%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET991+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 00:23:39 EDT 2022 % Result : Theorem 2.58s 1.26s % Output : Proof 3.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET991+1 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n007.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jul 11 04:54:02 EDT 2022 % 0.12/0.33 % 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/sandbox/benchmark/theBenchmark.p ... % 0.62/0.61 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.53/0.89 Prover 0: Preprocessing ... % 2.06/1.11 Prover 0: Warning: ignoring some quantifiers % 2.06/1.13 Prover 0: Constructing countermodel ... % 2.58/1.26 Prover 0: proved (649ms) % 2.58/1.26 % 2.58/1.26 No countermodel exists, formula is valid % 2.58/1.26 % SZS status Theorem for theBenchmark % 2.58/1.26 % 2.58/1.26 Generating proof ... Warning: ignoring some quantifiers % 3.84/1.54 found it (size 10) % 3.84/1.54 % 3.84/1.54 % SZS output start Proof for theBenchmark % 3.84/1.54 Assumed formulas after preprocessing and simplification: % 3.84/1.54 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (apply(v1, v0) = v3 & relation_rng(v1) = v4 & relation_dom(v1) = v2 & in(v0, v2) & function(v10) & function(v1) & relation_empty_yielding(v7) & relation_empty_yielding(empty_set) & relation(v10) & relation(v9) & relation(v8) & relation(v7) & relation(v1) & relation(empty_set) & empty(v9) & empty(v6) & empty(empty_set) & ~ in(v3, v4) & ~ empty(v8) & ~ empty(v5) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (apply(v14, v13) = v12) | ~ (apply(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ in(v11, v12) | ~ element(v12, v14) | ~ empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ in(v11, v12) | ~ element(v12, v14) | element(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_rng(v13) = v12) | ~ (relation_rng(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_dom(v13) = v12) | ~ (relation_dom(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | subset(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ subset(v11, v12) | element(v11, v13)) & ! [v11] : ! [v12] : (v12 = v11 | ~ empty(v12) | ~ empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ function(v11) | ~ relation(v11) | ? [v13] : (relation_dom(v11) = v13 & ! [v14] : ! [v15] : ( ~ (apply(v11, v15) = v14) | ~ in(v15, v13) | in(v14, v12)) & ! [v14] : ( ~ in(v14, v12) | ? [v15] : (apply(v11, v15) = v14 & in(v15, v13))) & ? [v14] : (v14 = v12 | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v14) | ! [v18] : ( ~ (apply(v11, v18) = v15) | ~ in(v18, v13))) & (in(v15, v14) | (v17 = v15 & apply(v11, v16) = v15 & in(v16, v13))))))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ function(v11) | ~ relation(v11) | ? [v13] : (relation_rng(v11) = v13 & ! [v14] : ! [v15] : ( ~ (apply(v11, v15) = v14) | ~ in(v15, v12) | in(v14, v13)) & ! [v14] : ( ~ in(v14, v13) | ? [v15] : (apply(v11, v15) = v14 & in(v15, v12))) & ? [v14] : (v14 = v13 | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v14) | ! [v18] : ( ~ (apply(v11, v18) = v15) | ~ in(v18, v12))) & (in(v15, v14) | (v17 = v15 & apply(v11, v16) = v15 & in(v16, v12))))))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | empty(v11) | ? [v13] : (element(v13, v12) & ~ empty(v13))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) & empty(v13))) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) & ! [v11] : ! [v12] : ( ~ element(v11, v12) | in(v11, v12) | empty(v12)) & ! [v11] : (v11 = empty_set | ~ empty(v11)) & ! [v11] : ( ~ empty(v11) | function(v11)) & ! [v11] : ( ~ empty(v11) | relation(v11)) & ? [v11] : ? [v12] : element(v12, v11) & ? [v11] : subset(v11, v11)) % 3.84/1.58 | 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: % 3.84/1.58 | (1) apply(all_0_9_9, all_0_10_10) = all_0_7_7 & relation_rng(all_0_9_9) = all_0_6_6 & relation_dom(all_0_9_9) = all_0_8_8 & in(all_0_10_10, all_0_8_8) & function(all_0_0_0) & function(all_0_9_9) & relation_empty_yielding(all_0_3_3) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_2_2) & relation(all_0_3_3) & relation(all_0_9_9) & relation(empty_set) & empty(all_0_1_1) & empty(all_0_4_4) & empty(empty_set) & ~ in(all_0_7_7, all_0_6_6) & ~ empty(all_0_2_2) & ~ empty(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | 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) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ function(v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [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) | ~ function(v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, 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] : ( ~ (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] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 3.84/1.59 | % 3.84/1.59 | Applying alpha-rule on (1) yields: % 3.84/1.59 | (2) empty(all_0_1_1) % 3.84/1.59 | (3) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 3.84/1.59 | (4) ? [v0] : subset(v0, v0) % 3.84/1.59 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 3.84/1.59 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 3.84/1.59 | (7) relation(all_0_9_9) % 3.84/1.59 | (8) relation(all_0_2_2) % 