%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 1.51s % Output : Proof 7.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n017.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 18:30:27 EDT 2022 % 0.12/0.33 % CPUTime : % 0.58/0.58 ____ _ % 0.58/0.58 ___ / __ \_____(_)___ ________ __________ % 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.59 % 0.58/0.59 A Theorem Prover for First-Order Logic % 0.58/0.59 (ePrincess v.1.0) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2015 % 0.58/0.59 (c) Peter Backeman, 2014-2015 % 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.59 Bug reports to peter@backeman.se % 0.58/0.59 % 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.59 % 0.58/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.69/0.95 Prover 0: Preprocessing ... % 2.74/1.25 Prover 0: Warning: ignoring some quantifiers % 2.74/1.27 Prover 0: Constructing countermodel ... % 3.77/1.51 Prover 0: proved (878ms) % 3.77/1.51 % 3.77/1.51 No countermodel exists, formula is valid % 3.77/1.51 % SZS status Theorem for theBenchmark % 3.77/1.51 % 3.77/1.51 Generating proof ... Warning: ignoring some quantifiers % 6.15/2.05 found it (size 118) % 6.15/2.05 % 6.15/2.05 % SZS output start Proof for theBenchmark % 6.15/2.05 Assumed formulas after preprocessing and simplification: % 6.15/2.05 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v2 = v0) & function_inverse(v1) = v2 & function_inverse(v0) = v1 & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v4) & one_to_one(v0) & relation(v10) & relation(v9) & relation(v7) & relation(v6) & relation(v4) & relation(v3) & relation(v0) & relation(empty_set) & function(v10) & function(v7) & function(v4) & function(v0) & empty(v9) & empty(v8) & empty(v7) & empty(empty_set) & ~ empty(v6) & ~ empty(v5) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_composition(v14, v13) = v12) | ~ (relation_composition(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | ~ empty(v13) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | ~ in(v11, v12) | element(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_rng(v13) = v12) | ~ (relation_rng(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_dom(v13) = v12) | ~ (relation_dom(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (identity_relation(v13) = v12) | ~ (identity_relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (function_inverse(v13) = v12) | ~ (function_inverse(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ subset(v11, v12) | element(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | subset(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ (function_inverse(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v14] : ? [v15] : ? [v16] : (relation_rng(v11) = v16 & relation_dom(v11) = v15 & identity_relation(v16) = v13 & identity_relation(v15) = v14 & relation_composition(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ relation(v12) | ~ empty(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ relation(v12) | ~ empty(v11) | empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ (function_inverse(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v14] : ? [v15] : ? [v16] : (relation_rng(v11) = v16 & relation_dom(v11) = v14 & identity_relation(v16) = v15 & identity_relation(v14) = v13 & relation_composition(v12, v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | ~ function(v12) | ~ function(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | ~ function(v12) | ~ function(v11) | function(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ empty(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ empty(v11) | empty(v13)) & ! [v11] : ! [v12] : (v12 = v11 | ~ empty(v12) | ~ empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (relation_dom(v11) = v15 & identity_relation(v15) = v14 & identity_relation(v12) = v16 & relation_composition(v13, v11) = v16 & relation_composition(v11, v13) = v14 & function_inverse(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : (relation_rng(v13) = v14 & relation_dom(v13) = v12 & relation_dom(v11) = v14 & function_inverse(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : ? [v15] : (relation_dom(v11) = v13 & identity_relation(v13) = v14 & function_inverse(v11) = v15 & ! [v16] : (v16 = v15 | ~ (relation_dom(v16) = v12) | ~ one_to_one(v11) | ~ relation(v16) | ~ function(v16) | ? [v17] : ( ~ (v17 = v14) & relation_composition(v11, v16) = v17)) & ! [v16] : (v16 = v15 | ~ (relation_composition(v11, v16) = v14) | ~ one_to_one(v11) | ~ relation(v16) | ~ function(v16) | ? [v17] : ( ~ (v17 = v12) & relation_dom(v16) = v17)))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (relation_rng(v11) = v16 & identity_relation(v16) = v15 & identity_relation(v12) = v14 & relation_composition(v13, v11) = v15 & relation_composition(v11, v13) = v14 & function_inverse(v11) = v13)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : (relation_rng(v14) = v12 & relation_rng(v11) = v13 & relation_dom(v14) = v13 & function_inverse(v11) = v14)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : ? [v15] : (relation_rng(v11) = v13 & identity_relation(v12) = v14 & function_inverse(v11) = v15 & ! [v16] : (v16 = v15 | ~ (relation_dom(v16) = v13) | ~ one_to_one(v11) | ~ relation(v16) | ~ function(v16) | ? [v17] : ( ~ (v17 = v14) & relation_composition(v11, v16) = v17)) & ! [v16] : (v16 = v15 | ~ (relation_composition(v11, v16) = v14) | ~ one_to_one(v11) | ~ relation(v16) | ~ function(v16) | ? [v17] : ( ~ (v17 = v13) & relation_dom(v16) = v17)))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | empty(v11) | ? [v13] : (element(v13, v12) & ~ empty(v13))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) & empty(v13))) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | function(v12)) & ! [v11] : ! [v12] : ( ~ (function_inverse(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | one_to_one(v12)) & ! [v11] : ! [v12] : ( ~ (function_inverse(v11) = v12) | ~ one_to_one(v11) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : (relation_rng(v12) = v14 & relation_rng(v11) = v13 & relation_dom(v12) = v13 & relation_dom(v11) = v14)) & ! [v11] : ! [v12] : ( ~ (function_inverse(v11) = v12) | ~ relation(v11) | ~ function(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (function_inverse(v11) = v12) | ~ relation(v11) | ~ function(v11) | function(v12)) & ! [v11] : ! [v12] : ( ~ (function_inverse(v11) = v12) | ~ relation(v11) | ~ function(v11) | ? [v13] : ? [v14] : ? [v15] : (relation_rng(v11) = v13 & relation_dom(v11) = v14 & identity_relation(v14) = v15 & ! [v16] : (v16 = v12 | ~ (relation_dom(v16) = v13) | ~ one_to_one(v11) | ~ relation(v16) | ~ function(v16) | ? [v17] : ( ~ (v17 = v15) & relation_composition(v11, v16) = v17)) & ! [v16] : (v16 = v12 | ~ (relation_composition(v11, v16) = v15) | ~ one_to_one(v11) | ~ relation(v16) | ~ function(v16) | ? [v17] : ( ~ (v17 = v13) & relation_dom(v16) = v17)))) & ! [v11] : ! [v12] : ( ~ element(v11, v12) | empty(v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ empty(v12) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) & ! [v11] : (v11 = empty_set | ~ empty(v11)) & ! [v11] : ( ~ relation(v11) | ~ function(v11) | ~ empty(v11) | one_to_one(v11)) & ! [v11] : ( ~ empty(v11) | relation(v11)) & ! [v11] : ( ~ empty(v11) | function(v11)) & ? [v11] : ? [v12] : element(v12, v11) & ? [v11] : subset(v11, v11)) % 6.53/2.09 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10 yields: % 6.53/2.09 | (1) ~ (all_0_8_8 = all_0_10_10) & function_inverse(all_0_9_9) = all_0_8_8 & function_inverse(all_0_10_10) = 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_10_10) & 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_10_10) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_10_10) & 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] : (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) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v2 & identity_relation(v2) = v3 & function_inverse(v0) = v4 & ! [v5] : (v5 = v4 | ~ (relation_dom(v5) = v1) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v3) & relation_composition(v0, v5) = v6)) & ! [v5] : (v5 = v4 | ~ (relation_composition(v0, v5) = v3) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v1) & relation_dom(v5) = v6)))) & ! [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) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v2 & identity_relation(v1) = v3 & function_inverse(v0) = v4 & ! [v5] : (v5 = v4 | ~ (relation_dom(v5) = v2) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v3) & relation_composition(v0, v5) = v6)) & ! [v5] : (v5 = v4 | ~ (relation_composition(v0, v5) = v3) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v2) & relation_dom(v5) = v6)))) & ! [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) | one_to_one(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] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & identity_relation(v3) = v4 & ! [v5] : (v5 = v1 | ~ (relation_dom(v5) = v2) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v4) & relation_composition(v0, v5) = v6)) & ! [v5] : (v5 = v1 | ~ (relation_composition(v0, v5) = v4) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v2) & relation_dom(v5) = v6)))) & ! [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) % 6.53/2.11 | % 6.53/2.11 | Applying alpha-rule on (1) yields: % 6.53/2.11 | (2) ! [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)) % 6.53/2.11 | (3) function(all_0_0_0) % 6.53/2.11 | (4) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1)) % 6.53/2.11 | (5) function_inverse(all_0_9_9) = all_0_8_8 % 6.53/2.11 | (6) ~ empty(all_0_4_4) % 6.53/2.11 | (7) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 6.53/2.11 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 6.53/2.11 | (9) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 6.53/2.11 | (10) empty(all_0_2_2) % 6.53/2.11 | (11) ! [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)) % 6.53/2.11 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 6.53/2.11 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 6.53/2.11 | (14) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 6.53/2.11 | (15) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 6.53/2.11 | (16) ! [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)) % 6.53/2.11 | (17) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 6.53/2.12 | (18) ! [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)) % 6.53/2.12 | (19) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) % 6.53/2.12 | (20) function(all_0_6_6) % 6.53/2.12 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) % 6.53/2.12 | (22) empty(all_0_3_3) % 6.53/2.12 | (23) empty(empty_set) % 6.53/2.12 | (24) relation(all_0_4_4) % 6.53/2.12 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 6.53/2.12 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 6.53/2.12 | (27) ! [v0] : ( ~ empty(v0) | function(v0)) % 6.53/2.12 | (28) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v2 & identity_relation(v2) = v3 & function_inverse(v0) = v4 & ! [v5] : (v5 = v4 | ~ (relation_dom(v5) = v1) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v3) & relation_composition(v0, v5) = v6)) & ! [v5] : (v5 = v4 | ~ (relation_composition(v0, v5) = v3) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v1) & relation_dom(v5) = v6)))) % 6.53/2.12 | (29) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 6.53/2.12 | (30) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 6.53/2.12 | (31) relation(all_0_3_3) % 6.53/2.12 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 6.53/2.12 | (33) ? [v0] : ? [v1] : element(v1, v0) % 6.53/2.12 | (34) empty(all_0_1_1) % 6.53/2.12 | (35) relation(all_0_10_10) % 6.53/2.12 | (36) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 6.53/2.12 | (37) ! [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)) % 6.53/2.12 | (38) ! [v0] : ( ~ empty(v0) | relation(v0)) % 6.53/2.12 | (39) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 6.53/2.12 