%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU031+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n015.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 08:46:17 EDT 2022 % Result : Theorem 3.77s 1.50s % Output : Proof 6.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU031+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n015.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jun 19 20:14:15 EDT 2022 % 0.13/0.34 % CPUTime : % 0.48/0.60 ____ _ % 0.48/0.60 ___ / __ \_____(_)___ ________ __________ % 0.48/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.60 % 0.48/0.60 A Theorem Prover for First-Order Logic % 0.48/0.60 (ePrincess v.1.0) % 0.48/0.60 % 0.48/0.60 (c) Philipp Rümmer, 2009-2015 % 0.48/0.60 (c) Peter Backeman, 2014-2015 % 0.48/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.60 Bug reports to peter@backeman.se % 0.48/0.60 % 0.48/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.60 % 0.48/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.76/0.98 Prover 0: Preprocessing ... % 2.91/1.27 Prover 0: Warning: ignoring some quantifiers % 2.91/1.30 Prover 0: Constructing countermodel ... % 3.77/1.50 Prover 0: proved (849ms) % 3.77/1.50 % 3.77/1.50 No countermodel exists, formula is valid % 3.77/1.50 % SZS status Theorem for theBenchmark % 3.77/1.50 % 3.77/1.50 Generating proof ... Warning: ignoring some quantifiers % 5.61/1.93 found it (size 68) % 5.61/1.93 % 5.61/1.93 % SZS output start Proof for theBenchmark % 5.61/1.93 Assumed formulas after preprocessing and simplification: % 5.61/1.93 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ( ~ (v5 = v4) & relation_rng(v5) = v1 & relation_rng(v0) = v2 & relation_dom(v0) = v1 & identity_relation(v2) = v3 & relation_composition(v5, v0) = v3 & function_inverse(v0) = v4 & relation_empty_yielding(v6) & relation_empty_yielding(empty_set) & one_to_one(v7) & one_to_one(v0) & relation(v13) & relation(v12) & relation(v10) & relation(v9) & relation(v7) & relation(v6) & relation(v5) & relation(v0) & relation(empty_set) & function(v13) & function(v10) & function(v7) & function(v5) & function(v0) & empty(v12) & empty(v11) & empty(v10) & empty(empty_set) & ~ empty(v9) & ~ empty(v8) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = v15 | ~ (relation_rng(v15) = v14) | ~ (relation_dom(v19) = v20) | ~ (identity_relation(v14) = v16) | ~ (relation_composition(v15, v17) = v18) | ~ relation(v19) | ~ relation(v17) | ~ relation(v15) | ~ function(v19) | ~ function(v17) | ~ function(v15) | ? [v21] : ? [v22] : (identity_relation(v20) = v21 & relation_composition(v17, v19) = v22 & ( ~ (v22 = v16) | ~ (v21 = v18)))) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v15 | ~ (relation_rng(v15) = v14) | ~ (identity_relation(v14) = v16) | ~ (relation_composition(v17, v19) = v16) | ~ (relation_composition(v15, v17) = v18) | ~ relation(v19) | ~ relation(v17) | ~ relation(v15) | ~ function(v19) | ~ function(v17) | ~ function(v15) | ? [v20] : ? [v21] : ( ~ (v21 = v18) & relation_dom(v19) = v20 & identity_relation(v20) = v21)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = v14 | ~ (relation_composition(v17, v16) = v15) | ~ (relation_composition(v17, v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | ~ empty(v16) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | ~ in(v14, v15) | element(v14, v16)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_rng(v16) = v15) | ~ (relation_rng(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_dom(v16) = v15) | ~ (relation_dom(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (powerset(v16) = v15) | ~ (powerset(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (identity_relation(v16) = v15) | ~ (identity_relation(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (function_inverse(v16) = v15) | ~ (function_inverse(v16) = v14)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ subset(v14, v15) | element(v14, v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ element(v14, v16) | subset(v14, v15)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v14) = v16) | ~ (function_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v17] : ? [v18] : ? [v19] : (relation_rng(v14) = v19 & relation_dom(v14) = v18 & identity_relation(v19) = v16 & identity_relation(v18) = v17 & relation_composition(v14, v15) = v17)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v14) = v16) | ~ relation(v15) | ~ empty(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v14) = v16) | ~ relation(v15) | ~ empty(v14) | empty(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ (function_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v17] : ? [v18] : ? [v19] : (relation_rng(v14) = v19 & relation_dom(v14) = v17 & identity_relation(v19) = v18 & identity_relation(v17) = v16 & relation_composition(v15, v14) = v18)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | ~ function(v15) | ~ function(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | ~ function(v15) | ~ function(v14) | function(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ relation(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ empty(v14) | relation(v16)) & ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v15) = v16) | ~ relation(v15) | ~ empty(v14) | empty(v16)) & ! [v14] : ! [v15] : (v15 = v14 | ~ empty(v15) | ~ empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (relation_dom(v14) = v18 & identity_relation(v18) = v17 & identity_relation(v15) = v19 & relation_composition(v16, v14) = v19 & relation_composition(v14, v16) = v17 & function_inverse(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : (relation_rng(v16) = v17 & relation_dom(v16) = v15 & relation_dom(v14) = v17 & function_inverse(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ relation(v14) | ~ empty(v15) | empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ empty(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ empty(v14) | empty(v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (relation_rng(v14) = v19 & identity_relation(v19) = v18 & identity_relation(v15) = v17 & relation_composition(v16, v14) = v18 & relation_composition(v14, v16) = v17 & function_inverse(v14) = v16)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : (relation_rng(v17) = v15 & relation_rng(v14) = v16 & relation_dom(v17) = v16 & function_inverse(v14) = v17)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ relation(v14) | ~ empty(v15) | empty(v14)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ empty(v14) | empty(v15)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ empty(v15)) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | empty(v14) | ? [v16] : (element(v16, v15) & ~ empty(v16))) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ? [v16] : (element(v16, v15) & empty(v16))) & ! [v14] : ! [v15] : ( ~ (identity_relation(v14) = v15) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (identity_relation(v14) = v15) | function(v15)) & ! [v14] : ! [v15] : ( ~ (function_inverse(v14) = v15) | ~ one_to_one(v14) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : (relation_rng(v15) = v17 & relation_rng(v14) = v16 & relation_dom(v15) = v16 & relation_dom(v14) = v17)) & ! [v14] : ! [v15] : ( ~ (function_inverse(v14) = v15) | ~ relation(v14) | ~ function(v14) | relation(v15)) & ! [v14] : ! [v15] : ( ~ (function_inverse(v14) = v15) | ~ relation(v14) | ~ function(v14) | function(v15)) & ! [v14] : ! [v15] : ( ~ element(v14, v15) | empty(v15) | in(v14, v15)) & ! [v14] : ! [v15] : ( ~ empty(v15) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v15, v14) | ~ in(v14, v15)) & ! [v14] : ! [v15] : ( ~ in(v14, v15) | element(v14, v15)) & ! [v14] : (v14 = empty_set | ~ empty(v14)) & ! [v14] : ( ~ relation(v14) | ~ function(v14) | ~ empty(v14) | one_to_one(v14)) & ! [v14] : ( ~ empty(v14) | relation(v14)) & ! [v14] : ( ~ empty(v14) | function(v14)) & ? [v14] : ? [v15] : element(v15, v14) & ? [v14] : subset(v14, v14)) % 6.17/1.98 | 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 