%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU188+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n006.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 08:47:27 EDT 2022 % Result : Theorem 11.19s 3.30s % Output : Proof 16.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU188+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sun Jun 19 23:03:10 EDT 2022 % 0.13/0.35 % CPUTime : % 0.61/0.61 ____ _ % 0.61/0.61 ___ / __ \_____(_)___ ________ __________ % 0.61/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.61/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.61/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.61/0.61 % 0.61/0.61 A Theorem Prover for First-Order Logic % 0.61/0.61 (ePrincess v.1.0) % 0.61/0.61 % 0.61/0.61 (c) Philipp Rümmer, 2009-2015 % 0.61/0.61 (c) Peter Backeman, 2014-2015 % 0.61/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.61/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.61/0.61 Bug reports to peter@backeman.se % 0.61/0.61 % 0.61/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.61/0.61 % 0.61/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.57/1.18 Prover 0: Preprocessing ... % 5.16/1.86 Prover 0: Warning: ignoring some quantifiers % 5.16/1.90 Prover 0: Constructing countermodel ... % 11.19/3.30 Prover 0: proved (2638ms) % 11.19/3.30 % 11.19/3.30 No countermodel exists, formula is valid % 11.19/3.30 % SZS status Theorem for theBenchmark % 11.19/3.30 % 11.19/3.30 Generating proof ... Warning: ignoring some quantifiers % 15.19/4.20 found it (size 113) % 15.19/4.20 % 15.19/4.20 % SZS output start Proof for theBenchmark % 15.19/4.20 Assumed formulas after preprocessing and simplification: % 15.19/4.20 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v1 = empty_set) & 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] : ( ~ (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 | ~ (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)) % 15.83/4.29 | 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: % 15.83/4.29 | (1) ~ (all_0_6_6 = empty_set) & 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] : ( ~ (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 | ~ (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) % 15.83/4.33 | % 15.83/4.33 | Applying alpha-rule on (1) yields: % 15.83/4.33 | (2) ! [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)) % 15.83/4.33 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) % 15.83/4.33 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) % 15.83/4.33 | (5) ! [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))) % 15.83/4.33 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) % 15.83/4.33 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 15.83/4.33 | (8) ? [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))))) % 15.83/4.33 | (9) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) % 15.83/4.33 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 15.83/4.33 | (11) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) % 15.83/4.33 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) % 15.83/4.33 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 15.83/4.33 | (14) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) % 15.83/4.33 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) % 15.83/4.33 | (16) relation_rng(empty_set) = empty_set % 15.83/4.33 | (17) ! [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)))) % 15.83/4.33 | (18) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) % 15.83/4.33 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) % 15.83/4.34 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) % 15.83/4.34 | (21) ! [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)) % 15.83/4.34 | (22) relation(all_0_0_0) % 15.83/4.34 | (23) relation(empty_set) % 15.83/4.34 | (24) ! [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)))) % 15.83/4.34 | (25) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 15.83/4.34 | (26) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 15.83/4.34 | (27) ! [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))) % 15.83/4.34 | (28) ! [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)))) % 15.83/4.34 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 15.83/4.34 | (30) ! [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))) % 15.83/4.34 | (31) ! [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)) % 15.83/4.34 | (32) ! [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)))) % 15.83/4.34 | (33) ! [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))) % 15.83/4.34 | (34) ! [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))))) % 15.83/4.34 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 15.83/4.34 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 15.83/4.34 | (37) ? [v0] : subset(empty_set, v0) % 15.83/4.34 | (38) ! [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)))) % 15.83/4.34 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 15.83/4.34 | (40) all_0_4_4 = empty_set | all_0_5_5 = empty_set % 15.83/4.34 | (41) ! [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)) % 15.83/4.34 | (42) ! [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))) % 15.83/4.34 | (43) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 15.83/4.34 | (44) ! [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)))) % 15.83/4.34 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) % 15.83/4.34 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) % 15.83/4.34 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) % 15.83/4.34 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 15.83/4.34 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 15.83/4.34 | (50) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1))) % 