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 6.53/2.12 | (41) ! [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)) % 6.53/2.12 | (42) ? [v0] : subset(v0, v0) % 6.53/2.12 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 6.53/2.12 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 6.53/2.12 | (45) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) % 6.53/2.12 | (46) relation_empty_yielding(empty_set) % 6.53/2.12 | (47) relation(all_0_6_6) % 6.53/2.12 | (48) relation(all_0_7_7) % 6.53/2.12 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 6.53/2.12 | (50) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 6.53/2.12 | (51) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 6.53/2.13 | (52) function_inverse(all_0_10_10) = all_0_9_9 % 6.53/2.13 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 6.53/2.13 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 6.53/2.13 | (55) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 6.53/2.13 | (56) ~ empty(all_0_5_5) % 6.53/2.13 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 6.53/2.13 | (58) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 6.53/2.13 | (59) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 6.53/2.13 | (60) function(all_0_3_3) % 6.53/2.13 | (61) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & identity_relation(v3) = v4 & ! [v5] : (v5 = v1 | ~ (relation_dom(v5) = v2) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v4) & relation_composition(v0, v5) = v6)) & ! [v5] : (v5 = v1 | ~ (relation_composition(v0, v5) = v4) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v2) & relation_dom(v5) = v6)))) % 6.53/2.13 | (62) relation(empty_set) % 6.53/2.13 | (63) one_to_one(all_0_10_10) % 6.53/2.13 | (64) relation(all_0_1_1) % 6.53/2.13 | (65) relation_empty_yielding(all_0_7_7) % 6.53/2.13 | (66) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 6.53/2.13 | (67) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 6.53/2.13 | (68) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 6.53/2.13 | (69) function(all_0_10_10) % 6.53/2.13 | (70) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 6.53/2.13 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 6.53/2.13 | (72) ! [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)) % 6.53/2.13 | (73) relation(all_0_0_0) % 6.53/2.13 | (74) one_to_one(all_0_6_6) % 6.53/2.13 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 6.53/2.13 | (76) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v2 & identity_relation(v1) = v3 & function_inverse(v0) = v4 & ! [v5] : (v5 = v4 | ~ (relation_dom(v5) = v2) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v3) & relation_composition(v0, v5) = v6)) & ! [v5] : (v5 = v4 | ~ (relation_composition(v0, v5) = v3) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6] : ( ~ (v6 = v2) & relation_dom(v5) = v6)))) % 6.53/2.13 | (77) ~ (all_0_8_8 = all_0_10_10) % 6.53/2.13 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 6.53/2.13 | % 6.53/2.13 | Instantiating formula (4) with all_0_9_9, all_0_10_10 and discharging atoms function_inverse(all_0_10_10) = all_0_9_9, one_to_one(all_0_10_10), relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.14 | (79) one_to_one(all_0_9_9) % 6.53/2.14 | % 6.53/2.14 | Instantiating formula (41) with all_0_9_9, all_0_10_10 and discharging atoms function_inverse(all_0_10_10) = all_0_9_9, one_to_one(all_0_10_10), relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.14 | (80) ? [v0] : ? [v1] : (relation_rng(all_0_9_9) = v1 & relation_rng(all_0_10_10) = v0 & relation_dom(all_0_9_9) = v0 & relation_dom(all_0_10_10) = v1) % 6.53/2.14 | % 6.53/2.14 | Instantiating formula (55) with all_0_9_9, all_0_10_10 and discharging atoms function_inverse(all_0_10_10) = all_0_9_9, relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.14 | (81) relation(all_0_9_9) % 6.53/2.14 | % 6.53/2.14 | Instantiating formula (45) with all_0_9_9, all_0_10_10 and discharging atoms function_inverse(all_0_10_10) = all_0_9_9, relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.14 | (82) function(all_0_9_9) % 6.53/2.14 | % 6.53/2.14 | Instantiating formula (61) with all_0_9_9, all_0_10_10 and discharging atoms function_inverse(all_0_10_10) = all_0_9_9, relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.14 | (83) ? [v0] : ? [v1] : ? [v2] : (relation_rng(all_0_10_10) = v0 & relation_dom(all_0_10_10) = v1 & identity_relation(v1) = v2 & ! [v3] : (v3 = all_0_9_9 | ~ (relation_dom(v3) = v0) | ~ one_to_one(all_0_10_10) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v2) & relation_composition(all_0_10_10, v3) = v4)) & ! [v3] : (v3 = all_0_9_9 | ~ (relation_composition(all_0_10_10, v3) = v2) | ~ one_to_one(all_0_10_10) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v0) & relation_dom(v3) = v4))) % 6.53/2.14 | % 6.53/2.14 | Instantiating (80) with all_17_0_14, all_17_1_15 yields: % 6.53/2.14 | (84) relation_rng(all_0_9_9) = all_17_0_14 & relation_rng(all_0_10_10) = all_17_1_15 & relation_dom(all_0_9_9) = all_17_1_15 & relation_dom(all_0_10_10) = all_17_0_14 % 6.53/2.14 | % 6.53/2.14 | Applying alpha-rule on (84) yields: % 6.53/2.14 | (85) relation_rng(all_0_9_9) = all_17_0_14 % 6.53/2.14 | (86) relation_rng(all_0_10_10) = all_17_1_15 % 6.53/2.14 | (87) relation_dom(all_0_9_9) = all_17_1_15 % 6.53/2.14 | (88) relation_dom(all_0_10_10) = all_17_0_14 % 6.53/2.14 | % 6.53/2.14 | Instantiating (83) with all_19_0_16, all_19_1_17, all_19_2_18 yields: % 6.53/2.14 | (89) relation_rng(all_0_10_10) = all_19_2_18 & relation_dom(all_0_10_10) = all_19_1_17 & identity_relation(all_19_1_17) = all_19_0_16 & ! [v0] : (v0 = all_0_9_9 | ~ (relation_dom(v0) = all_19_2_18) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_19_0_16) & relation_composition(all_0_10_10, v0) = v1)) & ! [v0] : (v0 = all_0_9_9 | ~ (relation_composition(all_0_10_10, v0) = all_19_0_16) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_19_2_18) & relation_dom(v0) = v1)) % 6.53/2.14 | % 6.53/2.14 | Applying