%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU044+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n004.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 08:46:21 EDT 2022 % Result : Theorem 3.55s 1.48s % Output : Proof 5.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU044+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n004.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 20:27:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.53/0.58 ____ _ % 0.53/0.58 ___ / __ \_____(_)___ ________ __________ % 0.53/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.53/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.53/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.53/0.58 % 0.53/0.58 A Theorem Prover for First-Order Logic % 0.59/0.58 (ePrincess v.1.0) % 0.59/0.58 % 0.59/0.58 (c) Philipp Rümmer, 2009-2015 % 0.59/0.58 (c) Peter Backeman, 2014-2015 % 0.59/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.58 Bug reports to peter@backeman.se % 0.59/0.58 % 0.59/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.58 % 0.59/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.59/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.57/0.92 Prover 0: Preprocessing ... % 2.10/1.15 Prover 0: Warning: ignoring some quantifiers % 2.33/1.18 Prover 0: Constructing countermodel ... % 3.55/1.48 Prover 0: proved (854ms) % 3.55/1.48 % 3.55/1.48 No countermodel exists, formula is valid % 3.55/1.48 % SZS status Theorem for theBenchmark % 3.55/1.48 % 3.55/1.48 Generating proof ... Warning: ignoring some quantifiers % 5.19/1.89 found it (size 45) % 5.19/1.89 % 5.19/1.89 % SZS output start Proof for theBenchmark % 5.19/1.89 Assumed formulas after preprocessing and simplification: % 5.19/1.89 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (apply(v2, v1) = v6 & relation_rng_restriction(v0, v2) = v3 & relation_dom(v3) = v4 & relation_dom(v2) = v5 & one_to_one(v12) & function(v14) & function(v13) & function(v12) & function(v2) & relation_empty_yielding(v9) & relation_empty_yielding(empty_set) & relation(v14) & relation(v13) & relation(v12) & relation(v11) & relation(v10) & relation(v9) & relation(v2) & relation(empty_set) & empty(v13) & empty(v11) & empty(v8) & empty(empty_set) & ~ empty(v10) & ~ empty(v7) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v15, v18) = v19) | ~ (relation_dom(v16) = v17) | ~ function(v18) | ~ function(v16) | ~ relation(v18) | ~ relation(v16) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_dom(v18) = v20 & ( ~ (v19 = v16) | ( ! [v24] : ! [v25] : ( ~ (apply(v18, v24) = v25) | ~ in(v25, v15) | ~ in(v24, v20) | in(v24, v17)) & ! [v24] : ! [v25] : ( ~ (apply(v18, v24) = v25) | ~ in(v24, v17) | apply(v16, v24) = v25) & ! [v24] : ! [v25] : ( ~ (apply(v18, v24) = v25) | ~ in(v24, v17) | in(v25, v15)) & ! [v24] : ! [v25] : ( ~ (apply(v18, v24) = v25) | ~ in(v24, v17) | in(v24, v20)) & ! [v24] : ! [v25] : ( ~ (apply(v16, v24) = v25) | ~ in(v24, v17) | apply(v18, v24) = v25))) & (v19 = v16 | ( ~ (v23 = v22) & apply(v18, v21) = v23 & apply(v16, v21) = v22 & in(v21, v17)) | (apply(v18, v21) = v22 & ( ~ in(v22, v15) | ~ in(v21, v20) | ~ in(v21, v17)) & (in(v21, v17) | (in(v22, v15) & in(v21, v20))))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ (relation_dom(v16) = v17) | ~ function(v18) | ~ function(v16) | ~ relation(v18) | ~ relation(v16) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_rng_restriction(v15, v18) = v20 & ( ~ (v20 = v16) | ( ! [v24] : ! [v25] : ( ~ (apply(v18, v24) = v25) | ~ in(v25, v15) | ~ in(v24, v19) | in(v24, v17)) & ! [v24] : ! [v25] : ( ~ (apply(v18, v24) = v25) | ~ in(v24, v17) | apply(v16, v24) = v25) & ! [v24] : ! [v25] : ( ~ (apply(v18, v24) = v25) | ~ in(v24, v17) | in(v25, v15)) & ! [v24] : ! [v25] : ( ~ (apply(v18, v24) = v25) | ~ in(v24, v17) | in(v24, v19)) & ! [v24] : ! [v25] : ( ~ (apply(v16, v24) = v25) | ~ in(v24, v17) | apply(v18, v24) = v25))) & (v20 = v16 | ( ~ (v23 = v22) & apply(v18, v21) = v23 & apply(v16, v21) = v22 & in(v21, v17)) | (apply(v18, v21) = v22 & ( ~ in(v22, v15) | ~ in(v21, v19) | ~ in(v21, v17)) & (in(v21, v17) | (in(v22, v15) & in(v21, v19))))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (apply(v18, v17) = v16) | ~ (apply(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_rng_restriction(v18, v17) = v16) | ~ (relation_rng_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ in(v15, v16) | ~ element(v16, v18) | ~ empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ in(v15, v16) | ~ element(v16, v18) | element(v15, v17)) & ! [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_rng_restriction(v15, v16) = v17) | ~ function(v16) | ~ relation(v16) | function(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ function(v16) | ~ relation(v16) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ subset(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : (v16 = v15 | ~ empty(v16) | ~ empty(v15)) & ! [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] : ( ~ in(v16, v15) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v15, v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) & ! [v15] : ! [v16] : ( ~ element(v15, v16) | in(v15, v16) | empty(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) & ((in(v6, v0) & in(v1, v5) & ~ in(v1, v4)) | (in(v1, v4) & ( ~ in(v6, v0) | ~ in(v1, v5))))) % 5.55/1.93 | 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: % 5.55/1.93 | (1) apply(all_0_12_12, all_0_13_13) = all_0_8_8 & relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11 & relation_dom(all_0_11_11) = all_0_10_10 & relation_dom(all_0_12_12) = all_0_9_9 & 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_12_12) & 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_12_12) & 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] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ function(v3) | ~ function(v1) | ~ relation(v3) | ~ relation(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v3) = v5 & ( ~ (v4 = v1) | ( ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v10, v0) | ~ in(v9, v5) | in(v9, v2)) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | apply(v1, v9) = v10) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | in(v10, v0)) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | in(v9, v5)) & ! [v9] : ! [v10] : ( ~ (apply(v1, v9) = v10) | ~ in(v9, v2) | apply(v3, v9) = v10))) & (v4 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) | ~ in(v6, v5) | ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v5))))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ function(v3) | ~ function(v1) | ~ relation(v3) | ~ relation(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng_restriction(v0, v3) = v5 & ( ~ (v5 = v1) | ( ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v10, v0) | ~ in(v9, v4) | in(v9, v2)) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | apply(v1, v9) = v10) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | in(v10, v0)) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | in(v9, v4)) & ! [v9] : ! [v10] : ( ~ (apply(v1, v9) = v10) | ~ in(v9, v2) | apply(v3, v9) = v10))) & (v5 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) | ~ in(v6, v4) | ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v4))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(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_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ function(v1) | ~ relation(v1) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ function(v1) | ~ relation(v1) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) & ! [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_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] : ( ~ 