yields: % 6.17/1.98 | (1) ~ (all_0_8_8 = all_0_9_9) & relation_rng(all_0_8_8) = all_0_12_12 & relation_rng(all_0_13_13) = all_0_11_11 & relation_dom(all_0_13_13) = all_0_12_12 & identity_relation(all_0_11_11) = all_0_10_10 & relation_composition(all_0_8_8, all_0_13_13) = all_0_10_10 & function_inverse(all_0_13_13) = all_0_9_9 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & one_to_one(all_0_13_13) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_8_8) & relation(all_0_13_13) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_8_8) & function(all_0_13_13) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ (relation_dom(v5) = v6) | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v1, v3) = v4) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) | ? [v7] : ? [v8] : (identity_relation(v6) = v7 & relation_composition(v3, v5) = v8 & ( ~ (v8 = v2) | ~ (v7 = v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v3, v5) = v2) | ~ (relation_composition(v1, v3) = v4) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ( ~ (v7 = v4) & relation_dom(v5) = v6 & identity_relation(v6) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(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] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(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] : ( ~ (relation_composition(v1, v0) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v4 & identity_relation(v5) = v2 & identity_relation(v4) = v3 & relation_composition(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3) = v2 & relation_composition(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v4 & identity_relation(v4) = v3 & identity_relation(v1) = v5 & relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & function_inverse(v0) = 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) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & identity_relation(v5) = v4 & identity_relation(v1) = v3 & relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & function_inverse(v0) = v3)) & ! [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] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [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] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0) % 6.17/2.00 | % 6.17/2.00 | Applying alpha-rule on (1) yields: % 6.17/2.00 | (2) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 6.17/2.00 | (3) one_to_one(all_0_6_6) % 6.17/2.00 | (4) function(all_0_3_3) % 6.17/2.00 | (5) identity_relation(all_0_11_11) = all_0_10_10 % 6.17/2.00 | (6) empty(all_0_3_3) % 6.17/2.00 | (7) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 6.17/2.00 | (8) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & function_inverse(v0) = v3)) % 6.17/2.00 | (9) ~ empty(all_0_4_4) % 6.17/2.00 | (10) empty(all_0_1_1) % 6.17/2.00 | (11) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 6.17/2.00 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ (relation_dom(v5) = v6) | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v1, v3) = v4) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) | ? [v7] : ? [v8] : (identity_relation(v6) = v7 & relation_composition(v3, v5) = v8 & ( ~ (v8 = v2) | ~ (v7 = v4)))) % 6.17/2.00 | (13) function(all_0_6_6) % 6.17/2.00 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 6.17/2.00 | (15) function(all_0_8_8) % 6.17/2.00 | (16) relation(all_0_4_4) % 6.17/2.00 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 6.17/2.00 | (18) function(all_0_0_0) % 6.17/2.00 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 6.17/2.00 | (20) relation(all_0_6_6) % 6.17/2.00 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 6.17/2.00 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 6.17/2.00 | (23) relation_dom(all_0_13_13) = all_0_12_12 % 6.17/2.00 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 6.17/2.00 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 6.17/2.00 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v4 & identity_relation(v5) = v2 & identity_relation(v4) = v3 & relation_composition(v0, v1) = v3)) % 6.17/2.01 | (27) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 6.17/2.01 | (28) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) % 6.17/2.01 | (29) relation_rng(all_0_13_13) = all_0_11_11 % 6.17/2.01 | (30) ! [v0] : ( ~ empty(v0) | function(v0)) % 6.17/2.01 | (31) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 6.17/2.01 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 6.17/2.01 | (33) relation(all_0_13_13) % 6.17/2.01 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 6.17/2.01 | (35) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 6.17/2.01 | (36) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 6.17/2.01 | (37) relation(all_0_7_7) % 6.17/2.01 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 6.17/2.01 | (39) empty(empty_set) % 6.17/2.01 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ (relation_composition(v3, v5) = v2) | ~ (relation_composition(v1, v3) = v4) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ( ~ (v7 = v4) & relation_dom(v5) = v6 & identity_relation(v6) = v7)) % 6.17/2.01 | (41) relation(all_0_0_0) % 6.17/2.01 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 6.17/2.01 | (43) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3 & function_inverse(v0) = v2)) % 6.17/2.01 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 6.17/2.01 | (45) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 6.17/2.01 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 6.17/2.01 | (47) relation(all_0_1_1) % 6.17/2.01 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 6.17/2.01 | (49) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 6.17/2.01 | (50) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) % 6.17/2.01 | (51) function(all_0_13_13) % 6.17/2.01 | (52) relation_rng(all_0_8_8) = all_0_12_12 % 6.17/2.01 | (53) relation(empty_set) % 6.17/2.01 | (54) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 6.17/2.01 | (55) relation_composition(all_0_8_8, all_0_13_13) = all_0_10_10 % 6.17/2.01 | (56) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 6.17/2.01 | (57) ? [v0] : subset(v0, v0) % 6.17/2.01 | (58) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_dom(v0) = v4 & identity_relation(v4) = v3 & identity_relation(v1) = v5 & relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) % 6.17/2.01 | (59) function_inverse(all_0_13_13) = all_0_9_9 % 6.17/2.01 | (60) relation_empty_yielding(empty_set) % 6.17/2.02 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 6.17/2.02 | (62) relation_empty_yielding(all_0_7_7) % 6.17/2.02 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 6.17/2.02 | (64) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 6.17/2.02 | (65) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) % 6.17/2.02 | (66) ! [v0] : ( ~ empty(v0) | relation(v0)) % 6.17/2.02 | (67) one_to_one(all_0_13_13) % 6.17/2.02 | (68) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 6.17/2.02 | (69) ~ (all_0_8_8 = all_0_9_9) % 6.17/2.02 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) % 6.17/2.02 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3) = v2 & relation_composition(v1, v0) = v4)) % 6.17/2.02 | (72) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 6.17/2.02 | (73) ~ empty(all_0_5_5) % 6.17/2.02 | (74) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 6.17/2.02 | (75) relation(all_0_3_3) % 6.17/2.02 | (76) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_rng(v0) = v5 & identity_relation(v5) = v4 & identity_relation(v1) = v3 & relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 & function_inverse(v0) = v2)) % 6.17/2.02 | (77) empty(all_0_2_2) % 6.17/2.02 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 6.17/2.02 | (79) ? [v0] : ? [v1] : element(v1, v0) % 6.17/2.02 | (80) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 6.17/2.02 | (81) relation(all_0_8_8) % 6.17/2.02 | (82) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 