%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU196+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 08:47:31 EDT 2022 % Result : Theorem 2.46s 1.33s % Output : Proof 4.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU196+1 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.34 % Computer : n012.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sun Jun 19 20:01:52 EDT 2022 % 0.14/0.34 % CPUTime : % 0.20/0.59 ____ _ % 0.20/0.59 ___ / __ \_____(_)___ ________ __________ % 0.20/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.20/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.20/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic % 0.20/0.59 (ePrincess v.1.0) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2015 % 0.20/0.59 (c) Peter Backeman, 2014-2015 % 0.20/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.20/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.20/0.59 Bug reports to peter@backeman.se % 0.20/0.59 % 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.20/0.59 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.55/0.94 Prover 0: Preprocessing ... % 1.90/1.12 Prover 0: Warning: ignoring some quantifiers % 1.90/1.15 Prover 0: Constructing countermodel ... % 2.46/1.32 Prover 0: proved (678ms) % 2.46/1.33 % 2.46/1.33 No countermodel exists, formula is valid % 2.46/1.33 % SZS status Theorem for theBenchmark % 2.46/1.33 % 2.46/1.33 Generating proof ... Warning: ignoring some quantifiers % 3.69/1.58 found it (size 9) % 3.69/1.58 % 3.69/1.58 % SZS output start Proof for theBenchmark % 3.69/1.58 Assumed formulas after preprocessing and simplification: % 3.69/1.59 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & relation_dom_restriction(v1, v0) = v2 & relation(v8) & relation(v6) & relation(v1) & relation(empty_set) & empty(v8) & empty(v7) & empty(empty_set) & ~ subset(v3, v4) & ~ empty(v6) & ~ empty(v5) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (relation_dom_restriction(v12, v11) = v10) | ~ (relation_dom_restriction(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ element(v10, v12) | ~ empty(v11) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ element(v10, v12) | ~ in(v9, v10) | element(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (relation_rng(v11) = v10) | ~ (relation_rng(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (relation_dom(v11) = v10) | ~ (relation_dom(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (powerset(v11) = v10) | ~ (powerset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ subset(v9, v10) | element(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ element(v9, v11) | subset(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_dom_restriction(v10, v9) = v11) | ~ relation(v10) | subset(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_dom_restriction(v9, v10) = v11) | ~ relation(v9) | relation(v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ empty(v10) | ~ empty(v9)) & ! [v9] : ! [v10] : ( ~ (relation_rng(v9) = v10) | ~ relation(v9) | ~ empty(v10) | empty(v9)) & ! [v9] : ! [v10] : ( ~ (relation_rng(v9) = v10) | ~ relation(v9) | ? [v11] : (relation_dom(v9) = v11 & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ subset(v9, v12) | ~ relation(v12) | subset(v10, v13)) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ subset(v9, v12) | ~ relation(v12) | ? [v14] : (relation_dom(v12) = v14 & subset(v11, v14))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ subset(v9, v12) | ~ relation(v12) | subset(v11, v13)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ subset(v9, v12) | ~ relation(v12) | ? [v14] : (relation_rng(v12) = v14 & subset(v10, v14))))) & ! [v9] : ! [v10] : ( ~ (relation_rng(v9) = v10) | ~ empty(v9) | relation(v10)) & ! [v9] : ! [v10] : ( ~ (relation_rng(v9) = v10) | ~ empty(v9) | empty(v10)) & ! [v9] : ! [v10] : ( ~ (relation_dom(v9) = v10) | ~ relation(v9) | ~ empty(v10) | empty(v9)) & ! [v9] : ! [v10] : ( ~ (relation_dom(v9) = v10) | ~ relation(v9) | ? [v11] : (relation_rng(v9) = v11 & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ subset(v9, v12) | ~ relation(v12) | subset(v11, v13)) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ subset(v9, v12) | ~ relation(v12) | ? [v14] : (relation_dom(v12) = v14 & subset(v10, v14))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ subset(v9, v12) | ~ relation(v12) | subset(v10, v13)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ subset(v9, v12) | ~ relation(v12) | ? [v14] : (relation_rng(v12) = v14 & subset(v11, v14))))) & ! [v9] : ! [v10] : ( ~ (relation_dom(v9) = v10) | ~ empty(v9) | relation(v10)) & ! [v9] : ! [v10] : ( ~ (relation_dom(v9) = v10) | ~ empty(v9) | empty(v10)) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ empty(v10)) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | empty(v9) | ? [v11] : (element(v11, v10) & ~ empty(v11))) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ? [v11] : (element(v11, v10) & empty(v11))) & ! [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) & ? [v9] : subset(v9, v9)) % 3.69/1.63 | 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: % 3.69/1.63 | (1) relation_rng(all_0_6_6) = all_0_5_5 & relation_rng(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) & ~ subset(all_0_5_5, all_0_4_4) & ~ empty(all_0_2_2) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [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] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5))))) & ! [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) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [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) & ? [v0] : subset(v0, v0) % 4.08/1.64 | % 4.08/1.64 | Applying alpha-rule on (1) yields: % 4.08/1.64 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) % 4.08/1.64 | (3) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.08/1.64 | (4) ~ empty(all_0_2_2) % 4.08/1.64 | (5) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) % 4.08/1.64 | (6) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.08/1.64 | (7) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 4.08/1.64 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 4.08/1.64 | (9) relation_rng(all_0_7_7) = all_0_4_4 % 4.08/1.64 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.08/1.64 | (11) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 4.08/1.64 | (12) relation(all_0_2_2) % 4.08/1.64 | (13) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 4.08/1.64 | (14) empty(empty_set) % 4.08/1.64 | (15) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 4.08/1.64 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 4.08/1.64 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 4.08/1.64 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 4.08/1.64 | (19) ? [v0] : subset(v0, v0) % 4.08/1.64 | (20) ! [v0] : ( ~ empty(v0) | relation(v0)) % 4.08/1.64 | (21) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5))))) % 4.08/1.65 | (22) relation_dom_restriction(all_0_7_7, all_0_8_8) = all_0_6_6 % 4.08/1.65 | (23) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 4.08/1.65 | (24) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 4.08/1.65 | (25) ~ subset(all_0_5_5, all_0_4_4) % 4.08/1.65 | (26) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 4.08/1.65 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 4.08/1.65 | (28) empty(all_0_1_1) % 4.08/1.65 | (29) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 4.08/1.65 | (30) empty(all_0_0_0) % 4.08/1.65 | (31) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.08/1.65 | (32) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 4.08/1.65 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 4.08/1.65 | (34) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.08/1.65 | (35) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 4.08/1.65 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 4.08/1.65 | (37) relation(all_0_7_7) % 4.08/1.65 | (38) relation(empty_set) % 4.08/1.65 | (39) relation(all_0_0_0) % 4.08/1.65 | (40) relation_rng(all_0_6_6) = all_0_5_5 % 4.08/1.65 | (41) ? [v0] : ? [v1] : element(v1, v0) % 4.08/1.65 | (42) ~ empty(all_0_3_3) % 4.08/1.65 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 4.08/1.65 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 4.08/1.65 | % 4.08/1.65 | Instantiating formula (2) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms relation_dom_restriction(all_0_7_7, all_0_8_8) = all_0_6_6, relation(all_0_7_7), yields: % 4.08/1.65 | (45) subset(all_0_6_6, all_0_7_7) % 4.08/1.65 | % 4.08/1.65 | Instantiating formula (8) 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: % 4.08/1.65 | (46) relation(all_0_6_6) % 4.08/1.65 | % 4.08/1.65 | Instantiating formula (21) with all_0_5_5, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_5_5, relation(all_0_6_6), yields: % 4.08/1.65 | (47) ? [v0] : (relation_dom(all_0_6_6) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | subset(all_0_5_5, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v0, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(all_0_5_5, v3)))) % 4.08/1.66 | % 4.08/1.66 | Instantiating (47) with all_25_0_13 yields: % 4.08/1.66 | (48) relation_dom(all_0_6_6) = all_25_0_13 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_5_5, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_25_0_13, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_25_0_13, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_0_5_5, v2))) % 4.08/1.66 | % 4.08/1.66 | Applying alpha-rule on (48) yields: % 4.08/1.66 | (49) relation_dom(all_0_6_6) = all_25_0_13 % 4.08/1.66 | (50) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_25_0_13, v1)) % 4.08/1.66 | (51) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_0_5_5, v2))) % 4.08/1.66 | (52) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_5_5, v1)) % 4.08/1.66 | (53) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_25_0_13, v2))) % 4.08/1.66 | % 4.08/1.66 | Instantiating formula (52) with all_0_4_4, all_0_7_7 and discharging atoms relation_rng(all_0_7_7) = all_0_4_4, subset(all_0_6_6, all_0_7_7), relation(all_0_7_7), ~ subset(all_0_5_5, all_0_4_4), yields: % 4.08/1.66 | (54) $false % 4.08/1.66 | % 4.08/1.66 |-The branch is then unsatisfiable % 4.08/1.66 % SZS output end Proof for theBenchmark % 4.08/1.66 % 4.08/1.66 1056ms %------------------------------------------------------------------------------