%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU189+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 08:47:28 EDT 2022 % Result : Theorem 11.92s 3.28s % Output : Proof 17.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SEU189+2 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.32 % Computer : n027.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Sun Jun 19 12:32:54 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.69/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.33/1.06 Prover 0: Preprocessing ... % 5.36/1.76 Prover 0: Warning: ignoring some quantifiers % 5.91/1.80 Prover 0: Constructing countermodel ... % 11.92/3.28 Prover 0: proved (2657ms) % 11.92/3.28 % 11.92/3.28 No countermodel exists, formula is valid % 11.92/3.28 % SZS status Theorem for theBenchmark % 11.92/3.28 % 11.92/3.28 Generating proof ... Warning: ignoring some quantifiers % 15.89/4.15 found it (size 202) % 15.89/4.15 % 15.89/4.15 % SZS output start Proof for theBenchmark % 15.89/4.15 Assumed formulas after preprocessing and simplification: % 15.89/4.15 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_rng(v1) = v3 & relation_rng(empty_set) = empty_set & relation_dom(v1) = v2 & relation_dom(empty_set) = empty_set & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation(v7) & relation(v5) & relation(v1) & relation(empty_set) & empty(v7) & empty(v6) & empty(empty_set) & ~ empty(v5) & ~ empty(v4) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v8, v9) = v10) | ~ (ordered_pair(v14, v12) = v15) | ~ (ordered_pair(v11, v12) = v13) | ~ relation(v10) | ~ relation(v9) | ~ relation(v8) | ~ in(v15, v9) | in(v13, v10) | ? [v16] : (ordered_pair(v11, v14) = v16 & ~ in(v16, v8))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v8, v9) = v10) | ~ (ordered_pair(v11, v14) = v15) | ~ (ordered_pair(v11, v12) = v13) | ~ relation(v10) | ~ relation(v9) | ~ relation(v8) | ~ in(v15, v8) | in(v13, v10) | ? [v16] : (ordered_pair(v14, v12) = v16 & ~ in(v16, v9))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v8, v9) = v10) | ~ (ordered_pair(v11, v12) = v13) | ~ relation(v10) | ~ relation(v9) | ~ relation(v8) | ~ in(v13, v10) | ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v12) = v16 & ordered_pair(v11, v14) = v15 & in(v16, v9) & in(v15, v8))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ in(v12, v13) | in(v9, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ in(v12, v13) | in(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ in(v9, v11) | ~ in(v8, v10) | in(v12, v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v9, v11) = v13) | ~ (cartesian_product2(v8, v10) = v12) | ~ subset(v10, v11) | ~ subset(v8, v9) | subset(v12, v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v8, v9) = v10) | ~ (ordered_pair(v12, v13) = v11) | ~ in(v13, v9) | ~ in(v12, v8) | in(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | ~ (ordered_pair(v10, v11) = v12) | ~ (ordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v8 | v10 = v8 | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v8 | ~ (ordered_pair(v10, v11) = v12) | ~ (ordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (subset_difference(v12, v11, v10) = v9) | ~ (subset_difference(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = empty_set | ~ (subset_difference(v8, v10, v11) = v12) | ~ (meet_of_subsets(v8, v9) = v11) | ~ (cast_to_subset(v8) = v10) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (union_of_subsets(v8, v15) = v16 & complements_of_subsets(v8, v9) = v15 & powerset(v13) = v14 & powerset(v8) = v13 & (v16 = v12 | ~ element(v9, v14)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = empty_set | ~ (subset_difference(v8, v10, v11) = v12) | ~ (union_of_subsets(v8, v9) = v11) | ~ (cast_to_subset(v8) = v10) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (meet_of_subsets(v8, v15) = v16 & complements_of_subsets(v8, v9) = v15 & powerset(v13) = v14 & powerset(v8) = v13 & (v16 = v12 | ~ element(v9, v14)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = empty_set | ~ (subset_complement(v8, v10) = v11) | ~ (powerset(v8) = v9) | ~ element(v12, v8) | ~ element(v10, v9) | in(v12, v11) | in(v12, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_inverse(v8) = v9) | ~ (ordered_pair(v11, v10) = v12) | ~ relation(v9) | ~ relation(v8) | ~ in(v12, v8) | ? [v13] : (ordered_pair(v10, v11) = v13 & in(v13, v9))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_inverse(v8) = v9) | ~ (ordered_pair(v11, v10) = v12) | ~ relation(v9) | ~ relation(v8) | in(v12, v8) | ? [v13] : (ordered_pair(v10, v11) = v13 & ~ in(v13, v9))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_inverse(v8) = v9) | ~ (ordered_pair(v10, v11) = v12) | ~ relation(v9) | ~ relation(v8) | ~ in(v12, v9) | ? [v13] : (ordered_pair(v11, v10) = v13 & in(v13, v8))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_inverse(v8) = v9) | ~ (ordered_pair(v10, v11) = v12) | ~ relation(v9) | ~ relation(v8) | in(v12, v9) | ? [v13] : (ordered_pair(v11, v10) = v13 & ~ in(v13, v8))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_field(v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ relation(v10) | ~ in(v11, v10) | in(v9, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_field(v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ relation(v10) | ~ in(v11, v10) | in(v8, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_complement(v8, v11) = v12) | ~ (powerset(v8) = v10) | ~ disjoint(v9, v11) | ~ element(v11, v10) | ~ element(v9, v10) | subset(v9, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_complement(v8, v11) = v12) | ~ (powerset(v8) = v10) | ~ element(v11, v10) | ~ element(v9, v10) | ~ subset(v9, v12) | disjoint(v9, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng(v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ relation(v10) | ~ in(v11, v10) | in(v9, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng(v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ relation(v10) | ~ in(v11, v10) | ? [v13] : (relation_dom(v10) = v13 & in(v8, v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng(v8) = v9) | ~ (ordered_pair(v11, v10) = v12) | ~ relation(v8) | ~ in(v12, v8) | in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v11) = v12) | ~ (singleton(v10) = v11) | ~ subset(v8, v9) | subset(v8, v12) | in(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v10) = v12) | ~ (set_difference(v8, v10) = v11) | ~ subset(v8, v9) | subset(v11, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v9, v10) = v12) | ~ (powerset(v8) = v11) | ~ element(v10, v11) | ~ element(v9, v11) | subset_difference(v8, v9, v10) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom(v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ relation(v10) | ~ in(v11, v10) | in(v8, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom(v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ relation(v10) | ~ in(v11, v10) | ? [v13] : (relation_rng(v10) = v13 & in(v9, v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom(v8) = v9) | ~ (ordered_pair(v10, v11) = v12) | ~ relation(v8) | ~ in(v12, v8) | in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v10, v9) = v12) | ~ (cartesian_product2(v10, v8) = v11) | ~ subset(v8, v9) | subset(v11, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v10, v9) = v12) | ~ (cartesian_product2(v10, v8) = v11) | ~ subset(v8, v9) | ? [v13] : ? [v14] : (cartesian_product2(v9, v10) = v14 & cartesian_product2(v8, v10) = v13 & subset(v13, v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v10, v9) = v12) | ~ (cartesian_product2(v8, v10) = v11) | ~ subset(v8, v9) | ? [v13] : ? [v14] : (cartesian_product2(v10, v8) = v14 & cartesian_product2(v9, v10) = v13 & subset(v14, v12) & subset(v11, v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v10, v8) = v12) | ~ (cartesian_product2(v9, v10) = v11) | ~ subset(v8, v9) | ? [v13] : ? [v14] : (cartesian_product2(v10, v9) = v14 & cartesian_product2(v8, v10) = v13 & subset(v13, v11) & subset(v12, v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v9, v10) = v12) | ~ (cartesian_product2(v8, v10) = v11) | ~ subset(v8, v9) | subset(v11, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v9, v10) = v12) | ~ (cartesian_product2(v8, v10) = v11) | ~ subset(v8, v9) | ? [v13] : ? [v14] : (cartesian_product2(v10, v9) = v14 & cartesian_product2(v10, v8) = v13 & subset(v13, v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v8) = v11) | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v10) | ordered_pair(v8, v9) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v9, v10) = v12) | ~ (set_intersection2(v8, v10) = v11) | ~ subset(v8, v9) | subset(v11, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v10 | ~ (relation_composition(v8, v9) = v10) | ~ relation(v11) | ~ relation(v9) | ~ relation(v8) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v12, v13) = v14 & ( ~ in(v14, v11) | ( ! [v18] : ! [v19] : ( ~ (ordered_pair(v18, v13) = v19) | ~ in(v19, v9) | ? [v20] : (ordered_pair(v12, v18) = v20 & ~ in(v20, v8))) & ! [v18] : ! [v19] : ( ~ (ordered_pair(v12, v18) = v19) | ~ in(v19, v8) | ? [v20] : (ordered_pair(v18, v13) = v20 & ~ in(v20, v9))))) & (in(v14, v11) | (ordered_pair(v15, v13) = v17 & ordered_pair(v12, v15) = v16 & in(v17, v9) & in(v16, v8))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | v11 = v8 | ~ (unordered_pair(v8, v9) = v10) | ~ in(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (complements_of_subsets(v8, v10) = v11) | ~ (complements_of_subsets(v8, v9) = v10) | ? [v12] : ? [v13] : (powerset(v12) = v13 & powerset(v8) = v12 & ~ element(v9, v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (subset_complement(v8, v10) = v11) | ~ (subset_complement(v8, v9) = v10) | ? [v12] : (powerset(v8) = v12 & ~ element(v9, v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v8, v10) = v11) | ~ subset(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (singleton(v8) = v10) | ~ (set_union2(v10, v9) = v11) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_difference(v8, v10) = v11) | ~ (singleton(v9) = v10) | in(v9, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v8) = v11) | ~ (unordered_pair(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (meet_of_subsets(v11, v10) = v9) | ~ (meet_of_subsets(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union_of_subsets(v11, v10) = v9) | ~ (union_of_subsets(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (complements_of_subsets(v11, v10) = v9) | ~ (complements_of_subsets(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (relation_composition(v11, v10) = v9) | ~ (relation_composition(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset_complement(v11, v10) = v9) | ~ (subset_complement(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_difference(v11, v10) = v9) | ~ (set_difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cartesian_product2(v11, v10) = v9) | ~ (cartesian_product2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (singleton(v9) = v11) | ~ (singleton(v8) = v10) | ~ subset(v10, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (singleton(v8) = v11) | ~ (unordered_pair(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (ordered_pair(v11, v10) = v9) | ~ (ordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_intersection2(v11, v10) = v9) | ~ (set_intersection2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_union2(v11, v10) = v9) | ~ (set_union2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = empty_set | ~ (meet_of_subsets(v8, v10) = v11) | ~ (complements_of_subsets(v8, v9) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (subset_difference(v8, v14, v15) = v16 & union_of_subsets(v8, v9) = v15 & cast_to_subset(v8) = v14 & powerset(v12) = v13 & powerset(v8) = v12 & (v16 = v11 | ~ element(v9, v13)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = empty_set | ~ (union_of_subsets(v8, v10) = v11) | ~ (complements_of_subsets(v8, v9) = v10) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (subset_difference(v8, v14, v15) = v16 & meet_of_subsets(v8, v9) = v15 & cast_to_subset(v8) = v14 & powerset(v12) = v13 & powerset(v8) = v12 & (v16 = v11 | ~ element(v9, v13)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = empty_set | ~ (set_meet(v8) = v9) | ~ in(v11, v8) | ~ in(v10, v9) | in(v10, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_difference(v8, v9, v10) = v11) | ? [v12] : ? [v13] : (set_difference(v9, v10) = v13 & powerset(v8) = v12 & (v13 = v11 | ~ element(v10, v12) | ~ element(v9, v12)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_difference(v8, v9, v10) = v11) | ? [v12] : (powerset(v8) = v12 & ( ~ element(v10, v12) | ~ element(v9, v12) | element(v11, v12)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_composition(v8, v10) = v11) | ~ (relation_dom(v8) = v9) | ~ relation(v10) | ~ relation(v8) | ? [v12] : (relation_dom(v11) = v12 & subset(v12, v9))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_complement(v8, v10) = v11) | ~ in(v9, v11) | ~ in(v9, v10) | ? [v12] : (powerset(v8) = v12 & ~ element(v10, v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_rng(v8) = v10) | ~ (relation_dom(v8) = v9) | ~ (cartesian_product2(v9, v10) = v11) | ~ relation(v8) | subset(v8, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (relation_rng(v8) = v10) | ~ (relation_dom(v8) = v9) | ~ (set_union2(v9, v10) = v11) | ~ relation(v8) | relation_field(v8) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v10, v9) = v11) | ~ (set_union2(v8, v9) = v10) | set_difference(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v8, v10) = v11) | set_union2(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v10) = v11) | ~ (set_difference(v8, v9) = v10) | set_intersection2(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v10) | ~ in(v11, v10) | ~ in(v11, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v10) | ~ in(v11, v10) | in(v11, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v10) | ~ in(v11, v8) | in(v11, v10) | in(v11, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9) = v11) | ~ (powerset(v8) = v10) | ? [v12] : ? [v13] : (union_of_subsets(v8, v9) = v13 & powerset(v10) = v12 & (v13 = v11 | ~ element(v9, v12)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v8) = v9) | ~ in(v11, v8) | ~ in(v10, v11) | in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cartesian_product2(v8, v9) = v10) | ~ in(v11, v10) | ? [v12] : ? [v13] : (ordered_pair(v12, v13) = v11 & in(v13, v9) & in(v12, v8))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ element(v9, v11) | ~ empty(v10) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ element(v9, v11) | ~ in(v8, v9) | element(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v8) = v10) | ~ (set_meet(v9) = v11) | ? [v12] : ? [v13] : (meet_of_subsets(v8, v9) = v13 & powerset(v10) = v12 & (v13 = v11 | ~ element(v9, v12)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v8) = v10) | ~ element(v9, v10) | ~ in(v11, v9) | in(v11, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v9, v10) = v11) | ~ subset(v8, v10) | ~ subset(v8, v9) | subset(v8, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ disjoint(v8, v9) | ~ in(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ in(v11, v10) | in(v11, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ in(v11, v10) | in(v11, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ in(v11, v9) | ~ in(v11, v8) | in(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v10) = v11) | ~ subset(v10, v9) | ~ subset(v8, v9) | subset(v11, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v9) = v10) | ~ in(v11, v10) | in(v11, v9) | in(v11, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v9) = v10) | ~ in(v11, v9) | in(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_union2(v8, v9) = v10) | ~ in(v11, v8) | in(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v8, v9) = v11) | ~ subset(v11, v10) | in(v9, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v8, v9) = v11) | ~ subset(v11, v10) | in(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v8, v9) = v11) | ~ in(v9, v10) | ~ in(v8, v10) | subset(v11, v10)) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_difference(v9, v10) = v11) | ? [v12] : (( ~ in(v12, v9) | ~ in(v12, v8) | in(v12, v10)) & (in(v12, v8) | (in(v12, v9) & ~ in(v12, v10))))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (cartesian_product2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (( ~ in(v12, v8) | ! [v16] : ! [v17] : ( ~ (ordered_pair(v16, v17) = v12) | ~ in(v17, v10) | ~ in(v16, v9))) & (in(v12, v8) | (v15 = v12 & ordered_pair(v13, v14) = v12 & in(v14, v10) & in(v13, v9))))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : (( ~ in(v12, v10) | ~ in(v12, v9) | ~ in(v12, v8)) & (in(v12, v8) | (in(v12, v10) & in(v12, v9))))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_union2(v9, v10) = v11) | ? [v12] : (( ~ in(v12, v8) | ( ~ in(v12, v10) & ~ in(v12, v9))) & (in(v12, v10) | in(v12, v9) | in(v12, v8)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (unordered_pair(v9, v10) = v11) | ? [v12] : ((v12 = v10 | v12 = v9 | in(v12, v8)) & ( ~ in(v12, v8) | ( ~ (v12 = v10) & ~ (v12 = v9))))) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (relation_inverse(v8) = v9) | ~ relation(v10) | ~ relation(v8) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (ordered_pair(v12, v11) = v14 & ordered_pair(v11, v12) = v13 & ( ~ in(v14, v8) | ~ in(v13, v10)) & (in(v14, v8) | in(v13, v10)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v8, v9) = v10) | ~ subset(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v8 = empty_set | ~ (singleton(v9) = v10) | ~ subset(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_difference(v8, v9) = v10) | ~ disjoint(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v8) = v9) | ~ in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_intersection2(v8, v9) = v10) | ~ subset(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(v8, v9) = v10) | ~ subset(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_intersection2(v8, v9) = v10) | ~ disjoint(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_inverse(v10) = v9) | ~ (relation_inverse(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_field(v10) = v9) | ~ (relation_field(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_rng(v10) = v9) | ~ (relation_rng(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (union(v10) = v9) | ~ (union(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (cast_to_subset(v10) = v9) | ~ (cast_to_subset(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (relation_dom(v10) = v9) | ~ (relation_dom(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (powerset(v10) = v9) | ~ (powerset(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (set_meet(v10) = v9) | ~ (set_meet(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (meet_of_subsets(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (powerset(v11) = v12 & powerset(v8) = v11 & set_meet(v9) = v13 & (v13 = v10 | ~ element(v9, v12)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (meet_of_subsets(v8, v9) = v10) | ? [v11] : ? [v12] : (powerset(v11) = v12 & powerset(v8) = v11 & ( ~ element(v9, v12) | element(v10, v11)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union_of_subsets(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (union(v9) = v13 & powerset(v11) = v12 & powerset(v8) = v11 & (v13 = v10 | ~ element(v9, v12)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union_of_subsets(v8, v9) = v10) | ? [v11] : ? [v12] : (powerset(v11) = v12 & powerset(v8) = v11 & ( ~ element(v9, v12) | element(v10, v11)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (complements_of_subsets(v8, v9) = v10) | ? [v11] : ? [v12] : (powerset(v11) = v12 & powerset(v8) = v11 & ( ~ element(v9, v12) | element(v10, v12)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (complements_of_subsets(v8, v9) = v10) | ? [v11] : ? [v12] : (powerset(v11) = v12 & powerset(v8) = v11 & ( ~ element(v9, v12) | ( ! [v13] : ! [v14] : ( ~ (subset_complement(v8, v13) = v14) | ~ element(v13, v11) | ~ element(v10, v12) | ~ in(v14, v9) | in(v13, v10)) & ! [v13] : ! [v14] : ( ~ (subset_complement(v8, v13) = v14) | ~ element(v13, v11) | ~ element(v10, v12) | ~ in(v13, v10) | in(v14, v9)) & ! [v13] : (v13 = v10 | ~ element(v13, v12) | ? [v14] : ? [v15] : (subset_complement(v8, v14) = v15 & element(v14, v11) & ( ~ in(v15, v9) | ~ in(v14, v13)) & (in(v15, v9) | in(v14, v13)))))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (relation_composition(v8, v9) = v10) | ~ relation(v9) | ~ relation(v8) | relation(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (relation_composition(v8, v9) = v10) | ~ relation(v9) | ~ relation(v8) | ? [v11] : ? [v12] : (relation_rng(v10) = v11 & relation_rng(v9) = v12 & subset(v11, v12))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset_complement(v8, v9) = v10) | ? [v11] : ? [v12] : (set_difference(v8, v9) = v12 & powerset(v8) = v11 & (v12 = v10 | ~ element(v9, v11)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset_complement(v8, v9) = v10) | ? [v11] : (powerset(v8) = v11 & ( ~ element(v9, v11) | element(v10, v11)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (relation_rng(v9) = v10) | ~ relation(v9) | ~ relation(v8) | ? [v11] : ? [v12] : (relation_composition(v8, v9) = v11 & relation_rng(v11) = v12 & subset(v12, v10))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (relation_rng(v8) = v9) | ~ relation(v8) | ~ in(v10, v9) | ? [v11] : ? [v12] : (ordered_pair(v11, v10) = v12 & in(v12, v8))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v10) = v8) | ~ (singleton(v9) = v10) | ~ in(v9, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v9) = v10) | subset(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v9) = v10) | ? [v11] : ? [v12] : (subset_complement(v8, v9) = v12 & powerset(v8) = v11 & (v12 = v10 | ~ element(v9, v11)))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v9) = v10) | ? [v11] : (set_difference(v11, v9) = v10 & set_union2(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v9) = v10) | ~ in(v8, v9) | subset(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8) = v9) | ~ in(v10, v9) | ? [v11] : (in(v11, v8) & in(v10, v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (relation_dom(v8) = v9) | ~ relation(v8) | ~ in(v10, v9) | ? [v11] : ? [v12] : (ordered_pair(v10, v11) = v12 & in(v12, v8))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (cartesian_product2(v8, v9) = v10) | ~ empty(v10) | empty(v9) | empty(v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ element(v8, v10) | subset(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ subset(v8, v9) | element(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v8) = v9) | ~ subset(v10, v8) | in(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v8) = v9) | ~ in(v10, v9) | subset(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v8) = v10) | ~ disjoint(v10, v9) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v8) = v10) | ~ subset(v10, v9) | in(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v8) = v10) | ~ in(v8, v9) | subset(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ empty(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : (singleton(v8) = v12 & unordered_pair(v11, v12) = v10 & unordered_pair(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v9, v8) = v10) | set_intersection2(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | set_intersection2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | disjoint(v8, v9) | ? [v11] : in(v11, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | subset(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | ? [v11] : (set_difference(v8, v11) = v10 & set_difference(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | ~ empty(v10) | empty(v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | set_union2(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ~ relation(v9) | ~ relation(v8) | relation(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ~ empty(v10) | empty(v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | subset(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ? [v11] : (set_difference(v9, v8) = v11 & set_union2(v8, v11) = v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v8) = v10) | unordered_pair(v8, v9) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | ~ empty(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | in(v9, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | in(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ disjoint(v9, v10) | ~ subset(v8, v9) | disjoint(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ disjoint(v8, v9) | ~ in(v10, v9) | ~ in(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ subset(v9, v10) | ~ subset(v8, v9) | subset(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ subset(v8, v9) | ~ in(v10, v8) | in(v10, v9)) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | v9 = empty_set | ~ (set_meet(v9) = v10) | ? [v11] : ? [v12] : (( ~ in(v11, v8) | (in(v12, v9) & ~ in(v11, v12))) & (in(v11, v8) | ! [v13] : ( ~ in(v13, v9) | in(v11, v13))))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (relation_rng(v9) = v10) | ~ relation(v9) | ? [v11] : ? [v12] : ? [v13] : (( ~ in(v11, v8) | ! [v14] : ! [v15] : ( ~ (ordered_pair(v14, v11) = v15) | ~ in(v15, v9))) & (in(v11, v8) | (ordered_pair(v12, v11) = v13 & in(v13, v9))))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (union(v9) = v10) | ? [v11] : ? [v12] : (( ~ in(v11, v8) | ! [v13] : ( ~ in(v13, v9) | ~ in(v11, v13))) & (in(v11, v8) | (in(v12, v9) & in(v11, v12))))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (relation_dom(v9) = v10) | ~ relation(v9) | ? [v11] : ? [v12] : ? [v13] : (( ~ in(v11, v8) | ! [v14] : ! [v15] : ( ~ (ordered_pair(v11, v14) = v15) | ~ in(v15, v9))) & (in(v11, v8) | (ordered_pair(v11, v12) = v13 & in(v13, v9))))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (powerset(v9) = v10) | ? [v11] : (( ~ subset(v11, v9) | ~ in(v11, v8)) & (subset(v11, v9) | in(v11, v8)))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v9) = v10) | ? [v11] : (( ~ (v11 = v9) | ~ in(v9, v8)) & (v11 = v9 | in(v11, v8)))) & ? [v8] : ! [v9] : ! [v10] : (v9 = empty_set | ~ (set_meet(v9) = v10) | in(v8, v10) | ? [v11] : (in(v11, v9) & ~ in(v8, v11))) & ? [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | element(v8, v10) | ? [v11] : (in(v11, v8) & ~ in(v11, v9))) & ? [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v9) = v10) | disjoint(v10, v8) | in(v9, v8)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_difference(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (cast_to_subset(v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_intersection2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ subset(v9, v8) | ~ subset(v8, v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ subset(v8, v9) | proper_subset(v8, v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ empty(v9) | ~ empty(v8)) & ! [v8] : ! [v9] : (v9 = empty_set | ~ (complements_of_subsets(v8, v9) = empty_set) | ? [v10] : ? [v11] : (powerset(v10) = v11 & powerset(v8) = v10 & ~ element(v9, v11))) & ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(empty_set, v8) = v9)) & ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_intersection2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v8 = empty_set | ~ (relation_rng(v8) = v9) | ~ relation(v8) | ? [v10] : ( ~ (v10 = empty_set) & relation_dom(v8) = v10)) & ! [v8] : ! [v9] : (v8 = empty_set | ~ (relation_dom(v8) = v9) | ~ relation(v8) | ? [v10] : ( ~ (v10 = empty_set) & relation_rng(v8) = v10)) & ! [v8] : ! [v9] : ( ~ (relation_inverse(v8) = v9) | ~ relation(v8) | relation_inverse(v9) = v8) & ! [v8] : ! [v9] : ( ~ (relation_inverse(v8) = v9) | ~ relation(v8) | relation(v9)) & ! [v8] : ! [v9] : ( ~ (relation_inverse(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : (relation_rng(v9) = v11 & relation_rng(v8) = v10 & relation_dom(v9) = v10 & relation_dom(v8) = v11)) & ! [v8] : ! [v9] : ( ~ (relation_field(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : (relation_rng(v8) = v11 & relation_dom(v8) = v10 & set_union2(v10, v11) = v9)) & ! [v8] : ! [v9] : ( ~ (relation_rng(v8) = v9) | ~ relation(v8) | ~ empty(v9) | empty(v8)) & ! [v8] : ! [v9] : ( ~ (relation_rng(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : (relation_inverse(v8) = v10 & relation_rng(v10) = v11 & relation_dom(v10) = v9 & relation_dom(v8) = v11)) & ! [v8] : ! [v9] : ( ~ (relation_rng(v8) = v9) | ~ relation(v8) | ? [v10] : (relation_dom(v8) = v10 & ! [v11] : ! [v12] : ( ~ (relation_composition(v11, v8) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_rng(v12) = v14 & relation_rng(v11) = v13 & (v14 = v9 | ~ subset(v10, v13)))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ subset(v10, v12) | ~ relation(v11) | ? [v13] : (relation_composition(v11, v8) = v13 & relation_rng(v13) = v9)))) & ! [v8] : ! [v9] : ( ~ (relation_rng(v8) = v9) | ~ relation(v8) | ? [v10] : (relation_dom(v8) = v10 & ! [v11] : ! [v12] : ( ~ (relation_composition(v8, v11) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_dom(v12) = v14 & relation_dom(v11) = v13 & (v14 = v10 | ~ subset(v9, v13)))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ subset(v9, v12) | ~ relation(v11) | ? [v13] : (relation_composition(v8, v11) = v13 & relation_dom(v13) = v10)))) & ! [v8] : ! [v9] : ( ~ (relation_rng(v8) = v9) | ~ relation(v8) | ? [v10] : (relation_dom(v8) = v10 & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ subset(v8, v11) | ~ relation(v11) | subset(v9, v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ subset(v8, v11) | ~ relation(v11) | ? [v13] : (relation_dom(v11) = v13 & subset(v10, v13))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ subset(v8, v11) | ~ relation(v11) | subset(v10, v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ subset(v8, v11) | ~ relation(v11) | ? [v13] : (relation_rng(v11) = v13 & subset(v9, v13))))) & ! [v8] : ! [v9] : ( ~ (relation_rng(v8) = v9) | ~ empty(v8) | relation(v9)) & ! [v8] : ! [v9] : ( ~ (relation_rng(v8) = v9) | ~ empty(v8) | empty(v9)) & ! [v8] : ! [v9] : ( ~ (set_difference(v8, v9) = v8) | disjoint(v8, v9)) & ! [v8] : ! [v9] : ( ~ (set_difference(v8, v9) = empty_set) | subset(v8, v9)) & ! [v8] : ! [v9] : ( ~ (cast_to_subset(v8) = v9) | ? [v10] : (powerset(v8) = v10 & element(v9, v10))) & ! [v8] : ! [v9] : ( ~ (relation_dom(v8) = v9) | ~ relation(v8) | ~ empty(v9) | empty(v8)) & ! [v8] : ! [v9] : ( ~ (relation_dom(v8) = v9) | ~ relation(v8) | ? [v10] : ? [v11] : (relation_inverse(v8) = v11 & relation_rng(v11) = v9 & relation_rng(v8) = v10 & relation_dom(v11) = v10)) & ! [v8] : ! [v9] : ( ~ (relation_dom(v8) = v9) | ~ relation(v8) | ? [v10] : (relation_rng(v8) = v10 & ! [v11] : ! [v12] : ( ~ (relation_composition(v11, v8) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_rng(v12) = v14 & relation_rng(v11) = v13 & (v14 = v10 | ~ subset(v9, v13)))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ subset(v9, v12) | ~ relation(v11) | ? [v13] : (relation_composition(v11, v8) = v13 & relation_rng(v13) = v10)))) & ! [v8] : ! [v9] : ( ~ (relation_dom(v8) = v9) | ~ relation(v8) | ? [v10] : (relation_rng(v8) = v10 & ! [v11] : ! [v12] : ( ~ (relation_composition(v8, v11) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_dom(v12) = v14 & relation_dom(v11) = v13 & (v14 = v9 | ~ subset(v10, v13)))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ subset(v10, v12) | ~ relation(v11) | ? [v13] : (relation_composition(v8, v11) = v13 & relation_dom(v13) = v9)))) & ! [v8] : ! [v9] : ( ~ (relation_dom(v8) = v9) | ~ relation(v8) | ? [v10] : (relation_rng(v8) = v10 & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ subset(v8, v11) | ~ relation(v11) | subset(v10, v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ subset(v8, v11) | ~ relation(v11) | ? [v13] : (relation_dom(v11) = v13 & subset(v9, v13))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ subset(v8, v11) | ~ relation(v11) | subset(v9, v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ subset(v8, v11) | ~ relation(v11) | ? [v13] : (relation_rng(v11) = v13 & subset(v10, v13))))) & ! [v8] : ! [v9] : ( ~ (relation_dom(v8) = v9) | ~ empty(v8) | relation(v9)) & ! [v8] : ! [v9] : ( ~ (relation_dom(v8) = v9) | ~ empty(v8) | empty(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ~ empty(v9)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | union(v9) = v8) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | empty(v8) | ? [v10] : (element(v10, v9) & ~ empty(v10))) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ? [v10] : (cast_to_subset(v8) = v10 & element(v10, v9))) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ? [v10] : (element(v10, v9) & empty(v10))) & ! [v8] : ! [v9] : ( ~ (singleton(v9) = v8) | subset(v8, v8)) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | ~ empty(v9)) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | unordered_pair(v8, v8) = v9) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | subset(empty_set, v9)) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | in(v8, v9)) & ! [v8] : ! [v9] : ( ~ (set_intersection2(v8, v9) = empty_set) | disjoint(v8, v9)) & ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v8) = v9) | singleton(v8) = v9) & ! [v8] : ! [v9] : ( ~ disjoint(v8, v9) | disjoint(v9, v8)) & ! [v8] : ! [v9] : ( ~ element(v9, v8) | ~ empty(v8) | empty(v9)) & ! [v8] : ! [v9] : ( ~ element(v9, v8) | empty(v8) | in(v9, v8)) & ! [v8] : ! [v9] : ( ~ element(v8, v9) | empty(v9) | in(v8, v9)) & ! [v8] : ! [v9] : ( ~ subset(v8, v9) | ~ proper_subset(v9, v8)) & ! [v8] : ! [v9] : ( ~ relation(v8) | ~ in(v9, v8) | ? [v10] : ? [v11] : ordered_pair(v10, v11) = v9) & ! [v8] : ! [v9] : ( ~ empty(v9) | ~ empty(v8) | element(v9, v8)) & ! [v8] : ! [v9] : ( ~ empty(v9) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ( ~ proper_subset(v9, v8) | ~ proper_subset(v8, v9)) & ! [v8] : ! [v9] : ( ~ proper_subset(v8, v9) | subset(v8, v9)) & ! [v8] : ! [v9] : ( ~ in(v9, v8) | ~ in(v8, v9)) & ! [v8] : ! [v9] : ( ~ in(v9, v8) | element(v9, v8) | empty(v8)) & ! [v8] : ! [v9] : ( ~ in(v8, v9) | element(v8, v9)) & ! [v8] : (v8 = empty_set | ~ (relation_rng(v8) = empty_set) | ~ relation(v8)) & ! [v8] : (v8 = empty_set | ~ (relation_dom(v8) = empty_set) | ~ relation(v8)) & ! [v8] : (v8 = empty_set | ~ (set_meet(empty_set) = v8)) & ! [v8] : (v8 = empty_set | ~ subset(v8, empty_set)) & ! [v8] : (v8 = empty_set | ~ relation(v8) | ? [v9] : ? [v10] : ? [v11] : (ordered_pair(v9, v10) = v11 & in(v11, v8))) & ! [v8] : (v8 = empty_set | ~ empty(v8)) & ! [v8] : ~ (singleton(v8) = empty_set) & ! [v8] : ( ~ empty(v8) | relation(v8)) & ! [v8] : ~ proper_subset(v8, v8) & ! [v8] : ~ in(v8, empty_set) & ? [v8] : ? [v9] : (v9 = v8 | ? [v10] : (( ~ in(v10, v9) | ~ in(v10, v8)) & (in(v10, v9) | in(v10, v8)))) & ? [v8] : ? [v9] : (disjoint(v8, v9) | ? [v10] : (in(v10, v9) & in(v10, v8))) & ? [v8] : ? [v9] : element(v9, v8) & ? [v8] : ? [v9] : (subset(v8, v9) | ? [v10] : (in(v10, v8) & ~ in(v10, v9))) & ? [v8] : ? [v9] : (in(v8, v9) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ in(v10, v9) | in(v11, v9)) & ! [v10] : ! [v11] : ( ~ subset(v11, v10) | ~ in(v10, v9) | in(v11, v9)) & ! [v10] : ( ~ subset(v10, v9) | are_equipotent(v10, v9) | in(v10, v9))) & ? [v8] : ? [v9] : (in(v8, v9) & ! [v10] : ! [v11] : ( ~ subset(v11, v10) | ~ in(v10, v9) | in(v11, v9)) & ! [v10] : ( ~ subset(v10, v9) | are_equipotent(v10, v9) | in(v10, v9)) & ! [v10] : ( ~ in(v10, v9) | ? [v11] : (in(v11, v9) & ! [v12] : ( ~ subset(v12, v10) | in(v12, v11))))) & ? [v8] : (v8 = empty_set | ? [v9] : in(v9, v8)) & ? [v8] : subset(v8, v8) & ? [v8] : subset(empty_set, v8) & ? [v8] : (relation(v8) | ? [v9] : (in(v9, v8) & ! [v10] : ! [v11] : ~ (ordered_pair(v10, v11) = v9))) & ((v3 = empty_set & ~ (v2 = empty_set)) | (v2 = empty_set & ~ (v3 = empty_set)))) % 16.45/4.26 | 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 yields: % 16.45/4.26 | (1) relation_rng(all_0_6_6) = all_0_4_4 & relation_rng(empty_set) = empty_set & relation_dom(all_0_6_6) = all_0_5_5 & relation_dom(empty_set) = empty_set & powerset(empty_set) = all_0_7_7 & singleton(empty_set) = all_0_7_7 & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_6_6) & relation(empty_set) & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) & ~ empty(all_0_2_2) & ~ empty(all_0_3_3) & ! [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] : ( ~ (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] : (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_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) | ~ 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(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [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] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, 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 = 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] : (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 | ~ (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 | ~ (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(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(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] : ( ~ (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] : ( ~ (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] : ( ~ (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 | ~ (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] : (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 | ~ (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] : ( ~ (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(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] : ( ~ (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(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] : ( ~ (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) | 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 | ~ 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] : ( ~ (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 & ! [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) | ~ 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) | ~ 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] : ( ~ (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(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] : ~ 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))) & ((all_0_4_4 = empty_set & ~ (all_0_5_5 = empty_set)) | (all_0_5_5 = empty_set & ~ (all_0_4_4 = empty_set))) % 16.57/4.31 | % 16.57/4.31 | Applying alpha-rule on (1) yields: % 16.57/4.31 | (2) ! [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)) % 16.57/4.31 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 16.57/4.31 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 16.57/4.31 | (5) ? [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))))) % 16.57/4.31 | (6) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 16.57/4.31 | (7) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 16.57/4.31 | (8) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) % 16.57/4.31 | (9) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) % 16.57/4.31 | (10) powerset(empty_set) = all_0_7_7 % 16.57/4.31 | (11) ! [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))) % 16.57/4.31 | (12) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) % 16.57/4.31 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 16.57/4.31 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 16.57/4.31 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 16.57/4.32 | (16) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) % 16.57/4.32 | (17) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) % 16.57/4.32 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 16.57/4.32 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 16.57/4.32 | (20) ! [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)))) % 16.57/4.32 | (21) ! [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)))) % 16.57/4.32 | (22) ! [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))) % 16.57/4.32 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 16.57/4.32 | (24) ! [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)) % 16.57/4.32 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 16.57/4.32 | (26) relation(all_0_2_2) % 16.57/4.32 | (27) ! [v0] : ~ in(v0, empty_set) % 16.57/4.32 | (28) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 16.57/4.32 | (29) ? [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))))) % 16.57/4.32 | (30) ! [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)) % 16.57/4.32 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) % 16.57/4.32 | (32) ! [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))) % 16.57/4.32 | (33) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 16.57/4.32 | (34) ! [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)) % 16.57/4.32 | (35) ! [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))) % 16.57/4.32 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 16.57/4.32 | (37) ~ empty(all_0_3_3) % 16.57/4.32 | (38) ! [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))) % 16.57/4.32 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 16.57/4.32 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) % 16.57/4.32 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 16.57/4.32 | (42) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 16.57/4.32 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) % 16.57/4.32 | (44) ! [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))) % 16.57/4.32 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 16.83/4.32 | (46) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 16.83/4.32 | (47) ! [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) % 16.83/4.32 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 16.83/4.32 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 16.83/4.32 | (50) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 16.83/4.32 | (51) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 16.83/4.32 | (52) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 16.83/4.32 | (53) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) % 16.83/4.32 | (54) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1))) % 16.83/4.32 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 16.83/4.32 | (56) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) % 16.83/4.32 | (57) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 16.83/4.32 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 16.83/4.32 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) % 16.83/4.32 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 16.83/4.32 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 16.83/4.32 | (62) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 16.83/4.32 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 16.83/4.32 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 16.83/4.32 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 16.83/4.32 | (66) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 16.83/4.32 | (67) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 16.83/4.32 | (68) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) % 16.83/4.33 | (69) ! [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))))) % 16.83/4.33 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 16.83/4.33 | (71) ! [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))) % 16.83/4.33 | (72) ! [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)))) % 16.83/4.33 | (73) relation(all_0_0_0) % 16.83/4.33 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) % 16.83/4.33 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 16.83/4.33 | (76) ! [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))) % 16.83/4.33 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 16.83/4.33 | (78) ? [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))) % 16.83/4.33 | (79) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 16.83/4.33 | (80) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) % 16.83/4.33 | (81) ! [v0] : ~ proper_subset(v0, v0) % 16.83/4.33 | (82) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 16.83/4.33 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 16.83/4.33 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 16.83/4.33 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) % 16.83/4.33 | (86) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 16.83/4.33 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) % 16.83/4.33 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) % 16.83/4.33 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) % 16.83/4.33 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 16.83/4.33 | (91) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 16.83/4.33 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 16.83/4.33 | (93) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 16.83/4.33 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) % 16.83/4.33 | (95) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 16.83/4.33 | (96) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) % 16.83/4.33 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 16.83/4.33 | (98) ~ empty(all_0_2_2) % 16.83/4.33 | (99) ! [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))) % 16.83/4.33 | (100) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 16.83/4.33 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 16.83/4.33 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 16.83/4.33 | (103) ? [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))))) % 16.83/4.33 | (104) ! [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))) % 16.83/4.33 | (105) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 16.83/4.33 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) % 16.83/4.33 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 16.83/4.33 | (108) ! [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)) % 16.83/4.33 | (109) empty(all_0_0_0) % 16.83/4.33 | (110) ? [v0] : subset(empty_set, v0) % 16.83/4.33 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 16.83/4.33 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 16.83/4.33 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 16.83/4.33 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 16.83/4.33 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 16.83/4.33 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 16.83/4.33 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 16.83/4.33 | (118) relation_dom(empty_set) = empty_set % 16.83/4.33 | (119) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) % 16.83/4.34 | (120) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 16.83/4.34 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) % 16.83/4.34 | (122) ? [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)))) % 16.83/4.34 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 16.83/4.34 | (124) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 16.83/4.34 | (125) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 16.83/4.34 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 16.83/4.34 | (127) ! [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)))) % 16.83/4.34 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 16.83/4.34 | (129) ! [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)) % 16.83/4.34 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 16.83/4.34 | (131) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 16.83/4.34 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 16.83/4.34 | (133) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) % 16.83/4.34 | (134) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 16.83/4.34 | (135) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 16.83/4.34 | (136) ! [v0] : ( ~ empty(v0) | relation(v0)) % 16.83/4.34 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 16.83/4.34 | (138) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 16.83/4.34 | (139) ! [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))) % 16.83/4.34 | (140) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 16.83/4.34 | (141) ! [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))) % 16.83/4.34 | (142) ! [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)) % 16.83/4.34 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 16.83/4.34 | (144) ? [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))))) % 16.83/4.34 | (145) ! [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)))) % 16.83/4.34 | (146) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 16.83/4.34 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 16.83/4.34 | (148) ? [v0] : ? [v1] : element(v1, v0) % 16.83/4.34 | (149) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 16.83/4.34 | (150) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 16.83/4.34 | (151) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 16.83/4.34 | (152) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 16.83/4.34 | (153) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 16.83/4.34 | (154) empty(all_0_1_1) % 16.83/4.34 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 16.83/4.34 | (156) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) % 16.83/4.34 | (157) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 16.83/4.34 | (158) ? [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))))) % 16.83/4.34 | (159) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) % 16.83/4.34 | (160) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) % 16.83/4.34 | (161) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 16.83/4.34 | (162) empty(empty_set) % 16.83/4.34 | (163) ? [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))))) % 16.83/4.34 | (164) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 16.83/4.34 | (165) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) % 16.83/4.34 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 16.83/4.34 | (167) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 16.83/4.35 | (168) ! [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)))) % 16.83/4.35 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 16.83/4.35 | (170) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 16.83/4.35 | (171) ! [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))) % 16.83/4.35 | (172) relation_dom(all_0_6_6) = all_0_5_5 % 16.83/4.35 | (173) ! [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)))) % 16.83/4.35 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 16.83/4.35 | (175) ! [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)))) % 16.83/4.35 | (176) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 16.83/4.35 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) % 16.83/4.35 | (178) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 16.83/4.35 | (179) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 16.83/4.35 | (180) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 16.83/4.35 | (181) singleton(empty_set) = all_0_7_7 % 16.83/4.35 | (182) ! [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)) % 16.83/4.35 | (183) ! [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)))) % 16.83/4.35 | (184) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) % 16.83/4.35 | (185) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) % 16.83/4.35 | (186) ! [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)))) % 16.83/4.35 | (187) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) % 16.83/4.35 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 16.83/4.35 | (189) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 16.83/4.35 | (190) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 16.83/4.35 | (191) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) % 16.83/4.35 | (192) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 16.83/4.35 | (193) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 16.83/4.35 | (194) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 16.83/4.35 | (195) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 16.83/4.35 | (196) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) % 16.97/4.35 | (197) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 16.97/4.35 | (198) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 16.97/4.35 | (199) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) % 16.97/4.35 | (200) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 16.97/4.35 | (201) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) % 16.97/4.35 | (202) ! [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))))) % 16.97/4.35 | (203) ? [v0] : subset(v0, v0) % 16.97/4.35 | (204) ! [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))) % 16.97/4.35 | (205) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) % 16.97/4.35 | (206) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) % 16.97/4.35 | (207) ! [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)))) % 16.97/4.35 | (208) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 16.97/4.35 | (209) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) % 16.97/4.35 | (210) relation_rng(empty_set) = empty_set % 16.97/4.35 | (211) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) % 16.97/4.35 | (212) ! [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))) % 16.97/4.35 | (213) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 16.97/4.35 | (214) ! [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))))) % 16.97/4.35 | (215) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 16.97/4.36 | (216) ? [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))))) % 16.97/4.36 | (217) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 16.97/4.36 | (218) ! [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))) % 16.97/4.36 | (219) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) % 16.97/4.36 | (220) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) % 16.97/4.36 | (221) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 16.97/4.36 | (222) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 16.97/4.36 | (223) ! [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))) % 16.97/4.36 | (224) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 16.97/4.36 | (225) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 16.97/4.36 | (226) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) % 16.97/4.36 | (227) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) % 16.97/4.36 | (228) ! [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))) % 16.97/4.36 | (229) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) % 16.97/4.36 | (230) ! [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)))) % 16.97/4.36 | (231) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) % 16.97/4.36 | (232) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) % 16.97/4.36 | (233) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 16.97/4.36 | (234) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 16.97/4.36 | (235) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) % 16.97/4.36 | (236) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 16.97/4.36 | (237) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) % 16.97/4.36 | (238) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) % 16.97/4.36 | (239) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) % 16.97/4.36 | (240) ? [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))))) % 16.97/4.36 | (241) relation(empty_set) % 16.97/4.36 | (242) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 16.97/4.36 | (243) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 16.97/4.36 | (244) relation(all_0_6_6) % 16.97/4.36 | (245) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) % 16.97/4.36 | (246) ! [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)))))))) % 16.97/4.36 | (247) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 16.97/4.36 | (248) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 16.97/4.36 | (249) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 16.97/4.36 | (250) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 16.97/4.36 | (251) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 16.97/4.36 | (252) ! [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)) % 16.97/4.36 | (253) ! [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)))) % 16.97/4.36 | (254) ! [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)))) % 16.97/4.36 | (255) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 16.97/4.36 | (256) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) % 16.97/4.36 | (257) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 16.97/4.36 | (258) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 16.97/4.36 | (259) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) % 16.97/4.36 | (260) ? [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))))) % 16.97/4.36 | (261) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 16.97/4.36 | (262) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) % 16.97/4.36 | (263) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 16.97/4.36 | (264) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) % 16.97/4.37 | (265) ! [v0] : ~ (singleton(v0) = empty_set) % 16.97/4.37 | (266) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 16.97/4.37 | (267) (all_0_4_4 = empty_set & ~ (all_0_5_5 = empty_set)) | (all_0_5_5 = empty_set & ~ (all_0_4_4 = empty_set)) % 16.97/4.37 | (268) relation_rng(all_0_6_6) = all_0_4_4 % 16.97/4.37 | (269) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 16.97/4.37 | (270) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 16.97/4.37 | (271) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 16.97/4.37 | (272) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (178) with all_0_1_1, all_0_0_0 and discharging atoms empty(all_0_0_0), empty(all_0_1_1), yields: % 16.97/4.37 | (273) all_0_0_0 = all_0_1_1 % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (178) with empty_set, all_0_0_0 and discharging atoms empty(all_0_0_0), empty(empty_set), yields: % 16.97/4.37 | (274) all_0_0_0 = empty_set % 16.97/4.37 | % 16.97/4.37 | Combining equations (274,273) yields a new equation: % 16.97/4.37 | (275) all_0_1_1 = empty_set % 16.97/4.37 | % 16.97/4.37 | Combining equations (275,273) yields a new equation: % 16.97/4.37 | (274) all_0_0_0 = empty_set % 16.97/4.37 | % 16.97/4.37 | From (274) and (73) follows: % 16.97/4.37 | (241) relation(empty_set) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (108) with all_0_4_4, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_4_4, relation(all_0_6_6), yields: % 16.97/4.37 | (278) ? [v0] : ? [v1] : (relation_inverse(all_0_6_6) = v0 & relation_rng(v0) = v1 & relation_dom(v0) = all_0_4_4 & relation_dom(all_0_6_6) = v1) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (253) with all_0_4_4, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_4_4, relation(all_0_6_6), yields: % 16.97/4.37 | (279) ? [v0] : (relation_dom(all_0_6_6) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(v1, all_0_6_6) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v4 & relation_rng(v1) = v3 & (v4 = all_0_4_4 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(v1, all_0_6_6) = v3 & relation_rng(v3) = all_0_4_4))) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (72) with all_0_4_4, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_4_4, relation(all_0_6_6), yields: % 16.97/4.37 | (280) ? [v0] : (relation_dom(all_0_6_6) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_6_6, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_0_4_4, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_4_4, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_6_6, v1) = v3 & relation_dom(v3) = v0))) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (202) with all_0_4_4, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_4_4, relation(all_0_6_6), yields: % 16.97/4.37 | (281) ? [v0] : (relation_dom(all_0_6_6) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | subset(all_0_4_4, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v0, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(all_0_4_4, v3)))) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (30) with all_0_5_5, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, relation(all_0_6_6), yields: % 16.97/4.37 | (282) ? [v0] : ? [v1] : (relation_inverse(all_0_6_6) = v1 & relation_rng(v1) = all_0_5_5 & relation_rng(all_0_6_6) = v0 & relation_dom(v1) = v0) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (127) with all_0_5_5, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, relation(all_0_6_6), yields: % 16.97/4.37 | (283) ? [v0] : (relation_rng(all_0_6_6) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(v1, all_0_6_6) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v4 & relation_rng(v1) = v3 & (v4 = v0 | ~ subset(all_0_5_5, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_5_5, v2) | ~ relation(v1) | ? [v3] : (relation_composition(v1, all_0_6_6) = v3 & relation_rng(v3) = v0))) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (186) with all_0_5_5, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, relation(all_0_6_6), yields: % 16.97/4.37 | (284) ? [v0] : (relation_rng(all_0_6_6) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_6_6, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = all_0_5_5 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_6_6, v1) = v3 & relation_dom(v3) = all_0_5_5))) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (69) with all_0_5_5, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, relation(all_0_6_6), yields: % 16.97/4.37 | (285) ? [v0] : (relation_rng(all_0_6_6) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(all_0_5_5, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | subset(all_0_5_5, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_6_6, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v0, v3)))) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (32) with all_0_4_4, all_0_6_6, empty_set and discharging atoms relation_rng(all_0_6_6) = all_0_4_4, relation(all_0_6_6), relation(empty_set), yields: % 16.97/4.37 | (286) ? [v0] : ? [v1] : (relation_composition(empty_set, all_0_6_6) = v0 & relation_rng(v0) = v1 & subset(v1, all_0_4_4)) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (32) with empty_set, empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 16.97/4.37 | (287) ? [v0] : ? [v1] : (relation_composition(empty_set, empty_set) = v0 & relation_rng(v0) = v1 & subset(v1, empty_set)) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (32) with empty_set, empty_set, all_0_6_6 and discharging atoms relation_rng(empty_set) = empty_set, relation(all_0_6_6), relation(empty_set), yields: % 16.97/4.37 | (288) ? [v0] : ? [v1] : (relation_composition(all_0_6_6, empty_set) = v0 & relation_rng(v0) = v1 & subset(v1, empty_set)) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (108) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 16.97/4.37 | (289) ? [v0] : ? [v1] : (relation_inverse(empty_set) = v0 & relation_rng(v0) = v1 & relation_dom(v0) = empty_set & relation_dom(empty_set) = v1) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (253) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 16.97/4.37 | (290) ? [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))) % 16.97/4.37 | % 16.97/4.37 | Instantiating formula (72) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 16.97/4.38 | (291) ? [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))) % 16.97/4.38 | % 16.97/4.38 | Instantiating formula (202) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 16.97/4.38 | (292) ? [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)))) % 16.97/4.38 | % 16.97/4.38 | Instantiating formula (30) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, relation(empty_set), yields: % 16.97/4.38 | (293) ? [v0] : ? [v1] : (relation_inverse(empty_set) = v1 & relation_rng(v1) = empty_set & relation_rng(empty_set) = v0 & relation_dom(v1) = v0) % 16.97/4.38 | % 16.97/4.38 | Instantiating formula (127) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, relation(empty_set), yields: % 16.97/4.38 | (294) ? [v0] : (relation_rng(empty_set) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(v1, empty_set) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v4 & relation_rng(v1) = v3 & (v4 = v0 | ~ subset(empty_set, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(empty_set, v2) | ~ relation(v1) | ? [v3] : (relation_composition(v1, empty_set) = v3 & relation_rng(v3) = v0))) % 16.97/4.38 | % 16.97/4.38 | Instantiating formula (186) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, relation(empty_set), yields: % 16.97/4.38 | (295) ? [v0] : (relation_rng(empty_set) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(empty_set, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = empty_set | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(empty_set, v1) = v3 & relation_dom(v3) = empty_set))) % 16.97/4.38 | % 16.97/4.38 | Instantiating formula (69) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, relation(empty_set), yields: % 16.97/4.38 | (296) ? [v0] : (relation_rng(empty_set) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(empty_set, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | subset(empty_set, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v0, v3)))) % 16.97/4.38 | % 16.97/4.38 | Instantiating (281) with all_58_0_38 yields: % 16.97/4.38 | (297) relation_dom(all_0_6_6) = all_58_0_38 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_4_4, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_58_0_38, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_58_0_38, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_0_4_4, v2))) % 16.97/4.38 | % 16.97/4.38 | Applying alpha-rule on (297) yields: % 16.97/4.38 | (298) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_0_4_4, v2))) % 16.97/4.38 | (299) relation_dom(all_0_6_6) = all_58_0_38 % 16.97/4.38 | (300) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_58_0_38, v2))) % 16.97/4.38 | (301) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_4_4, v1)) % 16.97/4.38 | (302) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_58_0_38, v1)) % 16.97/4.38 | % 16.97/4.38 | Instantiating (280) with all_61_0_39 yields: % 16.97/4.38 | (303) relation_dom(all_0_6_6) = all_61_0_39 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_6_6, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_61_0_39 | ~ subset(all_0_4_4, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_4_4, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_6_6, v0) = v2 & relation_dom(v2) = all_61_0_39)) % 16.97/4.38 | % 16.97/4.38 | Applying alpha-rule on (303) yields: % 16.97/4.38 | (304) relation_dom(all_0_6_6) = all_61_0_39 % 16.97/4.38 | (305) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_6_6, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_61_0_39 | ~ subset(all_0_4_4, v2)))) % 16.97/4.38 | (306) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_4_4, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_6_6, v0) = v2 & relation_dom(v2) = all_61_0_39)) % 16.97/4.38 | % 16.97/4.38 | Instantiating (295) with all_66_0_42 yields: % 16.97/4.38 | (307) relation_rng(empty_set) = all_66_0_42 & ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = empty_set | ~ subset(all_66_0_42, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_66_0_42, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = empty_set)) % 16.97/4.38 | % 16.97/4.38 | Applying alpha-rule on (307) yields: % 16.97/4.38 | (308) relation_rng(empty_set) = all_66_0_42 % 16.97/4.38 | (309) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = empty_set | ~ subset(all_66_0_42, v2)))) % 16.97/4.38 | (310) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_66_0_42, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = empty_set)) % 16.97/4.38 | % 16.97/4.38 | Instantiating (294) with all_69_0_43 yields: % 16.97/4.38 | (311) relation_rng(empty_set) = all_69_0_43 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_69_0_43 | ~ subset(empty_set, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, empty_set) = v2 & relation_rng(v2) = all_69_0_43)) % 16.97/4.38 | % 16.97/4.38 | Applying alpha-rule on (311) yields: % 16.97/4.38 | (312) relation_rng(empty_set) = all_69_0_43 % 16.97/4.38 | (313) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_69_0_43 | ~ subset(empty_set, v2)))) % 16.97/4.38 | (314) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, empty_set) = v2 & relation_rng(v2) = all_69_0_43)) % 16.97/4.38 | % 16.97/4.38 | Instantiating (279) with all_72_0_44 yields: % 16.97/4.38 | (315) relation_dom(all_0_6_6) = all_72_0_44 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_6_6) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_0_4_4 | ~ subset(all_72_0_44, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_72_0_44, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_6_6) = v2 & relation_rng(v2) = all_0_4_4)) % 16.97/4.38 | % 16.97/4.38 | Applying alpha-rule on (315) yields: % 16.97/4.38 | (316) relation_dom(all_0_6_6) = all_72_0_44 % 16.97/4.38 | (317) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_6_6) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_0_4_4 | ~ subset(all_72_0_44, v2)))) % 16.97/4.38 | (318) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_72_0_44, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_6_6) = v2 & relation_rng(v2) = all_0_4_4)) % 16.97/4.38 | % 16.97/4.38 | Instantiating (278) with all_75_0_45, all_75_1_46 yields: % 16.97/4.38 | (319) relation_inverse(all_0_6_6) = all_75_1_46 & relation_rng(all_75_1_46) = all_75_0_45 & relation_dom(all_75_1_46) = all_0_4_4 & relation_dom(all_0_6_6) = all_75_0_45 % 16.97/4.38 | % 16.97/4.38 | Applying alpha-rule on (319) yields: % 16.97/4.38 | (320) relation_inverse(all_0_6_6) = all_75_1_46 % 16.97/4.38 | (321) relation_rng(all_75_1_46) = all_75_0_45 % 16.97/4.39 | (322) relation_dom(all_75_1_46) = all_0_4_4 % 16.97/4.39 | (323) relation_dom(all_0_6_6) = all_75_0_45 % 16.97/4.39 | % 16.97/4.39 | Instantiating (293) with all_82_0_49, all_82_1_50 yields: % 16.97/4.39 | (324) relation_inverse(empty_set) = all_82_0_49 & relation_rng(all_82_0_49) = empty_set & relation_rng(empty_set) = all_82_1_50 & relation_dom(all_82_0_49) = all_82_1_50 % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (324) yields: % 16.97/4.39 | (325) relation_inverse(empty_set) = all_82_0_49 % 16.97/4.39 | (326) relation_rng(all_82_0_49) = empty_set % 16.97/4.39 | (327) relation_rng(empty_set) = all_82_1_50 % 16.97/4.39 | (328) relation_dom(all_82_0_49) = all_82_1_50 % 16.97/4.39 | % 16.97/4.39 | Instantiating (292) with all_84_0_51 yields: % 16.97/4.39 | (329) relation_dom(empty_set) = all_84_0_51 & ! [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_84_0_51, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(all_84_0_51, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(empty_set, v2))) % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (329) yields: % 16.97/4.39 | (330) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(empty_set, v2))) % 16.97/4.39 | (331) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(all_84_0_51, v1)) % 16.97/4.39 | (332) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_84_0_51, v2))) % 16.97/4.39 | (333) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1)) % 16.97/4.39 | (334) relation_dom(empty_set) = all_84_0_51 % 16.97/4.39 | % 16.97/4.39 | Instantiating (287) with all_89_0_54, all_89_1_55 yields: % 16.97/4.39 | (335) relation_composition(empty_set, empty_set) = all_89_1_55 & relation_rng(all_89_1_55) = all_89_0_54 & subset(all_89_0_54, empty_set) % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (335) yields: % 16.97/4.39 | (336) relation_composition(empty_set, empty_set) = all_89_1_55 % 16.97/4.39 | (337) relation_rng(all_89_1_55) = all_89_0_54 % 16.97/4.39 | (338) subset(all_89_0_54, empty_set) % 16.97/4.39 | % 16.97/4.39 | Instantiating (285) with all_91_0_56 yields: % 16.97/4.39 | (339) relation_rng(all_0_6_6) = all_91_0_56 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_91_0_56, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_0_5_5, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_5_5, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_91_0_56, v2))) % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (339) yields: % 16.97/4.39 | (340) relation_rng(all_0_6_6) = all_91_0_56 % 16.97/4.39 | (341) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_91_0_56, v1)) % 16.97/4.39 | (342) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_0_5_5, v2))) % 16.97/4.39 | (343) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_91_0_56, v2))) % 16.97/4.39 | (344) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_5_5, v1)) % 16.97/4.39 | % 16.97/4.39 | Instantiating (283) with all_94_0_57 yields: % 16.97/4.39 | (345) relation_rng(all_0_6_6) = all_94_0_57 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_6_6) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_94_0_57 | ~ subset(all_0_5_5, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_5_5, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_6_6) = v2 & relation_rng(v2) = all_94_0_57)) % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (345) yields: % 16.97/4.39 | (346) relation_rng(all_0_6_6) = all_94_0_57 % 16.97/4.39 | (347) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_6_6) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_94_0_57 | ~ subset(all_0_5_5, v2)))) % 16.97/4.39 | (348) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_5_5, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_6_6) = v2 & relation_rng(v2) = all_94_0_57)) % 16.97/4.39 | % 16.97/4.39 | Instantiating (291) with all_97_0_58 yields: % 16.97/4.39 | (349) relation_dom(empty_set) = all_97_0_58 & ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_97_0_58 | ~ 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_97_0_58)) % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (349) yields: % 16.97/4.39 | (350) relation_dom(empty_set) = all_97_0_58 % 16.97/4.39 | (351) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_97_0_58 | ~ subset(empty_set, v2)))) % 16.97/4.39 | (352) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = all_97_0_58)) % 16.97/4.39 | % 16.97/4.39 | Instantiating (282) with all_100_0_59, all_100_1_60 yields: % 16.97/4.39 | (353) relation_inverse(all_0_6_6) = all_100_0_59 & relation_rng(all_100_0_59) = all_0_5_5 & relation_rng(all_0_6_6) = all_100_1_60 & relation_dom(all_100_0_59) = all_100_1_60 % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (353) yields: % 16.97/4.39 | (354) relation_inverse(all_0_6_6) = all_100_0_59 % 16.97/4.39 | (355) relation_rng(all_100_0_59) = all_0_5_5 % 16.97/4.39 | (356) relation_rng(all_0_6_6) = all_100_1_60 % 16.97/4.39 | (357) relation_dom(all_100_0_59) = all_100_1_60 % 16.97/4.39 | % 16.97/4.39 | Instantiating (284) with all_102_0_61 yields: % 16.97/4.39 | (358) relation_rng(all_0_6_6) = all_102_0_61 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_6_6, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_0_5_5 | ~ subset(all_102_0_61, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_102_0_61, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_6_6, v0) = v2 & relation_dom(v2) = all_0_5_5)) % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (358) yields: % 16.97/4.39 | (359) relation_rng(all_0_6_6) = all_102_0_61 % 16.97/4.39 | (360) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_6_6, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_0_5_5 | ~ subset(all_102_0_61, v2)))) % 16.97/4.39 | (361) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_102_0_61, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_6_6, v0) = v2 & relation_dom(v2) = all_0_5_5)) % 16.97/4.39 | % 16.97/4.39 | Instantiating (286) with all_105_0_62, all_105_1_63 yields: % 16.97/4.39 | (362) relation_composition(empty_set, all_0_6_6) = all_105_1_63 & relation_rng(all_105_1_63) = all_105_0_62 & subset(all_105_0_62, all_0_4_4) % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (362) yields: % 16.97/4.39 | (363) relation_composition(empty_set, all_0_6_6) = all_105_1_63 % 16.97/4.39 | (364) relation_rng(all_105_1_63) = all_105_0_62 % 16.97/4.39 | (365) subset(all_105_0_62, all_0_4_4) % 16.97/4.39 | % 16.97/4.39 | Instantiating (296) with all_107_0_64 yields: % 16.97/4.39 | (366) relation_rng(empty_set) = all_107_0_64 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(all_107_0_64, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(empty_set, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_107_0_64, v2))) % 16.97/4.39 | % 16.97/4.39 | Applying alpha-rule on (366) yields: % 16.97/4.39 | (367) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1)) % 16.97/4.39 | (368) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(empty_set, v2))) % 16.97/4.40 | (369) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(all_107_0_64, v1)) % 16.97/4.40 | (370) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_107_0_64, v2))) % 16.97/4.40 | (371) relation_rng(empty_set) = all_107_0_64 % 16.97/4.40 | % 16.97/4.40 | Instantiating (290) with all_112_0_67 yields: % 16.97/4.40 | (372) relation_dom(empty_set) = all_112_0_67 & ! [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_112_0_67, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_112_0_67, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, empty_set) = v2 & relation_rng(v2) = empty_set)) % 16.97/4.40 | % 16.97/4.40 | Applying alpha-rule on (372) yields: % 16.97/4.40 | (373) relation_dom(empty_set) = all_112_0_67 % 16.97/4.40 | (374) ! [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_112_0_67, v2)))) % 16.97/4.40 | (375) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_112_0_67, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, empty_set) = v2 & relation_rng(v2) = empty_set)) % 16.97/4.40 | % 16.97/4.40 | Instantiating (289) with all_115_0_68, all_115_1_69 yields: % 16.97/4.40 | (376) relation_inverse(empty_set) = all_115_1_69 & relation_rng(all_115_1_69) = all_115_0_68 & relation_dom(all_115_1_69) = empty_set & relation_dom(empty_set) = all_115_0_68 % 16.97/4.40 | % 16.97/4.40 | Applying alpha-rule on (376) yields: % 16.97/4.40 | (377) relation_inverse(empty_set) = all_115_1_69 % 16.97/4.40 | (378) relation_rng(all_115_1_69) = all_115_0_68 % 16.97/4.40 | (379) relation_dom(all_115_1_69) = empty_set % 16.97/4.40 | (380) relation_dom(empty_set) = all_115_0_68 % 16.97/4.40 | % 16.97/4.40 | Instantiating (288) with all_117_0_70, all_117_1_71 yields: % 16.97/4.40 | (381) relation_composition(all_0_6_6, empty_set) = all_117_1_71 & relation_rng(all_117_1_71) = all_117_0_70 & subset(all_117_0_70, empty_set) % 16.97/4.40 | % 16.97/4.40 | Applying alpha-rule on (381) yields: % 16.97/4.40 | (382) relation_composition(all_0_6_6, empty_set) = all_117_1_71 % 16.97/4.40 | (383) relation_rng(all_117_1_71) = all_117_0_70 % 16.97/4.40 | (384) subset(all_117_0_70, empty_set) % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (18) with all_0_6_6, all_100_1_60, all_102_0_61 and discharging atoms