%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET018+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.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 00:16:10 EDT 2022 % Result : Theorem 2.79s 1.31s % Output : Proof 4.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SET018+4 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n005.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 01:09:22 EDT 2022 % 0.12/0.33 % CPUTime : % 0.51/0.58 ____ _ % 0.51/0.58 ___ / __ \_____(_)___ ________ __________ % 0.51/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.51/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.51/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.51/0.58 % 0.51/0.58 A Theorem Prover for First-Order Logic % 0.51/0.58 (ePrincess v.1.0) % 0.51/0.58 % 0.51/0.58 (c) Philipp Rümmer, 2009-2015 % 0.51/0.58 (c) Peter Backeman, 2014-2015 % 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.51/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.51/0.58 Bug reports to peter@backeman.se % 0.51/0.58 % 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.51/0.58 % 0.51/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.49/0.88 Prover 0: Preprocessing ... % 1.96/1.07 Prover 0: Warning: ignoring some quantifiers % 2.06/1.09 Prover 0: Constructing countermodel ... % 2.79/1.30 Prover 0: proved (677ms) % 2.79/1.31 % 2.79/1.31 No countermodel exists, formula is valid % 2.79/1.31 % SZS status Theorem for theBenchmark % 2.79/1.31 % 2.79/1.31 Generating proof ... Warning: ignoring some quantifiers % 3.98/1.55 found it (size 78) % 3.98/1.55 % 3.98/1.55 % SZS output start Proof for theBenchmark % 3.98/1.55 Assumed formulas after preprocessing and simplification: % 3.98/1.55 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v3 = v1) & 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)))) % 4.13/1.59 | 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: % 4.13/1.59 | (1) ~ (all_0_6_6 = all_0_8_8) & 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))) % 4.13/1.60 | % 4.13/1.60 | Applying alpha-rule on (1) yields: % 4.13/1.60 | (2) equal_set(all_0_3_3, all_0_0_0) % 4.13/1.60 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 4.13/1.61 | (4) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1)) % 4.13/1.61 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 4.13/1.61 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ subset(v0, v1) | member(v0, v2)) % 4.13/1.61 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ member(v0, v2) | subset(v0, v1)) % 4.13/1.61 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.13/1.61 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v2) | member(v0, v3)) % 4.13/1.61 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v2) | ~ member(v0, v1) | member(v0, v3)) % 4.13/1.61 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) % 4.13/1.61 | (12) singleton(all_0_9_9) = all_0_5_5 % 4.13/1.61 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) % 4.13/1.61 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2)) % 4.13/1.61 | (15) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 4.13/1.61 | (16) singleton(all_0_7_7) = all_0_2_2 % 4.13/1.61 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2)) % 4.13/1.61 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) % 4.13/1.61 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v1) | member(v0, v3)) % 4.13/1.61 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v1)) % 4.13/1.61 | (21) ! [v0] : ~ member(v0, empty_set) % 4.13/1.61 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v3) | member(v0, v2) | member(v0, v1)) % 4.13/1.61 | (23) ~ (all_0_6_6 = all_0_8_8) % 4.13/1.61 | (24) unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4 % 4.13/1.61 | (25) ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v1, v0)) % 4.13/1.61 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 4.13/1.61 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) % 4.13/1.61 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) % 