15.83/4.34 | (51) ? [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))))) % 15.83/4.34 | (52) relation_rng(all_0_6_6) = all_0_4_4 % 15.83/4.34 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 15.83/4.34 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 15.83/4.34 | (55) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 15.83/4.34 | (56) ? [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))))) % 15.83/4.34 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 15.83/4.34 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 15.83/4.34 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 15.83/4.34 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) % 15.83/4.34 | (61) empty(all_0_1_1) % 15.83/4.34 | (62) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) % 15.83/4.34 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 15.83/4.34 | (64) powerset(empty_set) = all_0_7_7 % 15.83/4.34 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 15.83/4.34 | (66) relation_dom(empty_set) = empty_set % 15.83/4.34 | (67) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 15.83/4.34 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) % 15.83/4.34 | (69) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 15.83/4.34 | (70) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 15.83/4.34 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 15.83/4.34 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 15.83/4.35 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) % 15.83/4.35 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) % 15.83/4.35 | (75) ! [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))) % 15.83/4.35 | (76) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 15.83/4.35 | (77) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) % 15.83/4.35 | (78) ? [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))))) % 15.83/4.35 | (79) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 15.83/4.35 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) % 15.83/4.35 | (81) ! [v0] : ~ proper_subset(v0, v0) % 15.83/4.35 | (82) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) % 15.83/4.35 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 15.83/4.35 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 15.83/4.35 | (85) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 15.83/4.35 | (86) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 15.83/4.35 | (87) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 15.83/4.35 | (88) ! [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)) % 15.83/4.35 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 15.83/4.35 | (90) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 15.83/4.35 | (91) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 15.83/4.35 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 15.83/4.35 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 15.83/4.35 | (94) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) % 15.83/4.35 | (95) ? [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))))) % 15.83/4.35 | (96) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 15.83/4.35 | (97) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 15.83/4.35 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 15.83/4.35 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 15.83/4.35 | (100) ! [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))) % 15.83/4.35 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 15.83/4.35 | (102) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) % 15.83/4.35 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 15.83/4.35 | (104) ! [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))) % 15.83/4.35 | (105) ! [v0] : ~ (singleton(v0) = empty_set) % 15.83/4.35 | (106) ? [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))))) % 15.83/4.35 | (107) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 15.83/4.35 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 15.83/4.35 | (109) ? [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))))) % 15.83/4.35 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 15.83/4.35 | (111) ? [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))) % 15.83/4.35 | (112) ! [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))) % 15.83/4.35 | (113) ? [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))))) % 15.83/4.35 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 15.83/4.35 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 15.83/4.35 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 15.83/4.35 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 15.83/4.35 | (118) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) % 15.83/4.35 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 15.83/4.35 | (120) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 15.83/4.35 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 15.83/4.35 | (122) singleton(empty_set) = all_0_7_7 % 15.83/4.35 | (123) ! [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)))) % 15.83/4.35 | (124) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 15.83/4.35 | (125) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 15.83/4.36 | (126) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) % 15.83/4.36 | (127) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 15.83/4.36 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 15.83/4.36 | (129) ! [v0] : ( ~ empty(v0) | relation(v0)) % 15.83/4.36 | (130) ! [v0] : ~ in(v0, empty_set) % 15.83/4.36 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 15.83/4.36 | (132) ! [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))) % 15.83/4.36 | (133) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 15.83/4.36 | (134) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 