%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET694+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 00:21:27 EDT 2022 % Result : Theorem 6.79s 2.26s % Output : Proof 9.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET694+4 : TPTP v8.1.0. Released v2.2.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n008.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sun Jul 10 09:11:53 EDT 2022 % 0.14/0.34 % CPUTime : % 0.63/0.61 ____ _ % 0.63/0.61 ___ / __ \_____(_)___ ________ __________ % 0.63/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.63/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.63/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.63/0.61 % 0.63/0.61 A Theorem Prover for First-Order Logic % 0.63/0.61 (ePrincess v.1.0) % 0.63/0.61 % 0.63/0.61 (c) Philipp Rümmer, 2009-2015 % 0.63/0.61 (c) Peter Backeman, 2014-2015 % 0.63/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.63/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.63/0.61 Bug reports to peter@backeman.se % 0.63/0.61 % 0.63/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.63/0.61 % 0.63/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.62/0.96 Prover 0: Preprocessing ... % 1.99/1.16 Prover 0: Warning: ignoring some quantifiers % 1.99/1.18 Prover 0: Constructing countermodel ... % 5.67/2.04 Prover 0: gave up % 5.67/2.04 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 5.67/2.07 Prover 1: Preprocessing ... % 6.33/2.15 Prover 1: Constructing countermodel ... % 6.79/2.25 Prover 1: proved (210ms) % 6.79/2.26 % 6.79/2.26 No countermodel exists, formula is valid % 6.79/2.26 % SZS status Theorem for theBenchmark % 6.79/2.26 % 6.79/2.26 Generating proof ... found it (size 54) % 8.51/2.63 % 8.51/2.63 % SZS output start Proof for theBenchmark % 8.51/2.63 Assumed formulas after preprocessing and simplification: % 8.51/2.63 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = 0) & union(v2, v3) = v4 & union(v0, v1) = v5 & power_set(v5) = v6 & power_set(v1) = v3 & power_set(v0) = v2 & subset(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)) % 8.51/2.66 | 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: % 8.51/2.66 | (1) ~ (all_0_0_0 = 0) & 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 & power_set(all_0_2_2) = all_0_1_1 & power_set(all_0_6_6) = all_0_4_4 & power_set(all_0_7_7) = all_0_5_5 & subset(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) % 8.51/2.68 | % 8.51/2.68 | Applying alpha-rule on (1) yields: % 8.51/2.68 | (2) power_set(all_0_6_6) = all_0_4_4 % 8.51/2.68 | (3) union(all_0_5_5, all_0_4_4) = all_0_3_3 % 8.51/2.68 | (4) ! [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))) % 8.51/2.68 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 8.51/2.68 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 8.51/2.68 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 8.51/2.68 | (8) ! [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)) % 8.51/2.68 | (9) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 8.51/2.68 | (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)) % 8.51/2.68 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 8.51/2.68 | (12) subset(all_0_3_3, all_0_1_1) = all_0_0_0 % 8.51/2.68 | (13) ! [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)))) % 8.51/2.68 | (14) union(all_0_7_7, all_0_6_6) = all_0_2_2 % 8.51/2.68 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 8.51/2.68 | (16) power_set(all_0_7_7) = all_0_5_5 % 8.51/2.68 | (17) ! [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)) % 8.51/2.68 | (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)))) % 8.51/2.68 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 