_1_27 yields: % 6.68/2.20 | (142) ~ (all_84_0_26 = 0) & ~ (all_84_1_27 = 0) & member(all_42_1_21, all_0_5_5) = all_84_0_26 & member(all_42_1_21, all_0_6_6) = all_84_1_27 % 6.68/2.20 | % 6.68/2.20 | Applying alpha-rule on (142) yields: % 6.68/2.20 | (143) ~ (all_84_0_26 = 0) % 6.68/2.20 | (144) ~ (all_84_1_27 = 0) % 6.68/2.20 | (145) member(all_42_1_21, all_0_5_5) = all_84_0_26 % 6.68/2.20 | (146) member(all_42_1_21, all_0_6_6) = all_84_1_27 % 6.68/2.20 | % 6.68/2.20 +-Applying beta-rule and splitting (123), into two cases. % 6.68/2.20 |-Branch one: % 6.68/2.20 | (147) ~ (member(all_42_1_21, all_0_4_4) = 0) % 6.68/2.20 | % 6.68/2.20 | Instantiating formula (3) with all_42_1_21, all_0_5_5, all_84_0_26, all_57_0_22 and discharging atoms member(all_42_1_21, all_0_5_5) = all_84_0_26, member(all_42_1_21, all_0_5_5) = all_57_0_22, yields: % 6.68/2.20 | (148) all_84_0_26 = all_57_0_22 % 6.68/2.20 | % 6.68/2.20 | Using (125) and (147) yields: % 6.68/2.20 | (149) ~ (all_57_1_23 = 0) % 6.68/2.20 | % 6.68/2.20 | Equations (148) can reduce 143 to: % 6.68/2.20 | (150) ~ (all_57_0_22 = 0) % 6.68/2.20 | % 6.68/2.20 +-Applying beta-rule and splitting (127), into two cases. % 6.68/2.20 |-Branch one: % 6.68/2.20 | (151) all_57_0_22 = 0 % 6.68/2.20 | % 6.68/2.20 | Equations (151) can reduce 150 to: % 6.68/2.20 | (43) $false % 6.68/2.20 | % 6.68/2.20 |-The branch is then unsatisfiable % 6.68/2.20 |-Branch two: % 6.68/2.20 | (150) ~ (all_57_0_22 = 0) % 6.68/2.20 | (154) all_57_1_23 = 0 % 6.68/2.20 | % 6.68/2.20 | Equations (154) can reduce 149 to: % 6.68/2.20 | (43) $false % 6.68/2.20 | % 6.68/2.20 |-The branch is then unsatisfiable % 6.68/2.20 |-Branch two: % 6.68/2.20 | (156) member(all_42_1_21, all_0_4_4) = 0 % 6.68/2.20 | (157) ? [v0] : ? [v1] : (member(all_42_1_21, all_0_6_6) = v1 & member(all_42_1_21, all_0_7_7) = v0 & (v1 = 0 | v0 = 0)) % 6.68/2.20 | % 6.68/2.20 | Instantiating (157) with all_90_0_28, all_90_1_29 yields: % 6.68/2.20 | (158) member(all_42_1_21, all_0_6_6) = all_90_0_28 & member(all_42_1_21, all_0_7_7) = all_90_1_29 & (all_90_0_28 = 0 | all_90_1_29 = 0) % 6.68/2.20 | % 6.68/2.20 | Applying alpha-rule on (158) yields: % 6.68/2.20 | (159) member(all_42_1_21, all_0_6_6) = all_90_0_28 % 6.68/2.20 | (160) member(all_42_1_21, all_0_7_7) = all_90_1_29 % 6.68/2.21 | (161) all_90_0_28 = 0 | all_90_1_29 = 0 % 6.68/2.21 | % 6.68/2.21 | Instantiating formula (3) with all_42_1_21, all_0_6_6, all_84_1_27, all_90_0_28 and discharging atoms member(all_42_1_21, all_0_6_6) = all_90_0_28, member(all_42_1_21, all_0_6_6) = all_84_1_27, yields: % 6.68/2.21 | (162) all_90_0_28 = all_84_1_27 % 6.68/2.21 | % 6.68/2.21 | Instantiating formula (3) with all_42_1_21, all_0_7_7, all_90_1_29, all_63_1_25 and discharging atoms member(all_42_1_21, all_0_7_7) = all_90_1_29, member(all_42_1_21, all_0_7_7) = all_63_1_25, yields: % 6.68/2.21 | (163) all_90_1_29 = all_63_1_25 % 6.68/2.21 | % 6.68/2.21 +-Applying beta-rule and splitting (161), into two cases. % 6.68/2.21 |-Branch one: % 6.68/2.21 | (164) all_90_0_28 = 0 % 6.68/2.21 | % 6.68/2.21 | Combining equations (164,162) yields a new equation: % 6.68/2.21 | (165) all_84_1_27 = 0 % 6.68/2.21 | % 6.68/2.21 | Equations (165) can reduce 144 to: % 6.68/2.21 | (43) $false % 6.68/2.21 | % 6.68/2.21 |-The branch is then unsatisfiable % 6.68/2.21 |-Branch two: % 6.68/2.21 | (167) ~ (all_90_0_28 = 0) % 6.68/2.21 | (168) all_90_1_29 = 0 % 6.68/2.21 | % 6.68/2.21 | Combining equations (163,168) yields a new equation: % 6.68/2.21 | (169) all_63_1_25 = 0 % 6.68/2.21 | % 6.68/2.21 | Simplifying 169 yields: % 6.68/2.21 | (170) all_63_1_25 = 0 % 6.68/2.21 | % 6.68/2.21 | Equations (170) can reduce 134 to: % 6.68/2.21 | (43) $false % 6.68/2.21 | % 6.68/2.21 |-The branch is then unsatisfiable % 6.68/2.21 % SZS output end Proof for theBenchmark % 6.68/2.21 % 6.68/2.21 1612ms %------------------------------------------------------------------------------