%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU195+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n032.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 08:47:31 EDT 2022 % Result : Theorem 43.98s 14.78s % Output : Proof 49.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SEU195+1 : TPTP v8.1.0. Released v3.3.0. % 0.00/0.09 % Command : ePrincess-casc -timeout=%d %s % 0.09/0.28 % Computer : n032.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 600 % 0.09/0.28 % DateTime : Sun Jun 19 00:00:17 EDT 2022 % 0.09/0.29 % CPUTime : % 0.13/0.48 ____ _ % 0.13/0.48 ___ / __ \_____(_)___ ________ __________ % 0.13/0.48 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.13/0.48 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.13/0.48 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.13/0.48 % 0.13/0.48 A Theorem Prover for First-Order Logic % 0.13/0.49 (ePrincess v.1.0) % 0.13/0.49 % 0.13/0.49 (c) Philipp Rümmer, 2009-2015 % 0.13/0.49 (c) Peter Backeman, 2014-2015 % 0.13/0.49 (contributions by Angelo Brillout, Peter Baumgartner) % 0.13/0.49 Free software under GNU Lesser General Public License (LGPL). % 0.13/0.49 Bug reports to peter@backeman.se % 0.13/0.49 % 0.13/0.49 For more information, visit http://user.uu.se/~petba168/breu/ % 0.13/0.49 % 0.13/0.49 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.13/0.53 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.11/0.77 Prover 0: Preprocessing ... % 1.63/0.98 Prover 0: Warning: ignoring some quantifiers % 1.63/1.00 Prover 0: Constructing countermodel ... % 19.81/5.82 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 19.81/5.86 Prover 1: Preprocessing ... % 20.24/5.97 Prover 1: Warning: ignoring some quantifiers % 20.24/5.97 Prover 1: Constructing countermodel ... % 30.40/8.42 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 30.75/8.45 Prover 2: Preprocessing ... % 31.09/8.54 Prover 2: Warning: ignoring some quantifiers % 31.09/8.54 Prover 2: Constructing countermodel ... % 37.76/11.43 Prover 0: stopped % 38.07/11.63 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 38.26/11.66 Prover 3: Preprocessing ... % 38.36/11.69 Prover 3: Warning: ignoring some quantifiers % 38.36/11.70 Prover 3: Constructing countermodel ... % 43.97/14.77 Prover 3: proved (3140ms) % 43.97/14.78 Prover 1: stopped % 43.97/14.78 Prover 2: stopped % 43.98/14.78 % 43.98/14.78 No countermodel exists, formula is valid % 43.98/14.78 % SZS status Theorem for theBenchmark % 43.98/14.78 % 43.98/14.78 Generating proof ... Warning: ignoring some quantifiers % 49.05/16.00 found it (size 27) % 49.05/16.00 % 49.05/16.00 % SZS output start Proof for theBenchmark % 49.05/16.00 Assumed formulas after preprocessing and simplification: % 49.05/16.00 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v4 = v2) & identity_relation(v0) = v3 & relation_composition(v3, v1) = v4 & relation_dom_restriction(v1, v0) = v2 & relation(v8) & relation(v6) & relation(v1) & relation(empty_set) & empty(v8) & empty(v7) & empty(empty_set) & ~ empty(v6) & ~ empty(v5) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (identity_relation(v11) = v14) | ~ (relation_composition(v14, v12) = v15) | ~ (ordered_pair(v9, v10) = v13) | ~ relation(v12) | ~ in(v13, v15) | in(v13, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (identity_relation(v11) = v14) | ~ (relation_composition(v14, v12) = v15) | ~ (ordered_pair(v9, v10) = v13) | ~ relation(v12) | ~ in(v13, v15) | in(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (identity_relation(v11) = v14) | ~ (relation_composition(v14, v12) = v15) | ~ (ordered_pair(v9, v10) = v13) | ~ relation(v12) | ~ in(v13, v12) | ~ in(v9, v11) | in(v13, v15)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v9, v10) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ relation(v11) | ~ relation(v9) | ~ in(v14, v11) | in(v14, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v9, v10) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ relation(v11) | ~ relation(v9) | ~ in(v14, v11) | in(v12, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v9, v10) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ relation(v11) | ~ relation(v9) | ~ in(v14, v9) | ~ in(v12, v10) | in(v14, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v9) = v12) | ~ (unordered_pair(v11, v12) = v13) | ~ (unordered_pair(v9, v10) = v11) | ordered_pair(v9, v10) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (relation_dom_restriction(v9, v10) = v12) | ~ relation(v11) | ~ relation(v9) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v13, v14) = v15 & ( ~ in(v15, v11) | ~ in(v15, v9) | ~ in(v13, v10)) & (in(v15, v11) | (in(v15, v9) & in(v13, v10))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (relation_composition(v12, v11) = v10) | ~ (relation_composition(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (relation_dom_restriction(v12, v11) = v10) | ~ (relation_dom_restriction(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (ordered_pair(v12, v11) = v10) | ~ (ordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (identity_relation(v11) = v10) | ~ (identity_relation(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_composition(v10, v9) = v11) | ~ relation(v10) | ~ empty(v9) | relation(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_composition(v10, v9) = v11) | ~ relation(v10) | ~ empty(v9) | empty(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_composition(v9, v10) = v11) | ~ relation(v10) | ~ relation(v9) | relation(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_composition(v9, v10) = v11) | ~ relation(v10) | ~ empty(v9) | relation(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_composition(v9, v10) = v11) | ~ relation(v10) | ~ empty(v9) | empty(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_dom_restriction(v9, v10) = v11) | ~ relation(v9) | relation(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ empty(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | ~ empty(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | unordered_pair(v10, v9) = v11) & ! [v9] : ! [v10] : (v10 = v9 | ~ relation(v10) | ~ relation(v9) | ? [v11] : ? [v12] : ? [v13] : (ordered_pair(v11, v12) = v13 & ( ~ in(v13, v10) | ~ in(v13, v9)) & (in(v13, v10) | in(v13, v9)))) & ! [v9] : ! [v10] : (v10 = v9 | ~ empty(v10) | ~ empty(v9)) & ! [v9] : ! [v10] : ( ~ (identity_relation(v9) = v10) | relation(v10)) & ! [v9] : ! [v10] : ( ~ (singleton(v9) = v10) | ~ empty(v10)) & ! [v9] : ! [v10] : ( ~ element(v9, v10) | empty(v10) | in(v9, v10)) & ! [v9] : ! [v10] : ( ~ empty(v10) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v10, v9) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v9, v10) | element(v9, v10)) & ! [v9] : (v9 = empty_set | ~ empty(v9)) & ! [v9] : ( ~ empty(v9) | relation(v9)) & ? [v9] : ? [v10] : element(v10, v9)) % 49.15/16.03 | 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 yields: % 49.15/16.03 | (1) ~ (all_0_4_4 = all_0_6_6) & identity_relation(all_0_8_8) = all_0_5_5 & relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4 & relation_dom_restriction(all_0_7_7, all_0_8_8) = 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] : ( ~ (identity_relation(v2) = v5) | ~ (relation_composition(v5, v3) = v6) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (identity_relation(v2) = v5) | ~ (relation_composition(v5, v3) = v6) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (identity_relation(v2) = v5) | ~ (relation_composition(v5, v3) = v6) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v3) | ~ in(v0, v2) | in(v4, v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) & ! [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] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(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] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(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] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(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 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ 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 | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ? [v0] : ? [v1] : element(v1, v0) % 49.15/16.04 | % 49.15/16.04 | Applying alpha-rule on (1) yields: % 49.15/16.04 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) % 49.15/16.04 | (3) ! [v0] : ( ~ empty(v0) | relation(v0)) % 49.15/16.04 | (4) ~ empty(all_0_2_2) % 49.15/16.04 | (5) relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4 % 49.15/16.04 | (6) ~ empty(all_0_3_3) % 49.15/16.04 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 49.15/16.04 