6.17/2.02 | % 6.17/2.02 | Instantiating formula (58) with all_0_11_11, all_0_13_13 and discharging atoms relation_rng(all_0_13_13) = all_0_11_11, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields: % 6.17/2.02 | (83) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_13_13) = v2 & identity_relation(v2) = v1 & identity_relation(all_0_11_11) = v3 & relation_composition(v0, all_0_13_13) = v3 & relation_composition(all_0_13_13, v0) = v1 & function_inverse(all_0_13_13) = v0) % 6.17/2.02 | % 6.17/2.02 | Instantiating formula (43) with all_0_11_11, all_0_13_13 and discharging atoms relation_rng(all_0_13_13) = all_0_11_11, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields: % 6.17/2.02 | (84) ? [v0] : ? [v1] : (relation_rng(v0) = v1 & relation_dom(v0) = all_0_11_11 & relation_dom(all_0_13_13) = v1 & function_inverse(all_0_13_13) = v0) % 6.17/2.02 | % 6.17/2.02 | Instantiating formula (76) with all_0_12_12, all_0_13_13 and discharging atoms relation_dom(all_0_13_13) = all_0_12_12, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields: % 6.17/2.02 | (85) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng(all_0_13_13) = v3 & identity_relation(v3) = v2 & identity_relation(all_0_12_12) = v1 & relation_composition(v0, all_0_13_13) = v2 & relation_composition(all_0_13_13, v0) = v1 & function_inverse(all_0_13_13) = v0) % 6.17/2.02 | % 6.17/2.02 | Instantiating formula (8) with all_0_12_12, all_0_13_13 and discharging atoms relation_dom(all_0_13_13) = all_0_12_12, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields: % 6.17/2.02 | (86) ? [v0] : ? [v1] : (relation_rng(v1) = all_0_12_12 & relation_rng(all_0_13_13) = v0 & relation_dom(v1) = v0 & function_inverse(all_0_13_13) = v1) % 6.17/2.03 | % 6.17/2.03 | Instantiating formula (50) with all_0_9_9, all_0_13_13 and discharging atoms function_inverse(all_0_13_13) = all_0_9_9, one_to_one(all_0_13_13), relation(all_0_13_13), function(all_0_13_13), yields: % 6.17/2.03 | (87) ? [v0] : ? [v1] : (relation_rng(all_0_9_9) = v1 & relation_rng(all_0_13_13) = v0 & relation_dom(all_0_9_9) = v0 & relation_dom(all_0_13_13) = v1) % 6.17/2.03 | % 6.17/2.03 | Instantiating formula (2) with all_0_9_9, all_0_13_13 and discharging atoms function_inverse(all_0_13_13) = all_0_9_9, relation(all_0_13_13), function(all_0_13_13), yields: % 6.17/2.03 | (88) relation(all_0_9_9) % 6.17/2.03 | % 6.17/2.03 | Instantiating formula (28) with all_0_9_9, all_0_13_13 and discharging atoms function_inverse(all_0_13_13) = all_0_9_9, relation(all_0_13_13), function(all_0_13_13), yields: % 6.17/2.03 | (89) function(all_0_9_9) % 6.17/2.03 | % 6.17/2.03 | Instantiating (87) with all_17_0_17, all_17_1_18 yields: % 6.17/2.03 | (90) relation_rng(all_0_9_9) = all_17_0_17 & relation_rng(all_0_13_13) = all_17_1_18 & relation_dom(all_0_9_9) = all_17_1_18 & relation_dom(all_0_13_13) = all_17_0_17 % 6.17/2.03 | % 6.17/2.03 | Applying alpha-rule on (90) yields: % 6.17/2.03 | (91) relation_rng(all_0_9_9) = all_17_0_17 % 6.17/2.03 | (92) relation_rng(all_0_13_13) = all_17_1_18 % 6.17/2.03 | (93) relation_dom(all_0_9_9) = all_17_1_18 % 6.17/2.03 | (94) relation_dom(all_0_13_13) = all_17_0_17 % 6.17/2.03 | % 6.17/2.03 | Instantiating (85) with all_19_0_19, all_19_1_20, all_19_2_21, all_19_3_22 yields: % 6.17/2.03 | (95) relation_rng(all_0_13_13) = all_19_0_19 & identity_relation(all_19_0_19) = all_19_1_20 & identity_relation(all_0_12_12) = all_19_2_21 & relation_composition(all_19_3_22, all_0_13_13) = all_19_1_20 & relation_composition(all_0_13_13, all_19_3_22) = all_19_2_21 & function_inverse(all_0_13_13) = all_19_3_22 % 6.17/2.03 | % 6.17/2.03 | Applying alpha-rule on (95) yields: % 6.17/2.03 | (96) identity_relation(all_19_0_19) = all_19_1_20 % 6.17/2.03 | (97) relation_rng(all_0_13_13) = all_19_0_19 % 6.17/2.03 | (98) identity_relation(all_0_12_12) = all_19_2_21 % 6.17/2.03 | (99) function_inverse(all_0_13_13) = all_19_3_22 % 6.17/2.03 | (100) relation_composition(all_0_13_13, all_19_3_22) = all_19_2_21 % 6.17/2.03 | (101) relation_composition(all_19_3_22, all_0_13_13) = all_19_1_20 % 6.17/2.03 | % 6.17/2.03 | Instantiating (84) with all_21_0_23, all_21_1_24 yields: % 6.17/2.03 | (102) relation_rng(all_21_1_24) = all_21_0_23 & relation_dom(all_21_1_24) = all_0_11_11 & relation_dom(all_0_13_13) = all_21_0_23 & function_inverse(all_0_13_13) = all_21_1_24 % 6.17/2.03 | % 6.17/2.03 | Applying alpha-rule on (102) yields: % 6.17/2.03 | (103) relation_rng(all_21_1_24) = all_21_0_23 % 6.17/2.03 | (104) relation_dom(all_21_1_24) = all_0_11_11 % 6.17/2.03 | (105) relation_dom(all_0_13_13) = all_21_0_23 % 6.17/2.03 | (106) function_inverse(all_0_13_13) = all_21_1_24 % 6.17/2.03 | % 6.17/2.03 | Instantiating (86) with all_23_0_25, all_23_1_26 yields: % 6.17/2.03 | (107) relation_rng(all_23_0_25) = all_0_12_12 & relation_rng(all_0_13_13) = all_23_1_26 & relation_dom(all_23_0_25) = all_23_1_26 & function_inverse(all_0_13_13) = all_23_0_25 % 6.17/2.03 | % 6.17/2.03 | Applying alpha-rule on (107) yields: % 6.17/2.03 | (108) relation_rng(all_23_0_25) = all_0_12_12 % 6.17/2.03 | (109) relation_rng(all_0_13_13) = all_23_1_26 % 6.17/2.03 | (110) relation_dom(all_23_0_25) = all_23_1_26 % 6.17/2.03 | (111) function_inverse(all_0_13_13) = all_23_0_25 % 6.17/2.03 | % 6.17/2.03 | Instantiating (83) with all_25_0_27, all_25_1_28, all_25_2_29, all_25_3_30 yields: % 6.17/2.03 | (112) relation_dom(all_0_13_13) = all_25_1_28 & identity_relation(all_25_1_28) = all_25_2_29 & identity_relation(all_0_11_11) = all_25_0_27 & relation_composition(all_25_3_30, all_0_13_13) = all_25_0_27 & relation_composition(all_0_13_13, all_25_3_30) = all_25_2_29 & function_inverse(all_0_13_13) = all_25_3_30 % 6.17/2.03 | % 6.17/2.03 | Applying alpha-rule on (112) yields: % 6.17/2.03 | (113) function_inverse(all_0_13_13) = all_25_3_30 % 6.17/2.03 | (114) identity_relation(all_0_11_11) = all_25_0_27 % 6.17/2.03 | (115) relation_composition(all_25_3_30, all_0_13_13) = all_25_0_27 % 6.17/2.03 | (116) relation_dom(all_0_13_13) = all_25_1_28 % 6.17/2.03 | (117) relation_composition(all_0_13_13, all_25_3_30) = all_25_2_29 % 6.17/2.03 | (118) identity_relation(all_25_1_28) = all_25_2_29 % 6.17/2.03 | % 6.17/2.03 | Instantiating formula (19) with all_0_13_13, all_23_1_26, all_0_11_11 and discharging atoms relation_rng(all_0_13_13) = all_23_1_26, relation_rng(all_0_13_13) = all_0_11_11, yields: % 6.17/2.03 | (119) all_23_1_26 = all_0_11_11 % 6.17/2.03 | % 6.17/2.03 | Instantiating formula (19) with all_0_13_13, all_19_0_19, all_23_1_26 and discharging atoms relation_rng(all_0_13_13) = all_23_1_26, relation_rng(all_0_13_13) = all_19_0_19, yields: % 6.17/2.03 | (120) all_23_1_26 = all_19_0_19 % 6.17/2.03 | % 6.17/2.03 | Instantiating formula (19) with all_0_13_13, all_17_1_18, all_23_1_26 and discharging atoms relation_rng(all_0_13_13) = all_23_1_26, relation_rng(all_0_13_13) = all_17_1_18, yields: % 6.17/2.03 | (121) all_23_1_26 = all_17_1_18 % 6.17/2.03 | % 6.17/2.03 | Instantiating formula (32) with all_0_13_13, all_25_1_28, all_0_12_12 and discharging atoms relation_dom(all_0_13_13) = all_25_1_28, relation_dom(all_0_13_13) = all_0_12_12, yields: % 6.17/2.03 | (122) all_25_1_28 = all_0_12_12 % 6.17/2.03 | % 6.17/2.03 | Instantiating formula (48) with all_0_11_11, all_25_0_27, all_0_10_10 and discharging atoms identity_relation(all_0_11_11) = all_25_0_27, identity_relation(all_0_11_11) = all_0_10_10, yields: % 6.17/2.04 | (123) all_25_0_27 = all_0_10_10 % 6.17/2.04 | % 6.17/2.04 | Instantiating formula (63) with all_0_13_13, all_23_0_25, all_0_9_9 and discharging atoms function_inverse(all_0_13_13) = all_23_0_25, function_inverse(all_0_13_13) = all_0_9_9, yields: % 6.17/2.04 | (124) all_23_0_25 = all_0_9_9 % 6.17/2.04 | % 6.17/2.04 | Instantiating formula (63) with all_0_13_13, all_21_1_24, all_25_3_30 and discharging atoms function_inverse(all_0_13_13) = all_25_3_30, function_inverse(all_0_13_13) = all_21_1_24, yields: % 6.17/2.04 | (125) all_25_3_30 = all_21_1_24 % 6.17/2.04 | % 