%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU191+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.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 08:47:29 EDT 2022 % Result : Theorem 3.00s 1.44s % Output : Proof 5.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SEU191+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.11 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n027.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Mon Jun 20 00:46:54 EDT 2022 % 0.11/0.33 % CPUTime : % 0.18/0.55 ____ _ % 0.18/0.55 ___ / __ \_____(_)___ ________ __________ % 0.18/0.55 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.55 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.55 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.55 % 0.18/0.55 A Theorem Prover for First-Order Logic % 0.18/0.55 (ePrincess v.1.0) % 0.18/0.55 % 0.18/0.55 (c) Philipp Rümmer, 2009-2015 % 0.18/0.55 (c) Peter Backeman, 2014-2015 % 0.18/0.55 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.55 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.55 Bug reports to peter@backeman.se % 0.18/0.55 % 0.18/0.55 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.55 % 0.18/0.55 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.61/0.60 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.59/0.94 Prover 0: Preprocessing ... % 2.17/1.18 Prover 0: Warning: ignoring some quantifiers % 2.27/1.20 Prover 0: Constructing countermodel ... % 3.00/1.44 Prover 0: proved (833ms) % 3.00/1.44 % 3.00/1.44 No countermodel exists, formula is valid % 3.00/1.44 % SZS status Theorem for theBenchmark % 3.00/1.44 % 3.00/1.44 Generating proof ... Warning: ignoring some quantifiers % 4.38/1.77 found it (size 25) % 4.38/1.77 % 4.38/1.77 % SZS output start Proof for theBenchmark % 4.38/1.77 Assumed formulas after preprocessing and simplification: % 4.38/1.77 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_composition(v5, v3) = v6 & identity_relation(v2) = v5 & ordered_pair(v0, v1) = v4 & relation(v10) & relation(v8) & relation(v3) & relation(empty_set) & empty(v10) & empty(v9) & empty(empty_set) & ~ empty(v8) & ~ empty(v7) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v11, v12) = v13) | ~ (ordered_pair(v17, v15) = v18) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ relation(v11) | ~ in(v18, v12) | in(v16, v13) | ? [v19] : (ordered_pair(v14, v17) = v19 & ~ in(v19, v11))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v11, v12) = v13) | ~ (ordered_pair(v14, v17) = v18) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ relation(v11) | ~ in(v18, v11) | in(v16, v13) | ? [v19] : (ordered_pair(v17, v15) = v19 & ~ in(v19, v12))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ relation(v11) | ~ in(v16, v13) | ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v17, v15) = v19 & ordered_pair(v14, v17) = v18 & in(v19, v12) & in(v18, v11))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (identity_relation(v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ in(v15, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (singleton(v11) = v14) | ~ (unordered_pair(v13, v14) = v15) | ~ (unordered_pair(v11, v12) = v13) | ordered_pair(v11, v12) = v15) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (identity_relation(v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ in(v15, v12) | in(v13, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (relation_composition(v11, v12) = v13) | ~ relation(v14) | ~ relation(v12) | ~ relation(v11) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v15, v16) = v17 & ( ~ in(v17, v14) | ( ! [v21] : ! [v22] : ( ~ (ordered_pair(v21, v16) = v22) | ~ in(v22, v12) | ? [v23] : (ordered_pair(v15, v21) = v23 & ~ in(v23, v11))) & ! [v21] : ! [v22] : ( ~ (ordered_pair(v15, v21) = v22) | ~ in(v22, v11) | ? [v23] : (ordered_pair(v21, v16) = v23 & ~ in(v23, v12))))) & (in(v17, v14) | (ordered_pair(v18, v16) = v20 & ordered_pair(v15, v18) = v19 & in(v20, v12) & in(v19, v11))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_composition(v14, v13) = v12) | ~ (relation_composition(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (ordered_pair(v14, v13) = v12) | ~ (ordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (unordered_pair(v14, v13) = v12) | ~ (unordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (identity_relation(v11) = v12) | ~ (ordered_pair(v13, v13) = v14) | ~ relation(v12) | ~ in(v13, v11) | in(v14, v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (identity_relation(v11) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & ( ~ (v15 = v14) | ~ in(v16, v12) | ~ in(v14, v11)) & (in(v16, v12) | (v15 = v14 & in(v14, v11))))) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (identity_relation(v13) = v12) | ~ (identity_relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ relation(v12) | ~ empty(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ relation(v12) | ~ empty(v11) | empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ empty(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ empty(v11) | empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ~ empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (singleton(v11) = v15 & unordered_pair(v14, v15) = v13 & unordered_pair(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v12, v11) = v13) | unordered_pair(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | ~ empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | unordered_pair(v12, v11) = v13) & ! [v11] : ! [v12] : (v12 = v11 | ~ empty(v12) | ~ empty(v11)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | relation(v12)) & ! [v11] : ! [v12] : ( ~ element(v11, v12) | empty(v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ empty(v12) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) & ! [v11] : (v11 = empty_set | ~ empty(v11)) & ! [v11] : ( ~ empty(v11) | relation(v11)) & ? [v11] : ? [v12] : element(v12, v11) & ((in(v4, v6) & ( ~ in(v4, v3) | ~ in(v0, v2))) | (in(v4, v3) & in(v0, v2) & ~ in(v4, v6)))) % 4.88/1.81 | 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, all_0_10_10 yields: % 4.88/1.81 | (1) relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4 & identity_relation(all_0_8_8) = all_0_5_5 & ordered_pair(all_0_10_10, all_0_9_9) = all_0_6_6 & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_7_7) & 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] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v1) | in(v5, v2) | ? [v8] : (ordered_pair(v3, v6) = v8 & ~ in(v8, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8] : (ordered_pair(v6, v4) = v8 & ~ in(v8, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & in(v8, v1) & in(v7, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) & ! [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] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [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] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ( ~ (v4 = v3) | ~ in(v5, v1) | ~ in(v3, v0)) & (in(v5, v1) | (v4 = v3 & in(v3, v0))))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [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] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(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 | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ((in(all_0_6_6, all_0_4_4) & ( ~ in(all_0_6_6, all_0_7_7) | ~ in(all_0_10_10, all_0_8_8))) | (in(all_0_6_6, all_0_7_7) & in(all_0_10_10, all_0_8_8) & ~ in(all_0_6_6, all_0_4_4))) % 5.00/1.82 | % 5.00/1.82 | Applying alpha-rule on (1) yields: % 5.04/1.82 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 5.04/1.82 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8] : (ordered_pair(v6, v4) = v8 & ~ in(v8, v1))) % 5.04/1.82 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 5.04/1.82 | (5) empty(all_0_0_0) % 5.04/1.82 | (6) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 5.04/1.82 | (7) empty(empty_set) % 5.04/1.82 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 5.04/1.83 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 5.04/1.83 