%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET016+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n020.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 00:16:05 EDT 2022 % Result : Theorem 3.03s 1.37s % Output : Proof 4.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET016+4 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n020.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 : Sun Jul 10 07:01:13 EDT 2022 % 0.12/0.34 % CPUTime : % 0.55/0.60 ____ _ % 0.55/0.60 ___ / __ \_____(_)___ ________ __________ % 0.55/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.60 % 0.55/0.60 A Theorem Prover for First-Order Logic % 0.55/0.60 (ePrincess v.1.0) % 0.55/0.60 % 0.55/0.60 (c) Philipp Rümmer, 2009-2015 % 0.55/0.60 (c) Peter Backeman, 2014-2015 % 0.55/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.60 Bug reports to peter@backeman.se % 0.55/0.60 % 0.55/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.60 % 0.55/0.60 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 % 1.56/0.94 Prover 0: Preprocessing ... % 1.96/1.14 Prover 0: Warning: ignoring some quantifiers % 2.18/1.17 Prover 0: Constructing countermodel ... % 3.03/1.37 Prover 0: proved (713ms) % 3.03/1.37 % 3.03/1.37 No countermodel exists, formula is valid % 3.03/1.37 % SZS status Theorem for theBenchmark % 3.03/1.37 % 3.03/1.37 Generating proof ... Warning: ignoring some quantifiers % 3.85/1.59 found it (size 52) % 3.85/1.59 % 3.85/1.59 % SZS output start Proof for theBenchmark % 3.85/1.59 Assumed formulas after preprocessing and simplification: % 3.85/1.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v2 = v0) & unordered_pair(v7, v8) = v9 & unordered_pair(v4, v5) = v6 & unordered_pair(v2, v3) = v8 & unordered_pair(v0, v1) = v5 & singleton(v2) = v7 & singleton(v0) = v4 & equal_set(v6, v9) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v10 | v11 = v10 | ~ (unordered_pair(v11, v12) = v13) | ~ member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (difference(v13, v12) = v11) | ~ (difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (union(v13, v12) = v11) | ~ (union(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (intersection(v13, v12) = v11) | ~ (intersection(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (product(v11) = v12) | ~ member(v13, v11) | ~ member(v10, v12) | member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (sum(v11) = v12) | ~ member(v13, v11) | ~ member(v10, v13) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (difference(v12, v11) = v13) | ~ member(v10, v13) | ~ member(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (difference(v12, v11) = v13) | ~ member(v10, v13) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (difference(v12, v11) = v13) | ~ member(v10, v12) | member(v10, v13) | member(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11, v12) = v13) | ~ member(v10, v13) | member(v10, v12) | member(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11, v12) = v13) | ~ member(v10, v12) | member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11, v12) = v13) | ~ member(v10, v11) | member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (intersection(v11, v12) = v13) | ~ member(v10, v13) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (intersection(v11, v12) = v13) | ~ member(v10, v13) | member(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (intersection(v11, v12) = v13) | ~ member(v10, v12) | ~ member(v10, v11) | member(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (product(v12) = v11) | ~ (product(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (sum(v12) = v11) | ~ (sum(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v11) = v12) | ~ member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (power_set(v12) = v11) | ~ (power_set(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (sum(v11) = v12) | ~ member(v10, v12) | ? [v13] : (member(v13, v11) & member(v10, v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (power_set(v11) = v12) | ~ member(v10, v12) | subset(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (power_set(v11) = v12) | ~ subset(v10, v11) | member(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ member(v12, v10) | ~ subset(v10, v11) | member(v12, v11)) & ? [v10] : ! [v11] : ! [v12] : ( ~ (product(v11) = v12) | member(v10, v12) | ? [v13] : (member(v13, v11) & ~ member(v10, v13))) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | member(v10, v11)) & ! [v10] : ! [v11] : ( ~ equal_set(v10, v11) | subset(v11, v10)) & ! [v10] : ! [v11] : ( ~ equal_set(v10, v11) | subset(v10, v11)) & ! [v10] : ! [v11] : ( ~ subset(v11, v10) | ~ subset(v10, v11) | equal_set(v10, v11)) & ! [v10] : ~ member(v10, empty_set) & ? [v10] : ? [v11] : (subset(v10, v11) | ? [v12] : (member(v12, v10) & ~ member(v12, v11)))) % 4.18/1.64 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields: % 4.18/1.64 | (1) ~ (all_0_7_7 = all_0_9_9) & unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0 & unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3 & unordered_pair(all_0_7_7, all_0_6_6) = all_0_1_1 & unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4 & singleton(all_0_7_7) = all_0_2_2 & singleton(all_0_9_9) = all_0_5_5 & equal_set(all_0_3_3, all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) & ! [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] : ( ~ (product(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v2) | member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | ~ member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v2) | member(v0, v3) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v2) | member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v1) | member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v2) | ~ member(v0, v1) | member(v0, v3)) & ! [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)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ member(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ subset(v0, v1) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (product(v1) = v2) | member(v0, v2) | ? [v3] : (member(v3, v1) & ~ member(v0, v3))) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1)) & ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1)) & ! [v0] : ~ member(v0, empty_set) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 4.18/1.65 | % 4.18/1.65 | Applying alpha-rule on (1) yields: % 4.18/1.65 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v1)) % 4.18/1.65 | (3) unordered_pair(all_0_7_7, all_0_6_6) = all_0_1_1 % 4.18/1.65 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 4.18/1.65 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v2) | member(v0, v3)) % 4.18/1.65 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) % 4.18/1.65 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.18/1.65 | (8) singleton(all_0_9_9) = all_0_5_5 % 4.18/1.65 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.18/1.65 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.18/1.65 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2)) % 4.18/1.65 | (12) equal_set(all_0_3_3, all_0_0_0) % 4.18/1.65 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v1) | member(v0, v3)) % 4.18/1.65 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2)) % 4.18/1.65 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v2) | member(v0, v3)) % 4.18/1.65 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2) | member(v0, v1)) % 4.18/1.65 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 4.18/1.65 | (18) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 4.18/1.65 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ member(v0, v2)) % 4.18/1.65 | (20) singleton(all_0_7_7) = all_0_2_2 % 4.18/1.65 | (21) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1)) % 4.18/1.65 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | member(v0, v2)) % 4.18/1.65 | (23) ? [v0] : ! [v1] : ! [v2] : ( ~ (product(v1) = v2) | member(v0, v2) | ? [v3] : (member(v3, v1) & ~ member(v0, v3))) % 4.18/1.66 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) % 4.18/1.66 | (25) ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v0, v1)) % 4.18/1.66 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.18/1.66 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v2) | ~ member(v0, v1) | member(v0, v3)) % 4.18/1.66 | (28) unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.18/1.66 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | member(v0, v2)) % 4.18/1.66 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.18/1.66 | (31) unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3 % 4.18/1.66 | (32) unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4 % 4.18/1.66 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ subset(v0, v1) | member(v0, v2)) % 4.18/1.66 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ member(v0, v2) | subset(v0, v1)) % 