%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET595+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n022.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 00:20:34 EDT 2022 % Result : Theorem 3.72s 1.55s % Output : Proof 5.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET595+4 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n022.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 10:17:40 EDT 2022 % 0.12/0.33 % CPUTime : % 0.56/0.58 ____ _ % 0.56/0.58 ___ / __ \_____(_)___ ________ __________ % 0.56/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.56/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.56/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.56/0.58 % 0.56/0.58 A Theorem Prover for First-Order Logic % 0.56/0.58 (ePrincess v.1.0) % 0.56/0.58 % 0.56/0.58 (c) Philipp Rümmer, 2009-2015 % 0.56/0.58 (c) Peter Backeman, 2014-2015 % 0.56/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.56/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.56/0.58 Bug reports to peter@backeman.se % 0.56/0.58 % 0.56/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.56/0.58 % 0.56/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.56/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.46/0.92 Prover 0: Preprocessing ... % 2.01/1.11 Prover 0: Warning: ignoring some quantifiers % 2.01/1.13 Prover 0: Constructing countermodel ... % 2.72/1.30 Prover 0: gave up % 2.72/1.30 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.72/1.33 Prover 1: Preprocessing ... % 2.96/1.44 Prover 1: Constructing countermodel ... % 3.72/1.55 Prover 1: proved (241ms) % 3.72/1.55 % 3.72/1.55 No countermodel exists, formula is valid % 3.72/1.55 % SZS status Theorem for theBenchmark % 3.72/1.55 % 3.72/1.55 Generating proof ... found it (size 76) % 4.88/1.88 % 4.88/1.88 % SZS output start Proof for theBenchmark % 4.88/1.88 Assumed formulas after preprocessing and simplification: % 4.88/1.88 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & difference(v1, v0) = v2 & union(v2, v0) = v3 & equal_set(v3, v1) = v4 & subset(v0, v1) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v8) = v9) | ~ (member(v5, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v8, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : (member(v5, v7) = v10 & member(v5, v6) = v11 & ( ~ (v10 = 0) | v11 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & member(v5, v7) = v11 & member(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = v9) | ? [v10] : ? [v11] : (member(v5, v7) = v11 & member(v5, v6) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum(v6) = v7) | ~ (member(v5, v9) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = 0 & member(v5, v9) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v6, v5) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (power_set(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & subset(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | v6 = v5 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unordered_pair(v8, v7) = v6) | ~ (unordered_pair(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (difference(v8, v7) = v6) | ~ (difference(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equal_set(v8, v7) = v6) | ~ (equal_set(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subset(v8, v7) = v6) | ~ (subset(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (difference(v7, v6) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v5, v7) = 0 & member(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v6, v7) = v8) | ~ (member(v5, v8) = 