%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU200+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 08:47:34 EDT 2022 % Result : Theorem 8.35s 2.50s % Output : Proof 14.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU200+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jun 20 13:35:26 EDT 2022 % 0.13/0.34 % CPUTime : % 0.52/0.58 ____ _ % 0.52/0.58 ___ / __ \_____(_)___ ________ __________ % 0.52/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.58 % 0.52/0.58 A Theorem Prover for First-Order Logic % 0.52/0.58 (ePrincess v.1.0) % 0.52/0.58 % 0.52/0.58 (c) Philipp Rümmer, 2009-2015 % 0.52/0.58 (c) Peter Backeman, 2014-2015 % 0.52/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.58 Bug reports to peter@backeman.se % 0.52/0.58 % 0.52/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.58 % 0.52/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.52/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.41/1.08 Prover 0: Preprocessing ... % 5.64/1.89 Prover 0: Warning: ignoring some quantifiers % 6.00/1.93 Prover 0: Constructing countermodel ... % 8.35/2.50 Prover 0: proved (1869ms) % 8.35/2.50 % 8.35/2.50 No countermodel exists, formula is valid % 8.35/2.50 % SZS status Theorem for theBenchmark % 8.35/2.50 % 8.35/2.50 Generating proof ... Warning: ignoring some quantifiers % 13.04/3.51 found it (size 22) % 13.04/3.51 % 13.04/3.51 % SZS output start Proof for theBenchmark % 13.04/3.52 Assumed formulas after preprocessing and simplification: % 13.04/3.52 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v3) = v4 & relation_rng(v2) = v5 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation_rng_restriction(v1, v2) = v3 & relation(v9) & relation(v7) & relation(v2) & relation(empty_set) & empty(v9) & empty(v8) & empty(empty_set) & ~ subset(v4, v5) & ~ empty(v7) & ~ empty(v6) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v10, v11) = v12) | ~ (ordered_pair(v16, v14) = v17) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v11) | ~ relation(v10) | ~ in(v17, v11) | in(v15, v12) | ? [v18] : (ordered_pair(v13, v16) = v18 & ~ in(v18, v10))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v10, v11) = v12) | ~ (ordered_pair(v13, v16) = v17) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v11) | ~ relation(v10) | ~ in(v17, v10) | in(v15, v12) | ? [v18] : (ordered_pair(v16, v14) = v18 & ~ in(v18, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v13) = v16) | ~ (identity_relation(v12) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ relation(v13) | ~ in(v14, v16) | in(v14, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v13) = v16) | ~ (identity_relation(v12) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ relation(v13) | ~ in(v14, v16) | in(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v13) = v16) | ~ (identity_relation(v12) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ relation(v13) | ~ in(v14, v13) | ~ in(v10, v12) | in(v14, v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v11) | ~ relation(v10) | ~ in(v15, v12) | ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v16, v14) = v18 & ordered_pair(v13, v16) = v17 & in(v18, v11) & in(v17, v10))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ in(v14, v15) | in(v11, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ in(v14, v15) | in(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ in(v11, v13) | ~ in(v10, v12) | in(v14, v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v11, v13) = v15) | ~ (cartesian_product2(v10, v12) = v14) | ~ subset(v12, v13) | ~ subset(v10, v11) | subset(v14, v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v10, v11) = v12) | ~ (ordered_pair(v14, v15) = v13) | ~ in(v15, v11) | ~ in(v14, v10) | in(v13, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng_restriction(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v11) | ~ in(v15, v12) | in(v15, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng_restriction(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v11) | ~ in(v15, v12) | in(v14, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng_restriction(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v11) | ~ in(v15, v11) | ~ in(v14, v10) | in(v15, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom_restriction(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v10) | ~ in(v15, v12) | in(v15, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom_restriction(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v10) | ~ in(v15, v12) | in(v13, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom_restriction(v10, v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v10) | ~ in(v15, v10) | ~ in(v13, v11) | in(v15, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (identity_relation(v10) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ relation(v11) | ~ in(v14, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v11 | ~ (ordered_pair(v12, v13) = v14) | ~ (ordered_pair(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v10 | v12 = v10 | ~ (unordered_pair(v12, v13) = v14) | ~ (unordered_pair(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v10 | ~ (ordered_pair(v12, v13) = v14) | ~ (ordered_pair(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (subset_difference(v14, v13, v12) = v11) | ~ (subset_difference(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = empty_set | ~ (subset_difference(v10, v12, v13) = v14) | ~ (meet_of_subsets(v10, v11) = v13) | ~ (cast_to_subset(v10) = v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (union_of_subsets(v10, v17) = v18 & complements_of_subsets(v10, v11) = v17 & powerset(v15) = v16 & powerset(v10) = v15 & (v18 = v14 | ~ element(v11, v16)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = empty_set | ~ (subset_difference(v10, v12, v13) = v14) | ~ (union_of_subsets(v10, v11) = v13) | ~ (cast_to_subset(v10) = v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (meet_of_subsets(v10, v17) = v18 & complements_of_subsets(v10, v11) = v17 & powerset(v15) = v16 & powerset(v10) = v15 & (v18 = v14 | ~ element(v11, v16)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = empty_set | ~ (subset_complement(v10, v12) = v13) | ~ (powerset(v10) = v11) | ~ element(v14, v10) | ~ element(v12, v11) | in(v14, v13) | in(v14, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_inverse(v10) = v11) | ~ (ordered_pair(v13, v12) = v14) | ~ relation(v11) | ~ relation(v10) | ~ in(v14, v10) | ? [v15] : (ordered_pair(v12, v13) = v15 & in(v15, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_inverse(v10) = v11) | ~ (ordered_pair(v13, v12) = v14) | ~ relation(v11) | ~ relation(v10) | in(v14, v10) | ? [v15] : (ordered_pair(v12, v13) = v15 & ~ in(v15, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_inverse(v10) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ relation(v11) | ~ relation(v10) | ~ in(v14, v11) | ? [v15] : (ordered_pair(v13, v12) = v15 & in(v15, v10))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_inverse(v10) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ relation(v11) | ~ relation(v10) | in(v14, v11) | ? [v15] : (ordered_pair(v13, v12) = v15 & ~ in(v15, v10))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_field(v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ relation(v12) | ~ in(v13, v12) | in(v11, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_field(v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ relation(v12) | ~ in(v13, v12) | in(v10, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (subset_complement(v10, v13) = v14) | ~ (powerset(v10) = v12) | ~ disjoint(v11, v13) | ~ element(v13, v12) | ~ element(v11, v12) | subset(v11, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (subset_complement(v10, v13) = v14) | ~ (powerset(v10) = v12) | ~ element(v13, v12) | ~ element(v11, v12) | ~ subset(v11, v14) | disjoint(v11, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ relation(v12) | ~ in(v13, v12) | in(v11, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ relation(v12) | ~ in(v13, v12) | ? [v15] : (relation_dom(v12) = v15 & in(v10, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v10) = v11) | ~ (ordered_pair(v13, v12) = v14) | ~ relation(v10) | ~ in(v14, v10) | in(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v11, v13) = v14) | ~ (singleton(v12) = v13) | ~ subset(v10, v11) | subset(v10, v14) | in(v12, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v11, v12) = v14) | ~ (set_difference(v10, v12) = v13) | ~ subset(v10, v11) | subset(v13, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v11, v12) = v14) | ~ (powerset(v10) = v13) | ~ element(v12, v13) | ~ element(v11, v13) | subset_difference(v10, v11, v12) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ relation(v12) | ~ in(v13, v12) | in(v10, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ relation(v12) | ~ in(v13, v12) | ? [v15] : (relation_rng(v12) = v15 & in(v11, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v10) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ relation(v10) | ~ in(v14, v10) | in(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v12, v11) = v14) | ~ (cartesian_product2(v12, v10) = v13) | ~ subset(v10, v11) | subset(v13, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v12, v11) = v14) | ~ (cartesian_product2(v12, v10) = v13) | ~ subset(v10, v11) | ? [v15] : ? [v16] : (cartesian_product2(v11, v12) = v16 & cartesian_product2(v10, v12) = v15 & subset(v15, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v12, v11) = v14) | ~ (cartesian_product2(v10, v12) = v13) | ~ subset(v10, v11) | ? [v15] : ? [v16] : (cartesian_product2(v12, v10) = v16 & cartesian_product2(v11, v12) = v15 & subset(v16, v14) & subset(v13, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v12, v10) = v14) | ~ (cartesian_product2(v11, v12) = v13) | ~ subset(v10, v11) | ? [v15] : ? [v16] : (cartesian_product2(v12, v11) = v16 & cartesian_product2(v10, v12) = v15 & subset(v15, v13) & subset(v14, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v11, v12) = v14) | ~ (cartesian_product2(v10, v12) = v13) | ~ subset(v10, v11) | subset(v13, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v11, v12) = v14) | ~ (cartesian_product2(v10, v12) = v13) | ~ subset(v10, v11) | ? [v15] : ? [v16] : (cartesian_product2(v12, v11) = v16 & cartesian_product2(v12, v10) = v15 & subset(v15, v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v10) = v13) | ~ (unordered_pair(v12, v13) = v14) | ~ (unordered_pair(v10, v11) = v12) | ordered_pair(v10, v11) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (identity_relation(v10) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ relation(v11) | ~ in(v14, v11) | in(v12, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ~ subset(v10, v11) | ~ relation(v11) | ~ relation(v10) | ~ in(v14, v10) | in(v14, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v14) | ~ (set_intersection2(v10, v12) = v13) | ~ subset(v10, v11) | subset(v13, v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (relation_composition(v10, v11) = v12) | ~ relation(v13) | ~ relation(v11) | ~ relation(v10) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v14, v15) = v16 & ( ~ in(v16, v13) | ( ! [v20] : ! [v21] : ( ~ (ordered_pair(v20, v15) = v21) | ~ in(v21, v11) | ? [v22] : (ordered_pair(v14, v20) = v22 & ~ in(v22, v10))) & ! [v20] : ! [v21] : ( ~ (ordered_pair(v14, v20) = v21) | ~ in(v21, v10) | ? [v22] : (ordered_pair(v20, v15) = v22 & ~ in(v22, v11))))) & (in(v16, v13) | (ordered_pair(v17, v15) = v19 & ordered_pair(v14, v17) = v18 & in(v19, v11) & in(v18, v10))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (relation_rng_restriction(v10, v11) = v12) | ~ relation(v13) | ~ relation(v11) | ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & ( ~ in(v16, v13) | ~ in(v16, v11) | ~ in(v15, v10)) & (in(v16, v13) | (in(v16, v11) & in(v15, v10))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (relation_dom_restriction(v10, v11) = v13) | ~ relation(v12) | ~ relation(v10) | ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & ( ~ in(v16, v12) | ~ in(v16, v10) | ~ in(v14, v11)) & (in(v16, v12) | (in(v16, v10) & in(v14, v11))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v13 = v10 | ~ (unordered_pair(v10, v11) = v12) | ~ in(v13, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (complements_of_subsets(v10, v12) = v13) | ~ (complements_of_subsets(v10, v11) = v12) | ? [v14] : ? [v15] : (powerset(v14) = v15 & powerset(v10) = v14 & ~ element(v11, v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (subset_complement(v10, v12) = v13) | ~ (subset_complement(v10, v11) = v12) | ? [v14] : (powerset(v10) = v14 & ~ element(v11, v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (set_difference(v11, v10) = v12) | ~ (set_union2(v10, v12) = v13) | ~ subset(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v10) = v12) | ~ (set_union2(v12, v11) = v13) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_difference(v10, v12) = v13) | ~ (singleton(v11) = v12) | in(v11, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v10) = v13) | ~ (unordered_pair(v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (meet_of_subsets(v13, v12) = v11) | ~ (meet_of_subsets(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (union_of_subsets(v13, v12) = v11) | ~ (union_of_subsets(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (complements_of_subsets(v13, v12) = v11) | ~ (complements_of_subsets(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_composition(v13, v12) = v11) | ~ (relation_composition(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset_complement(v13, v12) = v11) | ~ (subset_complement(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_difference(v13, v12) = v11) | ~ (set_difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (singleton(v11) = v13) | ~ (singleton(v10) = v12) | ~ subset(v12, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (singleton(v10) = v13) | ~ (unordered_pair(v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_rng_restriction(v13, v12) = v11) | ~ (relation_rng_restriction(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (relation_dom_restriction(v13, v12) = v11) | ~ (relation_dom_restriction(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_union2(v13, v12) = v11) | ~ (set_union2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = empty_set | ~ (meet_of_subsets(v10, v12) = v13) | ~ (complements_of_subsets(v10, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (subset_difference(v10, v16, v17) = v18 & union_of_subsets(v10, v11) = v17 & cast_to_subset(v10) = v16 & powerset(v14) = v15 & powerset(v10) = v14 & (v18 = v13 | ~ element(v11, v15)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = empty_set | ~ (union_of_subsets(v10, v12) = v13) | ~ (complements_of_subsets(v10, v11) = v12) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (subset_difference(v10, v16, v17) = v18 & meet_of_subsets(v10, v11) = v17 & cast_to_subset(v10) = v16 & powerset(v14) = v15 & powerset(v10) = v14 & (v18 = v13 | ~ element(v11, v15)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = empty_set | ~ (set_meet(v10) = v11) | ~ in(v13, v10) | ~ in(v12, v11) | in(v12, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (subset_difference(v10, v11, v12) = v13) | ? [v14] : ? [v15] : (set_difference(v11, v12) = v15 & powerset(v10) = v14 & (v15 = v13 | ~ element(v12, v14) | ~ element(v11, v14)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (subset_difference(v10, v11, v12) = v13) | ? [v14] : (powerset(v10) = v14 & ( ~ element(v12, v14) | ~ element(v11, v14) | element(v13, v14)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ (identity_relation(v10) = v12) | ~ relation(v11) | relation_dom_restriction(v11, v10) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v10, v12) = v13) | ~ (relation_dom(v10) = v11) | ~ relation(v12) | ~ relation(v10) | ? [v14] : (relation_dom(v13) = v14 & subset(v14, v11))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (subset_complement(v10, v12) = v13) | ~ in(v11, v13) | ~ in(v11, v12) | ? [v14] : (powerset(v10) = v14 & ~ element(v12, v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v10) = v12) | ~ (relation_dom(v10) = v11) | ~ (cartesian_product2(v11, v12) = v13) | ~ relation(v10) | subset(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v10) = v12) | ~ (relation_dom(v10) = v11) | ~ (set_union2(v11, v12) = v13) | ~ relation(v10) | relation_field(v10) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v12, v11) = v13) | ~ (set_union2(v10, v11) = v12) | set_difference(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v10) = v12) | ~ (set_union2(v10, v12) = v13) | set_union2(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v12) = v13) | ~ (set_difference(v10, v11) = v12) | set_intersection2(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v11) = v12) | ~ in(v13, v12) | ~ in(v13, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v11) = v12) | ~ in(v13, v12) | in(v13, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v11) = v12) | ~ in(v13, v10) | in(v13, v12) | in(v13, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11) = v13) | ~ (powerset(v10) = v12) | ? [v14] : ? [v15] : (union_of_subsets(v10, v11) = v15 & powerset(v12) = v14 & (v15 = v13 | ~ element(v11, v14)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v10) = v11) | ~ in(v13, v10) | ~ in(v12, v13) | in(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom(v11) = v12) | ~ (set_intersection2(v12, v10) = v13) | ~ relation(v11) | ? [v14] : (relation_dom(v14) = v13 & relation_dom_restriction(v11, v10) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v12) | ~ in(v13, v12) | ? [v14] : ? [v15] : (ordered_pair(v14, v15) = v13 & in(v15, v11) & in(v14, v10))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | ~ empty(v12) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | ~ in(v10, v11) | element(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v10) = v12) | ~ (set_meet(v11) = v13) | ? [v14] : ? [v15] : (meet_of_subsets(v10, v11) = v15 & powerset(v12) = v14 & (v15 = v13 | ~ element(v11, v14)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v10) = v12) | ~ element(v11, v12) | ~ in(v13, v11) | in(v13, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (identity_relation(v10) = v11) | ~ (ordered_pair(v12, v12) = v13) | ~ relation(v11) | ~ in(v12, v10) | in(v13, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | ~ subset(v10, v12) | ~ subset(v10, v11) | subset(v10, v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ disjoint(v10, v11) | ~ in(v13, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ in(v13, v12) | in(v13, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ in(v13, v12) | in(v13, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ in(v13, v11) | ~ in(v13, v10) | in(v13, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v10, v12) = v13) | ~ subset(v12, v11) | ~ subset(v10, v11) | subset(v13, v11)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v10, v11) = v12) | ~ in(v13, v12) | in(v13, v11) | in(v13, v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v10, v11) = v12) | ~ in(v13, v11) | in(v13, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v10, v11) = v12) | ~ in(v13, v10) | in(v13, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v10, v11) = v13) | ~ subset(v13, v12) | in(v11, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v10, v11) = v13) | ~ subset(v13, v12) | in(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v10, v11) = v13) | ~ in(v11, v12) | ~ in(v10, v12) | subset(v13, v12)) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_difference(v11, v12) = v13) | ? [v14] : (( ~ in(v14, v11) | ~ in(v14, v10) | in(v14, v12)) & (in(v14, v10) | (in(v14, v11) & ~ in(v14, v12))))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (cartesian_product2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ in(v14, v10) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v18, v19) = v14) | ~ in(v19, v12) | ~ in(v18, v11))) & (in(v14, v10) | (v17 = v14 & ordered_pair(v15, v16) = v14 & in(v16, v12) & in(v15, v11))))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_intersection2(v11, v12) = v13) | ? [v14] : (( ~ in(v14, v12) | ~ in(v14, v11) | ~ in(v14, v10)) & (in(v14, v10) | (in(v14, v12) & in(v14, v11))))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_union2(v11, v12) = v13) | ? [v14] : (( ~ in(v14, v10) | ( ~ in(v14, v12) & ~ in(v14, v11))) & (in(v14, v12) | in(v14, v11) | in(v14, v10)))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ((v14 = v12 | v14 = v11 | in(v14, v10)) & ( ~ in(v14, v10) | ( ~ (v14 = v12) & ~ (v14 = v11))))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_rng(v13) = v14 & relation_rng(v12) = v15 & ( ~ in(v10, v15) | ~ in(v10, v11) | in(v10, v14)) & ( ~ in(v10, v14) | (in(v10, v15) & in(v10, v11))))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom_restriction(v12, v11) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_dom(v13) = v14 & relation_dom(v12) = v15 & ( ~ in(v10, v15) | ~ in(v10, v11) | in(v10, v14)) & ( ~ in(v10, v14) | (in(v10, v15) & in(v10, v11))))) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (relation_inverse(v10) = v11) | ~ relation(v12) | ~ relation(v10) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v13) = v16 & ordered_pair(v13, v14) = v15 & ( ~ in(v16, v10) | ~ in(v15, v12)) & (in(v16, v10) | in(v15, v12)))) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (identity_relation(v10) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v13, v14) = v15 & ( ~ (v14 = v13) | ~ in(v15, v11) | ~ in(v13, v10)) & (in(v15, v11) | (v14 = v13 & in(v13, v10))))) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v10, v11) = v12) | ~ subset(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | v10 = empty_set | ~ (singleton(v11) = v12) | ~ subset(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (set_difference(v10, v11) = v12) | ~ disjoint(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (singleton(v10) = v11) | ~ in(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (set_intersection2(v10, v11) = v12) | ~ subset(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_difference(v10, v11) = v12) | ~ subset(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_intersection2(v10, v11) = v12) | ~ disjoint(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_inverse(v12) = v11) | ~ (relation_inverse(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_field(v12) = v11) | ~ (relation_field(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_rng(v12) = v11) | ~ (relation_rng(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (union(v12) = v11) | ~ (union(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (cast_to_subset(v12) = v11) | ~ (cast_to_subset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_dom(v12) = v11) | ~ (relation_dom(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (set_meet(v12) = v11) | ~ (set_meet(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (identity_relation(v12) = v11) | ~ (identity_relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (meet_of_subsets(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (powerset(v13) = v14 & powerset(v10) = v13 & set_meet(v11) = v15 & (v15 = v12 | ~ element(v11, v14)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (meet_of_subsets(v10, v11) = v12) | ? [v13] : ? [v14] : (powerset(v13) = v14 & powerset(v10) = v13 & ( ~ element(v11, v14) | element(v12, v13)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (union_of_subsets(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (union(v11) = v15 & powerset(v13) = v14 & powerset(v10) = v13 & (v15 = v12 | ~ element(v11, v14)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (union_of_subsets(v10, v11) = v12) | ? [v13] : ? [v14] : (powerset(v13) = v14 & powerset(v10) = v13 & ( ~ element(v11, v14) | element(v12, v13)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (complements_of_subsets(v10, v11) = v12) | ? [v13] : ? [v14] : (powerset(v13) = v14 & powerset(v10) = v13 & ( ~ element(v11, v14) | element(v12, v14)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (complements_of_subsets(v10, v11) = v12) | ? [v13] : ? [v14] : (powerset(v13) = v14 & powerset(v10) = v13 & ( ~ element(v11, v14) | ( ! [v15] : ! [v16] : ( ~ (subset_complement(v10, v15) = v16) | ~ element(v15, v13) | ~ element(v12, v14) | ~ in(v16, v11) | in(v15, v12)) & ! [v15] : ! [v16] : ( ~ (subset_complement(v10, v15) = v16) | ~ element(v15, v13) | ~ element(v12, v14) | ~ in(v15, v12) | in(v16, v11)) & ! [v15] : (v15 = v12 | ~ element(v15, v14) | ? [v16] : ? [v17] : (subset_complement(v10, v16) = v17 & element(v16, v13) & ( ~ in(v17, v11) | ~ in(v16, v15)) & (in(v17, v11) | in(v16, v15)))))))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v11, v10) = v12) | ~ relation(v11) | ~ empty(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v11, v10) = v12) | ~ relation(v11) | ~ empty(v10) | empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ~ relation(v11) | ~ relation(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ~ relation(v11) | ~ relation(v10) | ? [v13] : ? [v14] : (relation_rng(v12) = v13 & relation_rng(v11) = v14 & subset(v13, v14))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ~ relation(v11) | ~ empty(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_composition(v10, v11) = v12) | ~ relation(v11) | ~ empty(v10) | empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_complement(v10, v11) = v12) | ? [v13] : ? [v14] : (set_difference(v10, v11) = v14 & powerset(v10) = v13 & (v14 = v12 | ~ element(v11, v13)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_complement(v10, v11) = v12) | ? [v13] : (powerset(v10) = v13 & ( ~ element(v11, v13) | element(v12, v13)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ relation(v10) | ? [v13] : ? [v14] : (relation_composition(v10, v11) = v13 & relation_rng(v13) = v14 & subset(v14, v12))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng(v10) = v11) | ~ relation(v10) | ~ in(v12, v11) | ? [v13] : ? [v14] : (ordered_pair(v13, v12) = v14 & in(v14, v10))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v10, v12) = v10) | ~ (singleton(v11) = v12) | ~ in(v11, v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v10, v11) = v12) | subset(v12, v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v10, v11) = v12) | ? [v13] : ? [v14] : (subset_complement(v10, v11) = v14 & powerset(v10) = v13 & (v14 = v12 | ~ element(v11, v13)))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v10, v11) = v12) | ? [v13] : (set_difference(v13, v11) = v12 & set_union2(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v11) = v12) | ~ in(v10, v11) | subset(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v10) = v11) | ~ in(v12, v11) | ? [v13] : (in(v13, v10) & in(v12, v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ~ in(v12, v11) | ? [v13] : ? [v14] : (ordered_pair(v12, v13) = v14 & in(v14, v10))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v10, v11) = v12) | ~ empty(v12) | empty(v11) | empty(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ element(v10, v12) | subset(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ subset(v10, v11) | element(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v10) = v11) | ~ subset(v12, v10) | in(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v10) = v11) | ~ in(v12, v11) | subset(v12, v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v10) = v12) | ~ disjoint(v12, v11) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v10) = v12) | ~ subset(v12, v11) | in(v10, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v10) = v12) | ~ in(v10, v11) | subset(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng_restriction(v10, v11) = v12) | ~ relation(v11) | subset(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng_restriction(v10, v11) = v12) | ~ relation(v11) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng_restriction(v10, v11) = v12) | ~ relation(v11) | ? [v13] : (relation_rng(v12) = v13 & subset(v13, v10))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom_restriction(v11, v10) = v12) | ~ relation(v11) | subset(v12, v11)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom_restriction(v11, v10) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_rng(v12) = v13 & relation_rng(v11) = v14 & subset(v13, v14))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom_restriction(v11, v10) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_dom(v12) = v13 & relation_dom(v11) = v14 & set_intersection2(v14, v10) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom_restriction(v11, v10) = v12) | ~ relation(v11) | ? [v13] : (relation_composition(v13, v11) = v12 & identity_relation(v10) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom_restriction(v10, v11) = v12) | ~ relation(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ~ empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ? [v14] : (singleton(v10) = v14 & unordered_pair(v13, v14) = v12 & unordered_pair(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v11, v10) = v12) | set_intersection2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | ~ relation(v11) | ~ relation(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | disjoint(v10, v11) | ? [v13] : in(v13, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | subset(v12, v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | ? [v13] : (set_difference(v10, v13) = v12 & set_difference(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | ~ empty(v12) | empty(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | set_union2(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ~ relation(v11) | ~ relation(v10) | relation(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ~ empty(v12) | empty(v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | set_union2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | subset(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : (set_difference(v11, v10) = v13 & set_union2(v10, v13) = v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v10) = v12) | unordered_pair(v10, v11) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ~ empty(v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | in(v11, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | in(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ disjoint(v11, v12) | ~ subset(v10, v11) | disjoint(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ disjoint(v10, v11) | ~ in(v12, v11) | ~ in(v12, v10)) & ! [v10] : ! [v11] : ! [v12] : ( ~ subset(v11, v12) | ~ subset(v10, v11) | subset(v10, v12)) & ! [v10] : ! [v11] : ! [v12] : ( ~ subset(v10, v11) | ~ in(v12, v10) | in(v12, v11)) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | v11 = empty_set | ~ (set_meet(v11) = v12) | ? [v13] : ? [v14] : (( ~ in(v13, v10) | (in(v14, v11) & ~ in(v13, v14))) & (in(v13, v10) | ! [v15] : ( ~ in(v15, v11) | in(v13, v15))))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (relation_rng(v11) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : ? [v15] : (( ~ in(v13, v10) | ! [v16] : ! [v17] : ( ~ (ordered_pair(v16, v13) = v17) | ~ in(v17, v11))) & (in(v13, v10) | (ordered_pair(v14, v13) = v15 & in(v15, v11))))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (union(v11) = v12) | ? [v13] : ? [v14] : (( ~ in(v13, v10) | ! [v15] : ( ~ in(v15, v11) | ~ in(v13, v15))) & (in(v13, v10) | (in(v14, v11) & in(v13, v14))))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (relation_dom(v11) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : ? [v15] : (( ~ in(v13, v10) | ! [v16] : ! [v17] : ( ~ (ordered_pair(v13, v16) = v17) | ~ in(v17, v11))) & (in(v13, v10) | (ordered_pair(v13, v14) = v15 & in(v15, v11))))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (powerset(v11) = v12) | ? [v13] : (( ~ subset(v13, v11) | ~ in(v13, v10)) & (subset(v13, v11) | in(v13, v10)))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (singleton(v11) = v12) | ? [v13] : (( ~ (v13 = v11) | ~ in(v11, v10)) & (v13 = v11 | in(v13, v10)))) & ? [v10] : ! [v11] : ! [v12] : (v11 = empty_set | ~ (set_meet(v11) = v12) | in(v10, v12) | ? [v13] : (in(v13, v11) & ~ in(v10, v13))) & ? [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | element(v10, v12) | ? [v13] : (in(v13, v10) & ~ in(v13, v11))) & ? [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | disjoint(v12, v10) | in(v11, v10)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_difference(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (cast_to_subset(v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ subset(v11, v10) | ~ subset(v10, v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ subset(v10, v11) | proper_subset(v10, v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ relation(v11) | ~ relation(v10) | ? [v12] : ? [v13] : ? [v14] : (ordered_pair(v12, v13) = v14 & ( ~ in(v14, v11) | ~ in(v14, v10)) & (in(v14, v11) | in(v14, v10)))) & ! [v10] : ! [v11] : (v11 = v10 | ~ empty(v11) | ~ empty(v10)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (complements_of_subsets(v10, v11) = empty_set) | ? [v12] : ? [v13] : (powerset(v12) = v13 & powerset(v10) = v12 & ~ element(v11, v13))) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_difference(empty_set, v10) = v11)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v10 = empty_set | ~ (relation_rng(v10) = v11) | ~ relation(v10) | ? [v12] : ( ~ (v12 = empty_set) & relation_dom(v10) = v12)) & ! [v10] : ! [v11] : (v10 = empty_set | ~ (relation_dom(v10) = v11) | ~ relation(v10) | ? [v12] : ( ~ (v12 = empty_set) & relation_rng(v10) = v12)) & ! [v10] : ! [v11] : ( ~ (relation_inverse(v10) = v11) | ~ relation(v10) | relation_inverse(v11) = v10) & ! [v10] : ! [v11] : ( ~ (relation_inverse(v10) = v11) | ~ relation(v10) | relation(v11)) & ! [v10] : ! [v11] : ( ~ (relation_inverse(v10) = v11) | ~ relation(v10) | ? [v12] : ? [v13] : (relation_rng(v11) = v13 & relation_rng(v10) = v12 & relation_dom(v11) = v12 & relation_dom(v10) = v13)) & ! [v10] : ! [v11] : ( ~ (relation_field(v10) = v11) | ~ relation(v10) | ? [v12] : ? [v13] : (relation_rng(v10) = v13 & relation_dom(v10) = v12 & set_union2(v12, v13) = v11)) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ relation(v10) | ~ empty(v11) | empty(v10)) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ relation(v10) | ? [v12] : ? [v13] : (relation_inverse(v10) = v12 & relation_rng(v12) = v13 & relation_dom(v12) = v11 & relation_dom(v10) = v13)) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ relation(v10) | ? [v12] : (relation_dom(v10) = v12 & ! [v13] : ! [v14] : ( ~ (relation_composition(v13, v10) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_rng(v14) = v16 & relation_rng(v13) = v15 & (v16 = v11 | ~ subset(v12, v15)))) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ subset(v12, v14) | ~ relation(v13) | ? [v15] : (relation_composition(v13, v10) = v15 & relation_rng(v15) = v11)))) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ relation(v10) | ? [v12] : (relation_dom(v10) = v12 & ! [v13] : ! [v14] : ( ~ (relation_composition(v10, v13) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_dom(v14) = v16 & relation_dom(v13) = v15 & (v16 = v12 | ~ subset(v11, v15)))) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ subset(v11, v14) | ~ relation(v13) | ? [v15] : (relation_composition(v10, v13) = v15 & relation_dom(v15) = v12)))) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ relation(v10) | ? [v12] : (relation_dom(v10) = v12 & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ subset(v10, v13) | ~ relation(v13) | subset(v11, v14)) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ subset(v10, v13) | ~ relation(v13) | ? [v15] : (relation_dom(v13) = v15 & subset(v12, v15))) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ subset(v10, v13) | ~ relation(v13) | subset(v12, v14)) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ subset(v10, v13) | ~ relation(v13) | ? [v15] : (relation_rng(v13) = v15 & subset(v11, v15))))) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ relation(v10) | ? [v12] : (relation_dom(v10) = v12 & ( ~ (v12 = empty_set) | v11 = empty_set) & ( ~ (v11 = empty_set) | v12 = empty_set))) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ empty(v10) | relation(v11)) & ! [v10] : ! [v11] : ( ~ (relation_rng(v10) = v11) | ~ empty(v10) | empty(v11)) & ! [v10] : ! [v11] : ( ~ (set_difference(v10, v11) = v10) | disjoint(v10, v11)) & ! [v10] : ! [v11] : ( ~ (set_difference(v10, v11) = empty_set) | subset(v10, v11)) & ! [v10] : ! [v11] : ( ~ (cast_to_subset(v10) = v11) | ? [v12] : (powerset(v10) = v12 & element(v11, v12))) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ~ empty(v11) | empty(v10)) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ? [v12] : ? [v13] : (relation_inverse(v10) = v13 & relation_rng(v13) = v11 & relation_rng(v10) = v12 & relation_dom(v13) = v12)) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ? [v12] : (relation_rng(v10) = v12 & ! [v13] : ! [v14] : ( ~ (relation_composition(v13, v10) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_rng(v14) = v16 & relation_rng(v13) = v15 & (v16 = v12 | ~ subset(v11, v15)))) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ subset(v11, v14) | ~ relation(v13) | ? [v15] : (relation_composition(v13, v10) = v15 & relation_rng(v15) = v12)))) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ? [v12] : (relation_rng(v10) = v12 & ! [v13] : ! [v14] : ( ~ (relation_composition(v10, v13) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_dom(v14) = v16 & relation_dom(v13) = v15 & (v16 = v11 | ~ subset(v12, v15)))) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ subset(v12, v14) | ~ relation(v13) | ? [v15] : (relation_composition(v10, v13) = v15 & relation_dom(v15) = v11)))) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ? [v12] : (relation_rng(v10) = v12 & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ subset(v10, v13) | ~ relation(v13) | subset(v12, v14)) & ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ subset(v10, v13) | ~ relation(v13) | ? [v15] : (relation_dom(v13) = v15 & subset(v11, v15))) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ subset(v10, v13) | ~ relation(v13) | subset(v11, v14)) & ! [v13] : ! [v14] : ( ~ (relation_dom(v13) = v14) | ~ subset(v10, v13) | ~ relation(v13) | ? [v15] : (relation_rng(v13) = v15 & subset(v12, v15))))) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ relation(v10) | ? [v12] : (relation_rng(v10) = v12 & ( ~ (v12 = empty_set) | v11 = empty_set) & ( ~ (v11 = empty_set) | v12 = empty_set))) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ empty(v10) | relation(v11)) & ! [v10] : ! [v11] : ( ~ (relation_dom(v10) = v11) | ~ empty(v10) | empty(v11)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ empty(v11)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | union(v11) = v10) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | empty(v10) | ? [v12] : (element(v12, v11) & ~ empty(v12))) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : (cast_to_subset(v10) = v12 & element(v12, v11))) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : (element(v12, v11) & empty(v12))) & ! [v10] : ! [v11] : ( ~ (singleton(v11) = v10) | subset(v10, v10)) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | ~ empty(v11)) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | unordered_pair(v10, v10) = v11) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | subset(empty_set, v11)) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | in(v10, v11)) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | relation_rng(v11) = v10) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | relation_dom(v11) = v10) & ! [v10] : ! [v11] : ( ~ (identity_relation(v10) = v11) | relation(v11)) & ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v11) = empty_set) | disjoint(v10, v11)) & ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v10) = v11) | singleton(v10) = v11) & ! [v10] : ! [v11] : ( ~ disjoint(v10, v11) | disjoint(v11, v10)) & ! [v10] : ! [v11] : ( ~ element(v11, v10) | ~ empty(v10) | empty(v11)) & ! [v10] : ! [v11] : ( ~ element(v11, v10) | empty(v10) | in(v11, v10)) & ! [v10] : ! [v11] : ( ~ element(v10, v11) | empty(v11) | in(v10, v11)) & ! [v10] : ! [v11] : ( ~ subset(v10, v11) | ~ proper_subset(v11, v10)) & ! [v10] : ! [v11] : ( ~ relation(v11) | ~ relation(v10) | subset(v10, v11) | ? [v12] : ? [v13] : ? [v14] : (ordered_pair(v12, v13) = v14 & in(v14, v10) & ~ in(v14, v11))) & ! [v10] : ! [v11] : ( ~ relation(v10) | ~ in(v11, v10) | ? [v12] : ? [v13] : ordered_pair(v12, v13) = v11) & ! [v10] : ! [v11] : ( ~ empty(v11) | ~ empty(v10) | element(v11, v10)) & ! [v10] : ! [v11] : ( ~ empty(v11) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ proper_subset(v11, v10) | ~ proper_subset(v10, v11)) & ! [v10] : ! [v11] : ( ~ proper_subset(v10, v11) | subset(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | ~ in(v10, v11)) & ! [v10] : ! [v11] : ( ~ in(v11, v10) | element(v11, v10) | empty(v10)) & ! [v10] : ! [v11] : ( ~ in(v10, v11) | element(v10, v11)) & ! [v10] : (v10 = empty_set | ~ (relation_rng(v10) = empty_set) | ~ relation(v10)) & ! [v10] : (v10 = empty_set | ~ (relation_dom(v10) = empty_set) | ~ relation(v10)) & ! [v10] : (v10 = empty_set | ~ (set_meet(empty_set) = v10)) & ! [v10] : (v10 = empty_set | ~ subset(v10, empty_set)) & ! [v10] : (v10 = empty_set | ~ relation(v10) | ? [v11] : ? [v12] : ? [v13] : (ordered_pair(v11, v12) = v13 & in(v13, v10))) & ! [v10] : (v10 = empty_set | ~ empty(v10)) & ! [v10] : ~ (singleton(v10) = empty_set) & ! [v10] : ( ~ empty(v10) | relation(v10)) & ! [v10] : ~ proper_subset(v10, v10) & ! [v10] : ~ in(v10, empty_set) & ? [v10] : ? [v11] : (v11 = v10 | ? [v12] : (( ~ in(v12, v11) | ~ in(v12, v10)) & (in(v12, v11) | in(v12, v10)))) & ? [v10] : ? [v11] : (disjoint(v10, v11) | ? [v12] : (in(v12, v11) & in(v12, v10))) & ? [v10] : ? [v11] : element(v11, v10) & ? [v10] : ? [v11] : (subset(v10, v11) | ? [v12] : (in(v12, v10) & ~ in(v12, v11))) & ? [v10] : ? [v11] : (in(v10, v11) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ in(v12, v11) | in(v13, v11)) & ! [v12] : ! [v13] : ( ~ subset(v13, v12) | ~ in(v12, v11) | in(v13, v11)) & ! [v12] : ( ~ subset(v12, v11) | are_equipotent(v12, v11) | in(v12, v11))) & ? [v10] : ? [v11] : (in(v10, v11) & ! [v12] : ! [v13] : ( ~ subset(v13, v12) | ~ in(v12, v11) | in(v13, v11)) & ! [v12] : ( ~ subset(v12, v11) | are_equipotent(v12, v11) | in(v12, v11)) & ! [v12] : ( ~ in(v12, v11) | ? [v13] : (in(v13, v11) & ! [v14] : ( ~ subset(v14, v12) | in(v14, v13))))) & ? [v10] : (v10 = empty_set | ? [v11] : in(v11, v10)) & ? [v10] : subset(v10, v10) & ? [v10] : subset(empty_set, v10) & ? [v10] : (relation(v10) | ? [v11] : (in(v11, v10) & ! [v12] : ! [v13] : ~ (ordered_pair(v12, v13) = v11)))) % 13.57/3.63 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields: % 13.57/3.63 | (1) relation_rng(all_0_6_6) = all_0_5_5 & relation_rng(all_0_7_7) = all_0_4_4 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & powerset(empty_set) = all_0_9_9 & singleton(empty_set) = all_0_9_9 & relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6 & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_7_7) & relation(empty_set) & empty(all_0_0_0) & empty(all_0_1_1) & empty(empty_set) & ~ subset(all_0_5_5, all_0_4_4) & ~ 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] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v3) | ~ in(v0, v2) | in(v4, v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & in(v8, v1) & in(v7, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ subset(v2, v3) | ~ subset(v0, v1) | subset(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (meet_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (union_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (meet_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ element(v4, v0) | ~ element(v2, v1) | in(v4, v3) | in(v4, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_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] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (complements_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v0) = v4 & ~ element(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (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 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (meet_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (union_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & meet_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_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] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_dom(v4) = v3 & relation_dom_restriction(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (set_meet(v1) = v3) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_rng(v3) = v4 & relation_rng(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v3) = v6 & ordered_pair(v3, v4) = v5 & ( ~ in(v6, v0) | ~ in(v5, v2)) & (in(v6, v0) | in(v5, v2)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ( ~ (v4 = v3) | ~ in(v5, v1) | ~ in(v3, v0)) & (in(v5, v1) | (v4 = v3 & in(v3, v0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (powerset(v3) = v4 & powerset(v0) = v3 & set_meet(v1) = v5 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | ( ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v6, v1) | in(v5, v2)) & ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v5, v2) | in(v6, v1)) & ! [v5] : (v5 = v2 | ~ element(v5, v4) | ? [v6] : ? [v7] : (subset_complement(v0, v6) = v7 & element(v6, v3) & ( ~ in(v7, v1) | ~ in(v6, v5)) & (in(v7, v1) | in(v6, v5)))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_composition(v0, v1) = v3 & relation_rng(v3) = v4 & subset(v4, v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & set_intersection2(v4, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | (in(v4, v1) & ~ in(v3, v4))) & (in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | in(v3, v5))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (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) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) & ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) & ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ~ 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))) % 13.86/3.68 | % 13.86/3.68 | Applying alpha-rule on (1) yields: % 13.86/3.69 | (2) ! [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)))) % 13.86/3.69 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 