relation_rng(all_0_6_6) = all_102_0_61, relation_rng(all_0_6_6) = all_100_1_60, yields: % 16.97/4.40 | (385) all_102_0_61 = all_100_1_60 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (18) with all_0_6_6, all_94_0_57, all_0_4_4 and discharging atoms relation_rng(all_0_6_6) = all_94_0_57, relation_rng(all_0_6_6) = all_0_4_4, yields: % 16.97/4.40 | (386) all_94_0_57 = all_0_4_4 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (18) with all_0_6_6, all_94_0_57, all_102_0_61 and discharging atoms relation_rng(all_0_6_6) = all_102_0_61, relation_rng(all_0_6_6) = all_94_0_57, yields: % 16.97/4.40 | (387) all_102_0_61 = all_94_0_57 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (18) with all_0_6_6, all_91_0_56, all_102_0_61 and discharging atoms relation_rng(all_0_6_6) = all_102_0_61, relation_rng(all_0_6_6) = all_91_0_56, yields: % 16.97/4.40 | (388) all_102_0_61 = all_91_0_56 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (18) with empty_set, all_82_1_50, empty_set and discharging atoms relation_rng(empty_set) = all_82_1_50, relation_rng(empty_set) = empty_set, yields: % 16.97/4.40 | (389) all_82_1_50 = empty_set % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (18) with empty_set, all_82_1_50, all_107_0_64 and discharging atoms relation_rng(empty_set) = all_107_0_64, relation_rng(empty_set) = all_82_1_50, yields: % 16.97/4.40 | (390) all_107_0_64 = all_82_1_50 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (18) with empty_set, all_69_0_43, all_107_0_64 and discharging atoms relation_rng(empty_set) = all_107_0_64, relation_rng(empty_set) = all_69_0_43, yields: % 16.97/4.40 | (391) all_107_0_64 = all_69_0_43 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (18) with empty_set, all_66_0_42, all_82_1_50 and discharging atoms relation_rng(empty_set) = all_82_1_50, relation_rng(empty_set) = all_66_0_42, yields: % 16.97/4.40 | (392) all_82_1_50 = all_66_0_42 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (15) with all_0_6_6, all_72_0_44, all_0_5_5 and discharging atoms relation_dom(all_0_6_6) = all_72_0_44, relation_dom(all_0_6_6) = all_0_5_5, yields: % 16.97/4.40 | (393) all_72_0_44 = all_0_5_5 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (15) with all_0_6_6, all_61_0_39, all_75_0_45 and discharging atoms relation_dom(all_0_6_6) = all_75_0_45, relation_dom(all_0_6_6) = all_61_0_39, yields: % 16.97/4.40 | (394) all_75_0_45 = all_61_0_39 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (15) with all_0_6_6, all_61_0_39, all_72_0_44 and discharging atoms relation_dom(all_0_6_6) = all_72_0_44, relation_dom(all_0_6_6) = all_61_0_39, yields: % 16.97/4.40 | (395) all_72_0_44 = all_61_0_39 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (15) with all_0_6_6, all_58_0_38, all_75_0_45 and discharging atoms relation_dom(all_0_6_6) = all_75_0_45, relation_dom(all_0_6_6) = all_58_0_38, yields: % 16.97/4.40 | (396) all_75_0_45 = all_58_0_38 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (15) with empty_set, all_115_0_68, empty_set and discharging atoms relation_dom(empty_set) = all_115_0_68, relation_dom(empty_set) = empty_set, yields: % 16.97/4.40 | (397) all_115_0_68 = empty_set % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (15) with empty_set, all_112_0_67, all_115_0_68 and discharging atoms relation_dom(empty_set) = all_115_0_68, relation_dom(empty_set) = all_112_0_67, yields: % 16.97/4.40 | (398) all_115_0_68 = all_112_0_67 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (15) with empty_set, all_97_0_58, all_115_0_68 and discharging atoms relation_dom(empty_set) = all_115_0_68, relation_dom(empty_set) = all_97_0_58, yields: % 16.97/4.40 | (399) all_115_0_68 = all_97_0_58 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (15) with empty_set, all_84_0_51, all_115_0_68 and discharging atoms relation_dom(empty_set) = all_115_0_68, relation_dom(empty_set) = all_84_0_51, yields: % 16.97/4.40 | (400) all_115_0_68 = all_84_0_51 % 16.97/4.40 | % 16.97/4.40 | Instantiating formula (42) with all_117_0_70 and discharging atoms subset(all_117_0_70, empty_set), yields: % 16.97/4.40 | (401) all_117_0_70 = empty_set % 16.97/4.40 | % 16.97/4.40 | Combining equations (397,398) yields a new equation: % 16.97/4.40 | (402) all_112_0_67 = empty_set % 16.97/4.40 | % 16.97/4.40 | Combining equations (400,398) yields a new equation: % 16.97/4.40 | (403) all_112_0_67 = all_84_0_51 % 16.97/4.40 | % 16.97/4.40 | Combining equations (399,398) yields a new equation: % 16.97/4.40 | (404) all_112_0_67 = all_97_0_58 % 16.97/4.40 | % 16.97/4.40 | Combining equations (402,404) yields a new equation: % 16.97/4.40 | (405) all_97_0_58 = empty_set % 16.97/4.40 | % 16.97/4.40 | Combining equations (403,404) yields a new equation: % 16.97/4.40 | (406) all_97_0_58 = all_84_0_51 % 16.97/4.40 | % 16.97/4.40 | Combining equations (390,391) yields a new equation: % 16.97/4.40 | (407) all_82_1_50 = all_69_0_43 % 16.97/4.40 | % 16.97/4.40 | Simplifying 407 yields: % 16.97/4.40 | (408) all_82_1_50 = all_69_0_43 % 16.97/4.40 | % 16.97/4.40 | Combining equations (387,385) yields a new equation: % 16.97/4.40 | (409) all_100_1_60 = all_94_0_57 % 16.97/4.40 | % 16.97/4.40 | Combining equations (388,385) yields a new equation: % 16.97/4.40 | (410) all_100_1_60 = all_91_0_56 % 16.97/4.40 | % 16.97/4.40 | Combining equations (409,410) yields a new equation: % 16.97/4.40 | (411) all_94_0_57 = all_91_0_56 % 16.97/4.40 | % 16.97/4.40 | Simplifying 411 yields: % 16.97/4.40 | (412) all_94_0_57 = all_91_0_56 % 16.97/4.40 | % 16.97/4.40 | Combining equations (406,405) yields a new equation: % 16.97/4.40 | (413) all_84_0_51 = empty_set % 16.97/4.40 | % 16.97/4.40 | Simplifying 413 yields: % 16.97/4.40 | (414) all_84_0_51 = empty_set % 16.97/4.40 | % 16.97/4.40 | Combining equations (412,386) yields a new equation: % 16.97/4.40 | (415) all_91_0_56 = all_0_4_4 % 16.97/4.40 | % 16.97/4.40 | Simplifying 415 yields: % 16.97/4.40 | (416) all_91_0_56 = all_0_4_4 % 16.97/4.40 | % 16.97/4.40 | Combining equations (392,408) yields a new equation: % 16.97/4.40 | (417) all_69_0_43 = all_66_0_42 % 16.97/4.40 | % 16.97/4.40 | Combining equations (389,408) yields a new equation: % 16.97/4.40 | (418) all_69_0_43 = empty_set % 16.97/4.40 | % 16.97/4.40 | Combining equations (394,396) yields a new equation: % 16.97/4.40 | (419) all_61_0_39 = all_58_0_38 % 16.97/4.40 | % 16.97/4.40 | Simplifying 419 yields: % 16.97/4.40 | (420) all_61_0_39 = all_58_0_38 % 16.97/4.40 | % 16.97/4.40 | Combining equations (395,393) yields a new equation: % 16.97/4.40 | (421) all_61_0_39 = all_0_5_5 % 16.97/4.40 | % 16.97/4.40 | Simplifying 421 yields: % 16.97/4.40 | (422) all_61_0_39 = all_0_5_5 % 16.97/4.40 | % 16.97/4.40 | Combining equations (418,417) yields a new equation: % 16.97/4.40 | (423) all_66_0_42 = empty_set % 16.97/4.40 | % 16.97/4.40 | Combining equations (420,422) yields a new equation: % 16.97/4.40 | (424) all_58_0_38 = all_0_5_5 % 16.97/4.40 | % 16.97/4.40 | Simplifying 424 yields: % 16.97/4.40 | (425) all_58_0_38 = all_0_5_5 % 16.97/4.40 | % 16.97/4.40 | Combining equations (416,410) yields a new equation: % 16.97/4.40 | (426) all_100_1_60 = all_0_4_4 % 16.97/4.40 | % 16.97/4.40 | Combining equations (426,385) yields a new equation: % 16.97/4.40 | (427) all_102_0_61 = all_0_4_4 % 16.97/4.40 | % 16.97/4.40 | From (401) and (383) follows: % 16.97/4.40 | (428) relation_rng(all_117_1_71) = empty_set % 16.97/4.40 | % 16.97/4.40 | From (423) and (308) follows: % 16.97/4.40 | (210) relation_rng(empty_set) = empty_set % 16.97/4.40 | % 16.97/4.40 | From (425) and (299) follows: % 16.97/4.40 | (172) relation_dom(all_0_6_6) = all_0_5_5 % 16.97/4.41 | % 16.97/4.41 | From (414) and (334) follows: % 16.97/4.41 | (118) relation_dom(empty_set) = empty_set % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (23) with all_117_1_71, empty_set, all_0_6_6 and discharging atoms relation_composition(all_0_6_6, empty_set) = all_117_1_71, relation(all_0_6_6), relation(empty_set), yields: % 16.97/4.41 | (432) relation(all_117_1_71) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (11) with all_117_1_71, empty_set, all_0_5_5, all_0_6_6 and discharging atoms relation_composition(all_0_6_6, empty_set) = all_117_1_71, relation_dom(all_0_6_6) = all_0_5_5, relation(all_0_6_6), relation(empty_set), yields: % 16.97/4.41 | (433) ? [v0] : (relation_dom(all_117_1_71) = v0 & subset(v0, all_0_5_5)) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (305) with all_117_1_71, empty_set and discharging atoms relation_composition(all_0_6_6, empty_set) = all_117_1_71, relation(empty_set), yields: % 16.97/4.41 | (434) ? [v0] : ? [v1] : (relation_dom(all_117_1_71) = v1 & relation_dom(empty_set) = v0 & (v1 = all_61_0_39 | ~ subset(all_0_4_4, v0))) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (360) with all_117_1_71, empty_set and discharging atoms relation_composition(all_0_6_6, empty_set) = all_117_1_71, relation(empty_set), yields: % 16.97/4.41 | (435) ? [v0] : ? [v1] : (relation_dom(all_117_1_71) = v1 & relation_dom(empty_set) = v0 & (v1 = all_0_5_5 | ~ subset(all_102_0_61, v0))) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (23) with all_105_1_63, all_0_6_6, empty_set and discharging atoms relation_composition(empty_set, all_0_6_6) = all_105_1_63, relation(all_0_6_6), relation(empty_set), yields: % 16.97/4.41 | (436) relation(all_105_1_63) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (11) with all_105_1_63, all_0_6_6, empty_set, empty_set and discharging atoms relation_composition(empty_set, all_0_6_6) = all_105_1_63, relation_dom(empty_set) = empty_set, relation(all_0_6_6), relation(empty_set), yields: % 16.97/4.41 | (437) ? [v0] : (relation_dom(all_105_1_63) = v0 & subset(v0, empty_set)) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (347) with all_105_1_63, empty_set and discharging atoms relation_composition(empty_set, all_0_6_6) = all_105_1_63, relation(empty_set), yields: % 16.97/4.41 | (438) ? [v0] : ? [v1] : (relation_rng(all_105_1_63) = v1 & relation_rng(empty_set) = v0 & (v1 = all_94_0_57 | ~ subset(all_0_5_5, v0))) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (317) with all_105_1_63, empty_set and discharging atoms relation_composition(empty_set, all_0_6_6) = all_105_1_63, relation(empty_set), yields: % 16.97/4.41 | (439) ? [v0] : ? [v1] : (relation_rng(all_105_1_63) = v1 & relation_rng(empty_set) = v0 & (v1 = all_0_4_4 | ~ subset(all_72_0_44, v0))) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (351) with all_105_1_63, all_0_6_6 and discharging atoms relation_composition(empty_set, all_0_6_6) = all_105_1_63, relation(all_0_6_6), yields: % 16.97/4.41 | (440) ? [v0] : ? [v1] : (relation_dom(all_105_1_63) = v1 & relation_dom(all_0_6_6) = v0 & (v1 = all_97_0_58 | ~ subset(empty_set, v0))) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (309) with all_105_1_63, all_0_6_6 and discharging atoms relation_composition(empty_set, all_0_6_6) = all_105_1_63, relation(all_0_6_6), yields: % 16.97/4.41 | (441) ? [v0] : ? [v1] : (relation_dom(all_105_1_63) = v1 & relation_dom(all_0_6_6) = v0 & (v1 = empty_set | ~ subset(all_66_0_42, v0))) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (351) with all_89_1_55, empty_set and discharging atoms relation_composition(empty_set, empty_set) = all_89_1_55, relation(empty_set), yields: % 16.97/4.41 | (442) ? [v0] : ? [v1] : (relation_dom(all_89_1_55) = v1 & relation_dom(empty_set) = v0 & (v1 = all_97_0_58 | ~ subset(empty_set, v0))) % 16.97/4.41 | % 16.97/4.41 | Instantiating formula (309) with all_89_1_55, empty_set and discharging atoms relation_composition(empty_set, empty_set) = all_89_1_55, relation(empty_set), yields: % 16.97/4.41 | (443) ? [v0] : ? [v1] : (relation_dom(all_89_1_55) = v1 & relation_dom(empty_set) = v0 & (v1 = empty_set | ~ subset(all_66_0_42, v0))) % 16.97/4.41 | % 16.97/4.41 | Instantiating (435) with all_131_0_73, all_131_1_74 yields: % 16.97/4.41 | (444) relation_dom(all_117_1_71) = all_131_0_73 & relation_dom(empty_set) = all_131_1_74 & (all_131_0_73 = all_0_5_5 | ~ subset(all_102_0_61, all_131_1_74)) % 16.97/4.41 | % 16.97/4.41 | Applying alpha-rule on (444) yields: % 16.97/4.41 | (445) relation_dom(all_117_1_71) = all_131_0_73 % 16.97/4.41 | (446) relation_dom(empty_set) = all_131_1_74 % 16.97/4.41 | (447) all_131_0_73 = all_0_5_5 | ~ subset(all_102_0_61, all_131_1_74) % 16.97/4.41 | % 16.97/4.41 | Instantiating (434) with all_133_0_75, all_133_1_76 yields: % 16.97/4.41 | (448) relation_dom(all_117_1_71) = all_133_0_75 & relation_dom(empty_set) = all_133_1_76 & (all_133_0_75 = all_61_0_39 | ~ subset(all_0_4_4, all_133_1_76)) % 16.97/4.41 | % 16.97/4.41 | Applying alpha-rule on (448) yields: % 16.97/4.41 | (449) relation_dom(all_117_1_71) = all_133_0_75 % 16.97/4.41 | (450) relation_dom(empty_set) = all_133_1_76 % 16.97/4.41 | (451) all_133_0_75 = all_61_0_39 | ~ subset(all_0_4_4, all_133_1_76) % 16.97/4.41 | % 16.97/4.41 | Instantiating (443) with all_147_0_88, all_147_1_89 yields: % 16.97/4.41 | (452) relation_dom(all_89_1_55) = all_147_0_88 & relation_dom(empty_set) = all_147_1_89 & (all_147_0_88 = empty_set | ~ subset(all_66_0_42, all_147_1_89)) % 16.97/4.41 | % 16.97/4.41 | Applying alpha-rule on (452) yields: % 16.97/4.41 | (453) relation_dom(all_89_1_55) = all_147_0_88 % 16.97/4.41 | (454) relation_dom(empty_set) = all_147_1_89 % 16.97/4.41 | (455) all_147_0_88 = empty_set | ~ subset(all_66_0_42, all_147_1_89) % 16.97/4.41 | % 16.97/4.41 | Instantiating (442) with all_149_0_90, all_149_1_91 yields: % 16.97/4.41 | (456) relation_dom(all_89_1_55) = all_149_0_90 & relation_dom(empty_set) = all_149_1_91 & (all_149_0_90 = all_97_0_58 | ~ subset(empty_set, all_149_1_91)) % 16.97/4.41 | % 16.97/4.41 | Applying alpha-rule on (456) yields: % 16.97/4.41 | (457) relation_dom(all_89_1_55) = all_149_0_90 % 16.97/4.41 | (458) relation_dom(empty_set) = all_149_1_91 % 16.97/4.41 | (459) all_149_0_90 = all_97_0_58 | ~ subset(empty_set, all_149_1_91) % 16.97/4.41 | % 16.97/4.41 | Instantiating (433) with all_153_0_94 yields: % 16.97/4.41 | (460) relation_dom(all_117_1_71) = all_153_0_94 & subset(all_153_0_94, all_0_5_5) % 16.97/4.41 | % 16.97/4.41 | Applying alpha-rule on (460) yields: % 16.97/4.41 | (461) relation_dom(all_117_1_71) = all_153_0_94 % 16.97/4.41 | (462) subset(all_153_0_94, all_0_5_5) % 16.97/4.41 | % 16.97/4.41 | Instantiating (441) with all_168_0_104, all_168_1_105 yields: % 16.97/4.41 | (463) relation_dom(all_105_1_63) = all_168_0_104 & relation_dom(all_0_6_6) = all_168_1_105 & (all_168_0_104 = empty_set | ~ subset(all_66_0_42, all_168_1_105)) % 16.97/4.41 | % 16.97/4.41 | Applying alpha-rule on (463) yields: % 16.97/4.41 | (464) relation_dom(all_105_1_63) = all_168_0_104 % 16.97/4.41 | (465) relation_dom(all_0_6_6) = all_168_1_105 % 16.97/4.41 | (466) all_168_0_104 = empty_set | ~ subset(all_66_0_42, all_168_1_105) % 16.97/4.41 | % 16.97/4.41 | Instantiating (440) with all_170_0_106, all_170_1_107 yields: % 16.97/4.41 | (467) relation_dom(all_105_1_63) = all_170_0_106 & relation_dom(all_0_6_6) = all_170_1_107 & (all_170_0_106 = all_97_0_58 | ~ subset(empty_set, all_170_1_107)) % 16.97/4.41 | % 16.97/4.41 | Applying alpha-rule on (467) yields: % 16.97/4.41 | (468) relation_dom(all_105_1_63) = all_170_0_106 % 16.97/4.41 | (469) relation_dom(all_0_6_6) = all_170_1_107 % 16.97/4.41 | (470) all_170_0_106 = all_97_0_58 | ~ subset(empty_set, all_170_1_107) % 16.97/4.41 | % 16.97/4.41 | Instantiating (439) with all_172_0_108, all_172_1_109 yields: % 16.97/4.41 | (471) relation_rng(all_105_1_63) = all_172_0_108 & relation_rng(empty_set) = all_172_1_109 & (all_172_0_108 = all_0_4_4 | ~ subset(all_72_0_44, all_172_1_109)) % 16.97/4.41 | % 16.97/4.41 | Applying alpha-rule on (471) yields: % 16.97/4.41 | (472) relation_rng(all_105_1_63) = all_172_0_108 % 16.97/4.41 | (473) relation_rng(empty_set) = all_172_1_109 % 16.97/4.41 | (474) all_172_0_108 = all_0_4_4 | ~ subset(all_72_0_44, all_172_1_109) % 16.97/4.41 | % 16.97/4.41 | Instantiating (438) with all_174_0_110, all_174_1_111 yields: % 16.97/4.42 | (475) relation_rng(all_105_1_63) = all_174_0_110 & relation_rng(empty_set) = all_174_1_111 & (all_174_0_110 = all_94_0_57 | ~ subset(all_0_5_5, all_174_1_111)) % 16.97/4.42 | % 16.97/4.42 | Applying alpha-rule on (475) yields: % 16.97/4.42 | (476) relation_rng(all_105_1_63) = all_174_0_110 % 16.97/4.42 | (477) relation_rng(empty_set) = all_174_1_111 % 16.97/4.42 | (478) all_174_0_110 = all_94_0_57 | ~ subset(all_0_5_5, all_174_1_111) % 16.97/4.42 | % 16.97/4.42 | Instantiating (437) with all_176_0_112 yields: % 16.97/4.42 | (479) relation_dom(all_105_1_63) = all_176_0_112 & subset(all_176_0_112, empty_set) % 16.97/4.42 | % 16.97/4.42 | Applying alpha-rule on (479) yields: % 16.97/4.42 | (480) relation_dom(all_105_1_63) = all_176_0_112 % 16.97/4.42 | (481) subset(all_176_0_112, empty_set) % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (18) with all_105_1_63, all_174_0_110, all_105_0_62 and discharging atoms relation_rng(all_105_1_63) = all_174_0_110, relation_rng(all_105_1_63) = all_105_0_62, yields: % 16.97/4.42 | (482) all_174_0_110 = all_105_0_62 % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (18) with all_105_1_63, all_172_0_108, all_174_0_110 and discharging atoms relation_rng(all_105_1_63) = all_174_0_110, relation_rng(all_105_1_63) = all_172_0_108, yields: % 16.97/4.42 | (483) all_174_0_110 = all_172_0_108 % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (18) with empty_set, all_174_1_111, empty_set and discharging atoms relation_rng(empty_set) = all_174_1_111, relation_rng(empty_set) = empty_set, yields: % 16.97/4.42 | (484) all_174_1_111 = empty_set % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (18) with empty_set, all_172_1_109, all_174_1_111 and discharging atoms relation_rng(empty_set) = all_174_1_111, relation_rng(empty_set) = all_172_1_109, yields: % 16.97/4.42 | (485) all_174_1_111 = all_172_1_109 % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (15) with all_117_1_71, all_131_0_73, all_153_0_94 and discharging atoms relation_dom(all_117_1_71) = all_153_0_94, relation_dom(all_117_1_71) = all_131_0_73, yields: % 16.97/4.42 | (486) all_153_0_94 = all_131_0_73 % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (15) with all_105_1_63, all_170_0_106, all_176_0_112 and discharging atoms relation_dom(all_105_1_63) = all_176_0_112, relation_dom(all_105_1_63) = all_170_0_106, yields: % 16.97/4.42 | (487) all_176_0_112 = all_170_0_106 % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (15) with all_105_1_63, all_168_0_104, all_170_0_106 and discharging atoms relation_dom(all_105_1_63) = all_170_0_106, relation_dom(all_105_1_63) = all_168_0_104, yields: % 16.97/4.42 | (488) all_170_0_106 = all_168_0_104 % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (15) with empty_set, all_147_1_89, empty_set and discharging atoms relation_dom(empty_set) = all_147_1_89, relation_dom(empty_set) = empty_set, yields: % 16.97/4.42 | (489) all_147_1_89 = empty_set % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (15) with empty_set, all_133_1_76, all_149_1_91 and discharging atoms relation_dom(empty_set) = all_149_1_91, relation_dom(empty_set) = all_133_1_76, yields: % 16.97/4.42 | (490) all_149_1_91 = all_133_1_76 % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (15) with empty_set, all_133_1_76, all_147_1_89 and discharging atoms relation_dom(empty_set) = all_147_1_89, relation_dom(empty_set) = all_133_1_76, yields: % 16.97/4.42 | (491) all_147_1_89 = all_133_1_76 % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (15) with empty_set, all_131_1_74, all_149_1_91 and discharging atoms relation_dom(empty_set) = all_149_1_91, relation_dom(empty_set) = all_131_1_74, yields: % 16.97/4.42 | (492) all_149_1_91 = all_131_1_74 % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (42) with all_176_0_112 and discharging atoms subset(all_176_0_112, empty_set), yields: % 16.97/4.42 | (493) all_176_0_112 = empty_set % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (68) with all_117_1_71 and discharging atoms relation_rng(all_117_1_71) = empty_set, relation(all_117_1_71), yields: % 16.97/4.42 | (494) all_117_1_71 = empty_set % 16.97/4.42 | % 16.97/4.42 | Combining equations (487,493) yields a new equation: % 16.97/4.42 | (495) all_170_0_106 = empty_set % 16.97/4.42 | % 16.97/4.42 | Simplifying 495 yields: % 16.97/4.42 | (496) all_170_0_106 = empty_set % 16.97/4.42 | % 16.97/4.42 | Combining equations (482,483) yields a new equation: % 16.97/4.42 | (497) all_172_0_108 = all_105_0_62 % 16.97/4.42 | % 16.97/4.42 | Combining equations (484,485) yields a new equation: % 16.97/4.42 | (498) all_172_1_109 = empty_set % 16.97/4.42 | % 16.97/4.42 | Combining equations (488,496) yields a new equation: % 16.97/4.42 | (499) all_168_0_104 = empty_set % 16.97/4.42 | % 16.97/4.42 | Simplifying 499 yields: % 16.97/4.42 | (500) all_168_0_104 = empty_set % 16.97/4.42 | % 16.97/4.42 | Combining equations (490,492) yields a new equation: % 16.97/4.42 | (501) all_133_1_76 = all_131_1_74 % 16.97/4.42 | % 16.97/4.42 | Simplifying 501 yields: % 16.97/4.42 | (502) all_133_1_76 = all_131_1_74 % 16.97/4.42 | % 16.97/4.42 | Combining equations (491,489) yields a new equation: % 16.97/4.42 | (503) all_133_1_76 = empty_set % 16.97/4.42 | % 16.97/4.42 | Simplifying 503 yields: % 16.97/4.42 | (504) all_133_1_76 = empty_set % 16.97/4.42 | % 16.97/4.42 | Combining equations (504,502) yields a new equation: % 16.97/4.42 | (505) all_131_1_74 = empty_set % 16.97/4.42 | % 16.97/4.42 | From (497) and (472) follows: % 16.97/4.42 | (364) relation_rng(all_105_1_63) = all_105_0_62 % 16.97/4.42 | % 16.97/4.42 | From (498) and (473) follows: % 16.97/4.42 | (210) relation_rng(empty_set) = empty_set % 16.97/4.42 | % 16.97/4.42 | From (494) and (445) follows: % 16.97/4.42 | (508) relation_dom(empty_set) = all_131_0_73 % 16.97/4.42 | % 16.97/4.42 | From (500) and (464) follows: % 16.97/4.42 | (509) relation_dom(all_105_1_63) = empty_set % 16.97/4.42 | % 16.97/4.42 | From (505) and (446) follows: % 16.97/4.42 | (118) relation_dom(empty_set) = empty_set % 16.97/4.42 | % 16.97/4.42 | From (486) and (462) follows: % 16.97/4.42 | (511) subset(all_131_0_73, all_0_5_5) % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (160) with all_105_1_63 and discharging atoms relation_dom(all_105_1_63) = empty_set, relation(all_105_1_63), yields: % 16.97/4.42 | (512) all_105_1_63 = empty_set % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (15) with empty_set, all_131_0_73, empty_set and discharging atoms relation_dom(empty_set) = all_131_0_73, relation_dom(empty_set) = empty_set, yields: % 16.97/4.42 | (513) all_131_0_73 = empty_set % 16.97/4.42 | % 16.97/4.42 | From (512) and (364) follows: % 16.97/4.42 | (514) relation_rng(empty_set) = all_105_0_62 % 16.97/4.42 | % 16.97/4.42 | From (513) and (511) follows: % 16.97/4.42 | (515) subset(empty_set, all_0_5_5) % 16.97/4.42 | % 16.97/4.42 | Instantiating formula (18) with empty_set, all_105_0_62, empty_set and discharging atoms relation_rng(empty_set) = all_105_0_62, relation_rng(empty_set) = empty_set, yields: % 16.97/4.42 | (516) all_105_0_62 = empty_set % 16.97/4.42 | % 16.97/4.42 | Combining equations (516,497) yields a new equation: % 16.97/4.42 | (517) all_172_0_108 = empty_set % 16.97/4.42 | % 16.97/4.42 | From (516) and (365) follows: % 16.97/4.42 | (518) subset(empty_set, all_0_4_4) % 16.97/4.42 | % 16.97/4.42 +-Applying beta-rule and splitting (267), into two cases. % 16.97/4.42 |-Branch one: % 16.97/4.42 | (519) all_0_4_4 = empty_set & ~ (all_0_5_5 = empty_set) % 16.97/4.42 | % 16.97/4.42 | Applying alpha-rule on (519) yields: % 16.97/4.42 | (520) all_0_4_4 = empty_set % 16.97/4.42 | (521) ~ (all_0_5_5 = empty_set) % 16.97/4.42 | % 16.97/4.42 | Combining equations (520,427) yields a new equation: % 16.97/4.42 | (522) all_102_0_61 = empty_set % 16.97/4.42 | % 16.97/4.42 | From (520) and (518) follows: % 16.97/4.42 | (523) subset(empty_set, empty_set) % 16.97/4.42 | % 16.97/4.42 +-Applying beta-rule and splitting (447), into two cases. % 16.97/4.42 |-Branch one: % 16.97/4.42 | (524) ~ subset(all_102_0_61, all_131_1_74) % 16.97/4.42 | % 16.97/4.42 | From (522)(505) and (524) follows: % 16.97/4.42 | (525) ~ subset(empty_set, empty_set) % 16.97/4.42 | % 16.97/4.42 | Using (523) and (525) yields: % 16.97/4.42 | (526) $false % 16.97/4.42 | % 16.97/4.42 |-The branch is then unsatisfiable % 16.97/4.42 |-Branch two: % 16.97/4.42 | (527) subset(all_102_0_61, all_131_1_74) % 16.97/4.43 | (528) all_131_0_73 = all_0_5_5 % 16.97/4.43 | % 16.97/4.43 | Combining equations (528,513) yields a new equation: % 16.97/4.43 | (529) all_0_5_5 = empty_set % 16.97/4.43 | % 16.97/4.43 | Simplifying 529 yields: % 16.97/4.43 | (530) all_0_5_5 = empty_set % 16.97/4.43 | % 16.97/4.43 | Equations (530) can reduce 521 to: % 16.97/4.43 | (531) $false % 16.97/4.43 | % 16.97/4.43 |-The branch is then unsatisfiable % 16.97/4.43 |-Branch two: % 16.97/4.43 | (532) all_0_5_5 = empty_set & ~ (all_0_4_4 = empty_set) % 16.97/4.43 | % 16.97/4.43 | Applying alpha-rule on (532) yields: % 16.97/4.43 | (530) all_0_5_5 = empty_set % 16.97/4.43 | (534) ~ (all_0_4_4 = empty_set) % 16.97/4.43 | % 16.97/4.43 | Combining equations (530,393) yields a new equation: % 16.97/4.43 | (535) all_72_0_44 = empty_set % 16.97/4.43 | % 16.97/4.43 | From (530) and (515) follows: % 16.97/4.43 | (523) subset(empty_set, empty_set) % 17.35/4.43 | % 17.35/4.43 +-Applying beta-rule and splitting (474), into two cases. % 17.35/4.43 |-Branch one: % 17.35/4.43 | (537) ~ subset(all_72_0_44, all_172_1_109) % 17.35/4.43 | % 17.35/4.43 | From (535)(498) and (537) follows: % 17.35/4.43 | (525) ~ subset(empty_set, empty_set) % 17.35/4.43 | % 17.35/4.43 | Using (523) and (525) yields: % 17.35/4.43 | (526) $false % 17.35/4.43 | % 17.35/4.43 |-The branch is then unsatisfiable % 17.35/4.43 |-Branch two: % 17.35/4.43 | (540) subset(all_72_0_44, all_172_1_109) % 17.35/4.43 | (541) all_172_0_108 = all_0_4_4 % 17.35/4.43 | % 17.35/4.43 | Combining equations (517,541) yields a new equation: % 17.35/4.43 | (520) all_0_4_4 = empty_set % 17.35/4.43 | % 17.35/4.43 | Equations (520) can reduce 534 to: % 17.35/4.43 | (531) $false % 17.35/4.43 | % 17.35/4.43 |-The branch is then unsatisfiable % 17.35/4.43 % SZS output end Proof for theBenchmark % 17.35/4.43 % 17.35/4.43 3848ms %------------------------------------------------------------------------------