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (identity_relation(v2) = v5) | ~ (relation_composition(v5, v3) = v6) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v3) | ~ in(v0, v2) | in(v4, v6)) % 49.15/16.04 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 49.15/16.04 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) % 49.15/16.04 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) % 49.15/16.04 | (12) empty(all_0_1_1) % 49.15/16.04 | (13) relation_dom_restriction(all_0_7_7, all_0_8_8) = all_0_6_6 % 49.15/16.05 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 49.15/16.05 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) % 49.15/16.05 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) % 49.15/16.05 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 49.15/16.05 | (18) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 49.15/16.05 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 49.15/16.05 | (20) identity_relation(all_0_8_8) = all_0_5_5 % 49.15/16.05 | (21) ? [v0] : ? [v1] : element(v1, v0) % 49.15/16.05 | (22) relation(empty_set) % 49.15/16.05 | (23) ~ (all_0_4_4 = all_0_6_6) % 49.15/16.05 | (24) relation(all_0_7_7) % 49.15/16.05 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 49.15/16.05 | (26) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 49.15/16.05 | (27) relation(all_0_0_0) % 49.15/16.05 | (28) relation(all_0_2_2) % 49.15/16.05 | (29) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 49.15/16.05 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 49.15/16.05 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 49.15/16.05 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (identity_relation(v2) = v5) | ~ (relation_composition(v5, v3) = v6) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3)) % 49.15/16.05 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (identity_relation(v2) = v5) | ~ (relation_composition(v5, v3) = v6) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2)) % 49.15/16.05 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 49.15/16.05 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 49.15/16.05 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 49.15/16.05 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 49.15/16.05 | (38) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 49.15/16.05 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 49.15/16.05 | (40) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 49.15/16.05 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 49.15/16.05 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 49.15/16.05 | (43) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 49.15/16.05 | (44) empty(empty_set) % 49.15/16.05 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 49.15/16.05 | (46) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 49.15/16.05 | (47) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 49.15/16.05 | (48) empty(all_0_0_0) % 49.15/16.05 | % 49.15/16.05 | Instantiating formula (18) with all_0_5_5, all_0_8_8 and discharging atoms identity_relation(all_0_8_8) = all_0_5_5, yields: % 49.15/16.05 | (49) relation(all_0_5_5) % 49.15/16.05 | % 49.15/16.05 | Instantiating formula (7) 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_7_7), yields: % 49.15/16.05 | (50) ~ relation(all_0_5_5) | relation(all_0_4_4) % 49.15/16.05 | % 49.15/16.05 +-Applying beta-rule and splitting (50), into two cases. % 49.15/16.05 |-Branch one: % 49.15/16.05 | (51) ~ relation(all_0_5_5) % 49.15/16.05 | % 49.15/16.05 | Using (49) and (51) yields: % 49.15/16.05 | (52) $false % 49.15/16.05 | % 49.15/16.05 |-The branch is then unsatisfiable % 49.15/16.05 |-Branch two: % 49.15/16.05 | (49) relation(all_0_5_5) % 49.15/16.05 | (54) relation(all_0_4_4) % 49.15/16.06 | % 49.15/16.06 | Instantiating formula (16) with all_0_6_6, all_0_4_4, all_0_8_8, all_0_7_7 and discharging atoms relation_dom_restriction(all_0_7_7, all_0_8_8) = all_0_6_6, relation(all_0_4_4), relation(all_0_7_7), yields: % 49.15/16.06 | (55) all_0_4_4 = all_0_6_6 | ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & ( ~ in(v2, all_0_4_4) | ~ in(v2, all_0_7_7) | ~ in(v0, all_0_8_8)) & (in(v2, all_0_4_4) | (in(v2, all_0_7_7) & in(v0, all_0_8_8)))) % 49.15/16.06 | % 49.15/16.06 +-Applying beta-rule and splitting (55), into two cases. % 49.15/16.06 |-Branch