%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU321+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n007.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 08:48:50 EDT 2022 % Result : Theorem 76.16s 23.20s % Output : Proof 89.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.09 % Problem : SEU321+2 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.09 % Command : ePrincess-casc -timeout=%d %s % 0.09/0.29 % Computer : n007.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 600 % 0.09/0.29 % DateTime : Mon Jun 20 06:52:29 EDT 2022 % 0.09/0.29 % CPUTime : % 0.50/0.53 ____ _ % 0.50/0.53 ___ / __ \_____(_)___ ________ __________ % 0.50/0.53 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.50/0.53 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.50/0.53 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.50/0.53 % 0.50/0.53 A Theorem Prover for First-Order Logic % 0.50/0.53 (ePrincess v.1.0) % 0.50/0.53 % 0.50/0.53 (c) Philipp Rümmer, 2009-2015 % 0.50/0.53 (c) Peter Backeman, 2014-2015 % 0.50/0.53 (contributions by Angelo Brillout, Peter Baumgartner) % 0.50/0.53 Free software under GNU Lesser General Public License (LGPL). % 0.50/0.53 Bug reports to peter@backeman.se % 0.50/0.53 % 0.50/0.53 For more information, visit http://user.uu.se/~petba168/breu/ % 0.50/0.53 % 0.50/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.53/0.59 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.57/1.70 Prover 0: Preprocessing ... % 14.67/4.01 Prover 0: Warning: ignoring some quantifiers % 15.22/4.13 Prover 0: Constructing countermodel ... % 22.51/5.88 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 25.13/6.50 Prover 1: Preprocessing ... % 30.95/7.93 Prover 1: Warning: ignoring some quantifiers % 31.12/8.00 Prover 1: Constructing countermodel ... % 33.13/8.47 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 35.07/9.00 Prover 2: Preprocessing ... % 51.79/13.31 Prover 2: Warning: ignoring some quantifiers % 52.62/13.53 Prover 2: Constructing countermodel ... % 65.61/19.91 Prover 0: stopped % 66.33/20.11 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 68.17/20.62 Prover 3: Preprocessing ... % 70.41/21.24 Prover 3: Warning: ignoring some quantifiers % 70.88/21.29 Prover 3: Constructing countermodel ... % 76.16/23.20 Prover 3: proved (3086ms) % 76.16/23.20 Prover 1: stopped % 76.16/23.20 Prover 2: stopped % 76.16/23.20 % 76.16/23.20 No countermodel exists, formula is valid % 76.16/23.20 % SZS status Theorem for theBenchmark % 76.16/23.20 % 76.16/23.20 Generating proof ... Warning: ignoring some quantifiers % 87.27/26.58 found it (size 56) % 87.27/26.58 % 87.27/26.58 % SZS output start Proof for theBenchmark % 87.27/26.58 Assumed formulas after preprocessing and simplification: % 87.27/26.58 | (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] : ? [v41] : (subset_complement(v3, v5) = v6 & singleton(empty_set) = v0 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & the_carrier(v2) = v3 & powerset(v3) = v4 & 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) & top_str(v40) & meet_semilatt_str(v41) & 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(v7, v3) & element(v5, v4) & v1_membered(v33) & v1_membered(empty_set) & in(empty_set, omega) & ~ empty_carrier(v20) & ~ empty_carrier(v2) & ~ empty(v36) & ~ empty(v35) & ~ empty(v33) & ~ empty(v25) & ~ empty(v24) & ~ empty(v22) & ~ empty(omega) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ! [v49] : (v43 = v42 | ~ (apply_binary_as_element(v49, v48, v47, v46, v45, v44) = v43) | ~ (apply_binary_as_element(v49, v48, v47, v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ! [v49] : (v43 = empty_set | ~ (relation_composition(v45, v47) = v48) | ~ (apply(v48, v44) = v49) | ~ (apply(v45, v44) = v46) | ~ quasi_total(v45, v42, v43) | ~ relation_of2_as_subset(v45, v42, v43) | ~ relation(v47) | ~ function(v47) | ~ function(v45) | ~ in(v44, v42) | apply(v47, v46) = v49) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ! [v49] : ( ~ (relation_composition(v42, v43) = v44) | ~ (ordered_pair(v45, v48) = v49) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v44) | ~ relation(v43) | ~ relation(v42) | ~ in(v49, v42) | in(v47, v44) | ? [v50] : (ordered_pair(v48, v46) = v50 & ~ in(v50, v43))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v43 = empty_set | ~ (relation_inverse_image(v45, v44) = v46) | ~ (apply(v45, v47) = v48) | ~ quasi_total(v45, v42, v43) | ~ relation_of2_as_subset(v45, v42, v43) | ~ function(v45) | ~ in(v48, v44) | ~ in(v47, v42) | in(v47, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v43 = empty_set | ~ (relation_inverse_image(v45, v44) = v46) | ~ (apply(v45, v47) = v48) | ~ quasi_total(v45, v42, v43) | ~ relation_of2_as_subset(v45, v42, v43) | ~ function(v45) | ~ in(v47, v46) | in(v48, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : (v43 = empty_set | ~ (relation_inverse_image(v45, v44) = v46) | ~ (apply(v45, v47) = v48) | ~ quasi_total(v45, v42, v43) | ~ relation_of2_as_subset(v45, v42, v43) | ~ function(v45) | ~ in(v47, v46) | in(v47, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_composition(v47, v45) = v48) | ~ (identity_relation(v44) = v47) | ~ (ordered_pair(v42, v43) = v46) | ~ relation(v45) | ~ in(v46, v48) | in(v46, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_composition(v47, v45) = v48) | ~ (identity_relation(v44) = v47) | ~ (ordered_pair(v42, v43) = v46) | ~ relation(v45) | ~ in(v46, v48) | in(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_composition(v47, v45) = v48) | ~ (identity_relation(v44) = v47) | ~ (ordered_pair(v42, v43) = v46) | ~ relation(v45) | ~ in(v46, v45) | ~ in(v42, v44) | in(v46, v48)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (apply_binary_as_element(v42, v43, v44, v45, v46, v47) = v48) | ~ function(v45) | ~ element(v47, v43) | ~ element(v46, v42) | empty(v43) | empty(v42) | element(v48, v44) | ? [v49] : (cartesian_product2(v42, v43) = v49 & ( ~ relation_of2(v45, v49, v44) | ~ quasi_total(v45, v49, v44)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (apply_binary_as_element(v42, v43, v44, v45, v46, v47) = v48) | ~ function(v45) | ~ element(v47, v43) | ~ element(v46, v42) | empty(v43) | empty(v42) | ? [v49] : ((v49 = v48 & apply_binary(v45, v46, v47) = v48) | (cartesian_product2(v42, v43) = v49 & ( ~ relation_of2(v45, v49, v44) | ~ quasi_total(v45, v49, v44))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (ordered_pair(v44, v46) = v48) | ~ (ordered_pair(v44, v45) = v47) | ~ is_transitive_in(v42, v43) | ~ relation(v42) | ~ in(v47, v42) | ~ in(v46, v43) | ~ in(v45, v43) | ~ in(v44, v43) | in(v48, v42) | ? [v49] : (ordered_pair(v45, v46) = v49 & ~ in(v49, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : (v47 = v45 | ~ (meet(v42, v44, v45) = v46) | ~ (join(v42, v46, v45) = v47) | ~ (the_carrier(v42) = v43) | ~ meet_absorbing(v42) | ~ latt_str(v42) | ~ element(v45, v43) | ~ element(v44, v43) | empty_carrier(v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : (v45 = v44 | ~ (ordered_pair(v43, v45) = v47) | ~ (ordered_pair(v43, v44) = v46) | ~ function(v42) | ~ in(v47, v42) | ~ in(v46, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : (v45 = v43 | ~ (pair_second(v42) = v43) | ~ (ordered_pair(v46, v47) = v42) | ~ (ordered_pair(v44, v45) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : (v44 = v43 | ~ (pair_first(v42) = v43) | ~ (ordered_pair(v46, v47) = v42) | ~ (ordered_pair(v44, v45) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_composition(v42, v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v44) | ~ relation(v43) | ~ relation(v42) | ~ in(v47, v44) | ? [v48] : ? [v49] : ? [v50] : (ordered_pair(v48, v46) = v50 & ordered_pair(v45, v48) = v49 & in(v50, v43) & in(v49, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (inclusion_relation(v42) = v43) | ~ (relation_field(v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ subset(v45, v46) | ~ relation(v43) | ~ in(v46, v42) | ~ in(v45, v42) | in(v47, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (inclusion_relation(v42) = v43) | ~ (relation_field(v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v43) | ~ in(v47, v43) | ~ in(v46, v42) | ~ in(v45, v42) | subset(v45, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_rng(v46) = v47) | ~ (relation_field(v44) = v45) | ~ (relation_field(v42) = v43) | ~ relation(v46) | ~ relation(v44) | ~ relation(v42) | ~ function(v46) | ? [v48] : ? [v49] : ? [v50] : ? [v51] : ? [v52] : ? [v53] : ? [v54] : (( ~ (v47 = v45) | ~ one_to_one(v46) | relation_isomorphism(v42, v44, v46) | ( ~ (v48 = v43) & relation_dom(v46) = v48) | (( ~ in(v50, v43) | ~ in(v49, v43) | (apply(v46, v50) = v53 & apply(v46, v49) = v52 & ordered_pair(v52, v53) = v54 & ~ in(v54, v44)) | (ordered_pair(v49, v50) = v51 & ~ in(v51, v42))) & ((apply(v46, v50) = v53 & apply(v46, v49) = v52 & ordered_pair(v52, v53) = v54 & in(v54, v44) & in(v50, v43) & in(v49, v43)) | (ordered_pair(v49, v50) = v51 & in(v51, v42))))) & ( ~ relation_isomorphism(v42, v44, v46) | (v48 = v43 & v47 = v45 & relation_dom(v46) = v43 & one_to_one(v46) & ! [v55] : ! [v56] : ! [v57] : ! [v58] : ! [v59] : ( ~ (apply(v46, v56) = v58) | ~ (apply(v46, v55) = v57) | ~ (ordered_pair(v57, v58) = v59) | ~ in(v59, v44) | ~ in(v56, v43) | ~ in(v55, v43) | ? [v60] : (ordered_pair(v55, v56) = v60 & in(v60, v42))) & ! [v55] : ! [v56] : ! [v57] : ! [v58] : ! [v59] : ( ~ (apply(v46, v56) = v58) | ~ (apply(v46, v55) = v57) | ~ (ordered_pair(v57, v58) = v59) | in(v59, v44) | ? [v60] : (ordered_pair(v55, v56) = v60 & ~ in(v60, v42))) & ! [v55] : ! [v56] : ! [v57] : ! [v58] : ! [v59] : ( ~ (apply(v46, v56) = v58) | ~ (apply(v46, v55) = v57) | ~ (ordered_pair(v57, v58) = v59) | in(v56, v43) | ? [v60] : (ordered_pair(v55, v56) = v60 & ~ in(v60, v42))) & ! [v55] : ! [v56] : ! [v57] : ! [v58] : ! [v59] : ( ~ (apply(v46, v56) = v58) | ~ (apply(v46, v55) = v57) | ~ (ordered_pair(v57, v58) = v59) | in(v55, v43) | ? [v60] : (ordered_pair(v55, v56) = v60 & ~ in(v60, v42))))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_inverse_image(v42, v44) = v45) | ~ (relation_dom(v42) = v43) | ~ (apply(v42, v46) = v47) | ~ relation(v42) | ~ function(v42) | ~ in(v47, v44) | ~ in(v46, v43) | in(v46, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_inverse_image(v42, v44) = v45) | ~ (relation_dom(v42) = v43) | ~ (apply(v42, v46) = v47) | ~ relation(v42) | ~ function(v42) | ~ in(v46, v45) | in(v47, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_inverse_image(v42, v44) = v45) | ~ (relation_dom(v42) = v43) | ~ (apply(v42, v46) = v47) | ~ relation(v42) | ~ function(v42) | ~ in(v46, v45) | in(v46, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_inverse_image(v42, v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v42) | ~ in(v47, v42) | ~ in(v46, v43) | in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v44) | ~ relation(v43) | ~ in(v47, v44) | in(v47, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v44) | ~ relation(v43) | ~ in(v47, v44) | in(v46, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v44) | ~ relation(v43) | ~ in(v47, v43) | ~ in(v46, v42) | in(v47, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_dom(v45) = v46) | ~ (relation_dom(v43) = v44) | ~ (set_intersection2(v46, v42) = v47) | ~ relation(v45) | ~ relation(v43) | ~ function(v45) | ~ function(v43) | ? [v48] : ? [v49] : ? [v50] : ? [v51] : (( ~ (v47 = v44) | (v48 = v43 & relation_dom_restriction(v45, v42) = v43) | ( ~ (v51 = v50) & apply(v45, v49) = v51 & apply(v43, v49) = v50 & in(v49, v44))) & ((v47 = v44 & ! [v52] : ! [v53] : ( ~ (apply(v43, v52) = v53) | ~ in(v52, v44) | apply(v45, v52) = v53)) | ( ~ (v48 = v43) & relation_dom_restriction(v45, v42) = v48)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_dom(v42) = v43) | ~ (relation_image(v42, v44) = v45) | ~ (apply(v42, v47) = v46) | ~ relation(v42) | ~ function(v42) | ~ in(v47, v44) | ~ in(v47, v43) | in(v46, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_image(v42, v43) = v44) | ~ (ordered_pair(v46, v45) = v47) | ~ relation(v42) | ~ in(v47, v42) | ~ in(v46, v43) | in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_dom_restriction(v42, v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v44) | ~ relation(v42) | ~ in(v47, v44) | in(v47, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_dom_restriction(v42, v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v44) | ~ relation(v42) | ~ in(v47, v44) | in(v45, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (relation_dom_restriction(v42, v43) = v44) | ~ (ordered_pair(v45, v46) = v47) | ~ relation(v44) | ~ relation(v42) | ~ in(v47, v42) | ~ in(v45, v43) | in(v47, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v46, v47) = v45) | ~ (cartesian_product2(v42, v43) = v44) | ~ in(v47, v43) | ~ in(v46, v42) | in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v43, v45) = v47) | ~ (ordered_pair(v43, v44) = v46) | ~ transitive(v42) | ~ relation(v42) | ~ in(v46, v42) | in(v47, v42) | ? [v48] : (ordered_pair(v44, v45) = v48 & ~ in(v48, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v42, v43) = v46) | ~ (cartesian_product2(v44, v45) = v47) | ~ in(v46, v47) | in(v43, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v42, v43) = v46) | ~ (cartesian_product2(v44, v45) = v47) | ~ in(v46, v47) | in(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (ordered_pair(v42, v43) = v46) | ~ (cartesian_product2(v44, v45) = v47) | ~ in(v43, v45) | ~ in(v42, v44) | in(v46, v47)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ! [v47] : ( ~ (cartesian_product2(v43, v45) = v47) | ~ (cartesian_product2(v42, v44) = v46) | ~ subset(v44, v45) | ~ subset(v42, v43) | subset(v46, v47)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v46 = v45 | ~ (join(v42, v44, v45) = v46) | ~ (the_carrier(v42) = v43) | ~ below(v42, v44, v45) | ~ join_semilatt_str(v42) | ~ element(v45, v43) | ~ element(v44, v43) | empty_carrier(v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v46 = v45 | ~ (relation_dom(v43) = v44) | ~ (apply(v43, v45) = v46) | ~ (identity_relation(v42) = v43) | ~ relation(v43) | ~ function(v43) | ~ in(v45, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v46 = v44 | v46 = v43 | v46 = v42 | ~ (unordered_triple(v42, v43, v44) = v45) | ~ in(v46, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v45 = v44 | ~ (relation_field(v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ connected(v42) | ~ relation(v42) | ~ in(v45, v43) | ~ in(v44, v43) | in(v46, v42) | ? [v47] : (ordered_pair(v45, v44) = v47 & in(v47, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v45 = v44 | ~ (relation_dom(v42) = v43) | ~ (apply(v42, v45) = v46) | ~ (apply(v42, v44) = v46) | ~ one_to_one(v42) | ~ relation(v42) | ~ function(v42) | ~ in(v45, v43) | ~ in(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v45 = v44 | ~ (identity_relation(v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ in(v46, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v45 = v44 | ~ (ordered_pair(v44, v45) = v46) | ~ is_connected_in(v42, v43) | ~ relation(v42) | ~ in(v45, v43) | ~ in(v44, v43) | in(v46, v42) | ? [v47] : (ordered_pair(v45, v44) = v47 & in(v47, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v45 = v44 | ~ (ordered_pair(v44, v45) = v46) | ~ is_antisymmetric_in(v42, v43) | ~ relation(v42) | ~ in(v46, v42) | ~ in(v45, v43) | ~ in(v44, v43) | ? [v47] : (ordered_pair(v45, v44) = v47 & ~ in(v47, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v45 = v43 | ~ (fiber(v42, v43) = v44) | ~ (ordered_pair(v45, v43) = v46) | ~ relation(v42) | ~ in(v46, v42) | in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v45 = v43 | ~ (ordered_pair(v44, v45) = v46) | ~ (ordered_pair(v42, v43) = v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v45 = v42 | v44 = v42 | ~ (unordered_pair(v44, v45) = v46) | ~ (unordered_pair(v42, v43) = v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v44 = v42 | ~ (ordered_pair(v44, v45) = v46) | ~ (ordered_pair(v42, v43) = v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (apply_binary(v46, v45, v44) = v43) | ~ (apply_binary(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (relation_rng_as_subset(v46, v45, v44) = v43) | ~ (relation_rng_as_subset(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (subset_difference(v46, v45, v44) = v43) | ~ (subset_difference(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (meet(v46, v45, v44) = v43) | ~ (meet(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (join(v46, v45, v44) = v43) | ~ (join(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (relation_dom_as_subset(v46, v45, v44) = v43) | ~ (relation_dom_as_subset(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (unordered_triple(v46, v45, v44) = v43) | ~ (unordered_triple(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (subset_intersection2(v46, v45, v44) = v43) | ~ (subset_intersection2(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (meet_commut(v46, v45, v44) = v43) | ~ (meet_commut(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = v42 | ~ (join_commut(v46, v45, v44) = v43) | ~ (join_commut(v46, v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = empty_set | ~ (meet_of_subsets(v42, v43) = v45) | ~ (subset_difference(v42, v44, v45) = v46) | ~ (cast_to_subset(v42) = v44) | ? [v47] : ? [v48] : ((v48 = v46 & complements_of_subsets(v42, v43) = v47 & union_of_subsets(v42, v47) = v46) | (powerset(v47) = v48 & powerset(v42) = v47 & ~ element(v43, v48)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = empty_set | ~ (subset_difference(v42, v44, v45) = v46) | ~ (cast_to_subset(v42) = v44) | ~ (union_of_subsets(v42, v43) = v45) | ? [v47] : ? [v48] : ((v48 = v46 & meet_of_subsets(v42, v47) = v46 & complements_of_subsets(v42, v43) = v47) | (powerset(v47) = v48 & powerset(v42) = v47 & ~ element(v43, v48)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v43 = empty_set | ~ (apply(v45, v44) = v46) | ~ quasi_total(v45, v42, v43) | ~ relation_of2_as_subset(v45, v42, v43) | ~ function(v45) | ~ in(v44, v42) | ? [v47] : (relation_rng(v45) = v47 & in(v46, v47))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v42 = empty_set | ~ (subset_complement(v42, v44) = v45) | ~ (powerset(v42) = v43) | ~ element(v46, v42) | ~ element(v44, v43) | in(v46, v45) | in(v46, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (function_inverse(v43) = v44) | ~ (relation_composition(v44, v43) = v45) | ~ (apply(v45, v42) = v46) | ~ one_to_one(v43) | ~ relation(v43) | ~ function(v43) | ? [v47] : ? [v48] : ((v48 = v42 & v46 = v42 & apply(v44, v42) = v47 & apply(v43, v47) = v42) | (relation_rng(v43) = v47 & ~ in(v42, v47)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_composition(v44, v43) = v45) | ~ (apply(v45, v42) = v46) | ~ relation(v44) | ~ relation(v43) | ~ function(v44) | ~ function(v43) | ? [v47] : ? [v48] : ((v48 = v46 & apply(v44, v42) = v47 & apply(v43, v47) = v46) | (relation_dom(v45) = v47 & ~ in(v42, v47)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_inverse(v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v42) | ~ in(v46, v43) | ? [v47] : (ordered_pair(v45, v44) = v47 & in(v47, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_inverse(v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ relation(v42) | in(v46, v43) | ? [v47] : (ordered_pair(v45, v44) = v47 & ~ in(v47, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_restriction(v44, v42) = v45) | ~ (fiber(v45, v43) = v46) | ~ relation(v44) | ? [v47] : (fiber(v44, v43) = v47 & subset(v46, v47))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (subset_complement(v42, v45) = v46) | ~ (powerset(v42) = v44) | ~ disjoint(v43, v45) | ~ element(v45, v44) | ~ element(v43, v44) | subset(v43, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (subset_complement(v42, v45) = v46) | ~ (powerset(v42) = v44) | ~ subset(v43, v46) | ~ element(v45, v44) | ~ element(v43, v44) | disjoint(v43, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (set_difference(v43, v45) = v46) | ~ (singleton(v44) = v45) | ~ subset(v42, v43) | subset(v42, v46) | in(v44, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (set_difference(v43, v44) = v46) | ~ (set_difference(v42, v44) = v45) | ~ subset(v42, v43) | subset(v45, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (fiber(v42, v43) = v44) | ~ (ordered_pair(v45, v43) = v46) | ~ relation(v42) | ~ in(v45, v44) | in(v46, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (singleton(v42) = v45) | ~ (unordered_pair(v44, v45) = v46) | ~ (unordered_pair(v42, v43) = v44) | ordered_pair(v42, v43) = v46) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_rng(v45) = v46) | ~ relation_of2_as_subset(v45, v44, v42) | ~ subset(v46, v43) | relation_of2_as_subset(v45, v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_rng(v44) = v46) | ~ (ordered_pair(v42, v43) = v45) | ~ relation(v44) | ~ in(v45, v44) | in(v43, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_rng(v44) = v46) | ~ (ordered_pair(v42, v43) = v45) | ~ relation(v44) | ~ in(v45, v44) | ? [v47] : (relation_dom(v44) = v47 & in(v42, v47))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_rng(v42) = v43) | ~ (ordered_pair(v45, v44) = v46) | ~ relation(v42) | ~ in(v46, v42) | in(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_inverse_image(v44, v43) = v46) | ~ (relation_inverse_image(v44, v42) = v45) | ~ subset(v42, v43) | ~ relation(v44) | subset(v45, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_field(v44) = v46) | ~ (ordered_pair(v42, v43) = v45) | ~ relation(v44) | ~ in(v45, v44) | in(v43, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_field(v44) = v46) | ~ (ordered_pair(v42, v43) = v45) | ~ relation(v44) | ~ in(v45, v44) | in(v42, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_rng_restriction(v42, v45) = v46) | ~ (relation_dom_restriction(v44, v43) = v45) | ~ relation(v44) | ? [v47] : (relation_rng_restriction(v42, v44) = v47 & relation_dom_restriction(v47, v43) = v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom(v43) = v44) | ~ (relation_image(v43, v45) = v46) | ~ (set_intersection2(v44, v42) = v45) | ~ relation(v43) | relation_image(v43, v42) = v46) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom(v42) = v43) | ~ (relation_image(v42, v44) = v45) | ~ relation(v42) | ~ function(v42) | ~ in(v46, v45) | ? [v47] : (apply(v42, v47) = v46 & in(v47, v44) & in(v47, v43))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom(v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v42) | ~ function(v42) | ~ in(v44, v43) | ? [v47] : (( ~ in(v46, v42) | (v47 = v45 & apply(v42, v44) = v45)) & (in(v46, v42) | ( ~ (v47 = v45) & apply(v42, v44) = v47)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom(v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v42) | ~ in(v46, v42) | in(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (apply(v45, v43) = v46) | ~ (relation_dom_restriction(v44, v42) = v45) | ~ relation(v44) | ~ function(v44) | ~ in(v43, v42) | apply(v44, v43) = v46) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (apply(v45, v43) = v46) | ~ (relation_dom_restriction(v44, v42) = v45) | ~ relation(v44) | ~ function(v44) | ? [v47] : ((v47 = v46 & apply(v44, v43) = v46) | (relation_dom(v45) = v47 & ~ in(v43, v47)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (apply(v44, v42) = v46) | ~ (ordered_pair(v42, v43) = v45) | ~ relation(v44) | ~ function(v44) | ? [v47] : (( ~ (v46 = v43) | in(v45, v44) | (relation_dom(v44) = v47 & ~ in(v42, v47))) & ( ~ in(v45, v44) | (v46 = v43 & relation_dom(v44) = v47 & in(v42, v47))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (identity_relation(v42) = v43) | ~ (ordered_pair(v44, v45) = v46) | ~ relation(v43) | ~ in(v46, v43) | in(v44, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v44, v45) = v46) | ~ subset(v42, v43) | ~ relation(v43) | ~ relation(v42) | ~ in(v46, v42) | in(v46, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (meet_commut(v42, v44, v45) = v46) | ~ (the_carrier(v42) = v43) | ~ meet_absorbing(v42) | ~ latt_str(v42) | ~ meet_commutative(v42) | ~ element(v45, v43) | ~ element(v44, v43) | below(v42, v46, v44) | empty_carrier(v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (set_intersection2(v43, v44) = v46) | ~ (set_intersection2(v42, v44) = v45) | ~ subset(v42, v43) | subset(v45, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (cartesian_product2(v43, v44) = v46) | ~ (cartesian_product2(v42, v44) = v45) | ~ subset(v42, v43) | subset(v45, v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (cartesian_product2(v43, v44) = v46) | ~ (cartesian_product2(v42, v44) = v45) | ~ subset(v42, v43) | ? [v47] : ? [v48] : (cartesian_product2(v44, v43) = v48 & cartesian_product2(v44, v42) = v47 & subset(v47, v48))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v46 = v42 | ~ (unordered_triple(v43, v44, v45) = v46) | ? [v47] : ((v47 = v45 | v47 = v44 | v47 = v43 | in(v47, v42)) & ( ~ in(v47, v42) | ( ~ (v47 = v45) & ~ (v47 = v44) & ~ (v47 = v43))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v46 = v42 | ~ (relation_inverse_image(v43, v45) = v46) | ~ (relation_dom(v43) = v44) | ~ relation(v43) | ~ function(v43) | ? [v47] : ? [v48] : (( ~ in(v47, v44) | ~ in(v47, v42) | (apply(v43, v47) = v48 & ~ in(v48, v45))) & (in(v47, v42) | (apply(v43, v47) = v48 & in(v48, v45) & in(v47, v44))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v46 = v42 | ~ (relation_dom(v43) = v44) | ~ (relation_image(v43, v45) = v46) | ~ relation(v43) | ~ function(v43) | ? [v47] : ? [v48] : ? [v49] : (( ~ in(v47, v42) | ! [v50] : ( ~ (apply(v43, v50) = v47) | ~ in(v50, v45) | ~ in(v50, v44))) & (in(v47, v42) | (v49 = v47 & apply(v43, v48) = v47 & in(v48, v45) & in(v48, v44))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v44 = v42 | ~ (pair_second(v43) = v44) | ~ (ordered_pair(v45, v46) = v43) | ? [v47] : ? [v48] : ( ~ (v48 = v42) & ordered_pair(v47, v48) = v43)) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : (v44 = v42 | ~ (pair_first(v43) = v44) | ~ (ordered_pair(v45, v46) = v43) | ? [v47] : ? [v48] : ( ~ (v47 = v42) & ordered_pair(v47, v48) = v43)) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_composition(v45, v43) = v46) | ~ (relation_dom(v43) = v44) | ~ relation(v45) | ~ relation(v43) | ~ function(v45) | ~ function(v43) | ? [v47] : ? [v48] : ? [v49] : (((relation_dom(v46) = v47 & in(v42, v47)) | (relation_dom(v45) = v48 & ~ in(v42, v48)) | (apply(v45, v42) = v49 & ~ in(v49, v44))) & ((relation_dom(v46) = v47 & ~ in(v42, v47)) | (relation_dom(v45) = v48 & apply(v45, v42) = v49 & in(v49, v44) & in(v42, v48))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ! [v46] : ( ~ (relation_dom(v44) = v46) | ~ (powerset(v43) = v45) | ~ relation(v44) | ~ function(v44) | ? [v47] : ? [v48] : ((powerset(v46) = v47 & ! [v49] : ! [v50] : ( ~ (relation_image(v44, v49) = v50) | ~ in(v50, v42) | ~ in(v49, v47) | in(v49, v48)) & ! [v49] : ! [v50] : ( ~ (relation_image(v44, v49) = v50) | ~ in(v49, v48) | in(v50, v42)) & ! [v49] : ! [v50] : ( ~ (relation_image(v44, v49) = v50) | ~ in(v49, v48) | in(v49, v47))) | (powerset(v45) = v47 & ~ element(v42, v47)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v44 | ~ (relation_composition(v42, v43) = v44) | ~ relation(v45) | ~ relation(v43) | ~ relation(v42) | ? [v46] : ? [v47] : ? [v48] : ? [v49] : ? [v50] : ? [v51] : (( ! [v52] : ! [v53] : ( ~ (ordered_pair(v46, v52) = v53) | ~ in(v53, v42) | ? [v54] : (ordered_pair(v52, v47) = v54 & ~ in(v54, v43))) | (ordered_pair(v46, v47) = v48 & ~ in(v48, v45))) & ((ordered_pair(v49, v47) = v51 & ordered_pair(v46, v49) = v50 & in(v51, v43) & in(v50, v42)) | (ordered_pair(v46, v47) = v48 & in(v48, v45))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v44 | ~ (relation_rng_restriction(v42, v43) = v44) | ~ relation(v45) | ~ relation(v43) | ? [v46] : ? [v47] : ? [v48] : (ordered_pair(v46, v47) = v48 & ( ~ in(v48, v45) | ~ in(v48, v43) | ~ in(v47, v42)) & (in(v48, v45) | (in(v48, v43) & in(v47, v42))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v44 | ~ (relation_dom_restriction(v42, v43) = v45) | ~ relation(v44) | ~ relation(v42) | ? [v46] : ? [v47] : ? [v48] : (ordered_pair(v46, v47) = v48 & ( ~ in(v48, v44) | ~ in(v48, v42) | ~ in(v46, v43)) & (in(v48, v44) | (in(v48, v42) & in(v46, v43))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v44 | ~ (the_carrier(v42) = v43) | ~ below(v42, v45, v44) | ~ below(v42, v44, v45) | ~ join_semilatt_str(v42) | ~ join_commutative(v42) | ~ element(v45, v43) | ~ element(v44, v43) | empty_carrier(v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v43 | v45 = v42 | ~ (unordered_pair(v42, v43) = v44) | ~ in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v43 | ~ (relation_rng_as_subset(v42, v43, v44) = v45) | ~ relation_of2_as_subset(v44, v42, v43) | ? [v46] : (in(v46, v43) & ! [v47] : ! [v48] : ( ~ (ordered_pair(v47, v46) = v48) | ~ in(v48, v44)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v43 | ~ (complements_of_subsets(v42, v44) = v45) | ~ (complements_of_subsets(v42, v43) = v44) | ? [v46] : ? [v47] : (powerset(v46) = v47 & powerset(v42) = v46 & ~ element(v43, v47))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v43 | ~ (subset_complement(v42, v44) = v45) | ~ (subset_complement(v42, v43) = v44) | ? [v46] : (powerset(v42) = v46 & ~ element(v43, v46))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v43 | ~ (set_difference(v43, v42) = v44) | ~ (set_union2(v42, v44) = v45) | ~ subset(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v43 | ~ (singleton(v42) = v44) | ~ (set_union2(v44, v43) = v45) | ~ in(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v43 | ~ (relation_dom_as_subset(v43, v42, v44) = v45) | ~ relation_of2_as_subset(v44, v43, v42) | ? [v46] : (in(v46, v43) & ! [v47] : ! [v48] : ( ~ (ordered_pair(v46, v47) = v48) | ~ in(v48, v44)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v43 | ~ (apply(v44, v43) = v45) | ~ (identity_relation(v42) = v44) | ~ in(v43, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | v43 = empty_set | ~ (relation_dom_as_subset(v42, v43, v44) = v45) | ~ quasi_total(v44, v42, v43) | ~ relation_of2_as_subset(v44, v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (set_difference(v42, v44) = v45) | ~ (singleton(v43) = v44) | in(v43, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (relation_inverse_image(v43, v42) = v44) | ~ (relation_image(v43, v44) = v45) | ~ relation(v43) | ~ function(v43) | ? [v46] : (relation_rng(v43) = v46 & ~ subset(v42, v46))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = empty_set | ~ (relation_dom(v42) = v43) | ~ (apply(v42, v44) = v45) | ~ relation(v42) | ~ function(v42) | in(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (singleton(v42) = v45) | ~ (unordered_pair(v43, v44) = v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v44 = v43 | ~ (ordered_pair(v43, v44) = v45) | ~ antisymmetric(v42) | ~ relation(v42) | ~ in(v45, v42) | ? [v46] : (ordered_pair(v44, v43) = v46 & ~ in(v46, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (meet_of_subsets(v45, v44) = v43) | ~ (meet_of_subsets(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (complements_of_subsets(v45, v44) = v43) | ~ (complements_of_subsets(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (relation_composition(v45, v44) = v43) | ~ (relation_composition(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (relation_restriction(v45, v44) = v43) | ~ (relation_restriction(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (subset_complement(v45, v44) = v43) | ~ (subset_complement(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (set_difference(v45, v44) = v43) | ~ (set_difference(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (fiber(v45, v44) = v43) | ~ (fiber(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (union_of_subsets(v45, v44) = v43) | ~ (union_of_subsets(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (singleton(v43) = v45) | ~ (singleton(v42) = v44) | ~ subset(v44, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (singleton(v42) = v45) | ~ (unordered_pair(v43, v44) = v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (topstr_closure(v45, v44) = v43) | ~ (topstr_closure(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (relation_inverse_image(v45, v44) = v43) | ~ (relation_inverse_image(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (relation_rng_restriction(v45, v44) = v43) | ~ (relation_rng_restriction(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (relation_image(v45, v44) = v43) | ~ (relation_image(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (apply(v45, v44) = v43) | ~ (apply(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (relation_dom_restriction(v45, v44) = v43) | ~ (relation_dom_restriction(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (ordered_pair(v45, v44) = v43) | ~ (ordered_pair(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (set_intersection2(v45, v44) = v43) | ~ (set_intersection2(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (set_union2(v45, v44) = v43) | ~ (set_union2(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (unordered_pair(v45, v44) = v43) | ~ (unordered_pair(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = v42 | ~ (cartesian_product2(v45, v44) = v43) | ~ (cartesian_product2(v45, v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = empty_set | ~ quasi_total(v45, v42, v43) | ~ relation_of2_as_subset(v45, v42, v43) | ~ subset(v43, v44) | ~ function(v45) | quasi_total(v45, v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v43 = empty_set | ~ quasi_total(v45, v42, v43) | ~ relation_of2_as_subset(v45, v42, v43) | ~ subset(v43, v44) | ~ function(v45) | relation_of2_as_subset(v45, v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : (v42 = empty_set | ~ (set_meet(v42) = v43) | ~ in(v45, v42) | ~ in(v44, v43) | in(v44, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng_as_subset(v42, v43, v44) = v45) | ~ relation_of2(v44, v42, v43) | relation_rng(v44) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng_as_subset(v42, v43, v44) = v45) | ~ relation_of2(v44, v42, v43) | ? [v46] : (powerset(v43) = v46 & element(v45, v46))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng_as_subset(v42, v43, v44) = v43) | ~ relation_of2_as_subset(v44, v42, v43) | ~ in(v45, v43) | ? [v46] : ? [v47] : (ordered_pair(v46, v45) = v47 & in(v47, v44))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (function_inverse(v44) = v45) | ~ relation_isomorphism(v42, v43, v44) | ~ relation(v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v44) | relation_isomorphism(v43, v42, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_composition(v44, v43) = v45) | ~ (identity_relation(v42) = v44) | ~ relation(v43) | relation_dom_restriction(v43, v42) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_composition(v42, v44) = v45) | ~ (relation_dom(v42) = v43) | ~ relation(v44) | ~ relation(v42) | ? [v46] : (relation_dom(v45) = v46 & subset(v46, v43))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (subset_difference(v42, v43, v44) = v45) | ? [v46] : (powerset(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46) | element(v45, v46)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (subset_difference(v42, v43, v44) = v45) | ? [v46] : ((v46 = v45 & set_difference(v43, v44) = v45) | (powerset(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (subset_complement(v42, v44) = v45) | ~ in(v43, v45) | ~ in(v43, v44) | ? [v46] : (powerset(v42) = v46 & ~ element(v44, v46))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_difference(v44, v43) = v45) | ~ (set_union2(v42, v43) = v44) | set_difference(v42, v43) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_difference(v43, v42) = v44) | ~ (set_union2(v42, v44) = v45) | set_union2(v42, v43) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_difference(v42, v44) = v45) | ~ (set_difference(v42, v43) = v44) | set_intersection2(v42, v43) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_difference(v42, v43) = v44) | ~ in(v45, v44) | ~ in(v45, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_difference(v42, v43) = v44) | ~ in(v45, v44) | in(v45, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_difference(v42, v43) = v44) | ~ in(v45, v42) | in(v45, v44) | in(v45, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (union(v42) = v43) | ~ in(v45, v42) | ~ in(v44, v45) | in(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (meet(v42, v43, v44) = v45) | ~ meet_semilatt_str(v42) | empty_carrier(v42) | ? [v46] : (the_carrier(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46) | element(v45, v46)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (fiber(v42, v43) = v44) | ~ (ordered_pair(v43, v43) = v45) | ~ relation(v42) | ~ in(v43, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_meet(v43) = v45) | ~ (powerset(v42) = v44) | ? [v46] : ((v46 = v45 & meet_of_subsets(v42, v43) = v45) | (powerset(v44) = v46 & ~ element(v43, v46)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (join(v42, v44, v45) = v45) | ~ (the_carrier(v42) = v43) | ~ join_semilatt_str(v42) | ~ element(v45, v43) | ~ element(v44, v43) | below(v42, v44, v45) | empty_carrier(v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (join(v42, v43, v44) = v45) | ~ join_semilatt_str(v42) | empty_carrier(v42) | ? [v46] : (the_carrier(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46) | element(v45, v46)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom_as_subset(v43, v42, v44) = v43) | ~ relation_of2_as_subset(v44, v43, v42) | ~ in(v45, v43) | ? [v46] : ? [v47] : (ordered_pair(v45, v46) = v47 & in(v47, v44))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom_as_subset(v42, v43, v44) = v45) | ~ relation_of2(v44, v42, v43) | relation_dom(v44) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom_as_subset(v42, v43, v44) = v45) | ~ relation_of2(v44, v42, v43) | ? [v46] : (powerset(v42) = v46 & element(v45, v46))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v44) = v45) | ~ relation_of2_as_subset(v44, v42, v43) | subset(v45, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v44) = v45) | ~ relation_of2_as_subset(v44, v42, v43) | ? [v46] : (relation_dom(v44) = v46 & subset(v46, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v43) = v44) | ~ (set_intersection2(v44, v42) = v45) | ~ relation(v43) | ? [v46] : (relation_rng(v46) = v45 & relation_rng_restriction(v42, v43) = v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v42) = v44) | ~ (relation_dom(v42) = v43) | ~ (set_union2(v43, v44) = v45) | ~ relation(v42) | relation_field(v42) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v42) = v44) | ~ (relation_dom(v42) = v43) | ~ (cartesian_product2(v43, v44) = v45) | ~ relation(v42) | subset(v42, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng(v42) = v43) | ~ (relation_image(v44, v43) = v45) | ~ relation(v44) | ~ relation(v42) | ? [v46] : (relation_composition(v42, v44) = v46 & relation_rng(v46) = v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (unordered_triple(v42, v43, v44) = v45) | in(v44, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (unordered_triple(v42, v43, v44) = v45) | in(v43, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (unordered_triple(v42, v43, v44) = v45) | in(v42, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_inverse_image(v43, v44) = v45) | ~ (relation_image(v43, v42) = v44) | ~ relation(v43) | subset(v42, v45) | ? [v46] : (relation_dom(v43) = v46 & ~ subset(v42, v46))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_inverse_image(v43, v42) = v44) | ~ (relation_image(v43, v44) = v45) | ~ relation(v43) | ~ function(v43) | subset(v45, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_inverse_image(v42, v43) = v44) | ~ relation(v42) | ~ in(v45, v44) | ? [v46] : ? [v47] : (ordered_pair(v45, v46) = v47 & in(v47, v42) & in(v46, v43))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_field(v42) = v43) | ~ (ordered_pair(v44, v44) = v45) | ~ reflexive(v42) | ~ relation(v42) | ~ in(v44, v43) | in(v45, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng_restriction(v42, v44) = v45) | ~ (relation_dom_restriction(v43, v42) = v44) | ~ relation(v43) | relation_restriction(v43, v42) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ (relation_dom_restriction(v44, v42) = v45) | ~ relation(v43) | relation_restriction(v43, v42) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom(v43) = v44) | ~ (set_intersection2(v44, v42) = v45) | ~ relation(v43) | ? [v46] : (relation_dom(v46) = v45 & relation_dom_restriction(v43, v42) = v46)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_image(v42, v43) = v44) | ~ relation(v42) | ~ in(v45, v44) | ? [v46] : ? [v47] : (ordered_pair(v46, v45) = v47 & in(v47, v42) & in(v46, v43))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (identity_relation(v42) = v43) | ~ (ordered_pair(v44, v44) = v45) | ~ relation(v43) | ~ in(v44, v42) | in(v45, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (ordered_pair(v44, v44) = v45) | ~ is_reflexive_in(v42, v43) | ~ relation(v42) | ~ in(v44, v43) | in(v45, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (subset_intersection2(v42, v43, v44) = v45) | ? [v46] : (powerset(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46) | element(v45, v46)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (subset_intersection2(v42, v43, v44) = v45) | ? [v46] : ((v46 = v45 & subset_intersection2(v42, v44, v43) = v45) | (powerset(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (subset_intersection2(v42, v43, v44) = v45) | ? [v46] : ((v46 = v45 & set_intersection2(v43, v44) = v45) | (powerset(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (meet_commut(v42, v43, v44) = v45) | ~ meet_semilatt_str(v42) | ~ meet_commutative(v42) | empty_carrier(v42) | ? [v46] : (the_carrier(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46) | element(v45, v46)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (meet_commut(v42, v43, v44) = v45) | ~ meet_semilatt_str(v42) | ~ meet_commutative(v42) | empty_carrier(v42) | ? [v46] : ((v46 = v45 & meet(v42, v43, v44) = v45) | (the_carrier(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (meet_commut(v42, v43, v44) = v45) | ~ meet_semilatt_str(v42) | ~ meet_commutative(v42) | empty_carrier(v42) | ? [v46] : ((v46 = v45 & meet_commut(v42, v44, v43) = v45) | (the_carrier(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_intersection2(v43, v44) = v45) | ~ subset(v42, v44) | ~ subset(v42, v43) | subset(v42, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_intersection2(v42, v44) = v45) | ~ (cartesian_product2(v43, v43) = v44) | ~ relation(v42) | relation_restriction(v42, v43) = v45) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_intersection2(v42, v43) = v44) | ~ disjoint(v42, v43) | ~ in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_intersection2(v42, v43) = v44) | ~ in(v45, v44) | in(v45, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_intersection2(v42, v43) = v44) | ~ in(v45, v44) | in(v45, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_intersection2(v42, v43) = v44) | ~ in(v45, v43) | ~ in(v45, v42) | in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (join_commut(v42, v43, v44) = v45) | ~ join_semilatt_str(v42) | ~ join_commutative(v42) | empty_carrier(v42) | ? [v46] : (the_carrier(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46) | element(v45, v46)))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (join_commut(v42, v43, v44) = v45) | ~ join_semilatt_str(v42) | ~ join_commutative(v42) | empty_carrier(v42) | ? [v46] : ((v46 = v45 & join(v42, v43, v44) = v45) | (the_carrier(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (join_commut(v42, v43, v44) = v45) | ~ join_semilatt_str(v42) | ~ join_commutative(v42) | empty_carrier(v42) | ? [v46] : ((v46 = v45 & join_commut(v42, v44, v43) = v45) | (the_carrier(v42) = v46 & ( ~ element(v44, v46) | ~ element(v43, v46))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_union2(v42, v44) = v45) | ~ subset(v44, v43) | ~ subset(v42, v43) | subset(v45, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_union2(v42, v43) = v44) | ~ in(v45, v44) | in(v45, v43) | in(v45, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_union2(v42, v43) = v44) | ~ in(v45, v43) | in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (set_union2(v42, v43) = v44) | ~ in(v45, v42) | in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (unordered_pair(v42, v43) = v45) | ~ subset(v45, v44) | in(v43, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (unordered_pair(v42, v43) = v45) | ~ subset(v45, v44) | in(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (unordered_pair(v42, v43) = v45) | ~ in(v43, v44) | ~ in(v42, v44) | subset(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v42, v44) = v45) | ~ relation(v43) | empty(v42) | ? [v46] : ( ! [v47] : ! [v48] : ! [v49] : ( ~ (ordered_pair(v48, v49) = v47) | ~ in(v49, v48) | ~ in(v48, v42) | ~ in(v47, v45) | in(v47, v46) | ? [v50] : ? [v51] : (ordered_pair(v49, v50) = v51 & in(v50, v48) & ~ in(v51, v43))) & ! [v47] : ( ~ in(v47, v46) | in(v47, v45)) & ! [v47] : ( ~ in(v47, v46) | ? [v48] : ? [v49] : (ordered_pair(v48, v49) = v47 & in(v49, v48) & in(v48, v42) & ! [v50] : ! [v51] : ( ~ (ordered_pair(v49, v50) = v51) | ~ in(v50, v48) | in(v51, v43)))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v42, v43) = v45) | ~ relation_of2(v44, v42, v43) | subset(v44, v45)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v42, v43) = v45) | ~ relation_of2_as_subset(v44, v42, v43) | ? [v46] : (powerset(v45) = v46 & element(v44, v46))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v42, v43) = v45) | ~ subset(v44, v45) | relation_of2(v44, v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v42, v43) = v44) | ~ in(v45, v44) | ? [v46] : ? [v47] : (ordered_pair(v46, v47) = v45 & in(v47, v43) & in(v46, v42))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v42, v42) = v45) | ~ relation(v44) | ~ relation(v43) | ~ function(v44) | ? [v46] : ( ! [v47] : ! [v48] : ! [v49] : ! [v50] : ! [v51] : ! [v52] : ( ~ (apply(v44, v49) = v51) | ~ (apply(v44, v48) = v50) | ~ (ordered_pair(v50, v51) = v52) | ~ in(v52, v43) | ~ in(v47, v45) | in(v47, v46) | ? [v53] : ( ~ (v53 = v47) & ordered_pair(v48, v49) = v53)) & ! [v47] : ( ~ in(v47, v46) | in(v47, v45)) & ! [v47] : ( ~ in(v47, v46) | ? [v48] : ? [v49] : ? [v50] : ? [v51] : ? [v52] : (apply(v44, v49) = v51 & apply(v44, v48) = v50 & ordered_pair(v50, v51) = v52 & ordered_pair(v48, v49) = v47 & in(v52, v43))))) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (powerset(v44) = v45) | ~ empty(v44) | ~ element(v43, v45) | ~ in(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (powerset(v44) = v45) | ~ element(v43, v45) | ~ in(v42, v43) | element(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (powerset(v42) = v44) | ~ element(v43, v44) | ~ in(v45, v43) | in(v45, v42)) & ! [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ relation_of2_as_subset(v45, v44, v42) | ~ subset(v42, v43) | relation_of2_as_subset(v45, v44, v43)) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v44 | ~ (subset_intersection2(v43, v44, v44) = v45) | ? [v46] : (powerset(v43) = v46 & ( ~ element(v44, v46) | ~ element(v42, v46)))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (set_difference(v43, v44) = v45) | ? [v46] : (( ~ in(v46, v43) | ~ in(v46, v42) | in(v46, v44)) & (in(v46, v42) | (in(v46, v43) & ~ in(v46, v44))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (fiber(v43, v44) = v45) | ~ relation(v43) | ? [v46] : ? [v47] : ((v46 = v44 | ~ in(v46, v42) | (ordered_pair(v46, v44) = v47 & ~ in(v47, v43))) & (in(v46, v42) | ( ~ (v46 = v44) & ordered_pair(v46, v44) = v47 & in(v47, v43))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (relation_inverse_image(v43, v44) = v45) | ~ relation(v43) | ? [v46] : ? [v47] : ? [v48] : (( ~ in(v46, v42) | ! [v49] : ! [v50] : ( ~ (ordered_pair(v46, v49) = v50) | ~ in(v50, v43) | ~ in(v49, v44))) & (in(v46, v42) | (ordered_pair(v46, v47) = v48 & in(v48, v43) & in(v47, v44))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (relation_image(v43, v44) = v45) | ~ relation(v43) | ? [v46] : ? [v47] : ? [v48] : (( ~ in(v46, v42) | ! [v49] : ! [v50] : ( ~ (ordered_pair(v49, v46) = v50) | ~ in(v50, v43) | ~ in(v49, v44))) & (in(v46, v42) | (ordered_pair(v47, v46) = v48 & in(v48, v43) & in(v47, v44))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (set_intersection2(v43, v44) = v45) | ? [v46] : (( ~ in(v46, v44) | ~ in(v46, v43) | ~ in(v46, v42)) & (in(v46, v42) | (in(v46, v44) & in(v46, v43))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (set_union2(v43, v44) = v45) | ? [v46] : (( ~ in(v46, v42) | ( ~ in(v46, v44) & ~ in(v46, v43))) & (in(v46, v44) | in(v46, v43) | in(v46, v42)))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (unordered_pair(v43, v44) = v45) | ? [v46] : ((v46 = v44 | v46 = v43 | in(v46, v42)) & ( ~ in(v46, v42) | ( ~ (v46 = v44) & ~ (v46 = v43))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : (v45 = v42 | ~ (cartesian_product2(v43, v44) = v45) | ? [v46] : ? [v47] : ? [v48] : ? [v49] : (( ~ in(v46, v42) | ! [v50] : ! [v51] : ( ~ (ordered_pair(v50, v51) = v46) | ~ in(v51, v44) | ~ in(v50, v43))) & (in(v46, v42) | (v49 = v46 & ordered_pair(v47, v48) = v46 & in(v48, v44) & in(v47, v43))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_restriction(v44, v43) = v45) | ~ relation(v44) | ? [v46] : (( ~ in(v42, v45) | (cartesian_product2(v43, v43) = v46 & in(v42, v46) & in(v42, v44))) & ( ~ in(v42, v44) | in(v42, v45) | (cartesian_product2(v43, v43) = v46 & ~ in(v42, v46))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_restriction(v44, v43) = v45) | ~ relation(v44) | ? [v46] : ((relation_field(v45) = v46 & ~ in(v42, v46)) | (relation_field(v44) = v46 & in(v42, v46) & in(v42, v43)))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_inverse_image(v44, v43) = v45) | ~ relation(v44) | ? [v46] : ? [v47] : ? [v48] : (( ~ in(v42, v45) | (relation_rng(v44) = v46 & ordered_pair(v42, v47) = v48 & in(v48, v44) & in(v47, v46) & in(v47, v43))) & (in(v42, v45) | (relation_rng(v44) = v46 & ! [v49] : ! [v50] : ( ~ (ordered_pair(v42, v49) = v50) | ~ in(v50, v44) | ~ in(v49, v46) | ~ in(v49, v43)))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_rng_restriction(v43, v44) = v45) | ~ relation(v44) | ? [v46] : ? [v47] : (( ~ in(v42, v43) | (relation_rng(v45) = v46 & in(v42, v46)) | (relation_rng(v44) = v47 & ~ in(v42, v47))) & ((relation_rng(v45) = v46 & ~ in(v42, v46)) | (relation_rng(v44) = v47 & in(v42, v47) & in(v42, v43))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_image(v44, v43) = v45) | ~ relation(v44) | ? [v46] : ? [v47] : ? [v48] : (( ~ in(v42, v45) | (relation_dom(v44) = v46 & ordered_pair(v47, v42) = v48 & in(v48, v44) & in(v47, v46) & in(v47, v43))) & (in(v42, v45) | (relation_dom(v44) = v46 & ! [v49] : ! [v50] : ( ~ (ordered_pair(v49, v42) = v50) | ~ in(v50, v44) | ~ in(v49, v46) | ~ in(v49, v43)))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom_restriction(v44, v43) = v45) | ~ relation(v44) | ~ function(v44) | ? [v46] : ? [v47] : (( ~ in(v42, v43) | (relation_dom(v45) = v46 & in(v42, v46)) | (relation_dom(v44) = v47 & ~ in(v42, v47))) & ((relation_dom(v45) = v46 & ~ in(v42, v46)) | (relation_dom(v44) = v47 & in(v42, v47) & in(v42, v43))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (relation_dom_restriction(v44, v43) = v45) | ~ relation(v44) | ? [v46] : ? [v47] : (( ~ in(v42, v43) | (relation_dom(v45) = v46 & in(v42, v46)) | (relation_dom(v44) = v47 & ~ in(v42, v47))) & ((relation_dom(v45) = v46 & ~ in(v42, v46)) | (relation_dom(v44) = v47 & in(v42, v47) & in(v42, v43))))) & ? [v42] : ! [v43] : ! [v44] : ! [v45] : ( ~ (cartesian_product2(v43, v44) = v45) | relation(v42) | ? [v46] : (powerset(v45) = v46 & ~ element(v42, v46))) & ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (relation_inverse(v42) = v43) | ~ relation(v44) | ~ relation(v42) | ? [v45] : ? [v46] : ? [v47] : ? [v48] : (((ordered_pair(v46, v45) = v48 & in(v48, v42)) | (ordered_pair(v45, v46) = v47 & in(v47, v44))) & ((ordered_pair(v46, v45) = v48 & ~ in(v48, v42)) | (ordered_pair(v45, v46) = v47 & ~ in(v47, v44))))) & ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (inclusion_relation(v42) = v44) | ~ (relation_field(v43) = v42) | ~ relation(v43) | ? [v45] : ? [v46] : ? [v47] : (in(v46, v42) & in(v45, v42) & ( ~ subset(v45, v46) | (ordered_pair(v45, v46) = v47 & ~ in(v47, v43))) & (subset(v45, v46) | (ordered_pair(v45, v46) = v47 & in(v47, v43))))) & ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (relation_dom(v43) = v42) | ~ (identity_relation(v42) = v44) | ~ relation(v43) | ~ function(v43) | ? [v45] : ? [v46] : ( ~ (v46 = v45) & apply(v43, v45) = v46 & in(v45, v42))) & ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (identity_relation(v42) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : ? [v47] : (( ~ (v46 = v45) | ~ in(v45, v42) | (ordered_pair(v45, v45) = v47 & ~ in(v47, v43))) & ((v46 = v45 & in(v45, v42)) | (ordered_pair(v45, v46) = v47 & in(v47, v43))))) & ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ (set_union2(v42, v43) = v44) | ~ subset(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : (v44 = v43 | ~ epsilon_connected(v42) | ~ in(v44, v42) | ~ in(v43, v42) | in(v44, v43) | in(v43, v44)) & ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | v42 = empty_set | ~ (singleton(v43) = v44) | ~ subset(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (set_difference(v42, v43) = v44) | ~ disjoint(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (inclusion_relation(v42) = v43) | ~ (relation_field(v43) = v44) | ~ relation(v43)) & ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (singleton(v42) = v43) | ~ in(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (relation_dom(v43) = v44) | ~ (identity_relation(v42) = v43) | ~ relation(v43) | ~ function(v43)) & ! [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (set_intersection2(v42, v43) = v44) | ~ subset(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : (v44 = empty_set | ~ (set_difference(v42, v43) = v44) | ~ subset(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : (v44 = empty_set | ~ (relation_dom_as_subset(empty_set, v42, v43) = v44) | ~ quasi_total(v43, empty_set, v42) | ~ relation_of2_as_subset(v43, empty_set, v42)) & ! [v42] : ! [v43] : ! [v44] : (v44 = empty_set | ~ (relation_field(v42) = v43) | ~ well_founded_relation(v42) | ~ subset(v44, v43) | ~ relation(v42) | ? [v45] : ? [v46] : (fiber(v42, v45) = v46 & disjoint(v46, v44) & in(v45, v44))) & ! [v42] : ! [v43] : ! [v44] : (v44 = empty_set | ~ (set_intersection2(v42, v43) = v44) | ~ disjoint(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : (v44 = empty_set | ~ is_well_founded_in(v42, v43) | ~ subset(v44, v43) | ~ relation(v42) | ? [v45] : ? [v46] : (fiber(v42, v45) = v46 & disjoint(v46, v44) & in(v45, v44))) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (function_inverse(v44) = v43) | ~ (function_inverse(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (relation_inverse(v44) = v43) | ~ (relation_inverse(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (union(v44) = v43) | ~ (union(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (cast_to_subset(v44) = v43) | ~ (cast_to_subset(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (cast_as_carrier_subset(v44) = v43) | ~ (cast_as_carrier_subset(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (empty_carrier_subset(v44) = v43) | ~ (empty_carrier_subset(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (pair_second(v44) = v43) | ~ (pair_second(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (the_L_meet(v44) = v43) | ~ (the_L_meet(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (inclusion_relation(v44) = v43) | ~ (inclusion_relation(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (set_meet(v44) = v43) | ~ (set_meet(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (the_topology(v44) = v43) | ~ (the_topology(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (singleton(v44) = v43) | ~ (singleton(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (succ(v44) = v43) | ~ (succ(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (pair_first(v44) = v43) | ~ (pair_first(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (the_L_join(v44) = v43) | ~ (the_L_join(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (relation_rng(v44) = v43) | ~ (relation_rng(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (relation_field(v44) = v43) | ~ (relation_field(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (relation_dom(v44) = v43) | ~ (relation_dom(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (identity_relation(v44) = v43) | ~ (identity_relation(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (the_carrier(v44) = v43) | ~ (the_carrier(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = v42 | ~ (powerset(v44) = v43) | ~ (powerset(v44) = v42)) & ! [v42] : ! [v43] : ! [v44] : (v43 = empty_set | v42 = empty_set | ~ (relation_dom_as_subset(v42, empty_set, v43) = v44) | ~ quasi_total(v43, v42, empty_set) | ~ relation_of2_as_subset(v43, v42, empty_set)) & ! [v42] : ! [v43] : ! [v44] : (v43 = empty_set | ~ (relation_dom_as_subset(v42, v43, v44) = v42) | ~ relation_of2_as_subset(v44, v42, v43) | quasi_total(v44, v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (meet_of_subsets(v42, v43) = v44) | ? [v45] : ? [v46] : (powerset(v42) = v45 & (element(v44, v45) | (powerset(v45) = v46 & ~ element(v43, v46))))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (complements_of_subsets(v42, v43) = v44) | ? [v45] : ? [v46] : (powerset(v45) = v46 & powerset(v42) = v45 & ( ~ element(v43, v46) | element(v44, v46)))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (complements_of_subsets(v42, v43) = v44) | ? [v45] : ? [v46] : (powerset(v45) = v46 & powerset(v42) = v45 & ( ~ element(v43, v46) | ( ! [v47] : ! [v48] : ( ~ (subset_complement(v42, v47) = v48) | ~ element(v47, v45) | ~ element(v44, v46) | ~ in(v48, v43) | in(v47, v44)) & ! [v47] : ! [v48] : ( ~ (subset_complement(v42, v47) = v48) | ~ element(v47, v45) | ~ element(v44, v46) | ~ in(v47, v44) | in(v48, v43)) & ! [v47] : (v47 = v44 | ~ element(v47, v46) | ? [v48] : ? [v49] : (element(v48, v45) & ( ~ in(v48, v47) | (subset_complement(v42, v48) = v49 & ~ in(v49, v43))) & (in(v48, v47) | (subset_complement(v42, v48) = v49 & in(v49, v43))))))))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v43, v42) = v44) | ~ relation(v43) | ~ empty(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v43, v42) = v44) | ~ relation(v43) | ~ empty(v42) | empty(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v42, v43) = v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v43) | ~ function(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v42, v43) = v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v43) | ~ function(v42) | function(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v42, v43) = v44) | ~ relation(v43) | ~ relation(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v42, v43) = v44) | ~ relation(v43) | ~ relation(v42) | ? [v45] : ? [v46] : (relation_rng(v44) = v45 & relation_rng(v43) = v46 & subset(v45, v46))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v42, v43) = v44) | ~ relation(v43) | ~ empty(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_composition(v42, v43) = v44) | ~ relation(v43) | ~ empty(v42) | empty(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ well_orders(v43, v42) | ~ relation(v43) | relation_field(v44) = v42) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ well_orders(v43, v42) | ~ relation(v43) | well_ordering(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ reflexive(v43) | ~ relation(v43) | reflexive(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ well_ordering(v43) | ~ relation(v43) | well_ordering(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ well_ordering(v43) | ~ relation(v43) | ? [v45] : ((v45 = v42 & relation_field(v44) = v42) | (relation_field(v43) = v45 & ~ subset(v42, v45)))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ well_founded_relation(v43) | ~ relation(v43) | well_founded_relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ transitive(v43) | ~ relation(v43) | transitive(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ connected(v43) | ~ relation(v43) | connected(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ antisymmetric(v43) | ~ relation(v43) | antisymmetric(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v43, v42) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : (relation_field(v44) = v45 & relation_field(v43) = v46 & subset(v45, v46) & subset(v45, v42))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_restriction(v42, v43) = v44) | ~ relation(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (subset_complement(v42, v43) = v44) | ? [v45] : (powerset(v42) = v45 & ( ~ element(v43, v45) | element(v44, v45)))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (subset_complement(v42, v43) = v44) | ? [v45] : ((v45 = v44 & set_difference(v42, v43) = v44) | (powerset(v42) = v45 & ~ element(v43, v45)))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v44) = v42) | ~ (singleton(v43) = v44) | ~ in(v43, v42)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ relation(v43) | ~ relation(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ finite(v42) | finite(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v5_membered(v42) | v5_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v5_membered(v42) | v4_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v5_membered(v42) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v5_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v5_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v4_membered(v42) | v4_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v4_membered(v42) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v4_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v4_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v3_membered(v42) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v3_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v3_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v2_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v2_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | ~ v1_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_difference(v42, v43) = v44) | subset(v44, v42)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (union(v43) = v44) | ~ in(v42, v43) | subset(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (union(v42) = v43) | ~ in(v44, v43) | ? [v45] : (in(v45, v42) & in(v44, v45))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (union_of_subsets(v42, v43) = v44) | ? [v45] : ? [v46] : (powerset(v42) = v45 & (element(v44, v45) | (powerset(v45) = v46 & ~ element(v43, v46))))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (union_of_subsets(v42, v43) = v44) | ? [v45] : ? [v46] : ((v45 = v44 & union(v43) = v44) | (powerset(v45) = v46 & powerset(v42) = v45 & ~ element(v43, v46)))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (singleton(v42) = v44) | ~ disjoint(v44, v43) | ~ in(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (singleton(v42) = v44) | ~ subset(v44, v43) | in(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (singleton(v42) = v44) | ~ in(v42, v43) | subset(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (singleton(v42) = v43) | ~ (set_union2(v42, v43) = v44) | succ(v42) = v44) & ! [v42] : ! [v43] : ! [v44] : ( ~ (succ(v43) = v44) | ~ being_limit_ordinal(v42) | ~ ordinal(v43) | ~ ordinal(v42) | ~ in(v43, v42) | in(v44, v42)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (succ(v42) = v43) | ~ ordinal_subset(v43, v44) | ~ ordinal(v44) | ~ ordinal(v42) | in(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (succ(v42) = v43) | ~ ordinal(v44) | ~ ordinal(v42) | ~ in(v42, v44) | ordinal_subset(v43, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng(v42) = v43) | ~ relation(v42) | ~ in(v44, v43) | ? [v45] : ? [v46] : (ordered_pair(v45, v44) = v46 & in(v46, v42))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (topstr_closure(v42, v43) = v44) | ~ top_str(v42) | ? [v45] : ? [v46] : (the_carrier(v42) = v45 & powerset(v45) = v46 & ( ~ element(v43, v46) | element(v44, v46)))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_inverse_image(v43, v42) = v44) | ~ relation(v43) | ? [v45] : (relation_dom(v43) = v45 & subset(v44, v45))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_field(v43) = v44) | ~ equipotent(v42, v44) | ~ well_ordering(v43) | ~ relation(v43) | ? [v45] : (well_orders(v45, v42) & relation(v45))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ relation(v43) | ~ function(v43) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ relation(v43) | ~ function(v43) | function(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ relation(v43) | subset(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ relation(v43) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : (relation_rng(v44) = v45 & relation_rng(v43) = v46 & subset(v45, v46))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : (relation_dom(v44) = v45 & relation_dom(v43) = v46 & subset(v45, v46))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng_restriction(v42, v43) = v44) | ~ relation(v43) | ? [v45] : (relation_rng(v44) = v45 & subset(v45, v42))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom(v42) = v43) | ~ (relation_image(v42, v43) = v44) | ~ relation(v42) | relation_rng(v42) = v44) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom(v42) = v43) | ~ relation(v42) | ~ in(v44, v43) | ? [v45] : ? [v46] : (ordered_pair(v44, v45) = v46 & in(v46, v42))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_image(v43, v42) = v44) | ~ relation(v43) | ~ function(v43) | ~ finite(v42) | finite(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_image(v43, v42) = v44) | ~ relation(v43) | ? [v45] : (relation_rng(v43) = v45 & subset(v44, v45))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_image(v42, v43) = v44) | ~ relation(v42) | ~ function(v42) | ~ finite(v43) | finite(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (apply(v43, v42) = v44) | ~ relation(v43) | ~ function(v43) | ? [v45] : (relation_dom(v43) = v45 & ! [v46] : ! [v47] : ! [v48] : ( ~ (relation_composition(v43, v46) = v47) | ~ (apply(v47, v42) = v48) | ~ relation(v46) | ~ function(v46) | ~ in(v42, v45) | apply(v46, v44) = v48))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_restriction(v43, v42) = v44) | ~ relation(v43) | subset(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_restriction(v43, v42) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : (relation_rng(v44) = v45 & relation_rng(v43) = v46 & subset(v45, v46))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_restriction(v42, v43) = v44) | ~ relation_empty_yielding(v42) | ~ relation(v42) | relation_empty_yielding(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_restriction(v42, v43) = v44) | ~ relation_empty_yielding(v42) | ~ relation(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_restriction(v42, v43) = v44) | ~ relation(v42) | ~ function(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_restriction(v42, v43) = v44) | ~ relation(v42) | ~ function(v42) | function(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (relation_dom_restriction(v42, v43) = v44) | ~ relation(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (ordered_pair(v42, v43) = v44) | ~ empty(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (ordered_pair(v42, v43) = v44) | pair_second(v44) = v43) & ! [v42] : ! [v43] : ! [v44] : ( ~ (ordered_pair(v42, v43) = v44) | pair_first(v44) = v42) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v5_membered(v42) | v5_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v5_membered(v42) | v4_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v5_membered(v42) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v5_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v5_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v4_membered(v42) | v4_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v4_membered(v42) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v4_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v4_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v3_membered(v42) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v3_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v3_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v2_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v2_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v43, v42) = v44) | ~ v1_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ relation(v43) | ~ relation(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ finite(v43) | finite(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ finite(v42) | finite(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v5_membered(v42) | v5_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v5_membered(v42) | v4_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v5_membered(v42) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v5_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v5_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v4_membered(v42) | v4_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v4_membered(v42) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v4_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v4_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v3_membered(v42) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v3_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v3_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v2_membered(v42) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v2_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | ~ v1_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | set_intersection2(v43, v42) = v44) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | disjoint(v42, v43) | ? [v45] : in(v45, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_intersection2(v42, v43) = v44) | subset(v44, v42)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (the_carrier(v42) = v43) | ~ (cartesian_product2(v43, v43) = v44) | ~ meet_semilatt_str(v42) | ? [v45] : (the_L_meet(v42) = v45 & quasi_total(v45, v44, v43) & relation_of2_as_subset(v45, v44, v43) & function(v45))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (the_carrier(v42) = v43) | ~ (cartesian_product2(v43, v43) = v44) | ~ join_semilatt_str(v42) | ? [v45] : (the_L_join(v42) = v45 & quasi_total(v45, v44, v43) & relation_of2_as_subset(v45, v44, v43) & function(v45))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v43, v42) = v44) | ~ empty(v44) | empty(v42)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v42, v43) = v44) | ~ relation(v43) | ~ relation(v42) | relation(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v42, v43) = v44) | ~ finite(v43) | ~ finite(v42) | finite(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v42, v43) = v44) | ~ empty(v44) | empty(v42)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v42, v43) = v44) | set_union2(v43, v42) = v44) & ! [v42] : ! [v43] : ! [v44] : ( ~ (set_union2(v42, v43) = v44) | subset(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_pair(v42, v43) = v44) | ~ empty(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_pair(v42, v43) = v44) | unordered_pair(v43, v42) = v44) & ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_pair(v42, v43) = v44) | in(v43, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (unordered_pair(v42, v43) = v44) | in(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (cartesian_product2(v42, v43) = v44) | ~ empty(v44) | empty(v43) | empty(v42)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (cartesian_product2(v42, v43) = v44) | ? [v45] : ( ! [v46] : ! [v47] : ! [v48] : ( ~ (ordered_pair(v47, v48) = v46) | ~ in(v47, v42) | ~ in(v46, v44) | in(v46, v45) | ? [v49] : ( ~ (v49 = v48) & singleton(v47) = v49)) & ! [v46] : ( ~ in(v46, v45) | in(v46, v44)) & ! [v46] : ( ~ in(v46, v45) | ? [v47] : ? [v48] : (singleton(v47) = v48 & ordered_pair(v47, v48) = v46 & in(v47, v42))))) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v43) = v44) | ~ subset(v42, v43) | element(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v43) = v44) | ~ element(v42, v44) | subset(v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ subset(v44, v42) | in(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ finite(v42) | ~ element(v44, v43) | finite(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v5_membered(v42) | ~ element(v44, v43) | v5_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v5_membered(v42) | ~ element(v44, v43) | v4_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v5_membered(v42) | ~ element(v44, v43) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v5_membered(v42) | ~ element(v44, v43) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v5_membered(v42) | ~ element(v44, v43) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v4_membered(v42) | ~ element(v44, v43) | v4_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v4_membered(v42) | ~ element(v44, v43) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v4_membered(v42) | ~ element(v44, v43) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v4_membered(v42) | ~ element(v44, v43) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v3_membered(v42) | ~ element(v44, v43) | v3_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v3_membered(v42) | ~ element(v44, v43) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v3_membered(v42) | ~ element(v44, v43) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v2_membered(v42) | ~ element(v44, v43) | v2_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ v2_membered(v42) | ~ element(v44, v43) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ element(v44, v43) | ~ v1_membered(v42) | v1_membered(v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v42) = v43) | ~ in(v44, v43) | subset(v44, v42)) & ! [v42] : ! [v43] : ! [v44] : ( ~ relation_isomorphism(v42, v43, v44) | ~ reflexive(v42) | ~ relation(v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v44) | reflexive(v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ relation_isomorphism(v42, v43, v44) | ~ well_ordering(v42) | ~ relation(v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v44) | well_ordering(v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ relation_isomorphism(v42, v43, v44) | ~ well_founded_relation(v42) | ~ relation(v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v44) | well_founded_relation(v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ relation_isomorphism(v42, v43, v44) | ~ transitive(v42) | ~ relation(v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v44) | transitive(v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ relation_isomorphism(v42, v43, v44) | ~ connected(v42) | ~ relation(v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v44) | connected(v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ relation_isomorphism(v42, v43, v44) | ~ antisymmetric(v42) | ~ relation(v44) | ~ relation(v43) | ~ relation(v42) | ~ function(v44) | antisymmetric(v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ relation_of2(v44, v42, v43) | relation_of2_as_subset(v44, v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ quasi_total(v44, empty_set, v42) | ~ relation_of2_as_subset(v44, empty_set, v42) | ~ subset(v42, v43) | ~ function(v44) | quasi_total(v44, empty_set, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ quasi_total(v44, empty_set, v42) | ~ relation_of2_as_subset(v44, empty_set, v42) | ~ subset(v42, v43) | ~ function(v44) | relation_of2_as_subset(v44, empty_set, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ relation_of2_as_subset(v44, v42, v43) | relation_of2(v44, v42, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ disjoint(v43, v44) | ~ subset(v42, v43) | disjoint(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ disjoint(v42, v43) | ~ in(v44, v43) | ~ in(v44, v42)) & ! [v42] : ! [v43] : ! [v44] : ( ~ subset(v43, v44) | ~ subset(v42, v43) | subset(v42, v44)) & ! [v42] : ! [v43] : ! [v44] : ( ~ subset(v42, v43) | ~ in(v44, v42) | in(v44, v43)) & ! [v42] : ! [v43] : ! [v44] : ( ~ in(v44, v42) | ~ in(v43, v44) | ~ in(v42, v43)) & ? [v42] : ! [v43] : ! [v44] : (v44 = v42 | v43 = empty_set | ~ (set_meet(v43) = v44) | ? [v45] : ? [v46] : (( ~ in(v45, v42) | (in(v46, v43) & ~ in(v45, v46))) & (in(v45, v42) | ! [v47] : ( ~ in(v47, v43) | in(v45, v47))))) & ? [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (union(v43) = v44) | ? [v45] : ? [v46] : (( ~ in(v45, v42) | ! [v47] : ( ~ in(v47, v43) | ~ in(v45, v47))) & (in(v45, v42) | (in(v46, v43) & in(v45, v46))))) & ? [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (singleton(v43) = v44) | ? [v45] : (( ~ (v45 = v43) | ~ in(v43, v42)) & (v45 = v43 | in(v45, v42)))) & ? [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (relation_rng(v43) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : ? [v47] : (( ~ in(v45, v42) | ! [v48] : ! [v49] : ( ~ (ordered_pair(v48, v45) = v49) | ~ in(v49, v43))) & (in(v45, v42) | (ordered_pair(v46, v45) = v47 & in(v47, v43))))) & ? [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (relation_dom(v43) = v44) | ~ relation(v43) | ? [v45] : ? [v46] : ? [v47] : (( ~ in(v45, v42) | ! [v48] : ! [v49] : ( ~ (ordered_pair(v45, v48) = v49) | ~ in(v49, v43))) & (in(v45, v42) | (ordered_pair(v45, v46) = v47 & in(v47, v43))))) & ? [v42] : ! [v43] : ! [v44] : (v44 = v42 | ~ (powerset(v43) = v44) | ? [v45] : (( ~ subset(v45, v43) | ~ in(v45, v42)) & (subset(v45, v43) | in(v45, v42)))) & ? [v42] : ! [v43] : ! [v44] : (v43 = empty_set | ~ (set_meet(v43) = v44) | in(v42, v44) | ? [v45] : (in(v45, v43) & ~ in(v42, v45))) & ? [v42] : ! [v43] : ! [v44] : ( ~ (cast_as_carrier_subset(v43) = v44) | ~ topological_space(v43) | ~ top_str(v43) | ? [v45] : ? [v46] : ? [v47] : ? [v48] : (the_carrier(v43) = v45 & powerset(v46) = v47 & powerset(v45) = v46 & ( ~ element(v42, v47) | (element(v48, v47) & ! [v49] : ! [v50] : ( ~ (set_difference(v44, v49) = v50) | ~ element(v49, v46) | ~ in(v50, v42) | in(v49, v48)) & ! [v49] : ! [v50] : ( ~ (set_difference(v44, v49) = v50) | ~ element(v49, v46) | ~ in(v49, v48) | in(v50, v42)))))) & ? [v42] : ! [v43] : ! [v44] : ( ~ (cast_as_carrier_subset(v43) = v44) | ~ topological_space(v43) | ~ top_str(v43) | ? [v45] : ? [v46] : ? [v47] : (the_carrier(v43) = v45 & powerset(v45) = v46 & ((powerset(v46) = v47 & ~ element(v42, v47)) | ( ! [v48] : ! [v49] : ( ~ (set_difference(v44, v48) = v49) | ~ in(v49, v42) | ~ in(v48, v46) | in(v48, v47)) & ! [v48] : ! [v49] : ( ~ (set_difference(v44, v48) = v49) | ~ in(v48, v47) | in(v49, v42)) & ! [v48] : ! [v49] : ( ~ (set_difference(v44, v48) = v49) | ~ in(v48, v47) | in(v48, v46)))))) & ? [v42] : ! [v43] : ! [v44] : ( ~ (singleton(v43) = v44) | disjoint(v44, v42) | in(v43, v42)) & ? [v42] : ! [v43] : ! [v44] : ( ~ (succ(v43) = v44) | ~ ordinal(v43) | ? [v45] : ? [v46] : ? [v47] : ((singleton(v43) = v46 & powerset(v43) = v45 & ! [v48] : ! [v49] : ( ~ (set_difference(v49, v46) = v48) | ~ in(v49, v42) | ~ in(v48, v45) | in(v48, v47)) & ! [v48] : ( ~ in(v48, v47) | in(v48, v45)) & ! [v48] : ( ~ in(v48, v47) | ? [v49] : (set_difference(v49, v46) = v48 & in(v49, v42)))) | (powerset(v45) = v46 & powerset(v44) = v45 & ~ element(v42, v46)))) & ? [v42] : ! [v43] : ! [v44] : ( ~ (succ(v43) = v44) | ~ ordinal(v43) | ? [v45] : ? [v46] : ? [v47] : ((singleton(v43) = v45 & powerset(v43) = v46 & ! [v48] : ! [v49] : ( ~ (set_difference(v49, v45) = v48) | ~ in(v49, v42) | ~ in(v48, v46) | in(v48, v47)) & ! [v48] : ( ~ in(v48, v47) | in(v48, v46)) & ! [v48] : ( ~ in(v48, v47) | ? [v49] : (set_difference(v49, v45) = v48 & in(v49, v42)))) | (powerset(v45) = v46 & powerset(v44) = v45 & ~ element(v42, v46)))) & ? [v42] : ! [v43] : ! [v44] : ( ~ (succ(v43) = v44) | ~ ordinal(v43) | ? [v45] : ( ! [v46] : ( ~ ordinal(v46) | ~ in(v46, v44) | ~ in(v46, v42) | in(v46, v45)) & ! [v46] : ( ~ in(v46, v45) | in(v46, v44)) & ! [v46] : ( ~ in(v46, v45) | (ordinal(v46) & in(v46, v42))))) & ? [v42] : ! [v43] : ! [v44] : ( ~ (relation_rng(v44) = v43) | ~ one_to_one(v44) | ~ relation(v44) | ~ function(v44) | equipotent(v42, v43) | ? [v45] : ( ~ (v45 = v42) & relation_dom(v44) = v45)) & ? [v42] : ! [v43] : ! [v44] : ( ~ (the_carrier(v43) = v44) | ~ topological_space(v43) | ~ top_str(v43) | ? [v45] : ? [v46] : ? [v47] : (powerset(v44) = v45 & ( ~ element(v42, v45) | (powerset(v45) = v46 & element(v47, v46) & ! [v48] : ( ~ closed_subset(v48, v43) | ~ subset(v42, v48) | ~ element(v48, v45) | in(v48, v47)) & ! [v48] : ( ~ element(v48, v45) | ~ in(v48, v47) | closed_subset(v48, v43)) & ! [v48] : ( ~ element(v48, v45) | ~ in(v48, v47) | subset(v42, v48)))))) & ? [v42] : ! [v43] : ! [v44] : ( ~ (the_carrier(v43) = v44) | ~ topological_space(v43) | ~ top_str(v43) | ? [v45] : ? [v46] : (powerset(v44) = v45 & ( ~ element(v42, v45) | ( ! [v47] : ( ~ closed_subset(v47, v43) | ~ subset(v42, v47) | ~ element(v47, v45) | ~ in(v47, v45) | in(v47, v46)) & ! [v47] : ( ~ in(v47, v46) | subset(v42, v47)) & ! [v47] : ( ~ in(v47, v46) | in(v47, v45)) & ! [v47] : ( ~ in(v47, v46) | (closed_subset(v47, v43) & element(v47, v45))))))) & ? [v42] : ! [v43] : ! [v44] : ( ~ (powerset(v43) = v44) | element(v42, v44) | ? [v45] : (in(v45, v42) & ~ in(v45, v43))) & ? [v42] : ! [v43] : ! [v44] : ( ~ relation(v44) | ~ relation(v43) | ~ function(v44) | ? [v45] : (relation(v45) & ! [v46] : ! [v47] : ! [v48] : ! [v49] : ! [v50] : ( ~ (apply(v44, v47) = v49) | ~ (apply(v44, v46) = v48) | ~ (ordered_pair(v48, v49) = v50) | ~ in(v50, v43) | ~ in(v47, v42) | ~ in(v46, v42) | ? [v51] : (ordered_pair(v46, v47) = v51 & in(v51, v45))) & ! [v46] : ! [v47] : ! [v48] : ! [v49] : ! [v50] : ( ~ (apply(v44, v47) = v49) | ~ (apply(v44, v46) = v48) | ~ (ordered_pair(v48, v49) = v50) | in(v50, v43) | ? [v51] : (ordered_pair(v46, v47) = v51 & ~ in(v51, v45))) & ! [v46] : ! [v47] : ! [v48] : ! [v49] : ! [v50] : ( ~ (apply(v44, v47) = v49) | ~ (apply(v44, v46) = v48) | ~ (ordered_pair(v48, v49) = v50) | in(v47, v42) | ? [v51] : (ordered_pair(v46, v47) = v51 & ~ in(v51, v45))) & ! [v46] : ! [v47] : ! [v48] : ! [v49] : ! [v50] : ( ~ (apply(v44, v47) = v49) | ~ (apply(v44, v46) = v48) | ~ (ordered_pair(v48, v49) = v50) | in(v46, v42) | ? [v51] : (ordered_pair(v46, v47) = v51 & ~ in(v51, v45))))) & ! [v42] : ! [v43] : (v43 = v42 | ~ (set_difference(v42, empty_set) = v43)) & ! [v42] : ! [v43] : (v43 = v42 | ~ (union(v42) = v43) | ~ being_limit_ordinal(v42)) & ! [v42] : ! [v43] : (v43 = v42 | ~ (cast_to_subset(v42) = v43)) & ! [v42] : ! [v43] : (v43 = v42 | ~ (set_intersection2(v42, v42) = v43)) & ! [v42] : ! [v43] : (v43 = v42 | ~ (set_union2(v42, v42) = v43)) & ! [v42] : ! [v43] : (v43 = v42 | ~ (set_union2(v42, empty_set) = v43)) & ! [v42] : ! [v43] : (v43 = v42 | ~ subset(v43, v42) | ~ subset(v42, v43)) & ! [v42] : ! [v43] : (v43 = v42 | ~ subset(v42, v43) | proper_subset(v42, v43)) & ! [v42] : ! [v43] : (v43 = v42 | ~ relation(v43) | ~ relation(v42) | ? [v44] : ? [v45] : ? [v46] : (ordered_pair(v44, v45) = v46 & ( ~ in(v46, v43) | ~ in(v46, v42)) & (in(v46, v43) | in(v46, v42)))) & ! [v42] : ! [v43] : (v43 = v42 | ~ ordinal(v43) | ~ ordinal(v42) | in(v43, v42) | in(v42, v43)) & ! [v42] : ! [v43] : (v43 = v42 | ~ empty(v43) | ~ empty(v42)) & ! [v42] : ! [v43] : (v43 = empty_set | ~ (complements_of_subsets(v42, v43) = empty_set) | ? [v44] : ? [v45] : (powerset(v44) = v45 & powerset(v42) = v44 & ~ element(v43, v45))) & ! [v42] : ! [v43] : (v43 = empty_set | ~ (set_difference(empty_set, v42) = v43)) & ! [v42] : ! [v43] : (v43 = empty_set | ~ (empty_carrier_subset(v42) = v43) | ~ one_sorted_str(v42)) & ! [v42] : ! [v43] : (v43 = empty_set | ~ (set_intersection2(v42, empty_set) = v43)) & ! [v42] : ! [v43] : (v42 = empty_set | ~ (relation_dom_as_subset(v42, empty_set, empty_set) = v43) | ~ relation_of2_as_subset(empty_set, v42, empty_set) | quasi_total(empty_set, v42, empty_set)) & ! [v42] : ! [v43] : (v42 = empty_set | ~ (relation_rng(v42) = v43) | ~ relation(v42) | ? [v44] : ( ~ (v44 = empty_set) & relation_dom(v42) = v44)) & ! [v42] : ! [v43] : (v42 = empty_set | ~ (relation_inverse_image(v43, v42) = empty_set) | ~ relation(v43) | ? [v44] : (relation_rng(v43) = v44 & ~ subset(v42, v44))) & ! [v42] : ! [v43] : (v42 = empty_set | ~ subset(v42, v43) | ~ ordinal(v43) | ? [v44] : (ordinal(v44) & in(v44, v42) & ! [v45] : ( ~ ordinal(v45) | ~ in(v45, v42) | ordinal_subset(v44, v45)))) & ! [v42] : ! [v43] : ( ~ (function_inverse(v42) = v43) | ~ one_to_one(v42) | ~ relation(v42) | ~ function(v42) | relation_inverse(v42) = v43) & ! [v42] : ! [v43] : ( ~ (function_inverse(v42) = v43) | ~ one_to_one(v42) | ~ relation(v42) | ~ function(v42) | one_to_one(v43)) & ! [v42] : ! [v43] : ( ~ (function_inverse(v42) = v43) | ~ one_to_one(v42) | ~ relation(v42) | ~ function(v42) | ? [v44] : ? [v45] : (relation_rng(v43) = v45 & relation_rng(v42) = v44 & relation_dom(v43) = v44 & relation_dom(v42) = v45)) & ! [v42] : ! [v43] : ( ~ (function_inverse(v42) = v43) | ~ one_to_one(v42) | ~ relation(v42) | ~ function(v42) | ? [v44] : ? [v45] : (relation_rng(v42) = v44 & relation_dom(v42) = v45 & ! [v46] : ! [v47] : ! [v48] : ! [v49] : (v49 = v48 | ~ (relation_dom(v43) = v46) | ~ (apply(v43, v47) = v49) | ~ (apply(v42, v48) = v47) | ~ relation(v43) | ~ function(v43) | ~ in(v48, v45)) & ! [v46] : ! [v47] : ! [v48] : ! [v49] : (v49 = v47 | ~ (relation_dom(v43) = v46) | ~ (apply(v43, v47) = v48) | ~ (apply(v42, v48) = v49) | ~ relation(v43) | ~ function(v43) | ~ in(v47, v44)) & ! [v46] : ! [v47] : ! [v48] : ! [v49] : ( ~ (relation_dom(v43) = v46) | ~ (apply(v43, v47) = v49) | ~ (apply(v42, v48) = v47) | ~ relation(v43) | ~ function(v43) | ~ in(v48, v45) | in(v47, v44)) & ! [v46] : ! [v47] : ! [v48] : ! [v49] : ( ~ (relation_dom(v43) = v46) | ~ (apply(v43, v47) = v48) | ~ (apply(v42, v48) = v49) | ~ relation(v43) | ~ function(v43) | ~ in(v47, v44) | in(v48, v45)) & ! [v46] : (v46 = v44 | ~ (relation_dom(v43) = v46) | ~ relation(v43) | ~ function(v43)) & ! [v46] : (v46 = v43 | ~ (relation_dom(v46) = v44) | ~ relation(v46) | ~ function(v46) | ? [v47] : ? [v48] : ? [v49] : ? [v50] : ((v50 = v47 & apply(v42, v48) = v47 & in(v48, v45) & ( ~ in(v47, v44) | ( ~ (v49 = v48) & apply(v46, v47) = v49))) | (v49 = v48 & apply(v46, v47) = v48 & in(v47, v44) & ( ~ in(v48, v45) | ( ~ (v50 = v47) & apply(v42, v48) = v50))))))) & ! [v42] : ! [v43] : ( ~ (function_inverse(v42) = v43) | ~ relation(v42) | ~ function(v42) | relation(v43)) & ! [v42] : ! [v43] : ( ~ (function_inverse(v42) = v43) | ~ relation(v42) | ~ function(v42) | function(v43)) & ! [v42] : ! [v43] : ( ~ (relation_inverse(v42) = v43) | ~ one_to_one(v42) | ~ relation(v42) | ~ function(v42) | relation(v43)) & ! [v42] : ! [v43] : ( ~ (relation_inverse(v42) = v43) | ~ one_to_one(v42) | ~ relation(v42) | ~ function(v42) | function(v43)) & ! [v42] : ! [v43] : ( ~ (relation_inverse(v42) = v43) | ~ relation(v42) | relation_inverse(v43) = v42) & ! [v42] : ! [v43] : ( ~ (relation_inverse(v42) = v43) | ~ relation(v42) | relation(v43)) & ! [v42] : ! [v43] : ( ~ (relation_inverse(v42) = v43) | ~ relation(v42) | ? [v44] : ? [v45] : (relation_rng(v43) = v45 & relation_rng(v42) = v44 & relation_dom(v43) = v44 & relation_dom(v42) = v45)) & ! [v42] : ! [v43] : ( ~ (relation_inverse(v42) = v43) | ~ empty(v42) | relation(v43)) & ! [v42] : ! [v43] : ( ~ (relation_inverse(v42) = v43) | ~ empty(v42) | empty(v43)) & ! [v42] : ! [v43] : ( ~ (set_difference(v42, v43) = v42) | disjoint(v42, v43)) & ! [v42] : ! [v43] : ( ~ (set_difference(v42, v43) = empty_set) | subset(v42, v43)) & ! [v42] : ! [v43] : ( ~ (union(v42) = v43) | ~ ordinal(v42) | epsilon_connected(v43)) & ! [v42] : ! [v43] : ( ~ (union(v42) = v43) | ~ ordinal(v42) | epsilon_transitive(v43)) & ! [v42] : ! [v43] : ( ~ (union(v42) = v43) | ~ ordinal(v42) | ordinal(v43)) & ! [v42] : ! [v43] : ( ~ (cast_to_subset(v42) = v43) | ? [v44] : (powerset(v42) = v44 & element(v43, v44))) & ! [v42] : ! [v43] : ( ~ (cast_as_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | the_carrier(v42) = v43) & ! [v42] : ! [v43] : ( ~ (cast_as_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | ? [v44] : ? [v45] : (the_carrier(v42) = v44 & powerset(v44) = v45 & element(v43, v45))) & ! [v42] : ! [v43] : ( ~ (cast_as_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | ? [v44] : ? [v45] : (the_carrier(v42) = v44 & powerset(v44) = v45 & ! [v46] : ! [v47] : ! [v48] : (v48 = v46 | ~ (subset_difference(v44, v43, v47) = v48) | ~ (subset_difference(v44, v43, v46) = v47) | ~ element(v46, v45)))) & ! [v42] : ! [v43] : ( ~ (cast_as_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | ? [v44] : ? [v45] : (the_carrier(v42) = v44 & powerset(v44) = v45 & ! [v46] : ! [v47] : (v47 = v46 | ~ (subset_intersection2(v44, v46, v43) = v47) | ~ element(v46, v45)))) & ! [v42] : ! [v43] : ( ~ (cast_as_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | ? [v44] : ? [v45] : (the_carrier(v42) = v44 & powerset(v44) = v45 & ! [v46] : ! [v47] : ( ~ (subset_difference(v44, v43, v46) = v47) | ~ element(v46, v45) | subset_complement(v44, v46) = v47))) & ! [v42] : ! [v43] : ( ~ (cast_as_carrier_subset(v42) = v43) | ~ topological_space(v42) | ~ top_str(v42) | closed_subset(v43, v42)) & ! [v42] : ! [v43] : ( ~ (cast_as_carrier_subset(v42) = v43) | ~ top_str(v42) | ? [v44] : ? [v45] : (the_carrier(v42) = v44 & powerset(v44) = v45 & ! [v46] : ! [v47] : ( ~ (subset_difference(v44, v43, v46) = v47) | ~ closed_subset(v46, v42) | ~ element(v46, v45) | open_subset(v47, v42)) & ! [v46] : ! [v47] : ( ~ (subset_difference(v44, v43, v46) = v47) | ~ open_subset(v47, v42) | ~ element(v46, v45) | closed_subset(v46, v42)))) & ! [v42] : ! [v43] : ( ~ (empty_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | empty(v43)) & ! [v42] : ! [v43] : ( ~ (empty_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | v5_membered(v43)) & ! [v42] : ! [v43] : ( ~ (empty_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | v4_membered(v43)) & ! [v42] : ! [v43] : ( ~ (empty_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | v3_membered(v43)) & ! [v42] : ! [v43] : ( ~ (empty_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | v2_membered(v43)) & ! [v42] : ! [v43] : ( ~ (empty_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | v1_membered(v43)) & ! [v42] : ! [v43] : ( ~ (empty_carrier_subset(v42) = v43) | ~ one_sorted_str(v42) | ? [v44] : ? [v45] : (the_carrier(v42) = v44 & powerset(v44) = v45 & element(v43, v45))) & ! [v42] : ! [v43] : ( ~ (the_L_meet(v42) = v43) | ~ meet_semilatt_str(v42) | empty_carrier(v42) | ? [v44] : (the_carrier(v42) = v44 & ! [v45] : ! [v46] : ! [v47] : ( ~ (apply_binary_as_element(v44, v44, v44, v43, v45, v46) = v47) | ~ element(v46, v44) | ~ element(v45, v44) | meet(v42, v45, v46) = v47))) & ! [v42] : ! [v43] : ( ~ (inclusion_relation(v42) = v43) | ~ ordinal(v42) | well_ordering(v43)) & ! [v42] : ! [v43] : ( ~ (inclusion_relation(v42) = v43) | ~ ordinal(v42) | well_founded_relation(v43)) & ! [v42] : ! [v43] : ( ~ (inclusion_relation(v42) = v43) | ~ ordinal(v42) | connected(v43)) & ! [v42] : ! [v43] : ( ~ (inclusion_relation(v42) = v43) | reflexive(v43)) & ! [v42] : ! [v43] : ( ~ (inclusion_relation(v42) = v43) | transitive(v43)) & ! [v42] : ! [v43] : ( ~ (inclusion_relation(v42) = v43) | antisymmetric(v43)) & ! [v42] : ! [v43] : ( ~ (inclusion_relation(v42) = v43) | relation(v43)) & ! [v42] : ! [v43] : ( ~ (the_topology(v42) = v43) | ~ top_str(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : ? [v49] : (( ~ topological_space(v42) | (the_carrier(v42) = v44 & powerset(v45) = v46 & powerset(v44) = v45 & in(v44, v43) & ! [v50] : ! [v51] : ! [v52] : ( ~ (subset_intersection2(v44, v50, v51) = v52) | ~ element(v51, v45) | ~ element(v50, v45) | ~ in(v51, v43) | ~ in(v50, v43) | in(v52, v43)) & ! [v50] : ! [v51] : ( ~ (union_of_subsets(v44, v50) = v51) | ~ subset(v50, v43) | ~ element(v50, v46) | in(v51, v43)))) & (topological_space(v42) | (the_carrier(v42) = v44 & ( ~ in(v44, v43) | (union_of_subsets(v44, v47) = v48 & powerset(v45) = v46 & powerset(v44) = v45 & subset(v47, v43) & element(v47, v46) & ~ in(v48, v43)) | (subset_intersection2(v44, v47, v48) = v49 & powerset(v44) = v45 & element(v48, v45) & element(v47, v45) & in(v48, v43) & in(v47, v43) & ~ in(v49, v43))))))) & ! [v42] : ! [v43] : ( ~ (the_topology(v42) = v43) | ~ top_str(v42) | ? [v44] : ? [v45] : ? [v46] : (the_carrier(v42) = v44 & powerset(v45) = v46 & powerset(v44) = v45 & element(v43, v46))) & ! [v42] : ! [v43] : ( ~ (the_topology(v42) = v43) | ~ top_str(v42) | ? [v44] : ? [v45] : (the_carrier(v42) = v44 & powerset(v44) = v45 & ! [v46] : ( ~ open_subset(v46, v42) | ~ element(v46, v45) | in(v46, v43)) & ! [v46] : ( ~ element(v46, v45) | ~ in(v46, v43) | open_subset(v46, v42)))) & ! [v42] : ! [v43] : ( ~ (singleton(v43) = v42) | subset(v42, v42)) & ! [v42] : ! [v43] : ( ~ (singleton(v42) = v43) | ~ empty(v43)) & ! [v42] : ! [v43] : ( ~ (singleton(v42) = v43) | subset(empty_set, v43)) & ! [v42] : ! [v43] : ( ~ (singleton(v42) = v43) | finite(v43)) & ! [v42] : ! [v43] : ( ~ (singleton(v42) = v43) | in(v42, v43)) & ! [v42] : ! [v43] : ( ~ (succ(v43) = v42) | ~ being_limit_ordinal(v42) | ~ ordinal(v43) | ~ ordinal(v42)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ~ empty(v43) | ~ natural(v42)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ~ empty(v43)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ~ natural(v42) | epsilon_connected(v43)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ~ natural(v42) | epsilon_transitive(v43)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ~ natural(v42) | ordinal(v43)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ~ natural(v42) | natural(v43)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | epsilon_connected(v43)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | epsilon_transitive(v43)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ordinal(v43)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ ordinal(v42) | ? [v44] : ( ! [v45] : ! [v46] : ( ~ (powerset(v45) = v46) | ~ ordinal(v45) | ~ in(v45, v43) | in(v45, v44) | in(v45, omega)) & ! [v45] : ! [v46] : ( ~ (powerset(v45) = v46) | ~ ordinal(v45) | ~ in(v45, v43) | in(v45, v44) | ? [v47] : ? [v48] : ( ~ (v48 = empty_set) & powerset(v46) = v47 & element(v48, v47) & ! [v49] : ( ~ in(v49, v48) | ? [v50] : ( ~ (v50 = v49) & subset(v49, v50) & in(v50, v48))))) & ! [v45] : ( ~ in(v45, v44) | in(v45, v43)) & ! [v45] : ( ~ in(v45, v44) | ? [v46] : ? [v47] : (ordinal(v45) & ( ~ in(v45, omega) | (powerset(v46) = v47 & powerset(v45) = v46 & ! [v48] : (v48 = empty_set | ~ element(v48, v47) | ? [v49] : (in(v49, v48) & ! [v50] : (v50 = v49 | ~ subset(v49, v50) | ~ in(v50, v48)))))))))) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | ~ empty(v43)) & ! [v42] : ! [v43] : ( ~ (succ(v42) = v43) | in(v42, v43)) & ! [v42] : ! [v43] : ( ~ (the_L_join(v42) = v43) | ~ join_semilatt_str(v42) | empty_carrier(v42) | ? [v44] : (the_carrier(v42) = v44 & ! [v45] : ! [v46] : ! [v47] : ( ~ (apply_binary_as_element(v44, v44, v44, v43, v45, v46) = v47) | ~ element(v46, v44) | ~ element(v45, v44) | join(v42, v45, v46) = v47))) & ! [v42] : ! [v43] : ( ~ (relation_dom_as_subset(empty_set, v42, v43) = empty_set) | ~ relation_of2_as_subset(v43, empty_set, v42) | quasi_total(v43, empty_set, v42)) & ! [v42] : ! [v43] : ( ~ (relation_rng(v43) = v42) | ~ relation(v43) | ~ function(v43) | finite(v42) | ? [v44] : (relation_dom(v43) = v44 & ~ in(v44, omega))) & ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ relation(v42) | ~ function(v42) | finite(v43) | ? [v44] : (relation_dom(v42) = v44 & ~ finite(v44))) & ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ relation(v42) | ~ function(v42) | ? [v44] : (relation_dom(v42) = v44 & ! [v45] : ! [v46] : ( ~ (apply(v42, v46) = v45) | ~ in(v46, v44) | in(v45, v43)) & ! [v45] : ( ~ in(v45, v43) | ? [v46] : (apply(v42, v46) = v45 & in(v46, v44))) & ? [v45] : (v45 = v43 | ? [v46] : ? [v47] : ? [v48] : (( ~ in(v46, v45) | ! [v49] : ( ~ (apply(v42, v49) = v46) | ~ in(v49, v44))) & (in(v46, v45) | (v48 = v46 & apply(v42, v47) = v46 & in(v47, v44))))))) & ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ relation(v42) | ~ empty(v43) | empty(v42)) & ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ relation(v42) | ? [v44] : (relation_dom(v42) = v44 & ! [v45] : ! [v46] : ( ~ (relation_composition(v45, v42) = v46) | ~ relation(v45) | ? [v47] : ((v47 = v43 & relation_rng(v46) = v43) | (relation_rng(v45) = v47 & ~ subset(v44, v47)))))) & ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ relation(v42) | ? [v44] : (relation_dom(v42) = v44 & ! [v45] : ! [v46] : ( ~ (relation_composition(v42, v45) = v46) | ~ relation(v45) | ? [v47] : ((v47 = v44 & relation_dom(v46) = v44) | (relation_dom(v45) = v47 & ~ subset(v43, v47)))))) & ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ relation(v42) | ? [v44] : (relation_dom(v42) = v44 & ! [v45] : ! [v46] : ( ~ (relation_rng(v45) = v46) | ~ subset(v42, v45) | ~ relation(v45) | subset(v43, v46)) & ! [v45] : ! [v46] : ( ~ (relation_rng(v45) = v46) | ~ subset(v42, v45) | ~ relation(v45) | ? [v47] : (relation_dom(v45) = v47 & subset(v44, v47))))) & ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ relation(v42) | ? [v44] : (( ~ (v43 = empty_set) | (v44 = empty_set & relation_dom(v42) = empty_set)) & (v43 = empty_set | ( ~ (v44 = empty_set) & relation_dom(v42) = v44)))) & ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ empty(v42) | relation(v43)) & ! [v42] : ! [v43] : ( ~ (relation_rng(v42) = v43) | ~ empty(v42) | empty(v43)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ well_orders(v42, v43) | ~ relation(v42) | well_ordering(v42)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ reflexive(v42) | ~ relation(v42) | is_reflexive_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ well_ordering(v42) | ~ relation(v42) | well_orders(v42, v43)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ is_well_founded_in(v42, v43) | ~ relation(v42) | well_founded_relation(v42)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ well_founded_relation(v42) | ~ relation(v42) | is_well_founded_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ is_reflexive_in(v42, v43) | ~ relation(v42) | reflexive(v42)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ is_transitive_in(v42, v43) | ~ relation(v42) | transitive(v42)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ transitive(v42) | ~ relation(v42) | is_transitive_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ is_connected_in(v42, v43) | ~ relation(v42) | connected(v42)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ connected(v42) | ~ relation(v42) | is_connected_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ is_antisymmetric_in(v42, v43) | ~ relation(v42) | antisymmetric(v42)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ antisymmetric(v42) | ~ relation(v42) | is_antisymmetric_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ relation(v42) | reflexive(v42) | ? [v44] : ? [v45] : (ordered_pair(v44, v44) = v45 & in(v44, v43) & ~ in(v45, v42))) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ relation(v42) | well_founded_relation(v42) | ? [v44] : ( ~ (v44 = empty_set) & subset(v44, v43) & ! [v45] : ! [v46] : ( ~ (fiber(v42, v45) = v46) | ~ disjoint(v46, v44) | ~ in(v45, v44)))) & ! [v42] : ! [v43] : ( ~ (relation_field(v42) = v43) | ~ relation(v42) | connected(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ( ~ (v45 = v44) & ordered_pair(v45, v44) = v47 & ordered_pair(v44, v45) = v46 & in(v45, v43) & in(v44, v43) & ~ in(v47, v42) & ~ in(v46, v42))) & ! [v42] : ! [v43] : ( ~ (relation_dom(v42) = v43) | ~ relation(v42) | ~ function(v42) | one_to_one(v42) | ? [v44] : ? [v45] : ? [v46] : ( ~ (v45 = v44) & apply(v42, v45) = v46 & apply(v42, v44) = v46 & in(v45, v43) & in(v44, v43))) & ! [v42] : ! [v43] : ( ~ (relation_dom(v42) = v43) | ~ relation(v42) | ~ empty(v43) | empty(v42)) & ! [v42] : ! [v43] : ( ~ (relation_dom(v42) = v43) | ~ empty(v42) | relation(v43)) & ! [v42] : ! [v43] : ( ~ (relation_dom(v42) = v43) | ~ empty(v42) | empty(v43)) & ! [v42] : ! [v43] : ( ~ (identity_relation(v42) = v43) | relation_rng(v43) = v42) & ! [v42] : ! [v43] : ( ~ (identity_relation(v42) = v43) | relation_dom(v43) = v42) & ! [v42] : ! [v43] : ( ~ (identity_relation(v42) = v43) | relation(v43)) & ! [v42] : ! [v43] : ( ~ (identity_relation(v42) = v43) | function(v43)) & ! [v42] : ! [v43] : ( ~ (set_intersection2(v42, v43) = empty_set) | disjoint(v42, v43)) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ latt_str(v42) | meet_absorbing(v42) | empty_carrier(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ( ~ (v47 = v45) & meet(v42, v44, v45) = v46 & join(v42, v46, v45) = v47 & element(v45, v43) & element(v44, v43))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ one_sorted_str(v42) | ~ empty(v43) | empty_carrier(v42)) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ one_sorted_str(v42) | empty_carrier(v42) | ? [v44] : ? [v45] : (powerset(v43) = v44 & element(v45, v44) & ~ empty(v45))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ topological_space(v42) | ~ top_str(v42) | ? [v44] : ? [v45] : (powerset(v44) = v45 & powerset(v43) = v44 & ! [v46] : ! [v47] : ( ~ (meet_of_subsets(v43, v46) = v47) | ~ element(v46, v45) | closed_subset(v47, v42) | ? [v48] : (element(v48, v44) & in(v48, v46) & ~ closed_subset(v48, v42))))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ topological_space(v42) | ~ top_str(v42) | ? [v44] : ? [v45] : (powerset(v44) = v45 & powerset(v43) = v44 & ! [v46] : ! [v47] : ( ~ (topstr_closure(v42, v46) = v47) | ~ element(v46, v44) | ? [v48] : (meet_of_subsets(v43, v48) = v47 & element(v48, v45) & ! [v49] : ( ~ closed_subset(v49, v42) | ~ subset(v46, v49) | ~ element(v49, v44) | in(v49, v48)) & ! [v49] : ( ~ element(v49, v44) | ~ in(v49, v48) | closed_subset(v49, v42)) & ! [v49] : ( ~ element(v49, v44) | ~ in(v49, v48) | subset(v46, v49)))))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ topological_space(v42) | ~ top_str(v42) | ? [v44] : ? [v45] : (powerset(v43) = v44 & closed_subset(v45, v42) & element(v45, v44))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ top_str(v42) | ? [v44] : (powerset(v43) = v44 & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (topstr_closure(v42, v45) = v46) | ~ closed_subset(v48, v42) | ~ subset(v45, v48) | ~ element(v48, v44) | ~ element(v45, v44) | ~ in(v47, v46) | ~ in(v47, v43) | in(v47, v48)) & ! [v45] : ! [v46] : ! [v47] : ( ~ (topstr_closure(v42, v45) = v46) | ~ element(v45, v44) | ~ in(v47, v43) | in(v47, v46) | ? [v48] : (closed_subset(v48, v42) & subset(v45, v48) & element(v48, v44) & ~ in(v47, v48))))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ top_str(v42) | ? [v44] : (powerset(v43) = v44 & ! [v45] : ! [v46] : ! [v47] : ! [v48] : ( ~ (topstr_closure(v42, v45) = v46) | ~ disjoint(v45, v48) | ~ open_subset(v48, v42) | ~ element(v48, v44) | ~ element(v46, v44) | ~ element(v45, v44) | ~ in(v47, v48) | ~ in(v47, v46) | ~ in(v47, v43)) & ! [v45] : ! [v46] : ! [v47] : (v47 = v46 | ~ (topstr_closure(v42, v45) = v46) | ~ element(v47, v44) | ~ element(v45, v44) | ? [v48] : ? [v49] : (in(v48, v43) & ( ~ in(v48, v47) | (disjoint(v45, v49) & open_subset(v49, v42) & element(v49, v44) & in(v48, v49))) & (in(v48, v47) | ! [v50] : ( ~ disjoint(v45, v50) | ~ open_subset(v50, v42) | ~ element(v50, v44) | ~ in(v48, v50))))) & ! [v45] : ! [v46] : ! [v47] : ( ~ (topstr_closure(v42, v45) = v46) | ~ element(v46, v44) | ~ element(v45, v44) | ~ in(v47, v43) | in(v47, v46) | ? [v48] : (disjoint(v45, v48) & open_subset(v48, v42) & element(v48, v44) & in(v47, v48))))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ top_str(v42) | ? [v44] : (powerset(v43) = v44 & ! [v45] : ! [v46] : (v46 = v45 | ~ (topstr_closure(v42, v45) = v46) | ~ closed_subset(v45, v42) | ~ element(v45, v44)) & ! [v45] : ( ~ (topstr_closure(v42, v45) = v45) | ~ topological_space(v42) | ~ element(v45, v44) | closed_subset(v45, v42)))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ top_str(v42) | ? [v44] : (powerset(v43) = v44 & ! [v45] : ! [v46] : ( ~ (subset_complement(v43, v45) = v46) | ~ closed_subset(v46, v42) | ~ element(v45, v44) | open_subset(v45, v42)) & ! [v45] : ! [v46] : ( ~ (subset_complement(v43, v45) = v46) | ~ open_subset(v45, v42) | ~ element(v45, v44) | closed_subset(v46, v42)))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ top_str(v42) | ? [v44] : (powerset(v43) = v44 & ! [v45] : ! [v46] : ( ~ (subset_complement(v43, v45) = v46) | ~ closed_subset(v45, v42) | ~ element(v45, v44) | open_subset(v46, v42)) & ! [v45] : ! [v46] : ( ~ (subset_complement(v43, v45) = v46) | ~ open_subset(v46, v42) | ~ element(v45, v44) | closed_subset(v45, v42)))) & ! [v42] : ! [v43] : ( ~ (the_carrier(v42) = v43) | ~ top_str(v42) | ? [v44] : (powerset(v43) = v44 & ! [v45] : ! [v46] : ( ~ (topstr_closure(v42, v45) = v46) | ~ element(v45, v44) | subset(v45, v46)))) & ! [v42] : ! [v43] : ( ~ (unordered_pair(v42, v42) = v43) | singleton(v42) = v43) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ~ finite(v42) | ? [v44] : (powerset(v43) = v44 & ! [v45] : (v45 = empty_set | ~ element(v45, v44) | ? [v46] : (in(v46, v45) & ! [v47] : (v47 = v46 | ~ subset(v46, v47) | ~ in(v47, v45)))))) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ~ empty(v43)) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | union(v43) = v42) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | diff_closed(v43)) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | cup_closed(v43)) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | preboolean(v43)) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | empty(v42) | ? [v44] : (finite(v44) & element(v44, v43) & ~ empty(v44))) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | empty(v42) | ? [v44] : (element(v44, v43) & ~ empty(v44))) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ? [v44] : (one_to_one(v44) & relation(v44) & function(v44) & finite(v44) & epsilon_connected(v44) & epsilon_transitive(v44) & ordinal(v44) & empty(v44) & natural(v44) & element(v44, v43))) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ? [v44] : (empty(v44) & element(v44, v43))) & ! [v42] : ! [v43] : ( ~ are_equipotent(v42, v43) | equipotent(v42, v43)) & ! [v42] : ! [v43] : ( ~ well_orders(v42, v43) | ~ relation(v42) | is_well_founded_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ well_orders(v42, v43) | ~ relation(v42) | is_reflexive_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ well_orders(v42, v43) | ~ relation(v42) | is_transitive_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ well_orders(v42, v43) | ~ relation(v42) | is_connected_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ well_orders(v42, v43) | ~ relation(v42) | is_antisymmetric_in(v42, v43)) & ! [v42] : ! [v43] : ( ~ equipotent(v42, v43) | are_equipotent(v42, v43)) & ! [v42] : ! [v43] : ( ~ equipotent(v42, v43) | equipotent(v43, v42)) & ! [v42] : ! [v43] : ( ~ equipotent(v42, v43) | ? [v44] : (relation_rng(v44) = v43 & relation_dom(v44) = v42 & one_to_one(v44) & relation(v44) & function(v44))) & ! [v42] : ! [v43] : ( ~ is_well_founded_in(v42, v43) | ~ is_reflexive_in(v42, v43) | ~ is_transitive_in(v42, v43) | ~ is_connected_in(v42, v43) | ~ is_antisymmetric_in(v42, v43) | ~ relation(v42) | well_orders(v42, v43)) & ! [v42] : ! [v43] : ( ~ disjoint(v42, v43) | disjoint(v43, v42)) & ! [v42] : ! [v43] : ( ~ subset(v42, v43) | ~ finite(v43) | finite(v42)) & ! [v42] : ! [v43] : ( ~ subset(v42, v43) | ~ ordinal(v43) | ~ ordinal(v42) | ordinal_subset(v42, v43)) & ! [v42] : ! [v43] : ( ~ subset(v42, v43) | ~ proper_subset(v43, v42)) & ! [v42] : ! [v43] : ( ~ ordinal_subset(v42, v43) | ~ ordinal(v43) | ~ ordinal(v42) | subset(v42, v43)) & ! [v42] : ! [v43] : ( ~ relation(v43) | ~ relation(v42) | subset(v42, v43) | ? [v44] : ? [v45] : ? [v46] : (ordered_pair(v44, v45) = v46 & in(v46, v42) & ~ in(v46, v43))) & ! [v42] : ! [v43] : ( ~ relation(v42) | ~ in(v43, v42) | ? [v44] : ? [v45] : ordered_pair(v44, v45) = v43) & ! [v42] : ! [v43] : ( ~ epsilon_transitive(v42) | ~ ordinal(v43) | ~ proper_subset(v42, v43) | in(v42, v43)) & ! [v42] : ! [v43] : ( ~ epsilon_transitive(v42) | ~ in(v43, v42) | subset(v43, v42)) & ! [v42] : ! [v43] : ( ~ ordinal(v43) | ~ ordinal(v42) | ordinal_subset(v43, v42) | ordinal_subset(v42, v43)) & ! [v42] : ! [v43] : ( ~ ordinal(v43) | ~ ordinal(v42) | ordinal_subset(v42, v42)) & ! [v42] : ! [v43] : ( ~ ordinal(v43) | ~ in(v43, v42) | ? [v44] : (ordinal(v44) & in(v44, v42) & ! [v45] : ( ~ ordinal(v45) | ~ in(v45, v42) | ordinal_subset(v44, v45)))) & ! [v42] : ! [v43] : ( ~ ordinal(v43) | ~ in(v42, v43) | ordinal(v42)) & ! [v42] : ! [v43] : ( ~ ordinal(v42) | ~ element(v43, v42) | epsilon_connected(v43)) & ! [v42] : ! [v43] : ( ~ ordinal(v42) | ~ element(v43, v42) | epsilon_transitive(v43)) & ! [v42] : ! [v43] : ( ~ ordinal(v42) | ~ element(v43, v42) | ordinal(v43)) & ! [v42] : ! [v43] : ( ~ empty(v43) | ~ empty(v42) | element(v43, v42)) & ! [v42] : ! [v43] : ( ~ empty(v43) | ~ in(v42, v43)) & ! [v42] : ! [v43] : ( ~ empty(v42) | ~ element(v43, v42) | empty(v43)) & ! [v42] : ! [v43] : ( ~ v5_membered(v42) | ~ element(v43, v42) | natural(v43)) & ! [v42] : ! [v43] : ( ~ v5_membered(v42) | ~ element(v43, v42) | v1_int_1(v43)) & ! [v42] : ! [v43] : ( ~ v5_membered(v42) | ~ element(v43, v42) | v1_rat_1(v43)) & ! [v42] : ! [v43] : ( ~ v5_membered(v42) | ~ element(v43, v42) | v1_xreal_0(v43)) & ! [v42] : ! [v43] : ( ~ v5_membered(v42) | ~ element(v43, v42) | v1_xcmplx_0(v43)) & ! [v42] : ! [v43] : ( ~ v4_membered(v42) | ~ element(v43, v42) | v1_int_1(v43)) & ! [v42] : ! [v43] : ( ~ v4_membered(v42) | ~ element(v43, v42) | v1_rat_1(v43)) & ! [v42] : ! [v43] : ( ~ v4_membered(v42) | ~ element(v43, v42) | v1_xreal_0(v43)) & ! [v42] : ! [v43] : ( ~ v4_membered(v42) | ~ element(v43, v42) | v1_xcmplx_0(v43)) & ! [v42] : ! [v43] : ( ~ v3_membered(v42) | ~ element(v43, v42) | v1_rat_1(v43)) & ! [v42] : ! [v43] : ( ~ v3_membered(v42) | ~ element(v43, v42) | v1_xreal_0(v43)) & ! [v42] : ! [v43] : ( ~ v3_membered(v42) | ~ element(v43, v42) | v1_xcmplx_0(v43)) & ! [v42] : ! [v43] : ( ~ v2_membered(v42) | ~ element(v43, v42) | v1_xreal_0(v43)) & ! [v42] : ! [v43] : ( ~ v2_membered(v42) | ~ element(v43, v42) | v1_xcmplx_0(v43)) & ! [v42] : ! [v43] : ( ~ element(v43, v42) | ~ v1_membered(v42) | v1_xcmplx_0(v43)) & ! [v42] : ! [v43] : ( ~ element(v43, v42) | empty(v42) | in(v43, v42)) & ! [v42] : ! [v43] : ( ~ element(v42, v43) | empty(v43) | in(v42, v43)) & ! [v42] : ! [v43] : ( ~ proper_subset(v43, v42) | ~ proper_subset(v42, v43)) & ! [v42] : ! [v43] : ( ~ proper_subset(v42, v43) | subset(v42, v43)) & ! [v42] : ! [v43] : ( ~ in(v43, v42) | ~ in(v42, v43)) & ! [v42] : ! [v43] : ( ~ in(v43, v42) | empty(v42) | element(v43, v42)) & ! [v42] : ! [v43] : ( ~ in(v42, v43) | element(v42, v43)) & ! [v42] : ! [v43] : ( ~ in(v42, v43) | ? [v44] : (in(v44, v43) & ! [v45] : ( ~ in(v45, v44) | ~ in(v45, v43)))) & ? [v42] : ! [v43] : ( ~ relation(v43) | is_well_founded_in(v43, v42) | ? [v44] : ( ~ (v44 = empty_set) & subset(v44, v42) & ! [v45] : ! [v46] : ( ~ (fiber(v43, v45) = v46) | ~ disjoint(v46, v44) | ~ in(v45, v44)))) & ? [v42] : ! [v43] : ( ~ relation(v43) | is_reflexive_in(v43, v42) | ? [v44] : ? [v45] : (ordered_pair(v44, v44) = v45 & in(v44, v42) & ~ in(v45, v43))) & ? [v42] : ! [v43] : ( ~ relation(v43) | is_transitive_in(v43, v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : ? [v49] : (ordered_pair(v45, v46) = v48 & ordered_pair(v44, v46) = v49 & ordered_pair(v44, v45) = v47 & in(v48, v43) & in(v47, v43) & in(v46, v42) & in(v45, v42) & in(v44, v42) & ~ in(v49, v43))) & ? [v42] : ! [v43] : ( ~ relation(v43) | is_connected_in(v43, v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ( ~ (v45 = v44) & ordered_pair(v45, v44) = v47 & ordered_pair(v44, v45) = v46 & in(v45, v42) & in(v44, v42) & ~ in(v47, v43) & ~ in(v46, v43))) & ? [v42] : ! [v43] : ( ~ relation(v43) | is_antisymmetric_in(v43, v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ( ~ (v45 = v44) & ordered_pair(v45, v44) = v47 & ordered_pair(v44, v45) = v46 & in(v47, v43) & in(v46, v43) & in(v45, v42) & in(v44, v42))) & ? [v42] : ! [v43] : ( ~ relation(v43) | empty(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : ((v48 = v44 & v47 = v44 & ~ (v46 = v45) & in(v46, v44) & in(v45, v44) & in(v44, v42) & ! [v49] : ! [v50] : ( ~ (ordered_pair(v46, v49) = v50) | ~ in(v49, v44) | in(v50, v43)) & ! [v49] : ! [v50] : ( ~ (ordered_pair(v45, v49) = v50) | ~ in(v49, v44) | in(v50, v43))) | (v45 = v42 & relation_dom(v44) = v42 & relation(v44) & function(v44) & ! [v49] : ! [v50] : ( ~ (apply(v44, v49) = v50) | ~ in(v49, v42) | (in(v50, v49) & ! [v51] : ! [v52] : ( ~ (ordered_pair(v50, v51) = v52) | ~ in(v51, v49) | in(v52, v43))))) | (in(v44, v42) & ! [v49] : ( ~ in(v49, v44) | ? [v50] : ? [v51] : (ordered_pair(v49, v50) = v51 & in(v50, v44) & ~ in(v51, v43)))))) & ? [v42] : ! [v43] : ( ~ relation(v43) | empty(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : ((v48 = v44 & v47 = v44 & ~ (v46 = v45) & in(v46, v44) & in(v45, v44) & in(v44, v42) & ! [v49] : ! [v50] : ( ~ (ordered_pair(v46, v49) = v50) | ~ in(v49, v44) | in(v50, v43)) & ! [v49] : ! [v50] : ( ~ (ordered_pair(v45, v49) = v50) | ~ in(v49, v44) | in(v50, v43))) | (relation(v44) & function(v44) & ! [v49] : ! [v50] : ! [v51] : ( ~ (ordered_pair(v49, v50) = v51) | ~ in(v51, v44) | in(v49, v42)) & ! [v49] : ! [v50] : ! [v51] : ( ~ (ordered_pair(v49, v50) = v51) | ~ in(v51, v44) | (in(v50, v49) & ! [v52] : ! [v53] : ( ~ (ordered_pair(v50, v52) = v53) | ~ in(v52, v49) | in(v53, v43)))) & ! [v49] : ! [v50] : ! [v51] : ( ~ (ordered_pair(v49, v50) = v51) | ~ in(v50, v49) | ~ in(v49, v42) | in(v51, v44) | ? [v52] : ? [v53] : (ordered_pair(v50, v52) = v53 & in(v52, v49) & ~ in(v53, v43)))))) & ? [v42] : ! [v43] : ( ~ relation(v43) | empty(v42) | ? [v44] : ? [v45] : ? [v46] : ? [v47] : ? [v48] : ((v48 = v44 & v47 = v44 & ~ (v46 = v45) & in(v46, v44) & in(v45, v44) & in(v44, v42) & ! [v49] : ! [v50] : ( ~ (ordered_pair(v46, v49) = v50) | ~ in(v49, v44) | in(v50, v43)) & ! [v49] : ! [v50] : ( ~ (ordered_pair(v45, v49) = v50) | ~ in(v49, v44) | in(v50, v43))) | ( ! [v49] : ! [v50] : ( ~ in(v50, v42) | ~ in(v49, v50) | in(v49, v44) | ? [v51] : ? [v52] : (ordered_pair(v49, v51) = v52 & in(v51, v50) & ~ in(v52, v43))) & ! [v49] : ( ~ in(v49, v44) | ? [v50] : (in(v50, v42) & in(v49, v50) & ! [v51] : ! [v52] : ( ~ (ordered_pair(v49, v51) = v52) | ~ in(v51, v50) | in(v52, v43))))))) & ! [v42] : (v42 = empty_set | ~ (set_meet(empty_set) = v42)) & ! [v42] : (v42 = empty_set | ~ (relation_rng(v42) = empty_set) | ~ relation(v42)) & ! [v42] : (v42 = empty_set | ~ subset(v42, empty_set)) & ! [v42] : (v42 = empty_set | ~ relation(v42) | ? [v43] : ? [v44] : ? [v45] : (ordered_pair(v43, v44) = v45 & in(v45, v42))) & ! [v42] : (v42 = empty_set | ~ empty(v42)) & ! [v42] : (v42 = omega | ~ being_limit_ordinal(v42) | ~ ordinal(v42) | ~ in(empty_set, v42) | ? [v43] : (being_limit_ordinal(v43) & ordinal(v43) & in(empty_set, v43) & ~ subset(v42, v43))) & ! [v42] : ( ~ (union(v42) = v42) | being_limit_ordinal(v42)) & ! [v42] : ~ (singleton(v42) = empty_set) & ! [v42] : ( ~ latt_str(v42) | meet_semilatt_str(v42)) & ! [v42] : ( ~ latt_str(v42) | join_semilatt_str(v42)) & ! [v42] : ( ~ being_limit_ordinal(v42) | ~ ordinal(v42) | ~ in(empty_set, v42) | subset(omega, v42)) & ! [v42] : ( ~ reflexive(v42) | ~ well_founded_relation(v42) | ~ transitive(v42) | ~ connected(v42) | ~ antisymmetric(v42) | ~ relation(v42) | well_ordering(v42)) & ! [v42] : ( ~ well_ordering(v42) | ~ relation(v42) | reflexive(v42)) & ! [v42] : ( ~ well_ordering(v42) | ~ relation(v42) | well_founded_relation(v42)) & ! [v42] : ( ~ well_ordering(v42) | ~ relation(v42) | transitive(v42)) & ! [v42] : ( ~ well_ordering(v42) | ~ relation(v42) | connected(v42)) & ! [v42] : ( ~ well_ordering(v42) | ~ relation(v42) | antisymmetric(v42)) & ! [v42] : ( ~ top_str(v42) | one_sorted_str(v42)) & ! [v42] : ( ~ meet_semilatt_str(v42) | one_sorted_str(v42)) & ! [v42] : ( ~ join_semilatt_str(v42) | one_sorted_str(v42)) & ! [v42] : ( ~ relation(v42) | ~ function(v42) | ~ empty(v42) | one_to_one(v42)) & ! [v42] : ( ~ relation(v42) | transitive(v42) | ? [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(v48, v42))) & ! [v42] : ( ~ relation(v42) | antisymmetric(v42) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ( ~ (v44 = v43) & ordered_pair(v44, v43) = v46 & ordered_pair(v43, v44) = v45 & in(v46, v42) & in(v45, v42))) & ! [v42] : ( ~ diff_closed(v42) | ~ cup_closed(v42) | preboolean(v42)) & ! [v42] : ( ~ preboolean(v42) | diff_closed(v42)) & ! [v42] : ( ~ preboolean(v42) | cup_closed(v42)) & ! [v42] : ( ~ finite(v42) | ? [v43] : ? [v44] : (relation_rng(v43) = v42 & relation_dom(v43) = v44 & relation(v43) & function(v43) & in(v44, omega))) & ! [v42] : ( ~ epsilon_connected(v42) | ~ epsilon_transitive(v42) | ordinal(v42)) & ! [v42] : ( ~ ordinal(v42) | ~ empty(v42) | epsilon_connected(v42)) & ! [v42] : ( ~ ordinal(v42) | ~ empty(v42) | epsilon_transitive(v42)) & ! [v42] : ( ~ ordinal(v42) | ~ empty(v42) | natural(v42)) & ! [v42] : ( ~ ordinal(v42) | being_limit_ordinal(v42) | ? [v43] : ? [v44] : (succ(v43) = v44 & ordinal(v43) & in(v43, v42) & ~ in(v44, v42))) & ! [v42] : ( ~ ordinal(v42) | being_limit_ordinal(v42) | ? [v43] : (succ(v43) = v42 & ordinal(v43))) & ! [v42] : ( ~ ordinal(v42) | epsilon_connected(v42)) & ! [v42] : ( ~ ordinal(v42) | epsilon_transitive(v42)) & ! [v42] : ( ~ empty(v42) | relation(v42)) & ! [v42] : ( ~ empty(v42) | function(v42)) & ! [v42] : ( ~ empty(v42) | finite(v42)) & ! [v42] : ( ~ empty(v42) | epsilon_connected(v42)) & ! [v42] : ( ~ empty(v42) | epsilon_transitive(v42)) & ! [v42] : ( ~ empty(v42) | ordinal(v42)) & ! [v42] : ( ~ empty(v42) | v5_membered(v42)) & ! [v42] : ( ~ empty(v42) | v4_membered(v42)) & ! [v42] : ( ~ empty(v42) | v3_membered(v42)) & ! [v42] : ( ~ empty(v42) | v2_membered(v42)) & ! [v42] : ( ~ empty(v42) | v1_membered(v42)) & ! [v42] : ( ~ v5_membered(v42) | v4_membered(v42)) & ! [v42] : ( ~ v4_membered(v42) | v3_membered(v42)) & ! [v42] : ( ~ v3_membered(v42) | v2_membered(v42)) & ! [v42] : ( ~ v2_membered(v42) | v1_membered(v42)) & ! [v42] : ( ~ element(v42, omega) | epsilon_connected(v42)) & ! [v42] : ( ~ element(v42, omega) | epsilon_transitive(v42)) & ! [v42] : ( ~ element(v42, omega) | ordinal(v42)) & ! [v42] : ( ~ element(v42, omega) | natural(v42)) & ! [v42] : ~ proper_subset(v42, v42) & ! [v42] : ~ in(v42, empty_set) & ? [v42] : ? [v43] : ? [v44] : relation_of2(v44, v42, v43) & ? [v42] : ? [v43] : ? [v44] : relation_of2_as_subset(v44, v42, v43) & ? [v42] : ? [v43] : ? [v44] : (relation_of2(v44, v42, v43) & quasi_total(v44, v42, v43) & relation(v44) & function(v44)) & ? [v42] : ? [v43] : ? [v44] : (relation_of2(v44, v42, v43) & relation(v44) & function(v44)) & ? [v42] : ? [v43] : (v43 = v42 | ? [v44] : (( ~ in(v44, v43) | ~ in(v44, v42)) & (in(v44, v43) | in(v44, v42)))) & ? [v42] : ? [v43] : (disjoint(v42, v43) | ? [v44] : (in(v44, v43) & in(v44, v42))) & ? [v42] : ? [v43] : (subset(v42, v43) | ? [v44] : (in(v44, v42) & ~ in(v44, v43))) & ? [v42] : ? [v43] : element(v43, v42) & ? [v42] : ? [v43] : (relation_dom(v43) = v42 & relation(v43) & function(v43) & ! [v44] : ! [v45] : ( ~ (singleton(v44) = v45) | ~ in(v44, v42) | apply(v43, v44) = v45)) & ? [v42] : ? [v43] : (well_orders(v43, v42) & relation(v43)) & ? [v42] : ? [v43] : (relation(v43) & function(v43) & ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v44, v45) = v46) | ~ in(v46, v43) | singleton(v44) = v45) & ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v44, v45) = v46) | ~ in(v46, v43) | in(v44, v42)) & ! [v44] : ! [v45] : ! [v46] : ( ~ (ordered_pair(v44, v45) = v46) | ~ in(v44, v42) | in(v46, v43) | ? [v47] : ( ~ (v47 = v45) & singleton(v44) = v47))) & ? [v42] : ? [v43] : (in(v42, v43) & ! [v44] : ! [v45] : ( ~ (powerset(v44) = v45) | ~ in(v44, v43) | in(v45, v43)) & ! [v44] : ! [v45] : ( ~ subset(v45, v44) | ~ in(v44, v43) | in(v45, v43)) & ! [v44] : ( ~ subset(v44, v43) | are_equipotent(v44, v43) | in(v44, v43))) & ? [v42] : ? [v43] : (in(v42, v43) & ! [v44] : ! [v45] : ( ~ subset(v45, v44) | ~ in(v44, v43) | in(v45, v43)) & ! [v44] : ( ~ subset(v44, v43) | are_equipotent(v44, v43) | in(v44, v43)) & ! [v44] : ( ~ in(v44, v43) | ? [v45] : (in(v45, v43) & ! [v46] : ( ~ subset(v46, v44) | in(v46, v45))))) & ? [v42] : ? [v43] : ( ! [v44] : ! [v45] : ( ~ (singleton(v45) = v44) | ~ in(v45, v42) | in(v44, v43)) & ! [v44] : ( ~ in(v44, v43) | ? [v45] : (singleton(v45) = v44 & in(v45, v42)))) & ? [v42] : ? [v43] : ( ! [v44] : ( ~ ordinal(v44) | ~ in(v44, v42) | in(v44, v43)) & ! [v44] : ( ~ in(v44, v43) | ordinal(v44)) & ! [v44] : ( ~ in(v44, v43) | in(v44, v42))) & ? [v42] : (v42 = empty_set | ? [v43] : in(v43, v42)) & ? [v42] : equipotent(v42, v42) & ? [v42] : subset(v42, v42) & ? [v42] : subset(empty_set, v42) & ? [v42] : (relation(v42) | ? [v43] : (in(v43, v42) & ! [v44] : ! [v45] : ~ (ordered_pair(v44, v45) = v43))) & ? [v42] : (function(v42) | ? [v43] : ? [v44] : ? [v45] : ? [v46] : ? [v47] : ( ~ (v45 = v44) & ordered_pair(v43, v45) = v47 & ordered_pair(v43, v44) = v46 & in(v47, v42) & in(v46, v42))) & ? [v42] : (epsilon_connected(v42) | ? [v43] : ? [v44] : ( ~ (v44 = v43) & in(v44, v42) & in(v43, v42) & ~ in(v44, v43) & ~ in(v43, v44))) & ? [v42] : (epsilon_transitive(v42) | ? [v43] : (in(v43, v42) & ~ subset(v43, v42))) & ? [v42] : (ordinal(v42) | ? [v43] : (in(v43, v42) & ( ~ subset(v43, v42) | ~ ordinal(v43)))) & ? [v42] : (empty(v42) | ? [v43] : ? [v44] : ((v44 = v42 & relation_dom(v43) = v42 & relation(v43) & function(v43) & ! [v45] : ! [v46] : ( ~ (apply(v43, v45) = v46) | ~ in(v45, v42) | in(v46, v45))) | (v43 = empty_set & in(empty_set, v42)))) & ( ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ~ ordinal(v42) | ~ in(v42, omega) | ? [v44] : (powerset(v43) = v44 & ! [v45] : (v45 = empty_set | ~ element(v45, v44) | ? [v46] : (in(v46, v45) & ! [v47] : (v47 = v46 | ~ subset(v46, v47) | ~ in(v47, v45)))))) | ( ~ (v18 = empty_set) & succ(v12) = v15 & powerset(v16) = v17 & powerset(v15) = v16 & ordinal(v12) & element(v18, v17) & in(v15, omega) & ! [v42] : ( ~ in(v42, v18) | ? [v43] : ( ~ (v43 = v42) & subset(v42, v43) & in(v43, v18))) & ( ~ in(v12, omega) | (powerset(v13) = v14 & powerset(v12) = v13 & ! [v42] : (v42 = empty_set | ~ element(v42, v14) | ? [v43] : (in(v43, v42) & ! [v44] : (v44 = v43 | ~ subset(v43, v44) | ~ in(v44, v42))))))) | ( ~ (v15 = empty_set) & ~ (v12 = empty_set) & powerset(v13) = v14 & powerset(v12) = v13 & being_limit_ordinal(v12) & ordinal(v12) & element(v15, v14) & in(v12, omega) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ~ ordinal(v42) | ~ in(v42, v12) | ~ in(v42, omega) | ? [v44] : (powerset(v43) = v44 & ! [v45] : (v45 = empty_set | ~ element(v45, v44) | ? [v46] : (in(v46, v45) & ! [v47] : (v47 = v46 | ~ subset(v46, v47) | ~ in(v47, v45)))))) & ! [v42] : ( ~ in(v42, v15) | ? [v43] : ( ~ (v43 = v42) & subset(v42, v43) & in(v43, v15)))) | ( ~ (v12 = empty_set) & powerset(v0) = v1 & element(v12, v1) & ! [v42] : ( ~ in(v42, v12) | ? [v43] : ( ~ (v43 = v42) & subset(v42, v43) & in(v43, v12))))) & ( ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ~ ordinal(v42) | ~ in(v42, omega) | ? [v44] : (powerset(v43) = v44 & ! [v45] : (v45 = empty_set | ~ element(v45, v44) | ? [v46] : (in(v46, v45) & ! [v47] : (v47 = v46 | ~ subset(v46, v47) | ~ in(v47, v45)))))) | ( ~ (v11 = empty_set) & powerset(v9) = v10 & powerset(v8) = v9 & ordinal(v8) & element(v11, v10) & in(v8, omega) & ! [v42] : ! [v43] : ( ~ (powerset(v42) = v43) | ~ ordinal(v42) | ~ in(v42, v8) | ~ in(v42, omega) | ? [v44] : (powerset(v43) = v44 & ! [v45] : (v45 = empty_set | ~ element(v45, v44) | ? [v46] : (in(v46, v45) & ! [v47] : (v47 = v46 | ~ subset(v46, v47) | ~ in(v47, v45)))))) & ! [v42] : ( ~ in(v42, v11) | ? [v43] : ( ~ (v43 = v42) & subset(v42, v43) & in(v43, v11))))) & ((in(v7, v6) & in(v7, v5)) | ( ~ in(v7, v6) & ~ in(v7, v5)))) % 88.25/26.79 | 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, all_0_41_41 yields: % 88.25/26.79 | (1) subset_complement(all_0_38_38, all_0_36_36) = all_0_35_35 & singleton(empty_set) = all_0_41_41 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & the_carrier(all_0_39_39) = all_0_38_38 & powerset(all_0_38_38) = all_0_37_37 & powerset(empty_set) = all_0_41_41 & relation_empty_yielding(all_0_20_20) & relation_empty_yielding(all_0_22_22) & relation_empty_yielding(empty_set) & latt_str(all_0_4_4) & being_limit_ordinal(all_0_10_10) & being_limit_ordinal(omega) & one_sorted_str(all_0_2_2) & one_sorted_str(all_0_21_21) & one_sorted_str(all_0_39_39) & top_str(all_0_1_1) & meet_semilatt_str(all_0_0_0) & join_semilatt_str(all_0_3_3) & one_to_one(all_0_11_11) & one_to_one(all_0_15_15) & one_to_one(all_0_18_18) & one_to_one(empty_set) & relation(all_0_7_7) & relation(all_0_11_11) & relation(all_0_12_12) & relation(all_0_14_14) & relation(all_0_15_15) & relation(all_0_16_16) & relation(all_0_18_18) & relation(all_0_20_20) & relation(all_0_22_22) & relation(empty_set) & function(all_0_7_7) & function(all_0_11_11) & function(all_0_14_14) & function(all_0_15_15) & function(all_0_18_18) & function(all_0_22_22) & function(empty_set) & finite(all_0_6_6) & epsilon_connected(all_0_5_5) & epsilon_connected(all_0_9_9) & epsilon_connected(all_0_10_10) & epsilon_connected(all_0_15_15) & epsilon_connected(all_0_19_19) & epsilon_connected(empty_set) & epsilon_connected(omega) & epsilon_transitive(all_0_5_5) & epsilon_transitive(all_0_9_9) & epsilon_transitive(all_0_10_10) & epsilon_transitive(all_0_15_15) & epsilon_transitive(all_0_19_19) & epsilon_transitive(empty_set) & epsilon_transitive(omega) & ordinal(all_0_5_5) & ordinal(all_0_9_9) & ordinal(all_0_10_10) & ordinal(all_0_15_15) & ordinal(all_0_19_19) & ordinal(empty_set) & ordinal(omega) & empty(all_0_11_11) & empty(all_0_12_12) & empty(all_0_13_13) & empty(all_0_14_14) & empty(all_0_15_15) & empty(empty_set) & natural(all_0_5_5) & v5_membered(all_0_8_8) & v5_membered(empty_set) & v4_membered(all_0_8_8) & v4_membered(empty_set) & v3_membered(all_0_8_8) & v3_membered(empty_set) & v2_membered(all_0_8_8) & v2_membered(empty_set) & element(all_0_34_34, all_0_38_38) & element(all_0_36_36, all_0_37_37) & v1_membered(all_0_8_8) & v1_membered(empty_set) & in(empty_set, omega) & ~ empty_carrier(all_0_21_21) & ~ empty_carrier(all_0_39_39) & ~ empty(all_0_5_5) & ~ empty(all_0_6_6) & ~ empty(all_0_8_8) & ~ empty(all_0_16_16) & ~ empty(all_0_17_17) & ~ empty(all_0_19_19) & ~ 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(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] : ( ~ (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] : ((v7 = v6 & apply_binary(v3, v4, v5) = v6) | (cartesian_product2(v0, v1) = v7 & ( ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2))))) & ! [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] : (( ~ (v5 = v3) | ~ one_to_one(v4) | relation_isomorphism(v0, v2, v4) | ( ~ (v6 = v1) & relation_dom(v4) = v6) | (( ~ in(v8, v1) | ~ in(v7, v1) | (apply(v4, v8) = v11 & apply(v4, v7) = v10 & ordered_pair(v10, v11) = v12 & ~ in(v12, v2)) | (ordered_pair(v7, v8) = v9 & ~ in(v9, v0))) & ((apply(v4, v8) = v11 & apply(v4, v7) = v10 & ordered_pair(v10, v11) = v12 & in(v12, v2) & in(v8, v1) & in(v7, v1)) | (ordered_pair(v7, v8) = v9 & in(v9, v0))))) & ( ~ relation_isomorphism(v0, v2, v4) | (v6 = v1 & v5 = v3 & relation_dom(v4) = 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))))))) & ! [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_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] : (( ~ (v5 = v2) | (v6 = v1 & relation_dom_restriction(v3, v0) = v1) | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ((v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11)) | ( ~ (v6 = v1) & relation_dom_restriction(v3, v0) = v6)))) & ! [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(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(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(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 | ~ (relation_rng_as_subset(v4, v3, v2) = v1) | ~ (relation_rng_as_subset(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 | ~ (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 | ~ (meet_of_subsets(v0, v1) = v3) | ~ (subset_difference(v0, v2, v3) = v4) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ((v6 = v4 & complements_of_subsets(v0, v1) = v5 & union_of_subsets(v0, v5) = v4) | (powerset(v5) = v6 & powerset(v0) = v5 & ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (cast_to_subset(v0) = v2) | ~ (union_of_subsets(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & meet_of_subsets(v0, v5) = v4 & complements_of_subsets(v0, v1) = v5) | (powerset(v5) = v6 & powerset(v0) = v5 & ~ 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] : ((v6 = v0 & v4 = v0 & apply(v2, v0) = v5 & apply(v1, v5) = v0) | (relation_rng(v1) = v5 & ~ in(v0, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ((v6 = v4 & apply(v2, v0) = v5 & apply(v1, v5) = v4) | (relation_dom(v3) = v5 & ~ in(v0, v5)))) & ! [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] : ( ~ (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_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(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] : (( ~ in(v4, v0) | (v5 = v3 & apply(v0, v2) = v3)) & (in(v4, v0) | ( ~ (v5 = v3) & apply(v0, v2) = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (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] : ((v5 = v4 & apply(v2, v1) = v4) | (relation_dom(v3) = v5 & ~ in(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (( ~ (v4 = v1) | in(v3, v2) | (relation_dom(v2) = v5 & ~ in(v0, v5))) & ( ~ in(v3, v2) | (v4 = v1 & relation_dom(v2) = v5 & in(v0, v5))))) & ! [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] : ( ~ (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] : (( ~ in(v5, v2) | ~ in(v5, v0) | (apply(v1, v5) = v6 & ~ in(v6, v3))) & (in(v5, v0) | (apply(v1, v5) = v6 & 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 & in(v0, v5)) | (relation_dom(v3) = v6 & ~ in(v0, v6)) | (apply(v3, v0) = v7 & ~ in(v7, v2))) & ((relation_dom(v4) = v5 & ~ in(v0, v5)) | (relation_dom(v3) = v6 & apply(v3, v0) = v7 & in(v7, v2) & in(v0, v6))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (powerset(v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : ((powerset(v4) = v5 & ! [v7] : ! [v8] : ( ~ (relation_image(v2, v7) = v8) | ~ in(v8, v0) | ~ in(v7, v5) | in(v7, v6)) & ! [v7] : ! [v8] : ( ~ (relation_image(v2, v7) = v8) | ~ in(v7, v6) | in(v8, v0)) & ! [v7] : ! [v8] : ( ~ (relation_image(v2, v7) = v8) | ~ in(v7, v6) | in(v7, v5))) | (powerset(v3) = v5 & ~ element(v0, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))) | (ordered_pair(v4, v5) = v6 & ~ in(v6, v3))) & ((ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0)) | (ordered_pair(v4, v5) = v6 & in(v6, v3))))) & ! [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(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 | ~ (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 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(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 | ~ (topstr_closure(v3, v2) = v1) | ~ (topstr_closure(v3, v2) = v0)) & ! [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 | ~ 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] : ( ~ (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_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_dom(v3) = v4 & subset(v4, v1))) & ! [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] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ((v4 = v3 & set_difference(v1, v2) = v3) | (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4))))) & ! [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(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) & ! [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] : ((v4 = v3 & meet_of_subsets(v0, v1) = v3) | (powerset(v2) = v4 & ~ 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) | 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(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, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ((v4 = v3 & subset_intersection2(v0, v2, v1) = v3) | (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ((v4 = v3 & set_intersection2(v1, v2) = v3) | (powerset(v0) = v4 & ( ~ 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] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ((v4 = v3 & meet(v0, v1, v2) = v3) | (the_carrier(v0) = v4 & ( ~ 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] : ((v4 = v3 & meet_commut(v0, v2, v1) = v3) | (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, 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, 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] : ( ~ (join_commut(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ((v4 = v3 & join(v0, v1, v2) = v3) | (the_carrier(v0) = v4 & ( ~ 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] : ((v4 = v3 & join_commut(v0, v2, v1) = v3) | (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, 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] : ( ~ 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] : ((v4 = v2 | ~ in(v4, v0) | (ordered_pair(v4, v2) = v5 & ~ in(v5, v1))) & (in(v4, v0) | ( ~ (v4 = v2) & ordered_pair(v4, v2) = v5 & 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_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : (( ~ in(v0, v3) | (cartesian_product2(v1, v1) = v4 & in(v0, v4) & in(v0, v2))) & ( ~ in(v0, v2) | in(v0, v3) | (cartesian_product2(v1, v1) = v4 & ~ in(v0, v4))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ((relation_field(v3) = v4 & ~ in(v0, v4)) | (relation_field(v2) = v4 & in(v0, v4) & in(v0, v1)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v0, v3) | (relation_rng(v2) = v4 & ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | (relation_rng(v2) = v4 & ! [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] : (( ~ in(v0, v1) | (relation_rng(v3) = v4 & in(v0, v4)) | (relation_rng(v2) = v5 & ~ in(v0, v5))) & ((relation_rng(v3) = v4 & ~ in(v0, v4)) | (relation_rng(v2) = v5 & in(v0, v5) & in(v0, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v0, v3) | (relation_dom(v2) = v4 & ordered_pair(v5, v0) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | (relation_dom(v2) = v4 & ! [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] : (( ~ in(v0, v1) | (relation_dom(v3) = v4 & in(v0, v4)) | (relation_dom(v2) = v5 & ~ in(v0, v5))) & ((relation_dom(v3) = v4 & ~ in(v0, v4)) | (relation_dom(v2) = v5 & in(v0, v5) & in(v0, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (( ~ in(v0, v1) | (relation_dom(v3) = v4 & in(v0, v4)) | (relation_dom(v2) = v5 & ~ in(v0, v5))) & ((relation_dom(v3) = v4 & ~ in(v0, v4)) | (relation_dom(v2) = v5 & 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 & in(v6, v0)) | (ordered_pair(v3, v4) = v5 & in(v5, v2))) & ((ordered_pair(v4, v3) = v6 & ~ in(v6, v0)) | (ordered_pair(v3, v4) = v5 & ~ in(v5, v2))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (in(v4, v0) & in(v3, v0) & ( ~ subset(v3, v4) | (ordered_pair(v3, v4) = v5 & ~ in(v5, v1))) & (subset(v3, v4) | (ordered_pair(v3, v4) = v5 & 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] : (( ~ (v4 = v3) | ~ in(v3, v0) | (ordered_pair(v3, v3) = v5 & ~ in(v5, v1))) & ((v4 = v3 & in(v3, v0)) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ! [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 | ~ (empty_carrier_subset(v2) = v1) | ~ (empty_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 | ~ (the_topology(v2) = v1) | ~ (the_topology(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] : (powerset(v0) = v3 & (element(v2, v3) | (powerset(v3) = v4 & ~ element(v1, v4))))) & ! [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] : (element(v6, v3) & ( ~ in(v6, v5) | (subset_complement(v0, v6) = v7 & ~ in(v7, v1))) & (in(v6, v5) | (subset_complement(v0, v6) = v7 & in(v7, v1))))))))) & ! [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] : ((v3 = v0 & relation_field(v2) = v0) | (relation_field(v1) = v3 & ~ 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(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ((v3 = v2 & set_difference(v0, v1) = v2) | (powerset(v0) = v3 & ~ element(v1, 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) | ~ v5_membered(v0) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) & ! [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] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v0) = v3 & (element(v2, v3) | (powerset(v3) = v4 & ~ element(v1, v4))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = v2 & union(v1) = v2) | (powerset(v3) = v4 & powerset(v0) = v3 & ~ element(v1, v4)))) & ! [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(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (topstr_closure(v0, v1) = v2) | ~ top_str(v0) | ? [v3] : ? [v4] : (the_carrier(v0) = v3 & powerset(v3) = v4 & ( ~ element(v1, v4) | element(v2, v4)))) & ! [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 & 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] : (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))) & ! [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(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] : ( ~ (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(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] : ( ~ (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(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] : ( ~ (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] : ( ~ 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] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ 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] : ( ~ (cast_as_carrier_subset(v1) = v2) | ~ topological_space(v1) | ~ top_str(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (the_carrier(v1) = v3 & powerset(v4) = v5 & powerset(v3) = v4 & ( ~ element(v0, v5) | (element(v6, v5) & ! [v7] : ! [v8] : ( ~ (set_difference(v2, v7) = v8) | ~ element(v7, v4) | ~ in(v8, v0) | in(v7, v6)) & ! [v7] : ! [v8] : ( ~ (set_difference(v2, v7) = v8) | ~ element(v7, v4) | ~ in(v7, v6) | in(v8, v0)))))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (cast_as_carrier_subset(v1) = v2) | ~ topological_space(v1) | ~ top_str(v1) | ? [v3] : ? [v4] : ? [v5] : (the_carrier(v1) = v3 & powerset(v3) = v4 & ((powerset(v4) = v5 & ~ element(v0, v5)) | ( ! [v6] : ! [v7] : ( ~ (set_difference(v2, v6) = v7) | ~ in(v7, v0) | ~ in(v6, v4) | in(v6, v5)) & ! [v6] : ! [v7] : ( ~ (set_difference(v2, v6) = v7) | ~ in(v6, v5) | in(v7, v0)) & ! [v6] : ! [v7] : ( ~ (set_difference(v2, v6) = v7) | ~ in(v6, v5) | in(v6, v4)))))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) & ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ((singleton(v1) = v4 & powerset(v1) = v3 & ! [v6] : ! [v7] : ( ~ (set_difference(v7, v4) = v6) | ~ in(v7, v0) | ~ in(v6, v3) | in(v6, v5)) & ! [v6] : ( ~ in(v6, v5) | in(v6, v3)) & ! [v6] : ( ~ in(v6, v5) | ? [v7] : (set_difference(v7, v4) = v6 & in(v7, v0)))) | (powerset(v3) = v4 & powerset(v2) = v3 & ~ element(v0, v4)))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ((singleton(v1) = v3 & powerset(v1) = v4 & ! [v6] : ! [v7] : ( ~ (set_difference(v7, v3) = v6) | ~ in(v7, v0) | ~ in(v6, v4) | in(v6, v5)) & ! [v6] : ( ~ in(v6, v5) | in(v6, v4)) & ! [v6] : ( ~ in(v6, v5) | ? [v7] : (set_difference(v7, v3) = v6 & in(v7, v0)))) | (powerset(v3) = v4 & powerset(v2) = v3 & ~ element(v0, v4)))) & ? [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] : ( ~ (the_carrier(v1) = v2) | ~ topological_space(v1) | ~ top_str(v1) | ? [v3] : ? [v4] : ? [v5] : (powerset(v2) = v3 & ( ~ element(v0, v3) | (powerset(v3) = v4 & element(v5, v4) & ! [v6] : ( ~ closed_subset(v6, v1) | ~ subset(v0, v6) | ~ element(v6, v3) | in(v6, v5)) & ! [v6] : ( ~ element(v6, v3) | ~ in(v6, v5) | closed_subset(v6, v1)) & ! [v6] : ( ~ element(v6, v3) | ~ in(v6, v5) | subset(v0, v6)))))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v1) = v2) | ~ topological_space(v1) | ~ top_str(v1) | ? [v3] : ? [v4] : (powerset(v2) = v3 & ( ~ element(v0, v3) | ( ! [v5] : ( ~ closed_subset(v5, v1) | ~ subset(v0, v5) | ~ element(v5, v3) | ~ in(v5, v3) | in(v5, v4)) & ! [v5] : ( ~ in(v5, v4) | subset(v0, v5)) & ! [v5] : ( ~ in(v5, v4) | in(v5, v3)) & ! [v5] : ( ~ in(v5, v4) | (closed_subset(v5, v1) & element(v5, v3))))))) & ? [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))))) & ! [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 | ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0)) & ! [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 | ~ 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] : ((v8 = v5 & apply(v0, v6) = v5 & in(v6, v3) & ( ~ in(v5, v2) | ( ~ (v7 = v6) & apply(v4, v5) = v7))) | (v7 = v6 & apply(v4, v5) = v6 & in(v5, v2) & ( ~ in(v6, v3) | ( ~ (v8 = v5) & apply(v0, v6) = v8))))))) & ! [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) | 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] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | ~ (subset_difference(v2, v1, v5) = v6) | ~ (subset_difference(v2, v1, v4) = v5) | ~ element(v4, v3)))) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : (v5 = v4 | ~ (subset_intersection2(v2, v4, v1) = v5) | ~ element(v4, v3)))) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ element(v4, v3) | subset_complement(v2, v4) = v5))) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ topological_space(v0) | ~ top_str(v0) | closed_subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ closed_subset(v4, v0) | ~ element(v4, v3) | open_subset(v5, v0)) & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ open_subset(v5, v0) | ~ element(v4, v3) | closed_subset(v4, v0)))) & ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v5_membered(v1)) & ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v4_membered(v1)) & ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v3_membered(v1)) & ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v2_membered(v1)) & ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v1_membered(v1)) & ! [v0] : ! [v1] : ( ~ (empty_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] : ( ~ (apply_binary_as_element(v2, v2, v2, v1, v3, v4) = v5) | ~ element(v4, v2) | ~ element(v3, v2) | meet(v0, v3, v4) = v5))) & ! [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] : ( ~ (the_topology(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ topological_space(v0) | (the_carrier(v0) = v2 & powerset(v3) = v4 & powerset(v2) = v3 & in(v2, v1) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset_intersection2(v2, v8, v9) = v10) | ~ element(v9, v3) | ~ element(v8, v3) | ~ in(v9, v1) | ~ in(v8, v1) | in(v10, v1)) & ! [v8] : ! [v9] : ( ~ (union_of_subsets(v2, v8) = v9) | ~ subset(v8, v1) | ~ element(v8, v4) | in(v9, v1)))) & (topological_space(v0) | (the_carrier(v0) = v2 & ( ~ in(v2, v1) | (union_of_subsets(v2, v5) = v6 & powerset(v3) = v4 & powerset(v2) = v3 & subset(v5, v1) & element(v5, v4) & ~ in(v6, v1)) | (subset_intersection2(v2, v5, v6) = v7 & powerset(v2) = v3 & element(v6, v3) & element(v5, v3) & in(v6, v1) & in(v5, v1) & ~ in(v7, v1))))))) & ! [v0] : ! [v1] : ( ~ (the_topology(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : ? [v4] : (the_carrier(v0) = v2 & powerset(v3) = v4 & powerset(v2) = v3 & element(v1, v4))) & ! [v0] : ! [v1] : ( ~ (the_topology(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ( ~ open_subset(v4, v0) | ~ element(v4, v3) | in(v4, v1)) & ! [v4] : ( ~ element(v4, v3) | ~ in(v4, v1) | open_subset(v4, v0)))) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(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] : (ordinal(v3) & ( ~ in(v3, omega) | (powerset(v4) = v5 & powerset(v3) = v4 & ! [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] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [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] : ( ~ (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) | ~ 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] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ((v5 = v1 & relation_rng(v4) = v1) | (relation_rng(v3) = v5 & ~ subset(v2, v5)))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ((v5 = v2 & relation_dom(v4) = v2) | (relation_dom(v3) = v5 & ~ subset(v1, v5)))))) & ! [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))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (( ~ (v1 = empty_set) | (v2 = empty_set & relation_dom(v0) = empty_set)) & (v1 = empty_set | ( ~ (v2 = empty_set) & relation_dom(v0) = v2)))) & ! [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_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) | ~ empty(v1) | empty(v0)) & ! [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) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ topological_space(v0) | ~ top_str(v0) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : ( ~ (meet_of_subsets(v1, v4) = v5) | ~ element(v4, v3) | closed_subset(v5, v0) | ? [v6] : (element(v6, v2) & in(v6, v4) & ~ closed_subset(v6, v0))))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ topological_space(v0) | ~ top_str(v0) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : ( ~ (topstr_closure(v0, v4) = v5) | ~ element(v4, v2) | ? [v6] : (meet_of_subsets(v1, v6) = v5 & element(v6, v3) & ! [v7] : ( ~ closed_subset(v7, v0) | ~ subset(v4, v7) | ~ element(v7, v2) | in(v7, v6)) & ! [v7] : ( ~ element(v7, v2) | ~ in(v7, v6) | closed_subset(v7, v0)) & ! [v7] : ( ~ element(v7, v2) | ~ in(v7, v6) | subset(v4, v7)))))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ topological_space(v0) | ~ top_str(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & element(v3, v2))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (topstr_closure(v0, v3) = v4) | ~ closed_subset(v6, v0) | ~ subset(v3, v6) | ~ element(v6, v2) | ~ element(v3, v2) | ~ in(v5, v4) | ~ in(v5, v1) | in(v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (topstr_closure(v0, v3) = v4) | ~ element(v3, v2) | ~ in(v5, v1) | in(v5, v4) | ? [v6] : (closed_subset(v6, v0) & subset(v3, v6) & element(v6, v2) & ~ in(v5, v6))))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (topstr_closure(v0, v3) = v4) | ~ disjoint(v3, v6) | ~ open_subset(v6, v0) | ~ element(v6, v2) | ~ element(v4, v2) | ~ element(v3, v2) | ~ in(v5, v6) | ~ in(v5, v4) | ~ in(v5, v1)) & ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (topstr_closure(v0, v3) = v4) | ~ element(v5, v2) | ~ element(v3, v2) | ? [v6] : ? [v7] : (in(v6, v1) & ( ~ in(v6, v5) | (disjoint(v3, v7) & open_subset(v7, v0) & element(v7, v2) & in(v6, v7))) & (in(v6, v5) | ! [v8] : ( ~ disjoint(v3, v8) | ~ open_subset(v8, v0) | ~ element(v8, v2) | ~ in(v6, v8))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (topstr_closure(v0, v3) = v4) | ~ element(v4, v2) | ~ element(v3, v2) | ~ in(v5, v1) | in(v5, v4) | ? [v6] : (disjoint(v3, v6) & open_subset(v6, v0) & element(v6, v2) & in(v5, v6))))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : (v4 = v3 | ~ (topstr_closure(v0, v3) = v4) | ~ closed_subset(v3, v0) | ~ element(v3, v2)) & ! [v3] : ( ~ (topstr_closure(v0, v3) = v3) | ~ topological_space(v0) | ~ element(v3, v2) | closed_subset(v3, v0)))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ~ closed_subset(v4, v0) | ~ element(v3, v2) | open_subset(v3, v0)) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ~ open_subset(v3, v0) | ~ element(v3, v2) | closed_subset(v4, v0)))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ~ closed_subset(v3, v0) | ~ element(v3, v2) | open_subset(v4, v0)) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ~ open_subset(v4, v0) | ~ element(v3, v2) | closed_subset(v3, v0)))) & ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (topstr_closure(v0, v3) = v4) | ~ element(v3, v2) | subset(v3, v4)))) & ! [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] : (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 | ~ 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] : ( ~ top_str(v0) | one_sorted_str(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)) & ? [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_23_23 = empty_set) & succ(all_0_29_29) = all_0_26_26 & powerset(all_0_25_25) = all_0_24_24 & powerset(all_0_26_26) = all_0_25_25 & ordinal(all_0_29_29) & element(all_0_23_23, all_0_24_24) & in(all_0_26_26, omega) & ! [v0] : ( ~ in(v0, all_0_23_23) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_23_23))) & ( ~ in(all_0_29_29, omega) | (powerset(all_0_28_28) = all_0_27_27 & powerset(all_0_29_29) = all_0_28_28 & ! [v0] : (v0 = empty_set | ~ element(v0, all_0_27_27) | ? [v1] : (in(v1, v0) & ! [v2] : (v2 = v1 | ~ subset(v1, v2) | ~ in(v2, v0))))))) | ( ~ (all_0_26_26 = empty_set) & ~ (all_0_29_29 = empty_set) & powerset(all_0_28_28) = all_0_27_27 & powerset(all_0_29_29) = all_0_28_28 & being_limit_ordinal(all_0_29_29) & ordinal(all_0_29_29) & element(all_0_26_26, all_0_27_27) & in(all_0_29_29, omega) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, all_0_29_29) | ~ 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_26_26) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_26_26)))) | ( ~ (all_0_29_29 = empty_set) & powerset(all_0_41_41) = all_0_40_40 & element(all_0_29_29, all_0_40_40) & ! [v0] : ( ~ in(v0, all_0_29_29) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_29_29))))) & ( ! [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_30_30 = empty_set) & powerset(all_0_32_32) = all_0_31_31 & powerset(all_0_33_33) = all_0_32_32 & ordinal(all_0_33_33) & element(all_0_30_30, all_0_31_31) & in(all_0_33_33, omega) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, all_0_33_33) | ~ 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_30_30) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_30_30))))) & ((in(all_0_34_34, all_0_35_35) & in(all_0_34_34, all_0_36_36)) | ( ~ in(all_0_34_34, all_0_35_35) & ~ in(all_0_34_34, all_0_36_36))) % 88.73/26.92 | % 88.73/26.92 | Applying alpha-rule on (1) yields: % 88.73/26.92 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) % 88.73/26.92 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) % 88.73/26.92 | (4) function(all_0_14_14) % 88.73/26.92 | (5) ? [v0] : equipotent(v0, v0) % 88.73/26.92 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 88.73/26.92 | (7) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 88.73/26.92 | (8) relation(all_0_14_14) % 88.73/26.92 | (9) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 88.73/26.92 | (10) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | preboolean(v1)) % 88.73/26.92 | (11) subset_complement(all_0_38_38, all_0_36_36) = all_0_35_35 % 88.73/26.92 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 88.73/26.92 | (13) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 88.73/26.92 | (14) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) % 88.73/26.92 | (15) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) % 88.73/26.92 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) % 88.73/26.92 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) % 88.73/26.92 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1)) % 88.73/26.92 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v0, v3)) % 88.73/26.92 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) % 88.73/26.92 | (21) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) % 88.73/26.92 | (22) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) % 88.73/26.92 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join_commut(v4, v3, v2) = v1) | ~ (join_commut(v4, v3, v2) = v0)) % 88.73/26.92 | (24) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | antisymmetric(v1)) % 88.73/26.92 | (25) ! [v0] : ( ~ top_str(v0) | one_sorted_str(v0)) % 88.73/26.92 | (26) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 88.73/26.92 | (27) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) & quasi_total(v2, v0, v1) & relation(v2) & function(v2)) % 88.73/26.92 | (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_23_23 = empty_set) & succ(all_0_29_29) = all_0_26_26 & powerset(all_0_25_25) = all_0_24_24 & powerset(all_0_26_26) = all_0_25_25 & ordinal(all_0_29_29) & element(all_0_23_23, all_0_24_24) & in(all_0_26_26, omega) & ! [v0] : ( ~ in(v0, all_0_23_23) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_23_23))) & ( ~ in(all_0_29_29, omega) | (powerset(all_0_28_28) = all_0_27_27 & powerset(all_0_29_29) = all_0_28_28 & ! [v0] : (v0 = empty_set | ~ element(v0, all_0_27_27) | ? [v1] : (in(v1, v0) & ! [v2] : (v2 = v1 | ~ subset(v1, v2) | ~ in(v2, v0))))))) | ( ~ (all_0_26_26 = empty_set) & ~ (all_0_29_29 = empty_set) & powerset(all_0_28_28) = all_0_27_27 & powerset(all_0_29_29) = all_0_28_28 & being_limit_ordinal(all_0_29_29) & ordinal(all_0_29_29) & element(all_0_26_26, all_0_27_27) & in(all_0_29_29, omega) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, all_0_29_29) | ~ 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_26_26) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_26_26)))) | ( ~ (all_0_29_29 = empty_set) & powerset(all_0_41_41) = all_0_40_40 & element(all_0_29_29, all_0_40_40) & ! [v0] : ( ~ in(v0, all_0_29_29) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_29_29)))) % 88.73/26.92 | (29) ! [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)) % 88.73/26.92 | (30) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) % 88.73/26.92 | (31) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) % 88.73/26.92 