%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET703+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 00:21:30 EDT 2022 % Result : Theorem 3.86s 1.56s % Output : Proof 5.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET703+4 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % 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 : Mon Jul 11 06:12:25 EDT 2022 % 0.12/0.33 % CPUTime : % 0.49/0.58 ____ _ % 0.49/0.58 ___ / __ \_____(_)___ ________ __________ % 0.49/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.49/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.49/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.49/0.58 % 0.49/0.58 A Theorem Prover for First-Order Logic % 0.49/0.58 (ePrincess v.1.0) % 0.49/0.58 % 0.49/0.58 (c) Philipp Rümmer, 2009-2015 % 0.49/0.58 (c) Peter Backeman, 2014-2015 % 0.49/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.49/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.49/0.58 Bug reports to peter@backeman.se % 0.49/0.58 % 0.49/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.49/0.58 % 0.49/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.76/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.51/0.90 Prover 0: Preprocessing ... % 2.01/1.08 Prover 0: Warning: ignoring some quantifiers % 2.08/1.10 Prover 0: Constructing countermodel ... % 3.03/1.35 Prover 0: gave up % 3.03/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.10/1.38 Prover 1: Preprocessing ... % 3.50/1.47 Prover 1: Constructing countermodel ... % 3.86/1.55 Prover 1: proved (201ms) % 3.86/1.56 % 3.86/1.56 No countermodel exists, formula is valid % 3.86/1.56 % SZS status Theorem for theBenchmark % 3.86/1.56 % 3.86/1.56 Generating proof ... found it (size 71) % 5.02/1.84 % 5.02/1.84 % SZS output start Proof for theBenchmark % 5.02/1.84 Assumed formulas after preprocessing and simplification: % 5.02/1.84 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & unordered_pair(v0, v1) = v5 & singleton(v1) = v3 & singleton(v0) = v2 & union(v2, v3) = v4 & equal_set(v4, v5) = v6 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v10) = v11) | ~ (member(v7, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v12 & member(v7, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v7, v9) = v13 & member(v7, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = v11) | ? [v12] : ? [v13] : (member(v7, v9) = v13 & member(v7, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (product(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = 0 & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_set(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (difference(v10, v9) = v8) | ~ (difference(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (equal_set(v10, v9) = v8) | ~ (equal_set(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subset(v10, v9) = v8) | ~ (subset(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (difference(v9, v8) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v7, v9) = 0 & member(v7, v8) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (member(v7, v10) = 0) | ? [v11] : ? [v12] : (member(v7, v9) = v12 & member(v7, v8) = v11 & (v12 = 0 | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v8, v9) = v10) | ~ (member(v7, v10) = 0) | (member(v7, v9) = 0 & member(v7, v8) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (singleton(v7) = v8) | ~ (member(v7, v8) = v9)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (equal_set(v7, v8) = v9) | ? [v10] : ? [v11] : (subset(v8, v7) = v11 & subset(v7, v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (product(v9) = v8) | ~ (product(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum(v9) = v8) | ~ (sum(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v8) = v9) | ~ (member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_set(v9) = v8) | ~ (power_set(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_set(v8) = v9) | ~ (member(v7, v9) = 0) | subset(v7, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subset(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ( ~ (equal_set(v7, v8) = 0) | (subset(v8, v7) = 0 & subset(v7, v8) = 0)) & ! [v7] : ~ (member(v7, empty_set) = 0)) % 5.20/1.88 | 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 yields: % 5.20/1.88 | (1) ~ (all_0_0_0 = 0) & unordered_pair(all_0_6_6, all_0_5_5) = all_0_1_1 & singleton(all_0_5_5) = all_0_3_3 & singleton(all_0_6_6) = all_0_4_4 & union(all_0_4_4, all_0_3_3) = all_0_2_2 & equal_set(all_0_2_2, 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) % 5.20/1.90 | % 5.20/1.90 | Applying alpha-rule on (1) yields: % 5.20/1.90 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 5.20/1.90 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.20/1.90 | (4) ~ (all_0_0_0 = 0) % 5.20/1.90 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 5.20/1.90 | (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))) % 5.20/1.90 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 5.20/1.90 | (8) ! [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))) % 5.20/1.90 | (9) ! [v0] : ~ (member(v0, empty_set) = 0) % 5.20/1.90 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 5.20/1.90 | (11) ! [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)) % 5.20/1.90 | (12) union(all_0_4_4, all_0_3_3) = all_0_2_2 % 5.20/1.90 | (13) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 5.20/1.90 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 5.20/1.90 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.20/1.90 | (16) ! [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)) % 5.20/1.90 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 5.20/1.90 | (18) equal_set(all_0_2_2, all_0_1_1) = all_0_0_0 % 5.20/1.90 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 5.20/1.90 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 5.20/1.90 | (21) singleton(all_0_6_6) = all_0_4_4 % 5.20/1.90 | (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)) % 5.20/1.91 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 5.20/1.91 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.20/1.91 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 5.20/1.91 | (26) singleton(all_0_5_5) = all_0_3_3 % 5.20/1.91 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.20/1.91 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 5.20/1.91 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 5.20/1.91 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 5.20/1.91 