%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 00:16:04 EDT 2022 % Result : Theorem 3.18s 1.44s % Output : Proof 5.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jul 10 07:03:16 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.58 ____ _ % 0.19/0.58 ___ / __ \_____(_)___ ________ __________ % 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.58 % 0.19/0.58 A Theorem Prover for First-Order Logic % 0.19/0.58 (ePrincess v.1.0) % 0.19/0.58 % 0.19/0.58 (c) Philipp Rümmer, 2009-2015 % 0.19/0.58 (c) Peter Backeman, 2014-2015 % 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.58 Bug reports to peter@backeman.se % 0.19/0.58 % 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.58 % 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.50/0.90 Prover 0: Preprocessing ... % 1.98/1.08 Prover 0: Warning: ignoring some quantifiers % 1.98/1.10 Prover 0: Constructing countermodel ... % 2.42/1.24 Prover 0: gave up % 2.42/1.24 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 2.49/1.26 Prover 1: Preprocessing ... % 2.90/1.37 Prover 1: Constructing countermodel ... % 3.18/1.44 Prover 1: proved (200ms) % 3.18/1.44 % 3.18/1.44 No countermodel exists, formula is valid % 3.18/1.44 % SZS status Theorem for theBenchmark % 3.18/1.44 % 3.18/1.44 Generating proof ... found it (size 57) % 4.46/1.75 % 4.46/1.75 % SZS output start Proof for theBenchmark % 4.46/1.75 Assumed formulas after preprocessing and simplification: % 4.46/1.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & union(v1, v0) = v3 & union(v0, v1) = v2 & equal_set(v2, v3) = v4 & ! [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)) % 4.88/1.80 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 4.88/1.80 | (1) ~ (all_0_0_0 = 0) & union(all_0_3_3, all_0_4_4) = all_0_1_1 & 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) % 4.88/1.81 | % 4.88/1.81 | Applying alpha-rule on (1) yields: % 4.88/1.81 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.88/1.81 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 4.88/1.81 | (4) ! [v0] : ~ (member(v0, empty_set) = 0) % 4.88/1.81 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 4.88/1.81 | (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))) % 4.88/1.81 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 4.88/1.81 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 4.88/1.81 | (9) ! [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)) % 4.88/1.81 | (10) ! [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)))) % 4.88/1.81 | (11) ~ (all_0_0_0 = 0) % 4.88/1.81 | (12) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 4.88/1.81 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 4.88/1.81 | (14) ! [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)) % 4.88/1.81 | (15) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 4.88/1.81 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.88/1.81 | (17) ! [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)) % 4.88/1.82 | (18) ! [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))) % 4.88/1.82 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.88/1.82 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 4.88/1.82 | (21) union(all_0_3_3, all_0_4_4) = all_0_1_1 % 4.88/1.82 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.88/1.82 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 4.88/1.82 | (24) ! [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)) % 4.88/1.82 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 4.88/1.82 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 4.88/1.82 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 4.88/1.82 | (28) equal_set(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.88/1.82 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 