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_founded_relation(v1) | ~ relation(v1) | well_founded_relation(v2)) % 88.73/26.92 | (33) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | the_carrier(v0) = v1) % 88.73/26.92 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | relation_restriction(v1, v0) = v3) % 88.73/26.92 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ((v4 = v3 & set_intersection2(v1, v2) = v3) | (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4))))) % 88.73/26.92 | (36) empty(all_0_13_13) % 88.73/26.92 | (37) ! [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)))) % 88.73/26.92 | (38) ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v4_membered(v1)) % 88.73/26.92 | (39) ? [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)) % 88.73/26.93 | (40) ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1)) % 88.73/26.93 | (41) ? [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))) % 88.73/26.93 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) % 88.73/26.93 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (join(v4, v3, v2) = v1) | ~ (join(v4, v3, v2) = v0)) % 88.73/26.93 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) % 88.73/26.93 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) % 88.73/26.93 | (46) ! [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] : (ordinal(v3) & ( ~ in(v3, omega) | (powerset(v4) = v5 & powerset(v3) = v4 & ! [v6] : (v6 = empty_set | ~ element(v6, v5) | ? [v7] : (in(v7, v6) & ! [v8] : (v8 = v7 | ~ subset(v7, v8) | ~ in(v8, v6)))))))))) % 88.73/26.93 | (47) v4_membered(all_0_8_8) % 88.73/26.93 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v1) | finite(v2)) % 88.73/26.93 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join_commut(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ((v4 = v3 & join_commut(v0, v2, v1) = v3) | (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4))))) % 88.73/26.93 | (50) top_str(all_0_1_1) % 88.73/26.93 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 88.73/26.93 | (52) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | transitive(v1)) % 88.73/26.93 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_ordering(v1) | ~ relation(v1) | well_ordering(v2)) % 88.73/26.93 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) % 88.73/26.93 | (55) ! [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))) % 88.73/26.93 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) % 88.73/26.93 | (57) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) % 88.73/26.93 | (58) ! [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))) % 88.73/26.93 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 88.73/26.93 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = v1 | ~ (pair_first(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) % 88.73/26.93 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | relation_rng(v2) = v3) % 88.73/26.93 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 88.73/26.93 | (63) ? [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)))) % 88.73/26.93 | (64) ? [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))))) % 88.73/26.93 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2)) % 88.73/26.93 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v2, v3)) % 88.73/26.93 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) % 88.73/26.93 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_orders(v1, v0) | ~ relation(v1) | well_ordering(v2)) % 88.73/26.93 | (69) one_to_one(all_0_18_18) % 88.73/26.93 | (70) ~ empty(omega) % 88.73/26.93 | (71) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) % 88.73/26.93 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) % 88.73/26.93 | (73) relation(all_0_7_7) % 88.73/26.93 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 88.73/26.93 | (75) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | connected(v1)) % 88.73/26.93 | (76) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) % 88.73/26.93 | (77) ! [v0] : ( ~ being_limit_ordinal(v0) | ~ ordinal(v0) | ~ in(empty_set, v0) | subset(omega, v0)) % 88.73/26.93 | (78) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | natural(v1)) % 88.73/26.93 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 88.73/26.93 | (80) ordinal(omega) % 88.73/26.93 | (81) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) % 88.73/26.93 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) % 88.73/26.93 | (83) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ antisymmetric(v0) | ~ relation(v0) | is_antisymmetric_in(v0, v1)) % 88.73/26.93 | (84) element(all_0_34_34, all_0_38_38) % 88.73/26.93 | (85) ? [v0] : ? [v1] : ? [v2] : relation_of2_as_subset(v2, v0, v1) % 88.73/26.93 | (86) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | connected(v0)) % 88.73/26.93 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) % 88.73/26.93 | (88) ! [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))))) % 88.73/26.93 | (89) ! [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))) % 88.73/26.93 | (90) ! [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)))) % 88.73/26.93 | (91) v1_membered(all_0_8_8) % 88.73/26.93 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v1, v3)) % 88.73/26.93 | (93) ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | empty(v1)) % 88.73/26.93 | (94) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) % 88.73/26.93 | (95) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 88.73/26.93 | (96) ! [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)) % 88.73/26.93 | (97) v3_membered(empty_set) % 88.73/26.93 | (98) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ((relation_field(v3) = v4 & ~ in(v0, v4)) | (relation_field(v2) = v4 & in(v0, v4) & in(v0, v1)))) % 88.73/26.94 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 88.73/26.94 | (100) ? [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))))) % 88.73/26.94 | (101) ! [v0] : ( ~ empty(v0) | ordinal(v0)) % 88.73/26.94 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v2, v2) = v3) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | ~ in(v2, v1) | in(v3, v0)) % 88.73/26.94 | (103) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_join(v2) = v1) | ~ (the_L_join(v2) = v0)) % 88.73/26.94 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ transitive(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | transitive(v1)) % 88.73/26.94 | (105) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 88.73/26.94 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) % 88.73/26.94 | (107) ! [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)) % 88.73/26.94 | (108) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_first(v2) = v1) | ~ (pair_first(v2) = v0)) % 88.73/26.94 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ reflexive(v1) | ~ relation(v1) | reflexive(v2)) % 88.73/26.94 | (110) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (fiber(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ((v4 = v2 | ~ in(v4, v0) | (ordered_pair(v4, v2) = v5 & ~ in(v5, v1))) & (in(v4, v0) | ( ~ (v4 = v2) & ordered_pair(v4, v2) = v5 & in(v5, v1))))) % 88.73/26.94 | (111) function(all_0_15_15) % 88.73/26.94 | (112) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_L_meet(v2) = v1) | ~ (the_L_meet(v2) = v0)) % 88.73/26.94 | (113) ! [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)) % 88.73/26.94 | (114) relation(all_0_22_22) % 88.73/26.94 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v1_membered(v2)) % 88.73/26.94 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 88.73/26.94 | (117) ! [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)) % 88.73/26.94 | (118) ! [v0] : ! [v1] : (v1 = empty_set | ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0)) % 88.73/26.94 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v2_membered(v0) | v2_membered(v2)) % 88.73/26.94 | (120) ! [v0] : ! [v1] : ( ~ empty(v0) | ~ element(v1, v0) | empty(v1)) % 88.73/26.94 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) % 88.73/26.94 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) % 88.73/26.94 | (123) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 88.73/26.94 | (124) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) % 88.73/26.94 | (125) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1)) % 88.73/26.94 | (126) relation(all_0_18_18) % 88.73/26.94 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (relation_dom(v2) = v4 & subset(v4, v0))) % 88.73/26.94 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) % 88.73/26.94 | (129) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | cup_closed(v1)) % 88.73/26.94 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) % 88.73/26.94 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ((v4 = v3 & meet_commut(v0, v2, v1) = v3) | (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4))))) % 88.73/26.94 | (132) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) % 88.73/26.94 | (133) one_sorted_str(all_0_39_39) % 88.73/26.94 | (134) (in(all_0_34_34, all_0_35_35) & in(all_0_34_34, all_0_36_36)) | ( ~ in(all_0_34_34, all_0_35_35) & ~ in(all_0_34_34, all_0_36_36)) % 88.73/26.94 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 88.73/26.94 | (136) function(all_0_18_18) % 88.73/26.94 | (137) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) % 88.73/26.94 | (138) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) % 88.73/26.94 | (139) ! [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)) % 88.73/26.94 | (140) ! [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)))) % 88.73/26.94 | (141) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) % 88.73/26.94 | (142) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & element(v3, v2) & ~ empty(v3))) % 88.73/26.94 | (143) ! [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)) % 88.73/26.94 | (144) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) % 88.73/26.94 | (145) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (pair_second(v2) = v1) | ~ (pair_second(v2) = v0)) % 88.73/26.94 | (146) ! [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)) % 88.73/26.94 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~ (unordered_triple(v4, v3, v2) = v0)) % 88.73/26.94 | (148) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0) | ~ in(v1, v0) | in(v2, v0)) % 88.73/26.94 | (149) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 88.73/26.94 | (150) one_sorted_str(all_0_2_2) % 88.73/26.94 | (151) ? [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))))) % 88.73/26.94 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) % 88.73/26.94 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ((v6 = v4 & apply(v2, v0) = v5 & apply(v1, v5) = v4) | (relation_dom(v3) = v5 & ~ in(v0, v5)))) % 88.73/26.94 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))) | (ordered_pair(v4, v5) = v6 & ~ in(v6, v3))) & ((ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0)) | (ordered_pair(v4, v5) = v6 & in(v6, v3))))) % 88.73/26.94 | (155) ? [v0] : subset(v0, v0) % 88.73/26.94 | (156) latt_str(all_0_4_4) % 88.73/26.94 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) % 88.73/26.94 | (158) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | diff_closed(v1)) % 88.73/26.94 | (159) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 88.73/26.94 | (160) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) % 88.73/26.94 | (161) epsilon_connected(all_0_5_5) % 88.73/26.94 | (162) ! [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)) % 88.73/26.95 | (163) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 88.73/26.95 | (164) empty(all_0_14_14) % 88.73/26.95 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 88.73/26.95 | (166) ? [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))))) % 88.73/26.95 | (167) ! [v0] : ( ~ (union(v0) = v0) | being_limit_ordinal(v0)) % 88.73/26.95 | (168) ! [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)) % 88.73/26.95 | (169) ! [v0] : ! [v1] : ( ~ ordinal(v0) | ~ element(v1, v0) | ordinal(v1)) % 88.73/26.95 | (170) ! [v0] : ! [v1] : ( ~ ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0, v1)) % 88.73/26.95 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 88.73/26.95 | (172) ! [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)) % 88.73/26.95 | (173) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 88.73/26.95 | (174) ? [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))))) % 88.73/26.95 | (175) v4_membered(empty_set) % 88.73/26.95 | (176) ! [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))) % 88.73/26.95 | (177) ! [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] : (( ~ (v5 = v3) | ~ one_to_one(v4) | relation_isomorphism(v0, v2, v4) | ( ~ (v6 = v1) & relation_dom(v4) = v6) | (( ~ in(v8, v1) | ~ in(v7, v1) | (apply(v4, v8) = v11 & apply(v4, v7) = v10 & ordered_pair(v10, v11) = v12 & ~ in(v12, v2)) | (ordered_pair(v7, v8) = v9 & ~ in(v9, v0))) & ((apply(v4, v8) = v11 & apply(v4, v7) = v10 & ordered_pair(v10, v11) = v12 & in(v12, v2) & in(v8, v1) & in(v7, v1)) | (ordered_pair(v7, v8) = v9 & in(v9, v0))))) & ( ~ relation_isomorphism(v0, v2, v4) | (v6 = v1 & v5 = v3 & relation_dom(v4) = 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))))))) % 88.73/26.95 | (178) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2)) % 88.73/26.95 | (179) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 88.73/26.95 | (180) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) % 88.73/26.95 | (181) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ epsilon_connected(v0) | ~ in(v2, v0) | ~ in(v1, v0) | in(v2, v1) | in(v1, v2)) % 88.73/26.95 | (182) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 88.73/26.95 | (183) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2)) % 88.73/26.95 | (184) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) % 88.73/26.95 | (185) ! [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))) % 88.73/26.95 | (186) epsilon_transitive(omega) % 88.73/26.95 | (187) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) % 88.73/26.95 | (188) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 88.73/26.95 | (189) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_connected_in(v0, v1)) % 88.73/26.95 | (190) ! [v0] : ! [v1] : ! [v2] : ( ~ (topstr_closure(v0, v1) = v2) | ~ top_str(v0) | ? [v3] : ? [v4] : (the_carrier(v0) = v3 & powerset(v3) = v4 & ( ~ element(v1, v4) | element(v2, v4)))) % 88.73/26.95 | (191) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 88.73/26.95 | (192) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) % 88.73/26.95 | (193) ! [v0] : ( ~ element(v0, omega) | ordinal(v0)) % 88.73/26.95 | (194) ~ empty(all_0_6_6) % 88.73/26.95 | (195) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ antisymmetric(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | antisymmetric(v1)) % 88.73/26.95 | (196) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 88.73/26.95 | (197) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) % 88.73/26.95 | (198) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ finite(v1) | finite(v0)) % 88.73/26.95 | (199) ! [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))) % 88.73/26.95 | (200) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2) % 88.73/26.95 | (201) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) % 88.73/26.95 | (202) ? [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))))) % 88.73/26.95 | (203) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 88.73/26.95 | (204) ! [v0] : (v0 = empty_set | ~ empty(v0)) % 88.73/26.95 | (205) ? [v0] : ? [v1] : ( ! [v2] : ( ~ ordinal(v2) | ~ in(v2, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ordinal(v2)) & ! [v2] : ( ~ in(v2, v1) | in(v2, v0))) % 88.73/26.95 | (206) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | relation(v1)) % 88.73/26.95 | (207) ! [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)) % 88.73/26.95 | (208) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) % 88.73/26.95 | (209) ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v5_membered(v1)) % 88.73/26.95 | (210) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | in(v0, v1)) % 88.73/26.96 | (211) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ topological_space(v0) | ~ top_str(v0) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : ( ~ (topstr_closure(v0, v4) = v5) | ~ element(v4, v2) | ? [v6] : (meet_of_subsets(v1, v6) = v5 & element(v6, v3) & ! [v7] : ( ~ closed_subset(v7, v0) | ~ subset(v4, v7) | ~ element(v7, v2) | in(v7, v6)) & ! [v7] : ( ~ element(v7, v2) | ~ in(v7, v6) | closed_subset(v7, v0)) & ! [v7] : ( ~ element(v7, v2) | ~ in(v7, v6) | subset(v4, v7)))))) % 88.73/26.96 | (212) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) % 88.73/26.96 | (213) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ (v4 = v3) | ~ in(v3, v0) | (ordered_pair(v3, v3) = v5 & ~ in(v5, v1))) & ((v4 = v3 & in(v3, v0)) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) % 88.73/26.96 | (214) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : ((v4 = v3 & subset_intersection2(v0, v2, v1) = v3) | (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4))))) % 88.73/26.96 | (215) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) % 88.73/26.96 | (216) ? [v0] : ! [v1] : ! [v2] : ( ~ (cast_as_carrier_subset(v1) = v2) | ~ topological_space(v1) | ~ top_str(v1) | ? [v3] : ? [v4] : ? [v5] : (the_carrier(v1) = v3 & powerset(v3) = v4 & ((powerset(v4) = v5 & ~ element(v0, v5)) | ( ! [v6] : ! [v7] : ( ~ (set_difference(v2, v6) = v7) | ~ in(v7, v0) | ~ in(v6, v4) | in(v6, v5)) & ! [v6] : ! [v7] : ( ~ (set_difference(v2, v6) = v7) | ~ in(v6, v5) | in(v7, v0)) & ! [v6] : ! [v7] : ( ~ (set_difference(v2, v6) = v7) | ~ in(v6, v5) | in(v6, v4)))))) % 88.73/26.96 | (217) ! [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))) % 88.73/26.96 | (218) ~ empty(all_0_19_19) % 88.73/26.96 | (219) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) % 88.73/26.96 | (220) ! [v0] : ! [v1] : ( ~ (the_topology(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ( ~ open_subset(v4, v0) | ~ element(v4, v3) | in(v4, v1)) & ! [v4] : ( ~ element(v4, v3) | ~ in(v4, v1) | open_subset(v4, v0)))) % 88.73/26.96 | (221) relation_rng(empty_set) = empty_set % 88.73/26.96 | (222) ! [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))) % 88.73/26.96 | (223) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ~ function(v1) | function(v2)) % 88.73/26.96 | (224) ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v3_membered(v1)) % 88.73/26.96 | (225) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ in(v4, v5) | in(v0, v2)) % 88.73/26.96 | (226) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v5_membered(v2)) % 88.73/26.96 | (227) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ((v5 = v2 & relation_dom(v4) = v2) | (relation_dom(v3) = v5 & ~ subset(v1, v5)))))) % 88.73/26.96 | (228) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) % 88.73/26.96 | (229) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) % 88.73/26.96 | (230) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ closed_subset(v4, v0) | ~ element(v4, v3) | open_subset(v5, v0)) & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ open_subset(v5, v0) | ~ element(v4, v3) | closed_subset(v4, v0)))) % 88.73/26.96 | (231) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) % 88.73/26.96 | (232) one_to_one(all_0_15_15) % 88.73/26.96 | (233) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) % 88.73/26.96 | (234) ! [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))) % 88.73/26.96 | (235) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1)) % 88.73/26.96 | (236) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (subset_intersection2(v1, v2, v2) = v3) | ? [v4] : (powerset(v1) = v4 & ( ~ element(v2, v4) | ~ element(v0, v4)))) % 88.73/26.96 | (237) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 88.73/26.96 | (238) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 88.73/26.96 | (239) ! [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)) % 88.73/26.96 | (240) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ relation_of2_as_subset(v3, v2, v0) | ~ subset(v0, v1) | relation_of2_as_subset(v3, v2, v1)) % 88.73/26.96 | (241) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | ordinal(v1)) % 88.73/26.96 | (242) ! [v0] : ( ~ meet_semilatt_str(v0) | one_sorted_str(v0)) % 88.73/26.96 | (243) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) % 88.73/26.96 | (244) ? [v0] : ? [v1] : element(v1, v0) % 88.73/26.96 | (245) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 88.73/26.96 | (246) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) % 88.73/26.96 | (247) element(all_0_36_36, all_0_37_37) % 88.73/26.96 | (248) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) % 88.73/26.96 | (249) relation(all_0_20_20) % 88.73/26.96 | (250) ! [v0] : ! [v1] : ( ~ (the_L_join(v0) = v1) | ~ join_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [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))) % 89.13/26.96 | (251) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) % 89.13/26.96 | (252) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_inverse_image(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : (( ~ in(v5, v2) | ~ in(v5, v0) | (apply(v1, v5) = v6 & ~ in(v6, v3))) & (in(v5, v0) | (apply(v1, v5) = v6 & in(v6, v3) & in(v5, v2))))) % 89.13/26.96 | (253) ! [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)) % 89.13/26.96 | (254) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) % 89.13/26.96 | (255) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v5_membered(v2)) % 89.13/26.96 | (256) ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v1_membered(v1)) % 89.13/26.96 | (257) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_rng_as_subset(v4, v3, v2) = v1) | ~ (relation_rng_as_subset(v4, v3, v2) = v0)) % 89.13/26.96 | (258) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | finite(v1) | ? [v2] : (relation_dom(v0) = v2 & ~ finite(v2))) % 89.13/26.96 | (259) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) % 89.13/26.96 | (260) ! [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)) % 89.13/26.96 | (261) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 89.13/26.97 | (262) ! [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] : ((v6 = v0 & v4 = v0 & apply(v2, v0) = v5 & apply(v1, v5) = v0) | (relation_rng(v1) = v5 & ~ in(v0, v5)))) % 89.13/26.97 | (263) v5_membered(empty_set) % 89.13/26.97 | (264) ! [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)) % 89.13/26.97 | (265) epsilon_transitive(all_0_15_15) % 89.13/26.97 | (266) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) % 89.13/26.97 | (267) function(all_0_7_7) % 89.13/26.97 | (268) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 89.13/26.97 | (269) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3))) % 89.13/26.97 | (270) ! [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))) % 89.13/26.97 | (271) empty(empty_set) % 89.13/26.97 | (272) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v3_membered(v2)) % 89.13/26.97 | (273) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ in(v1, v0) | ? [v2] : (ordinal(v2) & in(v2, v0) & ! [v3] : ( ~ ordinal(v3) | ~ in(v3, v0) | ordinal_subset(v2, v3)))) % 89.13/26.97 | (274) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : (v4 = v3 | ~ (topstr_closure(v0, v3) = v4) | ~ closed_subset(v3, v0) | ~ element(v3, v2)) & ! [v3] : ( ~ (topstr_closure(v0, v3) = v3) | ~ topological_space(v0) | ~ element(v3, v2) | closed_subset(v3, v0)))) % 89.13/26.97 | (275) ~ empty(all_0_17_17) % 89.13/26.97 | (276) v2_membered(empty_set) % 89.13/26.97 | (277) ! [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)) % 89.13/26.97 | (278) ! [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))) % 89.13/26.97 | (279) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) % 89.13/26.97 | (280) ! [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))) % 89.13/26.97 | (281) ~ empty(all_0_8_8) % 89.13/26.97 | (282) ! [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)) % 89.13/26.97 | (283) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_connected_in(v0, v1) | ~ relation(v0) | connected(v0)) % 89.13/26.97 | (284) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) % 89.13/26.97 | (285) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 89.13/26.97 | (286) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (join_commut(v0, v1, v2) = v3) | ~ join_semilatt_str(v0) | ~ join_commutative(v0) | empty_carrier(v0) | ? [v4] : ((v4 = v3 & join(v0, v1, v2) = v3) | (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4))))) % 89.13/26.97 | (287) ! [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))) % 89.13/26.97 | (288) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (( ~ in(v0, v1) | (relation_rng(v3) = v4 & in(v0, v4)) | (relation_rng(v2) = v5 & ~ in(v0, v5))) & ((relation_rng(v3) = v4 & ~ in(v0, v4)) | (relation_rng(v2) = v5 & in(v0, v5) & in(v0, v1))))) % 89.13/26.97 | (289) ! [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)) % 89.13/26.97 | (290) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v4_membered(v2)) % 89.13/26.97 | (291) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) % 89.13/26.97 | (292) ! [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)) % 89.13/26.97 | (293) epsilon_transitive(all_0_10_10) % 89.13/26.97 | (294) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 89.13/26.97 | (295) relation(all_0_11_11) % 89.13/26.97 | (296) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ in(v0, v1) | ordinal(v0)) % 89.13/26.97 | (297) ! [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)) % 89.13/26.97 | (298) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) % 89.13/26.97 | (299) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 89.13/26.97 | (300) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) % 89.13/26.97 | (301) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) % 89.13/26.97 | (302) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) % 89.13/26.97 | (303) relation(empty_set) % 89.13/26.97 | (304) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) % 89.13/26.97 | (305) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 89.13/26.97 | (306) ! [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)) % 89.13/26.97 | (307) ! [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)) % 89.13/26.97 | (308) ! [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)) % 89.13/26.97 | (309) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) % 89.13/26.97 | (310) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | pair_second(v2) = v1) % 89.13/26.97 | (311) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (powerset(v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : ((powerset(v4) = v5 & ! [v7] : ! [v8] : ( ~ (relation_image(v2, v7) = v8) | ~ in(v8, v0) | ~ in(v7, v5) | in(v7, v6)) & ! [v7] : ! [v8] : ( ~ (relation_image(v2, v7) = v8) | ~ in(v7, v6) | in(v8, v0)) & ! [v7] : ! [v8] : ( ~ (relation_image(v2, v7) = v8) | ~ in(v7, v6) | in(v7, v5))) | (powerset(v3) = v5 & ~ element(v0, v5)))) % 89.13/26.97 | (312) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) % 89.13/26.97 | (313) ! [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)))) % 89.13/26.97 | (314) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v2_membered(v2)) % 89.13/26.98 | (315) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ transitive(v0) | ~ relation(v0) | is_transitive_in(v0, v1)) % 89.13/26.98 | (316) epsilon_transitive(all_0_19_19) % 89.13/26.98 | (317) ? [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))))) % 89.13/26.98 | (318) v5_membered(all_0_8_8) % 89.13/26.98 | (319) ! [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)) % 89.13/26.98 | (320) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) % 89.13/26.98 | (321) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) % 89.13/26.98 | (322) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) % 89.13/26.98 | (323) ! [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)) % 89.13/26.98 | (324) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | reflexive(v1)) % 89.13/26.98 | (325) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1)) % 89.13/26.98 | (326) ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) % 89.13/26.98 | (327) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 89.13/26.98 | (328) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (meet_commut(v0, v1, v2) = v3) | ~ meet_semilatt_str(v0) | ~ meet_commutative(v0) | empty_carrier(v0) | ? [v4] : ((v4 = v3 & meet(v0, v1, v2) = v3) | (the_carrier(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4))))) % 89.13/26.98 | (329) finite(all_0_6_6) % 89.13/26.98 | (330) ! [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)) % 89.13/26.98 | (331) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 89.13/26.98 | (332) ! [v0] : ( ~ preboolean(v0) | diff_closed(v0)) % 89.13/26.98 | (333) ! [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))) % 89.13/26.98 | (334) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) % 89.13/26.98 | (335) being_limit_ordinal(omega) % 89.13/26.98 | (336) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) % 89.13/26.98 | (337) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | v4 = v1 | v4 = v0 | ~ (unordered_triple(v0, v1, v2) = v3) | ~ in(v4, v3)) % 89.13/26.98 | (338) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v2) = v3) | ~ (cartesian_product2(v1, v1) = v2) | ~ relation(v0) | relation_restriction(v0, v1) = v3) % 89.13/26.98 | (339) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 89.13/26.98 | (340) ! [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) % 89.13/26.98 | (341) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) % 89.13/26.98 | (342) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) % 89.13/26.98 | (343) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1)) % 89.13/26.98 | (344) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet_commut(v4, v3, v2) = v1) | ~ (meet_commut(v4, v3, v2) = v0)) % 89.13/26.98 | (345) ! [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))) % 89.13/26.98 | (346) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) % 89.13/26.98 | (347) ! [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)) % 89.13/26.98 | (348) ! [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)) % 89.13/26.98 | (349) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0)) % 89.13/26.98 | (350) relation_empty_yielding(all_0_22_22) % 89.13/26.98 | (351) ! [v0] : ( ~ empty(v0) | relation(v0)) % 89.13/26.98 | (352) ! [v0] : ! [v1] : ( ~ (the_topology(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : ? [v4] : (the_carrier(v0) = v2 & powerset(v3) = v4 & powerset(v2) = v3 & element(v1, v4))) % 89.13/26.98 | (353) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ finite(v1) | ~ finite(v0) | finite(v2)) % 89.13/26.98 | (354) ! [v0] : ( ~ reflexive(v0) | ~ well_founded_relation(v0) | ~ transitive(v0) | ~ connected(v0) | ~ antisymmetric(v0) | ~ relation(v0) | well_ordering(v0)) % 89.13/26.98 | (355) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | well_founded_relation(v1)) % 89.13/26.98 | (356) ordinal(all_0_5_5) % 89.13/26.98 | (357) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v0) = v3 & (element(v2, v3) | (powerset(v3) = v4 & ~ element(v1, v4))))) % 89.13/26.98 | (358) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) % 89.13/26.98 | (359) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) % 89.13/26.98 | (360) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ finite(v0) | finite(v2)) % 89.13/26.98 | (361) ! [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)) % 89.13/26.98 | (362) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 89.13/26.98 | (363) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1)) % 89.13/26.98 | (364) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | subset(v3, v1)) % 89.13/26.98 | (365) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_meet(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ((v4 = v3 & meet_of_subsets(v0, v1) = v3) | (powerset(v2) = v4 & ~ element(v1, v4)))) % 89.13/26.98 | (366) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v2_membered(v2)) % 89.13/26.98 | (367) ! [v0] : ~ proper_subset(v0, v0) % 89.13/26.98 | (368) ! [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)))) % 89.13/26.98 | (369) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 89.13/26.98 | (370) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ topological_space(v0) | ~ top_str(v0) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v1) = v2 & ! [v4] : ! [v5] : ( ~ (meet_of_subsets(v1, v4) = v5) | ~ element(v4, v3) | closed_subset(v5, v0) | ? [v6] : (element(v6, v2) & in(v6, v4) & ~ closed_subset(v6, v0))))) % 89.13/26.98 | (371) ! [v0] : ( ~ ordinal(v0) | ~ empty(v0) | epsilon_connected(v0)) % 89.13/26.98 | (372) ! [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) % 89.13/26.98 | (373) function(empty_set) % 89.13/26.98 | (374) ! [v0] : ! [v1] : ( ~ (the_L_meet(v0) = v1) | ~ meet_semilatt_str(v0) | empty_carrier(v0) | ? [v2] : (the_carrier(v0) = v2 & ! [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))) % 89.13/26.98 | (375) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (inclusion_relation(v0) = v1) | ~ (relation_field(v1) = v2) | ~ relation(v1)) % 89.13/26.98 | (376) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) % 89.13/26.98 | (377) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) % 89.13/26.99 | (378) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) % 89.13/26.99 | (379) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (finite(v2) & element(v2, v1) & ~ empty(v2))) % 89.13/26.99 | (380) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 89.13/26.99 | (381) ! [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)) % 89.13/26.99 | (382) ordinal(all_0_19_19) % 89.13/26.99 | (383) powerset(empty_set) = all_0_41_41 % 89.13/26.99 | (384) ! [v0] : ( ~ finite(v0) | ? [v1] : ? [v2] : (relation_rng(v1) = v0 & relation_dom(v1) = v2 & relation(v1) & function(v1) & in(v2, omega))) % 89.13/26.99 | (385) ! [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))) % 89.13/26.99 | (386) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) % 89.13/26.99 | (387) ! [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)))) % 89.13/26.99 | (388) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ transitive(v1) | ~ relation(v1) | transitive(v2)) % 89.13/26.99 | (389) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 89.13/26.99 | (390) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1))) % 89.13/26.99 | (391) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1)) % 89.13/26.99 | (392) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v1_membered(v2)) % 89.13/26.99 | (393) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 89.13/26.99 | (394) ! [v0] : ! [v1] : ( ~ equipotent(v0, v1) | equipotent(v1, v0)) % 89.13/26.99 | (395) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 89.13/26.99 | (396) ! [v0] : ! [v1] : ( ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v0)) % 89.13/26.99 | (397) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | relation_dom(v2) = v3) % 89.13/26.99 | (398) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v1 | ~ (pair_second(v0) = v1) | ~ (ordered_pair(v4, v5) = v0) | ~ (ordered_pair(v2, v3) = v0)) % 89.13/26.99 | (399) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v1) | relation_restriction(v1, v0) = v3) % 89.13/26.99 | (400) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) % 89.13/26.99 | (401) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) % 89.13/26.99 | (402) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 89.13/26.99 | (403) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ relation(v0) | ~ in(v3, v2) | in(v4, v0)) % 89.13/26.99 | (404) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) % 89.13/26.99 | (405) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) % 89.13/26.99 | (406) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ well_founded_relation(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | well_founded_relation(v1)) % 89.13/26.99 | (407) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) % 89.13/26.99 | (408) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 89.13/26.99 | (409) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ connected(v1) | ~ relation(v1) | connected(v2)) % 89.13/26.99 | (410) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) % 89.13/26.99 | (411) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_intersection2(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) % 89.13/26.99 | (412) ! [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)))) % 89.13/26.99 | (413) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | ~ finite(v1) | finite(v2)) % 89.13/26.99 | (414) ? [v0] : ! [v1] : ( ~ relation(v1) | is_reflexive_in(v1, v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v2) = v3 & in(v2, v0) & ~ in(v3, v1))) % 89.13/26.99 | (415) ! [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))) % 89.13/26.99 | (416) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal_subset(v1, v2) | ~ ordinal(v2) | ~ ordinal(v0) | in(v0, v2)) % 89.13/26.99 | (417) ? [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))) % 89.13/26.99 | (418) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ( ~ (subset_difference(v2, v1, v4) = v5) | ~ element(v4, v3) | subset_complement(v2, v4) = v5))) % 89.13/26.99 | (419) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) % 89.13/26.99 | (420) v1_membered(empty_set) % 89.13/26.99 | (421) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) % 89.13/26.99 | (422) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ topological_space(v0) | ~ top_str(v0) | ? [v2] : ? [v3] : (powerset(v1) = v2 & closed_subset(v3, v0) & element(v3, v2))) % 89.13/26.99 | (423) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v0, v1) = v4) | ~ (cartesian_product2(v2, v3) = v5) | ~ in(v4, v5) | in(v1, v3)) % 89.13/26.99 | (424) ! [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)))) % 89.13/26.99 | (425) ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ((singleton(v1) = v4 & powerset(v1) = v3 & ! [v6] : ! [v7] : ( ~ (set_difference(v7, v4) = v6) | ~ in(v7, v0) | ~ in(v6, v3) | in(v6, v5)) & ! [v6] : ( ~ in(v6, v5) | in(v6, v3)) & ! [v6] : ( ~ in(v6, v5) | ? [v7] : (set_difference(v7, v4) = v6 & in(v7, v0)))) | (powerset(v3) = v4 & powerset(v2) = v3 & ~ element(v0, v4)))) % 89.13/26.99 | (426) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ((v3 = v2 & set_difference(v0, v1) = v2) | (powerset(v0) = v3 & ~ element(v1, v3)))) % 89.13/26.99 | (427) ! [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))))))) % 89.13/26.99 | (428) ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : ? [v2] : (succ(v1) = v2 & ordinal(v1) & in(v1, v0) & ~ in(v2, v0))) % 89.13/26.99 | (429) ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) % 89.13/26.99 | (430) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) % 89.13/26.99 | (431) ! [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)) % 89.13/26.99 | (432) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) % 89.13/26.99 | (433) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) % 89.13/26.99 | (434) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) % 89.13/26.99 | (435) relation_empty_yielding(empty_set) % 89.13/26.99 | (436) ! [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))))) % 89.13/27.00 | (437) ! [v0] : ( ~ ordinal(v0) | being_limit_ordinal(v0) | ? [v1] : (succ(v1) = v0 & ordinal(v1))) % 89.13/27.00 | (438) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_well_founded_in(v0, v1) | ~ relation(v0) | well_founded_relation(v0)) % 89.13/27.00 | (439) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 89.13/27.00 | (440) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) % 89.13/27.00 | (441) relation_empty_yielding(all_0_20_20) % 89.13/27.00 | (442) ! [v0] : ! [v1] : ! [v2] : ( ~ (succ(v0) = v1) | ~ ordinal(v2) | ~ ordinal(v0) | ~ in(v0, v2) | ordinal_subset(v1, v2)) % 89.13/27.00 | (443) ! [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)) % 89.13/27.00 | (444) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) % 89.13/27.00 | (445) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) % 89.28/27.00 | (446) ! [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))) % 89.28/27.00 | (447) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1)) % 89.28/27.00 | (448) ! [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)) % 89.28/27.00 | (449) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ((v4 = v3 & set_difference(v1, v2) = v3) | (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4))))) % 89.28/27.00 | (450) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) % 89.28/27.00 | (451) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v2_membered(v2)) % 89.28/27.00 | (452) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_antisymmetric_in(v0, v1) | ~ relation(v0) | antisymmetric(v0)) % 89.28/27.00 | (453) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ connected(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | connected(v1)) % 89.28/27.00 | (454) ! [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))) % 89.28/27.00 | (455) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) % 89.28/27.00 | (456) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) % 89.28/27.00 | (457) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1) | ~ natural(v0)) % 89.28/27.00 | (458) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) % 89.28/27.00 | (459) ordinal(empty_set) % 89.28/27.00 | (460) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1)) % 89.28/27.00 | (461) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_ordering(v1) | ~ relation(v1) | ? [v3] : ((v3 = v0 & relation_field(v2) = v0) | (relation_field(v1) = v3 & ~ subset(v0, v3)))) % 89.28/27.00 | (462) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_transitive_in(v0, v1)) % 89.28/27.00 | (463) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) % 89.28/27.00 | (464) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) % 89.28/27.00 | (465) ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) % 89.28/27.00 | (466) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) % 89.28/27.00 | (467) ? [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)) % 89.28/27.00 | (468) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 89.28/27.00 | (469) being_limit_ordinal(all_0_10_10) % 89.28/27.00 | (470) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) % 89.28/27.00 | (471) one_to_one(empty_set) % 89.28/27.00 | (472) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 89.28/27.00 | (473) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ordinal(v1)) % 89.28/27.00 | (474) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v1_membered(v0) | v1_membered(v2)) % 89.28/27.00 | (475) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) % 89.28/27.00 | (476) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | epsilon_connected(v1)) % 89.28/27.00 | (477) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) % 89.28/27.00 | (478) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3, v2) = v0)) % 89.28/27.00 | (479) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 89.28/27.00 | (480) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 89.28/27.00 | (481) v3_membered(all_0_8_8) % 89.28/27.00 | (482) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) % 89.28/27.00 | (483) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v4] : ? [v5] : (( ~ in(v0, v1) | (relation_dom(v3) = v4 & in(v0, v4)) | (relation_dom(v2) = v5 & ~ in(v0, v5))) & ((relation_dom(v3) = v4 & ~ in(v0, v4)) | (relation_dom(v2) = v5 & in(v0, v5) & in(v0, v1))))) % 89.28/27.00 | (484) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) % 89.28/27.00 | (485) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | finite(v1)) % 89.28/27.00 | (486) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_orders(v0, v1) | ~ relation(v0) | well_ordering(v0)) % 89.28/27.00 | (487) ? [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))))) % 89.28/27.00 | (488) ! [v0] : ( ~ preboolean(v0) | cup_closed(v0)) % 89.28/27.00 | (489) v2_membered(all_0_8_8) % 89.28/27.00 | (490) ! [v0] : ( ~ ordinal(v0) | epsilon_transitive(v0)) % 89.28/27.00 | (491) ? [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 & in(v0, v5)) | (relation_dom(v3) = v6 & ~ in(v0, v6)) | (apply(v3, v0) = v7 & ~ in(v7, v2))) & ((relation_dom(v4) = v5 & ~ in(v0, v5)) | (relation_dom(v3) = v6 & apply(v3, v0) = v7 & in(v7, v2) & in(v0, v6))))) % 89.28/27.00 | (492) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) % 89.28/27.00 | (493) ? [v0] : ! [v1] : ! [v2] : ( ~ (succ(v1) = v2) | ~ ordinal(v1) | ? [v3] : ? [v4] : ? [v5] : ((singleton(v1) = v3 & powerset(v1) = v4 & ! [v6] : ! [v7] : ( ~ (set_difference(v7, v3) = v6) | ~ in(v7, v0) | ~ in(v6, v4) | in(v6, v5)) & ! [v6] : ( ~ in(v6, v5) | in(v6, v4)) & ! [v6] : ( ~ in(v6, v5) | ? [v7] : (set_difference(v7, v3) = v6 & in(v7, v0)))) | (powerset(v3) = v4 & powerset(v2) = v3 & ~ element(v0, v4)))) % 89.28/27.00 | (494) ! [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))) % 89.28/27.00 | (495) ? [v0] : ? [v1] : (well_orders(v1, v0) & relation(v1)) % 89.28/27.00 | (496) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v0, v3) | (relation_dom(v2) = v4 & ordered_pair(v5, v0) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | (relation_dom(v2) = v4 & ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v0) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1)))))) % 89.28/27.00 | (497) ! [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] : ( ~ 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))))) % 89.28/27.00 | (498) function(all_0_22_22) % 89.28/27.00 | (499) ! [v0] : ! [v1] : ( ~ ordinal(v0) | ~ element(v1, v0) | epsilon_transitive(v1)) % 89.28/27.00 | (500) ! [v0] : ! [v1] : ( ~ (union(v0) = v1) | ~ ordinal(v0) | epsilon_transitive(v1)) % 89.28/27.00 | (501) join_semilatt_str(all_0_3_3) % 89.28/27.00 | (502) ! [v0] : ( ~ empty(v0) | v1_membered(v0)) % 89.28/27.00 | (503) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) % 89.28/27.01 | (504) ? [v0] : (epsilon_transitive(v0) | ? [v1] : (in(v1, v0) & ~ subset(v1, v0))) % 89.28/27.01 | (505) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 89.28/27.01 | (506) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | reflexive(v0) | ? [v2] : ? [v3] : (ordered_pair(v2, v2) = v3 & in(v2, v1) & ~ in(v3, v0))) % 89.28/27.01 | (507) ! [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))) % 89.28/27.01 | (508) ? [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v1) = v2) | ~ topological_space(v1) | ~ top_str(v1) | ? [v3] : ? [v4] : (powerset(v2) = v3 & ( ~ element(v0, v3) | ( ! [v5] : ( ~ closed_subset(v5, v1) | ~ subset(v0, v5) | ~ element(v5, v3) | ~ in(v5, v3) | in(v5, v4)) & ! [v5] : ( ~ in(v5, v4) | subset(v0, v5)) & ! [v5] : ( ~ in(v5, v4) | in(v5, v3)) & ! [v5] : ( ~ in(v5, v4) | (closed_subset(v5, v1) & element(v5, v3))))))) % 89.28/27.01 | (509) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 89.28/27.01 | (510) ? [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))))) % 89.28/27.01 | (511) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) % 89.28/27.01 | (512) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v1, v2) = v3) | relation(v0) | ? [v4] : (powerset(v3) = v4 & ~ element(v0, v4))) % 89.28/27.01 | (513) ! [v0] : ( ~ element(v0, omega) | epsilon_connected(v0)) % 89.28/27.01 | (514) ! [v0] : ( ~ latt_str(v0) | meet_semilatt_str(v0)) % 89.28/27.01 | (515) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : (( ~ in(v0, v3) | (cartesian_product2(v1, v1) = v4 & in(v0, v4) & in(v0, v2))) & ( ~ in(v0, v2) | in(v0, v3) | (cartesian_product2(v1, v1) = v4 & ~ in(v0, v4))))) % 89.28/27.01 | (516) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 89.28/27.01 | (517) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (meet_of_subsets(v0, v1) = v3) | ~ (subset_difference(v0, v2, v3) = v4) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ((v6 = v4 & complements_of_subsets(v0, v1) = v5 & union_of_subsets(v0, v5) = v4) | (powerset(v5) = v6 & powerset(v0) = v5 & ~ element(v1, v6)))) % 89.28/27.01 | (518) meet_semilatt_str(all_0_0_0) % 89.28/27.01 | (519) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : ! [v6] : (v6 = v4 | ~ (subset_difference(v2, v1, v5) = v6) | ~ (subset_difference(v2, v1, v4) = v5) | ~ element(v4, v3)))) % 89.28/27.01 | (520) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) % 89.28/27.01 | (521) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 89.28/27.01 | (522) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (topstr_closure(v3, v2) = v1) | ~ (topstr_closure(v3, v2) = v0)) % 89.28/27.01 | (523) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) % 89.28/27.01 | (524) in(empty_set, omega) % 89.28/27.01 | (525) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_as_carrier_subset(v2) = v1) | ~ (cast_as_carrier_subset(v2) = v0)) % 89.28/27.01 | (526) ! [v0] : ! [v1] : ( ~ (the_topology(v0) = v1) | ~ top_str(v0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ topological_space(v0) | (the_carrier(v0) = v2 & powerset(v3) = v4 & powerset(v2) = v3 & in(v2, v1) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset_intersection2(v2, v8, v9) = v10) | ~ element(v9, v3) | ~ element(v8, v3) | ~ in(v9, v1) | ~ in(v8, v1) | in(v10, v1)) & ! [v8] : ! [v9] : ( ~ (union_of_subsets(v2, v8) = v9) | ~ subset(v8, v1) | ~ element(v8, v4) | in(v9, v1)))) & (topological_space(v0) | (the_carrier(v0) = v2 & ( ~ in(v2, v1) | (union_of_subsets(v2, v5) = v6 & powerset(v3) = v4 & powerset(v2) = v3 & subset(v5, v1) & element(v5, v4) & ~ in(v6, v1)) | (subset_intersection2(v2, v5, v6) = v7 & powerset(v2) = v3 & element(v6, v3) & element(v5, v3) & in(v6, v1) & in(v5, v1) & ~ in(v7, v1))))))) % 89.28/27.01 | (527) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) % 89.28/27.01 | (528) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) % 89.28/27.01 | (529) ! [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))) % 89.28/27.01 | (530) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) % 89.28/27.01 | (531) ! [v0] : ~ (singleton(v0) = empty_set) % 89.28/27.01 | (532) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) % 89.28/27.01 | (533) ! [v0] : ! [v1] : (v1 = v0 | ~ (union(v0) = v1) | ~ being_limit_ordinal(v0)) % 89.28/27.01 | (534) epsilon_connected(omega) % 89.28/27.01 | (535) one_sorted_str(all_0_21_21) % 89.28/27.01 | (536) ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) % 89.28/27.01 | (537) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | natural(v1)) % 89.28/27.01 | (538) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 89.28/27.01 | (539) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 89.28/27.01 | (540) ordinal(all_0_15_15) % 89.28/27.01 | (541) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2)) % 89.28/27.01 | (542) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 89.28/27.01 | (543) epsilon_transitive(all_0_9_9) % 89.28/27.01 | (544) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ~ finite(v0) | finite(v2)) % 89.28/27.01 | (545) epsilon_connected(all_0_9_9) % 89.28/27.01 | (546) epsilon_connected(empty_set) % 89.28/27.01 | (547) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ subset(v2, v3) | relation_of2(v2, v0, v1)) % 89.28/27.01 | (548) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2(v2, v0, v1) | subset(v2, v3)) % 89.28/27.01 | (549) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) % 89.28/27.01 | (550) ? [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))))) % 89.28/27.01 | (551) ? [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)))))) % 89.28/27.01 | (552) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) % 89.28/27.01 | (553) powerset(all_0_38_38) = all_0_37_37 % 89.28/27.01 | (554) ! [v0] : ( ~ epsilon_connected(v0) | ~ epsilon_transitive(v0) | ordinal(v0)) % 89.28/27.01 | (555) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) % 89.28/27.01 | (556) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 89.28/27.01 | (557) ? [v0] : ? [v1] : ( ! [v2] : ! [v3] : ( ~ (singleton(v3) = v2) | ~ in(v3, v0) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : (singleton(v3) = v2 & in(v3, v0)))) % 89.28/27.01 | (558) ! [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)) % 89.28/27.01 | (559) ? [v0] : (ordinal(v0) | ? [v1] : (in(v1, v0) & ( ~ subset(v1, v0) | ~ ordinal(v1)))) % 89.28/27.01 | (560) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) % 89.28/27.01 | (561) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) % 89.28/27.01 | (562) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) % 89.28/27.01 | (563) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 89.28/27.01 | (564) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 89.28/27.01 | (565) ? [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)))))) % 89.28/27.02 | (566) ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) % 89.28/27.02 | (567) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | epsilon_connected(v1)) % 89.28/27.02 | (568) empty(all_0_12_12) % 89.28/27.02 | (569) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_reflexive_in(v0, v1)) % 89.28/27.02 | (570) the_carrier(all_0_39_39) = all_0_38_38 % 89.28/27.02 | (571) ! [v0] : ! [v1] : ( ~ (succ(v1) = v0) | ~ being_limit_ordinal(v0) | ~ ordinal(v1) | ~ ordinal(v0)) % 89.28/27.02 | (572) ! [v0] : ! [v1] : ( ~ (empty_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | v2_membered(v1)) % 89.28/27.02 | (573) ! [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))) % 89.28/27.02 | (574) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ topological_space(v0) | ~ top_str(v0) | closed_subset(v1, v0)) % 89.28/27.02 | (575) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v1_membered(v2)) % 89.28/27.02 | (576) relation_dom(empty_set) = empty_set % 89.28/27.02 | (577) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) % 89.28/27.02 | (578) ? [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))))))) % 89.28/27.02 | (579) ! [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)))))) % 89.28/27.02 | (580) ! [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))) % 89.28/27.02 | (581) ! [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))) % 89.28/27.02 | (582) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 89.28/27.02 | (583) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (topstr_closure(v0, v3) = v4) | ~ closed_subset(v6, v0) | ~ subset(v3, v6) | ~ element(v6, v2) | ~ element(v3, v2) | ~ in(v5, v4) | ~ in(v5, v1) | in(v5, v6)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (topstr_closure(v0, v3) = v4) | ~ element(v3, v2) | ~ in(v5, v1) | in(v5, v4) | ? [v6] : (closed_subset(v6, v0) & subset(v3, v6) & element(v6, v2) & ~ in(v5, v6))))) % 89.28/27.02 | (584) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_field(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ reflexive(v0) | ~ relation(v0) | ~ in(v2, v1) | in(v3, v0)) % 89.28/27.02 | (585) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 89.28/27.02 | (586) ! [v0] : ( ~ latt_str(v0) | join_semilatt_str(v0)) % 89.28/27.02 | (587) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) % 89.28/27.02 | (588) ! [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))))) % 89.28/27.02 | (589) ? [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)))) % 89.28/27.02 | (590) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (( ~ (v4 = v1) | in(v3, v2) | (relation_dom(v2) = v5 & ~ in(v0, v5))) & ( ~ in(v3, v2) | (v4 = v1 & relation_dom(v2) = v5 & in(v0, v5))))) % 89.28/27.02 | (591) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) % 89.28/27.02 | (592) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v0, v3) | (relation_rng(v2) = v4 & ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | (relation_rng(v2) = v4 & ! [v7] : ! [v8] : ( ~ (ordered_pair(v0, v7) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1)))))) % 89.28/27.02 | (593) ! [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)) % 89.28/27.02 | (594) one_to_one(all_0_11_11) % 89.28/27.02 | (595) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 89.28/27.02 | (596) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) % 89.28/27.02 | (597) ! [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)) % 89.28/27.02 | (598) ! [v0] : ( ~ empty(v0) | function(v0)) % 89.28/27.02 | (599) ! [v0] : ! [v1] : ( ~ well_orders(v0, v1) | ~ relation(v0) | is_well_founded_in(v0, v1)) % 89.28/27.02 | (600) ! [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] : (element(v6, v3) & ( ~ in(v6, v5) | (subset_complement(v0, v6) = v7 & ~ in(v7, v1))) & (in(v6, v5) | (subset_complement(v0, v6) = v7 & in(v7, v1))))))))) % 89.28/27.02 | (601) ! [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)) % 89.28/27.02 | (602) ! [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))) % 89.28/27.02 | (603) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (topstr_closure(v0, v3) = v4) | ~ disjoint(v3, v6) | ~ open_subset(v6, v0) | ~ element(v6, v2) | ~ element(v4, v2) | ~ element(v3, v2) | ~ in(v5, v6) | ~ in(v5, v4) | ~ in(v5, v1)) & ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (topstr_closure(v0, v3) = v4) | ~ element(v5, v2) | ~ element(v3, v2) | ? [v6] : ? [v7] : (in(v6, v1) & ( ~ in(v6, v5) | (disjoint(v3, v7) & open_subset(v7, v0) & element(v7, v2) & in(v6, v7))) & (in(v6, v5) | ! [v8] : ( ~ disjoint(v3, v8) | ~ open_subset(v8, v0) | ~ element(v8, v2) | ~ in(v6, v8))))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (topstr_closure(v0, v3) = v4) | ~ element(v4, v2) | ~ element(v3, v2) | ~ in(v5, v1) | in(v5, v4) | ? [v6] : (disjoint(v3, v6) & open_subset(v6, v0) & element(v6, v2) & in(v5, v6))))) % 89.28/27.02 | (604) ! [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)) % 89.28/27.02 | (605) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (((ordered_pair(v4, v3) = v6 & in(v6, v0)) | (ordered_pair(v3, v4) = v5 & in(v5, v2))) & ((ordered_pair(v4, v3) = v6 & ~ in(v6, v0)) | (ordered_pair(v3, v4) = v5 & ~ in(v5, v2))))) % 89.28/27.02 | (606) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) % 89.28/27.02 | (607) epsilon_connected(all_0_19_19) % 89.28/27.02 | (608) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | ? [v4] : (powerset(v0) = v4 & element(v3, v4))) % 89.28/27.02 | (609) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) % 89.28/27.02 | (610) ? [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))) % 89.28/27.02 | (611) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) % 89.28/27.02 | (612) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) % 89.28/27.02 | (613) ! [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))) % 89.28/27.02 | (614) natural(all_0_5_5) % 89.28/27.02 | (615) ! [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))) % 89.28/27.02 | (616) ! [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)) % 89.28/27.02 | (617) ! [v0] : ( ~ ordinal(v0) | ~ empty(v0) | epsilon_transitive(v0)) % 89.28/27.02 | (618) ? [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))) % 89.28/27.03 | (619) ! [v0] : ( ~ ordinal(v0) | ~ empty(v0) | natural(v0)) % 89.28/27.03 | (620) ? [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))))) % 89.28/27.03 | (621) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) % 89.28/27.03 | (622) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 89.28/27.03 | (623) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) % 89.28/27.03 | (624) ? [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))))) % 89.28/27.03 | (625) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ connected(v0) | ~ relation(v0) | is_connected_in(v0, v1)) % 89.28/27.03 | (626) ! [v0] : ~ in(v0, empty_set) % 89.28/27.03 | (627) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_as_subset(v0, v1, v2) = v3) | ~ relation_of2(v2, v0, v1) | ? [v4] : (powerset(v1) = v4 & element(v3, v4))) % 89.28/27.03 | (628) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & element(v1, v3))) % 89.28/27.03 | (629) ! [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] : ((v8 = v5 & apply(v0, v6) = v5 & in(v6, v3) & ( ~ in(v5, v2) | ( ~ (v7 = v6) & apply(v4, v5) = v7))) | (v7 = v6 & apply(v4, v5) = v6 & in(v5, v2) & ( ~ in(v6, v3) | ( ~ (v8 = v5) & apply(v0, v6) = v8))))))) % 89.28/27.03 | (630) ! [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)) % 89.28/27.03 | (631) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 89.28/27.03 | (632) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | transitive(v0)) % 89.28/27.03 | (633) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_topology(v2) = v1) | ~ (the_topology(v2) = v0)) % 89.28/27.03 | (634) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) % 89.28/27.03 | (635) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ reflexive(v0) | ~ relation(v0) | is_reflexive_in(v0, v1)) % 89.28/27.03 | (636) ! [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)) % 89.28/27.03 | (637) ! [v0] : ! [v1] : ( ~ (cast_as_carrier_subset(v0) = v1) | ~ one_sorted_str(v0) | ? [v2] : ? [v3] : (the_carrier(v0) = v2 & powerset(v2) = v3 & ! [v4] : ! [v5] : (v5 = v4 | ~ (subset_intersection2(v2, v4, v1) = v5) | ~ element(v4, v3)))) % 89.28/27.03 | (638) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v1, v1) = v3) | ~ relation(v0) | ~ in(v1, v2)) % 89.28/27.03 | (639) ! [v0] : ! [v1] : ( ~ (inclusion_relation(v0) = v1) | ~ ordinal(v0) | well_ordering(v1)) % 89.28/27.03 | (640) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) % 89.28/27.03 | (641) ordinal(all_0_9_9) % 89.28/27.03 | (642) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) % 89.28/27.03 | (643) epsilon_connected(all_0_15_15) % 89.28/27.03 | (644) ! [v0] : ( ~ empty(v0) | v4_membered(v0)) % 89.28/27.03 | (645) ! [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)))) % 89.28/27.03 | (646) ! [v0] : ( ~ empty(v0) | v5_membered(v0)) % 89.28/27.03 | (647) ! [v0] : ( ~ element(v0, omega) | epsilon_transitive(v0)) % 89.28/27.03 | (648) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) % 89.28/27.03 | (649) ? [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))) % 89.28/27.03 | (650) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_reflexive_in(v0, v1) | ~ relation(v0) | reflexive(v0)) % 89.28/27.03 | (651) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) % 89.28/27.03 | (652) relation(all_0_12_12) % 89.28/27.03 | (653) ! [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))) % 89.28/27.03 | (654) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (meet(v4, v3, v2) = v1) | ~ (meet(v4, v3, v2) = v0)) % 89.40/27.03 | (655) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 89.40/27.03 | (656) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (cast_to_subset(v0) = v2) | ~ (union_of_subsets(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & meet_of_subsets(v0, v5) = v4 & complements_of_subsets(v0, v1) = v5) | (powerset(v5) = v6 & powerset(v0) = v5 & ~ element(v1, v6)))) % 89.40/27.03 | (657) ? [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))))) % 89.40/27.03 | (658) relation(all_0_16_16) % 89.40/27.03 | (659) ! [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)) % 89.40/27.03 | (660) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) % 89.40/27.03 | (661) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 89.40/27.03 | (662) epsilon_transitive(all_0_5_5) % 89.40/27.03 | (663) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) % 89.40/27.03 | (664) ~ empty(all_0_16_16) % 89.40/27.03 | (665) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v3_membered(v2)) % 89.40/27.03 | (666) ! [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)) % 89.40/27.03 | (667) ? [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))))) % 89.40/27.03 | (668) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (inclusion_relation(v0) = v2) | ~ (relation_field(v1) = v0) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (in(v4, v0) & in(v3, v0) & ( ~ subset(v3, v4) | (ordered_pair(v3, v4) = v5 & ~ in(v5, v1))) & (subset(v3, v4) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) % 89.40/27.03 | (669) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) % 89.40/27.03 | (670) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) % 89.40/27.03 | (671) ! [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)) % 89.40/27.03 | (672) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) % 89.40/27.03 | (673) ! [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) % 89.40/27.03 | (674) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 89.40/27.03 | (675) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) % 89.40/27.03 | (676) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1)) % 89.40/27.03 | (677) ? [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))) % 89.40/27.04 | (678) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v5_membered(v0) | v4_membered(v2)) % 89.40/27.04 | (679) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) % 89.40/27.04 | (680) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 89.40/27.04 | (681) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 89.40/27.04 | (682) function(all_0_11_11) % 89.40/27.04 | (683) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | pair_first(v2) = v0) % 89.40/27.04 | (684) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) % 89.40/27.04 | (685) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | subset(v3, v0)) % 89.40/27.04 | (686) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (topstr_closure(v0, v3) = v4) | ~ element(v3, v2) | subset(v3, v4)))) % 89.40/27.04 | (687) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) % 89.40/27.04 | (688) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (fiber(v0, v1) = v2) | ~ (ordered_pair(v3, v1) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v3, v2)) % 89.40/27.04 | (689) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1)) % 89.40/27.04 | (690) ! [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))) % 89.40/27.04 | (691) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) = v0)) % 89.40/27.04 | (692) empty(all_0_15_15) % 89.40/27.04 | (693) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 89.40/27.04 | (694) ! [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_30_30 = empty_set) & powerset(all_0_32_32) = all_0_31_31 & powerset(all_0_33_33) = all_0_32_32 & ordinal(all_0_33_33) & element(all_0_30_30, all_0_31_31) & in(all_0_33_33, omega) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ ordinal(v0) | ~ in(v0, all_0_33_33) | ~ 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_30_30) | ? [v1] : ( ~ (v1 = v0) & subset(v0, v1) & in(v1, all_0_30_30)))) % 89.40/27.04 | (695) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ~ function(v1) | relation(v2)) % 89.40/27.04 | (696) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ is_transitive_in(v0, v1) | ~ relation(v0) | transitive(v0)) % 89.40/27.04 | (697) ! [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))) % 89.40/27.04 | (698) ! [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))) % 89.40/27.04 | (699) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_field(v1) = v2) | ~ equipotent(v0, v2) | ~ well_ordering(v1) | ~ relation(v1) | ? [v3] : (well_orders(v3, v0) & relation(v3))) % 89.40/27.04 | (700) ? [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))))) % 89.40/27.04 | (701) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & subset(v3, v4))) % 89.40/27.04 | (702) ! [v0] : ! [v1] : ! [v2] : ( ~ in(v2, v0) | ~ in(v1, v2) | ~ in(v0, v1)) % 89.40/27.04 | (703) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 89.40/27.04 | (704) ? [v0] : ? [v1] : ? [v2] : (relation_of2(v2, v0, v1) & relation(v2) & function(v2)) % 89.40/27.04 | (705) ! [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))) % 89.40/27.04 | (706) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 89.40/27.04 | (707) ! [v0] : ( ~ empty(v0) | finite(v0)) % 89.40/27.04 | (708) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) % 89.40/27.04 | (709) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | ordinal(v1)) % 89.40/27.04 | (710) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply_binary(v4, v3, v2) = v1) | ~ (apply_binary(v4, v3, v2) = v0)) % 89.40/27.04 | (711) ! [v0] : ( ~ ordinal(v0) | epsilon_connected(v0)) % 89.40/27.04 | (712) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ finite(v0) | ~ element(v2, v1) | finite(v2)) % 89.40/27.04 | (713) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) % 89.40/27.04 | (714) ! [v0] : ! [v1] : ( ~ in(v1, v0) | empty(v0) | element(v1, v0)) % 89.40/27.04 | (715) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) % 89.40/27.04 | (716) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) % 89.40/27.04 | (717) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 89.40/27.04 | (718) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) % 89.40/27.04 | (719) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) % 89.40/27.04 | (720) ! [v0] : ( ~ join_semilatt_str(v0) | one_sorted_str(v0)) % 89.40/27.04 | (721) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) % 89.40/27.04 | (722) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) % 89.40/27.04 | (723) ! [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)) % 89.40/27.04 | (724) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) % 89.40/27.04 | (725) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) % 89.40/27.04 | (726) ! [v0] : ! [v1] : ( ~ equipotent(v0, v1) | ? [v2] : (relation_rng(v2) = v1 & relation_dom(v2) = v0 & one_to_one(v2) & relation(v2) & function(v2))) % 89.40/27.04 | (727) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v3_membered(v0) | v1_membered(v2)) % 89.40/27.04 | (728) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) % 89.40/27.04 | (729) ~ empty_carrier(all_0_21_21) % 89.40/27.04 | (730) ! [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))) % 89.40/27.04 | (731) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 89.40/27.04 | (732) ! [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)) % 89.40/27.04 | (733) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ well_ordering(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | well_ordering(v1)) % 89.40/27.04 | (734) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (( ~ in(v4, v0) | (v5 = v3 & apply(v0, v2) = v3)) & (in(v4, v0) | ( ~ (v5 = v3) & apply(v0, v2) = v5)))) % 89.40/27.04 | (735) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v0) = v3 & (element(v2, v3) | (powerset(v3) = v4 & ~ element(v1, v4))))) % 89.40/27.04 | (736) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty_carrier_subset(v2) = v1) | ~ (empty_carrier_subset(v2) = v0)) % 89.40/27.04 | (737) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v3) | ~ relation_of2_as_subset(v2, v0, v1) | ? [v4] : (powerset(v3) = v4 & element(v2, v4))) % 89.40/27.04 | (738) ! [v0] : ( ~ empty(v0) | v2_membered(v0)) % 89.40/27.04 | (739) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) % 89.40/27.04 | (740) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) % 89.40/27.04 | (741) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 89.40/27.04 | (742) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ natural(v0) | epsilon_transitive(v1)) % 89.40/27.04 | (743) ! [v0] : ! [v1] : ( ~ equipotent(v0, v1) | are_equipotent(v0, v1)) % 89.40/27.04 | (744) ! [v0] : ! [v1] : ( ~ are_equipotent(v0, v1) | equipotent(v0, v1)) % 89.40/27.04 | (745) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3))) % 89.40/27.05 | (746) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) % 89.40/27.05 | (747) ! [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)))))) % 89.40/27.05 | (748) ! [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)) % 89.40/27.05 | (749) ? [v0] : ! [v1] : ! [v2] : ( ~ (the_carrier(v1) = v2) | ~ topological_space(v1) | ~ top_str(v1) | ? [v3] : ? [v4] : ? [v5] : (powerset(v2) = v3 & ( ~ element(v0, v3) | (powerset(v3) = v4 & element(v5, v4) & ! [v6] : ( ~ closed_subset(v6, v1) | ~ subset(v0, v6) | ~ element(v6, v3) | in(v6, v5)) & ! [v6] : ( ~ element(v6, v3) | ~ in(v6, v5) | closed_subset(v6, v1)) & ! [v6] : ( ~ element(v6, v3) | ~ in(v6, v5) | subset(v0, v6)))))) % 89.40/27.05 | (750) epsilon_connected(all_0_10_10) % 89.40/27.05 | (751) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) % 89.40/27.05 | (752) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) % 89.40/27.05 | (753) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) % 89.40/27.05 | (754) ! [v0] : ( ~ element(v0, omega) | natural(v0)) % 89.40/27.05 | (755) ? [v0] : ? [v1] : ? [v2] : relation_of2(v2, v0, v1) % 89.40/27.05 | (756) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 89.40/27.05 | (757) ! [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)) % 89.40/27.05 | (758) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ? [v2] : (in(v2, v1) & ! [v3] : ( ~ in(v3, v2) | ~ in(v3, v1)))) % 89.40/27.05 | (759) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) % 89.40/27.05 | (760) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | well_founded_relation(v0)) % 89.40/27.05 | (761) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 89.40/27.05 | (762) ! [v0] : ! [v1] : ! [v2] : ( ~ relation_isomorphism(v0, v1, v2) | ~ reflexive(v0) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v2) | reflexive(v1)) % 89.40/27.05 | (763) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ finite(v0) | finite(v2)) % 89.40/27.05 | (764) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ((v5 = v4 & apply(v2, v1) = v4) | (relation_dom(v3) = v5 & ~ in(v1, v5)))) % 89.40/27.05 | (765) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1) % 89.40/27.05 | (766) ! [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)) % 89.40/27.05 | (767) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) % 89.40/27.05 | (768) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | ~ v4_membered(v0) | v3_membered(v2)) % 89.40/27.05 | (769) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ~ closed_subset(v3, v0) | ~ element(v3, v2) | open_subset(v4, v0)) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ~ open_subset(v4, v0) | ~ element(v3, v2) | closed_subset(v3, v0)))) % 89.40/27.05 | (770) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) % 89.40/27.05 | (771) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ ordinal(v0) | ~ empty(v1)) % 89.40/27.05 | (772) ! [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] : (( ~ (v5 = v2) | (v6 = v1 & relation_dom_restriction(v3, v0) = v1) | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ((v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11)) | ( ~ (v6 = v1) & relation_dom_restriction(v3, v0) = v6)))) % 89.40/27.05 | (773) ! [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)) % 89.40/27.05 | (774) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ antisymmetric(v1) | ~ relation(v1) | antisymmetric(v2)) % 89.40/27.05 | (775) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) % 89.40/27.05 | (776) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) % 89.40/27.05 | (777) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) % 89.40/27.05 | (778) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) % 89.40/27.05 | (779) ! [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] : ((v7 = v6 & apply_binary(v3, v4, v5) = v6) | (cartesian_product2(v0, v1) = v7 & ( ~ relation_of2(v3, v7, v2) | ~ quasi_total(v3, v7, v2))))) % 89.40/27.05 | (780) ! [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))) % 89.40/27.05 | (781) ! [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)) % 89.40/27.05 | (782) ~ empty(all_0_5_5) % 89.40/27.05 | (783) ? [v0] : subset(empty_set, v0) % 89.40/27.05 | (784) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (( ~ (v1 = empty_set) | (v2 = empty_set & relation_dom(v0) = empty_set)) & (v1 = empty_set | ( ~ (v2 = empty_set) & relation_dom(v0) = v2)))) % 89.40/27.05 | (785) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_ordering(v0) | ~ relation(v0) | well_orders(v0, v1)) % 89.40/27.05 | (786) ! [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))))) % 89.40/27.05 | (787) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) % 89.40/27.05 | (788) ! [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))) % 89.40/27.05 | (789) ! [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)) % 89.40/27.05 | (790) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0)) % 89.40/27.05 | (791) ! [v0] : ! [v1] : ( ~ ordinal(v0) | ~ element(v1, v0) | epsilon_connected(v1)) % 89.40/27.05 | (792) ! [v0] : ! [v1] : ( ~ epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0)) % 89.40/27.05 | (793) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = v2 & union(v1) = v2) | (powerset(v3) = v4 & powerset(v0) = v3 & ~ element(v1, v4)))) % 89.40/27.05 | (794) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_intersection2(v4, v3, v2) = v1) | ~ (subset_intersection2(v4, v3, v2) = v0)) % 89.40/27.05 | (795) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) % 89.40/27.05 | (796) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) % 89.40/27.05 | (797) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) % 89.40/27.05 | (798) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) % 89.40/27.05 | (799) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) % 89.40/27.05 | (800) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_restriction(v2, v0) = v3) | ~ (fiber(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (fiber(v2, v1) = v5 & subset(v4, v5))) % 89.40/27.05 | (801) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | antisymmetric(v0)) % 89.40/27.05 | (802) singleton(empty_set) = all_0_41_41 % 89.40/27.05 | (803) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ well_founded_relation(v0) | ~ relation(v0) | is_well_founded_in(v0, v1)) % 89.40/27.05 | (804) ~ empty_carrier(all_0_39_39) % 89.40/27.05 | (805) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (( ~ in(v0, v1) | (relation_dom(v3) = v4 & in(v0, v4)) | (relation_dom(v2) = v5 & ~ in(v0, v5))) & ((relation_dom(v3) = v4 & ~ in(v0, v4)) | (relation_dom(v2) = v5 & in(v0, v5) & in(v0, v1))))) % 89.40/27.05 | (806) ! [v0] : ( ~ empty(v0) | epsilon_transitive(v0)) % 89.40/27.05 | (807) ? [v0] : ? [v1] : (relation_dom(v1) = v0 & relation(v1) & function(v1) & ! [v2] : ! [v3] : ( ~ (singleton(v2) = v3) | ~ in(v2, v0) | apply(v1, v2) = v3)) % 89.40/27.06 | (808) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 89.40/27.06 | (809) ! [v0] : ( ~ diff_closed(v0) | ~ cup_closed(v0) | preboolean(v0)) % 89.40/27.06 | (810) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) % 89.40/27.06 | (811) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) % 89.40/27.06 | (812) ! [v0] : ! [v1] : ( ~ (the_carrier(v0) = v1) | ~ top_str(v0) | ? [v2] : (powerset(v1) = v2 & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ~ closed_subset(v4, v0) | ~ element(v3, v2) | open_subset(v3, v0)) & ! [v3] : ! [v4] : ( ~ (subset_complement(v1, v3) = v4) | ~ open_subset(v3, v0) | ~ element(v3, v2) | closed_subset(v4, v0)))) % 89.40/27.06 | (813) ! [v0] : ( ~ empty(v0) | v3_membered(v0)) % 89.40/27.06 | (814) ? [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)) % 89.40/27.06 | (815) ! [v0] : ( ~ empty(v0) | epsilon_connected(v0)) % 89.40/27.06 | (816) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_restriction(v1, v0) = v2) | ~ well_orders(v1, v0) | ~ relation(v1) | relation_field(v2) = v0) % 89.40/27.06 | (817) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) % 89.40/27.06 | (818) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) % 89.40/27.06 | (819) relation(all_0_15_15) % 89.40/27.06 | (820) ! [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))) % 89.40/27.06 | (821) ! [v0] : ! [v1] : (v1 = v0 | ~ ordinal(v1) | ~ ordinal(v0) | in(v1, v0) | in(v0, v1)) % 89.40/27.06 | (822) ! [v0] : ! [v1] : ( ~ (relation_rng(v1) = v0) | ~ relation(v1) | ~ function(v1) | finite(v0) | ? [v2] : (relation_dom(v1) = v2 & ~ in(v2, omega))) % 89.40/27.06 | (823) ! [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)))) % 89.40/27.06 | (824) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ((v5 = v1 & relation_rng(v4) = v1) | (relation_rng(v3) = v5 & ~ subset(v2, v5)))))) % 89.40/27.06 | (825) epsilon_transitive(empty_set) % 89.40/27.06 | (826) ! [v0] : ( ~ well_ordering(v0) | ~ relation(v0) | reflexive(v0)) % 89.40/27.06 | (827) empty(all_0_11_11) % 89.40/27.06 | (828) ? [v0] : (epsilon_connected(v0) | ? [v1] : ? [v2] : ( ~ (v2 = v1) & in(v2, v0) & in(v1, v0) & ~ in(v2, v1) & ~ in(v1, v2))) % 89.40/27.06 | (829) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) % 89.40/27.06 | (830) ? [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)))) % 89.40/27.06 | (831) ! [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)) % 89.40/27.06 | (832) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) % 89.40/27.06 | (833) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) % 89.40/27.06 | (834) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 89.40/27.06 | (835) ? [v0] : ! [v1] : ! [v2] : ( ~ (cast_as_carrier_subset(v1) = v2) | ~ topological_space(v1) | ~ top_str(v1) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (the_carrier(v1) = v3 & powerset(v4) = v5 & powerset(v3) = v4 & ( ~ element(v0, v5) | (element(v6, v5) & ! [v7] : ! [v8] : ( ~ (set_difference(v2, v7) = v8) | ~ element(v7, v4) | ~ in(v8, v0) | in(v7, v6)) & ! [v7] : ! [v8] : ( ~ (set_difference(v2, v7) = v8) | ~ element(v7, v4) | ~ in(v7, v6) | in(v8, v0)))))) % 89.40/27.06 | (836) ordinal(all_0_10_10) % 89.40/27.06 | (837) ! [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))) % 89.40/27.06 | (838) ! [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)) % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (432) with all_0_12_12, all_0_11_11 and discharging atoms empty(all_0_11_11), empty(all_0_12_12), yields: % 89.40/27.06 | (839) all_0_11_11 = all_0_12_12 % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (432) with all_0_13_13, all_0_12_12 and discharging atoms empty(all_0_12_12), empty(all_0_13_13), yields: % 89.40/27.06 | (840) all_0_12_12 = all_0_13_13 % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (432) with all_0_14_14, all_0_13_13 and discharging atoms empty(all_0_13_13), empty(all_0_14_14), yields: % 89.40/27.06 | (841) all_0_13_13 = all_0_14_14 % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (432) with all_0_15_15, all_0_11_11 and discharging atoms empty(all_0_11_11), empty(all_0_15_15), yields: % 89.40/27.06 | (842) all_0_11_11 = all_0_15_15 % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (432) with empty_set, all_0_13_13 and discharging atoms empty(all_0_13_13), empty(empty_set), yields: % 89.40/27.06 | (843) all_0_13_13 = empty_set % 89.40/27.06 | % 89.40/27.06 | Combining equations (839,842) yields a new equation: % 89.40/27.06 | (844) all_0_12_12 = all_0_15_15 % 89.40/27.06 | % 89.40/27.06 | Simplifying 844 yields: % 89.40/27.06 | (845) all_0_12_12 = all_0_15_15 % 89.40/27.06 | % 89.40/27.06 | Combining equations (840,845) yields a new equation: % 89.40/27.06 | (846) all_0_13_13 = all_0_15_15 % 89.40/27.06 | % 89.40/27.06 | Simplifying 846 yields: % 89.40/27.06 | (847) all_0_13_13 = all_0_15_15 % 89.40/27.06 | % 89.40/27.06 | Combining equations (843,841) yields a new equation: % 89.40/27.06 | (848) all_0_14_14 = empty_set % 89.40/27.06 | % 89.40/27.06 | Combining equations (847,841) yields a new equation: % 89.40/27.06 | (849) all_0_14_14 = all_0_15_15 % 89.40/27.06 | % 89.40/27.06 | Combining equations (848,849) yields a new equation: % 89.40/27.06 | (850) all_0_15_15 = empty_set % 89.40/27.06 | % 89.40/27.06 | From (850) and (692) follows: % 89.40/27.06 | (271) empty(empty_set) % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (477) with all_0_35_35, all_0_36_36, all_0_38_38 and discharging atoms subset_complement(all_0_38_38, all_0_36_36) = all_0_35_35, yields: % 89.40/27.06 | (852) ? [v0] : (powerset(all_0_38_38) = v0 & ( ~ element(all_0_36_36, v0) | element(all_0_35_35, v0))) % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (426) with all_0_35_35, all_0_36_36, all_0_38_38 and discharging atoms subset_complement(all_0_38_38, all_0_36_36) = all_0_35_35, yields: % 89.40/27.06 | (853) ? [v0] : ((v0 = all_0_35_35 & set_difference(all_0_38_38, all_0_36_36) = all_0_35_35) | (powerset(all_0_38_38) = v0 & ~ element(all_0_36_36, v0))) % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (142) with all_0_38_38, all_0_39_39 and discharging atoms the_carrier(all_0_39_39) = all_0_38_38, one_sorted_str(all_0_39_39), ~ empty_carrier(all_0_39_39), yields: % 89.40/27.06 | (854) ? [v0] : ? [v1] : (powerset(all_0_38_38) = v0 & element(v1, v0) & ~ empty(v1)) % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (349) with empty_set, all_0_39_39 and discharging atoms one_sorted_str(all_0_39_39), empty(empty_set), ~ empty_carrier(all_0_39_39), yields: % 89.40/27.06 | (855) ~ (the_carrier(all_0_39_39) = empty_set) % 89.40/27.06 | % 89.40/27.06 | Instantiating formula (107) with all_0_34_34, all_0_35_35, all_0_36_36, all_0_37_37, all_0_38_38 and discharging atoms subset_complement(all_0_38_38, all_0_36_36) = all_0_35_35, powerset(all_0_38_38) = all_0_37_37, element(all_0_34_34, all_0_38_38), element(all_0_36_36, all_0_37_37), yields: % 89.40/27.06 | (856) all_0_38_38 = empty_set | in(all_0_34_34, all_0_35_35) | in(all_0_34_34, all_0_36_36) % 89.40/27.06 | % 89.40/27.06 | Instantiating (854) with all_194_0_147, all_194_1_148 yields: % 89.40/27.06 | (857) powerset(all_0_38_38) = all_194_1_148 & element(all_194_0_147, all_194_1_148) & ~ empty(all_194_0_147) % 89.40/27.06 | % 89.40/27.06 | Applying alpha-rule on (857) yields: % 89.40/27.06 | (858) powerset(all_0_38_38) = all_194_1_148 % 89.40/27.06 | (859) element(all_194_0_147, all_194_1_148) % 89.40/27.06 | (860) ~ empty(all_194_0_147) % 89.40/27.06 | % 89.40/27.06 | Instantiating (853) with all_412_0_230 yields: % 89.40/27.06 | (861) (all_412_0_230 = all_0_35_35 & set_difference(all_0_38_38, all_0_36_36) = all_0_35_35) | (powerset(all_0_38_38) = all_412_0_230 & ~ element(all_0_36_36, all_412_0_230)) % 89.40/27.06 | % 89.40/27.06 | Instantiating (852) with all_413_0_231 yields: % 89.40/27.06 | (862) powerset(all_0_38_38) = all_413_0_231 & ( ~ element(all_0_36_36, all_413_0_231) | element(all_0_35_35, all_413_0_231)) % 89.40/27.07 | % 89.40/27.07 | Applying alpha-rule on (862) yields: % 89.40/27.07 | (863) powerset(all_0_38_38) = all_413_0_231 % 89.40/27.07 | (864) ~ element(all_0_36_36, all_413_0_231) | element(all_0_35_35, all_413_0_231) % 89.40/27.07 | % 89.40/27.07 | Instantiating formula (105) with all_0_38_38, all_413_0_231, all_0_37_37 and discharging atoms powerset(all_0_38_38) = all_413_0_231, powerset(all_0_38_38) = all_0_37_37, yields: % 89.40/27.07 | (865) all_413_0_231 = all_0_37_37 % 89.40/27.07 | % 89.40/27.07 | Instantiating formula (105) with all_0_38_38, all_194_1_148, all_413_0_231 and discharging atoms powerset(all_0_38_38) = all_413_0_231, powerset(all_0_38_38) = all_194_1_148, yields: % 89.40/27.07 | (866) all_413_0_231 = all_194_1_148 % 89.40/27.07 | % 89.40/27.07 | Using (570) and (855) yields: % 89.40/27.07 | (867) ~ (all_0_38_38 = empty_set) % 89.40/27.07 | % 89.40/27.07 | Combining equations (866,865) yields a new equation: % 89.40/27.07 | (868) all_194_1_148 = all_0_37_37 % 89.40/27.07 | % 89.40/27.07 | Simplifying 868 yields: % 89.40/27.07 | (869) all_194_1_148 = all_0_37_37 % 89.40/27.07 | % 89.40/27.07 | From (869) and (858) follows: % 89.40/27.07 | (553) powerset(all_0_38_38) = all_0_37_37 % 89.40/27.07 | % 89.40/27.07 +-Applying beta-rule and splitting (864), into two cases. % 89.40/27.07 |-Branch one: % 89.40/27.07 | (871) ~ element(all_0_36_36, all_413_0_231) % 89.40/27.07 | % 89.40/27.07 | From (865) and (871) follows: % 89.40/27.07 | (872) ~ element(all_0_36_36, all_0_37_37) % 89.40/27.07 | % 89.40/27.07 | Using (247) and (872) yields: % 89.40/27.07 | (873) $false % 89.40/27.07 | % 89.40/27.07 |-The branch is then unsatisfiable % 89.40/27.07 |-Branch two: % 89.40/27.07 | (874) element(all_0_36_36, all_413_0_231) % 89.40/27.07 | (875) element(all_0_35_35, all_413_0_231) % 89.40/27.07 | % 89.40/27.07 | From (865) and (874) follows: % 89.40/27.07 | (247) element(all_0_36_36, all_0_37_37) % 89.40/27.07 | % 89.40/27.07 +-Applying beta-rule and splitting (861), into two cases. % 89.40/27.07 |-Branch one: % 89.40/27.07 | (877) all_412_0_230 = all_0_35_35 & set_difference(all_0_38_38, all_0_36_36) = all_0_35_35 % 89.40/27.07 | % 89.40/27.07 | Applying alpha-rule on (877) yields: % 89.40/27.07 | (878) all_412_0_230 = all_0_35_35 % 89.40/27.07 | (879) set_difference(all_0_38_38, all_0_36_36) = all_0_35_35 % 89.40/27.07 | % 89.40/27.07 +-Applying beta-rule and splitting (134), into two cases. % 89.40/27.07 |-Branch one: % 89.40/27.07 | (880) in(all_0_34_34, all_0_35_35) & in(all_0_34_34, all_0_36_36) % 89.40/27.07 | % 89.40/27.07 | Applying alpha-rule on (880) yields: % 89.40/27.07 | (881) in(all_0_34_34, all_0_35_35) % 89.40/27.07 | (882) in(all_0_34_34, all_0_36_36) % 89.40/27.07 | % 89.40/27.07 | Instantiating formula (336) with all_0_34_34, all_0_35_35, all_0_36_36, all_0_38_38 and discharging atoms set_difference(all_0_38_38, all_0_36_36) = all_0_35_35, in(all_0_34_34, all_0_35_35), in(all_0_34_34, all_0_36_36), yields: % 89.40/27.07 | (873) $false % 89.40/27.07 | % 89.40/27.07 |-The branch is then unsatisfiable % 89.40/27.07 |-Branch two: % 89.40/27.07 | (884) ~ in(all_0_34_34, all_0_35_35) & ~ in(all_0_34_34, all_0_36_36) % 89.40/27.07 | % 89.40/27.07 | Applying alpha-rule on (884) yields: % 89.40/27.07 | (885) ~ in(all_0_34_34, all_0_35_35) % 89.40/27.07 | (886) ~ in(all_0_34_34, all_0_36_36) % 89.40/27.07 | % 89.40/27.07 +-Applying beta-rule and splitting (856), into two cases. % 89.40/27.07 |-Branch one: % 89.40/27.07 | (881) in(all_0_34_34, all_0_35_35) % 89.40/27.07 | % 89.40/27.07 | Using (881) and (885) yields: % 89.40/27.07 | (873) $false % 89.40/27.07 | % 89.40/27.07 |-The branch is then unsatisfiable % 89.40/27.07 |-Branch two: % 89.40/27.07 | (885) ~ in(all_0_34_34, all_0_35_35) % 89.40/27.07 | (890) all_0_38_38 = empty_set | in(all_0_34_34, all_0_36_36) % 89.40/27.07 | % 89.40/27.07 +-Applying beta-rule and splitting (890), into two cases. % 89.40/27.07 |-Branch one: % 89.40/27.07 | (882) in(all_0_34_34, all_0_36_36) % 89.40/27.07 | % 89.40/27.07 | Using (882) and (886) yields: % 89.40/27.07 | (873) $false % 89.40/27.07 | % 89.40/27.07 |-The branch is then unsatisfiable % 89.40/27.07 |-Branch two: % 89.40/27.07 | (886) ~ in(all_0_34_34, all_0_36_36) % 89.40/27.07 | (894) all_0_38_38 = empty_set % 89.40/27.07 | % 89.40/27.07 | Equations (894) can reduce 867 to: % 89.40/27.07 | (895) $false % 89.40/27.07 | % 89.40/27.07 |-The branch is then unsatisfiable % 89.40/27.07 |-Branch two: % 89.40/27.07 | (896) powerset(all_0_38_38) = all_412_0_230 & ~ element(all_0_36_36, all_412_0_230) % 89.40/27.07 | % 89.40/27.07 | Applying alpha-rule on (896) yields: % 89.40/27.07 | (897) powerset(all_0_38_38) = all_412_0_230 % 89.40/27.07 | (898) ~ element(all_0_36_36, all_412_0_230) % 89.40/27.07 | % 89.40/27.07 | Instantiating formula (105) with all_0_38_38, all_412_0_230, all_0_37_37 and discharging atoms powerset(all_0_38_38) = all_412_0_230, powerset(all_0_38_38) = all_0_37_37, yields: % 89.40/27.07 | (899) all_412_0_230 = all_0_37_37 % 89.40/27.07 | % 89.40/27.07 | Using (247) and (898) yields: % 89.40/27.07 | (900) ~ (all_412_0_230 = all_0_37_37) % 89.40/27.07 | % 89.40/27.07 | Equations (899) can reduce 900 to: % 89.40/27.07 | (895) $false % 89.40/27.07 | % 89.40/27.07 |-The branch is then unsatisfiable % 89.40/27.07 % SZS output end Proof for theBenchmark % 89.40/27.07 % 89.40/27.07 26529ms %------------------------------------------------------------------------------