one: % 49.15/16.06 | (56) all_0_4_4 = all_0_6_6 % 49.15/16.06 | % 49.15/16.06 | Equations (56) can reduce 23 to: % 49.15/16.06 | (57) $false % 49.15/16.06 | % 49.15/16.06 |-The branch is then unsatisfiable % 49.15/16.06 |-Branch two: % 49.15/16.06 | (23) ~ (all_0_4_4 = all_0_6_6) % 49.15/16.06 | (59) ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & ( ~ in(v2, all_0_4_4) | ~ in(v2, all_0_7_7) | ~ in(v0, all_0_8_8)) & (in(v2, all_0_4_4) | (in(v2, all_0_7_7) & in(v0, all_0_8_8)))) % 49.15/16.06 | % 49.15/16.06 | Instantiating (59) with all_44_0_14, all_44_1_15, all_44_2_16 yields: % 49.15/16.06 | (60) ordered_pair(all_44_2_16, all_44_1_15) = all_44_0_14 & ( ~ in(all_44_0_14, all_0_4_4) | ~ in(all_44_0_14, all_0_7_7) | ~ in(all_44_2_16, all_0_8_8)) & (in(all_44_0_14, all_0_4_4) | (in(all_44_0_14, all_0_7_7) & in(all_44_2_16, all_0_8_8))) % 49.15/16.06 | % 49.15/16.06 | Applying alpha-rule on (60) yields: % 49.15/16.06 | (61) ordered_pair(all_44_2_16, all_44_1_15) = all_44_0_14 % 49.15/16.06 | (62) ~ in(all_44_0_14, all_0_4_4) | ~ in(all_44_0_14, all_0_7_7) | ~ in(all_44_2_16, all_0_8_8) % 49.15/16.06 | (63) in(all_44_0_14, all_0_4_4) | (in(all_44_0_14, all_0_7_7) & in(all_44_2_16, all_0_8_8)) % 49.15/16.06 | % 49.15/16.06 +-Applying beta-rule and splitting (62), into two cases. % 49.15/16.06 |-Branch one: % 49.15/16.06 | (64) ~ in(all_44_0_14, all_0_4_4) % 49.15/16.06 | % 49.15/16.06 +-Applying beta-rule and splitting (63), into two cases. % 49.15/16.06 |-Branch one: % 49.15/16.06 | (65) in(all_44_0_14, all_0_4_4) % 49.15/16.06 | % 49.15/16.06 | Using (65) and (64) yields: % 49.15/16.06 | (52) $false % 49.15/16.06 | % 49.15/16.06 |-The branch is then unsatisfiable % 49.15/16.06 |-Branch two: % 49.15/16.06 | (64) ~ in(all_44_0_14, all_0_4_4) % 49.15/16.06 | (68) in(all_44_0_14, all_0_7_7) & in(all_44_2_16, all_0_8_8) % 49.15/16.06 | % 49.15/16.06 | Applying alpha-rule on (68) yields: % 49.15/16.06 | (69) in(all_44_0_14, all_0_7_7) % 49.15/16.06 | (70) in(all_44_2_16, all_0_8_8) % 49.15/16.06 | % 49.15/16.06 | Instantiating formula (8) with all_0_4_4, all_0_5_5, all_44_0_14, all_0_7_7, all_0_8_8, all_44_1_15, all_44_2_16 and discharging atoms identity_relation(all_0_8_8) = all_0_5_5, relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4, ordered_pair(all_44_2_16, all_44_1_15) = all_44_0_14, relation(all_0_7_7), in(all_44_0_14, all_0_7_7), in(all_44_2_16, all_0_8_8), ~ in(all_44_0_14, all_0_4_4), yields: % 49.15/16.06 | (52) $false % 49.15/16.06 | % 49.15/16.06 |-The branch is then unsatisfiable % 49.15/16.06 |-Branch two: % 49.15/16.06 | (65) in(all_44_0_14, all_0_4_4) % 49.15/16.06 | (73) ~ in(all_44_0_14, all_0_7_7) | ~ in(all_44_2_16, all_0_8_8) % 49.15/16.06 | % 49.15/16.06 | Instantiating formula (32) with all_0_4_4, all_0_5_5, all_44_0_14, all_0_7_7, all_0_8_8, all_44_1_15, all_44_2_16 and discharging atoms identity_relation(all_0_8_8) = all_0_5_5, relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4, ordered_pair(all_44_2_16, all_44_1_15) = all_44_0_14, relation(all_0_7_7), in(all_44_0_14, all_0_4_4), yields: % 49.15/16.06 | (69) in(all_44_0_14, all_0_7_7) % 49.15/16.06 | % 49.15/16.06 | Instantiating formula (33) with all_0_4_4, all_0_5_5, all_44_0_14, all_0_7_7, all_0_8_8, all_44_1_15, all_44_2_16 and discharging atoms identity_relation(all_0_8_8) = all_0_5_5, relation_composition(all_0_5_5, all_0_7_7) = all_0_4_4, ordered_pair(all_44_2_16, all_44_1_15) = all_44_0_14, relation(all_0_7_7), in(all_44_0_14, all_0_4_4), yields: % 49.15/16.06 | (70) in(all_44_2_16, all_0_8_8) % 49.15/16.06 | % 49.15/16.06 +-Applying beta-rule and splitting (73), into two cases. % 49.15/16.06 |-Branch one: % 49.15/16.06 | (76) ~ in(all_44_0_14, all_0_7_7) % 49.15/16.06 | % 49.15/16.06 | Using (69) and (76) yields: % 49.15/16.06 | (52) $false % 49.15/16.06 | % 49.15/16.06 |-The branch is then unsatisfiable % 49.15/16.06 |-Branch two: % 49.15/16.06 | (69) in(all_44_0_14, all_0_7_7) % 49.15/16.06 | (79) ~ in(all_44_2_16, all_0_8_8) % 49.15/16.06 | % 49.15/16.06 | Using (70) and (79) yields: % 49.15/16.06 | (52) $false % 49.15/16.06 | % 49.15/16.06 |-The branch is then unsatisfiable % 49.15/16.06 % SZS output end Proof for theBenchmark % 49.15/16.06 % 49.15/16.06 15566ms %------------------------------------------------------------------------------