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 5.20/1.91 | (32) unordered_pair(all_0_6_6, all_0_5_5) = all_0_1_1 % 5.20/1.91 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 5.20/1.91 | (34) ! [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)) % 5.20/1.91 | (35) ! [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)))) % 5.20/1.91 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 5.20/1.91 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 5.20/1.91 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 5.20/1.91 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 5.20/1.91 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 5.20/1.91 | % 5.20/1.91 | Instantiating formula (29) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms equal_set(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 5.20/1.91 | (41) all_0_0_0 = 0 | ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_2_2) = v1 & subset(all_0_2_2, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.20/1.91 | % 5.20/1.91 +-Applying beta-rule and splitting (41), into two cases. % 5.20/1.91 |-Branch one: % 5.20/1.91 | (42) all_0_0_0 = 0 % 5.20/1.91 | % 5.20/1.92 | Equations (42) can reduce 4 to: % 5.20/1.92 | (43) $false % 5.20/1.92 | % 5.20/1.92 |-The branch is then unsatisfiable % 5.20/1.92 |-Branch two: % 5.20/1.92 | (4) ~ (all_0_0_0 = 0) % 5.20/1.92 | (45) ? [v0] : ? [v1] : (subset(all_0_1_1, all_0_2_2) = v1 & subset(all_0_2_2, all_0_1_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.20/1.92 | % 5.20/1.92 | Instantiating (45) with all_14_0_7, all_14_1_8 yields: % 5.20/1.92 | (46) subset(all_0_1_1, all_0_2_2) = all_14_0_7 & subset(all_0_2_2, all_0_1_1) = all_14_1_8 & ( ~ (all_14_0_7 = 0) | ~ (all_14_1_8 = 0)) % 5.20/1.92 | % 5.20/1.92 | Applying alpha-rule on (46) yields: % 5.20/1.92 | (47) subset(all_0_1_1, all_0_2_2) = all_14_0_7 % 5.20/1.92 | (48) subset(all_0_2_2, all_0_1_1) = all_14_1_8 % 5.20/1.92 | (49) ~ (all_14_0_7 = 0) | ~ (all_14_1_8 = 0) % 5.20/1.92 | % 5.20/1.92 | Instantiating formula (17) with all_14_0_7, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = all_14_0_7, yields: % 5.20/1.92 | (50) all_14_0_7 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1) % 5.20/1.92 | % 5.20/1.92 | Instantiating formula (17) with all_14_1_8, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = all_14_1_8, yields: % 5.20/1.92 | (51) all_14_1_8 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 5.20/1.92 | % 5.20/1.92 +-Applying beta-rule and splitting (49), into two cases. % 5.20/1.92 |-Branch one: % 5.20/1.92 | (52) ~ (all_14_0_7 = 0) % 5.20/1.92 | % 5.20/1.92 +-Applying beta-rule and splitting (50), into two cases. % 5.20/1.92 |-Branch one: % 5.20/1.92 | (53) all_14_0_7 = 0 % 5.20/1.92 | % 5.20/1.92 | Equations (53) can reduce 52 to: % 5.20/1.92 | (43) $false % 5.20/1.92 | % 5.20/1.92 |-The branch is then unsatisfiable % 5.20/1.92 |-Branch two: % 5.20/1.92 | (52) ~ (all_14_0_7 = 0) % 5.20/1.92 | (56) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1) % 5.20/1.92 | % 5.20/1.92 | Instantiating (56) with all_31_0_9, all_31_1_10 yields: % 5.20/1.92 | (57) ~ (all_31_0_9 = 0) & member(all_31_1_10, all_0_1_1) = 0 & member(all_31_1_10, all_0_2_2) = all_31_0_9 % 