4.88/1.82 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.88/1.82 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.88/1.82 | (32) union(all_0_4_4, all_0_3_3) = all_0_2_2 % 4.88/1.82 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.05/1.82 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 5.05/1.82 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 5.05/1.82 | (36) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 5.05/1.82 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 5.05/1.82 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 5.05/1.82 | % 5.05/1.82 | Instantiating formula (15) 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: % 5.05/1.83 | (39) 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))) % 5.05/1.83 | % 5.05/1.83 +-Applying beta-rule and splitting (39), into two cases. % 5.05/1.83 |-Branch one: % 5.05/1.83 | (40) all_0_0_0 = 0 % 5.05/1.83 | % 5.05/1.83 | Equations (40) can reduce 11 to: % 5.05/1.83 | (41) $false % 5.05/1.83 | % 5.05/1.83 |-The branch is then unsatisfiable % 5.05/1.83 |-Branch two: % 5.05/1.83 | (11) ~ (all_0_0_0 = 0) % 5.05/1.83 | (43) ? [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))) % 5.05/1.83 | % 5.05/1.83 | Instantiating (43) with all_10_0_5, all_10_1_6 yields: % 5.05/1.83 | (44) subset(all_0_1_1, all_0_2_2) = all_10_0_5 & subset(all_0_2_2, all_0_1_1) = all_10_1_6 & ( ~ (all_10_0_5 = 0) | ~ (all_10_1_6 = 0)) % 5.05/1.83 | % 5.05/1.83 | Applying alpha-rule on (44) yields: % 5.05/1.83 | (45) subset(all_0_1_1, all_0_2_2) = all_10_0_5 % 5.05/1.83 | (46) subset(all_0_2_2, all_0_1_1) = all_10_1_6 % 5.05/1.83 | (47) ~ (all_10_0_5 = 0) | ~ (all_10_1_6 = 0) % 5.05/1.83 | % 5.05/1.83 | Instantiating formula (12) with all_10_0_5, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = all_10_0_5, yields: % 5.05/1.83 | (48) all_10_0_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1) % 5.05/1.83 | % 5.05/1.83 | Instantiating formula (12) with all_10_1_6, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = all_10_1_6, yields: % 5.05/1.83 | (49) all_10_1_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 5.05/1.83 | % 5.05/1.83 +-Applying beta-rule and splitting (47), into two cases. % 5.05/1.83 |-Branch one: % 5.05/1.83 | (50) ~ (all_10_0_5 = 0) % 5.05/1.83 | % 5.05/1.83 +-Applying beta-rule and splitting (48), into two cases. % 5.05/1.83 |-Branch one: % 5.05/1.83 | (51) all_10_0_5 = 0 % 5.05/1.83 | % 5.05/1.83 | Equations (51) can reduce 50 to: % 5.05/1.83 | (41) $false % 5.05/1.83 | % 5.05/1.83 |-The branch is then unsatisfiable % 5.05/1.83 |-Branch two: % 5.05/1.83 | (50) ~ (all_10_0_5 = 0) % 5.05/1.83 | (54) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1) % 5.05/1.83 | % 5.05/1.83 | Instantiating (54) with all_23_0_7, all_23_1_8 yields: % 5.05/1.83 | (55) ~ (all_23_0_7 = 0) & member(all_23_1_8, all_0_1_1) = 0 & member(all_23_1_8, all_0_2_2) = all_23_0_7 % 5.05/1.83 | % 5.05/1.83 | Applying alpha-rule on (55) yields: % 5.05/1.83 | (56) ~ (all_23_0_7 = 0) % 5.05/1.83 | (57) member(all_23_1_8, all_0_1_1) = 0 % 5.05/1.83 | (58) member(all_23_1_8, all_0_2_2) = all_23_0_7 % 5.05/1.83 | % 5.05/1.83 | Instantiating formula (6) with all_0_1_1, all_0_4_4, all_0_3_3, all_23_1_8 and discharging atoms union(all_0_3_3, all_0_4_4) = all_0_1_1, member(all_23_1_8, all_0_1_1) = 0, yields: % 5.05/1.83 | (59) ? [v0] : ? [v1] : (member(all_23_1_8, all_0_3_3) = v0 & member(all_23_1_8, all_0_4_4) = v1 & (v1 = 0 | v0 = 0)) % 5.05/1.83 | % 5.05/1.83 | Instantiating formula (24) with all_23_0_7, all_0_2_2, all_0_3_3, all_0_4_4, all_23_1_8 and discharging atoms union(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_23_1_8, all_0_2_2) = all_23_0_7, yields: % 5.05/1.83 | (60) all_23_0_7 