%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU215+2 : TPTP v8.1.0. Released v3.3.0. % 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 08:47:43 EDT 2022 % Result : Theorem 10.95s 3.06s % Output : Proof 21.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEU215+2 : TPTP v8.1.0. Released v3.3.0. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.35 % Computer : n015.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sun Jun 19 17:24:29 EDT 2022 % 0.13/0.35 % CPUTime : % 0.52/0.60 ____ _ % 0.52/0.60 ___ / __ \_____(_)___ ________ __________ % 0.52/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.60 % 0.52/0.60 A Theorem Prover for First-Order Logic % 0.52/0.60 (ePrincess v.1.0) % 0.52/0.60 % 0.52/0.60 (c) Philipp Rümmer, 2009-2015 % 0.52/0.60 (c) Peter Backeman, 2014-2015 % 0.52/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.60 Bug reports to peter@backeman.se % 0.52/0.60 % 0.52/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.60 % 0.52/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.79/1.23 Prover 0: Preprocessing ... % 6.73/2.07 Prover 0: Warning: ignoring some quantifiers % 6.97/2.12 Prover 0: Constructing countermodel ... % 10.95/3.06 Prover 0: proved (2406ms) % 10.95/3.06 % 10.95/3.06 No countermodel exists, formula is valid % 10.95/3.06 % SZS status Theorem for theBenchmark % 10.95/3.06 % 10.95/3.06 Generating proof ... Warning: ignoring some quantifiers % 20.25/5.25 found it (size 407) % 20.25/5.25 % 20.25/5.25 % SZS output start Proof for theBenchmark % 20.25/5.25 Assumed formulas after preprocessing and simplification: % 20.25/5.25 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ( ~ (v8 = v7) & relation_composition(v2, v5) = v6 & relation_rng(empty_set) = empty_set & relation_dom(v2) = v3 & relation_dom(empty_set) = empty_set & apply(v6, v1) = v7 & apply(v5, v4) = v8 & apply(v2, v1) = v4 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation_empty_yielding(v9) & relation_empty_yielding(empty_set) & relation(v14) & relation(v13) & relation(v11) & relation(v9) & relation(v5) & relation(v2) & relation(empty_set) & function(v14) & function(v5) & function(v2) & empty(v13) & empty(v12) & empty(empty_set) & in(v1, v3) & ~ empty(v11) & ~ empty(v10) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v15, v16) = v17) | ~ (ordered_pair(v21, v19) = v22) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ in(v22, v16) | in(v20, v17) | ? [v23] : (ordered_pair(v18, v21) = v23 & ~ in(v23, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v15, v16) = v17) | ~ (ordered_pair(v18, v21) = v22) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ in(v22, v15) | in(v20, v17) | ? [v23] : (ordered_pair(v21, v19) = v23 & ~ in(v23, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (identity_relation(v17) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ relation(v18) | ~ in(v19, v21) | in(v19, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (identity_relation(v17) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ relation(v18) | ~ in(v19, v21) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (identity_relation(v17) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ relation(v18) | ~ in(v19, v18) | ~ in(v15, v17) | in(v19, v21)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ in(v20, v17) | ? [v21] : ? [v22] : ? [v23] : (ordered_pair(v21, v19) = v23 & ordered_pair(v18, v21) = v22 & in(v23, v16) & in(v22, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ in(v19, v20) | in(v16, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ in(v19, v20) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ in(v16, v18) | ~ in(v15, v17) | in(v19, v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v16, v18) = v20) | ~ (cartesian_product2(v15, v17) = v19) | ~ subset(v17, v18) | ~ subset(v15, v16) | subset(v19, v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v15, v16) = v17) | ~ (ordered_pair(v19, v20) = v18) | ~ in(v20, v16) | ~ in(v19, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v19, v16) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_image(v15, v16) = v17) | ~ (ordered_pair(v19, v18) = v20) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v19, v16) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v17) | in(v20, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v17) | in(v19, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v16) | ~ in(v19, v15) | in(v20, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v15) | ~ in(v20, v17) | in(v20, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v15) | ~ in(v20, v17) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v18, v16) | in(v20, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (identity_relation(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ in(v19, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v16 | ~ (ordered_pair(v17, v18) = v19) | ~ (ordered_pair(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v15 | v17 = v15 | ~ (unordered_pair(v17, v18) = v19) | ~ (unordered_pair(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v15 | ~ (ordered_pair(v17, v18) = v19) | ~ (ordered_pair(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = v15 | ~ (subset_difference(v19, v18, v17) = v16) | ~ (subset_difference(v19, v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = empty_set | ~ (subset_difference(v15, v17, v18) = v19) | ~ (meet_of_subsets(v15, v16) = v18) | ~ (cast_to_subset(v15) = v17) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (union_of_subsets(v15, v22) = v23 & complements_of_subsets(v15, v16) = v22 & powerset(v20) = v21 & powerset(v15) = v20 & (v23 = v19 | ~ element(v16, v21)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = empty_set | ~ (subset_difference(v15, v17, v18) = v19) | ~ (union_of_subsets(v15, v16) = v18) | ~ (cast_to_subset(v15) = v17) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (meet_of_subsets(v15, v22) = v23 & complements_of_subsets(v15, v16) = v22 & powerset(v20) = v21 & powerset(v15) = v20 & (v23 = v19 | ~ element(v16, v21)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v15 = empty_set | ~ (subset_complement(v15, v17) = v18) | ~ (powerset(v15) = v16) | ~ element(v19, v15) | ~ element(v17, v16) | in(v19, v18) | in(v19, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v16) = v18) | ~ (apply(v18, v15) = v19) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_dom(v18) = v20 & apply(v17, v15) = v21 & apply(v16, v21) = v22 & (v22 = v19 | ~ in(v15, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ relation(v16) | ~ relation(v15) | ~ in(v19, v15) | ? [v20] : (ordered_pair(v17, v18) = v20 & in(v20, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ relation(v16) | ~ relation(v15) | in(v19, v15) | ? [v20] : (ordered_pair(v17, v18) = v20 & ~ in(v20, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ relation(v15) | ~ in(v19, v16) | ? [v20] : (ordered_pair(v18, v17) = v20 & in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ relation(v15) | in(v19, v16) | ? [v20] : (ordered_pair(v18, v17) = v20 & ~ in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_field(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v16, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_field(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v15, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v15, v18) = v19) | ~ (powerset(v15) = v17) | ~ disjoint(v16, v18) | ~ element(v18, v17) | ~ element(v16, v17) | subset(v16, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v15, v18) = v19) | ~ (powerset(v15) = v17) | ~ element(v18, v17) | ~ element(v16, v17) | ~ subset(v16, v19) | disjoint(v16, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v16, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | ? [v20] : (relation_dom(v17) = v20 & in(v15, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ relation(v15) | ~ in(v19, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v18) = v19) | ~ (singleton(v17) = v18) | ~ subset(v15, v16) | subset(v15, v19) | in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v17) = v19) | ~ (set_difference(v15, v17) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v17) = v19) | ~ (powerset(v15) = v18) | ~ element(v17, v18) | ~ element(v16, v18) | subset_difference(v15, v16, v17) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : (apply(v17, v15) = v20 & ( ~ (v20 = v16) | ~ in(v15, v19) | in(v18, v17)) & ( ~ in(v18, v17) | (v20 = v16 & in(v15, v19))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v15, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | ? [v20] : (relation_rng(v17) = v20 & in(v16, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v16) = v17) | ~ (apply(v18, v15) = v19) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v18, v16) = v20 & relation_dom(v20) = v21 & relation_dom(v18) = v22 & ( ~ in(v19, v17) | ~ in(v15, v22) | in(v15, v21)) & ( ~ in(v15, v21) | (in(v19, v17) & in(v15, v22))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v16) = v17) | ~ (relation_image(v16, v18) = v19) | ~ (set_intersection2(v17, v15) = v18) | ~ relation(v16) | relation_image(v16, v15) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v15) | ~ function(v15) | ~ in(v17, v16) | ? [v20] : (apply(v15, v17) = v20 & ( ~ (v20 = v18) | in(v19, v15)) & (v20 = v18 | ~ in(v19, v15)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v15) | ~ in(v19, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v17, v15) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : (relation_dom(v17) = v20 & ( ~ (v19 = v16) | ~ in(v15, v20) | in(v18, v17)) & ( ~ in(v18, v17) | (v19 = v16 & in(v15, v20))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v17, v15) = v18) | ~ (apply(v16, v18) = v19) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v17, v16) = v20 & relation_dom(v20) = v21 & apply(v20, v15) = v22 & (v22 = v19 | ~ in(v15, v21)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v16) = v19) | ~ (cartesian_product2(v17, v15) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v16) = v19) | ~ (cartesian_product2(v17, v15) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v16, v17) = v21 & cartesian_product2(v15, v17) = v20 & subset(v20, v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v16) = v19) | ~ (cartesian_product2(v15, v17) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v17, v15) = v21 & cartesian_product2(v16, v17) = v20 & subset(v21, v19) & subset(v18, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v15) = v19) | ~ (cartesian_product2(v16, v17) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v17, v16) = v21 & cartesian_product2(v15, v17) = v20 & subset(v20, v18) & subset(v19, v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v16, v17) = v19) | ~ (cartesian_product2(v15, v17) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v16, v17) = v19) | ~ (cartesian_product2(v15, v17) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v17, v16) = v21 & cartesian_product2(v17, v15) = v20 & subset(v20, v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (singleton(v15) = v18) | ~ (unordered_pair(v17, v18) = v19) | ~ (unordered_pair(v15, v16) = v17) | ordered_pair(v15, v16) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse_image(v17, v16) = v19) | ~ (relation_inverse_image(v17, v15) = v18) | ~ subset(v15, v16) | ~ relation(v17) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v15, v18) = v19) | ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v20] : (relation_rng_restriction(v15, v17) = v20 & relation_dom_restriction(v20, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v15, v17) = v18) | ~ (relation_dom_restriction(v18, v16) = v19) | ~ relation(v17) | ? [v20] : (relation_rng_restriction(v15, v20) = v19 & relation_dom_restriction(v17, v16) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (identity_relation(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ in(v19, v16) | in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ~ subset(v15, v16) | ~ relation(v16) | ~ relation(v15) | ~ in(v19, v15) | in(v19, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v16, v17) = v19) | ~ (set_intersection2(v15, v17) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v16) = v19) | ~ (relation_dom(v16) = v17) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_dom(v19) = v20 & relation_dom(v18) = v21 & apply(v18, v15) = v22 & ( ~ in(v22, v17) | ~ in(v15, v21) | in(v15, v20)) & ( ~ in(v15, v20) | (in(v22, v17) & in(v15, v21))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ (relation_dom(v16) = v17) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v18, v16) = v20 & relation_dom(v20) = v21 & apply(v18, v15) = v22 & ( ~ in(v22, v17) | ~ in(v15, v19) | in(v15, v21)) & ( ~ in(v15, v21) | (in(v22, v17) & in(v15, v19))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_composition(v15, v16) = v17) | ~ relation(v18) | ~ relation(v16) | ~ relation(v15) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v18) | ( ! [v25] : ! [v26] : ( ~ (ordered_pair(v25, v20) = v26) | ~ in(v26, v16) | ? [v27] : (ordered_pair(v19, v25) = v27 & ~ in(v27, v15))) & ! [v25] : ! [v26] : ( ~ (ordered_pair(v19, v25) = v26) | ~ in(v26, v15) | ? [v27] : (ordered_pair(v25, v20) = v27 & ~ in(v27, v16))))) & (in(v21, v18) | (ordered_pair(v22, v20) = v24 & ordered_pair(v19, v22) = v23 & in(v24, v16) & in(v23, v15))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v18) | ~ in(v21, v16) | ~ in(v20, v15)) & (in(v21, v18) | (in(v21, v16) & in(v20, v15))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_dom_restriction(v15, v16) = v18) | ~ relation(v17) | ~ relation(v15) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v17) | ~ in(v21, v15) | ~ in(v19, v16)) & (in(v21, v17) | (in(v21, v15) & in(v19, v16))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | v18 = v15 | ~ (unordered_pair(v15, v16) = v17) | ~ in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (complements_of_subsets(v15, v17) = v18) | ~ (complements_of_subsets(v15, v16) = v17) | ? [v19] : ? [v20] : (powerset(v19) = v20 & powerset(v15) = v19 & ~ element(v16, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (subset_complement(v15, v17) = v18) | ~ (subset_complement(v15, v16) = v17) | ? [v19] : (powerset(v15) = v19 & ~ element(v16, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (set_difference(v16, v15) = v17) | ~ (set_union2(v15, v17) = v18) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (singleton(v15) = v17) | ~ (set_union2(v17, v16) = v18) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_difference(v15, v17) = v18) | ~ (singleton(v16) = v17) | in(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = empty_set | ~ (relation_dom(v15) = v16) | ~ (apply(v15, v17) = v18) | ~ relation(v15) | ~ function(v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (singleton(v15) = v18) | ~ (unordered_pair(v16, v17) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (meet_of_subsets(v18, v17) = v16) | ~ (meet_of_subsets(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (union_of_subsets(v18, v17) = v16) | ~ (union_of_subsets(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (complements_of_subsets(v18, v17) = v16) | ~ (complements_of_subsets(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_composition(v18, v17) = v16) | ~ (relation_composition(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (subset_complement(v18, v17) = v16) | ~ (subset_complement(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_difference(v18, v17) = v16) | ~ (set_difference(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (apply(v18, v17) = v16) | ~ (apply(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (cartesian_product2(v18, v17) = v16) | ~ (cartesian_product2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (singleton(v16) = v18) | ~ (singleton(v15) = v17) | ~ subset(v17, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (singleton(v15) = v18) | ~ (unordered_pair(v16, v17) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_inverse_image(v18, v17) = v16) | ~ (relation_inverse_image(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_image(v18, v17) = v16) | ~ (relation_image(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_rng_restriction(v18, v17) = v16) | ~ (relation_rng_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_dom_restriction(v18, v17) = v16) | ~ (relation_dom_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (ordered_pair(v18, v17) = v16) | ~ (ordered_pair(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_intersection2(v18, v17) = v16) | ~ (set_intersection2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_union2(v18, v17) = v16) | ~ (set_union2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (unordered_pair(v18, v17) = v16) | ~ (unordered_pair(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = empty_set | ~ (meet_of_subsets(v15, v17) = v18) | ~ (complements_of_subsets(v15, v16) = v17) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset_difference(v15, v21, v22) = v23 & union_of_subsets(v15, v16) = v22 & cast_to_subset(v15) = v21 & powerset(v19) = v20 & powerset(v15) = v19 & (v23 = v18 | ~ element(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = empty_set | ~ (union_of_subsets(v15, v17) = v18) | ~ (complements_of_subsets(v15, v16) = v17) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset_difference(v15, v21, v22) = v23 & meet_of_subsets(v15, v16) = v22 & cast_to_subset(v15) = v21 & powerset(v19) = v20 & powerset(v15) = v19 & (v23 = v18 | ~ element(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v15 = empty_set | ~ (set_meet(v15) = v16) | ~ in(v18, v15) | ~ in(v17, v16) | in(v17, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_difference(v15, v16, v17) = v18) | ? [v19] : ? [v20] : (set_difference(v16, v17) = v20 & powerset(v15) = v19 & (v20 = v18 | ~ element(v17, v19) | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_difference(v15, v16, v17) = v18) | ? [v19] : (powerset(v15) = v19 & ( ~ element(v17, v19) | ~ element(v16, v19) | element(v18, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ (identity_relation(v15) = v17) | ~ relation(v16) | relation_dom_restriction(v16, v15) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v15, v17) = v18) | ~ (relation_rng(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ? [v19] : (relation_rng(v18) = v19 & relation_image(v17, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v15, v17) = v18) | ~ (relation_dom(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ? [v19] : (relation_dom(v18) = v19 & subset(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v15, v17) = v18) | ~ in(v16, v18) | ~ in(v16, v17) | ? [v19] : (powerset(v15) = v19 & ~ element(v17, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v16) = v17) | ~ (set_intersection2(v17, v15) = v18) | ~ relation(v16) | ? [v19] : (relation_rng(v19) = v18 & relation_rng_restriction(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v15) = v17) | ~ (relation_dom(v15) = v16) | ~ (cartesian_product2(v16, v17) = v18) | ~ relation(v15) | subset(v15, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v15) = v17) | ~ (relation_dom(v15) = v16) | ~ (set_union2(v16, v17) = v18) | ~ relation(v15) | relation_field(v15) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v15) = v16) | ~ (relation_image(v17, v16) = v18) | ~ relation(v17) | ~ relation(v15) | ? [v19] : (relation_composition(v15, v17) = v19 & relation_rng(v19) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v17, v16) = v18) | ~ (set_union2(v15, v16) = v17) | set_difference(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v16, v15) = v17) | ~ (set_union2(v15, v17) = v18) | set_union2(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v17) = v18) | ~ (set_difference(v15, v16) = v17) | set_intersection2(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ in(v18, v17) | ~ in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ in(v18, v15) | in(v18, v17) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (union(v16) = v18) | ~ (powerset(v15) = v17) | ? [v19] : ? [v20] : (union_of_subsets(v15, v16) = v20 & powerset(v17) = v19 & (v20 = v18 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (union(v15) = v16) | ~ in(v18, v15) | ~ in(v17, v18) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v16) = v17) | ~ (set_intersection2(v17, v15) = v18) | ~ relation(v16) | ? [v19] : (relation_dom(v19) = v18 & relation_dom_restriction(v16, v15) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v15, v16) = v17) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v19, v20) = v18 & in(v20, v16) & in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ empty(v17) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ in(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v15) = v17) | ~ (set_meet(v16) = v18) | ? [v19] : ? [v20] : (meet_of_subsets(v15, v16) = v20 & powerset(v17) = v19 & (v20 = v18 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v15) = v17) | ~ element(v16, v17) | ~ in(v18, v16) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_inverse_image(v15, v16) = v17) | ~ relation(v15) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & in(v20, v15) & in(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_image(v15, v16) = v17) | ~ relation(v15) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v19, v18) = v20 & in(v20, v15) & in(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (identity_relation(v15) = v16) | ~ (ordered_pair(v17, v17) = v18) | ~ relation(v16) | ~ in(v17, v15) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | ~ subset(v15, v17) | ~ subset(v15, v16) | subset(v15, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ disjoint(v15, v16) | ~ in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ in(v18, v16) | ~ in(v18, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v17) = v18) | ~ subset(v17, v16) | ~ subset(v15, v16) | subset(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v16) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v16) = v17) | ~ in(v18, v16) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v16) = v17) | ~ in(v18, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v15, v16) = v18) | ~ subset(v18, v17) | in(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v15, v16) = v18) | ~ subset(v18, v17) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v15, v16) = v18) | ~ in(v16, v17) | ~ in(v15, v17) | subset(v18, v17)) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_difference(v16, v17) = v18) | ? [v19] : (( ~ in(v19, v16) | ~ in(v19, v15) | in(v19, v17)) & (in(v19, v15) | (in(v19, v16) & ~ in(v19, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (cartesian_product2(v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ in(v19, v15) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v23, v24) = v19) | ~ in(v24, v17) | ~ in(v23, v16))) & (in(v19, v15) | (v22 = v19 & ordered_pair(v20, v21) = v19 & in(v21, v17) & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (relation_inverse_image(v16, v17) = v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v15) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v19, v22) = v23) | ~ in(v23, v16) | ~ in(v22, v17))) & (in(v19, v15) | (ordered_pair(v19, v20) = v21 & in(v21, v16) & in(v20, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (relation_image(v16, v17) = v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v15) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v19) = v23) | ~ in(v23, v16) | ~ in(v22, v17))) & (in(v19, v15) | (ordered_pair(v20, v19) = v21 & in(v21, v16) & in(v20, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_intersection2(v16, v17) = v18) | ? [v19] : (( ~ in(v19, v17) | ~ in(v19, v16) | ~ in(v19, v15)) & (in(v19, v15) | (in(v19, v17) & in(v19, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_union2(v16, v17) = v18) | ? [v19] : (( ~ in(v19, v15) | ( ~ in(v19, v17) & ~ in(v19, v16))) & (in(v19, v17) | in(v19, v16) | in(v19, v15)))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (unordered_pair(v16, v17) = v18) | ? [v19] : ((v19 = v17 | v19 = v16 | in(v19, v15)) & ( ~ in(v19, v15) | ( ~ (v19 = v17) & ~ (v19 = v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_dom(v18) = v19 & apply(v18, v15) = v20 & apply(v17, v15) = v21 & apply(v16, v21) = v22 & (v22 = v20 | ~ in(v15, v19)))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_inverse_image(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (relation_rng(v17) = v19 & ( ~ in(v15, v18) | (ordered_pair(v15, v20) = v21 & in(v21, v17) & in(v20, v19) & in(v20, v16))) & (in(v15, v18) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v15, v22) = v23) | ~ in(v23, v17) | ~ in(v22, v19) | ~ in(v22, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_image(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (relation_dom(v17) = v19 & ( ~ in(v15, v18) | (ordered_pair(v20, v15) = v21 & in(v21, v17) & in(v20, v19) & in(v20, v16))) & (in(v15, v18) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v15) = v23) | ~ in(v23, v17) | ~ in(v22, v19) | ~ in(v22, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_rng(v18) = v19 & relation_rng(v17) = v20 & ( ~ in(v15, v20) | ~ in(v15, v16) | in(v15, v19)) & ( ~ in(v15, v19) | (in(v15, v20) & in(v15, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_dom(v18) = v19 & relation_dom(v17) = v20 & ( ~ in(v15, v20) | ~ in(v15, v16) | in(v15, v19)) & ( ~ in(v15, v19) | (in(v15, v20) & in(v15, v16))))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (relation_inverse(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v18) = v21 & ordered_pair(v18, v19) = v20 & ( ~ in(v21, v15) | ~ in(v20, v17)) & (in(v21, v15) | in(v20, v17)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (identity_relation(v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & ( ~ (v19 = v18) | ~ in(v20, v16) | ~ in(v18, v15)) & (in(v20, v16) | (v19 = v18 & in(v18, v15))))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v15, v16) = v17) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | v15 = empty_set | ~ (singleton(v16) = v17) | ~ subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (set_difference(v15, v16) = v17) | ~ disjoint(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (singleton(v15) = v16) | ~ in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (set_intersection2(v15, v16) = v17) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = empty_set | ~ (set_difference(v15, v16) = v17) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = empty_set | ~ (set_intersection2(v15, v16) = v17) | ~ disjoint(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_inverse(v17) = v16) | ~ (relation_inverse(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_field(v17) = v16) | ~ (relation_field(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_rng(v17) = v16) | ~ (relation_rng(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (union(v17) = v16) | ~ (union(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (cast_to_subset(v17) = v16) | ~ (cast_to_subset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_dom(v17) = v16) | ~ (relation_dom(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (powerset(v17) = v16) | ~ (powerset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (singleton(v17) = v16) | ~ (singleton(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (set_meet(v17) = v16) | ~ (set_meet(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (identity_relation(v17) = v16) | ~ (identity_relation(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (meet_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (powerset(v18) = v19 & powerset(v15) = v18 & set_meet(v16) = v20 & (v20 = v17 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (meet_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | element(v17, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (union(v16) = v20 & powerset(v18) = v19 & powerset(v15) = v18 & (v20 = v17 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | element(v17, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (complements_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | element(v17, v19)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (complements_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | ( ! [v20] : ! [v21] : ( ~ (subset_complement(v15, v20) = v21) | ~ element(v20, v18) | ~ element(v17, v19) | ~ in(v21, v16) | in(v20, v17)) & ! [v20] : ! [v21] : ( ~ (subset_complement(v15, v20) = v21) | ~ element(v20, v18) | ~ element(v17, v19) | ~ in(v20, v17) | in(v21, v16)) & ! [v20] : (v20 = v17 | ~ element(v20, v19) | ? [v21] : ? [v22] : (subset_complement(v15, v21) = v22 & element(v21, v18) & ( ~ in(v22, v16) | ~ in(v21, v20)) & (in(v22, v16) | in(v21, v20)))))))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v15) = v17) | ~ relation(v16) | ~ empty(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v15) = v17) | ~ relation(v16) | ~ empty(v15) | empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v16) | ~ function(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v16) | ~ function(v15) | function(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ empty(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ empty(v15) | empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset_complement(v15, v16) = v17) | ? [v18] : ? [v19] : (set_difference(v15, v16) = v19 & powerset(v15) = v18 & (v19 = v17 | ~ element(v16, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset_complement(v15, v16) = v17) | ? [v18] : (powerset(v15) = v18 & ( ~ element(v16, v18) | element(v17, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ~ relation(v15) | ? [v18] : ? [v19] : (relation_composition(v15, v16) = v18 & relation_rng(v18) = v19 & subset(v19, v17))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ~ in(v17, v16) | ? [v18] : ? [v19] : (ordered_pair(v18, v17) = v19 & in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v17) = v15) | ~ (singleton(v16) = v17) | ~ in(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | subset(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | ? [v18] : ? [v19] : (subset_complement(v15, v16) = v19 & powerset(v15) = v18 & (v19 = v17 | ~ element(v16, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | ? [v18] : (set_difference(v18, v16) = v17 & set_union2(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union(v16) = v17) | ~ in(v15, v16) | subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union(v15) = v16) | ~ in(v17, v16) | ? [v18] : (in(v18, v15) & in(v17, v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom(v15) = v16) | ~ (relation_image(v15, v16) = v17) | ~ relation(v15) | relation_rng(v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ in(v17, v16) | ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v15, v16) = v17) | ~ empty(v17) | empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ subset(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v15) = v16) | ~ subset(v17, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v15) = v16) | ~ in(v17, v16) | subset(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v17) | ~ disjoint(v17, v16) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v17) | ~ subset(v17, v16) | in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v17) | ~ in(v15, v16) | subset(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_inverse_image(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_dom(v16) = v18 & subset(v17, v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_image(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_dom(v16) = v18 & relation_image(v16, v19) = v17 & set_intersection2(v18, v15) = v19)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_image(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v16) = v18 & subset(v17, v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | subset(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & set_intersection2(v19, v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v17) = v18 & subset(v18, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | subset(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_dom(v17) = v18 & relation_dom(v16) = v19 & set_intersection2(v19, v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_composition(v18, v16) = v17 & identity_relation(v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (ordered_pair(v15, v16) = v17) | ~ empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (ordered_pair(v15, v16) = v17) | ? [v18] : ? [v19] : (singleton(v15) = v19 & unordered_pair(v18, v19) = v17 & unordered_pair(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v16, v15) = v17) | set_intersection2(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | set_intersection2(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | disjoint(v15, v16) | ? [v18] : in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | subset(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | ? [v18] : (set_difference(v15, v18) = v17 & set_difference(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v16, v15) = v17) | ~ empty(v17) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v16, v15) = v17) | set_union2(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ~ empty(v17) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | set_union2(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ? [v18] : (set_difference(v16, v15) = v18 & set_union2(v15, v18) = v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v16, v15) = v17) | unordered_pair(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | ~ empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | unordered_pair(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | in(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ disjoint(v16, v17) | ~ subset(v15, v16) | disjoint(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ disjoint(v15, v16) | ~ in(v17, v16) | ~ in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ subset(v16, v17) | ~ subset(v15, v16) | subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ subset(v15, v16) | ~ in(v17, v15) | in(v17, v16)) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | v16 = empty_set | ~ (set_meet(v16) = v17) | ? [v18] : ? [v19] : (( ~ in(v18, v15) | (in(v19, v16) & ~ in(v18, v19))) & (in(v18, v15) | ! [v20] : ( ~ in(v20, v16) | in(v18, v20))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (( ~ in(v18, v15) | ! [v21] : ! [v22] : ( ~ (ordered_pair(v21, v18) = v22) | ~ in(v22, v16))) & (in(v18, v15) | (ordered_pair(v19, v18) = v20 & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (union(v16) = v17) | ? [v18] : ? [v19] : (( ~ in(v18, v15) | ! [v20] : ( ~ in(v20, v16) | ~ in(v18, v20))) & (in(v18, v15) | (in(v19, v16) & in(v18, v19))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (relation_dom(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (( ~ in(v18, v15) | ! [v21] : ! [v22] : ( ~ (ordered_pair(v18, v21) = v22) | ~ in(v22, v16))) & (in(v18, v15) | (ordered_pair(v18, v19) = v20 & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (powerset(v16) = v17) | ? [v18] : (( ~ subset(v18, v16) | ~ in(v18, v15)) & (subset(v18, v16) | in(v18, v15)))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (singleton(v16) = v17) | ? [v18] : (( ~ (v18 = v16) | ~ in(v16, v15)) & (v18 = v16 | in(v18, v15)))) & ? [v15] : ! [v16] : ! [v17] : (v16 = empty_set | ~ (set_meet(v16) = v17) | in(v15, v17) | ? [v18] : (in(v18, v16) & ~ in(v15, v18))) & ? [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | element(v15, v17) | ? [v18] : (in(v18, v15) & ~ in(v18, v16))) & ? [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v16) = v17) | disjoint(v17, v15) | in(v16, v15)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_difference(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (cast_to_subset(v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_intersection2(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_union2(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_union2(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ subset(v16, v15) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ subset(v15, v16) | proper_subset(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ relation(v16) | ~ relation(v15) | ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & ( ~ in(v19, v16) | ~ in(v19, v15)) & (in(v19, v16) | in(v19, v15)))) & ! [v15] : ! [v16] : (v16 = v15 | ~ empty(v16) | ~ empty(v15)) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (complements_of_subsets(v15, v16) = empty_set) | ? [v17] : ? [v18] : (powerset(v17) = v18 & powerset(v15) = v17 & ~ element(v16, v18))) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (set_difference(empty_set, v15) = v16)) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (set_intersection2(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v15 = empty_set | ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : ( ~ (v17 = empty_set) & relation_dom(v15) = v17)) & ! [v15] : ! [v16] : (v15 = empty_set | ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : ( ~ (v17 = empty_set) & relation_rng(v15) = v17)) & ! [v15] : ! [v16] : (v15 = empty_set | ~ (relation_inverse_image(v16, v15) = empty_set) | ~ relation(v16) | ? [v17] : (relation_rng(v16) = v17 & ~ subset(v15, v17))) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ relation(v15) | relation_inverse(v16) = v15) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ relation(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_rng(v16) = v18 & relation_rng(v15) = v17 & relation_dom(v16) = v17 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_rng(v15) = v18 & relation_dom(v15) = v17 & set_union2(v17, v18) = v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ~ empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_inverse(v15) = v17 & relation_rng(v17) = v18 & relation_dom(v17) = v16 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & relation_image(v15, v17) = v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v15) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v21 & relation_rng(v18) = v20 & (v21 = v16 | ~ subset(v17, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v17, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v18, v15) = v20 & relation_rng(v20) = v16)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v15, v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_dom(v19) = v21 & relation_dom(v18) = v20 & (v21 = v17 | ~ subset(v16, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v16, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v15, v18) = v20 & relation_dom(v20) = v17)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v16, v19)) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_dom(v18) = v20 & subset(v17, v20))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v17, v19)) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_rng(v18) = v20 & subset(v16, v20))))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ( ~ (v17 = empty_set) | v16 = empty_set) & ( ~ (v16 = empty_set) | v17 = empty_set))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (set_difference(v15, v16) = v15) | disjoint(v15, v16)) & ! [v15] : ! [v16] : ( ~ (set_difference(v15, v16) = empty_set) | subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ (cast_to_subset(v15) = v16) | ? [v17] : (powerset(v15) = v17 & element(v16, v17))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_inverse(v15) = v18 & relation_rng(v18) = v16 & relation_rng(v15) = v17 & relation_dom(v18) = v17)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v15) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v21 & relation_rng(v18) = v20 & (v21 = v17 | ~ subset(v16, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v16, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v18, v15) = v20 & relation_rng(v20) = v17)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v15, v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_dom(v19) = v21 & relation_dom(v18) = v20 & (v21 = v16 | ~ subset(v17, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v17, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v15, v18) = v20 & relation_dom(v20) = v16)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v17, v19)) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_dom(v18) = v20 & subset(v16, v20))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v16, v19)) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_rng(v18) = v20 & subset(v17, v20))))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ( ~ (v17 = empty_set) | v16 = empty_set) & ( ~ (v16 = empty_set) | v17 = empty_set))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | union(v16) = v15) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | empty(v15) | ? [v17] : (element(v17, v16) & ~ empty(v17))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (cast_to_subset(v15) = v17 & element(v17, v16))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (element(v17, v16) & empty(v17))) & ! [v15] : ! [v16] : ( ~ (singleton(v16) = v15) | subset(v15, v15)) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | unordered_pair(v15, v15) = v16) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | subset(empty_set, v16)) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation_rng(v16) = v15) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation_dom(v16) = v15) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (set_intersection2(v15, v16) = empty_set) | disjoint(v15, v16)) & ! [v15] : ! [v16] : ( ~ (unordered_pair(v15, v15) = v16) | singleton(v15) = v16) & ! [v15] : ! [v16] : ( ~ disjoint(v15, v16) | disjoint(v16, v15)) & ! [v15] : ! [v16] : ( ~ element(v16, v15) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ element(v16, v15) | empty(v15) | in(v16, v15)) & ! [v15] : ! [v16] : ( ~ element(v15, v16) | empty(v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ subset(v15, v16) | ~ proper_subset(v16, v15)) & ! [v15] : ! [v16] : ( ~ relation(v16) | ~ relation(v15) | subset(v15, v16) | ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & in(v19, v15) & ~ in(v19, v16))) & ! [v15] : ! [v16] : ( ~ relation(v15) | ~ in(v16, v15) | ? [v17] : ? [v18] : ordered_pair(v17, v18) = v16) & ! [v15] : ! [v16] : ( ~ empty(v16) | ~ empty(v15) | element(v16, v15)) & ! [v15] : ! [v16] : ( ~ empty(v16) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ proper_subset(v16, v15) | ~ proper_subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ proper_subset(v15, v16) | subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v16, v15) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v16, v15) | element(v16, v15) | empty(v15)) & ! [v15] : ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) & ! [v15] : (v15 = empty_set | ~ (relation_rng(v15) = empty_set) | ~ relation(v15)) & ! [v15] : (v15 = empty_set | ~ (relation_dom(v15) = empty_set) | ~ relation(v15)) & ! [v15] : (v15 = empty_set | ~ (set_meet(empty_set) = v15)) & ! [v15] : (v15 = empty_set | ~ subset(v15, empty_set)) & ! [v15] : (v15 = empty_set | ~ relation(v15) | ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v16, v17) = v18 & in(v18, v15))) & ! [v15] : (v15 = empty_set | ~ empty(v15)) & ! [v15] : ~ (singleton(v15) = empty_set) & ! [v15] : ( ~ empty(v15) | relation(v15)) & ! [v15] : ( ~ empty(v15) | function(v15)) & ! [v15] : ~ proper_subset(v15, v15) & ! [v15] : ~ in(v15, empty_set) & ? [v15] : ? [v16] : (v16 = v15 | ? [v17] : (( ~ in(v17, v16) | ~ in(v17, v15)) & (in(v17, v16) | in(v17, v15)))) & ? [v15] : ? [v16] : (disjoint(v15, v16) | ? [v17] : (in(v17, v16) & in(v17, v15))) & ? [v15] : ? [v16] : element(v16, v15) & ? [v15] : ? [v16] : (subset(v15, v16) | ? [v17] : (in(v17, v15) & ~ in(v17, v16))) & ? [v15] : ? [v16] : (in(v15, v16) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ in(v17, v16) | in(v18, v16)) & ! [v17] : ! [v18] : ( ~ subset(v18, v17) | ~ in(v17, v16) | in(v18, v16)) & ! [v17] : ( ~ subset(v17, v16) | are_equipotent(v17, v16) | in(v17, v16))) & ? [v15] : ? [v16] : (in(v15, v16) & ! [v17] : ! [v18] : ( ~ subset(v18, v17) | ~ in(v17, v16) | in(v18, v16)) & ! [v17] : ( ~ subset(v17, v16) | are_equipotent(v17, v16) | in(v17, v16)) & ! [v17] : ( ~ in(v17, v16) | ? [v18] : (in(v18, v16) & ! [v19] : ( ~ subset(v19, v17) | in(v19, v18))))) & ? [v15] : (v15 = empty_set | ? [v16] : in(v16, v15)) & ? [v15] : subset(v15, v15) & ? [v15] : subset(empty_set, v15) & ? [v15] : (relation(v15) | ? [v16] : (in(v16, v15) & ! [v17] : ! [v18] : ~ (ordered_pair(v17, v18) = v16)))) % 20.99/5.38 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14 yields: % 20.99/5.38 | (1) ~ (all_0_6_6 = all_0_7_7) & relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8 & relation_rng(empty_set) = empty_set & relation_dom(all_0_12_12) = all_0_11_11 & relation_dom(empty_set) = empty_set & apply(all_0_8_8, all_0_13_13) = all_0_7_7 & apply(all_0_9_9, all_0_10_10) = all_0_6_6 & apply(all_0_12_12, all_0_13_13) = all_0_10_10 & powerset(empty_set) = all_0_14_14 & singleton(empty_set) = all_0_14_14 & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_5_5) & relation(all_0_9_9) & relation(all_0_12_12) & relation(empty_set) & function(all_0_0_0) & function(all_0_9_9) & function(all_0_12_12) & empty(all_0_1_1) & empty(all_0_2_2) & empty(empty_set) & in(all_0_13_13, all_0_11_11) & ~ empty(all_0_3_3) & ~ empty(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v1) | in(v5, v2) | ? [v8] : (ordered_pair(v3, v6) = v8 & ~ in(v8, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8] : (ordered_pair(v6, v4) = v8 & ~ in(v8, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v3) | ~ in(v0, v2) | in(v4, v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & in(v8, v1) & in(v7, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ subset(v2, v3) | ~ subset(v0, v1) | subset(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (meet_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (union_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (meet_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ element(v4, v0) | ~ element(v2, v1) | in(v4, v3) | in(v4, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ disjoint(v1, v3) | ~ element(v3, v2) | ~ element(v1, v2) | subset(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ element(v3, v2) | ~ element(v1, v2) | ~ subset(v1, v4) | disjoint(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_dom(v2) = v5 & in(v0, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (apply(v2, v0) = v5 & ( ~ (v5 = v1) | ~ in(v0, v4) | in(v3, v2)) & ( ~ in(v3, v2) | (v5 = v1 & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_rng(v2) = v5 & in(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (relation_dom(v2) = v5 & ( ~ (v4 = v1) | ~ in(v0, v5) | in(v3, v2)) & ( ~ in(v3, v2) | (v4 = v1 & in(v0, v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 | ~ in(v0, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v5 & subset(v6, v4) & subset(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v0) = v4) | ~ (cartesian_product2(v1, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v3) & subset(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & subset(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ subset(v0, v1) | ~ relation(v2) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v2) = v5 & relation_dom_restriction(v5, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v5) = v4 & relation_dom_restriction(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (complements_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v0) = v4 & ~ element(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (meet_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (union_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & meet_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_rng(v3) = v4 & relation_image(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_dom(v3) = v4 & subset(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_rng(v4) = v3 & relation_rng_restriction(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_dom(v4) = v3 & relation_dom_restriction(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, 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] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (set_meet(v1) = v3) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) & in(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) & in(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & in(v6, v1) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v4) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v5, v4) = v6 & in(v6, v1) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 | ~ in(v0, v4)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v0, v7) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v5, v0) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v0) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_rng(v3) = v4 & relation_rng(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v3) = v6 & ordered_pair(v3, v4) = v5 & ( ~ in(v6, v0) | ~ in(v5, v2)) & (in(v6, v0) | in(v5, v2)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ( ~ (v4 = v3) | ~ in(v5, v1) | ~ in(v3, v0)) & (in(v5, v1) | (v4 = v3 & in(v3, v0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(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 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (powerset(v3) = v4 & powerset(v0) = v3 & set_meet(v1) = v5 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | ( ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v6, v1) | in(v5, v2)) & ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v5, v2) | in(v6, v1)) & ! [v5] : (v5 = v2 | ~ element(v5, v4) | ? [v6] : ? [v7] : (subset_complement(v0, v6) = v7 & element(v6, v3) & ( ~ in(v7, v1) | ~ in(v6, v5)) & (in(v7, v1) | in(v6, v5)))))))) & ! [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) | ~ 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) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [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] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_composition(v0, v1) = v3 & relation_rng(v3) = v4 & subset(v4, v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v1) = v3 & relation_image(v1, v4) = v2 & set_intersection2(v3, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & set_intersection2(v4, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & set_intersection2(v4, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | (in(v4, v1) & ~ in(v3, v4))) & (in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | in(v3, v5))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [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) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) & ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) & ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ~ proper_subset(v0, v0) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1))) & ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v1) & ! [v4] : ( ~ subset(v4, v2) | in(v4, v3))))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) & ? [v0] : subset(v0, v0) & ? [v0] : subset(empty_set, v0) & ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1))) % 20.99/5.43 | % 20.99/5.43 | Applying alpha-rule on (1) yields: % 20.99/5.43 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 20.99/5.43 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 20.99/5.43 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 20.99/5.43 | (5) apply(all_0_9_9, all_0_10_10) = all_0_6_6 % 20.99/5.43 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) % 20.99/5.43 | (7) function(all_0_9_9) % 20.99/5.43 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 20.99/5.43 | (9) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & in(v6, v1) & in(v5, v2))))) % 20.99/5.43 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 20.99/5.43 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) % 20.99/5.43 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 20.99/5.43 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 20.99/5.43 | (14) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 20.99/5.43 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) % 20.99/5.43 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 20.99/5.43 | (17) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 20.99/5.43 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 20.99/5.43 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) % 20.99/5.43 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 20.99/5.43 | (21) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) % 20.99/5.43 | (22) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) % 20.99/5.43 | (23) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1)))) % 20.99/5.43 | (24) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 20.99/5.43 | (25) singleton(empty_set) = all_0_14_14 % 20.99/5.43 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 20.99/5.43 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) % 20.99/5.43 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 20.99/5.43 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) % 20.99/5.43 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ subset(v0, v1) | ~ relation(v2) | subset(v3, v4)) % 20.99/5.43 | (31) ! [v0] : ~ (singleton(v0) = empty_set) % 20.99/5.43 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 20.99/5.43 | (33) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) % 20.99/5.43 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 20.99/5.43 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) % 20.99/5.43 | (36) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) % 20.99/5.43 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (meet_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (union_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) % 20.99/5.43 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 20.99/5.43 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 20.99/5.43 | (40) function(all_0_0_0) % 20.99/5.43 | (41) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 20.99/5.43 | (42) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 20.99/5.43 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (union_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & meet_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) % 20.99/5.43 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 20.99/5.43 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 20.99/5.43 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 | ~ in(v0, v6)))) % 20.99/5.43 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) % 20.99/5.43 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) % 20.99/5.44 | (49) relation_rng(empty_set) = empty_set % 20.99/5.44 | (50) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) % 20.99/5.44 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 20.99/5.44 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 20.99/5.44 | (53) ! [v0] : ~ proper_subset(v0, v0) % 20.99/5.44 | (54) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 20.99/5.44 | (55) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) % 20.99/5.44 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) % 20.99/5.44 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) % 20.99/5.44 | (58) ? [v0] : ? [v1] : element(v1, v0) % 20.99/5.44 | (59) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) % 20.99/5.44 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) % 20.99/5.44 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2) % 20.99/5.44 | (62) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 20.99/5.44 | (63) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 20.99/5.44 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 20.99/5.44 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 20.99/5.44 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v5) = v4 & relation_dom_restriction(v2, v1) = v5)) % 20.99/5.44 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 20.99/5.44 | (68) ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) % 20.99/5.44 | (69) relation_dom(all_0_12_12) = all_0_11_11 % 20.99/5.44 | (70) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) % 20.99/5.44 | (71) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) % 20.99/5.44 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 20.99/5.44 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) % 20.99/5.44 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ disjoint(v1, v3) | ~ element(v3, v2) | ~ element(v1, v2) | subset(v1, v4)) % 20.99/5.44 | (75) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) % 20.99/5.44 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) % 20.99/5.44 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 20.99/5.44 | (78) in(all_0_13_13, all_0_11_11) % 20.99/5.44 | (79) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 20.99/5.44 | (80) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) % 20.99/5.44 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) % 20.99/5.44 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 20.99/5.44 | (83) ~ empty(all_0_4_4) % 20.99/5.44 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 20.99/5.44 | (85) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 20.99/5.44 | (86) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1)) % 20.99/5.44 | (87) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) % 20.99/5.44 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2)) % 20.99/5.44 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 20.99/5.44 | (90) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 20.99/5.44 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3))) % 20.99/5.44 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8] : (ordered_pair(v6, v4) = v8 & ~ in(v8, v1))) % 20.99/5.44 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 20.99/5.44 | (94) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 20.99/5.44 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) % 20.99/5.44 | (96) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) % 20.99/5.44 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) % 20.99/5.44 | (98) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ( ~ (v4 = v3) | ~ in(v5, v1) | ~ in(v3, v0)) & (in(v5, v1) | (v4 = v3 & in(v3, v0))))) % 20.99/5.44 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & in(v8, v1) & in(v7, v0))) % 20.99/5.45 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 20.99/5.45 | (101) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 20.99/5.45 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) % 20.99/5.45 | (103) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 20.99/5.45 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 20.99/5.45 | (105) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 20.99/5.45 | (106) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 | ~ in(v0, v4)))) % 20.99/5.45 | (107) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) % 20.99/5.45 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) % 20.99/5.45 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) % 20.99/5.45 | (110) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 20.99/5.45 | (111) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) % 20.99/5.45 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 20.99/5.45 | (113) ! [v0] : ( ~ empty(v0) | function(v0)) % 20.99/5.45 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_composition(v0, v1) = v3 & relation_rng(v3) = v4 & subset(v4, v2))) % 20.99/5.45 | (115) apply(all_0_12_12, all_0_13_13) = all_0_10_10 % 20.99/5.45 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & subset(v5, v6))) % 20.99/5.45 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 20.99/5.45 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 20.99/5.45 | (119) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 20.99/5.45 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 20.99/5.45 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) % 20.99/5.45 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 20.99/5.45 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 20.99/5.45 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (meet_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) % 20.99/5.45 | (125) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) % 20.99/5.45 | (126) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) % 20.99/5.45 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) % 20.99/5.45 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) % 20.99/5.45 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) & in(v4, v1))) % 20.99/5.45 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v1))) % 20.99/5.45 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 20.99/5.45 | (132) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 20.99/5.45 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) % 20.99/5.45 | (134) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) % 20.99/5.45 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v5 & subset(v6, v4) & subset(v3, v5))) % 20.99/5.45 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 20.99/5.45 | (137) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4))))) % 20.99/5.45 | (138) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 20.99/5.45 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 20.99/5.45 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 20.99/5.45 | (141) ! [v0] : ( ~ empty(v0) | relation(v0)) % 20.99/5.45 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_rng(v3) = v4 & relation_image(v2, v1) = v4)) % 20.99/5.45 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 20.99/5.45 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 20.99/5.45 | (145) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) % 20.99/5.45 | (146) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 20.99/5.45 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) % 20.99/5.45 | (148) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 20.99/5.45 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 20.99/5.45 | (150) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 20.99/5.45 | (151) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3)) % 20.99/5.46 | (152) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) % 20.99/5.46 | (153) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) % 20.99/5.46 | (154) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 20.99/5.46 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 20.99/5.46 | (156) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 20.99/5.46 | (157) relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8 % 20.99/5.46 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0))) % 20.99/5.46 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_dom(v2) = v5 & in(v0, v5))) % 20.99/5.46 | (160) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 20.99/5.46 | (161) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 20.99/5.46 | (162) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 20.99/5.46 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (set_meet(v1) = v3) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) % 20.99/5.46 | (164) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 20.99/5.46 | (165) relation(all_0_5_5) % 20.99/5.46 | (166) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 20.99/5.46 | (167) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 20.99/5.46 | (168) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 20.99/5.46 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) % 20.99/5.46 | (170) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 20.99/5.46 | (171) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) % 20.99/5.46 | (172) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) % 20.99/5.46 | (173) relation_dom(empty_set) = empty_set % 20.99/5.46 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3)) % 20.99/5.46 | (175) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (powerset(v3) = v4 & powerset(v0) = v3 & set_meet(v1) = v5 & (v5 = v2 | ~ element(v1, v4)))) % 20.99/5.46 | (176) relation(all_0_0_0) % 20.99/5.46 | (177) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) % 20.99/5.46 | (178) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) % 20.99/5.46 | (179) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v0) = v4) | ~ (cartesian_product2(v1, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v3) & subset(v4, v6))) % 20.99/5.46 | (180) relation_empty_yielding(empty_set) % 20.99/5.46 | (181) ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1))) % 20.99/5.46 | (182) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 20.99/5.46 | (183) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 20.99/5.46 | (184) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 20.99/5.46 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 20.99/5.46 | (186) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 20.99/5.46 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) % 20.99/5.46 | (188) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2)))) % 20.99/5.46 | (189) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 20.99/5.46 | (190) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 20.99/5.46 | (191) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) % 20.99/5.46 | (192) function(all_0_12_12) % 20.99/5.46 | (193) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v1) = v3 & relation_image(v1, v4) = v2 & set_intersection2(v3, v0) = v4)) % 20.99/5.46 | (194) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 20.99/5.46 | (195) empty(all_0_1_1) % 20.99/5.46 | (196) relation(empty_set) % 20.99/5.46 | (197) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 20.99/5.46 | (198) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 20.99/5.46 | (199) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & set_intersection2(v4, v0) = v3)) % 20.99/5.46 | (200) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) % 20.99/5.46 | (201) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) % 20.99/5.46 | (202) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) % 20.99/5.46 | (203) ~ empty(all_0_3_3) % 20.99/5.46 | (204) ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v1) & ! [v4] : ( ~ subset(v4, v2) | in(v4, v3))))) % 20.99/5.46 | (205) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 21.36/5.46 | (206) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 21.36/5.46 | (207) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (apply(v2, v0) = v5 & ( ~ (v5 = v1) | ~ in(v0, v4) | in(v3, v2)) & ( ~ in(v3, v2) | (v5 = v1 & in(v0, v4))))) % 21.36/5.47 | (208) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) % 21.36/5.47 | (209) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 21.36/5.47 | (210) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 21.36/5.47 | (211) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (relation_dom(v2) = v5 & ( ~ (v4 = v1) | ~ in(v0, v5) | in(v3, v2)) & ( ~ in(v3, v2) | (v4 = v1 & in(v0, v5))))) % 21.36/5.47 | (212) ! [v0] : ~ in(v0, empty_set) % 21.36/5.47 | (213) powerset(empty_set) = all_0_14_14 % 21.36/5.47 | (214) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v3) | ~ in(v0, v2) | in(v4, v6)) % 21.36/5.47 | (215) relation(all_0_12_12) % 21.36/5.47 | (216) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 21.36/5.47 | (217) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) % 21.36/5.47 | (218) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5))))) % 21.36/5.47 | (219) empty(all_0_2_2) % 21.36/5.47 | (220) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 21.36/5.47 | (221) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 21.36/5.47 | (222) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) % 21.36/5.47 | (223) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) % 21.36/5.47 | (224) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) % 21.36/5.47 | (225) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_dom(v3) = v4 & subset(v4, v1))) % 21.36/5.47 | (226) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 21.36/5.47 | (227) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) % 21.36/5.47 | (228) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) % 21.36/5.47 | (229) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v0, v7) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) % 21.36/5.47 | (230) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v3) = v6 & ordered_pair(v3, v4) = v5 & ( ~ in(v6, v0) | ~ in(v5, v2)) & (in(v6, v0) | in(v5, v2)))) % 21.36/5.47 | (231) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) % 21.36/5.47 | (232) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 21.36/5.47 | (233) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) % 21.36/5.47 | (234) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1))) % 21.36/5.47 | (235) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) % 21.36/5.47 | (236) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) % 21.36/5.47 | (237) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) % 21.36/5.47 | (238) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 21.36/5.47 | (239) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 21.36/5.47 | (240) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 21.36/5.47 | (241) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 21.36/5.47 | (242) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) % 21.36/5.47 | (243) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v6))) % 21.36/5.47 | (244) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 21.36/5.47 | (245) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) % 21.36/5.47 | (246) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v1))) % 21.36/5.47 | (247) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) % 21.36/5.47 | (248) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 21.36/5.47 | (249) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 21.36/5.47 | (250) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v1) | in(v5, v2) | ? [v8] : (ordered_pair(v3, v6) = v8 & ~ in(v8, v0))) % 21.36/5.47 | (251) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) % 21.36/5.47 | (252) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 21.36/5.47 | (253) ? [v0] : subset(empty_set, v0) % 21.36/5.47 | (254) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_rng(v3) = v4 & relation_rng(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) % 21.36/5.47 | (255) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (meet_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) % 21.36/5.48 | (256) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) % 21.36/5.48 | (257) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) % 21.36/5.48 | (258) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) % 21.36/5.48 | (259) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) & in(v4, v1))) % 21.36/5.48 | (260) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ subset(v2, v3) | ~ subset(v0, v1) | subset(v4, v5)) % 21.36/5.48 | (261) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) % 21.36/5.48 | (262) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 21.36/5.48 | (263) relation(all_0_1_1) % 21.36/5.48 | (264) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ element(v4, v0) | ~ element(v2, v1) | in(v4, v3) | in(v4, v2)) % 21.36/5.48 | (265) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 21.36/5.48 | (266) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) % 21.36/5.48 | (267) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) % 21.36/5.48 | (268) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 21.36/5.48 | (269) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 21.36/5.48 | (270) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 