%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU192+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n012.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 2.84s 1.36s % Output : Proof 4.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SEU192+1 : TPTP v8.1.0. Released v3.3.0. % 0.00/0.09 % Command : ePrincess-casc -timeout=%d %s % 0.08/0.29 % Computer : n012.cluster.edu % 0.08/0.29 % Model : x86_64 x86_64 % 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.29 % Memory : 8042.1875MB % 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.29 % CPULimit : 300 % 0.08/0.29 % WCLimit : 600 % 0.08/0.29 % DateTime : Sun Jun 19 22:16:37 EDT 2022 % 0.08/0.29 % CPUTime : % 0.14/0.54 ____ _ % 0.14/0.54 ___ / __ \_____(_)___ ________ __________ % 0.14/0.54 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.14/0.54 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.14/0.54 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.14/0.54 % 0.14/0.54 A Theorem Prover for First-Order Logic % 0.14/0.54 (ePrincess v.1.0) % 0.14/0.54 % 0.14/0.54 (c) Philipp Rümmer, 2009-2015 % 0.14/0.54 (c) Peter Backeman, 2014-2015 % 0.14/0.54 (contributions by Angelo Brillout, Peter Baumgartner) % 0.14/0.54 Free software under GNU Lesser General Public License (LGPL). % 0.14/0.54 Bug reports to peter@backeman.se % 0.14/0.54 % 0.14/0.54 For more information, visit http://user.uu.se/~petba168/breu/ % 0.14/0.54 % 0.14/0.54 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.52/0.91 Prover 0: Preprocessing ... % 2.03/1.12 Prover 0: Warning: ignoring some quantifiers % 2.03/1.14 Prover 0: Constructing countermodel ... % 2.84/1.35 Prover 0: proved (747ms) % 2.84/1.36 % 2.84/1.36 No countermodel exists, formula is valid % 2.84/1.36 % SZS status Theorem for theBenchmark % 2.84/1.36 % 2.84/1.36 Generating proof ... Warning: ignoring some quantifiers % 4.09/1.66 found it (size 22) % 4.09/1.66 % 4.09/1.66 % SZS output start Proof for theBenchmark % 4.09/1.66 Assumed formulas after preprocessing and simplification: % 4.09/1.66 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & relation_dom_restriction(v2, v1) = v3 & relation(v9) & relation(v7) & relation(v2) & relation(empty_set) & empty(v9) & empty(v8) & empty(empty_set) & ~ empty(v7) & ~ empty(v6) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom_restriction(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v10) | ~ in(v15, v12) | in(v15, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom_restriction(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v10) | ~ in(v15, v12) | in(v13, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom_restriction(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v10) | ~ in(v15, v10) | ~ in(v13, v11) | in(v15, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v10) = v13) | ~ (unordered_pair(v12, v13) = v14) | ~ (unordered_pair(v10, v11) = v12) | ordered_pair(v10, v11) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v10) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ relation(v10) | ~ in(v14, v10) | in(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (relation_dom_restriction(v10, v11) = v13) | ~ relation(v12) | ~ relation(v10) | ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & ( ~ in(v16, v12) | ~ in(v16, v10) | ~ in(v14, v11)) & (in(v16, v12) | (in(v16, v10) & in(v14, v11))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_dom_restriction(v13, v12) = v11) | ~ (relation_dom_restriction(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_dom(v12) = v11) | ~ (relation_dom(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ~ in(v12, v11) | ? [v13] : ? [v14] : (ordered_pair(v12, v13) = v14 & in(v14, v10))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom_restriction(v10, v11) = v12) | ~ relation(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ~ empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & unordered_pair(v13, v14) = v12 & unordered_pair(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ~ empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (relation_dom(v11) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : ? [v15] : (( ~ in(v13, v10) | ! [v16] : ! [v17] : ( ~ (ordered_pair(v13, v16) = v17) | ~ in(v17, v11))) & (in(v13, v10) | (ordered_pair(v13, v14) = v15 & in(v15, v11))))) & ! [v10] : ! [v11] : (v11 = v10 | ~ empty(v11) | ~ empty(v10)) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | ~ empty(v11)) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ~ empty(v11) | empty(v10)) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ empty(v10) | relation(v11)) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ empty(v10) | empty(v11)) & ! [v10] : ! [v11] : ( ~ element(v10, v11) | empty(v11) | in(v10, v11)) & ! [v10] : ! [v11] : ( ~ empty(v11) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v10, v11) | element(v10, v11)) & ! [v10] : (v10 = empty_set | ~ empty(v10)) & ! [v10] : ( ~ empty(v10) | relation(v10)) & ? [v10] : ? [v11] : element(v11, v10) & ((in(v0, v5) & in(v0, v1) & ~ in(v0, v4)) | (in(v0, v4) & ( ~ in(v0, v5) | ~ in(v0, v1))))) % 4.44/1.71 | 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: % 4.44/1.71 | (1) relation_dom(all_0_6_6) = all_0_5_5 & relation_dom(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] : ( ~ (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] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [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_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 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = 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] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(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] : ! [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_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 | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ((in(all_0_9_9, all_0_4_4) & in(all_0_9_9, all_0_8_8) & ~ in(all_0_9_9, all_0_5_5)) | (in(all_0_9_9, all_0_5_5) & ( ~ in(all_0_9_9, all_0_4_4) | ~ in(all_0_9_9, all_0_8_8)))) % 4.44/1.72 | % 4.44/1.72 | Applying alpha-rule on (1) yields: % 4.44/1.72 | (2) relation_dom(all_0_7_7) = all_0_4_4 % 4.44/1.72 | (3) empty(all_0_1_1) % 4.44/1.72 | (4) relation_dom(all_0_6_6) = all_0_5_5 % 4.44/1.72 | (5) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.44/1.72 | (6) ? [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))))) % 4.44/1.72 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 4.44/1.72 | (8) relation(all_0_2_2) % 4.44/1.72 | (9) ? [v0] : ? [v1] : element(v1, v0) % 4.44/1.72 | (10) (in(all_0_9_9, all_0_4_4) & in(all_0_9_9, all_0_8_8) & ~ in(all_0_9_9, all_0_5_5)) | (in(all_0_9_9, all_0_5_5) & ( ~ in(all_0_9_9, all_0_4_4) | ~ in(all_0_9_9, all_0_8_8))) % 4.44/1.72 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.44/1.72 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 4.44/1.72 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 4.44/1.72 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 4.44/1.72 | (15) ! [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))))) % 4.44/1.72 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 4.44/1.72 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 4.44/1.72 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 4.44/1.72 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 4.44/1.72 | (20) ! [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)) % 4.44/1.72 | (21) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 4.44/1.72 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 4.44/1.72 | (23) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 4.44/1.73 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 4.44/1.73 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 4.44/1.73 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 4.44/1.73 | (27) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.44/1.73 | (28) ~ empty(all_0_2_2) % 4.44/1.73 | (29) ! [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)) % 4.44/1.73 | (30) ~ empty(all_0_3_3) % 4.44/1.73 | (31) empty(empty_set) % 4.44/1.73 | (32) relation(all_0_7_7) % 4.44/1.73 | (33) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.44/1.73 | (34) ! [v0] : ( ~ empty(v0) | relation(v0)) % 4.44/1.73 | (35) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.44/1.73 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 4.44/1.73 | (37) relation(all_0_0_0) % 4.44/1.73 | (38) ! [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)) % 4.44/1.73 | (39) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 4.44/1.73 | (40) empty(all_0_0_0) % 4.44/1.73 | (41) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 4.44/1.73 | (42) relation_dom_restriction(all_0_7_7, all_0_8_8) = all_0_6_6 % 4.44/1.73 | (43) relation(empty_set) % 4.44/1.73 | (44) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 4.44/1.73 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 4.44/1.73 | % 4.44/1.73 | Instantiating formula (26) with all_0_6_6, 