6.17/2.04 | Instantiating formula (63) with all_0_13_13, all_21_1_24, all_23_0_25 and discharging atoms function_inverse(all_0_13_13) = all_23_0_25, function_inverse(all_0_13_13) = all_21_1_24, yields: % 6.17/2.04 | (126) all_23_0_25 = all_21_1_24 % 6.17/2.04 | % 6.17/2.04 | Instantiating formula (63) with all_0_13_13, all_19_3_22, all_25_3_30 and discharging atoms function_inverse(all_0_13_13) = all_25_3_30, function_inverse(all_0_13_13) = all_19_3_22, yields: % 6.17/2.04 | (127) all_25_3_30 = all_19_3_22 % 6.17/2.04 | % 6.17/2.04 | Combining equations (125,127) yields a new equation: % 6.17/2.04 | (128) all_21_1_24 = all_19_3_22 % 6.17/2.04 | % 6.17/2.04 | Simplifying 128 yields: % 6.17/2.04 | (129) all_21_1_24 = all_19_3_22 % 6.17/2.04 | % 6.17/2.04 | Combining equations (126,124) yields a new equation: % 6.17/2.04 | (130) all_21_1_24 = all_0_9_9 % 6.17/2.04 | % 6.17/2.04 | Simplifying 130 yields: % 6.17/2.04 | (131) all_21_1_24 = all_0_9_9 % 6.17/2.04 | % 6.17/2.04 | Combining equations (121,120) yields a new equation: % 6.17/2.04 | (132) all_19_0_19 = all_17_1_18 % 6.17/2.04 | % 6.17/2.04 | Combining equations (119,120) yields a new equation: % 6.17/2.04 | (133) all_19_0_19 = all_0_11_11 % 6.17/2.04 | % 6.17/2.04 | Combining equations (129,131) yields a new equation: % 6.17/2.04 | (134) all_19_3_22 = all_0_9_9 % 6.17/2.04 | % 6.17/2.04 | Simplifying 134 yields: % 6.17/2.04 | (135) all_19_3_22 = all_0_9_9 % 6.17/2.04 | % 6.17/2.04 | Combining equations (133,132) yields a new equation: % 6.17/2.04 | (136) all_17_1_18 = all_0_11_11 % 6.17/2.04 | % 6.17/2.04 | Combining equations (136,132) yields a new equation: % 6.17/2.04 | (133) all_19_0_19 = all_0_11_11 % 6.17/2.04 | % 6.17/2.04 | Combining equations (135,127) yields a new equation: % 6.17/2.04 | (138) all_25_3_30 = all_0_9_9 % 6.17/2.04 | % 6.17/2.04 | From (136) and (93) follows: % 6.17/2.04 | (139) relation_dom(all_0_9_9) = all_0_11_11 % 6.17/2.04 | % 6.17/2.04 | From (122) and (118) follows: % 6.17/2.04 | (140) identity_relation(all_0_12_12) = all_25_2_29 % 6.17/2.04 | % 6.17/2.04 | From (133) and (96) follows: % 6.17/2.04 | (141) identity_relation(all_0_11_11) = all_19_1_20 % 6.17/2.04 | % 6.17/2.04 | From (138)(123) and (115) follows: % 6.17/2.04 | (142) relation_composition(all_0_9_9, all_0_13_13) = all_0_10_10 % 6.17/2.04 | % 6.17/2.04 | From (135) and (101) follows: % 6.17/2.04 | (143) relation_composition(all_0_9_9, all_0_13_13) = all_19_1_20 % 6.17/2.04 | % 6.17/2.04 | From (138) and (117) follows: % 6.17/2.04 | (144) relation_composition(all_0_13_13, all_0_9_9) = all_25_2_29 % 6.48/2.04 | % 6.48/2.04 | From (135) and (100) follows: % 6.48/2.04 | (145) relation_composition(all_0_13_13, all_0_9_9) = all_19_2_21 % 6.48/2.04 | % 6.48/2.04 | Instantiating formula (34) with all_0_9_9, all_0_13_13, all_0_10_10, all_19_1_20 and discharging atoms relation_composition(all_0_9_9, all_0_13_13) = all_19_1_20, relation_composition(all_0_9_9, all_0_13_13) = all_0_10_10, yields: % 6.48/2.04 | (146) all_19_1_20 = all_0_10_10 % 6.48/2.04 | % 6.48/2.04 | Instantiating formula (34) with all_0_13_13, all_0_9_9, all_19_2_21, all_25_2_29 and discharging atoms relation_composition(all_0_13_13, all_0_9_9) = all_25_2_29, relation_composition(all_0_13_13, all_0_9_9) = all_19_2_21, yields: % 6.48/2.04 | (147) all_25_2_29 = all_19_2_21 % 6.48/2.04 | % 6.48/2.04 | From (146) and (141) follows: % 6.48/2.04 | (5) identity_relation(all_0_11_11) = all_0_10_10 % 6.48/2.04 | % 6.48/2.04 | From (147) and (140) follows: % 6.48/2.04 | (98) identity_relation(all_0_12_12) = all_19_2_21 % 6.48/2.04 | % 6.48/2.04 | From (147) and (144) follows: % 6.48/2.04 | (145) relation_composition(all_0_13_13, all_0_9_9) = all_19_2_21 % 6.48/2.04 | % 6.48/2.04 | Instantiating formula (12) with all_0_11_11, all_0_9_9, all_0_10_10, all_0_13_13, all_19_2_21, all_0_8_8, all_0_12_12 and discharging atoms