21.36/5.48 | (271) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 21.36/5.48 | (272) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5)))) % 21.36/5.48 | (273) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) % 21.36/5.48 | (274) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3))) % 21.36/5.48 | (275) ~ (all_0_6_6 = all_0_7_7) % 21.36/5.48 | (276) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 21.36/5.48 | (277) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 21.36/5.48 | (278) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 21.36/5.48 | (279) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) % 21.36/5.48 | (280) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 21.36/5.48 | (281) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 21.36/5.48 | (282) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) % 21.36/5.48 | (283) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v2) = v5 & relation_dom_restriction(v5, v1) = v4)) % 21.36/5.48 | (284) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 21.36/5.48 | (285) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v2)))) % 21.36/5.48 | (286) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 21.36/5.48 | (287) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 21.36/5.48 | (288) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 21.36/5.48 | (289) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) % 21.36/5.48 | (290) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 21.36/5.48 | (291) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) % 21.44/5.48 | (292) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) % 21.44/5.48 | (293) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 21.44/5.48 | (294) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) % 21.44/5.48 | (295) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) % 21.44/5.48 | (296) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 21.44/5.48 | (297) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) % 21.44/5.48 | (298) relation(all_0_9_9) % 21.44/5.48 | (299) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) % 21.44/5.48 | (300) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v1)))) % 21.44/5.48 | (301) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) % 21.44/5.48 | (302) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 21.44/5.48 | (303) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | ( ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v6, v1) | in(v5, v2)) & ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v5, v2) | in(v6, v1)) & ! [v5] : (v5 = v2 | ~ element(v5, v4) | ? [v6] : ? [v7] : (subset_complement(v0, v6) = v7 & element(v6, v3) & ( ~ in(v7, v1) | ~ in(v6, v5)) & (in(v7, v1) | in(v6, v5)))))))) % 21.44/5.49 | (304) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 21.44/5.49 | (305) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) % 21.44/5.49 | (306) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) % 21.44/5.49 | (307) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) % 21.44/5.49 | (308) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) % 21.44/5.49 | (309) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 21.44/5.49 | (310) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 21.44/5.49 | (311) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 21.44/5.49 | (312) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | (in(v4, v1) & ~ in(v3, v4))) & (in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | in(v3, v5))))) % 21.44/5.49 | (313) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 21.44/5.49 | (314) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) % 21.44/5.49 | (315) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) % 21.44/5.49 | (316) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) % 21.44/5.49 | (317) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) % 21.44/5.49 | (318) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) % 21.44/5.49 | (319) empty(empty_set) % 21.44/5.49 | (320) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_rng(v4) = v3 & relation_rng_restriction(v0, v1) = v4)) % 21.44/5.49 | (321) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 21.44/5.49 | (322) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) % 21.44/5.49 | (323) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 21.44/5.49 | (324) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 21.44/5.49 | (325) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) % 21.44/5.49 | (326) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 21.44/5.49 | (327) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 21.44/5.49 | (328) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 21.44/5.49 | (329) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & set_intersection2(v4, v0) = v3)) % 21.44/5.49 | (330) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) % 21.44/5.49 | (331) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) % 21.44/5.49 | (332) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 21.44/5.49 | (333) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) % 21.44/5.49 | (334) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) % 21.44/5.49 | (335) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3)) % 21.44/5.49 | (336) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 21.44/5.49 | (337) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_dom(v4) = v3 & relation_dom_restriction(v1, v0) = v4)) % 21.44/5.49 | (338) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 21.44/5.49 | (339) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ element(v3, v2) | ~ element(v1, v2) | ~ subset(v1, v4) | disjoint(v1, v3)) % 21.44/5.49 | (340) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) % 21.44/5.49 | (341) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 21.44/5.49 | (342) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 21.44/5.49 | (343) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (complements_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v0) = v4 & ~ element(v1, v5))) % 21.44/5.49 | (344) relation(all_0_3_3) % 21.44/5.49 | (345) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 21.44/5.49 | (346) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) % 21.44/5.49 | (347) apply(all_0_8_8, all_0_13_13) = all_0_7_7 % 21.44/5.49 | (348) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 21.44/5.49 | (349) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 21.44/5.49 | (350) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 21.44/5.49 | (351) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 21.44/5.49 | (352) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 21.44/5.49 | (353) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 21.44/5.50 | (354) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 21.44/5.50 | (355) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v4) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v5, v4) = v6 & in(v6, v1) & in(v5, v2))))) % 21.44/5.50 | (356) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) % 21.44/5.50 | (357) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) % 21.44/5.50 | (358) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v5, v0) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v0) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) % 21.44/5.50 | (359) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 21.44/5.50 | (360) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 21.44/5.50 | (361) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) % 21.44/5.50 | (362) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_rng(v2) = v5 & in(v1, v5))) % 21.44/5.50 | (363) relation_empty_yielding(all_0_5_5) % 21.44/5.50 | (364) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 21.44/5.50 | (365) ? [v0] : subset(v0, v0) % 21.44/5.50 | (366) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) % 21.44/5.50 | % 21.44/5.50 | Instantiating (317) with all_35_0_37 yields: % 21.44/5.50 | (367) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, v0) = v4 & relation_dom(v4) = v5 & apply(v2, all_35_0_37) = v6 & ( ~ in(v6, v1) | ~ in(all_35_0_37, v3) | in(all_35_0_37, v5)) & ( ~ in(all_35_0_37, v5) | (in(v6, v1) & in(all_35_0_37, v3))))) % 21.44/5.50 | % 21.44/5.50 | Instantiating (297) with all_37_0_38 yields: % 21.44/5.50 | (368) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v0) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & apply(v2, all_37_0_38) = v6 & ( ~ in(v6, v1) | ~ in(all_37_0_38, v5) | in(all_37_0_38, v4)) & ( ~ in(all_37_0_38, v4) | (in(v6, v1) & in(all_37_0_38, v5))))) % 21.44/5.50 | % 21.44/5.50 | Instantiating (106) with all_58_0_50 yields: % 21.44/5.50 | (369) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v3 & apply(v2, all_58_0_50) = v4 & apply(v1, all_58_0_50) = v5 & apply(v0, v5) = v6 & (v6 = v4 | ~ in(all_58_0_50, v3)))) % 21.44/5.50 | % 21.44/5.50 | Instantiating formula (241) with all_0_2_2, all_0_1_1 and discharging atoms empty(all_0_1_1), empty(all_0_2_2), yields: % 21.44/5.50 | (370) all_0_1_1 = all_0_2_2 % 21.44/5.50 | % 21.44/5.50 | Instantiating formula (241) with empty_set, all_0_1_1 and discharging atoms empty(all_0_1_1), empty(empty_set), yields: % 21.44/5.50 | (371) all_0_1_1 = empty_set % 21.44/5.50 | % 21.44/5.50 | Combining equations (371,370) yields a new equation: % 21.44/5.50 | (372) all_0_2_2 = empty_set % 21.44/5.50 | % 21.44/5.50 | Combining equations (372,370) yields a new equation: % 21.44/5.50 | (371) all_0_1_1 = empty_set % 21.44/5.50 | % 21.44/5.50 | From (371) and (263) follows: % 21.44/5.50 | (196) relation(empty_set) % 21.44/5.50 | % 21.44/5.50 | From (372) and (219) follows: % 21.44/5.50 | (319) empty(empty_set) % 21.44/5.50 | % 21.44/5.50 | Instantiating formula (328) with all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), yields: % 21.44/5.50 | (376) ? [v0] : ? [v1] : (relation_rng(all_0_8_8) = v0 & relation_rng(all_0_9_9) = v1 & subset(v0, v1)) % 21.44/5.50 | % 21.44/5.50 | Instantiating formula (225) with all_0_8_8, all_0_9_9, all_0_11_11, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_9_9), relation(all_0_12_12), yields: % 21.44/5.50 | (377) ? [v0] : (relation_dom(all_0_8_8) = v0 & subset(v0, all_0_11_11)) % 21.44/5.50 | % 21.44/5.50 | Instantiating formula (267) with all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), yields: % 21.44/5.50 | (378) ? [v0] : ? [v1] : (relation_inverse(all_0_12_12) = v1 & relation_rng(v1) = all_0_11_11 & relation_rng(all_0_12_12) = v0 & relation_dom(v1) = v0) % 21.44/5.50 | % 21.44/5.50 | Instantiating formula (285) with all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), yields: % 21.44/5.50 | (379) ? [v0] : (relation_rng(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(v1, all_0_12_12) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v4 & relation_rng(v1) = v3 & (v4 = v0 | ~ subset(all_0_11_11, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_11_11, v2) | ~ relation(v1) | ? [v3] : (relation_composition(v1, all_0_12_12) = v3 & relation_rng(v3) = v0))) % 21.44/5.50 | % 21.44/5.50 | Instantiating formula (23) with all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), yields: % 21.44/5.50 | (380) ? [v0] : (relation_rng(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_12_12, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = all_0_11_11 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_12_12, v1) = v3 & relation_dom(v3) = all_0_11_11))) % 21.44/5.50 | % 21.44/5.50 | Instantiating formula (201) with all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), yields: % 21.44/5.50 | (381) ? [v0] : (relation_rng(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(all_0_11_11, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | subset(all_0_11_11, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v0, v3)))) % 21.44/5.50 | % 21.44/5.50 | Instantiating formula (177) with all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), yields: % 21.44/5.50 | (382) ? [v0] : (relation_rng(all_0_12_12) = v0 & ( ~ (v0 = empty_set) | all_0_11_11 = empty_set) & ( ~ (all_0_11_11 = empty_set) | v0 = empty_set)) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (237) with all_0_12_12, all_0_12_12 and discharging atoms relation(all_0_12_12), yields: % 21.44/5.51 | (383) subset(all_0_12_12, all_0_12_12) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (114) with empty_set, empty_set, all_0_12_12 and discharging atoms relation_rng(empty_set) = empty_set, relation(all_0_12_12), relation(empty_set), yields: % 21.44/5.51 | (384) ? [v0] : ? [v1] : (relation_composition(all_0_12_12, empty_set) = v0 & relation_rng(v0) = v1 & subset(v1, empty_set)) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (340) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 21.44/5.51 | (385) ? [v0] : ? [v1] : (relation_inverse(empty_set) = v0 & relation_rng(v0) = v1 & relation_dom(v0) = empty_set & relation_dom(empty_set) = v1) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (86) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 21.44/5.51 | (386) ? [v0] : (relation_dom(empty_set) = v0 & relation_image(empty_set, v0) = empty_set) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (300) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 21.44/5.51 | (387) ? [v0] : (relation_dom(empty_set) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(v1, empty_set) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v4 & relation_rng(v1) = v3 & (v4 = empty_set | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(v1, empty_set) = v3 & relation_rng(v3) = empty_set))) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (188) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 21.44/5.51 | (388) ? [v0] : (relation_dom(empty_set) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(empty_set, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(empty_set, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(empty_set, v2) | ~ relation(v1) | ? [v3] : (relation_composition(empty_set, v1) = v3 & relation_dom(v3) = v0))) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (218) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 21.44/5.51 | (389) ? [v0] : (relation_dom(empty_set) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | subset(empty_set, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v0, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(empty_set, v3)))) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (272) with all_0_7_7, all_0_8_8, all_0_12_12, all_0_9_9, all_0_13_13 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.44/5.51 | (390) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_8_8) = v0 & apply(all_0_9_9, v1) = v2 & apply(all_0_12_12, all_0_13_13) = v1 & (v2 = all_0_7_7 | ~ in(all_0_13_13, v0))) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (247) with all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.44/5.51 | (391) relation(all_0_8_8) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (276) with all_0_8_8, all_0_9_9, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.44/5.51 | (392) function(all_0_8_8) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (369) with all_0_8_8, all_0_12_12, all_0_9_9 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.44/5.51 | (393) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_8_8) = v0 & apply(all_0_8_8, all_58_0_50) = v1 & apply(all_0_9_9, v2) = v3 & apply(all_0_12_12, all_58_0_50) = v2 & (v3 = v1 | ~ in(all_58_0_50, v0))) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (191) with all_0_10_10, all_0_12_12, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_12_12), function(all_0_12_12), yields: % 21.44/5.51 | (394) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, all_0_11_11) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, v2)))) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (367) with all_0_11_11, all_0_12_12, all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields: % 21.44/5.51 | (395) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & apply(all_0_12_12, all_35_0_37) = v2 & ( ~ in(v2, all_0_11_11) | ~ in(all_35_0_37, all_0_11_11) | in(all_35_0_37, v1)) & ( ~ in(all_35_0_37, v1) | (in(v2, all_0_11_11) & in(all_35_0_37, all_0_11_11)))) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (191) with all_0_6_6, all_0_9_9, all_0_11_11, all_0_12_12, all_0_10_10 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_9_9, all_0_10_10) = all_0_6_6, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.44/5.51 | (396) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_9_9, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_9_9) = v2 & ( ~ in(all_0_6_6, all_0_11_11) | ~ in(all_0_10_10, v2) | in(all_0_10_10, v1)) & ( ~ in(all_0_10_10, v1) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, v2)))) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (46) with all_0_6_6, all_0_10_10, all_0_12_12, all_0_9_9, all_0_13_13 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_0_6_6, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.44/5.51 | (397) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & apply(v0, all_0_13_13) = v2 & (v2 = all_0_6_6 | ~ in(all_0_13_13, v1))) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (113) with empty_set and discharging atoms empty(empty_set), yields: % 21.44/5.51 | (398) function(empty_set) % 21.44/5.51 | % 21.44/5.51 | Instantiating formula (3) with all_0_13_13, all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, relation(all_0_12_12), in(all_0_13_13, all_0_11_11), yields: % 21.44/5.51 | (399) ? [v0] : ? [v1] : (ordered_pair(all_0_13_13, v0) = v1 & in(v1, all_0_12_12)) % 21.44/5.51 | % 21.44/5.51 | Instantiating (382) with all_76_0_54 yields: % 21.44/5.51 | (400) relation_rng(all_0_12_12) = all_76_0_54 & ( ~ (all_76_0_54 = empty_set) | all_0_11_11 = empty_set) & ( ~ (all_0_11_11 = empty_set) | all_76_0_54 = empty_set) % 21.44/5.51 | % 21.44/5.51 | Applying alpha-rule on (400) yields: % 21.44/5.51 | (401) relation_rng(all_0_12_12) = all_76_0_54 % 21.44/5.51 | (402) ~ (all_76_0_54 = empty_set) | all_0_11_11 = empty_set % 21.44/5.51 | (403) ~ (all_0_11_11 = empty_set) | all_76_0_54 = empty_set % 21.44/5.51 | % 21.44/5.51 | Instantiating (381) with all_78_0_55 yields: % 21.44/5.51 | (404) relation_rng(all_0_12_12) = all_78_0_55 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_78_0_55, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_0_11_11, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_0_11_11, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_78_0_55, v2))) % 21.44/5.51 | % 21.44/5.51 | Applying alpha-rule on (404) yields: % 21.44/5.51 | (405) relation_rng(all_0_12_12) = all_78_0_55 % 21.44/5.51 | (406) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_0_11_11, v1)) % 21.44/5.51 | (407) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_0_11_11, v2))) % 21.44/5.51 | (408) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_78_0_55, v1)) % 21.44/5.51 | (409) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_78_0_55, v2))) % 21.44/5.51 | % 21.44/5.51 | Instantiating (376) with all_81_0_56, all_81_1_57 yields: % 21.44/5.51 | (410) relation_rng(all_0_8_8) = all_81_1_57 & relation_rng(all_0_9_9) = all_81_0_56 & subset(all_81_1_57, all_81_0_56) % 21.44/5.51 | % 21.44/5.51 | Applying alpha-rule on (410) yields: % 21.44/5.51 | (411) relation_rng(all_0_8_8) = all_81_1_57 % 21.44/5.51 | (412) relation_rng(all_0_9_9) = all_81_0_56 % 21.44/5.51 | (413) subset(all_81_1_57, all_81_0_56) % 21.44/5.51 | % 21.44/5.51 | Instantiating (380) with all_83_0_58 yields: % 21.44/5.51 | (414) relation_rng(all_0_12_12) = all_83_0_58 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_0_11_11 | ~ subset(all_83_0_58, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_83_0_58, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & relation_dom(v2) = all_0_11_11)) % 21.44/5.51 | % 21.44/5.51 | Applying alpha-rule on (414) yields: % 21.44/5.51 | (415) relation_rng(all_0_12_12) = all_83_0_58 % 21.59/5.51 | (416) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_0_11_11 | ~ subset(all_83_0_58, v2)))) % 21.59/5.51 | (417) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_83_0_58, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & relation_dom(v2) = all_0_11_11)) % 21.59/5.51 | % 21.59/5.51 | Instantiating formula (416) with all_0_8_8, all_0_9_9 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), yields: % 21.59/5.52 | (418) ? [v0] : ? [v1] : (relation_dom(all_0_8_8) = v1 & relation_dom(all_0_9_9) = v0 & (v1 = all_0_11_11 | ~ subset(all_83_0_58, v0))) % 21.59/5.52 | % 21.59/5.52 | Instantiating (378) with all_86_0_59, all_86_1_60 yields: % 21.59/5.52 | (419) relation_inverse(all_0_12_12) = all_86_0_59 & relation_rng(all_86_0_59) = all_0_11_11 & relation_rng(all_0_12_12) = all_86_1_60 & relation_dom(all_86_0_59) = all_86_1_60 % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (419) yields: % 21.59/5.52 | (420) relation_inverse(all_0_12_12) = all_86_0_59 % 21.59/5.52 | (421) relation_rng(all_86_0_59) = all_0_11_11 % 21.59/5.52 | (422) relation_rng(all_0_12_12) = all_86_1_60 % 21.59/5.52 | (423) relation_dom(all_86_0_59) = all_86_1_60 % 21.59/5.52 | % 21.59/5.52 | Instantiating (379) with all_88_0_61 yields: % 21.59/5.52 | (424) relation_rng(all_0_12_12) = all_88_0_61 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_12_12) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_88_0_61 | ~ subset(all_0_11_11, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_11_11, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_12_12) = v2 & relation_rng(v2) = all_88_0_61)) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (424) yields: % 21.59/5.52 | (425) relation_rng(all_0_12_12) = all_88_0_61 % 21.59/5.52 | (426) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_12_12) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_88_0_61 | ~ subset(all_0_11_11, v2)))) % 21.59/5.52 | (427) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_11_11, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_12_12) = v2 & relation_rng(v2) = all_88_0_61)) % 21.59/5.52 | % 21.59/5.52 | Instantiating (399) with all_91_0_62, all_91_1_63 yields: % 21.59/5.52 | (428) ordered_pair(all_0_13_13, all_91_1_63) = all_91_0_62 & in(all_91_0_62, all_0_12_12) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (428) yields: % 21.59/5.52 | (429) ordered_pair(all_0_13_13, all_91_1_63) = all_91_0_62 % 21.59/5.52 | (430) in(all_91_0_62, all_0_12_12) % 21.59/5.52 | % 21.59/5.52 | Instantiating (396) with all_96_0_65, all_96_1_66, all_96_2_67 yields: % 21.59/5.52 | (431) relation_composition(all_0_9_9, all_0_12_12) = all_96_2_67 & relation_dom(all_96_2_67) = all_96_1_66 & relation_dom(all_0_9_9) = all_96_0_65 & ( ~ in(all_0_6_6, all_0_11_11) | ~ in(all_0_10_10, all_96_0_65) | in(all_0_10_10, all_96_1_66)) & ( ~ in(all_0_10_10, all_96_1_66) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, all_96_0_65))) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (431) yields: % 21.59/5.52 | (432) ~ in(all_0_10_10, all_96_1_66) | (in(all_0_6_6, all_0_11_11) & in(all_0_10_10, all_96_0_65)) % 21.59/5.52 | (433) relation_dom(all_0_9_9) = all_96_0_65 % 21.59/5.52 | (434) relation_composition(all_0_9_9, all_0_12_12) = all_96_2_67 % 21.59/5.52 | (435) ~ in(all_0_6_6, all_0_11_11) | ~ in(all_0_10_10, all_96_0_65) | in(all_0_10_10, all_96_1_66) % 21.59/5.52 | (436) relation_dom(all_96_2_67) = all_96_1_66 % 21.59/5.52 | % 21.59/5.52 | Instantiating (395) with all_98_0_68, all_98_1_69, all_98_2_70 yields: % 21.59/5.52 | (437) relation_composition(all_0_12_12, all_0_12_12) = all_98_2_70 & relation_dom(all_98_2_70) = all_98_1_69 & apply(all_0_12_12, all_35_0_37) = all_98_0_68 & ( ~ in(all_98_0_68, all_0_11_11) | ~ in(all_35_0_37, all_0_11_11) | in(all_35_0_37, all_98_1_69)) & ( ~ in(all_35_0_37, all_98_1_69) | (in(all_98_0_68, all_0_11_11) & in(all_35_0_37, all_0_11_11))) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (437) yields: % 21.59/5.52 | (438) ~ in(all_35_0_37, all_98_1_69) | (in(all_98_0_68, all_0_11_11) & in(all_35_0_37, all_0_11_11)) % 21.59/5.52 | (439) ~ in(all_98_0_68, all_0_11_11) | ~ in(all_35_0_37, all_0_11_11) | in(all_35_0_37, all_98_1_69) % 21.59/5.52 | (440) relation_composition(all_0_12_12, all_0_12_12) = all_98_2_70 % 21.59/5.52 | (441) relation_dom(all_98_2_70) = all_98_1_69 % 21.59/5.52 | (442) apply(all_0_12_12, all_35_0_37) = all_98_0_68 % 21.59/5.52 | % 21.59/5.52 | Instantiating (390) with all_100_0_71, all_100_1_72, all_100_2_73 yields: % 21.59/5.52 | (443) relation_dom(all_0_8_8) = all_100_2_73 & apply(all_0_9_9, all_100_1_72) = all_100_0_71 & apply(all_0_12_12, all_0_13_13) = all_100_1_72 & (all_100_0_71 = all_0_7_7 | ~ in(all_0_13_13, all_100_2_73)) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (443) yields: % 21.59/5.52 | (444) relation_dom(all_0_8_8) = all_100_2_73 % 21.59/5.52 | (445) apply(all_0_9_9, all_100_1_72) = all_100_0_71 % 21.59/5.52 | (446) apply(all_0_12_12, all_0_13_13) = all_100_1_72 % 21.59/5.52 | (447) all_100_0_71 = all_0_7_7 | ~ in(all_0_13_13, all_100_2_73) % 21.59/5.52 | % 21.59/5.52 | Instantiating (394) with all_102_0_74, all_102_1_75, all_102_2_76 yields: % 21.59/5.52 | (448) relation_composition(all_0_12_12, all_0_12_12) = all_102_2_76 & relation_dom(all_102_2_76) = all_102_1_75 & relation_dom(all_0_12_12) = all_102_0_74 & ( ~ in(all_0_10_10, all_0_11_11) | ~ in(all_0_13_13, all_102_0_74) | in(all_0_13_13, all_102_1_75)) & ( ~ in(all_0_13_13, all_102_1_75) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, all_102_0_74))) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (448) yields: % 21.59/5.52 | (449) ~ in(all_0_13_13, all_102_1_75) | (in(all_0_10_10, all_0_11_11) & in(all_0_13_13, all_102_0_74)) % 21.59/5.52 | (450) relation_dom(all_0_12_12) = all_102_0_74 % 21.59/5.52 | (451) relation_composition(all_0_12_12, all_0_12_12) = all_102_2_76 % 21.59/5.52 | (452) relation_dom(all_102_2_76) = all_102_1_75 % 21.59/5.52 | (453) ~ in(all_0_10_10, all_0_11_11) | ~ in(all_0_13_13, all_102_0_74) | in(all_0_13_13, all_102_1_75) % 21.59/5.52 | % 21.59/5.52 | Instantiating (393) with all_104_0_77, all_104_1_78, all_104_2_79, all_104_3_80 yields: % 21.59/5.52 | (454) relation_dom(all_0_8_8) = all_104_3_80 & apply(all_0_8_8, all_58_0_50) = all_104_2_79 & apply(all_0_9_9, all_104_1_78) = all_104_0_77 & apply(all_0_12_12, all_58_0_50) = all_104_1_78 & (all_104_0_77 = all_104_2_79 | ~ in(all_58_0_50, all_104_3_80)) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (454) yields: % 21.59/5.52 | (455) apply(all_0_9_9, all_104_1_78) = all_104_0_77 % 21.59/5.52 | (456) relation_dom(all_0_8_8) = all_104_3_80 % 21.59/5.52 | (457) all_104_0_77 = all_104_2_79 | ~ in(all_58_0_50, all_104_3_80) % 21.59/5.52 | (458) apply(all_0_8_8, all_58_0_50) = all_104_2_79 % 21.59/5.52 | (459) apply(all_0_12_12, all_58_0_50) = all_104_1_78 % 21.59/5.52 | % 21.59/5.52 | Instantiating (377) with all_106_0_81 yields: % 21.59/5.52 | (460) relation_dom(all_0_8_8) = all_106_0_81 & subset(all_106_0_81, all_0_11_11) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (460) yields: % 21.59/5.52 | (461) relation_dom(all_0_8_8) = all_106_0_81 % 21.59/5.52 | (462) subset(all_106_0_81, all_0_11_11) % 21.59/5.52 | % 21.59/5.52 | Instantiating (397) with all_108_0_82, all_108_1_83, all_108_2_84 yields: % 21.59/5.52 | (463) relation_composition(all_0_12_12, all_0_9_9) = all_108_2_84 & relation_dom(all_108_2_84) = all_108_1_83 & apply(all_108_2_84, all_0_13_13) = all_108_0_82 & (all_108_0_82 = all_0_6_6 | ~ in(all_0_13_13, all_108_1_83)) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (463) yields: % 21.59/5.52 | (464) relation_composition(all_0_12_12, all_0_9_9) = all_108_2_84 % 21.59/5.52 | (465) relation_dom(all_108_2_84) = all_108_1_83 % 21.59/5.52 | (466) apply(all_108_2_84, all_0_13_13) = all_108_0_82 % 21.59/5.52 | (467) all_108_0_82 = all_0_6_6 | ~ in(all_0_13_13, all_108_1_83) % 21.59/5.52 | % 21.59/5.52 | Instantiating (389) with all_125_0_92 yields: % 21.59/5.52 | (468) relation_dom(empty_set) = all_125_0_92 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_125_0_92, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(all_125_0_92, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(empty_set, v2))) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (468) yields: % 21.59/5.52 | (469) relation_dom(empty_set) = all_125_0_92 % 21.59/5.52 | (470) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(all_125_0_92, v1)) % 21.59/5.52 | (471) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_125_0_92, v2))) % 21.59/5.52 | (472) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(empty_set, v2))) % 21.59/5.52 | (473) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1)) % 21.59/5.52 | % 21.59/5.52 | Instantiating (388) with all_132_0_97 yields: % 21.59/5.52 | (474) relation_dom(empty_set) = all_132_0_97 & ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_132_0_97 | ~ subset(empty_set, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = all_132_0_97)) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (474) yields: % 21.59/5.52 | (475) relation_dom(empty_set) = all_132_0_97 % 21.59/5.52 | (476) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_132_0_97 | ~ subset(empty_set, v2)))) % 21.59/5.52 | (477) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = all_132_0_97)) % 21.59/5.52 | % 21.59/5.52 | Instantiating (387) with all_135_0_98 yields: % 21.59/5.52 | (478) relation_dom(empty_set) = all_135_0_98 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = empty_set | ~ subset(all_135_0_98, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_135_0_98, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, empty_set) = v2 & relation_rng(v2) = empty_set)) % 21.59/5.52 | % 21.59/5.52 | Applying alpha-rule on (478) yields: % 21.59/5.52 | (479) relation_dom(empty_set) = all_135_0_98 % 21.59/5.53 | (480) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = empty_set | ~ subset(all_135_0_98, v2)))) % 21.59/5.53 | (481) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_135_0_98, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, empty_set) = v2 & relation_rng(v2) = empty_set)) % 21.59/5.53 | % 21.59/5.53 | Instantiating (386) with all_138_0_99 yields: % 21.59/5.53 | (482) relation_dom(empty_set) = all_138_0_99 & relation_image(empty_set, all_138_0_99) = empty_set % 21.59/5.53 | % 21.59/5.53 | Applying alpha-rule on (482) yields: % 21.59/5.53 | (483) relation_dom(empty_set) = all_138_0_99 % 21.59/5.53 | (484) relation_image(empty_set, all_138_0_99) = empty_set % 21.59/5.53 | % 21.59/5.53 | Instantiating (384) with all_140_0_100, all_140_1_101 yields: % 21.59/5.53 | (485) relation_composition(all_0_12_12, empty_set) = all_140_1_101 & relation_rng(all_140_1_101) = all_140_0_100 & subset(all_140_0_100, empty_set) % 21.59/5.53 | % 21.59/5.53 | Applying alpha-rule on (485) yields: % 21.59/5.53 | (486) relation_composition(all_0_12_12, empty_set) = all_140_1_101 % 21.59/5.53 | (487) relation_rng(all_140_1_101) = all_140_0_100 % 21.59/5.53 | (488) subset(all_140_0_100, empty_set) % 21.59/5.53 | % 21.59/5.53 | Instantiating (385) with all_146_0_106, all_146_1_107 yields: % 21.59/5.53 | (489) relation_inverse(empty_set) = all_146_1_107 & relation_rng(all_146_1_107) = all_146_0_106 & relation_dom(all_146_1_107) = empty_set & relation_dom(empty_set) = all_146_0_106 % 21.59/5.53 | % 21.59/5.53 | Applying alpha-rule on (489) yields: % 21.59/5.53 | (490) relation_inverse(empty_set) = all_146_1_107 % 21.59/5.53 | (491) relation_rng(all_146_1_107) = all_146_0_106 % 21.59/5.53 | (492) relation_dom(all_146_1_107) = empty_set % 21.59/5.53 | (493) relation_dom(empty_set) = all_146_0_106 % 21.59/5.53 | % 21.59/5.53 | Instantiating (418) with all_150_0_110, all_150_1_111 yields: % 21.59/5.53 | (494) relation_dom(all_0_8_8) = all_150_0_110 & relation_dom(all_0_9_9) = all_150_1_111 & (all_150_0_110 = all_0_11_11 | ~ subset(all_83_0_58, all_150_1_111)) % 21.59/5.53 | % 21.59/5.53 | Applying alpha-rule on (494) yields: % 21.59/5.53 | (495) relation_dom(all_0_8_8) = all_150_0_110 % 21.59/5.53 | (496) relation_dom(all_0_9_9) = all_150_1_111 % 21.59/5.53 | (497) all_150_0_110 = all_0_11_11 | ~ subset(all_83_0_58, all_150_1_111) % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (338) with all_0_12_12, all_0_9_9, all_108_2_84, all_0_8_8 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_108_2_84, relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, yields: % 21.59/5.53 | (498) all_108_2_84 = all_0_8_8 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (338) with all_0_12_12, all_0_12_12, all_98_2_70, all_102_2_76 and discharging atoms relation_composition(all_0_12_12, all_0_12_12) = all_102_2_76, relation_composition(all_0_12_12, all_0_12_12) = all_98_2_70, yields: % 21.59/5.53 | (499) all_102_2_76 = all_98_2_70 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (186) with all_0_12_12, all_86_1_60, all_88_0_61 and discharging atoms relation_rng(all_0_12_12) = all_88_0_61, relation_rng(all_0_12_12) = all_86_1_60, yields: % 21.59/5.53 | (500) all_88_0_61 = all_86_1_60 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (186) with all_0_12_12, all_83_0_58, all_88_0_61 and discharging atoms relation_rng(all_0_12_12) = all_88_0_61, relation_rng(all_0_12_12) = all_83_0_58, yields: % 21.59/5.53 | (501) all_88_0_61 = all_83_0_58 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (186) with all_0_12_12, all_78_0_55, all_88_0_61 and discharging atoms relation_rng(all_0_12_12) = all_88_0_61, relation_rng(all_0_12_12) = all_78_0_55, yields: % 21.59/5.53 | (502) all_88_0_61 = all_78_0_55 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (186) with all_0_12_12, all_76_0_54, all_83_0_58 and discharging atoms relation_rng(all_0_12_12) = all_83_0_58, relation_rng(all_0_12_12) = all_76_0_54, yields: % 21.59/5.53 | (503) all_83_0_58 = all_76_0_54 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with all_0_8_8, all_106_0_81, all_150_0_110 and discharging atoms relation_dom(all_0_8_8) = all_150_0_110, relation_dom(all_0_8_8) = all_106_0_81, yields: % 21.59/5.53 | (504) all_150_0_110 = all_106_0_81 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with all_0_8_8, all_104_3_80, all_106_0_81 and discharging atoms relation_dom(all_0_8_8) = all_106_0_81, relation_dom(all_0_8_8) = all_104_3_80, yields: % 21.59/5.53 | (505) all_106_0_81 = all_104_3_80 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with all_0_8_8, all_100_2_73, all_150_0_110 and discharging atoms relation_dom(all_0_8_8) = all_150_0_110, relation_dom(all_0_8_8) = all_100_2_73, yields: % 21.59/5.53 | (506) all_150_0_110 = all_100_2_73 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with all_0_9_9, all_96_0_65, all_150_1_111 and discharging atoms relation_dom(all_0_9_9) = all_150_1_111, relation_dom(all_0_9_9) = all_96_0_65, yields: % 21.59/5.53 | (507) all_150_1_111 = all_96_0_65 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with all_0_12_12, all_102_0_74, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_102_0_74, relation_dom(all_0_12_12) = all_0_11_11, yields: % 21.59/5.53 | (508) all_102_0_74 = all_0_11_11 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with empty_set, all_138_0_99, empty_set and discharging atoms relation_dom(empty_set) = all_138_0_99, relation_dom(empty_set) = empty_set, yields: % 21.59/5.53 | (509) all_138_0_99 = empty_set % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with empty_set, all_138_0_99, all_146_0_106 and discharging atoms relation_dom(empty_set) = all_146_0_106, relation_dom(empty_set) = all_138_0_99, yields: % 21.59/5.53 | (510) all_146_0_106 = all_138_0_99 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with empty_set, all_135_0_98, all_138_0_99 and discharging atoms relation_dom(empty_set) = all_138_0_99, relation_dom(empty_set) = all_135_0_98, yields: % 21.59/5.53 | (511) all_138_0_99 = all_135_0_98 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with empty_set, all_132_0_97, all_138_0_99 and discharging atoms relation_dom(empty_set) = all_138_0_99, relation_dom(empty_set) = all_132_0_97, yields: % 21.59/5.53 | (512) all_138_0_99 = all_132_0_97 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with empty_set, all_125_0_92, all_146_0_106 and discharging atoms relation_dom(empty_set) = all_146_0_106, relation_dom(empty_set) = all_125_0_92, yields: % 21.59/5.53 | (513) all_146_0_106 = all_125_0_92 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (140) with all_0_12_12, all_0_13_13, all_100_1_72, all_0_10_10 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_100_1_72, apply(all_0_12_12, all_0_13_13) = all_0_10_10, yields: % 21.59/5.53 | (514) all_100_1_72 = all_0_10_10 % 21.59/5.53 | % 21.59/5.53 | Combining equations (504,506) yields a new equation: % 21.59/5.53 | (515) all_106_0_81 = all_100_2_73 % 21.59/5.53 | % 21.59/5.53 | Simplifying 515 yields: % 21.59/5.53 | (516) all_106_0_81 = all_100_2_73 % 21.59/5.53 | % 21.59/5.53 | Combining equations (510,513) yields a new equation: % 21.59/5.53 | (517) all_138_0_99 = all_125_0_92 % 21.59/5.53 | % 21.59/5.53 | Simplifying 517 yields: % 21.59/5.53 | (518) all_138_0_99 = all_125_0_92 % 21.59/5.53 | % 21.59/5.53 | Combining equations (509,511) yields a new equation: % 21.59/5.53 | (519) all_135_0_98 = empty_set % 21.59/5.53 | % 21.59/5.53 | Combining equations (512,511) yields a new equation: % 21.59/5.53 | (520) all_135_0_98 = all_132_0_97 % 21.59/5.53 | % 21.59/5.53 | Combining equations (518,511) yields a new equation: % 21.59/5.53 | (521) all_135_0_98 = all_125_0_92 % 21.59/5.53 | % 21.59/5.53 | Combining equations (519,520) yields a new equation: % 21.59/5.53 | (522) all_132_0_97 = empty_set % 21.59/5.53 | % 21.59/5.53 | Combining equations (521,520) yields a new equation: % 21.59/5.53 | (523) all_132_0_97 = all_125_0_92 % 21.59/5.53 | % 21.59/5.53 | Combining equations (522,523) yields a new equation: % 21.59/5.53 | (524) all_125_0_92 = empty_set % 21.59/5.53 | % 21.59/5.53 | Combining equations (516,505) yields a new equation: % 21.59/5.53 | (525) all_104_3_80 = all_100_2_73 % 21.59/5.53 | % 21.59/5.53 | Combining equations (501,500) yields a new equation: % 21.59/5.53 | (526) all_86_1_60 = all_83_0_58 % 21.59/5.53 | % 21.59/5.53 | Combining equations (502,500) yields a new equation: % 21.59/5.53 | (527) all_86_1_60 = all_78_0_55 % 21.59/5.53 | % 21.59/5.53 | Combining equations (526,527) yields a new equation: % 21.59/5.53 | (528) all_83_0_58 = all_78_0_55 % 21.59/5.53 | % 21.59/5.53 | Simplifying 528 yields: % 21.59/5.53 | (529) all_83_0_58 = all_78_0_55 % 21.59/5.53 | % 21.59/5.53 | Combining equations (529,503) yields a new equation: % 21.59/5.53 | (530) all_78_0_55 = all_76_0_54 % 21.59/5.53 | % 21.59/5.53 | Simplifying 530 yields: % 21.59/5.53 | (531) all_78_0_55 = all_76_0_54 % 21.59/5.53 | % 21.59/5.53 | From (498) and (464) follows: % 21.59/5.53 | (157) relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8 % 21.59/5.53 | % 21.59/5.53 | From (499) and (451) follows: % 21.59/5.53 | (440) relation_composition(all_0_12_12, all_0_12_12) = all_98_2_70 % 21.59/5.53 | % 21.59/5.53 | From (531) and (405) follows: % 21.59/5.53 | (401) relation_rng(all_0_12_12) = all_76_0_54 % 21.59/5.53 | % 21.59/5.53 | From (498) and (465) follows: % 21.59/5.53 | (535) relation_dom(all_0_8_8) = all_108_1_83 % 21.59/5.53 | % 21.59/5.53 | From (525) and (456) follows: % 21.59/5.53 | (444) relation_dom(all_0_8_8) = all_100_2_73 % 21.59/5.53 | % 21.59/5.53 | From (507) and (496) follows: % 21.59/5.53 | (433) relation_dom(all_0_9_9) = all_96_0_65 % 21.59/5.53 | % 21.59/5.53 | From (508) and (450) follows: % 21.59/5.53 | (69) relation_dom(all_0_12_12) = all_0_11_11 % 21.59/5.53 | % 21.59/5.53 | From (524) and (469) follows: % 21.59/5.53 | (173) relation_dom(empty_set) = empty_set % 21.59/5.53 | % 21.59/5.53 | From (498) and (466) follows: % 21.59/5.53 | (540) apply(all_0_8_8, all_0_13_13) = all_108_0_82 % 21.59/5.53 | % 21.59/5.53 | From (514) and (445) follows: % 21.59/5.53 | (541) apply(all_0_9_9, all_0_10_10) = all_100_0_71 % 21.59/5.53 | % 21.59/5.53 | From (514) and (446) follows: % 21.59/5.53 | (115) apply(all_0_12_12, all_0_13_13) = all_0_10_10 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (146) with all_0_8_8, all_108_1_83, all_100_2_73 and discharging atoms relation_dom(all_0_8_8) = all_108_1_83, relation_dom(all_0_8_8) = all_100_2_73, yields: % 21.59/5.53 | (543) all_108_1_83 = all_100_2_73 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (140) with all_0_8_8, all_0_13_13, all_108_0_82, all_0_7_7 and discharging atoms apply(all_0_8_8, all_0_13_13) = all_108_0_82, apply(all_0_8_8, all_0_13_13) = all_0_7_7, yields: % 21.59/5.53 | (544) all_108_0_82 = all_0_7_7 % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (140) with all_0_9_9, all_0_10_10, all_100_0_71, all_0_6_6 and discharging atoms apply(all_0_9_9, all_0_10_10) = all_100_0_71, apply(all_0_9_9, all_0_10_10) = all_0_6_6, yields: % 21.59/5.53 | (545) all_100_0_71 = all_0_6_6 % 21.59/5.53 | % 21.59/5.53 | From (543) and (535) follows: % 21.59/5.53 | (444) relation_dom(all_0_8_8) = all_100_2_73 % 21.59/5.53 | % 21.59/5.53 | From (544) and (540) follows: % 21.59/5.53 | (347) apply(all_0_8_8, all_0_13_13) = all_0_7_7 % 21.59/5.53 | % 21.59/5.53 | From (545) and (541) follows: % 21.59/5.53 | (5) apply(all_0_9_9, all_0_10_10) = all_0_6_6 % 21.59/5.53 | % 21.59/5.53 +-Applying beta-rule and splitting (447), into two cases. % 21.59/5.53 |-Branch one: % 21.59/5.53 | (549) ~ in(all_0_13_13, all_100_2_73) % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (188) with all_81_0_56, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_81_0_56, relation(all_0_9_9), yields: % 21.59/5.53 | (550) ? [v0] : (relation_dom(all_0_9_9) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_9_9, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_81_0_56, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_81_0_56, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_9_9, v1) = v3 & relation_dom(v3) = v0))) % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (86) with all_76_0_54, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_76_0_54, relation(all_0_12_12), yields: % 21.59/5.53 | (551) ? [v0] : (relation_dom(all_0_12_12) = v0 & relation_image(all_0_12_12, v0) = all_76_0_54) % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (188) with all_76_0_54, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_76_0_54, relation(all_0_12_12), yields: % 21.59/5.53 | (552) ? [v0] : (relation_dom(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_12_12, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_76_0_54, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_76_0_54, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_12_12, v1) = v3 & relation_dom(v3) = v0))) % 21.59/5.53 | % 21.59/5.53 | Instantiating formula (218) with all_76_0_54, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_76_0_54, relation(all_0_12_12), yields: % 21.59/5.53 | (553) ? [v0] : (relation_dom(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | subset(all_76_0_54, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v0, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(all_76_0_54, v3)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (301) with all_0_6_6, all_0_10_10, all_96_0_65, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_96_0_65, apply(all_0_9_9, all_0_10_10) = all_0_6_6, relation(all_0_9_9), function(all_0_9_9), yields: % 21.59/5.54 | (554) all_0_6_6 = empty_set | in(all_0_10_10, all_96_0_65) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (191) with all_0_10_10, all_0_12_12, all_96_0_65, all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_9_9) = all_96_0_65, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.59/5.54 | (555) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, all_96_0_65) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_96_0_65) & in(all_0_13_13, v2)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (368) with all_0_8_8, all_0_12_12, all_96_0_65, all_0_9_9 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation_dom(all_0_9_9) = all_96_0_65, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.59/5.54 | (556) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_8_8) = v0 & relation_dom(all_0_12_12) = v1 & apply(all_0_12_12, all_37_0_38) = v2 & ( ~ in(v2, all_96_0_65) | ~ in(all_37_0_38, v1) | in(all_37_0_38, v0)) & ( ~ in(all_37_0_38, v0) | (in(v2, all_96_0_65) & in(all_37_0_38, v1)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (23) with all_96_0_65, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_96_0_65, relation(all_0_9_9), yields: % 21.59/5.54 | (557) ? [v0] : (relation_rng(all_0_9_9) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_9_9, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = all_96_0_65 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_9_9, v1) = v3 & relation_dom(v3) = all_96_0_65))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (272) with all_104_2_79, all_0_8_8, all_0_12_12, all_0_9_9, all_58_0_50 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, apply(all_0_8_8, all_58_0_50) = all_104_2_79, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.59/5.54 | (558) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_8_8) = v0 & apply(all_0_9_9, v1) = v2 & apply(all_0_12_12, all_58_0_50) = v1 & (v2 = all_104_2_79 | ~ in(all_58_0_50, v0))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (191) with all_104_1_78, all_0_12_12, all_96_0_65, all_0_9_9, all_58_0_50 and discharging atoms relation_dom(all_0_9_9) = all_96_0_65, apply(all_0_12_12, all_58_0_50) = all_104_1_78, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.59/5.54 | (559) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_104_1_78, all_96_0_65) | ~ in(all_58_0_50, v2) | in(all_58_0_50, v1)) & ( ~ in(all_58_0_50, v1) | (in(all_104_1_78, all_96_0_65) & in(all_58_0_50, v2)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (46) with all_104_0_77, all_104_1_78, all_0_12_12, all_0_9_9, all_58_0_50 and discharging atoms apply(all_0_9_9, all_104_1_78) = all_104_0_77, apply(all_0_12_12, all_58_0_50) = all_104_1_78, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.59/5.54 | (560) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & apply(v0, all_58_0_50) = v2 & (v2 = all_104_0_77 | ~ in(all_58_0_50, v1))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (191) with all_98_0_68, all_0_12_12, all_96_0_65, all_0_9_9, all_35_0_37 and discharging atoms relation_dom(all_0_9_9) = all_96_0_65, apply(all_0_12_12, all_35_0_37) = all_98_0_68, relation(all_0_9_9), relation(all_0_12_12), function(all_0_9_9), function(all_0_12_12), yields: % 21.59/5.54 | (561) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_98_0_68, all_96_0_65) | ~ in(all_35_0_37, v2) | in(all_35_0_37, v1)) & ( ~ in(all_35_0_37, v1) | (in(all_98_0_68, all_96_0_65) & in(all_35_0_37, v2)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (266) with all_91_0_62, all_91_1_63, all_0_13_13, all_0_11_11, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, ordered_pair(all_0_13_13, all_91_1_63) = all_91_0_62, relation(all_0_12_12), function(all_0_12_12), in(all_0_13_13, all_0_11_11), yields: % 21.59/5.54 | (562) ? [v0] : (apply(all_0_12_12, all_0_13_13) = v0 & ( ~ (v0 = all_91_1_63) | in(all_91_0_62, all_0_12_12)) & (v0 = all_91_1_63 | ~ in(all_91_0_62, all_0_12_12))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (207) with all_0_11_11, all_91_0_62, all_0_12_12, all_91_1_63, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, ordered_pair(all_0_13_13, all_91_1_63) = all_91_0_62, relation(all_0_12_12), function(all_0_12_12), yields: % 21.59/5.54 | (563) ? [v0] : (apply(all_0_12_12, all_0_13_13) = v0 & ( ~ (v0 = all_91_1_63) | ~ in(all_0_13_13, all_0_11_11) | in(all_91_0_62, all_0_12_12)) & ( ~ in(all_91_0_62, all_0_12_12) | (v0 = all_91_1_63 & in(all_0_13_13, all_0_11_11)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (211) with all_0_10_10, all_91_0_62, all_0_12_12, all_91_1_63, all_0_13_13 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_10_10, ordered_pair(all_0_13_13, all_91_1_63) = all_91_0_62, relation(all_0_12_12), function(all_0_12_12), yields: % 21.59/5.54 | (564) ? [v0] : (relation_dom(all_0_12_12) = v0 & ( ~ (all_91_1_63 = all_0_10_10) | ~ in(all_0_13_13, v0) | in(all_91_0_62, all_0_12_12)) & ( ~ in(all_91_0_62, all_0_12_12) | (all_91_1_63 = all_0_10_10 & in(all_0_13_13, v0)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (340) with all_81_1_57, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_81_1_57, relation(all_0_8_8), yields: % 21.59/5.54 | (565) ? [v0] : ? [v1] : (relation_inverse(all_0_8_8) = v0 & relation_rng(v0) = v1 & relation_dom(v0) = all_81_1_57 & relation_dom(all_0_8_8) = v1) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (86) with all_81_1_57, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_81_1_57, relation(all_0_8_8), yields: % 21.59/5.54 | (566) ? [v0] : (relation_dom(all_0_8_8) = v0 & relation_image(all_0_8_8, v0) = all_81_1_57) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (300) with all_81_1_57, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_81_1_57, relation(all_0_8_8), yields: % 21.59/5.54 | (567) ? [v0] : (relation_dom(all_0_8_8) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(v1, all_0_8_8) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v4 & relation_rng(v1) = v3 & (v4 = all_81_1_57 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(v1, all_0_8_8) = v3 & relation_rng(v3) = all_81_1_57))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (188) with all_81_1_57, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_81_1_57, relation(all_0_8_8), yields: % 21.59/5.54 | (568) ? [v0] : (relation_dom(all_0_8_8) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_8_8, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_81_1_57, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_81_1_57, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_8_8, v1) = v3 & relation_dom(v3) = v0))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (218) with all_81_1_57, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_81_1_57, relation(all_0_8_8), yields: % 21.59/5.54 | (569) ? [v0] : (relation_dom(all_0_8_8) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_8_8, v1) | ~ relation(v1) | subset(all_81_1_57, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_8_8, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v0, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_8_8, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_8_8, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(all_81_1_57, v3)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (202) with all_81_1_57, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_81_1_57, relation(all_0_8_8), yields: % 21.59/5.54 | (570) ? [v0] : (relation_dom(all_0_8_8) = v0 & ( ~ (v0 = empty_set) | all_81_1_57 = empty_set) & ( ~ (all_81_1_57 = empty_set) | v0 = empty_set)) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (191) with all_0_7_7, all_0_8_8, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields: % 21.59/5.54 | (571) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, all_0_11_11) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, v2)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (191) with all_104_2_79, all_0_8_8, all_0_11_11, all_0_12_12, all_58_0_50 and discharging atoms relation_dom(all_0_12_12) = all_0_11_11, apply(all_0_8_8, all_58_0_50) = all_104_2_79, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields: % 21.59/5.54 | (572) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_104_2_79, all_0_11_11) | ~ in(all_58_0_50, v2) | in(all_58_0_50, v1)) & ( ~ in(all_58_0_50, v1) | (in(all_104_2_79, all_0_11_11) & in(all_58_0_50, v2)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (191) with all_0_7_7, all_0_8_8, all_100_2_73, all_0_8_8, all_0_13_13 and discharging atoms relation_dom(all_0_8_8) = all_100_2_73, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), function(all_0_8_8), yields: % 21.59/5.54 | (573) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, all_100_2_73) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_100_2_73) & in(all_0_13_13, v2)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (191) with all_104_2_79, all_0_8_8, all_100_2_73, all_0_8_8, all_58_0_50 and discharging atoms relation_dom(all_0_8_8) = all_100_2_73, apply(all_0_8_8, all_58_0_50) = all_104_2_79, relation(all_0_8_8), function(all_0_8_8), yields: % 21.59/5.54 | (574) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_104_2_79, all_100_2_73) | ~ in(all_58_0_50, v2) | in(all_58_0_50, v1)) & ( ~ in(all_58_0_50, v1) | (in(all_104_2_79, all_100_2_73) & in(all_58_0_50, v2)))) % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (301) with all_0_7_7, all_0_13_13, all_100_2_73, all_0_8_8 and discharging atoms relation_dom(all_0_8_8) = all_100_2_73, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), function(all_0_8_8), ~ in(all_0_13_13, all_100_2_73), yields: % 21.59/5.54 | (575) all_0_7_7 = empty_set % 21.59/5.54 | % 21.59/5.54 | Instantiating formula (191) with all_0_10_10, all_0_12_12, all_100_2_73, all_0_8_8, all_0_13_13 and discharging atoms relation_dom(all_0_8_8) = all_100_2_73, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields: % 21.59/5.55 | (576) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, all_100_2_73) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, all_100_2_73) & in(all_0_13_13, v2)))) % 21.59/5.55 | % 21.59/5.55 | Instantiating formula (191) with all_104_1_78, all_0_12_12, all_100_2_73, all_0_8_8, all_58_0_50 and discharging atoms relation_dom(all_0_8_8) = all_100_2_73, apply(all_0_12_12, all_58_0_50) = all_104_1_78, relation(all_0_8_8), relation(all_0_12_12), function(all_0_8_8), function(all_0_12_12), yields: % 21.59/5.55 | (577) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_8_8) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_104_1_78, all_100_2_73) | ~ in(all_58_0_50, v2) | in(all_58_0_50, v1)) & ( ~ in(all_58_0_50, v1) | (in(all_104_1_78, all_100_2_73) & in(all_58_0_50, v2)))) % 21.59/5.55 | % 21.59/5.55 | Instantiating formula (191) with all_0_7_7, all_0_8_8, all_96_0_65, all_0_9_9, all_0_13_13 and discharging atoms relation_dom(all_0_9_9) = all_96_0_65, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), relation(all_0_9_9), function(all_0_8_8), function(all_0_9_9), yields: % 21.59/5.55 | (578) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, all_96_0_65) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, all_96_0_65) & in(all_0_13_13, v2)))) % 21.59/5.55 | % 21.59/5.55 | Instantiating formula (191) with all_104_2_79, all_0_8_8, all_96_0_65, all_0_9_9, all_58_0_50 and discharging atoms relation_dom(all_0_9_9) = all_96_0_65, apply(all_0_8_8, all_58_0_50) = all_104_2_79, relation(all_0_8_8), relation(all_0_9_9), function(all_0_8_8), function(all_0_9_9), yields: % 21.59/5.55 | (579) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, all_0_9_9) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_104_2_79, all_96_0_65) | ~ in(all_58_0_50, v2) | in(all_58_0_50, v1)) & ( ~ in(all_58_0_50, v1) | (in(all_104_2_79, all_96_0_65) & in(all_58_0_50, v2)))) % 21.59/5.55 | % 21.59/5.55 | Instantiating formula (211) with all_0_7_7, all_91_0_62, all_0_8_8, all_91_1_63, all_0_13_13 and discharging atoms apply(all_0_8_8, all_0_13_13) = all_0_7_7, ordered_pair(all_0_13_13, all_91_1_63) = all_91_0_62, relation(all_0_8_8), function(all_0_8_8), yields: % 21.59/5.55 | (580) ? [v0] : (relation_dom(all_0_8_8) = v0 & ( ~ (all_91_1_63 = all_0_7_7) | ~ in(all_0_13_13, v0) | in(all_91_0_62, all_0_8_8)) & ( ~ in(all_91_0_62, all_0_8_8) | (all_91_1_63 = all_0_7_7 & in(all_0_13_13, v0)))) % 21.59/5.55 | % 21.59/5.55 | Instantiating formula (368) with all_140_1_101, all_0_12_12, empty_set, empty_set and discharging atoms relation_composition(all_0_12_12, empty_set) = all_140_1_101, relation_dom(empty_set) = empty_set, relation(all_0_12_12), relation(empty_set), function(all_0_12_12), function(empty_set), yields: % 21.59/5.55 | (581) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_140_1_101) = v0 & relation_dom(all_0_12_12) = v1 & apply(all_0_12_12, all_37_0_38) = v2 & ( ~ in(v2, empty_set) | ~ in(all_37_0_38, v1) | in(all_37_0_38, v0)) & ( ~ in(all_37_0_38, v0) | (in(v2, empty_set) & in(all_37_0_38, v1)))) % 21.59/5.55 | % 21.59/5.55 | Instantiating formula (191) with all_0_7_7, all_0_8_8, empty_set, empty_set, all_0_13_13 and discharging atoms relation_dom(empty_set) = empty_set, apply(all_0_8_8, all_0_13_13) = all_0_7_7, relation(all_0_8_8), relation(empty_set), function(all_0_8_8), function(empty_set), yields: % 21.59/5.55 | (582) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, empty_set) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_0_7_7, empty_set) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_7_7, empty_set) & in(all_0_13_13, v2)))) % 21.59/5.55 | % 21.59/5.55 | Instantiating formula (191) with all_0_10_10, all_0_12_12, empty_set, empty_set, all_0_13_13 and discharging atoms relation_dom(empty_set) = empty_set, apply(all_0_12_12, all_0_13_13) = all_0_10_10, relation(all_0_12_12), relation(empty_set), function(all_0_12_12), function(empty_set), yields: % 21.71/5.55 | (583) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, empty_set) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_10_10, empty_set) | ~ in(all_0_13_13, v2) | in(all_0_13_13, v1)) & ( ~ in(all_0_13_13, v1) | (in(all_0_10_10, empty_set) & in(all_0_13_13, v2)))) % 21.71/5.55 | % 21.71/5.55 | Instantiating formula (191) with all_104_2_79, all_0_8_8, empty_set, empty_set, all_58_0_50 and discharging atoms relation_dom(empty_set) = empty_set, apply(all_0_8_8, all_58_0_50) = all_104_2_79, relation(all_0_8_8), relation(empty_set), function(all_0_8_8), function(empty_set), yields: % 21.71/5.55 | (584) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_8_8, empty_set) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_8_8) = v2 & ( ~ in(all_104_2_79, empty_set) | ~ in(all_58_0_50, v2) | in(all_58_0_50, v1)) & ( ~ in(all_58_0_50, v1) | (in(all_104_2_79, empty_set) & in(all_58_0_50, v2)))) % 21.71/5.55 | % 21.71/5.55 | Instantiating formula (191) with all_104_1_78, all_0_12_12, empty_set, empty_set, all_58_0_50 and discharging atoms relation_dom(empty_set) = empty_set, apply(all_0_12_12, all_58_0_50) = all_104_1_78, relation(all_0_12_12), relation(empty_set), function(all_0_12_12), function(empty_set), yields: % 21.71/5.55 | (585) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, empty_set) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_104_1_78, empty_set) | ~ in(all_58_0_50, v2) | in(all_58_0_50, v1)) & ( ~ in(all_58_0_50, v1) | (in(all_104_1_78, empty_set) & in(all_58_0_50, v2)))) % 21.71/5.55 | % 21.71/5.55 | Instantiating formula (191) with all_98_0_68, all_0_12_12, empty_set, empty_set, all_35_0_37 and discharging atoms relation_dom(empty_set) = empty_set, apply(all_0_12_12, all_35_0_37) = all_98_0_68, relation(all_0_12_12), relation(empty_set), function(all_0_12_12), function(empty_set), yields: % 21.71/5.55 | (586) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, empty_set) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_98_0_68, empty_set) | ~ in(all_35_0_37, v2) | in(all_35_0_37, v1)) & ( ~ in(all_35_0_37, v1) | (in(all_98_0_68, empty_set) & in(all_35_0_37, v2)))) % 21.71/5.55 | % 21.71/5.55 | Instantiating (572) with all_170_0_112, all_170_1_113, all_170_2_114 yields: % 21.71/5.55 | (587) relation_composition(all_0_8_8, all_0_12_12) = all_170_2_114 & relation_dom(all_170_2_114) = all_170_1_113 & relation_dom(all_0_8_8) = all_170_0_112 & ( ~ in(all_104_2_79, all_0_11_11) | ~ in(all_58_0_50, all_170_0_112) | in(all_58_0_50, all_170_1_113)) & ( ~ in(all_58_0_50, all_170_1_113) | (in(all_104_2_79, all_0_11_11) & in(all_58_0_50, all_170_0_112))) % 21.71/5.55 | % 21.71/5.55 | Applying alpha-rule on (587) yields: % 21.71/5.55 | (588) ~ in(all_104_2_79, all_0_11_11) | ~ in(all_58_0_50, all_170_0_112) | in(all_58_0_50, all_170_1_113) % 21.71/5.55 | (589) relation_dom(all_170_2_114) = all_170_1_113 % 21.71/5.55 | (590) relation_composition(all_0_8_8, all_0_12_12) = all_170_2_114 % 21.71/5.55 | (591) ~ in(all_58_0_50, all_170_1_113) | (in(all_104_2_79, all_0_11_11) & in(all_58_0_50, all_170_0_112)) % 21.71/5.55 | (592) relation_dom(all_0_8_8) = all_170_0_112 % 21.71/5.55 | % 21.71/5.55 | Instantiating (571) with all_172_0_115, all_172_1_116, all_172_2_117 yields: % 21.71/5.55 | (593) relation_composition(all_0_8_8, all_0_12_12) = all_172_2_117 & relation_dom(all_172_2_117) = all_172_1_116 & relation_dom(all_0_8_8) = all_172_0_115 & ( ~ in(all_0_7_7, all_0_11_11) | ~ in(all_0_13_13, all_172_0_115) | in(all_0_13_13, all_172_1_116)) & ( ~ in(all_0_13_13, all_172_1_116) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, all_172_0_115))) % 21.71/5.55 | % 21.71/5.55 | Applying alpha-rule on (593) yields: % 21.71/5.55 | (594) relation_dom(all_0_8_8) = all_172_0_115 % 21.71/5.55 | (595) relation_dom(all_172_2_117) = all_172_1_116 % 21.71/5.55 | (596) ~ in(all_0_13_13, all_172_1_116) | (in(all_0_7_7, all_0_11_11) & in(all_0_13_13, all_172_0_115)) % 21.71/5.55 | (597) ~ in(all_0_7_7, all_0_11_11) | ~ in(all_0_13_13, all_172_0_115) | in(all_0_13_13, all_172_1_116) % 21.71/5.55 | (598) relation_composition(all_0_8_8, all_0_12_12) = all_172_2_117 % 21.71/5.55 | % 21.71/5.55 | Instantiating (552) with all_218_0_166 yields: % 21.71/5.55 | (599) relation_dom(all_0_12_12) = all_218_0_166 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_218_0_166 | ~ subset(all_76_0_54, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_76_0_54, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & relation_dom(v2) = all_218_0_166)) % 21.71/5.55 | % 21.71/5.55 | Applying alpha-rule on (599) yields: % 21.71/5.55 | (600) relation_dom(all_0_12_12) = all_218_0_166 % 21.71/5.55 | (601) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_218_0_166 | ~ subset(all_76_0_54, v2)))) % 21.71/5.55 | (602) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_76_0_54, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & relation_dom(v2) = all_218_0_166)) % 21.71/5.55 | % 21.71/5.55 | Instantiating formula (601) with all_0_8_8, all_0_9_9 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, relation(all_0_9_9), yields: % 21.71/5.55 | (603) ? [v0] : ? [v1] : (relation_dom(all_0_8_8) = v1 & relation_dom(all_0_9_9) = v0 & (v1 = all_218_0_166 | ~ subset(all_76_0_54, v0))) % 21.71/5.55 | % 21.71/5.55 | Instantiating formula (601) with all_98_2_70, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_12_12) = all_98_2_70, relation(all_0_12_12), yields: % 21.71/5.55 | (604) ? [v0] : ? [v1] : (relation_dom(all_98_2_70) = v1 & relation_dom(all_0_12_12) = v0 & (v1 = all_218_0_166 | ~ subset(all_76_0_54, v0))) % 21.71/5.55 | % 21.71/5.55 | Instantiating (553) with all_223_0_170 yields: % 21.71/5.55 | (605) relation_dom(all_0_12_12) = all_223_0_170 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_76_0_54, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_223_0_170, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_223_0_170, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_76_0_54, v2))) % 21.71/5.55 | % 21.71/5.55 | Applying alpha-rule on (605) yields: % 21.71/5.55 | (606) relation_dom(all_0_12_12) = all_223_0_170 % 21.71/5.55 | (607) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_76_0_54, v1)) % 21.71/5.55 | (608) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_76_0_54, v2))) % 21.71/5.55 | (609) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_223_0_170, v1)) % 21.71/5.55 | (610) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_223_0_170, v2))) % 21.71/5.55 | % 21.71/5.55 | Instantiating formula (610) with all_76_0_54, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_76_0_54, subset(all_0_12_12, all_0_12_12), relation(all_0_12_12), yields: % 21.71/5.55 | (611) ? [v0] : (relation_dom(all_0_12_12) = v0 & subset(all_223_0_170, v0)) % 21.71/5.55 | % 21.71/5.55 | Instantiating (556) with all_230_0_172, all_230_1_173, all_230_2_174 yields: % 21.71/5.55 | (612) relation_dom(all_0_8_8) = all_230_2_174 & relation_dom(all_0_12_12) = all_230_1_173 & apply(all_0_12_12, all_37_0_38) = all_230_0_172 & ( ~ in(all_230_0_172, all_96_0_65) | ~ in(all_37_0_38, all_230_1_173) | in(all_37_0_38, all_230_2_174)) & ( ~ in(all_37_0_38, all_230_2_174) | (in(all_230_0_172, all_96_0_65) & in(all_37_0_38, all_230_1_173))) % 21.71/5.55 | % 21.71/5.55 | Applying alpha-rule on (612) yields: % 21.71/5.55 | (613) ~ in(all_230_0_172, all_96_0_65) | ~ in(all_37_0_38, all_230_1_173) | in(all_37_0_38, all_230_2_174) % 21.71/5.55 | (614) relation_dom(all_0_12_12) = all_230_1_173 % 21.71/5.55 | (615) apply(all_0_12_12, all_37_0_38) = all_230_0_172 % 21.71/5.55 | (616) relation_dom(all_0_8_8) = all_230_2_174 % 21.71/5.56 | (617) ~ in(all_37_0_38, all_230_2_174) | (in(all_230_0_172, all_96_0_65) & in(all_37_0_38, all_230_1_173)) % 21.71/5.56 | % 21.71/5.56 | Instantiating (560) with all_232_0_175, all_232_1_176, all_232_2_177 yields: % 21.71/5.56 | (618) relation_composition(all_0_12_12, all_0_9_9) = all_232_2_177 & relation_dom(all_232_2_177) = all_232_1_176 & apply(all_232_2_177, all_58_0_50) = all_232_0_175 & (all_232_0_175 = all_104_0_77 | ~ in(all_58_0_50, all_232_1_176)) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (618) yields: % 21.71/5.56 | (619) relation_composition(all_0_12_12, all_0_9_9) = all_232_2_177 % 21.71/5.56 | (620) relation_dom(all_232_2_177) = all_232_1_176 % 21.71/5.56 | (621) apply(all_232_2_177, all_58_0_50) = all_232_0_175 % 21.71/5.56 | (622) all_232_0_175 = all_104_0_77 | ~ in(all_58_0_50, all_232_1_176) % 21.71/5.56 | % 21.71/5.56 | Instantiating (559) with all_234_0_178, all_234_1_179, all_234_2_180 yields: % 21.71/5.56 | (623) relation_composition(all_0_12_12, all_0_9_9) = all_234_2_180 & relation_dom(all_234_2_180) = all_234_1_179 & relation_dom(all_0_12_12) = all_234_0_178 & ( ~ in(all_104_1_78, all_96_0_65) | ~ in(all_58_0_50, all_234_0_178) | in(all_58_0_50, all_234_1_179)) & ( ~ in(all_58_0_50, all_234_1_179) | (in(all_104_1_78, all_96_0_65) & in(all_58_0_50, all_234_0_178))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (623) yields: % 21.71/5.56 | (624) relation_dom(all_234_2_180) = all_234_1_179 % 21.71/5.56 | (625) relation_dom(all_0_12_12) = all_234_0_178 % 21.71/5.56 | (626) ~ in(all_104_1_78, all_96_0_65) | ~ in(all_58_0_50, all_234_0_178) | in(all_58_0_50, all_234_1_179) % 21.71/5.56 | (627) ~ in(all_58_0_50, all_234_1_179) | (in(all_104_1_78, all_96_0_65) & in(all_58_0_50, all_234_0_178)) % 21.71/5.56 | (628) relation_composition(all_0_12_12, all_0_9_9) = all_234_2_180 % 21.71/5.56 | % 21.71/5.56 | Instantiating (555) with all_236_0_181, all_236_1_182, all_236_2_183 yields: % 21.71/5.56 | (629) relation_composition(all_0_12_12, all_0_9_9) = all_236_2_183 & relation_dom(all_236_2_183) = all_236_1_182 & relation_dom(all_0_12_12) = all_236_0_181 & ( ~ in(all_0_10_10, all_96_0_65) | ~ in(all_0_13_13, all_236_0_181) | in(all_0_13_13, all_236_1_182)) & ( ~ in(all_0_13_13, all_236_1_182) | (in(all_0_10_10, all_96_0_65) & in(all_0_13_13, all_236_0_181))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (629) yields: % 21.71/5.56 | (630) ~ in(all_0_13_13, all_236_1_182) | (in(all_0_10_10, all_96_0_65) & in(all_0_13_13, all_236_0_181)) % 21.71/5.56 | (631) relation_composition(all_0_12_12, all_0_9_9) = all_236_2_183 % 21.71/5.56 | (632) relation_dom(all_236_2_183) = all_236_1_182 % 21.71/5.56 | (633) ~ in(all_0_10_10, all_96_0_65) | ~ in(all_0_13_13, all_236_0_181) | in(all_0_13_13, all_236_1_182) % 21.71/5.56 | (634) relation_dom(all_0_12_12) = all_236_0_181 % 21.71/5.56 | % 21.71/5.56 | Instantiating (558) with all_246_0_196, all_246_1_197, all_246_2_198 yields: % 21.71/5.56 | (635) relation_dom(all_0_8_8) = all_246_2_198 & apply(all_0_9_9, all_246_1_197) = all_246_0_196 & apply(all_0_12_12, all_58_0_50) = all_246_1_197 & (all_246_0_196 = all_104_2_79 | ~ in(all_58_0_50, all_246_2_198)) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (635) yields: % 21.71/5.56 | (636) relation_dom(all_0_8_8) = all_246_2_198 % 21.71/5.56 | (637) apply(all_0_9_9, all_246_1_197) = all_246_0_196 % 21.71/5.56 | (638) apply(all_0_12_12, all_58_0_50) = all_246_1_197 % 21.71/5.56 | (639) all_246_0_196 = all_104_2_79 | ~ in(all_58_0_50, all_246_2_198) % 21.71/5.56 | % 21.71/5.56 | Instantiating (557) with all_248_0_199 yields: % 21.71/5.56 | (640) relation_rng(all_0_9_9) = all_248_0_199 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_9_9, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_96_0_65 | ~ subset(all_248_0_199, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_248_0_199, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_9_9, v0) = v2 & relation_dom(v2) = all_96_0_65)) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (640) yields: % 21.71/5.56 | (641) relation_rng(all_0_9_9) = all_248_0_199 % 21.71/5.56 | (642) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_9_9, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_96_0_65 | ~ subset(all_248_0_199, v2)))) % 21.71/5.56 | (643) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_248_0_199, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_9_9, v0) = v2 & relation_dom(v2) = all_96_0_65)) % 21.71/5.56 | % 21.71/5.56 | Instantiating formula (642) with all_96_2_67, all_0_12_12 and discharging atoms relation_composition(all_0_9_9, all_0_12_12) = all_96_2_67, relation(all_0_12_12), yields: % 21.71/5.56 | (644) ? [v0] : ? [v1] : (relation_dom(all_96_2_67) = v1 & relation_dom(all_0_12_12) = v0 & (v1 = all_96_0_65 | ~ subset(all_248_0_199, v0))) % 21.71/5.56 | % 21.71/5.56 | Instantiating (581) with all_266_0_218, all_266_1_219, all_266_2_220 yields: % 21.71/5.56 | (645) relation_dom(all_140_1_101) = all_266_2_220 & relation_dom(all_0_12_12) = all_266_1_219 & apply(all_0_12_12, all_37_0_38) = all_266_0_218 & ( ~ in(all_266_0_218, empty_set) | ~ in(all_37_0_38, all_266_1_219) | in(all_37_0_38, all_266_2_220)) & ( ~ in(all_37_0_38, all_266_2_220) | (in(all_266_0_218, empty_set) & in(all_37_0_38, all_266_1_219))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (645) yields: % 21.71/5.56 | (646) apply(all_0_12_12, all_37_0_38) = all_266_0_218 % 21.71/5.56 | (647) relation_dom(all_0_12_12) = all_266_1_219 % 21.71/5.56 | (648) ~ in(all_266_0_218, empty_set) | ~ in(all_37_0_38, all_266_1_219) | in(all_37_0_38, all_266_2_220) % 21.71/5.56 | (649) ~ in(all_37_0_38, all_266_2_220) | (in(all_266_0_218, empty_set) & in(all_37_0_38, all_266_1_219)) % 21.71/5.56 | (650) relation_dom(all_140_1_101) = all_266_2_220 % 21.71/5.56 | % 21.71/5.56 | Instantiating (577) with all_272_0_226, all_272_1_227, all_272_2_228 yields: % 21.71/5.56 | (651) relation_composition(all_0_12_12, all_0_8_8) = all_272_2_228 & relation_dom(all_272_2_228) = all_272_1_227 & relation_dom(all_0_12_12) = all_272_0_226 & ( ~ in(all_104_1_78, all_100_2_73) | ~ in(all_58_0_50, all_272_0_226) | in(all_58_0_50, all_272_1_227)) & ( ~ in(all_58_0_50, all_272_1_227) | (in(all_104_1_78, all_100_2_73) & in(all_58_0_50, all_272_0_226))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (651) yields: % 21.71/5.56 | (652) relation_dom(all_272_2_228) = all_272_1_227 % 21.71/5.56 | (653) ~ in(all_104_1_78, all_100_2_73) | ~ in(all_58_0_50, all_272_0_226) | in(all_58_0_50, all_272_1_227) % 21.71/5.56 | (654) relation_composition(all_0_12_12, all_0_8_8) = all_272_2_228 % 21.71/5.56 | (655) relation_dom(all_0_12_12) = all_272_0_226 % 21.71/5.56 | (656) ~ in(all_58_0_50, all_272_1_227) | (in(all_104_1_78, all_100_2_73) & in(all_58_0_50, all_272_0_226)) % 21.71/5.56 | % 21.71/5.56 | Instantiating (551) with all_280_0_233 yields: % 21.71/5.56 | (657) relation_dom(all_0_12_12) = all_280_0_233 & relation_image(all_0_12_12, all_280_0_233) = all_76_0_54 % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (657) yields: % 21.71/5.56 | (658) relation_dom(all_0_12_12) = all_280_0_233 % 21.71/5.56 | (659) relation_image(all_0_12_12, all_280_0_233) = all_76_0_54 % 21.71/5.56 | % 21.71/5.56 | Instantiating (564) with all_290_0_242 yields: % 21.71/5.56 | (660) relation_dom(all_0_12_12) = all_290_0_242 & ( ~ (all_91_1_63 = all_0_10_10) | ~ in(all_0_13_13, all_290_0_242) | in(all_91_0_62, all_0_12_12)) & ( ~ in(all_91_0_62, all_0_12_12) | (all_91_1_63 = all_0_10_10 & in(all_0_13_13, all_290_0_242))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (660) yields: % 21.71/5.56 | (661) relation_dom(all_0_12_12) = all_290_0_242 % 21.71/5.56 | (662) ~ (all_91_1_63 = all_0_10_10) | ~ in(all_0_13_13, all_290_0_242) | in(all_91_0_62, all_0_12_12) % 21.71/5.56 | (663) ~ in(all_91_0_62, all_0_12_12) | (all_91_1_63 = all_0_10_10 & in(all_0_13_13, all_290_0_242)) % 21.71/5.56 | % 21.71/5.56 | Instantiating (574) with all_308_0_258, all_308_1_259, all_308_2_260 yields: % 21.71/5.56 | (664) relation_composition(all_0_8_8, all_0_8_8) = all_308_2_260 & relation_dom(all_308_2_260) = all_308_1_259 & relation_dom(all_0_8_8) = all_308_0_258 & ( ~ in(all_104_2_79, all_100_2_73) | ~ in(all_58_0_50, all_308_0_258) | in(all_58_0_50, all_308_1_259)) & ( ~ in(all_58_0_50, all_308_1_259) | (in(all_104_2_79, all_100_2_73) & in(all_58_0_50, all_308_0_258))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (664) yields: % 21.71/5.56 | (665) ~ in(all_104_2_79, all_100_2_73) | ~ in(all_58_0_50, all_308_0_258) | in(all_58_0_50, all_308_1_259) % 21.71/5.56 | (666) ~ in(all_58_0_50, all_308_1_259) | (in(all_104_2_79, all_100_2_73) & in(all_58_0_50, all_308_0_258)) % 21.71/5.56 | (667) relation_composition(all_0_8_8, all_0_8_8) = all_308_2_260 % 21.71/5.56 | (668) relation_dom(all_308_2_260) = all_308_1_259 % 21.71/5.56 | (669) relation_dom(all_0_8_8) = all_308_0_258 % 21.71/5.56 | % 21.71/5.56 | Instantiating (573) with all_331_0_276, all_331_1_277, all_331_2_278 yields: % 21.71/5.56 | (670) relation_composition(all_0_8_8, all_0_8_8) = all_331_2_278 & relation_dom(all_331_2_278) = all_331_1_277 & relation_dom(all_0_8_8) = all_331_0_276 & ( ~ in(all_0_7_7, all_100_2_73) | ~ in(all_0_13_13, all_331_0_276) | in(all_0_13_13, all_331_1_277)) & ( ~ in(all_0_13_13, all_331_1_277) | (in(all_0_7_7, all_100_2_73) & in(all_0_13_13, all_331_0_276))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (670) yields: % 21.71/5.56 | (671) relation_dom(all_0_8_8) = all_331_0_276 % 21.71/5.56 | (672) relation_dom(all_331_2_278) = all_331_1_277 % 21.71/5.56 | (673) relation_composition(all_0_8_8, all_0_8_8) = all_331_2_278 % 21.71/5.56 | (674) ~ in(all_0_7_7, all_100_2_73) | ~ in(all_0_13_13, all_331_0_276) | in(all_0_13_13, all_331_1_277) % 21.71/5.56 | (675) ~ in(all_0_13_13, all_331_1_277) | (in(all_0_7_7, all_100_2_73) & in(all_0_13_13, all_331_0_276)) % 21.71/5.56 | % 21.71/5.56 | Instantiating (563) with all_343_0_291 yields: % 21.71/5.56 | (676) apply(all_0_12_12, all_0_13_13) = all_343_0_291 & ( ~ (all_343_0_291 = all_91_1_63) | ~ in(all_0_13_13, all_0_11_11) | in(all_91_0_62, all_0_12_12)) & ( ~ in(all_91_0_62, all_0_12_12) | (all_343_0_291 = all_91_1_63 & in(all_0_13_13, all_0_11_11))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (676) yields: % 21.71/5.56 | (677) apply(all_0_12_12, all_0_13_13) = all_343_0_291 % 21.71/5.56 | (678) ~ (all_343_0_291 = all_91_1_63) | ~ in(all_0_13_13, all_0_11_11) | in(all_91_0_62, all_0_12_12) % 21.71/5.56 | (679) ~ in(all_91_0_62, all_0_12_12) | (all_343_0_291 = all_91_1_63 & in(all_0_13_13, all_0_11_11)) % 21.71/5.56 | % 21.71/5.56 | Instantiating (561) with all_353_0_299, all_353_1_300, all_353_2_301 yields: % 21.71/5.56 | (680) relation_composition(all_0_12_12, all_0_9_9) = all_353_2_301 & relation_dom(all_353_2_301) = all_353_1_300 & relation_dom(all_0_12_12) = all_353_0_299 & ( ~ in(all_98_0_68, all_96_0_65) | ~ in(all_35_0_37, all_353_0_299) | in(all_35_0_37, all_353_1_300)) & ( ~ in(all_35_0_37, all_353_1_300) | (in(all_98_0_68, all_96_0_65) & in(all_35_0_37, all_353_0_299))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (680) yields: % 21.71/5.56 | (681) relation_composition(all_0_12_12, all_0_9_9) = all_353_2_301 % 21.71/5.56 | (682) ~ in(all_98_0_68, all_96_0_65) | ~ in(all_35_0_37, all_353_0_299) | in(all_35_0_37, all_353_1_300) % 21.71/5.56 | (683) relation_dom(all_353_2_301) = all_353_1_300 % 21.71/5.56 | (684) ~ in(all_35_0_37, all_353_1_300) | (in(all_98_0_68, all_96_0_65) & in(all_35_0_37, all_353_0_299)) % 21.71/5.56 | (685) relation_dom(all_0_12_12) = all_353_0_299 % 21.71/5.56 | % 21.71/5.56 | Instantiating (550) with all_357_0_303 yields: % 21.71/5.56 | (686) relation_dom(all_0_9_9) = all_357_0_303 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_9_9, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_357_0_303 | ~ subset(all_81_0_56, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_81_0_56, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_9_9, v0) = v2 & relation_dom(v2) = all_357_0_303)) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (686) yields: % 21.71/5.56 | (687) relation_dom(all_0_9_9) = all_357_0_303 % 21.71/5.56 | (688) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_9_9, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_357_0_303 | ~ subset(all_81_0_56, v2)))) % 21.71/5.56 | (689) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_81_0_56, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_9_9, v0) = v2 & relation_dom(v2) = all_357_0_303)) % 21.71/5.56 | % 21.71/5.56 | Instantiating formula (688) with all_96_2_67, all_0_12_12 and discharging atoms relation_composition(all_0_9_9, all_0_12_12) = all_96_2_67, relation(all_0_12_12), yields: % 21.71/5.56 | (690) ? [v0] : ? [v1] : (relation_dom(all_96_2_67) = v1 & relation_dom(all_0_12_12) = v0 & (v1 = all_357_0_303 | ~ subset(all_81_0_56, v0))) % 21.71/5.56 | % 21.71/5.56 | Instantiating (579) with all_399_0_339, all_399_1_340, all_399_2_341 yields: % 21.71/5.56 | (691) relation_composition(all_0_8_8, all_0_9_9) = all_399_2_341 & relation_dom(all_399_2_341) = all_399_1_340 & relation_dom(all_0_8_8) = all_399_0_339 & ( ~ in(all_104_2_79, all_96_0_65) | ~ in(all_58_0_50, all_399_0_339) | in(all_58_0_50, all_399_1_340)) & ( ~ in(all_58_0_50, all_399_1_340) | (in(all_104_2_79, all_96_0_65) & in(all_58_0_50, all_399_0_339))) % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (691) yields: % 21.71/5.56 | (692) ~ in(all_58_0_50, all_399_1_340) | (in(all_104_2_79, all_96_0_65) & in(all_58_0_50, all_399_0_339)) % 21.71/5.56 | (693) ~ in(all_104_2_79, all_96_0_65) | ~ in(all_58_0_50, all_399_0_339) | in(all_58_0_50, all_399_1_340) % 21.71/5.56 | (694) relation_dom(all_0_8_8) = all_399_0_339 % 21.71/5.56 | (695) relation_dom(all_399_2_341) = all_399_1_340 % 21.71/5.56 | (696) relation_composition(all_0_8_8, all_0_9_9) = all_399_2_341 % 21.71/5.56 | % 21.71/5.56 | Instantiating (565) with all_409_0_352, all_409_1_353 yields: % 21.71/5.56 | (697) relation_inverse(all_0_8_8) = all_409_1_353 & relation_rng(all_409_1_353) = all_409_0_352 & relation_dom(all_409_1_353) = all_81_1_57 & relation_dom(all_0_8_8) = all_409_0_352 % 21.71/5.56 | % 21.71/5.56 | Applying alpha-rule on (697) yields: % 21.71/5.56 | (698) relation_inverse(all_0_8_8) = all_409_1_353 % 21.71/5.57 | (699) relation_rng(all_409_1_353) = all_409_0_352 % 21.71/5.57 | (700) relation_dom(all_409_1_353) = all_81_1_57 % 21.71/5.57 | (701) relation_dom(all_0_8_8) = all_409_0_352 % 21.71/5.57 | % 21.71/5.57 | Instantiating (570) with all_419_0_362 yields: % 21.71/5.57 | (702) relation_dom(all_0_8_8) = all_419_0_362 & ( ~ (all_419_0_362 = empty_set) | all_81_1_57 = empty_set) & ( ~ (all_81_1_57 = empty_set) | all_419_0_362 = empty_set) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (702) yields: % 21.71/5.57 | (703) relation_dom(all_0_8_8) = all_419_0_362 % 21.71/5.57 | (704) ~ (all_419_0_362 = empty_set) | all_81_1_57 = empty_set % 21.71/5.57 | (705) ~ (all_81_1_57 = empty_set) | all_419_0_362 = empty_set % 21.71/5.57 | % 21.71/5.57 | Instantiating (569) with all_423_0_365 yields: % 21.71/5.57 | (706) relation_dom(all_0_8_8) = all_423_0_365 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_8_8, v0) | ~ relation(v0) | subset(all_81_1_57, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_8_8, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_423_0_365, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_8_8, v0) | ~ relation(v0) | subset(all_423_0_365, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_8_8, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_81_1_57, v2))) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (706) yields: % 21.71/5.57 | (707) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_8_8, v0) | ~ relation(v0) | subset(all_423_0_365, v1)) % 21.71/5.57 | (708) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_8_8, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_81_1_57, v2))) % 21.71/5.57 | (709) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_8_8, v0) | ~ relation(v0) | subset(all_81_1_57, v1)) % 21.71/5.57 | (710) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_8_8, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_423_0_365, v2))) % 21.71/5.57 | (711) relation_dom(all_0_8_8) = all_423_0_365 % 21.71/5.57 | % 21.71/5.57 | Instantiating (567) with all_426_0_366 yields: % 21.71/5.57 | (712) relation_dom(all_0_8_8) = all_426_0_366 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_8_8) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_81_1_57 | ~ subset(all_426_0_366, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_426_0_366, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_8_8) = v2 & relation_rng(v2) = all_81_1_57)) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (712) yields: % 21.71/5.57 | (713) relation_dom(all_0_8_8) = all_426_0_366 % 21.71/5.57 | (714) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_8_8) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_81_1_57 | ~ subset(all_426_0_366, v2)))) % 21.71/5.57 | (715) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_426_0_366, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_8_8) = v2 & relation_rng(v2) = all_81_1_57)) % 21.71/5.57 | % 21.71/5.57 | Instantiating (568) with all_429_0_367 yields: % 21.71/5.57 | (716) relation_dom(all_0_8_8) = all_429_0_367 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_8_8, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_429_0_367 | ~ subset(all_81_1_57, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_81_1_57, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_8_8, v0) = v2 & relation_dom(v2) = all_429_0_367)) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (716) yields: % 21.71/5.57 | (717) relation_dom(all_0_8_8) = all_429_0_367 % 21.71/5.57 | (718) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_8_8, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_429_0_367 | ~ subset(all_81_1_57, v2)))) % 21.71/5.57 | (719) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_81_1_57, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_8_8, v0) = v2 & relation_dom(v2) = all_429_0_367)) % 21.71/5.57 | % 21.71/5.57 | Instantiating (580) with all_432_0_368 yields: % 21.71/5.57 | (720) relation_dom(all_0_8_8) = all_432_0_368 & ( ~ (all_91_1_63 = all_0_7_7) | ~ in(all_0_13_13, all_432_0_368) | in(all_91_0_62, all_0_8_8)) & ( ~ in(all_91_0_62, all_0_8_8) | (all_91_1_63 = all_0_7_7 & in(all_0_13_13, all_432_0_368))) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (720) yields: % 21.71/5.57 | (721) relation_dom(all_0_8_8) = all_432_0_368 % 21.71/5.57 | (722) ~ (all_91_1_63 = all_0_7_7) | ~ in(all_0_13_13, all_432_0_368) | in(all_91_0_62, all_0_8_8) % 21.71/5.57 | (723) ~ in(all_91_0_62, all_0_8_8) | (all_91_1_63 = all_0_7_7 & in(all_0_13_13, all_432_0_368)) % 21.71/5.57 | % 21.71/5.57 | Instantiating (566) with all_436_0_372 yields: % 21.71/5.57 | (724) relation_dom(all_0_8_8) = all_436_0_372 & relation_image(all_0_8_8, all_436_0_372) = all_81_1_57 % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (724) yields: % 21.71/5.57 | (725) relation_dom(all_0_8_8) = all_436_0_372 % 21.71/5.57 | (726) relation_image(all_0_8_8, all_436_0_372) = all_81_1_57 % 21.71/5.57 | % 21.71/5.57 | Instantiating (576) with all_444_0_378, all_444_1_379, all_444_2_380 yields: % 21.71/5.57 | (727) relation_composition(all_0_12_12, all_0_8_8) = all_444_2_380 & relation_dom(all_444_2_380) = all_444_1_379 & relation_dom(all_0_12_12) = all_444_0_378 & ( ~ in(all_0_10_10, all_100_2_73) | ~ in(all_0_13_13, all_444_0_378) | in(all_0_13_13, all_444_1_379)) & ( ~ in(all_0_13_13, all_444_1_379) | (in(all_0_10_10, all_100_2_73) & in(all_0_13_13, all_444_0_378))) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (727) yields: % 21.71/5.57 | (728) ~ in(all_0_10_10, all_100_2_73) | ~ in(all_0_13_13, all_444_0_378) | in(all_0_13_13, all_444_1_379) % 21.71/5.57 | (729) relation_composition(all_0_12_12, all_0_8_8) = all_444_2_380 % 21.71/5.57 | (730) relation_dom(all_0_12_12) = all_444_0_378 % 21.71/5.57 | (731) ~ in(all_0_13_13, all_444_1_379) | (in(all_0_10_10, all_100_2_73) & in(all_0_13_13, all_444_0_378)) % 21.71/5.57 | (732) relation_dom(all_444_2_380) = all_444_1_379 % 21.71/5.57 | % 21.71/5.57 | Instantiating (578) with all_450_0_387, all_450_1_388, all_450_2_389 yields: % 21.71/5.57 | (733) relation_composition(all_0_8_8, all_0_9_9) = all_450_2_389 & relation_dom(all_450_2_389) = all_450_1_388 & relation_dom(all_0_8_8) = all_450_0_387 & ( ~ in(all_0_7_7, all_96_0_65) | ~ in(all_0_13_13, all_450_0_387) | in(all_0_13_13, all_450_1_388)) & ( ~ in(all_0_13_13, all_450_1_388) | (in(all_0_7_7, all_96_0_65) & in(all_0_13_13, all_450_0_387))) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (733) yields: % 21.71/5.57 | (734) ~ in(all_0_13_13, all_450_1_388) | (in(all_0_7_7, all_96_0_65) & in(all_0_13_13, all_450_0_387)) % 21.71/5.57 | (735) relation_dom(all_0_8_8) = all_450_0_387 % 21.71/5.57 | (736) relation_composition(all_0_8_8, all_0_9_9) = all_450_2_389 % 21.71/5.57 | (737) relation_dom(all_450_2_389) = all_450_1_388 % 21.71/5.57 | (738) ~ in(all_0_7_7, all_96_0_65) | ~ in(all_0_13_13, all_450_0_387) | in(all_0_13_13, all_450_1_388) % 21.71/5.57 | % 21.71/5.57 | Instantiating (586) with all_457_0_392, all_457_1_393, all_457_2_394 yields: % 21.71/5.57 | (739) relation_composition(all_0_12_12, empty_set) = all_457_2_394 & relation_dom(all_457_2_394) = all_457_1_393 & relation_dom(all_0_12_12) = all_457_0_392 & ( ~ in(all_98_0_68, empty_set) | ~ in(all_35_0_37, all_457_0_392) | in(all_35_0_37, all_457_1_393)) & ( ~ in(all_35_0_37, all_457_1_393) | (in(all_98_0_68, empty_set) & in(all_35_0_37, all_457_0_392))) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (739) yields: % 21.71/5.57 | (740) relation_dom(all_457_2_394) = all_457_1_393 % 21.71/5.57 | (741) ~ in(all_35_0_37, all_457_1_393) | (in(all_98_0_68, empty_set) & in(all_35_0_37, all_457_0_392)) % 21.71/5.57 | (742) relation_dom(all_0_12_12) = all_457_0_392 % 21.71/5.57 | (743) relation_composition(all_0_12_12, empty_set) = all_457_2_394 % 21.71/5.57 | (744) ~ in(all_98_0_68, empty_set) | ~ in(all_35_0_37, all_457_0_392) | in(all_35_0_37, all_457_1_393) % 21.71/5.57 | % 21.71/5.57 | Instantiating (562) with all_461_0_398 yields: % 21.71/5.57 | (745) apply(all_0_12_12, all_0_13_13) = all_461_0_398 & ( ~ (all_461_0_398 = all_91_1_63) | in(all_91_0_62, all_0_12_12)) & (all_461_0_398 = all_91_1_63 | ~ in(all_91_0_62, all_0_12_12)) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (745) yields: % 21.71/5.57 | (746) apply(all_0_12_12, all_0_13_13) = all_461_0_398 % 21.71/5.57 | (747) ~ (all_461_0_398 = all_91_1_63) | in(all_91_0_62, all_0_12_12) % 21.71/5.57 | (748) all_461_0_398 = all_91_1_63 | ~ in(all_91_0_62, all_0_12_12) % 21.71/5.57 | % 21.71/5.57 | Instantiating (583) with all_463_0_399, all_463_1_400, all_463_2_401 yields: % 21.71/5.57 | (749) relation_composition(all_0_12_12, empty_set) = all_463_2_401 & relation_dom(all_463_2_401) = all_463_1_400 & relation_dom(all_0_12_12) = all_463_0_399 & ( ~ in(all_0_10_10, empty_set) | ~ in(all_0_13_13, all_463_0_399) | in(all_0_13_13, all_463_1_400)) & ( ~ in(all_0_13_13, all_463_1_400) | (in(all_0_10_10, empty_set) & in(all_0_13_13, all_463_0_399))) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (749) yields: % 21.71/5.57 | (750) ~ in(all_0_10_10, empty_set) | ~ in(all_0_13_13, all_463_0_399) | in(all_0_13_13, all_463_1_400) % 21.71/5.57 | (751) relation_dom(all_0_12_12) = all_463_0_399 % 21.71/5.57 | (752) ~ in(all_0_13_13, all_463_1_400) | (in(all_0_10_10, empty_set) & in(all_0_13_13, all_463_0_399)) % 21.71/5.57 | (753) relation_dom(all_463_2_401) = all_463_1_400 % 21.71/5.57 | (754) relation_composition(all_0_12_12, empty_set) = all_463_2_401 % 21.71/5.57 | % 21.71/5.57 | Instantiating (582) with all_469_0_409, all_469_1_410, all_469_2_411 yields: % 21.71/5.57 | (755) relation_composition(all_0_8_8, empty_set) = all_469_2_411 & relation_dom(all_469_2_411) = all_469_1_410 & relation_dom(all_0_8_8) = all_469_0_409 & ( ~ in(all_0_7_7, empty_set) | ~ in(all_0_13_13, all_469_0_409) | in(all_0_13_13, all_469_1_410)) & ( ~ in(all_0_13_13, all_469_1_410) | (in(all_0_7_7, empty_set) & in(all_0_13_13, all_469_0_409))) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (755) yields: % 21.71/5.57 | (756) ~ in(all_0_13_13, all_469_1_410) | (in(all_0_7_7, empty_set) & in(all_0_13_13, all_469_0_409)) % 21.71/5.57 | (757) ~ in(all_0_7_7, empty_set) | ~ in(all_0_13_13, all_469_0_409) | in(all_0_13_13, all_469_1_410) % 21.71/5.57 | (758) relation_dom(all_0_8_8) = all_469_0_409 % 21.71/5.57 | (759) relation_dom(all_469_2_411) = all_469_1_410 % 21.71/5.57 | (760) relation_composition(all_0_8_8, empty_set) = all_469_2_411 % 21.71/5.57 | % 21.71/5.57 | Instantiating (584) with all_471_0_412, all_471_1_413, all_471_2_414 yields: % 21.71/5.57 | (761) relation_composition(all_0_8_8, empty_set) = all_471_2_414 & relation_dom(all_471_2_414) = all_471_1_413 & relation_dom(all_0_8_8) = all_471_0_412 & ( ~ in(all_104_2_79, empty_set) | ~ in(all_58_0_50, all_471_0_412) | in(all_58_0_50, all_471_1_413)) & ( ~ in(all_58_0_50, all_471_1_413) | (in(all_104_2_79, empty_set) & in(all_58_0_50, all_471_0_412))) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (761) yields: % 21.71/5.57 | (762) relation_dom(all_471_2_414) = all_471_1_413 % 21.71/5.57 | (763) relation_composition(all_0_8_8, empty_set) = all_471_2_414 % 21.71/5.57 | (764) relation_dom(all_0_8_8) = all_471_0_412 % 21.71/5.57 | (765) ~ in(all_58_0_50, all_471_1_413) | (in(all_104_2_79, empty_set) & in(all_58_0_50, all_471_0_412)) % 21.71/5.57 | (766) ~ in(all_104_2_79, empty_set) | ~ in(all_58_0_50, all_471_0_412) | in(all_58_0_50, all_471_1_413) % 21.71/5.57 | % 21.71/5.57 | Instantiating (585) with all_473_0_415, all_473_1_416, all_473_2_417 yields: % 21.71/5.57 | (767) relation_composition(all_0_12_12, empty_set) = all_473_2_417 & relation_dom(all_473_2_417) = all_473_1_416 & relation_dom(all_0_12_12) = all_473_0_415 & ( ~ in(all_104_1_78, empty_set) | ~ in(all_58_0_50, all_473_0_415) | in(all_58_0_50, all_473_1_416)) & ( ~ in(all_58_0_50, all_473_1_416) | (in(all_104_1_78, empty_set) & in(all_58_0_50, all_473_0_415))) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (767) yields: % 21.71/5.57 | (768) relation_dom(all_473_2_417) = all_473_1_416 % 21.71/5.57 | (769) ~ in(all_104_1_78, empty_set) | ~ in(all_58_0_50, all_473_0_415) | in(all_58_0_50, all_473_1_416) % 21.71/5.57 | (770) ~ in(all_58_0_50, all_473_1_416) | (in(all_104_1_78, empty_set) & in(all_58_0_50, all_473_0_415)) % 21.71/5.57 | (771) relation_dom(all_0_12_12) = all_473_0_415 % 21.71/5.57 | (772) relation_composition(all_0_12_12, empty_set) = all_473_2_417 % 21.71/5.57 | % 21.71/5.57 | Instantiating (604) with all_481_0_422, all_481_1_423 yields: % 21.71/5.57 | (773) relation_dom(all_98_2_70) = all_481_0_422 & relation_dom(all_0_12_12) = all_481_1_423 & (all_481_0_422 = all_218_0_166 | ~ subset(all_76_0_54, all_481_1_423)) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (773) yields: % 21.71/5.57 | (774) relation_dom(all_98_2_70) = all_481_0_422 % 21.71/5.57 | (775) relation_dom(all_0_12_12) = all_481_1_423 % 21.71/5.57 | (776) all_481_0_422 = all_218_0_166 | ~ subset(all_76_0_54, all_481_1_423) % 21.71/5.57 | % 21.71/5.57 | Instantiating (603) with all_483_0_424, all_483_1_425 yields: % 21.71/5.57 | (777) relation_dom(all_0_8_8) = all_483_0_424 & relation_dom(all_0_9_9) = all_483_1_425 & (all_483_0_424 = all_218_0_166 | ~ subset(all_76_0_54, all_483_1_425)) % 21.71/5.57 | % 21.71/5.57 | Applying alpha-rule on (777) yields: % 21.71/5.57 | (778) relation_dom(all_0_8_8) = all_483_0_424 % 21.71/5.58 | (779) relation_dom(all_0_9_9) = all_483_1_425 % 21.71/5.58 | (780) all_483_0_424 = all_218_0_166 | ~ subset(all_76_0_54, all_483_1_425) % 21.71/5.58 | % 21.71/5.58 | Instantiating (611) with all_487_0_427 yields: % 21.71/5.58 | (781) relation_dom(all_0_12_12) = all_487_0_427 & subset(all_223_0_170, all_487_0_427) % 21.71/5.58 | % 21.71/5.58 | Applying alpha-rule on (781) yields: % 21.71/5.58 | (782) relation_dom(all_0_12_12) = all_487_0_427 % 21.71/5.58 | (783) subset(all_223_0_170, all_487_0_427) % 21.71/5.58 | % 21.71/5.58 | Instantiating (644) with all_495_0_434, all_495_1_435 yields: % 21.71/5.58 | (784) relation_dom(all_96_2_67) = all_495_0_434 & relation_dom(all_0_12_12) = all_495_1_435 & (all_495_0_434 = all_96_0_65 | ~ subset(all_248_0_199, all_495_1_435)) % 21.71/5.58 | % 21.71/5.58 | Applying alpha-rule on (784) yields: % 21.71/5.58 | (785) relation_dom(all_96_2_67) = all_495_0_434 % 21.71/5.58 | (786) relation_dom(all_0_12_12) = all_495_1_435 % 21.71/5.58 | (787) all_495_0_434 = all_96_0_65 | ~ subset(all_248_0_199, all_495_1_435) % 21.71/5.58 | % 21.71/5.58 | Instantiating (690) with all_505_0_442, all_505_1_443 yields: % 21.71/5.58 | (788) relation_dom(all_96_2_67) = all_505_0_442 & relation_dom(all_0_12_12) = all_505_1_443 & (all_505_0_442 = all_357_0_303 | ~ subset(all_81_0_56, all_505_1_443)) % 21.71/5.58 | % 21.71/5.58 | Applying alpha-rule on (788) yields: % 21.71/5.58 | (789) relation_dom(all_96_2_67) = all_505_0_442 % 21.71/5.58 | (790) relation_dom(all_0_12_12) = all_505_1_443 % 21.71/5.58 | (791) all_505_0_442 = all_357_0_303 | ~ subset(all_81_0_56, all_505_1_443) % 21.71/5.58 | % 21.71/5.58 | Equations (575) can reduce 275 to: % 21.71/5.58 | (792) ~ (all_0_6_6 = empty_set) % 21.71/5.58 | % 21.71/5.58 +-Applying beta-rule and splitting (748), into two cases. % 21.71/5.58 |-Branch one: % 21.71/5.58 | (793) ~ in(all_91_0_62, all_0_12_12) % 21.71/5.58 | % 21.71/5.58 | Using (430) and (793) yields: % 21.71/5.58 | (794) $false % 21.71/5.58 | % 21.71/5.58 |-The branch is then unsatisfiable % 21.71/5.58 |-Branch two: % 21.71/5.58 | (430) in(all_91_0_62, all_0_12_12) % 21.71/5.58 | (796) all_461_0_398 = all_91_1_63 % 21.71/5.58 | % 21.71/5.58 +-Applying beta-rule and splitting (679), into two cases. % 21.71/5.58 |-Branch one: % 21.71/5.58 | (793) ~ in(all_91_0_62, all_0_12_12) % 21.71/5.58 | % 21.71/5.58 | Using (430) and (793) yields: % 21.71/5.58 | (794) $false % 21.71/5.58 | % 21.71/5.58 |-The branch is then unsatisfiable % 21.71/5.58 |-Branch two: % 21.71/5.58 | (430) in(all_91_0_62, all_0_12_12) % 21.71/5.58 | (800) all_343_0_291 = all_91_1_63 & in(all_0_13_13, all_0_11_11) % 21.71/5.58 | % 21.71/5.58 +-Applying beta-rule and splitting (554), into two cases. % 21.71/5.58 |-Branch one: % 21.71/5.58 | (801) in(all_0_10_10, all_96_0_65) % 