%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU275+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.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 08:48:24 EDT 2022 % Result : Theorem 12.92s 3.44s % Output : Proof 21.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.13 % Problem : SEU275+2 : TPTP v8.1.0. Released v3.3.0. % 0.09/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.14/0.35 % Computer : n007.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sun Jun 19 02:42:13 EDT 2022 % 0.14/0.36 % CPUTime : % 0.58/0.62 ____ _ % 0.58/0.62 ___ / __ \_____(_)___ ________ __________ % 0.58/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.62 % 0.58/0.62 A Theorem Prover for First-Order Logic % 0.58/0.62 (ePrincess v.1.0) % 0.58/0.62 % 0.58/0.62 (c) Philipp Rümmer, 2009-2015 % 0.58/0.62 (c) Peter Backeman, 2014-2015 % 0.58/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.62 Bug reports to peter@backeman.se % 0.58/0.62 % 0.58/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.62 % 0.58/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.25/1.31 Prover 0: Preprocessing ... % 8.85/2.53 Prover 0: Warning: ignoring some quantifiers % 8.85/2.59 Prover 0: Constructing countermodel ... % 12.92/3.44 Prover 0: proved (2765ms) % 12.92/3.44 % 12.92/3.44 No countermodel exists, formula is valid % 12.92/3.44 % SZS status Theorem for theBenchmark % 12.92/3.44 % 12.92/3.44 Generating proof ... Warning: ignoring some quantifiers % 19.26/4.92 found it (size 10) % 19.26/4.92 % 19.26/4.92 % SZS output start Proof for theBenchmark % 19.26/4.92 Assumed formulas after preprocessing and simplification: % 19.26/4.92 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (relation_rng(empty_set) = empty_set & inclusion_relation(v1) = v2 & singleton(empty_set) = v0 & relation_dom(empty_set) = empty_set & powerset(empty_set) = v0 & relation_empty_yielding(v4) & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v9) & one_to_one(v6) & one_to_one(empty_set) & relation(v14) & relation(v12) & relation(v10) & relation(v9) & relation(v8) & relation(v6) & relation(v4) & relation(v3) & relation(empty_set) & epsilon_connected(v13) & epsilon_connected(v9) & epsilon_connected(v5) & epsilon_connected(empty_set) & epsilon_transitive(v13) & epsilon_transitive(v9) & epsilon_transitive(v5) & epsilon_transitive(empty_set) & ordinal(v13) & ordinal(v9) & ordinal(v5) & ordinal(v1) & ordinal(empty_set) & function(v14) & function(v10) & function(v9) & function(v6) & function(v3) & function(empty_set) & empty(v12) & empty(v11) & empty(v10) & empty(v9) & empty(empty_set) & ~ well_ordering(v2) & ~ empty(v8) & ~ empty(v7) & ~ empty(v5) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v15, v16) = v17) | ~ (ordered_pair(v21, v19) = v22) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ in(v22, v16) | in(v20, v17) | ? [v23] : (ordered_pair(v18, v21) = v23 & ~ in(v23, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v15, v16) = v17) | ~ (ordered_pair(v18, v21) = v22) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ in(v22, v15) | in(v20, v17) | ? [v23] : (ordered_pair(v21, v19) = v23 & ~ in(v23, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (identity_relation(v17) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ relation(v18) | ~ in(v19, v21) | in(v19, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (identity_relation(v17) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ relation(v18) | ~ in(v19, v21) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (identity_relation(v17) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ relation(v18) | ~ in(v19, v18) | ~ in(v15, v17) | in(v19, v21)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v18, v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ is_transitive_in(v15, v16) | ~ relation(v15) | ~ in(v21, v15) | ~ in(v20, v15) | ~ in(v19, v16) | ~ in(v18, v16) | ~ in(v17, v16) | ? [v22] : (ordered_pair(v17, v19) = v22 & in(v22, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v18, v19) = v20) | ~ (ordered_pair(v17, v19) = v21) | ~ is_transitive_in(v15, v16) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v19, v16) | ~ in(v18, v16) | ~ in(v17, v16) | in(v21, v15) | ? [v22] : (ordered_pair(v17, v18) = v22 & ~ in(v22, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v17, v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ is_transitive_in(v15, v16) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v19, v16) | ~ in(v18, v16) | ~ in(v17, v16) | in(v21, v15) | ? [v22] : (ordered_pair(v18, v19) = v22 & ~ in(v22, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v16 | ~ (pair_second(v15) = v16) | ~ (ordered_pair(v19, v20) = v15) | ~ (ordered_pair(v17, v18) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v17 = v16 | ~ (pair_first(v15) = v16) | ~ (ordered_pair(v19, v20) = v15) | ~ (ordered_pair(v17, v18) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ in(v20, v17) | ? [v21] : ? [v22] : ? [v23] : (ordered_pair(v21, v19) = v23 & ordered_pair(v18, v21) = v22 & in(v23, v16) & in(v22, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v19) = v20) | ~ (relation_field(v17) = v18) | ~ (relation_field(v15) = v16) | ~ relation(v19) | ~ relation(v17) | ~ relation(v15) | ~ function(v19) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (relation_dom(v19) = v21 & ( ~ (v21 = v16) | ~ (v20 = v18) | ~ one_to_one(v19) | relation_isomorphism(v15, v17, v19) | (apply(v19, v23) = v26 & apply(v19, v22) = v25 & ordered_pair(v25, v26) = v27 & ordered_pair(v22, v23) = v24 & ( ~ in(v27, v17) | ~ in(v24, v15) | ~ in(v23, v16) | ~ in(v22, v16)) & (in(v24, v15) | (in(v27, v17) & in(v23, v16) & in(v22, v16))))) & ( ~ relation_isomorphism(v15, v17, v19) | (v21 = v16 & v20 = v18 & one_to_one(v19) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : ( ~ (apply(v19, v29) = v31) | ~ (apply(v19, v28) = v30) | ~ (ordered_pair(v30, v31) = v32) | ~ in(v32, v17) | ~ in(v29, v16) | ~ in(v28, v16) | ? [v33] : (ordered_pair(v28, v29) = v33 & in(v33, v15))) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : ( ~ (apply(v19, v29) = v31) | ~ (apply(v19, v28) = v30) | ~ (ordered_pair(v30, v31) = v32) | in(v32, v17) | ? [v33] : (ordered_pair(v28, v29) = v33 & ~ in(v33, v15))) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : ( ~ (apply(v19, v29) = v31) | ~ (apply(v19, v28) = v30) | ~ (ordered_pair(v30, v31) = v32) | in(v29, v16) | ? [v33] : (ordered_pair(v28, v29) = v33 & ~ in(v33, v15))) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : ( ~ (apply(v19, v29) = v31) | ~ (apply(v19, v28) = v30) | ~ (ordered_pair(v30, v31) = v32) | in(v28, v16) | ? [v33] : (ordered_pair(v28, v29) = v33 & ~ in(v33, v15))) & ! [v28] : ! [v29] : ! [v30] : ( ~ (ordered_pair(v28, v29) = v30) | ~ in(v30, v15) | in(v29, v16)) & ! [v28] : ! [v29] : ! [v30] : ( ~ (ordered_pair(v28, v29) = v30) | ~ in(v30, v15) | in(v28, v16)) & ! [v28] : ! [v29] : ! [v30] : ( ~ (ordered_pair(v28, v29) = v30) | ~ in(v30, v15) | ? [v31] : ? [v32] : ? [v33] : (apply(v19, v29) = v32 & apply(v19, v28) = v31 & ordered_pair(v31, v32) = v33 & in(v33, v17))) & ! [v28] : ! [v29] : ! [v30] : ( ~ (ordered_pair(v28, v29) = v30) | ~ in(v29, v16) | ~ in(v28, v16) | in(v30, v15) | ? [v31] : ? [v32] : ? [v33] : (apply(v19, v29) = v32 & apply(v19, v28) = v31 & ordered_pair(v31, v32) = v33 & ~ in(v33, v17))))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (inclusion_relation(v15) = v16) | ~ (relation_field(v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ subset(v18, v19) | ~ relation(v16) | ~ in(v19, v15) | ~ in(v18, v15) | in(v20, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (inclusion_relation(v15) = v16) | ~ (relation_field(v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v16) | ~ in(v20, v16) | ~ in(v19, v15) | ~ in(v18, v15) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v15, v17) = v18) | ~ (relation_dom(v15) = v16) | ~ (apply(v15, v19) = v20) | ~ relation(v15) | ~ function(v15) | ~ in(v20, v17) | ~ in(v19, v16) | in(v19, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v15, v17) = v18) | ~ (relation_dom(v15) = v16) | ~ (apply(v15, v19) = v20) | ~ relation(v15) | ~ function(v15) | ~ in(v19, v18) | in(v20, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v15, v17) = v18) | ~ (relation_dom(v15) = v16) | ~ (apply(v15, v19) = v20) | ~ relation(v15) | ~ function(v15) | ~ in(v19, v18) | in(v19, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v19, v16) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_field(v17) = v18) | ~ (relation_field(v15) = v16) | ~ (relation_dom(v19) = v20) | ~ relation(v19) | ~ relation(v17) | ~ relation(v15) | ~ function(v19) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (relation_rng(v19) = v21 & ( ~ (v21 = v18) | ~ (v20 = v16) | ~ one_to_one(v19) | relation_isomorphism(v15, v17, v19) | (apply(v19, v23) = v26 & apply(v19, v22) = v25 & ordered_pair(v25, v26) = v27 & ordered_pair(v22, v23) = v24 & ( ~ in(v27, v17) | ~ in(v24, v15) | ~ in(v23, v16) | ~ in(v22, v16)) & (in(v24, v15) | (in(v27, v17) & in(v23, v16) & in(v22, v16))))) & ( ~ relation_isomorphism(v15, v17, v19) | (v21 = v18 & v20 = v16 & one_to_one(v19) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : ( ~ (apply(v19, v29) = v31) | ~ (apply(v19, v28) = v30) | ~ (ordered_pair(v30, v31) = v32) | ~ in(v32, v17) | ~ in(v29, v16) | ~ in(v28, v16) | ? [v33] : (ordered_pair(v28, v29) = v33 & in(v33, v15))) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : ( ~ (apply(v19, v29) = v31) | ~ (apply(v19, v28) = v30) | ~ (ordered_pair(v30, v31) = v32) | in(v32, v17) | ? [v33] : (ordered_pair(v28, v29) = v33 & ~ in(v33, v15))) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : ( ~ (apply(v19, v29) = v31) | ~ (apply(v19, v28) = v30) | ~ (ordered_pair(v30, v31) = v32) | in(v29, v16) | ? [v33] : (ordered_pair(v28, v29) = v33 & ~ in(v33, v15))) & ! [v28] : ! [v29] : ! [v30] : ! [v31] : ! [v32] : ( ~ (apply(v19, v29) = v31) | ~ (apply(v19, v28) = v30) | ~ (ordered_pair(v30, v31) = v32) | in(v28, v16) | ? [v33] : (ordered_pair(v28, v29) = v33 & ~ in(v33, v15))) & ! [v28] : ! [v29] : ! [v30] : ( ~ (ordered_pair(v28, v29) = v30) | ~ in(v30, v15) | in(v29, v16)) & ! [v28] : ! [v29] : ! [v30] : ( ~ (ordered_pair(v28, v29) = v30) | ~ in(v30, v15) | in(v28, v16)) & ! [v28] : ! [v29] : ! [v30] : ( ~ (ordered_pair(v28, v29) = v30) | ~ in(v30, v15) | ? [v31] : ? [v32] : ? [v33] : (apply(v19, v29) = v32 & apply(v19, v28) = v31 & ordered_pair(v31, v32) = v33 & in(v33, v17))) & ! [v28] : ! [v29] : ! [v30] : ( ~ (ordered_pair(v28, v29) = v30) | ~ in(v29, v16) | ~ in(v28, v16) | in(v30, v15) | ? [v31] : ? [v32] : ? [v33] : (apply(v19, v29) = v32 & apply(v19, v28) = v31 & ordered_pair(v31, v32) = v33 & ~ in(v33, v17))))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v17) | in(v20, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v17) | in(v19, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v16) | ~ in(v19, v15) | in(v20, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v18) = v19) | ~ (relation_dom(v16) = v17) | ~ (set_intersection2(v19, v15) = v20) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_dom_restriction(v18, v15) = v21 & ( ~ (v21 = v16) | (v20 = v17 & ! [v25] : ! [v26] : ( ~ (apply(v18, v25) = v26) | ~ in(v25, v17) | apply(v16, v25) = v26) & ! [v25] : ! [v26] : ( ~ (apply(v16, v25) = v26) | ~ in(v25, v17) | apply(v18, v25) = v26))) & ( ~ (v20 = v17) | v21 = v16 | ( ~ (v24 = v23) & apply(v18, v22) = v24 & apply(v16, v22) = v23 & in(v22, v17))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v15) = v16) | ~ (relation_image(v15, v17) = v18) | ~ (apply(v15, v20) = v19) | ~ relation(v15) | ~ function(v15) | ~ in(v20, v17) | ~ in(v20, v16) | in(v19, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_image(v15, v16) = v17) | ~ (ordered_pair(v19, v18) = v20) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v19, v16) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v15) | ~ in(v20, v17) | in(v20, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v15) | ~ in(v20, v17) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v18, v16) | in(v20, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v19, v20) = v18) | ~ (cartesian_product2(v15, v16) = v17) | ~ in(v20, v16) | ~ in(v19, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v17, v18) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ transitive(v15) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v19, v15) | ? [v21] : (ordered_pair(v16, v18) = v21 & in(v21, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v17, v18) = v19) | ~ (ordered_pair(v16, v18) = v20) | ~ transitive(v15) | ~ relation(v15) | ~ in(v19, v15) | in(v20, v15) | ? [v21] : (ordered_pair(v16, v17) = v21 & ~ in(v21, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v16, v18) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ transitive(v15) | ~ relation(v15) | ~ in(v19, v15) | in(v20, v15) | ? [v21] : (ordered_pair(v17, v18) = v21 & ~ in(v21, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v15, v16) = v19) | ~ (cartesian_product2(v17, v18) = v20) | ~ in(v19, v20) | in(v16, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v15, v16) = v19) | ~ (cartesian_product2(v17, v18) = v20) | ~ in(v19, v20) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v15, v16) = v19) | ~ (cartesian_product2(v17, v18) = v20) | ~ in(v16, v18) | ~ in(v15, v17) | in(v19, v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v16, v18) = v20) | ~ (cartesian_product2(v15, v17) = v19) | ~ subset(v17, v18) | ~ subset(v15, v16) | subset(v19, v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_dom(v16) = v17) | ~ (apply(v16, v18) = v19) | ~ (identity_relation(v15) = v16) | ~ relation(v16) | ~ function(v16) | ~ in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | v19 = v16 | v19 = v15 | ~ (unordered_triple(v15, v16, v17) = v18) | ~ in(v19, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_field(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ connected(v15) | ~ relation(v15) | ~ in(v18, v16) | ~ in(v17, v16) | in(v19, v15) | ? [v20] : (ordered_pair(v17, v18) = v20 & in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_field(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ connected(v15) | ~ relation(v15) | ~ in(v18, v16) | ~ in(v17, v16) | in(v19, v15) | ? [v20] : (ordered_pair(v18, v17) = v20 & in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_dom(v15) = v16) | ~ (apply(v15, v18) = v19) | ~ (apply(v15, v17) = v19) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ~ in(v18, v16) | ~ in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (identity_relation(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ in(v19, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (ordered_pair(v18, v17) = v19) | ~ is_connected_in(v15, v16) | ~ relation(v15) | ~ in(v18, v16) | ~ in(v17, v16) | in(v19, v15) | ? [v20] : (ordered_pair(v17, v18) = v20 & in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (ordered_pair(v18, v17) = v19) | ~ is_antisymmetric_in(v15, v16) | ~ relation(v15) | ~ in(v19, v15) | ~ in(v18, v16) | ~ in(v17, v16) | ? [v20] : (ordered_pair(v17, v18) = v20 & ~ in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (ordered_pair(v17, v18) = v19) | ~ is_connected_in(v15, v16) | ~ relation(v15) | ~ in(v18, v16) | ~ in(v17, v16) | in(v19, v15) | ? [v20] : (ordered_pair(v18, v17) = v20 & in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (ordered_pair(v17, v18) = v19) | ~ is_antisymmetric_in(v15, v16) | ~ relation(v15) | ~ in(v19, v15) | ~ in(v18, v16) | ~ in(v17, v16) | ? [v20] : (ordered_pair(v18, v17) = v20 & ~ in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v16 | ~ (fiber(v15, v16) = v17) | ~ (ordered_pair(v18, v16) = v19) | ~ relation(v15) | ~ in(v19, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v16 | ~ (ordered_pair(v17, v18) = v19) | ~ (ordered_pair(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v15 | v17 = v15 | ~ (unordered_pair(v17, v18) = v19) | ~ (unordered_pair(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v15 | ~ (ordered_pair(v17, v18) = v19) | ~ (ordered_pair(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = v15 | ~ (subset_difference(v19, v18, v17) = v16) | ~ (subset_difference(v19, v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = v15 | ~ (relation_rng_as_subset(v19, v18, v17) = v16) | ~ (relation_rng_as_subset(v19, v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = v15 | ~ (relation_dom_as_subset(v19, v18, v17) = v16) | ~ (relation_dom_as_subset(v19, v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = v15 | ~ (unordered_triple(v19, v18, v17) = v16) | ~ (unordered_triple(v19, v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = empty_set | ~ (subset_difference(v15, v17, v18) = v19) | ~ (meet_of_subsets(v15, v16) = v18) | ~ (cast_to_subset(v15) = v17) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (union_of_subsets(v15, v22) = v23 & complements_of_subsets(v15, v16) = v22 & powerset(v20) = v21 & powerset(v15) = v20 & (v23 = v19 | ~ element(v16, v21)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = empty_set | ~ (subset_difference(v15, v17, v18) = v19) | ~ (union_of_subsets(v15, v16) = v18) | ~ (cast_to_subset(v15) = v17) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (meet_of_subsets(v15, v22) = v23 & complements_of_subsets(v15, v16) = v22 & powerset(v20) = v21 & powerset(v15) = v20 & (v23 = v19 | ~ element(v16, v21)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v15 = empty_set | ~ (subset_complement(v15, v17) = v18) | ~ (powerset(v15) = v16) | ~ element(v19, v15) | ~ element(v17, v16) | in(v19, v18) | in(v19, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (function_inverse(v16) = v17) | ~ (relation_composition(v17, v16) = v18) | ~ (apply(v18, v15) = v19) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_rng(v16) = v20 & apply(v17, v15) = v21 & apply(v16, v21) = v22 & ( ~ in(v15, v20) | (v22 = v15 & v19 = v15)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (function_inverse(v16) = v17) | ~ (apply(v17, v15) = v18) | ~ (apply(v16, v18) = v19) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v17, v16) = v21 & relation_rng(v16) = v20 & apply(v21, v15) = v22 & ( ~ in(v15, v20) | (v22 = v15 & v19 = v15)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v16) = v18) | ~ (apply(v18, v15) = v19) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_dom(v18) = v20 & apply(v17, v15) = v21 & apply(v16, v21) = v22 & (v22 = v19 | ~ in(v15, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ relation(v16) | ~ relation(v15) | ~ in(v19, v15) | ? [v20] : (ordered_pair(v17, v18) = v20 & in(v20, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ relation(v16) | ~ relation(v15) | in(v19, v15) | ? [v20] : (ordered_pair(v17, v18) = v20 & ~ in(v20, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ relation(v15) | ~ in(v19, v16) | ? [v20] : (ordered_pair(v18, v17) = v20 & in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ relation(v15) | in(v19, v16) | ? [v20] : (ordered_pair(v18, v17) = v20 & ~ in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_restriction(v17, v15) = v18) | ~ (fiber(v18, v16) = v19) | ~ relation(v17) | ? [v20] : (fiber(v17, v16) = v20 & subset(v19, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v15, v18) = v19) | ~ (powerset(v15) = v17) | ~ disjoint(v16, v18) | ~ element(v18, v17) | ~ element(v16, v17) | subset(v16, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v15, v18) = v19) | ~ (powerset(v15) = v17) | ~ subset(v16, v19) | ~ element(v18, v17) | ~ element(v16, v17) | disjoint(v16, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ relation_of2_as_subset(v18, v17, v15) | ~ subset(v19, v16) | relation_of2_as_subset(v18, v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v16, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | ? [v20] : (relation_dom(v17) = v20 & in(v15, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ relation(v15) | ~ in(v19, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v18) = v19) | ~ (singleton(v17) = v18) | ~ subset(v15, v16) | subset(v15, v19) | in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v17) = v19) | ~ (set_difference(v15, v17) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v17) = v19) | ~ (powerset(v15) = v18) | ~ element(v17, v18) | ~ element(v16, v18) | subset_difference(v15, v16, v17) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (fiber(v15, v16) = v17) | ~ (ordered_pair(v18, v16) = v19) | ~ relation(v15) | ~ in(v18, v17) | in(v19, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (singleton(v15) = v18) | ~ (unordered_pair(v17, v18) = v19) | ~ (unordered_pair(v15, v16) = v17) | ordered_pair(v15, v16) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse_image(v17, v16) = v19) | ~ (relation_inverse_image(v17, v15) = v18) | ~ subset(v15, v16) | ~ relation(v17) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_field(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v16, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_field(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v15, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v15, v18) = v19) | ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v20] : (relation_rng_restriction(v15, v17) = v20 & relation_dom_restriction(v20, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v15, v17) = v18) | ~ (relation_dom_restriction(v18, v16) = v19) | ~ relation(v17) | ? [v20] : (relation_rng_restriction(v15, v20) = v19 & relation_dom_restriction(v17, v16) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : (apply(v17, v15) = v20 & ( ~ (v20 = v16) | ~ in(v15, v19) | in(v18, v17)) & ( ~ in(v18, v17) | (v20 = v16 & in(v15, v19))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v15, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | ? [v20] : (relation_rng(v17) = v20 & in(v16, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v16) = v17) | ~ (relation_image(v16, v18) = v19) | ~ (set_intersection2(v17, v15) = v18) | ~ relation(v16) | relation_image(v16, v15) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v16) = v17) | ~ (apply(v18, v15) = v19) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v18, v16) = v20 & relation_dom(v20) = v21 & relation_dom(v18) = v22 & ( ~ in(v19, v17) | ~ in(v15, v22) | in(v15, v21)) & ( ~ in(v15, v21) | (in(v19, v17) & in(v15, v22))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v16) = v17) | ~ (relation_dom_restriction(v18, v15) = v19) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_dom(v18) = v20 & set_intersection2(v20, v15) = v21 & ( ~ (v21 = v17) | v19 = v16 | ( ~ (v24 = v23) & apply(v18, v22) = v24 & apply(v16, v22) = v23 & in(v22, v17))) & ( ~ (v19 = v16) | (v21 = v17 & ! [v25] : ! [v26] : ( ~ (apply(v18, v25) = v26) | ~ in(v25, v17) | apply(v16, v25) = v26) & ! [v25] : ! [v26] : ( ~ (apply(v16, v25) = v26) | ~ in(v25, v17) | apply(v18, v25) = v26))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v15) = v16) | ~ (relation_image(v15, v17) = v18) | ~ relation(v15) | ~ function(v15) | ~ in(v19, v18) | ? [v20] : (apply(v15, v20) = v19 & in(v20, v17) & in(v20, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v15) | ~ function(v15) | ~ in(v17, v16) | ? [v20] : (apply(v15, v17) = v20 & ( ~ (v20 = v18) | in(v19, v15)) & (v20 = v18 | ~ in(v19, v15)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v15) | ~ in(v19, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v18, v16) = v19) | ~ (relation_dom_restriction(v17, v15) = v18) | ~ relation(v17) | ~ function(v17) | ~ in(v16, v15) | apply(v17, v16) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v18, v16) = v19) | ~ (relation_dom_restriction(v17, v15) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : ? [v21] : (relation_dom(v18) = v20 & apply(v17, v16) = v21 & (v21 = v19 | ~ in(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v17, v16) = v19) | ~ (relation_dom_restriction(v17, v15) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : ? [v21] : (relation_dom(v18) = v20 & apply(v18, v16) = v21 & (v21 = v19 | ~ in(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v17, v15) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : (relation_dom(v17) = v20 & ( ~ (v19 = v16) | ~ in(v15, v20) | in(v18, v17)) & ( ~ in(v18, v17) | (v19 = v16 & in(v15, v20))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v17, v15) = v18) | ~ (apply(v16, v18) = v19) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v17, v16) = v20 & relation_dom(v20) = v21 & apply(v20, v15) = v22 & (v22 = v19 | ~ in(v15, v21)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (identity_relation(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ in(v19, v16) | in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ~ subset(v15, v16) | ~ relation(v16) | ~ relation(v15) | ~ in(v19, v15) | in(v19, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v16, v17) = v19) | ~ (set_intersection2(v15, v17) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v16) = v19) | ~ (cartesian_product2(v17, v15) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v16) = v19) | ~ (cartesian_product2(v17, v15) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v16, v17) = v21 & cartesian_product2(v15, v17) = v20 & subset(v20, v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v16) = v19) | ~ (cartesian_product2(v15, v17) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v17, v15) = v21 & cartesian_product2(v16, v17) = v20 & subset(v21, v19) & subset(v18, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v15) = v19) | ~ (cartesian_product2(v16, v17) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v17, v16) = v21 & cartesian_product2(v15, v17) = v20 & subset(v20, v18) & subset(v19, v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v16, v17) = v19) | ~ (cartesian_product2(v15, v17) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v16, v17) = v19) | ~ (cartesian_product2(v15, v17) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v17, v16) = v21 & cartesian_product2(v17, v15) = v20 & subset(v20, v21))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v15 | ~ (unordered_triple(v16, v17, v18) = v19) | ? [v20] : ((v20 = v18 | v20 = v17 | v20 = v16 | in(v20, v15)) & ( ~ in(v20, v15) | ( ~ (v20 = v18) & ~ (v20 = v17) & ~ (v20 = v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v15 | ~ (relation_inverse_image(v16, v18) = v19) | ~ (relation_dom(v16) = v17) | ~ relation(v16) | ~ function(v16) | ? [v20] : ? [v21] : (apply(v16, v20) = v21 & ( ~ in(v21, v18) | ~ in(v20, v17) | ~ in(v20, v15)) & (in(v20, v15) | (in(v21, v18) & in(v20, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v15 | ~ (relation_dom(v16) = v17) | ~ (relation_image(v16, v18) = v19) | ~ relation(v16) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (( ~ in(v20, v15) | ! [v23] : ( ~ (apply(v16, v23) = v20) | ~ in(v23, v18) | ~ in(v23, v17))) & (in(v20, v15) | (v22 = v20 & apply(v16, v21) = v20 & in(v21, v18) & in(v21, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v15 | ~ (pair_second(v16) = v17) | ~ (ordered_pair(v18, v19) = v16) | ? [v20] : ? [v21] : ( ~ (v21 = v15) & ordered_pair(v20, v21) = v16)) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v15 | ~ (pair_first(v16) = v17) | ~ (ordered_pair(v18, v19) = v16) | ? [v20] : ? [v21] : ( ~ (v20 = v15) & ordered_pair(v20, v21) = v16)) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v16) = v19) | ~ (relation_dom(v16) = v17) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_dom(v19) = v20 & relation_dom(v18) = v21 & apply(v18, v15) = v22 & ( ~ in(v22, v17) | ~ in(v15, v21) | in(v15, v20)) & ( ~ in(v15, v20) | (in(v22, v17) & in(v15, v21))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ (relation_dom(v16) = v17) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v18, v16) = v20 & relation_dom(v20) = v21 & apply(v18, v15) = v22 & ( ~ in(v22, v17) | ~ in(v15, v19) | in(v15, v21)) & ( ~ in(v15, v21) | (in(v22, v17) & in(v15, v19))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_composition(v15, v16) = v17) | ~ relation(v18) | ~ relation(v16) | ~ relation(v15) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v18) | ( ! [v25] : ! [v26] : ( ~ (ordered_pair(v25, v20) = v26) | ~ in(v26, v16) | ? [v27] : (ordered_pair(v19, v25) = v27 & ~ in(v27, v15))) & ! [v25] : ! [v26] : ( ~ (ordered_pair(v19, v25) = v26) | ~ in(v26, v15) | ? [v27] : (ordered_pair(v25, v20) = v27 & ~ in(v27, v16))))) & (in(v21, v18) | (ordered_pair(v22, v20) = v24 & ordered_pair(v19, v22) = v23 & in(v24, v16) & in(v23, v15))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v18) | ~ in(v21, v16) | ~ in(v20, v15)) & (in(v21, v18) | (in(v21, v16) & in(v20, v15))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_dom_restriction(v15, v16) = v18) | ~ relation(v17) | ~ relation(v15) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v17) | ~ in(v21, v15) | ~ in(v19, v16)) & (in(v21, v17) | (in(v21, v15) & in(v19, v16))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | v18 = v15 | ~ (unordered_pair(v15, v16) = v17) | ~ in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (relation_rng_as_subset(v15, v16, v17) = v18) | ~ relation_of2_as_subset(v17, v15, v16) | ? [v19] : (in(v19, v16) & ! [v20] : ! [v21] : ( ~ (ordered_pair(v20, v19) = v21) | ~ in(v21, v17)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (relation_dom_as_subset(v16, v15, v17) = v18) | ~ relation_of2_as_subset(v17, v16, v15) | ? [v19] : (in(v19, v16) & ! [v20] : ! [v21] : ( ~ (ordered_pair(v19, v20) = v21) | ~ in(v21, v17)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (complements_of_subsets(v15, v17) = v18) | ~ (complements_of_subsets(v15, v16) = v17) | ? [v19] : ? [v20] : (powerset(v19) = v20 & powerset(v15) = v19 & ~ element(v16, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (subset_complement(v15, v17) = v18) | ~ (subset_complement(v15, v16) = v17) | ? [v19] : (powerset(v15) = v19 & ~ element(v16, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (set_difference(v16, v15) = v17) | ~ (set_union2(v15, v17) = v18) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (singleton(v15) = v17) | ~ (set_union2(v17, v16) = v18) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (apply(v17, v16) = v18) | ~ (identity_relation(v15) = v17) | ~ in(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_difference(v15, v17) = v18) | ~ (singleton(v16) = v17) | in(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (relation_inverse_image(v16, v15) = v17) | ~ (relation_image(v16, v17) = v18) | ~ relation(v16) | ~ function(v16) | ? [v19] : (relation_rng(v16) = v19 & ~ subset(v15, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = empty_set | ~ (relation_dom(v15) = v16) | ~ (apply(v15, v17) = v18) | ~ relation(v15) | ~ function(v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (singleton(v15) = v18) | ~ (unordered_pair(v16, v17) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (ordered_pair(v17, v16) = v18) | ~ antisymmetric(v15) | ~ relation(v15) | ~ in(v18, v15) | ? [v19] : (ordered_pair(v16, v17) = v19 & ~ in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (ordered_pair(v16, v17) = v18) | ~ antisymmetric(v15) | ~ relation(v15) | ~ in(v18, v15) | ? [v19] : (ordered_pair(v17, v16) = v19 & ~ in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (meet_of_subsets(v18, v17) = v16) | ~ (meet_of_subsets(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (union_of_subsets(v18, v17) = v16) | ~ (union_of_subsets(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (complements_of_subsets(v18, v17) = v16) | ~ (complements_of_subsets(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_composition(v18, v17) = v16) | ~ (relation_composition(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_restriction(v18, v17) = v16) | ~ (relation_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (subset_complement(v18, v17) = v16) | ~ (subset_complement(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_difference(v18, v17) = v16) | ~ (set_difference(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (fiber(v18, v17) = v16) | ~ (fiber(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (singleton(v16) = v18) | ~ (singleton(v15) = v17) | ~ subset(v17, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (singleton(v15) = v18) | ~ (unordered_pair(v16, v17) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_inverse_image(v18, v17) = v16) | ~ (relation_inverse_image(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_rng_restriction(v18, v17) = v16) | ~ (relation_rng_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_image(v18, v17) = v16) | ~ (relation_image(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (apply(v18, v17) = v16) | ~ (apply(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_dom_restriction(v18, v17) = v16) | ~ (relation_dom_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (ordered_pair(v18, v17) = v16) | ~ (ordered_pair(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_intersection2(v18, v17) = v16) | ~ (set_intersection2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_union2(v18, v17) = v16) | ~ (set_union2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (unordered_pair(v18, v17) = v16) | ~ (unordered_pair(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (cartesian_product2(v18, v17) = v16) | ~ (cartesian_product2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = empty_set | ~ (meet_of_subsets(v15, v17) = v18) | ~ (complements_of_subsets(v15, v16) = v17) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset_difference(v15, v21, v22) = v23 & union_of_subsets(v15, v16) = v22 & cast_to_subset(v15) = v21 & powerset(v19) = v20 & powerset(v15) = v19 & (v23 = v18 | ~ element(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = empty_set | ~ (union_of_subsets(v15, v17) = v18) | ~ (complements_of_subsets(v15, v16) = v17) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset_difference(v15, v21, v22) = v23 & meet_of_subsets(v15, v16) = v22 & cast_to_subset(v15) = v21 & powerset(v19) = v20 & powerset(v15) = v19 & (v23 = v18 | ~ element(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v15 = empty_set | ~ (set_meet(v15) = v16) | ~ in(v18, v15) | ~ in(v17, v16) | in(v17, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_difference(v15, v16, v17) = v18) | ? [v19] : ? [v20] : (set_difference(v16, v17) = v20 & powerset(v15) = v19 & (v20 = v18 | ~ element(v17, v19) | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_difference(v15, v16, v17) = v18) | ? [v19] : (powerset(v15) = v19 & ( ~ element(v17, v19) | ~ element(v16, v19) | element(v18, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_as_subset(v15, v16, v17) = v18) | ~ relation_of2(v17, v15, v16) | relation_rng(v17) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_as_subset(v15, v16, v17) = v18) | ~ relation_of2(v17, v15, v16) | ? [v19] : (powerset(v16) = v19 & element(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_as_subset(v15, v16, v17) = v16) | ~ relation_of2_as_subset(v17, v15, v16) | ~ in(v18, v16) | ? [v19] : ? [v20] : (ordered_pair(v19, v18) = v20 & in(v20, v17))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_as_subset(v16, v15, v17) = v16) | ~ relation_of2_as_subset(v17, v16, v15) | ~ in(v18, v16) | ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & in(v20, v17))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_as_subset(v15, v16, v17) = v18) | ~ relation_of2(v17, v15, v16) | relation_dom(v17) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_as_subset(v15, v16, v17) = v18) | ~ relation_of2(v17, v15, v16) | ? [v19] : (powerset(v15) = v19 & element(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (function_inverse(v17) = v18) | ~ relation_isomorphism(v15, v16, v17) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v17) | relation_isomorphism(v16, v15, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ (identity_relation(v15) = v17) | ~ relation(v16) | relation_dom_restriction(v16, v15) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v15, v17) = v18) | ~ (relation_rng(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ? [v19] : (relation_rng(v18) = v19 & relation_image(v17, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v15, v17) = v18) | ~ (relation_dom(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ? [v19] : (relation_dom(v18) = v19 & subset(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v15, v17) = v18) | ~ in(v16, v18) | ~ in(v16, v17) | ? [v19] : (powerset(v15) = v19 & ~ element(v17, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation_of2_as_subset(v17, v15, v16) | subset(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation_of2_as_subset(v17, v15, v16) | ? [v19] : (relation_dom(v17) = v19 & subset(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v16) = v17) | ~ (set_intersection2(v17, v15) = v18) | ~ relation(v16) | ? [v19] : (relation_rng(v19) = v18 & relation_rng_restriction(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v15) = v17) | ~ (relation_dom(v15) = v16) | ~ (set_union2(v16, v17) = v18) | ~ relation(v15) | relation_field(v15) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v15) = v17) | ~ (relation_dom(v15) = v16) | ~ (cartesian_product2(v16, v17) = v18) | ~ relation(v15) | subset(v15, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v15) = v16) | ~ (relation_image(v17, v16) = v18) | ~ relation(v17) | ~ relation(v15) | ? [v19] : (relation_composition(v15, v17) = v19 & relation_rng(v19) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v17, v16) = v18) | ~ (set_union2(v15, v16) = v17) | set_difference(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v16, v15) = v17) | ~ (set_union2(v15, v17) = v18) | set_union2(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v17) = v18) | ~ (set_difference(v15, v16) = v17) | set_intersection2(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ in(v18, v17) | ~ in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ in(v18, v15) | in(v18, v17) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (union(v16) = v18) | ~ (powerset(v15) = v17) | ? [v19] : ? [v20] : (union_of_subsets(v15, v16) = v20 & powerset(v17) = v19 & (v20 = v18 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (union(v15) = v16) | ~ in(v18, v15) | ~ in(v17, v18) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (fiber(v15, v16) = v17) | ~ (ordered_pair(v16, v16) = v18) | ~ relation(v15) | ~ in(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_meet(v16) = v18) | ~ (powerset(v15) = v17) | ? [v19] : ? [v20] : (meet_of_subsets(v15, v16) = v20 & powerset(v17) = v19 & (v20 = v18 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_triple(v15, v16, v17) = v18) | in(v17, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_triple(v15, v16, v17) = v18) | in(v16, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_triple(v15, v16, v17) = v18) | in(v15, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_inverse_image(v16, v17) = v18) | ~ (relation_image(v16, v15) = v17) | ~ relation(v16) | subset(v15, v18) | ? [v19] : (relation_dom(v16) = v19 & ~ subset(v15, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_inverse_image(v16, v15) = v17) | ~ (relation_image(v16, v17) = v18) | ~ relation(v16) | ~ function(v16) | subset(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_inverse_image(v15, v16) = v17) | ~ relation(v15) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & in(v20, v15) & in(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_field(v15) = v16) | ~ (ordered_pair(v17, v17) = v18) | ~ reflexive(v15) | ~ relation(v15) | ~ in(v17, v16) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v15, v17) = v18) | ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | relation_restriction(v16, v15) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (relation_dom_restriction(v17, v15) = v18) | ~ relation(v16) | relation_restriction(v16, v15) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation_of2_as_subset(v17, v15, v16) | subset(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation_of2_as_subset(v17, v15, v16) | ? [v19] : (relation_rng(v17) = v19 & subset(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v16) = v17) | ~ (set_intersection2(v17, v15) = v18) | ~ relation(v16) | ? [v19] : (relation_dom(v19) = v18 & relation_dom_restriction(v16, v15) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_image(v15, v16) = v17) | ~ relation(v15) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v19, v18) = v20 & in(v20, v15) & in(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (identity_relation(v15) = v16) | ~ (ordered_pair(v17, v17) = v18) | ~ relation(v16) | ~ in(v17, v15) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (ordered_pair(v17, v17) = v18) | ~ is_reflexive_in(v15, v16) | ~ relation(v15) | ~ in(v17, v16) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | ~ subset(v15, v17) | ~ subset(v15, v16) | subset(v15, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v17) = v18) | ~ (cartesian_product2(v16, v16) = v17) | ~ relation(v15) | relation_restriction(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ disjoint(v15, v16) | ~ in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ in(v18, v16) | ~ in(v18, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v17) = v18) | ~ subset(v17, v16) | ~ subset(v15, v16) | subset(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v16) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v16) = v17) | ~ in(v18, v16) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v16) = v17) | ~ in(v18, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v15, v16) = v18) | ~ subset(v18, v17) | in(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v15, v16) = v18) | ~ subset(v18, v17) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v15, v16) = v18) | ~ in(v16, v17) | ~ in(v15, v17) | subset(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v15, v16) = v18) | ~ relation_of2_as_subset(v17, v15, v16) | ? [v19] : (powerset(v18) = v19 & element(v17, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v15, v16) = v18) | ~ relation_of2(v17, v15, v16) | subset(v17, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v15, v16) = v18) | ~ subset(v17, v18) | relation_of2(v17, v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v15, v16) = v17) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v19, v20) = v18 & in(v20, v16) & in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ empty(v17) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ in(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v15) = v17) | ~ element(v16, v17) | ~ in(v18, v16) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ relation_of2_as_subset(v18, v17, v15) | ~ subset(v15, v16) | relation_of2_as_subset(v18, v17, v16)) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_difference(v16, v17) = v18) | ? [v19] : (( ~ in(v19, v16) | ~ in(v19, v15) | in(v19, v17)) & (in(v19, v15) | (in(v19, v16) & ~ in(v19, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (fiber(v16, v17) = v18) | ~ relation(v16) | ? [v19] : ? [v20] : (ordered_pair(v19, v17) = v20 & (v19 = v17 | ~ in(v20, v16) | ~ in(v19, v15)) & (in(v19, v15) | ( ~ (v19 = v17) & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (relation_inverse_image(v16, v17) = v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v15) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v19, v22) = v23) | ~ in(v23, v16) | ~ in(v22, v17))) & (in(v19, v15) | (ordered_pair(v19, v20) = v21 & in(v21, v16) & in(v20, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (relation_image(v16, v17) = v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v15) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v19) = v23) | ~ in(v23, v16) | ~ in(v22, v17))) & (in(v19, v15) | (ordered_pair(v20, v19) = v21 & in(v21, v16) & in(v20, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_intersection2(v16, v17) = v18) | ? [v19] : (( ~ in(v19, v17) | ~ in(v19, v16) | ~ in(v19, v15)) & (in(v19, v15) | (in(v19, v17) & in(v19, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_union2(v16, v17) = v18) | ? [v19] : (( ~ in(v19, v15) | ( ~ in(v19, v17) & ~ in(v19, v16))) & (in(v19, v17) | in(v19, v16) | in(v19, v15)))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (unordered_pair(v16, v17) = v18) | ? [v19] : ((v19 = v17 | v19 = v16 | in(v19, v15)) & ( ~ in(v19, v15) | ( ~ (v19 = v17) & ~ (v19 = v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (cartesian_product2(v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ in(v19, v15) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v23, v24) = v19) | ~ in(v24, v17) | ~ in(v23, v16))) & (in(v19, v15) | (v22 = v19 & ordered_pair(v20, v21) = v19 & in(v21, v17) & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_dom(v18) = v19 & apply(v18, v15) = v20 & apply(v17, v15) = v21 & apply(v16, v21) = v22 & (v22 = v20 | ~ in(v15, v19)))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_field(v18) = v19 & relation_field(v17) = v20 & ( ~ in(v15, v19) | (in(v15, v20) & in(v15, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v19] : (cartesian_product2(v16, v16) = v19 & ( ~ in(v15, v19) | ~ in(v15, v17) | in(v15, v18)) & ( ~ in(v15, v18) | (in(v15, v19) & in(v15, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_inverse_image(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (relation_rng(v17) = v19 & ( ~ in(v15, v18) | (ordered_pair(v15, v20) = v21 & in(v21, v17) & in(v20, v19) & in(v20, v16))) & (in(v15, v18) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v15, v22) = v23) | ~ in(v23, v17) | ~ in(v22, v19) | ~ in(v22, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_rng(v18) = v19 & relation_rng(v17) = v20 & ( ~ in(v15, v20) | ~ in(v15, v16) | in(v15, v19)) & ( ~ in(v15, v19) | (in(v15, v20) & in(v15, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_image(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (relation_dom(v17) = v19 & ( ~ in(v15, v18) | (ordered_pair(v20, v15) = v21 & in(v21, v17) & in(v20, v19) & in(v20, v16))) & (in(v15, v18) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v15) = v23) | ~ in(v23, v17) | ~ in(v22, v19) | ~ in(v22, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : (relation_dom(v18) = v19 & relation_dom(v17) = v20 & ( ~ in(v15, v20) | ~ in(v15, v16) | in(v15, v19)) & ( ~ in(v15, v19) | (in(v15, v20) & in(v15, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_dom(v18) = v19 & relation_dom(v17) = v20 & ( ~ in(v15, v20) | ~ in(v15, v16) | in(v15, v19)) & ( ~ in(v15, v19) | (in(v15, v20) & in(v15, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v16, v17) = v18) | relation(v15) | ? [v19] : (powerset(v18) = v19 & ~ element(v15, v19))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (relation_inverse(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v18) = v21 & ordered_pair(v18, v19) = v20 & ( ~ in(v21, v15) | ~ in(v20, v17)) & (in(v21, v15) | in(v20, v17)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (inclusion_relation(v15) = v17) | ~ (relation_field(v16) = v15) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & in(v19, v15) & in(v18, v15) & ( ~ subset(v18, v19) | ~ in(v20, v16)) & (subset(v18, v19) | in(v20, v16)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (relation_dom(v16) = v15) | ~ (identity_relation(v15) = v17) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : ( ~ (v19 = v18) & apply(v16, v18) = v19 & in(v18, v15))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (identity_relation(v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & ( ~ (v19 = v18) | ~ in(v20, v16) | ~ in(v18, v15)) & (in(v20, v16) | (v19 = v18 & in(v18, v15))))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v15, v16) = v17) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ epsilon_connected(v15) | ~ in(v17, v15) | ~ in(v16, v15) | in(v17, v16) | in(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | v15 = empty_set | ~ (singleton(v16) = v17) | ~ subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (set_difference(v15, v16) = v17) | ~ disjoint(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (inclusion_relation(v15) = v16) | ~ (relation_field(v16) = v17) | ~ relation(v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (singleton(v15) = v16) | ~ in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (relation_dom(v16) = v17) | ~ (identity_relation(v15) = v16) | ~ relation(v16) | ~ function(v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (set_intersection2(v15, v16) = v17) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = empty_set | ~ (set_difference(v15, v16) = v17) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = empty_set | ~ (relation_field(v15) = v16) | ~ well_founded_relation(v15) | ~ subset(v17, v16) | ~ relation(v15) | ? [v18] : ? [v19] : (fiber(v15, v18) = v19 & disjoint(v19, v17) & in(v18, v17))) & ! [v15] : ! [v16] : ! [v17] : (v17 = empty_set | ~ (set_intersection2(v15, v16) = v17) | ~ disjoint(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = empty_set | ~ is_well_founded_in(v15, v16) | ~ subset(v17, v16) | ~ relation(v15) | ? [v18] : ? [v19] : (fiber(v15, v18) = v19 & disjoint(v19, v17) & in(v18, v17))) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (function_inverse(v17) = v16) | ~ (function_inverse(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_inverse(v17) = v16) | ~ (relation_inverse(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_rng(v17) = v16) | ~ (relation_rng(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (union(v17) = v16) | ~ (union(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (cast_to_subset(v17) = v16) | ~ (cast_to_subset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (pair_second(v17) = v16) | ~ (pair_second(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (inclusion_relation(v17) = v16) | ~ (inclusion_relation(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (set_meet(v17) = v16) | ~ (set_meet(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (singleton(v17) = v16) | ~ (singleton(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (succ(v17) = v16) | ~ (succ(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (pair_first(v17) = v16) | ~ (pair_first(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_field(v17) = v16) | ~ (relation_field(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_dom(v17) = v16) | ~ (relation_dom(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (identity_relation(v17) = v16) | ~ (identity_relation(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (powerset(v17) = v16) | ~ (powerset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (meet_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (set_meet(v16) = v20 & powerset(v18) = v19 & powerset(v15) = v18 & (v20 = v17 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (meet_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | element(v17, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (union(v16) = v20 & powerset(v18) = v19 & powerset(v15) = v18 & (v20 = v17 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | element(v17, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (complements_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | element(v17, v19)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (complements_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | ( ! [v20] : ! [v21] : ( ~ (subset_complement(v15, v20) = v21) | ~ element(v20, v18) | ~ element(v17, v19) | ~ in(v21, v16) | in(v20, v17)) & ! [v20] : ! [v21] : ( ~ (subset_complement(v15, v20) = v21) | ~ element(v20, v18) | ~ element(v17, v19) | ~ in(v20, v17) | in(v21, v16)) & ! [v20] : (v20 = v17 | ~ element(v20, v19) | ? [v21] : ? [v22] : (subset_complement(v15, v21) = v22 & element(v21, v18) & ( ~ in(v22, v16) | ~ in(v21, v20)) & (in(v22, v16) | in(v21, v20)))))))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v15) = v17) | ~ relation(v16) | ~ empty(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v15) = v17) | ~ relation(v16) | ~ empty(v15) | empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v16) | ~ function(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v16) | ~ function(v15) | function(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ empty(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ empty(v15) | empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ reflexive(v16) | ~ relation(v16) | reflexive(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ well_ordering(v16) | ~ relation(v16) | well_ordering(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ well_ordering(v16) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_field(v17) = v19 & relation_field(v16) = v18 & (v19 = v15 | ~ subset(v15, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ well_founded_relation(v16) | ~ relation(v16) | well_founded_relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ transitive(v16) | ~ relation(v16) | transitive(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ connected(v16) | ~ relation(v16) | connected(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ antisymmetric(v16) | ~ relation(v16) | antisymmetric(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_field(v17) = v18 & relation_field(v16) = v19 & subset(v18, v19) & subset(v18, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_rng_restriction(v15, v18) = v17 & relation_dom_restriction(v16, v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_rng_restriction(v15, v16) = v18 & relation_dom_restriction(v18, v15) = v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v15, v16) = v17) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_restriction(v15, v16) = v17) | ~ relation(v15) | ? [v18] : (set_intersection2(v15, v18) = v17 & cartesian_product2(v16, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset_complement(v15, v16) = v17) | ? [v18] : ? [v19] : (set_difference(v15, v16) = v19 & powerset(v15) = v18 & (v19 = v17 | ~ element(v16, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset_complement(v15, v16) = v17) | ? [v18] : (powerset(v15) = v18 & ( ~ element(v16, v18) | element(v17, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ~ relation(v15) | ? [v18] : ? [v19] : (relation_composition(v15, v16) = v18 & relation_rng(v18) = v19 & subset(v19, v17))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ~ in(v17, v16) | ? [v18] : ? [v19] : (ordered_pair(v18, v17) = v19 & in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v17) = v15) | ~ (singleton(v16) = v17) | ~ in(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | subset(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | ? [v18] : ? [v19] : (subset_complement(v15, v16) = v19 & powerset(v15) = v18 & (v19 = v17 | ~ element(v16, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | ? [v18] : (set_difference(v18, v16) = v17 & set_union2(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union(v16) = v17) | ~ in(v15, v16) | subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union(v15) = v16) | ~ in(v17, v16) | ? [v18] : (in(v18, v15) & in(v17, v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v17) | ~ disjoint(v17, v16) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v17) | ~ subset(v17, v16) | in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v17) | ~ in(v15, v16) | subset(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v16) | ~ (set_union2(v15, v16) = v17) | succ(v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | ~ being_limit_ordinal(v15) | ~ ordinal(v16) | ~ ordinal(v15) | ~ in(v16, v15) | in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (succ(v15) = v16) | ~ ordinal_subset(v16, v17) | ~ ordinal(v17) | ~ ordinal(v15) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (succ(v15) = v16) | ~ ordinal(v17) | ~ ordinal(v15) | ~ in(v15, v17) | ordinal_subset(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_inverse_image(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_dom(v16) = v18 & subset(v17, v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ~ function(v16) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ~ function(v16) | function(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | subset(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & set_intersection2(v19, v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_dom(v17) = v18 & relation_dom(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v17) = v18 & subset(v18, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom(v15) = v16) | ~ (relation_image(v15, v16) = v17) | ~ relation(v15) | relation_rng(v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ in(v17, v16) | ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_image(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_dom(v16) = v18 & relation_image(v16, v19) = v17 & set_intersection2(v18, v15) = v19)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_image(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v16) = v18 & subset(v17, v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v16, v15) = v17) | ~ relation(v16) | ~ function(v16) | ? [v18] : (relation_dom(v16) = v18 & ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v16, v19) = v20) | ~ (apply(v20, v15) = v21) | ~ relation(v19) | ~ function(v19) | ~ in(v15, v18) | apply(v19, v17) = v21) & ! [v19] : ! [v20] : ( ~ (apply(v19, v17) = v20) | ~ relation(v19) | ~ function(v19) | ~ in(v15, v18) | ? [v21] : (relation_composition(v16, v19) = v21 & apply(v21, v15) = v20)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | subset(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_dom(v17) = v18 & relation_dom(v16) = v19 & set_intersection2(v19, v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_composition(v18, v16) = v17 & identity_relation(v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation_empty_yielding(v15) | ~ relation(v15) | relation_empty_yielding(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation_empty_yielding(v15) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation(v15) | ~ function(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation(v15) | ~ function(v15) | function(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (ordered_pair(v15, v16) = v17) | ~ empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (ordered_pair(v15, v16) = v17) | pair_second(v17) = v16) & ! [v15] : ! [v16] : ! [v17] : ( ~ (ordered_pair(v15, v16) = v17) | pair_first(v17) = v15) & ! [v15] : ! [v16] : ! [v17] : ( ~ (ordered_pair(v15, v16) = v17) | ? [v18] : ? [v19] : (singleton(v15) = v19 & unordered_pair(v18, v19) = v17 & unordered_pair(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v16, v15) = v17) | set_intersection2(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | set_intersection2(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | disjoint(v15, v16) | ? [v18] : in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | subset(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | ? [v18] : (set_difference(v15, v18) = v17 & set_difference(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v16, v15) = v17) | ~ empty(v17) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v16, v15) = v17) | set_union2(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ~ empty(v17) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | set_union2(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ? [v18] : (set_difference(v16, v15) = v18 & set_union2(v15, v18) = v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v16, v15) = v17) | unordered_pair(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | ~ empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | unordered_pair(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | in(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v15, v16) = v17) | ~ empty(v17) | empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ subset(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v15) = v16) | ~ subset(v17, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v15) = v16) | ~ in(v17, v16) | subset(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ relation_of2_as_subset(v17, v15, v16) | relation_of2(v17, v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ relation_isomorphism(v15, v16, v17) | ~ reflexive(v15) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v17) | reflexive(v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ relation_isomorphism(v15, v16, v17) | ~ well_ordering(v15) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v17) | well_ordering(v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ relation_isomorphism(v15, v16, v17) | ~ well_founded_relation(v15) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v17) | well_founded_relation(v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ relation_isomorphism(v15, v16, v17) | ~ transitive(v15) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v17) | transitive(v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ relation_isomorphism(v15, v16, v17) | ~ connected(v15) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v17) | connected(v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ relation_isomorphism(v15, v16, v17) | ~ antisymmetric(v15) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v17) | antisymmetric(v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ disjoint(v16, v17) | ~ subset(v15, v16) | disjoint(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ disjoint(v15, v16) | ~ in(v17, v16) | ~ in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ relation_of2(v17, v15, v16) | relation_of2_as_subset(v17, v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ subset(v16, v17) | ~ subset(v15, v16) | subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ subset(v15, v16) | ~ in(v17, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ in(v17, v15) | ~ in(v16, v17) | ~ in(v15, v16)) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | v16 = empty_set | ~ (set_meet(v16) = v17) | ? [v18] : ? [v19] : (( ~ in(v18, v15) | (in(v19, v16) & ~ in(v18, v19))) & (in(v18, v15) | ! [v20] : ( ~ in(v20, v16) | in(v18, v20))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (( ~ in(v18, v15) | ! [v21] : ! [v22] : ( ~ (ordered_pair(v21, v18) = v22) | ~ in(v22, v16))) & (in(v18, v15) | (ordered_pair(v19, v18) = v20 & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (union(v16) = v17) | ? [v18] : ? [v19] : (( ~ in(v18, v15) | ! [v20] : ( ~ in(v20, v16) | ~ in(v18, v20))) & (in(v18, v15) | (in(v19, v16) & in(v18, v19))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (singleton(v16) = v17) | ? [v18] : (( ~ (v18 = v16) | ~ in(v16, v15)) & (v18 = v16 | in(v18, v15)))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (relation_dom(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (( ~ in(v18, v15) | ! [v21] : ! [v22] : ( ~ (ordered_pair(v18, v21) = v22) | ~ in(v22, v16))) & (in(v18, v15) | (ordered_pair(v18, v19) = v20 & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (powerset(v16) = v17) | ? [v18] : (( ~ subset(v18, v16) | ~ in(v18, v15)) & (subset(v18, v16) | in(v18, v15)))) & ? [v15] : ! [v16] : ! [v17] : (v16 = empty_set | ~ (set_meet(v16) = v17) | in(v15, v17) | ? [v18] : (in(v18, v16) & ~ in(v15, v18))) & ? [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v16) = v17) | disjoint(v17, v15) | in(v16, v15)) & ? [v15] : ! [v16] : ! [v17] : ( ~ (succ(v16) = v17) | ~ ordinal(v16) | ? [v18] : ( ! [v19] : ( ~ ordinal(v19) | ~ in(v19, v17) | ~ in(v19, v15) | in(v19, v18)) & ! [v19] : ( ~ in(v19, v18) | in(v19, v17)) & ! [v19] : ( ~ in(v19, v18) | (ordinal(v19) & in(v19, v15))))) & ? [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | element(v15, v17) | ? [v18] : (in(v18, v15) & ~ in(v18, v16))) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_difference(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (union(v15) = v16) | ~ being_limit_ordinal(v15)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (cast_to_subset(v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_intersection2(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_union2(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_union2(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ subset(v16, v15) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ subset(v15, v16) | proper_subset(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ relation(v16) | ~ relation(v15) | ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & ( ~ in(v19, v16) | ~ in(v19, v15)) & (in(v19, v16) | in(v19, v15)))) & ! [v15] : ! [v16] : (v16 = v15 | ~ ordinal(v16) | ~ ordinal(v15) | in(v16, v15) | in(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ empty(v16) | ~ empty(v15)) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (complements_of_subsets(v15, v16) = empty_set) | ? [v17] : ? [v18] : (powerset(v17) = v18 & powerset(v15) = v17 & ~ element(v16, v18))) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (set_difference(empty_set, v15) = v16)) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (set_intersection2(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v15 = empty_set | ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : ( ~ (v17 = empty_set) & relation_dom(v15) = v17)) & ! [v15] : ! [v16] : (v15 = empty_set | ~ (relation_inverse_image(v16, v15) = empty_set) | ~ relation(v16) | ? [v17] : (relation_rng(v16) = v17 & ~ subset(v15, v17))) & ! [v15] : ! [v16] : (v15 = empty_set | ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : ( ~ (v17 = empty_set) & relation_rng(v15) = v17)) & ! [v15] : ! [v16] : (v15 = empty_set | ~ subset(v15, v16) | ~ ordinal(v16) | ? [v17] : (ordinal(v17) & in(v17, v15) & ! [v18] : ( ~ ordinal(v18) | ~ in(v18, v15) | ordinal_subset(v17, v18)))) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | relation_inverse(v15) = v16) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | one_to_one(v16)) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (relation_rng(v16) = v18 & relation_rng(v15) = v17 & relation_dom(v16) = v17 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (relation_rng(v15) = v17 & relation_dom(v15) = v18 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (relation_dom(v16) = v19) | ~ (apply(v16, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v16) | ~ function(v16) | ~ in(v21, v18)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (relation_dom(v16) = v19) | ~ (apply(v16, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v16) | ~ function(v16) | ~ in(v20, v17)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v16) = v19) | ~ (apply(v16, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v16) | ~ function(v16) | ~ in(v21, v18) | in(v20, v17)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v16) = v19) | ~ (apply(v16, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v16) | ~ function(v16) | ~ in(v20, v17) | in(v21, v18)) & ! [v19] : (v19 = v17 | ~ (relation_dom(v16) = v19) | ~ relation(v16) | ~ function(v16)) & ! [v19] : (v19 = v16 | ~ (relation_dom(v19) = v17) | ~ relation(v19) | ~ function(v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (apply(v19, v20) = v22 & apply(v15, v21) = v23 & ((v23 = v20 & in(v21, v18) & ( ~ (v22 = v21) | ~ in(v20, v17))) | (v22 = v21 & in(v20, v17) & ( ~ (v23 = v20) | ~ in(v21, v18)))))))) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ relation(v15) | ~ function(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ relation(v15) | ~ function(v15) | function(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | function_inverse(v15) = v16) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | function(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ relation(v15) | relation_inverse(v16) = v15) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ relation(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_rng(v16) = v18 & relation_rng(v15) = v17 & relation_dom(v16) = v17 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (function_inverse(v15) = v17 & relation_rng(v17) = v18 & relation_dom(v17) = v16 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (function_inverse(v15) = v17 & relation_dom(v15) = v18 