5.20/1.92 | % 5.20/1.92 | Applying alpha-rule on (57) yields: % 5.20/1.92 | (58) ~ (all_31_0_9 = 0) % 5.20/1.92 | (59) member(all_31_1_10, all_0_1_1) = 0 % 5.20/1.92 | (60) member(all_31_1_10, all_0_2_2) = all_31_0_9 % 5.20/1.92 | % 5.20/1.92 | Instantiating formula (7) with all_0_1_1, all_0_5_5, all_0_6_6, all_31_1_10 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_1_1, member(all_31_1_10, all_0_1_1) = 0, yields: % 5.20/1.92 | (61) all_31_1_10 = all_0_5_5 | all_31_1_10 = all_0_6_6 % 5.20/1.92 | % 5.20/1.92 | Instantiating formula (34) with all_31_0_9, all_0_2_2, all_0_3_3, all_0_4_4, all_31_1_10 and discharging atoms union(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_31_1_10, all_0_2_2) = all_31_0_9, yields: % 5.20/1.92 | (62) all_31_0_9 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_31_1_10, all_0_3_3) = v1 & member(all_31_1_10, all_0_4_4) = v0) % 5.20/1.92 | % 5.20/1.92 +-Applying beta-rule and splitting (62), into two cases. % 5.20/1.92 |-Branch one: % 5.20/1.92 | (63) all_31_0_9 = 0 % 5.20/1.92 | % 5.20/1.92 | Equations (63) can reduce 58 to: % 5.20/1.92 | (43) $false % 5.20/1.92 | % 5.20/1.92 |-The branch is then unsatisfiable % 5.20/1.92 |-Branch two: % 5.20/1.92 | (58) ~ (all_31_0_9 = 0) % 5.20/1.92 | (66) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_31_1_10, all_0_3_3) = v1 & member(all_31_1_10, all_0_4_4) = v0) % 5.20/1.92 | % 5.20/1.92 | Instantiating (66) with all_52_0_11, all_52_1_12 yields: % 5.20/1.92 | (67) ~ (all_52_0_11 = 0) & ~ (all_52_1_12 = 0) & member(all_31_1_10, all_0_3_3) = all_52_0_11 & member(all_31_1_10, all_0_4_4) = all_52_1_12 % 5.20/1.92 | % 5.20/1.92 | Applying alpha-rule on (67) yields: % 5.20/1.92 | (68) ~ (all_52_0_11 = 0) % 5.20/1.92 | (69) ~ (all_52_1_12 = 0) % 5.20/1.92 | (70) member(all_31_1_10, all_0_3_3) = all_52_0_11 % 5.20/1.92 | (71) member(all_31_1_10, all_0_4_4) = all_52_1_12 % 5.20/1.92 | % 5.20/1.92 | Instantiating formula (19) with all_52_0_11, all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, yields: % 5.20/1.92 | (72) all_52_0_11 = 0 | ~ (member(all_0_5_5, all_0_3_3) = all_52_0_11) % 5.20/1.92 | % 5.20/1.92 | Instantiating formula (19) with all_52_1_12, all_0_4_4, all_0_6_6 and discharging atoms singleton(all_0_6_6) = all_0_4_4, yields: % 5.20/1.92 | (73) all_52_1_12 = 0 | ~ (member(all_0_6_6, all_0_4_4) = all_52_1_12) % 5.20/1.92 | % 5.20/1.92 +-Applying beta-rule and splitting (73), into two cases. % 5.20/1.92 |-Branch one: % 5.20/1.92 | (74) ~ (member(all_0_6_6, all_0_4_4) = all_52_1_12) % 5.20/1.93 | % 5.20/1.93 +-Applying beta-rule and splitting (72), into two cases. % 5.20/1.93 |-Branch one: % 5.20/1.93 | (75) ~ (member(all_0_5_5, all_0_3_3) = all_52_0_11) % 5.20/1.93 | % 5.20/1.93 | Using (70) and (75) yields: % 5.20/1.93 | (76) ~ (all_31_1_10 = all_0_5_5) % 5.20/1.93 | % 5.20/1.93 | Using (71) and (74) yields: % 5.20/1.93 | (77) ~ (all_31_1_10 = all_0_6_6) % 5.20/1.93 | % 5.20/1.93 +-Applying beta-rule and splitting (61), into two cases. % 5.20/1.93 |-Branch one: % 5.20/1.93 | (78) all_31_1_10 = all_0_5_5 % 5.20/1.93 | % 5.20/1.93 | Equations (78) can reduce 76 to: % 5.20/1.93 | (43) $false % 5.20/1.93 | % 5.20/1.93 |-The branch is then unsatisfiable % 5.20/1.93 |-Branch two: % 5.20/1.93 | (76) ~ (all_31_1_10 = all_0_5_5) % 5.20/1.93 | (81) all_31_1_10 = all_0_6_6 % 5.20/1.93 | % 5.20/1.93 | Equations (81) can reduce 77 to: % 5.20/1.93 | (43) $false % 5.20/1.93 | % 5.20/1.93 |-The branch is then unsatisfiable % 5.20/1.93 |-Branch two: % 5.20/1.93 | (83) member(all_0_5_5, all_0_3_3) = all_52_0_11 % 5.20/1.93 | (84) all_52_0_11 = 0 % 5.20/1.93 | % 5.20/1.93 | Equations (84) can reduce 68 to: % 5.20/1.93 | (43) $false % 5.20/1.93 | % 5.20/1.93 |-The branch is then unsatisfiable % 5.20/1.93 |-Branch two: % 5.20/1.93 | (86) member(all_0_6_6, all_0_4_4) = all_52_1_12 % 5.20/1.93 | (87) all_52_1_12 = 0 % 5.20/1.93 | % 5.20/1.93 | Equations (87) can reduce 69 to: % 5.20/1.93 | (43) $false % 5.20/1.93 | % 5.20/1.93 |-The branch is then unsatisfiable % 5.20/1.93 |-Branch two: % 5.20/1.93 | (53) all_14_0_7 = 0 % 5.20/1.93 | (90) ~ (all_14_1_8 = 0) % 5.20/1.93 | % 5.20/1.93 +-Applying beta-rule and splitting (51), into two cases. % 5.20/1.93 |-Branch one: % 5.20/1.93 | (91) all_14_1_8 = 0 % 5.20/1.93 | % 5.20/1.93 | Equations (91) can reduce 90 to: % 5.20/1.93 | (43) $false % 5.20/1.93 | % 5.20/1.93 |-The branch is then unsatisfiable % 5.20/1.93 |-Branch two: % 5.20/1.93 | (90) ~ (all_14_1_8 = 0) % 5.20/1.93 | (94) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 5.20/1.93 | % 5.20/1.93 | Instantiating (94) with all_31_0_13, all_31_1_14 yields: % 5.20/1.93 | (95) ~ (all_31_0_13 = 0) & member(all_31_1_14, all_0_1_1) = all_31_0_13 & member(all_31_1_14, all_0_2_2) = 0 % 5.20/1.93 | % 5.20/1.93 | Applying alpha-rule on (95) yields: % 5.20/1.93 | (96) ~ (all_31_0_13 = 0) % 5.20/1.93 | (97) member(all_31_1_14, all_0_1_1) = all_31_0_13 % 5.20/1.93 | (98) member(all_31_1_14, all_0_2_2) = 0 % 5.20/1.93 | % 5.20/1.93 | Instantiating formula (37) with all_31_0_13, all_0_1_1, all_0_6_6, all_0_5_5 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_1_1, yields: % 5.20/1.93 | (99) all_31_0_13 = 0 | ~ (member(all_0_5_5, all_0_1_1) = all_31_0_13) % 5.20/1.93 | % 5.20/1.93 | Instantiating formula (31) with all_31_0_13, all_0_1_1, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_1_1, yields: % 5.20/1.93 | (100) all_31_0_13 = 0 | ~ (member(all_0_6_6, all_0_1_1) = all_31_0_13) % 5.20/1.93 | % 5.20/1.93 | Instantiating formula (39) with all_0_3_3, all_0_5_5, all_31_1_14 and discharging atoms singleton(all_0_5_5) = all_0_3_3, yields: % 5.20/1.93 | (101) all_31_1_14 = all_0_5_5 | ~ (member(all_31_1_14, all_0_3_3) = 0) % 5.20/1.93 | % 5.20/1.93 | Instantiating formula (39) with all_0_4_4, all_0_6_6, all_31_1_14 and discharging atoms singleton(all_0_6_6) = all_0_4_4, yields: % 5.20/1.93 | (102) all_31_1_14 = all_0_6_6 | ~ (member(all_31_1_14, all_0_4_4) = 0) % 5.20/1.93 | % 5.20/1.93 +-Applying beta-rule and splitting (99), into two cases. % 5.20/1.93 |-Branch one: % 5.20/1.93 | (103) ~ (member(all_0_5_5, all_0_1_1) = all_31_0_13) % 5.20/1.93 | % 5.20/1.93 +-Applying beta-rule and splitting (100), into two cases. % 5.20/1.93 |-Branch one: % 5.20/1.93 | (104) ~ (member(all_0_6_6, all_0_1_1) = all_31_0_13) % 5.20/1.93 | % 5.20/1.93 | Using (97) and (103) yields: % 5.20/1.93 | (105) ~ (all_31_1_14 = all_0_5_5) % 5.20/1.93 | % 5.20/1.93 | Using (97) and (104) yields: % 