%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU188+1 : TPTP v8.1.0. Released v3.3.0. % 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 08:47:27 EDT 2022 % Result : Theorem 3.65s 1.53s % Output : Proof 4.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU188+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n007.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 : Sun Jun 19 01:58:13 EDT 2022 % 0.12/0.33 % CPUTime : % 0.58/0.58 ____ _ % 0.58/0.58 ___ / __ \_____(_)___ ________ __________ % 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.58 % 0.58/0.58 A Theorem Prover for First-Order Logic % 0.58/0.58 (ePrincess v.1.0) % 0.58/0.58 % 0.58/0.58 (c) Philipp Rümmer, 2009-2015 % 0.58/0.58 (c) Peter Backeman, 2014-2015 % 0.58/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.58 Bug reports to peter@backeman.se % 0.58/0.58 % 0.58/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.58 % 0.58/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.62/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.49/0.91 Prover 0: Preprocessing ... % 1.99/1.14 Prover 0: Warning: ignoring some quantifiers % 1.99/1.16 Prover 0: Constructing countermodel ... % 3.65/1.53 Prover 0: proved (899ms) % 3.65/1.53 % 3.65/1.53 No countermodel exists, formula is valid % 3.65/1.53 % SZS status Theorem for theBenchmark % 3.65/1.53 % 3.65/1.53 Generating proof ... Warning: ignoring some quantifiers % 4.84/1.79 found it (size 26) % 4.84/1.79 % 4.84/1.79 % SZS output start Proof for theBenchmark % 4.84/1.79 Assumed formulas after preprocessing and simplification: % 4.84/1.79 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v0 = empty_set) & relation_rng(v0) = v2 & relation_dom(v0) = v1 & relation(v6) & relation(v4) & relation(v0) & relation(empty_set) & empty(v6) & empty(v5) & empty(empty_set) & ~ empty(v4) & ~ empty(v3) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v7) = v10) | ~ (unordered_pair(v9, v10) = v11) | ~ (unordered_pair(v7, v8) = v9) | ordered_pair(v7, v8) = v11) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_rng(v7) = v8) | ~ (ordered_pair(v10, v9) = v11) | ~ relation(v7) | ~ in(v11, v7) | in(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_dom(v7) = v8) | ~ (ordered_pair(v9, v10) = v11) | ~ relation(v7) | ~ in(v11, v7) | in(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (ordered_pair(v10, v9) = v8) | ~ (ordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (relation_rng(v9) = v8) | ~ (relation_rng(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (relation_dom(v9) = v8) | ~ (relation_dom(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (relation_rng(v7) = v8) | ~ relation(v7) | ~ in(v9, v8) | ? [v10] : ? [v11] : (ordered_pair(v10, v9) = v11 & in(v11, v7))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (relation_dom(v7) = v8) | ~ relation(v7) | ~ in(v9, v8) | ? [v10] : ? [v11] : (ordered_pair(v9, v10) = v11 & in(v11, v7))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ empty(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ? [v11] : (singleton(v7) = v11 & unordered_pair(v10, v11) = v9 & unordered_pair(v7, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | ~ empty(v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (relation_rng(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : ? [v12] : (( ~ in(v10, v7) | ! [v13] : ! [v14] : ( ~ (ordered_pair(v13, v10) = v14) | ~ in(v14, v8))) & (in(v10, v7) | (ordered_pair(v11, v10) = v12 & in(v12, v8))))) & ? [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (relation_dom(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : ? [v12] : (( ~ in(v10, v7) | ! [v13] : ! [v14] : ( ~ (ordered_pair(v10, v13) = v14) | ~ in(v14, v8))) & (in(v10, v7) | (ordered_pair(v10, v11) = v12 & in(v12, v8))))) & ! [v7] : ! [v8] : (v8 = v7 | ~ empty(v8) | ~ empty(v7)) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ (relation_rng(v7) = v8) | ~ relation(v7) | ~ empty(v8) | empty(v7)) & ! [v7] : ! [v8] : ( ~ (relation_rng(v7) = v8) | ~ empty(v7) | relation(v8)) & ! [v7] : ! [v8] : ( ~ (relation_rng(v7) = v8) | ~ empty(v7) | empty(v8)) & ! [v7] : ! [v8] : ( ~ (relation_dom(v7) = v8) | ~ relation(v7) | ~ empty(v8) | empty(v7)) & ! [v7] : ! [v8] : ( ~ (relation_dom(v7) = v8) | ~ empty(v7) | relation(v8)) & ! [v7] : ! [v8] : ( ~ (relation_dom(v7) = v8) | ~ empty(v7) | empty(v8)) & ! [v7] : ! [v8] : ( ~ element(v7, v8) | empty(v8) | in(v7, v8)) & ! [v7] : ! [v8] : ( ~ empty(v8) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v8, v7) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ( ~ in(v7, v8) | element(v7, v8)) & ! [v7] : (v7 = empty_set | ~ relation(v7) | ? [v8] : ? [v9] : ? [v10] : (ordered_pair(v8, v9) = v10 & in(v10, v7))) & ! [v7] : (v7 = empty_set | ~ empty(v7)) & ! [v7] : ( ~ empty(v7) | relation(v7)) & ? [v7] : ? [v8] : element(v8, v7) & (v2 = empty_set | v1 = empty_set)) % 4.95/1.83 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields: % 4.95/1.83 | (1) ~ (all_0_6_6 = empty_set) & relation_rng(all_0_6_6) = all_0_4_4 & relation_dom(all_0_6_6) = all_0_5_5 & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_6_6) & relation(empty_set) & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) & ~ empty(all_0_2_2) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ? [v0] : ? [v1] : element(v1, v0) & (all_0_4_4 = empty_set | all_0_5_5 = empty_set) % 4.95/1.84 | % 4.95/1.84 | Applying alpha-rule on (1) yields: % 4.95/1.84 | (2) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 4.95/1.84 | (3) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 4.95/1.84 | (4) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 4.95/1.84 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 4.95/1.84 | (6) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.95/1.84 | (7) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) % 4.95/1.84 | (8) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 4.95/1.84 | (9) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 4.95/1.84 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 4.95/1.84 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 4.95/1.85 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 4.95/1.85 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 4.95/1.85 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.95/1.85 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.95/1.85 | (16) relation(empty_set) % 4.95/1.85 | (17) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.95/1.85 | (18) relation(all_0_6_6) % 4.95/1.85 | (19) empty(all_0_1_1) % 4.95/1.85 | (20) empty(all_0_0_0) % 4.95/1.85 | (21) all_0_4_4 = empty_set | all_0_5_5 = empty_set % 4.95/1.85 | (22) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 4.95/1.85 | (23) empty(empty_set) % 4.95/1.85 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 4.95/1.85 | (25) ! [v0] : ( ~ empty(v0) | relation(v0)) % 4.95/1.85 | (26) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 4.95/1.85 | (27) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.95/1.85 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 4.95/1.85 | (29) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.95/1.85 | (30) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) % 4.95/1.85 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 4.95/1.85 | (32) relation_dom(all_0_6_6) = all_0_5_5 % 4.95/1.85 | (33) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) % 4.95/1.85 | (34) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 4.95/1.85 | (35) relation(all_0_0_0) % 4.95/1.85 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 4.95/1.85 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 4.95/1.85 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.95/1.85 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 4.95/1.85 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 4.95/1.85 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 4.95/1.86 | (42) ~ empty(all_0_2_2) % 4.95/1.86 | (43) ? [v0] : ? [v1] : element(v1, v0) % 4.95/1.86 | (44) ~ (all_0_6_6 = empty_set) % 4.95/1.86 | (45) relation_rng(all_0_6_6) = all_0_4_4 % 4.95/1.86 | (46) ~ empty(all_0_3_3) % 4.95/1.86 | (47) relation(all_0_2_2) % 4.95/1.86 | % 4.95/1.86 | Instantiating formula (38) with all_0_1_1, all_0_0_0 and discharging atoms empty(all_0_0_0), empty(all_0_1_1), yields: % 4.95/1.86 | (48) all_0_0_0 = all_0_1_1 % 4.95/1.86 | % 4.95/1.86 | Instantiating formula (38) with empty_set, all_0_0_0 and discharging atoms empty(all_0_0_0), empty(empty_set), yields: % 4.95/1.86 | (49) all_0_0_0 = empty_set % 4.95/1.86 | % 4.95/1.86 | Combining equations (49,48) yields a new equation: % 4.95/1.86 | (50) all_0_1_1 = empty_set % 4.95/1.86 | % 4.95/1.86 | From (50) and (19) follows: % 4.95/1.86 | (23) empty(empty_set) % 4.95/1.86 | % 4.95/1.86 | Instantiating formula (7) with all_0_6_6 and discharging atoms relation(all_0_6_6), yields: % 4.95/1.86 | (52) all_0_6_6 = empty_set | ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_6_6)) % 4.95/1.86 | % 4.95/1.86 +-Applying beta-rule and splitting (21), into two cases. % 4.95/1.86 |-Branch one: % 4.95/1.86 | (53) all_0_4_4 = empty_set % 4.95/1.86 | % 4.95/1.86 | From (53) and (45) follows: % 4.95/1.86 | (54) relation_rng(all_0_6_6) = empty_set % 4.95/1.86 | % 4.95/1.86 +-Applying beta-rule and splitting (52), into two cases. % 4.95/1.86 |-Branch one: % 4.95/1.86 | (55) all_0_6_6 = empty_set % 4.95/1.86 | % 4.95/1.86 | Equations (55) can reduce 44 to: % 4.95/1.86 | (56) $false % 4.95/1.86 | % 4.95/1.86 |-The branch is then unsatisfiable % 4.95/1.86 |-Branch two: % 4.95/1.86 | (44) ~ (all_0_6_6 = empty_set) % 4.95/1.86 | (58) ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_6_6)) % 4.95/1.86 | % 4.95/1.86 | Instantiating (58) with all_24_0_11, all_24_1_12, all_24_2_13 yields: % 4.95/1.86 | (59) ordered_pair(all_24_2_13, all_24_1_12) = all_24_0_11 & in(all_24_0_11, all_0_6_6) % 4.95/1.86 | % 4.95/1.86 | Applying alpha-rule on (59) yields: % 4.95/1.86 | (60) ordered_pair(all_24_2_13, all_24_1_12) = all_24_0_11 % 4.95/1.86 | (61) in(all_24_0_11, all_0_6_6) % 4.95/1.86 | % 4.95/1.86 | Instantiating formula (10) with all_24_0_11, all_24_2_13, all_24_1_12, empty_set, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = empty_set, ordered_pair(all_24_2_13, all_24_1_12) = all_24_0_11, relation(all_0_6_6), in(all_24_0_11, all_0_6_6), yields: % 4.95/1.86 | (62) in(all_24_1_12, empty_set) % 4.95/1.86 | % 4.95/1.86 | Instantiating formula (27) with empty_set, all_24_1_12 and discharging atoms empty(empty_set), in(all_24_1_12, empty_set), yields: % 4.95/1.86 | (63) $false % 4.95/1.86 | % 4.95/1.86 |-The branch is then unsatisfiable % 4.95/1.86 |-Branch two: % 4.95/1.86 | (64) ~ (all_0_4_4 = empty_set) % 4.95/1.86 | (65) all_0_5_5 = empty_set % 4.95/1.86 | % 4.95/1.86 | From (65) and (32) follows: % 4.95/1.86 | (66) relation_dom(all_0_6_6) = empty_set % 4.95/1.86 | % 4.95/1.86 +-Applying beta-rule and splitting (52), into two cases. % 4.95/1.86 |-Branch one: % 4.95/1.86 | (55) all_0_6_6 = empty_set % 4.95/1.86 | % 4.95/1.86 | Equations (55) can reduce 44 to: % 4.95/1.86 | (56) $false % 4.95/1.86 | % 4.95/1.86 |-The branch is then unsatisfiable % 4.95/1.86 |-Branch two: % 4.95/1.86 | (44) ~ (all_0_6_6 = empty_set) % 4.95/1.86 | (58) ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_6_6)) % 4.95/1.87 | % 4.95/1.87 | Instantiating (58) with all_24_0_16, all_24_1_17, all_24_2_18 yields: % 4.95/1.87 | (71) ordered_pair(all_24_2_18, all_24_1_17) = all_24_0_16 & in(all_24_0_16, all_0_6_6) % 4.95/1.87 | % 4.95/1.87 | Applying alpha-rule on (71) yields: % 4.95/1.87 | (72) ordered_pair(all_24_2_18, all_24_1_17) = all_24_0_16 % 4.95/1.87 | (73) in(all_24_0_16, all_0_6_6) % 4.95/1.87 | % 4.95/1.87 | Instantiating formula (39) with all_24_0_16, all_24_1_17, all_24_2_18, empty_set, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = empty_set, ordered_pair(all_24_2_18, all_24_1_17) = all_24_0_16, relation(all_0_6_6), in(all_24_0_16, all_0_6_6), yields: % 4.95/1.87 | (74) in(all_24_2_18, empty_set) % 4.95/1.87 | % 4.95/1.87 | Instantiating formula (27) with empty_set, all_24_2_18 and discharging atoms empty(empty_set), in(all_24_2_18, empty_set), yields: % 4.95/1.87 | (63) $false % 4.95/1.87 | % 4.95/1.87 |-The branch is then unsatisfiable % 4.95/1.87 % SZS output end Proof for theBenchmark % 4.95/1.87 % 4.95/1.87 1278ms %------------------------------------------------------------------------------