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_23_1_8, all_0_3_3) = v1 & member(all_23_1_8, all_0_4_4) = v0) % 5.05/1.83 | % 5.05/1.83 | Instantiating (59) with all_38_0_9, all_38_1_10 yields: % 5.05/1.83 | (61) member(all_23_1_8, all_0_3_3) = all_38_1_10 & member(all_23_1_8, all_0_4_4) = all_38_0_9 & (all_38_0_9 = 0 | all_38_1_10 = 0) % 5.05/1.83 | % 5.05/1.83 | Applying alpha-rule on (61) yields: % 5.05/1.83 | (62) member(all_23_1_8, all_0_3_3) = all_38_1_10 % 5.05/1.83 | (63) member(all_23_1_8, all_0_4_4) = all_38_0_9 % 5.05/1.83 | (64) all_38_0_9 = 0 | all_38_1_10 = 0 % 5.05/1.83 | % 5.05/1.83 +-Applying beta-rule and splitting (60), into two cases. % 5.05/1.83 |-Branch one: % 5.05/1.84 | (65) all_23_0_7 = 0 % 5.05/1.84 | % 5.05/1.84 | Equations (65) can reduce 56 to: % 5.05/1.84 | (41) $false % 5.05/1.84 | % 5.05/1.84 |-The branch is then unsatisfiable % 5.05/1.84 |-Branch two: % 5.05/1.84 | (56) ~ (all_23_0_7 = 0) % 5.05/1.84 | (68) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_23_1_8, all_0_3_3) = v1 & member(all_23_1_8, all_0_4_4) = v0) % 5.05/1.84 | % 5.05/1.84 | Instantiating (68) with all_44_0_11, all_44_1_12 yields: % 5.05/1.84 | (69) ~ (all_44_0_11 = 0) & ~ (all_44_1_12 = 0) & member(all_23_1_8, all_0_3_3) = all_44_0_11 & member(all_23_1_8, all_0_4_4) = all_44_1_12 % 5.05/1.84 | % 5.05/1.84 | Applying alpha-rule on (69) yields: % 5.05/1.84 | (70) ~ (all_44_0_11 = 0) % 5.05/1.84 | (71) ~ (all_44_1_12 = 0) % 5.05/1.84 | (72) member(all_23_1_8, all_0_3_3) = all_44_0_11 % 5.05/1.84 | (73) member(all_23_1_8, all_0_4_4) = all_44_1_12 % 5.05/1.84 | % 5.05/1.84 | Instantiating formula (16) with all_23_1_8, all_0_3_3, all_38_1_10, all_44_0_11 and discharging atoms member(all_23_1_8, all_0_3_3) = all_44_0_11, member(all_23_1_8, all_0_3_3) = all_38_1_10, yields: % 5.05/1.84 | (74) all_44_0_11 = all_38_1_10 % 5.05/1.84 | % 5.05/1.84 | Instantiating formula (16) with all_23_1_8, all_0_4_4, all_38_0_9, all_44_1_12 and discharging atoms member(all_23_1_8, all_0_4_4) = all_44_1_12, member(all_23_1_8, all_0_4_4) = all_38_0_9, yields: % 5.12/1.84 | (75) all_44_1_12 = all_38_0_9 % 5.12/1.84 | % 5.12/1.84 | Equations (74) can reduce 70 to: % 5.12/1.84 | (76) ~ (all_38_1_10 = 0) % 5.12/1.84 | % 5.12/1.84 | Equations (75) can reduce 71 to: % 5.12/1.84 | (77) ~ (all_38_0_9 = 0) % 5.12/1.84 | % 5.12/1.84 +-Applying beta-rule and splitting (64), into two cases. % 5.12/1.84 |-Branch one: % 5.12/1.84 | (78) all_38_0_9 = 0 % 5.12/1.84 | % 5.12/1.84 | Equations (78) can reduce 77 to: % 5.12/1.84 | (41) $false % 5.12/1.84 | % 5.12/1.84 |-The branch is then unsatisfiable % 5.12/1.84 |-Branch two: % 5.12/1.84 | (77) ~ (all_38_0_9 = 0) % 5.12/1.84 | (81) all_38_1_10 = 0 % 5.12/1.84 | % 5.12/1.84 | Equations (81) can reduce 76 to: % 5.12/1.84 | (41) $false % 5.12/1.84 | % 5.12/1.84 |-The branch is then unsatisfiable % 5.12/1.84 |-Branch two: % 5.12/1.84 | (51) all_10_0_5 = 0 % 5.12/1.84 | (84) ~ (all_10_1_6 = 0) % 5.12/1.84 | % 5.12/1.84 +-Applying beta-rule and splitting (49), into two cases. % 5.12/1.84 |-Branch one: % 5.12/1.84 | (85) all_10_1_6 = 0 % 5.12/1.84 | % 5.12/1.84 | Equations (85) can reduce 84 to: % 5.12/1.84 | (41) $false % 5.12/1.84 | % 5.12/1.84 |-The branch is then unsatisfiable % 5.12/1.84 |-Branch two: % 5.12/1.84 | (84) ~ (all_10_1_6 = 0) % 5.12/1.84 | (88) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0) % 5.12/1.84 | % 5.12/1.84 | Instantiating (88) with all_23_0_13, all_23_1_14 yields: % 5.12/1.84 | (89) ~ (all_23_0_13 = 0) & member(all_23_1_14, all_0_1_1) = all_23_0_13 & member(all_23_1_14, all_0_2_2) = 0 % 5.12/1.84 | % 5.12/1.84 | Applying alpha-rule on (89) yields: % 5.12/1.84 | (90) ~ (all_23_0_13 = 0) % 5.12/1.84 | (91) member(all_23_1_14, all_0_1_1) = all_23_0_13 % 5.12/1.84 | (92) member(all_23_1_14, all_0_2_2) = 0 % 5.12/1.84 | % 5.12/1.84 | Instantiating formula (24) with all_23_0_13, all_0_1_1, all_0_4_4, all_0_3_3, all_23_1_14 and discharging atoms union(all_0_3_3, all_0_4_4) = all_0_1_1, member(all_23_1_14, all_0_1_1) = all_23_0_13, yields: % 5.12/1.84 | (93) all_23_0_13 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_23_1_14, all_0_3_3) = v0 & member(all_23_1_14, all_0_4_4) = v1) % 5.12/1.84 | % 5.12/1.84 | Instantiating formula (6) with all_0_2_2, all_0_3_3, all_0_4_4, all_23_1_14 and discharging atoms union(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_23_1_14, all_0_2_2) = 0, yields: % 5.12/1.84 | (94) ? [v0] : ? [v1] : (member(all_23_1_14, all_0_3_3) = v1 & member(all_23_1_14, all_0_4_4) = v0 & (v1 = 0 | v0 = 0)) % 5.12/1.84 | % 5.12/1.84 | Instantiating (94) with all_38_0_15, all_38_1_16 yields: % 5.12/1.84 | (95) member(all_23_1_14, all_0_3_3) = all_38_0_15 & member(all_23_1_14, all_0_4_4) = all_38_1_16 & (all_38_0_15 = 0 | all_38_1_16 = 0) % 5.12/1.84 | % 5.12/1.84 | Applying alpha-rule on (95) yields: % 5.12/1.84 | (96) member(all_23_1_14, all_0_3_3) = all_38_0_15 % 5.12/1.84 | (97) member(all_23_1_14, all_0_4_4) = all_38_1_16 % 5.12/1.85 | (98) all_38_0_15 = 0 | all_38_1_16 = 0 % 5.12/1.85 | % 5.12/1.85 +-Applying beta-rule and splitting (93), into two cases. % 5.12/1.85 |-Branch one: % 5.12/1.85 | (99) all_23_0_13 = 0 % 5.12/1.85 | % 5.12/1.85 | Equations (99) can reduce 90 to: % 5.12/1.85 | (41) $false % 5.12/1.85 | % 5.12/1.85 |-The branch is then unsatisfiable % 5.12/1.85 |-Branch two: % 5.12/1.85 | (90) ~ (all_23_0_13 = 0) % 5.12/1.85 | (102) ? [v0] : ? [v1] : ( ~ (v1 = 0) & ~ (v0 = 0) & member(all_23_1_14, all_0_3_3) = v0 & member(all_23_1_14, all_0_4_4) = v1) % 5.12/1.85 | % 5.12/1.85 | Instantiating (102) with all_44_0_17, all_44_1_18 yields: % 5.12/1.85 | (103) ~ (all_44_0_17 = 0) & ~ (all_44_1_18 = 0) & member(all_23_1_14, all_0_3_3) = all_44_1_18 & member(all_23_1_14, all_0_4_4) = all_44_0_17 % 5.12/1.85 | % 5.12/1.85 | Applying alpha-rule on (103) yields: % 5.12/1.85 | (104) ~ (all_44_0_17 = 0) % 5.12/1.85 | (105) ~ (all_44_1_18 = 0) % 5.12/1.85 | (106) member(all_23_1_14, all_0_3_3) = all_44_1_18 % 5.12/1.85 | (107) member(all_23_1_14, all_0_4_4) = all_44_0_17 % 5.12/1.85 | % 5.12/1.85 | Instantiating formula (16) with all_23_1_14, all_0_3_3, all_38_0_15, all_44_1_18 and discharging atoms member(all_23_1_14, all_0_3_3) = all_44_1_18, member(all_23_1_14, all_0_3_3) = all_38_0_15, yields: % 5.12/1.85 | (108) all_44_1_18 = all_38_0_15 % 5.12/1.85 | % 5.12/1.85 | Instantiating formula (16) with all_23_1_14, all_0_4_4, all_38_1_16, all_44_0_17 and discharging atoms member(all_23_1_14, all_0_4_4) = all_44_0_17, member(all_23_1_14, all_0_4_4) = all_38_1_16, yields: % 5.12/1.85 | (109) all_44_0_17 = all_38_1_16 % 5.12/1.85 | % 5.12/1.85 | Equations (109) can reduce 104 to: % 5.12/1.85 | (110) ~ (all_38_1_16 = 0) % 5.12/1.85 | % 5.12/1.85 | Equations (108) can reduce 105 to: % 5.12/1.85 | (111) ~ (all_38_0_15 = 0) % 5.12/1.85 | % 5.12/1.85 +-Applying beta-rule and splitting (98), into two cases. % 5.12/1.85 |-Branch one: % 5.12/1.85 | (112) all_38_0_15 = 0 % 5.12/1.85 | % 5.12/1.85 | Equations (112) can reduce 111 to: % 5.12/1.85 | (41) $false % 5.12/1.85 | % 5.12/1.85 |-The branch is then unsatisfiable % 5.12/1.85 |-Branch two: % 5.12/1.85 | (111) ~ (all_38_0_15 = 0) % 5.12/1.85 | (115) all_38_1_16 = 0 % 5.12/1.85 | % 5.12/1.85 | Equations (115) can reduce 110 to: % 5.12/1.85 | (41) $false % 5.12/1.85 | % 5.12/1.85 |-The branch is then unsatisfiable % 5.12/1.85 % SZS output end Proof for theBenchmark % 5.12/1.85 % 5.12/1.85 1265ms %------------------------------------------------------------------------------