%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU199+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 08:47:33 EDT 2022 % Result : Theorem 2.83s 1.33s % Output : Proof 3.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SEU199+1 : TPTP v8.1.0. Released v3.3.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.33 % Computer : n026.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Sun Jun 19 01:30:40 EDT 2022 % 0.11/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.49/0.92 Prover 0: Preprocessing ... % 1.94/1.13 Prover 0: Warning: ignoring some quantifiers % 1.94/1.15 Prover 0: Constructing countermodel ... % 2.49/1.33 Prover 0: proved (710ms) % 2.83/1.33 % 2.83/1.33 No countermodel exists, formula is valid % 2.83/1.33 % SZS status Theorem for theBenchmark % 2.83/1.33 % 2.83/1.33 Generating proof ... Warning: ignoring some quantifiers % 3.70/1.53 found it (size 8) % 3.70/1.53 % 3.70/1.53 % SZS output start Proof for theBenchmark % 3.70/1.53 Assumed formulas after preprocessing and simplification: % 3.70/1.53 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng_restriction(v0, v1) = v2 & relation(v6) & relation(v4) & relation(v1) & relation(empty_set) & empty(v6) & empty(v5) & empty(empty_set) & ~ subset(v2, v1) & ~ empty(v4) & ~ empty(v3) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng_restriction(v7, v8) = v9) | ~ (ordered_pair(v10, v11) = v12) | ~ relation(v9) | ~ relation(v8) | ~ in(v12, v9) | in(v12, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng_restriction(v7, v8) = v9) | ~ (ordered_pair(v10, v11) = v12) | ~ relation(v9) | ~ relation(v8) | ~ in(v12, v9) | in(v11, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng_restriction(v7, v8) = v9) | ~ (ordered_pair(v10, v11) = v12) | ~ relation(v9) | ~ relation(v8) | ~ in(v12, v8) | ~ in(v11, v7) | in(v12, v9)) & ! [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] : ( ~ (ordered_pair(v9, v10) = v11) | ~ subset(v7, v8) | ~ relation(v8) | ~ relation(v7) | ~ in(v11, v7) | in(v11, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (relation_rng_restriction(v7, v8) = v9) | ~ relation(v10) | ~ relation(v8) | ? [v11] : ? [v12] : ? [v13] : (ordered_pair(v11, v12) = v13 & ( ~ in(v13, v10) | ~ in(v13, v8) | ~ in(v12, v7)) & (in(v13, v10) | (in(v13, v8) & in(v12, v7))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (relation_rng_restriction(v10, v9) = v8) | ~ (relation_rng_restriction(v10, v9) = v7)) & ! [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] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ element(v8, v10) | ~ empty(v9) | ~ in(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ element(v8, v10) | ~ in(v7, v8) | element(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (powerset(v9) = v8) | ~ (powerset(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ element(v7, v9) | subset(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ subset(v7, v8) | element(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (relation_rng_restriction(v7, v8) = v9) | ~ relation(v8) | relation(v9)) & ! [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] : (v8 = v7 | ~ empty(v8) | ~ empty(v7)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | empty(v7) | ? [v9] : (element(v9, v8) & ~ empty(v9))) & ! [v7] : ! [v8] : ( ~ (powerset(v7) = v8) | ? [v9] : (element(v9, v8) & empty(v9))) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | ~ empty(v8)) & ! [v7] : ! [v8] : ( ~ element(v7, v8) | empty(v8) | in(v7, v8)) & ! [v7] : ! [v8] : ( ~ relation(v8) | ~ relation(v7) | subset(v7, v8) | ? [v9] : ? [v10] : ? [v11] : (ordered_pair(v9, v10) = v11 & in(v11, v7) & ~ in(v11, 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 | ~ empty(v7)) & ! [v7] : ( ~ empty(v7) | relation(v7)) & ? [v7] : ? [v8] : element(v8, v7) & ? [v7] : subset(v7, v7)) % 3.84/1.57 | 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: % 3.84/1.57 | (1) relation_rng_restriction(all_0_6_6, all_0_5_5) = all_0_4_4 & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_5_5) & relation(empty_set) & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) & ~ subset(all_0_4_4, all_0_5_5) & ~ empty(all_0_2_2) & ~ empty(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | 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] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_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] : ! [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 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | 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] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [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] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, 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) % 3.84/1.58 | % 3.84/1.58 | Applying alpha-rule on (1) yields: % 3.84/1.58 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 3.84/1.58 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) % 3.84/1.58 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 3.84/1.58 | (5) relation(all_0_5_5) % 3.84/1.58 | (6) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 3.84/1.58 | (7) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.84/1.58 | (8) relation(all_0_0_0) % 3.84/1.58 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 3.84/1.58 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 3.84/1.58 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) % 3.84/1.58 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 3.84/1.58 | (13) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 3.84/1.58 | (14) ! [v0] : ( ~ empty(v0) | relation(v0)) % 3.84/1.58 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 3.84/1.58 | (16) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 3.84/1.58 | (17) ? [v0] : subset(v0, v0) % 3.84/1.59 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 3.84/1.59 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 3.84/1.59 | (20) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 3.84/1.59 | (21) ? [v0] : ? [v1] : element(v1, v0) % 3.84/1.59 | (22) relation(empty_set) % 3.84/1.59 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) % 3.84/1.59 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 3.84/1.59 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 3.84/1.59 | (26) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.84/1.59 | (27) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 3.84/1.59 | (28) relation(all_0_2_2) % 3.84/1.59 | (29) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) % 3.84/1.59 | (30) empty(all_0_0_0) % 3.84/1.59 | (31) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 3.84/1.59 | (32) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 3.84/1.59 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 3.84/1.59 | (34) empty(empty_set) % 3.84/1.59 | (35) ~ subset(all_0_4_4, all_0_5_5) % 3.84/1.59 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) % 3.84/1.59 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 3.84/1.59 | (38) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.84/1.59 | (39) ~ empty(all_0_2_2) % 3.84/1.59 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) % 3.84/1.59 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 3.84/1.59 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 3.84/1.59 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 3.84/1.59 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) % 3.84/1.59 | (45) empty(all_0_1_1) % 3.84/1.59 | (46) relation_rng_restriction(all_0_6_6, all_0_5_5) = all_0_4_4 % 3.84/1.59 | (47) ~ empty(all_0_3_3) % 3.84/1.59 | % 3.84/1.59 | Instantiating formula (40) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms relation_rng_restriction(all_0_6_6, all_0_5_5) = all_0_4_4, relation(all_0_5_5), yields: % 3.84/1.59 | (48) relation(all_0_4_4) % 3.84/1.59 | % 3.84/1.59 | Instantiating formula (29) with all_0_5_5, all_0_4_4 and discharging atoms relation(all_0_4_4), relation(all_0_5_5), ~ subset(all_0_4_4, all_0_5_5), yields: % 3.84/1.59 | (49) ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_4_4) & ~ in(v2, all_0_5_5)) % 3.84/1.60 | % 3.84/1.60 | Instantiating (49) with all_23_0_10, all_23_1_11, all_23_2_12 yields: % 3.84/1.60 | (50) ordered_pair(all_23_2_12, all_23_1_11) = all_23_0_10 & in(all_23_0_10, all_0_4_4) & ~ in(all_23_0_10, all_0_5_5) % 3.84/1.60 | % 3.84/1.60 | Applying alpha-rule on (50) yields: % 3.84/1.60 | (51) ordered_pair(all_23_2_12, all_23_1_11) = all_23_0_10 % 3.84/1.60 | (52) in(all_23_0_10, all_0_4_4) % 3.84/1.60 | (53) ~ in(all_23_0_10, all_0_5_5) % 3.84/1.60 | % 3.84/1.60 | Instantiating formula (23) with all_23_0_10, all_23_1_11, all_23_2_12, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms relation_rng_restriction(all_0_6_6, all_0_5_5) = all_0_4_4, ordered_pair(all_23_2_12, all_23_1_11) = all_23_0_10, relation(all_0_4_4), relation(all_0_5_5), in(all_23_0_10, all_0_4_4), ~ in(all_23_0_10, all_0_5_5), yields: % 3.84/1.60 | (54) $false % 3.84/1.60 | % 3.84/1.60 |-The branch is then unsatisfiable % 3.84/1.60 % SZS output end Proof for theBenchmark % 3.84/1.60 % 3.84/1.60 1019ms %------------------------------------------------------------------------------