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) & ((in(all_0_8_8, all_0_14_14) & in(all_0_13_13, all_0_9_9) & ~ in(all_0_13_13, all_0_10_10)) | (in(all_0_13_13, all_0_10_10) & ( ~ in(all_0_8_8, all_0_14_14) | ~ in(all_0_13_13, all_0_9_9)))) % 5.55/1.94 | % 5.55/1.94 | Applying alpha-rule on (1) yields: % 5.55/1.94 | (2) empty(all_0_3_3) % 5.55/1.94 | (3) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 5.55/1.94 | (4) relation_empty_yielding(all_0_5_5) % 5.55/1.94 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 5.55/1.94 | (6) relation_dom(all_0_11_11) = all_0_10_10 % 5.55/1.94 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 5.55/1.94 | (8) ~ empty(all_0_4_4) % 5.55/1.94 | (9) empty(all_0_1_1) % 5.55/1.94 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 5.55/1.94 | (11) function(all_0_2_2) % 5.55/1.94 | (12) empty(empty_set) % 5.55/1.94 | (13) ! [v0] : ! [v1] : ( ~ element(v0, v1) | in(v0, v1) | empty(v1)) % 5.55/1.94 | (14) relation(all_0_12_12) % 5.55/1.94 | (15) relation(all_0_3_3) % 5.55/1.94 | (16) ! [v0] : ( ~ empty(v0) | relation(v0)) % 5.55/1.94 | (17) one_to_one(all_0_2_2) % 5.55/1.94 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | element(v0, v2)) % 5.55/1.94 | (19) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 5.55/1.94 | (20) relation(all_0_2_2) % 5.55/1.94 | (21) empty(all_0_6_6) % 5.55/1.95 | (22) ~ empty(all_0_7_7) % 5.55/1.95 | (23) relation(empty_set) % 5.55/1.95 | (24) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ~ empty(v1)) % 5.55/1.95 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v0, v1) | ~ element(v1, v3) | ~ empty(v2)) % 5.55/1.95 | (26) (in(all_0_8_8, all_0_14_14) & in(all_0_13_13, all_0_9_9) & ~ in(all_0_13_13, all_0_10_10)) | (in(all_0_13_13, all_0_10_10) & ( ~ in(all_0_8_8, all_0_14_14) | ~ in(all_0_13_13, all_0_9_9))) % 5.55/1.95 | (27) ! [v0] : ( ~ function(v0) | ~ relation(v0) | ~ empty(v0) | one_to_one(v0)) % 5.55/1.95 | (28) relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11 % 5.55/1.95 | (29) relation(all_0_5_5) % 5.55/1.95 | (30) relation_empty_yielding(empty_set) % 5.55/1.95 | (31) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 5.55/1.95 | (32) function(all_0_0_0) % 5.55/1.95 | (33) ? [v0] : subset(v0, v0) % 5.55/1.95 | (34) function(all_0_1_1) % 5.55/1.95 | (35) relation_dom(all_0_12_12) = all_0_9_9 % 5.55/1.95 | (36) apply(all_0_12_12, all_0_13_13) = all_0_8_8 % 5.55/1.95 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ function(v1) | ~ relation(v1) | relation(v2)) % 5.55/1.95 | (38) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 5.55/1.95 | (39) relation(all_0_1_1) % 5.55/1.95 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ function(v3) | ~ function(v1) | ~ relation(v3) | ~ relation(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_dom(v3) = v5 & ( ~ (v4 = v1) | ( ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v10, v0) | ~ in(v9, v5) | in(v9, v2)) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | apply(v1, v9) = v10) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | in(v10, v0)) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | in(v9, v5)) & ! [v9] : ! [v10] : ( ~ (apply(v1, v9) = v10) | ~ in(v9, v2) | apply(v3, v9) = v10))) & (v4 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) | ~ in(v6, v5) | ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v5))))))) % 5.55/1.95 | (41) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 5.55/1.95 | (42) relation(all_0_0_0) % 5.55/1.95 | (43) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 5.55/1.95 | (44) function(all_0_12_12) % 5.55/1.95 | (45) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 5.55/1.95 | (46) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 5.55/1.95 | (47) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 5.55/1.95 | (48) ? [v0] : ? [v1] : element(v1, v0) % 5.55/1.95 | (49) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ function(v3) | ~ function(v1) | ~ relation(v3) | ~ relation(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng_restriction(v0, v3) = v5 & ( ~ (v5 = v1) | ( ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v10, v0) | ~ in(v9, v4) | in(v9, v2)) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | apply(v1, v9) = v10) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | in(v10, v0)) & ! [v9] : ! [v10] : ( ~ (apply(v3, v9) = v10) | ~ in(v9, v2) | in(v9, v4)) & ! [v9] : ! [v10] : ( ~ (apply(v1, v9) = v10) | ~ in(v9, v2) | apply(v3, v9) = v10))) & (v5 = v1 | ( ~ (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & in(v6, v2)) | (apply(v3, v6) = v7 & ( ~ in(v7, v0) | ~ in(v6, v4) | ~ in(v6, v2)) & (in(v6, v2) | (in(v7, v0) & in(v6, v4))))))) % 5.55/1.95 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) % 5.55/1.96 | (51) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 5.55/1.96 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 5.55/1.96 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 5.55/1.96 | (54) ! [v0] : ( ~ empty(v0) | function(v0)) % 5.55/1.96 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 5.55/1.96 | (56) relation(all_0_4_4) % 5.55/1.96 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ function(v1) | ~ relation(v1) | function(v2)) % 5.55/1.96 | % 5.55/1.96 | Instantiating (49) with all_7_0_18 yields: % 5.55/1.96 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ (relation_dom(v0) = v1) | ~ function(v2) | ~ function(v0) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(all_7_0_18, v2) = v4 & ( ~ (v4 = v0) | ( ! [v8] : ! [v9] : ( ~ (apply(v2, v8) = v9) | ~ in(v9, all_7_0_18) | ~ in(v8, v3) | in(v8, v1)) & ! [v8] : ! [v9] : ( ~ (apply(v2, v8) = v9) | ~ in(v8, v1) | apply(v0, v8) = v9) & ! [v8] : ! [v9] : ( ~ (apply(v2, v8) = v9) | ~ in(v8, v1) | in(v9, all_7_0_18)) & ! [v8] : ! [v9] : ( ~ (apply(v2, v8) = v9) | ~ in(v8, v1) | in(v8, v3)) & ! [v8] : ! [v9] : ( ~ (apply(v0, v8) = v9) | ~ in(v8, v1) | apply(v2, v8) = v9))) & (v4 = v0 | ( ~ (v7 = v6) & apply(v2, v5) = v7 & apply(v0, v5) = v6 & in(v5, v1)) | (apply(v2, v5) = v6 & ( ~ in(v6, all_7_0_18) | ~ in(v5, v3) | ~ in(v5, v1)) & (in(v5, v1) | (in(v6, all_7_0_18) & in(v5, v3))))))) % 5.55/1.96 | % 5.55/1.96 | Instantiating formula (40) with all_0_11_11, all_0_12_12, all_0_9_9, all_0_12_12, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, relation_dom(all_0_12_12) = all_0_9_9, function(all_0_12_12), relation(all_0_12_12), yields: % 5.55/1.96 | (59) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_12_12) = v0 & ( ~ (all_0_11_11 = all_0_12_12) | ( ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v5, all_0_14_14) | ~ in(v4, v0) | in(v4, all_0_9_9)) & ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v4, all_0_9_9) | in(v5, all_0_14_14)) & ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v4, all_0_9_9) | in(v4, v0)))) & (all_0_11_11 = all_0_12_12 | ( ~ (v3 = v2) & apply(all_0_12_12, v1) = v3 & apply(all_0_12_12, v1) = v2 & in(v1, all_0_9_9)) | (apply(all_0_12_12, v1) = v2 & ( ~ in(v2, all_0_14_14) | ~ in(v1, v0) | ~ in(v1, all_0_9_9)) & (in(v1, all_0_9_9) | (in(v2, all_0_14_14) & in(v1, v0)))))) % 5.55/1.96 | % 5.55/1.96 | Instantiating formula (57) with all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, function(all_0_12_12), relation(all_0_12_12), yields: % 5.55/1.96 | (60) function(all_0_11_11) % 5.55/1.96 | % 5.55/1.96 | Instantiating formula (50) with all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, relation(all_0_12_12), yields: % 5.55/1.96 | (61) relation(all_0_11_11) % 5.55/1.96 | % 5.55/1.96 | Instantiating formula (58) with all_0_9_9, all_0_12_12, all_0_9_9, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_9_9, function(all_0_12_12), relation(all_0_12_12), yields: % 5.55/1.96 | (62) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng_restriction(all_7_0_18, all_0_12_12) = v0 & ( ~ (v0 = all_0_12_12) | ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v4, all_0_9_9) | in(v5, all_7_0_18))) & (v0 = all_0_12_12 | ( ~ (v3 = v2) & apply(all_0_12_12, v1) = v3 & apply(all_0_12_12, v1) = v2 & in(v1, all_0_9_9)) | (apply(all_0_12_12, v1) = v2 & in(v1, all_0_9_9) & ~ in(v2, all_7_0_18)))) % 5.55/1.96 | % 5.55/1.96 | Instantiating (62) with all_19_0_19, all_19_1_20, all_19_2_21, all_19_3_22 yields: % 5.55/1.96 | (63) relation_rng_restriction(all_7_0_18, all_0_12_12) = all_19_3_22 & ( ~ (all_19_3_22 = all_0_12_12) | ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v1, all_7_0_18))) & (all_19_3_22 = all_0_12_12 | ( ~ (all_19_0_19 = all_19_1_20) & apply(all_0_12_12, all_19_2_21) = all_19_0_19 & apply(all_0_12_12, all_19_2_21) = all_19_1_20 & in(all_19_2_21, all_0_9_9)) | (apply(all_0_12_12, all_19_2_21) = all_19_1_20 & in(all_19_2_21, all_0_9_9) & ~ in(all_19_1_20, all_7_0_18))) % 5.55/1.96 | % 5.55/1.96 | Applying alpha-rule on (63) yields: % 5.55/1.96 | (64) relation_rng_restriction(all_7_0_18, all_0_12_12) = all_19_3_22 % 5.55/1.96 | (65) ~ (all_19_3_22 = all_0_12_12) | ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v1, all_7_0_18)) % 5.55/1.97 | (66) all_19_3_22 = all_0_12_12 | ( ~ (all_19_0_19 = all_19_1_20) & apply(all_0_12_12, all_19_2_21) = all_19_0_19 & apply(all_0_12_12, all_19_2_21) = all_19_1_20 & in(all_19_2_21, all_0_9_9)) | (apply(all_0_12_12, all_19_2_21) = all_19_1_20 & in(all_19_2_21, all_0_9_9) & ~ in(all_19_1_20, all_7_0_18)) % 5.55/1.97 | % 5.55/1.97 | Instantiating (59) with all_21_0_23, all_21_1_24, all_21_2_25, all_21_3_26 yields: % 5.55/1.97 | (67) relation_dom(all_0_12_12) = all_21_3_26 & ( ~ (all_0_11_11 = all_0_12_12) | ( ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v1, all_0_14_14) | ~ in(v0, all_21_3_26) | in(v0, all_0_9_9)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v1, all_0_14_14)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v0, all_21_3_26)))) & (all_0_11_11 = all_0_12_12 | ( ~ (all_21_0_23 = all_21_1_24) & apply(all_0_12_12, all_21_2_25) = all_21_0_23 & apply(all_0_12_12, all_21_2_25) = all_21_1_24 & in(all_21_2_25, all_0_9_9)) | (apply(all_0_12_12, all_21_2_25) = all_21_1_24 & ( ~ in(all_21_1_24, all_0_14_14) | ~ in(all_21_2_25, all_21_3_26) | ~ in(all_21_2_25, all_0_9_9)) & (in(all_21_2_25, all_0_9_9) | (in(all_21_1_24, all_0_14_14) & in(all_21_2_25, all_21_3_26))))) % 5.55/1.97 | % 5.55/1.97 | Applying alpha-rule on (67) yields: % 5.55/1.97 | (68) relation_dom(all_0_12_12) = all_21_3_26 % 5.55/1.97 | (69) ~ (all_0_11_11 = all_0_12_12) | ( ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v1, all_0_14_14) | ~ in(v0, all_21_3_26) | in(v0, all_0_9_9)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v1, all_0_14_14)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v0, all_21_3_26))) % 5.55/1.97 | (70) all_0_11_11 = all_0_12_12 | ( ~ (all_21_0_23 = all_21_1_24) & apply(all_0_12_12, all_21_2_25) = all_21_0_23 & apply(all_0_12_12, all_21_2_25) = all_21_1_24 & in(all_21_2_25, all_0_9_9)) | (apply(all_0_12_12, all_21_2_25) = all_21_1_24 & ( ~ in(all_21_1_24, all_0_14_14) | ~ in(all_21_2_25, all_21_3_26) | ~ in(all_21_2_25, all_0_9_9)) & (in(all_21_2_25, all_0_9_9) | (in(all_21_1_24, all_0_14_14) & in(all_21_2_25, all_21_3_26)))) % 5.55/1.97 | % 5.55/1.97 | Instantiating formula (55) with all_0_12_12, all_21_3_26, all_0_9_9 and discharging atoms relation_dom(all_0_12_12) = all_21_3_26, relation_dom(all_0_12_12) = all_0_9_9, yields: % 5.55/1.97 | (71) all_21_3_26 = all_0_9_9 % 5.55/1.97 | % 5.55/1.97 | From (71) and (68) follows: % 5.55/1.97 | (35) relation_dom(all_0_12_12) = all_0_9_9 % 5.55/1.97 | % 5.55/1.97 | Instantiating formula (40) with all_19_3_22, all_0_12_12, all_0_9_9, all_0_12_12, all_7_0_18 and discharging atoms