0) | ? [v9] : ? [v10] : (member(v5, v7) = v10 & member(v5, v6) = v9 & (v10 = 0 | v9 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v6, v7) = v8) | ~ (member(v5, v8) = 0) | (member(v5, v7) = 0 & member(v5, v6) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (singleton(v5) = v6) | ~ (member(v5, v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equal_set(v5, v6) = v7) | ? [v8] : ? [v9] : (subset(v6, v5) = v9 & subset(v5, v6) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (product(v7) = v6) | ~ (product(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sum(v7) = v6) | ~ (sum(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v6) = v7) | ~ (member(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (power_set(v7) = v6) | ~ (power_set(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum(v6) = v7) | ~ (member(v5, v7) = 0) | ? [v8] : (member(v8, v6) = 0 & member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (power_set(v6) = v7) | ~ (member(v5, v7) = 0) | subset(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subset(v5, v6) = 0) | ~ (member(v7, v5) = 0) | member(v7, v6) = 0) & ! [v5] : ! [v6] : ( ~ (equal_set(v5, v6) = 0) | (subset(v6, v5) = 0 & subset(v5, v6) = 0)) & ! [v5] : ~ (member(v5, empty_set) = 0)) % 5.26/1.92 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 5.26/1.92 | (1) ~ (all_0_0_0 = 0) & difference(all_0_3_3, all_0_4_4) = all_0_2_2 & union(all_0_2_2, all_0_4_4) = all_0_1_1 & equal_set(all_0_1_1, all_0_3_3) = all_0_0_0 & subset(all_0_4_4, all_0_3_3) = 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) % 5.26/1.93 | % 5.26/1.93 | Applying alpha-rule on (1) yields: % 5.26/1.93 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 5.26/1.93 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 5.26/1.93 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.26/1.93 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 5.26/1.93 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 5.26/1.93 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 5.26/1.93 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 5.26/1.93 | (9) difference(all_0_3_3, all_0_4_4) = all_0_2_2 % 5.26/1.93 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 5.26/1.93 | (11) ! [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))) % 5.26/1.93 | (12) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 5.26/1.94 | (13) ! [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))) % 5.26/1.94 | (14) ! [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)) % 5.26/1.94 | (15) ~ (all_0_0_0 = 0) % 5.26/1.94 | (16) ! [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)))) % 5.26/1.94 | (17) ! [v0] : ~ (member(v0, empty_set) = 0) % 5.26/1.94 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 5.26/1.94 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 5.26/1.94 | (20) ! [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)) % 5.26/1.94 | (21) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 5.26/1.94 | (22) ! [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)) % 5.26/1.94 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 5.26/1.94 | (24) union(all_0_2_2, all_0_4_4) = all_0_1_1 % 5.26/1.94 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.26/1.94 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.26/1.94 | (27) ! [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)) % 5.26/1.94 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 5.26/1.94 | (29) subset(all_0_4_4, all_0_3_3) = 0 % 5.26/1.94 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 