4.13/1.61 | (29) unordered_pair(all_0_7_7, all_0_6_6) = all_0_1_1 % 4.13/1.61 | (30) ? [v0] : ! [v1] : ! [v2] : ( ~ (product(v1) = v2) | member(v0, v2) | ? [v3] : (member(v3, v1) & ~ member(v0, v3))) % 4.13/1.61 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) % 4.13/1.61 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ member(v0, v2) | member(v0, v3)) % 4.13/1.61 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v0, v2)) % 4.13/1.62 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | member(v0, v2)) % 4.13/1.62 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ member(v0, v2)) % 4.13/1.62 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v2) | member(v0, v3) | member(v0, v1)) % 4.13/1.62 | (37) unordered_pair(all_0_2_2, all_0_1_1) = all_0_0_0 % 4.13/1.62 | (38) ! [v0] : ! [v1] : ( ~ equal_set(v0, v1) | subset(v0, v1)) % 4.13/1.62 | (39) unordered_pair(all_0_5_5, all_0_4_4) = all_0_3_3 % 4.13/1.62 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | member(v0, v2)) % 4.13/1.62 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ member(v0, v3) | ~ member(v0, v1)) % 4.13/1.62 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.13/1.62 | (43) ! [v0] : ! [v1] : ( ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1)) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (34) 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: % 4.13/1.62 | (44) member(all_0_1_1, all_0_0_0) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (33) 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: % 4.13/1.62 | (45) member(all_0_2_2, all_0_0_0) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (34) 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: % 4.13/1.62 | (46) member(all_0_4_4, all_0_3_3) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (33) 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: % 4.13/1.62 | (47) member(all_0_5_5, all_0_3_3) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (34) with all_0_1_1, all_0_7_7, all_0_6_6 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_1_1, yields: % 4.13/1.62 | (48) member(all_0_6_6, all_0_1_1) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (33) 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: % 4.13/1.62 | (49) member(all_0_7_7, all_0_1_1) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (34) with all_0_4_4, all_0_9_9, all_0_8_8 and discharging atoms unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4, yields: % 4.13/1.62 | (50) member(all_0_8_8, all_0_4_4) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (4) with all_0_2_2, all_0_7_7 and discharging atoms singleton(all_0_7_7) = all_0_2_2, yields: % 4.13/1.62 | (51) member(all_0_7_7, all_0_2_2) % 4.13/1.62 | % 4.13/1.62 | 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: % 4.13/1.62 | (52) subset(all_0_0_0, all_0_3_3) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (38) with all_0_0_0, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_0_0), yields: % 4.13/1.62 | (53) subset(all_0_3_3, all_0_0_0) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (31) 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: % 4.13/1.62 | (54) member(all_0_1_1, all_0_3_3) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (31) 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: % 4.13/1.62 | (55) member(all_0_2_2, all_0_3_3) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (31) 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: % 4.13/1.62 | (56) member(all_0_4_4, all_0_0_0) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (31) 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: % 4.13/1.62 | (57) member(all_0_5_5, all_0_0_0) % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (27) 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: % 4.13/1.62 | (58) all_0_1_1 = all_0_4_4 | all_0_1_1 = all_0_5_5 % 4.13/1.62 | % 4.13/1.62 | Instantiating formula (27) 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: % 4.13/1.63 | (59) all_0_2_2 = all_0_4_4 | all_0_2_2 = all_0_5_5 % 4.13/1.63 | % 