alpha-rule on (89) yields: % 6.53/2.14 | (90) relation_rng(all_0_10_10) = all_19_2_18 % 6.53/2.14 | (91) relation_dom(all_0_10_10) = all_19_1_17 % 6.53/2.14 | (92) ! [v0] : (v0 = all_0_9_9 | ~ (relation_composition(all_0_10_10, v0) = all_19_0_16) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_19_2_18) & relation_dom(v0) = v1)) % 6.53/2.14 | (93) identity_relation(all_19_1_17) = all_19_0_16 % 6.53/2.14 | (94) ! [v0] : (v0 = all_0_9_9 | ~ (relation_dom(v0) = all_19_2_18) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_19_0_16) & relation_composition(all_0_10_10, v0) = v1)) % 6.53/2.14 | % 6.53/2.14 | Instantiating formula (67) with all_0_10_10, all_17_1_15, all_19_2_18 and discharging atoms relation_rng(all_0_10_10) = all_19_2_18, relation_rng(all_0_10_10) = all_17_1_15, yields: % 6.53/2.14 | (95) all_19_2_18 = all_17_1_15 % 6.53/2.14 | % 6.53/2.14 | Instantiating formula (43) with all_0_10_10, all_17_0_14, all_19_1_17 and discharging atoms relation_dom(all_0_10_10) = all_19_1_17, relation_dom(all_0_10_10) = all_17_0_14, yields: % 6.53/2.14 | (96) all_19_1_17 = all_17_0_14 % 6.53/2.14 | % 6.53/2.14 | From (95) and (90) follows: % 6.53/2.14 | (86) relation_rng(all_0_10_10) = all_17_1_15 % 6.53/2.14 | % 6.53/2.14 | From (96) and (91) follows: % 6.53/2.14 | (88) relation_dom(all_0_10_10) = all_17_0_14 % 6.53/2.14 | % 6.53/2.14 | Instantiating formula (2) with all_17_1_15, all_0_10_10 and discharging atoms relation_rng(all_0_10_10) = all_17_1_15, one_to_one(all_0_10_10), relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.14 | (99) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_10_10) = v2 & identity_relation(v2) = v1 & identity_relation(all_17_1_15) = v3 & relation_composition(v0, all_0_10_10) = v3 & relation_composition(all_0_10_10, v0) = v1 & function_inverse(all_0_10_10) = v0) % 6.53/2.14 | % 6.53/2.14 | Instantiating formula (28) with all_17_1_15, all_0_10_10 and discharging atoms relation_rng(all_0_10_10) = all_17_1_15, relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.15 | (100) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_10_10) = v0 & identity_relation(v0) = v1 & function_inverse(all_0_10_10) = v2 & ! [v3] : (v3 = v2 | ~ (relation_dom(v3) = all_17_1_15) | ~ one_to_one(all_0_10_10) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v1) & relation_composition(all_0_10_10, v3) = v4)) & ! [v3] : (v3 = v2 | ~ (relation_composition(all_0_10_10, v3) = v1) | ~ one_to_one(all_0_10_10) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = all_17_1_15) & relation_dom(v3) = v4))) % 6.53/2.15 | % 6.53/2.15 | Instantiating formula (18) with all_17_0_14, all_0_10_10 and discharging atoms relation_dom(all_0_10_10) = all_17_0_14, one_to_one(all_0_10_10), relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.15 | (101) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng(all_0_10_10) = v3 & identity_relation(v3) = v2 & identity_relation(all_17_0_14) = v1 & relation_composition(v0, all_0_10_10) = v2 & relation_composition(all_0_10_10, v0) = v1 & function_inverse(all_0_10_10) = v0) % 6.53/2.15 | % 6.53/2.15 | Instantiating formula (76) with all_17_0_14, all_0_10_10 and discharging atoms relation_dom(all_0_10_10) = all_17_0_14, relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.15 | (102) ? [v0] : ? [v1] : ? [v2] : (relation_rng(all_0_10_10) = v0 & identity_relation(all_17_0_14) = v1 & function_inverse(all_0_10_10) = v2 & ! [v3] : (v3 = v2 | ~ (relation_dom(v3) = v0) | ~ one_to_one(all_0_10_10) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v1) & relation_composition(all_0_10_10, v3) = v4)) & ! [v3] : (v3 = v2 | ~ (relation_composition(all_0_10_10, v3) = v1) | ~ one_to_one(all_0_10_10) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v0) & relation_dom(v3) = v4))) % 6.53/2.15 | % 6.53/2.15 | Instantiating formula (2) with all_17_0_14, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_17_0_14, one_to_one(all_0_9_9), relation(all_0_9_9), function(all_0_9_9), yields: % 6.53/2.15 | (103) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_9_9) = v2 & identity_relation(v2) = v1 & identity_relation(all_17_0_14) = v3 & relation_composition(v0, all_0_9_9) = v3 & relation_composition(all_0_9_9, v0) = v1 & function_inverse(all_0_9_9) = v0) % 6.53/2.15 | % 6.53/2.15 | Instantiating formula (37) with all_17_0_14, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_17_0_14, one_to_one(all_0_9_9), relation(all_0_9_9), function(all_0_9_9), yields: % 6.53/2.15 | (104) ? [v0] : ? [v1] : (relation_rng(v0) = v1 & relation_dom(v0) = all_17_0_14 & relation_dom(all_0_9_9) = v1 & function_inverse(all_0_9_9) = v0) % 6.53/2.15 | % 6.53/2.15 | Instantiating formula (28) with all_17_0_14, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_17_0_14, relation(all_0_9_9), function(all_0_9_9), yields: % 6.53/2.15 | (105) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_9_9) = v0 & identity_relation(v0) = v1 & function_inverse(all_0_9_9) = v2 & ! [v3] : (v3 = v2 | ~ (relation_dom(v3) = all_17_0_14) | ~ one_to_one(all_0_9_9) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v1) & relation_composition(all_0_9_9, v3) = v4)) & ! [v3] : (v3 = v2 | ~ (relation_composition(all_0_9_9, v3) = v1) | ~ one_to_one(all_0_9_9) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = all_17_0_14) & relation_dom(v3) = v4))) % 6.53/2.15 | % 6.53/2.15 | Instantiating formula (18) with all_17_1_15, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_17_1_15, one_to_one(all_0_9_9), relation(all_0_9_9), function(all_0_9_9), yields: % 6.53/2.15 | (106) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng(all_0_9_9) = v3 & identity_relation(v3) = v2 & identity_relation(all_17_1_15) = v1 & relation_composition(v0, all_0_9_9) = v2 & relation_composition(all_0_9_9, v0) = v1 & function_inverse(all_0_9_9) = v0) % 6.53/2.15 | % 6.53/2.15 | Instantiating formula (76) with all_17_1_15, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_17_1_15, relation(all_0_9_9), function(all_0_9_9), yields: % 6.53/2.15 | (107) ? [v0] : ? [v1] : ? [v2] : (relation_rng(all_0_9_9) = v0 & identity_relation(all_17_1_15) = v1 & function_inverse(all_0_9_9) = v2 & ! [v3] : (v3 = v2 | ~ (relation_dom(v3) = v0) | ~ one_to_one(all_0_9_9) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v1) & relation_composition(all_0_9_9, v3) = v4)) & ! [v3] : (v3 = v2 | ~ (relation_composition(all_0_9_9, v3) = v1) | ~ one_to_one(all_0_9_9) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v0) & relation_dom(v3) = v4))) % 6.53/2.15 | % 6.53/2.15 | Instantiating formula (61) with all_0_8_8, all_0_9_9 and discharging atoms function_inverse(all_0_9_9) = all_0_8_8, relation(all_0_9_9), function(all_0_9_9), yields: % 6.53/2.15 | (108) ? [v0] : ? [v1] : ? [v2] : (relation_rng(all_0_9_9) = v0 & relation_dom(all_0_9_9) = v1 & identity_relation(v1) = v2 & ! [v3] : (v3 = all_0_8_8 | ~ (relation_dom(v3) = v0) | ~ one_to_one(all_0_9_9) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v2) & relation_composition(all_0_9_9, v3) = v4)) & ! [v3] : (v3 = all_0_8_8 | ~ (relation_composition(all_0_9_9, v3) = v2) | ~ one_to_one(all_0_9_9) | ~ relation(v3) | ~ function(v3) | ? [v4] : ( ~ (v4 = v0) & relation_dom(v3) = v4))) % 6.53/2.16 | % 6.53/2.16 | Instantiating (105) with all_36_0_23, all_36_1_24, all_36_2_25 yields: % 6.53/2.16 | (109) relation_dom(all_0_9_9) = all_36_2_25 & identity_relation(all_36_2_25) = all_36_1_24 & function_inverse(all_0_9_9) = all_36_0_23 & ! [v0] : (v0 = all_36_0_23 | ~ (relation_dom(v0) = all_17_0_14) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_36_1_24) & relation_composition(all_0_9_9, v0) = v1)) & ! [v0] : (v0 = all_36_0_23 | ~ (relation_composition(all_0_9_9, v0) = all_36_1_24) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_17_0_14) & relation_dom(v0) = v1)) % 6.53/2.16 | % 6.53/2.16 | Applying alpha-rule on (109) yields: % 6.53/2.16 | (110) relation_dom(all_0_9_9) = all_36_2_25 % 6.53/2.16 | (111) identity_relation(all_36_2_25) = all_36_1_24 % 6.53/2.16 | (112) ! [v0] : (v0 = all_36_0_23 | ~ (relation_dom(v0) = all_17_0_14) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_36_1_24) & relation_composition(all_0_9_9, v0) = v1)) % 6.53/2.16 | (113) function_inverse(all_0_9_9) = all_36_0_23 % 6.53/2.16 | (114) ! [v0] : (v0 = all_36_0_23 | ~ (relation_composition(all_0_9_9, v0) = all_36_1_24) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_17_0_14) & relation_dom(v0) = v1)) % 6.53/2.16 | % 6.53/2.16 | Instantiating formula (112) with all_0_10_10 and discharging atoms relation_dom(all_0_10_10) = all_17_0_14, one_to_one(all_0_9_9), relation(all_0_10_10), function(all_0_10_10), yields: % 6.53/2.16 | (115) all_36_0_23 = all_0_10_10 | ? [v0] : ( ~ (v0 = all_36_1_24) & relation_composition(all_0_9_9, all_0_10_10) = v0) % 6.53/2.16 | % 6.53/2.16 | Instantiating (108) with all_39_0_26, all_39_1_27, all_39_2_28 yields: % 6.53/2.16 | (116) relation_rng(all_0_9_9) = all_39_2_28 & relation_dom(all_0_9_9) = all_39_1_27 & identity_relation(all_39_1_27) = all_39_0_26 & ! [v0] : (v0 = all_0_8_8 | ~ (relation_dom(v0) = all_39_2_28) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_39_0_26) & relation_composition(all_0_9_9, v0) = v1)) & ! [v0] : (v0 = all_0_8_8 | ~ (relation_composition(all_0_9_9, v0) = all_39_0_26) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_39_2_28) & relation_dom(v0) = v1)) % 6.53/2.16 | % 6.53/2.16 | Applying alpha-rule on (116) yields: % 6.53/2.16 | (117) identity_relation(all_39_1_27) = all_39_0_26 % 6.53/2.16 | (118) relation_rng(all_0_9_9) = all_39_2_28 % 6.53/2.16 | (119) ! [v0] : (v0 = all_0_8_8 | ~ (relation_dom(v0) = all_39_2_28) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_39_0_26) & relation_composition(all_0_9_9, v0) = v1)) % 6.53/2.16 | (120) relation_dom(all_0_9_9) = all_39_1_27 % 6.53/2.16 | (121) ! [v0] : (v0 = all_0_8_8 | ~ (relation_composition(all_0_9_9, v0) = all_39_0_26) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_39_2_28) & relation_dom(v0) = v1)) % 6.53/2.16 | % 6.53/2.16 | Instantiating (102) with all_42_0_29, all_42_1_30, all_42_2_31 yields: % 6.53/2.16 | (122) relation_rng(all_0_10_10) = all_42_2_31 & identity_relation(all_17_0_14) = all_42_1_30 & function_inverse(all_0_10_10) = all_42_0_29 & ! [v0] : (v0 = all_42_0_29 | ~ (relation_dom(v0) = all_42_2_31) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_42_1_30) & relation_composition(all_0_10_10, v0) = v1)) & ! [v0] : (v0 = all_42_0_29 | ~ (relation_composition(all_0_10_10, v0) = all_42_1_30) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_42_2_31) & relation_dom(v0) = v1)) % 6.53/2.16 | % 6.53/2.16 | Applying alpha-rule on (122) yields: % 6.53/2.16 | (123) function_inverse(all_0_10_10) = all_42_0_29 % 6.53/2.16 | (124) relation_rng(all_0_10_10) = all_42_2_31 % 6.53/2.16 | (125) ! [v0] : (v0 = all_42_0_29 | ~ (relation_dom(v0) = all_42_2_31) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_42_1_30) & relation_composition(all_0_10_10, v0) = v1)) % 6.53/2.16 | (126) identity_relation(all_17_0_14) = all_42_1_30 % 6.53/2.16 | (127) ! [v0] : (v0 = all_42_0_29 | ~ (relation_composition(all_0_10_10, v0) = all_42_1_30) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_42_2_31) & relation_dom(v0) = v1)) % 6.53/2.16 | % 6.53/2.16 | Instantiating (103) with all_45_0_32, all_45_1_33, all_45_2_34, all_45_3_35 yields: % 6.53/2.16 | (128) relation_dom(all_0_9_9) = all_45_1_33 & identity_relation(all_45_1_33) = all_45_2_34 & identity_relation(all_17_0_14) = all_45_0_32 & relation_composition(all_45_3_35, all_0_9_9) = all_45_0_32 & relation_composition(all_0_9_9, all_45_3_35) = all_45_2_34 & function_inverse(all_0_9_9) = all_45_3_35 % 6.53/2.16 | % 6.53/2.16 | Applying alpha-rule on (128) yields: % 6.53/2.16 | (129) relation_composition(all_45_3_35, all_0_9_9) = all_45_0_32 % 6.53/2.16 | (130) relation_composition(all_0_9_9, all_45_3_35) = all_45_2_34 % 6.53/2.16 | (131) identity_relation(all_17_0_14) = all_45_0_32 % 6.53/2.16 | (132) function_inverse(all_0_9_9) = all_45_3_35 % 6.53/2.16 | (133) relation_dom(all_0_9_9) = all_45_1_33 % 6.53/2.16 | (134) identity_relation(all_45_1_33) = all_45_2_34 % 6.53/2.16 | % 6.53/2.16 | Instantiating (107) with all_47_0_36, all_47_1_37, all_47_2_38 yields: % 6.53/2.16 | (135) relation_rng(all_0_9_9) = all_47_2_38 & identity_relation(all_17_1_15) = all_47_1_37 & function_inverse(all_0_9_9) = all_47_0_36 & ! [v0] : (v0 = all_47_0_36 | ~ (relation_dom(v0) = all_47_2_38) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_47_1_37) & relation_composition(all_0_9_9, v0) = v1)) & ! [v0] : (v0 = all_47_0_36 | ~ (relation_composition(all_0_9_9, v0) = all_47_1_37) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_47_2_38) & relation_dom(v0) = v1)) % 6.53/2.16 | % 6.53/2.16 | Applying alpha-rule on (135) yields: % 6.53/2.16 | (136) relation_rng(all_0_9_9) = all_47_2_38 % 6.53/2.16 | (137) identity_relation(all_17_1_15) = all_47_1_37 % 6.53/2.16 | (138) ! [v0] : (v0 = all_47_0_36 | ~ (relation_composition(all_0_9_9, v0) = all_47_1_37) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_47_2_38) & relation_dom(v0) = v1)) % 6.53/2.16 | (139) function_inverse(all_0_9_9) = all_47_0_36 % 6.53/2.16 | (140) ! [v0] : (v0 = all_47_0_36 | ~ (relation_dom(v0) = all_47_2_38) | ~ one_to_one(all_0_9_9) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_47_1_37) & relation_composition(all_0_9_9, v0) = v1)) % 6.53/2.16 | % 6.53/2.16 | Instantiating (104) with all_50_0_39, all_50_1_40 yields: % 6.53/2.16 | (141) relation_rng(all_50_1_40) = all_50_0_39 & relation_dom(all_50_1_40) = all_17_0_14 & relation_dom(all_0_9_9) = all_50_0_39 & function_inverse(all_0_9_9) = all_50_1_40 % 6.53/2.16 | % 6.53/2.16 | Applying alpha-rule on (141) yields: % 6.53/2.17 | (142) relation_rng(all_50_1_40) = all_50_0_39 % 6.53/2.17 | (143) relation_dom(all_50_1_40) = all_17_0_14 % 6.53/2.17 | (144) relation_dom(all_0_9_9) = all_50_0_39 % 6.53/2.17 | (145) function_inverse(all_0_9_9) = all_50_1_40 % 6.53/2.17 | % 6.53/2.17 | Instantiating (106) with all_52_0_41, all_52_1_42, all_52_2_43, all_52_3_44 yields: % 6.53/2.17 | (146) relation_rng(all_0_9_9) = all_52_0_41 & identity_relation(all_52_0_41) = all_52_1_42 & identity_relation(all_17_1_15) = all_52_2_43 & relation_composition(all_52_3_44, all_0_9_9) = all_52_1_42 & relation_composition(all_0_9_9, all_52_3_44) = all_52_2_43 & function_inverse(all_0_9_9) = all_52_3_44 % 6.53/2.17 | % 6.53/2.17 | Applying alpha-rule on (146) yields: % 6.53/2.17 | (147) relation_composition(all_0_9_9, all_52_3_44) = all_52_2_43 % 6.53/2.17 | (148) identity_relation(all_52_0_41) = all_52_1_42 % 6.53/2.17 | (149) function_inverse(all_0_9_9) = all_52_3_44 % 6.53/2.17 | (150) relation_composition(all_52_3_44, all_0_9_9) = all_52_1_42 % 6.53/2.17 | (151) identity_relation(all_17_1_15) = all_52_2_43 % 6.53/2.17 | (152) relation_rng(all_0_9_9) = all_52_0_41 % 6.53/2.17 | % 6.53/2.17 | Instantiating (101) with all_54_0_45, all_54_1_46, all_54_2_47, all_54_3_48 yields: % 6.53/2.17 | (153) relation_rng(all_0_10_10) = all_54_0_45 & identity_relation(all_54_0_45) = all_54_1_46 & identity_relation(all_17_0_14) = all_54_2_47 & relation_composition(all_54_3_48, all_0_10_10) = all_54_1_46 & relation_composition(all_0_10_10, all_54_3_48) = all_54_2_47 & function_inverse(all_0_10_10) = all_54_3_48 % 6.53/2.17 | % 6.53/2.17 | Applying alpha-rule on (153) yields: % 6.53/2.17 | (154) identity_relation(all_54_0_45) = all_54_1_46 % 6.53/2.17 | (155) identity_relation(all_17_0_14) = all_54_2_47 % 6.53/2.17 | (156) function_inverse(all_0_10_10) = all_54_3_48 % 6.53/2.17 | (157) relation_rng(all_0_10_10) = all_54_0_45 % 6.53/2.17 | (158) relation_composition(all_54_3_48, all_0_10_10) = all_54_1_46 % 6.53/2.17 | (159) relation_composition(all_0_10_10, all_54_3_48) = all_54_2_47 % 6.53/2.17 | % 6.53/2.17 | Instantiating (99) with all_56_0_49, all_56_1_50, all_56_2_51, all_56_3_52 yields: % 6.53/2.17 | (160) relation_dom(all_0_10_10) = all_56_1_50 & identity_relation(all_56_1_50) = all_56_2_51 & identity_relation(all_17_1_15) = all_56_0_49 & relation_composition(all_56_3_52, all_0_10_10) = all_56_0_49 & relation_composition(all_0_10_10, all_56_3_52) = all_56_2_51 & function_inverse(all_0_10_10) = all_56_3_52 % 6.53/2.17 | % 6.53/2.17 | Applying alpha-rule on (160) yields: % 6.53/2.17 | (161) function_inverse(all_0_10_10) = all_56_3_52 % 6.53/2.17 | (162) identity_relation(all_17_1_15) = all_56_0_49 % 6.53/2.17 | (163) relation_composition(all_56_3_52, all_0_10_10) = all_56_0_49 % 6.53/2.17 | (164) relation_dom(all_0_10_10) = all_56_1_50 % 6.53/2.17 | (165) relation_composition(all_0_10_10, all_56_3_52) = all_56_2_51 % 6.53/2.17 | (166) identity_relation(all_56_1_50) = all_56_2_51 % 6.53/2.17 | % 6.53/2.17 | Instantiating (100) with all_58_0_53, all_58_1_54, all_58_2_55 yields: % 6.53/2.17 | (167) relation_dom(all_0_10_10) = all_58_2_55 & identity_relation(all_58_2_55) = all_58_1_54 & function_inverse(all_0_10_10) = all_58_0_53 & ! [v0] : (v0 = all_58_0_53 | ~ (relation_dom(v0) = all_17_1_15) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_58_1_54) & relation_composition(all_0_10_10, v0) = v1)) & ! [v0] : (v0 = all_58_0_53 | ~ (relation_composition(all_0_10_10, v0) = all_58_1_54) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_17_1_15) & relation_dom(v0) = v1)) % 6.53/2.17 | % 6.53/2.17 | Applying alpha-rule on (167) yields: % 6.53/2.17 | (168) identity_relation(all_58_2_55) = all_58_1_54 % 6.53/2.17 | (169) ! [v0] : (v0 = all_58_0_53 | ~ (relation_dom(v0) = all_17_1_15) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_58_1_54) & relation_composition(all_0_10_10, v0) = v1)) % 6.53/2.17 | (170) ! [v0] : (v0 = all_58_0_53 | ~ (relation_composition(all_0_10_10, v0) = all_58_1_54) | ~ one_to_one(all_0_10_10) | ~ relation(v0) | ~ function(v0) | ? [v1] : ( ~ (v1 = all_17_1_15) & relation_dom(v0) = v1)) % 6.53/2.17 | (171) relation_dom(all_0_10_10) = all_58_2_55 % 6.53/2.17 | (172) function_inverse(all_0_10_10) = all_58_0_53 