5.20/1.93 | (106) ~ (all_31_1_14 = all_0_6_6) % 5.20/1.93 | % 5.20/1.93 +-Applying beta-rule and splitting (101), into two cases. % 5.20/1.93 |-Branch one: % 5.20/1.93 | (107) ~ (member(all_31_1_14, all_0_3_3) = 0) % 5.20/1.93 | % 5.20/1.93 +-Applying beta-rule and splitting (102), into two cases. % 5.20/1.93 |-Branch one: % 5.20/1.93 | (108) ~ (member(all_31_1_14, all_0_4_4) = 0) % 5.20/1.94 | % 5.20/1.94 | Instantiating formula (6) with all_0_2_2, all_0_3_3, all_0_4_4, all_31_1_14 and discharging atoms union(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_31_1_14, all_0_2_2) = 0, yields: % 5.20/1.94 | (109) ? [v0] : ? [v1] : (member(all_31_1_14, all_0_3_3) = v1 & member(all_31_1_14, all_0_4_4) = v0 & (v1 = 0 | v0 = 0)) % 5.20/1.94 | % 5.20/1.94 | Instantiating (109) with all_70_0_15, all_70_1_16 yields: % 5.56/1.94 | (110) member(all_31_1_14, all_0_3_3) = all_70_0_15 & member(all_31_1_14, all_0_4_4) = all_70_1_16 & (all_70_0_15 = 0 | all_70_1_16 = 0) % 5.56/1.94 | % 5.56/1.94 | Applying alpha-rule on (110) yields: % 5.56/1.94 | (111) member(all_31_1_14, all_0_3_3) = all_70_0_15 % 5.56/1.94 | (112) member(all_31_1_14, all_0_4_4) = all_70_1_16 % 5.56/1.94 | (113) all_70_0_15 = 0 | all_70_1_16 = 0 % 5.56/1.94 | % 5.56/1.94 | Using (111) and (107) yields: % 5.56/1.94 | (114) ~ (all_70_0_15 = 0) % 5.56/1.94 | % 5.56/1.94 | Using (112) and (108) yields: % 5.56/1.94 | (115) ~ (all_70_1_16 = 0) % 5.56/1.94 | % 5.56/1.94 +-Applying beta-rule and splitting (113), into two cases. % 5.56/1.94 |-Branch one: % 5.56/1.94 | (116) all_70_0_15 = 0 % 5.56/1.94 | % 5.56/1.94 | Equations (116) can reduce 114 to: % 5.56/1.94 | (43) $false % 5.56/1.94 | % 5.56/1.94 |-The branch is then unsatisfiable % 5.56/1.94 |-Branch two: % 5.56/1.94 | (114) ~ (all_70_0_15 = 0) % 5.56/1.94 | (119) all_70_1_16 = 0 % 5.56/1.94 | % 5.56/1.94 | Equations (119) can reduce 115 to: % 5.56/1.94 | (43) $false % 5.56/1.94 | % 5.56/1.94 |-The branch is then unsatisfiable % 5.56/1.94 |-Branch two: % 5.56/1.94 | (121) member(all_31_1_14, all_0_4_4) = 0 % 5.56/1.94 | (122) all_31_1_14 = all_0_6_6 % 5.56/1.94 | % 5.56/1.94 | Equations (122) can reduce 106 to: % 5.56/1.94 | (43) $false % 5.56/1.94 | % 5.56/1.94 |-The branch is then unsatisfiable % 5.56/1.94 |-Branch two: % 5.56/1.94 | (124) member(all_31_1_14, all_0_3_3) = 0 % 5.56/1.94 | (125) all_31_1_14 = all_0_5_5 % 5.56/1.94 | % 5.56/1.94 | Equations (125) can reduce 105 to: % 5.56/1.94 | (43) $false % 5.56/1.94 | % 5.56/1.94 |-The branch is then unsatisfiable % 5.56/1.94 |-Branch two: % 5.56/1.94 | (127) member(all_0_6_6, all_0_1_1) = all_31_0_13 % 5.56/1.94 | (128) all_31_0_13 = 0 % 5.56/1.94 | % 5.56/1.94 | Equations (128) can reduce 96 to: % 5.56/1.94 | (43) $false % 5.56/1.94 | % 5.56/1.94 |-The branch is then unsatisfiable % 5.56/1.94 |-Branch two: % 5.56/1.94 | (130) member(all_0_5_5, all_0_1_1) = all_31_0_13 % 5.56/1.94 | (128) all_31_0_13 = 0 % 5.56/1.94 | % 5.56/1.94 | Equations (128) can reduce 96 to: % 5.56/1.94 | (43) $false % 5.56/1.94 | % 5.56/1.94 |-The branch is then unsatisfiable % 5.56/1.94 % SZS output end Proof for theBenchmark % 5.56/1.94 % 5.56/1.94 1350ms %------------------------------------------------------------------------------