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v18)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v17) | ~ function(v17) | ~ in(v20, v16)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v18) | in(v20, v16)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v17) | ~ function(v17) | ~ in(v20, v16) | in(v21, v18)) & ! [v19] : (v19 = v17 | ~ (relation_dom(v19) = v16) | ~ relation(v19) | ~ function(v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (apply(v19, v20) = v22 & apply(v15, v21) = v23 & ((v23 = v20 & in(v21, v18) & ( ~ (v22 = v21) | ~ in(v20, v16))) | (v22 = v21 & in(v20, v16) & ( ~ (v23 = v20) | ~ in(v21, v18)))))) & ! [v19] : (v19 = v16 | ~ (relation_dom(v17) = v19) | ~ relation(v17) | ~ function(v17)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ~ function(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (apply(v15, v19) = v18) | ~ in(v19, v17) | in(v18, v16)) & ! [v18] : ( ~ in(v18, v16) | ? [v19] : (apply(v15, v19) = v18 & in(v19, v17))) & ? [v18] : (v18 = v16 | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v18) | ! [v22] : ( ~ (apply(v15, v22) = v19) | ~ in(v22, v17))) & (in(v19, v18) | (v21 = v19 & apply(v15, v20) = v19 & in(v20, v17))))))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ~ empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_inverse(v15) = v17 & relation_rng(v17) = v18 & relation_dom(v17) = v16 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & relation_image(v15, v17) = v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v15) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v21 & relation_rng(v18) = v20 & (v21 = v16 | ~ subset(v17, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v17, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v18, v15) = v20 & relation_rng(v20) = v16)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v15, v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_dom(v19) = v21 & relation_dom(v18) = v20 & (v21 = v17 | ~ subset(v16, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v16, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v15, v18) = v20 & relation_dom(v20) = v17)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v16, v19)) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_dom(v18) = v20 & subset(v17, v20))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v17, v19)) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_rng(v18) = v20 & subset(v16, v20))))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ( ~ (v17 = empty_set) | v16 = empty_set) & ( ~ (v16 = empty_set) | v17 = empty_set))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (set_difference(v15, v16) = v15) | disjoint(v15, v16)) & ! [v15] : ! [v16] : ( ~ (set_difference(v15, v16) = empty_set) | subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ (union(v15) = v16) | ~ ordinal(v15) | epsilon_connected(v16)) & ! [v15] : ! [v16] : ( ~ (union(v15) = v16) | ~ ordinal(v15) | epsilon_transitive(v16)) & ! [v15] : ! [v16] : ( ~ (union(v15) = v16) | ~ ordinal(v15) | ordinal(v16)) & ! [v15] : ! [v16] : ( ~ (cast_to_subset(v15) = v16) | ? [v17] : (powerset(v15) = v17 & element(v16, v17))) & ! [v15] : ! [v16] : ( ~ (inclusion_relation(v15) = v16) | ~ ordinal(v15) | well_founded_relation(v16)) & ! [v15] : ! [v16] : ( ~ (inclusion_relation(v15) = v16) | ~ ordinal(v15) | connected(v16)) & ! [v15] : ! [v16] : ( ~ (inclusion_relation(v15) = v16) | reflexive(v16)) & ! [v15] : ! [v16] : ( ~ (inclusion_relation(v15) = v16) | transitive(v16)) & ! [v15] : ! [v16] : ( ~ (inclusion_relation(v15) = v16) | antisymmetric(v16)) & ! [v15] : ! [v16] : ( ~ (inclusion_relation(v15) = v16) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (singleton(v16) = v15) | subset(v15, v15)) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | unordered_pair(v15, v15) = v16) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | subset(empty_set, v16)) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (succ(v16) = v15) | ~ being_limit_ordinal(v15) | ~ ordinal(v16) | ~ ordinal(v15)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ ordinal(v15) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ ordinal(v15) | epsilon_connected(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ ordinal(v15) | epsilon_transitive(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ ordinal(v15) | ordinal(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (succ(v15) = v16) | ? [v17] : (singleton(v15) = v17 & set_union2(v15, v17) = v16)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ well_orders(v15, v16) | ~ relation(v15) | well_ordering(v15)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ reflexive(v15) | ~ relation(v15) | is_reflexive_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ well_ordering(v15) | ~ relation(v15) | well_orders(v15, v16)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ is_well_founded_in(v15, v16) | ~ relation(v15) | well_founded_relation(v15)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ well_founded_relation(v15) | ~ relation(v15) | is_well_founded_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ is_reflexive_in(v15, v16) | ~ relation(v15) | reflexive(v15)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ is_transitive_in(v15, v16) | ~ relation(v15) | transitive(v15)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ transitive(v15) | ~ relation(v15) | is_transitive_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ is_connected_in(v15, v16) | ~ relation(v15) | connected(v15)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ connected(v15) | ~ relation(v15) | is_connected_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ is_antisymmetric_in(v15, v16) | ~ relation(v15) | antisymmetric(v15)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ antisymmetric(v15) | ~ relation(v15) | is_antisymmetric_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ relation(v15) | reflexive(v15) | ? [v17] : ? [v18] : (ordered_pair(v17, v17) = v18 & in(v17, v16) & ~ in(v18, v15))) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ relation(v15) | well_founded_relation(v15) | ? [v17] : ( ~ (v17 = empty_set) & subset(v17, v16) & ! [v18] : ! [v19] : ( ~ (fiber(v15, v18) = v19) | ~ disjoint(v19, v17) | ~ in(v18, v17)))) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ relation(v15) | connected(v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ( ~ (v18 = v17) & ordered_pair(v18, v17) = v20 & ordered_pair(v17, v18) = v19 & in(v18, v16) & in(v17, v16) & ~ in(v20, v15) & ~ in(v19, v15))) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_rng(v15) = v18 & relation_dom(v15) = v17 & set_union2(v17, v18) = v16)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (function_inverse(v15) = v18 & relation_rng(v18) = v16 & relation_rng(v15) = v17 & relation_dom(v18) = v17)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (function_inverse(v15) = v17 & relation_rng(v15) = v18 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v16)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v17) | ~ function(v17) | ~ in(v20, v18)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v16) | in(v20, v18)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v17) | ~ function(v17) | ~ in(v20, v18) | in(v21, v16)) & ! [v19] : (v19 = v18 | ~ (relation_dom(v17) = v19) | ~ relation(v17) | ~ function(v17)) & ! [v19] : (v19 = v17 | ~ (relation_dom(v19) = v18) | ~ relation(v19) | ~ function(v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (apply(v19, v20) = v22 & apply(v15, v21) = v23 & ((v23 = v20 & in(v21, v16) & ( ~ (v22 = v21) | ~ in(v20, v18))) | (v22 = v21 & in(v20, v18) & ( ~ (v23 = v20) | ~ in(v21, v16)))))))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ function(v15) | one_to_one(v15) | ? [v17] : ? [v18] : ? [v19] : ( ~ (v18 = v17) & apply(v15, v18) = v19 & apply(v15, v17) = v19 & in(v18, v16) & in(v17, v16))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ function(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (apply(v15, v19) = v18) | ~ in(v19, v16) | in(v18, v17)) & ! [v18] : ( ~ in(v18, v17) | ? [v19] : (apply(v15, v19) = v18 & in(v19, v16))) & ? [v18] : (v18 = v17 | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v18) | ! [v22] : ( ~ (apply(v15, v22) = v19) | ~ in(v22, v16))) & (in(v19, v18) | (v21 = v19 & apply(v15, v20) = v19 & in(v20, v16))))))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_inverse(v15) = v18 & relation_rng(v18) = v16 & relation_rng(v15) = v17 & relation_dom(v18) = v17)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v15) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v21 & relation_rng(v18) = v20 & (v21 = v17 | ~ subset(v16, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v16, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v18, v15) = v20 & relation_rng(v20) = v17)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v15, v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_dom(v19) = v21 & relation_dom(v18) = v20 & (v21 = v16 | ~ subset(v17, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v17, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v15, v18) = v20 & relation_dom(v20) = v16)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v17, v19)) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_dom(v18) = v20 & subset(v16, v20))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v16, v19)) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_rng(v18) = v20 & subset(v17, v20))))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ( ~ (v17 = empty_set) | v16 = empty_set) & ( ~ (v16 = empty_set) | v17 = empty_set))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation_rng(v16) = v15) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation_dom(v16) = v15) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | function(v16)) & ! [v15] : ! [v16] : ( ~ (set_intersection2(v15, v16) = empty_set) | disjoint(v15, v16)) & ! [v15] : ! [v16] : ( ~ (unordered_pair(v15, v15) = v16) | singleton(v15) = v16) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | union(v16) = v15) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | empty(v15) | ? [v17] : (element(v17, v16) & ~ empty(v17))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (cast_to_subset(v15) = v17 & element(v17, v16))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (element(v17, v16) & empty(v17))) & ! [v15] : ! [v16] : ( ~ well_orders(v15, v16) | ~ relation(v15) | is_well_founded_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ well_orders(v15, v16) | ~ relation(v15) | is_reflexive_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ well_orders(v15, v16) | ~ relation(v15) | is_transitive_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ well_orders(v15, v16) | ~ relation(v15) | is_connected_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ well_orders(v15, v16) | ~ relation(v15) | is_antisymmetric_in(v15, v16)) & ! [v15] : ! [v16] : ( ~ is_well_founded_in(v15, v16) | ~ is_reflexive_in(v15, v16) | ~ is_transitive_in(v15, v16) | ~ is_connected_in(v15, v16) | ~ is_antisymmetric_in(v15, v16) | ~ relation(v15) | well_orders(v15, v16)) & ! [v15] : ! [v16] : ( ~ disjoint(v15, v16) | disjoint(v16, v15)) & ! [v15] : ! [v16] : ( ~ subset(v15, v16) | ~ ordinal(v16) | ~ ordinal(v15) | ordinal_subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ subset(v15, v16) | ~ proper_subset(v16, v15)) & ! [v15] : ! [v16] : ( ~ ordinal_subset(v15, v16) | ~ ordinal(v16) | ~ ordinal(v15) | subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ element(v16, v15) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ element(v16, v15) | empty(v15) | in(v16, v15)) & ! [v15] : ! [v16] : ( ~ element(v15, v16) | empty(v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ relation(v16) | ~ relation(v15) | subset(v15, v16) | ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & in(v19, v15) & ~ in(v19, v16))) & ! [v15] : ! [v16] : ( ~ relation(v15) | ~ in(v16, v15) | ? [v17] : ? [v18] : ordered_pair(v17, v18) = v16) & ! [v15] : ! [v16] : ( ~ epsilon_transitive(v15) | ~ ordinal(v16) | ~ proper_subset(v15, v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ epsilon_transitive(v15) | ~ in(v16, v15) | subset(v16, v15)) & ! [v15] : ! [v16] : ( ~ ordinal(v16) | ~ ordinal(v15) | ordinal_subset(v16, v15) | ordinal_subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ ordinal(v16) | ~ ordinal(v15) | ordinal_subset(v15, v15)) & ! [v15] : ! [v16] : ( ~ ordinal(v16) | ~ in(v16, v15) | ? [v17] : (ordinal(v17) & in(v17, v15) & ! [v18] : ( ~ ordinal(v18) | ~ in(v18, v15) | ordinal_subset(v17, v18)))) & ! [v15] : ! [v16] : ( ~ ordinal(v16) | ~ in(v15, v16) | ordinal(v15)) & ! [v15] : ! [v16] : ( ~ empty(v16) | ~ empty(v15) | element(v16, v15)) & ! [v15] : ! [v16] : ( ~ empty(v16) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ proper_subset(v16, v15) | ~ proper_subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ proper_subset(v15, v16) | subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v16, v15) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v16, v15) | element(v16, v15) | empty(v15)) & ! [v15] : ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v15, v16) | ? [v17] : (in(v17, v16) & ! [v18] : ( ~ in(v18, v17) | ~ in(v18, v16)))) & ? [v15] : ! [v16] : ( ~ relation(v16) | is_well_founded_in(v16, v15) | ? [v17] : ( ~ (v17 = empty_set) & subset(v17, v15) & ! [v18] : ! [v19] : ( ~ (fiber(v16, v18) = v19) | ~ disjoint(v19, v17) | ~ in(v18, v17)))) & ? [v15] : ! [v16] : ( ~ relation(v16) | is_reflexive_in(v16, v15) | ? [v17] : ? [v18] : (ordered_pair(v17, v17) = v18 & in(v17, v15) & ~ in(v18, v16))) & ? [v15] : ! [v16] : ( ~ relation(v16) | is_transitive_in(v16, v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (ordered_pair(v18, v19) = v21 & ordered_pair(v17, v19) = v22 & ordered_pair(v17, v18) = v20 & in(v21, v16) & in(v20, v16) & in(v19, v15) & in(v18, v15) & in(v17, v15) & ~ in(v22, v16))) & ? [v15] : ! [v16] : ( ~ relation(v16) | is_connected_in(v16, v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ( ~ (v18 = v17) & ordered_pair(v18, v17) = v20 & ordered_pair(v17, v18) = v19 & in(v18, v15) & in(v17, v15) & ~ in(v20, v16) & ~ in(v19, v16))) & ? [v15] : ! [v16] : ( ~ relation(v16) | is_antisymmetric_in(v16, v15) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ( ~ (v18 = v17) & ordered_pair(v18, v17) = v20 & ordered_pair(v17, v18) = v19 & in(v20, v16) & in(v19, v16) & in(v18, v15) & in(v17, v15))) & ! [v15] : (v15 = empty_set | ~ (relation_rng(v15) = empty_set) | ~ relation(v15)) & ! [v15] : (v15 = empty_set | ~ (set_meet(empty_set) = v15)) & ! [v15] : (v15 = empty_set | ~ (relation_dom(v15) = empty_set) | ~ relation(v15)) & ! [v15] : (v15 = empty_set | ~ subset(v15, empty_set)) & ! [v15] : (v15 = empty_set | ~ relation(v15) | ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v16, v17) = v18 & in(v18, v15))) & ! [v15] : (v15 = empty_set | ~ empty(v15)) & ! [v15] : ( ~ (union(v15) = v15) | being_limit_ordinal(v15)) & ! [v15] : ~ (singleton(v15) = empty_set) & ! [v15] : ( ~ reflexive(v15) | ~ well_founded_relation(v15) | ~ transitive(v15) | ~ connected(v15) | ~ antisymmetric(v15) | ~ relation(v15) | well_ordering(v15)) & ! [v15] : ( ~ well_ordering(v15) | ~ relation(v15) | reflexive(v15)) & ! [v15] : ( ~ well_ordering(v15) | ~ relation(v15) | well_founded_relation(v15)) & ! [v15] : ( ~ well_ordering(v15) | ~ relation(v15) | transitive(v15)) & ! [v15] : ( ~ well_ordering(v15) | ~ relation(v15) | connected(v15)) & ! [v15] : ( ~ well_ordering(v15) | ~ relation(v15) | antisymmetric(v15)) & ! [v15] : ( ~ relation(v15) | ~ function(v15) | ~ empty(v15) | one_to_one(v15)) & ! [v15] : ( ~ relation(v15) | transitive(v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v17, v18) = v20 & ordered_pair(v16, v18) = v21 & ordered_pair(v16, v17) = v19 & in(v20, v15) & in(v19, v15) & ~ in(v21, v15))) & ! [v15] : ( ~ relation(v15) | antisymmetric(v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ( ~ (v17 = v16) & ordered_pair(v17, v16) = v19 & ordered_pair(v16, v17) = v18 & in(v19, v15) & in(v18, v15))) & ! [v15] : ( ~ epsilon_connected(v15) | ~ epsilon_transitive(v15) | ordinal(v15)) & ! [v15] : ( ~ ordinal(v15) | being_limit_ordinal(v15) | ? [v16] : ? [v17] : (succ(v16) = v17 & ordinal(v16) & in(v16, v15) & ~ in(v17, v15))) & ! [v15] : ( ~ ordinal(v15) | being_limit_ordinal(v15) | ? [v16] : (succ(v16) = v15 & ordinal(v16))) & ! [v15] : ( ~ ordinal(v15) | epsilon_connected(v15)) & ! [v15] : ( ~ ordinal(v15) | epsilon_transitive(v15)) & ! [v15] : ( ~ empty(v15) | relation(v15)) & ! [v15] : ( ~ empty(v15) | epsilon_connected(v15)) & ! [v15] : ( ~ empty(v15) | epsilon_transitive(v15)) & ! [v15] : ( ~ empty(v15) | ordinal(v15)) & ! [v15] : ( ~ empty(v15) | function(v15)) & ! [v15] : ~ proper_subset(v15, v15) & ! [v15] : ~ in(v15, empty_set) & ? [v15] : ? [v16] : ? [v17] : relation_of2_as_subset(v17, v15, v16) & ? [v15] : ? [v16] : ? [v17] : relation_of2(v17, v15, v16) & ? [v15] : ? [v16] : (v16 = v15 | ? [v17] : (( ~ in(v17, v16) | ~ in(v17, v15)) & (in(v17, v16) | in(v17, v15)))) & ? [v15] : ? [v16] : (disjoint(v15, v16) | ? [v17] : (in(v17, v16) & in(v17, v15))) & ? [v15] : ? [v16] : (subset(v15, v16) | ? [v17] : (in(v17, v15) & ~ in(v17, v16))) & ? [v15] : ? [v16] : element(v16, v15) & ? [v15] : ? [v16] : (in(v15, v16) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ in(v17, v16) | in(v18, v16)) & ! [v17] : ! [v18] : ( ~ subset(v18, v17) | ~ in(v17, v16) | in(v18, v16)) & ! [v17] : ( ~ subset(v17, v16) | are_equipotent(v17, v16) | in(v17, v16))) & ? [v15] : ? [v16] : (in(v15, v16) & ! [v17] : ! [v18] : ( ~ subset(v18, v17) | ~ in(v17, v16) | in(v18, v16)) & ! [v17] : ( ~ subset(v17, v16) | are_equipotent(v17, v16) | in(v17, v16)) & ! [v17] : ( ~ in(v17, v16) | ? [v18] : (in(v18, v16) & ! [v19] : ( ~ subset(v19, v17) | in(v19, v18))))) & ? [v15] : (v15 = empty_set | ? [v16] : in(v16, v15)) & ? [v15] : subset(v15, v15) & ? [v15] : subset(empty_set, v15) & ? [v15] : (relation(v15) | ? [v16] : (in(v16, v15) & ! [v17] : ! [v18] : ~ (ordered_pair(v17, v18) = v16))) & ? [v15] : (epsilon_connected(v15) | ? [v16] : ? [v17] : ( ~ (v17 = v16) & in(v17, v15) & in(v16, v15) & ~ in(v17, v16) & ~ in(v16, v17))) & ? [v15] : (epsilon_transitive(v15) | ? [v16] : (in(v16, v15) & ~ subset(v16, v15))) & ? [v15] : (ordinal(v15) | ? [v16] : (in(v16, v15) & ( ~ subset(v16, v15) | ~ ordinal(v16))))) % 19.97/5.08 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14 yields: % 19.97/5.08 | (1) relation_rng(empty_set) = empty_set & inclusion_relation(all_0_13_13) = all_0_12_12 & singleton(empty_set) = all_0_14_14 & relation_dom(empty_set) = empty_set & powerset(empty_set) = all_0_14_14 & relation_empty_yielding(all_0_10_10) & relation_empty_yielding(all_0_11_11) & relation_empty_yielding(empty_set) & one_to_one(all_0_5_5) & one_to_one(all_0_8_8) & one_to_one(empty_set) & relation(all_0_0_0) & relation(all_0_2_2) & relation(all_0_4_4) & relation(all_0_5_5) & relation(all_0_6_6) & relation(all_0_8_8) & relation(all_0_10_10) & relation(all_0_11_11) & relation(empty_set) & epsilon_connected(all_0_1_1) & epsilon_connected(all_0_5_5) & epsilon_connected(all_0_9_9) & epsilon_connected(empty_set) & epsilon_transitive(all_0_1_1) & epsilon_transitive(all_0_5_5) & epsilon_transitive(all_0_9_9) & epsilon_transitive(empty_set) & ordinal(all_0_1_1) & ordinal(all_0_5_5) & ordinal(all_0_9_9) & ordinal(all_0_13_13) & ordinal(empty_set) & function(all_0_0_0) & function(all_0_4_4) & function(all_0_5_5) & function(all_0_8_8) & function(all_0_11_11) & function(empty_set) & empty(all_0_2_2) & empty(all_0_3_3) & empty(all_0_4_4) & empty(all_0_5_5) & empty(empty_set) & ~ well_ordering(all_0_12_12) & ~ empty(all_0_6_6) & ~ empty(all_0_7_7) & ~ empty(all_0_9_9) & ! [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] : ! [v6] : ( ~ (ordered_pair(v3, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | ~ in(v6, v0) | ~ in(v5, v0) | ~ in(v4, v1) | ~ in(v3, v1) | ~ in(v2, v1) | ? [v7] : (ordered_pair(v2, v4) = v7 & in(v7, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (ordered_pair(v2, v4) = v6) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | ~ in(v3, v1) | ~ in(v2, v1) | in(v6, v0) | ? [v7] : (ordered_pair(v2, v3) = v7 & ~ in(v7, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v2, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | ~ in(v3, v1) | ~ in(v2, v1) | in(v6, v0) | ? [v7] : (ordered_pair(v3, v4) = v7 & ~ in(v7, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v1 | ~ (pair_second(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair_first(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) & ! [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] : ( ~ (relation_rng(v4) = v5) | ~ (relation_field(v2) = v3) | ~ (relation_field(v0) = v1) | ~ relation(v4) | ~ relation(v2) | ~ relation(v0) | ~ function(v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (relation_dom(v4) = v6 & ( ~ (v6 = v1) | ~ (v5 = v3) | ~ one_to_one(v4) | relation_isomorphism(v0, v2, v4) | (apply(v4, v8) = v11 & apply(v4, v7) = v10 & ordered_pair(v10, v11) = v12 & ordered_pair(v7, v8) = v9 & ( ~ in(v12, v2) | ~ in(v9, v0) | ~ in(v8, v1) | ~ in(v7, v1)) & (in(v9, v0) | (in(v12, v2) & in(v8, v1) & in(v7, v1))))) & ( ~ relation_isomorphism(v0, v2, v4) | (v6 = v1 & v5 = v3 & one_to_one(v4) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | ~ in(v17, v2) | ~ in(v14, v1) | ~ in(v13, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v17, v2) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v14, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v13, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | in(v14, v1)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | in(v13, v1)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | ? [v16] : ? [v17] : ? [v18] : (apply(v4, v14) = v17 & apply(v4, v13) = v16 & ordered_pair(v16, v17) = v18 & in(v18, v2))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v14, v1) | ~ in(v13, v1) | in(v15, v0) | ? [v16] : ? [v17] : ? [v18] : (apply(v4, v14) = v17 & apply(v4, v13) = v16 & ordered_pair(v16, v17) = v18 & ~ in(v18, v2))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ subset(v3, v4) | ~ relation(v1) | ~ in(v4, v0) | ~ in(v3, v0) | in(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | ~ in(v3, v0) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v5, v2) | ~ in(v4, v1) | in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_field(v2) = v3) | ~ (relation_field(v0) = v1) | ~ (relation_dom(v4) = v5) | ~ relation(v4) | ~ relation(v2) | ~ relation(v0) | ~ function(v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (relation_rng(v4) = v6 & ( ~ (v6 = v3) | ~ (v5 = v1) | ~ one_to_one(v4) | relation_isomorphism(v0, v2, v4) | (apply(v4, v8) = v11 & apply(v4, v7) = v10 & ordered_pair(v10, v11) = v12 & ordered_pair(v7, v8) = v9 & ( ~ in(v12, v2) | ~ in(v9, v0) | ~ in(v8, v1) | ~ in(v7, v1)) & (in(v9, v0) | (in(v12, v2) & in(v8, v1) & in(v7, v1))))) & ( ~ relation_isomorphism(v0, v2, v4) | (v6 = v3 & v5 = v1 & one_to_one(v4) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | ~ in(v17, v2) | ~ in(v14, v1) | ~ in(v13, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v17, v2) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v14, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v13, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | in(v14, v1)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | in(v13, v1)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | ? [v16] : ? [v17] : ? [v18] : (apply(v4, v14) = v17 & apply(v4, v13) = v16 & ordered_pair(v16, v17) = v18 & in(v18, v2))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v14, v1) | ~ in(v13, v1) | in(v15, v0) | ? [v16] : ? [v17] : ? [v18] : (apply(v4, v14) = v17 & apply(v4, v13) = v16 & ordered_pair(v16, v17) = v18 & ~ in(v18, 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(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v4, v0) = v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | ~ (apply(v0, v5) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v5, v2) | ~ in(v5, v1) | in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_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] : ! [v5] : ( ~ (ordered_pair(v4, v5) = v3) | ~ (cartesian_product2(v0, v1) = v2) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v2, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ transitive(v0) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v0) | ? [v6] : (ordered_pair(v1, v3) = v6 & in(v6, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v1, v3) = v5) | ~ transitive(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v5, v0) | ? [v6] : (ordered_pair(v1, v2) = v6 & ~ in(v6, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v1, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ transitive(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v5, v0) | ? [v6] : (ordered_pair(v2, v3) = v6 & ~ in(v6, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ 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] : (v4 = v3 | ~ (relation_dom(v1) = v2) | ~ (apply(v1, v3) = v4) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | v4 = v1 | v4 = v0 | ~ (unordered_triple(v0, v1, v2) = v3) | ~ in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_field(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ connected(v0) | ~ relation(v0) | ~ in(v3, v1) | ~ in(v2, v1) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_field(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ connected(v0) | ~ relation(v0) | ~ in(v3, v1) | ~ in(v2, v1) | in(v4, v0) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) = v4) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1) | ~ in(v2, v1)) & ! [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 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ is_connected_in(v0, v1) | ~ relation(v0) | ~ in(v3, v1) | ~ in(v2, v1) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | ~ in(v4, v0) | ~ in(v3, v1) | ~ in(v2, v1) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ is_connected_in(v0, v1) | ~ relation(v0) | ~ in(v3, v1) | ~ in(v2, v1) | in(v4, v0) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | ~ in(v4, v0) | ~ in(v3, v1) | ~ in(v2, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_rng_as_subset(v4, v3, v2) = v1) | ~ (relation_rng_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~ (unordered_triple(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] : ( ~ (function_inverse(v1) = v2) | ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_rng(v1) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v6 & relation_rng(v1) = v5 & apply(v6, v0) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v0) = v3) | ~ (fiber(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (fiber(v2, v1) = v5 & subset(v4, v5))) & ! [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) | ~ subset(v1, v4) | ~ element(v3, v2) | ~ element(v1, v2) | disjoint(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ relation_of2_as_subset(v3, v2, v0) | ~ subset(v4, v1) | relation_of2_as_subset(v3, v2, v1)) & ! [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] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ relation(v0) | ~ in(v3, v2) | in(v4, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ subset(v0, v1) | ~ relation(v2) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_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] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v2) = v5 & relation_dom_restriction(v5, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v5) = v4 & relation_dom_restriction(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (apply(v2, v0) = v5 & ( ~ (v5 = v1) | ~ in(v0, v4) | in(v3, v2)) & ( ~ in(v3, v2) | (v5 = v1 & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_rng(v2) = v5 & in(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | ? [v5] : (apply(v0, v5) = v4 & in(v5, v2) & in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ~ in(v1, v0) | apply(v2, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : (relation_dom(v3) = v5 & apply(v2, v1) = v6 & (v6 = v4 | ~ in(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : (relation_dom(v3) = v5 & apply(v3, v1) = v6 & (v6 = v4 | ~ in(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (relation_dom(v2) = v5 & ( ~ (v4 = v1) | ~ in(v0, v5) | in(v3, v2)) & ( ~ in(v3, v2) | (v4 = v1 & in(v0, v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 | ~ in(v0, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (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] : (v4 = v0 | ~ (unordered_triple(v1, v2, v3) = v4) | ? [v5] : ((v5 = v3 | v5 = v2 | v5 = v1 | in(v5, v0)) & ( ~ in(v5, v0) | ( ~ (v5 = v3) & ~ (v5 = v2) & ~ (v5 = v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_inverse_image(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : (apply(v1, v5) = v6 & ( ~ in(v6, v3) | ~ in(v5, v2) | ~ in(v5, v0)) & (in(v5, v0) | (in(v6, v3) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (( ~ in(v5, v0) | ! [v8] : ( ~ (apply(v1, v8) = v5) | ~ in(v8, v3) | ~ in(v8, v2))) & (in(v5, v0) | (v7 = v5 & apply(v1, v6) = v5 & in(v6, v3) & in(v6, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (pair_second(v1) = v2) | ~ (ordered_pair(v3, v4) = v1) | ? [v5] : ? [v6] : ( ~ (v6 = v0) & ordered_pair(v5, v6) = v1)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (pair_first(v1) = v2) | ~ (ordered_pair(v3, v4) = v1) | ? [v5] : ? [v6] : ( ~ (v5 = v0) & ordered_pair(v5, v6) = v1)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (in(v4, v1) & ! [v5] : ! [v6] : ( ~ (ordered_pair(v5, v4) = v6) | ~ in(v6, v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom_as_subset(v1, v0, v2) = v3) | ~ relation_of2_as_subset(v2, v1, v0) | ? [v4] : (in(v4, v1) & ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v6, 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 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | ? [v4] : (relation_rng(v1) = v4 & ~ subset(v0, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (ordered_pair(v2, v1) = v3) | ~ antisymmetric(v0) | ~ relation(v0) | ~ in(v3, v0) | ? [v4] : (ordered_pair(v1, v2) = v4 & ~ in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (ordered_pair(v1, v2) = v3) | ~ antisymmetric(v0) | ~ relation(v0) | ~ in(v3, v0) | ? [v4] : (ordered_pair(v2, v1) = v4 & ~ in(v4, v0))) & ! [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 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(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 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(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 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(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_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | relation_rng(v2) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | ? [v4] : (powerset(v1) = v4 & element(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_as_subset(v0, v1, v2) = v1) | ~ relation_of2_as_subset(v2, v0, v1) | ~ in(v3, v1) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v1, v0, v2) = v1) | ~ relation_of2_as_subset(v2, v1, v0) | ~ in(v3, v1) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v2))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | relation_dom(v2) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | ? [v4] : (powerset(v0) = v4 & element(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (function_inverse(v2) = v3) | ~ relation_isomorphism(v0, v1, v2) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | relation_isomorphism(v1, v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_rng(v3) = v4 & relation_image(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_dom(v3) = v4 & subset(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (relation_dom(v2) = v4 & subset(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_rng(v4) = v3 & relation_rng_restriction(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) & ! [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) = v1) | ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v1, v1) = v3) | ~ relation(v0) | ~ in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_meet(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | subset(v0, v3) | ? [v4] : (relation_dom(v1) = v4 & ~ subset(v0, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | subset(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) & in(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_field(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ reflexive(v0) | ~ relation(v0) | ~ in(v2, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | relation_restriction(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v1) | relation_restriction(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | subset(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (relation_rng(v2) = v4 & subset(v4, 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] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) & in(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v2, v2) = v3) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | ~ in(v2, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v2) = v3) | ~ (cartesian_product2(v1, v1) = v2) | ~ relation(v0) | relation_restriction(v0, v1) = 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] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (powerset(v3) = v4 & element(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2(v2, v0, v1) | subset(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ subset(v2, v3) | relation_of2(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ relation_of2_as_subset(v3, v2, v0) | ~ subset(v0, v1) | relation_of2_as_subset(v3, v2, v1)) & ? [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 | ~ (fiber(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : (ordered_pair(v4, v2) = v5 & (v4 = v2 | ~ in(v5, v1) | ~ in(v4, v0)) & (in(v4, v0) | ( ~ (v4 = v2) & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & in(v6, v1) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v4) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v5, v4) = v6 & in(v6, v1) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (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] : ( ~ (relation_composition(v2, v1) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 | ~ in(v0, v4)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_field(v3) = v4 & relation_field(v2) = v5 & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : (cartesian_product2(v1, v1) = v4 & ( ~ in(v0, v4) | ~ in(v0, v2) | in(v0, v3)) & ( ~ in(v0, v3) | (in(v0, v4) & in(v0, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v0, v7) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_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_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v5, v0) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v0) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ~ function(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] : ! [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] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) | ? [v4] : (powerset(v3) = v4 & ~ element(v0, v4))) & ! [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 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v4, v0) & in(v3, v0) & ( ~ subset(v3, v4) | ~ in(v5, v1)) & (subset(v3, v4) | in(v5, v1)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_dom(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v3) = v4 & in(v3, v0))) & ! [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 = v1 | ~ epsilon_connected(v0) | ~ in(v2, v0) | ~ in(v1, v0) | in(v2, v1) | in(v1, v2)) & ! [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 | ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ relation(v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(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 | ~ (relation_field(v0) = v1) | ~ well_founded_relation(v0) | ~ subset(v2, v1) | ~ relation(v0) | ? [v3] : ? [v4] : (fiber(v0, v3) = v4 & disjoint(v4, v2) & in(v3, v2))) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ is_well_founded_in(v0, v1) | ~ subset(v2, v1) | ~ relation(v0) | ? [v3] : ? [v4] : (fiber(v0, v3) = v4 & disjoint(v4, v2) & in(v3, v2))) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(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 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_first(v2) = v1) | ~ (pair_first(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (set_meet(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | ( ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v6, v1) | in(v5, v2)) & ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v5, v2) | in(v6, v1)) & ! [v5] : (v5 = v2 | ~ element(v5, v4) | ? [v6] : ? [v7] : (subset_complement(v0, v6) = v7 & element(v6, v3) & ( ~ in(v7, v1) | ~ in(v6, v5)) & (in(v7, v1) | in(v6, v5)))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ reflexive(v1) | ~ relation(v1) | reflexive(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_ordering(v1) | ~ relation(v1) | well_ordering(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_ordering(v1) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_field(v2) = v4 & relation_field(v1) = v3 & (v4 = v0 | ~ subset(v0, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_founded_relation(v1) | ~ relation(v1) | well_founded_relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ transitive(v1) | ~ relation(v1) | transitive(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ connected(v1) | ~ relation(v1) | connected(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ antisymmetric(v1) | ~ relation(v1) | antisymmetric(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_field(v2) = v3 & relation_field(v1) = v4 & subset(v3, v4) & subset(v3, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng_restriction(v0, v3) = v2 & relation_dom_restriction(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng_restriction(v0, v1) = v3 & relation_dom_restriction(v3, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | ? [v3] : (set_intersection2(v0, v3) = v2 & cartesian_product2(v1, v1) = v3)) & ! [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) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [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] : ( ~ (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] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~ in(v1, v0) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) | ordinal_subset(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ~ function(v1) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ~ function(v1) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & set_intersection2(v4, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v1) = v3 & relation_image(v1, v4) = v2 & set_intersection2(v3, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | apply(v4, v2) = v6) & ! [v4] : ! [v5] : ( ~ (apply(v4, v2) = v5) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | ? [v6] : (relation_composition(v1, v4) = v6 & apply(v6, v0) = v5)))) & ! [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_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2)) & ! [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) | pair_second(v2) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | pair_first(v2) = v0) & ! [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] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ reflexive(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | reflexive(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ well_ordering(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | well_ordering(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ well_founded_relation(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | well_founded_relation(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ transitive(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | transitive(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ connected(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | connected(v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ antisymmetric(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | antisymmetric(v1)) & ! [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] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1)) & ! [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] : ( ~ in(v2, v0) | ~ in(v1, v2) | ~ in(v0, 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 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ? [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] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ( ! [v4] : ( ~ ordinal(v4) | ~ in(v4, v2) | ~ in(v4, v0) | in(v4, v3)) & ! [v4] : ( ~ in(v4, v3) | in(v4, v2)) & ! [v4] : ( ~ in(v4, v3) | (ordinal(v4) & in(v4, v0))))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0) = v1) | ~ being_limit_ordinal(v0)) & ! [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 | ~ ordinal(v1) | ~ ordinal(v0) | in(v1, v0) | in(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ subset(v0, v1) | ~ ordinal(v1) | ? [v2] : (ordinal(v2) & in(v2, v0) & ! [v3] : ( ~ ordinal(v3) | ~ in(v3, v0) | ordinal_subset(v2, v3)))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1)) & ! [v4] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v2))) | (v7 = v6 & in(v5, v2) & ( ~ (v8 = v5) | ~ in(v6, v3)))))))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3) | in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v1) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v1))) | (v7 = v6 & in(v5, v1) & ( ~ (v8 = v5) | ~ in(v6, v3)))))) & ! [v4] : (v4 = v1 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1)) & ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1)) & ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | ordinal(v1)) & ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) & ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | well_founded_relation(v1)) & ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | connected(v1)) & ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | reflexive(v1)) & ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | transitive(v1)) & ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | antisymmetric(v1)) & ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1)) & ! [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] : ( ~ (succ(v1) = v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ordinal(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_orders(v0, v1) | ~ relation(v0) | well_ordering(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ reflexive(v0) | ~ relation(v0) | is_reflexive_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_ordering(v0) | ~ relation(v0) | well_orders(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_well_founded_in(v0, v1) | ~ relation(v0) | well_founded_relation(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_founded_relation(v0) | ~ relation(v0) | is_well_founded_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | reflexive(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | transitive(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ transitive(v0) | ~ relation(v0) | is_transitive_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_connected_in(v0, v1) | ~ relation(v0) | connected(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ connected(v0) | ~ relation(v0) | is_connected_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | antisymmetric(v0)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ antisymmetric(v0) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | reflexive(v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v2) = v3 & in(v2, v1) & ~ in(v3, v0))) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | well_founded_relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & subset(v2, v1) & ! [v3] : ! [v4] : ( ~ (fiber(v0, v3) = v4) | ~ disjoint(v4, v2) | ~ in(v3, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | connected(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v2) & ordered_pair(v3, v2) = v5 & ordered_pair(v2, v3) = v4 & in(v3, v1) & in(v2, v1) & ~ in(v5, v0) & ~ in(v4, v0))) & ! [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_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1) | in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3) | in(v6, v1)) & ! [v4] : (v4 = v3 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v3) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v1) & ( ~ (v7 = v6) | ~ in(v5, v3))) | (v7 = v6 & in(v5, v3) & ( ~ (v8 = v5) | ~ in(v6, v1)))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | one_to_one(v0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v3 = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 & in(v3, v1) & in(v2, v1))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1))))))) & ! [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] : ( ~ (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] : ( ~ (identity_relation(v0) = v1) | function(v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = 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] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_well_founded_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_reflexive_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_transitive_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_connected_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) & ! [v0] : ! [v1] : ( ~ is_well_founded_in(v0, v1) | ~ is_reflexive_in(v0, v1) | ~ is_transitive_in(v0, v1) | ~ is_connected_in(v0, v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | well_orders(v0, v1)) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1)) & ! [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] : ( ~ 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] : ( ~ epsilon_transitive(v0) | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ in(v1, v0) | ? [v2] : (ordinal(v2) & in(v2, v0) & ! [v3] : ( ~ ordinal(v3) | ~ in(v3, v0) | ordinal_subset(v2, v3)))) & ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ in(v0, v1) | ordinal(v0)) & ! [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] : ! [v1] : ( ~ in(v0, v1) | ? [v2] : (in(v2, v1) & ! [v3] : ( ~ in(v3, v2) | ~ in(v3, v1)))) & ? [v0] : ! [v1] : ( ~ relation(v1) | is_well_founded_in(v1, v0) | ? [v2] : ( ~ (v2 = empty_set) & subset(v2, v0) & ! [v3] : ! [v4] : ( ~ (fiber(v1, v3) = v4) | ~ disjoint(v4, v2) | ~ in(v3, v2)))) & ? [v0] : ! [v1] : ( ~ relation(v1) | is_reflexive_in(v1, v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v2) = v3 & in(v2, v0) & ~ in(v3, v1))) & ? [v0] : ! [v1] : ( ~ relation(v1) | is_transitive_in(v1, v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v4) = v6 & ordered_pair(v2, v4) = v7 & ordered_pair(v2, v3) = v5 & in(v6, v1) & in(v5, v1) & in(v4, v0) & in(v3, v0) & in(v2, v0) & ~ in(v7, v1))) & ? [v0] : ! [v1] : ( ~ relation(v1) | is_connected_in(v1, v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v2) & ordered_pair(v3, v2) = v5 & ordered_pair(v2, v3) = v4 & in(v3, v0) & in(v2, v0) & ~ in(v5, v1) & ~ in(v4, v1))) & ? [v0] : ! [v1] : ( ~ relation(v1) | is_antisymmetric_in(v1, v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v2) & ordered_pair(v3, v2) = v5 & ordered_pair(v2, v3) = v4 & in(v5, v1) & in(v4, v1) & in(v3, v0) & in(v2, v0))) & ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(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] : ( ~ (union(v0) = v0) | being_limit_ordinal(v0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ reflexive(v0) | ~ well_founded_relation(v0) | ~ transitive(v0) | ~ connected(v0) | ~ antisymmetric(v0) | ~ relation(v0) | well_ordering(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | reflexive(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | well_founded_relation(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | transitive(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | connected(v0)) & ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | antisymmetric(v0)) & ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ relation(v0) | transitive(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v2, v3) = v5 & ordered_pair(v1, v3) = v6 & ordered_pair(v1, v2) = v4 & in(v5, v0) & in(v4, v0) & ~ in(v6, v0))) & ! [v0] : ( ~ relation(v0) | antisymmetric(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v2 = v1) & ordered_pair(v2, v1) = v4 & ordered_pair(v1, v2) = v3 & in(v4, v0) & in(v3, v0))) & ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) & ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : ? [v2] : (succ(v1) = v2 & ordinal(v1) & in(v1, v0) & ~ in(v2, v0))) & ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : (succ(v1) = v0 & ordinal(v1))) & ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | ordinal(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ~ proper_subset(v0, v0) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) & ? [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] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : ? [v1] : element(v1, v0) & ? [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))) & ? [v0] : (epsilon_connected(v0) | ? [v1] : ? [v2] : ( ~ (v2 = v1) & in(v2, v0) & in(v1, v0) & ~ in(v2, v1) & ~ in(v1, v2))) & ? [v0] : (epsilon_transitive(v0) | ? [v1] : (in(v1, v0) & ~ subset(v1, v0))) & ? [v0] : (ordinal(v0) | ? [v1] : (in(v1, v0) & ( ~ subset(v1, v0) | ~ ordinal(v1)))) % 20.30/5.17 | % 20.30/5.17 | Applying alpha-rule on (1) yields: % 20.30/5.17 | (2) ! [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)))) % 20.30/5.17 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0)) % 20.30/5.17 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v1) | in(v5, v2) | ? [v8] : (ordered_pair(v3, v6) = v8 & ~ in(v8, v0))) % 20.30/5.17 | (5) ! [v0] : ( ~ reflexive(v0) | ~ well_founded_relation(v0) | ~ transitive(v0) | ~ connected(v0) | ~ antisymmetric(v0) | ~ relation(v0) | well_ordering(v0)) % 20.30/5.17 | (6) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 20.30/5.17 | (7) ordinal(all_0_13_13) % 20.30/5.17 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8] : (ordered_pair(v6, v4) = v8 & ~ in(v8, v1))) % 20.30/5.17 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (function_inverse(v2) = v3) | ~ relation_isomorphism(v0, v1, v2) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | relation_isomorphism(v1, v0, v3)) % 20.30/5.17 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_rng(v4) = v3 & relation_rng_restriction(v0, v1) = v4)) % 20.30/5.17 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | ? [v4] : (powerset(v0) = v4 & element(v3, v4))) % 20.30/5.17 | (12) one_to_one(all_0_8_8) % 20.30/5.17 | (13) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 | ~ in(v0, v4)))) % 20.30/5.17 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v5) = v4 & relation_dom_restriction(v2, v1) = v5)) % 20.30/5.17 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | subset(v3, v1)) % 20.30/5.17 | (16) ~ empty(all_0_9_9) % 20.30/5.17 | (17) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) % 20.30/5.17 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (in(v4, v1) & ! [v5] : ! [v6] : ( ~ (ordered_pair(v5, v4) = v6) | ~ in(v6, v2)))) % 20.30/5.17 | (19) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | reflexive(v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v2) = v3 & in(v2, v1) & ~ in(v3, v0))) % 20.30/5.17 | (20) function(empty_set) % 20.30/5.17 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 20.30/5.17 | (22) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) % 20.30/5.17 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 20.30/5.17 | (24) function(all_0_0_0) % 20.30/5.17 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v0) = v4) | ~ (cartesian_product2(v1, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v3) & subset(v4, v6))) % 20.30/5.17 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 20.30/5.17 | (27) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1)) % 20.30/5.17 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 20.30/5.17 | (29) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 20.30/5.17 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3)) % 20.30/5.17 | (31) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) % 20.30/5.17 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (meet_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) % 20.30/5.17 | (33) ? [v0] : subset(empty_set, v0) % 20.30/5.17 | (34) ? [v0] : ! [v1] : ( ~ relation(v1) | is_reflexive_in(v1, v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v2) = v3 & in(v2, v0) & ~ in(v3, v1))) % 20.30/5.17 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 20.30/5.17 | (36) ? [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))))) % 20.30/5.17 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0) = v1) | ~ being_limit_ordinal(v0)) % 20.30/5.17 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 20.52/5.17 | (39) ordinal(all_0_1_1) % 20.52/5.17 | (40) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1)) % 20.52/5.17 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | ~ in(v4, v0) | ~ in(v3, v1) | ~ in(v2, v1) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v0))) % 20.52/5.17 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2)) % 20.52/5.17 | (43) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) % 20.52/5.17 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 20.52/5.17 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | ? [v3] : (set_intersection2(v0, v3) = v2 & cartesian_product2(v1, v1) = v3)) % 20.52/5.17 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 20.52/5.17 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) % 20.52/5.17 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (relation_dom(v2) = v5 & ( ~ (v4 = v1) | ~ in(v0, v5) | in(v3, v2)) & ( ~ in(v3, v2) | (v4 = v1 & in(v0, v5))))) % 20.52/5.18 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 20.52/5.18 | (50) ! [v0] : ( ~ relation(v0) | transitive(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v2, v3) = v5 & ordered_pair(v1, v3) = v6 & ordered_pair(v1, v2) = v4 & in(v5, v0) & in(v4, v0) & ~ in(v6, v0))) % 20.52/5.18 | (51) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v0, v7) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) % 20.52/5.18 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 20.52/5.18 | (53) relation_dom(empty_set) = empty_set % 20.52/5.18 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | pair_second(v2) = v1) % 20.52/5.18 | (55) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 20.52/5.18 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v2, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | ~ in(v3, v1) | ~ in(v2, v1) | in(v6, v0) | ? [v7] : (ordered_pair(v3, v4) = v7 & ~ in(v7, v0))) % 20.52/5.18 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) % 20.52/5.18 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ~ function(v1) | relation(v2)) % 20.52/5.18 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) % 20.52/5.18 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v3, v2) = v4) | ~ is_connected_in(v0, v1) | ~ relation(v0) | ~ in(v3, v1) | ~ in(v2, v1) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v0))) % 20.52/5.18 | (61) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (pair_first(v1) = v2) | ~ (ordered_pair(v3, v4) = v1) | ? [v5] : ? [v6] : ( ~ (v5 = v0) & ordered_pair(v5, v6) = v1)) % 20.52/5.18 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 20.52/5.18 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (relation_field(v0) = v1) | ~ well_founded_relation(v0) | ~ subset(v2, v1) | ~ relation(v0) | ? [v3] : ? [v4] : (fiber(v0, v3) = v4 & disjoint(v4, v2) & in(v3, v2))) % 20.52/5.18 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_composition(v0, v1) = v3 & relation_rng(v3) = v4 & subset(v4, v2))) % 20.52/5.18 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) % 20.52/5.18 | (66) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 20.52/5.18 | (67) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) % 20.52/5.18 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ subset(v0, v1) | ~ relation(v2) | subset(v3, v4)) % 20.52/5.18 | (69) one_to_one(all_0_5_5) % 20.52/5.18 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 20.52/5.18 | (71) ! [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)) % 20.52/5.18 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : (relation_dom(v3) = v5 & apply(v2, v1) = v6 & (v6 = v4 | ~ in(v1, v5)))) % 20.52/5.18 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v1 | ~ (pair_second(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) % 20.52/5.18 | (74) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : (cartesian_product2(v1, v1) = v4 & ( ~ in(v0, v4) | ~ in(v0, v2) | in(v0, v3)) & ( ~ in(v0, v3) | (in(v0, v4) & in(v0, v2))))) % 20.52/5.18 | (75) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) % 20.52/5.18 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 20.52/5.18 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) % 20.52/5.18 | (78) powerset(empty_set) = all_0_14_14 % 20.52/5.18 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 20.52/5.18 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) % 20.52/5.18 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) % 20.52/5.18 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) % 20.52/5.18 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ reflexive(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | reflexive(v1)) % 20.52/5.18 | (84) ! [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))))) % 20.52/5.18 | (85) ? [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))))) % 20.52/5.18 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 20.52/5.18 | (87) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ relation(v1)) % 20.52/5.18 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 20.52/5.19 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 20.52/5.19 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 20.52/5.19 | (91) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 20.52/5.19 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 20.52/5.19 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 20.52/5.19 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_dom(v2) = v5 & in(v0, v5))) % 20.52/5.19 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | ~ (apply(v0, v5) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v5, v2) | ~ in(v5, v1) | in(v4, v3)) % 20.52/5.19 | (96) ! [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)) % 20.52/5.19 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom_as_subset(v1, v0, v2) = v3) | ~ relation_of2_as_subset(v2, v1, v0) | ? [v4] : (in(v4, v1) & ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v6, v2)))) % 20.52/5.19 | (98) ~ empty(all_0_7_7) % 20.52/5.19 | (99) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | ordinal(v1)) % 20.52/5.19 | (100) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1) % 20.52/5.19 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) % 20.52/5.19 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) % 20.52/5.19 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) | ordinal_subset(v1, v2)) % 20.52/5.19 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (union_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & meet_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) % 20.52/5.19 | (105) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) % 20.52/5.19 | (106) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_founded_relation(v0) | ~ relation(v0) | is_well_founded_in(v0, v1)) % 20.52/5.19 | (107) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_inverse_image(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : (apply(v1, v5) = v6 & ( ~ in(v6, v3) | ~ in(v5, v2) | ~ in(v5, v0)) & (in(v5, v0) | (in(v6, v3) & in(v5, v2))))) % 20.52/5.19 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_field(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ connected(v0) | ~ relation(v0) | ~ in(v3, v1) | ~ in(v2, v1) | in(v4, v0) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) % 20.52/5.19 | (109) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 20.52/5.19 | (110) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ transitive(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | transitive(v1)) % 20.52/5.19 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 20.52/5.19 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 20.52/5.19 | (113) ? [v0] : (ordinal(v0) | ? [v1] : (in(v1, v0) & ( ~ subset(v1, v0) | ~ ordinal(v1)))) % 20.52/5.19 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) % 20.52/5.19 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ disjoint(v1, v3) | ~ element(v3, v2) | ~ element(v1, v2) | subset(v1, v4)) % 20.52/5.19 | (116) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) % 20.52/5.19 | (117) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) % 20.52/5.19 | (118) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3) | in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v1) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v1))) | (v7 = v6 & in(v5, v1) & ( ~ (v8 = v5) | ~ in(v6, v3)))))) & ! [v4] : (v4 = v1 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)))) % 20.52/5.19 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 20.52/5.19 | (120) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) % 20.52/5.19 | (121) ? [v0] : ? [v1] : element(v1, v0) % 20.52/5.19 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 20.52/5.19 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) % 20.52/5.19 | (124) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 20.52/5.19 | (125) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) % 20.52/5.19 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ relation(v0) | ~ in(v3, v2) | in(v4, v0)) % 20.52/5.19 | (127) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | pair_first(v2) = v0) % 20.52/5.19 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) % 20.52/5.19 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3))) % 20.52/5.19 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 20.52/5.19 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | ~ in(v4, v0) | ~ in(v3, v1) | ~ in(v2, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0))) % 20.52/5.20 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 20.52/5.20 | (133) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 20.52/5.20 | (134) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2)) % 20.52/5.20 | (135) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) % 20.52/5.20 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) % 20.52/5.20 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | relation_dom(v2) = v3) % 20.52/5.20 | (138) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v4) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v5, v4) = v6 & in(v6, v1) & in(v5, v2))))) % 20.52/5.20 | (139) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 20.52/5.20 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v3, v4) = v6) | ~ (ordered_pair(v2, v3) = v5) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | ~ in(v6, v0) | ~ in(v5, v0) | ~ in(v4, v1) | ~ in(v3, v1) | ~ in(v2, v1) | ? [v7] : (ordered_pair(v2, v4) = v7 & in(v7, v0))) % 20.52/5.20 | (141) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1)) % 20.52/5.20 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v1, v0, v2) = v1) | ~ relation_of2_as_subset(v2, v1, v0) | ~ in(v3, v1) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v2))) % 20.52/5.20 | (143) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) % 20.52/5.20 | (144) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_field(v3) = v4 & relation_field(v2) = v5 & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) % 20.52/5.20 | (145) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) % 20.52/5.20 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_meet(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) % 20.52/5.20 | (147) ! [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))))) % 20.52/5.20 | (148) relation(empty_set) % 20.52/5.20 | (149) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 20.52/5.20 | (150) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) % 20.52/5.20 | (151) ! [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)) % 20.52/5.20 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) % 20.52/5.20 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 20.52/5.20 | (154) ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) % 20.52/5.20 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) % 20.52/5.20 | (156) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) % 20.52/5.20 | (157) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_ordering(v1) | ~ relation(v1) | well_ordering(v2)) % 20.52/5.20 | (158) epsilon_connected(all_0_5_5) % 20.52/5.20 | (159) ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : (succ(v1) = v0 & ordinal(v1))) % 20.52/5.20 | (160) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_reflexive_in(v0, v1)) % 20.52/5.20 | (161) relation(all_0_0_0) % 20.52/5.20 | (162) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 20.52/5.20 | (163) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1)) % 20.52/5.20 | (164) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 20.52/5.20 | (165) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) % 20.52/5.20 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 20.52/5.20 | (167) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 20.52/5.20 | (168) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 20.52/5.20 | (169) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) % 20.52/5.20 | (170) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ is_well_founded_in(v0, v1) | ~ subset(v2, v1) | ~ relation(v0) | ? [v3] : ? [v4] : (fiber(v0, v3) = v4 & disjoint(v4, v2) & in(v3, v2))) % 20.52/5.20 | (171) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 20.52/5.20 | (172) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | well_founded_relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & subset(v2, v1) & ! [v3] : ! [v4] : ( ~ (fiber(v0, v3) = v4) | ~ disjoint(v4, v2) | ~ in(v3, v2)))) % 20.52/5.20 | (173) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ? [v2] : (in(v2, v1) & ! [v3] : ( ~ in(v3, v2) | ~ in(v3, v1)))) % 20.52/5.20 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 20.52/5.20 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) % 20.52/5.20 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) % 20.52/5.20 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 20.52/5.20 | (178) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1) | in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3) | in(v6, v1)) & ! [v4] : (v4 = v3 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v3) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v1) & ( ~ (v7 = v6) | ~ in(v5, v3))) | (v7 = v6 & in(v5, v3) & ( ~ (v8 = v5) | ~ in(v6, v1)))))))) % 20.52/5.21 | (179) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 20.52/5.21 | (180) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) % 20.52/5.21 | (181) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) % 20.52/5.21 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & subset(v5, v6))) % 20.52/5.21 | (183) ~ empty(all_0_6_6) % 20.52/5.21 | (184) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 20.52/5.21 | (185) singleton(empty_set) = all_0_14_14 % 20.52/5.21 | (186) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 20.52/5.21 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v0) = v3) | ~ (fiber(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (fiber(v2, v1) = v5 & subset(v4, v5))) % 20.52/5.21 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) % 