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (67) with all_0_10_10, all_54_0_45, all_17_1_15 and discharging atoms relation_rng(all_0_10_10) = all_54_0_45, relation_rng(all_0_10_10) = all_17_1_15, yields: % 6.53/2.17 | (173) all_54_0_45 = all_17_1_15 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (67) with all_0_10_10, all_42_2_31, all_54_0_45 and discharging atoms relation_rng(all_0_10_10) = all_54_0_45, relation_rng(all_0_10_10) = all_42_2_31, yields: % 6.53/2.17 | (174) all_54_0_45 = all_42_2_31 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (43) with all_0_9_9, all_39_1_27, all_17_1_15 and discharging atoms relation_dom(all_0_9_9) = all_39_1_27, relation_dom(all_0_9_9) = all_17_1_15, yields: % 6.53/2.17 | (175) all_39_1_27 = all_17_1_15 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (43) with all_0_9_9, all_39_1_27, all_45_1_33 and discharging atoms relation_dom(all_0_9_9) = all_45_1_33, relation_dom(all_0_9_9) = all_39_1_27, yields: % 6.53/2.17 | (176) all_45_1_33 = all_39_1_27 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (43) with all_0_9_9, all_36_2_25, all_45_1_33 and discharging atoms relation_dom(all_0_9_9) = all_45_1_33, relation_dom(all_0_9_9) = all_36_2_25, yields: % 6.53/2.17 | (177) all_45_1_33 = all_36_2_25 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (57) with all_17_1_15, all_52_2_43, all_56_0_49 and discharging atoms identity_relation(all_17_1_15) = all_56_0_49, identity_relation(all_17_1_15) = all_52_2_43, yields: % 6.53/2.17 | (178) all_56_0_49 = all_52_2_43 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (57) with all_17_1_15, all_47_1_37, all_56_0_49 and discharging atoms identity_relation(all_17_1_15) = all_56_0_49, identity_relation(all_17_1_15) = all_47_1_37, yields: % 6.53/2.17 | (179) all_56_0_49 = all_47_1_37 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (53) with all_0_9_9, all_50_1_40, all_52_3_44 and discharging atoms function_inverse(all_0_9_9) = all_52_3_44, function_inverse(all_0_9_9) = all_50_1_40, yields: % 6.53/2.17 | (180) all_52_3_44 = all_50_1_40 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (53) with all_0_9_9, all_47_0_36, all_0_8_8 and discharging atoms function_inverse(all_0_9_9) = all_47_0_36, function_inverse(all_0_9_9) = all_0_8_8, yields: % 6.53/2.17 | (181) all_47_0_36 = all_0_8_8 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (53) with all_0_9_9, all_47_0_36, all_52_3_44 and discharging atoms function_inverse(all_0_9_9) = all_52_3_44, function_inverse(all_0_9_9) = all_47_0_36, yields: % 6.53/2.17 | (182) all_52_3_44 = all_47_0_36 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (53) with all_0_9_9, all_45_3_35, all_52_3_44 and discharging atoms function_inverse(all_0_9_9) = all_52_3_44, function_inverse(all_0_9_9) = all_45_3_35, yields: % 6.53/2.17 | (183) all_52_3_44 = all_45_3_35 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (53) with all_0_9_9, all_36_0_23, all_50_1_40 and discharging atoms function_inverse(all_0_9_9) = all_50_1_40, function_inverse(all_0_9_9) = all_36_0_23, yields: % 6.53/2.17 | (184) all_50_1_40 = all_36_0_23 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (53) with all_0_10_10, all_58_0_53, all_0_9_9 and discharging atoms function_inverse(all_0_10_10) = all_58_0_53, function_inverse(all_0_10_10) = all_0_9_9, yields: % 6.53/2.17 | (185) all_58_0_53 = all_0_9_9 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (53) with all_0_10_10, all_56_3_52, all_58_0_53 and discharging atoms function_inverse(all_0_10_10) = all_58_0_53, function_inverse(all_0_10_10) = all_56_3_52, yields: % 6.53/2.17 | (186) all_58_0_53 = all_56_3_52 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (53) with all_0_10_10, all_54_3_48, all_58_0_53 and discharging atoms function_inverse(all_0_10_10) = all_58_0_53, function_inverse(all_0_10_10) = all_54_3_48, yields: % 6.53/2.17 | (187) all_58_0_53 = all_54_3_48 % 6.53/2.17 | % 6.53/2.17 | Instantiating formula (53) with all_0_10_10, all_42_0_29, all_56_3_52 and discharging atoms function_inverse(all_0_10_10) = all_56_3_52, function_inverse(all_0_10_10) = all_42_0_29, yields: % 6.53/2.17 | (188) all_56_3_52 = all_42_0_29 % 6.53/2.17 | % 6.53/2.18 | Combining equations (186,187) yields a new equation: % 6.53/2.18 | (189) all_56_3_52 = all_54_3_48 % 6.53/2.18 | % 6.53/2.18 | Simplifying 189 yields: % 6.53/2.18 | (190) all_56_3_52 = all_54_3_48 % 6.53/2.18 | % 6.53/2.18 | Combining equations (185,187) yields a new equation: % 6.53/2.18 | (191) all_54_3_48 = all_0_9_9 % 6.53/2.18 | % 6.53/2.18 | Combining equations (178,179) yields a new equation: % 6.53/2.18 | (192) all_52_2_43 = all_47_1_37 % 6.53/2.18 | % 6.53/2.18 | Simplifying 192 yields: % 6.53/2.18 | (193) all_52_2_43 = all_47_1_37 % 6.53/2.18 | % 6.53/2.18 | Combining equations (190,188) yields a new equation: % 6.53/2.18 | (194) all_54_3_48 = all_42_0_29 % 6.53/2.18 | % 6.53/2.18 | Simplifying 194 yields: % 6.53/2.18 | (195) all_54_3_48 = all_42_0_29 % 6.53/2.18 | % 6.53/2.18 | Combining equations (173,174) yields a new equation: % 6.53/2.18 | (196) all_42_2_31 = all_17_1_15 % 6.53/2.18 | % 6.53/2.18 | Combining equations (191,195) yields a new equation: % 6.53/2.18 | (197) all_42_0_29 = all_0_9_9 % 6.53/2.18 | % 6.53/2.18 | Combining equations (180,183) yields a new equation: % 6.53/2.18 | (198) all_50_1_40 = all_45_3_35 % 6.53/2.18 | % 6.53/2.18 | Simplifying 198 yields: % 6.53/2.18 | (199) all_50_1_40 = all_45_3_35 % 6.53/2.18 | % 6.53/2.18 | Combining equations (182,183) yields a new equation: % 6.53/2.18 | (200) all_47_0_36 = all_45_3_35 % 6.53/2.18 | % 6.53/2.18 | Simplifying 200 yields: % 6.53/2.18 | (201) all_47_0_36 = all_45_3_35 % 6.53/2.18 | % 6.53/2.18 | Combining equations (199,184) yields a new equation: % 6.53/2.18 | (202) all_45_3_35 = all_36_0_23 % 6.53/2.18 | % 6.53/2.18 | Simplifying 202 yields: % 6.53/2.18 | (203) all_45_3_35 = all_36_0_23 % 6.53/2.18 | % 6.53/2.18 | Combining equations (201,181) yields a new