15.83/4.36 | (135) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) % 15.83/4.36 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 15.83/4.36 | (137) ? [v0] : ? [v1] : element(v1, v0) % 15.83/4.36 | (138) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 15.83/4.36 | (139) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 15.83/4.36 | (140) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) % 15.83/4.36 | (141) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) % 15.83/4.36 | (142) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 15.83/4.36 | (143) ! [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))))) % 15.83/4.36 | (144) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) % 15.83/4.36 | (145) ! [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))) % 15.83/4.36 | (146) ! [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)))) % 15.83/4.36 | (147) ! [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)) % 15.83/4.36 | (148) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) % 15.83/4.36 | (149) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 15.83/4.36 | (150) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 15.83/4.36 | (151) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 15.83/4.36 | (152) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) % 15.83/4.36 | (153) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 15.83/4.36 | (154) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 15.83/4.36 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 15.83/4.36 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 15.83/4.36 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) % 15.83/4.36 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 15.83/4.36 | (159) ! [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))) % 15.83/4.36 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 15.83/4.36 | (161) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) % 15.83/4.36 | (162) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 15.83/4.36 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 15.83/4.36 | (164) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 15.83/4.36 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 15.83/4.36 | (166) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 15.83/4.36 | (167) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) % 15.83/4.36 | (168) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 15.83/4.36 | (169) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 15.83/4.36 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 15.83/4.36 | (171) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 15.83/4.36 | (172) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 15.83/4.36 | (173) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) % 15.83/4.36 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) % 15.83/4.36 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) % 15.83/4.36 | (176) ? [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))))) % 15.83/4.36 | (177) ? [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)))) % 15.83/4.36 | (178) ! [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)) % 15.83/4.36 | (179) ! [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)) % 15.83/4.36 | (180) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 15.83/4.36 | (181) ~ empty(all_0_2_2) % 15.83/4.36 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 15.83/4.37 | (183) ! [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))) % 15.83/4.37 | (184) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) % 15.83/4.37 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 15.83/4.37 | (186) ! [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) % 15.83/4.37 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 15.83/4.37 | (188) empty(empty_set) % 15.83/4.37 | (189) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 15.83/4.37 | (190) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) % 15.83/4.37 | (191) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 15.83/4.37 | (192) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 15.83/4.37 | (193) ! [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))) % 15.83/4.37 | (194) ! [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))) % 15.83/4.37 | (195) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 15.83/4.37 | (196) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 15.83/4.37 | (197) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) % 15.83/4.37 | (198) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 15.83/4.37 | (199) ? [v0] : subset(v0, v0) % 15.83/4.37 | (200) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 15.83/4.37 | (201) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 15.83/4.37 | (202) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 15.83/4.37 | (203) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) % 15.83/4.37 | (204) ! [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))))) % 15.83/4.37 | (205) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 15.83/4.37 | (206) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 15.83/4.37 | (207) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 15.83/4.37 | (208) relation_dom(all_0_6_6) = all_0_5_5 % 15.83/4.37 | (209) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 15.83/4.37 | (210) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 15.83/4.37 | (211) ~ (all_0_6_6 = empty_set) % 15.83/4.37 | (212) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 15.83/4.37 | (213) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 15.83/4.37 | (214) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 15.83/4.37 | (215) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 15.83/4.37 | (216) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) % 15.83/4.37 | (217) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) % 15.83/4.37 | (218) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 15.83/4.37 | (219) relation(all_0_6_6) % 15.83/4.37 | (220) ! [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)))) % 15.83/4.37 | (221) ! [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)))) % 15.83/4.37 | (222) empty(all_0_0_0) % 15.83/4.37 | (223) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) % 15.83/4.37 | (224) ! [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))) % 15.83/4.37 | (225) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 15.83/4.37 | (226) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) % 15.83/4.37 | (227) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 15.83/4.37 | (228) ! [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))) % 15.83/4.37 | (229) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 15.83/4.37 | (230) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 15.83/4.37 | (231) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) % 15.83/4.37 | (232) relation(all_0_2_2) % 15.83/4.37 | (233) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 15.83/4.37 | (234) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 15.83/4.37 | (235) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 15.83/4.37 | (236) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 15.83/4.37 | (237) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 15.83/4.37 | (238) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 15.83/4.37 | (239) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 15.83/4.37 | (240) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 15.83/4.37 | (241) ! [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)) % 15.83/4.38 | (242) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 15.83/4.38 | (243) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 15.83/4.38 | (244) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 15.83/4.38 | (245) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) % 15.83/4.38 | (246) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 15.83/4.38 | (247) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 15.83/4.38 | (248) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 15.83/4.38 | (249) ! [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)))) % 15.83/4.38 | (250) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 15.83/4.38 | (251) ! [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))) % 15.83/4.38 | (252) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 15.83/4.38 | (253) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) % 15.83/4.38 | (254) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) % 15.83/4.38 | (255) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 15.83/4.38 | (256) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 15.83/4.38 | (257) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 15.83/4.38 | (258) ! [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)))) % 15.83/4.38 | (259) ! [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)))) % 15.83/4.38 | (260) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 15.83/4.38 | (261) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 15.83/4.38 | (262) ~ empty(all_0_3_3) % 15.83/4.38 | (263) ! [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)))))))) % 15.83/4.38 | (264) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 15.83/4.38 | (265) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) % 15.83/4.38 | (266) ! [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)))) % 15.83/4.38 | (267) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 15.83/4.38 | (268) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 15.83/4.38 | (269) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) % 15.83/4.38 | % 15.83/4.38 | Instantiating formula (171) with all_0_1_1, all_0_0_0 and discharging atoms empty(all_0_0_0), empty(all_0_1_1), yields: % 15.83/4.38 | (270) all_0_0_0 = all_0_1_1 % 15.83/4.38 | % 15.83/4.38 | Instantiating formula (171) with empty_set, all_0_0_0 and discharging atoms empty(all_0_0_0), empty(empty_set), yields: % 15.83/4.38 | (271) all_0_0_0 = empty_set % 15.83/4.38 | % 15.83/4.38 | Combining equations (271,270) yields a new equation: % 15.83/4.38 | (272) all_0_1_1 = empty_set % 16.31/4.38 | % 16.31/4.38 | Combining equations (272,270) yields a new equation: % 16.31/4.38 | (271) all_0_0_0 = empty_set % 16.31/4.38 | % 16.31/4.38 | From (271) and (22) follows: % 16.31/4.38 | (23) relation(empty_set) % 16.31/4.38 | % 16.31/4.38 | Instantiating formula (193) with all_0_4_4, all_0_6_6, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_4_4, relation(all_0_6_6), yields: % 16.31/4.38 | (275) ? [v0] : ? [v1] : (relation_composition(all_0_6_6, all_0_6_6) = v0 & relation_rng(v0) = v1 & subset(v1, all_0_4_4)) % 16.31/4.38 | % 16.31/4.38 | Instantiating formula (21) 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: % 16.31/4.38 | (276) ? [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) % 16.31/4.38 | % 16.31/4.38 | Instantiating formula (249) 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: % 16.31/4.38 | (277) ? [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))) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (221) 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: % 16.31/4.39 | (278) ? [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))) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (34) 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: % 16.31/4.39 | (279) ? [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)))) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (88) 