20.52/5.21 | (189) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | connected(v1)) % 20.52/5.21 | (190) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 20.52/5.21 | (191) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v6 & relation_rng(v1) = v5 & apply(v6, v0) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) % 20.52/5.21 | (192) ! [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)) % 20.52/5.21 | (193) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 20.52/5.21 | (194) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 20.52/5.21 | (195) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v2, v2) = v3) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | ~ in(v2, v1) | in(v3, v0)) % 20.52/5.21 | (196) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) % 20.52/5.21 | (197) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) % 20.52/5.21 | (198) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 20.52/5.21 | (199) function(all_0_4_4) % 20.52/5.21 | (200) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (meet_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (union_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) % 20.52/5.21 | (201) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 20.52/5.21 | (202) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v2, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ transitive(v0) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v0) | ? [v6] : (ordered_pair(v1, v3) = v6 & in(v6, v0))) % 20.52/5.21 | (203) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 20.52/5.21 | (204) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v5, v2) | ~ in(v4, v1) | in(v4, v3)) % 20.52/5.21 | (205) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 20.52/5.21 | (206) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) | ? [v4] : (powerset(v3) = v4 & ~ element(v0, v4))) % 20.52/5.22 | (207) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 20.52/5.23 | (208) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 20.52/5.23 | (209) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) % 20.52/5.23 | (210) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 20.52/5.23 | (211) function(all_0_11_11) % 20.52/5.23 | (212) ? [v0] : (epsilon_connected(v0) | ? [v1] : ? [v2] : ( ~ (v2 = v1) & in(v2, v0) & in(v1, v0) & ~ in(v2, v1) & ~ in(v1, v2))) % 20.52/5.23 | (213) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) % 20.52/5.23 | (214) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3)) % 20.52/5.23 | (215) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 20.52/5.23 | (216) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 | ~ in(v0, v6)))) % 20.52/5.23 | (217) ! [v0] : ! [v1] : ! [v2] : ( ~ in(v2, v0) | ~ in(v1, v2) | ~ in(v0, v1)) % 20.52/5.23 | (218) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & in(v8, v1) & in(v7, v0))) % 20.52/5.23 | (219) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) % 20.52/5.23 | (220) ! [v0] : ~ proper_subset(v0, v0) % 20.52/5.23 | (221) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 20.52/5.23 | (222) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) % 20.52/5.23 | (223) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 20.52/5.23 | (224) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) % 20.52/5.23 | (225) epsilon_transitive(empty_set) % 20.52/5.23 | (226) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) % 20.52/5.23 | (227) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_rng_as_subset(v4, v3, v2) = v1) | ~ (relation_rng_as_subset(v4, v3, v2) = v0)) % 20.52/5.23 | (228) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | ? [v5] : (apply(v0, v5) = v4 & in(v5, v2) & in(v5, v1))) % 20.52/5.23 | (229) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 20.52/5.23 | (230) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 20.52/5.23 | (231) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 20.52/5.23 | (232) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) % 20.52/5.23 | (233) ! [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)) % 20.52/5.23 | (234) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 20.52/5.23 | (235) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) % 20.52/5.23 | (236) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 20.52/5.23 | (237) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 20.52/5.23 | (238) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v1))) % 20.52/5.23 | (239) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_field(v2) = v3 & relation_field(v1) = v4 & subset(v3, v4) & subset(v3, v0))) % 20.52/5.23 | (240) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0))) % 20.52/5.23 | (241) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | antisymmetric(v0)) % 20.52/5.23 | (242) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) % 20.52/5.23 | (243) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) % 20.52/5.23 | (244) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_ordering(v0) | ~ relation(v0) | well_orders(v0, v1)) % 20.52/5.23 | (245) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) | in(v0, v2)) % 20.52/5.23 | (246) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) % 20.52/5.23 | (247) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 20.52/5.23 | (248) ~ well_ordering(all_0_12_12) % 20.52/5.23 | (249) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & in(v6, v1) & in(v5, v2))))) % 20.52/5.23 | (250) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) % 20.52/5.23 | (251) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) % 20.52/5.23 | (252) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (ordered_pair(v1, v2) = v3) | ~ antisymmetric(v0) | ~ relation(v0) | ~ in(v3, v0) | ? [v4] : (ordered_pair(v2, v1) = v4 & ~ in(v4, v0))) % 20.52/5.23 | (253) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | well_founded_relation(v0)) % 20.52/5.23 | (254) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 20.52/5.23 | (255) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_well_founded_in(v0, v1) | ~ relation(v0) | well_founded_relation(v0)) % 20.52/5.23 | (256) ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0)) % 20.52/5.23 | (257) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 20.52/5.23 | (258) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) % 20.52/5.23 | (259) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (( ~ in(v5, v0) | ! [v8] : ( ~ (apply(v1, v8) = v5) | ~ in(v8, v3) | ~ in(v8, v2))) & (in(v5, v0) | (v7 = v5 & apply(v1, v6) = v5 & in(v6, v3) & in(v6, v2))))) % 20.52/5.23 | (260) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) % 20.52/5.23 | (261) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 20.52/5.24 | (262) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 20.52/5.24 | (263) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 20.52/5.24 | (264) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2)) % 20.52/5.24 | (265) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0)) % 20.52/5.24 | (266) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 20.52/5.24 | (267) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | connected(v0)) % 20.52/5.24 | (268) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 20.52/5.24 | (269) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 20.52/5.24 | (270) ! [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))) % 20.52/5.24 | (271) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ~ function(v1) | function(v2)) % 20.52/5.24 | (272) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) % 20.52/5.24 | (273) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v3, v2)) % 20.52/5.24 | (274) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v1, v1) = v3) | ~ relation(v0) | ~ in(v1, v2)) % 20.52/5.24 | (275) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1)) % 20.52/5.24 | (276) ! [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)) % 20.52/5.24 | (277) epsilon_transitive(all_0_9_9) % 20.52/5.24 | (278) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ reflexive(v0) | ~ relation(v0) | is_reflexive_in(v0, v1)) % 20.52/5.24 | (279) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ antisymmetric(v0) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) % 20.52/5.24 | (280) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 20.52/5.24 | (281) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 20.52/5.24 | (282) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 20.52/5.24 | (283) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 20.52/5.24 | (284) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) % 20.52/5.24 | (285) ? [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))))) % 20.52/5.24 | (286) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v4, v5) = v3) | ~ (cartesian_product2(v0, v1) = v2) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) % 20.52/5.24 | (287) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v4, v0) & in(v3, v0) & ( ~ subset(v3, v4) | ~ in(v5, v1)) & (subset(v3, v4) | in(v5, v1)))) % 20.52/5.24 | (288) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ antisymmetric(v1) | ~ relation(v1) | antisymmetric(v2)) % 20.52/5.24 | (289) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1)) % 20.52/5.24 | (290) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 20.52/5.24 | (291) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) % 20.52/5.24 | (292) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ well_founded_relation(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | well_founded_relation(v1)) % 20.52/5.24 | (293) relation(all_0_11_11) % 20.52/5.24 | (294) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ well_ordering(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | well_ordering(v1)) % 20.52/5.24 | (295) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ antisymmetric(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | antisymmetric(v1)) % 20.52/5.24 | (296) ! [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)) % 20.52/5.24 | (297) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (ordered_pair(v2, v1) = v3) | ~ antisymmetric(v0) | ~ relation(v0) | ~ in(v3, v0) | ? [v4] : (ordered_pair(v1, v2) = v4 & ~ in(v4, v0))) % 20.52/5.24 | (298) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | apply(v4, v2) = v6) & ! [v4] : ! [v5] : ( ~ (apply(v4, v2) = v5) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | ? [v6] : (relation_composition(v1, v4) = v6 & apply(v6, v0) = v5)))) % 20.52/5.24 | (299) ordinal(all_0_9_9) % 20.52/5.24 | (300) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~ (unordered_triple(v4, v3, v2) = v0)) % 20.52/5.24 | (301) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) % 20.52/5.24 | (302) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ subset(v1, v4) | ~ element(v3, v2) | ~ element(v1, v2) | disjoint(v1, v3)) % 20.52/5.24 | (303) ! [v0] : ~ (singleton(v0) = empty_set) % 20.52/5.24 | (304) relation(all_0_4_4) % 20.52/5.24 | (305) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) % 20.52/5.24 | (306) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 20.52/5.24 | (307) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))))) % 20.52/5.25 | (308) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 20.52/5.25 | (309) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v4, v0) = v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))))) % 20.52/5.25 | (310) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 20.52/5.25 | (311) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (relation_dom(v1) = v2) | ~ (apply(v1, v3) = v4) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0)) % 20.52/5.25 | (312) ? [v0] : ! [v1] : ( ~ relation(v1) | is_antisymmetric_in(v1, v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v2) & ordered_pair(v3, v2) = v5 & ordered_pair(v2, v3) = v4 & in(v5, v1) & in(v4, v1) & in(v3, v0) & in(v2, v0))) % 20.52/5.25 | (313) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 20.52/5.25 | (314) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_ordering(v1) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_field(v2) = v4 & relation_field(v1) = v3 & (v4 = v0 | ~ subset(v0, v3)))) % 20.52/5.25 | (315) ! [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)))) % 20.52/5.25 | (316) relation_empty_yielding(all_0_10_10) % 20.52/5.25 | (317) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) % 20.52/5.25 | (318) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (apply(v2, v0) = v5 & ( ~ (v5 = v1) | ~ in(v0, v4) | in(v3, v2)) & ( ~ in(v3, v2) | (v5 = v1 & in(v0, v4))))) % 20.52/5.25 | (319) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) & in(v4, v1))) % 20.52/5.25 | (320) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 20.52/5.25 | (321) ! [v0] : ( ~ (union(v0) = v0) | being_limit_ordinal(v0)) % 20.52/5.25 | (322) ! [v0] : ~ in(v0, empty_set) % 20.52/5.25 | (323) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (set_meet(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) % 20.52/5.25 | (324) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) % 20.52/5.25 | (325) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v0, v3)) % 20.52/5.25 | (326) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) % 20.52/5.25 | (327) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) % 20.52/5.25 | (328) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) % 20.52/5.25 | (329) ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1)) % 20.52/5.25 | (330) epsilon_transitive(all_0_1_1) % 20.52/5.25 | (331) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) % 20.52/5.25 | (332) empty(all_0_5_5) % 20.52/5.25 | (333) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 20.52/5.25 | (334) ! [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)))))))) % 20.52/5.25 | (335) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | antisymmetric(v1)) % 20.52/5.25 | (336) empty(empty_set) % 20.52/5.25 | (337) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ~ (relation_field(v2) = v3) | ~ (relation_field(v0) = v1) | ~ relation(v4) | ~ relation(v2) | ~ relation(v0) | ~ function(v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (relation_dom(v4) = v6 & ( ~ (v6 = v1) | ~ (v5 = v3) | ~ one_to_one(v4) | relation_isomorphism(v0, v2, v4) | (apply(v4, v8) = v11 & apply(v4, v7) = v10 & ordered_pair(v10, v11) = v12 & ordered_pair(v7, v8) = v9 & ( ~ in(v12, v2) | ~ in(v9, v0) | ~ in(v8, v1) | ~ in(v7, v1)) & (in(v9, v0) | (in(v12, v2) & in(v8, v1) & in(v7, v1))))) & ( ~ relation_isomorphism(v0, v2, v4) | (v6 = v1 & v5 = v3 & one_to_one(v4) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | ~ in(v17, v2) | ~ in(v14, v1) | ~ in(v13, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v17, v2) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v14, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v13, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | in(v14, v1)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | in(v13, v1)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | ? [v16] : ? [v17] : ? [v18] : (apply(v4, v14) = v17 & apply(v4, v13) = v16 & ordered_pair(v16, v17) = v18 & in(v18, v2))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v14, v1) | ~ in(v13, v1) | in(v15, v0) | ? [v16] : ? [v17] : ? [v18] : (apply(v4, v14) = v17 & apply(v4, v13) = v16 & ordered_pair(v16, v17) = v18 & ~ in(v18, v2))))))) % 20.88/5.26 | (338) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 20.88/5.26 | (339) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 20.88/5.26 | (340) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | relation_rng(v2) = v3) % 20.88/5.26 | (341) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng_restriction(v0, v3) = v2 & relation_dom_restriction(v1, v0) = v3)) % 20.88/5.26 | (342) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | reflexive(v0)) % 20.88/5.26 | (343) ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) % 20.88/5.26 | (344) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | antisymmetric(v0)) % 20.88/5.26 | (345) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1))) % 20.88/5.26 | (346) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (relation_dom(v2) = v4 & subset(v4, v0))) % 20.88/5.26 | (347) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v4] : ? [v5] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) % 20.88/5.26 | (348) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 20.88/5.26 | (349) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 20.88/5.26 | (350) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 20.88/5.26 | (351) ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1))) % 20.88/5.26 | (352) ! [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)) % 20.88/5.26 | (353) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) % 20.88/5.26 | (354) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v2) = v3) | ~ (cartesian_product2(v1, v1) = v2) | ~ relation(v0) | relation_restriction(v0, v1) = v3) % 20.88/5.26 | (355) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1)) % 20.88/5.26 | (356) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 20.88/5.26 | (357) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v1) = v3 & relation_image(v1, v4) = v2 & set_intersection2(v3, v0) = v4)) % 20.88/5.26 | (358) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) % 20.88/5.26 | (359) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 20.88/5.26 | (360) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 20.88/5.26 | (361) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) % 20.88/5.26 | (362) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 20.88/5.26 | (363) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 20.88/5.26 | (364) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 20.88/5.26 | (365) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ connected(v1) | ~ relation(v1) | connected(v2)) % 20.88/5.26 | (366) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (unordered_triple(v1, v2, v3) = v4) | ? [v5] : ((v5 = v3 | v5 = v2 | v5 = v1 | in(v5, v0)) & ( ~ in(v5, v0) | ( ~ (v5 = v3) & ~ (v5 = v2) & ~ (v5 = v1))))) % 20.88/5.26 | (367) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair_first(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) % 20.88/5.26 | (368) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) % 20.88/5.26 | (369) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | v4 = v1 | v4 = v0 | ~ (unordered_triple(v0, v1, v2) = v3) | ~ in(v4, v3)) % 20.88/5.26 | (370) ! [v0] : ! [v1] : (v1 = v0 | ~ ordinal(v1) | ~ ordinal(v0) | in(v1, v0) | in(v0, v1)) % 20.88/5.26 | (371) ! [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))) % 20.88/5.26 | (372) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 20.88/5.26 | (373) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | subset(v0, v3) | ? [v4] : (relation_dom(v1) = v4 & ~ subset(v0, v4))) % 20.88/5.26 | (374) empty(all_0_2_2) % 20.88/5.26 | (375) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) % 20.88/5.26 | (376) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | ? [v4] : (powerset(v1) = v4 & element(v3, v4))) % 20.88/5.26 | (377) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 20.88/5.26 | (378) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_founded_relation(v1) | ~ relation(v1) | well_founded_relation(v2)) % 20.88/5.26 | (379) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 20.88/5.26 | (380) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) % 20.88/5.27 | (381) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) % 20.88/5.27 | (382) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) % 20.88/5.27 | (383) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0)) % 20.88/5.27 | (384) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_dom(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v3) = v4 & in(v3, v0))) % 20.88/5.27 | (385) ! [v0] : ( ~ empty(v0) | function(v0)) % 20.88/5.27 | (386) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2)))) % 20.88/5.27 | (387) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 20.88/5.27 | (388) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 20.88/5.27 | (389) ! [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)) % 20.88/5.27 | (390) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v1, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ transitive(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v5, v0) | ? [v6] : (ordered_pair(v2, v3) = v6 & ~ in(v6, v0))) % 20.88/5.27 | (391) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1)) % 20.88/5.27 | (392) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 20.88/5.27 | (393) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 20.88/5.27 | (394) ! [v0] : ! [v1] : ( ~ (succ(v1) = v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0)) % 20.88/5.27 | (395) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v5, v0) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v0) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) % 20.88/5.27 | (396) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 20.88/5.27 | (397) relation_empty_yielding(all_0_11_11) % 20.88/5.27 | (398) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3))) % 20.88/5.27 | (399) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_transitive_in(v0, v1)) % 20.88/5.27 | (400) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 20.88/5.27 | (401) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 20.88/5.27 | (402) ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1)) % 20.88/5.27 | (403) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 20.88/5.27 | (404) ? [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))))) % 20.88/5.27 | (405) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & subset(v3, v4))) % 20.88/5.27 | (406) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) % 20.88/5.27 | (407) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ in(v4, v5) | in(v0, v2)) % 20.88/5.27 | (408) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | transitive(v0)) % 20.88/5.27 | (409) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) % 20.88/5.27 | (410) ! [v0] : ( ~ empty(v0) | relation(v0)) % 20.88/5.27 | (411) ordinal(empty_set) % 20.88/5.27 | (412) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 20.88/5.27 | (413) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 20.88/5.27 | (414) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v2, v3)) % 20.88/5.27 | (415) ! [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)))) % 20.88/5.27 | (416) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) % 