%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU307+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n025.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 08:48:42 EDT 2022 % Result : Theorem 16.63s 4.34s % Output : Proof 30.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SEU307+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n025.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Mon Jun 20 08:38:14 EDT 2022 % 0.12/0.33 % CPUTime : % 0.59/0.57 ____ _ % 0.59/0.57 ___ / __ \_____(_)___ ________ __________ % 0.59/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.57 % 0.59/0.57 A Theorem Prover for First-Order Logic % 0.59/0.57 (ePrincess v.1.0) % 0.59/0.57 % 0.59/0.57 (c) Philipp Rümmer, 2009-2015 % 0.59/0.57 (c) Peter Backeman, 2014-2015 % 0.59/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.57 Bug reports to peter@backeman.se % 0.59/0.57 % 0.59/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.57 % 0.59/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.59/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.54/1.42 Prover 0: Preprocessing ... % 10.18/2.87 Prover 0: Warning: ignoring some quantifiers % 10.43/2.94 Prover 0: Constructing countermodel ... % 16.63/4.34 Prover 0: proved (3715ms) % 16.63/4.34 % 16.63/4.34 No countermodel exists, formula is valid % 16.63/4.34 % SZS status Theorem for theBenchmark % 16.63/4.34 % 16.63/4.34 Generating proof ... Warning: ignoring some quantifiers % 27.87/7.08 found it (size 54) % 27.87/7.08 % 27.87/7.08 % SZS output start Proof for theBenchmark % 27.87/7.09 Assumed formulas after preprocessing and simplification: % 27.87/7.09 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : ? [v34] : ? [v35] : ? [v36] : ? [v37] : ? [v38] : ? [v39] : ? [v40] : ( ~ (v7 = v6) & cast_as_carrier_subset(v2) = v5 & singleton(empty_set) = v0 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & subset_intersection2(v3, v6, v5) = v7 & the_carrier(v2) = v3 & powerset(v3) = v4 & powerset(v0) = v1 & powerset(empty_set) = v0 & relation_empty_yielding(v21) & relation_empty_yielding(v19) & relation_empty_yielding(empty_set) & latt_str(v37) & being_limit_ordinal(v31) & being_limit_ordinal(omega) & one_sorted_str(v39) & one_sorted_str(v20) & one_sorted_str(v2) & meet_semilatt_str(v40) & join_semilatt_str(v38) & one_to_one(v30) & one_to_one(v26) & one_to_one(v23) & one_to_one(empty_set) & relation(v34) & relation(v30) & relation(v29) & relation(v27) & relation(v26) & relation(v25) & relation(v23) & relation(v21) & relation(v19) & relation(empty_set) & function(v34) & function(v30) & function(v27) & function(v26) & function(v23) & function(v19) & function(empty_set) & finite(v35) & epsilon_connected(v36) & epsilon_connected(v32) & epsilon_connected(v31) & epsilon_connected(v26) & epsilon_connected(v22) & epsilon_connected(empty_set) & epsilon_connected(omega) & epsilon_transitive(v36) & epsilon_transitive(v32) & epsilon_transitive(v31) & epsilon_transitive(v26) & epsilon_transitive(v22) & epsilon_transitive(empty_set) & epsilon_transitive(omega) & ordinal(v36) & ordinal(v32) & ordinal(v31) & ordinal(v26) & ordinal(v22) & ordinal(empty_set) & ordinal(omega) & empty(v30) & empty(v29) & empty(v28) & empty(v27) & empty(v26) & empty(empty_set) & natural(v36) & v5_membered(v33) & v5_membered(empty_set) & v4_membered(v33) & v4_membered(empty_set) & v3_membered(v33) & v3_membered(empty_set) & v2_membered(v33) & v2_membered(empty_set) & element(v6, v4) & v1_membered(v33) & v1_membered(empty_set) & in(empty_set, omega) & ~ empty_carrier(v20) & ~ empty(v36) & ~ empty(v35) & ~ empty(v33) & ~ empty(v25) & ~ empty(v24) & ~ empty(v22) & ~ empty(omega) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v42 = v41 | ~ (apply_binary_as_element(v48, v47, v46, v45, v44, v43) = v42) | ~ (apply_binary_as_element(v48, v47, v46, v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v42 = empty_set | ~ (relation_composition(v44, v46) = v47) | ~ (apply(v47, v43) = v48) | ~ (apply(v44, v43) = v45) | ~ quasi_total(v44, v41, v42) | ~ relation_of2_as_subset(v44, v41, v42) | ~ relation(v46) | ~ function(v46) | ~ function(v44) | ~ in(v43, v41) | apply(v46, v45) = v48) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_composition(v41, v42) = v43) | ~ (ordered_pair(v47, v45) = v48) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ in(v48, v42) | in(v46, v43) | ? [v49] : (ordered_pair(v44, v47) = v49 & ~ in(v49, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_composition(v41, v42) = v43) | ~ (ordered_pair(v44, v47) = v48) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ in(v48, v41) | in(v46, v43) | ? [v49] : (ordered_pair(v47, v45) = v49 & ~ in(v49, v42))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : (v42 = empty_set | ~ (relation_inverse_image(v44, v43) = v45) | ~ (apply(v44, v46) = v47) | ~ quasi_total(v44, v41, v42) | ~ relation_of2_as_subset(v44, v41, v42) | ~ function(v44) | ~ in(v47, v43) | ~ in(v46, v41) | in(v46, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : (v42 = empty_set | ~ (relation_inverse_image(v44, v43) = v45) | ~ (apply(v44, v46) = v47) | ~ quasi_total(v44, v41, v42) | ~ relation_of2_as_subset(v44, v41, v42) | ~ function(v44) | ~ in(v46, v45) | in(v47, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : (v42 = empty_set | ~ (relation_inverse_image(v44, v43) = v45) | ~ (apply(v44, v46) = v47) | ~ quasi_total(v44, v41, v42) | ~ relation_of2_as_subset(v44, v41, v42) | ~ function(v44) | ~ in(v46, v45) | in(v46, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : (v42 = empty_set | ~ (apply(v46, v45) = v47) | ~ (apply(v44, v43) = v45) | ~ quasi_total(v44, v41, v42) | ~ relation_of2_as_subset(v44, v41, v42) | ~ relation(v46) | ~ function(v46) | ~ function(v44) | ~ in(v43, v41) | ? [v48] : (relation_composition(v44, v46) = v48 & apply(v48, v43) = v47)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_composition(v46, v44) = v47) | ~ (identity_relation(v43) = v46) | ~ (ordered_pair(v41, v42) = v45) | ~ relation(v44) | ~ in(v45, v47) | in(v45, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_composition(v46, v44) = v47) | ~ (identity_relation(v43) = v46) | ~ (ordered_pair(v41, v42) = v45) | ~ relation(v44) | ~ in(v45, v47) | in(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_composition(v46, v44) = v47) | ~ (identity_relation(v43) = v46) | ~ (ordered_pair(v41, v42) = v45) | ~ relation(v44) | ~ in(v45, v44) | ~ in(v41, v43) | in(v45, v47)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (apply_binary_as_element(v41, v42, v43, v44, v45, v46) = v47) | ~ function(v44) | ~ element(v46, v42) | ~ element(v45, v41) | empty(v42) | empty(v41) | element(v47, v43) | ? [v48] : (cartesian_product2(v41, v42) = v48 & ( ~ relation_of2(v44, v48, v43) | ~ quasi_total(v44, v48, v43)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (apply_binary_as_element(v41, v42, v43, v44, v45, v46) = v47) | ~ function(v44) | ~ element(v46, v42) | ~ element(v45, v41) | empty(v42) | empty(v41) | ? [v48] : ? [v49] : (apply_binary(v44, v45, v46) = v49 & cartesian_product2(v41, v42) = v48 & (v49 = v47 | ~ relation_of2(v44, v48, v43) | ~ quasi_total(v44, v48, v43)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v44, v45) = v47) | ~ (ordered_pair(v43, v44) = v46) | ~ is_transitive_in(v41, v42) | ~ relation(v41) | ~ in(v47, v41) | ~ in(v46, v41) | ~ in(v45, v42) | ~ in(v44, v42) | ~ in(v43, v42) | ? [v48] : (ordered_pair(v43, v45) = v48 & in(v48, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v44, v45) = v46) | ~ (ordered_pair(v43, v45) = v47) | ~ is_transitive_in(v41, v42) | ~ relation(v41) | ~ in(v46, v41) | ~ in(v45, v42) | ~ in(v44, v42) | ~ in(v43, v42) | in(v47, v41) | ? [v48] : (ordered_pair(v43, v44) = v48 & ~ in(v48, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v43, v45) = v47) | ~ (ordered_pair(v43, v44) = v46) | ~ is_transitive_in(v41, v42) | ~ relation(v41) | ~ in(v46, v41) | ~ in(v45, v42) | ~ in(v44, v42) | ~ in(v43, v42) | in(v47, v41) | ? [v48] : (ordered_pair(v44, v45) = v48 & ~ in(v48, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v46 = v44 | ~ (meet(v41, v43, v44) = v45) | ~ (join(v41, v45, v44) = v46) | ~ (the_carrier(v41) = v42) | ~ meet_absorbing(v41) | ~ latt_str(v41) | ~ element(v44, v42) | ~ element(v43, v42) | empty_carrier(v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v44 = v43 | ~ (ordered_pair(v42, v44) = v46) | ~ (ordered_pair(v42, v43) = v45) | ~ function(v41) | ~ in(v46, v41) | ~ in(v45, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v44 = v42 | ~ (pair_second(v41) = v42) | ~ (ordered_pair(v45, v46) = v41) | ~ (ordered_pair(v43, v44) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (pair_first(v41) = v42) | ~ (ordered_pair(v45, v46) = v41) | ~ (ordered_pair(v43, v44) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_composition(v41, v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ in(v46, v43) | ? [v47] : ? [v48] : ? [v49] : (ordered_pair(v47, v45) = v49 & ordered_pair(v44, v47) = v48 & in(v49, v42) & in(v48, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (inclusion_relation(v41) = v42) | ~ (relation_field(v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ subset(v44, v45) | ~ relation(v42) | ~ in(v45, v41) | ~ in(v44, v41) | in(v46, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (inclusion_relation(v41) = v42) | ~ (relation_field(v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v42) | ~ in(v46, v42) | ~ in(v45, v41) | ~ in(v44, v41) | subset(v44, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_rng(v45) = v46) | ~ (relation_field(v43) = v44) | ~ (relation_field(v41) = v42) | ~ relation(v45) | ~ relation(v43) | ~ relation(v41) | ~ function(v45) | ? [v47] : ? [v48] : ? [v49] : ? [v50] : ? [v51] : ? [v52] : ? [v53] : (relation_dom(v45) = v47 & ( ~ (v47 = v42) | ~ (v46 = v44) | ~ one_to_one(v45) | relation_isomorphism(v41, v43, v45) | (apply(v45, v49) = v52 & apply(v45, v48) = v51 & ordered_pair(v51, v52) = v53 & ordered_pair(v48, v49) = v50 & ( ~ in(v53, v43) | ~ in(v50, v41) | ~ in(v49, v42) | ~ in(v48, v42)) & (in(v50, v41) | (in(v53, v43) & in(v49, v42) & in(v48, v42))))) & ( ~ relation_isomorphism(v41, v43, v45) | (v47 = v42 & v46 = v44 & one_to_one(v45) & ! [v54] : ! [v55] : ! [v56] : ! [v57] : ! [v58] : ( ~ (apply(v45, v55) = v57) | ~ (apply(v45, v54) = v56) | ~ (ordered_pair(v56, v57) = v58) | ~ in(v58, v43) | ~ in(v55, v42) | ~ in(v54, v42) | ? [v59] : (ordered_pair(v54, v55) = v59 & in(v59, v41))) & ! [v54] : ! [v55] : ! [v56] : ! [v57] : ! [v58] : ( ~ (apply(v45, v55) = v57) | ~ (apply(v45, v54) = v56) | ~ (ordered_pair(v56, v57) = v58) | in(v58, v43) | ? [v59] : (ordered_pair(v54, v55) = v59 & ~ in(v59, v41))) & ! [v54] : ! [v55] : ! [v56] : ! [v57] : ! [v58] : ( ~ (apply(v45, v55) = v57) | ~ (apply(v45, v54) = v56) | ~ (ordered_pair(v56, v57) = v58) | in(v55, v42) | ? [v59] : (ordered_pair(v54, v55) = v59 & ~ in(v59, v41))) & ! [v54] : ! [v55] : ! [v56] : ! [v57] : ! [v58] : ( ~ (apply(v45, v55) = v57) | ~ (apply(v45, v54) = v56) | ~ (ordered_pair(v56, v57) = v58) | in(v54, v42) | ? [v59] : (ordered_pair(v54, v55) = v59 & ~ in(v59, v41))) & ! [v54] : ! [v55] : ! [v56] : ( ~ (ordered_pair(v54, v55) = v56) | ~ in(v56, v41) | in(v55, v42)) & ! [v54] : ! [v55] : ! [v56] : ( ~ (ordered_pair(v54, v55) = v56) | ~ in(v56, v41) | in(v54, v42)) & ! [v54] : ! [v55] : ! [v56] : ( ~ (ordered_pair(v54, v55) = v56) | ~ in(v56, v41) | ? [v57] : ? [v58] : ? [v59] : (apply(v45, v55) = v58 & apply(v45, v54) = v57 & ordered_pair(v57, v58) = v59 & in(v59, v43))) & ! [v54] : ! [v55] : ! [v56] : ( ~ (ordered_pair(v54, v55) = v56) | ~ in(v55, v42) | ~ in(v54, v42) | in(v56, v41) | ? [v57] : ? [v58] : ? [v59] : (apply(v45, v55) = v58 & apply(v45, v54) = v57 & ordered_pair(v57, v58) = v59 & ~ in(v59, v43))))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_inverse_image(v41, v43) = v44) | ~ (relation_dom(v41) = v42) | ~ (apply(v41, v45) = v46) | ~ relation(v41) | ~ function(v41) | ~ in(v46, v43) | ~ in(v45, v42) | in(v45, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_inverse_image(v41, v43) = v44) | ~ (relation_dom(v41) = v42) | ~ (apply(v41, v45) = v46) | ~ relation(v41) | ~ function(v41) | ~ in(v45, v44) | in(v46, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_inverse_image(v41, v43) = v44) | ~ (relation_dom(v41) = v42) | ~ (apply(v41, v45) = v46) | ~ relation(v41) | ~ function(v41) | ~ in(v45, v44) | in(v45, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_inverse_image(v41, v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v41) | ~ in(v46, v41) | ~ in(v45, v42) | in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_field(v43) = v44) | ~ (relation_field(v41) = v42) | ~ (relation_dom(v45) = v46) | ~ relation(v45) | ~ relation(v43) | ~ relation(v41) | ~ function(v45) | ? [v47] : ? [v48] : ? [v49] : ? [v50] : ? [v51] : ? [v52] : ? [v53] : (relation_rng(v45) = v47 & ( ~ (v47 = v44) | ~ (v46 = v42) | ~ one_to_one(v45) | relation_isomorphism(v41, v43, v45) | (apply(v45, v49) = v52 & apply(v45, v48) = v51 & ordered_pair(v51, v52) = v53 & ordered_pair(v48, v49) = v50 & ( ~ in(v53, v43) | ~ in(v50, v41) | ~ in(v49, v42) | ~ in(v48, v42)) & (in(v50, v41) | (in(v53, v43) & in(v49, v42) & in(v48, v42))))) & ( ~ relation_isomorphism(v41, v43, v45) | (v47 = v44 & v46 = v42 & one_to_one(v45) & ! [v54] : ! [v55] : ! [v56] : ! [v57] : ! [v58] : ( ~ (apply(v45, v55) = v57) | ~ (apply(v45, v54) = v56) | ~ (ordered_pair(v56, v57) = v58) | ~ in(v58, v43) | ~ in(v55, v42) | ~ in(v54, v42) | ? [v59] : (ordered_pair(v54, v55) = v59 & in(v59, v41))) & ! [v54] : ! [v55] : ! [v56] : ! [v57] : ! [v58] : ( ~ (apply(v45, v55) = v57) | ~ (apply(v45, v54) = v56) | ~ (ordered_pair(v56, v57) = v58) | in(v58, v43) | ? [v59] : (ordered_pair(v54, v55) = v59 & ~ in(v59, v41))) & ! [v54] : ! [v55] : ! [v56] : ! [v57] : ! [v58] : ( ~ (apply(v45, v55) = v57) | ~ (apply(v45, v54) = v56) | ~ (ordered_pair(v56, v57) = v58) | in(v55, v42) | ? [v59] : (ordered_pair(v54, v55) = v59 & ~ in(v59, v41))) & ! [v54] : ! [v55] : ! [v56] : ! [v57] : ! [v58] : ( ~ (apply(v45, v55) = v57) | ~ (apply(v45, v54) = v56) | ~ (ordered_pair(v56, v57) = v58) | in(v54, v42) | ? [v59] : (ordered_pair(v54, v55) = v59 & ~ in(v59, v41))) & ! [v54] : ! [v55] : ! [v56] : ( ~ (ordered_pair(v54, v55) = v56) | ~ in(v56, v41) | in(v55, v42)) & ! [v54] : ! [v55] : ! [v56] : ( ~ (ordered_pair(v54, v55) = v56) | ~ in(v56, v41) | in(v54, v42)) & ! [v54] : ! [v55] : ! [v56] : ( ~ (ordered_pair(v54, v55) = v56) | ~ in(v56, v41) | ? [v57] : ? [v58] : ? [v59] : (apply(v45, v55) = v58 & apply(v45, v54) = v57 & ordered_pair(v57, v58) = v59 & in(v59, v43))) & ! [v54] : ! [v55] : ! [v56] : ( ~ (ordered_pair(v54, v55) = v56) | ~ in(v55, v42) | ~ in(v54, v42) | in(v56, v41) | ? [v57] : ? [v58] : ? [v59] : (apply(v45, v55) = v58 & apply(v45, v54) = v57 & ordered_pair(v57, v58) = v59 & ~ in(v59, v43))))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v42) | ~ in(v46, v43) | in(v46, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v42) | ~ in(v46, v43) | in(v45, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v42) | ~ in(v46, v42) | ~ in(v45, v41) | in(v46, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom(v44) = v45) | ~ (relation_dom(v42) = v43) | ~ (set_intersection2(v45, v41) = v46) | ~ relation(v44) | ~ relation(v42) | ~ function(v44) | ~ function(v42) | ? [v47] : ? [v48] : ? [v49] : ? [v50] : (relation_dom_restriction(v44, v41) = v47 & ( ~ (v47 = v42) | (v46 = v43 & ! [v51] : ! [v52] : ( ~ (apply(v44, v51) = v52) | ~ in(v51, v43) | apply(v42, v51) = v52) & ! [v51] : ! [v52] : ( ~ (apply(v42, v51) = v52) | ~ in(v51, v43) | apply(v44, v51) = v52))) & ( ~ (v46 = v43) | v47 = v42 | ( ~ (v50 = v49) & apply(v44, v48) = v50 & apply(v42, v48) = v49 & in(v48, v43))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom(v41) = v42) | ~ (relation_image(v41, v43) = v44) | ~ (apply(v41, v46) = v45) | ~ relation(v41) | ~ function(v41) | ~ in(v46, v43) | ~ in(v46, v42) | in(v45, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_image(v41, v42) = v43) | ~ (ordered_pair(v45, v44) = v46) | ~ relation(v41) | ~ in(v46, v41) | ~ in(v45, v42) | in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom_restriction(v41, v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v41) | ~ in(v46, v43) | in(v46, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom_restriction(v41, v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v41) | ~ in(v46, v43) | in(v44, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom_restriction(v41, v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v41) | ~ in(v46, v41) | ~ in(v44, v42) | in(v46, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v45, v46) = v44) | ~ (cartesian_product2(v41, v42) = v43) | ~ in(v46, v42) | ~ in(v45, v41) | in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v43, v44) = v46) | ~ (ordered_pair(v42, v43) = v45) | ~ transitive(v41) | ~ relation(v41) | ~ in(v46, v41) | ~ in(v45, v41) | ? [v47] : (ordered_pair(v42, v44) = v47 & in(v47, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v43, v44) = v45) | ~ (ordered_pair(v42, v44) = v46) | ~ transitive(v41) | ~ relation(v41) | ~ in(v45, v41) | in(v46, v41) | ? [v47] : (ordered_pair(v42, v43) = v47 & ~ in(v47, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v42, v44) = v46) | ~ (ordered_pair(v42, v43) = v45) | ~ transitive(v41) | ~ relation(v41) | ~ in(v45, v41) | in(v46, v41) | ? [v47] : (ordered_pair(v43, v44) = v47 & ~ in(v47, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v41, v42) = v45) | ~ (cartesian_product2(v43, v44) = v46) | ~ in(v45, v46) | in(v42, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v41, v42) = v45) | ~ (cartesian_product2(v43, v44) = v46) | ~ in(v45, v46) | in(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v41, v42) = v45) | ~ (cartesian_product2(v43, v44) = v46) | ~ in(v42, v44) | ~ in(v41, v43) | in(v45, v46)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (cartesian_product2(v42, v44) = v46) | ~ (cartesian_product2(v41, v43) = v45) | ~ subset(v43, v44) | ~ subset(v41, v42) | subset(v45, v46)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v44 | ~ (join(v41, v43, v44) = v45) | ~ (the_carrier(v41) = v42) | ~ below(v41, v43, v44) | ~ join_semilatt_str(v41) | ~ element(v44, v42) | ~ element(v43, v42) | empty_carrier(v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v44 | ~ (relation_dom(v42) = v43) | ~ (apply(v42, v44) = v45) | ~ (identity_relation(v41) = v42) | ~ relation(v42) | ~ function(v42) | ~ in(v44, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v43 | v45 = v42 | v45 = v41 | ~ (unordered_triple(v41, v42, v43) = v44) | ~ in(v45, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (relation_field(v41) = v42) | ~ (ordered_pair(v44, v43) = v45) | ~ connected(v41) | ~ relation(v41) | ~ in(v44, v42) | ~ in(v43, v42) | in(v45, v41) | ? [v46] : (ordered_pair(v43, v44) = v46 & in(v46, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (relation_field(v41) = v42) | ~ (ordered_pair(v43, v44) = v45) | ~ connected(v41) | ~ relation(v41) | ~ in(v44, v42) | ~ in(v43, v42) | in(v45, v41) | ? [v46] : (ordered_pair(v44, v43) = v46 & in(v46, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (relation_dom(v41) = v42) | ~ (apply(v41, v44) = v45) | ~ (apply(v41, v43) = v45) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | ~ in(v44, v42) | ~ in(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (identity_relation(v41) = v42) | ~ (ordered_pair(v43, v44) = v45) | ~ relation(v42) | ~ in(v45, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (ordered_pair(v44, v43) = v45) | ~ is_connected_in(v41, v42) | ~ relation(v41) | ~ in(v44, v42) | ~ in(v43, v42) | in(v45, v41) | ? [v46] : (ordered_pair(v43, v44) = v46 & in(v46, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (ordered_pair(v44, v43) = v45) | ~ is_antisymmetric_in(v41, v42) | ~ relation(v41) | ~ in(v45, v41) | ~ in(v44, v42) | ~ in(v43, v42) | ? [v46] : (ordered_pair(v43, v44) = v46 & ~ in(v46, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (ordered_pair(v43, v44) = v45) | ~ is_connected_in(v41, v42) | ~ relation(v41) | ~ in(v44, v42) | ~ in(v43, v42) | in(v45, v41) | ? [v46] : (ordered_pair(v44, v43) = v46 & in(v46, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (ordered_pair(v43, v44) = v45) | ~ is_antisymmetric_in(v41, v42) | ~ relation(v41) | ~ in(v45, v41) | ~ in(v44, v42) | ~ in(v43, v42) | ? [v46] : (ordered_pair(v44, v43) = v46 & ~ in(v46, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v42 | ~ (fiber(v41, v42) = v43) | ~ (ordered_pair(v44, v42) = v45) | ~ relation(v41) | ~ in(v45, v41) | in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v42 | ~ (ordered_pair(v43, v44) = v45) | ~ (ordered_pair(v41, v42) = v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v41 | v43 = v41 | ~ (unordered_pair(v43, v44) = v45) | ~ (unordered_pair(v41, v42) = v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v41 | ~ (ordered_pair(v43, v44) = v45) | ~ (ordered_pair(v41, v42) = v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (apply_binary(v45, v44, v43) = v42) | ~ (apply_binary(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (subset_difference(v45, v44, v43) = v42) | ~ (subset_difference(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (relation_rng_as_subset(v45, v44, v43) = v42) | ~ (relation_rng_as_subset(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (meet(v45, v44, v43) = v42) | ~ (meet(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (join(v45, v44, v43) = v42) | ~ (join(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (relation_dom_as_subset(v45, v44, v43) = v42) | ~ (relation_dom_as_subset(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (unordered_triple(v45, v44, v43) = v42) | ~ (unordered_triple(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (subset_intersection2(v45, v44, v43) = v42) | ~ (subset_intersection2(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (meet_commut(v45, v44, v43) = v42) | ~ (meet_commut(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = v41 | ~ (join_commut(v45, v44, v43) = v42) | ~ (join_commut(v45, v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = empty_set | ~ (subset_difference(v41, v43, v44) = v45) | ~ (meet_of_subsets(v41, v42) = v44) | ~ (cast_to_subset(v41) = v43) | ? [v46] : ? [v47] : ? [v48] : ? [v49] : (union_of_subsets(v41, v48) = v49 & complements_of_subsets(v41, v42) = v48 & powerset(v46) = v47 & powerset(v41) = v46 & (v49 = v45 | ~ element(v42, v47)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = empty_set | ~ (subset_difference(v41, v43, v44) = v45) | ~ (union_of_subsets(v41, v42) = v44) | ~ (cast_to_subset(v41) = v43) | ? [v46] : ? [v47] : ? [v48] : ? [v49] : (meet_of_subsets(v41, v48) = v49 & complements_of_subsets(v41, v42) = v48 & powerset(v46) = v47 & powerset(v41) = v46 & (v49 = v45 | ~ element(v42, v47)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = empty_set | ~ (apply(v44, v43) = v45) | ~ quasi_total(v44, v41, v42) | ~ relation_of2_as_subset(v44, v41, v42) | ~ function(v44) | ~ in(v43, v41) | ? [v46] : (relation_rng(v44) = v46 & in(v45, v46))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v41 = empty_set | ~ (subset_complement(v41, v43) = v44) | ~ (powerset(v41) = v42) | ~ element(v45, v41) | ~ element(v43, v42) | in(v45, v44) | in(v45, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (function_inverse(v42) = v43) | ~ (relation_composition(v43, v42) = v44) | ~ (apply(v44, v41) = v45) | ~ one_to_one(v42) | ~ relation(v42) | ~ function(v42) | ? [v46] : ? [v47] : ? [v48] : (relation_rng(v42) = v46 & apply(v43, v41) = v47 & apply(v42, v47) = v48 & ( ~ in(v41, v46) | (v48 = v41 & v45 = v41)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (function_inverse(v42) = v43) | ~ (apply(v43, v41) = v44) | ~ (apply(v42, v44) = v45) | ~ one_to_one(v42) | ~ relation(v42) | ~ function(v42) | ? [v46] : ? [v47] : ? [v48] : (relation_composition(v43, v42) = v47 & relation_rng(v42) = v46 & apply(v47, v41) = v48 & ( ~ in(v41, v46) | (v48 = v41 & v45 = v41)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_composition(v43, v42) = v44) | ~ (apply(v44, v41) = v45) | ~ relation(v43) | ~ relation(v42) | ~ function(v43) | ~ function(v42) | ? [v46] : ? [v47] : ? [v48] : (relation_dom(v44) = v46 & apply(v43, v41) = v47 & apply(v42, v47) = v48 & (v48 = v45 | ~ in(v41, v46)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_inverse(v41) = v42) | ~ (ordered_pair(v44, v43) = v45) | ~ relation(v42) | ~ relation(v41) | ~ in(v45, v41) | ? [v46] : (ordered_pair(v43, v44) = v46 & in(v46, v42))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_inverse(v41) = v42) | ~ (ordered_pair(v44, v43) = v45) | ~ relation(v42) | ~ relation(v41) | in(v45, v41) | ? [v46] : (ordered_pair(v43, v44) = v46 & ~ in(v46, v42))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_inverse(v41) = v42) | ~ (ordered_pair(v43, v44) = v45) | ~ relation(v42) | ~ relation(v41) | ~ in(v45, v42) | ? [v46] : (ordered_pair(v44, v43) = v46 & in(v46, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_inverse(v41) = v42) | ~ (ordered_pair(v43, v44) = v45) | ~ relation(v42) | ~ relation(v41) | in(v45, v42) | ? [v46] : (ordered_pair(v44, v43) = v46 & ~ in(v46, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_restriction(v43, v41) = v44) | ~ (fiber(v44, v42) = v45) | ~ relation(v43) | ? [v46] : (fiber(v43, v42) = v46 & subset(v45, v46))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (subset_complement(v41, v44) = v45) | ~ (powerset(v41) = v43) | ~ disjoint(v42, v44) | ~ element(v44, v43) | ~ element(v42, v43) | subset(v42, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (subset_complement(v41, v44) = v45) | ~ (powerset(v41) = v43) | ~ subset(v42, v45) | ~ element(v44, v43) | ~ element(v42, v43) | disjoint(v42, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_difference(v42, v44) = v45) | ~ (singleton(v43) = v44) | ~ subset(v41, v42) | subset(v41, v45) | in(v43, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_difference(v42, v43) = v45) | ~ (set_difference(v41, v43) = v44) | ~ subset(v41, v42) | subset(v44, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_difference(v42, v43) = v45) | ~ (powerset(v41) = v44) | ~ element(v43, v44) | ~ element(v42, v44) | subset_difference(v41, v42, v43) = v45) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (fiber(v41, v42) = v43) | ~ (ordered_pair(v44, v42) = v45) | ~ relation(v41) | ~ in(v44, v43) | in(v45, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (singleton(v41) = v44) | ~ (unordered_pair(v43, v44) = v45) | ~ (unordered_pair(v41, v42) = v43) | ordered_pair(v41, v42) = v45) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v44) = v45) | ~ relation_of2_as_subset(v44, v43, v41) | ~ subset(v45, v42) | relation_of2_as_subset(v44, v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v43) = v45) | ~ (ordered_pair(v41, v42) = v44) | ~ relation(v43) | ~ in(v44, v43) | in(v42, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v43) = v45) | ~ (ordered_pair(v41, v42) = v44) | ~ relation(v43) | ~ in(v44, v43) | ? [v46] : (relation_dom(v43) = v46 & in(v41, v46))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v41) = v42) | ~ (ordered_pair(v44, v43) = v45) | ~ relation(v41) | ~ in(v45, v41) | in(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_inverse_image(v43, v42) = v45) | ~ (relation_inverse_image(v43, v41) = v44) | ~ subset(v41, v42) | ~ relation(v43) | subset(v44, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_field(v43) = v45) | ~ (ordered_pair(v41, v42) = v44) | ~ relation(v43) | ~ in(v44, v43) | in(v42, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_field(v43) = v45) | ~ (ordered_pair(v41, v42) = v44) | ~ relation(v43) | ~ in(v44, v43) | in(v41, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng_restriction(v41, v44) = v45) | ~ (relation_dom_restriction(v43, v42) = v44) | ~ relation(v43) | ? [v46] : (relation_rng_restriction(v41, v43) = v46 & relation_dom_restriction(v46, v42) = v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng_restriction(v41, v43) = v44) | ~ (relation_dom_restriction(v44, v42) = v45) | ~ relation(v43) | ? [v46] : (relation_rng_restriction(v41, v46) = v45 & relation_dom_restriction(v43, v42) = v46)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v43) = v45) | ~ (ordered_pair(v41, v42) = v44) | ~ relation(v43) | ~ function(v43) | ? [v46] : (apply(v43, v41) = v46 & ( ~ (v46 = v42) | ~ in(v41, v45) | in(v44, v43)) & ( ~ in(v44, v43) | (v46 = v42 & in(v41, v45))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v43) = v45) | ~ (ordered_pair(v41, v42) = v44) | ~ relation(v43) | ~ in(v44, v43) | in(v41, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v43) = v45) | ~ (ordered_pair(v41, v42) = v44) | ~ relation(v43) | ~ in(v44, v43) | ? [v46] : (relation_rng(v43) = v46 & in(v42, v46))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v42) = v43) | ~ (relation_image(v42, v44) = v45) | ~ (set_intersection2(v43, v41) = v44) | ~ relation(v42) | relation_image(v42, v41) = v45) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v42) = v43) | ~ (apply(v44, v41) = v45) | ~ relation(v44) | ~ relation(v42) | ~ function(v44) | ~ function(v42) | ? [v46] : ? [v47] : ? [v48] : (relation_composition(v44, v42) = v46 & relation_dom(v46) = v47 & relation_dom(v44) = v48 & ( ~ in(v45, v43) | ~ in(v41, v48) | in(v41, v47)) & ( ~ in(v41, v47) | (in(v45, v43) & in(v41, v48))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v42) = v43) | ~ (relation_dom_restriction(v44, v41) = v45) | ~ relation(v44) | ~ relation(v42) | ~ function(v44) | ~ function(v42) | ? [v46] : ? [v47] : ? [v48] : ? [v49] : ? [v50] : (relation_dom(v44) = v46 & set_intersection2(v46, v41) = v47 & ( ~ (v47 = v43) | v45 = v42 | ( ~ (v50 = v49) & apply(v44, v48) = v50 & apply(v42, v48) = v49 & in(v48, v43))) & ( ~ (v45 = v42) | (v47 = v43 & ! [v51] : ! [v52] : ( ~ (apply(v44, v51) = v52) | ~ in(v51, v43) | apply(v42, v51) = v52) & ! [v51] : ! [v52] : ( ~ (apply(v42, v51) = v52) | ~ in(v51, v43) | apply(v44, v51) = v52))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v41) = v42) | ~ (relation_image(v41, v43) = v44) | ~ relation(v41) | ~ function(v41) | ~ in(v45, v44) | ? [v46] : (apply(v41, v46) = v45 & in(v46, v43) & in(v46, v42))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v41) = v42) | ~ (ordered_pair(v43, v44) = v45) | ~ relation(v41) | ~ function(v41) | ~ in(v43, v42) | ? [v46] : (apply(v41, v43) = v46 & ( ~ (v46 = v44) | in(v45, v41)) & (v46 = v44 | ~ in(v45, v41)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v41) = v42) | ~ (ordered_pair(v43, v44) = v45) | ~ relation(v41) | ~ in(v45, v41) | in(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (apply(v44, v42) = v45) | ~ (relation_dom_restriction(v43, v41) = v44) | ~ relation(v43) | ~ function(v43) | ~ in(v42, v41) | apply(v43, v42) = v45) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (apply(v44, v42) = v45) | ~ (relation_dom_restriction(v43, v41) = v44) | ~ relation(v43) | ~ function(v43) | ? [v46] : ? [v47] : (relation_dom(v44) = v46 & apply(v43, v42) = v47 & (v47 = v45 | ~ in(v42, v46)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (apply(v43, v42) = v45) | ~ (relation_dom_restriction(v43, v41) = v44) | ~ relation(v43) | ~ function(v43) | ? [v46] : ? [v47] : (relation_dom(v44) = v46 & apply(v44, v42) = v47 & (v47 = v45 | ~ in(v42, v46)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (apply(v43, v41) = v45) | ~ (ordered_pair(v41, v42) = v44) | ~ relation(v43) | ~ function(v43) | ? [v46] : (relation_dom(v43) = v46 & ( ~ (v45 = v42) | ~ in(v41, v46) | in(v44, v43)) & ( ~ in(v44, v43) | (v45 = v42 & in(v41, v46))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (apply(v43, v41) = v44) | ~ (apply(v42, v44) = v45) | ~ relation(v43) | ~ relation(v42) | ~ function(v43) | ~ function(v42) | ? [v46] : ? [v47] : ? [v48] : (relation_composition(v43, v42) = v46 & relation_dom(v46) = v47 & apply(v46, v41) = v48 & (v48 = v45 | ~ in(v41, v47)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (identity_relation(v41) = v42) | ~ (ordered_pair(v43, v44) = v45) | ~ relation(v42) | ~ in(v45, v42) | in(v43, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (ordered_pair(v43, v44) = v45) | ~ subset(v41, v42) | ~ relation(v42) | ~ relation(v41) | ~ in(v45, v41) | in(v45, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (meet_commut(v41, v43, v44) = v45) | ~ (the_carrier(v41) = v42) | ~ meet_absorbing(v41) | ~ latt_str(v41) | ~ meet_commutative(v41) | ~ element(v44, v42) | ~ element(v43, v42) | below(v41, v45, v43) | empty_carrier(v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_intersection2(v42, v43) = v45) | ~ (set_intersection2(v41, v43) = v44) | ~ subset(v41, v42) | subset(v44, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_intersection2(v42, v43) = v45) | ~ (powerset(v41) = v44) | ~ element(v43, v44) | ~ element(v42, v44) | subset_intersection2(v41, v42, v43) = v45) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v43, v42) = v45) | ~ (cartesian_product2(v43, v41) = v44) | ~ subset(v41, v42) | subset(v44, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v43, v42) = v45) | ~ (cartesian_product2(v43, v41) = v44) | ~ subset(v41, v42) | ? [v46] : ? [v47] : (cartesian_product2(v42, v43) = v47 & cartesian_product2(v41, v43) = v46 & subset(v46, v47))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v43, v42) = v45) | ~ (cartesian_product2(v41, v43) = v44) | ~ subset(v41, v42) | ? [v46] : ? [v47] : (cartesian_product2(v43, v41) = v47 & cartesian_product2(v42, v43) = v46 & subset(v47, v45) & subset(v44, v46))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v43, v41) = v45) | ~ (cartesian_product2(v42, v43) = v44) | ~ subset(v41, v42) | ? [v46] : ? [v47] : (cartesian_product2(v43, v42) = v47 & cartesian_product2(v41, v43) = v46 & subset(v46, v44) & subset(v45, v47))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v42, v43) = v45) | ~ (cartesian_product2(v41, v43) = v44) | ~ subset(v41, v42) | subset(v44, v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v42, v43) = v45) | ~ (cartesian_product2(v41, v43) = v44) | ~ subset(v41, v42) | ? [v46] : ? [v47] : (cartesian_product2(v43, v42) = v47 & cartesian_product2(v43, v41) = v46 & subset(v46, v47))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v41 | ~ (unordered_triple(v42, v43, v44) = v45) | ? [v46] : ((v46 = v44 | v46 = v43 | v46 = v42 | in(v46, v41)) & ( ~ in(v46, v41) | ( ~ (v46 = v44) & ~ (v46 = v43) & ~ (v46 = v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v41 | ~ (relation_inverse_image(v42, v44) = v45) | ~ (relation_dom(v42) = v43) | ~ relation(v42) | ~ function(v42) | ? [v46] : ? [v47] : (apply(v42, v46) = v47 & ( ~ in(v47, v44) | ~ in(v46, v43) | ~ in(v46, v41)) & (in(v46, v41) | (in(v47, v44) & in(v46, v43))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v41 | ~ (relation_dom(v42) = v43) | ~ (relation_image(v42, v44) = v45) | ~ relation(v42) | ~ function(v42) | ? [v46] : ? [v47] : ? [v48] : (( ~ in(v46, v41) | ! [v49] : ( ~ (apply(v42, v49) = v46) | ~ in(v49, v44) | ~ in(v49, v43))) & (in(v46, v41) | (v48 = v46 & apply(v42, v47) = v46 & in(v47, v44) & in(v47, v43))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v41 | ~ (pair_second(v42) = v43) | ~ (ordered_pair(v44, v45) = v42) | ? [v46] : ? [v47] : ( ~ (v47 = v41) & ordered_pair(v46, v47) = v42)) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v41 | ~ (pair_first(v42) = v43) | ~ (ordered_pair(v44, v45) = v42) | ? [v46] : ? [v47] : ( ~ (v46 = v41) & ordered_pair(v46, v47) = v42)) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_composition(v44, v42) = v45) | ~ (relation_dom(v42) = v43) | ~ relation(v44) | ~ relation(v42) | ~ function(v44) | ~ function(v42) | ? [v46] : ? [v47] : ? [v48] : (relation_dom(v45) = v46 & relation_dom(v44) = v47 & apply(v44, v41) = v48 & ( ~ in(v48, v43) | ~ in(v41, v47) | in(v41, v46)) & ( ~ in(v41, v46) | (in(v48, v43) & in(v41, v47))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v44) = v45) | ~ (relation_dom(v42) = v43) | ~ relation(v44) | ~ relation(v42) | ~ function(v44) | ~ function(v42) | ? [v46] : ? [v47] : ? [v48] : (relation_composition(v44, v42) = v46 & relation_dom(v46) = v47 & apply(v44, v41) = v48 & ( ~ in(v48, v43) | ~ in(v41, v45) | in(v41, v47)) & ( ~ in(v41, v47) | (in(v48, v43) & in(v41, v45))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v43) = v45) | ~ (powerset(v42) = v44) | ~ relation(v43) | ~ function(v43) | ? [v46] : ? [v47] : ? [v48] : (powerset(v45) = v47 & powerset(v44) = v46 & ( ~ element(v41, v46) | ( ! [v49] : ! [v50] : ( ~ (relation_image(v43, v49) = v50) | ~ in(v50, v41) | ~ in(v49, v47) | in(v49, v48)) & ! [v49] : ! [v50] : ( ~ (relation_image(v43, v49) = v50) | ~ in(v49, v48) | in(v50, v41)) & ! [v49] : ! [v50] : ( ~ (relation_image(v43, v49) = v50) | ~ in(v49, v48) | in(v49, v47)))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (relation_composition(v41, v42) = v43) | ~ relation(v44) | ~ relation(v42) | ~ relation(v41) | ? [v45] : ? [v46] : ? [v47] : ? [v48] : ? [v49] : ? [v50] : (ordered_pair(v45, v46) = v47 & ( ~ in(v47, v44) | ( ! [v51] : ! [v52] : ( ~ (ordered_pair(v51, v46) = v52) | ~ in(v52, v42) | ? [v53] : (ordered_pair(v45, v51) = v53 & ~ in(v53, v41))) & ! [v51] : ! [v52] : ( ~ (ordered_pair(v45, v51) = v52) | ~ in(v52, v41) | ? [v53] : (ordered_pair(v51, v46) = v53 & ~ in(v53, v42))))) & (in(v47, v44) | (ordered_pair(v48, v46) = v50 & ordered_pair(v45, v48) = v49 & in(v50, v42) & in(v49, v41))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (relation_rng_restriction(v41, v42) = v43) | ~ relation(v44) | ~ relation(v42) | ? [v45] : ? [v46] : ? [v47] : (ordered_pair(v45, v46) = v47 & ( ~ in(v47, v44) | ~ in(v47, v42) | ~ in(v46, v41)) & (in(v47, v44) | (in(v47, v42) & in(v46, v41))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (relation_dom_restriction(v41, v42) = v44) | ~ relation(v43) | ~ relation(v41) | ? [v45] : ? [v46] : ? [v47] : (ordered_pair(v45, v46) = v47 & ( ~ in(v47, v43) | ~ in(v47, v41) | ~ in(v45, v42)) & (in(v47, v43) | (in(v47, v41) & in(v45, v42))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (the_carrier(v41) = v42) | ~ below(v41, v44, v43) | ~ below(v41, v43, v44) | ~ join_semilatt_str(v41) | ~ join_commutative(v41) | ~ element(v44, v42) | ~ element(v43, v42) | empty_carrier(v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | v44 = v41 | ~ (unordered_pair(v41, v42) = v43) | ~ in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (relation_rng_as_subset(v41, v42, v43) = v44) | ~ relation_of2_as_subset(v43, v41, v42) | ? [v45] : (in(v45, v42) & ! [v46] : ! [v47] : ( ~ (ordered_pair(v46, v45) = v47) | ~ in(v47, v43)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (complements_of_subsets(v41, v43) = v44) | ~ (complements_of_subsets(v41, v42) = v43) | ? [v45] : ? [v46] : (powerset(v45) = v46 & powerset(v41) = v45 & ~ element(v42, v46))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (subset_complement(v41, v43) = v44) | ~ (subset_complement(v41, v42) = v43) | ? [v45] : (powerset(v41) = v45 & ~ element(v42, v45))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (set_difference(v42, v41) = v43) | ~ (set_union2(v41, v43) = v44) | ~ subset(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (singleton(v41) = v43) | ~ (set_union2(v43, v42) = v44) | ~ in(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (relation_dom_as_subset(v42, v41, v43) = v44) | ~ relation_of2_as_subset(v43, v42, v41) | ? [v45] : (in(v45, v42) & ! [v46] : ! [v47] : ( ~ (ordered_pair(v45, v46) = v47) | ~ in(v47, v43)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (apply(v43, v42) = v44) | ~ (identity_relation(v41) = v43) | ~ in(v42, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | v42 = empty_set | ~ (relation_dom_as_subset(v41, v42, v43) = v44) | ~ quasi_total(v43, v41, v42) | ~ relation_of2_as_subset(v43, v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (set_difference(v41, v43) = v44) | ~ (singleton(v42) = v43) | in(v42, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (relation_inverse_image(v42, v41) = v43) | ~ (relation_image(v42, v43) = v44) | ~ relation(v42) | ~ function(v42) | ? [v45] : (relation_rng(v42) = v45 & ~ subset(v41, v45))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = empty_set | ~ (relation_dom(v41) = v42) | ~ (apply(v41, v43) = v44) | ~ relation(v41) | ~ function(v41) | in(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (singleton(v41) = v44) | ~ (unordered_pair(v42, v43) = v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (ordered_pair(v43, v42) = v44) | ~ antisymmetric(v41) | ~ relation(v41) | ~ in(v44, v41) | ? [v45] : (ordered_pair(v42, v43) = v45 & ~ in(v45, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (ordered_pair(v42, v43) = v44) | ~ antisymmetric(v41) | ~ relation(v41) | ~ in(v44, v41) | ? [v45] : (ordered_pair(v43, v42) = v45 & ~ in(v45, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (meet_of_subsets(v44, v43) = v42) | ~ (meet_of_subsets(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (union_of_subsets(v44, v43) = v42) | ~ (union_of_subsets(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (complements_of_subsets(v44, v43) = v42) | ~ (complements_of_subsets(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (relation_composition(v44, v43) = v42) | ~ (relation_composition(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (relation_restriction(v44, v43) = v42) | ~ (relation_restriction(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (subset_complement(v44, v43) = v42) | ~ (subset_complement(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (set_difference(v44, v43) = v42) | ~ (set_difference(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (fiber(v44, v43) = v42) | ~ (fiber(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (singleton(v42) = v44) | ~ (singleton(v41) = v43) | ~ subset(v43, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (singleton(v41) = v44) | ~ (unordered_pair(v42, v43) = v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (relation_inverse_image(v44, v43) = v42) | ~ (relation_inverse_image(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (relation_rng_restriction(v44, v43) = v42) | ~ (relation_rng_restriction(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (relation_image(v44, v43) = v42) | ~ (relation_image(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (apply(v44, v43) = v42) | ~ (apply(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (relation_dom_restriction(v44, v43) = v42) | ~ (relation_dom_restriction(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (ordered_pair(v44, v43) = v42) | ~ (ordered_pair(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (set_intersection2(v44, v43) = v42) | ~ (set_intersection2(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (set_union2(v44, v43) = v42) | ~ (set_union2(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (unordered_pair(v44, v43) = v42) | ~ (unordered_pair(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = v41 | ~ (cartesian_product2(v44, v43) = v42) | ~ (cartesian_product2(v44, v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = empty_set | ~ (meet_of_subsets(v41, v43) = v44) | ~ (complements_of_subsets(v41, v42) = v43) | ? [v45] : ? [v46] : ? [v47] : ? [v48] : ? [v49] : (subset_difference(v41, v47, v48) = v49 & union_of_subsets(v41, v42) = v48 & cast_to_subset(v41) = v47 & powerset(v45) = v46 & powerset(v41) = v45 & (v49 = v44 | ~ element(v42, v46)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = empty_set | ~ (union_of_subsets(v41, v43) = v44) | ~ (complements_of_subsets(v41, v42) = v43) | ? [v45] : ? [v46] : ? [v47] : ? [v48] : ? [v49] : (subset_difference(v41, v47, v48) = v49 & meet_of_subsets(v41, v42) = v48 & cast_to_subset(v41) = v47 & powerset(v45) = v46 & powerset(v41) = v45 & (v49 = v44 | ~ element(v42, v46)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = empty_set | ~ quasi_total(v44, v41, v42) | ~ relation_of2_as_subset(v44, v41, v42) | ~ subset(v42, v43) | ~ function(v44) | quasi_total(v44, v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v42 = empty_set | ~ quasi_total(v44, v41, v42) | ~ relation_of2_as_subset(v44, v41, v42) | ~ subset(v42, v43) | ~ function(v44) | relation_of2_as_subset(v44, v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : (v41 = empty_set | ~ (set_meet(v41) = v42) | ~ in(v44, v41) | ~ in(v43, v42) | in(v43, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (subset_difference(v41, v42, v43) = v44) | ? [v45] : ? [v46] : (set_difference(v42, v43) = v46 & powerset(v41) = v45 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (subset_difference(v41, v42, v43) = v44) | ? [v45] : (powerset(v41) = v45 & ( ~ element(v43, v45) | ~ element(v42, v45) | element(v44, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_as_subset(v41, v42, v43) = v44) | ~ relation_of2(v43, v41, v42) | relation_rng(v43) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_as_subset(v41, v42, v43) = v44) | ~ relation_of2(v43, v41, v42) | ? [v45] : (powerset(v42) = v45 & element(v44, v45))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_as_subset(v41, v42, v43) = v42) | ~ relation_of2_as_subset(v43, v41, v42) | ~ in(v44, v42) | ? [v45] : ? [v46] : (ordered_pair(v45, v44) = v46 & in(v46, v43))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (function_inverse(v43) = v44) | ~ relation_isomorphism(v41, v42, v43) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ function(v43) | relation_isomorphism(v42, v41, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v43, v42) = v44) | ~ (identity_relation(v41) = v43) | ~ relation(v42) | relation_dom_restriction(v42, v41) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v41, v43) = v44) | ~ (relation_rng(v41) = v42) | ~ relation(v43) | ~ relation(v41) | ? [v45] : (relation_rng(v44) = v45 & relation_image(v43, v42) = v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v41, v43) = v44) | ~ (relation_dom(v41) = v42) | ~ relation(v43) | ~ relation(v41) | ? [v45] : (relation_dom(v44) = v45 & subset(v45, v42))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (subset_complement(v41, v43) = v44) | ~ in(v42, v44) | ~ in(v42, v43) | ? [v45] : (powerset(v41) = v45 & ~ element(v43, v45))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v43, v42) = v44) | ~ (set_union2(v41, v42) = v43) | set_difference(v41, v42) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v41) = v43) | ~ (set_union2(v41, v43) = v44) | set_union2(v41, v42) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v41, v43) = v44) | ~ (set_difference(v41, v42) = v43) | set_intersection2(v41, v42) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v41, v42) = v43) | ~ in(v44, v43) | ~ in(v44, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v41, v42) = v43) | ~ in(v44, v43) | in(v44, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v41, v42) = v43) | ~ in(v44, v41) | in(v44, v43) | in(v44, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (union(v42) = v44) | ~ (powerset(v41) = v43) | ? [v45] : ? [v46] : (union_of_subsets(v41, v42) = v46 & powerset(v43) = v45 & (v46 = v44 | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (union(v41) = v42) | ~ in(v44, v41) | ~ in(v43, v44) | in(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (meet(v41, v42, v43) = v44) | ~ meet_semilatt_str(v41) | ~ meet_commutative(v41) | empty_carrier(v41) | ? [v45] : ? [v46] : (meet_commut(v41, v42, v43) = v46 & the_carrier(v41) = v45 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (meet(v41, v42, v43) = v44) | ~ meet_semilatt_str(v41) | empty_carrier(v41) | ? [v45] : (the_carrier(v41) = v45 & ( ~ element(v43, v45) | ~ element(v42, v45) | element(v44, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (fiber(v41, v42) = v43) | ~ (ordered_pair(v42, v42) = v44) | ~ relation(v41) | ~ in(v42, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_meet(v42) = v44) | ~ (powerset(v41) = v43) | ? [v45] : ? [v46] : (meet_of_subsets(v41, v42) = v46 & powerset(v43) = v45 & (v46 = v44 | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (join(v41, v43, v44) = v44) | ~ (the_carrier(v41) = v42) | ~ join_semilatt_str(v41) | ~ element(v44, v42) | ~ element(v43, v42) | below(v41, v43, v44) | empty_carrier(v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (join(v41, v42, v43) = v44) | ~ join_semilatt_str(v41) | ~ join_commutative(v41) | empty_carrier(v41) | ? [v45] : ? [v46] : (the_carrier(v41) = v45 & join_commut(v41, v42, v43) = v46 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (join(v41, v42, v43) = v44) | ~ join_semilatt_str(v41) | empty_carrier(v41) | ? [v45] : (the_carrier(v41) = v45 & ( ~ element(v43, v45) | ~ element(v42, v45) | element(v44, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_as_subset(v42, v41, v43) = v42) | ~ relation_of2_as_subset(v43, v42, v41) | ~ in(v44, v42) | ? [v45] : ? [v46] : (ordered_pair(v44, v45) = v46 & in(v46, v43))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_as_subset(v41, v42, v43) = v44) | ~ relation_of2(v43, v41, v42) | relation_dom(v43) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_as_subset(v41, v42, v43) = v44) | ~ relation_of2(v43, v41, v42) | ? [v45] : (powerset(v41) = v45 & element(v44, v45))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng(v43) = v44) | ~ relation_of2_as_subset(v43, v41, v42) | subset(v44, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng(v43) = v44) | ~ relation_of2_as_subset(v43, v41, v42) | ? [v45] : (relation_dom(v43) = v45 & subset(v45, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng(v42) = v43) | ~ (set_intersection2(v43, v41) = v44) | ~ relation(v42) | ? [v45] : (relation_rng(v45) = v44 & relation_rng_restriction(v41, v42) = v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng(v41) = v43) | ~ (relation_dom(v41) = v42) | ~ (set_union2(v42, v43) = v44) | ~ relation(v41) | relation_field(v41) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng(v41) = v43) | ~ (relation_dom(v41) = v42) | ~ (cartesian_product2(v42, v43) = v44) | ~ relation(v41) | subset(v41, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng(v41) = v42) | ~ (relation_image(v43, v42) = v44) | ~ relation(v43) | ~ relation(v41) | ? [v45] : (relation_composition(v41, v43) = v45 & relation_rng(v45) = v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_triple(v41, v42, v43) = v44) | in(v43, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_triple(v41, v42, v43) = v44) | in(v42, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_triple(v41, v42, v43) = v44) | in(v41, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_inverse_image(v42, v43) = v44) | ~ (relation_image(v42, v41) = v43) | ~ relation(v42) | subset(v41, v44) | ? [v45] : (relation_dom(v42) = v45 & ~ subset(v41, v45))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_inverse_image(v42, v41) = v43) | ~ (relation_image(v42, v43) = v44) | ~ relation(v42) | ~ function(v42) | subset(v44, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_inverse_image(v41, v42) = v43) | ~ relation(v41) | ~ in(v44, v43) | ? [v45] : ? [v46] : (ordered_pair(v44, v45) = v46 & in(v46, v41) & in(v45, v42))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_field(v41) = v42) | ~ (ordered_pair(v43, v43) = v44) | ~ reflexive(v41) | ~ relation(v41) | ~ in(v43, v42) | in(v44, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v41, v43) = v44) | ~ (relation_dom_restriction(v42, v41) = v43) | ~ relation(v42) | relation_restriction(v42, v41) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ (relation_dom_restriction(v43, v41) = v44) | ~ relation(v42) | relation_restriction(v42, v41) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom(v43) = v44) | ~ relation_of2_as_subset(v43, v41, v42) | subset(v44, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom(v43) = v44) | ~ relation_of2_as_subset(v43, v41, v42) | ? [v45] : (relation_rng(v43) = v45 & subset(v45, v42))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom(v42) = v43) | ~ (set_intersection2(v43, v41) = v44) | ~ relation(v42) | ? [v45] : (relation_dom(v45) = v44 & relation_dom_restriction(v42, v41) = v45)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_image(v41, v42) = v43) | ~ relation(v41) | ~ in(v44, v43) | ? [v45] : ? [v46] : (ordered_pair(v45, v44) = v46 & in(v46, v41) & in(v45, v42))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (identity_relation(v41) = v42) | ~ (ordered_pair(v43, v43) = v44) | ~ relation(v42) | ~ in(v43, v41) | in(v44, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (ordered_pair(v43, v43) = v44) | ~ is_reflexive_in(v41, v42) | ~ relation(v41) | ~ in(v43, v42) | in(v44, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (subset_intersection2(v41, v43, v42) = v44) | ? [v45] : ? [v46] : (subset_intersection2(v41, v42, v43) = v46 & powerset(v41) = v45 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (subset_intersection2(v41, v42, v43) = v44) | ? [v45] : ? [v46] : (subset_intersection2(v41, v43, v42) = v46 & powerset(v41) = v45 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (subset_intersection2(v41, v42, v43) = v44) | ? [v45] : ? [v46] : (set_intersection2(v42, v43) = v46 & powerset(v41) = v45 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (subset_intersection2(v41, v42, v43) = v44) | ? [v45] : (powerset(v41) = v45 & ( ~ element(v43, v45) | ~ element(v42, v45) | element(v44, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (meet_commut(v41, v43, v42) = v44) | ~ meet_semilatt_str(v41) | ~ meet_commutative(v41) | empty_carrier(v41) | ? [v45] : ? [v46] : (meet_commut(v41, v42, v43) = v46 & the_carrier(v41) = v45 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (meet_commut(v41, v42, v43) = v44) | ~ meet_semilatt_str(v41) | ~ meet_commutative(v41) | empty_carrier(v41) | ? [v45] : ? [v46] : (meet(v41, v42, v43) = v46 & the_carrier(v41) = v45 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (meet_commut(v41, v42, v43) = v44) | ~ meet_semilatt_str(v41) | ~ meet_commutative(v41) | empty_carrier(v41) | ? [v45] : ? [v46] : (meet_commut(v41, v43, v42) = v46 & the_carrier(v41) = v45 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (meet_commut(v41, v42, v43) = v44) | ~ meet_semilatt_str(v41) | ~ meet_commutative(v41) | empty_carrier(v41) | ? [v45] : (the_carrier(v41) = v45 & ( ~ element(v43, v45) | ~ element(v42, v45) | element(v44, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ subset(v41, v43) | ~ subset(v41, v42) | subset(v41, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v41, v43) = v44) | ~ (cartesian_product2(v42, v42) = v43) | ~ relation(v41) | relation_restriction(v41, v42) = v44) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v41, v42) = v43) | ~ disjoint(v41, v42) | ~ in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v41, v42) = v43) | ~ in(v44, v43) | in(v44, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v41, v42) = v43) | ~ in(v44, v43) | in(v44, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v41, v42) = v43) | ~ in(v44, v42) | ~ in(v44, v41) | in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (join_commut(v41, v43, v42) = v44) | ~ join_semilatt_str(v41) | ~ join_commutative(v41) | empty_carrier(v41) | ? [v45] : ? [v46] : (the_carrier(v41) = v45 & join_commut(v41, v42, v43) = v46 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (join_commut(v41, v42, v43) = v44) | ~ join_semilatt_str(v41) | ~ join_commutative(v41) | empty_carrier(v41) | ? [v45] : ? [v46] : (join(v41, v42, v43) = v46 & the_carrier(v41) = v45 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (join_commut(v41, v42, v43) = v44) | ~ join_semilatt_str(v41) | ~ join_commutative(v41) | empty_carrier(v41) | ? [v45] : ? [v46] : (the_carrier(v41) = v45 & join_commut(v41, v43, v42) = v46 & (v46 = v44 | ~ element(v43, v45) | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (join_commut(v41, v42, v43) = v44) | ~ join_semilatt_str(v41) | ~ join_commutative(v41) | empty_carrier(v41) | ? [v45] : (the_carrier(v41) = v45 & ( ~ element(v43, v45) | ~ element(v42, v45) | element(v44, v45)))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v41, v43) = v44) | ~ subset(v43, v42) | ~ subset(v41, v42) | subset(v44, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v41, v42) = v43) | ~ in(v44, v43) | in(v44, v42) | in(v44, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v41, v42) = v43) | ~ in(v44, v42) | in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v41, v42) = v43) | ~ in(v44, v41) | in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_pair(v41, v42) = v44) | ~ subset(v44, v43) | in(v42, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_pair(v41, v42) = v44) | ~ subset(v44, v43) | in(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_pair(v41, v42) = v44) | ~ in(v42, v43) | ~ in(v41, v43) | subset(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (cartesian_product2(v41, v43) = v44) | ~ relation(v42) | empty(v41) | ? [v45] : ( ! [v46] : ! [v47] : ! [v48] : ( ~ (ordered_pair(v47, v48) = v46) | ~ in(v48, v47) | ~ in(v47, v41) | ~ in(v46, v44) | in(v46, v45) | ? [v49] : ? [v50] : (ordered_pair(v48, v49) = v50 & in(v49, v47) & ~ in(v50, v42))) & ! [v46] : ( ~ in(v46, v45) | in(v46, v44)) & ! [v46] : ( ~ in(v46, v45) | ? [v47] : ? [v48] : (ordered_pair(v47, v48) = v46 & in(v48, v47) & in(v47, v41) & ! [v49] : ! [v50] : ( ~ (ordered_pair(v48, v49) = v50) | ~ in(v49, v47) | in(v50, v42)))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (cartesian_product2(v41, v42) = v44) | ~ relation_of2(v43, v41, v42) | subset(v43, v44)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (cartesian_product2(v41, v42) = v44) | ~ relation_of2_as_subset(v43, v41, v42) | ? [v45] : (powerset(v44) = v45 & element(v43, v45))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (cartesian_product2(v41, v42) = v44) | ~ subset(v43, v44) | relation_of2(v43, v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (cartesian_product2(v41, v42) = v43) | ~ in(v44, v43) | ? [v45] : ? [v46] : (ordered_pair(v45, v46) = v44 & in(v46, v42) & in(v45, v41))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (cartesian_product2(v41, v41) = v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v43) | ? [v45] : ( ! [v46] : ! [v47] : ! [v48] : ! [v49] : ! [v50] : ! [v51] : ( ~ (apply(v43, v48) = v50) | ~ (apply(v43, v47) = v49) | ~ (ordered_pair(v49, v50) = v51) | ~ in(v51, v42) | ~ in(v46, v44) | in(v46, v45) | ? [v52] : ( ~ (v52 = v46) & ordered_pair(v47, v48) = v52)) & ! [v46] : ! [v47] : ! [v48] : ( ~ (ordered_pair(v47, v48) = v46) | ~ in(v46, v44) | in(v46, v45) | ? [v49] : ? [v50] : ? [v51] : (apply(v43, v48) = v50 & apply(v43, v47) = v49 & ordered_pair(v49, v50) = v51 & ~ in(v51, v42))) & ! [v46] : ( ~ in(v46, v45) | in(v46, v44)) & ! [v46] : ( ~ in(v46, v45) | ? [v47] : ? [v48] : ? [v49] : ? [v50] : ? [v51] : (apply(v43, v48) = v50 & apply(v43, v47) = v49 & ordered_pair(v49, v50) = v51 & ordered_pair(v47, v48) = v46 & in(v51, v42))))) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v43) = v44) | ~ empty(v43) | ~ element(v42, v44) | ~ in(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v43) = v44) | ~ element(v42, v44) | ~ in(v41, v42) | element(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v41) = v43) | ~ element(v42, v43) | ~ in(v44, v42) | in(v44, v41)) & ! [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ relation_of2_as_subset(v44, v43, v41) | ~ subset(v41, v42) | relation_of2_as_subset(v44, v43, v42)) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (subset_intersection2(v42, v43, v43) = v44) | ? [v45] : (powerset(v42) = v45 & ( ~ element(v43, v45) | ~ element(v41, v45)))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (set_difference(v42, v43) = v44) | ? [v45] : (( ~ in(v45, v42) | ~ in(v45, v41) | in(v45, v43)) & (in(v45, v41) | (in(v45, v42) & ~ in(v45, v43))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (fiber(v42, v43) = v44) | ~ relation(v42) | ? [v45] : ? [v46] : (ordered_pair(v45, v43) = v46 & (v45 = v43 | ~ in(v46, v42) | ~ in(v45, v41)) & (in(v45, v41) | ( ~ (v45 = v43) & in(v46, v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (relation_inverse_image(v42, v43) = v44) | ~ relation(v42) | ? [v45] : ? [v46] : ? [v47] : (( ~ in(v45, v41) | ! [v48] : ! [v49] : ( ~ (ordered_pair(v45, v48) = v49) | ~ in(v49, v42) | ~ in(v48, v43))) & (in(v45, v41) | (ordered_pair(v45, v46) = v47 & in(v47, v42) & in(v46, v43))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (relation_image(v42, v43) = v44) | ~ relation(v42) | ? [v45] : ? [v46] : ? [v47] : (( ~ in(v45, v41) | ! [v48] : ! [v49] : ( ~ (ordered_pair(v48, v45) = v49) | ~ in(v49, v42) | ~ in(v48, v43))) & (in(v45, v41) | (ordered_pair(v46, v45) = v47 & in(v47, v42) & in(v46, v43))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (set_intersection2(v42, v43) = v44) | ? [v45] : (( ~ in(v45, v43) | ~ in(v45, v42) | ~ in(v45, v41)) & (in(v45, v41) | (in(v45, v43) & in(v45, v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (set_union2(v42, v43) = v44) | ? [v45] : (( ~ in(v45, v41) | ( ~ in(v45, v43) & ~ in(v45, v42))) & (in(v45, v43) | in(v45, v42) | in(v45, v41)))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (unordered_pair(v42, v43) = v44) | ? [v45] : ((v45 = v43 | v45 = v42 | in(v45, v41)) & ( ~ in(v45, v41) | ( ~ (v45 = v43) & ~ (v45 = v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : (v44 = v41 | ~ (cartesian_product2(v42, v43) = v44) | ? [v45] : ? [v46] : ? [v47] : ? [v48] : (( ~ in(v45, v41) | ! [v49] : ! [v50] : ( ~ (ordered_pair(v49, v50) = v45) | ~ in(v50, v43) | ~ in(v49, v42))) & (in(v45, v41) | (v48 = v45 & ordered_pair(v46, v47) = v45 & in(v47, v43) & in(v46, v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v43, v42) = v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v43) | ~ function(v42) | ? [v45] : ? [v46] : ? [v47] : ? [v48] : (relation_dom(v44) = v45 & apply(v44, v41) = v46 & apply(v43, v41) = v47 & apply(v42, v47) = v48 & (v48 = v46 | ~ in(v41, v45)))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : (relation_field(v44) = v45 & relation_field(v43) = v46 & ( ~ in(v41, v45) | (in(v41, v46) & in(v41, v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ relation(v43) | ? [v45] : (cartesian_product2(v42, v42) = v45 & ( ~ in(v41, v45) | ~ in(v41, v43) | in(v41, v44)) & ( ~ in(v41, v44) | (in(v41, v45) & in(v41, v43))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_inverse_image(v43, v42) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : ? [v47] : (relation_rng(v43) = v45 & ( ~ in(v41, v44) | (ordered_pair(v41, v46) = v47 & in(v47, v43) & in(v46, v45) & in(v46, v42))) & (in(v41, v44) | ! [v48] : ! [v49] : ( ~ (ordered_pair(v41, v48) = v49) | ~ in(v49, v43) | ~ in(v48, v45) | ~ in(v48, v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : (relation_rng(v44) = v45 & relation_rng(v43) = v46 & ( ~ in(v41, v46) | ~ in(v41, v42) | in(v41, v45)) & ( ~ in(v41, v45) | (in(v41, v46) & in(v41, v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_image(v43, v42) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : ? [v47] : (relation_dom(v43) = v45 & ( ~ in(v41, v44) | (ordered_pair(v46, v41) = v47 & in(v47, v43) & in(v46, v45) & in(v46, v42))) & (in(v41, v44) | ! [v48] : ! [v49] : ( ~ (ordered_pair(v48, v41) = v49) | ~ in(v49, v43) | ~ in(v48, v45) | ~ in(v48, v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_restriction(v43, v42) = v44) | ~ relation(v43) | ~ function(v43) | ? [v45] : ? [v46] : (relation_dom(v44) = v45 & relation_dom(v43) = v46 & ( ~ in(v41, v46) | ~ in(v41, v42) | in(v41, v45)) & ( ~ in(v41, v45) | (in(v41, v46) & in(v41, v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_restriction(v43, v42) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : (relation_dom(v44) = v45 & relation_dom(v43) = v46 & ( ~ in(v41, v46) | ~ in(v41, v42) | in(v41, v45)) & ( ~ in(v41, v45) | (in(v41, v46) & in(v41, v42))))) & ? [v41] : ! [v42] : ! [v43] : ! [v44] : ( ~ (cartesian_product2(v42, v43) = v44) | relation(v41) | ? [v45] : (powerset(v44) = v45 & ~ element(v41, v45))) & ! [v41] : ! [v42] : ! [v43] : (v43 = v42 | ~ (relation_inverse(v41) = v42) | ~ relation(v43) | ~ relation(v41) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : (ordered_pair(v45, v44) = v47 & ordered_pair(v44, v45) = v46 & ( ~ in(v47, v41) | ~ in(v46, v43)) & (in(v47, v41) | in(v46, v43)))) & ! [v41] : ! [v42] : ! [v43] : (v43 = v42 | ~ (inclusion_relation(v41) = v43) | ~ (relation_field(v42) = v41) | ~ relation(v42) | ? [v44] : ? [v45] : ? [v46] : (ordered_pair(v44, v45) = v46 & in(v45, v41) & in(v44, v41) & ( ~ subset(v44, v45) | ~ in(v46, v42)) & (subset(v44, v45) | in(v46, v42)))) & ! [v41] : ! [v42] : ! [v43] : (v43 = v42 | ~ (relation_dom(v42) = v41) | ~ (identity_relation(v41) = v43) | ~ relation(v42) | ~ function(v42) | ? [v44] : ? [v45] : ( ~ (v45 = v44) & apply(v42, v44) = v45 & in(v44, v41))) & ! [v41] : ! [v42] : ! [v43] : (v43 = v42 | ~ (identity_relation(v41) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : ? [v46] : (ordered_pair(v44, v45) = v46 & ( ~ (v45 = v44) | ~ in(v46, v42) | ~ in(v44, v41)) & (in(v46, v42) | (v45 = v44 & in(v44, v41))))) & ! [v41] : ! [v42] : ! [v43] : (v43 = v42 | ~ (set_union2(v41, v42) = v43) | ~ subset(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : (v43 = v42 | ~ epsilon_connected(v41) | ~ in(v43, v41) | ~ in(v42, v41) | in(v43, v42) | in(v42, v43)) & ! [v41] : ! [v42] : ! [v43] : (v43 = v41 | v41 = empty_set | ~ (singleton(v42) = v43) | ~ subset(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (set_difference(v41, v42) = v43) | ~ disjoint(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (inclusion_relation(v41) = v42) | ~ (relation_field(v42) = v43) | ~ relation(v42)) & ! [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (singleton(v41) = v42) | ~ in(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (relation_dom(v42) = v43) | ~ (identity_relation(v41) = v42) | ~ relation(v42) | ~ function(v42)) & ! [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (set_intersection2(v41, v42) = v43) | ~ subset(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : (v43 = empty_set | ~ (set_difference(v41, v42) = v43) | ~ subset(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : (v43 = empty_set | ~ (relation_dom_as_subset(empty_set, v41, v42) = v43) | ~ quasi_total(v42, empty_set, v41) | ~ relation_of2_as_subset(v42, empty_set, v41)) & ! [v41] : ! [v42] : ! [v43] : (v43 = empty_set | ~ (relation_field(v41) = v42) | ~ well_founded_relation(v41) | ~ subset(v43, v42) | ~ relation(v41) | ? [v44] : ? [v45] : (fiber(v41, v44) = v45 & disjoint(v45, v43) & in(v44, v43))) & ! [v41] : ! [v42] : ! [v43] : (v43 = empty_set | ~ (set_intersection2(v41, v42) = v43) | ~ disjoint(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : (v43 = empty_set | ~ is_well_founded_in(v41, v42) | ~ subset(v43, v42) | ~ relation(v41) | ? [v44] : ? [v45] : (fiber(v41, v44) = v45 & disjoint(v45, v43) & in(v44, v43))) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (function_inverse(v43) = v42) | ~ (function_inverse(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (relation_inverse(v43) = v42) | ~ (relation_inverse(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (union(v43) = v42) | ~ (union(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (cast_to_subset(v43) = v42) | ~ (cast_to_subset(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (cast_as_carrier_subset(v43) = v42) | ~ (cast_as_carrier_subset(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (pair_second(v43) = v42) | ~ (pair_second(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (the_L_meet(v43) = v42) | ~ (the_L_meet(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (inclusion_relation(v43) = v42) | ~ (inclusion_relation(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (set_meet(v43) = v42) | ~ (set_meet(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (singleton(v43) = v42) | ~ (singleton(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (succ(v43) = v42) | ~ (succ(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (pair_first(v43) = v42) | ~ (pair_first(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (the_L_join(v43) = v42) | ~ (the_L_join(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (relation_rng(v43) = v42) | ~ (relation_rng(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (relation_field(v43) = v42) | ~ (relation_field(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (relation_dom(v43) = v42) | ~ (relation_dom(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (identity_relation(v43) = v42) | ~ (identity_relation(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (the_carrier(v43) = v42) | ~ (the_carrier(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = v41 | ~ (powerset(v43) = v42) | ~ (powerset(v43) = v41)) & ! [v41] : ! [v42] : ! [v43] : (v42 = empty_set | v41 = empty_set | ~ (relation_dom_as_subset(v41, empty_set, v42) = v43) | ~ quasi_total(v42, v41, empty_set) | ~ relation_of2_as_subset(v42, v41, empty_set)) & ! [v41] : ! [v42] : ! [v43] : (v42 = empty_set | ~ (relation_dom_as_subset(v41, v42, v43) = v41) | ~ relation_of2_as_subset(v43, v41, v42) | quasi_total(v43, v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (meet_of_subsets(v41, v42) = v43) | ? [v44] : ? [v45] : ? [v46] : (set_meet(v42) = v46 & powerset(v44) = v45 & powerset(v41) = v44 & (v46 = v43 | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (meet_of_subsets(v41, v42) = v43) | ? [v44] : ? [v45] : (powerset(v44) = v45 & powerset(v41) = v44 & ( ~ element(v42, v45) | element(v43, v44)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (union_of_subsets(v41, v42) = v43) | ? [v44] : ? [v45] : ? [v46] : (union(v42) = v46 & powerset(v44) = v45 & powerset(v41) = v44 & (v46 = v43 | ~ element(v42, v45)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (union_of_subsets(v41, v42) = v43) | ? [v44] : ? [v45] : (powerset(v44) = v45 & powerset(v41) = v44 & ( ~ element(v42, v45) | element(v43, v44)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (complements_of_subsets(v41, v42) = v43) | ? [v44] : ? [v45] : (powerset(v44) = v45 & powerset(v41) = v44 & ( ~ element(v42, v45) | element(v43, v45)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (complements_of_subsets(v41, v42) = v43) | ? [v44] : ? [v45] : (powerset(v44) = v45 & powerset(v41) = v44 & ( ~ element(v42, v45) | ( ! [v46] : ! [v47] : ( ~ (subset_complement(v41, v46) = v47) | ~ element(v46, v44) | ~ element(v43, v45) | ~ in(v47, v42) | in(v46, v43)) & ! [v46] : ! [v47] : ( ~ (subset_complement(v41, v46) = v47) | ~ element(v46, v44) | ~ element(v43, v45) | ~ in(v46, v43) | in(v47, v42)) & ! [v46] : (v46 = v43 | ~ element(v46, v45) | ? [v47] : ? [v48] : (subset_complement(v41, v47) = v48 & element(v47, v44) & ( ~ in(v48, v42) | ~ in(v47, v46)) & (in(v48, v42) | in(v47, v46)))))))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_composition(v42, v41) = v43) | ~ relation(v42) | ~ empty(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_composition(v42, v41) = v43) | ~ relation(v42) | ~ empty(v41) | empty(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_composition(v41, v42) = v43) | ~ relation(v42) | ~ relation(v41) | ~ function(v42) | ~ function(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_composition(v41, v42) = v43) | ~ relation(v42) | ~ relation(v41) | ~ function(v42) | ~ function(v41) | function(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_composition(v41, v42) = v43) | ~ relation(v42) | ~ relation(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_composition(v41, v42) = v43) | ~ relation(v42) | ~ relation(v41) | ? [v44] : ? [v45] : (relation_rng(v43) = v44 & relation_rng(v42) = v45 & subset(v44, v45))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_composition(v41, v42) = v43) | ~ relation(v42) | ~ empty(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_composition(v41, v42) = v43) | ~ relation(v42) | ~ empty(v41) | empty(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ well_orders(v42, v41) | ~ relation(v42) | relation_field(v43) = v41) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ well_orders(v42, v41) | ~ relation(v42) | well_ordering(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ reflexive(v42) | ~ relation(v42) | reflexive(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ well_ordering(v42) | ~ relation(v42) | well_ordering(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ well_ordering(v42) | ~ relation(v42) | ? [v44] : ? [v45] : (relation_field(v43) = v45 & relation_field(v42) = v44 & (v45 = v41 | ~ subset(v41, v44)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ well_founded_relation(v42) | ~ relation(v42) | well_founded_relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ transitive(v42) | ~ relation(v42) | transitive(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ connected(v42) | ~ relation(v42) | connected(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ antisymmetric(v42) | ~ relation(v42) | antisymmetric(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : (relation_field(v43) = v44 & relation_field(v42) = v45 & subset(v44, v45) & subset(v44, v41))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ relation(v42) | ? [v44] : (relation_rng_restriction(v41, v44) = v43 & relation_dom_restriction(v42, v41) = v44)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v42, v41) = v43) | ~ relation(v42) | ? [v44] : (relation_rng_restriction(v41, v42) = v44 & relation_dom_restriction(v44, v41) = v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v41, v42) = v43) | ~ relation(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_restriction(v41, v42) = v43) | ~ relation(v41) | ? [v44] : (set_intersection2(v41, v44) = v43 & cartesian_product2(v42, v42) = v44)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (subset_complement(v41, v42) = v43) | ? [v44] : ? [v45] : (set_difference(v41, v42) = v45 & powerset(v41) = v44 & (v45 = v43 | ~ element(v42, v44)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (subset_complement(v41, v42) = v43) | ? [v44] : (powerset(v41) = v44 & ( ~ element(v42, v44) | element(v43, v44)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_difference(v41, v43) = v41) | ~ (singleton(v42) = v43) | ~ in(v42, v41)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_difference(v41, v42) = v43) | ~ relation(v42) | ~ relation(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_difference(v41, v42) = v43) | ~ finite(v41) | finite(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_difference(v41, v42) = v43) | subset(v43, v41)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_difference(v41, v42) = v43) | ? [v44] : ? [v45] : (subset_complement(v41, v42) = v45 & powerset(v41) = v44 & (v45 = v43 | ~ element(v42, v44)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_difference(v41, v42) = v43) | ? [v44] : (set_difference(v44, v42) = v43 & set_union2(v41, v42) = v44)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (union(v42) = v43) | ~ in(v41, v42) | subset(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (union(v41) = v42) | ~ in(v43, v42) | ? [v44] : (in(v44, v41) & in(v43, v44))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (singleton(v41) = v43) | ~ disjoint(v43, v42) | ~ in(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (singleton(v41) = v43) | ~ subset(v43, v42) | in(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (singleton(v41) = v43) | ~ in(v41, v42) | subset(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (singleton(v41) = v42) | ~ (set_union2(v41, v42) = v43) | succ(v41) = v43) & ! [v41] : ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ being_limit_ordinal(v41) | ~ ordinal(v42) | ~ ordinal(v41) | ~ in(v42, v41) | in(v43, v41)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (succ(v41) = v42) | ~ ordinal_subset(v42, v43) | ~ ordinal(v43) | ~ ordinal(v41) | in(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (succ(v41) = v42) | ~ ordinal(v43) | ~ ordinal(v41) | ~ in(v41, v43) | ordinal_subset(v42, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ relation(v42) | ~ relation(v41) | ? [v44] : ? [v45] : (relation_composition(v41, v42) = v44 & relation_rng(v44) = v45 & subset(v45, v43))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ~ in(v43, v42) | ? [v44] : ? [v45] : (ordered_pair(v44, v43) = v45 & in(v45, v41))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_inverse_image(v42, v41) = v43) | ~ relation(v42) | ? [v44] : (relation_dom(v42) = v44 & subset(v43, v44))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ equipotent(v41, v43) | ~ well_ordering(v42) | ~ relation(v42) | ? [v44] : (well_orders(v44, v41) & relation(v44))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ relation(v42) | ~ function(v42) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ relation(v42) | ~ function(v42) | function(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ relation(v42) | subset(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ relation(v42) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : (relation_rng(v43) = v44 & relation_rng(v42) = v45 & set_intersection2(v45, v41) = v44)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : (relation_rng(v43) = v44 & relation_rng(v42) = v45 & subset(v44, v45))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : (relation_dom(v43) = v44 & relation_dom(v42) = v45 & subset(v44, v45))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng_restriction(v41, v42) = v43) | ~ relation(v42) | ? [v44] : (relation_rng(v43) = v44 & subset(v44, v41))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom(v41) = v42) | ~ (relation_image(v41, v42) = v43) | ~ relation(v41) | relation_rng(v41) = v43) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ~ in(v43, v42) | ? [v44] : ? [v45] : (ordered_pair(v43, v44) = v45 & in(v45, v41))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_image(v42, v41) = v43) | ~ relation(v42) | ~ function(v42) | ~ finite(v41) | finite(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_image(v42, v41) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : (relation_dom(v42) = v44 & relation_image(v42, v45) = v43 & set_intersection2(v44, v41) = v45)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_image(v42, v41) = v43) | ~ relation(v42) | ? [v44] : (relation_rng(v42) = v44 & subset(v43, v44))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_image(v41, v42) = v43) | ~ relation(v41) | ~ function(v41) | ~ finite(v42) | finite(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (apply(v42, v41) = v43) | ~ relation(v42) | ~ function(v42) | ? [v44] : (relation_dom(v42) = v44 & ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_composition(v42, v45) = v46) | ~ (apply(v46, v41) = v47) | ~ relation(v45) | ~ function(v45) | ~ in(v41, v44) | apply(v45, v43) = v47) & ! [v45] : ! [v46] : ( ~ (apply(v45, v43) = v46) | ~ relation(v45) | ~ function(v45) | ~ in(v41, v44) | ? [v47] : (relation_composition(v42, v45) = v47 & apply(v47, v41) = v46)))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom_restriction(v42, v41) = v43) | ~ relation(v42) | subset(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom_restriction(v42, v41) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : (relation_rng(v43) = v44 & relation_rng(v42) = v45 & subset(v44, v45))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom_restriction(v42, v41) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : (relation_dom(v43) = v44 & relation_dom(v42) = v45 & set_intersection2(v45, v41) = v44)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom_restriction(v42, v41) = v43) | ~ relation(v42) | ? [v44] : (relation_composition(v44, v42) = v43 & identity_relation(v41) = v44)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom_restriction(v41, v42) = v43) | ~ relation_empty_yielding(v41) | ~ relation(v41) | relation_empty_yielding(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom_restriction(v41, v42) = v43) | ~ relation_empty_yielding(v41) | ~ relation(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom_restriction(v41, v42) = v43) | ~ relation(v41) | ~ function(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom_restriction(v41, v42) = v43) | ~ relation(v41) | ~ function(v41) | function(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom_restriction(v41, v42) = v43) | ~ relation(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (ordered_pair(v41, v42) = v43) | ~ empty(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (ordered_pair(v41, v42) = v43) | pair_second(v43) = v42) & ! [v41] : ! [v42] : ! [v43] : ( ~ (ordered_pair(v41, v42) = v43) | pair_first(v43) = v41) & ! [v41] : ! [v42] : ! [v43] : ( ~ (ordered_pair(v41, v42) = v43) | ? [v44] : ? [v45] : (singleton(v41) = v45 & unordered_pair(v44, v45) = v43 & unordered_pair(v41, v42) = v44)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v5_membered(v41) | v5_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v5_membered(v41) | v4_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v5_membered(v41) | v3_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v5_membered(v41) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v5_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v4_membered(v41) | v4_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v4_membered(v41) | v3_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v4_membered(v41) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v4_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v3_membered(v41) | v3_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v3_membered(v41) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v3_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v2_membered(v41) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v2_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | ~ v1_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v41) = v43) | set_intersection2(v41, v42) = v43) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ relation(v42) | ~ relation(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ finite(v42) | finite(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ finite(v41) | finite(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v5_membered(v41) | v5_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v5_membered(v41) | v4_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v5_membered(v41) | v3_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v5_membered(v41) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v5_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v4_membered(v41) | v4_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v4_membered(v41) | v3_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v4_membered(v41) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v4_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v3_membered(v41) | v3_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v3_membered(v41) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v3_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v2_membered(v41) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v2_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ~ v1_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | set_intersection2(v42, v41) = v43) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | disjoint(v41, v42) | ? [v44] : in(v44, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | subset(v43, v41)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_intersection2(v41, v42) = v43) | ? [v44] : (set_difference(v41, v44) = v43 & set_difference(v41, v42) = v44)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (the_carrier(v41) = v42) | ~ (cartesian_product2(v42, v42) = v43) | ~ meet_semilatt_str(v41) | ? [v44] : (the_L_meet(v41) = v44 & quasi_total(v44, v43, v42) & relation_of2_as_subset(v44, v43, v42) & function(v44))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (the_carrier(v41) = v42) | ~ (cartesian_product2(v42, v42) = v43) | ~ join_semilatt_str(v41) | ? [v44] : (the_L_join(v41) = v44 & quasi_total(v44, v43, v42) & relation_of2_as_subset(v44, v43, v42) & function(v44))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_union2(v42, v41) = v43) | ~ empty(v43) | empty(v41)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_union2(v42, v41) = v43) | set_union2(v41, v42) = v43) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_union2(v41, v42) = v43) | ~ relation(v42) | ~ relation(v41) | relation(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_union2(v41, v42) = v43) | ~ finite(v42) | ~ finite(v41) | finite(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_union2(v41, v42) = v43) | ~ empty(v43) | empty(v41)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_union2(v41, v42) = v43) | set_union2(v42, v41) = v43) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_union2(v41, v42) = v43) | subset(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (set_union2(v41, v42) = v43) | ? [v44] : (set_difference(v42, v41) = v44 & set_union2(v41, v44) = v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (unordered_pair(v42, v41) = v43) | unordered_pair(v41, v42) = v43) & ! [v41] : ! [v42] : ! [v43] : ( ~ (unordered_pair(v41, v42) = v43) | ~ empty(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (unordered_pair(v41, v42) = v43) | unordered_pair(v42, v41) = v43) & ! [v41] : ! [v42] : ! [v43] : ( ~ (unordered_pair(v41, v42) = v43) | in(v42, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (unordered_pair(v41, v42) = v43) | in(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (cartesian_product2(v41, v42) = v43) | ~ empty(v43) | empty(v42) | empty(v41)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (cartesian_product2(v41, v42) = v43) | ? [v44] : ( ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v46, v47) = v45) | ~ in(v46, v41) | ~ in(v45, v43) | in(v45, v44) | ? [v48] : ( ~ (v48 = v47) & singleton(v46) = v48)) & ! [v45] : ( ~ in(v45, v44) | in(v45, v43)) & ! [v45] : ( ~ in(v45, v44) | ? [v46] : ? [v47] : (singleton(v46) = v47 & ordered_pair(v46, v47) = v45 & in(v46, v41))))) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ~ subset(v41, v42) | element(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ~ element(v41, v43) | subset(v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ subset(v43, v41) | in(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ finite(v41) | ~ element(v43, v42) | finite(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v5_membered(v41) | ~ element(v43, v42) | v5_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v5_membered(v41) | ~ element(v43, v42) | v4_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v5_membered(v41) | ~ element(v43, v42) | v3_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v5_membered(v41) | ~ element(v43, v42) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v5_membered(v41) | ~ element(v43, v42) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v4_membered(v41) | ~ element(v43, v42) | v4_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v4_membered(v41) | ~ element(v43, v42) | v3_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v4_membered(v41) | ~ element(v43, v42) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v4_membered(v41) | ~ element(v43, v42) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v3_membered(v41) | ~ element(v43, v42) | v3_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v3_membered(v41) | ~ element(v43, v42) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v3_membered(v41) | ~ element(v43, v42) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v2_membered(v41) | ~ element(v43, v42) | v2_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ v2_membered(v41) | ~ element(v43, v42) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ element(v43, v42) | ~ v1_membered(v41) | v1_membered(v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v41) = v42) | ~ in(v43, v42) | subset(v43, v41)) & ! [v41] : ! [v42] : ! [v43] : ( ~ relation_isomorphism(v41, v42, v43) | ~ reflexive(v41) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ function(v43) | reflexive(v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ relation_isomorphism(v41, v42, v43) | ~ well_ordering(v41) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ function(v43) | well_ordering(v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ relation_isomorphism(v41, v42, v43) | ~ well_founded_relation(v41) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ function(v43) | well_founded_relation(v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ relation_isomorphism(v41, v42, v43) | ~ transitive(v41) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ function(v43) | transitive(v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ relation_isomorphism(v41, v42, v43) | ~ connected(v41) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ function(v43) | connected(v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ relation_isomorphism(v41, v42, v43) | ~ antisymmetric(v41) | ~ relation(v43) | ~ relation(v42) | ~ relation(v41) | ~ function(v43) | antisymmetric(v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ disjoint(v42, v43) | ~ subset(v41, v42) | disjoint(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ disjoint(v41, v42) | ~ in(v43, v42) | ~ in(v43, v41)) & ! [v41] : ! [v42] : ! [v43] : ( ~ relation_of2(v43, v41, v42) | relation_of2_as_subset(v43, v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ quasi_total(v43, empty_set, v41) | ~ relation_of2_as_subset(v43, empty_set, v41) | ~ subset(v41, v42) | ~ function(v43) | quasi_total(v43, empty_set, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ quasi_total(v43, empty_set, v41) | ~ relation_of2_as_subset(v43, empty_set, v41) | ~ subset(v41, v42) | ~ function(v43) | relation_of2_as_subset(v43, empty_set, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ relation_of2_as_subset(v43, v41, v42) | relation_of2(v43, v41, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ subset(v42, v43) | ~ subset(v41, v42) | subset(v41, v43)) & ! [v41] : ! [v42] : ! [v43] : ( ~ subset(v41, v42) | ~ in(v43, v41) | in(v43, v42)) & ! [v41] : ! [v42] : ! [v43] : ( ~ in(v43, v41) | ~ in(v42, v43) | ~ in(v41, v42)) & ? [v41] : ! [v42] : ! [v43] : (v43 = v41 | v42 = empty_set | ~ (set_meet(v42) = v43) | ? [v44] : ? [v45] : (( ~ in(v44, v41) | (in(v45, v42) & ~ in(v44, v45))) & (in(v44, v41) | ! [v46] : ( ~ in(v46, v42) | in(v44, v46))))) & ? [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (union(v42) = v43) | ? [v44] : ? [v45] : (( ~ in(v44, v41) | ! [v46] : ( ~ in(v46, v42) | ~ in(v44, v46))) & (in(v44, v41) | (in(v45, v42) & in(v44, v45))))) & ? [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (singleton(v42) = v43) | ? [v44] : (( ~ (v44 = v42) | ~ in(v42, v41)) & (v44 = v42 | in(v44, v41)))) & ? [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (relation_rng(v42) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : ? [v46] : (( ~ in(v44, v41) | ! [v47] : ! [v48] : ( ~ (ordered_pair(v47, v44) = v48) | ~ in(v48, v42))) & (in(v44, v41) | (ordered_pair(v45, v44) = v46 & in(v46, v42))))) & ? [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (relation_dom(v42) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : ? [v46] : (( ~ in(v44, v41) | ! [v47] : ! [v48] : ( ~ (ordered_pair(v44, v47) = v48) | ~ in(v48, v42))) & (in(v44, v41) | (ordered_pair(v44, v45) = v46 & in(v46, v42))))) & ? [v41] : ! [v42] : ! [v43] : (v43 = v41 | ~ (powerset(v42) = v43) | ? [v44] : (( ~ subset(v44, v42) | ~ in(v44, v41)) & (subset(v44, v42) | in(v44, v41)))) & ? [v41] : ! [v42] : ! [v43] : (v42 = empty_set | ~ (set_meet(v42) = v43) | in(v41, v43) | ? [v44] : (in(v44, v42) & ~ in(v41, v44))) & ? [v41] : ! [v42] : ! [v43] : ( ~ (singleton(v42) = v43) | ~ ordinal(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : (succ(v42) = v44 & powerset(v45) = v46 & powerset(v44) = v45 & powerset(v42) = v47 & ( ~ element(v41, v46) | ( ! [v49] : ! [v50] : ( ~ (set_difference(v50, v43) = v49) | ~ in(v50, v41) | ~ in(v49, v47) | in(v49, v48)) & ! [v49] : ( ~ in(v49, v48) | in(v49, v47)) & ! [v49] : ( ~ in(v49, v48) | ? [v50] : (set_difference(v50, v43) = v49 & in(v50, v41))))))) & ? [v41] : ! [v42] : ! [v43] : ( ~ (singleton(v42) = v43) | disjoint(v43, v41) | in(v42, v41)) & ? [v41] : ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : (singleton(v42) = v47 & powerset(v44) = v45 & powerset(v43) = v44 & powerset(v42) = v46 & ( ~ element(v41, v45) | ( ! [v49] : ! [v50] : ( ~ (set_difference(v50, v47) = v49) | ~ in(v50, v41) | ~ in(v49, v46) | in(v49, v48)) & ! [v49] : ( ~ in(v49, v48) | in(v49, v46)) & ! [v49] : ( ~ in(v49, v48) | ? [v50] : (set_difference(v50, v47) = v49 & in(v50, v41))))))) & ? [v41] : ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : (singleton(v42) = v46 & powerset(v44) = v45 & powerset(v43) = v44 & powerset(v42) = v47 & ( ~ element(v41, v45) | ( ! [v49] : ! [v50] : ( ~ (set_difference(v50, v46) = v49) | ~ in(v50, v41) | ~ in(v49, v47) | in(v49, v48)) & ! [v49] : ( ~ in(v49, v48) | in(v49, v47)) & ! [v49] : ( ~ in(v49, v48) | ? [v50] : (set_difference(v50, v46) = v49 & in(v50, v41))))))) & ? [v41] : ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ? [v44] : ( ! [v45] : ( ~ ordinal(v45) | ~ in(v45, v43) | ~ in(v45, v41) | in(v45, v44)) & ! [v45] : ( ~ in(v45, v44) | in(v45, v43)) & ! [v45] : ( ~ in(v45, v44) | (ordinal(v45) & in(v45, v41))))) & ? [v41] : ! [v42] : ! [v43] : ( ~ (relation_rng(v43) = v42) | ~ one_to_one(v43) | ~ relation(v43) | ~ function(v43) | equipotent(v41, v42) | ? [v44] : ( ~ (v44 = v41) & relation_dom(v43) = v44)) & ? [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom(v43) = v42) | ~ one_to_one(v43) | ~ relation(v43) | ~ function(v43) | equipotent(v42, v41) | ? [v44] : ( ~ (v44 = v41) & relation_rng(v43) = v44)) & ? [v41] : ! [v42] : ! [v43] : ( ~ (relation_dom(v42) = v43) | ~ relation(v42) | ~ function(v42) | ~ in(v43, omega) | finite(v41) | ? [v44] : ( ~ (v44 = v41) & relation_rng(v42) = v44)) & ? [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ~ ordinal(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : (singleton(v42) = v47 & succ(v42) = v44 & powerset(v45) = v46 & powerset(v44) = v45 & ( ~ element(v41, v46) | ( ! [v49] : ! [v50] : ( ~ (set_difference(v50, v47) = v49) | ~ in(v50, v41) | ~ in(v49, v43) | in(v49, v48)) & ! [v49] : ( ~ in(v49, v48) | in(v49, v43)) & ! [v49] : ( ~ in(v49, v48) | ? [v50] : (set_difference(v50, v47) = v49 & in(v50, v41))))))) & ? [v41] : ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | element(v41, v43) | ? [v44] : (in(v44, v41) & ~ in(v44, v42))) & ? [v41] : ! [v42] : ! [v43] : ( ~ relation(v43) | ~ relation(v42) | ~ function(v43) | ? [v44] : (relation(v44) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ! [v49] : ( ~ (apply(v43, v46) = v48) | ~ (apply(v43, v45) = v47) | ~ (ordered_pair(v47, v48) = v49) | ~ in(v49, v42) | ~ in(v46, v41) | ~ in(v45, v41) | ? [v50] : (ordered_pair(v45, v46) = v50 & in(v50, v44))) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ! [v49] : ( ~ (apply(v43, v46) = v48) | ~ (apply(v43, v45) = v47) | ~ (ordered_pair(v47, v48) = v49) | in(v49, v42) | ? [v50] : (ordered_pair(v45, v46) = v50 & ~ in(v50, v44))) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ! [v49] : ( ~ (apply(v43, v46) = v48) | ~ (apply(v43, v45) = v47) | ~ (ordered_pair(v47, v48) = v49) | in(v46, v41) | ? [v50] : (ordered_pair(v45, v46) = v50 & ~ in(v50, v44))) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ! [v49] : ( ~ (apply(v43, v46) = v48) | ~ (apply(v43, v45) = v47) | ~ (ordered_pair(v47, v48) = v49) | in(v45, v41) | ? [v50] : (ordered_pair(v45, v46) = v50 & ~ in(v50, v44))) & ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v45, v46) = v47) | ~ in(v47, v44) | in(v46, v41)) & ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v45, v46) = v47) | ~ in(v47, v44) | in(v45, v41)) & ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v45, v46) = v47) | ~ in(v47, v44) | ? [v48] : ? [v49] : ? [v50] : (apply(v43, v46) = v49 & apply(v43, v45) = v48 & ordered_pair(v48, v49) = v50 & in(v50, v42))) & ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v45, v46) = v47) | ~ in(v46, v41) | ~ in(v45, v41) | in(v47, v44) | ? [v48] : ? [v49] : ? [v50] : (apply(v43, v46) = v49 & apply(v43, v45) = v48 & ordered_pair(v48, v49) = v50 & ~ in(v50, v42))))) & ! [v41] : ! [v42] : (v42 = v41 | ~ (set_difference(v41, empty_set) = v42)) & ! [v41] : ! [v42] : (v42 = v41 | ~ (union(v41) = v42) | ~ being_limit_ordinal(v41)) & ! [v41] : ! [v42] : (v42 = v41 | ~ (cast_to_subset(v41) = v42)) & ! [v41] : ! [v42] : (v42 = v41 | ~ (set_intersection2(v41, v41) = v42)) & ! [v41] : ! [v42] : (v42 = v41 | ~ (set_union2(v41, v41) = v42)) & ! [v41] : ! [v42] : (v42 = v41 | ~ (set_union2(v41, empty_set) = v42)) & ! [v41] : ! [v42] : (v42 = v41 | ~ subset(v42, v41) | ~ subset(v41, v42)) & ! [v41] : ! [v42] : (v42 = v41 | ~ subset(v41, v42) | proper_subset(v41, v42)) & ! [v41] : ! [v42] : (v42 = v41 | ~ relation(v42) | ~ relation(v41) | ? [v43] : ? [v44] : ? [v45] : (ordered_pair(v43, v44) = v45 & ( ~ in(v45, v42) | ~ in(v45, v41)) & (in(v45, v42) | in(v45, v41)))) & ! [v41] : ! [v42] : (v42 = v41 | ~ ordinal(v42) | ~ ordinal(v41) | in(v42, v41) | in(v41, v42)) & ! [v41] : ! [v42] : (v42 = v41 | ~ empty(v42) | ~ empty(v41)) & ! [v41] : ! [v42] : (v42 = empty_set | ~ (complements_of_subsets(v41, v42) = empty_set) | ? [v43] : ? [v44] : (powerset(v43) = v44 & powerset(v41) = v43 & ~ element(v42, v44))) & ! [v41] : ! [v42] : (v42 = empty_set | ~ (set_difference(empty_set, v41) = v42)) & ! [v41] : ! [v42] : (v42 = empty_set | ~ (set_intersection2(v41, empty_set) = v42)) & ! [v41] : ! [v42] : (v41 = empty_set | ~ (relation_dom_as_subset(v41, empty_set, empty_set) = v42) | ~ relation_of2_as_subset(empty_set, v41, empty_set) | quasi_total(empty_set, v41, empty_set)) & ! [v41] : ! [v42] : (v41 = empty_set | ~ (relation_rng(v41) = v42) | ~ relation(v41) | ? [v43] : ( ~ (v43 = empty_set) & relation_dom(v41) = v43)) & ! [v41] : ! [v42] : (v41 = empty_set | ~ (relation_inverse_image(v42, v41) = empty_set) | ~ relation(v42) | ? [v43] : (relation_rng(v42) = v43 & ~ subset(v41, v43))) & ! [v41] : ! [v42] : (v41 = empty_set | ~ (relation_dom(v41) = v42) | ~ relation(v41) | ? [v43] : ( ~ (v43 = empty_set) & relation_rng(v41) = v43)) & ! [v41] : ! [v42] : (v41 = empty_set | ~ subset(v41, v42) | ~ ordinal(v42) | ? [v43] : (ordinal(v43) & in(v43, v41) & ! [v44] : ( ~ ordinal(v44) | ~ in(v44, v41) | ordinal_subset(v43, v44)))) & ! [v41] : ! [v42] : ( ~ (function_inverse(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | relation_inverse(v41) = v42) & ! [v41] : ! [v42] : ( ~ (function_inverse(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | one_to_one(v42)) & ! [v41] : ! [v42] : ( ~ (function_inverse(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | ? [v43] : ? [v44] : (relation_rng(v42) = v44 & relation_rng(v41) = v43 & relation_dom(v42) = v43 & relation_dom(v41) = v44)) & ! [v41] : ! [v42] : ( ~ (function_inverse(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | ? [v43] : ? [v44] : (relation_rng(v41) = v43 & relation_dom(v41) = v44 & ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v48 = v47 | ~ (relation_dom(v42) = v45) | ~ (apply(v42, v46) = v48) | ~ (apply(v41, v47) = v46) | ~ relation(v42) | ~ function(v42) | ~ in(v47, v44)) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v48 = v46 | ~ (relation_dom(v42) = v45) | ~ (apply(v42, v46) = v47) | ~ (apply(v41, v47) = v48) | ~ relation(v42) | ~ function(v42) | ~ in(v46, v43)) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_dom(v42) = v45) | ~ (apply(v42, v46) = v48) | ~ (apply(v41, v47) = v46) | ~ relation(v42) | ~ function(v42) | ~ in(v47, v44) | in(v46, v43)) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_dom(v42) = v45) | ~ (apply(v42, v46) = v47) | ~ (apply(v41, v47) = v48) | ~ relation(v42) | ~ function(v42) | ~ in(v46, v43) | in(v47, v44)) & ! [v45] : (v45 = v43 | ~ (relation_dom(v42) = v45) | ~ relation(v42) | ~ function(v42)) & ! [v45] : (v45 = v42 | ~ (relation_dom(v45) = v43) | ~ relation(v45) | ~ function(v45) | ? [v46] : ? [v47] : ? [v48] : ? [v49] : (apply(v45, v46) = v48 & apply(v41, v47) = v49 & ((v49 = v46 & in(v47, v44) & ( ~ (v48 = v47) | ~ in(v46, v43))) | (v48 = v47 & in(v46, v43) & ( ~ (v49 = v46) | ~ in(v47, v44)))))))) & ! [v41] : ! [v42] : ( ~ (function_inverse(v41) = v42) | ~ relation(v41) | ~ function(v41) | relation(v42)) & ! [v41] : ! [v42] : ( ~ (function_inverse(v41) = v42) | ~ relation(v41) | ~ function(v41) | function(v42)) & ! [v41] : ! [v42] : ( ~ (relation_inverse(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | function_inverse(v41) = v42) & ! [v41] : ! [v42] : ( ~ (relation_inverse(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | relation(v42)) & ! [v41] : ! [v42] : ( ~ (relation_inverse(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | function(v42)) & ! [v41] : ! [v42] : ( ~ (relation_inverse(v41) = v42) | ~ relation(v41) | relation_inverse(v42) = v41) & ! [v41] : ! [v42] : ( ~ (relation_inverse(v41) = v42) | ~ relation(v41) | relation(v42)) & ! [v41] : ! [v42] : ( ~ (relation_inverse(v41) = v42) | ~ relation(v41) | ? [v43] : ? [v44] : (relation_rng(v42) = v44 & relation_rng(v41) = v43 & relation_dom(v42) = v43 & relation_dom(v41) = v44)) & ! [v41] : ! [v42] : ( ~ (relation_inverse(v41) = v42) | ~ empty(v41) | relation(v42)) & ! [v41] : ! [v42] : ( ~ (relation_inverse(v41) = v42) | ~ empty(v41) | empty(v42)) & ! [v41] : ! [v42] : ( ~ (set_difference(v41, v42) = v41) | disjoint(v41, v42)) & ! [v41] : ! [v42] : ( ~ (set_difference(v41, v42) = empty_set) | subset(v41, v42)) & ! [v41] : ! [v42] : ( ~ (union(v41) = v42) | ~ ordinal(v41) | epsilon_connected(v42)) & ! [v41] : ! [v42] : ( ~ (union(v41) = v42) | ~ ordinal(v41) | epsilon_transitive(v42)) & ! [v41] : ! [v42] : ( ~ (union(v41) = v42) | ~ ordinal(v41) | ordinal(v42)) & ! [v41] : ! [v42] : ( ~ (cast_to_subset(v41) = v42) | ? [v43] : (powerset(v41) = v43 & element(v42, v43))) & ! [v41] : ! [v42] : ( ~ (cast_as_carrier_subset(v41) = v42) | ~ one_sorted_str(v41) | the_carrier(v41) = v42) & ! [v41] : ! [v42] : ( ~ (cast_as_carrier_subset(v41) = v42) | ~ one_sorted_str(v41) | ? [v43] : ? [v44] : (the_carrier(v41) = v43 & powerset(v43) = v44 & element(v42, v44))) & ! [v41] : ! [v42] : ( ~ (the_L_meet(v41) = v42) | ~ meet_semilatt_str(v41) | empty_carrier(v41) | ? [v43] : (the_carrier(v41) = v43 & ! [v44] : ! [v45] : ! [v46] : ( ~ (meet(v41, v44, v45) = v46) | ~ element(v45, v43) | ~ element(v44, v43) | apply_binary_as_element(v43, v43, v43, v42, v44, v45) = v46) & ! [v44] : ! [v45] : ! [v46] : ( ~ (apply_binary_as_element(v43, v43, v43, v42, v44, v45) = v46) | ~ element(v45, v43) | ~ element(v44, v43) | meet(v41, v44, v45) = v46))) & ! [v41] : ! [v42] : ( ~ (the_L_meet(v41) = v42) | ~ meet_semilatt_str(v41) | function(v42)) & ! [v41] : ! [v42] : ( ~ (the_L_meet(v41) = v42) | ~ meet_semilatt_str(v41) | ? [v43] : ? [v44] : (the_carrier(v41) = v43 & cartesian_product2(v43, v43) = v44 & quasi_total(v42, v44, v43) & relation_of2_as_subset(v42, v44, v43))) & ! [v41] : ! [v42] : ( ~ (inclusion_relation(v41) = v42) | ~ ordinal(v41) | well_ordering(v42)) & ! [v41] : ! [v42] : ( ~ (inclusion_relation(v41) = v42) | ~ ordinal(v41) | well_founded_relation(v42)) & ! [v41] : ! [v42] : ( ~ (inclusion_relation(v41) = v42) | ~ ordinal(v41) | connected(v42)) & ! [v41] : ! [v42] : ( ~ (inclusion_relation(v41) = v42) | reflexive(v42)) & ! [v41] : ! [v42] : ( ~ (inclusion_relation(v41) = v42) | transitive(v42)) & ! [v41] : ! [v42] : ( ~ (inclusion_relation(v41) = v42) | antisymmetric(v42)) & ! [v41] : ! [v42] : ( ~ (inclusion_relation(v41) = v42) | relation(v42)) & ! [v41] : ! [v42] : ( ~ (singleton(v42) = v41) | subset(v41, v41)) & ! [v41] : ! [v42] : ( ~ (singleton(v41) = v42) | ~ empty(v42)) & ! [v41] : ! [v42] : ( ~ (singleton(v41) = v42) | unordered_pair(v41, v41) = v42) & ! [v41] : ! [v42] : ( ~ (singleton(v41) = v42) | subset(empty_set, v42)) & ! [v41] : ! [v42] : ( ~ (singleton(v41) = v42) | finite(v42)) & ! [v41] : ! [v42] : ( ~ (singleton(v41) = v42) | in(v41, v42)) & ! [v41] : ! [v42] : ( ~ (succ(v42) = v41) | ~ being_limit_ordinal(v41) | ~ ordinal(v42) | ~ ordinal(v41)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | ~ empty(v42) | ~ natural(v41)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | ~ empty(v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | ~ natural(v41) | epsilon_connected(v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | ~ natural(v41) | epsilon_transitive(v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | ~ natural(v41) | ordinal(v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | ~ natural(v41) | natural(v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | epsilon_connected(v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | epsilon_transitive(v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | ordinal(v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ ordinal(v41) | ? [v43] : ( ! [v44] : ! [v45] : ( ~ (powerset(v44) = v45) | ~ ordinal(v44) | ~ in(v44, v42) | in(v44, v43) | in(v44, omega)) & ! [v44] : ! [v45] : ( ~ (powerset(v44) = v45) | ~ ordinal(v44) | ~ in(v44, v42) | in(v44, v43) | ? [v46] : ? [v47] : ( ~ (v47 = empty_set) & powerset(v45) = v46 & element(v47, v46) & ! [v48] : ( ~ in(v48, v47) | ? [v49] : ( ~ (v49 = v48) & subset(v48, v49) & in(v49, v47))))) & ! [v44] : ( ~ in(v44, v43) | in(v44, v42)) & ! [v44] : ( ~ in(v44, v43) | ? [v45] : ? [v46] : (powerset(v45) = v46 & powerset(v44) = v45 & ordinal(v44) & ( ~ in(v44, omega) | ! [v47] : (v47 = empty_set | ~ element(v47, v46) | ? [v48] : (in(v48, v47) & ! [v49] : (v49 = v48 | ~ subset(v48, v49) | ~ in(v49, v47))))))))) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ~ empty(v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | in(v41, v42)) & ! [v41] : ! [v42] : ( ~ (succ(v41) = v42) | ? [v43] : (singleton(v41) = v43 & set_union2(v41, v43) = v42)) & ! [v41] : ! [v42] : ( ~ (the_L_join(v41) = v42) | ~ join_semilatt_str(v41) | empty_carrier(v41) | ? [v43] : (the_carrier(v41) = v43 & ! [v44] : ! [v45] : ! [v46] : ( ~ (join(v41, v44, v45) = v46) | ~ element(v45, v43) | ~ element(v44, v43) | apply_binary_as_element(v43, v43, v43, v42, v44, v45) = v46) & ! [v44] : ! [v45] : ! [v46] : ( ~ (apply_binary_as_element(v43, v43, v43, v42, v44, v45) = v46) | ~ element(v45, v43) | ~ element(v44, v43) | join(v41, v44, v45) = v46))) & ! [v41] : ! [v42] : ( ~ (the_L_join(v41) = v42) | ~ join_semilatt_str(v41) | function(v42)) & ! [v41] : ! [v42] : ( ~ (the_L_join(v41) = v42) | ~ join_semilatt_str(v41) | ? [v43] : ? [v44] : (the_carrier(v41) = v43 & cartesian_product2(v43, v43) = v44 & quasi_total(v42, v44, v43) & relation_of2_as_subset(v42, v44, v43))) & ! [v41] : ! [v42] : ( ~ (relation_dom_as_subset(empty_set, v41, v42) = empty_set) | ~ relation_of2_as_subset(v42, empty_set, v41) | quasi_total(v42, empty_set, v41)) & ! [v41] : ! [v42] : ( ~ (relation_rng(v42) = v41) | ~ relation(v42) | ~ function(v42) | finite(v41) | ? [v43] : (relation_dom(v42) = v43 & ~ in(v43, omega))) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | ? [v43] : ? [v44] : (function_inverse(v41) = v43 & relation_rng(v43) = v44 & relation_dom(v43) = v42 & relation_dom(v41) = v44)) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | ? [v43] : ? [v44] : (function_inverse(v41) = v43 & relation_dom(v41) = v44 & ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v48 = v47 | ~ (relation_dom(v43) = v45) | ~ (apply(v43, v46) = v48) | ~ (apply(v41, v47) = v46) | ~ relation(v43) | ~ function(v43) | ~ in(v47, v44)) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v48 = v46 | ~ (relation_dom(v43) = v45) | ~ (apply(v43, v46) = v47) | ~ (apply(v41, v47) = v48) | ~ relation(v43) | ~ function(v43) | ~ in(v46, v42)) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_dom(v43) = v45) | ~ (apply(v43, v46) = v48) | ~ (apply(v41, v47) = v46) | ~ relation(v43) | ~ function(v43) | ~ in(v47, v44) | in(v46, v42)) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_dom(v43) = v45) | ~ (apply(v43, v46) = v47) | ~ (apply(v41, v47) = v48) | ~ relation(v43) | ~ function(v43) | ~ in(v46, v42) | in(v47, v44)) & ! [v45] : (v45 = v43 | ~ (relation_dom(v45) = v42) | ~ relation(v45) | ~ function(v45) | ? [v46] : ? [v47] : ? [v48] : ? [v49] : (apply(v45, v46) = v48 & apply(v41, v47) = v49 & ((v49 = v46 & in(v47, v44) & ( ~ (v48 = v47) | ~ in(v46, v42))) | (v48 = v47 & in(v46, v42) & ( ~ (v49 = v46) | ~ in(v47, v44)))))) & ! [v45] : (v45 = v42 | ~ (relation_dom(v43) = v45) | ~ relation(v43) | ~ function(v43)))) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ~ function(v41) | finite(v42) | ? [v43] : (relation_dom(v41) = v43 & ~ finite(v43))) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ~ function(v41) | ? [v43] : (relation_dom(v41) = v43 & ! [v44] : ! [v45] : ( ~ (apply(v41, v45) = v44) | ~ in(v45, v43) | in(v44, v42)) & ! [v44] : ( ~ in(v44, v42) | ? [v45] : (apply(v41, v45) = v44 & in(v45, v43))) & ? [v44] : (v44 = v42 | ? [v45] : ? [v46] : ? [v47] : (( ~ in(v45, v44) | ! [v48] : ( ~ (apply(v41, v48) = v45) | ~ in(v48, v43))) & (in(v45, v44) | (v47 = v45 & apply(v41, v46) = v45 & in(v46, v43))))))) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ~ empty(v42) | empty(v41)) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ? [v43] : ? [v44] : (relation_inverse(v41) = v43 & relation_rng(v43) = v44 & relation_dom(v43) = v42 & relation_dom(v41) = v44)) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ? [v43] : (relation_dom(v41) = v43 & relation_image(v41, v43) = v42)) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ? [v43] : (relation_dom(v41) = v43 & ! [v44] : ! [v45] : ( ~ (relation_composition(v44, v41) = v45) | ~ relation(v44) | ? [v46] : ? [v47] : (relation_rng(v45) = v47 & relation_rng(v44) = v46 & (v47 = v42 | ~ subset(v43, v46)))) & ! [v44] : ! [v45] : ( ~ (relation_rng(v44) = v45) | ~ subset(v43, v45) | ~ relation(v44) | ? [v46] : (relation_composition(v44, v41) = v46 & relation_rng(v46) = v42)))) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ? [v43] : (relation_dom(v41) = v43 & ! [v44] : ! [v45] : ( ~ (relation_composition(v41, v44) = v45) | ~ relation(v44) | ? [v46] : ? [v47] : (relation_dom(v45) = v47 & relation_dom(v44) = v46 & (v47 = v43 | ~ subset(v42, v46)))) & ! [v44] : ! [v45] : ( ~ (relation_dom(v44) = v45) | ~ subset(v42, v45) | ~ relation(v44) | ? [v46] : (relation_composition(v41, v44) = v46 & relation_dom(v46) = v43)))) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ? [v43] : (relation_dom(v41) = v43 & ! [v44] : ! [v45] : ( ~ (relation_rng(v44) = v45) | ~ subset(v41, v44) | ~ relation(v44) | subset(v42, v45)) & ! [v44] : ! [v45] : ( ~ (relation_rng(v44) = v45) | ~ subset(v41, v44) | ~ relation(v44) | ? [v46] : (relation_dom(v44) = v46 & subset(v43, v46))) & ! [v44] : ! [v45] : ( ~ (relation_dom(v44) = v45) | ~ subset(v41, v44) | ~ relation(v44) | subset(v43, v45)) & ! [v44] : ! [v45] : ( ~ (relation_dom(v44) = v45) | ~ subset(v41, v44) | ~ relation(v44) | ? [v46] : (relation_rng(v44) = v46 & subset(v42, v46))))) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ relation(v41) | ? [v43] : (relation_dom(v41) = v43 & ( ~ (v43 = empty_set) | v42 = empty_set) & ( ~ (v42 = empty_set) | v43 = empty_set))) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ empty(v41) | relation(v42)) & ! [v41] : ! [v42] : ( ~ (relation_rng(v41) = v42) | ~ empty(v41) | empty(v42)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ well_orders(v41, v42) | ~ relation(v41) | well_ordering(v41)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ reflexive(v41) | ~ relation(v41) | is_reflexive_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ well_ordering(v41) | ~ relation(v41) | well_orders(v41, v42)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ is_well_founded_in(v41, v42) | ~ relation(v41) | well_founded_relation(v41)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ well_founded_relation(v41) | ~ relation(v41) | is_well_founded_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ is_reflexive_in(v41, v42) | ~ relation(v41) | reflexive(v41)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ is_transitive_in(v41, v42) | ~ relation(v41) | transitive(v41)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ transitive(v41) | ~ relation(v41) | is_transitive_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ is_connected_in(v41, v42) | ~ relation(v41) | connected(v41)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ connected(v41) | ~ relation(v41) | is_connected_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ is_antisymmetric_in(v41, v42) | ~ relation(v41) | antisymmetric(v41)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ antisymmetric(v41) | ~ relation(v41) | is_antisymmetric_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ relation(v41) | reflexive(v41) | ? [v43] : ? [v44] : (ordered_pair(v43, v43) = v44 & in(v43, v42) & ~ in(v44, v41))) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ relation(v41) | well_founded_relation(v41) | ? [v43] : ( ~ (v43 = empty_set) & subset(v43, v42) & ! [v44] : ! [v45] : ( ~ (fiber(v41, v44) = v45) | ~ disjoint(v45, v43) | ~ in(v44, v43)))) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ relation(v41) | connected(v41) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ( ~ (v44 = v43) & ordered_pair(v44, v43) = v46 & ordered_pair(v43, v44) = v45 & in(v44, v42) & in(v43, v42) & ~ in(v46, v41) & ~ in(v45, v41))) & ! [v41] : ! [v42] : ( ~ (relation_field(v41) = v42) | ~ relation(v41) | ? [v43] : ? [v44] : (relation_rng(v41) = v44 & relation_dom(v41) = v43 & set_union2(v43, v44) = v42)) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | ? [v43] : ? [v44] : (function_inverse(v41) = v44 & relation_rng(v44) = v42 & relation_rng(v41) = v43 & relation_dom(v44) = v43)) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ one_to_one(v41) | ~ relation(v41) | ~ function(v41) | ? [v43] : ? [v44] : (function_inverse(v41) = v43 & relation_rng(v41) = v44 & ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v48 = v47 | ~ (relation_dom(v43) = v45) | ~ (apply(v43, v46) = v48) | ~ (apply(v41, v47) = v46) | ~ relation(v43) | ~ function(v43) | ~ in(v47, v42)) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v48 = v46 | ~ (relation_dom(v43) = v45) | ~ (apply(v43, v46) = v47) | ~ (apply(v41, v47) = v48) | ~ relation(v43) | ~ function(v43) | ~ in(v46, v44)) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_dom(v43) = v45) | ~ (apply(v43, v46) = v48) | ~ (apply(v41, v47) = v46) | ~ relation(v43) | ~ function(v43) | ~ in(v47, v42) | in(v46, v44)) & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_dom(v43) = v45) | ~ (apply(v43, v46) = v47) | ~ (apply(v41, v47) = v48) | ~ relation(v43) | ~ function(v43) | ~ in(v46, v44) | in(v47, v42)) & ! [v45] : (v45 = v44 | ~ (relation_dom(v43) = v45) | ~ relation(v43) | ~ function(v43)) & ! [v45] : (v45 = v43 | ~ (relation_dom(v45) = v44) | ~ relation(v45) | ~ function(v45) | ? [v46] : ? [v47] : ? [v48] : ? [v49] : (apply(v45, v46) = v48 & apply(v41, v47) = v49 & ((v49 = v46 & in(v47, v42) & ( ~ (v48 = v47) | ~ in(v46, v44))) | (v48 = v47 & in(v46, v44) & ( ~ (v49 = v46) | ~ in(v47, v42)))))))) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ~ function(v41) | ~ finite(v42) | ? [v43] : (relation_rng(v41) = v43 & finite(v43))) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ~ function(v41) | one_to_one(v41) | ? [v43] : ? [v44] : ? [v45] : ( ~ (v44 = v43) & apply(v41, v44) = v45 & apply(v41, v43) = v45 & in(v44, v42) & in(v43, v42))) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ~ function(v41) | ? [v43] : (relation_rng(v41) = v43 & ! [v44] : ! [v45] : ( ~ (apply(v41, v45) = v44) | ~ in(v45, v42) | in(v44, v43)) & ! [v44] : ( ~ in(v44, v43) | ? [v45] : (apply(v41, v45) = v44 & in(v45, v42))) & ? [v44] : (v44 = v43 | ? [v45] : ? [v46] : ? [v47] : (( ~ in(v45, v44) | ! [v48] : ( ~ (apply(v41, v48) = v45) | ~ in(v48, v42))) & (in(v45, v44) | (v47 = v45 & apply(v41, v46) = v45 & in(v46, v42))))))) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ~ empty(v42) | empty(v41)) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ? [v43] : ? [v44] : (relation_inverse(v41) = v44 & relation_rng(v44) = v42 & relation_rng(v41) = v43 & relation_dom(v44) = v43)) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ? [v43] : (relation_rng(v41) = v43 & ! [v44] : ! [v45] : ( ~ (relation_composition(v44, v41) = v45) | ~ relation(v44) | ? [v46] : ? [v47] : (relation_rng(v45) = v47 & relation_rng(v44) = v46 & (v47 = v43 | ~ subset(v42, v46)))) & ! [v44] : ! [v45] : ( ~ (relation_rng(v44) = v45) | ~ subset(v42, v45) | ~ relation(v44) | ? [v46] : (relation_composition(v44, v41) = v46 & relation_rng(v46) = v43)))) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ? [v43] : (relation_rng(v41) = v43 & ! [v44] : ! [v45] : ( ~ (relation_composition(v41, v44) = v45) | ~ relation(v44) | ? [v46] : ? [v47] : (relation_dom(v45) = v47 & relation_dom(v44) = v46 & (v47 = v42 | ~ subset(v43, v46)))) & ! [v44] : ! [v45] : ( ~ (relation_dom(v44) = v45) | ~ subset(v43, v45) | ~ relation(v44) | ? [v46] : (relation_composition(v41, v44) = v46 & relation_dom(v46) = v42)))) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ? [v43] : (relation_rng(v41) = v43 & ! [v44] : ! [v45] : ( ~ (relation_rng(v44) = v45) | ~ subset(v41, v44) | ~ relation(v44) | subset(v43, v45)) & ! [v44] : ! [v45] : ( ~ (relation_rng(v44) = v45) | ~ subset(v41, v44) | ~ relation(v44) | ? [v46] : (relation_dom(v44) = v46 & subset(v42, v46))) & ! [v44] : ! [v45] : ( ~ (relation_dom(v44) = v45) | ~ subset(v41, v44) | ~ relation(v44) | subset(v42, v45)) & ! [v44] : ! [v45] : ( ~ (relation_dom(v44) = v45) | ~ subset(v41, v44) | ~ relation(v44) | ? [v46] : (relation_rng(v44) = v46 & subset(v43, v46))))) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ relation(v41) | ? [v43] : (relation_rng(v41) = v43 & ( ~ (v43 = empty_set) | v42 = empty_set) & ( ~ (v42 = empty_set) | v43 = empty_set))) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ empty(v41) | relation(v42)) & ! [v41] : ! [v42] : ( ~ (relation_dom(v41) = v42) | ~ empty(v41) | empty(v42)) & ! [v41] : ! [v42] : ( ~ (identity_relation(v41) = v42) | relation_rng(v42) = v41) & ! [v41] : ! [v42] : ( ~ (identity_relation(v41) = v42) | relation_dom(v42) = v41) & ! [v41] : ! [v42] : ( ~ (identity_relation(v41) = v42) | relation(v42)) & ! [v41] : ! [v42] : ( ~ (identity_relation(v41) = v42) | function(v42)) & ! [v41] : ! [v42] : ( ~ (set_intersection2(v41, v42) = empty_set) | disjoint(v41, v42)) & ! [v41] : ! [v42] : ( ~ (the_carrier(v41) = v42) | ~ latt_str(v41) | meet_absorbing(v41) | empty_carrier(v41) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ( ~ (v46 = v44) & meet(v41, v43, v44) = v45 & join(v41, v45, v44) = v46 & element(v44, v42) & element(v43, v42))) & ! [v41] : ! [v42] : ( ~ (the_carrier(v41) = v42) | ~ one_sorted_str(v41) | ~ empty(v42) | empty_carrier(v41)) & ! [v41] : ! [v42] : ( ~ (the_carrier(v41) = v42) | ~ one_sorted_str(v41) | cast_as_carrier_subset(v41) = v42) & ! [v41] : ! [v42] : ( ~ (the_carrier(v41) = v42) | ~ one_sorted_str(v41) | empty_carrier(v41) | ? [v43] : ? [v44] : (powerset(v42) = v43 & element(v44, v43) & ~ empty(v44))) & ! [v41] : ! [v42] : ( ~ (the_carrier(v41) = v42) | ~ one_sorted_str(v41) | ? [v43] : ? [v44] : (cast_as_carrier_subset(v41) = v43 & powerset(v42) = v44 & element(v43, v44))) & ! [v41] : ! [v42] : ( ~ (the_carrier(v41) = v42) | ~ meet_semilatt_str(v41) | empty_carrier(v41) | ? [v43] : (the_L_meet(v41) = v43 & ! [v44] : ! [v45] : ! [v46] : ( ~ (meet(v41, v44, v45) = v46) | ~ element(v45, v42) | ~ element(v44, v42) | apply_binary_as_element(v42, v42, v42, v43, v44, v45) = v46) & ! [v44] : ! [v45] : ! [v46] : ( ~ (apply_binary_as_element(v42, v42, v42, v43, v44, v45) = v46) | ~ element(v45, v42) | ~ element(v44, v42) | meet(v41, v44, v45) = v46))) & ! [v41] : ! [v42] : ( ~ (the_carrier(v41) = v42) | ~ meet_semilatt_str(v41) | ? [v43] : ? [v44] : (the_L_meet(v41) = v43 & cartesian_product2(v42, v42) = v44 & quasi_total(v43, v44, v42) & relation_of2_as_subset(v43, v44, v42) & function(v43))) & ! [v41] : ! [v42] : ( ~ (the_carrier(v41) = v42) | ~ join_semilatt_str(v41) | empty_carrier(v41) | ? [v43] : (the_L_join(v41) = v43 & ! [v44] : ! [v45] : ! [v46] : ( ~ (join(v41, v44, v45) = v46) | ~ element(v45, v42) | ~ element(v44, v42) | apply_binary_as_element(v42, v42, v42, v43, v44, v45) = v46) & ! [v44] : ! [v45] : ! [v46] : ( ~ (apply_binary_as_element(v42, v42, v42, v43, v44, v45) = v46) | ~ element(v45, v42) | ~ element(v44, v42) | join(v41, v44, v45) = v46))) & ! [v41] : ! [v42] : ( ~ (the_carrier(v41) = v42) | ~ join_semilatt_str(v41) | ? [v43] : ? [v44] : (the_L_join(v41) = v43 & cartesian_product2(v42, v42) = v44 & quasi_total(v43, v44, v42) & relation_of2_as_subset(v43, v44, v42) & function(v43))) & ! [v41] : ! [v42] : ( ~ (unordered_pair(v41, v41) = v42) | singleton(v41) = v42) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | ~ finite(v41) | ? [v43] : (powerset(v42) = v43 & ! [v44] : (v44 = empty_set | ~ element(v44, v43) | ? [v45] : (in(v45, v44) & ! [v46] : (v46 = v45 | ~ subset(v45, v46) | ~ in(v46, v44)))))) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | ~ empty(v42)) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | union(v42) = v41) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | diff_closed(v42)) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | cup_closed(v42)) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | preboolean(v42)) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | empty(v41) | ? [v43] : (finite(v43) & element(v43, v42) & ~ empty(v43))) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | empty(v41) | ? [v43] : (element(v43, v42) & ~ empty(v43))) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | ? [v43] : (cast_to_subset(v41) = v43 & element(v43, v42))) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | ? [v43] : (one_to_one(v43) & relation(v43) & function(v43) & finite(v43) & epsilon_connected(v43) & epsilon_transitive(v43) & ordinal(v43) & empty(v43) & natural(v43) & element(v43, v42))) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | ? [v43] : (empty(v43) & element(v43, v42))) & ! [v41] : ! [v42] : ( ~ are_equipotent(v41, v42) | equipotent(v41, v42)) & ! [v41] : ! [v42] : ( ~ well_orders(v41, v42) | ~ relation(v41) | is_well_founded_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ well_orders(v41, v42) | ~ relation(v41) | is_reflexive_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ well_orders(v41, v42) | ~ relation(v41) | is_transitive_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ well_orders(v41, v42) | ~ relation(v41) | is_connected_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ well_orders(v41, v42) | ~ relation(v41) | is_antisymmetric_in(v41, v42)) & ! [v41] : ! [v42] : ( ~ equipotent(v41, v42) | are_equipotent(v41, v42)) & ! [v41] : ! [v42] : ( ~ equipotent(v41, v42) | equipotent(v42, v41)) & ! [v41] : ! [v42] : ( ~ equipotent(v41, v42) | ? [v43] : (relation_rng(v43) = v42 & relation_dom(v43) = v41 & one_to_one(v43) & relation(v43) & function(v43))) & ! [v41] : ! [v42] : ( ~ is_well_founded_in(v41, v42) | ~ is_reflexive_in(v41, v42) | ~ is_transitive_in(v41, v42) | ~ is_connected_in(v41, v42) | ~ is_antisymmetric_in(v41, v42) | ~ relation(v41) | well_orders(v41, v42)) & ! [v41] : ! [v42] : ( ~ disjoint(v41, v42) | disjoint(v42, v41)) & ! [v41] : ! [v42] : ( ~ subset(v41, v42) | ~ finite(v42) | finite(v41)) & ! [v41] : ! [v42] : ( ~ subset(v41, v42) | ~ ordinal(v42) | ~ ordinal(v41) | ordinal_subset(v41, v42)) & ! [v41] : ! [v42] : ( ~ subset(v41, v42) | ~ proper_subset(v42, v41)) & ! [v41] : ! [v42] : ( ~ ordinal_subset(v41, v42) | ~ ordinal(v42) | ~ ordinal(v41) | subset(v41, v42)) & ! [v41] : ! [v42] : ( ~ relation(v42) | ~ relation(v41) | subset(v41, v42) | ? [v43] : ? [v44] : ? [v45] : (ordered_pair(v43, v44) = v45 & in(v45, v41) & ~ in(v45, v42))) & ! [v41] : ! [v42] : ( ~ relation(v41) | ~ in(v42, v41) | ? [v43] : ? [v44] : ordered_pair(v43, v44) = v42) & ! [v41] : ! [v42] : ( ~ epsilon_transitive(v41) | ~ ordinal(v42) | ~ proper_subset(v41, v42) | in(v41, v42)) & ! [v41] : ! [v42] : ( ~ epsilon_transitive(v41) | ~ in(v42, v41) | subset(v42, v41)) & ! [v41] : ! [v42] : ( ~ ordinal(v42) | ~ ordinal(v41) | ordinal_subset(v42, v41) | ordinal_subset(v41, v42)) & ! [v41] : ! [v42] : ( ~ ordinal(v42) | ~ ordinal(v41) | ordinal_subset(v41, v41)) & ! [v41] : ! [v42] : ( ~ ordinal(v42) | ~ in(v42, v41) | ? [v43] : (ordinal(v43) & in(v43, v41) & ! [v44] : ( ~ ordinal(v44) | ~ in(v44, v41) | ordinal_subset(v43, v44)))) & ! [v41] : ! [v42] : ( ~ ordinal(v42) | ~ in(v41, v42) | ordinal(v41)) & ! [v41] : ! [v42] : ( ~ ordinal(v41) | ~ element(v42, v41) | epsilon_connected(v42)) & ! [v41] : ! [v42] : ( ~ ordinal(v41) | ~ element(v42, v41) | epsilon_transitive(v42)) & ! [v41] : ! [v42] : ( ~ ordinal(v41) | ~ element(v42, v41) | ordinal(v42)) & ! [v41] : ! [v42] : ( ~ empty(v42) | ~ empty(v41) | element(v42, v41)) & ! [v41] : ! [v42] : ( ~ empty(v42) | ~ in(v41, v42)) & ! [v41] : ! [v42] : ( ~ empty(v41) | ~ element(v42, v41) | empty(v42)) & ! [v41] : ! [v42] : ( ~ v5_membered(v41) | ~ element(v42, v41) | natural(v42)) & ! [v41] : ! [v42] : ( ~ v5_membered(v41) | ~ element(v42, v41) | v1_int_1(v42)) & ! [v41] : ! [v42] : ( ~ v5_membered(v41) | ~ element(v42, v41) | v1_rat_1(v42)) & ! [v41] : ! [v42] : ( ~ v5_membered(v41) | ~ element(v42, v41) | v1_xreal_0(v42)) & ! [v41] : ! [v42] : ( ~ v5_membered(v41) | ~ element(v42, v41) | v1_xcmplx_0(v42)) & ! [v41] : ! [v42] : ( ~ v4_membered(v41) | ~ element(v42, v41) | v1_int_1(v42)) & ! [v41] : ! [v42] : ( ~ v4_membered(v41) | ~ element(v42, v41) | v1_rat_1(v42)) & ! [v41] : ! [v42] : ( ~ v4_membered(v41) | ~ element(v42, v41) | v1_xreal_0(v42)) & ! [v41] : ! [v42] : ( ~ v4_membered(v41) | ~ element(v42, v41) | v1_xcmplx_0(v42)) & ! [v41] : ! [v42] : ( ~ v3_membered(v41) | ~ element(v42, v41) | v1_rat_1(v42)) & ! [v41] : ! [v42] : ( ~ v3_membered(v41) | ~ element(v42, v41) | v1_xreal_0(v42)) & ! [v41] : ! [v42] : ( ~ v3_membered(v41) | ~ element(v42, v41) | v1_xcmplx_0(v42)) & ! [v41] : ! [v42] : ( ~ v2_membered(v41) | ~ element(v42, v41) | v1_xreal_0(v42)) & ! [v41] : ! [v42] : ( ~ v2_membered(v41) | ~ element(v42, v41) | v1_xcmplx_0(v42)) & ! [v41] : ! [v42] : ( ~ element(v42, v41) | ~ v1_membered(v41) | v1_xcmplx_0(v42)) & ! [v41] : ! [v42] : ( ~ element(v42, v41) | empty(v41) | in(v42, v41)) & ! [v41] : ! [v42] : ( ~ element(v41, v42) | empty(v42) | in(v41, v42)) & ! [v41] : ! [v42] : ( ~ proper_subset(v42, v41) | ~ proper_subset(v41, v42)) & ! [v41] : ! [v42] : ( ~ proper_subset(v41, v42) | subset(v41, v42)) & ! [v41] : ! [v42] : ( ~ in(v42, v41) | ~ in(v41, v42)) & ! [v41] : ! [v42] : ( ~ in(v42, v41) | empty(v41) | element(v42, v41)) & ! [v41] : ! [v42] : ( ~ in(v41, v42) | element(v41, v42)) & ! [v41] : ! [v42] : ( ~ in(v41, v42) | ? [v43] : (in(v43, v42) & ! [v44] : ( ~ in(v44, v43) | ~ in(v44, v42)))) & ? [v41] : ! [v42] : ( ~ relation(v42) | is_well_founded_in(v42, v41) | ? [v43] : ( ~ (v43 = empty_set) & subset(v43, v41) & ! [v44] : ! [v45] : ( ~ (fiber(v42, v44) = v45) | ~ disjoint(v45, v43) | ~ in(v44, v43)))) & ? [v41] : ! [v42] : ( ~ relation(v42) | is_reflexive_in(v42, v41) | ? [v43] : ? [v44] : (ordered_pair(v43, v43) = v44 & in(v43, v41) & ~ in(v44, v42))) & ? [v41] : ! [v42] : ( ~ relation(v42) | is_transitive_in(v42, v41) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : (ordered_pair(v44, v45) = v47 & ordered_pair(v43, v45) = v48 & ordered_pair(v43, v44) = v46 & in(v47, v42) & in(v46, v42) & in(v45, v41) & in(v44, v41) & in(v43, v41) & ~ in(v48, v42))) & ? [v41] : ! [v42] : ( ~ relation(v42) | is_connected_in(v42, v41) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ( ~ (v44 = v43) & ordered_pair(v44, v43) = v46 & ordered_pair(v43, v44) = v45 & in(v44, v41) & in(v43, v41) & ~ in(v46, v42) & ~ in(v45, v42))) & ? [v41] : ! [v42] : ( ~ relation(v42) | is_antisymmetric_in(v42, v41) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ( ~ (v44 = v43) & ordered_pair(v44, v43) = v46 & ordered_pair(v43, v44) = v45 & in(v46, v42) & in(v45, v42) & in(v44, v41) & in(v43, v41))) & ? [v41] : ! [v42] : ( ~ relation(v42) | empty(v41) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ? [v47] : ((v47 = v43 & v46 = v43 & ~ (v45 = v44) & in(v45, v43) & in(v44, v43) & in(v43, v41) & ! [v48] : ! [v49] : ( ~ (ordered_pair(v45, v48) = v49) | ~ in(v48, v43) | in(v49, v42)) & ! [v48] : ! [v49] : ( ~ (ordered_pair(v44, v48) = v49) | ~ in(v48, v43) | in(v49, v42))) | (v44 = v41 & relation_dom(v43) = v41 & relation(v43) & function(v43) & ! [v48] : ! [v49] : ( ~ (apply(v43, v48) = v49) | ~ in(v48, v41) | (in(v49, v48) & ! [v50] : ! [v51] : ( ~ (ordered_pair(v49, v50) = v51) | ~ in(v50, v48) | in(v51, v42))))) | (in(v43, v41) & ! [v48] : ( ~ in(v48, v43) | ? [v49] : ? [v50] : (ordered_pair(v48, v49) = v50 & in(v49, v43) & ~ in(v50, v42)))))) & ? [v41] : ! [v42] : ( ~ relation(v42) | empty(v41) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ? [v47] : ((v47 = v43 & v46 = v43 & ~ (v45 = v44) & in(v45, v43) & in(v44, v43) & in(v43, v41) & ! [v48] : ! [v49] : ( ~ (ordered_pair(v45, v48) = v49) | ~ in(v48, v43) | in(v49, v42)) & ! [v48] : ! [v49] : ( ~ (ordered_pair(v44, v48) = v49) | ~ in(v48, v43) | in(v49, v42))) | (relation(v43) & function(v43) & ! [v48] : ! [v49] : ! [v50] : ( ~ (ordered_pair(v48, v49) = v50) | ~ in(v50, v43) | in(v48, v41)) & ! [v48] : ! [v49] : ! [v50] : ( ~ (ordered_pair(v48, v49) = v50) | ~ in(v50, v43) | (in(v49, v48) & ! [v51] : ! [v52] : ( ~ (ordered_pair(v49, v51) = v52) | ~ in(v51, v48) | in(v52, v42)))) & ! [v48] : ! [v49] : ! [v50] : ( ~ (ordered_pair(v48, v49) = v50) | ~ in(v49, v48) | ~ in(v48, v41) | in(v50, v43) | ? [v51] : ? [v52] : (ordered_pair(v49, v51) = v52 & in(v51, v48) & ~ in(v52, v42)))))) & ? [v41] : ! [v42] : ( ~ relation(v42) | empty(v41) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ? [v47] : ((v47 = v43 & v46 = v43 & ~ (v45 = v44) & in(v45, v43) & in(v44, v43) & in(v43, v41) & ! [v48] : ! [v49] : ( ~ (ordered_pair(v45, v48) = v49) | ~ in(v48, v43) | in(v49, v42)) & ! [v48] : ! [v49] : ( ~ (ordered_pair(v44, v48) = v49) | ~ in(v48, v43) | in(v49, v42))) | ( ! [v48] : ! [v49] : ( ~ in(v49, v41) | ~ in(v48, v49) | in(v48, v43) | ? [v50] : ? [v51] : (ordered_pair(v48, v50) = v51 & in(v50, v49) & ~ in(v51, v42))) & ! [v48] : ( ~ in(v48, v43) | ? [v49] : (in(v49, v41) & in(v48, v49) & ! [v50] : ! [v51] : ( ~ (ordered_pair(v48, v50) = v51) | ~ in(v50, v49) | in(v51, v42))))))) & ! [v41] : (v41 = empty_set | ~ (set_meet(empty_set) = v41)) & ! [v41] : (v41 = empty_set | ~ (relation_rng(v41) = empty_set) | ~ relation(v41)) & ! [v41] : (v41 = empty_set | ~ (relation_dom(v41) = empty_set) | ~ relation(v41)) & ! [v41] : (v41 = empty_set | ~ subset(v41, empty_set)) & ! [v41] : (v41 = empty_set | ~ relation(v41) | ? [v42] : ? [v43] : ? [v44] : (ordered_pair(v42, v43) = v44 & in(v44, v41))) & ! [v41] : (v41 = empty_set | ~ empty(v41)) & ! [v41] : (v41 = omega | ~ being_limit_ordinal(v41) | ~ ordinal(v41) | ~ in(empty_set, v41) | ? [v42] : (being_limit_ordinal(v42) & ordinal(v42) & in(empty_set, v42) & ~ subset(v41, v42))) & ! [v41] : ( ~ (union(v41) = v41) | being_limit_ordinal(v41)) & ! [v41] : ~ (singleton(v41) = empty_set) & ! [v41] : ( ~ latt_str(v41) | meet_semilatt_str(v41)) & ! [v41] : ( ~ latt_str(v41) | join_semilatt_str(v41)) & ! [v41] : ( ~ being_limit_ordinal(v41) | ~ ordinal(v41) | ~ in(empty_set, v41) | subset(omega, v41)) & ! [v41] : ( ~ reflexive(v41) | ~ well_founded_relation(v41) | ~ transitive(v41) | ~ connected(v41) | ~ antisymmetric(v41) | ~ relation(v41) | well_ordering(v41)) & ! [v41] : ( ~ well_ordering(v41) | ~ relation(v41) | reflexive(v41)) & ! [v41] : ( ~ well_ordering(v41) | ~ relation(v41) | well_founded_relation(v41)) & ! [v41] : ( ~ well_ordering(v41) | ~ relation(v41) | transitive(v41)) & ! [v41] : ( ~ well_ordering(v41) | ~ relation(v41) | connected(v41)) & ! [v41] : ( ~ well_ordering(v41) | ~ relation(v41) | antisymmetric(v41)) & ! [v41] : ( ~ meet_semilatt_str(v41) | one_sorted_str(v41)) & ! [v41] : ( ~ join_semilatt_str(v41) | one_sorted_str(v41)) & ! [v41] : ( ~ relation(v41) | ~ function(v41) | ~ empty(v41) | one_to_one(v41)) & ! [v41] : ( ~ relation(v41) | transitive(v41) | ? [v42] : ? [v43] : ? [v44] : ? [v45] : ? [v46] : ? [v47] : (ordered_pair(v43, v44) = v46 & ordered_pair(v42, v44) = v47 & ordered_pair(v42, v43) = v45 & in(v46, v41) & in(v45, v41) & ~ in(v47, v41))) & ! [v41] : ( ~ relation(v41) | antisymmetric(v41) | ? [v42] : ? [v43] : ? [v44] : ? [v45] : ( ~ (v43 = v42) & ordered_pair(v43, v42) = v45 & ordered_pair(v42, v43) = v44 & in(v45, v41) & in(v44, v41))) & ! [v41] : ( ~ diff_closed(v41) | ~ cup_closed(v41) | preboolean(v41)) & ! [v41] : ( ~ preboolean(v41) | diff_closed(v41)) & ! [v41] : ( ~ preboolean(v41) | cup_closed(v41)) & ! [v41] : ( ~ finite(v41) | ? [v42] : ? [v43] : (relation_rng(v42) = v41 & relation_dom(v42) = v43 & relation(v42) & function(v42) & in(v43, omega))) & ! [v41] : ( ~ epsilon_connected(v41) | ~ epsilon_transitive(v41) | ordinal(v41)) & ! [v41] : ( ~ ordinal(v41) | ~ empty(v41) | epsilon_connected(v41)) & ! [v41] : ( ~ ordinal(v41) | ~ empty(v41) | epsilon_transitive(v41)) & ! [v41] : ( ~ ordinal(v41) | ~ empty(v41) | natural(v41)) & ! [v41] : ( ~ ordinal(v41) | being_limit_ordinal(v41) | ? [v42] : ? [v43] : (succ(v42) = v43 & ordinal(v42) & in(v42, v41) & ~ in(v43, v41))) & ! [v41] : ( ~ ordinal(v41) | being_limit_ordinal(v41) | ? [v42] : (succ(v42) = v41 & ordinal(v42))) & ! [v41] : ( ~ ordinal(v41) | epsilon_connected(v41)) & ! [v41] : ( ~ ordinal(v41) | epsilon_transitive(v41)) & ! [v41] : ( ~ empty(v41) | relation(v41)) & ! [v41] : ( ~ empty(v41) | function(v41)) & ! [v41] : ( ~ empty(v41) | finite(v41)) & ! [v41] : ( ~ empty(v41) | epsilon_connected(v41)) & ! [v41] : ( ~ empty(v41) | epsilon_transitive(v41)) & ! [v41] : ( ~ empty(v41) | ordinal(v41)) & ! [v41] : ( ~ empty(v41) | v5_membered(v41)) & ! [v41] : ( ~ empty(v41) | v4_membered(v41)) & ! [v41] : ( ~ empty(v41) | v3_membered(v41)) & ! [v41] : ( ~ empty(v41) | v2_membered(v41)) & ! [v41] : ( ~ empty(v41) | v1_membered(v41)) & ! [v41] : ( ~ v5_membered(v41) | v4_membered(v41)) & ! [v41] : ( ~ v4_membered(v41) | v3_membered(v41)) & ! [v41] : ( ~ v3_membered(v41) | v2_membered(v41)) & ! [v41] : ( ~ v2_membered(v41) | v1_membered(v41)) & ! [v41] : ( ~ element(v41, omega) | epsilon_connected(v41)) & ! [v41] : ( ~ element(v41, omega) | epsilon_transitive(v41)) & ! [v41] : ( ~ element(v41, omega) | ordinal(v41)) & ! [v41] : ( ~ element(v41, omega) | natural(v41)) & ! [v41] : ~ proper_subset(v41, v41) & ! [v41] : ~ in(v41, empty_set) & ? [v41] : ? [v42] : ? [v43] : relation_of2(v43, v41, v42) & ? [v41] : ? [v42] : ? [v43] : relation_of2_as_subset(v43, v41, v42) & ? [v41] : ? [v42] : ? [v43] : (relation_of2(v43, v41, v42) & quasi_total(v43, v41, v42) & relation(v43) & function(v43)) & ? [v41] : ? [v42] : ? [v43] : (relation_of2(v43, v41, v42) & relation(v43) & function(v43)) & ? [v41] : ? [v42] : (v42 = v41 | ? [v43] : (( ~ in(v43, v42) | ~ in(v43, v41)) & (in(v43, v42) | in(v43, v41)))) & ? [v41] : ? [v42] : (disjoint(v41, v42) | ? [v43] : (in(v43, v42) & in(v43, v41))) & ? [v41] : ? [v42] : (subset(v41, v42) | ? [v43] : (in(v43, v41) & ~ in(v43, v42))) & ? [v41] : ? [v42] : element(v42, v41) & ? [v41] : ? [v42] : (relation_dom(v42) = v41 & relation(v42) & function(v42) & ! [v43] : ! [v44] : ( ~ (singleton(v43) = v44) | ~ in(v43, v41) | apply(v42, v43) = v44) & ! [v43] : ! [v44] : ( ~ (apply(v42, v43) = v44) | ~ in(v43, v41) | singleton(v43) = v44)) & ? [v41] : ? [v42] : (well_orders(v42, v41) & relation(v42)) & ? [v41] : ? [v42] : (relation(v42) & function(v42) & ! [v43] : ! [v44] : ! [v45] : ( ~ (ordered_pair(v43, v44) = v45) | ~ in(v45, v42) | singleton(v43) = v44) & ! [v43] : ! [v44] : ! [v45] : ( ~ (ordered_pair(v43, v44) = v45) | ~ in(v45, v42) | in(v43, v41)) & ! [v43] : ! [v44] : ! [v45] : ( ~ (ordered_pair(v43, v44) = v45) | ~ in(v43, v41) | in(v45, v42) | ? [v46] : ( ~ (v46 = v44) & singleton(v43) = v46))) & ? [v41] : ? [v42] : (in(v41, v42) & ! [v43] : ! [v44] : ( ~ (powerset(v43) = v44) | ~ in(v43, v42) | in(v44, v42)) & ! [v43] : ! [v44] : ( ~ subset(v44, v43) | ~ in(v43, v42) | in(v44, v42)) & ! [v43] : ( ~ subset(v43, v42) | are_equipotent(v43, v42) | in(v43, v42))) & ? [v41] : ? [v42] : (in(v41, v42) & ! [v43] : ! [v44] : ( ~ subset(v44, v43) | ~ in(v43, v42) | in(v44, v42)) & ! [v43] : ( ~ subset(v43, v42) | are_equipotent(v43, v42) | in(v43, v42)) & ! [v43] : ( ~ in(v43, v42) | ? [v44] : (in(v44, v42) & ! [v45] : ( ~ subset(v45, v43) | in(v45, v44))))) & ? [v41] : ? [v42] : ( ! [v43] : ! [v44] : ( ~ (singleton(v44) = v43) | ~ in(v44, v41) | in(v43, v42)) & ! [v43] : ( ~ in(v43, v42) | ? [v44] : (singleton(v44) = v43 & in(v44, v41)))) & ? [v41] : ? [v42] : ( ! [v43] : ( ~ ordinal(v43) | ~ in(v43, v41) | in(v43, v42)) & ! [v43] : ( ~ in(v43, v42) | ordinal(v43)) & ! [v43] : ( ~ in(v43, v42) | in(v43, v41))) & ? [v41] : (v41 = empty_set | ? [v42] : in(v42, v41)) & ? [v41] : equipotent(v41, v41) & ? [v41] : subset(v41, v41) & ? [v41] : subset(empty_set, v41) & ? [v41] : (relation(v41) | ? [v42] : (in(v42, v41) & ! [v43] : ! [v44] : ~ (ordered_pair(v43, v44) = v42))) & ? [v41] : (function(v41) | ? [v42] : ? [v43] : ? [v44] : ? [v45] : ? [v46] : ( ~ (v44 = v43) & ordered_pair(v42, v44) = v46 & ordered_pair(v42, v43) = v45 & in(v46, v41) & in(v45, v41))) & ? [v41] : (epsilon_connected(v41) | ? [v42] : ? [v43] : ( ~ (v43 = v42) & in(v43, v41) & in(v42, v41) & ~ in(v43, v42) & ~ in(v42, v43))) & ? [v41] : (epsilon_transitive(v41) | ? [v42] : (in(v42, v41) & ~ subset(v42, v41))) & ? [v41] : (ordinal(v41) | ? [v42] : (in(v42, v41) & ( ~ subset(v42, v41) | ~ ordinal(v42)))) & ? [v41] : (empty(v41) | ? [v42] : ? [v43] : ((v43 = v41 & relation_dom(v42) = v41 & relation(v42) & function(v42) & ! [v44] : ! [v45] : ( ~ (apply(v42, v44) = v45) | ~ in(v44, v41) | in(v45, v44))) | (v42 = empty_set & in(empty_set, v41)))) & ( ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | ~ ordinal(v41) | ~ in(v41, omega) | ? [v43] : (powerset(v42) = v43 & ! [v44] : (v44 = empty_set | ~ element(v44, v43) | ? [v45] : (in(v45, v44) & ! [v46] : (v46 = v45 | ~ subset(v45, v46) | ~ in(v46, v44)))))) | ( ~ (v18 = empty_set) & succ(v12) = v15 & powerset(v16) = v17 & powerset(v15) = v16 & powerset(v13) = v14 & powerset(v12) = v13 & ordinal(v12) & element(v18, v17) & in(v15, omega) & ! [v41] : ( ~ in(v41, v18) | ? [v42] : ( ~ (v42 = v41) & subset(v41, v42) & in(v42, v18))) & ( ~ in(v12, omega) | ! [v41] : (v41 = empty_set | ~ element(v41, v14) | ? [v42] : (in(v42, v41) & ! [v43] : (v43 = v42 | ~ subset(v42, v43) | ~ in(v43, v41)))))) | ( ~ (v15 = empty_set) & ~ (v12 = empty_set) & powerset(v13) = v14 & powerset(v12) = v13 & being_limit_ordinal(v12) & ordinal(v12) & element(v15, v14) & in(v12, omega) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | ~ ordinal(v41) | ~ in(v41, v12) | ~ in(v41, omega) | ? [v43] : (powerset(v42) = v43 & ! [v44] : (v44 = empty_set | ~ element(v44, v43) | ? [v45] : (in(v45, v44) & ! [v46] : (v46 = v45 | ~ subset(v45, v46) | ~ in(v46, v44)))))) & ! [v41] : ( ~ in(v41, v15) | ? [v42] : ( ~ (v42 = v41) & subset(v41, v42) & in(v42, v15)))) | ( ~ (v12 = empty_set) & element(v12, v1) & ! [v41] : ( ~ in(v41, v12) | ? [v42] : ( ~ (v42 = v41) & subset(v41, v42) & in(v42, v12))))) & ( ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | ~ ordinal(v41) | ~ in(v41, omega) | ? [v43] : (powerset(v42) = v43 & ! [v44] : (v44 = empty_set | ~ element(v44, v43) | ? [v45] : (in(v45, v44) & ! [v46] : (v46 = v45 | ~ subset(v45, v46) | ~ in(v46, v44)))))) | ( ~ (v11 = empty_set) & powerset(v9) = v10 & powerset(v8) = v9 & ordinal(v8) & element(v11, v10) & in(v8, omega) & ! [v41] : ! [v42] : ( ~ (powerset(v41) = v42) | ~ ordinal(v41) | ~ in(v41, v8) | ~ in(v41, omega) | ? [v43] : (powerset(v42) = v43 & ! [v44] : (v44 = empty_set | ~ element(v44, v43) | ? [v45] : (in(v45, v44) & ! [v46] : (v46 = v45 | ~ subset(v45, v46) | ~ in(v46, v44)))))) & ! [v41] : ( ~ in(v41, v11) | ? [v42] : ( ~ (v42 = v41) & subset(v41, v42) & in(v42, v11)))))) % 28.94/7.30 | 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, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19, all_0_20_20, all_0_21_21, all_0_22_22, all_0_23_23, all_0_24_24, all_0_25_25, all_0_26_26, all_0_27_27, all_0_28_28, all_0_29_29, all_0_30_30, all_0_31_31, all_0_32_32, all_0_33_33, all_0_34_34, all_0_35_35, all_0_36_36, all_0_37_37, all_0_38_38, all_0_39_39, all_0_40_40 yields: % 28.94/7.30 | (1) ~ (all_0_33_33 = all_0_34_34) & cast_as_carrier_subset(all_0_38_38) = all_0_35_35 & singleton(empty_set) = all_0_40_40 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & subset_intersection2(all_0_37_37, all_0_34_34, all_0_35_35) = all_0_33_33 & the_carrier(all_0_38_38) = all_0_37_37 & powerset(all_0_37_37) = all_0_36_36 & powerset(all_0_40_40) = all_0_39_39 & powerset(empty_set) = all_0_40_40 & relation_empty_yielding(all_0_19_19) & relation_empty_yielding(all_0_21_21) & relation_empty_yielding(empty_set) & latt_str(all_0_3_3) & being_limit_ordinal(all_0_9_9) & being_limit_ordinal(omega) & one_sorted_str(all_0_1_1) & one_sorted_str(all_0_20_20) & one_sorted_str(all_0_38_38) & meet_semilatt_str(all_0_0_0) & join_semilatt_str(all_0_2_2) & one_to_one(all_0_10_10) & one_to_one(all_0_14_14) & one_to_one(all_0_17_17) & one_to_one(empty_set) & relation(all_0_6_6) & relation(all_0_10_10) & relation(all_0_11_11) & relation(all_0_13_13) & relation(all_0_14_14) & relation(all_0_15_15) & relation(all_0_17_17) & relation(all_0_19_19) & relation(all_0_21_21) & relation(empty_set) & function(all_0_6_6) & function(all_0_10_10) & function(all_0_13_13) & function(all_0_14_14) & function(all_0_17_17) & function(all_0_21_21) & function(empty_set) & finite(all_0_5_5) & epsilon_connected(all_0_4_4) & epsilon_connected(all_0_8_8) & epsilon_connected(all_0_9_9) & epsilon_connected(all_0_14_14) & epsilon_connected(all_0_18_18) & epsilon_connected(empty_set) & epsilon_connected(omega) & epsilon_transitive(all_0_4_4) & epsilon_transitive(all_0_8_8) & epsilon_transitive(all_0_9_9) & epsilon_transitive(all_0_14_14) & epsilon_transitive(all_0_18_18) & epsilon_transitive(empty_set) & epsilon_transitive(omega) & ordinal(all_0_4_4) & ordinal(all_0_8_8) & ordinal(all_0_9_9) & ordinal(all_0_14_14) & ordinal(all_0_18_18) & ordinal(empty_set) & ordinal(omega) & empty(all_0_10_10) & empty(all_0_11_11) & empty(all_0_12_12) & empty(all_0_13_13) & empty(all_0_14_14) & empty(empty_set) & natural(all_0_4_4) & v5_membered(all_0_7_7) & v5_membered(empty_set) & v4_membered(all_0_7_7) & v4_membered(empty_set) & v3_membered(all_0_7_7) & v3_membered(empty_set) & v2_membered(all_0_7_7) & v2_membered(empty_set) & element(all_0_34_34, all_0_36_36) & v1_membered(all_0_7_7) & v1_membered(empty_set) & in(empty_set, omega) & ~ empty_carrier(all_0_20_20) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ~ empty(all_0_7_7) & ~ empty(all_0_15_15) & ~ empty(all_0_16_16) & ~ empty(all_0_18_18) & ~ empty(omega) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (apply_binary_as_element(v7, v6, v5, v4, v3, v2) = v1) | ~ (apply_binary_as_element(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = empty_set | ~ (relation_composition(v3, v5) = v6) | ~ (apply(v6, v2) = v7) | ~ (apply(v3, v2) = v4) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ relation(v5) | ~ function(v5) | ~ function(v3) | ~ in(v2, v0) | apply(v5, v4) = v7) & ! [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] : (v1 = empty_set | ~ (relation_inverse_image(v3, v2) = v4) | ~ (apply(v3, v5) = v6) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ function(v3) | ~ in(v6, v2) | ~ in(v5, v0) | in(v5, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = empty_set | ~ (relation_inverse_image(v3, v2) = v4) | ~ (apply(v3, v5) = v6) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ function(v3) | ~ in(v5, v4) | in(v6, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = empty_set | ~ (relation_inverse_image(v3, v2) = v4) | ~ (apply(v3, v5) = v6) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ function(v3) | ~ in(v5, v4) | in(v5, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = empty_set | ~ (apply(v5, v4) = v6) | ~ (apply(v3, v2) = v4) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ relation(v5) | ~ function(v5) | ~ function(v3) | ~ in(v2, v0) | ? [v7] : (relation_composition(v3, v5) = v7 & apply(v7, v2) = v6)) & ! [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] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ~ function(v3) | ~ element(v5, v1) | ~ element(v4, v0) | empty(v1) | empty(v0) | element(v6, v2) | ? [v7] : (cartesian_product2(v0, v1) = v7 & ( ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ~ function(v3) | ~ element(v5, v1) | ~ element(v4, v0) | empty(v1) | empty(v0) | ? [v7] : ? [v8] : (apply_binary(v3, v4, v5) = v8 & cartesian_product2(v0, v1) = v7 & (v8 = v6 | ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2)))) & ! [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] : (v5 = v3 | ~ (meet(v0, v2, v3) = v4) | ~ (join(v0, v4, v3) = v5) | ~ (the_carrier(v0) = v1) | ~ meet_absorbing(v0) | ~ latt_str(v0) | ~ element(v3, v1) | ~ element(v2, v1) | empty_carrier(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (ordered_pair(v1, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ function(v0) | ~ in(v5, v0) | ~ in(v4, 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] : ( ~ (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_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] : ( ~ (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 | ~ (join(v0, v2, v3) = v4) | ~ (the_carrier(v0) = v1) | ~ below(v0, v2, v3) | ~ join_semilatt_str(v0) | ~ element(v3, v1) | ~ element(v2, v1) | empty_carrier(v0)) & ! [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 | ~ (apply_binary(v4, v3, v2) = v1) | ~ (apply_binary(v4, v3, v2) = v0)) & ! [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 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(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 = v0 | ~ (subset_intersection2(v4, v3, v2) = v1) | ~ (subset_intersection2(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet_commut(v4, v3, v2) = v1) | ~ (meet_commut(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join_commut(v4, v3, v2) = v1) | ~ (join_commut(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] : (v1 = empty_set | ~ (apply(v3, v2) = v4) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ function(v3) | ~ in(v2, v0) | ? [v5] : (relation_rng(v3) = v5 & in(v4, v5))) & ! [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] : ( ~ (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_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] : ( ~ (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] : ( ~ (meet_commut(v0, v2, v3) = v4) | ~ (the_carrier(v0) = v1) | ~ meet_absorbing(v0) | ~ latt_str(v0) | ~ meet_commutative(v0) | ~ element(v3, v1) | ~ element(v2, v1) | below(v0, v4, v2) | empty_carrier(v0)) & ! [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] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_intersection2(v0, v1, v2) = 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] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (powerset(v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : ? [v7] : (powerset(v4) = v6 & powerset(v3) = v5 & ( ~ element(v0, v5) | ( ! [v8] : ! [v9] : ( ~ (relation_image(v2, v8) = v9) | ~ in(v9, v0) | ~ in(v8, v6) | in(v8, v7)) & ! [v8] : ! [v9] : ( ~ (relation_image(v2, v8) = v9) | ~ in(v8, v7) | in(v9, v0)) & ! [v8] : ! [v9] : ( ~ (relation_image(v2, v8) = v9) | ~ in(v8, v7) | in(v8, v6)))))) & ! [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 = v2 | ~ (the_carrier(v0) = v1) | ~ below(v0, v3, v2) | ~ below(v0, v2, v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | ~ element(v3, v1) | ~ element(v2, v1) | empty_carrier(v0)) & ! [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 | ~ (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 | ~ (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 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v1 = empty_set | ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ quasi_total(v2, v0, v1) | ~ relation_of2_as_subset(v2, v0, v1)) & ! [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] : (v1 = empty_set | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ subset(v1, v2) | ~ function(v3) | quasi_total(v3, v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ subset(v1, v2) | ~ function(v3) | relation_of2_as_subset(v3, v0, v2)) & ! [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] : ( ~ (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] : ( ~ (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] : ( ~ (meet(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (meet_commut(v0, v1, v2) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [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] : ( ~ (join(v0, v2, v3) = v3) | ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | ~ element(v3, v1) | ~ element(v2, v1) | below(v0, v2, v3) | empty_carrier(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (the_carrier(v0) = v4 & join_commut(v0, v1, v2) = v5 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [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] : ( ~ (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] : ( ~ (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] : ( ~ (subset_intersection2(v0, v2, v1) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v2, v1) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_intersection2(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v2, v1) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (meet_commut(v0, v1, v2) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (meet(v0, v1, v2) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (meet_commut(v0, v2, v1) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [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] : ( ~ (join_commut(v0, v2, v1) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (the_carrier(v0) = v4 & join_commut(v0, v1, v2) = v5 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join_commut(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (join(v0, v1, v2) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join_commut(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (the_carrier(v0) = v4 & join_commut(v0, v2, v1) = v5 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join_commut(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [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, v2) = v3) | ~ relation(v1) | empty(v0) | ? [v4] : ( ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v7) = v5) | ~ in(v7, v6) | ~ in(v6, v0) | ~ in(v5, v3) | in(v5, v4) | ? [v8] : ? [v9] : (ordered_pair(v7, v8) = v9 & in(v8, v6) & ~ in(v9, v1))) & ! [v5] : ( ~ in(v5, v4) | in(v5, v3)) & ! [v5] : ( ~ in(v5, v4) | ? [v6] : ? [v7] : (ordered_pair(v6, v7) = v5 & in(v7, v6) & in(v6, v0) & ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ in(v8, v6) | in(v9, v1)))))) & ! [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) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (powerset(v3) = v4 & element(v2, v4))) & ! [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] : ( ~ (cartesian_product2(v0, v0) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ? [v4] : ( ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (apply(v2, v7) = v9) | ~ (apply(v2, v6) = v8) | ~ (ordered_pair(v8, v9) = v10) | ~ in(v10, v1) | ~ in(v5, v3) | in(v5, v4) | ? [v11] : ( ~ (v11 = v5) & ordered_pair(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v7) = v5) | ~ in(v5, v3) | in(v5, v4) | ? [v8] : ? [v9] : ? [v10] : (apply(v2, v7) = v9 & apply(v2, v6) = v8 & ordered_pair(v8, v9) = v10 & ~ in(v10, v1))) & ! [v5] : ( ~ in(v5, v4) | in(v5, v3)) & ! [v5] : ( ~ in(v5, v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (apply(v2, v7) = v9 & apply(v2, v6) = v8 & ordered_pair(v8, v9) = v10 & ordered_pair(v6, v7) = v5 & in(v10, v1))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ 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 = v2 | ~ (subset_intersection2(v1, v2, v2) = v3) | ? [v4] : (powerset(v1) = v4 & ( ~ element(v2, v4) | ~ element(v0, v4)))) & ? [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_dom_as_subset(empty_set, v0, v1) = v2) | ~ quasi_total(v1, empty_set, v0) | ~ relation_of2_as_subset(v1, empty_set, v0)) & ! [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 | ~ (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 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ (the_L_meet(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 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(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 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | v0 = empty_set | ~ (relation_dom_as_subset(v0, empty_set, v1) = v2) | ~ quasi_total(v1, v0, empty_set) | ~ relation_of2_as_subset(v1, v0, empty_set)) & ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (relation_dom_as_subset(v0, v1, v2) = v0) | ~ relation_of2_as_subset(v2, v0, v1) | quasi_total(v2, v0, v1)) & ! [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) | ~ well_orders(v1, v0) | ~ relation(v1) | relation_field(v2) = v0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_orders(v1, v0) | ~ relation(v1) | well_ordering(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] : ( ~ (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) | ~ finite(v0) | finite(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_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] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_field(v1) = v2) | ~ equipotent(v0, v2) | ~ well_ordering(v1) | ~ relation(v1) | ? [v3] : (well_orders(v3, v0) & relation(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) | ~ function(v1) | ~ finite(v0) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v1) = v3 & relation_image(v1, v4) = v2 & set_intersection2(v3, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | ~ finite(v1) | finite(v2)) & ! [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) | ~ v5_membered(v0) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v1_membered(v0) | v1_membered(v2)) & ! [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) | ~ finite(v1) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v0) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(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] : ( ~ (the_carrier(v0) = v1) | ~ (cartesian_product2(v1, v1) = v2) | ~ meet_semilatt_str(v0) | ? [v3] : (the_L_meet(v0) = v3 & quasi_total(v3, v2, v1) & relation_of2_as_subset(v3, v2, v1) & function(v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v1) | ~ (cartesian_product2(v1, v1) = v2) | ~ join_semilatt_str(v0) | ? [v3] : (the_L_join(v0) = v3 & quasi_total(v3, v2, v1) & relation_of2_as_subset(v3, v2, v1) & function(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) | ~ finite(v1) | ~ finite(v0) | finite(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] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ( ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v5, v6) = v4) | ~ in(v5, v0) | ~ in(v4, v2) | in(v4, v3) | ? [v7] : ( ~ (v7 = v6) & singleton(v5) = v7)) & ! [v4] : ( ~ in(v4, v3) | in(v4, v2)) & ! [v4] : ( ~ in(v4, v3) | ? [v5] : ? [v6] : (singleton(v5) = v6 & ordered_pair(v5, v6) = v4 & in(v5, 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) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [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] : ( ~ quasi_total(v2, empty_set, v0) | ~ relation_of2_as_subset(v2, empty_set, v0) | ~ subset(v0, v1) | ~ function(v2) | quasi_total(v2, empty_set, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ quasi_total(v2, empty_set, v0) | ~ relation_of2_as_subset(v2, empty_set, v0) | ~ subset(v0, v1) | ~ function(v2) | relation_of2_as_subset(v2, empty_set, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(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 | ~ (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_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 | ~ (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) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (succ(v1) = v3 & powerset(v4) = v5 & powerset(v3) = v4 & powerset(v1) = v6 & ( ~ element(v0, v5) | ( ! [v8] : ! [v9] : ( ~ (set_difference(v9, v2) = v8) | ~ in(v9, v0) | ~ in(v8, v6) | in(v8, v7)) & ! [v8] : ( ~ in(v8, v7) | in(v8, v6)) & ! [v8] : ( ~ in(v8, v7) | ? [v9] : (set_difference(v9, v2) = v8 & in(v9, v0))))))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (singleton(v1) = v6 & powerset(v3) = v4 & powerset(v2) = v3 & powerset(v1) = v5 & ( ~ element(v0, v4) | ( ! [v8] : ! [v9] : ( ~ (set_difference(v9, v6) = v8) | ~ in(v9, v0) | ~ in(v8, v5) | in(v8, v7)) & ! [v8] : ( ~ in(v8, v7) | in(v8, v5)) & ! [v8] : ( ~ in(v8, v7) | ? [v9] : (set_difference(v9, v6) = v8 & in(v9, v0))))))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (singleton(v1) = v5 & powerset(v3) = v4 & powerset(v2) = v3 & powerset(v1) = v6 & ( ~ element(v0, v4) | ( ! [v8] : ! [v9] : ( ~ (set_difference(v9, v5) = v8) | ~ in(v9, v0) | ~ in(v8, v6) | in(v8, v7)) & ! [v8] : ( ~ in(v8, v7) | in(v8, v6)) & ! [v8] : ( ~ in(v8, v7) | ? [v9] : (set_difference(v9, v5) = v8 & in(v9, 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] : ( ~ (relation_rng(v2) = v1) | ~ one_to_one(v2) | ~ relation(v2) | ~ function(v2) | equipotent(v0, v1) | ? [v3] : ( ~ (v3 = v0) & relation_dom(v2) = v3)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v2) = v1) | ~ one_to_one(v2) | ~ relation(v2) | ~ function(v2) | equipotent(v1, v0) | ? [v3] : ( ~ (v3 = v0) & relation_rng(v2) = v3)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(v2, omega) | finite(v0) | ? [v3] : ( ~ (v3 = v0) & relation_rng(v1) = v3)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (singleton(v1) = v6 & succ(v1) = v3 & powerset(v4) = v5 & powerset(v3) = v4 & ( ~ element(v0, v5) | ( ! [v8] : ! [v9] : ( ~ (set_difference(v9, v6) = v8) | ~ in(v9, v0) | ~ in(v8, v2) | in(v8, v7)) & ! [v8] : ( ~ in(v8, v7) | in(v8, v2)) & ! [v8] : ( ~ in(v8, v7) | ? [v9] : (set_difference(v9, v6) = v8 & in(v9, v0))))))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) & ? [v0] : ! [v1] : ! [v2] : ( ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ? [v3] : (relation(v3) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v2, v4) = v6) | ~ (ordered_pair(v6, v7) = v8) | ~ in(v8, v1) | ~ in(v5, v0) | ~ in(v4, v0) | ? [v9] : (ordered_pair(v4, v5) = v9 & in(v9, v3))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v2, v4) = v6) | ~ (ordered_pair(v6, v7) = v8) | in(v8, v1) | ? [v9] : (ordered_pair(v4, v5) = v9 & ~ in(v9, v3))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v2, v4) = v6) | ~ (ordered_pair(v6, v7) = v8) | in(v5, v0) | ? [v9] : (ordered_pair(v4, v5) = v9 & ~ in(v9, v3))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v2, v4) = v6) | ~ (ordered_pair(v6, v7) = v8) | in(v4, v0) | ? [v9] : (ordered_pair(v4, v5) = v9 & ~ in(v9, v3))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v6, v3) | in(v5, v0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v6, v3) | in(v4, v0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v6, v3) | ? [v7] : ? [v8] : ? [v9] : (apply(v2, v5) = v8 & apply(v2, v4) = v7 & ordered_pair(v7, v8) = v9 & in(v9, v1))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v5, v0) | ~ in(v4, v0) | in(v6, v3) | ? [v7] : ? [v8] : ? [v9] : (apply(v2, v5) = v8 & apply(v2, v4) = v7 & ordered_pair(v7, v8) = v9 & ~ in(v9, 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_dom_as_subset(v0, empty_set, empty_set) = v1) | ~ relation_of2_as_subset(empty_set, v0, empty_set) | quasi_total(empty_set, v0, empty_set)) & ! [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] : ( ~ (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] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | the_carrier(v0) = v1) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) & ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | meet(v0, v3, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & cartesian_product2(v2, v2) = v3 & quasi_total(v1, v3, v2) & relation_of2_as_subset(v1, v3, v2))) & ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | well_ordering(v1)) & ! [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) | finite(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) | ~ natural(v0)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | epsilon_connected(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | epsilon_transitive(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | ordinal(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | natural(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) | ~ ordinal(v0) | ? [v2] : ( ! [v3] : ! [v4] : ( ~ (powerset(v3) = v4) | ~ ordinal(v3) | ~ in(v3, v1) | in(v3, v2) | in(v3, omega)) & ! [v3] : ! [v4] : ( ~ (powerset(v3) = v4) | ~ ordinal(v3) | ~ in(v3, v1) | in(v3, v2) | ? [v5] : ? [v6] : ( ~ (v6 = empty_set) & powerset(v4) = v5 & element(v6, v5) & ! [v7] : ( ~ in(v7, v6) | ? [v8] : ( ~ (v8 = v7) & subset(v7, v8) & in(v8, v6))))) & ! [v3] : ( ~ in(v3, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v3) = v4 & ordinal(v3) & ( ~ in(v3, omega) | ! [v6] : (v6 = empty_set | ~ element(v6, v5) | ? [v7] : (in(v7, v6) & ! [v8] : (v8 = v7 | ~ subset(v7, v8) | ~ in(v8, v6))))))))) & ! [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] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | join(v0, v3, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & cartesian_product2(v2, v2) = v3 & quasi_total(v1, v3, v2) & relation_of2_as_subset(v1, v3, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom_as_subset(empty_set, v0, v1) = empty_set) | ~ relation_of2_as_subset(v1, empty_set, v0) | quasi_total(v1, empty_set, v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v1) = v0) | ~ relation(v1) | ~ function(v1) | finite(v0) | ? [v2] : (relation_dom(v1) = v2 & ~ in(v2, omega))) & ! [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) | finite(v1) | ? [v2] : (relation_dom(v0) = v2 & ~ finite(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] : ( ~ (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) | ~ finite(v1) | ? [v2] : (relation_rng(v0) = v2 & finite(v2))) & ! [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] : ( ~ (the_carrier(v0) = v1) | ~ latt_str(v0) | meet_absorbing(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v3) & meet(v0, v2, v3) = v4 & join(v0, v4, v3) = v5 & element(v3, v1) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0)) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | cast_as_carrier_subset(v0) = v1) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_L_meet(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | meet(v0, v3, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v2] : ? [v3] : (the_L_meet(v0) = v2 & cartesian_product2(v1, v1) = v3 & quasi_total(v2, v3, v1) & relation_of2_as_subset(v2, v3, v1) & function(v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_L_join(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | join(v0, v3, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | ? [v2] : ? [v3] : (the_L_join(v0) = v2 & cartesian_product2(v1, v1) = v3 & quasi_total(v2, v3, v1) & relation_of2_as_subset(v2, v3, v1) & function(v2))) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2))) & ! [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] : (one_to_one(v2) & relation(v2) & function(v2) & finite(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & ordinal(v2) & empty(v2) & natural(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ are_equipotent(v0, v1) | equipotent(v0, v1)) & ! [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] : ( ~ equipotent(v0, v1) | are_equipotent(v0, v1)) & ! [v0] : ! [v1] : ( ~ equipotent(v0, v1) | equipotent(v1, v0)) & ! [v0] : ! [v1] : ( ~ equipotent(v0, v1) | ? [v2] : (relation_rng(v2) = v1 & relation_dom(v2) = v0 & one_to_one(v2) & relation(v2) & function(v2))) & ! [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) | ~ finite(v1) | finite(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] : ( ~ 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] : ( ~ ordinal(v0) | ~ element(v1, v0) | epsilon_connected(v1)) & ! [v0] : ! [v1] : ( ~ ordinal(v0) | ~ element(v1, v0) | epsilon_transitive(v1)) & ! [v0] : ! [v1] : ( ~ ordinal(v0) | ~ element(v1, v0) | ordinal(v1)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ empty(v0) | ~ element(v1, v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | natural(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(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) | empty(v0) | element(v1, 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] : ! [v1] : ( ~ relation(v1) | empty(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = v2 & v5 = v2 & ~ (v4 = v3) & in(v4, v2) & in(v3, v2) & in(v2, v0) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v7, v2) | in(v8, v1)) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v3, v7) = v8) | ~ in(v7, v2) | in(v8, v1))) | (v3 = v0 & relation_dom(v2) = v0 & relation(v2) & function(v2) & ! [v7] : ! [v8] : ( ~ (apply(v2, v7) = v8) | ~ in(v7, v0) | (in(v8, v7) & ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ in(v9, v7) | in(v10, v1))))) | (in(v2, v0) & ! [v7] : ( ~ in(v7, v2) | ? [v8] : ? [v9] : (ordered_pair(v7, v8) = v9 & in(v8, v2) & ~ in(v9, v1)))))) & ? [v0] : ! [v1] : ( ~ relation(v1) | empty(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = v2 & v5 = v2 & ~ (v4 = v3) & in(v4, v2) & in(v3, v2) & in(v2, v0) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v7, v2) | in(v8, v1)) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v3, v7) = v8) | ~ in(v7, v2) | in(v8, v1))) | (relation(v2) & function(v2) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ in(v9, v2) | in(v7, v0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ in(v9, v2) | (in(v8, v7) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v8, v10) = v11) | ~ in(v10, v7) | in(v11, v1)))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ in(v8, v7) | ~ in(v7, v0) | in(v9, v2) | ? [v10] : ? [v11] : (ordered_pair(v8, v10) = v11 & in(v10, v7) & ~ in(v11, v1)))))) & ? [v0] : ! [v1] : ( ~ relation(v1) | empty(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = v2 & v5 = v2 & ~ (v4 = v3) & in(v4, v2) & in(v3, v2) & in(v2, v0) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v7, v2) | in(v8, v1)) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v3, v7) = v8) | ~ in(v7, v2) | in(v8, v1))) | ( ! [v7] : ! [v8] : ( ~ in(v8, v0) | ~ in(v7, v8) | in(v7, v2) | ? [v9] : ? [v10] : (ordered_pair(v7, v9) = v10 & in(v9, v8) & ~ in(v10, v1))) & ! [v7] : ( ~ in(v7, v2) | ? [v8] : (in(v8, v0) & in(v7, v8) & ! [v9] : ! [v10] : ( ~ (ordered_pair(v7, v9) = v10) | ~ in(v9, v8) | in(v10, v1))))))) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ 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] : (v0 = omega | ~ being_limit_ordinal(v0) | ~ ordinal(v0) | ~ in(empty_set, v0) | ? [v1] : (being_limit_ordinal(v1) & ordinal(v1) & in(empty_set, v1) & ~ subset(v0, v1))) & ! [v0] : ( ~ (union(v0) = v0) | being_limit_ordinal(v0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ latt_str(v0) | meet_semilatt_str(v0)) & ! [v0] : ( ~ latt_str(v0) | join_semilatt_str(v0)) & ! [v0] : ( ~ being_limit_ordinal(v0) | ~ ordinal(v0) | ~ in(empty_set, v0) | subset(omega, v0)) & ! [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] : ( ~ meet_semilatt_str(v0) | one_sorted_str(v0)) & ! [v0] : ( ~ join_semilatt_str(v0) | one_sorted_str(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] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) & ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) & ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) & ! [v0] : ( ~ finite(v0) | ? [v1] : ? [v2] : (relation_rng(v1) = v0 & relation_dom(v1) = v2 & relation(v1) & function(v1) & in(v2, omega))) & ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) & ! [v0] : ( ~ ordinal(v0) | ~ empty(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ ordinal(v0) | ~ empty(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ ordinal(v0) | ~ empty(v0) | natural(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) | function(v0)) & ! [v0] : ( ~ empty(v0) | finite(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) & ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) & ! [v0] : ( ~ empty(v0) | ordinal(v0)) & ! [v0] : ( ~ empty(v0) | v5_membered(v0)) & ! [v0] : ( ~ empty(v0) | v4_membered(v0)) & ! [v0] : ( ~ empty(v0) | v3_membered(v0)) & ! [v0] : ( ~ empty(v0) | v2_membered(v0)) & ! [v0] : ( ~ empty(v0) | v1_membered(v0)) & ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) & ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) & ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) & ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) & ! [v0] : ( ~ element(v0, omega) | epsilon_connected(v0)) & ! [v0] : ( ~ element(v0, omega) | epsilon_transitive(v0)) & ! [v0] : ( ~ element(v0, omega) | ordinal(v0)) & ! [v0] : ( ~ element(v0, omega) | natural(v0)) & ! [v0] : ~ proper_subset(v0, v0) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) & ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) & quasi_total(v2, v0, v1) & relation(v2) & function(v2)) & ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) & relation(v2) & function(v2)) & ? [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] : (relation_dom(v1) = v0 & relation(v1) & function(v1) & ! [v2] : ! [v3] : ( ~ (singleton(v2) = v3) | ~ in(v2, v0) | apply(v1, v2) = v3) & ! [v2] : ! [v3] : ( ~ (apply(v1, v2) = v3) | ~ in(v2, v0) | singleton(v2) = v3)) & ? [v0] : ? [v1] : (well_orders(v1, v0) & relation(v1)) & ? [v0] : ? [v1] : (relation(v1) & function(v1) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ in(v4, v1) | singleton(v2) = v3) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ in(v4, v1) | in(v2, v0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ in(v2, v0) | in(v4, v1) | ? [v5] : ( ~ (v5 = v3) & singleton(v2) = v5))) & ? [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] : ? [v1] : ( ! [v2] : ! [v3] : ( ~ (singleton(v3) = v2) | ~ in(v3, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : (singleton(v3) = v2 & in(v3, v0)))) & ? [v0] : ? [v1] : ( ! [v2] : ( ~ ordinal(v2) | ~ in(v2, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ordinal(v2)) & ! [v2] : ( ~ in(v2, v1) | in(v2, v0))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) & ? [v0] : equipotent(v0, 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] : (function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v2) & ordered_pair(v1, v3) = v5 & ordered_pair(v1, v2) = v4 & in(v5, v0) & in(v4, v0))) & ? [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)))) & ? [v0] : (empty(v0) | ? [v1] : ? [v2] : ((v2 = v0 & relation_dom(v1) = v0 & relation(v1) & function(v1) & ! [v3] : ! [v4] : ( ~ (apply(v1, v3) = v4) | ~ in(v3, v0) | in(v4, v3))) | (v1 = empty_set & in(empty_set, v0)))) & ( ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, omega) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) | ( ~ (all_0_22_22 = empty_set) & succ(all_0_28_28) = all_0_25_25 & powerset(all_0_24_24) = all_0_23_23 & powerset(all_0_25_25) = all_0_24_24 & powerset(all_0_27_27) = all_0_26_26 & powerset(all_0_28_28) = all_0_27_27 & ordinal(all_0_28_28) & element(all_0_22_22, all_0_23_23) & in(all_0_25_25, omega) & ! [v0] : ( ~ in(v0, all_0_22_22) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_22_22))) & ( ~ in(all_0_28_28, omega) | ! [v0] : (v0 = empty_set | ~ element(v0, all_0_26_26) | ? [v1] : (in(v1, v0) & ! [v2] : (v2 = v1 | ~ subset(v1, v2) | ~ in(v2, v0)))))) | ( ~ (all_0_25_25 = empty_set) & ~ (all_0_28_28 = empty_set) & powerset(all_0_27_27) = all_0_26_26 & powerset(all_0_28_28) = all_0_27_27 & being_limit_ordinal(all_0_28_28) & ordinal(all_0_28_28) & element(all_0_25_25, all_0_26_26) & in(all_0_28_28, omega) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, all_0_28_28) | ~ in(v0, omega) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) & ! [v0] : ( ~ in(v0, all_0_25_25) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_25_25)))) | ( ~ (all_0_28_28 = empty_set) & element(all_0_28_28, all_0_39_39) & ! [v0] : ( ~ in(v0, all_0_28_28) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_28_28))))) & ( ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, omega) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) | ( ~ (all_0_29_29 = empty_set) & powerset(all_0_31_31) = all_0_30_30 & powerset(all_0_32_32) = all_0_31_31 & ordinal(all_0_32_32) & element(all_0_29_29, all_0_30_30) & in(all_0_32_32, omega) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, all_0_32_32) | ~ in(v0, omega) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) & ! [v0] : ( ~ in(v0, all_0_29_29) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_29_29))))) % 29.27/7.40 | % 29.27/7.40 | Applying alpha-rule on (1) yields: % 29.27/7.40 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v2, v1) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (meet_commut(v0, v1, v2) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 29.27/7.41 | (3) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 29.27/7.41 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 29.27/7.41 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2)) % 29.27/7.41 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ~ function(v1) | function(v2)) % 29.27/7.41 | (7) v5_membered(all_0_7_7) % 29.27/7.41 | (8) ! [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)))) % 29.27/7.41 | (9) ! [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))) % 29.27/7.41 | (10) ? [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))))) % 29.27/7.41 | (11) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 29.27/7.41 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 29.27/7.41 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 29.27/7.41 | (14) ! [v0] : ! [v1] : ( ~ (relation_rng(v1) = v0) | ~ relation(v1) | ~ function(v1) | finite(v0) | ? [v2] : (relation_dom(v1) = v2 & ~ in(v2, omega))) % 29.27/7.41 | (15) ! [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)) % 29.27/7.41 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) % 29.27/7.41 | (17) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 29.27/7.41 | (18) ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (singleton(v1) = v5 & powerset(v3) = v4 & powerset(v2) = v3 & powerset(v1) = v6 & ( ~ element(v0, v4) | ( ! [v8] : ! [v9] : ( ~ (set_difference(v9, v5) = v8) | ~ in(v9, v0) | ~ in(v8, v6) | in(v8, v7)) & ! [v8] : ( ~ in(v8, v7) | in(v8, v6)) & ! [v8] : ( ~ in(v8, v7) | ? [v9] : (set_difference(v9, v5) = v8 & in(v9, v0))))))) % 29.27/7.41 | (19) ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) % 29.27/7.41 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v2, v1) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 29.27/7.41 | (21) ? [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))) % 29.27/7.41 | (22) epsilon_transitive(all_0_4_4) % 29.27/7.41 | (23) ? [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v2) = v1) | ~ one_to_one(v2) | ~ relation(v2) | ~ function(v2) | equipotent(v1, v0) | ? [v3] : ( ~ (v3 = v0) & relation_rng(v2) = v3)) % 29.27/7.41 | (24) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | finite(v1) | ? [v2] : (relation_dom(v0) = v2 & ~ finite(v2))) % 29.27/7.41 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) % 29.27/7.41 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0) = v1) | ~ being_limit_ordinal(v0)) % 29.27/7.41 | (27) singleton(empty_set) = all_0_40_40 % 29.27/7.41 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 29.27/7.41 | (29) ! [v0] : ( ~ element(v0, omega) | ordinal(v0)) % 29.27/7.41 | (30) ! [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))) % 29.27/7.41 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v1 = empty_set | ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ quasi_total(v2, v0, v1) | ~ relation_of2_as_subset(v2, v0, v1)) % 29.27/7.41 | (32) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) % 29.27/7.41 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 29.27/7.41 | (34) ! [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))) % 29.27/7.41 | (35) ! [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))))) % 29.27/7.41 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) % 29.27/7.41 | (37) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | antisymmetric(v1)) % 29.27/7.41 | (38) ! [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)))) % 29.27/7.41 | (39) empty(all_0_10_10) % 29.27/7.41 | (40) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) % 29.27/7.41 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 29.27/7.41 | (42) ! [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)))) % 29.27/7.41 | (43) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) % 29.27/7.41 | (44) ? [v0] : (epsilon_connected(v0) | ? [v1] : ? [v2] : ( ~ (v2 = v1) & in(v2, v0) & in(v1, v0) & ~ in(v2, v1) & ~ in(v1, v2))) % 29.27/7.41 | (45) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) % 29.27/7.41 | (46) ! [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))))) % 29.27/7.42 | (47) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | epsilon_transitive(v1)) % 29.27/7.42 | (48) epsilon_transitive(omega) % 29.27/7.42 | (49) ! [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))))))) % 29.27/7.42 | (50) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1)) % 29.27/7.42 | (51) ! [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))) % 29.27/7.42 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0)) % 29.27/7.42 | (53) ? [v0] : subset(v0, v0) % 29.27/7.42 | (54) ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) % 29.27/7.42 | (55) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | well_founded_relation(v0)) % 29.27/7.42 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 29.47/7.42 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v2_membered(v2)) % 29.47/7.42 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) % 29.47/7.42 | (59) ? [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))) % 29.47/7.42 | (60) ? [v0] : ? [v1] : (well_orders(v1, v0) & relation(v1)) % 29.47/7.42 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 29.47/7.42 | (62) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) % 29.47/7.42 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 29.47/7.42 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ relation(v1)) % 29.47/7.42 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) % 29.47/7.42 | (66) ! [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))) % 29.47/7.42 | (67) v5_membered(empty_set) % 29.47/7.42 | (68) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | well_ordering(v1)) % 29.47/7.42 | (69) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 29.47/7.42 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 29.47/7.42 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ~ finite(v0) | finite(v2)) % 29.47/7.42 | (72) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1)) % 29.47/7.42 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 29.47/7.42 | (74) ! [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)) % 29.47/7.42 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 29.47/7.42 | (76) ! [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))) % 29.47/7.42 | (77) ? [v0] : (ordinal(v0) | ? [v1] : (in(v1, v0) & ( ~ subset(v1, v0) | ~ ordinal(v1)))) % 29.47/7.42 | (78) ! [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)) % 29.47/7.42 | (79) ! [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)))) % 29.47/7.42 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) % 29.47/7.42 | (81) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & cartesian_product2(v2, v2) = v3 & quasi_total(v1, v3, v2) & relation_of2_as_subset(v1, v3, v2))) % 29.47/7.42 | (82) ! [v0] : ( ~ join_semilatt_str(v0) | one_sorted_str(v0)) % 29.47/7.42 | (83) ! [v0] : ( ~ ordinal(v0) | ~ empty(v0) | epsilon_connected(v0)) % 29.47/7.42 | (84) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | connected(v1)) % 29.47/7.42 | (85) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 29.47/7.42 | (86) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ latt_str(v0) | meet_absorbing(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v3) & meet(v0, v2, v3) = v4 & join(v0, v4, v3) = v5 & element(v3, v1) & element(v2, v1))) % 29.47/7.42 | (87) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 29.47/7.42 | (88) ! [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)))) % 29.47/7.43 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 29.47/7.43 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 29.47/7.43 | (91) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 29.47/7.43 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng_restriction(v0, v3) = v2 & relation_dom_restriction(v1, v0) = v3)) % 29.47/7.43 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) % 29.47/7.43 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 29.47/7.43 | (95) ? [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))))) % 29.47/7.43 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (relation_rng(v2) = v4 & subset(v4, v1))) % 29.47/7.43 | (97) ? [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))))) % 29.47/7.43 | (98) ! [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)) % 29.47/7.43 | (99) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | cast_as_carrier_subset(v0) = v1) % 29.47/7.43 | (100) ? [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))) % 29.47/7.43 | (101) ! [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))) % 29.47/7.43 | (102) element(all_0_34_34, all_0_36_36) % 29.47/7.43 | (103) ? [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))))) % 29.47/7.43 | (104) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | transitive(v1)) % 29.47/7.43 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) % 29.47/7.43 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v1 | ~ (pair_second(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) % 29.47/7.43 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair_first(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) % 29.47/7.43 | (108) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_orders(v0, v1) | ~ relation(v0) | well_ordering(v0)) % 29.47/7.43 | (109) ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (singleton(v1) = v6 & powerset(v3) = v4 & powerset(v2) = v3 & powerset(v1) = v5 & ( ~ element(v0, v4) | ( ! [v8] : ! [v9] : ( ~ (set_difference(v9, v6) = v8) | ~ in(v9, v0) | ~ in(v8, v5) | in(v8, v7)) & ! [v8] : ( ~ in(v8, v7) | in(v8, v5)) & ! [v8] : ( ~ in(v8, v7) | ? [v9] : (set_difference(v9, v6) = v8 & in(v9, v0))))))) % 29.47/7.43 | (110) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 29.47/7.43 | (111) v1_membered(empty_set) % 29.47/7.43 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 29.47/7.43 | (113) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) % 29.47/7.43 | (114) ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0)) % 29.47/7.43 | (115) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 29.47/7.43 | (116) ~ (all_0_33_33 = all_0_34_34) % 29.47/7.43 | (117) empty(all_0_13_13) % 29.47/7.43 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 29.47/7.43 | (119) ! [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)))) % 29.47/7.43 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 29.47/7.43 | (121) ! [v0] : (v0 = omega | ~ being_limit_ordinal(v0) | ~ ordinal(v0) | ~ in(empty_set, v0) | ? [v1] : (being_limit_ordinal(v1) & ordinal(v1) & in(empty_set, v1) & ~ subset(v0, v1))) % 29.47/7.43 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 29.47/7.43 | (123) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 29.47/7.43 | (124) ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) % 29.47/7.43 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) | ordinal_subset(v1, v2)) % 29.47/7.43 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 29.47/7.43 | (127) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) % 29.47/7.43 | (128) relation(all_0_21_21) % 29.47/7.43 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~ in(v1, v0) | in(v2, v0)) % 29.47/7.43 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 29.47/7.43 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) % 29.47/7.43 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (meet_commut(v0, v1, v2) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 29.47/7.44 | (133) ? [v0] : (epsilon_transitive(v0) | ? [v1] : (in(v1, v0) & ~ subset(v1, v0))) % 29.47/7.44 | (134) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 29.47/7.44 | (135) ! [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)))) % 29.47/7.44 | (136) epsilon_transitive(empty_set) % 29.47/7.44 | (137) ! [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) % 29.47/7.44 | (138) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3))) % 29.47/7.44 | (139) ! [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)) % 29.47/7.44 | (140) ! [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))))))) % 29.47/7.44 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) % 29.47/7.44 | (142) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2)) % 29.47/7.44 | (143) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1)) % 29.47/7.44 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) % 29.47/7.44 | (145) ~ empty(all_0_18_18) % 29.47/7.44 | (146) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 29.47/7.44 | (147) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 29.47/7.44 | (148) ! [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)))))))) % 29.47/7.44 | (149) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) % 29.47/7.44 | (150) ? [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))))) % 29.47/7.44 | (151) ! [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))) % 29.47/7.44 | (152) ? [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))))) % 29.47/7.44 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v1) | relation_restriction(v1, v0) = v3) % 29.47/7.44 | (154) ! [v0] : ( ~ ordinal(v0) | ~ empty(v0) | epsilon_transitive(v0)) % 29.47/7.44 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ subset(v2, v3) | relation_of2(v2, v0, v1)) % 29.47/7.44 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2(v2, v0, v1) | subset(v2, v3)) % 29.47/7.44 | (157) one_to_one(all_0_14_14) % 29.47/7.44 | (158) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 29.47/7.45 | (159) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 29.47/7.45 | (160) ? [v0] : ! [v1] : ( ~ relation(v1) | empty(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = v2 & v5 = v2 & ~ (v4 = v3) & in(v4, v2) & in(v3, v2) & in(v2, v0) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v7, v2) | in(v8, v1)) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v3, v7) = v8) | ~ in(v7, v2) | in(v8, v1))) | (v3 = v0 & relation_dom(v2) = v0 & relation(v2) & function(v2) & ! [v7] : ! [v8] : ( ~ (apply(v2, v7) = v8) | ~ in(v7, v0) | (in(v8, v7) & ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ in(v9, v7) | in(v10, v1))))) | (in(v2, v0) & ! [v7] : ( ~ in(v7, v2) | ? [v8] : ? [v9] : (ordered_pair(v7, v8) = v9 & in(v8, v2) & ~ in(v9, v1)))))) % 29.58/7.45 | (161) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v5_membered(v2)) % 29.58/7.45 | (162) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1) % 29.58/7.45 | (163) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) & quasi_total(v2, v0, v1) & relation(v2) & function(v2)) % 29.58/7.45 | (164) ! [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)) % 29.58/7.45 | (165) ! [v0] : ! [v1] : ( ~ (relation_dom_as_subset(empty_set, v0, v1) = empty_set) | ~ relation_of2_as_subset(v1, empty_set, v0) | quasi_total(v1, empty_set, v0)) % 29.58/7.45 | (166) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) % 29.58/7.45 | (167) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_ordering(v0) | ~ relation(v0) | well_orders(v0, v1)) % 29.58/7.45 | (168) one_to_one(all_0_10_10) % 29.58/7.45 | (169) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_first(v2) = v1) | ~ (pair_first(v2) = v0)) % 29.58/7.45 | (170) relation_dom(empty_set) = empty_set % 29.58/7.45 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 29.58/7.45 | (172) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) & relation(v2) & function(v2)) % 29.58/7.45 | (173) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ in(v0, v1) | ordinal(v0)) % 29.58/7.45 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | ? [v4] : (powerset(v0) = v4 & element(v3, v4))) % 29.58/7.45 | (175) ! [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))) % 29.58/7.45 | (176) empty(empty_set) % 29.58/7.45 | (177) ! [v0] : ! [v1] : ( ~ in(v1, v0) | empty(v0) | element(v1, v0)) % 29.58/7.45 | (178) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) % 29.58/7.45 | (179) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) % 29.58/7.45 | (180) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) % 29.58/7.45 | (181) ! [v0] : ~ in(v0, empty_set) % 29.58/7.45 | (182) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) | ? [v4] : (powerset(v3) = v4 & ~ element(v0, v4))) % 29.58/7.45 | (183) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 29.58/7.45 | (184) ! [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))) % 29.58/7.45 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ in(v4, v5) | in(v0, v2)) % 29.58/7.45 | (186) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | subset(v3, v0)) % 29.58/7.45 | (187) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) % 29.58/7.45 | (188) empty(all_0_14_14) % 29.58/7.45 | (189) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 29.58/7.45 | (190) ! [v0] : ~ (singleton(v0) = empty_set) % 29.58/7.45 | (191) ! [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)) % 29.58/7.45 | (192) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) % 29.58/7.45 | (193) ! [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))) % 29.58/7.45 | (194) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ( ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v5, v6) = v4) | ~ in(v5, v0) | ~ in(v4, v2) | in(v4, v3) | ? [v7] : ( ~ (v7 = v6) & singleton(v5) = v7)) & ! [v4] : ( ~ in(v4, v3) | in(v4, v2)) & ! [v4] : ( ~ in(v4, v3) | ? [v5] : ? [v6] : (singleton(v5) = v6 & ordered_pair(v5, v6) = v4 & in(v5, v0))))) % 29.58/7.45 | (195) ! [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))) % 29.58/7.45 | (196) ? [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))))) % 29.58/7.45 | (197) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ~ function(v3) | ~ element(v5, v1) | ~ element(v4, v0) | empty(v1) | empty(v0) | element(v6, v2) | ? [v7] : (cartesian_product2(v0, v1) = v7 & ( ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2)))) % 29.58/7.45 | (198) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 29.58/7.45 | (199) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) | in(v0, v2)) % 29.58/7.45 | (200) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ reflexive(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | reflexive(v1)) % 29.58/7.45 | (201) function(all_0_13_13) % 29.58/7.45 | (202) ordinal(all_0_4_4) % 29.58/7.45 | (203) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 29.58/7.45 | (204) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ~ function(v1) | relation(v2)) % 29.58/7.45 | (205) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) % 29.58/7.46 | (206) function(empty_set) % 29.58/7.46 | (207) epsilon_transitive(all_0_9_9) % 29.58/7.46 | (208) epsilon_connected(all_0_8_8) % 29.58/7.46 | (209) ! [v0] : ( ~ element(v0, omega) | natural(v0)) % 29.58/7.46 | (210) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) % 29.58/7.46 | (211) ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) % 29.58/7.46 | (212) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_well_founded_in(v0, v1)) % 29.58/7.46 | (213) ? [v0] : ! [v1] : ! [v2] : ( ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ? [v3] : (relation(v3) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v2, v4) = v6) | ~ (ordered_pair(v6, v7) = v8) | ~ in(v8, v1) | ~ in(v5, v0) | ~ in(v4, v0) | ? [v9] : (ordered_pair(v4, v5) = v9 & in(v9, v3))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v2, v4) = v6) | ~ (ordered_pair(v6, v7) = v8) | in(v8, v1) | ? [v9] : (ordered_pair(v4, v5) = v9 & ~ in(v9, v3))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v2, v4) = v6) | ~ (ordered_pair(v6, v7) = v8) | in(v5, v0) | ? [v9] : (ordered_pair(v4, v5) = v9 & ~ in(v9, v3))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v2, v5) = v7) | ~ (apply(v2, v4) = v6) | ~ (ordered_pair(v6, v7) = v8) | in(v4, v0) | ? [v9] : (ordered_pair(v4, v5) = v9 & ~ in(v9, v3))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v6, v3) | in(v5, v0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v6, v3) | in(v4, v0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v6, v3) | ? [v7] : ? [v8] : ? [v9] : (apply(v2, v5) = v8 & apply(v2, v4) = v7 & ordered_pair(v7, v8) = v9 & in(v9, v1))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v5) = v6) | ~ in(v5, v0) | ~ in(v4, v0) | in(v6, v3) | ? [v7] : ? [v8] : ? [v9] : (apply(v2, v5) = v8 & apply(v2, v4) = v7 & ordered_pair(v7, v8) = v9 & ~ in(v9, v1))))) % 29.58/7.46 | (214) relation_empty_yielding(all_0_21_21) % 29.58/7.46 | (215) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) % 29.58/7.46 | (216) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 29.58/7.46 | (217) ! [v0] : ( ~ empty(v0) | v5_membered(v0)) % 29.58/7.46 | (218) ! [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)) % 29.58/7.46 | (219) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join_commut(v0, v2, v1) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (the_carrier(v0) = v4 & join_commut(v0, v1, v2) = v5 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 29.58/7.46 | (220) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 29.58/7.46 | (221) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) % 29.58/7.46 | (222) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & subset(v3, v4))) % 29.58/7.46 | (223) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) % 29.58/7.46 | (224) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 29.58/7.46 | (225) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 29.58/7.46 | (226) ! [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) % 29.58/7.46 | (227) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | join(v0, v3, v4) = v5))) % 29.58/7.46 | (228) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | relation_restriction(v1, v0) = v3) % 29.58/7.46 | (229) ? [v0] : (function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v3 = v2) & ordered_pair(v1, v3) = v5 & ordered_pair(v1, v2) = v4 & in(v5, v0) & in(v4, v0))) % 29.58/7.46 | (230) ! [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)))) % 29.58/7.46 | (231) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 29.58/7.46 | (232) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_intersection2(v0, v1, v2) = v4) % 29.58/7.46 | (233) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 29.58/7.46 | (234) ! [v0] : ! [v1] : ( ~ ordinal(v0) | ~ element(v1, v0) | epsilon_connected(v1)) % 29.58/7.46 | (235) the_carrier(all_0_38_38) = all_0_37_37 % 29.58/7.46 | (236) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | well_founded_relation(v1)) % 29.58/7.46 | (237) ! [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))))) % 29.58/7.46 | (238) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_rng_as_subset(v4, v3, v2) = v1) | ~ (relation_rng_as_subset(v4, v3, v2) = v0)) % 29.58/7.46 | (239) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ relation(v0) | ~ in(v3, v2) | in(v4, v0)) % 29.58/7.46 | (240) ! [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)) % 29.58/7.46 | (241) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 29.58/7.46 | (242) ! [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))) % 29.58/7.46 | (243) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 29.58/7.46 | (244) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_founded_relation(v1) | ~ relation(v1) | well_founded_relation(v2)) % 29.58/7.46 | (245) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (the_carrier(v0) = v4 & join_commut(v0, v1, v2) = v5 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 29.58/7.47 | (246) ? [v0] : ? [v1] : ( ! [v2] : ! [v3] : ( ~ (singleton(v3) = v2) | ~ in(v3, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : (singleton(v3) = v2 & in(v3, v0)))) % 29.58/7.47 | (247) epsilon_transitive(all_0_14_14) % 29.58/7.47 | (248) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 29.58/7.47 | (249) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 29.58/7.47 | (250) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) % 29.58/7.47 | (251) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | antisymmetric(v0)) % 29.58/7.47 | (252) ! [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)))) % 29.58/7.47 | (253) ! [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)))) % 29.58/7.47 | (254) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ? [v2] : (in(v2, v1) & ! [v3] : ( ~ in(v3, v2) | ~ in(v3, v1)))) % 29.58/7.47 | (255) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 29.58/7.47 | (256) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_ordering(v1) | ~ relation(v1) | well_ordering(v2)) % 29.58/7.47 | (257) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~ (unordered_triple(v4, v3, v2) = v0)) % 29.58/7.47 | (258) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (singleton(v1) = v6 & succ(v1) = v3 & powerset(v4) = v5 & powerset(v3) = v4 & ( ~ element(v0, v5) | ( ! [v8] : ! [v9] : ( ~ (set_difference(v9, v6) = v8) | ~ in(v9, v0) | ~ in(v8, v2) | in(v8, v7)) & ! [v8] : ( ~ in(v8, v7) | in(v8, v2)) & ! [v8] : ( ~ in(v8, v7) | ? [v9] : (set_difference(v9, v6) = v8 & in(v9, v0))))))) % 29.58/7.47 | (259) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) % 29.58/7.47 | (260) ! [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)) % 29.58/7.47 | (261) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_orders(v1, v0) | ~ relation(v1) | well_ordering(v2)) % 29.58/7.47 | (262) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ connected(v1) | ~ relation(v1) | connected(v2)) % 29.58/7.47 | (263) one_sorted_str(all_0_1_1) % 29.58/7.47 | (264) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ transitive(v1) | ~ relation(v1) | transitive(v2)) % 29.58/7.47 | (265) ! [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)))) % 29.58/7.47 | (266) ! [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)) % 29.58/7.47 | (267) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (powerset(v3) = v4 & element(v2, v4))) % 29.58/7.47 | (268) ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : (succ(v1) = v0 & ordinal(v1))) % 29.58/7.47 | (269) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 29.58/7.47 | (270) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) % 29.58/7.47 | (271) ! [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))) % 29.58/7.47 | (272) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 29.58/7.47 | (273) ! [v0] : ( ~ empty(v0) | v2_membered(v0)) % 29.58/7.47 | (274) ! [v0] : ( ~ empty(v0) | finite(v0)) % 29.58/7.47 | (275) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 29.58/7.47 | (276) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 29.58/7.47 | (277) ! [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))) % 29.58/7.47 | (278) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 29.58/7.47 | (279) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (meet(v0, v1, v2) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 29.58/7.47 | (280) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 29.58/7.47 | (281) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 29.58/7.47 | (282) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) % 29.58/7.47 | (283) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (meet_commut(v0, v2, v3) = v4) | ~ (the_carrier(v0) = v1) | ~ meet_absorbing(v0) | ~ latt_str(v0) | ~ meet_commutative(v0) | ~ element(v3, v1) | ~ element(v2, v1) | below(v0, v4, v2) | empty_carrier(v0)) % 29.58/7.47 | (284) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1)) % 29.58/7.47 | (285) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 29.58/7.47 | (286) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) % 29.58/7.47 | (287) ! [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))) % 29.58/7.47 | (288) ~ empty(all_0_5_5) % 29.58/7.47 | (289) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) % 29.58/7.48 | (290) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) % 29.58/7.48 | (291) ! [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)))) % 29.58/7.48 | (292) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v1, v1) = v3) | ~ relation(v0) | ~ in(v1, v2)) % 29.58/7.48 | (293) ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) % 29.58/7.48 | (294) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_founded_relation(v0) | ~ relation(v0) | is_well_founded_in(v0, v1)) % 29.58/7.48 | (295) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | ordinal(v1)) % 29.58/7.48 | (296) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1) | ~ natural(v0)) % 29.58/7.48 | (297) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2) % 29.58/7.48 | (298) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) % 29.58/7.48 | (299) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) % 29.58/7.48 | (300) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng_restriction(v0, v1) = v3 & relation_dom_restriction(v3, v0) = v2)) % 29.58/7.48 | (301) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ antisymmetric(v0) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) % 29.58/7.48 | (302) ! [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))) % 29.58/7.48 | (303) ! [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)) % 29.58/7.48 | (304) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 29.58/7.48 | (305) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) % 29.58/7.48 | (306) v2_membered(empty_set) % 29.58/7.48 | (307) v1_membered(all_0_7_7) % 29.58/7.48 | (308) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) % 29.58/7.48 | (309) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ reflexive(v1) | ~ relation(v1) | reflexive(v2)) % 29.58/7.48 | (310) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ relation_of2_as_subset(v3, v2, v0) | ~ subset(v0, v1) | relation_of2_as_subset(v3, v2, v1)) % 29.58/7.48 | (311) ? [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))))) % 29.58/7.48 | (312) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 