21.71/5.58 | % 21.71/5.58 +-Applying beta-rule and splitting (663), into two cases. % 21.71/5.58 |-Branch one: % 21.71/5.58 | (793) ~ in(all_91_0_62, all_0_12_12) % 21.71/5.58 | % 21.71/5.58 | Using (430) and (793) yields: % 21.71/5.58 | (794) $false % 21.71/5.58 | % 21.71/5.58 |-The branch is then unsatisfiable % 21.71/5.58 |-Branch two: % 21.71/5.58 | (430) in(all_91_0_62, all_0_12_12) % 21.71/5.58 | (805) all_91_1_63 = all_0_10_10 & in(all_0_13_13, all_290_0_242) % 21.71/5.58 | % 21.71/5.58 | Applying alpha-rule on (805) yields: % 21.71/5.58 | (806) all_91_1_63 = all_0_10_10 % 21.71/5.58 | (807) in(all_0_13_13, all_290_0_242) % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (338) with all_0_12_12, all_0_9_9, all_236_2_183, all_353_2_301 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_353_2_301, relation_composition(all_0_12_12, all_0_9_9) = all_236_2_183, yields: % 21.71/5.58 | (808) all_353_2_301 = all_236_2_183 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (338) with all_0_12_12, all_0_9_9, all_234_2_180, all_0_8_8 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_234_2_180, relation_composition(all_0_12_12, all_0_9_9) = all_0_8_8, yields: % 21.71/5.58 | (809) all_234_2_180 = all_0_8_8 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (338) with all_0_12_12, all_0_9_9, all_234_2_180, all_353_2_301 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_353_2_301, relation_composition(all_0_12_12, all_0_9_9) = all_234_2_180, yields: % 21.71/5.58 | (810) all_353_2_301 = all_234_2_180 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (338) with all_0_12_12, all_0_9_9, all_232_2_177, all_353_2_301 and discharging atoms relation_composition(all_0_12_12, all_0_9_9) = all_353_2_301, relation_composition(all_0_12_12, all_0_9_9) = all_232_2_177, yields: % 21.71/5.58 | (811) all_353_2_301 = all_232_2_177 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_471_0_412, all_483_0_424 and discharging atoms relation_dom(all_0_8_8) = all_483_0_424, relation_dom(all_0_8_8) = all_471_0_412, yields: % 21.71/5.58 | (812) all_483_0_424 = all_471_0_412 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_469_0_409, all_471_0_412 and discharging atoms relation_dom(all_0_8_8) = all_471_0_412, relation_dom(all_0_8_8) = all_469_0_409, yields: % 21.71/5.58 | (813) all_471_0_412 = all_469_0_409 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_450_0_387, all_469_0_409 and discharging atoms relation_dom(all_0_8_8) = all_469_0_409, relation_dom(all_0_8_8) = all_450_0_387, yields: % 21.71/5.58 | (814) all_469_0_409 = all_450_0_387 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_436_0_372, all_450_0_387 and discharging atoms relation_dom(all_0_8_8) = all_450_0_387, relation_dom(all_0_8_8) = all_436_0_372, yields: % 21.71/5.58 | (815) all_450_0_387 = all_436_0_372 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_429_0_367, all_436_0_372 and discharging atoms relation_dom(all_0_8_8) = all_436_0_372, relation_dom(all_0_8_8) = all_429_0_367, yields: % 21.71/5.58 | (816) all_436_0_372 = all_429_0_367 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_426_0_366, all_432_0_368 and discharging atoms relation_dom(all_0_8_8) = all_432_0_368, relation_dom(all_0_8_8) = all_426_0_366, yields: % 21.71/5.58 | (817) all_432_0_368 = all_426_0_366 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_426_0_366, all_429_0_367 and discharging atoms relation_dom(all_0_8_8) = all_429_0_367, relation_dom(all_0_8_8) = all_426_0_366, yields: % 21.71/5.58 | (818) all_429_0_367 = all_426_0_366 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_423_0_365, all_432_0_368 and discharging atoms relation_dom(all_0_8_8) = all_432_0_368, relation_dom(all_0_8_8) = all_423_0_365, yields: % 21.71/5.58 | (819) all_432_0_368 = all_423_0_365 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_419_0_362, all_483_0_424 and discharging atoms relation_dom(all_0_8_8) = all_483_0_424, relation_dom(all_0_8_8) = all_419_0_362, yields: % 21.71/5.58 | (820) all_483_0_424 = all_419_0_362 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_399_0_339, all_409_0_352 and discharging atoms relation_dom(all_0_8_8) = all_409_0_352, relation_dom(all_0_8_8) = all_399_0_339, yields: % 21.71/5.58 | (821) all_409_0_352 = all_399_0_339 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_331_0_276, all_426_0_366 and discharging atoms relation_dom(all_0_8_8) = all_426_0_366, relation_dom(all_0_8_8) = all_331_0_276, yields: % 21.71/5.58 | (822) all_426_0_366 = all_331_0_276 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_331_0_276, all_409_0_352 and discharging atoms relation_dom(all_0_8_8) = all_409_0_352, relation_dom(all_0_8_8) = all_331_0_276, yields: % 21.71/5.58 | (823) all_409_0_352 = all_331_0_276 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_308_0_258, all_331_0_276 and discharging atoms relation_dom(all_0_8_8) = all_331_0_276, relation_dom(all_0_8_8) = all_308_0_258, yields: % 21.71/5.58 | (824) all_331_0_276 = all_308_0_258 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_246_2_198, all_426_0_366 and discharging atoms relation_dom(all_0_8_8) = all_426_0_366, relation_dom(all_0_8_8) = all_246_2_198, yields: % 21.71/5.58 | (825) all_426_0_366 = all_246_2_198 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_230_2_174, all_331_0_276 and discharging atoms relation_dom(all_0_8_8) = all_331_0_276, relation_dom(all_0_8_8) = all_230_2_174, yields: % 21.71/5.58 | (826) all_331_0_276 = all_230_2_174 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_172_0_115, all_100_2_73 and discharging atoms relation_dom(all_0_8_8) = all_172_0_115, relation_dom(all_0_8_8) = all_100_2_73, yields: % 21.71/5.58 | (827) all_172_0_115 = all_100_2_73 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_172_0_115, all_230_2_174 and discharging atoms relation_dom(all_0_8_8) = all_230_2_174, relation_dom(all_0_8_8) = all_172_0_115, yields: % 21.71/5.58 | (828) all_230_2_174 = all_172_0_115 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_8_8, all_170_0_112, all_409_0_352 and discharging atoms relation_dom(all_0_8_8) = all_409_0_352, relation_dom(all_0_8_8) = all_170_0_112, yields: % 21.71/5.58 | (829) all_409_0_352 = all_170_0_112 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_495_1_435, all_0_11_11 and discharging atoms relation_dom(all_0_12_12) = all_495_1_435, relation_dom(all_0_12_12) = all_0_11_11, yields: % 21.71/5.58 | (830) all_495_1_435 = all_0_11_11 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_495_1_435, all_505_1_443 and discharging atoms relation_dom(all_0_12_12) = all_505_1_443, relation_dom(all_0_12_12) = all_495_1_435, yields: % 21.71/5.58 | (831) all_505_1_443 = all_495_1_435 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_481_1_423, all_487_0_427 and discharging atoms relation_dom(all_0_12_12) = all_487_0_427, relation_dom(all_0_12_12) = all_481_1_423, yields: % 21.71/5.58 | (832) all_487_0_427 = all_481_1_423 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_473_0_415, all_481_1_423 and discharging atoms relation_dom(all_0_12_12) = all_481_1_423, relation_dom(all_0_12_12) = all_473_0_415, yields: % 21.71/5.58 | (833) all_481_1_423 = all_473_0_415 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_463_0_399, all_505_1_443 and discharging atoms relation_dom(all_0_12_12) = all_505_1_443, relation_dom(all_0_12_12) = all_463_0_399, yields: % 21.71/5.58 | (834) all_505_1_443 = all_463_0_399 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_444_0_378, all_457_0_392 and discharging atoms relation_dom(all_0_12_12) = all_457_0_392, relation_dom(all_0_12_12) = all_444_0_378, yields: % 21.71/5.58 | (835) all_457_0_392 = all_444_0_378 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_353_0_299, all_495_1_435 and discharging atoms relation_dom(all_0_12_12) = all_495_1_435, relation_dom(all_0_12_12) = all_353_0_299, yields: % 21.71/5.58 | (836) all_495_1_435 = all_353_0_299 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_353_0_299, all_473_0_415 and discharging atoms relation_dom(all_0_12_12) = all_473_0_415, relation_dom(all_0_12_12) = all_353_0_299, yields: % 21.71/5.58 | (837) all_473_0_415 = all_353_0_299 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_353_0_299, all_457_0_392 and discharging atoms relation_dom(all_0_12_12) = all_457_0_392, relation_dom(all_0_12_12) = all_353_0_299, yields: % 21.71/5.58 | (838) all_457_0_392 = all_353_0_299 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_290_0_242, all_487_0_427 and discharging atoms relation_dom(all_0_12_12) = all_487_0_427, relation_dom(all_0_12_12) = all_290_0_242, yields: % 21.71/5.58 | (839) all_487_0_427 = all_290_0_242 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_280_0_233, all_495_1_435 and discharging atoms relation_dom(all_0_12_12) = all_495_1_435, relation_dom(all_0_12_12) = all_280_0_233, yields: % 21.71/5.58 | (840) all_495_1_435 = all_280_0_233 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_272_0_226, all_457_0_392 and discharging atoms relation_dom(all_0_12_12) = all_457_0_392, relation_dom(all_0_12_12) = all_272_0_226, yields: % 21.71/5.58 | (841) all_457_0_392 = all_272_0_226 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_266_1_219, all_495_1_435 and discharging atoms relation_dom(all_0_12_12) = all_495_1_435, relation_dom(all_0_12_12) = all_266_1_219, yields: % 21.71/5.58 | (842) all_495_1_435 = all_266_1_219 % 21.71/5.58 | % 21.71/5.58 | Instantiating formula (146) with all_0_12_12, all_236_0_181, all_266_1_219 and discharging atoms relation_dom(all_0_12_12) = all_266_1_219, relation_dom(all_0_12_12) = all_236_0_181, yields: % 21.71/5.58 | (843) all_266_1_219 = all_236_0_181 % 21.71/5.58 | % 21.71/5.58 | Combining equations (831,834) yields a new equation: % 21.71/5.58 | (844) all_495_1_435 = all_463_0_399 % 21.71/5.58 | % 21.71/5.58 | Simplifying 844 yields: % 21.71/5.58 | (845) all_495_1_435 = all_463_0_399 % 21.71/5.58 | % 21.71/5.58 | Combining equations (836,845) yields a new equation: % 21.71/5.58 | (846) all_463_0_399 = all_353_0_299 % 21.71/5.58 | % 21.71/5.58 | Combining equations (840,845) yields a new equation: % 21.71/5.58 | (847) all_463_0_399 = all_280_0_233 % 21.71/5.58 | % 21.71/5.58 | Combining equations (830,845) yields a new equation: % 21.71/5.58 | (848) all_463_0_399 = all_0_11_11 % 21.71/5.58 | % 21.71/5.58 | Combining equations (842,845) yields a new equation: % 21.71/5.58 | (849) all_463_0_399 = all_266_1_219 % 21.71/5.58 | % 21.71/5.58 | Combining equations (832,839) yields a new equation: % 21.71/5.58 | (850) all_481_1_423 = all_290_0_242 % 21.71/5.58 | % 21.71/5.58 | Simplifying 850 yields: % 21.71/5.58 | (851) all_481_1_423 = all_290_0_242 % 21.71/5.58 | % 21.71/5.58 | Combining equations (812,820) yields a new equation: % 21.71/5.58 | (852) all_471_0_412 = all_419_0_362 % 21.71/5.58 | % 21.71/5.58 | Simplifying 852 yields: % 21.71/5.58 | (853) all_471_0_412 = all_419_0_362 % 21.71/5.58 | % 21.71/5.58 | Combining equations (833,851) yields a new equation: % 21.71/5.58 | (854) all_473_0_415 = all_290_0_242 % 21.71/5.58 | % 21.71/5.58 | Simplifying 854 yields: % 21.71/5.58 | (855) all_473_0_415 = all_290_0_242 % 21.71/5.58 | % 21.71/5.58 | Combining equations (837,855) yields a new equation: % 21.71/5.58 | (856) all_353_0_299 = all_290_0_242 % 21.71/5.58 | % 21.71/5.58 | Simplifying 856 yields: % 21.71/5.59 | (857) all_353_0_299 = all_290_0_242 % 21.71/5.59 | % 21.71/5.59 | Combining equations (813,853) yields a new equation: % 21.71/5.59 | (858) all_469_0_409 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Simplifying 858 yields: % 21.71/5.59 | (859) all_469_0_409 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Combining equations (814,859) yields a new equation: % 21.71/5.59 | (860) all_450_0_387 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Simplifying 860 yields: % 21.71/5.59 | (861) all_450_0_387 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Combining equations (846,847) yields a new equation: % 21.71/5.59 | (862) all_353_0_299 = all_280_0_233 % 21.71/5.59 | % 21.71/5.59 | Simplifying 862 yields: % 21.71/5.59 | (863) all_353_0_299 = all_280_0_233 % 21.71/5.59 | % 21.71/5.59 | Combining equations (848,847) yields a new equation: % 21.71/5.59 | (864) all_280_0_233 = all_0_11_11 % 21.71/5.59 | % 21.71/5.59 | Combining equations (849,847) yields a new equation: % 21.71/5.59 | (865) all_280_0_233 = all_266_1_219 % 21.71/5.59 | % 21.71/5.59 | Combining equations (838,835) yields a new equation: % 21.71/5.59 | (866) all_444_0_378 = all_353_0_299 % 21.71/5.59 | % 21.71/5.59 | Combining equations (841,835) yields a new equation: % 21.71/5.59 | (867) all_444_0_378 = all_272_0_226 % 21.71/5.59 | % 21.71/5.59 | Combining equations (815,861) yields a new equation: % 21.71/5.59 | (868) all_436_0_372 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Simplifying 868 yields: % 21.71/5.59 | (869) all_436_0_372 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Combining equations (866,867) yields a new equation: % 21.71/5.59 | (870) all_353_0_299 = all_272_0_226 % 21.71/5.59 | % 21.71/5.59 | Simplifying 870 yields: % 21.71/5.59 | (871) all_353_0_299 = all_272_0_226 % 21.71/5.59 | % 21.71/5.59 | Combining equations (816,869) yields a new equation: % 21.71/5.59 | (872) all_429_0_367 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Simplifying 872 yields: % 21.71/5.59 | (873) all_429_0_367 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Combining equations (817,819) yields a new equation: % 21.71/5.59 | (874) all_426_0_366 = all_423_0_365 % 21.71/5.59 | % 21.71/5.59 | Simplifying 874 yields: % 21.71/5.59 | (875) all_426_0_366 = all_423_0_365 % 21.71/5.59 | % 21.71/5.59 | Combining equations (818,873) yields a new equation: % 21.71/5.59 | (876) all_426_0_366 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Simplifying 876 yields: % 21.71/5.59 | (877) all_426_0_366 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Combining equations (825,875) yields a new equation: % 21.71/5.59 | (878) all_423_0_365 = all_246_2_198 % 21.71/5.59 | % 21.71/5.59 | Combining equations (822,875) yields a new equation: % 21.71/5.59 | (879) all_423_0_365 = all_331_0_276 % 21.71/5.59 | % 21.71/5.59 | Combining equations (877,875) yields a new equation: % 21.71/5.59 | (880) all_423_0_365 = all_419_0_362 % 21.71/5.59 | % 21.71/5.59 | Combining equations (878,880) yields a new equation: % 21.71/5.59 | (881) all_419_0_362 = all_246_2_198 % 21.71/5.59 | % 21.71/5.59 | Combining equations (879,880) yields a new equation: % 21.71/5.59 | (882) all_419_0_362 = all_331_0_276 % 21.71/5.59 | % 21.71/5.59 | Combining equations (882,881) yields a new equation: % 21.71/5.59 | (883) all_331_0_276 = all_246_2_198 % 21.71/5.59 | % 21.71/5.59 | Simplifying 883 yields: % 21.71/5.59 | (884) all_331_0_276 = all_246_2_198 % 21.71/5.59 | % 21.71/5.59 | Combining equations (823,821) yields a new equation: % 21.71/5.59 | (885) all_399_0_339 = all_331_0_276 % 21.71/5.59 | % 21.71/5.59 | Combining equations (829,821) yields a new equation: % 21.71/5.59 | (886) all_399_0_339 = all_170_0_112 % 21.71/5.59 | % 21.71/5.59 | Combining equations (885,886) yields a new equation: % 21.71/5.59 | (887) all_331_0_276 = all_170_0_112 % 21.71/5.59 | % 21.71/5.59 | Simplifying 887 yields: % 21.71/5.59 | (888) all_331_0_276 = all_170_0_112 % 21.71/5.59 | % 21.71/5.59 | Combining equations (871,857) yields a new equation: % 21.71/5.59 | (889) all_290_0_242 = all_272_0_226 % 21.71/5.59 | % 21.71/5.59 | Combining equations (863,857) yields a new equation: % 21.71/5.59 | (890) all_290_0_242 = all_280_0_233 % 21.71/5.59 | % 21.71/5.59 | Combining equations (811,808) yields a new equation: % 21.71/5.59 | (891) all_236_2_183 = all_232_2_177 % 21.71/5.59 | % 21.71/5.59 | Combining equations (810,808) yields a new equation: % 21.71/5.59 | (892) all_236_2_183 = all_234_2_180 % 21.71/5.59 | % 21.71/5.59 | Combining equations (826,824) yields a new equation: % 21.71/5.59 | (893) all_308_0_258 = all_230_2_174 % 21.71/5.59 | % 21.71/5.59 | Combining equations (888,824) yields a new equation: % 21.71/5.59 | (894) all_308_0_258 = all_170_0_112 % 21.71/5.59 | % 21.71/5.59 | Combining equations (884,824) yields a new equation: % 21.71/5.59 | (895) all_308_0_258 = all_246_2_198 % 21.71/5.59 | % 21.71/5.59 | Combining equations (893,895) yields a new equation: % 21.71/5.59 | (896) all_246_2_198 = all_230_2_174 % 21.71/5.59 | % 21.71/5.59 | Combining equations (894,895) yields a new equation: % 21.71/5.59 | (897) all_246_2_198 = all_170_0_112 % 21.71/5.59 | % 21.71/5.59 | Combining equations (890,889) yields a new equation: % 21.71/5.59 | (898) all_280_0_233 = all_272_0_226 % 21.71/5.59 | % 21.71/5.59 | Simplifying 898 yields: % 21.71/5.59 | (899) all_280_0_233 = all_272_0_226 % 21.71/5.59 | % 21.71/5.59 | Combining equations (864,899) yields a new equation: % 21.71/5.59 | (900) all_272_0_226 = all_0_11_11 % 21.71/5.59 | % 21.71/5.59 | Combining equations (865,899) yields a new equation: % 21.71/5.59 | (901) all_272_0_226 = all_266_1_219 % 21.71/5.59 | % 21.71/5.59 | Combining equations (901,900) yields a new equation: % 21.71/5.59 | (902) all_266_1_219 = all_0_11_11 % 21.71/5.59 | % 21.71/5.59 | Simplifying 902 yields: % 21.71/5.59 | (903) all_266_1_219 = all_0_11_11 % 21.71/5.59 | % 21.71/5.59 | Combining equations (843,903) yields a new equation: % 21.71/5.59 | (904) all_236_0_181 = all_0_11_11 % 21.71/5.59 | % 21.71/5.59 | Simplifying 904 yields: % 21.71/5.59 | (905) all_236_0_181 = all_0_11_11 % 21.71/5.59 | % 21.71/5.59 | Combining equations (896,897) yields a new equation: % 21.71/5.59 | (906) all_230_2_174 = all_170_0_112 % 21.71/5.59 | % 21.71/5.59 | Simplifying 906 yields: % 21.71/5.59 | (907) all_230_2_174 = all_170_0_112 % 21.71/5.59 | % 21.71/5.59 | Combining equations (892,891) yields a new equation: % 21.71/5.59 | (908) all_234_2_180 = all_232_2_177 % 21.71/5.59 | % 21.71/5.59 | Simplifying 908 yields: % 21.71/5.59 | (909) all_234_2_180 = all_232_2_177 % 21.71/5.59 | % 21.71/5.59 | Combining equations (909,809) yields a new equation: % 21.71/5.59 | (910) all_232_2_177 = all_0_8_8 % 21.71/5.59 | % 21.71/5.59 | Simplifying 910 yields: % 21.71/5.59 | (911) all_232_2_177 = all_0_8_8 % 21.71/5.59 | % 21.71/5.59 | Combining equations (828,907) yields a new equation: % 21.71/5.59 | (912) all_172_0_115 = all_170_0_112 % 21.71/5.59 | % 21.71/5.59 | Simplifying 912 yields: % 21.71/5.59 | (913) all_172_0_115 = all_170_0_112 % 21.71/5.59 | % 21.71/5.59 | Combining equations (913,827) yields a new equation: % 21.71/5.59 | (914) all_170_0_112 = all_100_2_73 % 21.71/5.59 | % 21.71/5.59 | Simplifying 914 yields: % 21.71/5.59 | (915) all_170_0_112 = all_100_2_73 % 21.71/5.59 | % 21.71/5.59 | Combining equations (911,891) yields a new equation: % 21.71/5.59 | (916) all_236_2_183 = all_0_8_8 % 21.71/5.59 | % 21.71/5.59 | Combining equations (900,889) yields a new equation: % 21.71/5.59 | (917) all_290_0_242 = all_0_11_11 % 21.71/5.59 | % 21.71/5.59 | Combining equations (916,808) yields a new equation: % 21.71/5.59 | (918) all_353_2_301 = all_0_8_8 % 21.71/5.59 | % 21.71/5.59 | From (918) and (683) follows: % 21.71/5.59 | (919) relation_dom(all_0_8_8) = all_353_1_300 % 21.71/5.59 | % 21.71/5.59 | From (916) and (632) follows: % 21.71/5.59 | (920) relation_dom(all_0_8_8) = all_236_1_182 % 21.71/5.59 | % 21.71/5.59 | From (809) and (624) follows: % 21.71/5.59 | (921) relation_dom(all_0_8_8) = all_234_1_179 % 21.71/5.59 | % 21.71/5.59 | From (911) and (620) follows: % 21.71/5.59 | (922) relation_dom(all_0_8_8) = all_232_1_176 % 21.71/5.59 | % 21.71/5.59 | From (915) and (592) follows: % 21.71/5.59 | (444) relation_dom(all_0_8_8) = all_100_2_73 % 21.71/5.59 | % 21.71/5.59 | From (917) and (807) follows: % 21.71/5.59 | (78) in(all_0_13_13, all_0_11_11) % 21.71/5.59 | % 21.71/5.59 +-Applying beta-rule and splitting (633), into two cases. % 21.71/5.59 |-Branch one: % 21.71/5.59 | (925) ~ in(all_0_10_10, all_96_0_65) % 21.71/5.59 | % 21.71/5.59 | Using (801) and (925) yields: % 21.71/5.59 | (794) $false % 21.71/5.59 | % 21.71/5.59 |-The branch is then unsatisfiable % 21.71/5.59 |-Branch two: % 21.71/5.59 | (801) in(all_0_10_10, all_96_0_65) % 21.71/5.59 | (928) ~ in(all_0_13_13, all_236_0_181) | in(all_0_13_13, all_236_1_182) % 21.71/5.59 | % 21.71/5.59 +-Applying beta-rule and splitting (928), into two cases. % 21.71/5.59 |-Branch one: % 21.71/5.59 | (929) ~ in(all_0_13_13, all_236_0_181) % 21.71/5.59 | % 21.71/5.59 | From (905) and (929) follows: % 21.71/5.59 | (930) ~ in(all_0_13_13, all_0_11_11) % 21.71/5.59 | % 21.71/5.59 | Using (78) and (930) yields: % 21.71/5.59 | (794) $false % 21.71/5.59 | % 21.71/5.59 |-The branch is then unsatisfiable % 21.71/5.59 |-Branch two: % 21.71/5.59 | (932) in(all_0_13_13, all_236_0_181) % 21.71/5.59 | (933) in(all_0_13_13, all_236_1_182) % 21.71/5.59 | % 21.71/5.59 | Instantiating formula (146) with all_0_8_8, all_236_1_182, all_353_1_300 and discharging atoms relation_dom(all_0_8_8) = all_353_1_300, relation_dom(all_0_8_8) = all_236_1_182, yields: % 21.71/5.59 | (934) all_353_1_300 = all_236_1_182 % 21.71/5.59 | % 21.71/5.59 | Instantiating formula (146) with all_0_8_8, all_234_1_179, all_100_2_73 and discharging atoms relation_dom(all_0_8_8) = all_234_1_179, relation_dom(all_0_8_8) = all_100_2_73, yields: % 21.71/5.59 | (935) all_234_1_179 = all_100_2_73 % 21.71/5.59 | % 21.71/5.59 | Instantiating formula (146) with all_0_8_8, all_234_1_179, all_353_1_300 and discharging atoms relation_dom(all_0_8_8) = all_353_1_300, relation_dom(all_0_8_8) = all_234_1_179, yields: % 21.71/5.59 | (936) all_353_1_300 = all_234_1_179 % 21.71/5.59 | % 21.71/5.59 | Instantiating formula (146) with all_0_8_8, all_232_1_176, all_353_1_300 and discharging atoms relation_dom(all_0_8_8) = all_353_1_300, relation_dom(all_0_8_8) = all_232_1_176, yields: % 21.71/5.59 | (937) all_353_1_300 = all_232_1_176 % 21.71/5.59 | % 21.71/5.59 | Combining equations (937,934) yields a new equation: % 21.71/5.59 | (938) all_236_1_182 = all_232_1_176 % 21.71/5.59 | % 21.71/5.59 | Combining equations (936,934) yields a new equation: % 21.71/5.59 | (939) all_236_1_182 = all_234_1_179 % 21.71/5.59 | % 21.71/5.59 | Combining equations (939,938) yields a new equation: % 21.71/5.59 | (940) all_234_1_179 = all_232_1_176 % 21.71/5.59 | % 21.71/5.59 | Simplifying 940 yields: % 21.71/5.59 | (941) all_234_1_179 = all_232_1_176 % 21.71/5.59 | % 21.71/5.59 | Combining equations (935,941) yields a new equation: % 21.71/5.59 | (942) all_232_1_176 = all_100_2_73 % 21.71/5.59 | % 21.71/5.59 | Combining equations (942,938) yields a new equation: % 21.71/5.59 | (943) all_236_1_182 = all_100_2_73 % 21.71/5.59 | % 21.71/5.59 | From (943) and (933) follows: % 21.71/5.59 | (944) in(all_0_13_13, all_100_2_73) % 21.71/5.59 | % 21.71/5.59 | Using (944) and (549) yields: % 21.71/5.59 | (794) $false % 21.71/5.59 | % 21.71/5.59 |-The branch is then unsatisfiable % 21.71/5.59 |-Branch two: % 21.71/5.59 | (925) ~ in(all_0_10_10, all_96_0_65) % 21.71/5.59 | (947) all_0_6_6 = empty_set % 21.71/5.59 | % 21.71/5.59 | Equations (947) can reduce 792 to: % 21.71/5.59 | (948) $false % 21.71/5.59 | % 21.71/5.59 |-The branch is then unsatisfiable % 21.71/5.59 |-Branch two: % 21.71/5.59 | (944) in(all_0_13_13, all_100_2_73) % 21.71/5.59 | (950) all_100_0_71 = all_0_7_7 % 21.71/5.59 | % 21.71/5.59 | Combining equations (545,950) yields a new equation: % 21.71/5.59 | (951) all_0_6_6 = all_0_7_7 % 21.71/5.59 | % 21.71/5.59 | Simplifying 951 yields: % 21.71/5.59 | (952) all_0_6_6 = all_0_7_7 % 21.71/5.59 | % 21.71/5.59 | Equations (952) can reduce 275 to: % 21.71/5.59 | (948) $false % 21.71/5.59 | % 21.71/5.59 |-The branch is then unsatisfiable % 21.71/5.59 % SZS output end Proof for theBenchmark % 21.71/5.60 % 21.71/5.60 4983ms %------------------------------------------------------------------------------