13.86/3.69 | (4) ! [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))) % 13.86/3.69 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 13.86/3.69 | (6) ? [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))))) % 13.86/3.69 | (7) ! [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)))) % 13.86/3.69 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) % 13.86/3.69 | (9) ! [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)))) % 13.86/3.69 | (10) ! [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))) % 13.86/3.69 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3)) % 13.86/3.69 | (12) ! [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))))) % 13.86/3.69 | (13) ! [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)))) % 13.86/3.69 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v3) | ~ in(v0, v2) | in(v4, v6)) % 13.86/3.69 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 13.86/3.69 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) % 13.86/3.69 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 13.86/3.69 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 13.86/3.69 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) % 13.86/3.69 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 13.86/3.69 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 13.86/3.69 | (22) ? [v0] : subset(v0, v0) % 13.86/3.69 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) % 13.86/3.69 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 13.86/3.69 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 13.86/3.69 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 13.86/3.69 | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) % 13.86/3.69 | (28) ! [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)) % 13.86/3.69 | (29) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) % 13.86/3.69 | (30) ! [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)) % 13.86/3.69 | (31) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 13.86/3.69 | (32) relation(all_0_7_7) % 13.86/3.69 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_dom(v4) = v3 & relation_dom_restriction(v1, v0) = v4)) % 13.86/3.69 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 13.86/3.69 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 13.86/3.69 | (36) ! [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))) % 13.86/3.69 | (37) ! [v0] : ( ~ empty(v0) | relation(v0)) % 13.86/3.69 | (38) empty(all_0_1_1) % 13.86/3.69 | (39) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 13.86/3.69 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 13.86/3.70 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 13.86/3.70 | (42) ! [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))) % 13.86/3.70 | (43) ! [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)))) % 13.86/3.70 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 13.86/3.70 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 13.86/3.70 | (46) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) % 13.86/3.70 | (47) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) % 13.86/3.70 | (48) ! [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))) % 13.86/3.70 | (49) empty(empty_set) % 13.86/3.70 | (50) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) % 13.86/3.70 | (51) ! [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)))) % 13.86/3.70 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 13.86/3.70 | (53) ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) % 13.86/3.70 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 13.86/3.70 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 13.86/3.70 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 13.86/3.70 | (57) ! [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))))) % 13.86/3.70 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 13.86/3.70 | (59) ? [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))))) % 13.86/3.70 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) % 13.86/3.70 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) % 13.86/3.70 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3)) % 13.86/3.70 | (63) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) % 13.86/3.70 | (64) ! [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))))) % 13.86/3.70 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 13.86/3.70 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 13.86/3.70 | (67) ! [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)))) % 13.86/3.70 | (68) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) % 13.86/3.70 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 13.86/3.71 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) % 13.86/3.71 | (71) relation(all_0_2_2) % 13.86/3.71 | (72) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 13.86/3.71 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 13.86/3.71 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) % 13.86/3.71 | (75) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 13.86/3.71 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 13.86/3.71 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 13.86/3.71 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) % 13.86/3.71 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) % 13.86/3.71 | (80) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 13.86/3.71 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 13.86/3.71 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 13.86/3.71 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 13.86/3.71 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 13.86/3.71 | (85) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 13.86/3.71 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 13.86/3.71 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 13.86/3.71 | (88) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 13.86/3.71 | (89) ~ empty(all_0_3_3) % 13.86/3.71 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 13.86/3.71 | (91) ! [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)))) % 13.86/3.71 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 13.86/3.71 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 13.86/3.71 | (94) empty(all_0_0_0) % 13.86/3.71 | (95) ! [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)))) % 13.86/3.71 | (96) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 13.86/3.71 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) % 13.86/3.71 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) % 13.86/3.71 | (99) ! [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)))) % 13.86/3.71 | (100) ! [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)) % 13.86/3.71 | (101) ! [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))) % 13.86/3.71 | (102) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 13.86/3.71 | (103) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) % 13.86/3.71 | (104) ! [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))) % 13.86/3.71 | (105) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 13.86/3.71 | (106) ! [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)))) % 13.86/3.71 | (107) ! [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))) % 13.86/3.71 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 13.86/3.71 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 13.86/3.71 | (110) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 13.86/3.71 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) % 13.86/3.71 | (112) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 13.86/3.71 | (113) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 13.86/3.71 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) % 13.86/3.71 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) % 13.86/3.71 | (116) ! [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))) % 13.86/3.71 | (117) ~ subset(all_0_5_5, all_0_4_4) % 13.86/3.72 | (118) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 13.86/3.72 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) % 13.86/3.72 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) % 13.86/3.72 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) % 13.86/3.72 | (122) ! [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)))) % 13.86/3.72 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 13.86/3.72 | (124) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 13.86/3.72 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 13.86/3.72 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 13.86/3.72 | (127) ! [v0] : ~ proper_subset(v0, v0) % 13.86/3.72 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) % 13.86/3.72 | (129) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) % 13.86/3.72 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) % 13.86/3.72 | (131) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) % 13.86/3.72 | (132) ! [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))) % 13.86/3.72 | (133) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) % 13.86/3.72 | (134) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 13.86/3.72 | (135) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) % 13.86/3.72 | (136) ! [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))) % 