29.58/7.48 | (313) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | reflexive(v1)) % 29.58/7.48 | (314) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 29.58/7.48 | (315) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) % 29.58/7.48 | (316) ! [v0] : ( ~ element(v0, omega) | epsilon_connected(v0)) % 29.58/7.48 | (317) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) % 29.58/7.48 | (318) ! [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))) % 29.58/7.48 | (319) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) % 29.58/7.48 | (320) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 29.58/7.48 | (321) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) % 29.58/7.48 | (322) ! [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)) % 29.58/7.48 | (323) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 29.58/7.48 | (324) epsilon_connected(empty_set) % 29.58/7.48 | (325) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ in(v1, v0) | ? [v2] : (ordinal(v2) & in(v2, v0) & ! [v3] : ( ~ ordinal(v3) | ~ in(v3, v0) | ordinal_subset(v2, v3)))) % 29.58/7.48 | (326) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0)) % 29.58/7.48 | (327) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 29.58/7.48 | (328) ! [v0] : ( ~ empty(v0) | relation(v0)) % 29.58/7.48 | (329) ! [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))) % 29.58/7.48 | (330) ! [v0] : ! [v1] : ! [v2] : ( ~ in(v2, v0) | ~ in(v1, v2) | ~ in(v0, v1)) % 29.58/7.48 | (331) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1)) % 29.58/7.48 | (332) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ subset(v1, v2) | ~ function(v3) | relation_of2_as_subset(v3, v0, v2)) % 29.58/7.48 | (333) ! [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)))) % 29.58/7.48 | (334) ! [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))) % 29.58/7.48 | (335) ! [v0] : ~ proper_subset(v0, v0) % 29.58/7.48 | (336) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v1_membered(v2)) % 29.58/7.48 | (337) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v2, v2) = v3) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | ~ in(v2, v1) | in(v3, v0)) % 29.58/7.48 | (338) function(all_0_17_17) % 29.58/7.48 | (339) ! [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))))) % 29.58/7.49 | (340) ! [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)) % 29.58/7.49 | (341) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) % 29.58/7.49 | (342) ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) % 29.58/7.49 | (343) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | the_carrier(v0) = v1) % 29.58/7.49 | (344) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 29.58/7.49 | (345) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) % 29.58/7.49 | (346) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | relation_rng(v2) = v3) % 29.58/7.49 | (347) ! [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))) % 29.58/7.49 | (348) ! [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))) % 29.58/7.49 | (349) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v2_membered(v2)) % 29.58/7.49 | (350) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_connected_in(v0, v1)) % 29.58/7.49 | (351) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3))) % 29.58/7.49 | (352) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 29.58/7.49 | (353) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (cast_as_carrier_subset(v0) = v2 & powerset(v1) = v3 & element(v2, v3))) % 29.58/7.49 | (354) relation(all_0_17_17) % 29.58/7.49 | (355) function(all_0_14_14) % 29.58/7.49 | (356) ~ empty(omega) % 29.58/7.49 | (357) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 29.58/7.49 | (358) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join_commut(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (the_carrier(v0) = v4 & join_commut(v0, v2, v1) = v5 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 29.58/7.49 | (359) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v3_membered(v2)) % 29.58/7.49 | (360) ! [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)) % 29.58/7.49 | (361) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) % 29.58/7.49 | (362) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1)) % 29.58/7.49 | (363) ! [v0] : ( ~ meet_semilatt_str(v0) | one_sorted_str(v0)) % 29.58/7.49 | (364) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 29.58/7.49 | (365) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | reflexive(v0)) % 29.58/7.49 | (366) ! [v0] : ! [v1] : ( ~ ordinal(v0) | ~ element(v1, v0) | epsilon_transitive(v1)) % 29.58/7.49 | (367) ! [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)))) % 29.58/7.49 | (368) ! [v0] : ( ~ being_limit_ordinal(v0) | ~ ordinal(v0) | ~ in(empty_set, v0) | subset(omega, v0)) % 29.58/7.49 | (369) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) % 29.58/7.49 | (370) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) % 29.58/7.49 | (371) ! [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)))) % 29.58/7.49 | (372) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ (the_L_meet(v2) = v0)) % 29.58/7.49 | (373) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) % 29.58/7.49 | (374) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 29.58/7.49 | (375) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) % 29.58/7.49 | (376) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) % 29.58/7.49 | (377) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (relation_dom_as_subset(empty_set, v0, v1) = v2) | ~ quasi_total(v1, empty_set, v0) | ~ relation_of2_as_subset(v1, empty_set, v0)) % 29.58/7.49 | (378) ? [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))))) % 29.58/7.49 | (379) ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1)) % 29.58/7.49 | (380) ! [v0] : ( ~ empty(v0) | v1_membered(v0)) % 29.58/7.49 | (381) ! [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))) % 29.58/7.49 | (382) ! [v0] : ( ~ empty(v0) | function(v0)) % 29.58/7.49 | (383) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | antisymmetric(v0)) % 29.58/7.49 | (384) ! [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))))) % 29.58/7.49 | (385) ! [v0] : ! [v1] : ( ~ equipotent(v0, v1) | equipotent(v1, v0)) % 29.58/7.49 | (386) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 29.58/7.50 | (387) ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v1) | ~ (cartesian_product2(v1, v1) = v2) | ~ meet_semilatt_str(v0) | ? [v3] : (the_L_meet(v0) = v3 & quasi_total(v3, v2, v1) & relation_of2_as_subset(v3, v2, v1) & function(v3))) % 29.58/7.50 | (388) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 29.58/7.50 | (389) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0)) % 29.58/7.50 | (390) ! [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)))) % 29.58/7.50 | (391) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ element(v1, v0) | empty(v1)) % 29.58/7.50 | (392) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 29.58/7.50 | (393) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | epsilon_connected(v1)) % 29.58/7.50 | (394) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) % 29.58/7.50 | (395) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 29.58/7.50 | (396) ? [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))))) % 29.58/7.50 | (397) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) % 29.58/7.50 | (398) relation_rng(empty_set) = empty_set % 29.58/7.50 | (399) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) % 29.58/7.50 | (400) ? [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))))) % 29.58/7.50 | (401) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 29.58/7.50 | (402) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v0, v3)) % 29.58/7.50 | (403) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 29.58/7.50 | (404) ! [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))))) % 29.58/7.50 | (405) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ antisymmetric(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | antisymmetric(v1)) % 29.58/7.50 | (406) ! [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))) % 29.58/7.50 | (407) one_sorted_str(all_0_38_38) % 29.58/7.50 | (408) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 29.58/7.50 | (409) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 29.58/7.50 | (410) in(empty_set, omega) % 29.58/7.50 | (411) ! [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)) % 29.58/7.50 | (412) empty(all_0_12_12) % 29.58/7.50 | (413) ! [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)))) % 29.58/7.50 | (414) powerset(all_0_37_37) = all_0_36_36 % 29.58/7.50 | (415) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 29.58/7.50 | (416) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) % 29.58/7.50 | (417) relation(empty_set) % 29.58/7.50 | (418) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 29.58/7.50 | (419) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v1_membered(v0) | v1_membered(v2)) % 29.58/7.50 | (420) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 29.58/7.50 | (421) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 29.58/7.50 | (422) ? [v0] : ! [v1] : ( ~ relation(v1) | empty(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = v2 & v5 = v2 & ~ (v4 = v3) & in(v4, v2) & in(v3, v2) & in(v2, v0) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v7, v2) | in(v8, v1)) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v3, v7) = v8) | ~ in(v7, v2) | in(v8, v1))) | (relation(v2) & function(v2) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ in(v9, v2) | in(v7, v0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ in(v9, v2) | (in(v8, v7) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v8, v10) = v11) | ~ in(v10, v7) | in(v11, v1)))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ in(v8, v7) | ~ in(v7, v0) | in(v9, v2) | ? [v10] : ? [v11] : (ordered_pair(v8, v10) = v11 & in(v10, v7) & ~ in(v11, v1)))))) % 29.58/7.50 | (423) ! [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)) % 29.58/7.50 | (424) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 29.58/7.50 | (425) ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (relation_dom_as_subset(v0, v1, v2) = v0) | ~ relation_of2_as_subset(v2, v0, v1) | quasi_total(v2, v0, v1)) % 29.58/7.50 | (426) empty(all_0_11_11) % 29.58/7.50 | (427) ordinal(omega) % 29.58/7.50 | (428) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) % 29.58/7.51 | (429) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2)) % 29.58/7.51 | (430) ! [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)))) % 29.58/7.51 | (431) ! [v0] : ! [v1] : ( ~ ordinal(v0) | ~ element(v1, v0) | ordinal(v1)) % 29.58/7.51 | (432) ! [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)) % 29.58/7.51 | (433) ! [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))) % 29.58/7.51 | (434) ! [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)) % 29.58/7.51 | (435) epsilon_connected(all_0_4_4) % 29.58/7.51 | (436) ! [v0] : ( ~ ordinal(v0) | ~ empty(v0) | natural(v0)) % 29.58/7.51 | (437) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v0) | finite(v2)) % 29.58/7.51 | (438) function(all_0_6_6) % 29.58/7.51 | (439) relation(all_0_6_6) % 29.58/7.51 | (440) ! [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)) % 29.58/7.51 | (441) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 29.58/7.51 | (442) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1))) % 29.58/7.51 | (443) ? [v0] : subset(empty_set, v0) % 29.58/7.51 | (444) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | ? [v4] : (powerset(v1) = v4 & element(v3, v4))) % 29.58/7.51 | (445) ! [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)))) % 29.58/7.51 | (446) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 29.58/7.51 | (447) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 29.58/7.51 | (448) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0)) % 29.58/7.51 | (449) ! [v0] : ! [v1] : ( ~ equipotent(v0, v1) | ? [v2] : (relation_rng(v2) = v1 & relation_dom(v2) = v0 & one_to_one(v2) & relation(v2) & function(v2))) % 29.58/7.51 | (450) v2_membered(all_0_7_7) % 29.58/7.51 | (451) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet_commut(v4, v3, v2) = v1) | ~ (meet_commut(v4, v3, v2) = v0)) % 29.58/7.51 | (452) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) % 29.58/7.51 | (453) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) % 29.58/7.51 | (454) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 29.58/7.51 | (455) ? [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))))) % 29.58/7.51 | (456) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 29.58/7.51 | (457) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join_commut(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (join(v0, v1, v2) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 29.58/7.51 | (458) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 29.58/7.51 | (459) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | natural(v1)) % 29.58/7.51 | (460) powerset(all_0_40_40) = all_0_39_39 % 29.58/7.51 | (461) ? [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))))) % 29.58/7.51 | (462) ? [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)) % 29.58/7.51 | (463) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, omega) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) | ( ~ (all_0_22_22 = empty_set) & succ(all_0_28_28) = all_0_25_25 & powerset(all_0_24_24) = all_0_23_23 & powerset(all_0_25_25) = all_0_24_24 & powerset(all_0_27_27) = all_0_26_26 & powerset(all_0_28_28) = all_0_27_27 & ordinal(all_0_28_28) & element(all_0_22_22, all_0_23_23) & in(all_0_25_25, omega) & ! [v0] : ( ~ in(v0, all_0_22_22) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_22_22))) & ( ~ in(all_0_28_28, omega) | ! [v0] : (v0 = empty_set | ~ element(v0, all_0_26_26) | ? [v1] : (in(v1, v0) & ! [v2] : (v2 = v1 | ~ subset(v1, v2) | ~ in(v2, v0)))))) | ( ~ (all_0_25_25 = empty_set) & ~ (all_0_28_28 = empty_set) & powerset(all_0_27_27) = all_0_26_26 & powerset(all_0_28_28) = all_0_27_27 & being_limit_ordinal(all_0_28_28) & ordinal(all_0_28_28) & element(all_0_25_25, all_0_26_26) & in(all_0_28_28, omega) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, all_0_28_28) | ~ in(v0, omega) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) & ! [v0] : ( ~ in(v0, all_0_25_25) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_25_25)))) | ( ~ (all_0_28_28 = empty_set) & element(all_0_28_28, all_0_39_39) & ! [v0] : ( ~ in(v0, all_0_28_28) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_28_28)))) % 29.58/7.51 | (464) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v0) = v3) | ~ (fiber(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (fiber(v2, v1) = v5 & subset(v4, v5))) % 29.58/7.51 | (465) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 29.58/7.51 | (466) ! [v0] : ( ~ latt_str(v0) | join_semilatt_str(v0)) % 29.58/7.51 | (467) ! [v0] : ( ~ empty(v0) | v3_membered(v0)) % 29.58/7.51 | (468) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ reflexive(v0) | ~ relation(v0) | is_reflexive_in(v0, v1)) % 29.58/7.52 | (469) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 29.58/7.52 | (470) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) % 29.58/7.52 | (471) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 29.58/7.52 | (472) ! [v0] : ! [v1] : (v1 = v0 | ~ ordinal(v1) | ~ ordinal(v0) | in(v1, v0) | in(v0, v1)) % 29.58/7.52 | (473) ? [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)))) % 29.58/7.52 | (474) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) % 29.58/7.52 | (475) ? [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))))) % 29.58/7.52 | (476) ordinal(all_0_9_9) % 29.58/7.52 | (477) ! [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))) % 29.58/7.52 | (478) ! [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)) % 29.58/7.52 | (479) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) % 29.58/7.52 | (480) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 29.58/7.52 | (481) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | pair_first(v2) = v0) % 29.58/7.52 | (482) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = empty_set | ~ (apply(v5, v4) = v6) | ~ (apply(v3, v2) = v4) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ relation(v5) | ~ function(v5) | ~ function(v3) | ~ in(v2, v0) | ? [v7] : (relation_composition(v3, v5) = v7 & apply(v7, v2) = v6)) % 29.58/7.52 | (483) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ? [v5] : (meet_commut(v0, v2, v1) = v5 & the_carrier(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 29.58/7.52 | (484) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 29.58/7.52 | (485) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = empty_set | ~ (relation_composition(v3, v5) = v6) | ~ (apply(v6, v2) = v7) | ~ (apply(v3, v2) = v4) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ relation(v5) | ~ function(v5) | ~ function(v3) | ~ in(v2, v0) | apply(v5, v4) = v7) % 29.58/7.52 | (486) ! [v0] : ( ~ empty(v0) | ordinal(v0)) % 29.58/7.52 | (487) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) % 29.58/7.52 | (488) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | reflexive(v0)) % 29.58/7.52 | (489) ! [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)) % 29.58/7.52 | (490) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) % 29.58/7.52 | (491) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 29.58/7.52 | (492) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) % 29.58/7.52 | (493) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (apply(v3, v2) = v4) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ function(v3) | ~ in(v2, v0) | ? [v5] : (relation_rng(v3) = v5 & in(v4, v5))) % 29.58/7.52 | (494) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) % 29.58/7.52 | (495) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 29.58/7.52 | (496) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) % 29.58/7.52 | (497) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 29.58/7.52 | (498) ! [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)))) % 29.58/7.52 | (499) relation(all_0_15_15) % 29.58/7.52 | (500) ! [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))) % 29.58/7.52 | (501) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join_commut(v4, v3, v2) = v1) | ~ (join_commut(v4, v3, v2) = v0)) % 29.58/7.52 | (502) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 29.58/7.52 | (503) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (succ(v1) = v3 & powerset(v4) = v5 & powerset(v3) = v4 & powerset(v1) = v6 & ( ~ element(v0, v5) | ( ! [v8] : ! [v9] : ( ~ (set_difference(v9, v2) = v8) | ~ in(v9, v0) | ~ in(v8, v6) | in(v8, v7)) & ! [v8] : ( ~ in(v8, v7) | in(v8, v6)) & ! [v8] : ( ~ in(v8, v7) | ? [v9] : (set_difference(v9, v2) = v8 & in(v9, v0))))))) % 29.58/7.52 | (504) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ finite(v0) | finite(v2)) % 29.58/7.52 | (505) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 29.91/7.52 | (506) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 29.91/7.52 | (507) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 29.91/7.52 | (508) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 29.91/7.52 | (509) ! [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))) % 29.91/7.52 | (510) ! [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))) % 29.91/7.53 | (511) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1)) % 29.91/7.53 | (512) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) % 29.91/7.53 | (513) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 29.91/7.53 | (514) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) % 29.91/7.53 | (515) ! [v0] : ( ~ (union(v0) = v0) | being_limit_ordinal(v0)) % 29.91/7.53 | (516) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 29.91/7.53 | (517) ! [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)) % 29.91/7.53 | (518) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 29.91/7.53 | (519) epsilon_transitive(all_0_18_18) % 29.91/7.53 | (520) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | ? [v3] : (set_intersection2(v0, v3) = v2 & cartesian_product2(v1, v1) = v3)) % 29.91/7.53 | (521) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = empty_set | ~ (relation_inverse_image(v3, v2) = v4) | ~ (apply(v3, v5) = v6) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ function(v3) | ~ in(v6, v2) | ~ in(v5, v0) | in(v5, v4)) % 29.91/7.53 | (522) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ well_founded_relation(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | well_founded_relation(v1)) % 29.91/7.53 | (523) ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) % 29.91/7.53 | (524) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply_binary_as_element(v0, v1, v2, v3, v4, v5) = v6) | ~ function(v3) | ~ element(v5, v1) | ~ element(v4, v0) | empty(v1) | empty(v0) | ? [v7] : ? [v8] : (apply_binary(v3, v4, v5) = v8 & cartesian_product2(v0, v1) = v7 & (v8 = v6 | ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2)))) % 29.91/7.53 | (525) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | pair_second(v2) = v1) % 29.91/7.53 | (526) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 29.91/7.53 | (527) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) % 29.91/7.53 | (528) one_to_one(empty_set) % 29.91/7.53 | (529) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 29.91/7.53 | (530) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_field(v1) = v2) | ~ equipotent(v0, v2) | ~ well_ordering(v1) | ~ relation(v1) | ? [v3] : (well_orders(v3, v0) & relation(v3))) % 29.91/7.53 | (531) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) % 29.91/7.53 | (532) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v1_membered(v2)) % 29.91/7.53 | (533) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 29.91/7.53 | (534) join_semilatt_str(all_0_2_2) % 29.91/7.53 | (535) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 29.91/7.53 | (536) ~ empty(all_0_15_15) % 29.91/7.53 | (537) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3))) % 29.91/7.53 | (538) ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) % 29.91/7.53 | (539) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | ? [v2] : ? [v3] : (the_L_join(v0) = v2 & cartesian_product2(v1, v1) = v3 & quasi_total(v2, v3, v1) & relation_of2_as_subset(v2, v3, v1) & function(v2))) % 29.91/7.53 | (540) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 29.91/7.53 | (541) natural(all_0_4_4) % 29.91/7.53 | (542) ! [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)) % 29.91/7.53 | (543) one_sorted_str(all_0_20_20) % 29.91/7.53 | (544) ! [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) % 29.91/7.53 | (545) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | v4 = v1 | v4 = v0 | ~ (unordered_triple(v0, v1, v2) = v3) | ~ in(v4, v3)) % 29.91/7.53 | (546) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_transitive_in(v0, v1)) % 29.91/7.53 | (547) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 29.91/7.53 | (548) ! [v0] : ! [v1] : ( ~ equipotent(v0, v1) | are_equipotent(v0, v1)) % 29.91/7.53 | (549) ! [v0] : ! [v1] : ( ~ are_equipotent(v0, v1) | equipotent(v0, v1)) % 29.91/7.53 | (550) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) % 29.91/7.53 | (551) relation(all_0_14_14) % 29.91/7.53 | (552) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join_commut(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 29.91/7.53 | (553) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) % 29.91/7.53 | (554) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 29.91/7.53 | (555) ? [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))))) % 29.91/7.53 | (556) ! [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)) % 29.91/7.53 | (557) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (relation_dom(v2) = v4 & subset(v4, v0))) % 29.91/7.54 | (558) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 29.91/7.54 | (559) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) % 29.91/7.54 | (560) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 29.91/7.54 | (561) ! [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))))) % 29.91/7.54 | (562) ! [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v0) = v1) | ~ (cartesian_product2(v1, v1) = v2) | ~ join_semilatt_str(v0) | ? [v3] : (the_L_join(v0) = v3 & quasi_total(v3, v2, v1) & relation_of2_as_subset(v3, v2, v1) & function(v3))) % 29.91/7.54 | (563) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) % 29.91/7.54 | (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))))) % 29.91/7.54 | (565) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v3_membered(v2)) % 29.91/7.54 | (566) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 29.91/7.54 | (567) ! [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)) % 29.91/7.54 | (568) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) % 29.91/7.54 | (569) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 29.91/7.54 | (570) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 29.91/7.54 | (571) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) % 29.91/7.54 | (572) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | reflexive(v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v2) = v3 & in(v2, v1) & ~ in(v3, v0))) % 29.91/7.54 | (573) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v1 = v0 | ~ (apply_binary_as_element(v7, v6, v5, v4, v3, v2) = v1) | ~ (apply_binary_as_element(v7, v6, v5, v4, v3, v2) = v0)) % 29.91/7.54 | (574) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (the_carrier(v0) = v1) | ~ below(v0, v3, v2) | ~ below(v0, v2, v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | ~ element(v3, v1) | ~ element(v2, v1) | empty_carrier(v0)) % 29.91/7.54 | (575) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 29.91/7.54 | (576) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | ordinal(v1)) % 29.91/7.54 | (577) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 29.91/7.54 | (578) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) % 29.91/7.54 | (579) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) % 29.91/7.54 | (580) ? [v0] : ? [v1] : ( ! [v2] : ( ~ ordinal(v2) | ~ in(v2, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ordinal(v2)) & ! [v2] : ( ~ in(v2, v1) | in(v2, v0))) % 29.91/7.54 | (581) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ well_ordering(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | well_ordering(v1)) % 29.91/7.54 | (582) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) % 29.91/7.54 | (583) ! [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)))) % 29.91/7.54 | (584) ! [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))) % 29.91/7.54 | (585) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 29.91/7.54 | (586) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) % 29.91/7.54 | (587) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v2) = v3) | ~ relation(v1) | empty(v0) | ? [v4] : ( ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v7) = v5) | ~ in(v7, v6) | ~ in(v6, v0) | ~ in(v5, v3) | in(v5, v4) | ? [v8] : ? [v9] : (ordered_pair(v7, v8) = v9 & in(v8, v6) & ~ in(v9, v1))) & ! [v5] : ( ~ in(v5, v4) | in(v5, v3)) & ! [v5] : ( ~ in(v5, v4) | ? [v6] : ? [v7] : (ordered_pair(v6, v7) = v5 & in(v7, v6) & in(v6, v0) & ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ in(v8, v6) | in(v9, v1)))))) % 29.91/7.54 | (588) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 29.91/7.54 | (589) epsilon_connected(all_0_9_9) % 29.91/7.54 | (590) ? [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)))) % 29.91/7.54 | (591) one_to_one(all_0_17_17) % 29.91/7.54 | (592) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 29.91/7.54 | (593) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ~ finite(v1) | ? [v2] : (relation_rng(v0) = v2 & finite(v2))) % 29.91/7.54 | (594) ! [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)) % 29.91/7.54 | (595) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 29.91/7.54 | (596) ! [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))))))) % 29.91/7.55 | (597) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 29.91/7.55 | (598) ! [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))) % 29.91/7.55 | (599) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_L_join(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (join(v0, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | join(v0, v3, v4) = v5))) % 29.91/7.55 | (600) ? [v0] : ? [v1] : (relation_dom(v1) = v0 & relation(v1) & function(v1) & ! [v2] : ! [v3] : ( ~ (singleton(v2) = v3) | ~ in(v2, v0) | apply(v1, v2) = v3) & ! [v2] : ! [v3] : ( ~ (apply(v1, v2) = v3) | ~ in(v2, v0) | singleton(v2) = v3)) % 29.91/7.55 | (601) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) % 29.91/7.55 | (602) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1)) % 29.91/7.55 | (603) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v2] : ? [v3] : (the_L_meet(v0) = v2 & cartesian_product2(v1, v1) = v3 & quasi_total(v2, v3, v1) & relation_of2_as_subset(v2, v3, v1) & function(v2))) % 29.91/7.55 | (604) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | connected(v0)) % 29.91/7.55 | (605) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 29.91/7.55 | (606) ! [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))))) % 29.91/7.55 | (607) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v1) | finite(v2)) % 29.91/7.55 | (608) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 29.91/7.55 | (609) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v5_membered(v2)) % 29.91/7.55 | (610) relation_empty_yielding(all_0_19_19) % 29.91/7.55 | (611) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_well_founded_in(v0, v1) | ~ relation(v0) | well_founded_relation(v0)) % 29.91/7.55 | (612) finite(all_0_5_5) % 29.91/7.55 | (613) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) % 29.91/7.55 | (614) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 29.91/7.55 | (615) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (powerset(v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : ? [v7] : (powerset(v4) = v6 & powerset(v3) = v5 & ( ~ element(v0, v5) | ( ! [v8] : ! [v9] : ( ~ (relation_image(v2, v8) = v9) | ~ in(v9, v0) | ~ in(v8, v6) | in(v8, v7)) & ! [v8] : ! [v9] : ( ~ (relation_image(v2, v8) = v9) | ~ in(v8, v7) | in(v9, v0)) & ! [v8] : ! [v9] : ( ~ (relation_image(v2, v8) = v9) | ~ in(v8, v7) | in(v8, v6)))))) % 29.91/7.55 | (616) ! [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))) % 29.91/7.55 | (617) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 29.91/7.55 | (618) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ transitive(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | transitive(v1)) % 29.91/7.55 | (619) ? [v0] : ? [v1] : element(v1, v0) % 29.91/7.55 | (620) ! [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)))) % 29.91/7.55 | (621) powerset(empty_set) = all_0_40_40 % 29.91/7.55 | (622) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | meet(v0, v3, v4) = v5))) % 29.91/7.55 | (623) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ antisymmetric(v1) | ~ relation(v1) | antisymmetric(v2)) % 29.91/7.55 | (624) ? [v0] : (empty(v0) | ? [v1] : ? [v2] : ((v2 = v0 & relation_dom(v1) = v0 & relation(v1) & function(v1) & ! [v3] : ! [v4] : ( ~ (apply(v1, v3) = v4) | ~ in(v3, v0) | in(v4, v3))) | (v1 = empty_set & in(empty_set, v0)))) % 29.91/7.55 | (625) ? [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))))) % 29.91/7.55 | (626) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 29.91/7.55 | (627) epsilon_connected(all_0_14_14) % 29.91/7.55 | (628) ! [v0] : ! [v1] : ( ~ (succ(v1) = v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0)) % 29.91/7.55 | (629) ! [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)) % 29.91/7.55 | (630) ? [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))))) % 29.91/7.55 | (631) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ connected(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | connected(v1)) % 29.91/7.55 | (632) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) % 29.91/7.55 | (633) being_limit_ordinal(all_0_9_9) % 29.91/7.55 | (634) ? [v0] : ? [v1] : (relation(v1) & function(v1) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ in(v4, v1) | singleton(v2) = v3) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ in(v4, v1) | in(v2, v0)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ in(v2, v0) | in(v4, v1) | ? [v5] : ( ~ (v5 = v3) & singleton(v2) = v5))) % 29.91/7.56 | (635) ! [v0] : ( ~ finite(v0) | ? [v1] : ? [v2] : (relation_rng(v1) = v0 & relation_dom(v1) = v2 & relation(v1) & function(v1) & in(v2, omega))) % 29.91/7.56 | (636) ! [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)) % 29.91/7.56 | (637) ! [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)) % 29.91/7.56 | (638) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) % 29.91/7.56 | (639) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 29.91/7.56 | (640) ! [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)) % 29.91/7.56 | (641) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 29.91/7.56 | (642) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = empty_set | ~ (relation_inverse_image(v3, v2) = v4) | ~ (apply(v3, v5) = v6) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ function(v3) | ~ in(v5, v4) | in(v5, v0)) % 29.91/7.56 | (643) ~ empty(all_0_4_4) % 29.91/7.56 | (644) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 29.91/7.56 | (645) ! [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)) % 29.91/7.56 | (646) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_reflexive_in(v0, v1)) % 29.91/7.56 | (647) ? [v0] : equipotent(v0, v0) % 29.91/7.56 | (648) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) % 29.91/7.56 | (649) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 29.91/7.56 | (650) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 29.91/7.56 | (651) ? [v0] : ! [v1] : ( ~ relation(v1) | empty(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = v2 & v5 = v2 & ~ (v4 = v3) & in(v4, v2) & in(v3, v2) & in(v2, v0) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v7, v2) | in(v8, v1)) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v3, v7) = v8) | ~ in(v7, v2) | in(v8, v1))) | ( ! [v7] : ! [v8] : ( ~ in(v8, v0) | ~ in(v7, v8) | in(v7, v2) | ? [v9] : ? [v10] : (ordered_pair(v7, v9) = v10 & in(v9, v8) & ~ in(v10, v1))) & ! [v7] : ( ~ in(v7, v2) | ? [v8] : (in(v8, v0) & in(v7, v8) & ! [v9] : ! [v10] : ( ~ (ordered_pair(v7, v9) = v10) | ~ in(v9, v8) | in(v10, v1))))))) % 29.91/7.56 | (652) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v3_membered(v2)) % 29.91/7.56 | (653) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) % 29.91/7.56 | (654) ? [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))))) % 29.91/7.56 | (655) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) % 29.91/7.56 | (656) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 29.91/7.56 | (657) function(all_0_10_10) % 29.91/7.56 | (658) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v4_membered(v2)) % 29.91/7.56 | (659) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 29.91/7.56 | (660) v3_membered(empty_set) % 29.91/7.56 | (661) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 29.91/7.56 | (662) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 29.91/7.56 | (663) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) % 29.91/7.56 | (664) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_connected_in(v0, v1) | ~ relation(v0) | connected(v0)) % 29.91/7.56 | (665) ! [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))))))) % 29.91/7.56 | (666) epsilon_transitive(all_0_8_8) % 29.91/7.56 | (667) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 29.91/7.56 | (668) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 29.91/7.56 | (669) ordinal(all_0_18_18) % 29.91/7.56 | (670) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 29.91/7.56 | (671) epsilon_connected(omega) % 29.91/7.56 | (672) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) % 29.91/7.56 | (673) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 29.91/7.56 | (674) ! [v0] : ! [v1] : ! [v2] : ( ~ quasi_total(v2, empty_set, v0) | ~ relation_of2_as_subset(v2, empty_set, v0) | ~ subset(v0, v1) | ~ function(v2) | quasi_total(v2, empty_set, v1)) % 29.91/7.56 | (675) ! [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))) % 29.91/7.57 | (676) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) % 29.91/7.57 | (677) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ epsilon_connected(v0) | ~ in(v2, v0) | ~ in(v1, v0) | in(v2, v1) | in(v1, v2)) % 29.91/7.57 | (678) ! [v0] : ( ~ element(v0, omega) | epsilon_transitive(v0)) % 29.91/7.57 | (679) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | transitive(v0)) % 29.91/7.57 | (680) ? [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)))) % 29.91/7.57 | (681) ! [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)) % 29.91/7.57 | (682) relation(all_0_11_11) % 29.91/7.57 | (683) ! [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))) % 29.91/7.57 | (684) ! [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)))) % 29.91/7.57 | (685) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 29.91/7.57 | (686) ! [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)))) % 29.91/7.57 | (687) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) % 29.91/7.57 | (688) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 29.91/7.57 | (689) ! [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)) % 29.91/7.57 | (690) ! [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))) % 29.91/7.57 | (691) relation(all_0_19_19) % 29.91/7.57 | (692) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1)) % 29.91/7.57 | (693) ? [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)) % 29.91/7.57 | (694) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 29.91/7.57 | (695) ! [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)) % 29.91/7.57 | (696) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) % 29.91/7.57 | (697) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 29.91/7.57 | (698) ! [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)))))))) % 29.91/7.57 | (699) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v1_membered(v2)) % 29.91/7.57 | (700) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | relation_dom(v2) = v3) % 29.91/7.57 | (701) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom_as_subset(v0, empty_set, empty_set) = v1) | ~ relation_of2_as_subset(empty_set, v0, empty_set) | quasi_total(empty_set, v0, empty_set)) % 29.91/7.57 | (702) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 29.91/7.57 | (703) ordinal(empty_set) % 29.91/7.57 | (704) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | function(v1)) % 29.91/7.57 | (705) epsilon_connected(all_0_18_18) % 29.91/7.57 | (706) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 29.91/7.57 | (707) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 29.91/7.57 | (708) ! [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))) % 29.91/7.57 | (709) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 29.91/7.57 | (710) ! [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))) % 30.12/7.57 | (711) ! [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)))) % 30.12/7.58 | (712) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_intersection2(v1, v2, v2) = v3) | ? [v4] : (powerset(v1) = v4 & ( ~ element(v2, v4) | ~ element(v0, v4)))) % 30.12/7.58 | (713) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v3, v2)) % 30.12/7.58 | (714) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 30.12/7.58 | (715) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0)) % 30.12/7.58 | (716) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 30.12/7.58 | (717) ! [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)) % 30.12/7.58 | (718) ? [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))))) % 30.12/7.58 | (719) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ transitive(v0) | ~ relation(v0) | is_transitive_in(v0, v1)) % 30.12/7.58 | (720) ! [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))) % 30.12/7.58 | (721) function(all_0_21_21) % 30.12/7.58 | (722) ? [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v2) = v1) | ~ one_to_one(v2) | ~ relation(v2) | ~ function(v2) | equipotent(v0, v1) | ? [v3] : ( ~ (v3 = v0) & relation_dom(v2) = v3)) % 30.12/7.58 | (723) ! [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))) % 30.12/7.58 | (724) ! [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)))) % 30.12/7.58 | (725) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v0) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ? [v4] : ( ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (apply(v2, v7) = v9) | ~ (apply(v2, v6) = v8) | ~ (ordered_pair(v8, v9) = v10) | ~ in(v10, v1) | ~ in(v5, v3) | in(v5, v4) | ? [v11] : ( ~ (v11 = v5) & ordered_pair(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v7) = v5) | ~ in(v5, v3) | in(v5, v4) | ? [v8] : ? [v9] : ? [v10] : (apply(v2, v7) = v9 & apply(v2, v6) = v8 & ordered_pair(v8, v9) = v10 & ~ in(v10, v1))) & ! [v5] : ( ~ in(v5, v4) | in(v5, v3)) & ! [v5] : ( ~ in(v5, v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (apply(v2, v7) = v9 & apply(v2, v6) = v8 & ordered_pair(v8, v9) = v10 & ordered_pair(v6, v7) = v5 & in(v10, v1))))) % 30.12/7.58 | (726) ! [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))) % 30.12/7.58 | (727) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | natural(v1)) % 30.12/7.58 | (728) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) % 30.12/7.58 | (729) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v1 = empty_set | ~ (relation_inverse_image(v3, v2) = v4) | ~ (apply(v3, v5) = v6) | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ function(v3) | ~ in(v5, v4) | in(v6, v2)) % 30.12/7.58 | (730) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_intersection2(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 30.12/7.58 | (731) ! [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)))) % 30.12/7.58 | (732) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 30.12/7.58 | (733) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ in(v4, v5) | in(v1, v3)) % 30.12/7.58 | (734) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2)) % 30.12/7.58 | (735) ! [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))) % 30.12/7.58 | (736) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v4_membered(v2)) % 30.12/7.58 | (737) ! [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))))) % 30.12/7.58 | (738) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 30.12/7.58 | (739) ! [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)) % 30.12/7.58 | (740) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | finite(v1)) % 30.12/7.58 | (741) ! [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)))) % 30.12/7.58 | (742) ? [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))))) % 30.12/7.59 | (743) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) % 30.12/7.59 | (744) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ finite(v1) | ~ finite(v0) | finite(v2)) % 30.12/7.59 | (745) ? [v0] : ! [v1] : ( ~ relation(v1) | is_reflexive_in(v1, v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v2) = v3 & in(v2, v0) & ~ in(v3, v1))) % 30.12/7.59 | (746) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v2_membered(v2)) % 30.12/7.59 | (747) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 30.12/7.59 | (748) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2))) % 30.12/7.59 | (749) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) % 30.12/7.59 | (750) ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) % 30.12/7.59 | (751) ? [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))) % 30.12/7.59 | (752) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 30.12/7.59 | (753) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) % 30.12/7.59 | (754) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ordinal(v1)) % 30.12/7.59 | (755) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (ordered_pair(v1, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ function(v0) | ~ in(v5, v0) | ~ in(v4, v0)) % 30.12/7.59 | (756) meet_semilatt_str(all_0_0_0) % 30.12/7.59 | (757) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) % 30.12/7.59 | (758) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 30.12/7.59 | (759) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 30.12/7.59 | (760) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) % 30.12/7.59 | (761) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v2) = v3) | ~ (cartesian_product2(v1, v1) = v2) | ~ relation(v0) | relation_restriction(v0, v1) = v3) % 30.12/7.59 | (762) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & cartesian_product2(v2, v2) = v3 & quasi_total(v1, v3, v2) & relation_of2_as_subset(v1, v3, v2))) % 30.12/7.59 | (763) latt_str(all_0_3_3) % 30.12/7.59 | (764) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 30.12/7.59 | (765) ! [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))) % 30.12/7.59 | (766) ! [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)) % 30.12/7.59 | (767) relation(all_0_10_10) % 30.12/7.59 | (768) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) % 30.12/7.59 | (769) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 30.12/7.59 | (770) ordinal(all_0_14_14) % 30.12/7.59 | (771) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ connected(v0) | ~ relation(v0) | is_connected_in(v0, v1)) % 30.12/7.59 | (772) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 30.12/7.59 | (773) ! [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)))))))) % 30.12/7.59 | (774) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) % 30.12/7.59 | (775) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 30.12/7.59 | (776) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 30.12/7.59 | (777) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_field(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ reflexive(v0) | ~ relation(v0) | ~ in(v2, v1) | in(v3, v0)) % 30.12/7.59 | (778) ~ empty(all_0_7_7) % 30.12/7.59 | (779) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1)) % 30.12/7.59 | (780) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) % 30.12/7.59 | (781) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | subset(v3, v1)) % 30.12/7.59 | (782) ! [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)))) % 30.12/7.59 | (783) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 30.12/7.60 | (784) ! [v0] : ( ~ reflexive(v0) | ~ well_founded_relation(v0) | ~ transitive(v0) | ~ connected(v0) | ~ antisymmetric(v0) | ~ relation(v0) | well_ordering(v0)) % 30.12/7.60 | (785) v4_membered(empty_set) % 30.12/7.60 | (786) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_orders(v1, v0) | ~ relation(v1) | relation_field(v2) = v0) % 30.12/7.60 | (787) relation_empty_yielding(empty_set) % 30.12/7.60 | (788) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) % 30.12/7.60 | (789) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3)) % 30.12/7.60 | (790) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 30.12/7.60 | (791) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 30.12/7.60 | (792) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~ (apply_binary(v4, v3, v2) = v0)) % 30.12/7.60 | (793) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1)) % 30.12/7.60 | (794) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1)) % 30.12/7.60 | (795) ! [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))) % 30.12/7.60 | (796) ! [v0] : ( ~ latt_str(v0) | meet_semilatt_str(v0)) % 30.12/7.60 | (797) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) % 30.12/7.60 | (798) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 30.12/7.60 | (799) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) % 30.12/7.60 | (800) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 30.12/7.60 | (801) ! [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)) % 30.12/7.60 | (802) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (one_to_one(v2) & relation(v2) & function(v2) & finite(v2) & epsilon_connected(v2) & epsilon_transitive(v2) & ordinal(v2) & empty(v2) & natural(v2) & element(v2, v1))) % 30.12/7.60 | (803) ! [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))) % 30.12/7.60 | (804) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 30.12/7.60 | (805) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) % 30.12/7.60 | (806) v3_membered(all_0_7_7) % 30.12/7.60 | (807) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) % 30.12/7.60 | (808) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v1, v3)) % 30.12/7.60 | (809) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (join(v0, v2, v3) = v4) | ~ (the_carrier(v0) = v1) | ~ below(v0, v2, v3) | ~ join_semilatt_str(v0) | ~ element(v3, v1) | ~ element(v2, v1) | empty_carrier(v0)) % 30.12/7.60 | (810) ~ empty_carrier(all_0_20_20) % 30.12/7.60 | (811) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) % 30.12/7.60 | (812) ! [v0] : ( ~ empty(v0) | v4_membered(v0)) % 30.12/7.60 | (813) ! [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))) % 30.12/7.60 | (814) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | subset(v3, v0)) % 30.12/7.60 | (815) ! [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)) % 30.12/7.60 | (816) ? [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))))) % 30.12/7.60 | (817) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1)) % 30.12/7.60 | (818) ~ empty(all_0_16_16) % 30.12/7.60 | (819) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 30.12/7.60 | (820) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1) % 30.12/7.60 | (821) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ finite(v1) | finite(v0)) % 30.12/7.60 | (822) ordinal(all_0_8_8) % 30.12/7.60 | (823) being_limit_ordinal(omega) % 30.12/7.60 | (824) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_L_meet(v0) = v2 & ! [v3] : ! [v4] : ! [v5] : ( ~ (meet(v0, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) & ! [v3] : ! [v4] : ! [v5] : ( ~ (apply_binary_as_element(v1, v1, v1, v2, v3, v4) = v5) | ~ element(v4, v1) | ~ element(v3, v1) | meet(v0, v3, v4) = v5))) % 30.12/7.60 | (825) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) % 30.12/7.60 | (826) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 30.12/7.60 | (827) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 30.12/7.60 | (828) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v2_membered(v2)) % 30.12/7.61 | (829) ! [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)) % 30.12/7.61 | (830) ! [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))) % 30.12/7.61 | (831) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v2, v1) = v3) | ? [v4] : ? [v5] : (subset_intersection2(v0, v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) % 30.12/7.61 | (832) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 30.12/7.61 | (833) ! [v0] : ! [v1] : ! [v2] : ( ~ quasi_total(v2, empty_set, v0) | ~ relation_of2_as_subset(v2, empty_set, v0) | ~ subset(v0, v1) | ~ function(v2) | relation_of2_as_subset(v2, empty_set, v1)) % 30.12/7.61 | (834) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | function(v1)) % 30.12/7.61 | (835) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ? [v2] : ( ! [v3] : ! [v4] : ( ~ (powerset(v3) = v4) | ~ ordinal(v3) | ~ in(v3, v1) | in(v3, v2) | in(v3, omega)) & ! [v3] : ! [v4] : ( ~ (powerset(v3) = v4) | ~ ordinal(v3) | ~ in(v3, v1) | in(v3, v2) | ? [v5] : ? [v6] : ( ~ (v6 = empty_set) & powerset(v4) = v5 & element(v6, v5) & ! [v7] : ( ~ in(v7, v6) | ? [v8] : ( ~ (v8 = v7) & subset(v7, v8) & in(v8, v6))))) & ! [v3] : ( ~ in(v3, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v3) = v4 & ordinal(v3) & ( ~ in(v3, omega) | ! [v6] : (v6 = empty_set | ~ element(v6, v5) | ? [v7] : (in(v7, v6) & ! [v8] : (v8 = v7 | ~ subset(v7, v8) | ~ in(v8, v6))))))))) % 30.12/7.61 | (836) ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1)) % 30.12/7.61 | (837) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) % 30.12/7.61 | (838) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ quasi_total(v3, v0, v1) | ~ relation_of2_as_subset(v3, v0, v1) | ~ subset(v1, v2) | ~ function(v3) | quasi_total(v3, v0, v2)) % 30.12/7.61 | (839) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_intersection2(v4, v3, v2) = v1) | ~ (subset_intersection2(v4, v3, v2) = v0)) % 30.12/7.61 | (840) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v2, v3)) % 30.12/7.61 | (841) ! [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))) % 30.12/7.61 | (842) ? [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))))) % 30.12/7.61 | (843) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) % 30.12/7.61 | (844) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | ~ finite(v1) | finite(v2)) % 30.12/7.61 | (845) ? [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))))) % 30.12/7.61 | (846) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 30.12/7.61 | (847) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) % 30.12/7.61 | (848) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v1_membered(v2)) % 30.12/7.61 | (849) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (meet(v0, v2, v3) = v4) | ~ (join(v0, v4, v3) = v5) | ~ (the_carrier(v0) = v1) | ~ meet_absorbing(v0) | ~ latt_str(v0) | ~ element(v3, v1) | ~ element(v2, v1) | empty_carrier(v0)) % 30.12/7.61 | (850) ! [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))) % 30.12/7.61 | (851) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) % 30.12/7.61 | (852) ! [v0] : ! [v1] : ! [v2] : (v1 = empty_set | v0 = empty_set | ~ (relation_dom_as_subset(v0, empty_set, v1) = v2) | ~ quasi_total(v1, v0, empty_set) | ~ relation_of2_as_subset(v1, v0, empty_set)) % 30.12/7.61 | (853) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 30.12/7.61 | (854) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) % 30.12/7.61 | (855) ! [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)) % 30.12/7.61 | (856) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1)) % 30.12/7.61 | (857) ? [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(v2, omega) | finite(v0) | ? [v3] : ( ~ (v3 = v0) & relation_rng(v1) = v3)) % 30.12/7.61 | (858) ! [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)) % 30.12/7.61 | (859) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) % 30.12/7.61 | (860) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) % 30.12/7.61 | (861) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0)) % 30.12/7.61 | (862) relation(all_0_13_13) % 30.12/7.61 | (863) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join(v0, v2, v3) = v3) | ~ (the_carrier(v0) = v1) | ~ join_semilatt_str(v0) | ~ element(v3, v1) | ~ element(v2, v1) | below(v0, v2, v3) | empty_carrier(v0)) % 30.12/7.61 | (864) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) % 30.12/7.61 | (865) ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : ? [v2] : (succ(v1) = v2 & ordinal(v1) & in(v1, v0) & ~ in(v2, v0))) % 30.12/7.62 | (866) subset_intersection2(all_0_37_37, all_0_34_34, all_0_35_35) = all_0_33_33 % 30.12/7.62 | (867) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 30.12/7.62 | (868) v4_membered(all_0_7_7) % 30.12/7.62 | (869) ? [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))))) % 30.12/7.62 | (870) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, omega) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) | ( ~ (all_0_29_29 = empty_set) & powerset(all_0_31_31) = all_0_30_30 & powerset(all_0_32_32) = all_0_31_31 & ordinal(all_0_32_32) & element(all_0_29_29, all_0_30_30) & in(all_0_32_32, omega) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, all_0_32_32) | ~ in(v0, omega) | ? [v2] : (powerset(v1) = v2 & ! [v3] : (v3 = empty_set | ~ element(v3, v2) | ? [v4] : (in(v4, v3) & ! [v5] : (v5 = v4 | ~ subset(v4, v5) | ~ in(v5, v3)))))) & ! [v0] : ( ~ in(v0, all_0_29_29) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_29_29)))) % 30.12/7.62 | (871) ! [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))))) % 30.12/7.62 | (872) ! [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))) % 30.12/7.62 | (873) ! [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)))) % 30.12/7.62 | (874) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1)) % 30.12/7.62 | (875) ! [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)) % 30.12/7.62 | (876) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 30.12/7.62 | (877) ! [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))))) % 30.12/7.62 | (878) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0)) % 30.12/7.62 | (879) cast_as_carrier_subset(all_0_38_38) = all_0_35_35 % 30.12/7.62 | (880) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | transitive(v0)) % 30.12/7.62 | % 30.12/7.62 | Instantiating formula (831) with all_0_33_33, all_0_34_34, all_0_35_35, all_0_37_37 and discharging atoms subset_intersection2(all_0_37_37, all_0_34_34, all_0_35_35) = all_0_33_33, yields: % 30.12/7.62 | (881) ? [v0] : ? [v1] : (subset_intersection2(all_0_37_37, all_0_35_35, all_0_34_34) = v1 & powerset(all_0_37_37) = v0 & (v1 = all_0_33_33 | ~ element(all_0_34_34, v0) | ~ element(all_0_35_35, v0))) % 30.12/7.62 | % 30.12/7.62 | Instantiating formula (730) with all_0_33_33, all_0_35_35, all_0_34_34, all_0_37_37 and discharging atoms subset_intersection2(all_0_37_37, all_0_34_34, all_0_35_35) = all_0_33_33, yields: % 30.12/7.62 | (882) ? [v0] : ? [v1] : (set_intersection2(all_0_34_34, all_0_35_35) = v1 & powerset(all_0_37_37) = v0 & (v1 = all_0_33_33 | ~ element(all_0_34_34, v0) | ~ element(all_0_35_35, v0))) % 30.12/7.62 | % 30.12/7.62 | Instantiating formula (215) with all_0_36_36, all_0_37_37 and discharging atoms powerset(all_0_37_37) = all_0_36_36, yields: % 30.12/7.62 | (883) ? [v0] : (cast_to_subset(all_0_37_37) = v0 & element(v0, all_0_36_36)) % 30.12/7.62 | % 30.12/7.62 | Instantiating formula (343) with all_0_35_35, all_0_38_38 and discharging atoms cast_as_carrier_subset(all_0_38_38) = all_0_35_35, one_sorted_str(all_0_38_38), yields: % 30.12/7.62 | (884) the_carrier(all_0_38_38) = all_0_35_35 % 30.12/7.62 | % 30.12/7.62 | Instantiating formula (851) with all_0_35_35, all_0_38_38 and discharging atoms cast_as_carrier_subset(all_0_38_38) = all_0_35_35, one_sorted_str(all_0_38_38), yields: % 30.12/7.62 | (885) ? [v0] : ? [v1] : (the_carrier(all_0_38_38) = v0 & powerset(v0) = v1 & element(all_0_35_35, v1)) % 30.12/7.62 | % 30.12/7.62 | Instantiating formula (353) with all_0_37_37, all_0_38_38 and discharging atoms the_carrier(all_0_38_38) = all_0_37_37, one_sorted_str(all_0_38_38), yields: % 30.12/7.62 | (886) ? [v0] : ? [v1] : (cast_as_carrier_subset(all_0_38_38) = v0 & powerset(all_0_37_37) = v1 & element(v0, v1)) % 30.12/7.62 | % 30.12/7.62 | Instantiating formula (505) with all_0_36_36, all_0_37_37, all_0_34_34 and discharging atoms powerset(all_0_37_37) = all_0_36_36, element(all_0_34_34, all_0_36_36), yields: % 30.12/7.62 | (887) subset(all_0_34_34, all_0_37_37) % 30.12/7.62 | % 30.12/7.62 | Instantiating (883) with all_226_0_171 yields: % 30.12/7.62 | (888) cast_to_subset(all_0_37_37) = all_226_0_171 & element(all_226_0_171, all_0_36_36) % 30.12/7.62 | % 30.12/7.62 | Applying alpha-rule on (888) yields: % 30.12/7.62 | (889) cast_to_subset(all_0_37_37) = all_226_0_171 % 30.12/7.62 | (890) element(all_226_0_171, all_0_36_36) % 30.12/7.62 | % 30.12/7.62 | Instantiating (885) with all_352_0_227, all_352_1_228 yields: % 30.12/7.62 | (891) the_carrier(all_0_38_38) = all_352_1_228 & powerset(all_352_1_228) = all_352_0_227 & element(all_0_35_35, all_352_0_227) % 30.12/7.62 | % 30.12/7.62 | Applying alpha-rule on (891) yields: % 30.12/7.62 | (892) the_carrier(all_0_38_38) = all_352_1_228 % 30.12/7.62 | (893) powerset(all_352_1_228) = all_352_0_227 % 30.12/7.62 | (894) element(all_0_35_35, all_352_0_227) % 30.12/7.62 | % 30.12/7.62 | Instantiating (882) with all_468_0_294, all_468_1_295 yields: % 30.12/7.62 | (895) set_intersection2(all_0_34_34, all_0_35_35) = all_468_0_294 & powerset(all_0_37_37) = all_468_1_295 & (all_468_0_294 = all_0_33_33 | ~ element(all_0_34_34, all_468_1_295) | ~ element(all_0_35_35, all_468_1_295)) % 30.12/7.62 | % 30.12/7.62 | Applying alpha-rule on (895) yields: % 30.12/7.62 | (896) set_intersection2(all_0_34_34, all_0_35_35) = all_468_0_294 % 30.12/7.63 | (897) powerset(all_0_37_37) = all_468_1_295 % 30.12/7.63 | (898) all_468_0_294 = all_0_33_33 | ~ element(all_0_34_34, all_468_1_295) | ~ element(all_0_35_35, all_468_1_295) % 30.12/7.63 | % 30.12/7.63 | Instantiating (881) with all_470_0_296, all_470_1_297 yields: % 30.12/7.63 | (899) subset_intersection2(all_0_37_37, all_0_35_35, all_0_34_34) = all_470_0_296 & powerset(all_0_37_37) = all_470_1_297 & (all_470_0_296 = all_0_33_33 | ~ element(all_0_34_34, all_470_1_297) | ~ element(all_0_35_35, all_470_1_297)) % 30.12/7.63 | % 30.12/7.63 | Applying alpha-rule on (899) yields: % 30.12/7.63 | (900) subset_intersection2(all_0_37_37, all_0_35_35, all_0_34_34) = all_470_0_296 % 30.12/7.63 | (901) powerset(all_0_37_37) = all_470_1_297 % 30.12/7.63 | (902) all_470_0_296 = all_0_33_33 | ~ element(all_0_34_34, all_470_1_297) | ~ element(all_0_35_35, all_470_1_297) % 30.12/7.63 | % 30.12/7.63 | Instantiating (886) with all_565_0_333, all_565_1_334 yields: % 30.12/7.63 | (903) cast_as_carrier_subset(all_0_38_38) = all_565_1_334 & powerset(all_0_37_37) = all_565_0_333 & element(all_565_1_334, all_565_0_333) % 30.12/7.63 | % 30.12/7.63 | Applying alpha-rule on (903) yields: % 30.12/7.63 | (904) cast_as_carrier_subset(all_0_38_38) = all_565_1_334 % 30.12/7.63 | (905) powerset(all_0_37_37) = all_565_0_333 % 30.12/7.63 | (906) element(all_565_1_334, all_565_0_333) % 30.12/7.63 | % 30.12/7.63 | Instantiating formula (494) with all_226_0_171, all_0_37_37 and discharging atoms cast_to_subset(all_0_37_37) = all_226_0_171, yields: % 30.12/7.63 | (907) all_226_0_171 = all_0_37_37 % 30.12/7.63 | % 30.12/7.63 | Instantiating formula (392) with all_0_38_38, all_352_1_228, all_0_37_37 and discharging atoms the_carrier(all_0_38_38) = all_352_1_228, the_carrier(all_0_38_38) = all_0_37_37, yields: % 30.12/7.63 | (908) all_352_1_228 = all_0_37_37 % 30.12/7.63 | % 30.12/7.63 | Instantiating formula (392) with all_0_38_38, all_0_35_35, all_352_1_228 and discharging atoms the_carrier(all_0_38_38) = all_352_1_228, the_carrier(all_0_38_38) = all_0_35_35, yields: % 30.12/7.63 | (909) all_352_1_228 = all_0_35_35 % 30.12/7.63 | % 30.12/7.63 | Instantiating formula (280) with all_0_37_37, all_565_0_333, all_0_36_36 and discharging atoms powerset(all_0_37_37) = all_565_0_333, powerset(all_0_37_37) = all_0_36_36, yields: % 30.12/7.63 | (910) all_565_0_333 = all_0_36_36 % 30.12/7.63 | % 30.12/7.63 | Instantiating formula (280) with all_0_37_37, all_470_1_297, all_565_0_333 and discharging atoms powerset(all_0_37_37) = all_565_0_333, powerset(all_0_37_37) = all_470_1_297, yields: % 30.12/7.63 | (911) all_565_0_333 = all_470_1_297 % 30.12/7.63 | % 30.12/7.63 | Instantiating formula (280) with all_0_37_37, all_468_1_295, all_470_1_297 and discharging atoms powerset(all_0_37_37) = all_470_1_297, powerset(all_0_37_37) = all_468_1_295, yields: % 30.12/7.63 | (912) all_470_1_297 = all_468_1_295 % 30.12/7.63 | % 30.12/7.63 | Combining equations (911,910) yields a new equation: % 30.12/7.63 | (913) all_470_1_297 = all_0_36_36 % 30.12/7.63 | % 30.12/7.63 | Simplifying 913 yields: % 30.12/7.63 | (914) all_470_1_297 = all_0_36_36 % 30.12/7.63 | % 30.12/7.63 | Combining equations (912,914) yields a new equation: % 30.12/7.63 | (915) all_468_1_295 = all_0_36_36 % 30.12/7.63 | % 30.12/7.63 | Simplifying 915 yields: % 30.12/7.63 | (916) all_468_1_295 = all_0_36_36 % 30.12/7.63 | % 30.12/7.63 | Combining equations (908,909) yields a new equation: % 30.12/7.63 | (917) all_0_35_35 = all_0_37_37 % 30.12/7.63 | % 30.12/7.63 | From (917) and (896) follows: % 30.12/7.63 | (918) set_intersection2(all_0_34_34, all_0_37_37) = all_468_0_294 % 30.12/7.63 | % 30.12/7.63 | From (907) and (890) follows: % 30.12/7.63 | (919) element(all_0_37_37, all_0_36_36) % 30.12/7.63 | % 30.12/7.63 +-Applying beta-rule and splitting (902), into two cases. % 30.12/7.63 |-Branch one: % 30.12/7.63 | (920) ~ element(all_0_34_34, all_470_1_297) % 30.12/7.63 | % 30.12/7.63 | From (914) and (920) follows: % 30.12/7.63 | (921) ~ element(all_0_34_34, all_0_36_36) % 30.12/7.63 | % 30.12/7.63 | Using (102) and (921) yields: % 30.12/7.63 | (922) $false % 30.12/7.63 | % 30.12/7.63 |-The branch is then unsatisfiable % 30.12/7.63 |-Branch two: % 30.12/7.63 | (923) element(all_0_34_34, all_470_1_297) % 30.12/7.63 | (924) all_470_0_296 = all_0_33_33 | ~ element(all_0_35_35, all_470_1_297) % 30.12/7.63 | % 30.12/7.63 | From (914) and (923) follows: % 30.12/7.63 | (102) element(all_0_34_34, all_0_36_36) % 30.12/7.63 | % 30.12/7.63 +-Applying beta-rule and splitting (924), into two cases. % 30.12/7.63 |-Branch one: % 30.12/7.63 | (926) ~ element(all_0_35_35, all_470_1_297) % 30.12/7.63 | % 30.12/7.63 | From (917)(914) and (926) follows: % 30.12/7.63 | (927) ~ element(all_0_37_37, all_0_36_36) % 30.12/7.63 | % 30.12/7.63 | Using (919) and (927) yields: % 30.12/7.63 | (922) $false % 30.12/7.63 | % 30.12/7.63 |-The branch is then unsatisfiable % 30.12/7.63 |-Branch two: % 30.12/7.63 | (929) element(all_0_35_35, all_470_1_297) % 30.12/7.63 | (930) all_470_0_296 = all_0_33_33 % 30.12/7.63 | % 30.12/7.63 | From (917)(914) and (929) follows: % 30.12/7.63 | (919) element(all_0_37_37, all_0_36_36) % 30.12/7.63 | % 30.12/7.63 +-Applying beta-rule and splitting (898), into two cases. % 30.12/7.63 |-Branch one: % 30.12/7.63 | (932) ~ element(all_0_34_34, all_468_1_295) % 30.12/7.63 | % 30.12/7.63 | From (916) and (932) follows: % 30.12/7.63 | (921) ~ element(all_0_34_34, all_0_36_36) % 30.12/7.63 | % 30.12/7.63 | Using (102) and (921) yields: % 30.12/7.63 | (922) $false % 30.12/7.63 | % 30.12/7.63 |-The branch is then unsatisfiable % 30.12/7.63 |-Branch two: % 30.12/7.63 | (935) element(all_0_34_34, all_468_1_295) % 30.12/7.63 | (936) all_468_0_294 = all_0_33_33 | ~ element(all_0_35_35, all_468_1_295) % 30.12/7.63 | % 30.12/7.63 +-Applying beta-rule and splitting (936), into two cases. % 30.12/7.63 |-Branch one: % 30.12/7.63 | (937) ~ element(all_0_35_35, all_468_1_295) % 30.12/7.63 | % 30.12/7.63 | From (917)(916) and (937) follows: % 30.12/7.63 | (927) ~ element(all_0_37_37, all_0_36_36) % 30.12/7.63 | % 30.12/7.64 | Using (919) and (927) yields: % 30.12/7.64 | (922) $false % 30.12/7.64 | % 30.12/7.64 |-The branch is then unsatisfiable % 30.12/7.64 |-Branch two: % 30.12/7.64 | (940) element(all_0_35_35, all_468_1_295) % 30.12/7.64 | (941) all_468_0_294 = all_0_33_33 % 30.12/7.64 | % 30.12/7.64 | From (941) and (918) follows: % 30.12/7.64 | (942) set_intersection2(all_0_34_34, all_0_37_37) = all_0_33_33 % 30.12/7.64 | % 30.12/7.64 | Instantiating formula (85) with all_0_33_33, all_0_37_37, all_0_34_34 and discharging atoms set_intersection2(all_0_34_34, all_0_37_37) = all_0_33_33, subset(all_0_34_34, all_0_37_37), yields: % 30.12/7.64 | (943) all_0_33_33 = all_0_34_34 % 30.12/7.64 | % 30.12/7.64 | Equations (943) can reduce 116 to: % 30.12/7.64 | (944) $false % 30.12/7.64 | % 30.12/7.64 |-The branch is then unsatisfiable % 30.12/7.64 % SZS output end Proof for theBenchmark % 30.12/7.64 % 30.12/7.64 7055ms %------------------------------------------------------------------------------