4.13/1.63 | Instantiating formula (27) 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: % 4.13/1.63 | (60) all_0_1_1 = all_0_4_4 | all_0_2_2 = all_0_4_4 % 4.13/1.63 | % 4.13/1.63 | Instantiating formula (27) 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: % 4.13/1.63 | (61) all_0_1_1 = all_0_5_5 | all_0_2_2 = all_0_5_5 % 4.13/1.63 | % 4.13/1.63 +-Applying beta-rule and splitting (60), into two cases. % 4.13/1.63 |-Branch one: % 4.13/1.63 | (62) all_0_1_1 = all_0_4_4 % 4.13/1.63 | % 4.13/1.63 | From (62) and (29) follows: % 4.13/1.63 | (63) unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4 % 4.13/1.63 | % 4.13/1.63 | From (62) and (48) follows: % 4.13/1.63 | (64) member(all_0_6_6, all_0_4_4) % 4.13/1.63 | % 4.13/1.63 | Instantiating formula (27) with all_0_4_4, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms unordered_pair(all_0_7_7, all_0_6_6) = all_0_4_4, member(all_0_8_8, all_0_4_4), yields: % 4.13/1.63 | (65) all_0_6_6 = all_0_8_8 | all_0_7_7 = all_0_8_8 % 4.13/1.63 | % 4.13/1.63 | Instantiating formula (27) with all_0_4_4, all_0_8_8, all_0_9_9, all_0_6_6 and discharging atoms unordered_pair(all_0_9_9, all_0_8_8) = all_0_4_4, member(all_0_6_6, all_0_4_4), yields: % 4.13/1.63 | (66) all_0_6_6 = all_0_8_8 | all_0_6_6 = all_0_9_9 % 4.13/1.63 | % 4.13/1.63 +-Applying beta-rule and splitting (61), into two cases. % 4.13/1.63 |-Branch one: % 4.13/1.63 | (67) all_0_1_1 = all_0_5_5 % 4.13/1.63 | % 4.13/1.63 | Combining equations (67,62) yields a new equation: % 4.13/1.63 | (68) all_0_4_4 = all_0_5_5 % 4.13/1.63 | % 4.13/1.63 +-Applying beta-rule and splitting (59), into two cases. % 4.13/1.63 |-Branch one: % 4.13/1.63 | (69) all_0_2_2 = all_0_4_4 % 4.13/1.63 | % 4.13/1.63 | Combining equations (68,69) yields a new equation: % 4.13/1.63 | (70) all_0_2_2 = all_0_5_5 % 4.13/1.63 | % 4.13/1.63 | From (70) and (51) follows: % 4.13/1.63 | (71) member(all_0_7_7, all_0_5_5) % 4.13/1.63 | % 4.13/1.63 +-Applying beta-rule and splitting (66), into two cases. % 4.13/1.63 |-Branch one: % 4.13/1.63 | (72) all_0_6_6 = all_0_8_8 % 4.13/1.63 | % 4.13/1.63 | Equations (72) can reduce 23 to: % 4.13/1.63 | (73) $false % 4.13/1.63 | % 4.13/1.63 |-The branch is then unsatisfiable % 4.13/1.63 |-Branch two: % 4.13/1.63 | (23) ~ (all_0_6_6 = all_0_8_8) % 4.13/1.63 | (75) all_0_6_6 = all_0_9_9 % 4.13/1.63 | % 4.13/1.63 | Equations (75) can reduce 23 to: % 4.13/1.63 | (76) ~ (all_0_8_8 = all_0_9_9) % 4.13/1.63 | % 4.13/1.63 | Simplifying 76 yields: % 4.13/1.63 | (77) ~ (all_0_8_8 = all_0_9_9) % 4.13/1.63 | % 4.13/1.63 +-Applying beta-rule and splitting (65), into two cases. % 4.13/1.63 |-Branch one: % 4.13/1.63 | (72) all_0_6_6 = all_0_8_8 % 4.13/1.63 | % 4.13/1.63 | Combining equations (72,75) yields a new equation: % 4.13/1.63 | (79) all_0_8_8 = all_0_9_9 % 4.13/1.63 | % 4.13/1.63 | Simplifying 79 yields: % 4.13/1.63 | (80) all_0_8_8 = all_0_9_9 % 4.13/1.63 | % 4.13/1.63 | Equations (80) can reduce 77 to: % 4.13/1.63 | (73) $false % 4.13/1.63 | % 4.13/1.63 |-The branch is then unsatisfiable % 4.13/1.63 |-Branch two: % 4.13/1.63 | (23) ~ (all_0_6_6 = all_0_8_8) % 4.13/1.63 | (83) all_0_7_7 = all_0_8_8 % 4.13/1.63 | % 4.13/1.63 | Equations (75) can reduce 23 to: % 4.13/1.63 | (76) ~ (all_0_8_8 = all_0_9_9) % 4.13/1.63 | % 4.13/1.63 | Simplifying 76 yields: % 4.13/1.63 | (77) ~ (all_0_8_8 = all_0_9_9) % 4.13/1.63 | % 4.13/1.63 | From (83) and (71) follows: % 4.13/1.63 | (86) member(all_0_8_8, all_0_5_5) % 4.13/1.63 | % 4.13/1.63 | Instantiating formula (35) 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: % 4.13/1.63 | (80) all_0_8_8 = all_0_9_9 % 4.13/1.64 | % 4.13/1.64 | Equations (80) can reduce 77 to: % 4.13/1.64 | (73) $false % 4.13/1.64 | % 4.13/1.64 |-The branch is then unsatisfiable % 4.13/1.64 |-Branch two: % 4.13/1.64 | (89) ~ (all_0_2_2 = all_0_4_4) % 4.13/1.64 | (70) all_0_2_2 = all_0_5_5 % 4.13/1.64 | % 4.13/1.64 | Equations (70,68) can reduce 89 to: % 4.13/1.64 | (73) $false % 4.13/1.64 | % 4.13/1.64 |-The branch is then unsatisfiable % 