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: % 16.31/4.39 | (280) ? [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) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (123) 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: % 16.31/4.39 | (281) ? [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))) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (28) 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: % 16.31/4.39 | (282) ? [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))) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (204) 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: % 16.31/4.39 | (283) ? [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)))) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (102) with all_0_6_6 and discharging atoms relation(all_0_6_6), yields: % 16.31/4.39 | (284) all_0_6_6 = empty_set | ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_6_6)) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (193) 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: % 16.31/4.39 | (285) ? [v0] : ? [v1] : (relation_composition(empty_set, all_0_6_6) = v0 & relation_rng(v0) = v1 & subset(v1, all_0_4_4)) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (221) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields: % 16.31/4.39 | (286) ? [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))) % 16.31/4.39 | % 16.31/4.39 | Instantiating formula (28) with empty_set, empty_set and discharging atoms relation_dom(empty_set) = empty_set, relation(empty_set), yields: % 16.31/4.39 | (287) ? [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))) % 16.31/4.39 | % 16.31/4.39 | Instantiating (275) with all_60_0_40, all_60_1_41 yields: % 16.31/4.39 | (288) relation_composition(all_0_6_6, all_0_6_6) = all_60_1_41 & relation_rng(all_60_1_41) = all_60_0_40 & subset(all_60_0_40, all_0_4_4) % 16.31/4.39 | % 16.31/4.39 | Applying alpha-rule on (288) yields: % 16.31/4.39 | (289) relation_composition(all_0_6_6, all_0_6_6) = all_60_1_41 % 16.31/4.39 | (290) relation_rng(all_60_1_41) = all_60_0_40 % 16.31/4.39 | (291) subset(all_60_0_40, all_0_4_4) % 16.31/4.39 | % 16.31/4.39 | Instantiating (281) with all_65_0_43 yields: % 16.31/4.39 | (292) relation_rng(all_0_6_6) = all_65_0_43 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_6_6) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_65_0_43 | ~ 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_65_0_43)) % 16.31/4.39 | % 16.31/4.39 | Applying alpha-rule on (292) yields: % 16.31/4.39 | (293) relation_rng(all_0_6_6) = all_65_0_43 % 16.31/4.39 | (294) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_6_6) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_65_0_43 | ~ subset(all_0_5_5, v2)))) % 16.31/4.39 | (295) ! [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_65_0_43)) % 16.31/4.39 | % 16.31/4.39 | Instantiating (279) with all_68_0_44 yields: % 16.31/4.39 | (296) relation_dom(all_0_6_6) = all_68_0_44 & ! [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_68_0_44, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_68_0_44, 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))) % 16.31/4.39 | % 16.31/4.39 | Applying alpha-rule on (296) yields: % 16.31/4.39 | (297) ! [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))) % 16.31/4.39 | (298) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_68_0_44, v2))) % 16.31/4.39 | (299) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_68_0_44, v1)) % 16.31/4.39 | (300) relation_dom(all_0_6_6) = all_68_0_44 % 16.31/4.39 | (301) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_4_4, v1)) % 16.31/4.39 | % 16.31/4.39 | Instantiating (280) with all_71_0_45, all_71_1_46 yields: % 16.31/4.39 | (302) relation_inverse(all_0_6_6) = all_71_0_45 & relation_rng(all_71_0_45) = all_0_5_5 & relation_rng(all_0_6_6) = all_71_1_46 & relation_dom(all_71_0_45) = all_71_1_46 % 16.31/4.39 | % 16.31/4.39 | Applying alpha-rule on (302) yields: % 16.31/4.39 | (303) relation_inverse(all_0_6_6) = all_71_0_45 % 16.31/4.39 | (304) relation_rng(all_71_0_45) = all_0_5_5 % 16.31/4.39 | (305) relation_rng(all_0_6_6) = all_71_1_46 % 16.31/4.39 | (306) relation_dom(all_71_0_45) = all_71_1_46 % 16.31/4.39 | % 16.31/4.39 | Instantiating (278) with all_78_0_49 yields: % 16.31/4.39 | (307) relation_dom(all_0_6_6) = all_78_0_49 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_6_6, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_78_0_49 | ~ 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_78_0_49)) % 16.31/4.39 | % 16.31/4.39 | Applying alpha-rule on (307) yields: % 16.31/4.39 | (308) relation_dom(all_0_6_6) = all_78_0_49 % 16.31/4.39 | (309) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_6_6, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_78_0_49 | ~ subset(all_0_4_4, v2)))) % 16.31/4.39 | (310) ! [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_78_0_49)) % 16.31/4.40 | % 16.31/4.40 | Instantiating (277) with all_81_0_50 yields: % 16.31/4.40 | (311) relation_dom(all_0_6_6) = all_81_0_50 & ! [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_81_0_50, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_81_0_50, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_6_6) = v2 & relation_rng(v2) = all_0_4_4)) % 16.31/4.40 | % 16.31/4.40 | Applying alpha-rule on (311) yields: % 16.31/4.40 | (312) relation_dom(all_0_6_6) = all_81_0_50 % 16.31/4.40 | (313) ! [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_81_0_50, v2)))) % 16.31/4.40 | (314) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_81_0_50, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_6_6) = v2 & relation_rng(v2) = all_0_4_4)) % 16.31/4.40 | % 16.31/4.40 | Instantiating (276) with all_84_0_51, all_84_1_52 yields: % 16.31/4.40 | (315) relation_inverse(all_0_6_6) = all_84_1_52 & relation_rng(all_84_1_52) = all_84_0_51 & relation_dom(all_84_1_52) = all_0_4_4 & relation_dom(all_0_6_6) = all_84_0_51 % 16.31/4.40 | % 16.31/4.40 | Applying alpha-rule on (315) yields: % 16.31/4.40 | (316) relation_inverse(all_0_6_6) = all_84_1_52 % 16.31/4.40 | (317) relation_rng(all_84_1_52) = all_84_0_51 % 16.31/4.40 | (318) relation_dom(all_84_1_52) = all_0_4_4 % 16.31/4.40 | (319) relation_dom(all_0_6_6) = all_84_0_51 % 16.31/4.40 | % 16.31/4.40 | Instantiating (287) with all_86_0_53 yields: % 16.31/4.40 | (320) relation_rng(empty_set) = all_86_0_53 & ! [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_86_0_53, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_86_0_53, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = empty_set)) % 16.31/4.40 | % 16.31/4.40 | Applying alpha-rule on (320) yields: % 16.31/4.40 | (321) relation_rng(empty_set) = all_86_0_53 % 16.31/4.40 | (322) ! [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_86_0_53, v2)))) % 16.31/4.40 | (323) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_86_0_53, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = empty_set)) % 16.31/4.40 | % 16.31/4.40 | Instantiating (285) with all_93_0_58, all_93_1_59 yields: % 16.31/4.40 | (324) relation_composition(empty_set, all_0_6_6) = all_93_1_59 & relation_rng(all_93_1_59) = all_93_0_58 & subset(all_93_0_58, all_0_4_4) % 16.31/4.40 | % 16.31/4.40 | Applying alpha-rule on (324) yields: % 16.31/4.40 | (325) relation_composition(empty_set, all_0_6_6) = all_93_1_59 % 16.31/4.40 | (326) relation_rng(all_93_1_59) = all_93_0_58 % 16.31/4.40 | (327) subset(all_93_0_58, all_0_4_4) % 16.31/4.40 | % 16.31/4.40 | Instantiating (286) with all_110_0_68 yields: % 16.31/4.40 | (328) relation_dom(empty_set) = all_110_0_68 & ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_110_0_68 | ~ 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_110_0_68)) % 16.31/4.40 | % 16.31/4.40 | Applying alpha-rule on (328) yields: % 16.31/4.40 | (329) relation_dom(empty_set) = all_110_0_68 % 16.31/4.40 | (330) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_110_0_68 | ~ subset(empty_set, v2)))) % 16.31/4.40 | (331) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = all_110_0_68)) % 16.31/4.40 | % 16.31/4.40 | Instantiating (283) with all_115_0_71 yields: % 16.31/4.40 | (332) relation_rng(all_0_6_6) = all_115_0_71 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_115_0_71, 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_115_0_71, v2))) % 16.31/4.40 | % 16.31/4.40 | Applying alpha-rule on (332) yields: % 16.31/4.40 | (333) ! [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))) % 16.31/4.40 | (334) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_115_0_71, v2))) % 16.31/4.40 | (335) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_115_0_71, v1)) % 16.31/4.40 | (336) relation_rng(all_0_6_6) = all_115_0_71 % 16.31/4.40 | (337) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_5_5, v1)) % 16.31/4.40 | % 16.31/4.40 | Instantiating (282) with all_118_0_72 yields: % 16.31/4.40 | (338) relation_rng(all_0_6_6) = all_118_0_72 & ! [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_118_0_72, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_118_0_72, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_6_6, v0) = v2 & relation_dom(v2) = all_0_5_5)) % 16.31/4.40 | % 16.31/4.40 | Applying alpha-rule on (338) yields: % 16.31/4.40 | (339) relation_rng(all_0_6_6) = all_118_0_72 % 16.31/4.40 | (340) ! [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_118_0_72, v2)))) % 16.31/4.40 | (341) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_118_0_72, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_6_6, v0) = v2 & relation_dom(v2) = all_0_5_5)) % 16.31/4.40 | % 16.31/4.40 +-Applying beta-rule and splitting (284), into two cases. % 16.31/4.40 |-Branch one: % 16.31/4.40 | (342) all_0_6_6 = empty_set % 16.31/4.40 | % 16.31/4.40 | Equations (342) can reduce 211 to: % 16.31/4.40 | (343) $false % 16.31/4.40 | % 16.31/4.40 |-The branch is then unsatisfiable % 16.31/4.40 |-Branch two: % 16.31/4.40 | (211) ~ (all_0_6_6 = empty_set) % 16.31/4.40 | (345) ? [v0] : ? [v1] : ? [v2] : (ordered_pair(v0, v1) = v2 & in(v2, all_0_6_6)) % 16.31/4.40 | % 16.31/4.40 | Instantiating (345) with all_125_0_73, all_125_1_74, all_125_2_75 yields: % 16.31/4.40 | (346) ordered_pair(all_125_2_75, all_125_1_74) = all_125_0_73 & in(all_125_0_73, all_0_6_6) % 16.31/4.40 | % 16.31/4.40 | Applying alpha-rule on (346) yields: % 16.31/4.40 | (347) ordered_pair(all_125_2_75, all_125_1_74) = all_125_0_73 % 16.31/4.40 | (348) in(all_125_0_73, all_0_6_6) % 16.31/4.40 | % 16.31/4.40 | Instantiating formula (257) with all_0_6_6, all_118_0_72, all_0_4_4 and discharging atoms relation_rng(all_0_6_6) = all_118_0_72, relation_rng(all_0_6_6) = all_0_4_4, yields: % 16.31/4.40 | (349) all_118_0_72 = all_0_4_4 % 16.31/4.40 | % 16.31/4.40 | Instantiating formula (257) with all_0_6_6, all_115_0_71, all_118_0_72 and discharging atoms relation_rng(all_0_6_6) = all_118_0_72, relation_rng(all_0_6_6) = all_115_0_71, yields: % 16.31/4.40 | (350) all_118_0_72 = all_115_0_71 % 16.31/4.40 | % 16.31/4.40 | Instantiating formula (257) with all_0_6_6, all_71_1_46, all_118_0_72 and discharging atoms relation_rng(all_0_6_6) = all_118_0_72, relation_rng(all_0_6_6) = all_71_1_46, yields: % 16.31/4.40 | (351) all_118_0_72 = all_71_1_46 % 16.31/4.40 | % 16.31/4.40 | Instantiating formula (257) with all_0_6_6, all_65_0_43, all_118_0_72 and discharging atoms relation_rng(all_0_6_6) = all_118_0_72, relation_rng(all_0_6_6) = all_65_0_43, yields: % 16.31/4.40 | (352) all_118_0_72 = all_65_0_43 % 16.31/4.40 | % 16.31/4.40 | Instantiating formula (65) with all_0_6_6, all_81_0_50, all_84_0_51 and