8.51/2.68 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 8.51/2.68 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 8.51/2.68 | (22) ~ (all_0_0_0 = 0) % 8.51/2.68 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 8.51/2.68 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 8.51/2.69 | (25) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 8.51/2.69 | (26) ! [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)) % 8.51/2.69 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 8.51/2.69 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 8.51/2.69 | (29) ! [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))) % 8.51/2.69 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 8.51/2.69 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 8.51/2.69 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 8.51/2.69 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 8.51/2.69 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 8.51/2.69 | (35) ! [v0] : ~ (member(v0, empty_set) = 0) % 8.51/2.69 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 8.51/2.69 | (37) power_set(all_0_2_2) = all_0_1_1 % 8.51/2.69 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 8.51/2.69 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 8.96/2.69 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 8.96/2.69 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 8.96/2.69 | % 8.96/2.69 | Instantiating formula (21) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_0_0_0, yields: % 8.97/2.69 | (42) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 8.97/2.69 | % 8.97/2.69 +-Applying beta-rule and splitting (42), into two cases. % 8.97/2.69 |-Branch one: % 8.97/2.69 | (43) all_0_0_0 = 0 % 8.97/2.69 | % 8.97/2.69 | Equations (43) can reduce 22 to: % 8.97/2.69 | (44) $false % 8.97/2.69 | % 8.97/2.69 |-The branch is then unsatisfiable % 8.97/2.69 |-Branch two: % 8.97/2.69 | (22) ~ (all_0_0_0 = 0) % 8.97/2.70 | (46) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 8.97/2.70 | % 8.97/2.70 | Instantiating (46) with all_14_0_8, all_14_1_9 yields: % 8.97/2.70 | (47) ~ (all_14_0_8 = 0) & member(all_14_1_9, all_0_1_1) = all_14_0_8 & member(all_14_1_9, all_0_3_3) = 0 % 8.97/2.70 | % 8.97/2.70 | Applying alpha-rule on (47) yields: % 8.97/2.70 | (48) ~ (all_14_0_8 = 0) % 8.97/2.70 | (49) member(all_14_1_9, all_0_1_1) = all_14_0_8 % 8.97/2.70 | (50) member(all_14_1_9, all_0_3_3) = 0 % 8.97/2.70 | % 8.97/2.70 | Instantiating formula (39) with all_14_0_8, all_0_1_1, all_0_2_2, all_14_1_9 and discharging atoms power_set(all_0_2_2) = all_0_1_1, member(all_14_1_9, all_0_1_1) = all_14_0_8, yields: % 8.97/2.70 | (51) all_14_0_8 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_14_1_9, all_0_2_2) = v0) % 8.97/2.70 | % 8.97/2.70 | Instantiating formula (4) with all_0_3_3, all_0_4_4, all_0_5_5, all_14_1_9 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_14_1_9, all_0_3_3) = 0, yields: % 8.97/2.70 | (52) ? [v0] : ? [v1] : (member(all_14_1_9, all_0_4_4) = v1 & member(all_14_1_9, all_0_5_5) = v0 & (v1 = 0 | v0 = 0)) % 8.97/2.70 | % 8.97/2.70 | Instantiating formula (24) with all_0_4_4, all_0_6_6, all_14_1_9 and discharging atoms power_set(all_0_6_6) = all_0_4_4, yields: % 8.97/2.70 | (53) ~ (member(all_14_1_9, all_0_4_4) = 0) | subset(all_14_1_9, all_0_6_6) = 0 % 8.97/2.70 | % 8.97/2.70 | Instantiating formula (24) with all_0_5_5, all_0_7_7, all_14_1_9 and discharging atoms power_set(all_0_7_7) = all_0_5_5, yields: % 8.97/2.70 | (54) ~ (member(all_14_1_9, all_0_5_5) = 0) | subset(all_14_1_9, all_0_7_7) = 0 % 8.97/2.70 | % 8.97/2.70 | Instantiating (52) with all_29_0_10, all_29_1_11 yields: % 8.97/2.70 | (55) member(all_14_1_9, all_0_4_4) = all_29_0_10 & member(all_14_1_9, all_0_5_5) = all_29_1_11 & (all_29_0_10 = 0 | all_29_1_11 = 0) % 9.00/2.70 | % 9.00/2.70 | Applying alpha-rule on (55) yields: % 9.00/2.70 | (56) member(all_14_1_9, all_0_4_4) = all_29_0_10 % 9.00/2.70 | (57) member(all_14_1_9, all_0_5_5) = all_29_1_11 % 9.00/2.70 | (58) all_29_0_10 = 0 | all_29_1_11 = 0 % 9.00/2.70 | % 9.00/2.70 +-Applying beta-rule and splitting (51), into two cases. % 9.00/2.70 |-Branch one: % 9.00/2.70 | (59) all_14_0_8 = 0 % 9.00/2.70 | % 9.00/2.70 | Equations (59) can reduce 48 to: % 9.00/2.70 | (44) $false % 9.00/2.70 | % 9.00/2.70 |-The branch is then unsatisfiable % 9.00/2.70 |-Branch two: % 9.00/2.70 | (48) ~ (all_14_0_8 = 0) % 9.00/2.70 | (62) ? [v0] : ( ~ (v0 = 0) & subset(all_14_1_9, all_0_2_2) = v0) % 9.00/2.70 | % 9.00/2.70 | Instantiating (62) with all_35_0_12 yields: % 9.00/2.70 | (63) ~ (all_35_0_12 = 0) & subset(all_14_1_9, all_0_2_2) = all_35_0_12 % 9.00/2.70 | % 9.00/2.70 | Applying alpha-rule on (63) yields: % 9.00/2.70 | (64) ~ (all_35_0_12 = 0) % 9.00/2.70 | (65) subset(all_14_1_9, all_0_2_2) = all_35_0_12 % 9.00/2.70 | % 9.00/2.70 | Instantiating formula (21) with all_35_0_12, all_0_2_2, all_14_1_9 and discharging atoms subset(all_14_1_9, all_0_2_2) = all_35_0_12, yields: % 9.00/2.70 | (66) all_35_0_12 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_14_1_9) = 0 & member(v0, all_0_2_2) = v1) % 9.00/2.70 | % 9.00/2.70 +-Applying beta-rule and splitting (66), into two cases. % 9.00/2.70 |-Branch one: % 9.00/2.70 | (67) all_35_0_12 = 0 % 9.00/2.70 | % 9.00/2.70 | Equations (67) can reduce 64 to: % 9.00/2.70 | (44) $false % 9.00/2.70 | % 9.00/2.70 |-The branch is then unsatisfiable % 9.00/2.70 |-Branch two: % 9.00/2.70 | (64) ~ (all_35_0_12 = 0) % 9.00/2.70 | (70) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_14_1_9) = 0 & member(v0, all_0_2_2) = v1) % 9.00/2.71 | % 9.00/2.71 | Instantiating (70) with all_56_0_13, all_56_1_14 yields: % 9.00/2.71 | (71) ~ (all_56_0_13 = 0) & member(all_56_1_14, all_14_1_9) = 0 & member(all_56_1_14, all_0_2_2) = all_56_0_13 % 9.00/2.71 | % 9.00/2.71 | Applying alpha-rule on (71) yields: % 9.00/2.71 | (72) ~ (all_56_0_13 = 0) % 9.00/2.71 | (73) member(all_56_1_14, all_14_1_9) = 0 % 9.00/2.71 | (74) member(all_56_1_14, all_0_2_2) = all_56_0_13 % 9.00/2.71 | % 9.00/2.71 | Instantiating formula (10) with all_56_0_13, all_0_2_2, all_0_6_6, all_0_7_7, all_56_1_14 and discharging atoms union(all_0_7_7, all_0_6_6) = all_0_2_2, member(all_56_1_14, all_0_2_2) = all_56_0_13, yields: % 9.00/2.71 | (75) all_56_0_13 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_56_1_14, all_0_6_6) = v1 & member(all_56_1_14, all_0_7_7) = v0) % 9.00/2.71 | % 9.00/2.71 +-Applying beta-rule and splitting (75), into two cases. % 9.00/2.71 |-Branch one: % 9.00/2.71 | (76) all_56_0_13 = 0 % 9.00/2.71 | % 9.00/2.71 | Equations (76) can reduce 72 to: % 9.00/2.71 | (44) $false % 9.00/2.71 | % 9.00/2.71 |-The branch is then unsatisfiable % 9.00/2.71 |-Branch two: % 9.00/2.71 | (72) ~ (all_56_0_13 = 0) % 9.00/2.71 | (79) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_56_1_14, all_0_6_6) = v1 & member(all_56_1_14, all_0_7_7) = v0) % 9.00/2.71 | % 9.00/2.71 | Instantiating (79) with all_77_0_15, all_77_1_16 yields: % 9.00/2.71 | (80) ~ (all_77_0_15 = 0) & ~ (all_77_1_16 = 0) & member(all_56_1_14, all_0_6_6) = all_77_0_15 & member(all_56_1_14, all_0_7_7) = all_77_1_16 % 9.00/2.71 | % 9.00/2.71 | Applying alpha-rule on (80) yields: % 9.00/2.71 | (81) ~ (all_77_0_15 = 0) % 9.00/2.71 | (82) ~ (all_77_1_16 = 0) % 9.00/2.71 | (83) member(all_56_1_14, all_0_6_6) = all_77_0_15 % 9.00/2.71 | (84) member(all_56_1_14, all_0_7_7) = all_77_1_16 % 9.00/2.71 | % 9.00/2.71 | Instantiating formula (38) with all_56_1_14, all_0_6_6, all_77_0_15, 0 and discharging atoms member(all_56_1_14, all_0_6_6) = all_77_0_15, yields: % 9.00/2.71 | (85) all_77_0_15 = 0 | ~ (member(all_56_1_14, all_0_6_6) = 0) % 9.00/2.71 | % 9.00/2.71 | Instantiating formula (38) with all_56_1_14, all_0_7_7, all_77_1_16, 0 and discharging atoms member(all_56_1_14, all_0_7_7) = all_77_1_16, yields: % 9.00/2.71 | (86) all_77_1_16 = 0 | ~ (member(all_56_1_14, all_0_7_7) = 0) % 9.00/2.71 | % 9.00/2.71 +-Applying beta-rule and splitting (54), into two cases. % 9.00/2.71 |-Branch one: % 9.00/2.71 | (87) ~ (member(all_14_1_9, all_0_5_5) = 0) % 9.00/2.71 | % 9.00/2.71 | Using (57) and (87) yields: % 9.00/2.71 | (88) ~ (all_29_1_11 = 0) % 9.00/2.71 | % 9.00/2.71 +-Applying beta-rule and splitting (58), into two cases. % 9.00/2.71 |-Branch one: % 9.00/2.71 | (89) all_29_0_10 = 0 % 9.00/2.71 | % 9.00/2.71 | From (89) and (56) follows: % 9.00/2.71 | (90) member(all_14_1_9, all_0_4_4) = 0 % 9.00/2.71 | % 9.00/2.71 +-Applying beta-rule and splitting (53), into two cases. % 9.00/2.71 |-Branch one: % 9.00/2.71 | (91) ~ (member(all_14_1_9, all_0_4_4) = 0) % 9.00/2.71 | % 9.00/2.71 | Using (90) and (91) yields: % 9.00/2.71 | (92) $false % 9.00/2.71 | % 9.00/2.71 |-The branch is then unsatisfiable % 9.00/2.71 |-Branch two: % 9.00/2.71 | (90) member(all_14_1_9, all_0_4_4) = 0 % 9.00/2.71 | (94) subset(all_14_1_9, all_0_6_6) = 0 % 9.00/2.71 | % 9.00/2.71 | Instantiating formula (40) with all_56_1_14, all_0_6_6, all_14_1_9 and discharging atoms subset(all_14_1_9, all_0_6_6) = 0, member(all_56_1_14, all_14_1_9) = 0, yields: % 9.00/2.71 | (95) member(all_56_1_14, all_0_6_6) = 0 % 9.00/2.71 | % 9.00/2.71 +-Applying beta-rule and splitting (85), into two cases. % 9.00/2.71 |-Branch one: % 9.00/2.71 | (96) ~ (member(all_56_1_14, all_0_6_6) = 0) % 9.00/2.71 | % 9.00/2.71 | Using (95) and (96) yields: % 9.00/2.71 | (92) $false % 9.00/2.71 | % 9.00/2.71 |-The branch is then unsatisfiable % 9.00/2.71 |-Branch two: % 9.00/2.71 | (95) member(all_56_1_14, all_0_6_6) = 0 % 9.00/2.71 | (99) all_77_0_15 = 0 % 9.00/2.71 | % 9.00/2.71 | Equations (99) can reduce 81 to: % 9.00/2.71 | (44) $false % 9.00/2.71 | % 9.00/2.71 |-The branch is then unsatisfiable % 9.00/2.71 |-Branch two: % 9.00/2.71 | (101) ~ (all_29_0_10 = 0) % 9.00/2.71 | (102) all_29_1_11 = 0 % 9.00/2.71 | % 9.00/2.71 | Equations (102) can reduce 88 to: % 9.00/2.71 | (44) $false % 9.00/2.71 | % 9.00/2.71 |-The branch is then unsatisfiable % 9.00/2.71 |-Branch two: % 9.00/2.71 | (104) member(all_14_1_9, all_0_5_5) = 0 % 9.00/2.71 | (105) subset(all_14_1_9, all_0_7_7) = 0 % 9.00/2.71 | % 9.00/2.71 | Instantiating formula (40) with all_56_1_14, all_0_7_7, all_14_1_9 and discharging atoms subset(all_14_1_9, all_0_7_7) = 0, member(all_56_1_14, all_14_1_9) = 0, yields: % 9.00/2.71 | (106) member(all_56_1_14, all_0_7_7) = 0 % 9.00/2.71 | % 9.00/2.71 +-Applying beta-rule and splitting (86), into two cases. % 9.00/2.71 |-Branch one: % 9.00/2.71 | (107) ~ (member(all_56_1_14, all_0_7_7) = 0) % 9.00/2.71 | % 9.00/2.71 | Using (106) and (107) yields: % 9.00/2.71 | (92) $false % 9.00/2.71 | % 9.00/2.71 |-The branch is then unsatisfiable % 9.00/2.71 |-Branch two: % 9.00/2.71 | (106) member(all_56_1_14, all_0_7_7) = 0 % 9.00/2.71 | (110) all_77_1_16 = 0 % 9.00/2.71 | % 9.00/2.71 | Equations (110) can reduce 82 to: % 9.00/2.71 | (44) $false % 9.00/2.71 | % 9.00/2.71 |-The branch is then unsatisfiable % 9.00/2.71 % SZS output end Proof for theBenchmark % 9.00/2.72 % 9.00/2.72 2097ms %------------------------------------------------------------------------------