relation_rng_restriction(all_7_0_18, all_0_12_12) = all_19_3_22, relation_dom(all_0_12_12) = all_0_9_9, function(all_0_12_12), relation(all_0_12_12), yields: % 5.55/1.97 | (73) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_12_12) = v0 & ( ~ (all_19_3_22 = all_0_12_12) | ( ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v5, all_7_0_18) | ~ in(v4, v0) | in(v4, all_0_9_9)) & ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v4, all_0_9_9) | in(v5, all_7_0_18)) & ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v4, all_0_9_9) | in(v4, v0)))) & (all_19_3_22 = all_0_12_12 | ( ~ (v3 = v2) & apply(all_0_12_12, v1) = v3 & apply(all_0_12_12, v1) = v2 & in(v1, all_0_9_9)) | (apply(all_0_12_12, v1) = v2 & ( ~ in(v2, all_7_0_18) | ~ in(v1, v0) | ~ in(v1, all_0_9_9)) & (in(v1, all_0_9_9) | (in(v2, all_7_0_18) & in(v1, v0)))))) % 5.55/1.97 | % 5.55/1.97 | Instantiating formula (40) with all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11, all_0_14_14 and discharging atoms relation_rng_restriction(all_0_14_14, all_0_12_12) = all_0_11_11, relation_dom(all_0_11_11) = all_0_10_10, function(all_0_11_11), function(all_0_12_12), relation(all_0_11_11), relation(all_0_12_12), yields: % 5.55/1.97 | (74) ? [v0] : (relation_dom(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (apply(all_0_11_11, v1) = v2) | ~ in(v1, all_0_10_10) | apply(all_0_12_12, v1) = v2) & ! [v1] : ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) | ~ in(v2, all_0_14_14) | ~ in(v1, v0) | in(v1, all_0_10_10)) & ! [v1] : ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) | ~ in(v1, all_0_10_10) | apply(all_0_11_11, v1) = v2) & ! [v1] : ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) | ~ in(v1, all_0_10_10) | in(v2, all_0_14_14)) & ! [v1] : ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) | ~ in(v1, all_0_10_10) | in(v1, v0))) % 5.55/1.97 | % 5.55/1.97 | Instantiating formula (40) with all_19_3_22, all_0_12_12, all_0_10_10, all_0_11_11, all_7_0_18 and discharging atoms relation_rng_restriction(all_7_0_18, all_0_12_12) = all_19_3_22, relation_dom(all_0_11_11) = all_0_10_10, function(all_0_11_11), function(all_0_12_12), relation(all_0_11_11), relation(all_0_12_12), yields: % 5.55/1.97 | (75) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_12_12) = v0 & ( ~ (all_19_3_22 = all_0_11_11) | ( ! [v4] : ! [v5] : ( ~ (apply(all_0_11_11, v4) = v5) | ~ in(v4, all_0_10_10) | apply(all_0_12_12, v4) = v5) & ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v5, all_7_0_18) | ~ in(v4, v0) | in(v4, all_0_10_10)) & ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v4, all_0_10_10) | apply(all_0_11_11, v4) = v5) & ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v4, all_0_10_10) | in(v5, all_7_0_18)) & ! [v4] : ! [v5] : ( ~ (apply(all_0_12_12, v4) = v5) | ~ in(v4, all_0_10_10) | in(v4, v0)))) & (all_19_3_22 = all_0_11_11 | ( ~ (v3 = v2) & apply(all_0_11_11, v1) = v2 & apply(all_0_12_12, v1) = v3 & in(v1, all_0_10_10)) | (apply(all_0_12_12, v1) = v2 & ( ~ in(v2, all_7_0_18) | ~ in(v1, v0) | ~ in(v1, all_0_10_10)) & (in(v1, all_0_10_10) | (in(v2, all_7_0_18) & in(v1, v0)))))) % 5.55/1.98 | % 5.93/1.98 | Instantiating (73) with all_33_0_27, all_33_1_28, all_33_2_29, all_33_3_30 yields: % 5.93/1.98 | (76) relation_dom(all_0_12_12) = all_33_3_30 & ( ~ (all_19_3_22 = all_0_12_12) | ( ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v1, all_7_0_18) | ~ in(v0, all_33_3_30) | in(v0, all_0_9_9)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v1, all_7_0_18)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v0, all_33_3_30)))) & (all_19_3_22 = all_0_12_12 | ( ~ (all_33_0_27 = all_33_1_28) & apply(all_0_12_12, all_33_2_29) = all_33_0_27 & apply(all_0_12_12, all_33_2_29) = all_33_1_28 & in(all_33_2_29, all_0_9_9)) | (apply(all_0_12_12, all_33_2_29) = all_33_1_28 & ( ~ in(all_33_1_28, all_7_0_18) | ~ in(all_33_2_29, all_33_3_30) | ~ in(all_33_2_29, all_0_9_9)) & (in(all_33_2_29, all_0_9_9) | (in(all_33_1_28, all_7_0_18) & in(all_33_2_29, all_33_3_30))))) % 5.93/1.98 | % 5.93/1.98 | Applying alpha-rule on (76) yields: % 5.93/1.98 | (77) relation_dom(all_0_12_12) = all_33_3_30 % 5.93/1.98 | (78) ~ (all_19_3_22 = all_0_12_12) | ( ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v1, all_7_0_18) | ~ in(v0, all_33_3_30) | in(v0, all_0_9_9)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v1, all_7_0_18)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_9_9) | in(v0, all_33_3_30))) % 5.93/1.98 | (79) all_19_3_22 = all_0_12_12 | ( ~ (all_33_0_27 = all_33_1_28) & apply(all_0_12_12, all_33_2_29) = all_33_0_27 & apply(all_0_12_12, all_33_2_29) = all_33_1_28 & in(all_33_2_29, all_0_9_9)) | (apply(all_0_12_12, all_33_2_29) = all_33_1_28 & ( ~ in(all_33_1_28, all_7_0_18) | ~ in(all_33_2_29, all_33_3_30) | ~ in(all_33_2_29, all_0_9_9)) & (in(all_33_2_29, all_0_9_9) | (in(all_33_1_28, all_7_0_18) & in(all_33_2_29, all_33_3_30)))) % 5.93/1.98 | % 5.93/1.98 | Instantiating (75) with all_39_0_39, all_39_1_40, all_39_2_41, all_39_3_42 yields: % 5.93/1.98 | (80) relation_dom(all_0_12_12) = all_39_3_42 & ( ~ (all_19_3_22 = all_0_11_11) | ( ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v1, all_7_0_18) | ~ in(v0, all_39_3_42) | in(v0, all_0_10_10)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | in(v1, all_7_0_18)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | in(v0, all_39_3_42)))) & (all_19_3_22 = all_0_11_11 | ( ~ (all_39_0_39 = all_39_1_40) & apply(all_0_11_11, all_39_2_41) = all_39_1_40 & apply(all_0_12_12, all_39_2_41) = all_39_0_39 & in(all_39_2_41, all_0_10_10)) | (apply(all_0_12_12, all_39_2_41) = all_39_1_40 & ( ~ in(all_39_1_40, all_7_0_18) | ~ in(all_39_2_41, all_39_3_42) | ~ in(all_39_2_41, all_0_10_10)) & (in(all_39_2_41, all_0_10_10) | (in(all_39_1_40, all_7_0_18) & in(all_39_2_41, all_39_3_42))))) % 5.93/1.98 | % 5.93/1.98 | Applying alpha-rule on (80) yields: % 5.93/1.98 | (81) relation_dom(all_0_12_12) = all_39_3_42 % 5.93/1.98 | (82) ~ (all_19_3_22 = all_0_11_11) | ( ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v1, all_7_0_18) | ~ in(v0, all_39_3_42) | in(v0, all_0_10_10)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | in(v1, all_7_0_18)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | in(v0, all_39_3_42))) % 5.93/1.99 | (83) all_19_3_22 = all_0_11_11 | ( ~ (all_39_0_39 = all_39_1_40) & apply(all_0_11_11, all_39_2_41) = all_39_1_40 & apply(all_0_12_12, all_39_2_41) = all_39_0_39 & in(all_39_2_41, all_0_10_10)) | (apply(all_0_12_12, all_39_2_41) = all_39_1_40 & ( ~ in(all_39_1_40, all_7_0_18) | ~ in(all_39_2_41, all_39_3_42) | ~ in(all_39_2_41, all_0_10_10)) & (in(all_39_2_41, all_0_10_10) | (in(all_39_1_40, all_7_0_18) & in(all_39_2_41, all_39_3_42)))) % 5.93/1.99 | % 5.93/1.99 | Instantiating (74) with all_43_0_47 yields: % 5.93/1.99 | (84) relation_dom(all_0_12_12) = all_43_0_47 & ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v1, all_0_14_14) | ~ in(v0, all_43_0_47) | in(v0, all_0_10_10)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | in(v1, all_0_14_14)) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | in(v0, all_43_0_47)) % 5.93/1.99 | % 5.93/1.99 | Applying alpha-rule on (84) yields: % 5.93/1.99 | (85) ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | in(v0, all_43_0_47)) % 5.93/1.99 | (86) ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v1, all_0_14_14) | ~ in(v0, all_43_0_47) | in(v0, all_0_10_10)) % 5.93/1.99 | (87) ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | in(v1, all_0_14_14)) % 5.93/1.99 | (88) ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1) % 5.93/1.99 | (89) relation_dom(all_0_12_12) = all_43_0_47 % 5.93/1.99 | (90) ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1) % 5.93/1.99 | % 5.93/1.99 | Instantiating