4.13/1.64 |-Branch two: % 4.13/1.64 | (92) ~ (all_0_1_1 = all_0_5_5) % 4.13/1.64 | (70) all_0_2_2 = all_0_5_5 % 4.13/1.64 | % 4.13/1.64 | From (70) and (51) follows: % 4.13/1.64 | (71) member(all_0_7_7, all_0_5_5) % 4.13/1.64 | % 4.13/1.64 +-Applying beta-rule and splitting (66), into two cases. % 4.13/1.64 |-Branch one: % 4.13/1.64 | (72) all_0_6_6 = all_0_8_8 % 4.13/1.64 | % 4.13/1.64 | Equations (72) can reduce 23 to: % 4.13/1.64 | (73) $false % 4.13/1.64 | % 4.13/1.64 |-The branch is then unsatisfiable % 4.13/1.64 |-Branch two: % 4.13/1.64 | (23) ~ (all_0_6_6 = all_0_8_8) % 4.13/1.64 | (75) all_0_6_6 = all_0_9_9 % 4.13/1.64 | % 4.13/1.64 | Equations (75) can reduce 23 to: % 4.13/1.64 | (76) ~ (all_0_8_8 = all_0_9_9) % 4.13/1.64 | % 4.13/1.64 | Simplifying 76 yields: % 4.13/1.64 | (77) ~ (all_0_8_8 = all_0_9_9) % 4.13/1.64 | % 4.13/1.64 +-Applying beta-rule and splitting (65), into two cases. % 4.13/1.64 |-Branch one: % 4.13/1.64 | (72) all_0_6_6 = all_0_8_8 % 4.13/1.64 | % 4.13/1.64 | Combining equations (72,75) yields a new equation: % 4.13/1.64 | (79) all_0_8_8 = all_0_9_9 % 4.13/1.64 | % 4.13/1.64 | Simplifying 79 yields: % 4.13/1.64 | (80) all_0_8_8 = all_0_9_9 % 4.13/1.64 | % 4.13/1.64 | Equations (80) can reduce 77 to: % 4.13/1.64 | (73) $false % 4.13/1.64 | % 4.13/1.64 |-The branch is then unsatisfiable % 4.13/1.64 |-Branch two: % 4.13/1.64 | (23) ~ (all_0_6_6 = all_0_8_8) % 4.13/1.64 | (83) all_0_7_7 = all_0_8_8 % 4.13/1.64 | % 4.13/1.64 | Equations (75) can reduce 23 to: % 4.13/1.64 | (76) ~ (all_0_8_8 = all_0_9_9) % 4.13/1.64 | % 4.13/1.64 | Simplifying 76 yields: % 4.13/1.64 | (77) ~ (all_0_8_8 = all_0_9_9) % 4.13/1.64 | % 4.13/1.64 | From (83) and (71) follows: % 4.13/1.64 | (86) member(all_0_8_8, all_0_5_5) % 4.13/1.64 | % 4.13/1.64 | Instantiating formula (35) 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: % 4.13/1.64 | (80) all_0_8_8 = all_0_9_9 % 4.13/1.64 | % 4.13/1.64 | Equations (80) can reduce 77 to: % 4.13/1.64 | (73) $false % 4.13/1.64 | % 4.13/1.64 |-The branch is then unsatisfiable % 4.13/1.64 |-Branch two: % 4.13/1.64 | (112) ~ (all_0_1_1 = all_0_4_4) % 4.13/1.64 | (69) all_0_2_2 = all_0_4_4 % 4.13/1.64 | % 4.13/1.64 | From (69) and (16) follows: % 4.13/1.64 | (114) singleton(all_0_7_7) = all_0_4_4 % 4.13/1.64 | % 4.13/1.64 +-Applying beta-rule and splitting (58), into two cases. % 4.13/1.64 |-Branch one: % 4.13/1.64 | (62) all_0_1_1 = all_0_4_4 % 4.13/1.64 | % 4.13/1.64 | Equations (62) can reduce 112 to: % 4.13/1.64 | (73) $false % 4.13/1.64 | % 4.13/1.64 |-The branch is then unsatisfiable % 4.13/1.64 |-Branch two: % 4.13/1.64 | (112) ~ (all_0_1_1 = all_0_4_4) % 4.13/1.64 | (67) all_0_1_1 = all_0_5_5 % 4.13/1.64 | % 4.13/1.64 | From (67) and (48) follows: % 4.13/1.64 | (119) member(all_0_6_6, all_0_5_5) % 4.13/1.64 | % 4.13/1.64 | From (67) and (49) follows: % 4.13/1.64 | (71) member(all_0_7_7, all_0_5_5) % 4.13/1.64 | % 4.13/1.64 | Instantiating formula (35) with all_0_4_4, all_0_7_7, all_0_8_8 and discharging atoms singleton(all_0_7_7) = all_0_4_4, member(all_0_8_8, all_0_4_4), yields: % 4.13/1.64 | (83) all_0_7_7 = all_0_8_8 % 4.13/1.64 | % 4.13/1.64 | Instantiating formula (35) with all_0_5_5, all_0_9_9, all_0_6_6 and discharging atoms singleton(all_0_9_9) = all_0_5_5, member(all_0_6_6, all_0_5_5), yields: % 4.46/1.64 | (75) all_0_6_6 = all_0_9_9 % 4.46/1.64 | % 4.46/1.64 | Instantiating formula (35) 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: % 4.46/1.64 | (123) all_0_7_7 = all_0_9_9 % 4.46/1.64 | % 4.46/1.64 | Combining equations (83,123) yields a new equation: % 4.46/1.64 | (79) all_0_8_8 = all_0_9_9 % 4.46/1.64 | % 4.46/1.64 | Simplifying 79 yields: % 4.46/1.64 | (80) all_0_8_8 = all_0_9_9 % 4.46/1.64 | % 4.46/1.64 | Equations (75,80) can reduce 23 to: % 4.46/1.64 | (73) $false % 4.46/1.64 | % 4.46/1.64 |-The branch is then unsatisfiable % 4.46/1.64 % SZS output end Proof for theBenchmark % 4.46/1.65 % 4.46/1.65 1055ms %------------------------------------------------------------------------------