%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU040+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.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 08:46:19 EDT 2022 % Result : Theorem 2.77s 1.30s % Output : Proof 3.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU040+1 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n027.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 : Sat Jun 18 22:11:53 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.58 ____ _ % 0.18/0.58 ___ / __ \_____(_)___ ________ __________ % 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.58 % 0.18/0.58 A Theorem Prover for First-Order Logic % 0.18/0.58 (ePrincess v.1.0) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2015 % 0.18/0.58 (c) Peter Backeman, 2014-2015 % 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.58 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.74/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.58/0.95 Prover 0: Preprocessing ... % 1.98/1.14 Prover 0: Warning: ignoring some quantifiers % 1.98/1.17 Prover 0: Constructing countermodel ... % 2.77/1.30 Prover 0: proved (669ms) % 2.77/1.30 % 2.77/1.30 No countermodel exists, formula is valid % 2.77/1.30 % SZS status Theorem for theBenchmark % 2.77/1.30 % 2.77/1.30 Generating proof ... Warning: ignoring some quantifiers % 3.58/1.53 found it (size 19) % 3.58/1.53 % 3.58/1.53 % SZS output start Proof for theBenchmark % 3.58/1.53 Assumed formulas after preprocessing and simplification: % 3.68/1.53 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (relation_dom_restriction(v1, v0) = v2 & relation_rng(v2) = v5 & relation_rng(v1) = v6 & relation_dom(v2) = v3 & relation_dom(v1) = v4 & one_to_one(v12) & function(v14) & function(v13) & function(v12) & function(v1) & relation_empty_yielding(v9) & relation_empty_yielding(empty_set) & relation(v14) & relation(v13) & relation(v12) & relation(v11) & relation(v10) & relation(v9) & relation(v1) & relation(empty_set) & empty(v13) & empty(v11) & empty(v8) & empty(empty_set) & ~ empty(v10) & ~ empty(v7) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_dom_restriction(v18, v17) = v16) | ~ (relation_dom_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ empty(v17) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ in(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_rng(v17) = v16) | ~ (relation_rng(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_dom(v17) = v16) | ~ (relation_dom(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (powerset(v17) = v16) | ~ (powerset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_dom(v17) = v18 & relation_dom(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ function(v15) | ~ relation(v15) | function(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ function(v15) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation_empty_yielding(v15) | ~ relation(v15) | relation_empty_yielding(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation_empty_yielding(v15) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ subset(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | subset(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ empty(v16) | ~ empty(v15)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ~ empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | empty(v15) | ? [v17] : (element(v17, v16) & ~ empty(v17))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (element(v17, v16) & empty(v17))) & ! [v15] : ! [v16] : ( ~ element(v15, v16) | empty(v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ empty(v16) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v16, v15) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) & ! [v15] : (v15 = empty_set | ~ empty(v15)) & ! [v15] : ( ~ function(v15) | ~ relation(v15) | ~ empty(v15) | one_to_one(v15)) & ! [v15] : ( ~ empty(v15) | function(v15)) & ! [v15] : ( ~ empty(v15) | relation(v15)) & ? [v15] : ? [v16] : element(v16, v15) & ? [v15] : subset(v15, v15) & ( ~ subset(v5, v6) | ~ subset(v3, v4))) % 3.68/1.57 | 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, 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 yields: % 3.68/1.57 | (1) relation_dom_restriction(all_0_13_13, all_0_14_14) = all_0_12_12 & relation_rng(all_0_12_12) = all_0_9_9 & relation_rng(all_0_13_13) = all_0_8_8 & relation_dom(all_0_12_12) = all_0_11_11 & relation_dom(all_0_13_13) = all_0_10_10 & one_to_one(all_0_2_2) & function(all_0_0_0) & function(all_0_1_1) & function(all_0_2_2) & function(all_0_13_13) & relation_empty_yielding(all_0_5_5) & 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_4_4) & relation(all_0_5_5) & relation(all_0_13_13) & relation(empty_set) & empty(all_0_1_1) & empty(all_0_3_3) & empty(all_0_6_6) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_7_7) & ! [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] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ function(v0) | ~ relation(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ function(v0) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [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] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [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) | ~ 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] : ( ~ 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] : ( ~ function(v0) | ~ relation(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) & ( ~ subset(all_0_9_9, all_0_8_8) | ~ subset(all_0_11_11, all_0_10_10)) % 3.68/1.58 | % 3.68/1.58 | Applying alpha-rule on (1) yields: % 3.68/1.58 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 3.68/1.58 | (3) relation(all_0_13_13) % 3.68/1.58 | (4) function(all_0_1_1) % 3.68/1.58 | (5) relation(all_0_2_2) % 3.68/1.58 | (6) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 3.68/1.58 | (7) function(all_0_2_2) % 3.68/1.58 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 3.68/1.58 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 3.68/1.58 | (10) ? [v0] : ? [v1] : element(v1, v0) % 3.68/1.58 | (11) ! [v0] : ( ~ function(v0) | ~ relation(v0) | ~ empty(v0) | one_to_one(v0)) % 3.68/1.58 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 3.68/1.58 | (13) relation_empty_yielding(all_0_5_5) % 3.68/1.58 | (14) ~ empty(all_0_4_4) % 3.68/1.58 | (15) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 3.68/1.58 | (16) ! [v0] : ( ~ empty(v0) | function(v0)) % 3.68/1.58 | (17) ? [v0] : subset(v0, v0) % 3.68/1.58 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 3.68/1.58 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 3.68/1.58 | (20) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 3.68/1.58 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ function(v0) | ~ relation(v0) | relation(v2)) % 3.68/1.58 | (22) relation_dom(all_0_12_12) = all_0_11_11 % 3.68/1.58 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 3.68/1.58 | (24) relation(all_0_5_5) % 3.68/1.58 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2)) % 3.68/1.58 | (26) relation(all_0_0_0) % 3.68/1.58 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 3.68/1.58 | (28) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 3.68/1.59 | (29) ~ subset(all_0_9_9, all_0_8_8) | ~ subset(all_0_11_11, all_0_10_10) % 3.68/1.59 | (30) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 3.68/1.59 | (31) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 3.68/1.59 | (32) function(all_0_13_13) % 3.68/1.59 | (33) ~ empty(all_0_7_7) % 3.68/1.59 | (34) ! [v0] : ( ~ empty(v0) | relation(v0)) % 3.68/1.59 | (35) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 3.68/1.59 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 3.68/1.59 | (37) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 3.68/1.59 | (38) relation(all_0_1_1) % 3.68/1.59 | (39) relation_rng(all_0_12_12) = all_0_9_9 % 3.68/1.59 | (40) relation_dom_restriction(all_0_13_13, all_0_14_14) = all_0_12_12 % 3.68/1.59 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 3.68/1.59 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 3.68/1.59 | (43) relation(empty_set) % 3.68/1.59 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & subset(v3, v4))) % 3.68/1.59 | (45) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 3.68/1.59 | (46) empty(all_0_3_3) % 3.68/1.59 | (47) relation(all_0_4_4) % 3.68/1.59 | (48) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 3.68/1.59 | (49) one_to_one(all_0_2_2) % 3.68/1.59 | (50) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 3.68/1.59 | (51) relation_dom(all_0_13_13) = all_0_10_10 % 3.68/1.59 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ function(v0) | ~ relation(v0) | function(v2)) % 3.68/1.59 | (53) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 3.68/1.59 | (54) relation_empty_yielding(empty_set) % 3.68/1.59 | (55) function(all_0_0_0) % 3.68/1.59 | (56) relation_rng(all_0_13_13) = all_0_8_8 % 3.68/1.59 | (57) empty(all_0_6_6) % 3.68/1.59 | (58) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 3.68/1.59 | (59) empty(all_0_1_1) % 3.68/1.59 | (60) empty(empty_set) % 3.68/1.59 | (61) relation(all_0_3_3) % 3.68/1.59 | (62) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 3.68/1.59 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2)) % 3.68/1.59 | % 3.68/1.59 | Instantiating formula (27) with all_0_12_12, all_0_13_13, all_0_14_14 and discharging atoms relation_dom_restriction(all_0_13_13, all_0_14_14) = all_0_12_12, relation(all_0_13_13), yields: % 3.68/1.59 | (64) ? [v0] : ? [v1] : (relation_rng(all_0_12_12) = v0 & relation_rng(all_0_13_13) = v1 & subset(v0, v1)) % 3.68/1.59 | % 3.68/1.60 | Instantiating formula (44) with all_0_12_12, all_0_13_13, all_0_14_14 and discharging atoms relation_dom_restriction(all_0_13_13, all_0_14_14) = all_0_12_12, relation(all_0_13_13), yields: % 3.68/1.60 | (65) ? [v0] : ? [v1] : (relation_dom(all_0_12_12) = v0 & relation_dom(all_0_13_13) = v1 & subset(v0, v1)) % 3.68/1.60 | % 3.68/1.60 | Instantiating (65) with all_17_0_18, all_17_1_19 yields: % 3.68/1.60 | (66) relation_dom(all_0_12_12) = all_17_1_19 & relation_dom(all_0_13_13) = all_17_0_18 & subset(all_17_1_19, all_17_0_18) % 3.68/1.60 | % 3.68/1.60 | Applying alpha-rule on (66) yields: % 3.68/1.60 | (67) relation_dom(all_0_12_12) = all_17_1_19 % 3.68/1.60 | (68) relation_dom(all_0_13_13) = all_17_0_18 % 3.68/1.60 | (69) subset(all_17_1_19, all_17_0_18) % 3.68/1.60 | % 3.68/1.60 | Instantiating (64) with all_19_0_20, all_19_1_21 yields: % 3.68/1.60 | (70) relation_rng(all_0_12_12) = all_19_1_21 & relation_rng(all_0_13_13) = all_19_0_20 & subset(all_19_1_21, all_19_0_20) % 3.68/1.60 | % 3.68/1.60 | Applying alpha-rule on (70) yields: % 3.68/1.60 | (71) relation_rng(all_0_12_12) = all_19_1_21 % 3.68/1.60 | (72) relation_rng(all_0_13_13) = all_19_0_20 % 3.68/1.60 | (73) subset(all_19_1_21, all_19_0_20) % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (36) with all_0_12_12, all_19_1_21, all_0_9_9 and discharging atoms relation_rng(all_0_12_12) = all_19_1_21, relation_rng(all_0_12_12) = all_0_9_9, yields: % 3.68/1.60 | (74) all_19_1_21 = all_0_9_9 % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (36) with all_0_13_13, all_19_0_20, all_0_8_8 and discharging atoms relation_rng(all_0_13_13) = all_19_0_20, relation_rng(all_0_13_13) = all_0_8_8, yields: % 3.68/1.60 | (75) all_19_0_20 = all_0_8_8 % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (2) with all_0_12_12, all_17_1_19, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_17_1_19, relation_dom(all_0_12_12) = all_0_11_11, yields: % 3.68/1.60 | (76) all_17_1_19 = all_0_11_11 % 3.68/1.60 | % 3.68/1.60 | Instantiating formula (2) with all_0_13_13, all_17_0_18, all_0_10_10 and discharging atoms relation_dom(all_0_13_13) = all_17_0_18, relation_dom(all_0_13_13) = all_0_10_10, yields: % 3.68/1.60 | (77) all_17_0_18 = all_0_10_10 % 3.68/1.60 | % 3.95/1.60 | From (74)(75) and (73) follows: % 3.95/1.60 | (78) subset(all_0_9_9, all_0_8_8) % 3.95/1.60 | % 3.95/1.60 | From (76)(77) and (69) follows: % 3.95/1.60 | (79) subset(all_0_11_11, all_0_10_10) % 3.95/1.60 | % 3.95/1.60 +-Applying beta-rule and splitting (29), into two cases. % 3.95/1.60 |-Branch one: % 3.95/1.60 | (80) ~ subset(all_0_9_9, all_0_8_8) % 3.95/1.60 | % 3.95/1.60 | Using (78) and (80) yields: % 3.95/1.60 | (81) $false % 3.95/1.60 | % 3.95/1.60 |-The branch is then unsatisfiable % 3.95/1.60 |-Branch two: % 3.95/1.60 | (78) subset(all_0_9_9, all_0_8_8) % 3.95/1.60 | (83) ~ subset(all_0_11_11, all_0_10_10) % 3.95/1.60 | % 3.95/1.60 | Using (79) and (83) yields: % 3.95/1.60 | (81) $false % 3.95/1.60 | % 3.95/1.60 |-The branch is then unsatisfiable % 3.95/1.60 % SZS output end Proof for theBenchmark % 3.95/1.60 % 3.95/1.60 1012ms %------------------------------------------------------------------------------