formula (55) with all_0_12_12, all_43_0_47, all_0_9_9 and discharging atoms relation_dom(all_0_12_12) = all_43_0_47, relation_dom(all_0_12_12) = all_0_9_9, yields: % 5.93/1.99 | (91) all_43_0_47 = all_0_9_9 % 5.93/1.99 | % 5.93/1.99 | Instantiating formula (55) with all_0_12_12, all_39_3_42, all_43_0_47 and discharging atoms relation_dom(all_0_12_12) = all_43_0_47, relation_dom(all_0_12_12) = all_39_3_42, yields: % 5.93/1.99 | (92) all_43_0_47 = all_39_3_42 % 5.93/1.99 | % 5.93/1.99 | Instantiating formula (55) with all_0_12_12, all_33_3_30, all_43_0_47 and discharging atoms relation_dom(all_0_12_12) = all_43_0_47, relation_dom(all_0_12_12) = all_33_3_30, yields: % 5.93/1.99 | (93) all_43_0_47 = all_33_3_30 % 5.93/1.99 | % 5.93/1.99 | Combining equations (93,92) yields a new equation: % 5.93/1.99 | (94) all_39_3_42 = all_33_3_30 % 5.93/1.99 | % 5.93/1.99 | Combining equations (91,92) yields a new equation: % 5.93/1.99 | (95) all_39_3_42 = all_0_9_9 % 5.93/1.99 | % 5.93/1.99 | Combining equations (95,94) yields a new equation: % 5.93/1.99 | (96) all_33_3_30 = all_0_9_9 % 5.93/1.99 | % 5.93/1.99 | Combining equations (96,94) yields a new equation: % 5.93/1.99 | (95) all_39_3_42 = all_0_9_9 % 5.93/1.99 | % 5.93/1.99 | Combining equations (95,92) yields a new equation: % 5.93/1.99 | (91) all_43_0_47 = all_0_9_9 % 5.93/1.99 | % 5.93/1.99 +-Applying beta-rule and splitting (26), into two cases. % 5.93/1.99 |-Branch one: % 5.93/1.99 | (99) in(all_0_8_8, all_0_14_14) & in(all_0_13_13, all_0_9_9) & ~ in(all_0_13_13, all_0_10_10) % 5.93/1.99 | % 5.93/1.99 | Applying alpha-rule on (99) yields: % 5.93/1.99 | (100) in(all_0_8_8, all_0_14_14) % 5.93/1.99 | (101) in(all_0_13_13, all_0_9_9) % 5.93/1.99 | (102) ~ in(all_0_13_13, all_0_10_10) % 5.93/1.99 | % 5.93/1.99 | Instantiating formula (86) with all_0_8_8, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_8_8, in(all_0_8_8, all_0_14_14), ~ in(all_0_13_13, all_0_10_10), yields: % 5.93/1.99 | (103) ~ in(all_0_13_13, all_43_0_47) % 5.93/1.99 | % 5.93/1.99 | From (91) and (103) follows: % 5.93/1.99 | (104) ~ in(all_0_13_13, all_0_9_9) % 5.93/1.99 | % 5.93/1.99 | Using (101) and (104) yields: % 5.93/1.99 | (105) $false % 5.93/1.99 | % 5.93/1.99 |-The branch is then unsatisfiable % 5.93/1.99 |-Branch two: % 5.93/1.99 | (106) in(all_0_13_13, all_0_10_10) & ( ~ in(all_0_8_8, all_0_14_14) | ~ in(all_0_13_13, all_0_9_9)) % 5.93/1.99 | % 5.93/1.99 | Applying alpha-rule on (106) yields: % 5.93/1.99 | (107) in(all_0_13_13, all_0_10_10) % 5.93/1.99 | (108) ~ in(all_0_8_8, all_0_14_14) | ~ in(all_0_13_13, all_0_9_9) % 5.93/1.99 | % 5.93/1.99 | Instantiating formula (87) with all_0_8_8, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_8_8, in(all_0_13_13, all_0_10_10), yields: % 5.93/1.99 | (100) in(all_0_8_8, all_0_14_14) % 5.93/1.99 | % 5.93/1.99 | Instantiating formula (85) with all_0_8_8, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_8_8, in(all_0_13_13, all_0_10_10), yields: % 5.93/1.99 | (110) in(all_0_13_13, all_43_0_47) % 5.93/1.99 | % 5.93/1.99 | From (91) and (110) follows: % 5.93/1.99 | (101) in(all_0_13_13, all_0_9_9) % 5.93/1.99 | % 5.93/1.99 +-Applying beta-rule and splitting (108), into two cases. % 5.93/1.99 |-Branch one: % 5.93/1.99 | (112) ~ in(all_0_8_8, all_0_14_14) % 5.93/1.99 | % 5.93/1.99 | Using (100) and (112) yields: % 5.93/1.99 | (105) $false % 5.93/1.99 | % 5.93/1.99 |-The branch is then unsatisfiable % 5.93/1.99 |-Branch two: % 5.93/1.99 | (100) in(all_0_8_8, all_0_14_14) % 5.93/1.99 | (104) ~ in(all_0_13_13, all_0_9_9) % 5.93/1.99 | % 5.93/1.99 | Using (101) and (104) yields: % 5.93/1.99 | (105) $false % 5.93/1.99 | % 5.93/2.00 |-The branch is then unsatisfiable % 5.93/2.00 % SZS output end Proof for theBenchmark % 5.93/2.00 % 5.93/2.00 1405ms %------------------------------------------------------------------------------