%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET351+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n011.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 00:19:09 EDT 2022 % Result : Theorem 3.84s 1.54s % Output : Proof 5.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET351+4 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n011.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jul 11 04:11:57 EDT 2022 % 0.12/0.34 % CPUTime : % 0.55/0.59 ____ _ % 0.55/0.59 ___ / __ \_____(_)___ ________ __________ % 0.55/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.59 % 0.55/0.59 A Theorem Prover for First-Order Logic % 0.55/0.59 (ePrincess v.1.0) % 0.55/0.59 % 0.55/0.59 (c) Philipp Rümmer, 2009-2015 % 0.55/0.59 (c) Peter Backeman, 2014-2015 % 0.55/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.59 Bug reports to peter@backeman.se % 0.55/0.59 % 0.55/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.59 % 0.55/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.53/0.90 Prover 0: Preprocessing ... % 2.06/1.09 Prover 0: Warning: ignoring some quantifiers % 2.06/1.11 Prover 0: Constructing countermodel ... % 2.92/1.35 Prover 0: gave up % 2.92/1.35 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.07/1.37 Prover 1: Preprocessing ... % 3.44/1.47 Prover 1: Constructing countermodel ... % 3.84/1.54 Prover 1: proved (185ms) % 3.84/1.54 % 3.84/1.54 No countermodel exists, formula is valid % 3.84/1.54 % SZS status Theorem for theBenchmark % 3.84/1.54 % 3.84/1.54 Generating proof ... found it (size 41) % 4.87/1.79 % 4.87/1.79 % SZS output start Proof for theBenchmark % 4.87/1.79 Assumed formulas after preprocessing and simplification: % 4.87/1.79 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & sum(v1) = v2 & singleton(v0) = v1 & equal_set(v2, v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v5) = v6) | ~ (member(v4, v7) = v8) | ~ (member(v4, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (difference(v6, v5) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : (member(v4, v6) = v9 & member(v4, v5) = v10 & ( ~ (v9 = 0) | v10 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (union(v5, v6) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & ~ (v9 = 0) & member(v4, v6) = v10 & member(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (intersection(v5, v6) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : (member(v4, v6) = v10 & member(v4, v5) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (sum(v5) = v6) | ~ (member(v4, v8) = 0) | ~ (member(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (product(v5) = v6) | ~ (member(v4, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = 0 & member(v4, v8) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unordered_pair(v5, v4) = v6) | ~ (member(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unordered_pair(v4, v5) = v6) | ~ (member(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (power_set(v5) = v6) | ~ (member(v4, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & subset(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v4 | v5 = v4 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unordered_pair(v7, v6) = v5) | ~ (unordered_pair(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (difference(v7, v6) = v5) | ~ (difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union(v7, v6) = v5) | ~ (union(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection(v7, v6) = v5) | ~ (intersection(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_set(v7, v6) = v5) | ~ (equal_set(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (subset(v7, v6) = v5) | ~ (subset(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (member(v7, v6) = v5) | ~ (member(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v6, v5) = v7) | ~ (member(v4, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v4, v6) = 0 & member(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | ~ (member(v4, v7) = 0) | ? [v8] : ? [v9] : (member(v4, v6) = v9 & member(v4, v5) = v8 & (v9 = 0 | v8 = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v5, v6) = v7) | ~ (member(v4, v7) = 0) | (member(v4, v6) = 0 & member(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (singleton(v4) = v5) | ~ (member(v4, v5) = v6)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_set(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v5, v4) = v8 & subset(v4, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8 & member(v7, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (product(v6) = v5) | ~ (product(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (sum(v6) = v5) | ~ (sum(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (singleton(v6) = v5) | ~ (singleton(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (singleton(v5) = v6) | ~ (member(v4, v6) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (power_set(v6) = v5) | ~ (power_set(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sum(v5) = v6) | ~ (member(v4, v6) = 0) | ? [v7] : (member(v7, v5) = 0 & member(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (power_set(v5) = v6) | ~ (member(v4, v6) = 0) | subset(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset(v4, v5) = 0) | ~ (member(v6, v4) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ( ~ (equal_set(v4, v5) = 0) | (subset(v5, v4) = 0 & subset(v4, v5) = 0)) & ! [v4] : ~ (member(v4, empty_set) = 0)) % 5.05/1.83 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 5.05/1.83 | (1) ~ (all_0_0_0 = 0) & sum(all_0_2_2) = all_0_1_1 & singleton(all_0_3_3) = all_0_2_2 & equal_set(all_0_1_1, all_0_3_3) = 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) % 5.10/1.84 | % 5.10/1.84 | Applying alpha-rule on (1) yields: % 5.10/1.84 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) % 5.10/1.84 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 5.10/1.84 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 5.10/1.84 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) % 5.10/1.84 | (6) sum(all_0_2_2) = all_0_1_1 % 5.10/1.84 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) % 5.10/1.84 | (8) singleton(all_0_3_3) = all_0_2_2 % 5.10/1.84 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.10/1.84 | (10) ! [v0] : ~ (member(v0, empty_set) = 0) % 5.10/1.84 | (11) ! [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)) % 5.10/1.84 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 5.10/1.84 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) % 5.10/1.85 | (14) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 5.10/1.85 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.10/1.85 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 5.10/1.85 | (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)) % 5.10/1.85 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 5.10/1.85 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) % 5.10/1.85 | (20) ! [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))) % 5.10/1.85 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 5.10/1.85 | (22) ~ (all_0_0_0 = 0) % 5.10/1.85 | (23) ! [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)))) % 5.10/1.85 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 5.10/1.85 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 5.10/1.85 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) % 5.10/1.85 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) % 5.10/1.85 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 5.10/1.85 | (29) ! [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)) % 