5.26/1.94 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 5.26/1.94 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 5.26/1.95 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 5.26/1.95 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 5.26/1.95 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 5.26/1.95 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.26/1.95 | (37) equal_set(all_0_1_1, all_0_3_3) = all_0_0_0 % 5.26/1.95 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 5.26/1.95 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 5.26/1.95 | % 5.26/1.95 | Instantiating formula (31) with all_0_0_0, all_0_3_3, all_0_1_1 and discharging atoms equal_set(all_0_1_1, all_0_3_3) = all_0_0_0, yields: % 5.26/1.95 | (40) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v0 & subset(all_0_3_3, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.26/1.95 | % 5.26/1.95 +-Applying beta-rule and splitting (40), into two cases. % 5.26/1.95 |-Branch one: % 5.26/1.95 | (41) all_0_0_0 = 0 % 5.26/1.95 | % 5.26/1.95 | Equations (41) can reduce 15 to: % 5.26/1.95 | (42) $false % 5.26/1.95 | % 5.26/1.95 |-The branch is then unsatisfiable % 5.26/1.95 |-Branch two: % 5.26/1.95 | (15) ~ (all_0_0_0 = 0) % 5.26/1.95 | (44) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_3_3) = v0 & subset(all_0_3_3, all_0_1_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.26/1.95 | % 5.26/1.95 | Instantiating (44) with all_10_0_5, all_10_1_6 yields: % 5.26/1.95 | (45) subset(all_0_1_1, all_0_3_3) = all_10_1_6 & subset(all_0_3_3, all_0_1_1) = all_10_0_5 & ( ~ (all_10_0_5 = 0) | ~ (all_10_1_6 = 0)) % 5.26/1.95 | % 5.26/1.95 | Applying alpha-rule on (45) yields: % 5.26/1.95 | (46) subset(all_0_1_1, all_0_3_3) = all_10_1_6 % 5.26/1.95 | (47) subset(all_0_3_3, all_0_1_1) = all_10_0_5 % 5.26/1.95 | (48) ~ (all_10_0_5 = 0) | ~ (all_10_1_6 = 0) % 5.26/1.95 | % 5.26/1.95 | Instantiating formula (4) with all_0_4_4, all_0_3_3, all_10_1_6, 0 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, yields: % 5.26/1.95 | (49) all_10_1_6 = 0 | ~ (subset(all_0_4_4, all_0_3_3) = all_10_1_6) % 5.26/1.95 | % 5.26/1.95 | Instantiating formula (21) with all_10_1_6, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_10_1_6, yields: % 5.26/1.95 | (50) all_10_1_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 5.26/1.95 | % 5.26/1.95 | Instantiating formula (21) with all_10_0_5, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_10_0_5, yields: % 5.26/1.95 | (51) all_10_0_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 5.26/1.95 | % 5.26/1.95 +-Applying beta-rule and splitting (49), into two cases. % 5.26/1.95 |-Branch one: % 5.26/1.95 | (52) ~ (subset(all_0_4_4, all_0_3_3) = all_10_1_6) % 5.26/1.95 | % 5.26/1.95 | Using (29) and (52) yields: % 5.26/1.95 | (53) ~ (all_10_1_6 = 0) % 5.26/1.95 | % 5.26/1.95 +-Applying beta-rule and splitting (50), into two cases. % 5.26/1.95 |-Branch one: % 5.26/1.95 | (54) all_10_1_6 = 0 % 5.26/1.96 | % 5.26/1.96 | Equations (54) can reduce 53 to: % 5.26/1.96 | (42) $false % 5.26/1.96 | % 5.26/1.96 |-The branch is then unsatisfiable % 5.26/1.96 |-Branch two: % 5.26/1.96 | (53) ~ (all_10_1_6 = 0) % 5.26/1.96 | (57) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 5.26/1.96 | % 5.26/1.96 | Instantiating (57) with all_27_0_7, all_27_1_8 yields: % 5.26/1.96 | (58) ~ (all_27_0_7 = 0) & member(all_27_1_8, all_0_1_1) = 0 & member(all_27_1_8, all_0_3_3) = all_27_0_7 % 5.26/1.96 | % 5.26/1.96 | Applying alpha-rule on (58) yields: % 5.26/1.96 | (59) ~ (all_27_0_7 = 0) % 