3.84/1.59 | (9) relation_empty_yielding(all_0_3_3) % 3.84/1.59 | (10) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 3.84/1.59 | (11) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.84/1.59 | (12) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ function(v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) % 3.84/1.60 | (13) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ function(v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1))))))) % 3.84/1.60 | (14) ! [v0] : ( ~ empty(v0) | relation(v0)) % 3.84/1.60 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.84/1.60 | (16) relation_dom(all_0_9_9) = all_0_8_8 % 3.84/1.60 | (17) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 3.84/1.60 | (18) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 3.84/1.60 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 3.84/1.60 | (20) ? [v0] : ? [v1] : element(v1, v0) % 3.84/1.60 | (21) relation(all_0_3_3) % 3.84/1.60 | (22) relation(all_0_0_0) % 3.84/1.60 | (23) empty(all_0_4_4) % 3.84/1.60 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | element(v0, v2)) % 3.84/1.60 | (25) relation_rng(all_0_9_9) = all_0_6_6 % 3.84/1.60 | (26) in(all_0_10_10, all_0_8_8) % 3.84/1.60 | (27) empty(empty_set) % 3.84/1.60 | (28) apply(all_0_9_9, all_0_10_10) = all_0_7_7 % 3.84/1.60 | (29) ! [v0] : ( ~ empty(v0) | function(v0)) % 3.84/1.60 | (30) function(all_0_9_9) % 3.84/1.60 | (31) function(all_0_0_0) % 3.84/1.60 | (32) relation(empty_set) % 3.84/1.60 | (33) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 3.84/1.60 | (34) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 3.84/1.60 | (35) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) % 3.84/1.60 | (36) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 3.84/1.60 | (37) ~ empty(all_0_2_2) % 3.84/1.60 | (38) relation_empty_yielding(empty_set) % 3.84/1.60 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 3.84/1.60 | (40) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 3.84/1.60 | (41) ~ empty(all_0_5_5) % 3.84/1.60 | (42) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 3.84/1.60 | (43) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 3.84/1.61 | (44) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 3.84/1.61 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | ~ empty(v2)) % 3.84/1.61 | (46) ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) % 3.84/1.61 | (47) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.84/1.61 | (48) ~ in(all_0_7_7, all_0_6_6) % 3.84/1.61 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 3.84/1.61 | (50) relation(all_0_1_1) % 3.84/1.61 | % 3.84/1.61 | Instantiating formula (13) with all_0_8_8, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_8_8, function(all_0_9_9), relation(all_0_9_9), yields: % 3.84/1.61 | (51) ? [v0] : (relation_rng(all_0_9_9) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_9_9, v2) = v1) | ~ in(v2, all_0_8_8) | in(v1, v0)) & ! [v1] : ( ~ in(v1, v0) | ? [v2] : (apply(all_0_9_9, v2) = v1 & in(v2, all_0_8_8))) & ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (( ~ in(v2, v1) | ! [v5] : ( ~ (apply(all_0_9_9, v5) = v2) | ~ in(v5, all_0_8_8))) & (in(v2, v1) | (v4 = v2 & apply(all_0_9_9, v3) = v2 & in(v3, all_0_8_8)))))) % 3.84/1.61 | % 3.84/1.61 | Instantiating (51) with all_17_0_14 yields: % 3.84/1.61 | (52) relation_rng(all_0_9_9) = all_17_0_14 & ! [v0] : ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) | ~ in(v1, all_0_8_8) | in(v0, all_17_0_14)) & ! [v0] : ( ~ in(v0, all_17_0_14) | ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_0_8_8))) & ? [v0] : (v0 = all_17_0_14 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) | ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_0_8_8))))) % 3.84/1.61 | % 3.84/1.61 | Applying alpha-rule on (52) yields: % 3.84/1.61 | (53) relation_rng(all_0_9_9) = all_17_0_14 % 3.84/1.61 | (54) ! [v0] : ! [v1] : ( ~ (apply(all_0_9_9, v1) = v0) | ~ in(v1, all_0_8_8) | in(v0, all_17_0_14)) % 3.84/1.61 | (55) ! [v0] : ( ~ in(v0, all_17_0_14) | ? [v1] : (apply(all_0_9_9, v1) = v0 & in(v1, all_0_8_8))) % 3.84/1.61 | (56) ? [v0] : (v0 = all_17_0_14 | ? [v1] : ? [v2] : ? [v3] : (( ~ in(v1, v0) | ! [v4] : ( ~ (apply(all_0_9_9, v4) = v1) | ~ in(v4, all_0_8_8))) & (in(v1, v0) | (v3 = v1 & apply(all_0_9_9, v2) = v1 & in(v2, all_0_8_8))))) % 3.84/1.61 | % 3.84/1.61 | Instantiating formula (54) with all_0_10_10, all_0_7_7 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_0_7_7, in(all_0_10_10, all_0_8_8), yields: % 3.84/1.61 | (57) in(all_0_7_7, all_17_0_14) % 3.84/1.62 | % 3.84/1.62 | Instantiating formula (39) with all_0_9_9, all_17_0_14, all_0_6_6 and discharging atoms relation_rng(all_0_9_9) = all_17_0_14, relation_rng(all_0_9_9) = all_0_6_6, yields: % 3.84/1.62 | (58) all_17_0_14 = all_0_6_6 % 3.84/1.62 | % 3.84/1.62 | From (58) and (57) follows: % 3.84/1.62 | (59) in(all_0_7_7, all_0_6_6) % 3.84/1.62 | % 3.84/1.62 | Using (59) and (48) yields: % 3.84/1.62 | (60) $false % 3.84/1.62 | % 3.84/1.62 |-The branch is then unsatisfiable % 3.84/1.62 % SZS output end Proof for theBenchmark % 3.84/1.62 % 3.84/1.62 1041ms %------------------------------------------------------------------------------