%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU295+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n022.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 08:48:34 EDT 2022 % Result : Theorem 2.77s 1.39s % Output : Proof 4.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU295+1 : TPTP v8.1.0. Released v3.3.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n022.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jun 20 06:36:16 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.59 ____ _ % 0.19/0.59 ___ / __ \_____(_)___ ________ __________ % 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic % 0.19/0.59 (ePrincess v.1.0) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2015 % 0.19/0.59 (c) Peter Backeman, 2014-2015 % 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.19/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.19/0.59 Bug reports to peter@backeman.se % 0.19/0.59 % 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.79/1.01 Prover 0: Preprocessing ... % 2.44/1.23 Prover 0: Warning: ignoring some quantifiers % 2.44/1.26 Prover 0: Constructing countermodel ... % 2.77/1.39 Prover 0: proved (717ms) % 2.77/1.39 % 2.77/1.39 No countermodel exists, formula is valid % 2.77/1.39 % SZS status Theorem for theBenchmark % 2.77/1.39 % 2.77/1.39 Generating proof ... Warning: ignoring some quantifiers % 4.16/1.67 found it (size 4) % 4.16/1.67 % 4.16/1.67 % SZS output start Proof for theBenchmark % 4.16/1.67 Assumed formulas after preprocessing and simplification: % 4.16/1.67 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (set_intersection2(v0, v1) = v2 & relation_empty_yielding(v4) & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v9) & one_to_one(v6) & one_to_one(empty_set) & natural(v16) & relation(v14) & relation(v12) & relation(v10) & relation(v9) & relation(v8) & relation(v6) & relation(v4) & relation(v3) & relation(empty_set) & function(v14) & function(v10) & function(v9) & function(v6) & function(v3) & function(empty_set) & finite(v15) & finite(v0) & empty(v12) & empty(v11) & empty(v10) & empty(v9) & empty(empty_set) & epsilon_connected(v16) & epsilon_connected(v13) & epsilon_connected(v9) & epsilon_connected(v5) & epsilon_connected(empty_set) & epsilon_transitive(v16) & epsilon_transitive(v13) & epsilon_transitive(v9) & epsilon_transitive(v5) & epsilon_transitive(empty_set) & ordinal(v16) & ordinal(v13) & ordinal(v9) & ordinal(v5) & ordinal(empty_set) & ~ finite(v2) & ~ empty(v16) & ~ empty(v15) & ~ empty(v8) & ~ empty(v7) & ~ empty(v5) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (set_intersection2(v20, v19) = v18) | ~ (set_intersection2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ empty(v19) | ~ element(v18, v20) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ element(v18, v20) | ~ in(v17, v18) | element(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (powerset(v19) = v18) | ~ (powerset(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v18, v17) = v19) | set_intersection2(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ~ finite(v18) | finite(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ~ finite(v17) | finite(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | set_intersection2(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | subset(v19, v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ subset(v17, v18) | element(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | subset(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v17) = v18) | ~ finite(v17) | ~ element(v19, v18) | finite(v19)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_intersection2(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ empty(v18) | ~ empty(v17)) & ! [v17] : ! [v18] : (v18 = empty_set | ~ (set_intersection2(v17, empty_set) = v18)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ empty(v18)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | empty(v17) | ? [v19] : (finite(v19) & element(v19, v18) & ~ empty(v19))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | empty(v17) | ? [v19] : (element(v19, v18) & ~ empty(v19))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : (one_to_one(v19) & natural(v19) & relation(v19) & function(v19) & finite(v19) & empty(v19) & epsilon_connected(v19) & epsilon_transitive(v19) & element(v19, v18) & ordinal(v19))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : (empty(v19) & element(v19, v18))) & ! [v17] : ! [v18] : ( ~ subset(v17, v18) | ~ finite(v18) | finite(v17)) & ! [v17] : ! [v18] : ( ~ empty(v18) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ( ~ element(v18, v17) | ~ ordinal(v17) | epsilon_connected(v18)) & ! [v17] : ! [v18] : ( ~ element(v18, v17) | ~ ordinal(v17) | epsilon_transitive(v18)) & ! [v17] : ! [v18] : ( ~ element(v18, v17) | ~ ordinal(v17) | ordinal(v18)) & ! [v17] : ! [v18] : ( ~ element(v17, v18) | empty(v18) | in(v17, v18)) & ! [v17] : ! [v18] : ( ~ in(v18, v17) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ( ~ in(v17, v18) | element(v17, v18)) & ! [v17] : (v17 = empty_set | ~ empty(v17)) & ! [v17] : ( ~ relation(v17) | ~ function(v17) | ~ empty(v17) | one_to_one(v17)) & ! [v17] : ( ~ empty(v17) | ~ ordinal(v17) | natural(v17)) & ! [v17] : ( ~ empty(v17) | ~ ordinal(v17) | epsilon_connected(v17)) & ! [v17] : ( ~ empty(v17) | ~ ordinal(v17) | epsilon_transitive(v17)) & ! [v17] : ( ~ empty(v17) | relation(v17)) & ! [v17] : ( ~ empty(v17) | function(v17)) & ! [v17] : ( ~ empty(v17) | finite(v17)) & ! [v17] : ( ~ empty(v17) | epsilon_connected(v17)) & ! [v17] : ( ~ empty(v17) | epsilon_transitive(v17)) & ! [v17] : ( ~ empty(v17) | ordinal(v17)) & ! [v17] : ( ~ epsilon_connected(v17) | ~ epsilon_transitive(v17) | ordinal(v17)) & ! [v17] : ( ~ ordinal(v17) | epsilon_connected(v17)) & ! [v17] : ( ~ ordinal(v17) | epsilon_transitive(v17)) & ? [v17] : ? [v18] : element(v18, v17) & ? [v17] : subset(v17, v17)) % 4.45/1.71 | 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, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16 yields: % 4.45/1.71 | (1) set_intersection2(all_0_16_16, all_0_15_15) = all_0_14_14 & relation_empty_yielding(all_0_12_12) & relation_empty_yielding(all_0_13_13) & relation_empty_yielding(empty_set) & one_to_one(all_0_7_7) & one_to_one(all_0_10_10) & one_to_one(empty_set) & natural(all_0_0_0) & relation(all_0_2_2) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_10_10) & relation(all_0_12_12) & relation(all_0_13_13) & relation(empty_set) & function(all_0_2_2) & function(all_0_6_6) & function(all_0_7_7) & function(all_0_10_10) & function(all_0_13_13) & function(empty_set) & finite(all_0_1_1) & finite(all_0_16_16) & empty(all_0_4_4) & empty(all_0_5_5) & empty(all_0_6_6) & empty(all_0_7_7) & empty(empty_set) & epsilon_connected(all_0_0_0) & epsilon_connected(all_0_3_3) & epsilon_connected(all_0_7_7) & epsilon_connected(all_0_11_11) & epsilon_connected(empty_set) & epsilon_transitive(all_0_0_0) & epsilon_transitive(all_0_3_3) & epsilon_transitive(all_0_7_7) & epsilon_transitive(all_0_11_11) & epsilon_transitive(empty_set) & ordinal(all_0_0_0) & ordinal(all_0_3_3) & ordinal(all_0_7_7) & ordinal(all_0_11_11) & ordinal(empty_set) & ~ finite(all_0_14_14) & ~ empty(all_0_0_0) & ~ empty(all_0_1_1) & ~ empty(all_0_8_8) & ~ empty(all_0_9_9) & ~ empty(all_0_11_11) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ 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] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v1) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v0) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(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] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (one_to_one(v2) & natural(v2) & relation(v2) & function(v2) & finite(v2) & empty(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & element(v2, v1) & ordinal(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ finite(v1) | finite(v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_connected(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_transitive(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | ordinal(v1)) & ! [v0] : ! [v1] : ( ~ element(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] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | natural(v0)) & ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ( ~ empty(v0) | finite(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | ordinal(v0)) & ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 4.45/1.73 | % 4.45/1.73 | Applying alpha-rule on (1) yields: % 4.45/1.73 | (2) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 4.45/1.73 | (3) ~ empty(all_0_0_0) % 4.45/1.73 | (4) one_to_one(all_0_7_7) % 4.45/1.73 | (5) ordinal(empty_set) % 4.45/1.73 | (6) relation_empty_yielding(all_0_13_13) % 4.45/1.73 | (7) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 4.45/1.73 | (8) function(empty_set) % 4.45/1.73 | (9) ! [v0] : ( ~ empty(v0) | relation(v0)) % 4.45/1.73 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 4.45/1.73 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 4.45/1.73 | (12) finite(all_0_1_1) % 4.45/1.73 | (13) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_transitive(v1)) % 4.45/1.73 | (14) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) % 4.45/1.73 | (15) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ finite(v1) | finite(v0)) % 4.45/1.73 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 4.45/1.73 | (17) ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_connected(v0)) % 4.45/1.73 | (18) relation(all_0_12_12) % 4.45/1.73 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 4.45/1.73 | (20) ! [v0] : ( ~ empty(v0) | ordinal(v0)) % 4.45/1.73 | (21) ordinal(all_0_0_0) % 4.45/1.73 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) % 4.45/1.73 | (23) relation_empty_yielding(all_0_12_12) % 4.45/1.73 | (24) epsilon_transitive(all_0_7_7) % 4.45/1.73 | (25) ~ empty(all_0_8_8) % 4.45/1.73 | (26) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 4.45/1.73 | (27) relation_empty_yielding(empty_set) % 4.45/1.73 | (28) ~ finite(all_0_14_14) % 4.45/1.73 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 4.45/1.73 | (30) finite(all_0_16_16) % 4.45/1.73 | (31) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 4.45/1.73 | (32) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (one_to_one(v2) & natural(v2) & relation(v2) & function(v2) & finite(v2) & empty(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & element(v2, v1) & ordinal(v2))) % 4.45/1.73 | (33) empty(all_0_7_7) % 4.45/1.73 | (34) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 4.45/1.73 | (35) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) % 4.45/1.73 | (36) ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) % 4.45/1.73 | (37) ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) % 4.45/1.73 | (38) relation(empty_set) % 4.45/1.73 | (39) set_intersection2(all_0_16_16, all_0_15_15) = all_0_14_14 % 4.45/1.73 | (40) epsilon_connected(empty_set) % 4.45/1.73 | (41) natural(all_0_0_0) % 4.45/1.73 | (42) empty(all_0_4_4) % 4.45/1.73 | (43) empty(empty_set) % 4.45/1.73 | (44) epsilon_transitive(all_0_0_0) % 4.45/1.74 | (45) epsilon_transitive(all_0_3_3) % 4.45/1.74 | (46) function(all_0_6_6) % 4.45/1.74 | (47) ! [v0] : ( ~ empty(v0) | function(v0)) % 4.45/1.74 | (48) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | epsilon_connected(v1)) % 4.45/1.74 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v1) | finite(v2)) % 4.45/1.74 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) % 4.45/1.74 | (51) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) % 4.45/1.74 | (52) ? [v0] : subset(v0, v0) % 4.45/1.74 | (53) ordinal(all_0_11_11) % 4.45/1.74 | (54) ! [v0] : ( ~ empty(v0) | finite(v0)) % 4.45/1.74 | (55) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 4.45/1.74 | (56) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ ordinal(v0) | ordinal(v1)) % 4.45/1.74 | (57) epsilon_transitive(empty_set) % 4.45/1.74 | (58) relation(all_0_2_2) % 4.45/1.74 | (59) epsilon_connected(all_0_7_7) % 4.45/1.74 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v0) | finite(v2)) % 4.45/1.74 | (61) function(all_0_10_10) % 4.45/1.74 | (62) epsilon_connected(all_0_0_0) % 4.45/1.74 | (63) ~ empty(all_0_9_9) % 4.45/1.74 | (64) ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | natural(v0)) % 4.45/1.74 | (65) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 4.45/1.74 | (66) relation(all_0_4_4) % 4.45/1.74 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 4.45/1.74 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 4.45/1.74 | (69) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) % 4.45/1.74 | (70) relation(all_0_6_6) % 4.45/1.74 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 4.45/1.74 | (72) ~ empty(all_0_11_11) % 4.45/1.74 | (73) one_to_one(empty_set) % 4.45/1.74 | (74) empty(all_0_6_6) % 4.45/1.74 | (75) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 4.45/1.74 | (76) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2))) % 4.45/1.74 | (77) relation(all_0_8_8) % 4.45/1.74 | (78) ! [v0] : ( ~ empty(v0) | ~ ordinal(v0) | epsilon_transitive(v0)) % 4.45/1.74 | (79) epsilon_transitive(all_0_11_11) % 4.45/1.74 | (80) function(all_0_13_13) % 4.45/1.74 | (81) relation(all_0_7_7) % 4.45/1.74 | (82) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 4.45/1.74 | (83) epsilon_connected(all_0_11_11) % 4.45/1.74 | (84) epsilon_connected(all_0_3_3) % 4.45/1.75 | (85) one_to_one(all_0_10_10) % 4.45/1.75 | (86) relation(all_0_13_13) % 4.45/1.75 | (87) relation(all_0_10_10) % 4.45/1.75 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 4.45/1.75 | (89) function(all_0_2_2) % 4.45/1.75 | (90) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 4.45/1.75 | (91) ordinal(all_0_3_3) % 4.45/1.75 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 4.45/1.75 | (93) ? [v0] : ? [v1] : element(v1, v0) % 4.45/1.75 | (94) function(all_0_7_7) % 4.45/1.75 | (95) empty(all_0_5_5) % 4.45/1.75 | (96) ~ empty(all_0_1_1) % 4.45/1.75 | (97) ordinal(all_0_7_7) % 4.45/1.75 | % 4.45/1.75 | Instantiating formula (60) with all_0_14_14, all_0_15_15, all_0_16_16 and discharging atoms set_intersection2(all_0_16_16, all_0_15_15) = all_0_14_14, finite(all_0_16_16), ~ finite(all_0_14_14), yields: % 4.45/1.75 | (98) $false % 4.45/1.75 | % 4.45/1.75 |-The branch is then unsatisfiable % 4.45/1.75 % SZS output end Proof for theBenchmark % 4.45/1.75 % 4.45/1.75 1140ms %------------------------------------------------------------------------------