relation_rng(all_0_8_8) = all_0_12_12, relation_dom(all_0_9_9) = all_0_11_11, identity_relation(all_0_12_12) = all_19_2_21, relation_composition(all_0_8_8, all_0_13_13) = all_0_10_10, relation(all_0_8_8), relation(all_0_9_9), relation(all_0_13_13), function(all_0_8_8), function(all_0_9_9), function(all_0_13_13), yields: % 6.48/2.04 | (151) all_0_8_8 = all_0_9_9 | ? [v0] : ? [v1] : (identity_relation(all_0_11_11) = v0 & relation_composition(all_0_13_13, all_0_9_9) = v1 & ( ~ (v1 = all_19_2_21) | ~ (v0 = all_0_10_10))) % 6.48/2.04 | % 6.48/2.04 | Instantiating formula (40) with all_0_9_9, all_0_10_10, all_0_13_13, all_19_2_21, all_0_8_8, all_0_12_12 and discharging atoms relation_rng(all_0_8_8) = all_0_12_12, identity_relation(all_0_12_12) = all_19_2_21, relation_composition(all_0_8_8, all_0_13_13) = all_0_10_10, relation_composition(all_0_13_13, all_0_9_9) = all_19_2_21, relation(all_0_8_8), relation(all_0_9_9), relation(all_0_13_13), function(all_0_8_8), function(all_0_9_9), function(all_0_13_13), yields: % 6.48/2.04 | (152) all_0_8_8 = all_0_9_9 | ? [v0] : ? [v1] : ( ~ (v1 = all_0_10_10) & relation_dom(all_0_9_9) = v0 & identity_relation(v0) = v1) % 6.48/2.04 | % 6.48/2.04 +-Applying beta-rule and splitting (152), into two cases. % 6.48/2.04 |-Branch one: % 6.48/2.04 | (153) all_0_8_8 = all_0_9_9 % 6.48/2.04 | % 6.48/2.04 | Equations (153) can reduce 69 to: % 6.48/2.04 | (154) $false % 6.48/2.04 | % 6.48/2.04 |-The branch is then unsatisfiable % 6.48/2.04 |-Branch two: % 6.48/2.04 | (69) ~ (all_0_8_8 = all_0_9_9) % 6.48/2.04 | (156) ? [v0] : ? [v1] : ( ~ (v1 = all_0_10_10) & relation_dom(all_0_9_9) = v0 & identity_relation(v0) = v1) % 6.48/2.04 | % 6.48/2.04 +-Applying beta-rule and splitting (151), into two cases. % 6.48/2.04 |-Branch one: % 6.48/2.04 | (153) all_0_8_8 = all_0_9_9 % 6.48/2.05 | % 6.48/2.05 | Equations (153) can reduce 69 to: % 6.48/2.05 | (154) $false % 6.48/2.05 | % 6.48/2.05 |-The branch is then unsatisfiable % 6.48/2.05 |-Branch two: % 6.48/2.05 | (69) ~ (all_0_8_8 = all_0_9_9) % 6.48/2.05 | (160) ? [v0] : ? [v1] : (identity_relation(all_0_11_11) = v0 & relation_composition(all_0_13_13, all_0_9_9) = v1 & ( ~ (v1 = all_19_2_21) | ~ (v0 = all_0_10_10))) % 6.48/2.05 | % 6.48/2.05 | Instantiating (160) with all_51_0_33, all_51_1_34 yields: % 6.48/2.05 | (161) identity_relation(all_0_11_11) = all_51_1_34 & relation_composition(all_0_13_13, all_0_9_9) = all_51_0_33 & ( ~ (all_51_0_33 = all_19_2_21) | ~ (all_51_1_34 = all_0_10_10)) % 6.48/2.05 | % 6.48/2.05 | Applying alpha-rule on (161) yields: % 6.48/2.05 | (162) identity_relation(all_0_11_11) = all_51_1_34 % 6.48/2.05 | (163) relation_composition(all_0_13_13, all_0_9_9) = all_51_0_33 % 6.48/2.05 | (164) ~ (all_51_0_33 = all_19_2_21) | ~ (all_51_1_34 = all_0_10_10) % 6.48/2.05 | % 6.48/2.05 | Instantiating formula (48) with all_0_11_11, all_51_1_34, all_0_10_10 and discharging atoms identity_relation(all_0_11_11) = all_51_1_34, identity_relation(all_0_11_11) = all_0_10_10, yields: % 6.48/2.05 | (165) all_51_1_34 = all_0_10_10 % 6.48/2.05 | % 6.48/2.05 | Instantiating formula (34) with all_0_13_13, all_0_9_9, all_51_0_33, all_19_2_21 and discharging atoms relation_composition(all_0_13_13, all_0_9_9) = all_51_0_33, relation_composition(all_0_13_13, all_0_9_9) = all_19_2_21, yields: % 6.48/2.05 | (166) all_51_0_33 = all_19_2_21 % 6.48/2.05 | % 6.48/2.05 +-Applying beta-rule and splitting (164), into two cases. % 6.48/2.05 |-Branch one: % 6.48/2.05 | (167) ~ (all_51_0_33 = all_19_2_21) % 6.48/2.05 | % 6.48/2.05 | Equations (166) can reduce 167 to: % 6.48/2.05 | (154) $false % 6.48/2.05 | % 6.48/2.05 |-The branch is then unsatisfiable % 6.48/2.05 |-Branch two: % 6.48/2.05 | (166) all_51_0_33 = all_19_2_21 % 6.48/2.05 | (170) ~ (all_51_1_34 = all_0_10_10) % 6.48/2.05 | % 6.48/2.05 | Equations (165) can reduce 170 to: % 6.48/2.05 | (154) $false % 6.48/2.05 | % 6.48/2.05 |-The branch is then unsatisfiable % 6.48/2.05 % SZS output end Proof for theBenchmark % 6.48/2.05 % 6.48/2.05 1435ms %------------------------------------------------------------------------------