5.10/1.85 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 5.10/1.85 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) % 5.10/1.85 | (32) ! [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))) % 5.10/1.85 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) % 5.10/1.85 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) % 5.10/1.85 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 5.10/1.86 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) % 5.10/1.86 | (37) equal_set(all_0_1_1, all_0_3_3) = all_0_0_0 % 5.10/1.86 | (38) ! [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)) % 5.10/1.86 | % 5.10/1.86 | Instantiating formula (13) 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: % 5.10/1.86 | (39) 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))) % 5.10/1.86 | % 5.10/1.86 +-Applying beta-rule and splitting (39), into two cases. % 5.10/1.86 |-Branch one: % 5.10/1.86 | (40) all_0_0_0 = 0 % 5.10/1.86 | % 5.10/1.86 | Equations (40) can reduce 22 to: % 5.10/1.86 | (41) $false % 5.10/1.86 | % 5.10/1.86 |-The branch is then unsatisfiable % 5.10/1.86 |-Branch two: % 5.10/1.86 | (22) ~ (all_0_0_0 = 0) % 5.10/1.86 | (43) ? [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))) % 5.10/1.86 | % 5.10/1.86 | Instantiating (43) with all_10_0_4, all_10_1_5 yields: % 5.10/1.86 | (44) subset(all_0_1_1, all_0_3_3) = all_10_1_5 & subset(all_0_3_3, all_0_1_1) = all_10_0_4 & ( ~ (all_10_0_4 = 0) | ~ (all_10_1_5 = 0)) % 5.10/1.86 | % 5.10/1.86 | Applying alpha-rule on (44) yields: % 5.10/1.86 | (45) subset(all_0_1_1, all_0_3_3) = all_10_1_5 % 5.10/1.86 | (46) subset(all_0_3_3, all_0_1_1) = all_10_0_4 % 5.10/1.86 | (47) ~ (all_10_0_4 = 0) | ~ (all_10_1_5 = 0) % 5.10/1.86 | % 5.10/1.86 | Instantiating formula (5) with all_10_1_5, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_10_1_5, yields: % 5.10/1.86 | (48) all_10_1_5 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 5.10/1.86 | % 5.10/1.86 | Instantiating formula (5) with all_10_0_4, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_10_0_4, yields: % 5.10/1.86 | (49) all_10_0_4 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 5.10/1.86 | % 5.10/1.86 +-Applying beta-rule and splitting (47), into two cases. % 5.10/1.86 |-Branch one: % 5.10/1.86 | (50) ~ (all_10_0_4 = 0) % 5.10/1.86 | % 5.10/1.86 +-Applying beta-rule and splitting (49), into two cases. % 5.10/1.86 |-Branch one: % 5.10/1.86 | (51) all_10_0_4 = 0 % 5.10/1.86 | % 5.10/1.86 | Equations (51) can reduce 50 to: % 5.10/1.86 | (41) $false % 5.10/1.86 | % 5.10/1.86 |-The branch is then unsatisfiable % 5.10/1.86 |-Branch two: % 5.10/1.86 | (50) ~ (all_10_0_4 = 0) % 5.10/1.86 | (54) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0) % 5.10/1.86 | % 5.10/1.86 | Instantiating (54) with all_23_0_6, all_23_1_7 yields: % 5.10/1.86 | (55) ~ (all_23_0_6 = 0) & member(all_23_1_7, all_0_1_1) = all_23_0_6 & member(all_23_1_7, all_0_3_3) = 0 % 5.10/1.86 | % 5.10/1.86 | Applying alpha-rule on (55) yields: % 5.10/1.86 | (56) ~ (all_23_0_6 = 0) % 5.10/1.86 | (57) member(all_23_1_7, all_0_1_1) = all_23_0_6 % 5.10/1.86 | (58) member(all_23_1_7, all_0_3_3) = 0 % 5.10/1.86 | % 5.10/1.86 | Instantiating formula (29) with all_0_3_3, all_23_0_6, all_0_1_1, all_0_2_2, all_23_1_7 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_23_1_7, all_0_1_1) = all_23_0_6, member(all_23_1_7, all_0_3_3) = 0, yields: % 5.10/1.86 | (59) all_23_0_6 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_2_2) = v0) % 5.10/1.86 | % 5.10/1.86 +-Applying beta-rule and splitting (59), into two cases. % 5.10/1.86 |-Branch one: % 5.10/1.86 | (60) all_23_0_6 = 0 % 5.10/1.86 | % 5.10/1.86 | Equations (60) can reduce 56 to: % 5.10/1.86 | (41) $false % 5.10/1.87 | % 5.10/1.87 |-The branch is then unsatisfiable % 5.10/1.87 |-Branch two: % 5.10/1.87 | (56) ~ (all_23_0_6 = 0) % 5.10/1.87 | (63) ? [v0] : ( ~ (v0 = 0) & member(all_0_3_3, all_0_2_2) = v0) % 5.10/1.87 | % 5.10/1.87 | Instantiating (63) with all_44_0_8 yields: % 5.10/1.87 | (64) ~ (all_44_0_8 = 0) & member(all_0_3_3, all_0_2_2) = all_44_0_8 % 5.10/1.87 | % 5.10/1.87 | Applying alpha-rule on (64) yields: % 5.10/1.87 | (65) ~ (all_44_0_8 = 0) % 5.10/1.87 | (66) member(all_0_3_3, all_0_2_2) = all_44_0_8 % 5.10/1.87 | % 5.10/1.87 | Instantiating formula (31) with all_44_0_8, all_0_2_2, all_0_3_3 and discharging atoms singleton(all_0_3_3) = all_0_2_2, member(all_0_3_3, all_0_2_2) = all_44_0_8, yields: % 5.10/1.87 | (67) all_44_0_8 = 0 % 5.10/1.87 | % 5.10/1.87 | Equations (67) can reduce 65 to: % 5.10/1.87 | (41) $false % 5.10/1.87 | % 5.10/1.87 |-The branch is then unsatisfiable % 5.10/1.87 |-Branch two: % 5.10/1.87 | (51) all_10_0_4 = 0 % 5.10/1.87 | (70) ~ (all_10_1_5 = 0) % 5.10/1.87 | % 5.10/1.87 +-Applying beta-rule and splitting (48), into two cases. % 5.10/1.87 |-Branch one: % 5.10/1.87 | (71) all_10_1_5 = 0 % 5.10/1.87 | % 5.10/1.87 | Equations (71) can reduce 70 to: % 5.10/1.87 | (41) $false % 5.10/1.87 | % 5.10/1.87 |-The branch is then unsatisfiable % 5.10/1.87 |-Branch two: % 5.10/1.87 | (70) ~ (all_10_1_5 = 0) % 5.10/1.87 | (74) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1) % 5.10/1.87 | % 5.10/1.87 | Instantiating (74) with all_23_0_9, all_23_1_10 yields: % 5.10/1.87 | (75) ~ (all_23_0_9 = 0) & member(all_23_1_10, all_0_1_1) = 0 & member(all_23_1_10, all_0_3_3) = all_23_0_9 % 5.10/1.87 | % 5.10/1.87 | Applying alpha-rule on (75) yields: % 5.10/1.87 | (76) ~ (all_23_0_9 = 0) % 5.10/1.87 | (77) member(all_23_1_10, all_0_1_1) = 0 % 5.10/1.87 | (78) member(all_23_1_10, all_0_3_3) = all_23_0_9 % 5.10/1.87 | % 5.10/1.87 | Instantiating formula (15) with all_23_1_10, all_0_3_3, all_23_0_9, 0 and discharging atoms member(all_23_1_10, all_0_3_3) = all_23_0_9, yields: % 5.10/1.87 | (79) all_23_0_9 = 0 | ~ (member(all_23_1_10, all_0_3_3) = 0) % 5.10/1.87 | % 5.10/1.87 | Instantiating formula (19) with all_0_1_1, all_0_2_2, all_23_1_10 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_23_1_10, all_0_1_1) = 0, yields: % 5.10/1.87 | (80) ? [v0] : (member(v0, all_0_2_2) = 0 & member(all_23_1_10, v0) = 0) % 5.10/1.87 | % 5.10/1.87 | Instantiating (80) with all_38_0_11 yields: % 5.10/1.87 | (81) member(all_38_0_11, all_0_2_2) = 0 & member(all_23_1_10, all_38_0_11) = 0 % 5.10/1.87 | % 5.10/1.87 | Applying alpha-rule on (81) yields: % 5.10/1.87 | (82) member(all_38_0_11, all_0_2_2) = 0 % 5.10/1.87 | (83) member(all_23_1_10, all_38_0_11) = 0 % 5.10/1.87 | % 5.10/1.87 | Instantiating formula (27) with all_0_2_2, all_0_3_3, all_38_0_11 and discharging atoms singleton(all_0_3_3) = all_0_2_2, member(all_38_0_11, all_0_2_2) = 0, yields: % 5.10/1.87 | (84) all_38_0_11 = all_0_3_3 % 5.10/1.87 | % 5.10/1.87 | From (84) and (83) follows: % 5.10/1.87 | (85) member(all_23_1_10, all_0_3_3) = 0 % 5.10/1.87 | % 5.10/1.87 +-Applying beta-rule and splitting (79), into two cases. % 5.10/1.87 |-Branch one: % 5.10/1.87 | (86) ~ (member(all_23_1_10, all_0_3_3) = 0) % 5.10/1.87 | % 5.10/1.87 | Using (85) and (86) yields: % 5.10/1.87 | (87) $false % 5.10/1.87 | % 5.10/1.87 |-The branch is then unsatisfiable % 5.10/1.87 |-Branch two: % 5.10/1.87 | (85) member(all_23_1_10, all_0_3_3) = 0 % 5.10/1.87 | (89) all_23_0_9 = 0 % 5.10/1.87 | % 5.10/1.87 | Equations (89) can reduce 76 to: % 5.10/1.87 | (41) $false % 5.10/1.87 | % 5.10/1.87 |-The branch is then unsatisfiable % 5.10/1.87 % SZS output end Proof for theBenchmark % 5.10/1.87 % 5.10/1.87 1277ms %------------------------------------------------------------------------------