13.86/3.72 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) % 13.86/3.72 | (138) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 13.86/3.72 | (139) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 13.86/3.72 | (140) ! [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)))))))) % 13.86/3.72 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 13.86/3.72 | (142) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 13.86/3.72 | (143) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 13.86/3.72 | (144) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 13.86/3.72 | (145) ? [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))))) % 13.86/3.72 | (146) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) % 13.86/3.72 | (147) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 13.86/3.72 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) % 13.86/3.72 | (149) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) % 13.86/3.72 | (150) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 13.86/3.72 | (151) ! [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))) % 13.86/3.72 | (152) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) % 13.86/3.72 | (153) ! [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)) % 13.86/3.72 | (154) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 13.86/3.72 | (155) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) % 13.86/3.72 | (156) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 13.86/3.72 | (157) ! [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)))) % 13.86/3.72 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 13.86/3.72 | (159) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) % 13.86/3.72 | (160) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) % 13.86/3.72 | (161) ! [v0] : ~ in(v0, empty_set) % 13.86/3.72 | (162) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) % 13.86/3.72 | (163) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_rng(v3) = v4 & relation_rng(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) % 13.86/3.72 | (164) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) % 13.86/3.72 | (165) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) % 13.86/3.72 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) % 13.86/3.72 | (167) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 13.86/3.72 | (168) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) % 13.86/3.72 | (169) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1))) % 13.86/3.72 | (170) singleton(empty_set) = all_0_9_9 % 13.86/3.72 | (171) ? [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))))) % 13.86/3.73 | (172) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) % 13.86/3.73 | (173) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 13.86/3.73 | (174) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 13.86/3.73 | (175) ! [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)) % 13.86/3.73 | (176) relation(all_0_0_0) % 13.86/3.73 | (177) ! [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)) % 13.86/3.73 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 13.86/3.73 | (179) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) % 13.86/3.73 | (180) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 13.86/3.73 | (181) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 13.86/3.73 | (182) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 13.86/3.73 | (183) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 13.86/3.73 | (184) ! [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))) % 13.86/3.73 | (185) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) % 13.86/3.73 | (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) % 13.86/3.73 | (187) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 13.86/3.73 | (188) ? [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))))) % 13.86/3.73 | (189) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) % 13.86/3.73 | (190) ? [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))))) % 13.86/3.73 | (191) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 13.86/3.73 | (192) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 13.86/3.73 | (193) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 13.86/3.73 | (194) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 13.86/3.73 | (195) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 13.86/3.73 | (196) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 13.86/3.73 | (197) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 13.86/3.73 | (198) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 13.86/3.73 | (199) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 13.86/3.73 | (200) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 13.86/3.73 | (201) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 13.86/3.73 | (202) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 13.86/3.73 | (203) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) % 13.86/3.73 | (204) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 13.86/3.73 | (205) ! [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))) % 13.86/3.73 | (206) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ( ~ (v4 = v3) | ~ in(v5, v1) | ~ in(v3, v0)) & (in(v5, v1) | (v4 = v3 & in(v3, v0))))) % 13.86/3.73 | (207) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 13.86/3.73 | (208) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 13.86/3.73 | (209) ? [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)))) % 13.86/3.73 | (210) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) % 13.86/3.73 | (211) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) % 13.86/3.73 | (212) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 13.86/3.73 | (213) ! [v0] : ~ (singleton(v0) = empty_set) % 13.86/3.73 | (214) relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6 % 13.86/3.73 | (215) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) % 13.86/3.73 | (216) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) % 13.86/3.73 | (217) ! [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))) % 13.86/3.73 | (218) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) % 13.86/3.73 | (219) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 13.86/3.73 | (220) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 13.86/3.73 | (221) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 13.86/3.73 | (222) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 13.86/3.73 | (223) ! [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)) % 13.86/3.73 | (224) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 13.86/3.73 | (225) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 13.86/3.74 | (226) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) % 13.86/3.74 | (227) relation_rng(empty_set) = empty_set % 13.86/3.74 | (228) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 13.86/3.74 | (229) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 13.86/3.74 | (230) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 13.86/3.74 | (231) ? [v0] : ? [v1] : element(v1, v0) % 13.86/3.74 | (232) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 13.86/3.74 | (233) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 13.86/3.74 | (234) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) % 13.86/3.74 | (235) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 13.86/3.74 | (236) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) % 13.86/3.74 | (237) ! [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))) % 13.86/3.74 | (238) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 13.86/3.74 | (239) relation(empty_set) % 13.86/3.74 | (240) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) % 13.86/3.74 | (241) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) % 13.86/3.74 | (242) powerset(empty_set) = all_0_9_9 % 13.86/3.74 | (243) ? [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))) % 13.86/3.74 | (244) ! [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))) % 13.86/3.74 | (245) ! [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)))) % 13.86/3.74 | (246) ? [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))))) % 13.86/3.74 | (247) ! [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))) % 13.86/3.74 | (248) relation_dom(empty_set) = empty_set % 13.86/3.74 | (249) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & set_intersection2(v4, v0) = v3)) % 13.86/3.74 | (250) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 13.86/3.74 | (251) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 13.86/3.74 | (252) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 13.86/3.74 | (253) ~ empty(all_0_2_2) % 13.86/3.74 | (254) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 13.86/3.74 | (255) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 13.86/3.74 | (256) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 13.86/3.74 | (257) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 13.86/3.74 | (258) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 13.86/3.74 | (259) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 13.86/3.74 | (260) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) % 13.86/3.74 | (261) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 13.86/3.74 | (262) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) % 13.86/3.74 | (263) relation_rng(all_0_6_6) = all_0_5_5 % 13.86/3.74 | (264) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 13.86/3.74 | (265) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) % 13.86/3.74 | (266) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 13.86/3.74 | (267) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 13.86/3.74 | (268) ! [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)) % 13.86/3.74 | (269) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2)) % 13.86/3.74 | (270) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 13.86/3.74 | (271) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 13.86/3.74 | (272) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) % 13.86/3.74 | (273) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 13.86/3.74 | (274) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 13.86/3.74 | (275) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 13.86/3.74 | (276) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 13.86/3.74 | (277) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 13.86/3.75 | (278) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 13.86/3.75 | (279) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) % 13.86/3.75 | (280) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) % 13.86/3.75 | (281) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 13.86/3.75 | (282) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) % 13.86/3.75 | (283) ? [v0] : subset(empty_set, v0) % 13.86/3.75 | (284) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 13.86/3.75 | (285) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 13.86/3.75 | (286) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) % 13.86/3.75 | (287) relation_rng(all_0_7_7) = all_0_4_4 % 13.86/3.75 | (288) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 13.86/3.75 | (289) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) % 13.86/3.75 | (290) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) % 13.86/3.75 | (291) ! [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)) % 13.86/3.75 | (292) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) % 13.86/3.75 | (293) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) % 13.86/3.75 | (294) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 13.86/3.75 | (295) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 13.86/3.75 | (296) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) % 13.86/3.75 | (297) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) % 13.86/3.75 | (298) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 13.86/3.75 | (299) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 13.86/3.75 | (300) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) % 13.86/3.75 | (301) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) % 13.86/3.75 | (302) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 13.86/3.75 | (303) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 13.86/3.75 | (304) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 13.86/3.75 | (305) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 13.86/3.75 | (306) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 13.86/3.75 | (307) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 13.86/3.75 | (308) ? [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))))) % 13.86/3.75 | (309) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 13.86/3.75 | (310) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 13.86/3.75 | (311) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 13.86/3.75 | (312) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) % 13.86/3.75 | (313) ? [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))))) % 13.86/3.75 | (314) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) % 13.86/3.75 | (315) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 13.86/3.75 | (316) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) % 13.86/3.75 | % 13.86/3.75 | Instantiating (163) with all_34_0_31 yields: % 13.86/3.75 | (317) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & ( ~ in(all_34_0_31, v4) | ~ in(all_34_0_31, v0) | in(all_34_0_31, v3)) & ( ~ in(all_34_0_31, v3) | (in(all_34_0_31, v4) & in(all_34_0_31, v0))))) % 13.86/3.75 | % 13.86/3.75 | Instantiating formula (128) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6, relation(all_0_7_7), yields: % 13.86/3.75 | (318) subset(all_0_6_6, all_0_7_7) % 13.86/3.75 | % 13.86/3.75 | Instantiating formula (272) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6, relation(all_0_7_7), yields: % 13.86/3.75 | (319) relation(all_0_6_6) % 13.86/3.75 | % 13.86/3.75 | Instantiating formula (317) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6, relation(all_0_7_7), yields: % 13.86/3.75 | (320) ? [v0] : ? [v1] : (relation_rng(all_0_6_6) = v0 & relation_rng(all_0_7_7) = v1 & ( ~ in(all_34_0_31, v1) | ~ in(all_34_0_31, all_0_8_8) | in(all_34_0_31, v0)) & ( ~ in(all_34_0_31, v0) | (in(all_34_0_31, v1) & in(all_34_0_31, all_0_8_8)))) % 13.86/3.75 | % 13.86/3.75 | Instantiating formula (78) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms relation_rng_restriction(all_0_8_8, all_0_7_7) = all_0_6_6, relation(all_0_7_7), yields: % 13.86/3.75 | (321) ? [v0] : (relation_rng(all_0_6_6) = v0 & subset(v0, all_0_8_8)) % 13.86/3.75 | % 13.86/3.75 | Instantiating (320) with all_87_0_56, all_87_1_57 yields: % 13.86/3.75 | (322) relation_rng(all_0_6_6) = all_87_1_57 & relation_rng(all_0_7_7) = all_87_0_56 & ( ~ in(all_34_0_31, all_87_0_56) | ~ in(all_34_0_31, all_0_8_8) | in(all_34_0_31, all_87_1_57)) & ( ~ in(all_34_0_31, all_87_1_57) | (in(all_34_0_31, all_87_0_56) & in(all_34_0_31, all_0_8_8))) % 14.20/3.76 | % 14.20/3.76 | Applying alpha-rule on (322) yields: % 14.20/3.76 | (323) relation_rng(all_0_6_6) = all_87_1_57 % 14.20/3.76 | (324) relation_rng(all_0_7_7) = all_87_0_56 % 14.20/3.76 | (325) ~ in(all_34_0_31, all_87_0_56) | ~ in(all_34_0_31, all_0_8_8) | in(all_34_0_31, all_87_1_57) % 14.20/3.76 | (326) ~ in(all_34_0_31, all_87_1_57) | (in(all_34_0_31, all_87_0_56) & in(all_34_0_31, all_0_8_8)) % 14.20/3.76 | % 14.20/3.76 | Instantiating (321) with all_95_0_60 yields: % 14.20/3.76 | (327) relation_rng(all_0_6_6) = all_95_0_60 & subset(all_95_0_60, all_0_8_8) % 14.20/3.76 | % 14.20/3.76 | Applying alpha-rule on (327) yields: % 14.20/3.76 | (328) relation_rng(all_0_6_6) = all_95_0_60 % 14.20/3.76 | (329) subset(all_95_0_60, all_0_8_8) % 14.20/3.76 | % 14.20/3.76 | Instantiating formula (201) with all_0_6_6, all_95_0_60, all_0_5_5 and discharging atoms relation_rng(all_0_6_6) = all_95_0_60, relation_rng(all_0_6_6) = all_0_5_5, yields: % 14.20/3.76 | (330) all_95_0_60 = all_0_5_5 % 14.20/3.76 | % 14.20/3.76 | Instantiating formula (201) with all_0_6_6, all_87_1_57, all_95_0_60 and discharging atoms relation_rng(all_0_6_6) = all_95_0_60, relation_rng(all_0_6_6) = all_87_1_57, yields: % 14.20/3.76 | (331) all_95_0_60 = all_87_1_57 % 14.20/3.76 | % 14.20/3.76 | Instantiating formula (201) with all_0_7_7, all_87_0_56, all_0_4_4 and discharging atoms relation_rng(all_0_7_7) = all_87_0_56, relation_rng(all_0_7_7) = all_0_4_4, yields: % 14.20/3.76 | (332) all_87_0_56 = all_0_4_4 % 14.20/3.76 | % 14.20/3.76 | Combining equations (330,331) yields a new equation: % 14.20/3.76 | (333) all_87_1_57 = all_0_5_5 % 14.20/3.76 | % 14.20/3.76 | From (333) and (323) follows: % 14.20/3.76 | (263) relation_rng(all_0_6_6) = all_0_5_5 % 14.20/3.76 | % 14.20/3.76 | From (332) and (324) follows: % 14.20/3.76 | (287) relation_rng(all_0_7_7) = all_0_4_4 % 14.20/3.76 | % 14.20/3.76 | Instantiating formula (64) with all_0_5_5, all_0_6_6 and discharging atoms relation_rng(all_0_6_6) = all_0_5_5, relation(all_0_6_6), yields: % 14.20/3.76 | (336) ? [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_5_5, 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_5_5, v3)))) % 14.20/3.76 | % 14.20/3.76 | Instantiating (336) with all_139_0_83 yields: % 14.20/3.76 | (337) relation_dom(all_0_6_6) = all_139_0_83 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_5_5, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_139_0_83, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_139_0_83, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_0_5_5, v2))) % 14.20/3.76 | % 14.20/3.76 | Applying alpha-rule on (337) yields: % 14.20/3.76 | (338) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_139_0_83, v1)) % 14.20/3.76 | (339) relation_dom(all_0_6_6) = all_139_0_83 % 14.20/3.76 | (340) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_0_5_5, v2))) % 14.20/3.76 | (341) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_139_0_83, v2))) % 14.20/3.76 | (342) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_6_6, v0) | ~ relation(v0) | subset(all_0_5_5, v1)) % 14.20/3.76 | % 14.20/3.76 | Instantiating formula (342) with all_0_4_4, all_0_7_7 and discharging atoms relation_rng(all_0_7_7) = all_0_4_4, subset(all_0_6_6, all_0_7_7), relation(all_0_7_7), ~ subset(all_0_5_5, all_0_4_4), yields: % 14.20/3.76 | (343) $false % 14.20/3.76 | % 14.20/3.76 |-The branch is then unsatisfiable % 14.20/3.76 % SZS output end Proof for theBenchmark % 14.20/3.76 % 14.20/3.76 3170ms %------------------------------------------------------------------------------