discharging atoms relation_dom(all_0_6_6) = all_84_0_51, relation_dom(all_0_6_6) = all_81_0_50, yields: % 16.31/4.40 | (353) all_84_0_51 = all_81_0_50 % 16.31/4.41 | % 16.31/4.41 | Instantiating formula (65) with all_0_6_6, all_78_0_49, all_0_5_5 and discharging atoms relation_dom(all_0_6_6) = all_78_0_49, relation_dom(all_0_6_6) = all_0_5_5, yields: % 16.31/4.41 | (354) all_78_0_49 = all_0_5_5 % 16.31/4.41 | % 16.31/4.41 | Instantiating formula (65) with all_0_6_6, all_78_0_49, all_81_0_50 and discharging atoms relation_dom(all_0_6_6) = all_81_0_50, relation_dom(all_0_6_6) = all_78_0_49, yields: % 16.31/4.41 | (355) all_81_0_50 = all_78_0_49 % 16.31/4.41 | % 16.31/4.41 | Instantiating formula (65) with all_0_6_6, all_68_0_44, all_84_0_51 and discharging atoms relation_dom(all_0_6_6) = all_84_0_51, relation_dom(all_0_6_6) = all_68_0_44, yields: % 16.31/4.41 | (356) all_84_0_51 = all_68_0_44 % 16.31/4.41 | % 16.31/4.41 | Combining equations (351,350) yields a new equation: % 16.31/4.41 | (357) all_115_0_71 = all_71_1_46 % 16.31/4.41 | % 16.31/4.41 | Combining equations (349,350) yields a new equation: % 16.31/4.41 | (358) all_115_0_71 = all_0_4_4 % 16.31/4.41 | % 16.31/4.41 | Combining equations (352,350) yields a new equation: % 16.31/4.41 | (359) all_115_0_71 = all_65_0_43 % 16.31/4.41 | % 16.31/4.41 | Combining equations (358,357) yields a new equation: % 16.31/4.41 | (360) all_71_1_46 = all_0_4_4 % 16.31/4.41 | % 16.31/4.41 | Combining equations (359,357) yields a new equation: % 16.31/4.41 | (361) all_71_1_46 = all_65_0_43 % 16.31/4.41 | % 16.31/4.41 | Combining equations (353,356) yields a new equation: % 16.31/4.41 | (362) all_81_0_50 = all_68_0_44 % 16.31/4.41 | % 16.31/4.41 | Simplifying 362 yields: % 16.31/4.41 | (363) all_81_0_50 = all_68_0_44 % 16.31/4.41 | % 16.31/4.41 | Combining equations (355,363) yields a new equation: % 16.31/4.41 | (364) all_78_0_49 = all_68_0_44 % 16.31/4.41 | % 16.31/4.41 | Simplifying 364 yields: % 16.31/4.41 | (365) all_78_0_49 = all_68_0_44 % 16.31/4.41 | % 16.31/4.41 | Combining equations (365,354) yields a new equation: % 16.31/4.41 | (366) all_68_0_44 = all_0_5_5 % 16.31/4.41 | % 16.31/4.41 | Simplifying 366 yields: % 16.31/4.41 | (367) all_68_0_44 = all_0_5_5 % 16.31/4.41 | % 16.31/4.41 | Combining equations (361,360) yields a new equation: % 16.31/4.41 | (368) all_65_0_43 = all_0_4_4 % 16.31/4.41 | % 16.31/4.41 | Simplifying 368 yields: % 16.31/4.41 | (369) all_65_0_43 = all_0_4_4 % 16.31/4.41 | % 16.31/4.41 | From (369) and (293) follows: % 16.31/4.41 | (52) relation_rng(all_0_6_6) = all_0_4_4 % 16.31/4.41 | % 16.31/4.41 | From (367) and (300) follows: % 16.31/4.41 | (208) relation_dom(all_0_6_6) = all_0_5_5 % 16.31/4.41 | % 16.31/4.41 | Instantiating formula (294) with all_60_1_41, all_0_6_6 and discharging atoms relation_composition(all_0_6_6, all_0_6_6) = all_60_1_41, relation(all_0_6_6), yields: % 16.31/4.41 | (372) ? [v0] : ? [v1] : (relation_rng(all_60_1_41) = v1 & relation_rng(all_0_6_6) = v0 & (v1 = all_65_0_43 | ~ subset(all_0_5_5, v0))) % 16.31/4.41 | % 16.31/4.41 | Instantiating formula (313) with all_60_1_41, all_0_6_6 and discharging atoms relation_composition(all_0_6_6, all_0_6_6) = all_60_1_41, relation(all_0_6_6), yields: % 16.31/4.41 | (373) ? [v0] : ? [v1] : (relation_rng(all_60_1_41) = v1 & relation_rng(all_0_6_6) = v0 & (v1 = all_0_4_4 | ~ subset(all_81_0_50, v0))) % 16.31/4.41 | % 16.31/4.41 | Instantiating formula (330) with all_93_1_59, all_0_6_6 and discharging atoms relation_composition(empty_set, all_0_6_6) = all_93_1_59, relation(all_0_6_6), yields: % 16.31/4.41 | (374) ? [v0] : ? [v1] : (relation_dom(all_93_1_59) = v1 & relation_dom(all_0_6_6) = v0 & (v1 = all_110_0_68 | ~ subset(empty_set, v0))) % 16.31/4.41 | % 16.31/4.41 | Instantiating formula (322) with all_93_1_59, all_0_6_6 and discharging atoms relation_composition(empty_set, all_0_6_6) = all_93_1_59, relation(all_0_6_6), yields: % 16.31/4.41 | (375) ? [v0] : ? [v1] : (relation_dom(all_93_1_59) = v1 & relation_dom(all_0_6_6) = v0 & (v1 = empty_set | ~ subset(all_86_0_53, v0))) % 16.31/4.41 | % 16.31/4.41 | Instantiating formula (30) with all_0_4_4, all_125_0_73, all_0_6_6, all_125_1_74, all_125_2_75 and discharging atoms relation_rng(all_0_6_6) = all_0_4_4, ordered_pair(all_125_2_75, all_125_1_74) = all_125_0_73, relation(all_0_6_6), in(all_125_0_73, all_0_6_6), yields: % 16.44/4.41 | (376) ? [v0] : (relation_dom(all_0_6_6) = v0 & in(all_125_2_75, v0)) % 16.44/4.41 | % 16.44/4.41 | Instantiating formula (183) with all_0_5_5, all_125_0_73, all_0_6_6, all_125_1_74, all_125_2_75 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, ordered_pair(all_125_2_75, all_125_1_74) = all_125_0_73, relation(all_0_6_6), in(all_125_0_73, all_0_6_6), yields: % 16.44/4.41 | (377) ? [v0] : (relation_rng(all_0_6_6) = v0 & in(all_125_1_74, v0)) % 16.44/4.41 | % 16.44/4.41 | Instantiating (372) with all_147_0_84, all_147_1_85 yields: % 16.44/4.41 | (378) relation_rng(all_60_1_41) = all_147_0_84 & relation_rng(all_0_6_6) = all_147_1_85 & (all_147_0_84 = all_65_0_43 | ~ subset(all_0_5_5, all_147_1_85)) % 16.44/4.41 | % 16.44/4.41 | Applying alpha-rule on (378) yields: % 16.44/4.41 | (379) relation_rng(all_60_1_41) = all_147_0_84 % 16.44/4.41 | (380) relation_rng(all_0_6_6) = all_147_1_85 % 16.44/4.41 | (381) all_147_0_84 = all_65_0_43 | ~ subset(all_0_5_5, all_147_1_85) % 16.44/4.41 | % 16.44/4.41 | Instantiating (376) with all_149_0_86 yields: % 16.44/4.41 | (382) relation_dom(all_0_6_6) = all_149_0_86 & in(all_125_2_75, all_149_0_86) % 16.44/4.41 | % 16.44/4.41 | Applying alpha-rule on (382) yields: % 16.44/4.41 | (383) relation_dom(all_0_6_6) = all_149_0_86 % 16.44/4.41 | (384) in(all_125_2_75, all_149_0_86) % 16.44/4.41 | % 16.44/4.41 | Instantiating (375) with