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ( ~ (v4 = v3) | ~ in(v5, v1) | ~ in(v3, v0)) & (in(v5, v1) | (v4 = v3 & in(v3, v0))))) % 5.04/1.83 | (11) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 5.04/1.83 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 5.04/1.83 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 5.04/1.83 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 5.04/1.83 | (15) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 5.04/1.83 | (16) relation(all_0_7_7) % 5.04/1.83 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & in(v8, v1) & in(v7, v0))) % 5.04/1.83 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) % 5.04/1.83 | (19) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 5.04/1.83 | (20) identity_relation(all_0_8_8) = all_0_5_5 % 5.04/1.83 | (21) empty(all_0_1_1) % 5.04/1.83 | (22) (in(all_0_6_6, all_0_4_4) & ( ~ in(all_0_6_6, all_0_7_7) | ~ in(all_0_10_10, all_0_8_8))) | (in(all_0_6_6, all_0_7_7) & in(all_0_10_10, all_0_8_8) & ~ in(all_0_6_6, all_0_4_4)) % 5.04/1.83 | (23) relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4 % 5.04/1.83 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 5.04/1.83 | (25) ~ empty(all_0_2_2) % 5.04/1.83 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 5.04/1.83 | (27) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 5.04/1.83 | (28) relation(empty_set) % 5.04/1.83 | (29) ordered_pair(all_0_10_10, all_0_9_9) = all_0_6_6 % 5.04/1.83 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 5.04/1.83 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 5.04/1.83 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 5.04/1.83 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 5.04/1.83 | (34) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 5.04/1.83 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 5.04/1.83 | (36) ~ empty(all_0_3_3) % 5.04/1.83 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) % 5.04/1.83 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 5.04/1.83 | (39) relation(all_0_2_2) % 5.04/1.83 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v1) | in(v5, v2) | ? [v8] : (ordered_pair(v3, v6) = v8 & ~ in(v8, v0))) % 5.04/1.83 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) % 5.04/1.84 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 5.04/1.84 | (43) ! [v0] : ( ~ empty(v0) | relation(v0)) % 5.04/1.84 | (44) relation(all_0_0_0) % 5.04/1.84 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 5.04/1.84 | (46) ? [v0] : ? [v1] : element(v1, v0) % 5.04/1.84 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) % 5.04/1.84 | (48) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 5.04/1.84 | % 5.04/1.84 | Instantiating formula (11) with all_0_5_5, all_0_8_8 and discharging atoms identity_relation(all_0_8_8) = all_0_5_5, yields: % 5.04/1.84 | (49) relation(all_0_5_5) % 5.04/1.84 | % 5.04/1.84 | Instantiating formula (4) with all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4, relation(all_0_5_5), relation(all_0_7_7), yields: % 5.04/1.84 | (50) relation(all_0_4_4) % 5.04/1.84 | % 5.04/1.84 +-Applying beta-rule and splitting (22), into two cases. % 5.04/1.84 |-Branch one: % 5.04/1.84 | (51) in(all_0_6_6, all_0_4_4) & ( ~ in(all_0_6_6, all_0_7_7) | ~ in(all_0_10_10, all_0_8_8)) % 5.04/1.84 | % 5.04/1.84 | Applying alpha-rule on (51) yields: % 5.04/1.84 | (52) in(all_0_6_6, all_0_4_4) % 5.04/1.84 | (53) ~ in(all_0_6_6, all_0_7_7) | ~ in(all_0_10_10, all_0_8_8) % 5.04/1.84 | % 5.04/1.84 | Instantiating formula (17) with all_0_6_6, all_0_9_9, all_0_10_10, all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4, ordered_pair(all_0_10_10, all_0_9_9) = all_0_6_6, relation(all_0_4_4), relation(all_0_5_5), relation(all_0_7_7), in(all_0_6_6, all_0_4_4), yields: % 5.04/1.84 | (54) ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, all_0_9_9) = v2 & ordered_pair(all_0_10_10, v0) = v1 & in(v2, all_0_7_7) & in(v1, all_0_5_5)) % 5.04/1.84 | % 5.04/1.84 | Instantiating (54) with all_36_0_15, all_36_1_16, all_36_2_17 yields: % 