equation: % 6.53/2.18 | (204) all_45_3_35 = all_0_8_8 % 6.53/2.18 | % 6.53/2.18 | Simplifying 204 yields: % 6.53/2.18 | (205) all_45_3_35 = all_0_8_8 % 6.53/2.18 | % 6.53/2.18 | Combining equations (176,177) yields a new equation: % 6.53/2.18 | (206) all_39_1_27 = all_36_2_25 % 6.53/2.18 | % 6.53/2.18 | Simplifying 206 yields: % 6.53/2.18 | (207) all_39_1_27 = all_36_2_25 % 6.53/2.18 | % 6.53/2.18 | Combining equations (203,205) yields a new equation: % 6.53/2.18 | (208) all_36_0_23 = all_0_8_8 % 6.53/2.18 | % 6.53/2.18 | Simplifying 208 yields: % 6.53/2.18 | (209) all_36_0_23 = all_0_8_8 % 6.53/2.18 | % 6.53/2.18 | Combining equations (207,175) yields a new equation: % 6.53/2.18 | (210) all_36_2_25 = all_17_1_15 % 6.53/2.18 | % 6.53/2.18 | Simplifying 210 yields: % 6.53/2.18 | (211) all_36_2_25 = all_17_1_15 % 6.53/2.18 | % 6.53/2.18 | Combining equations (211,177) yields a new equation: % 6.53/2.18 | (212) all_45_1_33 = all_17_1_15 % 6.53/2.18 | % 6.53/2.18 | Combining equations (205,183) yields a new equation: % 6.53/2.18 | (213) all_52_3_44 = all_0_8_8 % 6.53/2.18 | % 6.53/2.18 | Combining equations (196,174) yields a new equation: % 6.53/2.18 | (173) all_54_0_45 = all_17_1_15 % 6.53/2.18 | % 6.53/2.18 | Combining equations (197,188) yields a new equation: % 6.53/2.18 | (215) all_56_3_52 = all_0_9_9 % 6.53/2.18 | % 6.53/2.18 | From (173) and (154) follows: % 6.53/2.18 | (216) identity_relation(all_17_1_15) = all_54_1_46 % 6.53/2.18 | % 6.53/2.18 | From (212) and (134) follows: % 6.53/2.18 | (217) identity_relation(all_17_1_15) = all_45_2_34 % 6.53/2.18 | % 6.53/2.18 | From (175) and (117) follows: % 6.53/2.18 | (218) identity_relation(all_17_1_15) = all_39_0_26 % 6.53/2.18 | % 6.53/2.18 | From (211) and (111) follows: % 6.53/2.18 | (219) identity_relation(all_17_1_15) = all_36_1_24 % 6.53/2.18 | % 6.53/2.18 | From (193) and (151) follows: % 6.53/2.18 | (137) identity_relation(all_17_1_15) = all_47_1_37 % 6.53/2.18 | % 6.53/2.18 | From (215)(179) and (163) follows: % 6.53/2.18 | (221) relation_composition(all_0_9_9, all_0_10_10) = all_47_1_37 % 6.53/2.18 | % 6.53/2.18 | From (213)(193) and (147) follows: % 6.53/2.18 | (222) relation_composition(all_0_9_9, all_0_8_8) = all_47_1_37 % 6.53/2.18 | % 6.53/2.18 | From (205) and (130) follows: % 6.53/2.18 | (223) relation_composition(all_0_9_9, all_0_8_8) = all_45_2_34 % 6.53/2.18 | % 7.03/2.18 +-Applying beta-rule and splitting (115), into two cases. % 7.03/2.18 |-Branch one: % 7.03/2.18 | (224) all_36_0_23 = all_0_10_10 % 7.03/2.18 | % 7.03/2.18 | Combining equations (209,224) yields a new equation: % 7.03/2.18 | (225) all_0_8_8 = all_0_10_10 % 7.03/2.18 | % 7.03/2.18 | Simplifying 225 yields: % 7.03/2.18 | (226) all_0_8_8 = all_0_10_10 % 7.03/2.18 | % 7.03/2.18 | Equations (226) can reduce 77 to: % 7.03/2.18 | (227) $false % 7.03/2.18 | % 7.03/2.18 |-The branch is then unsatisfiable % 7.03/2.18 |-Branch two: % 7.03/2.18 | (228) ~ (all_36_0_23 = all_0_10_10) % 7.03/2.18 | (229) ? [v0] : ( ~ (v0 = all_36_1_24) & relation_composition(all_0_9_9, all_0_10_10) = v0) % 7.03/2.18 | % 7.03/2.18 | Instantiating (229) with all_69_0_56 yields: % 7.03/2.18 | (230) ~ (all_69_0_56 = all_36_1_24) & relation_composition(all_0_9_9, all_0_10_10) = all_69_0_56 % 7.03/2.18 | % 7.03/2.18 | Applying alpha-rule on (230) yields: % 7.03/2.18 | (231) ~ (all_69_0_56 = all_36_1_24) % 7.03/2.18 | (232) relation_composition(all_0_9_9, all_0_10_10) = all_69_0_56 % 7.03/2.18 | % 7.03/2.18 | Instantiating formula (57) with all_17_1_15, all_45_2_34, all_54_1_46 and discharging atoms identity_relation(all_17_1_15) = all_54_1_46, identity_relation(all_17_1_15) = all_45_2_34, yields: % 7.03/2.18 | (233) all_54_1_46 = all_45_2_34 % 7.03/2.18 | % 7.03/2.18 | Instantiating formula (57) with all_17_1_15, all_39_0_26, all_47_1_37 and discharging atoms identity_relation(all_17_1_15) = all_47_1_37, identity_relation(all_17_1_15) = all_39_0_26, yields: % 7.03/2.18 | (234) all_47_1_37 = all_39_0_26 % 7.03/2.18 | % 7.03/2.18 | Instantiating formula (57) with all_17_1_15, all_36_1_24, all_54_1_46 and discharging atoms identity_relation(all_17_1_15) = all_54_1_46, identity_relation(all_17_1_15) = all_36_1_24, yields: % 7.03/2.18 | (235) all_54_1_46 = all_36_1_24 % 7.03/2.18 | % 7.03/2.18 | Instantiating formula (32) with all_0_9_9, all_0_8_8, all_45_2_34, all_47_1_37 and discharging atoms relation_composition(all_0_9_9, all_0_8_8) = all_47_1_37, relation_composition(all_0_9_9, all_0_8_8) = all_45_2_34, yields: % 7.03/2.18 | (236) all_47_1_37 = all_45_2_34 % 7.03/2.18 | % 7.03/2.18 | Instantiating formula (32) with all_0_9_9, all_0_10_10, all_47_1_37, all_69_0_56 and discharging atoms relation_composition(all_0_9_9, all_0_10_10) = all_69_0_56, relation_composition(all_0_9_9, all_0_10_10) = all_47_1_37, yields: % 7.03/2.18 | (237) all_69_0_56 = all_47_1_37 % 7.03/2.18 | % 7.03/2.18 | Combining equations (233,235) yields a new equation: % 7.03/2.18 | (238) all_45_2_34 = all_36_1_24 % 7.03/2.18 | % 7.03/2.18 | Simplifying 238 yields: % 7.03/2.18 | (239) all_45_2_34 = all_36_1_24 % 7.03/2.18 | % 7.03/2.18 | Combining equations (236,234) yields a new equation: % 7.03/2.18 | (240) all_45_2_34 = all_39_0_26 % 7.03/2.18 | % 7.03/2.18 | Simplifying 240 yields: % 7.03/2.18 | (241) all_45_2_34 = all_39_0_26 % 7.03/2.18 | % 7.03/2.18 | Combining equations (239,241) yields a new equation: % 7.03/2.18 | (242) all_39_0_26 = all_36_1_24 % 7.03/2.18 | % 7.03/2.18 | Combining equations (242,234) yields a new equation: % 7.03/2.18 | (243) all_47_1_37 = all_36_1_24 % 7.03/2.18 | % 7.03/2.18 | Combining equations (243,237) yields a new equation: % 7.03/2.18 | (244) all_69_0_56 = all_36_1_24 % 7.03/2.18 | % 7.03/2.18 | Equations (244) can reduce 231 to: % 7.03/2.18 | (227) $false % 7.03/2.18 | % 7.03/2.18 |-The branch is then unsatisfiable % 7.03/2.18 % SZS output end Proof for theBenchmark % 7.03/2.18 % 7.03/2.18 1587ms %------------------------------------------------------------------------------