5.26/1.96 | (60) member(all_27_1_8, all_0_1_1) = 0 % 5.26/1.96 | (61) member(all_27_1_8, all_0_3_3) = all_27_0_7 % 5.26/1.96 | % 5.26/1.96 | Instantiating formula (26) with all_27_1_8, all_0_3_3, all_27_0_7, 0 and discharging atoms member(all_27_1_8, all_0_3_3) = all_27_0_7, yields: % 5.26/1.96 | (62) all_27_0_7 = 0 | ~ (member(all_27_1_8, all_0_3_3) = 0) % 5.26/1.96 | % 5.26/1.96 | Instantiating formula (8) with all_0_2_2, all_0_3_3, all_0_4_4, all_27_1_8 and discharging atoms difference(all_0_3_3, all_0_4_4) = all_0_2_2, yields: % 5.26/1.96 | (63) ~ (member(all_27_1_8, all_0_2_2) = 0) | ? [v0] : ( ~ (v0 = 0) & member(all_27_1_8, all_0_3_3) = 0 & member(all_27_1_8, all_0_4_4) = v0) % 5.26/1.96 | % 5.26/1.96 | Instantiating formula (11) with all_0_1_1, all_0_4_4, all_0_2_2, all_27_1_8 and discharging atoms union(all_0_2_2, all_0_4_4) = all_0_1_1, member(all_27_1_8, all_0_1_1) = 0, yields: % 5.26/1.96 | (64) ? [v0] : ? [v1] : (member(all_27_1_8, all_0_2_2) = v0 & member(all_27_1_8, all_0_4_4) = v1 & (v1 = 0 | v0 = 0)) % 5.26/1.96 | % 5.26/1.96 | Instantiating (64) with all_42_0_9, all_42_1_10 yields: % 5.26/1.96 | (65) member(all_27_1_8, all_0_2_2) = all_42_1_10 & member(all_27_1_8, all_0_4_4) = all_42_0_9 & (all_42_0_9 = 0 | all_42_1_10 = 0) % 5.26/1.96 | % 5.26/1.96 | Applying alpha-rule on (65) yields: % 5.26/1.96 | (66) member(all_27_1_8, all_0_2_2) = all_42_1_10 % 5.26/1.96 | (67) member(all_27_1_8, all_0_4_4) = all_42_0_9 % 5.26/1.96 | (68) all_42_0_9 = 0 | all_42_1_10 = 0 % 5.26/1.96 | % 5.26/1.96 +-Applying beta-rule and splitting (63), into two cases. % 5.26/1.96 |-Branch one: % 5.26/1.96 | (69) ~ (member(all_27_1_8, all_0_2_2) = 0) % 5.26/1.96 | % 5.26/1.96 | Using (66) and (69) yields: % 5.26/1.96 | (70) ~ (all_42_1_10 = 0) % 5.26/1.96 | % 5.26/1.96 +-Applying beta-rule and splitting (68), into two cases. % 5.26/1.96 |-Branch one: % 5.26/1.96 | (71) all_42_0_9 = 0 % 5.26/1.96 | % 5.26/1.96 | From (71) and (67) follows: % 5.26/1.96 | (72) member(all_27_1_8, all_0_4_4) = 0 % 5.26/1.96 | % 5.26/1.96 | Instantiating formula (18) with all_27_1_8, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, member(all_27_1_8, all_0_4_4) = 0, yields: % 5.26/1.96 | (73) member(all_27_1_8, all_0_3_3) = 0 % 5.26/1.96 | % 5.26/1.96 +-Applying beta-rule and splitting (62), into two cases. % 5.26/1.96 |-Branch one: % 5.26/1.96 | (74) ~ (member(all_27_1_8, all_0_3_3) = 0) % 5.26/1.96 | % 5.26/1.96 | Using (73) and (74) yields: % 5.26/1.96 | (75) $false % 5.26/1.96 | % 5.26/1.96 |-The branch is then unsatisfiable % 5.26/1.96 |-Branch two: % 5.26/1.96 | (73) member(all_27_1_8, all_0_3_3) = 0 % 5.26/1.96 | (77) all_27_0_7 = 0 % 5.26/1.96 | % 5.26/1.96 | Equations (77) can reduce 59 to: % 5.26/1.96 | (42) $false % 5.26/1.96 | % 5.26/1.96 |-The branch is then unsatisfiable % 5.26/1.96 |-Branch two: % 5.26/1.96 | (79) ~ (all_42_0_9 = 0) % 5.26/1.96 | (80) all_42_1_10 = 0 % 5.26/1.96 | % 5.26/1.96 | Equations (80) can reduce 70 to: % 5.26/1.96 | (42) $false % 5.26/1.96 | % 5.26/1.96 |-The branch is then unsatisfiable % 5.26/1.96 |-Branch two: % 5.26/1.96 | (82) member(all_27_1_8, all_0_2_2) = 0 % 5.26/1.96 | (83) ? [v0] : ( ~ (v0 = 0) & member(all_27_1_8, all_0_3_3) = 0 & member(all_27_1_8, all_0_4_4) = v0) % 5.26/1.96 | % 5.26/1.96 | Instantiating (83) with all_48_0_11 yields: % 5.26/1.96 | (84) ~ (all_48_0_11 = 0) & member(all_27_1_8, all_0_3_3) = 0 & member(all_27_1_8, all_0_4_4) = all_48_0_11 % 5.26/1.96 | % 5.26/1.96 | Applying alpha-rule on (84) yields: % 5.26/1.97 | (85) ~ (all_48_0_11 = 0) % 5.26/1.97 | (73) member(all_27_1_8, all_0_3_3) = 0 % 5.26/1.97 | (87) member(all_27_1_8, all_0_4_4) = all_48_0_11 % 5.26/1.97 | % 5.26/1.97 +-Applying beta-rule and splitting (62), into two cases. % 5.26/1.97 |-Branch one: % 5.26/1.97 | (74) ~ (member(all_27_1_8, all_0_3_3) = 0) % 5.26/1.97 | % 5.26/1.97 | Using (73) and (74) yields: % 5.26/1.97 | (75) $false % 5.26/1.97 | % 5.26/1.97 |-The branch is then unsatisfiable % 5.26/1.97 |-Branch two: % 5.26/1.97 | (73) member(all_27_1_8, all_0_3_3) = 0 % 5.26/1.97 | (77) all_27_0_7 = 0 % 5.26/1.97 | % 5.26/1.97 | Equations (77) can reduce 59 to: % 5.26/1.97 | (42) $false % 5.26/1.97 | % 5.26/1.97 |-The branch is then unsatisfiable % 5.26/1.97 |-Branch two: % 5.26/1.97 | (93) subset(all_0_4_4, all_0_3_3) = all_10_1_6 % 5.26/1.97 | (54) all_10_1_6 = 0 % 5.26/1.97 | % 5.26/1.97 +-Applying beta-rule and splitting (48), into two cases. % 5.26/1.97 |-Branch one: % 5.26/1.97 | (95) ~ (all_10_0_5 = 0) % 5.26/1.97 | % 5.26/1.97 +-Applying beta-rule and splitting (51), into two cases. % 5.26/1.97 |-Branch one: % 5.26/1.97 | (96) all_10_0_5 = 0 % 5.26/1.97 | % 5.26/1.97 | Equations (96) can reduce 95 to: % 5.26/1.97 | (42) $false % 5.26/1.97 | % 5.26/1.97 |-The branch is then unsatisfiable % 5.26/1.97 |-Branch two: % 5.26/1.97 | (95) ~ (all_10_0_5 = 0) % 5.26/1.97 | (99) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 5.26/1.97 | % 5.26/1.97 | Instantiating (99) with all_27_0_12, all_27_1_13 yields: % 5.26/1.97 | (100) ~ (all_27_0_12 = 0) & member(all_27_1_13, all_0_1_1) = all_27_0_12 & member(all_27_1_13, all_0_3_3) = 0 % 5.26/1.97 | % 5.26/1.97 | Applying alpha-rule on (100) yields: % 5.26/1.97 | (101) ~ (all_27_0_12 = 0) % 5.26/1.97 | (102) member(all_27_1_13, all_0_1_1) = all_27_0_12 % 5.26/1.97 | (103) member(all_27_1_13, all_0_3_3) = 0 % 5.26/1.97 | % 5.26/1.97 | Instantiating formula (14) with all_27_0_12, all_0_1_1, all_0_4_4, all_0_2_2, all_27_1_13 and discharging atoms union(all_0_2_2, all_0_4_4) = all_0_1_1, member(all_27_1_13, all_0_1_1) = all_27_0_12, yields: % 5.26/1.97 | (104) all_27_0_12 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_27_1_13, all_0_2_2) = v0 & member(all_27_1_13, all_0_4_4) = v1) % 5.26/1.97 | % 5.26/1.97 +-Applying beta-rule and splitting (104), into two cases. % 5.26/1.97 |-Branch one: % 5.26/1.97 | (105) all_27_0_12 = 0 % 5.26/1.97 | % 5.26/1.97 | Equations (105) can reduce 101 to: % 5.26/1.97 | (42) $false % 5.26/1.97 | % 5.26/1.97 |-The branch is then unsatisfiable % 5.26/1.97 |-Branch two: % 5.26/1.97 | (101) ~ (all_27_0_12 = 0) % 5.26/1.97 | (108) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_27_1_13, all_0_2_2) = v0 & member(all_27_1_13, all_0_4_4) = v1) % 5.26/1.97 | % 5.26/1.97 | Instantiating (108) with all_48_0_14, all_48_1_15 yields: % 5.26/1.97 | (109) ~ (all_48_0_14 = 0) & ~ (all_48_1_15 = 0) & member(all_27_1_13, all_0_2_2) = all_48_1_15 & member(all_27_1_13, all_0_4_4) = all_48_0_14 % 5.26/1.97 | % 5.26/1.97 | Applying alpha-rule on (109) yields: % 5.26/1.97 | (110) ~ (all_48_0_14 = 0) % 5.26/1.97 | (111) ~ (all_48_1_15 = 0) % 5.26/1.97 | (112) member(all_27_1_13, all_0_2_2) = all_48_1_15 % 5.26/1.98 | (113) member(all_27_1_13, all_0_4_4) = all_48_0_14 % 5.26/1.98 | % 5.26/1.98 | Instantiating formula (26) with all_27_1_13, all_0_4_4, all_48_0_14, 0 and discharging atoms member(all_27_1_13, all_0_4_4) = all_48_0_14, yields: % 5.26/1.98 | (114) all_48_0_14 = 0 | ~ (member(all_27_1_13, all_0_4_4) = 0) % 5.26/1.98 | % 5.26/1.98 | Instantiating formula (13) with all_48_1_15, all_0_2_2, all_0_3_3, all_0_4_4, all_27_1_13 