4.18/1.66 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v2) | member(v0, v3) | member(v0, v1)) % 4.18/1.66 | (36) ~ (all_0_7_7 = all_0_9_9) % 4.18/1.66 | (37) ! [v0] : ~ member(v0, empty_set) % 4.18/1.66 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v0, v2)) % 4.18/1.66 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) % 4.18/1.66 | (40) ! [v0] : ! [v1] : ( ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1)) % 4.18/1.66 | (41) ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v1, v0)) % 4.18/1.66 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | ~ member(v0, v1)) % 4.18/1.66 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 4.18/1.66 | % 4.18/1.66 | Instantiating formula (29) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.18/1.66 | (44) member(all_0_1_1, all_0_0_0) % 4.18/1.66 | % 4.18/1.66 | Instantiating formula (38) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0, yields: % 4.18/1.66 | (45) member(all_0_2_2, all_0_0_0) % 4.18/1.66 | % 4.18/1.66 | Instantiating formula (29) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.18/1.66 | (46) member(all_0_4_4, all_0_3_3) % 4.18/1.66 | % 4.18/1.66 | Instantiating formula (38) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3, yields: % 4.18/1.66 | (47) member(all_0_5_5, all_0_3_3) % 4.18/1.66 | % 4.18/1.66 | Instantiating formula (38) with all_0_1_1, all_0_6_6, all_0_7_7 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_1_1, yields: % 4.18/1.66 | (48) member(all_0_7_7, all_0_1_1) % 4.18/1.66 | % 4.18/1.66 | Instantiating formula (21) with all_0_2_2, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_2_2, yields: % 4.18/1.66 | (49) member(all_0_7_7, all_0_2_2) % 4.18/1.66 | % 4.18/1.66 | Instantiating formula (41) with all_0_0_0, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_0_0), yields: % 4.18/1.66 | (50) subset(all_0_0_0, all_0_3_3) % 4.18/1.66 | % 4.18/1.66 | Instantiating formula (25) with all_0_0_0, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_0_0), yields: % 4.18/1.66 | (51) subset(all_0_3_3, all_0_0_0) % 4.18/1.66 | % 4.18/1.66 | Instantiating formula (6) with all_0_1_1, all_0_3_3, all_0_0_0 and discharging atoms member(all_0_1_1, all_0_0_0), subset(all_0_0_0, all_0_3_3), yields: % 4.18/1.67 | (52) member(all_0_1_1, all_0_3_3) % 4.18/1.67 | % 4.18/1.67 | Instantiating formula (6) with all_0_2_2, all_0_3_3, all_0_0_0 and discharging atoms member(all_0_2_2, all_0_0_0), subset(all_0_0_0, all_0_3_3), yields: % 4.18/1.67 | (53) member(all_0_2_2, all_0_3_3) % 4.18/1.67 | % 4.18/1.67 | Instantiating formula (6) with all_0_4_4, all_0_0_0, all_0_3_3 and discharging atoms member(all_0_4_4, all_0_3_3), subset(all_0_3_3, all_0_0_0), yields: % 4.18/1.67 | (54) member(all_0_4_4, all_0_0_0) % 4.18/1.67 | % 4.18/1.67 | Instantiating formula (6) with all_0_5_5, all_0_0_0, all_0_3_3 and discharging atoms member(all_0_5_5, all_0_3_3), subset(all_0_3_3, all_0_0_0), yields: % 4.18/1.67 | (55) member(all_0_5_5, all_0_0_0) % 4.18/1.67 | % 4.18/1.67 | Instantiating formula (39) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_1_1 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_0_1_1, all_0_3_3), yields: % 4.18/1.67 | (56) all_0_1_1 = all_0_4_4 | all_0_1_1 = all_0_5_5 % 4.18/1.67 | % 4.18/1.67 | Instantiating formula (39) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_2_2 and discharging atoms unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3, member(all_0_2_2, all_0_3_3), yields: % 4.18/1.67 | (57) all_0_2_2 = all_0_4_4 | all_0_2_2 = all_0_5_5 % 4.18/1.67 | % 4.18/1.67 | Instantiating formula (39) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0, member(all_0_4_4, all_0_0_0), yields: % 4.18/1.67 | (58) all_0_1_1 = all_0_4_4 | all_0_2_2 = all_0_4_4 % 4.18/1.67 | % 4.18/1.67 | Instantiating formula (39) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_5_5 and discharging atoms unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0, member(all_0_5_5, all_0_0_0), yields: % 4.18/1.67 | (59) all_0_1_1 = all_0_5_5 | all_0_2_2 = all_0_5_5 % 4.18/1.67 | % 4.18/1.67 +-Applying beta-rule and splitting (58), into two cases. % 4.18/1.67 |-Branch one: % 4.18/1.67 | (60) all_0_1_1 = all_0_4_4 % 4.18/1.67 | % 4.18/1.67 | From (60) and (48) follows: % 4.18/1.67 | (61) member(all_0_7_7, all_0_4_4) % 4.18/1.67 | % 4.18/1.67 | Instantiating formula (39) with all_0_4_4, all_0_8_8, all_0_9_9, all_0_7_7 and discharging atoms unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4, member(all_0_7_7, all_0_4_4), yields: % 4.18/1.67 | (62) all_0_7_7 = all_0_8_8 | all_0_7_7 = all_0_9_9 % 4.18/1.67 | % 4.18/1.67 +-Applying beta-rule and splitting (59), into two cases. % 4.18/1.67 |-Branch one: % 4.18/1.67 | (63) all_0_1_1 = all_0_5_5 % 4.18/1.67 | % 4.18/1.67 | Combining equations (63,60) yields a new equation: % 4.18/1.67 | (64) all_0_4_4 = all_0_5_5 % 4.18/1.67 | % 4.18/1.67 +-Applying beta-rule and splitting (57), into two cases. % 4.18/1.67 |-Branch one: % 4.18/1.67 | (65) all_0_2_2 = all_0_4_4 % 4.18/1.67 | % 4.18/1.67 | Combining equations (64,65) yields a new equation: % 4.18/1.67 | (66) all_0_2_2 = all_0_5_5 % 4.18/1.67 | % 4.18/1.67 | From (66) and (49) follows: % 4.18/1.67 | (67) member(all_0_7_7, all_0_5_5) % 4.18/1.67 | % 4.18/1.67 +-Applying beta-rule and splitting (62), into two cases. % 4.18/1.67 |-Branch one: % 4.18/1.67 | (68) all_0_7_7 = all_0_8_8 % 4.18/1.67 | % 4.18/1.67 | Equations (68) can reduce 36 to: % 4.18/1.67 | (69) ~ (all_0_8_8 = all_0_9_9) % 4.18/1.67 | % 4.18/1.67 | From (68) and (67) follows: % 4.18/1.67 | (70) member(all_0_8_8, all_0_5_5) % 4.18/1.67 | % 4.18/1.67 | Instantiating formula (19) with all_0_5_5, all_0_9_9, all_0_8_8 and discharging atoms singleton(all_0_9_9) = all_0_5_5, member(all_0_8_8, all_0_5_5), yields: % 4.18/1.67 | (71) all_0_8_8 = all_0_9_9 % 4.18/1.67 | % 4.18/1.67 | Equations (71) can reduce 69 to: % 4.18/1.67 | (72) $false % 4.18/1.67 | % 4.18/1.67 |-The branch is then unsatisfiable % 4.18/1.67 |-Branch two: % 4.18/1.67 | (73) ~ (all_0_7_7 = all_0_8_8) % 4.18/1.67 | (74) all_0_7_7 = all_0_9_9 % 4.18/1.67 | % 4.18/1.67 | Equations (74) can reduce 36 to: % 4.18/1.67 | (72) $false % 4.18/1.67 | % 4.18/1.67 |-The branch is then unsatisfiable % 4.18/1.67 |-Branch two: % 4.18/1.67 | (76) ~ (all_0_2_2 = all_0_4_4) % 4.18/1.67 | (66) all_0_2_2 = all_0_5_5 % 4.18/1.67 | % 4.18/1.67 | Equations (66,64) can reduce 76 to: % 4.18/1.67 | (72) $false % 4.18/1.68 | % 4.18/1.68 |-The branch is then unsatisfiable % 4.18/1.68 |-Branch two: % 4.18/1.68 | (79) ~ (all_0_1_1 = all_0_5_5) % 4.18/1.68 | (66) all_0_2_2 = all_0_5_5 % 4.18/1.68 | % 4.18/1.68 | From (66) and (49) follows: % 4.18/1.68 | (67) member(all_0_7_7, all_0_5_5) % 4.18/1.68 | % 4.18/1.68 +-Applying beta-rule and splitting (62), into two cases. % 4.18/1.68 |-Branch one: % 4.18/1.68 | (68) all_0_7_7 = all_0_8_8 % 4.18/1.68 | % 4.18/1.68 | Equations (68) can reduce 36 to: % 4.18/1.68 | (69) ~ (all_0_8_8 = all_0_9_9) % 4.18/1.68 | % 4.18/1.68 | From (68) and (67) follows: % 4.18/1.68 | (70) member(all_0_8_8, all_0_5_5) % 4.18/1.68 | % 4.18/1.68 | Instantiating formula (19) with all_0_5_5, all_0_9_9, all_0_8_8 and discharging atoms singleton(all_0_9_9) = all_0_5_5, member(all_0_8_8, all_0_5_5), yields: % 4.18/1.68 | (71) all_0_8_8 = all_0_9_9 % 4.18/1.68 | % 4.18/1.68 | Equations (71) can reduce 69 to: % 4.18/1.68 | (72) $false % 4.18/1.68 | % 4.18/1.68 |-The branch is then unsatisfiable % 4.18/1.68 |-Branch two: % 4.18/1.68 | (73) ~ (all_0_7_7 = all_0_8_8) % 4.18/1.68 | (74) all_0_7_7 = all_0_9_9 % 4.18/1.68 | % 4.18/1.68 | Equations (74) can reduce 36 to: % 4.18/1.68 | (72) $false % 4.18/1.68 | % 4.18/1.68 |-The branch is then unsatisfiable % 4.18/1.68 |-Branch two: % 4.18/1.68 | (90) ~ (all_0_1_1 = all_0_4_4) % 4.18/1.68 | (65) all_0_2_2 = all_0_4_4 % 4.18/1.68 | % 4.18/1.68 +-Applying beta-rule and splitting (56), into two cases. % 4.18/1.68 |-Branch one: % 4.18/1.68 | (60) all_0_1_1 = all_0_4_4 % 4.18/1.68 | % 4.18/1.68 | Equations (60) can reduce 90 to: % 4.18/1.68 | (72) $false % 4.18/1.68 | % 4.18/1.68 |-The branch is then unsatisfiable % 4.18/1.68 |-Branch two: % 4.18/1.68 | (90) ~ (all_0_1_1 = all_0_4_4) % 4.18/1.68 | (63) all_0_1_1 = all_0_5_5 % 4.39/1.68 | % 4.39/1.68 | From (63) and (48) follows: % 4.39/1.68 | (67) member(all_0_7_7, all_0_5_5) % 4.39/1.68 | % 4.39/1.68 | Instantiating formula (19) with all_0_5_5, all_0_9_9, all_0_7_7 and discharging atoms singleton(all_0_9_9) = all_0_5_5, member(all_0_7_7, all_0_5_5), yields: % 4.39/1.68 | (74) all_0_7_7 = all_0_9_9 % 4.39/1.68 | % 4.39/1.68 | Equations (74) can reduce 36 to: % 4.39/1.68 | (72) $false % 4.39/1.68 | % 4.39/1.68 |-The branch is then unsatisfiable % 4.39/1.68 % SZS output end Proof for theBenchmark % 4.39/1.68 % 4.39/1.68 1068ms %------------------------------------------------------------------------------