all_161_0_96, all_161_1_97 yields: % 16.44/4.41 | (385) relation_dom(all_93_1_59) = all_161_0_96 & relation_dom(all_0_6_6) = all_161_1_97 & (all_161_0_96 = empty_set | ~ subset(all_86_0_53, all_161_1_97)) % 16.44/4.41 | % 16.44/4.41 | Applying alpha-rule on (385) yields: % 16.44/4.41 | (386) relation_dom(all_93_1_59) = all_161_0_96 % 16.44/4.41 | (387) relation_dom(all_0_6_6) = all_161_1_97 % 16.44/4.41 | (388) all_161_0_96 = empty_set | ~ subset(all_86_0_53, all_161_1_97) % 16.44/4.41 | % 16.44/4.41 | Instantiating (373) with all_171_0_105, all_171_1_106 yields: % 16.44/4.41 | (389) relation_rng(all_60_1_41) = all_171_0_105 & relation_rng(all_0_6_6) = all_171_1_106 & (all_171_0_105 = all_0_4_4 | ~ subset(all_81_0_50, all_171_1_106)) % 16.44/4.41 | % 16.44/4.41 | Applying alpha-rule on (389) yields: % 16.44/4.41 | (390) relation_rng(all_60_1_41) = all_171_0_105 % 16.44/4.41 | (391) relation_rng(all_0_6_6) = all_171_1_106 % 16.44/4.41 | (392) all_171_0_105 = all_0_4_4 | ~ subset(all_81_0_50, all_171_1_106) % 16.44/4.41 | % 16.44/4.41 | Instantiating (374) with all_179_0_113, all_179_1_114 yields: % 16.44/4.41 | (393) relation_dom(all_93_1_59) = all_179_0_113 & relation_dom(all_0_6_6) = all_179_1_114 & (all_179_0_113 = all_110_0_68 | ~ subset(empty_set, all_179_1_114)) % 16.44/4.41 | % 16.44/4.41 | Applying alpha-rule on (393) yields: % 16.44/4.41 | (394) relation_dom(all_93_1_59) = all_179_0_113 % 16.44/4.41 | (395) relation_dom(all_0_6_6) = all_179_1_114 % 16.44/4.41 | (396) all_179_0_113 = all_110_0_68 | ~ subset(empty_set, all_179_1_114) % 16.44/4.41 | % 16.44/4.41 | Instantiating (377) with all_190_0_121 yields: % 16.44/4.41 | (397) relation_rng(all_0_6_6) = all_190_0_121 & in(all_125_1_74, all_190_0_121) % 16.44/4.41 | % 16.44/4.41 | Applying alpha-rule on (397) yields: % 16.44/4.41 | (398) relation_rng(all_0_6_6) = all_190_0_121 % 16.44/4.41 | (399) in(all_125_1_74, all_190_0_121) % 16.44/4.41 | % 16.44/4.41 | Instantiating formula (257) with all_0_6_6, all_171_1_106, all_0_4_4 and discharging atoms relation_rng(all_0_6_6) = all_171_1_106, relation_rng(all_0_6_6) = all_0_4_4, yields: % 16.44/4.41 | (400) all_171_1_106 = all_0_4_4 % 16.44/4.41 | % 16.44/4.41 | Instantiating formula (257) with all_0_6_6, all_171_1_106, all_190_0_121 and discharging atoms relation_rng(all_0_6_6) = all_190_0_121, relation_rng(all_0_6_6) = all_171_1_106, yields: % 16.44/4.41 | (401) all_190_0_121 = all_171_1_106 % 16.44/4.41 | % 16.44/4.41 | Instantiating formula (257) with all_0_6_6, all_147_1_85, all_190_0_121 and discharging atoms relation_rng(all_0_6_6) = all_190_0_121, relation_rng(all_0_6_6) = all_147_1_85, yields: % 16.44/4.41 | (402) all_190_0_121 = all_147_1_85 % 16.44/4.41 | % 16.44/4.41 | Instantiating formula (65) with all_0_6_6, all_179_1_114, all_0_5_5 and discharging atoms relation_dom(all_0_6_6) = all_179_1_114, relation_dom(all_0_6_6) = all_0_5_5, yields: % 16.44/4.41 | (403) all_179_1_114 = all_0_5_5 % 16.44/4.41 | % 16.44/4.41 | Instantiating formula (65) with all_0_6_6, all_161_1_97, all_179_1_114 and discharging atoms relation_dom(all_0_6_6) = all_179_1_114, relation_dom(all_0_6_6) = all_161_1_97, yields: % 16.44/4.41 | (404) all_179_1_114 = all_161_1_97 % 16.44/4.41 | % 16.44/4.41 | Instantiating formula (65) with all_0_6_6, all_149_0_86, all_179_1_114 and discharging atoms relation_dom(all_0_6_6) = all_179_1_114, relation_dom(all_0_6_6) = all_149_0_86, yields: % 16.44/4.41 | (405) all_179_1_114 = all_149_0_86 % 16.44/4.41 | % 16.44/4.41 | Combining equations (401,402) yields a new equation: % 16.44/4.41 | (406) all_171_1_106 = all_147_1_85 % 16.44/4.41 | % 16.44/4.41 | Simplifying 406 yields: % 16.44/4.41 | (407) all_171_1_106 = all_147_1_85 % 16.44/4.41 | % 16.44/4.41 | Combining equations (405,404) yields a new equation: % 16.44/4.41 | (408) all_161_1_97 = all_149_0_86 % 16.44/4.41 | % 16.44/4.41 | Combining equations (403,404) yields a new equation: % 16.44/4.41 | (409) all_161_1_97 = all_0_5_5 % 16.44/4.41 | % 16.44/4.41 | Combining equations (400,407) yields a new equation: % 16.44/4.41 | (410) all_147_1_85 = all_0_4_4 % 16.44/4.41 | % 16.44/4.41 | Combining equations (408,409) yields a new equation: % 16.44/4.41 | (411) all_149_0_86 = all_0_5_5 % 16.44/4.41 | % 16.44/4.41 | Simplifying 411 yields: % 16.44/4.41 | (412) all_149_0_86 = all_0_5_5 % 16.44/4.41 | % 16.44/4.41 | Combining equations (410,402) yields a new equation: % 16.44/4.41 | (413) all_190_0_121 = all_0_4_4 % 16.44/4.41 | % 16.44/4.41 | From (413) and (399) follows: % 16.44/4.41 | (414) in(all_125_1_74, all_0_4_4) % 16.44/4.41 | % 16.44/4.41 | From (412) and (384) follows: % 16.44/4.41 | (415) in(all_125_2_75, all_0_5_5) % 16.44/4.41 | % 16.44/4.41 +-Applying beta-rule and splitting (40), into two cases. % 16.44/4.41 |-Branch one: % 16.44/4.41 | (416) all_0_4_4 = empty_set % 16.44/4.41 | % 16.44/4.41 | From (416) and (414) follows: % 16.44/4.41 | (417) in(all_125_1_74, empty_set) % 16.44/4.41 | % 16.44/4.41 | Instantiating formula (130) with all_125_1_74 and discharging atoms in(all_125_1_74, empty_set), yields: % 16.44/4.41 | (418) $false % 16.44/4.41 | % 16.44/4.41 |-The branch is then unsatisfiable % 16.44/4.41 |-Branch two: % 16.44/4.41 | (419) ~ (all_0_4_4 = empty_set) % 16.44/4.41 | (420) all_0_5_5 = empty_set % 16.44/4.41 | % 16.44/4.42 | From (420) and (415) follows: % 16.44/4.42 | (421) in(all_125_2_75, empty_set) % 16.44/4.42 | % 16.44/4.42 | Instantiating formula (130) with all_125_2_75 and discharging atoms in(all_125_2_75, empty_set), yields: % 16.44/4.42 | (418) $false % 16.44/4.42 | % 16.44/4.42 |-The branch is then unsatisfiable % 16.44/4.42 % SZS output end Proof for theBenchmark % 16.44/4.42 % 16.44/4.42 3791ms %------------------------------------------------------------------------------