20.88/5.27 | (417) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 20.88/5.27 | (418) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) % 20.88/5.27 | (419) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) % 20.88/5.27 | (420) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ in(v1, v0) | ? [v2] : (ordinal(v2) & in(v2, v0) & ! [v3] : ( ~ ordinal(v3) | ~ in(v3, v0) | ordinal_subset(v2, v3)))) % 20.88/5.27 | (421) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v1) | relation_restriction(v1, v0) = v3) % 20.88/5.27 | (422) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2) % 20.88/5.27 | (423) empty(all_0_3_3) % 20.88/5.27 | (424) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | ? [v4] : (relation_rng(v1) = v4 & ~ subset(v0, v4))) % 20.88/5.28 | (425) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_first(v2) = v1) | ~ (pair_first(v2) = v0)) % 20.88/5.28 | (426) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2)) % 20.88/5.28 | (427) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ in(v4, v5) | in(v1, v3)) % 20.88/5.28 | (428) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ reflexive(v1) | ~ relation(v1) | reflexive(v2)) % 20.88/5.28 | (429) function(all_0_5_5) % 20.88/5.28 | (430) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ relation_of2_as_subset(v3, v2, v0) | ~ subset(v4, v1) | relation_of2_as_subset(v3, v2, v1)) % 20.88/5.28 | (431) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ( ~ (v4 = v3) | ~ in(v5, v1) | ~ in(v3, v0)) & (in(v5, v1) | (v4 = v3 & in(v3, v0))))) % 20.88/5.28 | (432) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (powerset(v3) = v4 & element(v2, v4))) % 20.88/5.28 | (433) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) % 20.88/5.28 | (434) ? [v0] : subset(v0, v0) % 20.88/5.28 | (435) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) % 20.88/5.28 | (436) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3)) % 20.88/5.28 | (437) relation(all_0_2_2) % 20.88/5.28 | (438) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) % 20.98/5.28 | (439) empty(all_0_4_4) % 20.98/5.28 | (440) ! [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)))) % 20.98/5.28 | (441) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) % 20.98/5.28 | (442) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1)) % 20.98/5.28 | (443) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ transitive(v0) | ~ relation(v0) | is_transitive_in(v0, v1)) % 20.98/5.28 | (444) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 20.98/5.28 | (445) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5)))) % 20.98/5.28 | (446) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 20.98/5.28 | (447) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) % 20.98/5.28 | (448) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ relation_of2_as_subset(v3, v2, v0) | ~ subset(v0, v1) | relation_of2_as_subset(v3, v2, v1)) % 20.98/5.28 | (449) ? [v0] : (epsilon_transitive(v0) | ? [v1] : (in(v1, v0) & ~ subset(v1, v0))) % 20.98/5.28 | (450) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v1, v3) = v5) | ~ transitive(v0) | ~ relation(v0) | ~ in(v4, v0) | in(v5, v0) | ? [v6] : (ordered_pair(v1, v2) = v6 & ~ in(v6, v0))) % 20.98/5.28 | (451) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 20.98/5.28 | (452) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4))))) % 20.98/5.28 | (453) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 20.98/5.28 | (454) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) % 20.98/5.28 | (455) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | subset(v3, v0)) % 20.98/5.28 | (456) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | in(v5, v2)) % 20.98/5.28 | (457) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 20.98/5.28 | (458) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_field(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ reflexive(v0) | ~ relation(v0) | ~ in(v2, v1) | in(v3, v0)) % 20.98/5.28 | (459) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ subset(v3, v4) | ~ relation(v1) | ~ in(v4, v0) | ~ in(v3, v0) | in(v5, v1)) % 20.98/5.28 | (460) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) % 20.98/5.28 | (461) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ordinal(v1)) % 20.98/5.28 | (462) ! [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)))) % 20.98/5.28 | (463) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) % 20.98/5.28 | (464) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v1))) % 20.98/5.29 | (465) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1)) % 20.98/5.29 | (466) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 20.98/5.29 | (467) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2)) % 20.98/5.29 | (468) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 20.98/5.29 | (469) function(all_0_8_8) % 20.98/5.29 | (470) ! [v0] : ( ~ relation(v0) | antisymmetric(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v2 = v1) & ordered_pair(v2, v1) = v4 & ordered_pair(v1, v2) = v3 & in(v4, v0) & in(v3, v0))) % 20.98/5.29 | (471) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) % 20.98/5.29 | (472) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | transitive(v1)) % 20.98/5.29 | (473) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 20.98/5.29 | (474) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 20.98/5.29 | (475) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) % 20.98/5.29 | (476) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | well_founded_relation(v1)) % 20.98/5.29 | (477) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 20.98/5.29 | (478) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) % 20.98/5.29 | (479) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | reflexive(v0)) % 20.98/5.29 | (480) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 20.98/5.29 | (481) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) % 20.98/5.29 | (482) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) % 20.98/5.29 | (483) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) % 20.98/5.29 | (484) ! [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))) % 20.98/5.29 | (485) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) % 20.98/5.29 | (486) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) % 20.98/5.29 | (487) ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : ? [v2] : (succ(v1) = v2 & ordinal(v1) & in(v1, v0) & ~ in(v2, v0))) % 20.98/5.29 | (488) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 20.98/5.29 | (489) ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v1) & ! [v4] : ( ~ subset(v4, v2) | in(v4, v3))))) % 20.98/5.29 | (490) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (relation_rng(v2) = v4 & subset(v4, v1))) % 20.98/5.29 | (491) relation_empty_yielding(empty_set) % 20.98/5.29 | (492) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1)) % 20.98/5.29 | (493) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) % 20.98/5.29 | (494) epsilon_connected(empty_set) % 20.98/5.29 | (495) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_connected_in(v0, v1)) % 20.98/5.29 | (496) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) % 20.98/5.29 | (497) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 20.98/5.29 | (498) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ subset(v2, v3) | relation_of2(v2, v0, v1)) % 20.98/5.29 | (499) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2(v2, v0, v1) | subset(v2, v3)) % 20.98/5.29 | (500) ? [v0] : ! [v1] : ( ~ relation(v1) | is_connected_in(v1, v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v2) & ordered_pair(v3, v2) = v5 & ordered_pair(v2, v3) = v4 & in(v3, v0) & in(v2, v0) & ~ in(v5, v1) & ~ in(v4, v1))) % 20.98/5.29 | (501) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 20.98/5.29 | (502) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | reflexive(v1)) % 20.98/5.29 | (503) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ connected(v0) | ~ relation(v0) | is_connected_in(v0, v1)) % 20.98/5.29 | (504) ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) % 20.98/5.29 | (505) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) % 20.98/5.29 | (506) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 20.98/5.30 | (507) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) % 20.98/5.30 | (508) relation_rng(empty_set) = empty_set % 20.98/5.30 | (509) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (fiber(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : (ordered_pair(v4, v2) = v5 & (v4 = v2 | ~ in(v5, v1) | ~ in(v4, v0)) & (in(v4, v0) | ( ~ (v4 = v2) & in(v5, v1))))) % 20.98/5.30 | (510) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 20.98/5.30 | (511) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 20.98/5.30 | (512) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 20.98/5.30 | (513) ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ( ! [v4] : ( ~ ordinal(v4) | ~ in(v4, v2) | ~ in(v4, v0) | in(v4, v3)) & ! [v4] : ( ~ in(v4, v3) | in(v4, v2)) & ! [v4] : ( ~ in(v4, v3) | (ordinal(v4) & in(v4, v0))))) % 20.98/5.30 | (514) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 20.98/5.30 | (515) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 20.98/5.30 | (516) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1)) & ! [v4] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v2))) | (v7 = v6 & in(v5, v2) & ( ~ (v8 = v5) | ~ in(v6, v3)))))))) % 20.98/5.30 | (517) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : (relation_dom(v3) = v5 & apply(v3, v1) = v6 & (v6 = v4 | ~ in(v1, v5)))) % 20.98/5.30 | (518) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 20.98/5.30 | (519) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 20.98/5.30 | (520) ! [v0] : ! [v1] : ( ~ is_well_founded_in(v0, v1) | ~ is_reflexive_in(v0, v1) | ~ is_transitive_in(v0, v1) | ~ is_connected_in(v0, v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | well_orders(v0, v1)) % 20.98/5.30 | (521) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (pair_second(v1) = v2) | ~ (ordered_pair(v3, v4) = v1) | ? [v5] : ? [v6] : ( ~ (v6 = v0) & ordered_pair(v5, v6) = v1)) % 20.98/5.30 | (522) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 20.98/5.30 | (523) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) % 20.98/5.30 | (524) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | one_to_one(v0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v3 = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 & in(v3, v1) & in(v2, v1))) % 20.98/5.30 | (525) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~ in(v1, v0) | in(v2, v0)) % 20.98/5.30 | (526) relation(all_0_10_10) % 20.98/5.30 | (527) inclusion_relation(all_0_13_13) = all_0_12_12 % 20.98/5.30 | (528) ordinal(all_0_5_5) % 20.98/5.30 | (529) ! [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)) % 20.98/5.30 | (530) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 20.98/5.30 | (531) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 20.98/5.30 | (532) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 20.98/5.30 | (533) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) & in(v4, v1))) % 20.98/5.30 | (534) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | transitive(v0)) % 20.98/5.30 | (535) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 20.98/5.30 | (536) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 20.98/5.30 | (537) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1))))))) % 20.98/5.30 | (538) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (ordered_pair(v2, v3) = v4) | ~ is_connected_in(v0, v1) | ~ relation(v0) | ~ in(v3, v1) | ~ in(v2, v1) | in(v4, v0) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) % 20.98/5.30 | (539) ! [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)) % 20.98/5.30 | (540) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) % 20.98/5.30 | (541) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) % 20.98/5.31 | (542) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 20.98/5.31 | (543) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | connected(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v2) & ordered_pair(v3, v2) = v5 & ordered_pair(v2, v3) = v4 & in(v3, v1) & in(v2, v1) & ~ in(v5, v0) & ~ in(v4, v0))) % 20.98/5.31 | (544) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 20.98/5.31 | (545) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | in(v4, v1)) % 20.98/5.31 | (546) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 20.98/5.31 | (547) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 20.98/5.31 | (548) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 20.98/5.31 | (549) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 20.98/5.31 | (550) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1)) % 20.98/5.31 | (551) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1)))) % 20.98/5.31 | (552) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | relation_restriction(v1, v0) = v3) % 20.98/5.31 | (553) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_orders(v0, v1) | ~ relation(v0) | well_ordering(v0)) % 20.98/5.31 | (554) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) % 20.98/5.31 | (555) epsilon_connected(all_0_1_1) % 20.98/5.31 | (556) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1)) % 20.98/5.31 | (557) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) % 20.98/5.31 | (558) ! [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))) % 20.98/5.31 | (559) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 20.98/5.31 | (560) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ~ in(v1, v0) | apply(v2, v1) = v4) % 20.98/5.31 | (561) epsilon_connected(all_0_9_9) % 20.98/5.31 | (562) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) % 20.98/5.31 | (563) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 20.98/5.31 | (564) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) % 20.98/5.31 | (565) relation(all_0_5_5) % 20.98/5.31 | (566) ! [v0] : ( ~ empty(v0) | ordinal(v0)) % 20.98/5.31 | (567) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_well_founded_in(v0, v1)) % 20.98/5.31 | (568) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v2) = v5 & relation_dom_restriction(v5, v1) = v4)) % 20.98/5.31 | (569) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ in(v0, v1) | ordinal(v0)) % 20.98/5.31 | (570) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v5 & subset(v6, v4) & subset(v3, v5))) % 20.98/5.31 | (571) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) % 20.98/5.31 | (572) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | subset(v3, v0)) % 20.98/5.31 | (573) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) % 20.98/5.31 | (574) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | ~ in(v3, v0) | subset(v3, v4)) % 20.98/5.31 | (575) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_field(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ connected(v0) | ~ relation(v0) | ~ in(v3, v1) | ~ in(v2, v1) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v0))) % 20.98/5.31 | (576) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_field(v2) = v3) | ~ (relation_field(v0) = v1) | ~ (relation_dom(v4) = v5) | ~ relation(v4) | ~ relation(v2) | ~ relation(v0) | ~ function(v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (relation_rng(v4) = v6 & ( ~ (v6 = v3) | ~ (v5 = v1) | ~ one_to_one(v4) | relation_isomorphism(v0, v2, v4) | (apply(v4, v8) = v11 & apply(v4, v7) = v10 & ordered_pair(v10, v11) = v12 & ordered_pair(v7, v8) = v9 & ( ~ in(v12, v2) | ~ in(v9, v0) | ~ in(v8, v1) | ~ in(v7, v1)) & (in(v9, v0) | (in(v12, v2) & in(v8, v1) & in(v7, v1))))) & ( ~ relation_isomorphism(v0, v2, v4) | (v6 = v3 & v5 = v1 & one_to_one(v4) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | ~ in(v17, v2) | ~ in(v14, v1) | ~ in(v13, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v17, v2) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v14, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v4, v14) = v16) | ~ (apply(v4, v13) = v15) | ~ (ordered_pair(v15, v16) = v17) | in(v13, v1) | ? [v18] : (ordered_pair(v13, v14) = v18 & ~ in(v18, v0))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | in(v14, v1)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | in(v13, v1)) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v15, v0) | ? [v16] : ? [v17] : ? [v18] : (apply(v4, v14) = v17 & apply(v4, v13) = v16 & ordered_pair(v16, v17) = v18 & in(v18, v2))) & ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ in(v14, v1) | ~ in(v13, v1) | in(v15, v0) | ? [v16] : ? [v17] : ? [v18] : (apply(v4, v14) = v17 & apply(v4, v13) = v16 & ordered_pair(v16, v17) = v18 & ~ in(v18, v2))))))) % 20.98/5.32 | (577) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) % 20.98/5.32 | (578) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 20.98/5.32 | (579) one_to_one(empty_set) % 20.98/5.32 | (580) ? [v0] : ! [v1] : ( ~ relation(v1) | is_transitive_in(v1, v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v4) = v6 & ordered_pair(v2, v4) = v7 & ordered_pair(v2, v3) = v5 & in(v6, v1) & in(v5, v1) & in(v4, v0) & in(v3, v0) & in(v2, v0) & ~ in(v7, v1))) % 20.98/5.32 | (581) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 20.98/5.32 | (582) epsilon_transitive(all_0_5_5) % 20.98/5.32 | (583) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) % 20.98/5.32 | (584) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1)) % 20.98/5.32 | (585) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) % 20.98/5.32 | (586) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) % 20.98/5.32 | (587) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_as_subset(v0, v1, v2) = v1) | ~ relation_of2_as_subset(v2, v0, v1) | ~ in(v3, v1) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v2))) % 20.98/5.32 | (588) ? [v0] : ! [v1] : ( ~ relation(v1) | is_well_founded_in(v1, v0) | ? [v2] : ( ~ (v2 = empty_set) & subset(v2, v0) & ! [v3] : ! [v4] : ( ~ (fiber(v1, v3) = v4) | ~ disjoint(v4, v2) | ~ in(v3, v2)))) % 20.98/5.32 | (589) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1) % 20.98/5.32 | (590) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v1, v3)) % 20.98/5.32 | (591) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_rng(v1) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) % 20.98/5.32 | (592) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 20.98/5.32 | (593) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_connected_in(v0, v1) | ~ relation(v0) | connected(v0)) % 20.98/5.32 | (594) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ transitive(v1) | ~ relation(v1) | transitive(v2)) % 20.98/5.32 | (595) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & set_intersection2(v4, v0) = v3)) % 20.98/5.32 | (596) relation(all_0_8_8) % 20.98/5.32 | (597) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 20.98/5.32 | (598) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1)) % 20.98/5.32 | (599) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 20.98/5.32 | (600) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) % 20.98/5.32 | (601) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 20.98/5.32 | (602) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) % 21.16/5.32 | (603) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0)) % 21.16/5.32 | (604) ! [v0] : ! [v1] : (v0 = empty_set | ~ subset(v0, v1) | ~ ordinal(v1) | ? [v2] : (ordinal(v2) & in(v2, v0) & ! [v3] : ( ~ ordinal(v3) | ~ in(v3, v0) | ordinal_subset(v2, v3)))) % 21.16/5.32 | (605) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) % 21.16/5.32 | (606) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) = v4) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1) | ~ in(v2, v1)) % 21.16/5.32 | (607) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_rng(v3) = v4 & relation_image(v2, v1) = v4)) % 21.16/5.32 | (608) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_rng(v2) = v5 & in(v1, v5))) % 21.16/5.32 | (609) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng_restriction(v0, v1) = v3 & relation_dom_restriction(v3, v0) = v2)) % 21.16/5.32 | (610) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ connected(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | connected(v1)) % 21.16/5.32 | (611) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (ordered_pair(v2, v4) = v6) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | ~ in(v3, v1) | ~ in(v2, v1) | in(v6, v0) | ? [v7] : (ordered_pair(v2, v3) = v7 & ~ in(v7, v0))) % 21.16/5.32 | (612) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) % 21.16/5.32 | (613) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 21.16/5.32 | (614) relation(all_0_6_6) % 21.16/5.32 | (615) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ epsilon_connected(v0) | ~ in(v2, v0) | ~ in(v1, v0) | in(v2, v1) | in(v1, v2)) % 21.16/5.32 | (616) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) % 21.16/5.32 | % 21.16/5.32 | Instantiating formula (502) with all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, yields: % 21.16/5.33 | (617) reflexive(all_0_12_12) % 21.16/5.33 | % 21.16/5.33 | Instantiating formula (472) with all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, yields: % 21.16/5.33 | (618) transitive(all_0_12_12) % 21.16/5.33 | % 21.16/5.33 | Instantiating formula (335) with all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, yields: % 21.16/5.33 | (619) antisymmetric(all_0_12_12) % 21.16/5.33 | % 21.16/5.33 | Instantiating formula (492) with all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, yields: % 21.16/5.33 | (620) relation(all_0_12_12) % 21.16/5.33 | % 21.16/5.33 | Instantiating formula (476) with all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, ordinal(all_0_13_13), yields: % 21.16/5.33 | (621) well_founded_relation(all_0_12_12) % 21.16/5.33 | % 21.16/5.33 | Instantiating formula (189) with all_0_12_12, all_0_13_13 and discharging atoms inclusion_relation(all_0_13_13) = all_0_12_12, ordinal(all_0_13_13), yields: % 21.16/5.33 | (622) connected(all_0_12_12) % 21.16/5.33 | % 21.16/5.33 | Instantiating formula (5) with all_0_12_12 and discharging atoms reflexive(all_0_12_12), well_founded_relation(all_0_12_12), transitive(all_0_12_12), connected(all_0_12_12), antisymmetric(all_0_12_12), relation(all_0_12_12), ~ well_ordering(all_0_12_12), yields: % 21.16/5.33 | (623) $false % 21.16/5.33 | % 21.16/5.33 |-The branch is then unsatisfiable % 21.16/5.33 % SZS output end Proof for theBenchmark % 21.16/5.33 % 21.16/5.33 4697ms %------------------------------------------------------------------------------