5.04/1.84 | (55) ordered_pair(all_36_2_17, all_0_9_9) = all_36_0_15 & ordered_pair(all_0_10_10, all_36_2_17) = all_36_1_16 & in(all_36_0_15, all_0_7_7) & in(all_36_1_16, all_0_5_5) % 5.04/1.84 | % 5.04/1.84 | Applying alpha-rule on (55) yields: % 5.04/1.84 | (56) ordered_pair(all_36_2_17, all_0_9_9) = all_36_0_15 % 5.04/1.84 | (57) ordered_pair(all_0_10_10, all_36_2_17) = all_36_1_16 % 5.04/1.84 | (58) in(all_36_0_15, all_0_7_7) % 5.04/1.84 | (59) in(all_36_1_16, all_0_5_5) % 5.04/1.84 | % 5.04/1.84 | Instantiating formula (37) with all_36_1_16, all_36_2_17, all_0_10_10, all_0_5_5, all_0_8_8 and discharging atoms identity_relation(all_0_8_8) = all_0_5_5, ordered_pair(all_0_10_10, all_36_2_17) = all_36_1_16, relation(all_0_5_5), in(all_36_1_16, all_0_5_5), yields: % 5.04/1.84 | (60) all_36_2_17 = all_0_10_10 % 5.04/1.84 | % 5.04/1.84 | From (60) and (56) follows: % 5.04/1.84 | (61) ordered_pair(all_0_10_10, all_0_9_9) = all_36_0_15 % 5.04/1.84 | % 5.04/1.84 | From (60) and (57) follows: % 5.04/1.84 | (62) ordered_pair(all_0_10_10, all_0_10_10) = all_36_1_16 % 5.04/1.84 | % 5.04/1.85 | Instantiating formula (38) with all_0_10_10, all_0_9_9, all_36_0_15, all_0_6_6 and discharging atoms ordered_pair(all_0_10_10, all_0_9_9) = all_36_0_15, ordered_pair(all_0_10_10, all_0_9_9) = all_0_6_6, yields: % 5.04/1.85 | (63) all_36_0_15 = all_0_6_6 % 5.04/1.85 | % 5.04/1.85 | From (63) and (58) follows: % 5.04/1.85 | (64) in(all_0_6_6, all_0_7_7) % 5.04/1.85 | % 5.04/1.85 +-Applying beta-rule and splitting (53), into two cases. % 5.04/1.85 |-Branch one: % 5.04/1.85 | (65) ~ in(all_0_6_6, all_0_7_7) % 5.04/1.85 | % 5.04/1.85 | Using (64) and (65) yields: % 5.04/1.85 | (66) $false % 5.04/1.85 | % 5.04/1.85 |-The branch is then unsatisfiable % 5.04/1.85 |-Branch two: % 5.04/1.85 | (64) in(all_0_6_6, all_0_7_7) % 5.04/1.85 | (68) ~ in(all_0_10_10, all_0_8_8) % 5.04/1.85 | % 5.04/1.85 | Instantiating formula (47) with all_36_1_16, all_0_10_10, all_0_10_10, all_0_5_5, all_0_8_8 and discharging atoms identity_relation(all_0_8_8) = all_0_5_5, ordered_pair(all_0_10_10, all_0_10_10) = all_36_1_16, relation(all_0_5_5), in(all_36_1_16, all_0_5_5), ~ in(all_0_10_10, all_0_8_8), yields: % 5.04/1.85 | (66) $false % 5.04/1.85 | % 5.04/1.85 |-The branch is then unsatisfiable % 5.04/1.85 |-Branch two: % 5.04/1.85 | (70) in(all_0_6_6, all_0_7_7) & in(all_0_10_10, all_0_8_8) & ~ in(all_0_6_6, all_0_4_4) % 5.04/1.85 | % 5.04/1.85 | Applying alpha-rule on (70) yields: % 5.04/1.85 | (64) in(all_0_6_6, all_0_7_7) % 5.04/1.85 | (72) in(all_0_10_10, all_0_8_8) % 5.04/1.85 | (73) ~ in(all_0_6_6, all_0_4_4) % 5.04/1.85 | % 5.04/1.85 | Instantiating formula (40) with all_0_6_6, all_0_10_10, all_0_6_6, all_0_9_9, all_0_10_10, all_0_4_4, all_0_7_7, all_0_5_5 and discharging atoms relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4, ordered_pair(all_0_10_10, all_0_9_9) = all_0_6_6, relation(all_0_4_4), relation(all_0_5_5), relation(all_0_7_7), in(all_0_6_6, all_0_7_7), ~ in(all_0_6_6, all_0_4_4), yields: % 5.04/1.85 | (74) ? [v0] : (ordered_pair(all_0_10_10, all_0_10_10) = v0 & ~ in(v0, all_0_5_5)) % 5.04/1.85 | % 5.04/1.85 | Instantiating (74) with all_36_0_18 yields: % 5.04/1.85 | (75) ordered_pair(all_0_10_10, all_0_10_10) = all_36_0_18 & ~ in(all_36_0_18, all_0_5_5) % 5.04/1.85 | % 5.04/1.85 | Applying alpha-rule on (75) yields: % 5.04/1.85 | (76) ordered_pair(all_0_10_10, all_0_10_10) = all_36_0_18 % 5.04/1.85 | (77) ~ in(all_36_0_18, all_0_5_5) % 5.04/1.85 | % 5.04/1.85 | Instantiating formula (18) with all_36_0_18, all_0_10_10, all_0_5_5, all_0_8_8 and discharging atoms identity_relation(all_0_8_8) = all_0_5_5, ordered_pair(all_0_10_10, all_0_10_10) = all_36_0_18, relation(all_0_5_5), in(all_0_10_10, all_0_8_8), ~ in(all_36_0_18, all_0_5_5), yields: % 5.04/1.85 | (66) $false % 5.04/1.85 | % 5.04/1.85 |-The branch is then unsatisfiable % 5.04/1.85 % SZS output end Proof for theBenchmark % 5.04/1.85 % 5.04/1.85 1287ms %------------------------------------------------------------------------------