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_7_7), yields: % 4.44/1.73 | (46) relation(all_0_6_6) % 4.44/1.73 | % 4.44/1.73 +-Applying beta-rule and splitting (10), into two cases. % 4.44/1.73 |-Branch one: % 4.44/1.73 | (47) in(all_0_9_9, all_0_4_4) & in(all_0_9_9, all_0_8_8) & ~ in(all_0_9_9, all_0_5_5) % 4.44/1.73 | % 4.44/1.73 | Applying alpha-rule on (47) yields: % 4.44/1.73 | (48) in(all_0_9_9, all_0_4_4) % 4.44/1.73 | (49) in(all_0_9_9, all_0_8_8) % 4.44/1.73 | (50) ~ in(all_0_9_9, all_0_5_5) % 4.44/1.73 | % 4.44/1.73 | Instantiating formula (17) with all_0_9_9, all_0_4_4, all_0_7_7 and discharging atoms relation_dom(all_0_7_7) = all_0_4_4, relation(all_0_7_7), in(all_0_9_9, all_0_4_4), yields: % 4.44/1.73 | (51) ? [v0] : ? [v1] : (ordered_pair(all_0_9_9, v0) = v1 & in(v1, all_0_7_7)) % 4.44/1.73 | % 4.44/1.73 | Instantiating (51) with all_30_0_13, all_30_1_14 yields: % 4.44/1.73 | (52) ordered_pair(all_0_9_9, all_30_1_14) = all_30_0_13 & in(all_30_0_13, all_0_7_7) % 4.44/1.73 | % 4.44/1.73 | Applying alpha-rule on (52) yields: % 4.44/1.73 | (53) ordered_pair(all_0_9_9, all_30_1_14) = all_30_0_13 % 4.44/1.73 | (54) in(all_30_0_13, all_0_7_7) % 4.44/1.73 | % 4.44/1.73 | Instantiating formula (29) with all_30_0_13, all_30_1_14, all_0_9_9, all_0_6_6, 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, ordered_pair(all_0_9_9, all_30_1_14) = all_30_0_13, relation(all_0_6_6), relation(all_0_7_7), in(all_30_0_13, all_0_7_7), in(all_0_9_9, all_0_8_8), yields: % 4.44/1.74 | (55) in(all_30_0_13, all_0_6_6) % 4.44/1.74 | % 4.44/1.74 | Instantiating formula (45) with all_30_0_13, all_30_1_14, all_0_9_9, all_0_5_5, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, ordered_pair(all_0_9_9, all_30_1_14) = all_30_0_13, relation(all_0_6_6), in(all_30_0_13, all_0_6_6), ~ in(all_0_9_9, all_0_5_5), yields: % 4.44/1.74 | (56) $false % 4.44/1.74 | % 4.44/1.74 |-The branch is then unsatisfiable % 4.44/1.74 |-Branch two: % 4.44/1.74 | (57) in(all_0_9_9, all_0_5_5) & ( ~ in(all_0_9_9, all_0_4_4) | ~ in(all_0_9_9, all_0_8_8)) % 4.44/1.74 | % 4.44/1.74 | Applying alpha-rule on (57) yields: % 4.44/1.74 | (58) in(all_0_9_9, all_0_5_5) % 4.44/1.74 | (59) ~ in(all_0_9_9, all_0_4_4) | ~ in(all_0_9_9, all_0_8_8) % 4.44/1.74 | % 4.44/1.74 | Instantiating formula (17) with all_0_9_9, all_0_5_5, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, relation(all_0_6_6), in(all_0_9_9, all_0_5_5), yields: % 4.44/1.74 | (60) ? [v0] : ? [v1] : (ordered_pair(all_0_9_9, v0) = v1 & in(v1, all_0_6_6)) % 4.44/1.74 | % 4.44/1.74 | Instantiating (60) with all_30_0_17, all_30_1_18 yields: % 4.44/1.74 | (61) ordered_pair(all_0_9_9, all_30_1_18) = all_30_0_17 & in(all_30_0_17, all_0_6_6) % 4.44/1.74 | % 4.44/1.74 | Applying alpha-rule on (61) yields: % 4.44/1.74 | (62) ordered_pair(all_0_9_9, all_30_1_18) = all_30_0_17 % 4.44/1.74 | (63) in(all_30_0_17, all_0_6_6) % 4.44/1.74 | % 4.44/1.74 | Instantiating formula (20) with all_30_0_17, all_30_1_18, all_0_9_9, all_0_6_6, 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, ordered_pair(all_0_9_9, all_30_1_18) = all_30_0_17, relation(all_0_6_6), relation(all_0_7_7), in(all_30_0_17, all_0_6_6), yields: % 4.44/1.74 | (64) in(all_30_0_17, all_0_7_7) % 4.44/1.74 | % 4.44/1.74 | Instantiating formula (38) with all_30_0_17, all_30_1_18, all_0_9_9, all_0_6_6, 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, ordered_pair(all_0_9_9, all_30_1_18) = all_30_0_17, relation(all_0_6_6), relation(all_0_7_7), in(all_30_0_17, all_0_6_6), yields: % 4.44/1.74 | (49) in(all_0_9_9, all_0_8_8) % 4.44/1.74 | % 4.44/1.74 +-Applying beta-rule and splitting (59), into two cases. % 4.44/1.74 |-Branch one: % 4.44/1.74 | (66) ~ in(all_0_9_9, all_0_4_4) % 4.44/1.74 | % 4.44/1.74 | Instantiating formula (45) with all_30_0_17, all_30_1_18, all_0_9_9, all_0_4_4, all_0_7_7 and discharging atoms relation_dom(all_0_7_7) = all_0_4_4, ordered_pair(all_0_9_9, all_30_1_18) = all_30_0_17, relation(all_0_7_7), in(all_30_0_17, all_0_7_7), ~ in(all_0_9_9, all_0_4_4), yields: % 4.44/1.74 | (56) $false % 4.44/1.74 | % 4.44/1.74 |-The branch is then unsatisfiable % 4.44/1.74 |-Branch two: % 4.44/1.74 | (48) in(all_0_9_9, all_0_4_4) % 4.44/1.74 | (69) ~ in(all_0_9_9, all_0_8_8) % 4.44/1.74 | % 4.44/1.74 | Using (49) and (69) yields: % 4.44/1.74 | (56) $false % 4.44/1.74 | % 4.44/1.74 |-The branch is then unsatisfiable % 4.44/1.74 % SZS output end Proof for theBenchmark % 4.44/1.74 % 4.44/1.74 1190ms %------------------------------------------------------------------------------