and discharging atoms difference(all_0_3_3, all_0_4_4) = all_0_2_2, member(all_27_1_13, all_0_2_2) = all_48_1_15, yields: % 5.26/1.98 | (115) all_48_1_15 = 0 | ? [v0] : ? [v1] : (member(all_27_1_13, all_0_3_3) = v0 & member(all_27_1_13, all_0_4_4) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 5.26/1.98 | % 5.26/1.98 +-Applying beta-rule and splitting (114), into two cases. % 5.26/1.98 |-Branch one: % 5.26/1.98 | (116) ~ (member(all_27_1_13, all_0_4_4) = 0) % 5.26/1.98 | % 5.26/1.98 +-Applying beta-rule and splitting (115), into two cases. % 5.26/1.98 |-Branch one: % 5.26/1.98 | (117) all_48_1_15 = 0 % 5.26/1.98 | % 5.26/1.98 | Equations (117) can reduce 111 to: % 5.26/1.98 | (42) $false % 5.26/1.98 | % 5.26/1.98 |-The branch is then unsatisfiable % 5.26/1.98 |-Branch two: % 5.26/1.98 | (111) ~ (all_48_1_15 = 0) % 5.26/1.98 | (120) ? [v0] : ? [v1] : (member(all_27_1_13, all_0_3_3) = v0 & member(all_27_1_13, all_0_4_4) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 5.26/1.98 | % 5.26/1.98 | Instantiating (120) with all_73_0_16, all_73_1_17 yields: % 5.26/1.98 | (121) member(all_27_1_13, all_0_3_3) = all_73_1_17 & member(all_27_1_13, all_0_4_4) = all_73_0_16 & ( ~ (all_73_1_17 = 0) | all_73_0_16 = 0) % 5.26/1.98 | % 5.26/1.98 | Applying alpha-rule on (121) yields: % 5.26/1.98 | (122) member(all_27_1_13, all_0_3_3) = all_73_1_17 % 5.26/1.98 | (123) member(all_27_1_13, all_0_4_4) = all_73_0_16 % 5.26/1.98 | (124) ~ (all_73_1_17 = 0) | all_73_0_16 = 0 % 5.26/1.98 | % 5.26/1.98 | Instantiating formula (26) with all_27_1_13, all_0_3_3, all_73_1_17, 0 and discharging atoms member(all_27_1_13, all_0_3_3) = all_73_1_17, member(all_27_1_13, all_0_3_3) = 0, yields: % 5.26/1.98 | (125) all_73_1_17 = 0 % 5.26/1.98 | % 5.26/1.98 | Instantiating formula (26) with all_27_1_13, all_0_4_4, all_73_0_16, all_48_0_14 and discharging atoms member(all_27_1_13, all_0_4_4) = all_73_0_16, member(all_27_1_13, all_0_4_4) = all_48_0_14, yields: % 5.26/1.98 | (126) all_73_0_16 = all_48_0_14 % 5.26/1.98 | % 5.26/1.98 | Using (123) and (116) yields: % 5.26/1.98 | (127) ~ (all_73_0_16 = 0) % 5.26/1.98 | % 5.26/1.98 | Equations (126) can reduce 127 to: % 5.26/1.98 | (110) ~ (all_48_0_14 = 0) % 5.26/1.98 | % 5.26/1.98 +-Applying beta-rule and splitting (124), into two cases. % 5.26/1.98 |-Branch one: % 5.26/1.98 | (129) ~ (all_73_1_17 = 0) % 5.26/1.98 | % 5.26/1.98 | Equations (125) can reduce 129 to: % 5.26/1.98 | (42) $false % 5.26/1.98 | % 5.26/1.98 |-The branch is then unsatisfiable % 5.26/1.98 |-Branch two: % 5.26/1.98 | (125) all_73_1_17 = 0 % 5.26/1.98 | (132) all_73_0_16 = 0 % 5.26/1.98 | % 5.26/1.98 | Combining equations (132,126) yields a new equation: % 5.26/1.98 | (133) all_48_0_14 = 0 % 5.26/1.98 | % 5.26/1.98 | Equations (133) can reduce 110 to: % 5.26/1.98 | (42) $false % 5.26/1.98 | % 5.26/1.98 |-The branch is then unsatisfiable % 5.26/1.98 |-Branch two: % 5.26/1.98 | (135) member(all_27_1_13, all_0_4_4) = 0 % 5.26/1.98 | (133) all_48_0_14 = 0 % 5.26/1.98 | % 5.26/1.98 | Equations (133) can reduce 110 to: % 5.26/1.98 | (42) $false % 5.26/1.98 | % 5.26/1.98 |-The branch is then unsatisfiable % 5.26/1.98 |-Branch two: % 5.26/1.98 | (96) all_10_0_5 = 0 % 5.26/1.98 | (53) ~ (all_10_1_6 = 0) % 5.26/1.98 | % 5.26/1.98 | Equations (54) can reduce 53 to: % 5.26/1.98 | (42) $false % 5.26/1.98 | % 5.26/1.98 |-The branch is then unsatisfiable % 5.26/1.98 % SZS output end Proof for theBenchmark % 5.26/1.98 % 5.26/1.98 1395ms %------------------------------------------------------------------------------