%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU355+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n029.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  : 300s
% DateTime : Fri May 19 12:03:15 EDT 2023

% Result   : Theorem 5.81s 6.57s
% Output   : Proof 5.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU355+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.14/0.33  % Computer : n029.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Thu May 18 13:21:13 EDT 2023
% 0.14/0.33  % CPUTime  : 
% 5.81/6.57  
% 5.81/6.57  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 5.81/6.57  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.81/6.57  %-----------------------------------------------------
% 5.81/6.57  ncf(matrix, plain, [(14539 ^ _206269) ^ [] : [-(rel_str(14537 ^ []))], (14542 ^ _206269) ^ [] : [-(element(14540 ^ [], the_carrier(14537 ^ [])))], (14544 ^ _206269) ^ [] : [relstr_set_smaller(14537 ^ [], empty_set, 14540 ^ []), relstr_element_smaller(14537 ^ [], empty_set, 14540 ^ [])], (1156 ^ _206269) ^ [_243122, _243124, _243126, _243128, _243130, _243132] : [-(unordered_triple(_243132, _243128, _243124) = unordered_triple(_243130, _243126, _243122)), _243132 = _243130, _243128 = _243126, _243124 = _243122], (1170 ^ _206269) ^ [_243610, _243612, _243614, _243616] : [-(k8_filter_1(_243616, _243612) = k8_filter_1(_243614, _243610)), _243616 = _243614, _243612 = _243610], (1180 ^ _206269) ^ [_243941, _243943] : [_243943 = _243941, -(the_topology(_243943) = the_topology(_243941))], (1186 ^ _206269) ^ [_244159, _244161] : [_244161 = _244159, -(empty_carrier_subset(_244161) = empty_carrier_subset(_244159))], (1192 ^ _206269) ^ [_244377, _244379] : [_244379 = _244377, -(the_InternalRel(_244379) = the_InternalRel(_244377))], (1198 ^ _206269) ^ [_244595, _244597] : [_244597 = _244595, -(the_L_join(_244597) = the_L_join(_244595))], (1204 ^ _206269) ^ [_244813, _244815] : [_244815 = _244813, -(the_L_meet(_244815) = the_L_meet(_244813))], (1210 ^ _206269) ^ [_245031, _245033] : [_245033 = _245031, -(a_1_0_filter_1(_245033) = a_1_0_filter_1(_245031))], (1216 ^ _206269) ^ [_245277, _245279, _245281, _245283] : [-(a_2_2_lattice3(_245283, _245279) = a_2_2_lattice3(_245281, _245277)), _245283 = _245281, _245279 = _245277], (1226 ^ _206269) ^ [_245636, _245638, _245640, _245642] : [-(a_2_3_lattice3(_245642, _245638) = a_2_3_lattice3(_245640, _245636)), _245642 = _245640, _245638 = _245636], (1236 ^ _206269) ^ [_245995, _245997, _245999, _246001] : [-(rel_str_of(_246001, _245997) = rel_str_of(_245999, _245995)), _246001 = _245999, _245997 = _245995], (1246 ^ _206269) ^ [_246382, _246384, _246386, _246388, _246390, _246392] : [-(latt_str_of(_246392, _246388, _246384) = latt_str_of(_246390, _246386, _246382)), _246392 = _246390, _246388 = _246386, _246384 = _246382], (1260 ^ _206269) ^ [_246926, _246928, _246930, _246932, _246934, _246936, _246938, _246940] : [-(k10_filter_1(_246940, _246936, _246932, _246928) = k10_filter_1(_246938, _246934, _246930, _246926)), _246940 = _246938, _246936 = _246934, _246932 = _246930, _246928 = _246926], (1278 ^ _206269) ^ [_247531, _247533] : [_247533 = _247531, -(k1_pcomps_1(_247533) = k1_pcomps_1(_247531))], (1284 ^ _206269) ^ [_247889, _247891, _247893, _247895, _247897, _247899, _247901, _247903, _247905, _247907, _247909, _247911] : [-(apply_binary_as_element(_247911, _247907, _247903, _247899, _247895, _247891) = apply_binary_as_element(_247909, _247905, _247901, _247897, _247893, _247889)), _247911 = _247909, _247907 = _247905, _247903 = _247901, _247899 = _247897, _247895 = _247893, _247891 = _247889], (1310 ^ _206269) ^ [_248888, _248890, _248892, _248894, _248896, _248898] : [-(apply_binary(_248898, _248894, _248890) = apply_binary(_248896, _248892, _248888)), _248898 = _248896, _248894 = _248892, _248890 = _248888], (1324 ^ _206269) ^ [_249348, _249350] : [_249350 = _249348, -(k2_lattice3(_249350) = k2_lattice3(_249348))], (1330 ^ _206269) ^ [_249622, _249624, _249626, _249628, _249630, _249632] : [-(join_commut(_249632, _249628, _249624) = join_commut(_249630, _249626, _249622)), _249632 = _249630, _249628 = _249626, _249624 = _249622], (1344 ^ _206269) ^ [_250138, _250140, _250142, _250144, _250146, _250148] : [-(subset_union2(_250148, _250144, _250140) = subset_union2(_250146, _250142, _250138)), _250148 = _250146, _250144 = _250142, _250140 = _250138], (1358 ^ _206269) ^ [_250598, _250600] : [_250600 = _250598, -(identity_as_relation_of(_250600) = identity_as_relation_of(_250598))], (1364 ^ _206269) ^ [_250816, _250818] : [_250818 = _250816, -(set_meet(_250818) = set_meet(_250816))], (1370 ^ _206269) ^ [_251090, _251092, _251094, _251096, _251098, _251100] : [-(subset_intersection2(_251100, _251096, _251092) = subset_intersection2(_251098, _251094, _251090)), _251100 = _251098, _251096 = _251094, _251092 = _251090], (1384 ^ _206269) ^ [_251578, _251580, _251582, _251584] : [-(relation_image(_251584, _251580) = relation_image(_251582, _251578)), _251584 = _251582, _251580 = _251578], (1394 ^ _206269) ^ [_251937, _251939, _251941, _251943] : [-(relation_rng_restriction(_251943, _251939) = relation_rng_restriction(_251941, _251937)), _251943 = _251941, _251939 = _251937], (1404 ^ _206269) ^ [_252324, _252326, _252328, _252330, _252332, _252334] : [-(join(_252334, _252330, _252326) = join(_252332, _252328, _252324)), _252334 = _252332, _252330 = _252328, _252326 = _252324], (1418 ^ _206269) ^ [_252840, _252842, _252844, _252846, _252848, _252850] : [-(meet(_252850, _252846, _252842) = meet(_252848, _252844, _252840)), _252850 = _252848, _252846 = _252844, _252842 = _252840], (1432 ^ _206269) ^ [_253328, _253330, _253332, _253334] : [-(cartesian_product2(_253334, _253330) = cartesian_product2(_253332, _253328)), _253334 = _253332, _253330 = _253328], (1442 ^ _206269) ^ [_253687, _253689, _253691, _253693] : [-(fiber(_253693, _253689) = fiber(_253691, _253687)), _253693 = _253691, _253689 = _253687], (1452 ^ _206269) ^ [_254018, _254020] : [_254020 = _254018, -(cast_as_carrier_subset(_254020) = cast_as_carrier_subset(_254018))], (1458 ^ _206269) ^ [_254292, _254294, _254296, _254298, _254300, _254302] : [-(relation_dom_as_subset(_254302, _254298, _254294) = relation_dom_as_subset(_254300, _254296, _254292)), _254302 = _254300, _254298 = _254296, _254294 = _254292], (1472 ^ _206269) ^ [_254808, _254810, _254812, _254814, _254816, _254818] : [-(meet_commut(_254818, _254814, _254810) = meet_commut(_254816, _254812, _254808)), _254818 = _254816, _254814 = _254812, _254810 = _254808], (1486 ^ _206269) ^ [_255324, _255326, _255328, _255330, _255332, _255334] : [-(relation_rng_as_subset(_255334, _255330, _255326) = relation_rng_as_subset(_255332, _255328, _255324)), _255334 = _255332, _255330 = _255328, _255326 = _255324], (1500 ^ _206269) ^ [_255812, _255814, _255816, _255818] : [-(cast_to_el_of_lattice(_255818, _255814) = cast_to_el_of_lattice(_255816, _255812)), _255818 = _255816, _255814 = _255812], (1510 ^ _206269) ^ [_256227, _256229, _256231, _256233, _256235, _256237, _256239, _256241] : [-(ordered_pair_as_product_element(_256241, _256237, _256233, _256229) = ordered_pair_as_product_element(_256239, _256235, _256231, _256227)), _256241 = _256239, _256237 = _256235, _256233 = _256231, _256229 = _256227], (1528 ^ _206269) ^ [_256832, _256834] : [_256834 = _256832, -(relation_of_lattice(_256834) = relation_of_lattice(_256832))], (1534 ^ _206269) ^ [_257078, _257080, _257082, _257084] : [-(meet_of_latt_set(_257084, _257080) = meet_of_latt_set(_257082, _257078)), _257084 = _257082, _257080 = _257078], (1544 ^ _206269) ^ [_257409, _257411] : [_257411 = _257409, -(relation_inverse(_257411) = relation_inverse(_257409))], (1550 ^ _206269) ^ [_257655, _257657, _257659, _257661] : [-(relation_restriction(_257661, _257657) = relation_restriction(_257659, _257655)), _257661 = _257659, _257657 = _257655], (1560 ^ _206269) ^ [_257986, _257988] : [_257988 = _257986, -(boole_lattice(_257988) = boole_lattice(_257986))], (1566 ^ _206269) ^ [_258204, _258206] : [_258206 = _258204, -(succ(_258206) = succ(_258204))], (1572 ^ _206269) ^ [_258450, _258452, _258454, _258456] : [-(relation_inverse_image(_258456, _258452) = relation_inverse_image(_258454, _258450)), _258456 = _258454, _258452 = _258450], (1582 ^ _206269) ^ [_258809, _258811, _258813, _258815] : [-(union_of_subsets(_258815, _258811) = union_of_subsets(_258813, _258809)), _258815 = _258813, _258811 = _258809], (1592 ^ _206269) ^ [_259168, _259170, _259172, _259174] : [-(complements_of_subsets(_259174, _259170) = complements_of_subsets(_259172, _259168)), _259174 = _259172, _259170 = _259168], (1602 ^ _206269) ^ [_259555, _259557, _259559, _259561, _259563, _259565] : [-(subset_difference(_259565, _259561, _259557) = subset_difference(_259563, _259559, _259555)), _259565 = _259563, _259561 = _259559, _259557 = _259555], (1616 ^ _206269) ^ [_260015, _260017] : [_260017 = _260015, -(cast_to_subset(_260017) = cast_to_subset(_260015))], (1622 ^ _206269) ^ [_260261, _260263, _260265, _260267] : [-(meet_of_subsets(_260267, _260263) = meet_of_subsets(_260265, _260261)), _260267 = _260265, _260263 = _260261], (1632 ^ _206269) ^ [_260592, _260594] : [_260594 = _260592, -(bottom_of_semilattstr(_260594) = bottom_of_semilattstr(_260592))], (1638 ^ _206269) ^ [_260838, _260840, _260842, _260844] : [-(join_of_latt_set(_260844, _260840) = join_of_latt_set(_260842, _260838)), _260844 = _260842, _260840 = _260838], (1648 ^ _206269) ^ [_261197, _261199, _261201, _261203] : [-(topstr_closure(_261203, _261199) = topstr_closure(_261201, _261197)), _261203 = _261201, _261199 = _261197], (1658 ^ _206269) ^ [_261556, _261558, _261560, _261562] : [-(subset_complement(_261562, _261558) = subset_complement(_261560, _261556)), _261562 = _261560, _261558 = _261556], (1668 ^ _206269) ^ [_261915, _261917, _261919, _261921] : [-(interior(_261921, _261917) = interior(_261919, _261915)), _261921 = _261919, _261917 = _261915], (1678 ^ _206269) ^ [_262246, _262248] : [_262248 = _262246, -(function_inverse(_262248) = function_inverse(_262246))], (1684 ^ _206269) ^ [_262464, _262466] : [_262466 = _262464, -(poset_of_lattice(_262466) = poset_of_lattice(_262464))], (1690 ^ _206269) ^ [_262710, _262712, _262714, _262716] : [-(cast_to_el_of_LattPOSet(_262716, _262712) = cast_to_el_of_LattPOSet(_262714, _262710)), _262716 = _262714, _262712 = _262710], (1700 ^ _206269) ^ [_263041, _263043] : [_263043 = _263041, -(pair_first(_263043) = pair_first(_263041))], (1706 ^ _206269) ^ [_263259, _263261] : [_263261 = _263259, -(pair_second(_263261) = pair_second(_263259))], (1712 ^ _206269) ^ [_263477, _263479] : [_263479 = _263477, -(inclusion_relation(_263479) = inclusion_relation(_263477))], (1718 ^ _206269) ^ [_263723, _263725, _263727, _263729] : [-(set_difference(_263729, _263725) = set_difference(_263727, _263723)), _263729 = _263727, _263725 = _263723], (1728 ^ _206269) ^ [_264082, _264084, _264086, _264088] : [-(ordered_pair(_264088, _264084) = ordered_pair(_264086, _264082)), _264088 = _264086, _264084 = _264082], (1738 ^ _206269) ^ [_264441, _264443, _264445, _264447] : [-(apply(_264447, _264443) = apply(_264445, _264441)), _264447 = _264445, _264443 = _264441], (1748 ^ _206269) ^ [_264772, _264774] : [_264774 = _264772, -(relation_field(_264774) = relation_field(_264772))], (1754 ^ _206269) ^ [_265018, _265020, _265022, _265024] : [-(set_union2(_265024, _265020) = set_union2(_265022, _265018)), _265024 = _265022, _265020 = _265018], (1764 ^ _206269) ^ [_265377, _265379, _265381, _265383] : [-(set_intersection2(_265383, _265379) = set_intersection2(_265381, _265377)), _265383 = _265381, _265379 = _265377], (1774 ^ _206269) ^ [_265708, _265710] : [_265710 = _265708, -(relation_dom(_265710) = relation_dom(_265708))], (1780 ^ _206269) ^ [_266010, _266012, _266014, _266016, _266018, _266020, _266022, _266024] : [-(apply_as_element(_266024, _266020, _266016, _266012) = apply_as_element(_266022, _266018, _266014, _266010)), _266024 = _266022, _266020 = _266018, _266016 = _266014, _266012 = _266010], (1798 ^ _206269) ^ [_266615, _266617] : [_266617 = _266615, -(identity_on_carrier(_266617) = identity_on_carrier(_266615))], (1804 ^ _206269) ^ [_266861, _266863, _266865, _266867] : [-(relation_composition(_266867, _266863) = relation_composition(_266865, _266861)), _266867 = _266865, _266863 = _266861], (1814 ^ _206269) ^ [_267192, _267194] : [_267194 = _267192, -(identity_relation(_267194) = identity_relation(_267192))], (1820 ^ _206269) ^ [_267438, _267440, _267442, _267444] : [-(relation_dom_restriction(_267444, _267440) = relation_dom_restriction(_267442, _267438)), _267444 = _267442, _267440 = _267438], (1830 ^ _206269) ^ [_267769, _267771] : [_267771 = _267769, -(relation_rng(_267771) = relation_rng(_267769))], (1836 ^ _206269) ^ [_267987, _267989] : [_267989 = _267987, -(union(_267989) = union(_267987))], (1842 ^ _206269) ^ [_268205, _268207] : [_268207 = _268205, -(powerset(_268207) = powerset(_268205))], (1848 ^ _206269) ^ [_268423, _268425] : [_268425 = _268423, -(singleton(_268425) = singleton(_268423))], (1864 ^ _206269) ^ [_268980, _268982] : [_268982 = _268980, -(the_carrier(_268982) = the_carrier(_268980))], (1854 ^ _206269) ^ [_268669, _268671, _268673, _268675] : [-(unordered_pair(_268675, _268671) = unordered_pair(_268673, _268669)), _268675 = _268673, _268671 = _268669], (2 ^ _206269) ^ [_206413] : [-(_206413 = _206413)], (4 ^ _206269) ^ [_206520, _206522] : [_206522 = _206520, -(_206520 = _206522)], (10 ^ _206269) ^ [_206724, _206726, _206728] : [-(_206728 = _206724), _206728 = _206726, _206726 = _206724], (20 ^ _206269) ^ [_207037, _207039] : [-(v1_xcmplx_0(_207037)), _207039 = _207037, v1_xcmplx_0(_207039)], (30 ^ _206269) ^ [_207332, _207334] : [-(v1_xreal_0(_207332)), _207334 = _207332, v1_xreal_0(_207334)], (40 ^ _206269) ^ [_207627, _207629] : [-(v1_int_1(_207627)), _207629 = _207627, v1_int_1(_207629)], (50 ^ _206269) ^ [_207922, _207924] : [-(v1_rat_1(_207922)), _207924 = _207922, v1_rat_1(_207924)], (60 ^ _206269) ^ [_208245, _208247, _208249, _208251] : [-(is_antisymmetric_in(_208249, _208245)), is_antisymmetric_in(_208251, _208247), _208251 = _208249, _208247 = _208245], (74 ^ _206269) ^ [_208689, _208691, _208693, _208695] : [-(is_connected_in(_208693, _208689)), is_connected_in(_208695, _208691), _208695 = _208693, _208691 = _208689], (88 ^ _206269) ^ [_209133, _209135, _209137, _209139] : [-(is_transitive_in(_209137, _209133)), is_transitive_in(_209139, _209135), _209139 = _209137, _209135 = _209133], (102 ^ _206269) ^ [_209577, _209579, _209581, _209583] : [-(is_reflexive_in(_209581, _209577)), is_reflexive_in(_209583, _209579), _209583 = _209581, _209579 = _209577], (116 ^ _206269) ^ [_209993, _209995] : [-(cup_closed(_209993)), _209995 = _209993, cup_closed(_209995)], (126 ^ _206269) ^ [_210288, _210290] : [-(diff_closed(_210288)), _210290 = _210288, diff_closed(_210290)], (136 ^ _206269) ^ [_210583, _210585] : [-(preboolean(_210583)), _210585 = _210583, preboolean(_210585)], (146 ^ _206269) ^ [_210906, _210908, _210910, _210912] : [-(v1_binop_1(_210910, _210906)), v1_binop_1(_210912, _210908), _210912 = _210910, _210908 = _210906], (160 ^ _206269) ^ [_211350, _211352, _211354, _211356] : [-(v2_binop_1(_211354, _211350)), v2_binop_1(_211356, _211352), _211356 = _211354, _211352 = _211350], (174 ^ _206269) ^ [_211766, _211768] : [-(v1_membered(_211766)), _211768 = _211766, v1_membered(_211768)], (184 ^ _206269) ^ [_212061, _212063] : [-(v2_membered(_212061)), _212063 = _212061, v2_membered(_212063)], (194 ^ _206269) ^ [_212356, _212358] : [-(v3_membered(_212356)), _212358 = _212356, v3_membered(_212358)], (204 ^ _206269) ^ [_212651, _212653] : [-(v4_membered(_212651)), _212653 = _212651, v4_membered(_212653)], (214 ^ _206269) ^ [_212946, _212948] : [-(v5_membered(_212946)), _212948 = _212946, v5_membered(_212948)], (224 ^ _206269) ^ [_213241, _213243] : [-(natural(_213241)), _213243 = _213241, natural(_213243)], (234 ^ _206269) ^ [_213592, _213594, _213596, _213598, _213600, _213602] : [-(onto(_213600, _213596, _213592)), onto(_213602, _213598, _213594), _213602 = _213600, _213598 = _213596, _213594 = _213592], (252 ^ _206269) ^ [_214201, _214203, _214205, _214207, _214209, _214211] : [-(bijective(_214209, _214205, _214201)), bijective(_214211, _214207, _214203), _214211 = _214209, _214207 = _214205, _214203 = _214201], (270 ^ _206269) ^ [_214754, _214756] : [-(strict_rel_str(_214754)), _214756 = _214754, strict_rel_str(_214756)], (280 ^ _206269) ^ [_215049, _215051] : [-(epsilon_connected(_215049)), _215051 = _215049, epsilon_connected(_215051)], (290 ^ _206269) ^ [_215344, _215346] : [-(symmetric(_215344)), _215346 = _215344, symmetric(_215346)], (300 ^ _206269) ^ [_215695, _215697, _215699, _215701, _215703, _215705] : [-(v1_partfun1(_215703, _215699, _215695)), v1_partfun1(_215705, _215701, _215697), _215705 = _215703, _215701 = _215699, _215697 = _215695], (318 ^ _206269) ^ [_216248, _216250] : [-(relation_empty_yielding(_216248)), _216250 = _216248, relation_empty_yielding(_216250)], (328 ^ _206269) ^ [_216543, _216545] : [-(strict_latt_str(_216543)), _216545 = _216543, strict_latt_str(_216545)], (338 ^ _206269) ^ [_216838, _216840] : [-(join_associative(_216838)), _216840 = _216838, join_associative(_216840)], (348 ^ _206269) ^ [_217133, _217135] : [-(meet_associative(_217133)), _217135 = _217133, meet_associative(_217135)], (358 ^ _206269) ^ [_217428, _217430] : [-(meet_semilatt_str(_217428)), _217430 = _217428, meet_semilatt_str(_217430)], (368 ^ _206269) ^ [_217779, _217781, _217783, _217785, _217787, _217789] : [-(relation_of2(_217787, _217783, _217779)), relation_of2(_217789, _217785, _217781), _217789 = _217787, _217785 = _217783, _217781 = _217779], (386 ^ _206269) ^ [_218332, _218334] : [-(join_absorbing(_218332)), _218334 = _218332, join_absorbing(_218334)], (396 ^ _206269) ^ [_218627, _218629] : [-(reflexive_relstr(_218627)), _218629 = _218627, reflexive_relstr(_218629)], (406 ^ _206269) ^ [_218950, _218952, _218954, _218956] : [-(equipotent(_218954, _218950)), equipotent(_218956, _218952), _218956 = _218954, _218952 = _218950], (420 ^ _206269) ^ [_219366, _219368] : [-(compact_top_space(_219366)), _219368 = _219366, compact_top_space(_219368)], (430 ^ _206269) ^ [_219661, _219663] : [-(centered(_219661)), _219663 = _219661, centered(_219663)], (440 ^ _206269) ^ [_219984, _219986, _219988, _219990] : [-(open_subsets(_219988, _219984)), open_subsets(_219990, _219986), _219990 = _219988, _219986 = _219984], (454 ^ _206269) ^ [_220428, _220430, _220432, _220434] : [-(closed_subsets(_220432, _220428)), closed_subsets(_220434, _220430), _220434 = _220432, _220430 = _220428], (468 ^ _206269) ^ [_220844, _220846] : [-(epsilon_transitive(_220844)), _220846 = _220844, epsilon_transitive(_220846)], (478 ^ _206269) ^ [_221139, _221141] : [-(meet_commutative(_221139)), _221141 = _221139, meet_commutative(_221141)], (488 ^ _206269) ^ [_221434, _221436] : [-(meet_absorbing(_221434)), _221436 = _221434, meet_absorbing(_221436)], (498 ^ _206269) ^ [_221729, _221731] : [-(antisymmetric_relstr(_221729)), _221731 = _221729, antisymmetric_relstr(_221731)], (508 ^ _206269) ^ [_222024, _222026] : [-(finite(_222024)), _222026 = _222024, finite(_222026)], (518 ^ _206269) ^ [_222319, _222321] : [-(join_commutative(_222319)), _222321 = _222319, join_commutative(_222321)], (528 ^ _206269) ^ [_222614, _222616] : [-(join_semilatt_str(_222614)), _222616 = _222614, join_semilatt_str(_222616)], (538 ^ _206269) ^ [_222909, _222911] : [-(transitive_relstr(_222909)), _222911 = _222909, transitive_relstr(_222911)], (548 ^ _206269) ^ [_223260, _223262, _223264, _223266, _223268, _223270] : [-(related(_223268, _223264, _223260)), related(_223270, _223266, _223262), _223270 = _223268, _223266 = _223264, _223262 = _223260], (566 ^ _206269) ^ [_223869, _223871, _223873, _223875, _223877, _223879] : [-(below(_223877, _223873, _223869)), below(_223879, _223875, _223871), _223879 = _223877, _223875 = _223873, _223871 = _223869], (584 ^ _206269) ^ [_224478, _224480, _224482, _224484, _224486, _224488] : [-(latt_element_smaller(_224486, _224482, _224478)), latt_element_smaller(_224488, _224484, _224480), _224488 = _224486, _224484 = _224482, _224480 = _224478], (602 ^ _206269) ^ [_225059, _225061, _225063, _225065] : [-(ordinal_subset(_225063, _225059)), ordinal_subset(_225065, _225061), _225065 = _225063, _225061 = _225059], (616 ^ _206269) ^ [_225531, _225533, _225535, _225537, _225539, _225541] : [-(latt_set_smaller(_225539, _225535, _225531)), latt_set_smaller(_225541, _225537, _225533), _225541 = _225539, _225537 = _225535, _225533 = _225531], (634 ^ _206269) ^ [_226084, _226086] : [-(being_limit_ordinal(_226084)), _226086 = _226084, being_limit_ordinal(_226086)], (644 ^ _206269) ^ [_226379, _226381] : [-(complete_latt_str(_226379)), _226381 = _226379, complete_latt_str(_226381)], (654 ^ _206269) ^ [_226674, _226676] : [-(lower_bounded_semilattstr(_226674)), _226676 = _226674, lower_bounded_semilattstr(_226676)], (664 ^ _206269) ^ [_226997, _226999, _227001, _227003] : [-(closed_subset(_227001, _226997)), closed_subset(_227003, _226999), _227003 = _227001, _226999 = _226997], (678 ^ _206269) ^ [_227413, _227415] : [-(reflexive(_227413)), _227415 = _227413, reflexive(_227415)], (688 ^ _206269) ^ [_227708, _227710] : [-(transitive(_227708)), _227710 = _227708, transitive(_227710)], (698 ^ _206269) ^ [_228003, _228005] : [-(connected(_228003)), _228005 = _228003, connected(_228005)], (708 ^ _206269) ^ [_228354, _228356, _228358, _228360, _228362, _228364] : [-(relation_isomorphism(_228362, _228358, _228354)), relation_isomorphism(_228364, _228360, _228356), _228364 = _228362, _228360 = _228358, _228356 = _228354], (726 ^ _206269) ^ [_228907, _228909] : [-(topological_space(_228907)), _228909 = _228907, topological_space(_228909)], (736 ^ _206269) ^ [_229202, _229204] : [-(top_str(_229202)), _229204 = _229202, top_str(_229204)], (746 ^ _206269) ^ [_229525, _229527, _229529, _229531] : [-(open_subset(_229529, _229525)), open_subset(_229531, _229527), _229531 = _229529, _229527 = _229525], (760 ^ _206269) ^ [_229997, _229999, _230001, _230003, _230005, _230007] : [-(point_neighbourhood(_230005, _230001, _229997)), point_neighbourhood(_230007, _230003, _229999), _230007 = _230005, _230003 = _230001, _229999 = _229997], (778 ^ _206269) ^ [_230578, _230580, _230582, _230584] : [-(proper_element(_230582, _230578)), proper_element(_230584, _230580), _230584 = _230582, _230580 = _230578], (792 ^ _206269) ^ [_231022, _231024, _231026, _231028] : [-(is_a_cover_of_carrier(_231026, _231022)), is_a_cover_of_carrier(_231028, _231024), _231028 = _231026, _231024 = _231022], (806 ^ _206269) ^ [_231466, _231468, _231470, _231472] : [-(is_well_founded_in(_231470, _231466)), is_well_founded_in(_231472, _231468), _231472 = _231470, _231468 = _231466], (820 ^ _206269) ^ [_231882, _231884] : [-(antisymmetric(_231882)), _231884 = _231882, antisymmetric(_231884)], (830 ^ _206269) ^ [_232205, _232207, _232209, _232211] : [-(proper_subset(_232209, _232205)), proper_subset(_232211, _232207), _232211 = _232209, _232207 = _232205], (844 ^ _206269) ^ [_232621, _232623] : [-(one_to_one(_232621)), _232623 = _232621, one_to_one(_232623)], (854 ^ _206269) ^ [_232916, _232918] : [-(well_founded_relation(_232916)), _232918 = _232916, well_founded_relation(_232918)], (864 ^ _206269) ^ [_233211, _233213] : [-(lattice(_233211)), _233213 = _233211, lattice(_233213)], (874 ^ _206269) ^ [_233506, _233508] : [-(latt_str(_233506)), _233508 = _233506, latt_str(_233508)], (884 ^ _206269) ^ [_233857, _233859, _233861, _233863, _233865, _233867] : [-(below_refl(_233865, _233861, _233857)), below_refl(_233867, _233863, _233859), _233867 = _233865, _233863 = _233861, _233859 = _233857], (902 ^ _206269) ^ [_234466, _234468, _234470, _234472, _234474, _234476] : [-(related_reflexive(_234474, _234470, _234466)), related_reflexive(_234476, _234472, _234468), _234476 = _234474, _234472 = _234470, _234468 = _234466], (920 ^ _206269) ^ [_235019, _235021] : [-(ordinal(_235019)), _235021 = _235019, ordinal(_235021)], (930 ^ _206269) ^ [_235342, _235344, _235346, _235348] : [-(disjoint(_235346, _235342)), disjoint(_235348, _235344), _235348 = _235346, _235344 = _235342], (944 ^ _206269) ^ [_235758, _235760] : [-(empty(_235758)), _235760 = _235758, empty(_235760)], (954 ^ _206269) ^ [_236081, _236083, _236085, _236087] : [-(well_orders(_236085, _236081)), well_orders(_236087, _236083), _236087 = _236085, _236083 = _236081], (968 ^ _206269) ^ [_236497, _236499] : [-(well_ordering(_236497)), _236499 = _236497, well_ordering(_236499)], (978 ^ _206269) ^ [_236792, _236794] : [-(empty_carrier(_236792)), _236794 = _236792, empty_carrier(_236794)], (988 ^ _206269) ^ [_237087, _237089] : [-(one_sorted_str(_237087)), _237089 = _237087, one_sorted_str(_237089)], (998 ^ _206269) ^ [_237382, _237384] : [-(relation(_237382)), _237384 = _237382, relation(_237384)], (1008 ^ _206269) ^ [_237677, _237679] : [-(function(_237677)), _237679 = _237677, function(_237679)], (1018 ^ _206269) ^ [_238028, _238030, _238032, _238034, _238036, _238038] : [-(quasi_total(_238036, _238032, _238028)), quasi_total(_238038, _238034, _238030), _238038 = _238036, _238034 = _238032, _238030 = _238028], (1036 ^ _206269) ^ [_238637, _238639, _238641, _238643, _238645, _238647] : [-(relation_of2_as_subset(_238645, _238641, _238637)), relation_of2_as_subset(_238647, _238643, _238639), _238647 = _238645, _238643 = _238641, _238639 = _238637], (1054 ^ _206269) ^ [_239218, _239220, _239222, _239224] : [-(subset(_239222, _239218)), subset(_239224, _239220), _239224 = _239222, _239220 = _239218], (1068 ^ _206269) ^ [_239662, _239664, _239666, _239668] : [-(are_equipotent(_239666, _239662)), are_equipotent(_239668, _239664), _239668 = _239666, _239664 = _239662], (1082 ^ _206269) ^ [_240106, _240108, _240110, _240112] : [-(in(_240110, _240106)), in(_240112, _240108), _240112 = _240110, _240108 = _240106], (1096 ^ _206269) ^ [_240522, _240524] : [-(rel_str(_240522)), _240524 = _240522, rel_str(_240524)], (1106 ^ _206269) ^ [_240845, _240847, _240849, _240851] : [-(element(_240849, _240845)), element(_240851, _240847), _240851 = _240849, _240847 = _240845], (1120 ^ _206269) ^ [_241317, _241319, _241321, _241323, _241325, _241327] : [-(relstr_set_smaller(_241325, _241321, _241317)), relstr_set_smaller(_241327, _241323, _241319), _241327 = _241325, _241323 = _241321, _241319 = _241317], (1138 ^ _206269) ^ [_241906, _241908, _241910, _241912, _241914, _241916] : [-(relstr_element_smaller(_241914, _241910, _241906)), relstr_element_smaller(_241916, _241912, _241908), _241916 = _241914, _241912 = _241910, _241908 = _241906], (1870 ^ _206269) ^ [_269750] : [rel_str(_269750), strict_rel_str(_269750), -(_269750 = rel_str_of(the_carrier(_269750), the_InternalRel(_269750)))], (1880 ^ _206269) ^ [_270035] : [latt_str(_270035), strict_latt_str(_270035), -(_270035 = latt_str_of(the_carrier(_270035), the_L_join(_270035), the_L_meet(_270035)))], (1890 ^ _206269) ^ [_270340, _270342] : [in(_270342, _270340), in(_270340, _270342)], (1896 ^ _206269) ^ [_270551, _270553] : [proper_subset(_270553, _270551), proper_subset(_270551, _270553)], (1902 ^ _206269) ^ [_270748] : [v1_membered(_270748), 1905 ^ _206269 : [(1906 ^ _206269) ^ [_270878] : [element(_270878, _270748), -(v1_xcmplx_0(_270878))]]], (1912 ^ _206269) ^ [_271079] : [v2_membered(_271079), 1915 ^ _206269 : [(1916 ^ _206269) ^ [_271214] : [element(_271214, _271079), 1919 ^ _206269 : [(1920 ^ _206269) ^ [] : [-(v1_xcmplx_0(_271214))], (1922 ^ _206269) ^ [] : [-(v1_xreal_0(_271214))]]]]], (1924 ^ _206269) ^ [_271488] : [v3_membered(_271488), 1927 ^ _206269 : [(1928 ^ _206269) ^ [_271628] : [element(_271628, _271488), 1931 ^ _206269 : [(1932 ^ _206269) ^ [] : [-(v1_xcmplx_0(_271628))], (1934 ^ _206269) ^ [] : [-(v1_xreal_0(_271628))], (1936 ^ _206269) ^ [] : [-(v1_rat_1(_271628))]]]]], (1938 ^ _206269) ^ [_271974] : [v4_membered(_271974), 1941 ^ _206269 : [(1942 ^ _206269) ^ [_272119] : [element(_272119, _271974), 1945 ^ _206269 : [(1946 ^ _206269) ^ [] : [-(v1_xcmplx_0(_272119))], (1948 ^ _206269) ^ [] : [-(v1_xreal_0(_272119))], (1950 ^ _206269) ^ [] : [-(v1_int_1(_272119))], (1952 ^ _206269) ^ [] : [-(v1_rat_1(_272119))]]]]], (1954 ^ _206269) ^ [_272537] : [v5_membered(_272537), 1957 ^ _206269 : [(1958 ^ _206269) ^ [_272687] : [element(_272687, _272537), 1961 ^ _206269 : [(1962 ^ _206269) ^ [] : [-(v1_xcmplx_0(_272687))], (1964 ^ _206269) ^ [] : [-(natural(_272687))], (1966 ^ _206269) ^ [] : [-(v1_xreal_0(_272687))], (1968 ^ _206269) ^ [] : [-(v1_int_1(_272687))], (1970 ^ _206269) ^ [] : [-(v1_rat_1(_272687))]]]]], (1972 ^ _206269) ^ [_273177] : [empty(_273177), 1975 ^ _206269 : [(1976 ^ _206269) ^ [] : [-(v1_membered(_273177))], (1978 ^ _206269) ^ [] : [-(v2_membered(_273177))], (1980 ^ _206269) ^ [] : [-(v3_membered(_273177))], (1982 ^ _206269) ^ [] : [-(v4_membered(_273177))], (1984 ^ _206269) ^ [] : [-(v5_membered(_273177))]]], (1986 ^ _206269) ^ [_273644] : [v1_membered(_273644), 1989 ^ _206269 : [(1990 ^ _206269) ^ [_273776] : [element(_273776, powerset(_273644)), -(v1_membered(_273776))]]], (1996 ^ _206269) ^ [_273981] : [v2_membered(_273981), 1999 ^ _206269 : [(2000 ^ _206269) ^ [_274118] : [element(_274118, powerset(_273981)), 2003 ^ _206269 : [(2004 ^ _206269) ^ [] : [-(v1_membered(_274118))], (2006 ^ _206269) ^ [] : [-(v2_membered(_274118))]]]]], (2008 ^ _206269) ^ [_274396] : [v3_membered(_274396), 2011 ^ _206269 : [(2012 ^ _206269) ^ [_274538] : [element(_274538, powerset(_274396)), 2015 ^ _206269 : [(2016 ^ _206269) ^ [] : [-(v1_membered(_274538))], (2018 ^ _206269) ^ [] : [-(v2_membered(_274538))], (2020 ^ _206269) ^ [] : [-(v3_membered(_274538))]]]]], (2022 ^ _206269) ^ [_274888] : [v4_membered(_274888), 2025 ^ _206269 : [(2026 ^ _206269) ^ [_275035] : [element(_275035, powerset(_274888)), 2029 ^ _206269 : [(2030 ^ _206269) ^ [] : [-(v1_membered(_275035))], (2032 ^ _206269) ^ [] : [-(v2_membered(_275035))], (2034 ^ _206269) ^ [] : [-(v3_membered(_275035))], (2036 ^ _206269) ^ [] : [-(v4_membered(_275035))]]]]], (2038 ^ _206269) ^ [_275457] : [ordinal(_275457), 2041 ^ _206269 : [(2042 ^ _206269) ^ [_275597] : [element(_275597, _275457), 2045 ^ _206269 : [(2046 ^ _206269) ^ [] : [-(epsilon_transitive(_275597))], (2048 ^ _206269) ^ [] : [-(epsilon_connected(_275597))], (2050 ^ _206269) ^ [] : [-(ordinal(_275597))]]]]], (2052 ^ _206269) ^ [_275943] : [empty(_275943), -(finite(_275943))], (2058 ^ _206269) ^ [_276129] : [preboolean(_276129), 2061 ^ _206269 : [(2062 ^ _206269) ^ [] : [-(cup_closed(_276129))], (2064 ^ _206269) ^ [] : [-(diff_closed(_276129))]]], (2066 ^ _206269) ^ [_276386] : [empty(_276386), -(function(_276386))], (2072 ^ _206269) ^ [_276600, _276602, _276604] : [relation_of2(_276600, _276604, _276602), 2083 ^ _206269 : [(2084 ^ _206269) ^ [] : [-(function(_276600))], (2086 ^ _206269) ^ [] : [-(quasi_total(_276600, _276604, _276602))]], function(_276600), v1_partfun1(_276600, _276604, _276602)], (2088 ^ _206269) ^ [_277067] : [latt_str(_277067), 2099 ^ _206269 : [(2100 ^ _206269) ^ [] : [empty_carrier(_277067)], (2102 ^ _206269) ^ [] : [-(join_commutative(_277067))], (2104 ^ _206269) ^ [] : [-(join_associative(_277067))], (2106 ^ _206269) ^ [] : [-(meet_commutative(_277067))], (2108 ^ _206269) ^ [] : [-(meet_associative(_277067))], (2110 ^ _206269) ^ [] : [-(meet_absorbing(_277067))], (2112 ^ _206269) ^ [] : [-(join_absorbing(_277067))]], -(empty_carrier(_277067)), lattice(_277067)], (2114 ^ _206269) ^ [_277844] : [v5_membered(_277844), -(v4_membered(_277844))], (2120 ^ _206269) ^ [_278030] : [ordinal(_278030), 2123 ^ _206269 : [(2124 ^ _206269) ^ [] : [-(epsilon_transitive(_278030))], (2126 ^ _206269) ^ [] : [-(epsilon_connected(_278030))]]], (2128 ^ _206269) ^ [_278287] : [2139 ^ _206269 : [(2140 ^ _206269) ^ [] : [-(relation(_278287))], (2142 ^ _206269) ^ [] : [-(reflexive(_278287))]], relation(_278287), symmetric(_278287), transitive(_278287)], (2144 ^ _206269) ^ [_278710] : [empty(_278710), -(relation(_278710))], (2150 ^ _206269) ^ [_278924, _278926, _278928] : [element(_278924, powerset(cartesian_product2(_278928, _278926))), -(relation(_278924))], (2156 ^ _206269) ^ [_279134] : [v5_membered(_279134), 2159 ^ _206269 : [(2160 ^ _206269) ^ [_279286] : [element(_279286, powerset(_279134)), 2163 ^ _206269 : [(2164 ^ _206269) ^ [] : [-(v1_membered(_279286))], (2166 ^ _206269) ^ [] : [-(v2_membered(_279286))], (2168 ^ _206269) ^ [] : [-(v3_membered(_279286))], (2170 ^ _206269) ^ [] : [-(v4_membered(_279286))], (2172 ^ _206269) ^ [] : [-(v5_membered(_279286))]]]]], (2174 ^ _206269) ^ [_279780] : [2181 ^ _206269 : [(2182 ^ _206269) ^ [] : [-(epsilon_transitive(_279780))], (2184 ^ _206269) ^ [] : [-(epsilon_connected(_279780))], (2186 ^ _206269) ^ [] : [-(ordinal(_279780))], (2188 ^ _206269) ^ [] : [-(natural(_279780))]], empty(_279780), ordinal(_279780)], (2190 ^ _206269) ^ [_280260] : [finite(_280260), 2193 ^ _206269 : [(2194 ^ _206269) ^ [_280392] : [element(_280392, powerset(_280260)), -(finite(_280392))]]], (2200 ^ _206269) ^ [_280597] : [-(preboolean(_280597)), cup_closed(_280597), diff_closed(_280597)], (2210 ^ _206269) ^ [_280866] : [2221 ^ _206269 : [(2222 ^ _206269) ^ [] : [-(relation(_280866))], (2224 ^ _206269) ^ [] : [-(function(_280866))], (2226 ^ _206269) ^ [] : [-(one_to_one(_280866))]], relation(_280866), empty(_280866), function(_280866)], (2228 ^ _206269) ^ [_281387, _281389, _281391] : [relation_of2(_281387, _281391, _281389), 2243 ^ _206269 : [(2244 ^ _206269) ^ [] : [-(function(_281387))], (2246 ^ _206269) ^ [] : [-(one_to_one(_281387))], (2248 ^ _206269) ^ [] : [-(quasi_total(_281387, _281391, _281389))], (2250 ^ _206269) ^ [] : [-(onto(_281387, _281391, _281389))]], function(_281387), quasi_total(_281387, _281391, _281389), bijective(_281387, _281391, _281389)], (2252 ^ _206269) ^ [_282101] : [latt_str(_282101), 2283 ^ _206269 : [(2284 ^ _206269) ^ [] : [empty_carrier(_282101)], (2286 ^ _206269) ^ [] : [-(lattice(_282101))]], -(empty_carrier(_282101)), join_commutative(_282101), join_associative(_282101), meet_commutative(_282101), meet_associative(_282101), meet_absorbing(_282101), join_absorbing(_282101)], (2288 ^ _206269) ^ [_282943] : [v4_membered(_282943), -(v3_membered(_282943))], (2294 ^ _206269) ^ [_283129] : [-(ordinal(_283129)), epsilon_transitive(_283129), epsilon_connected(_283129)], (2304 ^ _206269) ^ [_283398] : [element(_283398, omega), 2307 ^ _206269 : [(2308 ^ _206269) ^ [] : [-(epsilon_transitive(_283398))], (2310 ^ _206269) ^ [] : [-(epsilon_connected(_283398))], (2312 ^ _206269) ^ [] : [-(ordinal(_283398))], (2314 ^ _206269) ^ [] : [-(natural(_283398))]]], (2316 ^ _206269) ^ [_283825, _283827, _283829] : [relation_of2(_283825, _283829, _283827), 2335 ^ _206269 : [(2336 ^ _206269) ^ [] : [-(function(_283825))], (2338 ^ _206269) ^ [] : [-(quasi_total(_283825, _283829, _283827))], (2340 ^ _206269) ^ [] : [-(bijective(_283825, _283829, _283827))]], function(_283825), one_to_one(_283825), quasi_total(_283825, _283829, _283827), onto(_283825, _283829, _283827)], (2342 ^ _206269) ^ [_284556] : [v3_membered(_284556), -(v2_membered(_284556))], (2348 ^ _206269) ^ [_284742] : [empty(_284742), 2351 ^ _206269 : [(2352 ^ _206269) ^ [] : [-(epsilon_transitive(_284742))], (2354 ^ _206269) ^ [] : [-(epsilon_connected(_284742))], (2356 ^ _206269) ^ [] : [-(ordinal(_284742))]]], (2358 ^ _206269) ^ [_285083, _285085] : [relation_of2(_285083, _285085, _285085), 2377 ^ _206269 : [(2378 ^ _206269) ^ [] : [-(function(_285083))], (2380 ^ _206269) ^ [] : [-(one_to_one(_285083))], (2382 ^ _206269) ^ [] : [-(quasi_total(_285083, _285085, _285085))], (2384 ^ _206269) ^ [] : [-(onto(_285083, _285085, _285085))], (2386 ^ _206269) ^ [] : [-(bijective(_285083, _285085, _285085))]], function(_285083), v1_partfun1(_285083, _285085, _285085), reflexive(_285083), quasi_total(_285083, _285085, _285085)], (2388 ^ _206269) ^ [_285936] : [v2_membered(_285936), -(v1_membered(_285936))], (2394 ^ _206269) ^ [_286136, _286138] : [-(empty(_286136)), 2397 ^ _206269 : [(2398 ^ _206269) ^ [_286300] : [relation_of2(_286300, _286138, _286136), 2409 ^ _206269 : [(2410 ^ _206269) ^ [] : [-(function(_286300))], (2412 ^ _206269) ^ [] : [-(v1_partfun1(_286300, _286138, _286136))], (2414 ^ _206269) ^ [] : [-(quasi_total(_286300, _286138, _286136))]], function(_286300), quasi_total(_286300, _286138, _286136)]]], (2416 ^ _206269) ^ [_286868, _286870] : [-(empty(_286870)), -(empty(_286868)), 2423 ^ _206269 : [(2424 ^ _206269) ^ [_287129] : [relation_of2(_287129, _286870, _286868), 2435 ^ _206269 : [(2436 ^ _206269) ^ [] : [-(function(_287129))], (2438 ^ _206269) ^ [] : [empty(_287129)], (2440 ^ _206269) ^ [] : [-(v1_partfun1(_287129, _286870, _286868))], (2442 ^ _206269) ^ [] : [-(quasi_total(_287129, _286870, _286868))]], function(_287129), quasi_total(_287129, _286870, _286868)]]], (2444 ^ _206269) ^ [_287759, _287761] : [-(unordered_pair(_287761, _287759) = unordered_pair(_287759, _287761))], (2446 ^ _206269) ^ [_287859, _287861] : [-(set_union2(_287861, _287859) = set_union2(_287859, _287861))], (2448 ^ _206269) ^ [_287988, _287990, _287992] : [-(join_commut(_287992, _287990, _287988) = join_commut(_287992, _287988, _287990)), -(empty_carrier(_287992)), join_commutative(_287992), join_semilatt_str(_287992), element(_287990, the_carrier(_287992)), element(_287988, the_carrier(_287992))], (2470 ^ _206269) ^ [_288582, _288584] : [-(set_intersection2(_288584, _288582) = set_intersection2(_288582, _288584))], (2472 ^ _206269) ^ [_288711, _288713, _288715] : [-(meet_commut(_288715, _288713, _288711) = meet_commut(_288715, _288711, _288713)), -(empty_carrier(_288715)), meet_commutative(_288715), meet_semilatt_str(_288715), element(_288713, the_carrier(_288715)), element(_288711, the_carrier(_288715))], (2494 ^ _206269) ^ [_289334, _289336, _289338] : [-(subset_union2(_289338, _289336, _289334) = subset_union2(_289338, _289334, _289336)), element(_289336, powerset(_289338)), element(_289334, powerset(_289338))], (2504 ^ _206269) ^ [_289681, _289683, _289685] : [-(subset_intersection2(_289685, _289683, _289681) = subset_intersection2(_289685, _289681, _289683)), element(_289683, powerset(_289685)), element(_289681, powerset(_289685))], (2514 ^ _206269) ^ [_290014, _290016] : [ordinal(_290016), ordinal(_290014), -(ordinal_subset(_290016, _290014)), -(ordinal_subset(_290014, _290016))], (2528 ^ _206269) ^ [_290401, _290403] : [relation(_290401), 2531 ^ _206269 : [(2554 ^ _206269) ^ [] : [-(_290401 = identity_relation(_290403)), 2567 ^ _206269 : [(2568 ^ _206269) ^ [] : [-(in(2555 ^ [_290401, _290403], _290403))], (2570 ^ _206269) ^ [] : [-(2555 ^ [_290401, _290403] = 2556 ^ [_290401, _290403])], (2572 ^ _206269) ^ [] : [in(ordered_pair(2555 ^ [_290401, _290403], 2556 ^ [_290401, _290403]), _290401)]], 2559 ^ _206269 : [(2560 ^ _206269) ^ [] : [-(in(ordered_pair(2555 ^ [_290401, _290403], 2556 ^ [_290401, _290403]), _290401))], (2562 ^ _206269) ^ [] : [in(2555 ^ [_290401, _290403], _290403), 2555 ^ [_290401, _290403] = 2556 ^ [_290401, _290403]]]], (2532 ^ _206269) ^ [] : [_290401 = identity_relation(_290403), 2535 ^ _206269 : [(2536 ^ _206269) ^ [_290711, _290713] : [in(ordered_pair(_290713, _290711), _290401), 2539 ^ _206269 : [(2540 ^ _206269) ^ [] : [-(in(_290713, _290403))], (2542 ^ _206269) ^ [] : [-(_290713 = _290711)]]], (2544 ^ _206269) ^ [_290974, _290976] : [-(in(ordered_pair(_290976, _290974), _290401)), in(_290976, _290403), _290976 = _290974]]]]], (2576 ^ _206269) ^ [_292082, _292084] : [_292084 = _292082, 2579 ^ _206269 : [(2580 ^ _206269) ^ [] : [-(subset(_292084, _292082))], (2582 ^ _206269) ^ [] : [-(subset(_292082, _292084))]]], (2584 ^ _206269) ^ [_292319, _292321] : [-(_292321 = _292319), subset(_292321, _292319), subset(_292319, _292321)], (2594 ^ _206269) ^ [_292606] : [one_sorted_str(_292606), -(identity_on_carrier(_292606) = identity_as_relation_of(the_carrier(_292606)))], (2600 ^ _206269) ^ [_292806] : [relation(_292806), 2603 ^ _206269 : [(2604 ^ _206269) ^ [_292992, _292994] : [relation(_292992), 2607 ^ _206269 : [(2630 ^ _206269) ^ [] : [-(_292992 = relation_dom_restriction(_292806, _292994)), 2643 ^ _206269 : [(2644 ^ _206269) ^ [] : [-(in(2631 ^ [_292806, _292992, _292994], _292994))], (2646 ^ _206269) ^ [] : [-(in(ordered_pair(2631 ^ [_292806, _292992, _292994], 2632 ^ [_292806, _292992, _292994]), _292806))], (2648 ^ _206269) ^ [] : [in(ordered_pair(2631 ^ [_292806, _292992, _292994], 2632 ^ [_292806, _292992, _292994]), _292992)]], 2635 ^ _206269 : [(2636 ^ _206269) ^ [] : [-(in(ordered_pair(2631 ^ [_292806, _292992, _292994], 2632 ^ [_292806, _292992, _292994]), _292992))], (2638 ^ _206269) ^ [] : [in(2631 ^ [_292806, _292992, _292994], _292994), in(ordered_pair(2631 ^ [_292806, _292992, _292994], 2632 ^ [_292806, _292992, _292994]), _292806)]]], (2608 ^ _206269) ^ [] : [_292992 = relation_dom_restriction(_292806, _292994), 2611 ^ _206269 : [(2612 ^ _206269) ^ [_293317, _293319] : [in(ordered_pair(_293319, _293317), _292992), 2615 ^ _206269 : [(2616 ^ _206269) ^ [] : [-(in(_293319, _292994))], (2618 ^ _206269) ^ [] : [-(in(ordered_pair(_293319, _293317), _292806))]]], (2620 ^ _206269) ^ [_293596, _293598] : [-(in(ordered_pair(_293598, _293596), _292992)), in(_293598, _292994), in(ordered_pair(_293598, _293596), _292806)]]]]]]], (2652 ^ _206269) ^ [_294751] : [relation(_294751), function(_294751), 2659 ^ _206269 : [(2689 ^ _206269) ^ [_296177, _296179] : [-(_296177 = relation_image(_294751, _296179)), 2706 ^ _206269 : [(2707 ^ _206269) ^ [] : [-(in(2705 ^ [_294751, _296177, _296179], relation_dom(_294751)))], (2709 ^ _206269) ^ [] : [-(in(2705 ^ [_294751, _296177, _296179], _296179))], (2711 ^ _206269) ^ [] : [-(2690 ^ [_294751, _296177, _296179] = apply(_294751, 2705 ^ [_294751, _296177, _296179]))], (2713 ^ _206269) ^ [] : [in(2690 ^ [_294751, _296177, _296179], _296177)]], 2693 ^ _206269 : [(2694 ^ _206269) ^ [] : [-(in(2690 ^ [_294751, _296177, _296179], _296177))], (2696 ^ _206269) ^ [_296497] : [in(_296497, relation_dom(_294751)), in(_296497, _296179), 2690 ^ [_294751, _296177, _296179] = apply(_294751, _296497)]]], (2660 ^ _206269) ^ [_295049, _295051] : [_295049 = relation_image(_294751, _295051), 2663 ^ _206269 : [(2664 ^ _206269) ^ [_295249] : [in(_295249, _295049), 2668 ^ _206269 : [(2669 ^ _206269) ^ [] : [-(in(2667 ^ [_294751, _295049, _295051, _295249], relation_dom(_294751)))], (2671 ^ _206269) ^ [] : [-(in(2667 ^ [_294751, _295049, _295051, _295249], _295051))], (2673 ^ _206269) ^ [] : [-(_295249 = apply(_294751, 2667 ^ [_294751, _295049, _295051, _295249]))]]], (2675 ^ _206269) ^ [_295704] : [-(in(_295704, _295049)), 2676 ^ _206269 : [(2677 ^ _206269) ^ [_295817] : [in(_295817, relation_dom(_294751)), in(_295817, _295051), _295704 = apply(_294751, _295817)]]]]]]], (2717 ^ _206269) ^ [_297307, _297309] : [relation(_297307), 2720 ^ _206269 : [(2721 ^ _206269) ^ [_297478] : [relation(_297478), 2724 ^ _206269 : [(2747 ^ _206269) ^ [] : [-(_297478 = relation_rng_restriction(_297309, _297307)), 2760 ^ _206269 : [(2761 ^ _206269) ^ [] : [-(in(2749 ^ [_297307, _297309, _297478], _297309))], (2763 ^ _206269) ^ [] : [-(in(ordered_pair(2748 ^ [_297307, _297309, _297478], 2749 ^ [_297307, _297309, _297478]), _297307))], (2765 ^ _206269) ^ [] : [in(ordered_pair(2748 ^ [_297307, _297309, _297478], 2749 ^ [_297307, _297309, _297478]), _297478)]], 2752 ^ _206269 : [(2753 ^ _206269) ^ [] : [-(in(ordered_pair(2748 ^ [_297307, _297309, _297478], 2749 ^ [_297307, _297309, _297478]), _297478))], (2755 ^ _206269) ^ [] : [in(2749 ^ [_297307, _297309, _297478], _297309), in(ordered_pair(2748 ^ [_297307, _297309, _297478], 2749 ^ [_297307, _297309, _297478]), _297307)]]], (2725 ^ _206269) ^ [] : [_297478 = relation_rng_restriction(_297309, _297307), 2728 ^ _206269 : [(2729 ^ _206269) ^ [_297805, _297807] : [in(ordered_pair(_297807, _297805), _297478), 2732 ^ _206269 : [(2733 ^ _206269) ^ [] : [-(in(_297805, _297309))], (2735 ^ _206269) ^ [] : [-(in(ordered_pair(_297807, _297805), _297307))]]], (2737 ^ _206269) ^ [_298084, _298086] : [-(in(ordered_pair(_298086, _298084), _297478)), in(_298084, _297309), in(ordered_pair(_298086, _298084), _297307)]]]]]]], (2769 ^ _206269) ^ [_299230] : [relation(_299230), 2772 ^ _206269 : [(2773 ^ _206269) ^ [] : [antisymmetric(_299230), -(is_antisymmetric_in(_299230, relation_field(_299230)))], (2779 ^ _206269) ^ [] : [is_antisymmetric_in(_299230, relation_field(_299230)), -(antisymmetric(_299230))]]], (2785 ^ _206269) ^ [_299661] : [relation(_299661), function(_299661), 2792 ^ _206269 : [(2815 ^ _206269) ^ [_300700, _300702] : [-(_300700 = relation_inverse_image(_299661, _300702)), 2827 ^ _206269 : [(2828 ^ _206269) ^ [] : [-(in(2816 ^ [_299661, _300700, _300702], relation_dom(_299661)))], (2830 ^ _206269) ^ [] : [-(in(apply(_299661, 2816 ^ [_299661, _300700, _300702]), _300702))], (2832 ^ _206269) ^ [] : [in(2816 ^ [_299661, _300700, _300702], _300700)]], 2819 ^ _206269 : [(2820 ^ _206269) ^ [] : [-(in(2816 ^ [_299661, _300700, _300702], _300700))], (2822 ^ _206269) ^ [] : [in(2816 ^ [_299661, _300700, _300702], relation_dom(_299661)), in(apply(_299661, 2816 ^ [_299661, _300700, _300702]), _300702)]]], (2793 ^ _206269) ^ [_299948, _299950] : [_299948 = relation_inverse_image(_299661, _299950), 2796 ^ _206269 : [(2797 ^ _206269) ^ [_300137] : [in(_300137, _299948), 2800 ^ _206269 : [(2801 ^ _206269) ^ [] : [-(in(_300137, relation_dom(_299661)))], (2803 ^ _206269) ^ [] : [-(in(apply(_299661, _300137), _299950))]]], (2805 ^ _206269) ^ [_300406] : [-(in(_300406, _299948)), in(_300406, relation_dom(_299661)), in(apply(_299661, _300406), _299950)]]]]], (2836 ^ _206269) ^ [_301468] : [-(empty_carrier(_301468)), meet_semilatt_str(_301468), 2843 ^ _206269 : [(2844 ^ _206269) ^ [] : [lower_bounded_semilattstr(_301468), 2848 ^ _206269 : [(2849 ^ _206269) ^ [] : [-(element(2847 ^ [_301468], the_carrier(_301468)))], (2851 ^ _206269) ^ [_301969] : [element(_301969, the_carrier(_301468)), 2854 ^ _206269 : [(2855 ^ _206269) ^ [] : [-(meet(_301468, 2847 ^ [_301468], _301969) = 2847 ^ [_301468])], (2857 ^ _206269) ^ [] : [-(meet(_301468, _301969, 2847 ^ [_301468]) = 2847 ^ [_301468])]]]]], (2859 ^ _206269) ^ [] : [-(lower_bounded_semilattstr(_301468)), 2860 ^ _206269 : [(2861 ^ _206269) ^ [_302321] : [element(_302321, the_carrier(_301468)), 2865 ^ _206269 : [(2866 ^ _206269) ^ [] : [-(element(2864 ^ [_301468, _302321], the_carrier(_301468)))], (2868 ^ _206269) ^ [] : [meet(_301468, _302321, 2864 ^ [_301468, _302321]) = _302321, meet(_301468, 2864 ^ [_301468, _302321], _302321) = _302321]]]]]]], (2876 ^ _206269) ^ [_302856] : [top_str(_302856), 2879 ^ _206269 : [(2880 ^ _206269) ^ [_303063] : [element(_303063, powerset(the_carrier(_302856))), 2883 ^ _206269 : [(2884 ^ _206269) ^ [_303271] : [element(_303271, powerset(the_carrier(_302856))), 2887 ^ _206269 : [(2927 ^ _206269) ^ [] : [-(_303271 = topstr_closure(_302856, _303063)), 2929 ^ _206269 : [(2930 ^ _206269) ^ [] : [-(in(2928 ^ [_302856, _303063, _303271], the_carrier(_302856)))], (2932 ^ _206269) ^ [] : [2933 ^ _206269 : [(2934 ^ _206269) ^ [] : [-(in(2928 ^ [_302856, _303063, _303271], _303271))], (2937 ^ _206269) ^ [] : [-(element(2935 ^ [_302856, _303063, _303271], powerset(the_carrier(_302856))))], (2939 ^ _206269) ^ [] : [-(open_subset(2935 ^ [_302856, _303063, _303271], _302856))], (2941 ^ _206269) ^ [] : [-(in(2928 ^ [_302856, _303063, _303271], 2935 ^ [_302856, _303063, _303271]))], (2943 ^ _206269) ^ [] : [-(disjoint(_303063, 2935 ^ [_302856, _303063, _303271]))]], 2944 ^ _206269 : [(2959 ^ _206269) ^ [] : [in(2928 ^ [_302856, _303063, _303271], _303271)], (2945 ^ _206269) ^ [_305534] : [element(_305534, powerset(the_carrier(_302856))), open_subset(_305534, _302856), in(2928 ^ [_302856, _303063, _303271], _305534), disjoint(_303063, _305534)]]]]], (2888 ^ _206269) ^ [] : [_303271 = topstr_closure(_302856, _303063), 2891 ^ _206269 : [(2892 ^ _206269) ^ [_303585] : [in(_303585, the_carrier(_302856)), 2895 ^ _206269 : [(2914 ^ _206269) ^ [] : [2916 ^ _206269 : [(2917 ^ _206269) ^ [] : [-(element(2915 ^ [_302856, _303063, _303271, _303585], powerset(the_carrier(_302856))))], (2919 ^ _206269) ^ [] : [-(open_subset(2915 ^ [_302856, _303063, _303271, _303585], _302856))], (2921 ^ _206269) ^ [] : [-(in(_303585, 2915 ^ [_302856, _303063, _303271, _303585]))], (2923 ^ _206269) ^ [] : [-(disjoint(_303063, 2915 ^ [_302856, _303063, _303271, _303585]))]], -(in(_303585, _303271))], (2896 ^ _206269) ^ [] : [in(_303585, _303271), 2899 ^ _206269 : [(2900 ^ _206269) ^ [_303880] : [element(_303880, powerset(the_carrier(_302856))), open_subset(_303880, _302856), in(_303585, _303880), disjoint(_303063, _303880)]]]]]]]]]]]]], (2963 ^ _206269) ^ [_306108] : [relation(_306108), 2966 ^ _206269 : [(2990 ^ _206269) ^ [_307221, _307223] : [-(_307221 = relation_image(_306108, _307223)), 3003 ^ _206269 : [(3004 ^ _206269) ^ [] : [-(in(ordered_pair(3002 ^ [_306108, _307221, _307223], 2991 ^ [_306108, _307221, _307223]), _306108))], (3006 ^ _206269) ^ [] : [-(in(3002 ^ [_306108, _307221, _307223], _307223))], (3008 ^ _206269) ^ [] : [in(2991 ^ [_306108, _307221, _307223], _307221)]], 2994 ^ _206269 : [(2995 ^ _206269) ^ [] : [-(in(2991 ^ [_306108, _307221, _307223], _307221))], (2997 ^ _206269) ^ [_307525] : [in(ordered_pair(_307525, 2991 ^ [_306108, _307221, _307223]), _306108), in(_307525, _307223)]]], (2967 ^ _206269) ^ [_306315, _306317] : [_306315 = relation_image(_306108, _306317), 2970 ^ _206269 : [(2971 ^ _206269) ^ [_306507] : [in(_306507, _306315), 2975 ^ _206269 : [(2976 ^ _206269) ^ [] : [-(in(ordered_pair(2974 ^ [_306108, _306315, _306317, _306507], _306507), _306108))], (2978 ^ _206269) ^ [] : [-(in(2974 ^ [_306108, _306315, _306317, _306507], _306317))]]], (2980 ^ _206269) ^ [_306861] : [-(in(_306861, _306315)), 2981 ^ _206269 : [(2982 ^ _206269) ^ [_306966] : [in(ordered_pair(_306966, _306861), _306108), in(_306966, _306317)]]]]]]], (3012 ^ _206269) ^ [_308127] : [relation(_308127), 3015 ^ _206269 : [(3039 ^ _206269) ^ [_309240, _309242] : [-(_309240 = relation_inverse_image(_308127, _309242)), 3052 ^ _206269 : [(3053 ^ _206269) ^ [] : [-(in(ordered_pair(3040 ^ [_308127, _309240, _309242], 3051 ^ [_308127, _309240, _309242]), _308127))], (3055 ^ _206269) ^ [] : [-(in(3051 ^ [_308127, _309240, _309242], _309242))], (3057 ^ _206269) ^ [] : [in(3040 ^ [_308127, _309240, _309242], _309240)]], 3043 ^ _206269 : [(3044 ^ _206269) ^ [] : [-(in(3040 ^ [_308127, _309240, _309242], _309240))], (3046 ^ _206269) ^ [_309544] : [in(ordered_pair(3040 ^ [_308127, _309240, _309242], _309544), _308127), in(_309544, _309242)]]], (3016 ^ _206269) ^ [_308334, _308336] : [_308334 = relation_inverse_image(_308127, _308336), 3019 ^ _206269 : [(3020 ^ _206269) ^ [_308526] : [in(_308526, _308334), 3024 ^ _206269 : [(3025 ^ _206269) ^ [] : [-(in(ordered_pair(_308526, 3023 ^ [_308127, _308334, _308336, _308526]), _308127))], (3027 ^ _206269) ^ [] : [-(in(3023 ^ [_308127, _308334, _308336, _308526], _308336))]]], (3029 ^ _206269) ^ [_308880] : [-(in(_308880, _308334)), 3030 ^ _206269 : [(3031 ^ _206269) ^ [_308985] : [in(ordered_pair(_308880, _308985), _308127), in(_308985, _308336)]]]]]]], (3061 ^ _206269) ^ [_310146] : [relation(_310146), 3064 ^ _206269 : [(3065 ^ _206269) ^ [] : [connected(_310146), -(is_connected_in(_310146, relation_field(_310146)))], (3071 ^ _206269) ^ [] : [is_connected_in(_310146, relation_field(_310146)), -(connected(_310146))]]], (3077 ^ _206269) ^ [_310577] : [-(empty_carrier(_310577)), latt_str(_310577), 3084 ^ _206269 : [(3085 ^ _206269) ^ [_310828] : [element(_310828, the_carrier(_310577)), 3088 ^ _206269 : [(3103 ^ _206269) ^ [_311465] : [3105 ^ _206269 : [(3106 ^ _206269) ^ [] : [-(element(3104 ^ [_310577, _310828, _311465], the_carrier(_310577)))], (3108 ^ _206269) ^ [] : [-(in(3104 ^ [_310577, _310828, _311465], _311465))], (3110 ^ _206269) ^ [] : [below(_310577, _310828, 3104 ^ [_310577, _310828, _311465])]], -(latt_set_smaller(_310577, _310828, _311465))], (3089 ^ _206269) ^ [_311021] : [latt_set_smaller(_310577, _310828, _311021), 3092 ^ _206269 : [(3093 ^ _206269) ^ [_311177] : [element(_311177, the_carrier(_310577)), in(_311177, _311021), -(below(_310577, _310828, _311177))]]]]]]], (3114 ^ _206269) ^ [_311942] : [-(empty_carrier(_311942)), meet_semilatt_str(_311942), lower_bounded_semilattstr(_311942), 3125 ^ _206269 : [(3126 ^ _206269) ^ [_312275] : [element(_312275, the_carrier(_311942)), 3129 ^ _206269 : [(3130 ^ _206269) ^ [] : [_312275 = bottom_of_semilattstr(_311942), 3133 ^ _206269 : [(3134 ^ _206269) ^ [_312552] : [element(_312552, the_carrier(_311942)), 3137 ^ _206269 : [(3138 ^ _206269) ^ [] : [-(meet(_311942, _312275, _312552) = _312275)], (3140 ^ _206269) ^ [] : [-(meet(_311942, _312552, _312275) = _312275)]]]]], (3142 ^ _206269) ^ [] : [-(_312275 = bottom_of_semilattstr(_311942)), 3144 ^ _206269 : [(3145 ^ _206269) ^ [] : [-(element(3143 ^ [_311942, _312275], the_carrier(_311942)))], (3147 ^ _206269) ^ [] : [meet(_311942, _312275, 3143 ^ [_311942, _312275]) = _312275, meet(_311942, 3143 ^ [_311942, _312275], _312275) = _312275]]]]]]], (3155 ^ _206269) ^ [_313259] : [relation(_313259), 3158 ^ _206269 : [(3159 ^ _206269) ^ [] : [transitive(_313259), -(is_transitive_in(_313259, relation_field(_313259)))], (3165 ^ _206269) ^ [] : [is_transitive_in(_313259, relation_field(_313259)), -(transitive(_313259))]]], (3171 ^ _206269) ^ [_313690] : [-(empty_carrier(_313690)), latt_str(_313690), 3178 ^ _206269 : [(3179 ^ _206269) ^ [_313941] : [element(_313941, the_carrier(_313690)), 3182 ^ _206269 : [(3197 ^ _206269) ^ [_314578] : [3199 ^ _206269 : [(3200 ^ _206269) ^ [] : [-(element(3198 ^ [_313690, _313941, _314578], the_carrier(_313690)))], (3202 ^ _206269) ^ [] : [-(in(3198 ^ [_313690, _313941, _314578], _314578))], (3204 ^ _206269) ^ [] : [below(_313690, 3198 ^ [_313690, _313941, _314578], _313941)]], -(latt_element_smaller(_313690, _313941, _314578))], (3183 ^ _206269) ^ [_314134] : [latt_element_smaller(_313690, _313941, _314134), 3186 ^ _206269 : [(3187 ^ _206269) ^ [_314290] : [element(_314290, the_carrier(_313690)), in(_314290, _314134), -(below(_313690, _314290, _313941))]]]]]]], (3208 ^ _206269) ^ [_315055] : [3215 ^ _206269 : [(3216 ^ _206269) ^ [_315277, _315279] : [-(apply_binary(_315055, _315279, _315277) = apply(_315055, ordered_pair(_315279, _315277)))]], relation(_315055), function(_315055)], (3218 ^ _206269) ^ [_315389] : [-(empty_carrier(_315389)), topological_space(_315389), top_str(_315389), 3229 ^ _206269 : [(3230 ^ _206269) ^ [_315716] : [element(_315716, the_carrier(_315389)), 3233 ^ _206269 : [(3234 ^ _206269) ^ [_315873] : [element(_315873, powerset(the_carrier(_315389))), 3237 ^ _206269 : [(3238 ^ _206269) ^ [] : [point_neighbourhood(_315873, _315389, _315716), -(in(_315716, interior(_315389, _315873)))], (3244 ^ _206269) ^ [] : [in(_315716, interior(_315389, _315873)), -(point_neighbourhood(_315873, _315389, _315716))]]]]]]], (3278 ^ _206269) ^ [_317408, _317410, _317412, _317414] : [-(_317408 = unordered_triple(_317414, _317412, _317410)), 3282 ^ _206269 : [(3283 ^ _206269) ^ [] : [-(in(3279 ^ [_317408, _317410, _317412, _317414], _317408))], (3285 ^ _206269) ^ [] : [3279 ^ [_317408, _317410, _317412, _317414] = _317414], (3287 ^ _206269) ^ [] : [3279 ^ [_317408, _317410, _317412, _317414] = _317412], (3289 ^ _206269) ^ [] : [3279 ^ [_317408, _317410, _317412, _317414] = _317410]], 3290 ^ _206269 : [(3301 ^ _206269) ^ [] : [in(3279 ^ [_317408, _317410, _317412, _317414], _317408)], (3291 ^ _206269) ^ [] : [-(3279 ^ [_317408, _317410, _317412, _317414] = _317414), -(3279 ^ [_317408, _317410, _317412, _317414] = _317412), -(3279 ^ [_317408, _317410, _317412, _317414] = _317410)]]], (3250 ^ _206269) ^ [_316444, _316446, _316448, _316450] : [_316444 = unordered_triple(_316450, _316448, _316446), 3253 ^ _206269 : [(3268 ^ _206269) ^ [_317046] : [3269 ^ _206269 : [(3270 ^ _206269) ^ [] : [_317046 = _316450], (3272 ^ _206269) ^ [] : [_317046 = _316448], (3274 ^ _206269) ^ [] : [_317046 = _316446]], -(in(_317046, _316444))], (3254 ^ _206269) ^ [_316646] : [in(_316646, _316444), -(_316646 = _316450), -(_316646 = _316448), -(_316646 = _316446)]]], (3305 ^ _206269) ^ [_318425] : [finite(_318425), 3309 ^ _206269 : [(3310 ^ _206269) ^ [] : [-(relation(3308 ^ [_318425]))], (3312 ^ _206269) ^ [] : [-(function(3308 ^ [_318425]))], (3314 ^ _206269) ^ [] : [-(relation_rng(3308 ^ [_318425]) = _318425)], (3316 ^ _206269) ^ [] : [-(in(relation_dom(3308 ^ [_318425]), omega))]]], (3318 ^ _206269) ^ [_318886] : [-(finite(_318886)), 3319 ^ _206269 : [(3320 ^ _206269) ^ [_318989] : [relation(_318989), function(_318989), relation_rng(_318989) = _318886, in(relation_dom(_318989), omega)]]], (3350 ^ _206269) ^ [_319918] : [3354 ^ _206269 : [(3355 ^ _206269) ^ [] : [-(in(ordered_pair(3351 ^ [_319918], 3352 ^ [_319918]), _319918))], (3357 ^ _206269) ^ [] : [-(in(ordered_pair(3351 ^ [_319918], 3353 ^ [_319918]), _319918))], (3359 ^ _206269) ^ [] : [3352 ^ [_319918] = 3353 ^ [_319918]]], -(function(_319918))], (3336 ^ _206269) ^ [_319447] : [function(_319447), 3339 ^ _206269 : [(3340 ^ _206269) ^ [_319628, _319630, _319632] : [-(_319630 = _319628), in(ordered_pair(_319632, _319630), _319447), in(ordered_pair(_319632, _319628), _319447)]]], (3363 ^ _206269) ^ [_320562, _320564, _320566] : [relation_of2_as_subset(_320562, _320566, _320564), 3366 ^ _206269 : [(3367 ^ _206269) ^ [] : [3368 ^ _206269 : [(3369 ^ _206269) ^ [] : [-(_320564 = empty_set)], (3371 ^ _206269) ^ [] : [_320566 = empty_set]], 3372 ^ _206269 : [(3373 ^ _206269) ^ [] : [quasi_total(_320562, _320566, _320564), -(_320566 = relation_dom_as_subset(_320566, _320564, _320562))], (3379 ^ _206269) ^ [] : [_320566 = relation_dom_as_subset(_320566, _320564, _320562), -(quasi_total(_320562, _320566, _320564))]]], (3385 ^ _206269) ^ [] : [_320564 = empty_set, -(_320566 = empty_set), 3392 ^ _206269 : [(3393 ^ _206269) ^ [] : [quasi_total(_320562, _320566, _320564), -(_320562 = empty_set)], (3399 ^ _206269) ^ [] : [_320562 = empty_set, -(quasi_total(_320562, _320566, _320564))]]]]], (3405 ^ _206269) ^ [_321752, _321754] : [strict_latt_str(_321752), latt_str(_321752), 3412 ^ _206269 : [(3413 ^ _206269) ^ [] : [_321752 = boole_lattice(_321754), 3416 ^ _206269 : [(3417 ^ _206269) ^ [] : [-(the_carrier(_321752) = powerset(_321754))], (3419 ^ _206269) ^ [_322213] : [element(_322213, powerset(_321754)), 3422 ^ _206269 : [(3423 ^ _206269) ^ [_322390] : [element(_322390, powerset(_321754)), 3426 ^ _206269 : [(3427 ^ _206269) ^ [] : [-(apply_binary(the_L_join(_321752), _322213, _322390) = subset_union2(_321754, _322213, _322390))], (3429 ^ _206269) ^ [] : [-(apply_binary(the_L_meet(_321752), _322213, _322390) = subset_intersection2(_321754, _322213, _322390))]]]]]]], (3431 ^ _206269) ^ [] : [-(_321752 = boole_lattice(_321754)), the_carrier(_321752) = powerset(_321754), 3437 ^ _206269 : [(3438 ^ _206269) ^ [] : [-(element(3436 ^ [_321752, _321754], powerset(_321754)))], (3441 ^ _206269) ^ [] : [-(element(3439 ^ [_321752, _321754], powerset(_321754)))], (3443 ^ _206269) ^ [] : [apply_binary(the_L_join(_321752), 3436 ^ [_321752, _321754], 3439 ^ [_321752, _321754]) = subset_union2(_321754, 3436 ^ [_321752, _321754], 3439 ^ [_321752, _321754]), apply_binary(the_L_meet(_321752), 3436 ^ [_321752, _321754], 3439 ^ [_321752, _321754]) = subset_intersection2(_321754, 3436 ^ [_321752, _321754], 3439 ^ [_321752, _321754])]]]]], (3451 ^ _206269) ^ [_323479] : [-(empty_carrier(_323479)), join_semilatt_str(_323479), 3458 ^ _206269 : [(3459 ^ _206269) ^ [_323730] : [element(_323730, the_carrier(_323479)), 3462 ^ _206269 : [(3463 ^ _206269) ^ [_323894] : [element(_323894, the_carrier(_323479)), -(join(_323479, _323730, _323894) = apply_binary_as_element(the_carrier(_323479), the_carrier(_323479), the_carrier(_323479), the_L_join(_323479), _323730, _323894))]]]]], (3469 ^ _206269) ^ [_324154] : [3470 ^ _206269 : [(3471 ^ _206269) ^ [_324276, _324278] : [_324154 = ordered_pair(_324278, _324276)]], 3472 ^ _206269 : [(3483 ^ _206269) ^ [_324739] : [3486 ^ _206269 : [(3487 ^ _206269) ^ [] : [-(_324154 = ordered_pair(3484 ^ [_324154, _324739], 3485 ^ [_324154, _324739]))], (3489 ^ _206269) ^ [] : [_324739 = 3484 ^ [_324154, _324739]]], -(_324739 = pair_first(_324154))], (3473 ^ _206269) ^ [_324385] : [_324385 = pair_first(_324154), 3476 ^ _206269 : [(3477 ^ _206269) ^ [_324550, _324552] : [_324154 = ordered_pair(_324552, _324550), -(_324385 = _324552)]]]]], (3493 ^ _206269) ^ [_325173] : [-(succ(_325173) = set_union2(_325173, singleton(_325173)))], (3495 ^ _206269) ^ [_325273] : [top_str(_325273), 3498 ^ _206269 : [(3533 ^ _206269) ^ [] : [-(topological_space(_325273)), in(the_carrier(_325273), the_topology(_325273)), 3541 ^ _206269 : [(3542 ^ _206269) ^ [] : [-(element(3540 ^ [_325273], powerset(powerset(the_carrier(_325273)))))], (3544 ^ _206269) ^ [] : [-(subset(3540 ^ [_325273], the_topology(_325273)))], (3546 ^ _206269) ^ [] : [in(union_of_subsets(the_carrier(_325273), 3540 ^ [_325273]), the_topology(_325273))]], 3548 ^ _206269 : [(3549 ^ _206269) ^ [] : [-(element(3547 ^ [_325273], powerset(the_carrier(_325273))))], (3552 ^ _206269) ^ [] : [-(element(3550 ^ [_325273], powerset(the_carrier(_325273))))], (3554 ^ _206269) ^ [] : [-(in(3547 ^ [_325273], the_topology(_325273)))], (3556 ^ _206269) ^ [] : [-(in(3550 ^ [_325273], the_topology(_325273)))], (3558 ^ _206269) ^ [] : [in(subset_intersection2(the_carrier(_325273), 3547 ^ [_325273], 3550 ^ [_325273]), the_topology(_325273))]]], (3499 ^ _206269) ^ [] : [topological_space(_325273), 3502 ^ _206269 : [(3503 ^ _206269) ^ [] : [-(in(the_carrier(_325273), the_topology(_325273)))], (3505 ^ _206269) ^ [_325691] : [element(_325691, powerset(powerset(the_carrier(_325273)))), subset(_325691, the_topology(_325273)), -(in(union_of_subsets(the_carrier(_325273), _325691), the_topology(_325273)))], (3515 ^ _206269) ^ [_325988] : [element(_325988, powerset(the_carrier(_325273))), 3518 ^ _206269 : [(3519 ^ _206269) ^ [_326163] : [element(_326163, powerset(the_carrier(_325273))), -(in(subset_intersection2(the_carrier(_325273), _325988, _326163), the_topology(_325273))), in(_325988, the_topology(_325273)), in(_326163, the_topology(_325273))]]]]]]], (3574 ^ _206269) ^ [_328105] : [3576 ^ _206269 : [(3577 ^ _206269) ^ [] : [-(in(3575 ^ [_328105], _328105))], (3579 ^ _206269) ^ [_328342, _328344] : [3575 ^ [_328105] = ordered_pair(_328344, _328342)]], -(relation(_328105))], (3562 ^ _206269) ^ [_327644] : [relation(_327644), 3565 ^ _206269 : [(3566 ^ _206269) ^ [_327792] : [in(_327792, _327644), -(_327792 = ordered_pair(3569 ^ [_327644, _327792], 3570 ^ [_327644, _327792]))]]], (3583 ^ _206269) ^ [_328499] : [relation(_328499), 3586 ^ _206269 : [(3597 ^ _206269) ^ [_328998] : [3599 ^ _206269 : [(3600 ^ _206269) ^ [] : [-(in(3598 ^ [_328499, _328998], _328998))], (3602 ^ _206269) ^ [] : [in(ordered_pair(3598 ^ [_328499, _328998], 3598 ^ [_328499, _328998]), _328499)]], -(is_reflexive_in(_328499, _328998))], (3587 ^ _206269) ^ [_328673] : [is_reflexive_in(_328499, _328673), 3590 ^ _206269 : [(3591 ^ _206269) ^ [_328815] : [in(_328815, _328673), -(in(ordered_pair(_328815, _328815), _328499))]]]]], (3606 ^ _206269) ^ [_329421, _329423, _329425] : [relation_of2(_329421, _329425, _329423), -(subset(_329421, cartesian_product2(_329425, _329423)))], (3612 ^ _206269) ^ [_329597, _329599, _329601] : [subset(_329597, cartesian_product2(_329601, _329599)), -(relation_of2(_329597, _329601, _329599))], (3667 ^ _206269) ^ [_331550, _331552] : [_331552 = empty_set, 3670 ^ _206269 : [(3671 ^ _206269) ^ [] : [_331550 = set_meet(_331552), -(_331550 = empty_set)], (3677 ^ _206269) ^ [] : [_331550 = empty_set, -(_331550 = set_meet(_331552))]]], (3618 ^ _206269) ^ [_329843, _329845] : [-(_329845 = empty_set), 3621 ^ _206269 : [(3645 ^ _206269) ^ [] : [-(_329843 = set_meet(_329845)), 3649 ^ _206269 : [(3650 ^ _206269) ^ [] : [-(in(3646 ^ [_329843, _329845], _329843))], (3653 ^ _206269) ^ [] : [-(in(3651 ^ [_329843, _329845], _329845))], (3655 ^ _206269) ^ [] : [in(3646 ^ [_329843, _329845], 3651 ^ [_329843, _329845])]], 3656 ^ _206269 : [(3663 ^ _206269) ^ [] : [in(3646 ^ [_329843, _329845], _329843)], (3657 ^ _206269) ^ [_331245] : [in(_331245, _329845), -(in(3646 ^ [_329843, _329845], _331245))]]], (3622 ^ _206269) ^ [] : [_329843 = set_meet(_329845), 3625 ^ _206269 : [(3636 ^ _206269) ^ [_330471] : [3638 ^ _206269 : [(3639 ^ _206269) ^ [] : [-(in(3637 ^ [_329843, _329845, _330471], _329845))], (3641 ^ _206269) ^ [] : [in(_330471, 3637 ^ [_329843, _329845, _330471])]], -(in(_330471, _329843))], (3626 ^ _206269) ^ [_330141] : [in(_330141, _329843), 3629 ^ _206269 : [(3630 ^ _206269) ^ [_330286] : [in(_330286, _329845), -(in(_330141, _330286))]]]]]]], (3683 ^ _206269) ^ [_332004] : [one_sorted_str(_332004), 3686 ^ _206269 : [(3687 ^ _206269) ^ [] : [empty_carrier(_332004), -(empty(the_carrier(_332004)))], (3693 ^ _206269) ^ [] : [empty(the_carrier(_332004)), -(empty_carrier(_332004))]]], (3715 ^ _206269) ^ [_332996, _332998] : [-(_332996 = singleton(_332998)), 3719 ^ _206269 : [(3720 ^ _206269) ^ [] : [-(in(3716 ^ [_332996, _332998], _332996))], (3722 ^ _206269) ^ [] : [3716 ^ [_332996, _332998] = _332998]], 3723 ^ _206269 : [(3724 ^ _206269) ^ [] : [-(3716 ^ [_332996, _332998] = _332998)], (3726 ^ _206269) ^ [] : [in(3716 ^ [_332996, _332998], _332996)]]], (3699 ^ _206269) ^ [_332475, _332477] : [_332475 = singleton(_332477), 3702 ^ _206269 : [(3703 ^ _206269) ^ [_332645] : [in(_332645, _332475), -(_332645 = _332477)], (3709 ^ _206269) ^ [_332817] : [_332817 = _332477, -(in(_332817, _332475))]]], (3730 ^ _206269) ^ [_333518] : [top_str(_333518), 3733 ^ _206269 : [(3734 ^ _206269) ^ [_333669] : [element(_333669, powerset(the_carrier(_333518))), -(interior(_333518, _333669) = subset_complement(the_carrier(_333518), topstr_closure(_333518, subset_complement(the_carrier(_333518), _333669))))]]], (3740 ^ _206269) ^ [_333912] : [top_str(_333912), 3743 ^ _206269 : [(3744 ^ _206269) ^ [_334076] : [element(_334076, powerset(powerset(the_carrier(_333912)))), 3747 ^ _206269 : [(3762 ^ _206269) ^ [] : [3764 ^ _206269 : [(3765 ^ _206269) ^ [] : [-(element(3763 ^ [_333912, _334076], powerset(the_carrier(_333912))))], (3767 ^ _206269) ^ [] : [-(in(3763 ^ [_333912, _334076], _334076))], (3769 ^ _206269) ^ [] : [open_subset(3763 ^ [_333912, _334076], _333912)]], -(open_subsets(_334076, _333912))], (3748 ^ _206269) ^ [] : [open_subsets(_334076, _333912), 3751 ^ _206269 : [(3752 ^ _206269) ^ [_334351] : [element(_334351, powerset(the_carrier(_333912))), in(_334351, _334076), -(open_subset(_334351, _333912))]]]]]]], (3773 ^ _206269) ^ [_335027] : [relation(_335027), 3776 ^ _206269 : [(3799 ^ _206269) ^ [_335979, _335981] : [-(_335979 = fiber(_335027, _335981)), 3811 ^ _206269 : [(3812 ^ _206269) ^ [] : [3800 ^ [_335027, _335979, _335981] = _335981], (3814 ^ _206269) ^ [] : [-(in(ordered_pair(3800 ^ [_335027, _335979, _335981], _335981), _335027))], (3816 ^ _206269) ^ [] : [in(3800 ^ [_335027, _335979, _335981], _335979)]], 3803 ^ _206269 : [(3804 ^ _206269) ^ [] : [-(in(3800 ^ [_335027, _335979, _335981], _335979))], (3806 ^ _206269) ^ [] : [-(3800 ^ [_335027, _335979, _335981] = _335981), in(ordered_pair(3800 ^ [_335027, _335979, _335981], _335981), _335027)]]], (3777 ^ _206269) ^ [_335231, _335233] : [_335231 = fiber(_335027, _335233), 3780 ^ _206269 : [(3781 ^ _206269) ^ [_335420] : [in(_335420, _335231), 3784 ^ _206269 : [(3785 ^ _206269) ^ [] : [_335420 = _335233], (3787 ^ _206269) ^ [] : [-(in(ordered_pair(_335420, _335233), _335027))]]], (3789 ^ _206269) ^ [_335686] : [-(in(_335686, _335231)), -(_335686 = _335233), in(ordered_pair(_335686, _335233), _335027)]]]]], (3820 ^ _206269) ^ [_336755, _336757] : [relation(_336755), 3823 ^ _206269 : [(3850 ^ _206269) ^ [] : [-(_336755 = inclusion_relation(_336757)), relation_field(_336755) = _336757, 3857 ^ _206269 : [(3858 ^ _206269) ^ [] : [-(in(3855 ^ [_336755, _336757], _336757))], (3860 ^ _206269) ^ [] : [-(in(3856 ^ [_336755, _336757], _336757))], (3862 ^ _206269) ^ [] : [3863 ^ _206269 : [(3864 ^ _206269) ^ [] : [-(in(ordered_pair(3855 ^ [_336755, _336757], 3856 ^ [_336755, _336757]), _336755))], (3866 ^ _206269) ^ [] : [subset(3855 ^ [_336755, _336757], 3856 ^ [_336755, _336757])]], 3867 ^ _206269 : [(3868 ^ _206269) ^ [] : [-(subset(3855 ^ [_336755, _336757], 3856 ^ [_336755, _336757]))], (3870 ^ _206269) ^ [] : [in(ordered_pair(3855 ^ [_336755, _336757], 3856 ^ [_336755, _336757]), _336755)]]]]], (3824 ^ _206269) ^ [] : [_336755 = inclusion_relation(_336757), 3827 ^ _206269 : [(3828 ^ _206269) ^ [] : [-(relation_field(_336755) = _336757)], (3830 ^ _206269) ^ [_337118, _337120] : [in(_337120, _336757), in(_337118, _336757), 3837 ^ _206269 : [(3838 ^ _206269) ^ [] : [in(ordered_pair(_337120, _337118), _336755), -(subset(_337120, _337118))], (3844 ^ _206269) ^ [] : [subset(_337120, _337118), -(in(ordered_pair(_337120, _337118), _336755))]]]]]]], (3874 ^ _206269) ^ [_338570] : [_338570 = empty_set, 3877 ^ _206269 : [(3878 ^ _206269) ^ [_338683] : [in(_338683, _338570)]]], (3880 ^ _206269) ^ [_338749] : [-(in(3881 ^ [_338749], _338749)), -(_338749 = empty_set)], (3903 ^ _206269) ^ [_339561, _339563] : [-(_339561 = powerset(_339563)), 3907 ^ _206269 : [(3908 ^ _206269) ^ [] : [-(in(3904 ^ [_339561, _339563], _339561))], (3910 ^ _206269) ^ [] : [subset(3904 ^ [_339561, _339563], _339563)]], 3911 ^ _206269 : [(3912 ^ _206269) ^ [] : [-(subset(3904 ^ [_339561, _339563], _339563))], (3914 ^ _206269) ^ [] : [in(3904 ^ [_339561, _339563], _339561)]]], (3887 ^ _206269) ^ [_339040, _339042] : [_339040 = powerset(_339042), 3890 ^ _206269 : [(3891 ^ _206269) ^ [_339210] : [in(_339210, _339040), -(subset(_339210, _339042))], (3897 ^ _206269) ^ [_339382] : [subset(_339382, _339042), -(in(_339382, _339040))]]], (3918 ^ _206269) ^ [_340083] : [-(empty_carrier(_340083)), latt_str(_340083), -(empty_carrier(_340083)), lattice(_340083), complete_latt_str(_340083), latt_str(_340083), 3941 ^ _206269 : [(3942 ^ _206269) ^ [_340689, _340691] : [element(_340689, the_carrier(_340083)), 3945 ^ _206269 : [(3962 ^ _206269) ^ [] : [-(_340689 = join_of_latt_set(_340083, _340691)), latt_element_smaller(_340083, _340689, _340691), 3968 ^ _206269 : [(3969 ^ _206269) ^ [] : [-(element(3967 ^ [_340083, _340689, _340691], the_carrier(_340083)))], (3971 ^ _206269) ^ [] : [-(latt_element_smaller(_340083, 3967 ^ [_340083, _340689, _340691], _340691))], (3973 ^ _206269) ^ [] : [below(_340083, _340689, 3967 ^ [_340083, _340689, _340691])]]], (3946 ^ _206269) ^ [] : [_340689 = join_of_latt_set(_340083, _340691), 3949 ^ _206269 : [(3950 ^ _206269) ^ [] : [-(latt_element_smaller(_340083, _340689, _340691))], (3952 ^ _206269) ^ [_341046] : [element(_341046, the_carrier(_340083)), latt_element_smaller(_340083, _341046, _340691), -(below(_340083, _340689, _341046))]]]]]]], (3977 ^ _206269) ^ [_341859] : [3984 ^ _206269 : [(3985 ^ _206269) ^ [_342064] : [-(meet_of_latt_set(_341859, _342064) = join_of_latt_set(_341859, a_2_2_lattice3(_341859, _342064)))]], -(empty_carrier(_341859)), latt_str(_341859)], (4007 ^ _206269) ^ [_342774] : [-(centered(_342774)), -(_342774 = empty_set), 4013 ^ _206269 : [(4014 ^ _206269) ^ [] : [4012 ^ [_342774] = empty_set], (4016 ^ _206269) ^ [] : [-(subset(4012 ^ [_342774], _342774))], (4018 ^ _206269) ^ [] : [-(finite(4012 ^ [_342774]))], (4020 ^ _206269) ^ [] : [-(set_meet(4012 ^ [_342774]) = empty_set)]]], (3987 ^ _206269) ^ [_342202] : [centered(_342202), 3990 ^ _206269 : [(3991 ^ _206269) ^ [] : [_342202 = empty_set], (3993 ^ _206269) ^ [_342421] : [-(_342421 = empty_set), subset(_342421, _342202), finite(_342421), set_meet(_342421) = empty_set]]], (4024 ^ _206269) ^ [_343364] : [-(poset_of_lattice(_343364) = rel_str_of(the_carrier(_343364), k2_lattice3(_343364))), -(empty_carrier(_343364)), lattice(_343364), latt_str(_343364)], (4038 ^ _206269) ^ [_343739] : [-(empty_carrier(_343739)), meet_semilatt_str(_343739), 4045 ^ _206269 : [(4046 ^ _206269) ^ [_343990] : [element(_343990, the_carrier(_343739)), 4049 ^ _206269 : [(4050 ^ _206269) ^ [_344154] : [element(_344154, the_carrier(_343739)), -(meet(_343739, _343990, _344154) = apply_binary_as_element(the_carrier(_343739), the_carrier(_343739), the_carrier(_343739), the_L_meet(_343739), _343990, _344154))]]]]], (4056 ^ _206269) ^ [_344414] : [4057 ^ _206269 : [(4058 ^ _206269) ^ [_344536, _344538] : [_344414 = ordered_pair(_344538, _344536)]], 4059 ^ _206269 : [(4070 ^ _206269) ^ [_344999] : [4073 ^ _206269 : [(4074 ^ _206269) ^ [] : [-(_344414 = ordered_pair(4071 ^ [_344414, _344999], 4072 ^ [_344414, _344999]))], (4076 ^ _206269) ^ [] : [_344999 = 4072 ^ [_344414, _344999]]], -(_344999 = pair_second(_344414))], (4060 ^ _206269) ^ [_344645] : [_344645 = pair_second(_344414), 4063 ^ _206269 : [(4064 ^ _206269) ^ [_344810, _344812] : [_344414 = ordered_pair(_344812, _344810), -(_344645 = _344810)]]]]], (4090 ^ _206269) ^ [_345770] : [4092 ^ _206269 : [(4093 ^ _206269) ^ [] : [-(in(4091 ^ [_345770], _345770))], (4095 ^ _206269) ^ [] : [subset(4091 ^ [_345770], _345770)]], -(epsilon_transitive(_345770))], (4080 ^ _206269) ^ [_345470] : [epsilon_transitive(_345470), 4083 ^ _206269 : [(4084 ^ _206269) ^ [_345601] : [in(_345601, _345470), -(subset(_345601, _345470))]]], (4099 ^ _206269) ^ [_346095] : [one_sorted_str(_346095), -(empty_carrier_subset(_346095) = empty_set)], (4105 ^ _206269) ^ [_346287] : [relation(_346287), 4108 ^ _206269 : [(4109 ^ _206269) ^ [_346445] : [relation(_346445), 4112 ^ _206269 : [(4129 ^ _206269) ^ [] : [-(_346287 = _346445), 4134 ^ _206269 : [(4135 ^ _206269) ^ [] : [-(in(ordered_pair(4130 ^ [_346287, _346445], 4131 ^ [_346287, _346445]), _346287))], (4137 ^ _206269) ^ [] : [in(ordered_pair(4130 ^ [_346287, _346445], 4131 ^ [_346287, _346445]), _346445)]], 4138 ^ _206269 : [(4139 ^ _206269) ^ [] : [-(in(ordered_pair(4130 ^ [_346287, _346445], 4131 ^ [_346287, _346445]), _346445))], (4141 ^ _206269) ^ [] : [in(ordered_pair(4130 ^ [_346287, _346445], 4131 ^ [_346287, _346445]), _346287)]]], (4113 ^ _206269) ^ [] : [_346287 = _346445, 4116 ^ _206269 : [(4117 ^ _206269) ^ [_346750, _346752] : [in(ordered_pair(_346752, _346750), _346287), -(in(ordered_pair(_346752, _346750), _346445))], (4123 ^ _206269) ^ [_346940, _346942] : [in(ordered_pair(_346942, _346940), _346445), -(in(ordered_pair(_346942, _346940), _346287))]]]]]]], (4145 ^ _206269) ^ [_347777, _347779] : [-(empty(_347779)), 4148 ^ _206269 : [(4149 ^ _206269) ^ [] : [element(_347777, _347779), -(in(_347777, _347779))], (4155 ^ _206269) ^ [] : [in(_347777, _347779), -(element(_347777, _347779))]]], (4161 ^ _206269) ^ [_348190, _348192] : [empty(_348192), 4164 ^ _206269 : [(4165 ^ _206269) ^ [] : [element(_348190, _348192), -(empty(_348190))], (4171 ^ _206269) ^ [] : [empty(_348190), -(element(_348190, _348192))]]], (4199 ^ _206269) ^ [_349415, _349417, _349419] : [-(_349415 = unordered_pair(_349419, _349417)), 4203 ^ _206269 : [(4204 ^ _206269) ^ [] : [-(in(4200 ^ [_349415, _349417, _349419], _349415))], (4206 ^ _206269) ^ [] : [4200 ^ [_349415, _349417, _349419] = _349419], (4208 ^ _206269) ^ [] : [4200 ^ [_349415, _349417, _349419] = _349417]], 4209 ^ _206269 : [(4216 ^ _206269) ^ [] : [in(4200 ^ [_349415, _349417, _349419], _349415)], (4210 ^ _206269) ^ [] : [-(4200 ^ [_349415, _349417, _349419] = _349419), -(4200 ^ [_349415, _349417, _349419] = _349417)]]], (4177 ^ _206269) ^ [_348690, _348692, _348694] : [_348690 = unordered_pair(_348694, _348692), 4180 ^ _206269 : [(4191 ^ _206269) ^ [_349150] : [4192 ^ _206269 : [(4193 ^ _206269) ^ [] : [_349150 = _348694], (4195 ^ _206269) ^ [] : [_349150 = _348692]], -(in(_349150, _348690))], (4181 ^ _206269) ^ [_348872] : [in(_348872, _348690), -(_348872 = _348694), -(_348872 = _348692)]]], (4220 ^ _206269) ^ [_350166, _350168] : [element(_350166, _350168), 4223 ^ _206269 : [(4224 ^ _206269) ^ [] : [proper_element(_350166, _350168), _350166 = union(_350168)], (4230 ^ _206269) ^ [] : [-(_350166 = union(_350168)), -(proper_element(_350166, _350168))]]], (4236 ^ _206269) ^ [_350620] : [top_str(_350620), 4239 ^ _206269 : [(4240 ^ _206269) ^ [_350784] : [element(_350784, powerset(powerset(the_carrier(_350620)))), 4243 ^ _206269 : [(4258 ^ _206269) ^ [] : [4260 ^ _206269 : [(4261 ^ _206269) ^ [] : [-(element(4259 ^ [_350620, _350784], powerset(the_carrier(_350620))))], (4263 ^ _206269) ^ [] : [-(in(4259 ^ [_350620, _350784], _350784))], (4265 ^ _206269) ^ [] : [closed_subset(4259 ^ [_350620, _350784], _350620)]], -(closed_subsets(_350784, _350620))], (4244 ^ _206269) ^ [] : [closed_subsets(_350784, _350620), 4247 ^ _206269 : [(4248 ^ _206269) ^ [_351059] : [element(_351059, powerset(the_carrier(_350620))), in(_351059, _350784), -(closed_subset(_351059, _350620))]]]]]]], (4269 ^ _206269) ^ [_351735] : [relation(_351735), 4272 ^ _206269 : [(4290 ^ _206269) ^ [] : [-(well_founded_relation(_351735)), 4292 ^ _206269 : [(4293 ^ _206269) ^ [] : [-(subset(4291 ^ [_351735], relation_field(_351735)))], (4295 ^ _206269) ^ [] : [4291 ^ [_351735] = empty_set], (4297 ^ _206269) ^ [_352685] : [in(_352685, 4291 ^ [_351735]), disjoint(fiber(_351735, _352685), 4291 ^ [_351735])]]], (4273 ^ _206269) ^ [] : [well_founded_relation(_351735), 4276 ^ _206269 : [(4277 ^ _206269) ^ [_352002] : [subset(_352002, relation_field(_351735)), -(_352002 = empty_set), 4285 ^ _206269 : [(4286 ^ _206269) ^ [] : [-(in(4284 ^ [_351735, _352002], _352002))], (4288 ^ _206269) ^ [] : [-(disjoint(fiber(_351735, 4284 ^ [_351735, _352002]), _352002))]]]]]]], (4327 ^ _206269) ^ [_353749, _353751, _353753] : [-(_353749 = set_union2(_353753, _353751)), 4331 ^ _206269 : [(4332 ^ _206269) ^ [] : [-(in(4328 ^ [_353749, _353751, _353753], _353749))], (4334 ^ _206269) ^ [] : [in(4328 ^ [_353749, _353751, _353753], _353753)], (4336 ^ _206269) ^ [] : [in(4328 ^ [_353749, _353751, _353753], _353751)]], 4337 ^ _206269 : [(4344 ^ _206269) ^ [] : [in(4328 ^ [_353749, _353751, _353753], _353749)], (4338 ^ _206269) ^ [] : [-(in(4328 ^ [_353749, _353751, _353753], _353753)), -(in(4328 ^ [_353749, _353751, _353753], _353751))]]], (4305 ^ _206269) ^ [_353024, _353026, _353028] : [_353024 = set_union2(_353028, _353026), 4308 ^ _206269 : [(4319 ^ _206269) ^ [_353484] : [4320 ^ _206269 : [(4321 ^ _206269) ^ [] : [in(_353484, _353028)], (4323 ^ _206269) ^ [] : [in(_353484, _353026)]], -(in(_353484, _353024))], (4309 ^ _206269) ^ [_353206] : [in(_353206, _353024), -(in(_353206, _353028)), -(in(_353206, _353026))]]], (4378 ^ _206269) ^ [_355800, _355802, _355804] : [-(_355800 = cartesian_product2(_355804, _355802)), 4396 ^ _206269 : [(4397 ^ _206269) ^ [] : [-(in(4394 ^ [_355800, _355802, _355804], _355804))], (4399 ^ _206269) ^ [] : [-(in(4395 ^ [_355800, _355802, _355804], _355802))], (4401 ^ _206269) ^ [] : [-(4379 ^ [_355800, _355802, _355804] = ordered_pair(4394 ^ [_355800, _355802, _355804], 4395 ^ [_355800, _355802, _355804]))], (4403 ^ _206269) ^ [] : [in(4379 ^ [_355800, _355802, _355804], _355800)]], 4382 ^ _206269 : [(4383 ^ _206269) ^ [] : [-(in(4379 ^ [_355800, _355802, _355804], _355800))], (4385 ^ _206269) ^ [_356138, _356140] : [in(_356140, _355804), in(_356138, _355802), 4379 ^ [_355800, _355802, _355804] = ordered_pair(_356140, _356138)]]], (4348 ^ _206269) ^ [_354543, _354545, _354547] : [_354543 = cartesian_product2(_354547, _354545), 4351 ^ _206269 : [(4352 ^ _206269) ^ [_354744] : [in(_354744, _354543), 4357 ^ _206269 : [(4358 ^ _206269) ^ [] : [-(in(4355 ^ [_354543, _354545, _354547, _354744], _354547))], (4360 ^ _206269) ^ [] : [-(in(4356 ^ [_354543, _354545, _354547, _354744], _354545))], (4362 ^ _206269) ^ [] : [-(_354744 = ordered_pair(4355 ^ [_354543, _354545, _354547, _354744], 4356 ^ [_354543, _354545, _354547, _354744]))]]], (4364 ^ _206269) ^ [_355304] : [-(in(_355304, _354543)), 4365 ^ _206269 : [(4366 ^ _206269) ^ [_355434, _355436] : [in(_355436, _354547), in(_355434, _354545), _355304 = ordered_pair(_355436, _355434)]]]]], (4407 ^ _206269) ^ [_357034] : [top_str(_357034), 4410 ^ _206269 : [(4411 ^ _206269) ^ [] : [compact_top_space(_357034), 4414 ^ _206269 : [(4415 ^ _206269) ^ [_357323] : [element(_357323, powerset(powerset(the_carrier(_357034)))), is_a_cover_of_carrier(_357034, _357323), open_subsets(_357323, _357034), 4427 ^ _206269 : [(4428 ^ _206269) ^ [] : [-(element(4426 ^ [_357034, _357323], powerset(powerset(the_carrier(_357034)))))], (4430 ^ _206269) ^ [] : [-(subset(4426 ^ [_357034, _357323], _357323))], (4432 ^ _206269) ^ [] : [-(is_a_cover_of_carrier(_357034, 4426 ^ [_357034, _357323]))], (4434 ^ _206269) ^ [] : [-(finite(4426 ^ [_357034, _357323]))]]]]], (4436 ^ _206269) ^ [] : [-(compact_top_space(_357034)), 4438 ^ _206269 : [(4439 ^ _206269) ^ [] : [-(element(4437 ^ [_357034], powerset(powerset(the_carrier(_357034)))))], (4441 ^ _206269) ^ [] : [-(is_a_cover_of_carrier(_357034, 4437 ^ [_357034]))], (4443 ^ _206269) ^ [] : [-(open_subsets(4437 ^ [_357034], _357034))], (4445 ^ _206269) ^ [_358378] : [element(_358378, powerset(powerset(the_carrier(_357034)))), subset(_358378, 4437 ^ [_357034]), is_a_cover_of_carrier(_357034, _358378), finite(_358378)]]]]], (4461 ^ _206269) ^ [_358836] : [4472 ^ _206269 : [(4473 ^ _206269) ^ [_359141] : [element(_359141, the_carrier(_358836)), -(cast_to_el_of_LattPOSet(_358836, _359141) = _359141)]], -(empty_carrier(_358836)), lattice(_358836), latt_str(_358836)], (4479 ^ _206269) ^ [_359354] : [-(empty_carrier(_359354)), join_semilatt_str(_359354), 4486 ^ _206269 : [(4487 ^ _206269) ^ [_359597] : [element(_359597, the_carrier(_359354)), 4490 ^ _206269 : [(4491 ^ _206269) ^ [_359753] : [element(_359753, the_carrier(_359354)), 4494 ^ _206269 : [(4495 ^ _206269) ^ [] : [below(_359354, _359597, _359753), -(join(_359354, _359597, _359753) = _359753)], (4501 ^ _206269) ^ [] : [join(_359354, _359597, _359753) = _359753, -(below(_359354, _359597, _359753))]]]]]]], (4529 ^ _206269) ^ [_360917] : [4532 ^ _206269 : [(4533 ^ _206269) ^ [] : [-(in(4530 ^ [_360917], _360917))], (4535 ^ _206269) ^ [] : [-(in(4531 ^ [_360917], _360917))], (4537 ^ _206269) ^ [] : [in(4530 ^ [_360917], 4531 ^ [_360917])], (4539 ^ _206269) ^ [] : [4530 ^ [_360917] = 4531 ^ [_360917]], (4541 ^ _206269) ^ [] : [in(4531 ^ [_360917], 4530 ^ [_360917])]], -(epsilon_connected(_360917))], (4507 ^ _206269) ^ [_360279] : [epsilon_connected(_360279), 4510 ^ _206269 : [(4511 ^ _206269) ^ [_360455, _360457] : [in(_360457, _360279), in(_360455, _360279), -(in(_360457, _360455)), -(_360457 = _360455), -(in(_360455, _360457))]]], (4545 ^ _206269) ^ [_361623] : [one_sorted_str(_361623), -(cast_as_carrier_subset(_361623) = the_carrier(_361623))], (4551 ^ _206269) ^ [_361819] : [relation(_361819), 4554 ^ _206269 : [(4555 ^ _206269) ^ [_361977] : [relation(_361977), 4558 ^ _206269 : [(4569 ^ _206269) ^ [] : [4572 ^ _206269 : [(4573 ^ _206269) ^ [] : [-(in(ordered_pair(4570 ^ [_361819, _361977], 4571 ^ [_361819, _361977]), _361819))], (4575 ^ _206269) ^ [] : [in(ordered_pair(4570 ^ [_361819, _361977], 4571 ^ [_361819, _361977]), _361977)]], -(subset(_361819, _361977))], (4559 ^ _206269) ^ [] : [subset(_361819, _361977), 4562 ^ _206269 : [(4563 ^ _206269) ^ [_362253, _362255] : [in(ordered_pair(_362255, _362253), _361819), -(in(ordered_pair(_362255, _362253), _361977))]]]]]]], (4589 ^ _206269) ^ [_363216, _363218] : [4591 ^ _206269 : [(4592 ^ _206269) ^ [] : [-(in(4590 ^ [_363216, _363218], _363218))], (4594 ^ _206269) ^ [] : [in(4590 ^ [_363216, _363218], _363216)]], -(subset(_363218, _363216))], (4579 ^ _206269) ^ [_362902, _362904] : [subset(_362904, _362902), 4582 ^ _206269 : [(4583 ^ _206269) ^ [_363039] : [in(_363039, _362904), -(in(_363039, _362902))]]], (4598 ^ _206269) ^ [_363559] : [relation(_363559), 4601 ^ _206269 : [(4619 ^ _206269) ^ [_364362] : [-(is_well_founded_in(_363559, _364362)), 4621 ^ _206269 : [(4622 ^ _206269) ^ [] : [-(subset(4620 ^ [_363559, _364362], _364362))], (4624 ^ _206269) ^ [] : [4620 ^ [_363559, _364362] = empty_set], (4626 ^ _206269) ^ [_364704] : [in(_364704, 4620 ^ [_363559, _364362]), disjoint(fiber(_363559, _364704), 4620 ^ [_363559, _364362])]]], (4602 ^ _206269) ^ [_363756] : [is_well_founded_in(_363559, _363756), 4605 ^ _206269 : [(4606 ^ _206269) ^ [_363921] : [subset(_363921, _363756), -(_363921 = empty_set), 4614 ^ _206269 : [(4615 ^ _206269) ^ [] : [-(in(4613 ^ [_363559, _363756, _363921], _363921))], (4617 ^ _206269) ^ [] : [-(disjoint(fiber(_363559, 4613 ^ [_363559, _363756, _363921]), _363921))]]]]]]], (4656 ^ _206269) ^ [_365787, _365789, _365791] : [-(_365787 = set_intersection2(_365791, _365789)), 4668 ^ _206269 : [(4669 ^ _206269) ^ [] : [-(in(4657 ^ [_365787, _365789, _365791], _365791))], (4671 ^ _206269) ^ [] : [-(in(4657 ^ [_365787, _365789, _365791], _365789))], (4673 ^ _206269) ^ [] : [in(4657 ^ [_365787, _365789, _365791], _365787)]], 4660 ^ _206269 : [(4661 ^ _206269) ^ [] : [-(in(4657 ^ [_365787, _365789, _365791], _365787))], (4663 ^ _206269) ^ [] : [in(4657 ^ [_365787, _365789, _365791], _365791), in(4657 ^ [_365787, _365789, _365791], _365789)]]], (4634 ^ _206269) ^ [_365062, _365064, _365066] : [_365062 = set_intersection2(_365066, _365064), 4637 ^ _206269 : [(4638 ^ _206269) ^ [_365244] : [in(_365244, _365062), 4641 ^ _206269 : [(4642 ^ _206269) ^ [] : [-(in(_365244, _365066))], (4644 ^ _206269) ^ [] : [-(in(_365244, _365064))]]], (4646 ^ _206269) ^ [_365503] : [-(in(_365503, _365062)), in(_365503, _365066), in(_365503, _365064)]]], (4677 ^ _206269) ^ [_366526] : [relation(_366526), function(_366526), 4684 ^ _206269 : [(4685 ^ _206269) ^ [_366818, _366820] : [in(_366820, relation_dom(_366526)), 4688 ^ _206269 : [(4689 ^ _206269) ^ [] : [_366818 = apply(_366526, _366820), -(in(ordered_pair(_366820, _366818), _366526))], (4695 ^ _206269) ^ [] : [in(ordered_pair(_366820, _366818), _366526), -(_366818 = apply(_366526, _366820))]]], (4701 ^ _206269) ^ [_367270, _367272] : [-(in(_367272, relation_dom(_366526))), 4704 ^ _206269 : [(4705 ^ _206269) ^ [] : [_367270 = apply(_366526, _367272), -(_367270 = empty_set)], (4711 ^ _206269) ^ [] : [_367270 = empty_set, -(_367270 = apply(_366526, _367272))]]]]], (4717 ^ _206269) ^ [_367759] : [4728 ^ _206269 : [(4729 ^ _206269) ^ [_368066] : [element(_368066, the_carrier(poset_of_lattice(_367759))), -(cast_to_el_of_lattice(_367759, _368066) = _368066)]], -(empty_carrier(_367759)), lattice(_367759), latt_str(_367759)], (4735 ^ _206269) ^ [_368312] : [ordinal(_368312), 4738 ^ _206269 : [(4739 ^ _206269) ^ [] : [-(epsilon_transitive(_368312))], (4741 ^ _206269) ^ [] : [-(epsilon_connected(_368312))]]], (4743 ^ _206269) ^ [_368535] : [-(ordinal(_368535)), epsilon_transitive(_368535), epsilon_connected(_368535)], (4753 ^ _206269) ^ [_368806] : [relation(_368806), 4756 ^ _206269 : [(4774 ^ _206269) ^ [_369618] : [-(_369618 = relation_dom(_368806)), 4778 ^ _206269 : [(4779 ^ _206269) ^ [] : [-(in(4775 ^ [_368806, _369618], _369618))], (4781 ^ _206269) ^ [_369881] : [in(ordered_pair(4775 ^ [_368806, _369618], _369881), _368806)]], 4783 ^ _206269 : [(4784 ^ _206269) ^ [] : [-(in(ordered_pair(4775 ^ [_368806, _369618], 4782 ^ [_368806, _369618]), _368806))], (4786 ^ _206269) ^ [] : [in(4775 ^ [_368806, _369618], _369618)]]], (4757 ^ _206269) ^ [_368987] : [_368987 = relation_dom(_368806), 4760 ^ _206269 : [(4761 ^ _206269) ^ [_369167] : [in(_369167, _368987), -(in(ordered_pair(_369167, 4764 ^ [_368806, _368987, _369167]), _368806))], (4768 ^ _206269) ^ [_369411] : [4769 ^ _206269 : [(4770 ^ _206269) ^ [_369490] : [in(ordered_pair(_369411, _369490), _368806)]], -(in(_369411, _368987))]]]]], (4790 ^ _206269) ^ [_370247] : [relation(_370247), 4793 ^ _206269 : [(4816 ^ _206269) ^ [_371115] : [4819 ^ _206269 : [(4820 ^ _206269) ^ [] : [-(in(4817 ^ [_370247, _371115], _371115))], (4822 ^ _206269) ^ [] : [-(in(4818 ^ [_370247, _371115], _371115))], (4824 ^ _206269) ^ [] : [-(in(ordered_pair(4817 ^ [_370247, _371115], 4818 ^ [_370247, _371115]), _370247))], (4826 ^ _206269) ^ [] : [-(in(ordered_pair(4818 ^ [_370247, _371115], 4817 ^ [_370247, _371115]), _370247))], (4828 ^ _206269) ^ [] : [4817 ^ [_370247, _371115] = 4818 ^ [_370247, _371115]]], -(is_antisymmetric_in(_370247, _371115))], (4794 ^ _206269) ^ [_370447] : [is_antisymmetric_in(_370247, _370447), 4797 ^ _206269 : [(4798 ^ _206269) ^ [_370629, _370631] : [-(_370631 = _370629), in(_370631, _370447), in(_370629, _370447), in(ordered_pair(_370631, _370629), _370247), in(ordered_pair(_370629, _370631), _370247)]]]]], (4832 ^ _206269) ^ [_371869] : [-(cast_to_subset(_371869) = _371869)], (4857 ^ _206269) ^ [_372852, _372854] : [-(_372852 = union(_372854)), 4870 ^ _206269 : [(4871 ^ _206269) ^ [] : [-(in(4858 ^ [_372852, _372854], 4869 ^ [_372852, _372854]))], (4873 ^ _206269) ^ [] : [-(in(4869 ^ [_372852, _372854], _372854))], (4875 ^ _206269) ^ [] : [in(4858 ^ [_372852, _372854], _372852)]], 4861 ^ _206269 : [(4862 ^ _206269) ^ [] : [-(in(4858 ^ [_372852, _372854], _372852))], (4864 ^ _206269) ^ [_373135] : [in(4858 ^ [_372852, _372854], _373135), in(_373135, _372854)]]], (4834 ^ _206269) ^ [_372007, _372009] : [_372007 = union(_372009), 4837 ^ _206269 : [(4838 ^ _206269) ^ [_372188] : [in(_372188, _372007), 4842 ^ _206269 : [(4843 ^ _206269) ^ [] : [-(in(_372188, 4841 ^ [_372007, _372009, _372188]))], (4845 ^ _206269) ^ [] : [-(in(4841 ^ [_372007, _372009, _372188], _372009))]]], (4847 ^ _206269) ^ [_372515] : [-(in(_372515, _372007)), 4848 ^ _206269 : [(4849 ^ _206269) ^ [_372613] : [in(_372515, _372613), in(_372613, _372009)]]]]], (4879 ^ _206269) ^ [_373685] : [relation(_373685), 4882 ^ _206269 : [(4883 ^ _206269) ^ [] : [well_ordering(_373685), 4886 ^ _206269 : [(4887 ^ _206269) ^ [] : [-(reflexive(_373685))], (4889 ^ _206269) ^ [] : [-(transitive(_373685))], (4891 ^ _206269) ^ [] : [-(antisymmetric(_373685))], (4893 ^ _206269) ^ [] : [-(connected(_373685))], (4895 ^ _206269) ^ [] : [-(well_founded_relation(_373685))]]], (4897 ^ _206269) ^ [] : [-(well_ordering(_373685)), reflexive(_373685), transitive(_373685), antisymmetric(_373685), connected(_373685), well_founded_relation(_373685)]]], (4919 ^ _206269) ^ [_374743, _374745] : [equipotent(_374745, _374743), 4923 ^ _206269 : [(4924 ^ _206269) ^ [] : [-(relation(4922 ^ [_374743, _374745]))], (4926 ^ _206269) ^ [] : [-(function(4922 ^ [_374743, _374745]))], (4928 ^ _206269) ^ [] : [-(one_to_one(4922 ^ [_374743, _374745]))], (4930 ^ _206269) ^ [] : [-(relation_dom(4922 ^ [_374743, _374745]) = _374745)], (4932 ^ _206269) ^ [] : [-(relation_rng(4922 ^ [_374743, _374745]) = _374743)]]], (4934 ^ _206269) ^ [_375314, _375316] : [-(equipotent(_375316, _375314)), 4935 ^ _206269 : [(4936 ^ _206269) ^ [_375425] : [relation(_375425), function(_375425), one_to_one(_375425), relation_dom(_375425) = _375316, relation_rng(_375425) = _375314]]], (4978 ^ _206269) ^ [_376752, _376754, _376756] : [-(_376752 = set_difference(_376756, _376754)), 4990 ^ _206269 : [(4991 ^ _206269) ^ [] : [-(in(4979 ^ [_376752, _376754, _376756], _376756))], (4993 ^ _206269) ^ [] : [in(4979 ^ [_376752, _376754, _376756], _376754)], (4995 ^ _206269) ^ [] : [in(4979 ^ [_376752, _376754, _376756], _376752)]], 4982 ^ _206269 : [(4983 ^ _206269) ^ [] : [-(in(4979 ^ [_376752, _376754, _376756], _376752))], (4985 ^ _206269) ^ [] : [in(4979 ^ [_376752, _376754, _376756], _376756), -(in(4979 ^ [_376752, _376754, _376756], _376754))]]], (4956 ^ _206269) ^ [_376021, _376023, _376025] : [_376021 = set_difference(_376025, _376023), 4959 ^ _206269 : [(4960 ^ _206269) ^ [_376205] : [in(_376205, _376021), 4963 ^ _206269 : [(4964 ^ _206269) ^ [] : [-(in(_376205, _376025))], (4966 ^ _206269) ^ [] : [in(_376205, _376023)]]], (4968 ^ _206269) ^ [_376465] : [-(in(_376465, _376021)), in(_376465, _376025), -(in(_376465, _376023))]]], (4999 ^ _206269) ^ [_377495] : [relation(_377495), function(_377495), 5006 ^ _206269 : [(5030 ^ _206269) ^ [_378649] : [-(_378649 = relation_rng(_377495)), 5043 ^ _206269 : [(5044 ^ _206269) ^ [] : [-(in(5042 ^ [_377495, _378649], relation_dom(_377495)))], (5046 ^ _206269) ^ [] : [-(5031 ^ [_377495, _378649] = apply(_377495, 5042 ^ [_377495, _378649]))], (5048 ^ _206269) ^ [] : [in(5031 ^ [_377495, _378649], _378649)]], 5034 ^ _206269 : [(5035 ^ _206269) ^ [] : [-(in(5031 ^ [_377495, _378649], _378649))], (5037 ^ _206269) ^ [_378944] : [in(_378944, relation_dom(_377495)), 5031 ^ [_377495, _378649] = apply(_377495, _378944)]]], (5007 ^ _206269) ^ [_377767] : [_377767 = relation_rng(_377495), 5010 ^ _206269 : [(5011 ^ _206269) ^ [_377955] : [in(_377955, _377767), 5015 ^ _206269 : [(5016 ^ _206269) ^ [] : [-(in(5014 ^ [_377495, _377767, _377955], relation_dom(_377495)))], (5018 ^ _206269) ^ [] : [-(_377955 = apply(_377495, 5014 ^ [_377495, _377767, _377955]))]]], (5020 ^ _206269) ^ [_378297] : [-(in(_378297, _377767)), 5021 ^ _206269 : [(5022 ^ _206269) ^ [_378400] : [in(_378400, relation_dom(_377495)), _378297 = apply(_377495, _378400)]]]]]]], (5052 ^ _206269) ^ [_379521] : [rel_str(_379521), 5055 ^ _206269 : [(5056 ^ _206269) ^ [] : [transitive_relstr(_379521), -(is_transitive_in(the_InternalRel(_379521), the_carrier(_379521)))], (5062 ^ _206269) ^ [] : [is_transitive_in(the_InternalRel(_379521), the_carrier(_379521)), -(transitive_relstr(_379521))]]], (5068 ^ _206269) ^ [_379987] : [_379987 = omega, 5071 ^ _206269 : [(5072 ^ _206269) ^ [] : [-(in(empty_set, _379987))], (5074 ^ _206269) ^ [] : [-(being_limit_ordinal(_379987))], (5076 ^ _206269) ^ [] : [-(ordinal(_379987))], (5078 ^ _206269) ^ [_380336] : [ordinal(_380336), -(subset(_379987, _380336)), in(empty_set, _380336), being_limit_ordinal(_380336)]]], (5092 ^ _206269) ^ [_380685] : [-(_380685 = omega), in(empty_set, _380685), being_limit_ordinal(_380685), ordinal(_380685), 5106 ^ _206269 : [(5107 ^ _206269) ^ [] : [-(ordinal(5105 ^ [_380685]))], (5109 ^ _206269) ^ [] : [-(in(empty_set, 5105 ^ [_380685]))], (5111 ^ _206269) ^ [] : [-(being_limit_ordinal(5105 ^ [_380685]))], (5113 ^ _206269) ^ [] : [subset(_380685, 5105 ^ [_380685])]]], (5117 ^ _206269) ^ [_381425] : [top_str(_381425), 5120 ^ _206269 : [(5121 ^ _206269) ^ [_381568] : [element(_381568, powerset(the_carrier(_381425))), 5124 ^ _206269 : [(5125 ^ _206269) ^ [] : [open_subset(_381568, _381425), -(in(_381568, the_topology(_381425)))], (5131 ^ _206269) ^ [] : [in(_381568, the_topology(_381425)), -(open_subset(_381568, _381425))]]]]], (5137 ^ _206269) ^ [_382035] : [relation(_382035), 5140 ^ _206269 : [(5158 ^ _206269) ^ [_382847] : [-(_382847 = relation_rng(_382035)), 5162 ^ _206269 : [(5163 ^ _206269) ^ [] : [-(in(5159 ^ [_382035, _382847], _382847))], (5165 ^ _206269) ^ [_383110] : [in(ordered_pair(_383110, 5159 ^ [_382035, _382847]), _382035)]], 5167 ^ _206269 : [(5168 ^ _206269) ^ [] : [-(in(ordered_pair(5166 ^ [_382035, _382847], 5159 ^ [_382035, _382847]), _382035))], (5170 ^ _206269) ^ [] : [in(5159 ^ [_382035, _382847], _382847)]]], (5141 ^ _206269) ^ [_382216] : [_382216 = relation_rng(_382035), 5144 ^ _206269 : [(5145 ^ _206269) ^ [_382396] : [in(_382396, _382216), -(in(ordered_pair(5148 ^ [_382035, _382216, _382396], _382396), _382035))], (5152 ^ _206269) ^ [_382640] : [5153 ^ _206269 : [(5154 ^ _206269) ^ [_382719] : [in(ordered_pair(_382719, _382640), _382035)]], -(in(_382640, _382216))]]]]], (5174 ^ _206269) ^ [_383490, _383492] : [element(_383490, powerset(_383492)), -(subset_complement(_383492, _383490) = set_difference(_383492, _383490))], (5180 ^ _206269) ^ [_383701, _383703] : [-(ordered_pair(_383703, _383701) = unordered_pair(unordered_pair(_383703, _383701), singleton(_383703)))], (5182 ^ _206269) ^ [_383807] : [relation(_383807), 5185 ^ _206269 : [(5186 ^ _206269) ^ [_383991] : [well_orders(_383807, _383991), 5189 ^ _206269 : [(5190 ^ _206269) ^ [] : [-(is_reflexive_in(_383807, _383991))], (5192 ^ _206269) ^ [] : [-(is_transitive_in(_383807, _383991))], (5194 ^ _206269) ^ [] : [-(is_antisymmetric_in(_383807, _383991))], (5196 ^ _206269) ^ [] : [-(is_connected_in(_383807, _383991))], (5198 ^ _206269) ^ [] : [-(is_well_founded_in(_383807, _383991))]]], (5200 ^ _206269) ^ [_384452] : [-(well_orders(_383807, _384452)), is_reflexive_in(_383807, _384452), is_transitive_in(_383807, _384452), is_antisymmetric_in(_383807, _384452), is_connected_in(_383807, _384452), is_well_founded_in(_383807, _384452)]]], (5222 ^ _206269) ^ [_385013] : [rel_str(_385013), 5225 ^ _206269 : [(5226 ^ _206269) ^ [] : [antisymmetric_relstr(_385013), -(is_antisymmetric_in(the_InternalRel(_385013), the_carrier(_385013)))], (5232 ^ _206269) ^ [] : [is_antisymmetric_in(the_InternalRel(_385013), the_carrier(_385013)), -(antisymmetric_relstr(_385013))]]], (5238 ^ _206269) ^ [_385479] : [being_limit_ordinal(_385479), -(_385479 = union(_385479))], (5244 ^ _206269) ^ [_385637] : [_385637 = union(_385637), -(being_limit_ordinal(_385637))], (5250 ^ _206269) ^ [_385831] : [top_str(_385831), 5253 ^ _206269 : [(5254 ^ _206269) ^ [_385980] : [element(_385980, powerset(the_carrier(_385831))), 5257 ^ _206269 : [(5258 ^ _206269) ^ [] : [closed_subset(_385980, _385831), -(open_subset(subset_difference(the_carrier(_385831), cast_as_carrier_subset(_385831), _385980), _385831))], (5264 ^ _206269) ^ [] : [open_subset(subset_difference(the_carrier(_385831), cast_as_carrier_subset(_385831), _385980), _385831), -(closed_subset(_385980, _385831))]]]]], (5270 ^ _206269) ^ [_386465] : [relation(_386465), -(relation_field(_386465) = set_union2(relation_dom(_386465), relation_rng(_386465)))], (5276 ^ _206269) ^ [_386671] : [relation(_386671), 5279 ^ _206269 : [(5302 ^ _206269) ^ [_387563] : [5305 ^ _206269 : [(5306 ^ _206269) ^ [] : [-(in(5303 ^ [_386671, _387563], _387563))], (5308 ^ _206269) ^ [] : [-(in(5304 ^ [_386671, _387563], _387563))], (5310 ^ _206269) ^ [] : [5303 ^ [_386671, _387563] = 5304 ^ [_386671, _387563]], (5312 ^ _206269) ^ [] : [in(ordered_pair(5303 ^ [_386671, _387563], 5304 ^ [_386671, _387563]), _386671)], (5314 ^ _206269) ^ [] : [in(ordered_pair(5304 ^ [_386671, _387563], 5303 ^ [_386671, _387563]), _386671)]], -(is_connected_in(_386671, _387563))], (5280 ^ _206269) ^ [_386879] : [is_connected_in(_386671, _386879), 5283 ^ _206269 : [(5284 ^ _206269) ^ [_387069, _387071] : [in(_387071, _386879), in(_387069, _386879), -(_387071 = _387069), -(in(ordered_pair(_387071, _387069), _386671)), -(in(ordered_pair(_387069, _387071), _386671))]]]]], (5318 ^ _206269) ^ [_388348] : [relation(_388348), 5321 ^ _206269 : [(5322 ^ _206269) ^ [_388467] : [-(relation_restriction(_388348, _388467) = set_intersection2(_388348, cartesian_product2(_388467, _388467)))]]], (5324 ^ _206269) ^ [_388576] : [relation(_388576), 5327 ^ _206269 : [(5328 ^ _206269) ^ [_388736] : [relation(_388736), 5331 ^ _206269 : [(5348 ^ _206269) ^ [] : [-(_388736 = relation_inverse(_388576)), 5353 ^ _206269 : [(5354 ^ _206269) ^ [] : [-(in(ordered_pair(5349 ^ [_388576, _388736], 5350 ^ [_388576, _388736]), _388736))], (5356 ^ _206269) ^ [] : [in(ordered_pair(5350 ^ [_388576, _388736], 5349 ^ [_388576, _388736]), _388576)]], 5357 ^ _206269 : [(5358 ^ _206269) ^ [] : [-(in(ordered_pair(5350 ^ [_388576, _388736], 5349 ^ [_388576, _388736]), _388576))], (5360 ^ _206269) ^ [] : [in(ordered_pair(5349 ^ [_388576, _388736], 5350 ^ [_388576, _388736]), _388736)]]], (5332 ^ _206269) ^ [] : [_388736 = relation_inverse(_388576), 5335 ^ _206269 : [(5336 ^ _206269) ^ [_389045, _389047] : [in(ordered_pair(_389047, _389045), _388736), -(in(ordered_pair(_389045, _389047), _388576))], (5342 ^ _206269) ^ [_389235, _389237] : [in(ordered_pair(_389235, _389237), _388576), -(in(ordered_pair(_389237, _389235), _388736))]]]]]]], (5364 ^ _206269) ^ [_390040] : [relation(_390040), 5367 ^ _206269 : [(5368 ^ _206269) ^ [_390261] : [relation(_390261), 5371 ^ _206269 : [(5372 ^ _206269) ^ [_390478] : [relation(_390478), function(_390478), 5379 ^ _206269 : [(5414 ^ _206269) ^ [] : [-(relation_isomorphism(_390040, _390261, _390478)), relation_dom(_390478) = relation_field(_390040), relation_rng(_390478) = relation_field(_390261), one_to_one(_390478), 5443 ^ _206269 : [(5444 ^ _206269) ^ [] : [-(in(5427 ^ [_390040, _390261, _390478], relation_field(_390040)))], (5446 ^ _206269) ^ [] : [-(in(5428 ^ [_390040, _390261, _390478], relation_field(_390040)))], (5448 ^ _206269) ^ [] : [-(in(ordered_pair(apply(_390478, 5427 ^ [_390040, _390261, _390478]), apply(_390478, 5428 ^ [_390040, _390261, _390478])), _390261))], (5450 ^ _206269) ^ [] : [in(ordered_pair(5427 ^ [_390040, _390261, _390478], 5428 ^ [_390040, _390261, _390478]), _390040)]], 5431 ^ _206269 : [(5432 ^ _206269) ^ [] : [-(in(ordered_pair(5427 ^ [_390040, _390261, _390478], 5428 ^ [_390040, _390261, _390478]), _390040))], (5434 ^ _206269) ^ [] : [in(5427 ^ [_390040, _390261, _390478], relation_field(_390040)), in(5428 ^ [_390040, _390261, _390478], relation_field(_390040)), in(ordered_pair(apply(_390478, 5427 ^ [_390040, _390261, _390478]), apply(_390478, 5428 ^ [_390040, _390261, _390478])), _390261)]]], (5380 ^ _206269) ^ [] : [relation_isomorphism(_390040, _390261, _390478), 5383 ^ _206269 : [(5384 ^ _206269) ^ [] : [-(relation_dom(_390478) = relation_field(_390040))], (5386 ^ _206269) ^ [] : [-(relation_rng(_390478) = relation_field(_390261))], (5388 ^ _206269) ^ [] : [-(one_to_one(_390478))], (5390 ^ _206269) ^ [_391144, _391146] : [in(ordered_pair(_391146, _391144), _390040), 5393 ^ _206269 : [(5394 ^ _206269) ^ [] : [-(in(_391146, relation_field(_390040)))], (5396 ^ _206269) ^ [] : [-(in(_391144, relation_field(_390040)))], (5398 ^ _206269) ^ [] : [-(in(ordered_pair(apply(_390478, _391146), apply(_390478, _391144)), _390261))]]], (5400 ^ _206269) ^ [_391523, _391525] : [-(in(ordered_pair(_391525, _391523), _390040)), in(_391525, relation_field(_390040)), in(_391523, relation_field(_390040)), in(ordered_pair(apply(_390478, _391525), apply(_390478, _391523)), _390261)]]]]]]]]], (5454 ^ _206269) ^ [_393350, _393352] : [disjoint(_393352, _393350), -(set_intersection2(_393352, _393350) = empty_set)], (5460 ^ _206269) ^ [_393518, _393520] : [set_intersection2(_393520, _393518) = empty_set, -(disjoint(_393520, _393518))], (5466 ^ _206269) ^ [_393722] : [-(relation_of_lattice(_393722) = a_1_0_filter_1(_393722)), -(empty_carrier(_393722)), lattice(_393722), latt_str(_393722)], (5480 ^ _206269) ^ [_394087] : [relation(_394087), function(_394087), 5487 ^ _206269 : [(5506 ^ _206269) ^ [] : [5509 ^ _206269 : [(5510 ^ _206269) ^ [] : [-(in(5507 ^ [_394087], relation_dom(_394087)))], (5512 ^ _206269) ^ [] : [-(in(5508 ^ [_394087], relation_dom(_394087)))], (5514 ^ _206269) ^ [] : [-(apply(_394087, 5507 ^ [_394087]) = apply(_394087, 5508 ^ [_394087]))], (5516 ^ _206269) ^ [] : [5507 ^ [_394087] = 5508 ^ [_394087]]], -(one_to_one(_394087))], (5488 ^ _206269) ^ [] : [one_to_one(_394087), 5491 ^ _206269 : [(5492 ^ _206269) ^ [_394450, _394452] : [-(_394452 = _394450), in(_394452, relation_dom(_394087)), in(_394450, relation_dom(_394087)), apply(_394087, _394452) = apply(_394087, _394450)]]]]], (5520 ^ _206269) ^ [_395397] : [rel_str(_395397), 5523 ^ _206269 : [(5524 ^ _206269) ^ [_395576, _395578] : [element(_395576, the_carrier(_395397)), 5527 ^ _206269 : [(5542 ^ _206269) ^ [] : [5544 ^ _206269 : [(5545 ^ _206269) ^ [] : [-(element(5543 ^ [_395397, _395576, _395578], the_carrier(_395397)))], (5547 ^ _206269) ^ [] : [-(in(5543 ^ [_395397, _395576, _395578], _395578))], (5549 ^ _206269) ^ [] : [related(_395397, _395576, 5543 ^ [_395397, _395576, _395578])]], -(relstr_element_smaller(_395397, _395578, _395576))], (5528 ^ _206269) ^ [] : [relstr_element_smaller(_395397, _395578, _395576), 5531 ^ _206269 : [(5532 ^ _206269) ^ [_395852] : [element(_395852, the_carrier(_395397)), in(_395852, _395578), -(related(_395397, _395576, _395852))]]]]]]], (5553 ^ _206269) ^ [_396557] : [-(empty_carrier(_396557)), latt_str(_396557), 5560 ^ _206269 : [(5575 ^ _206269) ^ [] : [5577 ^ _206269 : [(5578 ^ _206269) ^ [] : [-(element(5576 ^ [_396557], the_carrier(_396557)))], (5581 ^ _206269) ^ [] : [-(element(5579 ^ [_396557], the_carrier(_396557)))], (5583 ^ _206269) ^ [] : [join(_396557, meet(_396557, 5576 ^ [_396557], 5579 ^ [_396557]), 5579 ^ [_396557]) = 5579 ^ [_396557]]], -(meet_absorbing(_396557))], (5561 ^ _206269) ^ [] : [meet_absorbing(_396557), 5564 ^ _206269 : [(5565 ^ _206269) ^ [_396905] : [element(_396905, the_carrier(_396557)), 5568 ^ _206269 : [(5569 ^ _206269) ^ [_397058] : [element(_397058, the_carrier(_396557)), -(join(_396557, meet(_396557, _396905, _397058), _397058) = _397058)]]]]]]], (5587 ^ _206269) ^ [_397732] : [one_sorted_str(_397732), 5590 ^ _206269 : [(5591 ^ _206269) ^ [_397882] : [element(_397882, powerset(powerset(the_carrier(_397732)))), 5594 ^ _206269 : [(5595 ^ _206269) ^ [] : [is_a_cover_of_carrier(_397732, _397882), -(cast_as_carrier_subset(_397732) = union_of_subsets(the_carrier(_397732), _397882))], (5601 ^ _206269) ^ [] : [cast_as_carrier_subset(_397732) = union_of_subsets(the_carrier(_397732), _397882), -(is_a_cover_of_carrier(_397732, _397882))]]]]], (5607 ^ _206269) ^ [_398368] : [relation(_398368), 5610 ^ _206269 : [(5611 ^ _206269) ^ [_398553] : [relation(_398553), 5614 ^ _206269 : [(5615 ^ _206269) ^ [_398734] : [relation(_398734), 5618 ^ _206269 : [(5642 ^ _206269) ^ [] : [-(_398734 = relation_composition(_398368, _398553)), 5656 ^ _206269 : [(5657 ^ _206269) ^ [] : [-(in(ordered_pair(5643 ^ [_398368, _398553, _398734], 5655 ^ [_398368, _398553, _398734]), _398368))], (5659 ^ _206269) ^ [] : [-(in(ordered_pair(5655 ^ [_398368, _398553, _398734], 5644 ^ [_398368, _398553, _398734]), _398553))], (5661 ^ _206269) ^ [] : [in(ordered_pair(5643 ^ [_398368, _398553, _398734], 5644 ^ [_398368, _398553, _398734]), _398734)]], 5647 ^ _206269 : [(5648 ^ _206269) ^ [] : [-(in(ordered_pair(5643 ^ [_398368, _398553, _398734], 5644 ^ [_398368, _398553, _398734]), _398734))], (5650 ^ _206269) ^ [_400198] : [in(ordered_pair(5643 ^ [_398368, _398553, _398734], _400198), _398368), in(ordered_pair(_400198, 5644 ^ [_398368, _398553, _398734]), _398553)]]], (5619 ^ _206269) ^ [] : [_398734 = relation_composition(_398368, _398553), 5622 ^ _206269 : [(5623 ^ _206269) ^ [_399069, _399071] : [in(ordered_pair(_399071, _399069), _398734), 5627 ^ _206269 : [(5628 ^ _206269) ^ [] : [-(in(ordered_pair(_399071, 5626 ^ [_398368, _398553, _398734, _399069, _399071]), _398368))], (5630 ^ _206269) ^ [] : [-(in(ordered_pair(5626 ^ [_398368, _398553, _398734, _399069, _399071], _399069), _398553))]]], (5632 ^ _206269) ^ [_399454, _399456] : [-(in(ordered_pair(_399456, _399454), _398734)), 5633 ^ _206269 : [(5634 ^ _206269) ^ [_399567] : [in(ordered_pair(_399456, _399567), _398368), in(ordered_pair(_399567, _399454), _398553)]]]]]]]]]]], (5665 ^ _206269) ^ [_400870] : [relation(_400870), 5668 ^ _206269 : [(5695 ^ _206269) ^ [_401905] : [5699 ^ _206269 : [(5700 ^ _206269) ^ [] : [-(in(5696 ^ [_400870, _401905], _401905))], (5702 ^ _206269) ^ [] : [-(in(5697 ^ [_400870, _401905], _401905))], (5704 ^ _206269) ^ [] : [-(in(5698 ^ [_400870, _401905], _401905))], (5706 ^ _206269) ^ [] : [-(in(ordered_pair(5696 ^ [_400870, _401905], 5697 ^ [_400870, _401905]), _400870))], (5708 ^ _206269) ^ [] : [-(in(ordered_pair(5697 ^ [_400870, _401905], 5698 ^ [_400870, _401905]), _400870))], (5710 ^ _206269) ^ [] : [in(ordered_pair(5696 ^ [_400870, _401905], 5698 ^ [_400870, _401905]), _400870)]], -(is_transitive_in(_400870, _401905))], (5669 ^ _206269) ^ [_401084] : [is_transitive_in(_400870, _401084), 5672 ^ _206269 : [(5673 ^ _206269) ^ [_401294, _401296, _401298] : [-(in(ordered_pair(_401298, _401294), _400870)), in(_401298, _401084), in(_401296, _401084), in(_401294, _401084), in(ordered_pair(_401298, _401296), _400870), in(ordered_pair(_401296, _401294), _400870)]]]]], (5714 ^ _206269) ^ [_402929, _402931] : [element(_402929, powerset(powerset(_402931))), 5717 ^ _206269 : [(5718 ^ _206269) ^ [_403109] : [element(_403109, powerset(powerset(_402931))), 5721 ^ _206269 : [(5742 ^ _206269) ^ [] : [-(_403109 = complements_of_subsets(_402931, _402929)), 5744 ^ _206269 : [(5745 ^ _206269) ^ [] : [-(element(5743 ^ [_402929, _402931, _403109], powerset(_402931)))], (5747 ^ _206269) ^ [] : [5748 ^ _206269 : [(5749 ^ _206269) ^ [] : [-(in(5743 ^ [_402929, _402931, _403109], _403109))], (5751 ^ _206269) ^ [] : [in(subset_complement(_402931, 5743 ^ [_402929, _402931, _403109]), _402929)]], 5752 ^ _206269 : [(5753 ^ _206269) ^ [] : [-(in(subset_complement(_402931, 5743 ^ [_402929, _402931, _403109]), _402929))], (5755 ^ _206269) ^ [] : [in(5743 ^ [_402929, _402931, _403109], _403109)]]]]], (5722 ^ _206269) ^ [] : [_403109 = complements_of_subsets(_402931, _402929), 5725 ^ _206269 : [(5726 ^ _206269) ^ [_403397] : [element(_403397, powerset(_402931)), 5729 ^ _206269 : [(5730 ^ _206269) ^ [] : [in(_403397, _403109), -(in(subset_complement(_402931, _403397), _402929))], (5736 ^ _206269) ^ [] : [in(subset_complement(_402931, _403397), _402929), -(in(_403397, _403109))]]]]]]]]], (5759 ^ _206269) ^ [_404520, _404522] : [proper_subset(_404522, _404520), 5762 ^ _206269 : [(5763 ^ _206269) ^ [] : [-(subset(_404522, _404520))], (5765 ^ _206269) ^ [] : [_404522 = _404520]]], (5767 ^ _206269) ^ [_404758, _404760] : [-(proper_subset(_404760, _404758)), subset(_404760, _404758), -(_404760 = _404758)], (5777 ^ _206269) ^ [_405048] : [relation(_405048), function(_405048), one_to_one(_405048), -(function_inverse(_405048) = relation_inverse(_405048))], (5791 ^ _206269) ^ [_405412] : [rel_str(_405412), 5794 ^ _206269 : [(5795 ^ _206269) ^ [_405591, _405593] : [element(_405591, the_carrier(_405412)), 5798 ^ _206269 : [(5813 ^ _206269) ^ [] : [5815 ^ _206269 : [(5816 ^ _206269) ^ [] : [-(element(5814 ^ [_405412, _405591, _405593], the_carrier(_405412)))], (5818 ^ _206269) ^ [] : [-(in(5814 ^ [_405412, _405591, _405593], _405593))], (5820 ^ _206269) ^ [] : [related(_405412, 5814 ^ [_405412, _405591, _405593], _405591)]], -(relstr_set_smaller(_405412, _405593, _405591))], (5799 ^ _206269) ^ [] : [relstr_set_smaller(_405412, _405593, _405591), 5802 ^ _206269 : [(5803 ^ _206269) ^ [_405867] : [element(_405867, the_carrier(_405412)), in(_405867, _405593), -(related(_405412, _405867, _405591))]]]]]]], (5824 ^ _206269) ^ [_406572] : [rel_str(_406572), 5827 ^ _206269 : [(5828 ^ _206269) ^ [_406730] : [element(_406730, the_carrier(_406572)), 5831 ^ _206269 : [(5832 ^ _206269) ^ [_406887] : [element(_406887, the_carrier(_406572)), 5835 ^ _206269 : [(5836 ^ _206269) ^ [] : [related(_406572, _406730, _406887), -(in(ordered_pair(_406730, _406887), the_InternalRel(_406572)))], (5842 ^ _206269) ^ [] : [in(ordered_pair(_406730, _406887), the_InternalRel(_406572)), -(related(_406572, _406730, _406887))]]]]]]], (5848 ^ _206269) ^ [_407385] : [relation(_407385), 5851 ^ _206269 : [(5852 ^ _206269) ^ [] : [reflexive(_407385), -(is_reflexive_in(_407385, relation_field(_407385)))], (5858 ^ _206269) ^ [] : [is_reflexive_in(_407385, relation_field(_407385)), -(reflexive(_407385))]]], (5864 ^ _206269) ^ [_407830, _407832] : [relation_of2(_407830, _407832, _407832), 5867 ^ _206269 : [(5868 ^ _206269) ^ [] : [-(strict_rel_str(rel_str_of(_407832, _407830)))], (5870 ^ _206269) ^ [] : [-(rel_str(rel_str_of(_407832, _407830)))]]], (5872 ^ _206269) ^ [_408139, _408141, _408143] : [5895 ^ _206269 : [(5896 ^ _206269) ^ [] : [-(strict_latt_str(latt_str_of(_408143, _408141, _408139)))], (5898 ^ _206269) ^ [] : [-(latt_str(latt_str_of(_408143, _408141, _408139)))]], function(_408141), quasi_total(_408141, cartesian_product2(_408143, _408143), _408143), relation_of2(_408141, cartesian_product2(_408143, _408143), _408143), function(_408139), quasi_total(_408139, cartesian_product2(_408143, _408143), _408143), relation_of2(_408139, cartesian_product2(_408143, _408143), _408143)], (5900 ^ _206269) ^ [_408965, _408967, _408969, _408971] : [-(element(k10_filter_1(_408971, _408969, _408967, _408965), the_carrier(k8_filter_1(_408971, _408969)))), -(empty_carrier(_408971)), lattice(_408971), latt_str(_408971), -(empty_carrier(_408969)), lattice(_408969), latt_str(_408969), element(_408967, the_carrier(_408971)), element(_408965, the_carrier(_408969))], (5934 ^ _206269) ^ [] : [true___, -(true___)], (5940 ^ _206269) ^ [_410007, _410009] : [-(element(join_of_latt_set(_410009, _410007), the_carrier(_410009))), -(empty_carrier(_410009)), latt_str(_410009)], (5950 ^ _206269) ^ [_410315, _410317] : [-(element(meet_of_latt_set(_410317, _410315), the_carrier(_410317))), -(empty_carrier(_410317)), latt_str(_410317)], (5960 ^ _206269) ^ [] : [true___, -(true___)], (5966 ^ _206269) ^ [_410770, _410772, _410774, _410776] : [-(element(ordered_pair_as_product_element(_410776, _410774, _410772, _410770), cartesian_product2(_410776, _410774))), -(empty(_410776)), -(empty(_410774)), element(_410772, _410776), element(_410770, _410774)], (5984 ^ _206269) ^ [] : [true___, -(true___)], (5990 ^ _206269) ^ [] : [true___, -(true___)], (5996 ^ _206269) ^ [_411530] : [-(strict_latt_str(boole_lattice(_411530)))], (5998 ^ _206269) ^ [_411575] : [-(latt_str(boole_lattice(_411575)))], (6000 ^ _206269) ^ [_411699, _411701, _411703] : [-(element(join(_411703, _411701, _411699), the_carrier(_411703))), -(empty_carrier(_411703)), join_semilatt_str(_411703), element(_411701, the_carrier(_411703)), element(_411699, the_carrier(_411703))], (6018 ^ _206269) ^ [] : [true___, -(true___)], (6024 ^ _206269) ^ [] : [true___, -(true___)], (6030 ^ _206269) ^ [_412422] : [-(element(k1_pcomps_1(_412422), powerset(powerset(_412422))))], (6032 ^ _206269) ^ [_412521] : [one_sorted_str(_412521), -(element(empty_carrier_subset(_412521), powerset(the_carrier(_412521))))], (6038 ^ _206269) ^ [] : [true___, -(true___)], (6044 ^ _206269) ^ [] : [true___, -(true___)], (6050 ^ _206269) ^ [] : [true___, -(true___)], (6056 ^ _206269) ^ [_413092, _413094] : [-(element(interior(_413094, _413092), powerset(the_carrier(_413094)))), top_str(_413094), element(_413092, powerset(the_carrier(_413094)))], (6066 ^ _206269) ^ [] : [true___, -(true___)], (6072 ^ _206269) ^ [_413501] : [-(relation(inclusion_relation(_413501)))], (6074 ^ _206269) ^ [] : [true___, -(true___)], (6080 ^ _206269) ^ [] : [true___, -(true___)], (6086 ^ _206269) ^ [_413903, _413905, _413907, _413909, _413911, _413913] : [-(element(apply_binary_as_element(_413913, _413911, _413909, _413907, _413905, _413903), _413909)), -(empty(_413913)), -(empty(_413911)), function(_413907), quasi_total(_413907, cartesian_product2(_413913, _413911), _413909), relation_of2(_413907, cartesian_product2(_413913, _413911), _413909), element(_413905, _413913), element(_413903, _413911)], (6116 ^ _206269) ^ [_414783] : [6123 ^ _206269 : [(6124 ^ _206269) ^ [] : [-(relation(function_inverse(_414783)))], (6126 ^ _206269) ^ [] : [-(function(function_inverse(_414783)))]], relation(_414783), function(_414783)], (6128 ^ _206269) ^ [_415131] : [6139 ^ _206269 : [(6140 ^ _206269) ^ [] : [-(reflexive(k2_lattice3(_415131)))], (6142 ^ _206269) ^ [] : [-(antisymmetric(k2_lattice3(_415131)))], (6144 ^ _206269) ^ [] : [-(transitive(k2_lattice3(_415131)))], (6146 ^ _206269) ^ [] : [-(v1_partfun1(k2_lattice3(_415131), the_carrier(_415131), the_carrier(_415131)))], (6148 ^ _206269) ^ [] : [-(relation_of2_as_subset(k2_lattice3(_415131), the_carrier(_415131), the_carrier(_415131)))]], -(empty_carrier(_415131)), lattice(_415131), latt_str(_415131)], (6150 ^ _206269) ^ [_415839, _415841, _415843] : [-(element(meet(_415843, _415841, _415839), the_carrier(_415843))), -(empty_carrier(_415843)), meet_semilatt_str(_415843), element(_415841, the_carrier(_415843)), element(_415839, the_carrier(_415843))], (6168 ^ _206269) ^ [] : [true___, -(true___)], (6174 ^ _206269) ^ [_416458] : [one_sorted_str(_416458), -(element(cast_as_carrier_subset(_416458), powerset(the_carrier(_416458))))], (6180 ^ _206269) ^ [] : [true___, -(true___)], (6186 ^ _206269) ^ [_416762] : [-(element(cast_to_subset(_416762), powerset(_416762)))], (6188 ^ _206269) ^ [] : [true___, -(true___)], (6194 ^ _206269) ^ [_416992, _416994] : [relation(_416994), -(relation(relation_restriction(_416994, _416992)))], (6200 ^ _206269) ^ [] : [true___, -(true___)], (6206 ^ _206269) ^ [] : [true___, -(true___)], (6212 ^ _206269) ^ [_417428] : [6223 ^ _206269 : [(6224 ^ _206269) ^ [] : [-(strict_rel_str(poset_of_lattice(_417428)))], (6226 ^ _206269) ^ [] : [-(reflexive_relstr(poset_of_lattice(_417428)))], (6228 ^ _206269) ^ [] : [-(transitive_relstr(poset_of_lattice(_417428)))], (6230 ^ _206269) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_417428)))], (6232 ^ _206269) ^ [] : [-(rel_str(poset_of_lattice(_417428)))]], -(empty_carrier(_417428)), lattice(_417428), latt_str(_417428)], (6234 ^ _206269) ^ [_418112, _418114, _418116] : [-(element(join_commut(_418116, _418114, _418112), the_carrier(_418116))), -(empty_carrier(_418116)), join_commutative(_418116), join_semilatt_str(_418116), element(_418114, the_carrier(_418116)), element(_418112, the_carrier(_418116))], (6256 ^ _206269) ^ [] : [true___, -(true___)], (6262 ^ _206269) ^ [_418836, _418838] : [element(_418836, powerset(_418838)), -(element(subset_complement(_418838, _418836), powerset(_418838)))], (6268 ^ _206269) ^ [] : [true___, -(true___)], (6274 ^ _206269) ^ [] : [true___, -(true___)], (6280 ^ _206269) ^ [_419298, _419300] : [-(element(cast_to_el_of_LattPOSet(_419300, _419298), the_carrier(poset_of_lattice(_419300)))), -(empty_carrier(_419300)), lattice(_419300), latt_str(_419300), element(_419298, the_carrier(_419300))], (6298 ^ _206269) ^ [_419804, _419806, _419808] : [-(element(meet_commut(_419808, _419806, _419804), the_carrier(_419808))), -(empty_carrier(_419808)), meet_commutative(_419808), meet_semilatt_str(_419808), element(_419806, the_carrier(_419808)), element(_419804, the_carrier(_419808))], (6320 ^ _206269) ^ [_420395] : [relation(_420395), -(relation(relation_inverse(_420395)))], (6326 ^ _206269) ^ [_420613, _420615, _420617] : [relation_of2(_420613, _420617, _420615), -(element(relation_dom_as_subset(_420617, _420615, _420613), powerset(_420617)))], (6332 ^ _206269) ^ [_420857, _420859, _420861] : [-(element(subset_union2(_420861, _420859, _420857), powerset(_420861))), element(_420859, powerset(_420861)), element(_420857, powerset(_420861))], (6342 ^ _206269) ^ [] : [true___, -(true___)], (6348 ^ _206269) ^ [] : [true___, -(true___)], (6354 ^ _206269) ^ [_421424, _421426] : [-(element(cast_to_el_of_lattice(_421426, _421424), the_carrier(_421426))), -(empty_carrier(_421426)), lattice(_421426), latt_str(_421426), element(_421424, the_carrier(poset_of_lattice(_421426)))], (6372 ^ _206269) ^ [_421902] : [-(element(bottom_of_semilattstr(_421902), the_carrier(_421902))), -(empty_carrier(_421902)), meet_semilatt_str(_421902)], (6382 ^ _206269) ^ [] : [true___, -(true___)], (6388 ^ _206269) ^ [_422317, _422319] : [-(relation(relation_composition(_422319, _422317))), relation(_422319), relation(_422317)], (6398 ^ _206269) ^ [_422630, _422632, _422634] : [relation_of2(_422630, _422634, _422632), -(element(relation_rng_as_subset(_422634, _422632, _422630), powerset(_422632)))], (6404 ^ _206269) ^ [_422860, _422862] : [element(_422860, powerset(powerset(_422862))), -(element(union_of_subsets(_422862, _422860), powerset(_422862)))], (6410 ^ _206269) ^ [_423102, _423104, _423106] : [-(element(subset_intersection2(_423106, _423104, _423102), powerset(_423106))), element(_423104, powerset(_423106)), element(_423102, powerset(_423106))], (6420 ^ _206269) ^ [_423422] : [-(v1_partfun1(identity_as_relation_of(_423422), _423422, _423422))], (6422 ^ _206269) ^ [_423469] : [-(relation_of2_as_subset(identity_as_relation_of(_423469), _423469, _423469))], (6424 ^ _206269) ^ [_423581, _423583] : [-(element(topstr_closure(_423583, _423581), powerset(the_carrier(_423583)))), top_str(_423583), element(_423581, powerset(the_carrier(_423583)))], (6434 ^ _206269) ^ [_423871] : [-(relation(identity_relation(_423871)))], (6436 ^ _206269) ^ [_423979, _423981] : [element(_423979, powerset(powerset(_423981))), -(element(meet_of_subsets(_423981, _423979), powerset(_423981)))], (6442 ^ _206269) ^ [_424221, _424223, _424225] : [-(element(subset_difference(_424225, _424223, _424221), powerset(_424225))), element(_424223, powerset(_424225)), element(_424221, powerset(_424225))], (6452 ^ _206269) ^ [_424536] : [one_sorted_str(_424536), 6455 ^ _206269 : [(6456 ^ _206269) ^ [] : [-(function(identity_on_carrier(_424536)))], (6458 ^ _206269) ^ [] : [-(quasi_total(identity_on_carrier(_424536), the_carrier(_424536), the_carrier(_424536)))], (6460 ^ _206269) ^ [] : [-(relation_of2_as_subset(identity_on_carrier(_424536), the_carrier(_424536), the_carrier(_424536)))]]], (6462 ^ _206269) ^ [_424913, _424915] : [relation(_424915), -(relation(relation_dom_restriction(_424915, _424913)))], (6468 ^ _206269) ^ [_425125, _425127] : [element(_425125, powerset(powerset(_425127))), -(element(complements_of_subsets(_425127, _425125), powerset(powerset(_425127))))], (6474 ^ _206269) ^ [_425357, _425359] : [6489 ^ _206269 : [(6490 ^ _206269) ^ [] : [-(strict_latt_str(k8_filter_1(_425359, _425357)))], (6492 ^ _206269) ^ [] : [-(latt_str(k8_filter_1(_425359, _425357)))]], -(empty_carrier(_425359)), latt_str(_425359), -(empty_carrier(_425357)), latt_str(_425357)], (6494 ^ _206269) ^ [_425943, _425945, _425947, _425949] : [-(element(apply_as_element(_425949, _425947, _425945, _425943), _425947)), -(empty(_425949)), function(_425945), quasi_total(_425945, _425949, _425947), relation_of2(_425945, _425949, _425947), element(_425943, _425949)], (6516 ^ _206269) ^ [_426566, _426568] : [relation(_426566), -(relation(relation_rng_restriction(_426568, _426566)))], (6522 ^ _206269) ^ [_426764] : [-(relation(relation_of_lattice(_426764))), -(empty_carrier(_426764)), lattice(_426764), latt_str(_426764)], (6536 ^ _206269) ^ [] : [true___, -(true___)], (6542 ^ _206269) ^ [_427242] : [meet_semilatt_str(_427242), -(one_sorted_str(_427242))], (6548 ^ _206269) ^ [_427428] : [rel_str(_427428), -(one_sorted_str(_427428))], (6554 ^ _206269) ^ [_427614] : [top_str(_427614), -(one_sorted_str(_427614))], (6560 ^ _206269) ^ [] : [true___, -(true___)], (6566 ^ _206269) ^ [_427919] : [join_semilatt_str(_427919), -(one_sorted_str(_427919))], (6572 ^ _206269) ^ [_428105] : [latt_str(_428105), 6575 ^ _206269 : [(6576 ^ _206269) ^ [] : [-(meet_semilatt_str(_428105))], (6578 ^ _206269) ^ [] : [-(join_semilatt_str(_428105))]]], (6580 ^ _206269) ^ [_428376, _428378] : [6595 ^ _206269 : [(6596 ^ _206269) ^ [_428786] : [point_neighbourhood(_428786, _428378, _428376), -(element(_428786, powerset(the_carrier(_428378))))]], -(empty_carrier(_428378)), topological_space(_428378), top_str(_428378), element(_428376, the_carrier(_428378))], (6602 ^ _206269) ^ [] : [true___, -(true___)], (6608 ^ _206269) ^ [] : [true___, -(true___)], (6614 ^ _206269) ^ [_429273, _429275, _429277] : [relation_of2_as_subset(_429273, _429277, _429275), -(element(_429273, powerset(cartesian_product2(_429277, _429275))))], (6620 ^ _206269) ^ [_429487] : [meet_semilatt_str(_429487), 6623 ^ _206269 : [(6624 ^ _206269) ^ [] : [-(function(the_L_meet(_429487)))], (6626 ^ _206269) ^ [] : [-(quasi_total(the_L_meet(_429487), cartesian_product2(the_carrier(_429487), the_carrier(_429487)), the_carrier(_429487)))], (6628 ^ _206269) ^ [] : [-(relation_of2_as_subset(the_L_meet(_429487), cartesian_product2(the_carrier(_429487), the_carrier(_429487)), the_carrier(_429487)))]]], (6630 ^ _206269) ^ [_429870] : [rel_str(_429870), -(relation_of2_as_subset(the_InternalRel(_429870), the_carrier(_429870), the_carrier(_429870)))], (6636 ^ _206269) ^ [_430072] : [top_str(_430072), -(element(the_topology(_430072), powerset(powerset(the_carrier(_430072)))))], (6642 ^ _206269) ^ [] : [true___, -(true___)], (6648 ^ _206269) ^ [_430395] : [join_semilatt_str(_430395), 6651 ^ _206269 : [(6652 ^ _206269) ^ [] : [-(function(the_L_join(_430395)))], (6654 ^ _206269) ^ [] : [-(quasi_total(the_L_join(_430395), cartesian_product2(the_carrier(_430395), the_carrier(_430395)), the_carrier(_430395)))], (6656 ^ _206269) ^ [] : [-(relation_of2_as_subset(the_L_join(_430395), cartesian_product2(the_carrier(_430395), the_carrier(_430395)), the_carrier(_430395)))]]], (6659 ^ _206269) ^ [] : [-(meet_semilatt_str(6657 ^ []))], (6662 ^ _206269) ^ [] : [-(rel_str(6660 ^ []))], (6665 ^ _206269) ^ [] : [-(top_str(6663 ^ []))], (6668 ^ _206269) ^ [] : [-(one_sorted_str(6666 ^ []))], (6671 ^ _206269) ^ [] : [-(join_semilatt_str(6669 ^ []))], (6674 ^ _206269) ^ [] : [-(latt_str(6672 ^ []))], (6676 ^ _206269) ^ [_431326, _431328] : [-(point_neighbourhood(6691 ^ [_431326, _431328], _431328, _431326)), -(empty_carrier(_431328)), topological_space(_431328), top_str(_431328), element(_431326, the_carrier(_431328))], (6696 ^ _206269) ^ [_431891, _431893] : [-(relation_of2(6694 ^ [_431891, _431893], _431893, _431891))], (6699 ^ _206269) ^ [_432018] : [-(element(6697 ^ [_432018], _432018))], (6702 ^ _206269) ^ [_432157, _432159] : [-(relation_of2_as_subset(6700 ^ [_432157, _432159], _432159, _432157))], (6704 ^ _206269) ^ [_432274, _432276] : [finite(_432274), -(finite(set_intersection2(_432276, _432274)))], (6710 ^ _206269) ^ [_432486, _432488] : [6717 ^ _206269 : [(6718 ^ _206269) ^ [] : [-(empty(relation_composition(_432486, _432488)))], (6720 ^ _206269) ^ [] : [-(relation(relation_composition(_432486, _432488)))]], empty(_432488), relation(_432486)], (6722 ^ _206269) ^ [_432864, _432866] : [finite(_432866), -(finite(set_intersection2(_432866, _432864)))], (6728 ^ _206269) ^ [_433062] : [empty(_433062), 6731 ^ _206269 : [(6732 ^ _206269) ^ [] : [-(empty(relation_inverse(_433062)))], (6734 ^ _206269) ^ [] : [-(relation(relation_inverse(_433062)))]]], (6736 ^ _206269) ^ [_433341, _433343] : [finite(_433343), -(finite(set_difference(_433343, _433341)))], (6742 ^ _206269) ^ [] : [-(empty(empty_set))], (6744 ^ _206269) ^ [] : [-(relation(empty_set))], (6746 ^ _206269) ^ [] : [-(relation_empty_yielding(empty_set))], (6748 ^ _206269) ^ [_433716, _433718] : [-(finite(relation_image(_433718, _433716))), relation(_433718), function(_433718), finite(_433716)], (6762 ^ _206269) ^ [_434102, _434104] : [6769 ^ _206269 : [(6770 ^ _206269) ^ [] : [-(relation(relation_dom_restriction(_434104, _434102)))], (6772 ^ _206269) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_434104, _434102)))]], relation(_434104), relation_empty_yielding(_434104)], (6774 ^ _206269) ^ [_434470] : [empty(singleton(_434470))], (6776 ^ _206269) ^ [_434515] : [-(finite(singleton(_434515)))], (6778 ^ _206269) ^ [_434615] : [empty(powerset(_434615))], (6780 ^ _206269) ^ [_434680] : [-(cup_closed(powerset(_434680)))], (6782 ^ _206269) ^ [_434745] : [-(diff_closed(powerset(_434745)))], (6784 ^ _206269) ^ [_434790] : [-(preboolean(powerset(_434790)))], (6786 ^ _206269) ^ [_434904, _434906] : [6801 ^ _206269 : [(6802 ^ _206269) ^ [] : [-(relation(relation_composition(_434906, _434904)))], (6804 ^ _206269) ^ [] : [-(function(relation_composition(_434906, _434904)))]], relation(_434906), function(_434906), relation(_434904), function(_434904)], (6806 ^ _206269) ^ [_435446] : [empty_carrier(boole_lattice(_435446))], (6808 ^ _206269) ^ [_435491] : [-(strict_latt_str(boole_lattice(_435491)))], (6810 ^ _206269) ^ [_435601, _435603] : [6817 ^ _206269 : [(6818 ^ _206269) ^ [] : [empty_carrier(rel_str_of(_435603, _435601))], (6820 ^ _206269) ^ [] : [-(strict_rel_str(rel_str_of(_435603, _435601)))]], -(empty(_435603)), relation_of2(_435601, _435603, _435603)], (6822 ^ _206269) ^ [_435957] : [empty(succ(_435957))], (6824 ^ _206269) ^ [] : [-(epsilon_transitive(omega))], (6826 ^ _206269) ^ [] : [-(epsilon_connected(omega))], (6828 ^ _206269) ^ [] : [-(ordinal(omega))], (6830 ^ _206269) ^ [] : [empty(omega)], (6832 ^ _206269) ^ [_436268] : [one_sorted_str(_436268), 6835 ^ _206269 : [(6836 ^ _206269) ^ [] : [-(empty(empty_carrier_subset(_436268)))], (6838 ^ _206269) ^ [] : [-(v1_membered(empty_carrier_subset(_436268)))], (6840 ^ _206269) ^ [] : [-(v2_membered(empty_carrier_subset(_436268)))], (6842 ^ _206269) ^ [] : [-(v3_membered(empty_carrier_subset(_436268)))], (6844 ^ _206269) ^ [] : [-(v4_membered(empty_carrier_subset(_436268)))], (6846 ^ _206269) ^ [] : [-(v5_membered(empty_carrier_subset(_436268)))]]], (6848 ^ _206269) ^ [_436843, _436845] : [-(relation(set_intersection2(_436845, _436843))), relation(_436845), relation(_436843)], (6858 ^ _206269) ^ [_437128] : [empty(the_carrier(_437128)), -(empty_carrier(_437128)), one_sorted_str(_437128)], (6868 ^ _206269) ^ [_437389] : [empty(powerset(_437389))], (6870 ^ _206269) ^ [] : [-(empty(empty_set))], (6872 ^ _206269) ^ [_437534, _437536] : [empty(ordered_pair(_437536, _437534))], (6874 ^ _206269) ^ [_437645, _437647] : [v1_membered(_437647), -(v1_membered(set_intersection2(_437647, _437645)))], (6880 ^ _206269) ^ [_437857, _437859] : [v1_membered(_437859), -(v1_membered(set_intersection2(_437857, _437859)))], (6886 ^ _206269) ^ [_438069, _438071] : [v2_membered(_438071), 6889 ^ _206269 : [(6890 ^ _206269) ^ [] : [-(v1_membered(set_intersection2(_438071, _438069)))], (6892 ^ _206269) ^ [] : [-(v2_membered(set_intersection2(_438071, _438069)))]]], (6894 ^ _206269) ^ [_438346] : [6901 ^ _206269 : [(6902 ^ _206269) ^ [] : [empty(succ(_438346))], (6904 ^ _206269) ^ [] : [-(epsilon_transitive(succ(_438346)))], (6906 ^ _206269) ^ [] : [-(epsilon_connected(succ(_438346)))], (6908 ^ _206269) ^ [] : [-(ordinal(succ(_438346)))], (6910 ^ _206269) ^ [] : [-(natural(succ(_438346)))]], ordinal(_438346), natural(_438346)], (6912 ^ _206269) ^ [_438922] : [-(relation(identity_relation(_438922)))], (6914 ^ _206269) ^ [_438967] : [-(function(identity_relation(_438967)))], (6916 ^ _206269) ^ [_439063] : [6927 ^ _206269 : [(6928 ^ _206269) ^ [] : [-(relation(the_L_join(_439063)))], (6930 ^ _206269) ^ [] : [-(function(the_L_join(_439063)))], (6932 ^ _206269) ^ [] : [-(quasi_total(the_L_join(_439063), cartesian_product2(the_carrier(_439063), the_carrier(_439063)), the_carrier(_439063)))], (6934 ^ _206269) ^ [] : [-(v1_binop_1(the_L_join(_439063), the_carrier(_439063)))], (6936 ^ _206269) ^ [] : [-(v1_partfun1(the_L_join(_439063), cartesian_product2(the_carrier(_439063), the_carrier(_439063)), the_carrier(_439063)))]], -(empty_carrier(_439063)), join_commutative(_439063), join_semilatt_str(_439063)], (6938 ^ _206269) ^ [_439773] : [empty_carrier(boole_lattice(_439773))], (6940 ^ _206269) ^ [_439838] : [-(strict_latt_str(boole_lattice(_439838)))], (6942 ^ _206269) ^ [_439903] : [-(join_commutative(boole_lattice(_439903)))], (6944 ^ _206269) ^ [_439968] : [-(join_associative(boole_lattice(_439968)))], (6946 ^ _206269) ^ [_440033] : [-(meet_commutative(boole_lattice(_440033)))], (6948 ^ _206269) ^ [_440098] : [-(meet_associative(boole_lattice(_440098)))], (6950 ^ _206269) ^ [_440163] : [-(meet_absorbing(boole_lattice(_440163)))], (6952 ^ _206269) ^ [_440228] : [-(join_absorbing(boole_lattice(_440228)))], (6954 ^ _206269) ^ [_440273] : [-(lattice(boole_lattice(_440273)))], (6956 ^ _206269) ^ [_440383] : [6971 ^ _206269 : [(6972 ^ _206269) ^ [] : [-(relation(the_InternalRel(_440383)))], (6974 ^ _206269) ^ [] : [-(reflexive(the_InternalRel(_440383)))], (6976 ^ _206269) ^ [] : [-(antisymmetric(the_InternalRel(_440383)))], (6978 ^ _206269) ^ [] : [-(transitive(the_InternalRel(_440383)))], (6980 ^ _206269) ^ [] : [-(v1_partfun1(the_InternalRel(_440383), the_carrier(_440383), the_carrier(_440383)))]], reflexive_relstr(_440383), transitive_relstr(_440383), antisymmetric_relstr(_440383), rel_str(_440383)], (6982 ^ _206269) ^ [] : [-(relation(empty_set))], (6984 ^ _206269) ^ [] : [-(relation_empty_yielding(empty_set))], (6986 ^ _206269) ^ [] : [-(function(empty_set))], (6988 ^ _206269) ^ [] : [-(one_to_one(empty_set))], (6990 ^ _206269) ^ [] : [-(empty(empty_set))], (6992 ^ _206269) ^ [] : [-(epsilon_transitive(empty_set))], (6994 ^ _206269) ^ [] : [-(epsilon_connected(empty_set))], (6996 ^ _206269) ^ [] : [-(ordinal(empty_set))], (6998 ^ _206269) ^ [_441574] : [-(relation(identity_relation(_441574)))], (7000 ^ _206269) ^ [_441639] : [-(function(identity_relation(_441639)))], (7002 ^ _206269) ^ [_441704] : [-(reflexive(identity_relation(_441704)))], (7004 ^ _206269) ^ [_441769] : [-(symmetric(identity_relation(_441769)))], (7006 ^ _206269) ^ [_441834] : [-(antisymmetric(identity_relation(_441834)))], (7008 ^ _206269) ^ [_441879] : [-(transitive(identity_relation(_441879)))], (7010 ^ _206269) ^ [_441983] : [empty(cast_as_carrier_subset(_441983)), -(empty_carrier(_441983)), one_sorted_str(_441983)], (7020 ^ _206269) ^ [_442274, _442276] : [-(relation(set_union2(_442276, _442274))), relation(_442276), relation(_442274)], (7030 ^ _206269) ^ [_442543] : [empty(singleton(_442543))], (7032 ^ _206269) ^ [_442651, _442653] : [-(closed_subset(topstr_closure(_442653, _442651), _442653)), topological_space(_442653), top_str(_442653), element(_442651, powerset(the_carrier(_442653)))], (7046 ^ _206269) ^ [_443049, _443051] : [-(empty(_443051)), empty(set_union2(_443051, _443049))], (7052 ^ _206269) ^ [_443265, _443267] : [v2_membered(_443267), 7055 ^ _206269 : [(7056 ^ _206269) ^ [] : [-(v1_membered(set_intersection2(_443265, _443267)))], (7058 ^ _206269) ^ [] : [-(v2_membered(set_intersection2(_443265, _443267)))]]], (7060 ^ _206269) ^ [_443556, _443558] : [v3_membered(_443558), 7063 ^ _206269 : [(7064 ^ _206269) ^ [] : [-(v1_membered(set_intersection2(_443558, _443556)))], (7066 ^ _206269) ^ [] : [-(v2_membered(set_intersection2(_443558, _443556)))], (7068 ^ _206269) ^ [] : [-(v3_membered(set_intersection2(_443558, _443556)))]]], (7070 ^ _206269) ^ [_443925, _443927] : [v3_membered(_443927), 7073 ^ _206269 : [(7074 ^ _206269) ^ [] : [-(v1_membered(set_intersection2(_443925, _443927)))], (7076 ^ _206269) ^ [] : [-(v2_membered(set_intersection2(_443925, _443927)))], (7078 ^ _206269) ^ [] : [-(v3_membered(set_intersection2(_443925, _443927)))]]], (7080 ^ _206269) ^ [_444294, _444296] : [v4_membered(_444296), 7083 ^ _206269 : [(7084 ^ _206269) ^ [] : [-(v1_membered(set_intersection2(_444296, _444294)))], (7086 ^ _206269) ^ [] : [-(v2_membered(set_intersection2(_444296, _444294)))], (7088 ^ _206269) ^ [] : [-(v3_membered(set_intersection2(_444296, _444294)))], (7090 ^ _206269) ^ [] : [-(v4_membered(set_intersection2(_444296, _444294)))]]], (7092 ^ _206269) ^ [_444741, _444743] : [v4_membered(_444743), 7095 ^ _206269 : [(7096 ^ _206269) ^ [] : [-(v1_membered(set_intersection2(_444741, _444743)))], (7098 ^ _206269) ^ [] : [-(v2_membered(set_intersection2(_444741, _444743)))], (7100 ^ _206269) ^ [] : [-(v3_membered(set_intersection2(_444741, _444743)))], (7102 ^ _206269) ^ [] : [-(v4_membered(set_intersection2(_444741, _444743)))]]], (7104 ^ _206269) ^ [_445188, _445190] : [v5_membered(_445190), 7107 ^ _206269 : [(7108 ^ _206269) ^ [] : [-(v1_membered(set_intersection2(_445190, _445188)))], (7110 ^ _206269) ^ [] : [-(v2_membered(set_intersection2(_445190, _445188)))], (7112 ^ _206269) ^ [] : [-(v3_membered(set_intersection2(_445190, _445188)))], (7114 ^ _206269) ^ [] : [-(v4_membered(set_intersection2(_445190, _445188)))], (7116 ^ _206269) ^ [] : [-(v5_membered(set_intersection2(_445190, _445188)))]]], (7118 ^ _206269) ^ [_445713, _445715] : [v5_membered(_445715), 7121 ^ _206269 : [(7122 ^ _206269) ^ [] : [-(v1_membered(set_intersection2(_445713, _445715)))], (7124 ^ _206269) ^ [] : [-(v2_membered(set_intersection2(_445713, _445715)))], (7126 ^ _206269) ^ [] : [-(v3_membered(set_intersection2(_445713, _445715)))], (7128 ^ _206269) ^ [] : [-(v4_membered(set_intersection2(_445713, _445715)))], (7130 ^ _206269) ^ [] : [-(v5_membered(set_intersection2(_445713, _445715)))]]], (7132 ^ _206269) ^ [_446238, _446240] : [v1_membered(_446240), -(v1_membered(set_difference(_446240, _446238)))], (7138 ^ _206269) ^ [_446450, _446452] : [v2_membered(_446452), 7141 ^ _206269 : [(7142 ^ _206269) ^ [] : [-(v1_membered(set_difference(_446452, _446450)))], (7144 ^ _206269) ^ [] : [-(v2_membered(set_difference(_446452, _446450)))]]], (7146 ^ _206269) ^ [_446741, _446743] : [v3_membered(_446743), 7149 ^ _206269 : [(7150 ^ _206269) ^ [] : [-(v1_membered(set_difference(_446743, _446741)))], (7152 ^ _206269) ^ [] : [-(v2_membered(set_difference(_446743, _446741)))], (7154 ^ _206269) ^ [] : [-(v3_membered(set_difference(_446743, _446741)))]]], (7156 ^ _206269) ^ [_447096] : [7167 ^ _206269 : [(7168 ^ _206269) ^ [] : [-(relation(relation_inverse(_447096)))], (7170 ^ _206269) ^ [] : [-(function(relation_inverse(_447096)))]], relation(_447096), function(_447096), one_to_one(_447096)], (7172 ^ _206269) ^ [_447527] : [7183 ^ _206269 : [(7184 ^ _206269) ^ [] : [-(relation(the_L_join(_447527)))], (7186 ^ _206269) ^ [] : [-(function(the_L_join(_447527)))], (7188 ^ _206269) ^ [] : [-(quasi_total(the_L_join(_447527), cartesian_product2(the_carrier(_447527), the_carrier(_447527)), the_carrier(_447527)))], (7190 ^ _206269) ^ [] : [-(v2_binop_1(the_L_join(_447527), the_carrier(_447527)))], (7192 ^ _206269) ^ [] : [-(v1_partfun1(the_L_join(_447527), cartesian_product2(the_carrier(_447527), the_carrier(_447527)), the_carrier(_447527)))]], -(empty_carrier(_447527)), join_associative(_447527), join_semilatt_str(_447527)], (7194 ^ _206269) ^ [_448261, _448263, _448265] : [7221 ^ _206269 : [(7222 ^ _206269) ^ [] : [empty_carrier(latt_str_of(_448265, _448263, _448261))], (7224 ^ _206269) ^ [] : [-(strict_latt_str(latt_str_of(_448265, _448263, _448261)))]], -(empty(_448265)), function(_448263), quasi_total(_448263, cartesian_product2(_448265, _448265), _448265), relation_of2(_448263, cartesian_product2(_448265, _448265), _448265), function(_448261), quasi_total(_448261, cartesian_product2(_448265, _448265), _448265), relation_of2(_448261, cartesian_product2(_448265, _448265), _448265)], (7226 ^ _206269) ^ [_449154, _449156] : [7245 ^ _206269 : [(7246 ^ _206269) ^ [] : [-(strict_rel_str(rel_str_of(_449156, _449154)))], (7248 ^ _206269) ^ [] : [-(reflexive_relstr(rel_str_of(_449156, _449154)))], (7250 ^ _206269) ^ [] : [-(transitive_relstr(rel_str_of(_449156, _449154)))], (7252 ^ _206269) ^ [] : [-(antisymmetric_relstr(rel_str_of(_449156, _449154)))]], reflexive(_449154), antisymmetric(_449154), transitive(_449154), v1_partfun1(_449154, _449156, _449156), relation_of2(_449154, _449156, _449156)], (7254 ^ _206269) ^ [_449943] : [ordinal(_449943), 7257 ^ _206269 : [(7258 ^ _206269) ^ [] : [empty(succ(_449943))], (7260 ^ _206269) ^ [] : [-(epsilon_transitive(succ(_449943)))], (7262 ^ _206269) ^ [] : [-(epsilon_connected(succ(_449943)))], (7264 ^ _206269) ^ [] : [-(ordinal(succ(_449943)))]]], (7266 ^ _206269) ^ [_450371, _450373] : [-(relation(set_difference(_450373, _450371))), relation(_450373), relation(_450371)], (7276 ^ _206269) ^ [_450654, _450656] : [empty(unordered_pair(_450656, _450654))], (7278 ^ _206269) ^ [_450765, _450767] : [-(open_subset(subset_complement(the_carrier(_450767), _450765), _450767)), topological_space(_450767), top_str(_450767), closed_subset(_450765, _450767), element(_450765, powerset(the_carrier(_450767)))], (7296 ^ _206269) ^ [_451256, _451258] : [-(empty(_451258)), empty(set_union2(_451256, _451258))], (7302 ^ _206269) ^ [_451472, _451474] : [v4_membered(_451474), 7305 ^ _206269 : [(7306 ^ _206269) ^ [] : [-(v1_membered(set_difference(_451474, _451472)))], (7308 ^ _206269) ^ [] : [-(v2_membered(set_difference(_451474, _451472)))], (7310 ^ _206269) ^ [] : [-(v3_membered(set_difference(_451474, _451472)))], (7312 ^ _206269) ^ [] : [-(v4_membered(set_difference(_451474, _451472)))]]], (7314 ^ _206269) ^ [_451919, _451921] : [v5_membered(_451921), 7317 ^ _206269 : [(7318 ^ _206269) ^ [] : [-(v1_membered(set_difference(_451921, _451919)))], (7320 ^ _206269) ^ [] : [-(v2_membered(set_difference(_451921, _451919)))], (7322 ^ _206269) ^ [] : [-(v3_membered(set_difference(_451921, _451919)))], (7324 ^ _206269) ^ [] : [-(v4_membered(set_difference(_451921, _451919)))], (7326 ^ _206269) ^ [] : [-(v5_membered(set_difference(_451921, _451919)))]]], (7328 ^ _206269) ^ [_452444, _452446] : [7335 ^ _206269 : [(7336 ^ _206269) ^ [] : [-(relation(relation_dom_restriction(_452446, _452444)))], (7338 ^ _206269) ^ [] : [-(function(relation_dom_restriction(_452446, _452444)))]], relation(_452446), function(_452446)], (7340 ^ _206269) ^ [_452808] : [7351 ^ _206269 : [(7352 ^ _206269) ^ [] : [-(relation(the_L_meet(_452808)))], (7354 ^ _206269) ^ [] : [-(function(the_L_meet(_452808)))], (7356 ^ _206269) ^ [] : [-(quasi_total(the_L_meet(_452808), cartesian_product2(the_carrier(_452808), the_carrier(_452808)), the_carrier(_452808)))], (7358 ^ _206269) ^ [] : [-(v1_binop_1(the_L_meet(_452808), the_carrier(_452808)))], (7360 ^ _206269) ^ [] : [-(v1_partfun1(the_L_meet(_452808), cartesian_product2(the_carrier(_452808), the_carrier(_452808)), the_carrier(_452808)))]], -(empty_carrier(_452808)), meet_commutative(_452808), meet_semilatt_str(_452808)], (7362 ^ _206269) ^ [_453514] : [7373 ^ _206269 : [(7374 ^ _206269) ^ [] : [empty_carrier(poset_of_lattice(_453514))], (7376 ^ _206269) ^ [] : [-(strict_rel_str(poset_of_lattice(_453514)))], (7378 ^ _206269) ^ [] : [-(reflexive_relstr(poset_of_lattice(_453514)))], (7380 ^ _206269) ^ [] : [-(transitive_relstr(poset_of_lattice(_453514)))], (7382 ^ _206269) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_453514)))]], -(empty_carrier(_453514)), lattice(_453514), latt_str(_453514)], (7384 ^ _206269) ^ [_454171] : [ordinal(_454171), 7387 ^ _206269 : [(7388 ^ _206269) ^ [] : [-(epsilon_transitive(union(_454171)))], (7390 ^ _206269) ^ [] : [-(epsilon_connected(union(_454171)))], (7392 ^ _206269) ^ [] : [-(ordinal(union(_454171)))]]], (7394 ^ _206269) ^ [] : [-(empty(empty_set))], (7396 ^ _206269) ^ [] : [-(relation(empty_set))], (7398 ^ _206269) ^ [_454632, _454634] : [empty(cartesian_product2(_454634, _454632)), -(empty(_454634)), -(empty(_454632))], (7408 ^ _206269) ^ [_454938, _454940] : [-(closed_subset(subset_complement(the_carrier(_454940), _454938), _454940)), topological_space(_454940), top_str(_454940), open_subset(_454938, _454940), element(_454938, powerset(the_carrier(_454940)))], (7426 ^ _206269) ^ [_455429, _455431] : [7433 ^ _206269 : [(7434 ^ _206269) ^ [] : [-(relation(relation_rng_restriction(_455431, _455429)))], (7436 ^ _206269) ^ [] : [-(function(relation_rng_restriction(_455431, _455429)))]], relation(_455429), function(_455429)], (7438 ^ _206269) ^ [_455793] : [7449 ^ _206269 : [(7450 ^ _206269) ^ [] : [-(relation(the_L_meet(_455793)))], (7452 ^ _206269) ^ [] : [-(function(the_L_meet(_455793)))], (7454 ^ _206269) ^ [] : [-(quasi_total(the_L_meet(_455793), cartesian_product2(the_carrier(_455793), the_carrier(_455793)), the_carrier(_455793)))], (7456 ^ _206269) ^ [] : [-(v2_binop_1(the_L_meet(_455793), the_carrier(_455793)))], (7458 ^ _206269) ^ [] : [-(v1_partfun1(the_L_meet(_455793), cartesian_product2(the_carrier(_455793), the_carrier(_455793)), the_carrier(_455793)))]], -(empty_carrier(_455793)), meet_associative(_455793), meet_semilatt_str(_455793)], (7460 ^ _206269) ^ [_456499] : [-(closed_subset(cast_as_carrier_subset(_456499), _456499)), topological_space(_456499), top_str(_456499)], (7470 ^ _206269) ^ [_456774] : [empty(relation_dom(_456774)), -(empty(_456774)), relation(_456774)], (7480 ^ _206269) ^ [] : [-(empty(empty_set))], (7482 ^ _206269) ^ [] : [-(v1_membered(empty_set))], (7484 ^ _206269) ^ [] : [-(v2_membered(empty_set))], (7486 ^ _206269) ^ [] : [-(v3_membered(empty_set))], (7488 ^ _206269) ^ [] : [-(v4_membered(empty_set))], (7490 ^ _206269) ^ [] : [-(v5_membered(empty_set))], (7492 ^ _206269) ^ [_457379] : [empty(relation_rng(_457379)), -(empty(_457379)), relation(_457379)], (7502 ^ _206269) ^ [_457670, _457672] : [-(open_subset(interior(_457672, _457670), _457672)), topological_space(_457672), top_str(_457672), element(_457670, powerset(the_carrier(_457672)))], (7516 ^ _206269) ^ [_458054] : [empty(_458054), 7519 ^ _206269 : [(7520 ^ _206269) ^ [] : [-(empty(relation_dom(_458054)))], (7522 ^ _206269) ^ [] : [-(relation(relation_dom(_458054)))]]], (7524 ^ _206269) ^ [_458319] : [empty(_458319), 7527 ^ _206269 : [(7528 ^ _206269) ^ [] : [-(empty(relation_rng(_458319)))], (7530 ^ _206269) ^ [] : [-(relation(relation_rng(_458319)))]]], (7532 ^ _206269) ^ [_458598, _458600] : [-(finite(set_union2(_458600, _458598))), finite(_458600), finite(_458598)], (7542 ^ _206269) ^ [_458897, _458899] : [7549 ^ _206269 : [(7550 ^ _206269) ^ [] : [-(empty(relation_composition(_458899, _458897)))], (7552 ^ _206269) ^ [] : [-(relation(relation_composition(_458899, _458897)))]], empty(_458899), relation(_458897)], (7554 ^ _206269) ^ [_459275, _459277] : [-(empty_carrier(_459275)), lattice(_459275), latt_str(_459275), 7565 ^ _206269 : [(7566 ^ _206269) ^ [] : [in(_459277, a_1_0_filter_1(_459275)), 7571 ^ _206269 : [(7572 ^ _206269) ^ [] : [-(element(7569 ^ [_459275, _459277], the_carrier(_459275)))], (7574 ^ _206269) ^ [] : [-(element(7570 ^ [_459275, _459277], the_carrier(_459275)))], (7576 ^ _206269) ^ [] : [-(_459277 = ordered_pair_as_product_element(the_carrier(_459275), the_carrier(_459275), 7569 ^ [_459275, _459277], 7570 ^ [_459275, _459277]))], (7578 ^ _206269) ^ [] : [-(below_refl(_459275, 7569 ^ [_459275, _459277], 7570 ^ [_459275, _459277]))]]], (7580 ^ _206269) ^ [] : [-(in(_459277, a_1_0_filter_1(_459275))), 7581 ^ _206269 : [(7582 ^ _206269) ^ [_460275, _460277] : [element(_460277, the_carrier(_459275)), element(_460275, the_carrier(_459275)), _459277 = ordered_pair_as_product_element(the_carrier(_459275), the_carrier(_459275), _460277, _460275), below_refl(_459275, _460277, _460275)]]]]], (7598 ^ _206269) ^ [_460800, _460802, _460804] : [-(empty_carrier(_460802)), latt_str(_460802), 7605 ^ _206269 : [(7606 ^ _206269) ^ [] : [in(_460804, a_2_2_lattice3(_460802, _460800)), 7610 ^ _206269 : [(7611 ^ _206269) ^ [] : [-(element(7609 ^ [_460800, _460802, _460804], the_carrier(_460802)))], (7613 ^ _206269) ^ [] : [-(_460804 = 7609 ^ [_460800, _460802, _460804])], (7615 ^ _206269) ^ [] : [-(latt_set_smaller(_460802, 7609 ^ [_460800, _460802, _460804], _460800))]]], (7617 ^ _206269) ^ [] : [-(in(_460804, a_2_2_lattice3(_460802, _460800))), 7618 ^ _206269 : [(7619 ^ _206269) ^ [_461489] : [element(_461489, the_carrier(_460802)), _460804 = _461489, latt_set_smaller(_460802, _461489, _460800)]]]]], (7631 ^ _206269) ^ [_461898, _461900, _461902] : [-(empty_carrier(_461900)), lattice(_461900), complete_latt_str(_461900), latt_str(_461900), 7646 ^ _206269 : [(7647 ^ _206269) ^ [] : [in(_461902, a_2_3_lattice3(_461900, _461898)), 7651 ^ _206269 : [(7652 ^ _206269) ^ [] : [-(element(7650 ^ [_461898, _461900, _461902], the_carrier(_461900)))], (7654 ^ _206269) ^ [] : [-(_461902 = 7650 ^ [_461898, _461900, _461902])], (7656 ^ _206269) ^ [] : [-(latt_set_smaller(_461900, 7650 ^ [_461898, _461900, _461902], _461898))]]], (7658 ^ _206269) ^ [] : [-(in(_461902, a_2_3_lattice3(_461900, _461898))), 7659 ^ _206269 : [(7660 ^ _206269) ^ [_462769] : [element(_462769, the_carrier(_461900)), _461902 = _462769, latt_set_smaller(_461900, _462769, _461898)]]]]], (7672 ^ _206269) ^ [_463168, _463170] : [relation_of2(_463168, _463170, _463170), 7675 ^ _206269 : [(7676 ^ _206269) ^ [_463338, _463340] : [rel_str_of(_463170, _463168) = rel_str_of(_463340, _463338), 7679 ^ _206269 : [(7680 ^ _206269) ^ [] : [-(_463170 = _463340)], (7682 ^ _206269) ^ [] : [-(_463168 = _463338)]]]]], (7684 ^ _206269) ^ [_463674, _463676, _463678] : [7707 ^ _206269 : [(7708 ^ _206269) ^ [_464366, _464368, _464370] : [latt_str_of(_463678, _463676, _463674) = latt_str_of(_464370, _464368, _464366), 7711 ^ _206269 : [(7712 ^ _206269) ^ [] : [-(_463678 = _464370)], (7714 ^ _206269) ^ [] : [-(_463676 = _464368)], (7716 ^ _206269) ^ [] : [-(_463674 = _464366)]]]], function(_463676), quasi_total(_463676, cartesian_product2(_463678, _463678), _463678), relation_of2(_463676, cartesian_product2(_463678, _463678), _463678), function(_463674), quasi_total(_463674, cartesian_product2(_463678, _463678), _463678), relation_of2(_463674, cartesian_product2(_463678, _463678), _463678)], (7718 ^ _206269) ^ [_464777, _464779] : [-(set_union2(_464779, _464779) = _464779)], (7720 ^ _206269) ^ [_464874, _464876] : [-(set_intersection2(_464876, _464876) = _464876)], (7722 ^ _206269) ^ [_465000, _465002, _465004] : [-(subset_union2(_465004, _465002, _465002) = _465002), element(_465002, powerset(_465004)), element(_465000, powerset(_465004))], (7732 ^ _206269) ^ [_465339, _465341, _465343] : [-(subset_intersection2(_465343, _465341, _465341) = _465341), element(_465341, powerset(_465343)), element(_465339, powerset(_465343))], (7742 ^ _206269) ^ [_465664, _465666] : [element(_465664, powerset(_465666)), -(subset_complement(_465666, subset_complement(_465666, _465664)) = _465664)], (7748 ^ _206269) ^ [_465876] : [relation(_465876), -(relation_inverse(relation_inverse(_465876)) = _465876)], (7754 ^ _206269) ^ [_466086, _466088] : [element(_466086, powerset(powerset(_466088))), -(complements_of_subsets(_466088, complements_of_subsets(_466088, _466086)) = _466086)], (7760 ^ _206269) ^ [_466300, _466302] : [proper_subset(_466302, _466302)], (7762 ^ _206269) ^ [_466395] : [relation(_466395), 7765 ^ _206269 : [(7776 ^ _206269) ^ [] : [7778 ^ _206269 : [(7779 ^ _206269) ^ [] : [-(in(7777 ^ [_466395], relation_field(_466395)))], (7781 ^ _206269) ^ [] : [in(ordered_pair(7777 ^ [_466395], 7777 ^ [_466395]), _466395)]], -(reflexive(_466395))], (7766 ^ _206269) ^ [] : [reflexive(_466395), 7769 ^ _206269 : [(7770 ^ _206269) ^ [_466639] : [in(_466639, relation_field(_466395)), -(in(ordered_pair(_466639, _466639), _466395))]]]]], (7785 ^ _206269) ^ [_467104] : [singleton(_467104) = empty_set], (7787 ^ _206269) ^ [_467213, _467215] : [in(_467215, _467213), -(set_union2(singleton(_467215), _467213) = _467213)], (7793 ^ _206269) ^ [_467433, _467435] : [disjoint(singleton(_467435), _467433), in(_467435, _467433)], (7799 ^ _206269) ^ [_467646, _467648] : [-(in(_467648, _467646)), -(disjoint(singleton(_467648), _467646))], (7805 ^ _206269) ^ [_467863, _467865] : [relation(_467863), -(subset(relation_dom(relation_rng_restriction(_467865, _467863)), relation_dom(_467863)))], (7811 ^ _206269) ^ [_468071] : [relation(_468071), 7814 ^ _206269 : [(7829 ^ _206269) ^ [] : [7833 ^ _206269 : [(7834 ^ _206269) ^ [] : [-(in(ordered_pair(7830 ^ [_468071], 7831 ^ [_468071]), _468071))], (7836 ^ _206269) ^ [] : [-(in(ordered_pair(7831 ^ [_468071], 7832 ^ [_468071]), _468071))], (7838 ^ _206269) ^ [] : [in(ordered_pair(7830 ^ [_468071], 7832 ^ [_468071]), _468071)]], -(transitive(_468071))], (7815 ^ _206269) ^ [] : [transitive(_468071), 7818 ^ _206269 : [(7819 ^ _206269) ^ [_468363, _468365, _468367] : [-(in(ordered_pair(_468367, _468363), _468071)), in(ordered_pair(_468367, _468365), _468071), in(ordered_pair(_468365, _468363), _468071)]]]]], (7842 ^ _206269) ^ [_469270, _469272] : [subset(singleton(_469272), _469270), -(in(_469272, _469270))], (7848 ^ _206269) ^ [_469436, _469438] : [in(_469438, _469436), -(subset(singleton(_469438), _469436))], (7854 ^ _206269) ^ [_469652, _469654] : [relation(_469652), well_ordering(_469652), equipotent(_469654, relation_field(_469652)), 7866 ^ _206269 : [(7867 ^ _206269) ^ [] : [-(relation(7865 ^ [_469652, _469654]))], (7869 ^ _206269) ^ [] : [-(well_orders(7865 ^ [_469652, _469654], _469654))]]], (7871 ^ _206269) ^ [_470217, _470219] : [set_difference(_470219, _470217) = empty_set, -(subset(_470219, _470217))], (7877 ^ _206269) ^ [_470385, _470387] : [subset(_470387, _470385), -(set_difference(_470387, _470385) = empty_set)], (7883 ^ _206269) ^ [_470603, _470605] : [element(_470603, powerset(_470605)), 7886 ^ _206269 : [(7887 ^ _206269) ^ [_470744] : [in(_470744, _470603), -(in(_470744, _470605))]]], (7893 ^ _206269) ^ [_470955] : [relation(_470955), 7896 ^ _206269 : [(7911 ^ _206269) ^ [] : [7914 ^ _206269 : [(7915 ^ _206269) ^ [] : [-(in(ordered_pair(7912 ^ [_470955], 7913 ^ [_470955]), _470955))], (7917 ^ _206269) ^ [] : [-(in(ordered_pair(7913 ^ [_470955], 7912 ^ [_470955]), _470955))], (7919 ^ _206269) ^ [] : [7912 ^ [_470955] = 7913 ^ [_470955]]], -(antisymmetric(_470955))], (7897 ^ _206269) ^ [] : [antisymmetric(_470955), 7900 ^ _206269 : [(7901 ^ _206269) ^ [_471225, _471227] : [-(_471227 = _471225), in(ordered_pair(_471227, _471225), _470955), in(ordered_pair(_471225, _471227), _470955)]]]]], (7923 ^ _206269) ^ [_472005, _472007, _472009] : [subset(_472009, _472007), -(in(_472005, _472009)), -(subset(_472009, set_difference(_472007, singleton(_472005))))], (7933 ^ _206269) ^ [_472311] : [-(empty_carrier(_472311)), one_sorted_str(_472311), 7940 ^ _206269 : [(7941 ^ _206269) ^ [_472558] : [element(_472558, powerset(the_carrier(_472311))), 7944 ^ _206269 : [(7945 ^ _206269) ^ [_472720] : [element(_472720, the_carrier(_472311)), 7948 ^ _206269 : [(7949 ^ _206269) ^ [] : [in(_472720, subset_complement(the_carrier(_472311), _472558)), in(_472720, _472558)], (7955 ^ _206269) ^ [] : [-(in(_472720, _472558)), -(in(_472720, subset_complement(the_carrier(_472311), _472558)))]]]]]]], (7961 ^ _206269) ^ [_473219] : [relation(_473219), 7964 ^ _206269 : [(7987 ^ _206269) ^ [] : [7990 ^ _206269 : [(7991 ^ _206269) ^ [] : [-(in(7988 ^ [_473219], relation_field(_473219)))], (7993 ^ _206269) ^ [] : [-(in(7989 ^ [_473219], relation_field(_473219)))], (7995 ^ _206269) ^ [] : [7988 ^ [_473219] = 7989 ^ [_473219]], (7997 ^ _206269) ^ [] : [in(ordered_pair(7988 ^ [_473219], 7989 ^ [_473219]), _473219)], (7999 ^ _206269) ^ [] : [in(ordered_pair(7989 ^ [_473219], 7988 ^ [_473219]), _473219)]], -(connected(_473219))], (7965 ^ _206269) ^ [] : [connected(_473219), 7968 ^ _206269 : [(7969 ^ _206269) ^ [_473513, _473515] : [in(_473515, relation_field(_473219)), in(_473513, relation_field(_473219)), -(_473515 = _473513), -(in(ordered_pair(_473515, _473513), _473219)), -(in(ordered_pair(_473513, _473515), _473219))]]]]], (8013 ^ _206269) ^ [_474965, _474967] : [8014 ^ _206269 : [(8015 ^ _206269) ^ [] : [_474967 = empty_set], (8017 ^ _206269) ^ [] : [_474967 = singleton(_474965)]], -(subset(_474967, singleton(_474965)))], (8003 ^ _206269) ^ [_474705, _474707] : [subset(_474707, singleton(_474705)), -(_474707 = empty_set), -(_474707 = singleton(_474705))], (8021 ^ _206269) ^ [_475259, _475261] : [in(_475261, _475259), -(subset(_475261, union(_475259)))], (8027 ^ _206269) ^ [_475530, _475532, _475534, _475536] : [in(ordered_pair(_475536, _475534), cartesian_product2(_475532, _475530)), 8030 ^ _206269 : [(8031 ^ _206269) ^ [] : [-(in(_475536, _475532))], (8033 ^ _206269) ^ [] : [-(in(_475534, _475530))]]], (8035 ^ _206269) ^ [_475795, _475797, _475799, _475801] : [-(in(ordered_pair(_475801, _475799), cartesian_product2(_475797, _475795))), in(_475801, _475797), in(_475799, _475795)], (8045 ^ _206269) ^ [_476128, _476130] : [8047 ^ _206269 : [(8048 ^ _206269) ^ [] : [-(in(8046 ^ [_476128, _476130], _476130))], (8050 ^ _206269) ^ [] : [in(8046 ^ [_476128, _476130], _476128)]], -(element(_476130, powerset(_476128)))], (8054 ^ _206269) ^ [_476501, _476503, _476505] : [relation(_476501), function(_476501), 8061 ^ _206269 : [(8062 ^ _206269) ^ [] : [in(_476503, relation_dom(relation_dom_restriction(_476501, _476505))), 8065 ^ _206269 : [(8066 ^ _206269) ^ [] : [-(in(_476503, relation_dom(_476501)))], (8068 ^ _206269) ^ [] : [-(in(_476503, _476505))]]], (8070 ^ _206269) ^ [] : [-(in(_476503, relation_dom(relation_dom_restriction(_476501, _476505)))), in(_476503, relation_dom(_476501)), in(_476503, _476505)]]], (8081 ^ _206269) ^ [] : [empty(8079 ^ [])], (8083 ^ _206269) ^ [] : [-(epsilon_transitive(8079 ^ []))], (8085 ^ _206269) ^ [] : [-(epsilon_connected(8079 ^ []))], (8087 ^ _206269) ^ [] : [-(ordinal(8079 ^ []))], (8089 ^ _206269) ^ [] : [-(natural(8079 ^ []))], (8092 ^ _206269) ^ [] : [empty(8090 ^ [])], (8094 ^ _206269) ^ [] : [-(finite(8090 ^ []))], (8097 ^ _206269) ^ [] : [-(relation(8095 ^ []))], (8099 ^ _206269) ^ [] : [-(function(8095 ^ []))], (8102 ^ _206269) ^ [_477946, _477948] : [-(relation_of2(8100 ^ [_477946, _477948], _477948, _477946))], (8104 ^ _206269) ^ [_478020, _478022] : [-(relation(8100 ^ [_478020, _478022]))], (8106 ^ _206269) ^ [_478092, _478094] : [-(function(8100 ^ [_478092, _478094]))], (8108 ^ _206269) ^ [_478144, _478146] : [-(quasi_total(8100 ^ [_478144, _478146], _478146, _478144))], (8111 ^ _206269) ^ [] : [empty(8109 ^ [])], (8113 ^ _206269) ^ [] : [-(v1_membered(8109 ^ []))], (8115 ^ _206269) ^ [] : [-(v2_membered(8109 ^ []))], (8117 ^ _206269) ^ [] : [-(v3_membered(8109 ^ []))], (8119 ^ _206269) ^ [] : [-(v4_membered(8109 ^ []))], (8121 ^ _206269) ^ [] : [-(v5_membered(8109 ^ []))], (8124 ^ _206269) ^ [] : [-(rel_str(8122 ^ []))], (8126 ^ _206269) ^ [] : [-(strict_rel_str(8122 ^ []))], (8129 ^ _206269) ^ [] : [-(epsilon_transitive(8127 ^ []))], (8131 ^ _206269) ^ [] : [-(epsilon_connected(8127 ^ []))], (8133 ^ _206269) ^ [] : [-(ordinal(8127 ^ []))], (8136 ^ _206269) ^ [] : [-(epsilon_transitive(8134 ^ []))], (8138 ^ _206269) ^ [] : [-(epsilon_connected(8134 ^ []))], (8140 ^ _206269) ^ [] : [-(ordinal(8134 ^ []))], (8142 ^ _206269) ^ [] : [-(being_limit_ordinal(8134 ^ []))], (8145 ^ _206269) ^ [] : [-(relation(8143 ^ []))], (8147 ^ _206269) ^ [] : [-(function(8143 ^ []))], (8149 ^ _206269) ^ [] : [-(one_to_one(8143 ^ []))], (8151 ^ _206269) ^ [] : [-(empty(8143 ^ []))], (8154 ^ _206269) ^ [] : [-(empty(8152 ^ []))], (8156 ^ _206269) ^ [] : [-(relation(8152 ^ []))], (8158 ^ _206269) ^ [_479688] : [-(empty(_479688)), 8162 ^ _206269 : [(8163 ^ _206269) ^ [] : [-(element(8161 ^ [_479688], powerset(_479688)))], (8165 ^ _206269) ^ [] : [empty(8161 ^ [_479688])]]], (8167 ^ _206269) ^ [_480020] : [8175 ^ _206269 : [(8176 ^ _206269) ^ [] : [-(element(8174 ^ [_480020], powerset(the_carrier(_480020))))], (8178 ^ _206269) ^ [] : [-(open_subset(8174 ^ [_480020], _480020))]], topological_space(_480020), top_str(_480020)], (8181 ^ _206269) ^ [] : [-(empty(8179 ^ []))], (8184 ^ _206269) ^ [_480618] : [-(element(8182 ^ [_480618], powerset(_480618)))], (8186 ^ _206269) ^ [_480689] : [-(empty(8182 ^ [_480689]))], (8188 ^ _206269) ^ [_480757] : [-(relation(8182 ^ [_480757]))], (8190 ^ _206269) ^ [_480825] : [-(function(8182 ^ [_480825]))], (8192 ^ _206269) ^ [_480893] : [-(one_to_one(8182 ^ [_480893]))], (8194 ^ _206269) ^ [_480961] : [-(epsilon_transitive(8182 ^ [_480961]))], (8196 ^ _206269) ^ [_481029] : [-(epsilon_connected(8182 ^ [_481029]))], (8198 ^ _206269) ^ [_481097] : [-(ordinal(8182 ^ [_481097]))], (8200 ^ _206269) ^ [_481165] : [-(natural(8182 ^ [_481165]))], (8202 ^ _206269) ^ [_481213] : [-(finite(8182 ^ [_481213]))], (8205 ^ _206269) ^ [] : [-(relation(8203 ^ []))], (8207 ^ _206269) ^ [] : [-(empty(8203 ^ []))], (8209 ^ _206269) ^ [] : [-(function(8203 ^ []))], (8212 ^ _206269) ^ [_481618] : [-(relation_of2(8210 ^ [_481618], _481618, _481618))], (8214 ^ _206269) ^ [_481688] : [-(relation(8210 ^ [_481688]))], (8216 ^ _206269) ^ [_481756] : [-(function(8210 ^ [_481756]))], (8218 ^ _206269) ^ [_481824] : [-(one_to_one(8210 ^ [_481824]))], (8220 ^ _206269) ^ [_481892] : [-(quasi_total(8210 ^ [_481892], _481892, _481892))], (8222 ^ _206269) ^ [_481962] : [-(onto(8210 ^ [_481962], _481962, _481962))], (8224 ^ _206269) ^ [_482012] : [-(bijective(8210 ^ [_482012], _482012, _482012))], (8227 ^ _206269) ^ [] : [-(rel_str(8225 ^ []))], (8229 ^ _206269) ^ [] : [empty_carrier(8225 ^ [])], (8231 ^ _206269) ^ [] : [-(strict_rel_str(8225 ^ []))], (8233 ^ _206269) ^ [] : [-(reflexive_relstr(8225 ^ []))], (8235 ^ _206269) ^ [] : [-(transitive_relstr(8225 ^ []))], (8237 ^ _206269) ^ [] : [-(antisymmetric_relstr(8225 ^ []))], (8240 ^ _206269) ^ [] : [-(relation(8238 ^ []))], (8242 ^ _206269) ^ [] : [-(function(8238 ^ []))], (8244 ^ _206269) ^ [] : [-(one_to_one(8238 ^ []))], (8246 ^ _206269) ^ [] : [-(empty(8238 ^ []))], (8248 ^ _206269) ^ [] : [-(epsilon_transitive(8238 ^ []))], (8250 ^ _206269) ^ [] : [-(epsilon_connected(8238 ^ []))], (8252 ^ _206269) ^ [] : [-(ordinal(8238 ^ []))], (8255 ^ _206269) ^ [_483033, _483035] : [-(relation_of2(8253 ^ [_483033, _483035], _483035, _483033))], (8257 ^ _206269) ^ [_483107, _483109] : [-(relation(8253 ^ [_483107, _483109]))], (8259 ^ _206269) ^ [_483159, _483161] : [-(function(8253 ^ [_483159, _483161]))], (8262 ^ _206269) ^ [] : [empty(8260 ^ [])], (8264 ^ _206269) ^ [] : [-(relation(8260 ^ []))], (8267 ^ _206269) ^ [_483465] : [-(element(8265 ^ [_483465], powerset(_483465)))], (8269 ^ _206269) ^ [_483516] : [-(empty(8265 ^ [_483516]))], (8272 ^ _206269) ^ [_483671] : [-(element(8270 ^ [_483671], powerset(_483671)))], (8274 ^ _206269) ^ [_483721] : [proper_element(8270 ^ [_483721], powerset(_483721))], (8276 ^ _206269) ^ [_483823] : [8284 ^ _206269 : [(8285 ^ _206269) ^ [] : [-(element(8283 ^ [_483823], powerset(the_carrier(_483823))))], (8287 ^ _206269) ^ [] : [-(open_subset(8283 ^ [_483823], _483823))], (8289 ^ _206269) ^ [] : [-(closed_subset(8283 ^ [_483823], _483823))]], topological_space(_483823), top_str(_483823)], (8292 ^ _206269) ^ [] : [empty(8290 ^ [])], (8294 ^ _206269) ^ [_484414] : [-(empty(_484414)), 8298 ^ _206269 : [(8299 ^ _206269) ^ [] : [-(element(8297 ^ [_484414], powerset(_484414)))], (8301 ^ _206269) ^ [] : [empty(8297 ^ [_484414])], (8303 ^ _206269) ^ [] : [-(finite(8297 ^ [_484414]))]]], (8306 ^ _206269) ^ [] : [-(relation(8304 ^ []))], (8308 ^ _206269) ^ [] : [-(function(8304 ^ []))], (8310 ^ _206269) ^ [] : [-(one_to_one(8304 ^ []))], (8313 ^ _206269) ^ [] : [-(latt_str(8311 ^ []))], (8315 ^ _206269) ^ [] : [-(strict_latt_str(8311 ^ []))], (8318 ^ _206269) ^ [] : [empty(8316 ^ [])], (8320 ^ _206269) ^ [] : [-(epsilon_transitive(8316 ^ []))], (8322 ^ _206269) ^ [] : [-(epsilon_connected(8316 ^ []))], (8324 ^ _206269) ^ [] : [-(ordinal(8316 ^ []))], (8327 ^ _206269) ^ [_485531] : [-(relation_of2(8325 ^ [_485531], _485531, _485531))], (8329 ^ _206269) ^ [_485601] : [-(relation(8325 ^ [_485601]))], (8331 ^ _206269) ^ [_485669] : [-(reflexive(8325 ^ [_485669]))], (8333 ^ _206269) ^ [_485737] : [-(symmetric(8325 ^ [_485737]))], (8335 ^ _206269) ^ [_485805] : [-(antisymmetric(8325 ^ [_485805]))], (8337 ^ _206269) ^ [_485873] : [-(transitive(8325 ^ [_485873]))], (8339 ^ _206269) ^ [_485921] : [-(v1_partfun1(8325 ^ [_485921], _485921, _485921))], (8342 ^ _206269) ^ [] : [-(relation(8340 ^ []))], (8344 ^ _206269) ^ [] : [-(relation_empty_yielding(8340 ^ []))], (8347 ^ _206269) ^ [] : [-(one_sorted_str(8345 ^ []))], (8349 ^ _206269) ^ [] : [empty_carrier(8345 ^ [])], (8351 ^ _206269) ^ [_486331] : [-(empty(_486331)), 8355 ^ _206269 : [(8356 ^ _206269) ^ [] : [-(element(8354 ^ [_486331], powerset(_486331)))], (8358 ^ _206269) ^ [] : [empty(8354 ^ [_486331])], (8360 ^ _206269) ^ [] : [-(finite(8354 ^ [_486331]))]]], (8363 ^ _206269) ^ [] : [-(relation(8361 ^ []))], (8365 ^ _206269) ^ [] : [-(relation_empty_yielding(8361 ^ []))], (8367 ^ _206269) ^ [] : [-(function(8361 ^ []))], (8369 ^ _206269) ^ [_486952] : [8377 ^ _206269 : [(8378 ^ _206269) ^ [] : [-(element(8376 ^ [_486952], powerset(the_carrier(_486952))))], (8380 ^ _206269) ^ [] : [empty(8376 ^ [_486952])]], -(empty_carrier(_486952)), one_sorted_str(_486952)], (8383 ^ _206269) ^ [] : [-(latt_str(8381 ^ []))], (8385 ^ _206269) ^ [] : [empty_carrier(8381 ^ [])], (8387 ^ _206269) ^ [] : [-(strict_latt_str(8381 ^ []))], (8389 ^ _206269) ^ [_487583] : [8397 ^ _206269 : [(8398 ^ _206269) ^ [] : [-(element(8396 ^ [_487583], powerset(the_carrier(_487583))))], (8400 ^ _206269) ^ [] : [-(closed_subset(8396 ^ [_487583], _487583))]], topological_space(_487583), top_str(_487583)], (8402 ^ _206269) ^ [_488001] : [8414 ^ _206269 : [(8415 ^ _206269) ^ [] : [-(element(8413 ^ [_488001], powerset(the_carrier(_488001))))], (8417 ^ _206269) ^ [] : [empty(8413 ^ [_488001])], (8419 ^ _206269) ^ [] : [-(closed_subset(8413 ^ [_488001], _488001))]], -(empty_carrier(_488001)), topological_space(_488001), top_str(_488001)], (8422 ^ _206269) ^ [] : [-(latt_str(8420 ^ []))], (8424 ^ _206269) ^ [] : [empty_carrier(8420 ^ [])], (8426 ^ _206269) ^ [] : [-(strict_latt_str(8420 ^ []))], (8428 ^ _206269) ^ [] : [-(join_commutative(8420 ^ []))], (8430 ^ _206269) ^ [] : [-(join_associative(8420 ^ []))], (8432 ^ _206269) ^ [] : [-(meet_commutative(8420 ^ []))], (8434 ^ _206269) ^ [] : [-(meet_associative(8420 ^ []))], (8436 ^ _206269) ^ [] : [-(meet_absorbing(8420 ^ []))], (8438 ^ _206269) ^ [] : [-(join_absorbing(8420 ^ []))], (8440 ^ _206269) ^ [] : [-(lattice(8420 ^ []))], (8442 ^ _206269) ^ [_489260, _489262, _489264, _489266] : [-(k10_filter_1(_489266, _489264, _489262, _489260) = ordered_pair(_489262, _489260)), -(empty_carrier(_489266)), lattice(_489266), latt_str(_489266), -(empty_carrier(_489264)), lattice(_489264), latt_str(_489264), element(_489262, the_carrier(_489266)), element(_489260, the_carrier(_489264))], (8476 ^ _206269) ^ [_490207, _490209, _490211, _490213] : [-(ordered_pair_as_product_element(_490213, _490211, _490209, _490207) = ordered_pair(_490209, _490207)), -(empty(_490213)), -(empty(_490211)), element(_490209, _490213), element(_490207, _490211)], (8494 ^ _206269) ^ [_490709] : [-(k1_pcomps_1(_490709) = powerset(_490709))], (8496 ^ _206269) ^ [_490876, _490878, _490880, _490882, _490884, _490886] : [-(apply_binary_as_element(_490886, _490884, _490882, _490880, _490878, _490876) = apply_binary(_490880, _490878, _490876)), -(empty(_490886)), -(empty(_490884)), function(_490880), quasi_total(_490880, cartesian_product2(_490886, _490884), _490882), relation_of2(_490880, cartesian_product2(_490886, _490884), _490882), element(_490878, _490886), element(_490876, _490884)], (8526 ^ _206269) ^ [_491764] : [-(k2_lattice3(_491764) = relation_of_lattice(_491764)), -(empty_carrier(_491764)), lattice(_491764), latt_str(_491764)], (8540 ^ _206269) ^ [_492157, _492159, _492161] : [-(join_commut(_492161, _492159, _492157) = join(_492161, _492159, _492157)), -(empty_carrier(_492161)), join_commutative(_492161), join_semilatt_str(_492161), element(_492159, the_carrier(_492161)), element(_492157, the_carrier(_492161))], (8562 ^ _206269) ^ [_492780, _492782, _492784] : [-(meet_commut(_492784, _492782, _492780) = meet(_492784, _492782, _492780)), -(empty_carrier(_492784)), meet_commutative(_492784), meet_semilatt_str(_492784), element(_492782, the_carrier(_492784)), element(_492780, the_carrier(_492784))], (8584 ^ _206269) ^ [_493403, _493405, _493407] : [relation_of2(_493403, _493407, _493405), -(relation_dom_as_subset(_493407, _493405, _493403) = relation_dom(_493403))], (8590 ^ _206269) ^ [_493647, _493649, _493651] : [-(subset_union2(_493651, _493649, _493647) = set_union2(_493649, _493647)), element(_493649, powerset(_493651)), element(_493647, powerset(_493651))], (8600 ^ _206269) ^ [_493992, _493994, _493996] : [relation_of2(_493992, _493996, _493994), -(relation_rng_as_subset(_493996, _493994, _493992) = relation_rng(_493992))], (8606 ^ _206269) ^ [_494222, _494224] : [element(_494222, powerset(powerset(_494224))), -(union_of_subsets(_494224, _494222) = union(_494222))], (8612 ^ _206269) ^ [_494464, _494466, _494468] : [-(subset_intersection2(_494468, _494466, _494464) = set_intersection2(_494466, _494464)), element(_494466, powerset(_494468)), element(_494464, powerset(_494468))], (8622 ^ _206269) ^ [_494766] : [-(identity_as_relation_of(_494766) = identity_relation(_494766))], (8624 ^ _206269) ^ [_494877, _494879] : [element(_494877, powerset(powerset(_494879))), -(meet_of_subsets(_494879, _494877) = set_meet(_494877))], (8630 ^ _206269) ^ [_495119, _495121, _495123] : [-(subset_difference(_495123, _495121, _495119) = set_difference(_495121, _495119)), element(_495121, powerset(_495123)), element(_495119, powerset(_495123))], (8640 ^ _206269) ^ [_495478, _495480, _495482, _495484] : [-(apply_as_element(_495484, _495482, _495480, _495478) = apply(_495480, _495478)), -(empty(_495484)), function(_495480), quasi_total(_495480, _495484, _495482), relation_of2(_495480, _495484, _495482), element(_495478, _495484)], (8662 ^ _206269) ^ [_496150, _496152, _496154] : [relation_of2_as_subset(_496150, _496154, _496152), -(relation_of2(_496150, _496154, _496152))], (8668 ^ _206269) ^ [_496322, _496324, _496326] : [relation_of2(_496322, _496326, _496324), -(relation_of2_as_subset(_496322, _496326, _496324))], (8674 ^ _206269) ^ [_496544, _496546] : [ordinal(_496546), ordinal(_496544), 8681 ^ _206269 : [(8682 ^ _206269) ^ [] : [ordinal_subset(_496546, _496544), -(subset(_496546, _496544))], (8688 ^ _206269) ^ [] : [subset(_496546, _496544), -(ordinal_subset(_496546, _496544))]]], (8694 ^ _206269) ^ [_497120, _497122] : [equipotent(_497122, _497120), -(are_equipotent(_497122, _497120))], (8700 ^ _206269) ^ [_497282, _497284] : [are_equipotent(_497284, _497282), -(equipotent(_497284, _497282))], (8706 ^ _206269) ^ [_497508, _497510, _497512] : [8733 ^ _206269 : [(8734 ^ _206269) ^ [] : [below_refl(_497512, _497510, _497508), -(below(_497512, _497510, _497508))], (8740 ^ _206269) ^ [] : [below(_497512, _497510, _497508), -(below_refl(_497512, _497510, _497508))]], -(empty_carrier(_497512)), meet_commutative(_497512), meet_absorbing(_497512), join_absorbing(_497512), latt_str(_497512), element(_497510, the_carrier(_497512)), element(_497508, the_carrier(_497512))], (8746 ^ _206269) ^ [_498563, _498565, _498567] : [8765 ^ _206269 : [(8766 ^ _206269) ^ [] : [related_reflexive(_498567, _498565, _498563), -(related(_498567, _498565, _498563))], (8772 ^ _206269) ^ [] : [related(_498567, _498565, _498563), -(related_reflexive(_498567, _498565, _498563))]], -(empty_carrier(_498567)), reflexive_relstr(_498567), rel_str(_498567), element(_498565, the_carrier(_498567)), element(_498563, the_carrier(_498567))], (8778 ^ _206269) ^ [_499422, _499424] : [-(ordinal_subset(_499424, _499424)), ordinal(_499424), ordinal(_499422)], (8788 ^ _206269) ^ [_499702, _499704] : [-(subset(_499704, _499704))], (8790 ^ _206269) ^ [_499796, _499798] : [-(equipotent(_499798, _499798))], (8792 ^ _206269) ^ [_499919, _499921, _499923] : [-(below_refl(_499923, _499921, _499921)), -(empty_carrier(_499923)), meet_commutative(_499923), meet_absorbing(_499923), join_absorbing(_499923), latt_str(_499923), element(_499921, the_carrier(_499923)), element(_499919, the_carrier(_499923))], (8822 ^ _206269) ^ [_500710, _500712, _500714] : [-(related_reflexive(_500714, _500712, _500712)), -(empty_carrier(_500714)), reflexive_relstr(_500714), rel_str(_500714), element(_500712, the_carrier(_500714)), element(_500710, the_carrier(_500714))], (8844 ^ _206269) ^ [_501305, _501307] : [-(empty(_501307)), relation(_501305), 8856 ^ _206269 : [(8883 ^ _206269) ^ [] : [8854 ^ [_501305, _501307] = 8855 ^ [_501305, _501307]], (8857 ^ _206269) ^ [] : [-(in(8853 ^ [_501305, _501307], _501307))], (8860 ^ _206269) ^ [] : [-(8853 ^ [_501305, _501307] = 8858 ^ [_501305, _501307])], (8862 ^ _206269) ^ [] : [-(in(8854 ^ [_501305, _501307], 8858 ^ [_501305, _501307]))], (8864 ^ _206269) ^ [_502587] : [in(_502587, 8858 ^ [_501305, _501307]), -(in(ordered_pair(8854 ^ [_501305, _501307], _502587), _501305))], (8870 ^ _206269) ^ [] : [-(in(8853 ^ [_501305, _501307], _501307))], (8873 ^ _206269) ^ [] : [-(8853 ^ [_501305, _501307] = 8871 ^ [_501305, _501307])], (8875 ^ _206269) ^ [] : [-(in(8855 ^ [_501305, _501307], 8871 ^ [_501305, _501307]))], (8877 ^ _206269) ^ [_503136] : [in(_503136, 8871 ^ [_501305, _501307]), -(in(ordered_pair(8855 ^ [_501305, _501307], _503136), _501305))]], 8885 ^ _206269 : [(8886 ^ _206269) ^ [] : [-(relation(8884 ^ [_501305, _501307]))], (8888 ^ _206269) ^ [] : [-(function(8884 ^ [_501305, _501307]))], (8890 ^ _206269) ^ [_503735, _503737] : [in(ordered_pair(_503737, _503735), 8884 ^ [_501305, _501307]), 8893 ^ _206269 : [(8894 ^ _206269) ^ [] : [-(in(_503737, _501307))], (8896 ^ _206269) ^ [] : [-(in(_503737, _501307))], (8899 ^ _206269) ^ [] : [-(_503737 = 8897 ^ [_501305, _501307, _503735, _503737])], (8901 ^ _206269) ^ [] : [-(in(_503735, 8897 ^ [_501305, _501307, _503735, _503737]))], (8903 ^ _206269) ^ [_504317] : [in(_504317, 8897 ^ [_501305, _501307, _503735, _503737]), -(in(ordered_pair(_503735, _504317), _501305))]]], (8909 ^ _206269) ^ [_504546, _504548] : [-(in(ordered_pair(_504548, _504546), 8884 ^ [_501305, _501307])), in(_504548, _501307), in(_504548, _501307), 8918 ^ _206269 : [(8919 ^ _206269) ^ [_504862] : [_504548 = _504862, in(_504546, _504862), 8927 ^ _206269 : [(8928 ^ _206269) ^ [] : [-(in(8926 ^ [_501305, _501307, _504546, _504548, _504862], _504862))], (8930 ^ _206269) ^ [] : [in(ordered_pair(_504546, 8926 ^ [_501305, _501307, _504546, _504548, _504862]), _501305)]]]]]]], (8934 ^ _206269) ^ [_505459] : [8938 ^ _206269 : [(8939 ^ _206269) ^ [] : [-(in(8935 ^ [_505459], _505459))], (8941 ^ _206269) ^ [] : [-(8936 ^ [_505459] = singleton(8935 ^ [_505459]))], (8943 ^ _206269) ^ [] : [-(in(8935 ^ [_505459], _505459))], (8945 ^ _206269) ^ [] : [-(8937 ^ [_505459] = singleton(8935 ^ [_505459]))], (8947 ^ _206269) ^ [] : [8936 ^ [_505459] = 8937 ^ [_505459]]], 8949 ^ _206269 : [(8950 ^ _206269) ^ [] : [-(relation(8948 ^ [_505459]))], (8952 ^ _206269) ^ [] : [-(function(8948 ^ [_505459]))], (8954 ^ _206269) ^ [_506521, _506523] : [in(ordered_pair(_506523, _506521), 8948 ^ [_505459]), 8957 ^ _206269 : [(8958 ^ _206269) ^ [] : [-(in(_506523, _505459))], (8960 ^ _206269) ^ [] : [-(in(_506523, _505459))], (8962 ^ _206269) ^ [] : [-(_506521 = singleton(_506523))]]], (8964 ^ _206269) ^ [_506864, _506866] : [-(in(ordered_pair(_506866, _506864), 8948 ^ [_505459])), in(_506866, _505459), in(_506866, _505459), _506864 = singleton(_506866)]]], (8978 ^ _206269) ^ [_507300, _507302] : [one_sorted_str(_507302), element(_507300, powerset(powerset(the_carrier(_507302)))), 8990 ^ _206269 : [(9015 ^ _206269) ^ [] : [8988 ^ [_507300, _507302] = 8989 ^ [_507300, _507302]], (8991 ^ _206269) ^ [] : [-(in(8987 ^ [_507300, _507302], complements_of_subsets(the_carrier(_507302), _507300)))], (8993 ^ _206269) ^ [_508344] : [element(_508344, powerset(the_carrier(_507302))), _508344 = 8987 ^ [_507300, _507302], -(8988 ^ [_507300, _507302] = subset_complement(the_carrier(_507302), _508344))], (9003 ^ _206269) ^ [] : [-(in(8987 ^ [_507300, _507302], complements_of_subsets(the_carrier(_507302), _507300)))], (9005 ^ _206269) ^ [_508747] : [element(_508747, powerset(the_carrier(_507302))), _508747 = 8987 ^ [_507300, _507302], -(8989 ^ [_507300, _507302] = subset_complement(the_carrier(_507302), _508747))]], 9017 ^ _206269 : [(9018 ^ _206269) ^ [] : [-(relation(9016 ^ [_507300, _507302]))], (9020 ^ _206269) ^ [] : [-(function(9016 ^ [_507300, _507302]))], (9022 ^ _206269) ^ [_509448, _509450] : [in(ordered_pair(_509450, _509448), 9016 ^ [_507300, _507302]), 9025 ^ _206269 : [(9026 ^ _206269) ^ [] : [-(in(_509450, complements_of_subsets(the_carrier(_507302), _507300)))], (9028 ^ _206269) ^ [] : [-(in(_509450, complements_of_subsets(the_carrier(_507302), _507300)))], (9030 ^ _206269) ^ [_509804] : [element(_509804, powerset(the_carrier(_507302))), _509804 = _509450, -(_509448 = subset_complement(the_carrier(_507302), _509804))]]], (9040 ^ _206269) ^ [_510120, _510122] : [-(in(ordered_pair(_510122, _510120), 9016 ^ [_507300, _507302])), in(_510122, complements_of_subsets(the_carrier(_507302), _507300)), in(_510122, complements_of_subsets(the_carrier(_507302), _507300)), 9050 ^ _206269 : [(9051 ^ _206269) ^ [] : [-(element(9049 ^ [_507300, _507302, _510120, _510122], powerset(the_carrier(_507302))))], (9053 ^ _206269) ^ [] : [-(9049 ^ [_507300, _507302, _510120, _510122] = _510122)], (9055 ^ _206269) ^ [] : [_510120 = subset_complement(the_carrier(_507302), 9049 ^ [_507300, _507302, _510120, _510122])]]]]], (9059 ^ _206269) ^ [_510885, _510887] : [one_sorted_str(_510887), element(_510885, powerset(powerset(the_carrier(_510887)))), 9071 ^ _206269 : [(9096 ^ _206269) ^ [] : [9069 ^ [_510885, _510887] = 9070 ^ [_510885, _510887]], (9072 ^ _206269) ^ [] : [-(in(9068 ^ [_510885, _510887], _510885))], (9074 ^ _206269) ^ [_511874] : [element(_511874, powerset(the_carrier(_510887))), _511874 = 9068 ^ [_510885, _510887], -(9069 ^ [_510885, _510887] = subset_complement(the_carrier(_510887), _511874))], (9084 ^ _206269) ^ [] : [-(in(9068 ^ [_510885, _510887], _510885))], (9086 ^ _206269) ^ [_512272] : [element(_512272, powerset(the_carrier(_510887))), _512272 = 9068 ^ [_510885, _510887], -(9070 ^ [_510885, _510887] = subset_complement(the_carrier(_510887), _512272))]], 9098 ^ _206269 : [(9099 ^ _206269) ^ [] : [-(relation(9097 ^ [_510885, _510887]))], (9101 ^ _206269) ^ [] : [-(function(9097 ^ [_510885, _510887]))], (9103 ^ _206269) ^ [_512963, _512965] : [in(ordered_pair(_512965, _512963), 9097 ^ [_510885, _510887]), 9106 ^ _206269 : [(9107 ^ _206269) ^ [] : [-(in(_512965, _510885))], (9109 ^ _206269) ^ [] : [-(in(_512965, _510885))], (9111 ^ _206269) ^ [_513299] : [element(_513299, powerset(the_carrier(_510887))), _513299 = _512965, -(_512963 = subset_complement(the_carrier(_510887), _513299))]]], (9121 ^ _206269) ^ [_513615, _513617] : [-(in(ordered_pair(_513617, _513615), 9097 ^ [_510885, _510887])), in(_513617, _510885), in(_513617, _510885), 9131 ^ _206269 : [(9132 ^ _206269) ^ [] : [-(element(9130 ^ [_510885, _510887, _513615, _513617], powerset(the_carrier(_510887))))], (9134 ^ _206269) ^ [] : [-(9130 ^ [_510885, _510887, _513615, _513617] = _513617)], (9136 ^ _206269) ^ [] : [_513615 = subset_complement(the_carrier(_510887), 9130 ^ [_510885, _510887, _513615, _513617])]]]]], (9140 ^ _206269) ^ [_514346] : [9141 ^ _206269 : [(9142 ^ _206269) ^ [_514467] : [ordinal(_514467), in(_514467, _514346)]], 9148 ^ _206269 : [(9149 ^ _206269) ^ [] : [-(ordinal(9147 ^ [_514346]))], (9151 ^ _206269) ^ [] : [-(in(9147 ^ [_514346], _514346))], (9153 ^ _206269) ^ [_514847] : [ordinal(_514847), in(_514847, _514346), -(ordinal_subset(9147 ^ [_514346], _514847))]]], (9163 ^ _206269) ^ [] : [9290 ^ _206269 : [(9291 ^ _206269) ^ [_519614] : [ordinal(_519614), in(_519614, omega), 9298 ^ _206269 : [(9299 ^ _206269) ^ [_519870] : [element(_519870, powerset(powerset(_519614))), -(_519870 = empty_set), 9307 ^ _206269 : [(9308 ^ _206269) ^ [] : [-(in(9306 ^ [_519614, _519870], _519870))], (9310 ^ _206269) ^ [_520269] : [-(_520269 = 9306 ^ [_519614, _519870]), in(_520269, _519870), subset(9306 ^ [_519614, _519870], _520269)]]]]]], 9166 ^ _206269 : [(9167 ^ _206269) ^ [] : [-(in(empty_set, omega))], (9170 ^ _206269) ^ [] : [-(element(9168 ^ [], powerset(powerset(empty_set))))], (9172 ^ _206269) ^ [] : [9168 ^ [] = empty_set], (9174 ^ _206269) ^ [_515453] : [in(_515453, 9168 ^ []), 9178 ^ _206269 : [(9179 ^ _206269) ^ [] : [-(in(9177 ^ [_515453], 9168 ^ []))], (9181 ^ _206269) ^ [] : [-(subset(_515453, 9177 ^ [_515453]))], (9183 ^ _206269) ^ [] : [9177 ^ [_515453] = _515453]]]], 9187 ^ _206269 : [(9188 ^ _206269) ^ [] : [-(ordinal(9186 ^ []))], (9215 ^ _206269) ^ [] : [-(in(succ(9186 ^ []), omega))], (9218 ^ _206269) ^ [] : [-(element(9216 ^ [], powerset(powerset(succ(9186 ^ [])))))], (9220 ^ _206269) ^ [] : [9216 ^ [] = empty_set], (9222 ^ _206269) ^ [_517104] : [in(_517104, 9216 ^ []), 9226 ^ _206269 : [(9227 ^ _206269) ^ [] : [-(in(9225 ^ [_517104], 9216 ^ []))], (9229 ^ _206269) ^ [] : [-(subset(_517104, 9225 ^ [_517104]))], (9231 ^ _206269) ^ [] : [9225 ^ [_517104] = _517104]]], (9190 ^ _206269) ^ [] : [in(9186 ^ [], omega), 9193 ^ _206269 : [(9194 ^ _206269) ^ [_516187] : [element(_516187, powerset(powerset(9186 ^ []))), -(_516187 = empty_set), 9202 ^ _206269 : [(9203 ^ _206269) ^ [] : [-(in(9201 ^ [_516187], _516187))], (9205 ^ _206269) ^ [_516560] : [-(_516560 = 9201 ^ [_516187]), in(_516560, _516187), subset(9201 ^ [_516187], _516560)]]]]]], 9233 ^ _206269 : [(9234 ^ _206269) ^ [] : [-(ordinal(9232 ^ []))], (9271 ^ _206269) ^ [] : [9232 ^ [] = empty_set], (9273 ^ _206269) ^ [] : [-(in(9232 ^ [], omega))], (9276 ^ _206269) ^ [] : [-(element(9274 ^ [], powerset(powerset(9232 ^ []))))], (9278 ^ _206269) ^ [] : [9274 ^ [] = empty_set], (9280 ^ _206269) ^ [_519194] : [in(_519194, 9274 ^ []), 9284 ^ _206269 : [(9285 ^ _206269) ^ [] : [-(in(9283 ^ [_519194], 9274 ^ []))], (9287 ^ _206269) ^ [] : [-(subset(_519194, 9283 ^ [_519194]))], (9289 ^ _206269) ^ [] : [9283 ^ [_519194] = _519194]]], (9236 ^ _206269) ^ [] : [-(being_limit_ordinal(9232 ^ []))], (9238 ^ _206269) ^ [_517832] : [ordinal(_517832), in(_517832, 9232 ^ []), in(_517832, omega), 9249 ^ _206269 : [(9250 ^ _206269) ^ [_518169] : [element(_518169, powerset(powerset(_517832))), -(_518169 = empty_set), 9258 ^ _206269 : [(9259 ^ _206269) ^ [] : [-(in(9257 ^ [_517832, _518169], _518169))], (9261 ^ _206269) ^ [_518568] : [-(_518568 = 9257 ^ [_517832, _518169]), in(_518568, _518169), subset(9257 ^ [_517832, _518169], _518568)]]]]]]], (9320 ^ _206269) ^ [_520649, _520651, _520653] : [relation(_520651), relation(_520649), function(_520649), 9332 ^ _206269 : [(9333 ^ _206269) ^ [] : [-(relation(9331 ^ [_520649, _520651, _520653]))], (9335 ^ _206269) ^ [_521222, _521224] : [in(ordered_pair(_521224, _521222), 9331 ^ [_520649, _520651, _520653]), 9338 ^ _206269 : [(9339 ^ _206269) ^ [] : [-(in(_521224, _520653))], (9341 ^ _206269) ^ [] : [-(in(_521222, _520653))], (9343 ^ _206269) ^ [] : [-(in(ordered_pair(apply(_520649, _521224), apply(_520649, _521222)), _520651))]]], (9345 ^ _206269) ^ [_521611, _521613] : [-(in(ordered_pair(_521613, _521611), 9331 ^ [_520649, _520651, _520653])), in(_521613, _520653), in(_521611, _520653), in(ordered_pair(apply(_520649, _521613), apply(_520649, _521611)), _520651)]]], (9359 ^ _206269) ^ [_522102, _522104] : [-(empty(_522104)), relation(_522102), 9371 ^ _206269 : [(9398 ^ _206269) ^ [] : [9369 ^ [_522102, _522104] = 9370 ^ [_522102, _522104]], (9372 ^ _206269) ^ [] : [-(in(9368 ^ [_522102, _522104], _522104))], (9375 ^ _206269) ^ [] : [-(9368 ^ [_522102, _522104] = 9373 ^ [_522102, _522104])], (9377 ^ _206269) ^ [] : [-(in(9369 ^ [_522102, _522104], 9373 ^ [_522102, _522104]))], (9379 ^ _206269) ^ [_523371] : [in(_523371, 9373 ^ [_522102, _522104]), -(in(ordered_pair(9369 ^ [_522102, _522104], _523371), _522102))], (9385 ^ _206269) ^ [] : [-(in(9368 ^ [_522102, _522104], _522104))], (9388 ^ _206269) ^ [] : [-(9368 ^ [_522102, _522104] = 9386 ^ [_522102, _522104])], (9390 ^ _206269) ^ [] : [-(in(9370 ^ [_522102, _522104], 9386 ^ [_522102, _522104]))], (9392 ^ _206269) ^ [_523920] : [in(_523920, 9386 ^ [_522102, _522104]), -(in(ordered_pair(9370 ^ [_522102, _522104], _523920), _522102))]], 9400 ^ _206269 : [(9401 ^ _206269) ^ [_524348] : [in(_524348, 9399 ^ [_522102, _522104]), 9405 ^ _206269 : [(9406 ^ _206269) ^ [] : [-(in(9404 ^ [_522102, _522104, _524348], _522104))], (9408 ^ _206269) ^ [] : [-(in(9404 ^ [_522102, _522104, _524348], _522104))], (9411 ^ _206269) ^ [] : [-(9404 ^ [_522102, _522104, _524348] = 9409 ^ [_522102, _522104, _524348])], (9413 ^ _206269) ^ [] : [-(in(_524348, 9409 ^ [_522102, _522104, _524348]))], (9415 ^ _206269) ^ [_525037] : [in(_525037, 9409 ^ [_522102, _522104, _524348]), -(in(ordered_pair(_524348, _525037), _522102))]]], (9421 ^ _206269) ^ [_525254] : [-(in(_525254, 9399 ^ [_522102, _522104])), 9422 ^ _206269 : [(9423 ^ _206269) ^ [_525396] : [in(_525396, _522104), in(_525396, _522104), 9430 ^ _206269 : [(9431 ^ _206269) ^ [_525660] : [_525396 = _525660, in(_525254, _525660), 9439 ^ _206269 : [(9440 ^ _206269) ^ [] : [-(in(9438 ^ [_522102, _522104, _525254, _525396, _525660], _525660))], (9442 ^ _206269) ^ [] : [in(ordered_pair(_525254, 9438 ^ [_522102, _522104, _525254, _525396, _525660]), _522102)]]]]]]]]], (9446 ^ _206269) ^ [_526263, _526265] : [-(empty(_526265)), relation(_526263), 9453 ^ _206269 : [(9454 ^ _206269) ^ [_526731] : [9458 ^ _206269 : [(9497 ^ _206269) ^ [] : [9456 ^ [_526263, _526265, _526731] = 9457 ^ [_526263, _526265, _526731]], (9459 ^ _206269) ^ [] : [-(9455 ^ [_526263, _526265, _526731] = 9456 ^ [_526263, _526265, _526731])], (9463 ^ _206269) ^ [] : [-(ordered_pair(9460 ^ [_526263, _526265, _526731], 9461 ^ [_526263, _526265, _526731]) = 9456 ^ [_526263, _526265, _526731])], (9465 ^ _206269) ^ [] : [-(in(9460 ^ [_526263, _526265, _526731], _526265))], (9468 ^ _206269) ^ [] : [-(9460 ^ [_526263, _526265, _526731] = 9466 ^ [_526263, _526265, _526731])], (9470 ^ _206269) ^ [] : [-(in(9461 ^ [_526263, _526265, _526731], 9466 ^ [_526263, _526265, _526731]))], (9472 ^ _206269) ^ [_528509] : [in(_528509, 9466 ^ [_526263, _526265, _526731]), -(in(ordered_pair(9461 ^ [_526263, _526265, _526731], _528509), _526263))], (9478 ^ _206269) ^ [] : [-(9455 ^ [_526263, _526265, _526731] = 9457 ^ [_526263, _526265, _526731])], (9482 ^ _206269) ^ [] : [-(ordered_pair(9479 ^ [_526263, _526265, _526731], 9480 ^ [_526263, _526265, _526731]) = 9457 ^ [_526263, _526265, _526731])], (9484 ^ _206269) ^ [] : [-(in(9479 ^ [_526263, _526265, _526731], _526265))], (9487 ^ _206269) ^ [] : [-(9479 ^ [_526263, _526265, _526731] = 9485 ^ [_526263, _526265, _526731])], (9489 ^ _206269) ^ [] : [-(in(9480 ^ [_526263, _526265, _526731], 9485 ^ [_526263, _526265, _526731]))], (9491 ^ _206269) ^ [_529528] : [in(_529528, 9485 ^ [_526263, _526265, _526731]), -(in(ordered_pair(9480 ^ [_526263, _526265, _526731], _529528), _526263))]], 9499 ^ _206269 : [(9500 ^ _206269) ^ [_530018] : [in(_530018, 9498 ^ [_526263, _526265, _526731]), 9504 ^ _206269 : [(9505 ^ _206269) ^ [] : [-(in(9503 ^ [_526263, _526265, _526731, _530018], cartesian_product2(_526265, _526731)))], (9507 ^ _206269) ^ [] : [-(9503 ^ [_526263, _526265, _526731, _530018] = _530018)], (9511 ^ _206269) ^ [] : [-(ordered_pair(9508 ^ [_526263, _526265, _526731, _530018], 9509 ^ [_526263, _526265, _526731, _530018]) = _530018)], (9513 ^ _206269) ^ [] : [-(in(9508 ^ [_526263, _526265, _526731, _530018], _526265))], (9516 ^ _206269) ^ [] : [-(9508 ^ [_526263, _526265, _526731, _530018] = 9514 ^ [_526263, _526265, _526731, _530018])], (9518 ^ _206269) ^ [] : [-(in(9509 ^ [_526263, _526265, _526731, _530018], 9514 ^ [_526263, _526265, _526731, _530018]))], (9520 ^ _206269) ^ [_531249] : [in(_531249, 9514 ^ [_526263, _526265, _526731, _530018]), -(in(ordered_pair(9509 ^ [_526263, _526265, _526731, _530018], _531249), _526263))]]], (9526 ^ _206269) ^ [_531504] : [-(in(_531504, 9498 ^ [_526263, _526265, _526731])), 9527 ^ _206269 : [(9528 ^ _206269) ^ [_531680] : [in(_531680, cartesian_product2(_526265, _526731)), _531680 = _531504, 9535 ^ _206269 : [(9536 ^ _206269) ^ [_531999, _532001] : [ordered_pair(_532001, _531999) = _531504, in(_532001, _526265), 9543 ^ _206269 : [(9544 ^ _206269) ^ [_532297] : [_532001 = _532297, in(_531999, _532297), 9552 ^ _206269 : [(9553 ^ _206269) ^ [] : [-(in(9551 ^ [_526263, _526265, _526731, _531504, _531680, _531999, _532001, _532297], _532297))], (9555 ^ _206269) ^ [] : [in(ordered_pair(_531999, 9551 ^ [_526263, _526265, _526731, _531504, _531680, _531999, _532001, _532297]), _526263)]]]]]]]]]]]]], (9559 ^ _206269) ^ [_532966] : [9563 ^ _206269 : [(9564 ^ _206269) ^ [] : [-(in(9560 ^ [_532966], _532966))], (9566 ^ _206269) ^ [] : [-(9561 ^ [_532966] = singleton(9560 ^ [_532966]))], (9568 ^ _206269) ^ [] : [-(in(9560 ^ [_532966], _532966))], (9570 ^ _206269) ^ [] : [-(9562 ^ [_532966] = singleton(9560 ^ [_532966]))], (9572 ^ _206269) ^ [] : [9561 ^ [_532966] = 9562 ^ [_532966]]], 9574 ^ _206269 : [(9575 ^ _206269) ^ [_533852] : [in(_533852, 9573 ^ [_532966]), 9579 ^ _206269 : [(9580 ^ _206269) ^ [] : [-(in(9578 ^ [_532966, _533852], _532966))], (9582 ^ _206269) ^ [] : [-(in(9578 ^ [_532966, _533852], _532966))], (9584 ^ _206269) ^ [] : [-(_533852 = singleton(9578 ^ [_532966, _533852]))]]], (9586 ^ _206269) ^ [_534264] : [-(in(_534264, 9573 ^ [_532966])), 9587 ^ _206269 : [(9588 ^ _206269) ^ [_534371] : [in(_534371, _532966), in(_534371, _532966), _534264 = singleton(_534371)]]]]], (9600 ^ _206269) ^ [_534751, _534753] : [9604 ^ _206269 : [(9605 ^ _206269) ^ [] : [-(9601 ^ [_534751, _534753] = 9602 ^ [_534751, _534753])], (9609 ^ _206269) ^ [] : [-(ordered_pair(9606 ^ [_534751, _534753], 9607 ^ [_534751, _534753]) = 9602 ^ [_534751, _534753])], (9611 ^ _206269) ^ [] : [-(in(9606 ^ [_534751, _534753], _534753))], (9613 ^ _206269) ^ [] : [-(9607 ^ [_534751, _534753] = singleton(9606 ^ [_534751, _534753]))], (9615 ^ _206269) ^ [] : [-(9601 ^ [_534751, _534753] = 9603 ^ [_534751, _534753])], (9619 ^ _206269) ^ [] : [-(ordered_pair(9616 ^ [_534751, _534753], 9617 ^ [_534751, _534753]) = 9603 ^ [_534751, _534753])], (9621 ^ _206269) ^ [] : [-(in(9616 ^ [_534751, _534753], _534753))], (9623 ^ _206269) ^ [] : [-(9617 ^ [_534751, _534753] = singleton(9616 ^ [_534751, _534753]))], (9625 ^ _206269) ^ [] : [9602 ^ [_534751, _534753] = 9603 ^ [_534751, _534753]]], 9627 ^ _206269 : [(9628 ^ _206269) ^ [_536624] : [in(_536624, 9626 ^ [_534751, _534753]), 9632 ^ _206269 : [(9633 ^ _206269) ^ [] : [-(in(9631 ^ [_534751, _534753, _536624], cartesian_product2(_534753, _534751)))], (9635 ^ _206269) ^ [] : [-(9631 ^ [_534751, _534753, _536624] = _536624)], (9639 ^ _206269) ^ [] : [-(ordered_pair(9636 ^ [_534751, _534753, _536624], 9637 ^ [_534751, _534753, _536624]) = _536624)], (9641 ^ _206269) ^ [] : [-(in(9636 ^ [_534751, _534753, _536624], _534753))], (9643 ^ _206269) ^ [] : [-(9637 ^ [_534751, _534753, _536624] = singleton(9636 ^ [_534751, _534753, _536624]))]]], (9645 ^ _206269) ^ [_537464] : [-(in(_537464, 9626 ^ [_534751, _534753])), 9646 ^ _206269 : [(9647 ^ _206269) ^ [_537605] : [in(_537605, cartesian_product2(_534753, _534751)), _537605 = _537464, 9654 ^ _206269 : [(9655 ^ _206269) ^ [_537885, _537887] : [ordered_pair(_537887, _537885) = _537464, in(_537887, _534753), _537885 = singleton(_537887)]]]]]]], (9667 ^ _206269) ^ [_538304] : [ordinal(_538304), 9675 ^ _206269 : [(9740 ^ _206269) ^ [] : [9673 ^ [_538304] = 9674 ^ [_538304]], (9676 ^ _206269) ^ [] : [-(9672 ^ [_538304] = 9673 ^ [_538304])], (9679 ^ _206269) ^ [] : [-(ordinal(9677 ^ [_538304]))], (9681 ^ _206269) ^ [] : [-(9673 ^ [_538304] = 9677 ^ [_538304])], (9683 ^ _206269) ^ [] : [in(9677 ^ [_538304], omega), 9686 ^ _206269 : [(9687 ^ _206269) ^ [_539928] : [element(_539928, powerset(powerset(9677 ^ [_538304]))), -(_539928 = empty_set), 9695 ^ _206269 : [(9696 ^ _206269) ^ [] : [-(in(9694 ^ [_538304, _539928], _539928))], (9698 ^ _206269) ^ [_540337] : [-(_540337 = 9694 ^ [_538304, _539928]), in(_540337, _539928), subset(9694 ^ [_538304, _539928], _540337)]]]]], (9708 ^ _206269) ^ [] : [-(9672 ^ [_538304] = 9674 ^ [_538304])], (9711 ^ _206269) ^ [] : [-(ordinal(9709 ^ [_538304]))], (9713 ^ _206269) ^ [] : [-(9674 ^ [_538304] = 9709 ^ [_538304])], (9715 ^ _206269) ^ [] : [in(9709 ^ [_538304], omega), 9718 ^ _206269 : [(9719 ^ _206269) ^ [_541078] : [element(_541078, powerset(powerset(9709 ^ [_538304]))), -(_541078 = empty_set), 9727 ^ _206269 : [(9728 ^ _206269) ^ [] : [-(in(9726 ^ [_538304, _541078], _541078))], (9730 ^ _206269) ^ [_541487] : [-(_541487 = 9726 ^ [_538304, _541078]), in(_541487, _541078), subset(9726 ^ [_538304, _541078], _541487)]]]]]], 9742 ^ _206269 : [(9743 ^ _206269) ^ [_542056] : [in(_542056, 9741 ^ [_538304]), 9747 ^ _206269 : [(9748 ^ _206269) ^ [] : [-(in(9746 ^ [_538304, _542056], succ(_538304)))], (9750 ^ _206269) ^ [] : [-(9746 ^ [_538304, _542056] = _542056)], (9753 ^ _206269) ^ [] : [-(ordinal(9751 ^ [_538304, _542056]))], (9755 ^ _206269) ^ [] : [-(_542056 = 9751 ^ [_538304, _542056])], (9757 ^ _206269) ^ [] : [in(9751 ^ [_538304, _542056], omega), 9760 ^ _206269 : [(9761 ^ _206269) ^ [_542922] : [element(_542922, powerset(powerset(9751 ^ [_538304, _542056]))), -(_542922 = empty_set), 9769 ^ _206269 : [(9770 ^ _206269) ^ [] : [-(in(9768 ^ [_538304, _542056, _542922], _542922))], (9772 ^ _206269) ^ [_543353] : [-(_543353 = 9768 ^ [_538304, _542056, _542922]), in(_543353, _542922), subset(9768 ^ [_538304, _542056, _542922], _543353)]]]]]]], (9782 ^ _206269) ^ [_543695] : [-(in(_543695, 9741 ^ [_538304])), 9783 ^ _206269 : [(9784 ^ _206269) ^ [_543879] : [in(_543879, succ(_538304)), _543879 = _543695, 9791 ^ _206269 : [(9792 ^ _206269) ^ [_544183] : [ordinal(_544183), _543695 = _544183, 9799 ^ _206269 : [(9800 ^ _206269) ^ [] : [-(in(_544183, omega))], (9803 ^ _206269) ^ [] : [-(element(9801 ^ [_538304, _543695, _543879, _544183], powerset(powerset(_544183))))], (9805 ^ _206269) ^ [] : [9801 ^ [_538304, _543695, _543879, _544183] = empty_set], (9807 ^ _206269) ^ [_544813] : [in(_544813, 9801 ^ [_538304, _543695, _543879, _544183]), 9811 ^ _206269 : [(9812 ^ _206269) ^ [] : [-(in(9810 ^ [_538304, _543695, _543879, _544183, _544813], 9801 ^ [_538304, _543695, _543879, _544183]))], (9814 ^ _206269) ^ [] : [-(subset(_544813, 9810 ^ [_538304, _543695, _543879, _544183, _544813]))], (9816 ^ _206269) ^ [] : [9810 ^ [_538304, _543695, _543879, _544183, _544813] = _544813]]]]]]]]]]], (9820 ^ _206269) ^ [_545471, _545473] : [topological_space(_545473), top_str(_545473), element(_545471, powerset(the_carrier(_545473))), 9836 ^ _206269 : [(9837 ^ _206269) ^ [] : [-(9833 ^ [_545471, _545473] = 9834 ^ [_545471, _545473])], (9840 ^ _206269) ^ [] : [-(element(9838 ^ [_545471, _545473], powerset(the_carrier(_545473))))], (9842 ^ _206269) ^ [] : [-(9838 ^ [_545471, _545473] = 9834 ^ [_545471, _545473])], (9844 ^ _206269) ^ [] : [-(closed_subset(9838 ^ [_545471, _545473], _545473))], (9846 ^ _206269) ^ [] : [-(subset(_545471, 9834 ^ [_545471, _545473]))], (9848 ^ _206269) ^ [] : [-(9833 ^ [_545471, _545473] = 9835 ^ [_545471, _545473])], (9851 ^ _206269) ^ [] : [-(element(9849 ^ [_545471, _545473], powerset(the_carrier(_545473))))], (9853 ^ _206269) ^ [] : [-(9849 ^ [_545471, _545473] = 9835 ^ [_545471, _545473])], (9855 ^ _206269) ^ [] : [-(closed_subset(9849 ^ [_545471, _545473], _545473))], (9857 ^ _206269) ^ [] : [-(subset(_545471, 9835 ^ [_545471, _545473]))], (9859 ^ _206269) ^ [] : [9834 ^ [_545471, _545473] = 9835 ^ [_545471, _545473]]], 9861 ^ _206269 : [(9862 ^ _206269) ^ [_547580] : [in(_547580, 9860 ^ [_545471, _545473]), 9866 ^ _206269 : [(9867 ^ _206269) ^ [] : [-(in(9865 ^ [_545471, _545473, _547580], powerset(the_carrier(_545473))))], (9869 ^ _206269) ^ [] : [-(9865 ^ [_545471, _545473, _547580] = _547580)], (9872 ^ _206269) ^ [] : [-(element(9870 ^ [_545471, _545473, _547580], powerset(the_carrier(_545473))))], (9874 ^ _206269) ^ [] : [-(9870 ^ [_545471, _545473, _547580] = _547580)], (9876 ^ _206269) ^ [] : [-(closed_subset(9870 ^ [_545471, _545473, _547580], _545473))], (9878 ^ _206269) ^ [] : [-(subset(_545471, _547580))]]], (9880 ^ _206269) ^ [_548381] : [-(in(_548381, 9860 ^ [_545471, _545473])), 9881 ^ _206269 : [(9882 ^ _206269) ^ [_548523] : [in(_548523, powerset(the_carrier(_545473))), _548523 = _548381, 9889 ^ _206269 : [(9890 ^ _206269) ^ [_548791] : [element(_548791, powerset(the_carrier(_545473))), _548791 = _548381, closed_subset(_548791, _545473), subset(_545471, _548381)]]]]]]], (9906 ^ _206269) ^ [_549321, _549323] : [topological_space(_549323), top_str(_549323), element(_549321, powerset(powerset(the_carrier(_549323)))), 9922 ^ _206269 : [(9923 ^ _206269) ^ [] : [-(9919 ^ [_549321, _549323] = 9920 ^ [_549321, _549323])], (9925 ^ _206269) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_549323), 9920 ^ [_549321, _549323]), _549321))], (9927 ^ _206269) ^ [] : [-(9919 ^ [_549321, _549323] = 9921 ^ [_549321, _549323])], (9929 ^ _206269) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_549323), 9921 ^ [_549321, _549323]), _549321))], (9931 ^ _206269) ^ [] : [9920 ^ [_549321, _549323] = 9921 ^ [_549321, _549323]]], 9933 ^ _206269 : [(9934 ^ _206269) ^ [_550565] : [in(_550565, 9932 ^ [_549321, _549323]), 9938 ^ _206269 : [(9939 ^ _206269) ^ [] : [-(in(9937 ^ [_549321, _549323, _550565], powerset(the_carrier(_549323))))], (9941 ^ _206269) ^ [] : [-(9937 ^ [_549321, _549323, _550565] = _550565)], (9943 ^ _206269) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_549323), _550565), _549321))]]], (9945 ^ _206269) ^ [_551015] : [-(in(_551015, 9932 ^ [_549321, _549323])), 9946 ^ _206269 : [(9947 ^ _206269) ^ [_551135] : [in(_551135, powerset(the_carrier(_549323))), _551135 = _551015, in(set_difference(cast_as_carrier_subset(_549323), _551015), _549321)]]]]], (9959 ^ _206269) ^ [_551553, _551555] : [ordinal(_551555), element(_551553, powerset(powerset(succ(_551555)))), 9971 ^ _206269 : [(9972 ^ _206269) ^ [] : [-(9968 ^ [_551553, _551555] = 9969 ^ [_551553, _551555])], (9975 ^ _206269) ^ [] : [-(in(9973 ^ [_551553, _551555], _551553))], (9977 ^ _206269) ^ [] : [-(9969 ^ [_551553, _551555] = set_difference(9973 ^ [_551553, _551555], singleton(_551555)))], (9979 ^ _206269) ^ [] : [-(9968 ^ [_551553, _551555] = 9970 ^ [_551553, _551555])], (9982 ^ _206269) ^ [] : [-(in(9980 ^ [_551553, _551555], _551553))], (9984 ^ _206269) ^ [] : [-(9970 ^ [_551553, _551555] = set_difference(9980 ^ [_551553, _551555], singleton(_551555)))], (9986 ^ _206269) ^ [] : [9969 ^ [_551553, _551555] = 9970 ^ [_551553, _551555]]], 9988 ^ _206269 : [(9989 ^ _206269) ^ [_553112] : [in(_553112, 9987 ^ [_551553, _551555]), 9993 ^ _206269 : [(9994 ^ _206269) ^ [] : [-(in(9992 ^ [_551553, _551555, _553112], powerset(_551555)))], (9996 ^ _206269) ^ [] : [-(9992 ^ [_551553, _551555, _553112] = _553112)], (9999 ^ _206269) ^ [] : [-(in(9997 ^ [_551553, _551555, _553112], _551553))], (10001 ^ _206269) ^ [] : [-(_553112 = set_difference(9997 ^ [_551553, _551555, _553112], singleton(_551555)))]]], (10003 ^ _206269) ^ [_553726] : [-(in(_553726, 9987 ^ [_551553, _551555])), 10004 ^ _206269 : [(10005 ^ _206269) ^ [_553855] : [in(_553855, powerset(_551555)), _553855 = _553726, 10012 ^ _206269 : [(10013 ^ _206269) ^ [_554108] : [in(_554108, _551553), _553726 = set_difference(_554108, singleton(_551555))]]]]]]], (10021 ^ _206269) ^ [_554436, _554438] : [one_sorted_str(_554438), element(_554436, powerset(powerset(the_carrier(_554438)))), 10033 ^ _206269 : [(10058 ^ _206269) ^ [] : [10031 ^ [_554436, _554438] = 10032 ^ [_554436, _554438]], (10034 ^ _206269) ^ [] : [-(in(10030 ^ [_554436, _554438], complements_of_subsets(the_carrier(_554438), _554436)))], (10036 ^ _206269) ^ [_555467] : [element(_555467, powerset(the_carrier(_554438))), _555467 = 10030 ^ [_554436, _554438], -(10031 ^ [_554436, _554438] = subset_complement(the_carrier(_554438), _555467))], (10046 ^ _206269) ^ [] : [-(in(10030 ^ [_554436, _554438], complements_of_subsets(the_carrier(_554438), _554436)))], (10048 ^ _206269) ^ [_555870] : [element(_555870, powerset(the_carrier(_554438))), _555870 = 10030 ^ [_554436, _554438], -(10032 ^ [_554436, _554438] = subset_complement(the_carrier(_554438), _555870))]], 10060 ^ _206269 : [(10061 ^ _206269) ^ [_556400] : [in(_556400, 10059 ^ [_554436, _554438]), 10065 ^ _206269 : [(10066 ^ _206269) ^ [] : [-(in(10064 ^ [_554436, _554438, _556400], complements_of_subsets(the_carrier(_554438), _554436)))], (10068 ^ _206269) ^ [] : [-(in(10064 ^ [_554436, _554438, _556400], complements_of_subsets(the_carrier(_554438), _554436)))], (10070 ^ _206269) ^ [_556862] : [element(_556862, powerset(the_carrier(_554438))), _556862 = 10064 ^ [_554436, _554438, _556400], -(_556400 = subset_complement(the_carrier(_554438), _556862))]]], (10080 ^ _206269) ^ [_557184] : [-(in(_557184, 10059 ^ [_554436, _554438])), 10081 ^ _206269 : [(10082 ^ _206269) ^ [_557331] : [in(_557331, complements_of_subsets(the_carrier(_554438), _554436)), in(_557331, complements_of_subsets(the_carrier(_554438), _554436)), 10090 ^ _206269 : [(10091 ^ _206269) ^ [] : [-(element(10089 ^ [_554436, _554438, _557184, _557331], powerset(the_carrier(_554438))))], (10093 ^ _206269) ^ [] : [-(10089 ^ [_554436, _554438, _557184, _557331] = _557331)], (10095 ^ _206269) ^ [] : [_557184 = subset_complement(the_carrier(_554438), 10089 ^ [_554436, _554438, _557184, _557331])]]]]]]], (10099 ^ _206269) ^ [_558036, _558038] : [one_sorted_str(_558038), element(_558036, powerset(powerset(the_carrier(_558038)))), 10106 ^ _206269 : [(10107 ^ _206269) ^ [_558520] : [10111 ^ _206269 : [(10148 ^ _206269) ^ [] : [10109 ^ [_558036, _558038, _558520] = 10110 ^ [_558036, _558038, _558520]], (10112 ^ _206269) ^ [] : [-(10108 ^ [_558036, _558038, _558520] = 10109 ^ [_558036, _558038, _558520])], (10116 ^ _206269) ^ [] : [-(ordered_pair(10113 ^ [_558036, _558038, _558520], 10114 ^ [_558036, _558038, _558520]) = 10109 ^ [_558036, _558038, _558520])], (10118 ^ _206269) ^ [] : [-(in(10113 ^ [_558036, _558038, _558520], complements_of_subsets(the_carrier(_558038), _558036)))], (10120 ^ _206269) ^ [_560034] : [element(_560034, powerset(the_carrier(_558038))), _560034 = 10113 ^ [_558036, _558038, _558520], -(10114 ^ [_558036, _558038, _558520] = subset_complement(the_carrier(_558038), _560034))], (10130 ^ _206269) ^ [] : [-(10108 ^ [_558036, _558038, _558520] = 10110 ^ [_558036, _558038, _558520])], (10134 ^ _206269) ^ [] : [-(ordered_pair(10131 ^ [_558036, _558038, _558520], 10132 ^ [_558036, _558038, _558520]) = 10110 ^ [_558036, _558038, _558520])], (10136 ^ _206269) ^ [] : [-(in(10131 ^ [_558036, _558038, _558520], complements_of_subsets(the_carrier(_558038), _558036)))], (10138 ^ _206269) ^ [_560889] : [element(_560889, powerset(the_carrier(_558038))), _560889 = 10131 ^ [_558036, _558038, _558520], -(10132 ^ [_558036, _558038, _558520] = subset_complement(the_carrier(_558038), _560889))]], 10150 ^ _206269 : [(10151 ^ _206269) ^ [_561485] : [in(_561485, 10149 ^ [_558036, _558038, _558520]), 10155 ^ _206269 : [(10156 ^ _206269) ^ [] : [-(in(10154 ^ [_558036, _558038, _558520, _561485], cartesian_product2(complements_of_subsets(the_carrier(_558038), _558036), _558520)))], (10158 ^ _206269) ^ [] : [-(10154 ^ [_558036, _558038, _558520, _561485] = _561485)], (10162 ^ _206269) ^ [] : [-(ordered_pair(10159 ^ [_558036, _558038, _558520, _561485], 10160 ^ [_558036, _558038, _558520, _561485]) = _561485)], (10164 ^ _206269) ^ [] : [-(in(10159 ^ [_558036, _558038, _558520, _561485], complements_of_subsets(the_carrier(_558038), _558036)))], (10166 ^ _206269) ^ [_562440] : [element(_562440, powerset(the_carrier(_558038))), _562440 = 10159 ^ [_558036, _558038, _558520, _561485], -(10160 ^ [_558036, _558038, _558520, _561485] = subset_complement(the_carrier(_558038), _562440))]]], (10176 ^ _206269) ^ [_562804] : [-(in(_562804, 10149 ^ [_558036, _558038, _558520])), 10177 ^ _206269 : [(10178 ^ _206269) ^ [_562985] : [in(_562985, cartesian_product2(complements_of_subsets(the_carrier(_558038), _558036), _558520)), _562985 = _562804, 10185 ^ _206269 : [(10186 ^ _206269) ^ [_563314, _563316] : [ordered_pair(_563316, _563314) = _562804, in(_563316, complements_of_subsets(the_carrier(_558038), _558036)), 10194 ^ _206269 : [(10195 ^ _206269) ^ [] : [-(element(10193 ^ [_558036, _558038, _558520, _562804, _562985, _563314, _563316], powerset(the_carrier(_558038))))], (10197 ^ _206269) ^ [] : [-(10193 ^ [_558036, _558038, _558520, _562804, _562985, _563314, _563316] = _563316)], (10199 ^ _206269) ^ [] : [_563314 = subset_complement(the_carrier(_558038), 10193 ^ [_558036, _558038, _558520, _562804, _562985, _563314, _563316])]]]]]]]]]]], (10203 ^ _206269) ^ [_564105, _564107] : [one_sorted_str(_564107), element(_564105, powerset(powerset(the_carrier(_564107)))), 10215 ^ _206269 : [(10240 ^ _206269) ^ [] : [10213 ^ [_564105, _564107] = 10214 ^ [_564105, _564107]], (10216 ^ _206269) ^ [] : [-(in(10212 ^ [_564105, _564107], _564105))], (10218 ^ _206269) ^ [_565081] : [element(_565081, powerset(the_carrier(_564107))), _565081 = 10212 ^ [_564105, _564107], -(10213 ^ [_564105, _564107] = subset_complement(the_carrier(_564107), _565081))], (10228 ^ _206269) ^ [] : [-(in(10212 ^ [_564105, _564107], _564105))], (10230 ^ _206269) ^ [_565479] : [element(_565479, powerset(the_carrier(_564107))), _565479 = 10212 ^ [_564105, _564107], -(10214 ^ [_564105, _564107] = subset_complement(the_carrier(_564107), _565479))]], 10242 ^ _206269 : [(10243 ^ _206269) ^ [_565999] : [in(_565999, 10241 ^ [_564105, _564107]), 10247 ^ _206269 : [(10248 ^ _206269) ^ [] : [-(in(10246 ^ [_564105, _564107, _565999], _564105))], (10250 ^ _206269) ^ [] : [-(in(10246 ^ [_564105, _564107, _565999], _564105))], (10252 ^ _206269) ^ [_566431] : [element(_566431, powerset(the_carrier(_564107))), _566431 = 10246 ^ [_564105, _564107, _565999], -(_565999 = subset_complement(the_carrier(_564107), _566431))]]], (10262 ^ _206269) ^ [_566753] : [-(in(_566753, 10241 ^ [_564105, _564107])), 10263 ^ _206269 : [(10264 ^ _206269) ^ [_566890] : [in(_566890, _564105), in(_566890, _564105), 10272 ^ _206269 : [(10273 ^ _206269) ^ [] : [-(element(10271 ^ [_564105, _564107, _566753, _566890], powerset(the_carrier(_564107))))], (10275 ^ _206269) ^ [] : [-(10271 ^ [_564105, _564107, _566753, _566890] = _566890)], (10277 ^ _206269) ^ [] : [_566753 = subset_complement(the_carrier(_564107), 10271 ^ [_564105, _564107, _566753, _566890])]]]]]]], (10281 ^ _206269) ^ [_567575, _567577] : [one_sorted_str(_567577), element(_567575, powerset(powerset(the_carrier(_567577)))), 10288 ^ _206269 : [(10289 ^ _206269) ^ [_568039] : [10293 ^ _206269 : [(10330 ^ _206269) ^ [] : [10291 ^ [_567575, _567577, _568039] = 10292 ^ [_567575, _567577, _568039]], (10294 ^ _206269) ^ [] : [-(10290 ^ [_567575, _567577, _568039] = 10291 ^ [_567575, _567577, _568039])], (10298 ^ _206269) ^ [] : [-(ordered_pair(10295 ^ [_567575, _567577, _568039], 10296 ^ [_567575, _567577, _568039]) = 10291 ^ [_567575, _567577, _568039])], (10300 ^ _206269) ^ [] : [-(in(10295 ^ [_567575, _567577, _568039], _567575))], (10302 ^ _206269) ^ [_569488] : [element(_569488, powerset(the_carrier(_567577))), _569488 = 10295 ^ [_567575, _567577, _568039], -(10296 ^ [_567575, _567577, _568039] = subset_complement(the_carrier(_567577), _569488))], (10312 ^ _206269) ^ [] : [-(10290 ^ [_567575, _567577, _568039] = 10292 ^ [_567575, _567577, _568039])], (10316 ^ _206269) ^ [] : [-(ordered_pair(10313 ^ [_567575, _567577, _568039], 10314 ^ [_567575, _567577, _568039]) = 10292 ^ [_567575, _567577, _568039])], (10318 ^ _206269) ^ [] : [-(in(10313 ^ [_567575, _567577, _568039], _567575))], (10320 ^ _206269) ^ [_570328] : [element(_570328, powerset(the_carrier(_567577))), _570328 = 10313 ^ [_567575, _567577, _568039], -(10314 ^ [_567575, _567577, _568039] = subset_complement(the_carrier(_567577), _570328))]], 10332 ^ _206269 : [(10333 ^ _206269) ^ [_570914] : [in(_570914, 10331 ^ [_567575, _567577, _568039]), 10337 ^ _206269 : [(10338 ^ _206269) ^ [] : [-(in(10336 ^ [_567575, _567577, _568039, _570914], cartesian_product2(_567575, _568039)))], (10340 ^ _206269) ^ [] : [-(10336 ^ [_567575, _567577, _568039, _570914] = _570914)], (10344 ^ _206269) ^ [] : [-(ordered_pair(10341 ^ [_567575, _567577, _568039, _570914], 10342 ^ [_567575, _567577, _568039, _570914]) = _570914)], (10346 ^ _206269) ^ [] : [-(in(10341 ^ [_567575, _567577, _568039, _570914], _567575))], (10348 ^ _206269) ^ [_571829] : [element(_571829, powerset(the_carrier(_567577))), _571829 = 10341 ^ [_567575, _567577, _568039, _570914], -(10342 ^ [_567575, _567577, _568039, _570914] = subset_complement(the_carrier(_567577), _571829))]]], (10358 ^ _206269) ^ [_572193] : [-(in(_572193, 10331 ^ [_567575, _567577, _568039])), 10359 ^ _206269 : [(10360 ^ _206269) ^ [_572364] : [in(_572364, cartesian_product2(_567575, _568039)), _572364 = _572193, 10367 ^ _206269 : [(10368 ^ _206269) ^ [_572678, _572680] : [ordered_pair(_572680, _572678) = _572193, in(_572680, _567575), 10376 ^ _206269 : [(10377 ^ _206269) ^ [] : [-(element(10375 ^ [_567575, _567577, _568039, _572193, _572364, _572678, _572680], powerset(the_carrier(_567577))))], (10379 ^ _206269) ^ [] : [-(10375 ^ [_567575, _567577, _568039, _572193, _572364, _572678, _572680] = _572680)], (10381 ^ _206269) ^ [] : [_572678 = subset_complement(the_carrier(_567577), 10375 ^ [_567575, _567577, _568039, _572193, _572364, _572678, _572680])]]]]]]]]]]], (10385 ^ _206269) ^ [_573473, _573475, _573477] : [relation(_573475), relation(_573473), function(_573473), 10401 ^ _206269 : [(10402 ^ _206269) ^ [] : [-(10398 ^ [_573473, _573475, _573477] = 10399 ^ [_573473, _573475, _573477])], (10406 ^ _206269) ^ [] : [-(10399 ^ [_573473, _573475, _573477] = ordered_pair(10403 ^ [_573473, _573475, _573477], 10404 ^ [_573473, _573475, _573477]))], (10408 ^ _206269) ^ [] : [-(in(ordered_pair(apply(_573473, 10403 ^ [_573473, _573475, _573477]), apply(_573473, 10404 ^ [_573473, _573475, _573477])), _573475))], (10410 ^ _206269) ^ [] : [-(10398 ^ [_573473, _573475, _573477] = 10400 ^ [_573473, _573475, _573477])], (10414 ^ _206269) ^ [] : [-(10400 ^ [_573473, _573475, _573477] = ordered_pair(10411 ^ [_573473, _573475, _573477], 10412 ^ [_573473, _573475, _573477]))], (10416 ^ _206269) ^ [] : [-(in(ordered_pair(apply(_573473, 10411 ^ [_573473, _573475, _573477]), apply(_573473, 10412 ^ [_573473, _573475, _573477])), _573475))], (10418 ^ _206269) ^ [] : [10399 ^ [_573473, _573475, _573477] = 10400 ^ [_573473, _573475, _573477]]], 10420 ^ _206269 : [(10421 ^ _206269) ^ [_575583] : [in(_575583, 10419 ^ [_573473, _573475, _573477]), 10425 ^ _206269 : [(10426 ^ _206269) ^ [] : [-(in(10424 ^ [_573473, _573475, _573477, _575583], cartesian_product2(_573477, _573477)))], (10428 ^ _206269) ^ [] : [-(10424 ^ [_573473, _573475, _573477, _575583] = _575583)], (10432 ^ _206269) ^ [] : [-(_575583 = ordered_pair(10429 ^ [_573473, _573475, _573477, _575583], 10430 ^ [_573473, _573475, _573477, _575583]))], (10434 ^ _206269) ^ [] : [-(in(ordered_pair(apply(_573473, 10429 ^ [_573473, _573475, _573477, _575583]), apply(_573473, 10430 ^ [_573473, _573475, _573477, _575583])), _573475))]]], (10436 ^ _206269) ^ [_576392] : [-(in(_576392, 10419 ^ [_573473, _573475, _573477])), 10437 ^ _206269 : [(10438 ^ _206269) ^ [_576540] : [in(_576540, cartesian_product2(_573477, _573477)), _576540 = _576392, 10445 ^ _206269 : [(10446 ^ _206269) ^ [_576831, _576833] : [_576392 = ordered_pair(_576833, _576831), in(ordered_pair(apply(_573473, _576833), apply(_573473, _576831)), _573475)]]]]]]], (10454 ^ _206269) ^ [_577179] : [10458 ^ _206269 : [(10459 ^ _206269) ^ [] : [-(10455 ^ [_577179] = 10456 ^ [_577179])], (10461 ^ _206269) ^ [] : [-(ordinal(10456 ^ [_577179]))], (10463 ^ _206269) ^ [] : [-(10455 ^ [_577179] = 10457 ^ [_577179])], (10465 ^ _206269) ^ [] : [-(ordinal(10457 ^ [_577179]))], (10467 ^ _206269) ^ [] : [10456 ^ [_577179] = 10457 ^ [_577179]]], 10469 ^ _206269 : [(10470 ^ _206269) ^ [_578014] : [in(_578014, 10468 ^ [_577179]), 10474 ^ _206269 : [(10475 ^ _206269) ^ [] : [-(in(10473 ^ [_577179, _578014], _577179))], (10477 ^ _206269) ^ [] : [-(10473 ^ [_577179, _578014] = _578014)], (10479 ^ _206269) ^ [] : [-(ordinal(_578014))]]], (10481 ^ _206269) ^ [_578410] : [-(in(_578410, 10468 ^ [_577179])), 10482 ^ _206269 : [(10483 ^ _206269) ^ [_578514] : [in(_578514, _577179), _578514 = _578410, ordinal(_578410)]]]]], (10495 ^ _206269) ^ [_578902, _578904, _578906] : [element(_578904, powerset(powerset(_578906))), relation(_578902), function(_578902), 10511 ^ _206269 : [(10512 ^ _206269) ^ [] : [-(10508 ^ [_578902, _578904, _578906] = 10509 ^ [_578902, _578904, _578906])], (10514 ^ _206269) ^ [] : [-(in(relation_image(_578902, 10509 ^ [_578902, _578904, _578906]), _578904))], (10516 ^ _206269) ^ [] : [-(10508 ^ [_578902, _578904, _578906] = 10510 ^ [_578902, _578904, _578906])], (10518 ^ _206269) ^ [] : [-(in(relation_image(_578902, 10510 ^ [_578902, _578904, _578906]), _578904))], (10520 ^ _206269) ^ [] : [10509 ^ [_578902, _578904, _578906] = 10510 ^ [_578902, _578904, _578906]]], 10522 ^ _206269 : [(10523 ^ _206269) ^ [_580188] : [in(_580188, 10521 ^ [_578902, _578904, _578906]), 10527 ^ _206269 : [(10528 ^ _206269) ^ [] : [-(in(10526 ^ [_578902, _578904, _578906, _580188], powerset(relation_dom(_578902))))], (10530 ^ _206269) ^ [] : [-(10526 ^ [_578902, _578904, _578906, _580188] = _580188)], (10532 ^ _206269) ^ [] : [-(in(relation_image(_578902, _580188), _578904))]]], (10534 ^ _206269) ^ [_580656] : [-(in(_580656, 10521 ^ [_578902, _578904, _578906])), 10535 ^ _206269 : [(10536 ^ _206269) ^ [_580780] : [in(_580780, powerset(relation_dom(_578902))), _580780 = _580656, in(relation_image(_578902, _580656), _578904)]]]]], (10548 ^ _206269) ^ [_581210, _581212] : [ordinal(_581210), 10556 ^ _206269 : [(10557 ^ _206269) ^ [] : [-(10553 ^ [_581210, _581212] = 10554 ^ [_581210, _581212])], (10560 ^ _206269) ^ [] : [-(ordinal(10558 ^ [_581210, _581212]))], (10562 ^ _206269) ^ [] : [-(10554 ^ [_581210, _581212] = 10558 ^ [_581210, _581212])], (10564 ^ _206269) ^ [] : [-(in(10558 ^ [_581210, _581212], _581212))], (10566 ^ _206269) ^ [] : [-(10553 ^ [_581210, _581212] = 10555 ^ [_581210, _581212])], (10569 ^ _206269) ^ [] : [-(ordinal(10567 ^ [_581210, _581212]))], (10571 ^ _206269) ^ [] : [-(10555 ^ [_581210, _581212] = 10567 ^ [_581210, _581212])], (10573 ^ _206269) ^ [] : [-(in(10567 ^ [_581210, _581212], _581212))], (10575 ^ _206269) ^ [] : [10554 ^ [_581210, _581212] = 10555 ^ [_581210, _581212]]], 10577 ^ _206269 : [(10578 ^ _206269) ^ [_582812] : [in(_582812, 10576 ^ [_581210, _581212]), 10582 ^ _206269 : [(10583 ^ _206269) ^ [] : [-(in(10581 ^ [_581210, _581212, _582812], succ(_581210)))], (10585 ^ _206269) ^ [] : [-(10581 ^ [_581210, _581212, _582812] = _582812)], (10588 ^ _206269) ^ [] : [-(ordinal(10586 ^ [_581210, _581212, _582812]))], (10590 ^ _206269) ^ [] : [-(_582812 = 10586 ^ [_581210, _581212, _582812])], (10592 ^ _206269) ^ [] : [-(in(10586 ^ [_581210, _581212, _582812], _581212))]]], (10594 ^ _206269) ^ [_583499] : [-(in(_583499, 10576 ^ [_581210, _581212])), 10595 ^ _206269 : [(10596 ^ _206269) ^ [_583628] : [in(_583628, succ(_581210)), _583628 = _583499, 10603 ^ _206269 : [(10604 ^ _206269) ^ [_583881] : [ordinal(_583881), _583499 = _583881, in(_583881, _581212)]]]]]]], (10616 ^ _206269) ^ [_584296, _584298] : [-(empty(_584298)), relation(_584296), 10624 ^ _206269 : [(10625 ^ _206269) ^ [_584762, _584764] : [in(_584762, 10623 ^ [_584296, _584298, _584764]), 10628 ^ _206269 : [(10629 ^ _206269) ^ [] : [-(in(_584762, cartesian_product2(_584298, _584764)))], (10633 ^ _206269) ^ [] : [-(ordered_pair(10630 ^ [_584296, _584298, _584762, _584764], 10631 ^ [_584296, _584298, _584762, _584764]) = _584762)], (10635 ^ _206269) ^ [] : [-(in(10630 ^ [_584296, _584298, _584762, _584764], _584298))], (10638 ^ _206269) ^ [] : [-(10630 ^ [_584296, _584298, _584762, _584764] = 10636 ^ [_584296, _584298, _584762, _584764])], (10640 ^ _206269) ^ [] : [-(in(10631 ^ [_584296, _584298, _584762, _584764], 10636 ^ [_584296, _584298, _584762, _584764]))], (10642 ^ _206269) ^ [_585764] : [in(_585764, 10636 ^ [_584296, _584298, _584762, _584764]), -(in(ordered_pair(10631 ^ [_584296, _584298, _584762, _584764], _585764), _584296))]]], (10648 ^ _206269) ^ [_586017, _586019] : [-(in(_586017, 10623 ^ [_584296, _584298, _586019])), in(_586017, cartesian_product2(_584298, _586019)), 10653 ^ _206269 : [(10654 ^ _206269) ^ [_586284, _586286] : [ordered_pair(_586286, _586284) = _586017, in(_586286, _584298), 10661 ^ _206269 : [(10662 ^ _206269) ^ [_586572] : [_586286 = _586572, in(_586284, _586572), 10670 ^ _206269 : [(10671 ^ _206269) ^ [] : [-(in(10669 ^ [_584296, _584298, _586017, _586019, _586284, _586286, _586572], _586572))], (10673 ^ _206269) ^ [] : [in(ordered_pair(_586284, 10669 ^ [_584296, _584298, _586017, _586019, _586284, _586286, _586572]), _584296)]]]]]]]]], (10678 ^ _206269) ^ [_587353, _587355, _587357] : [in(_587353, 10676 ^ [_587355, _587357]), 10681 ^ _206269 : [(10682 ^ _206269) ^ [] : [-(in(_587353, cartesian_product2(_587357, _587355)))], (10686 ^ _206269) ^ [] : [-(ordered_pair(10683 ^ [_587353, _587355, _587357], 10684 ^ [_587353, _587355, _587357]) = _587353)], (10688 ^ _206269) ^ [] : [-(in(10683 ^ [_587353, _587355, _587357], _587357))], (10690 ^ _206269) ^ [] : [-(10684 ^ [_587353, _587355, _587357] = singleton(10683 ^ [_587353, _587355, _587357]))]]], (10692 ^ _206269) ^ [_587999, _588001, _588003] : [-(in(_587999, 10676 ^ [_588001, _588003])), in(_587999, cartesian_product2(_588003, _588001)), 10697 ^ _206269 : [(10698 ^ _206269) ^ [_588225, _588227] : [ordered_pair(_588227, _588225) = _587999, in(_588227, _588003), _588225 = singleton(_588227)]]], (10710 ^ _206269) ^ [_588621] : [ordinal(_588621), 10714 ^ _206269 : [(10751 ^ _206269) ^ [_590418] : [-(in(_590418, 10713 ^ [_588621])), in(_590418, succ(_588621)), 10756 ^ _206269 : [(10757 ^ _206269) ^ [_590672] : [ordinal(_590672), _590418 = _590672, 10764 ^ _206269 : [(10765 ^ _206269) ^ [] : [-(in(_590672, omega))], (10768 ^ _206269) ^ [] : [-(element(10766 ^ [_588621, _590418, _590672], powerset(powerset(_590672))))], (10770 ^ _206269) ^ [] : [10766 ^ [_588621, _590418, _590672] = empty_set], (10772 ^ _206269) ^ [_591278] : [in(_591278, 10766 ^ [_588621, _590418, _590672]), 10776 ^ _206269 : [(10777 ^ _206269) ^ [] : [-(in(10775 ^ [_588621, _590418, _590672, _591278], 10766 ^ [_588621, _590418, _590672]))], (10779 ^ _206269) ^ [] : [-(subset(_591278, 10775 ^ [_588621, _590418, _590672, _591278]))], (10781 ^ _206269) ^ [] : [10775 ^ [_588621, _590418, _590672, _591278] = _591278]]]]]]], (10715 ^ _206269) ^ [_589008] : [in(_589008, 10713 ^ [_588621]), 10718 ^ _206269 : [(10719 ^ _206269) ^ [] : [-(in(_589008, succ(_588621)))], (10722 ^ _206269) ^ [] : [-(ordinal(10720 ^ [_588621, _589008]))], (10724 ^ _206269) ^ [] : [-(_589008 = 10720 ^ [_588621, _589008])], (10726 ^ _206269) ^ [] : [in(10720 ^ [_588621, _589008], omega), 10729 ^ _206269 : [(10730 ^ _206269) ^ [_589647] : [element(_589647, powerset(powerset(10720 ^ [_588621, _589008]))), -(_589647 = empty_set), 10738 ^ _206269 : [(10739 ^ _206269) ^ [] : [-(in(10737 ^ [_588621, _589008, _589647], _589647))], (10741 ^ _206269) ^ [_590078] : [-(_590078 = 10737 ^ [_588621, _589008, _589647]), in(_590078, _589647), subset(10737 ^ [_588621, _589008, _589647], _590078)]]]]]]]]], (10785 ^ _206269) ^ [_591894, _591896] : [topological_space(_591896), top_str(_591896), element(_591894, powerset(the_carrier(_591896))), 10797 ^ _206269 : [(10798 ^ _206269) ^ [_592377] : [in(_592377, 10796 ^ [_591894, _591896]), 10801 ^ _206269 : [(10802 ^ _206269) ^ [] : [-(in(_592377, powerset(the_carrier(_591896))))], (10805 ^ _206269) ^ [] : [-(element(10803 ^ [_591894, _591896, _592377], powerset(the_carrier(_591896))))], (10807 ^ _206269) ^ [] : [-(10803 ^ [_591894, _591896, _592377] = _592377)], (10809 ^ _206269) ^ [] : [-(closed_subset(10803 ^ [_591894, _591896, _592377], _591896))], (10811 ^ _206269) ^ [] : [-(subset(_591894, _592377))]]], (10813 ^ _206269) ^ [_592987] : [-(in(_592987, 10796 ^ [_591894, _591896])), in(_592987, powerset(the_carrier(_591896))), 10818 ^ _206269 : [(10819 ^ _206269) ^ [_593205] : [element(_593205, powerset(the_carrier(_591896))), _593205 = _592987, closed_subset(_593205, _591896), subset(_591894, _592987)]]]]], (10835 ^ _206269) ^ [_593709, _593711] : [topological_space(_593711), top_str(_593711), element(_593709, powerset(powerset(the_carrier(_593711)))), 10847 ^ _206269 : [(10848 ^ _206269) ^ [_594152] : [in(_594152, 10846 ^ [_593709, _593711]), 10851 ^ _206269 : [(10852 ^ _206269) ^ [] : [-(in(_594152, powerset(the_carrier(_593711))))], (10854 ^ _206269) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_593711), _594152), _593709))]]], (10856 ^ _206269) ^ [_594433] : [-(in(_594433, 10846 ^ [_593709, _593711])), in(_594433, powerset(the_carrier(_593711))), in(set_difference(cast_as_carrier_subset(_593711), _594433), _593709)]]], (10866 ^ _206269) ^ [_594789, _594791] : [ordinal(_594791), element(_594789, powerset(powerset(succ(_594791)))), 10874 ^ _206269 : [(10875 ^ _206269) ^ [_595163] : [in(_595163, 10873 ^ [_594789, _594791]), 10878 ^ _206269 : [(10879 ^ _206269) ^ [] : [-(in(_595163, powerset(_594791)))], (10882 ^ _206269) ^ [] : [-(in(10880 ^ [_594789, _594791, _595163], _594789))], (10884 ^ _206269) ^ [] : [-(_595163 = set_difference(10880 ^ [_594789, _594791, _595163], singleton(_594791)))]]], (10886 ^ _206269) ^ [_595599] : [-(in(_595599, 10873 ^ [_594789, _594791])), in(_595599, powerset(_594791)), 10891 ^ _206269 : [(10892 ^ _206269) ^ [_595802] : [in(_595802, _594789), _595599 = set_difference(_595802, singleton(_594791))]]]]], (10900 ^ _206269) ^ [_596112, _596114] : [one_sorted_str(_596114), element(_596112, powerset(powerset(the_carrier(_596114)))), 10908 ^ _206269 : [(10909 ^ _206269) ^ [_596599, _596601] : [in(_596599, 10907 ^ [_596112, _596114, _596601]), 10912 ^ _206269 : [(10913 ^ _206269) ^ [] : [-(in(_596599, cartesian_product2(complements_of_subsets(the_carrier(_596114), _596112), _596601)))], (10917 ^ _206269) ^ [] : [-(ordered_pair(10914 ^ [_596112, _596114, _596599, _596601], 10915 ^ [_596112, _596114, _596599, _596601]) = _596599)], (10919 ^ _206269) ^ [] : [-(in(10914 ^ [_596112, _596114, _596599, _596601], complements_of_subsets(the_carrier(_596114), _596112)))], (10921 ^ _206269) ^ [_597320] : [element(_597320, powerset(the_carrier(_596114))), _597320 = 10914 ^ [_596112, _596114, _596599, _596601], -(10915 ^ [_596112, _596114, _596599, _596601] = subset_complement(the_carrier(_596114), _597320))]]], (10931 ^ _206269) ^ [_597682, _597684] : [-(in(_597682, 10907 ^ [_596112, _596114, _597684])), in(_597682, cartesian_product2(complements_of_subsets(the_carrier(_596114), _596112), _597684)), 10936 ^ _206269 : [(10937 ^ _206269) ^ [_597959, _597961] : [ordered_pair(_597961, _597959) = _597682, in(_597961, complements_of_subsets(the_carrier(_596114), _596112)), 10945 ^ _206269 : [(10946 ^ _206269) ^ [] : [-(element(10944 ^ [_596112, _596114, _597682, _597684, _597959, _597961], powerset(the_carrier(_596114))))], (10948 ^ _206269) ^ [] : [-(10944 ^ [_596112, _596114, _597682, _597684, _597959, _597961] = _597961)], (10950 ^ _206269) ^ [] : [_597959 = subset_complement(the_carrier(_596114), 10944 ^ [_596112, _596114, _597682, _597684, _597959, _597961])]]]]]]], (10954 ^ _206269) ^ [_598713, _598715] : [one_sorted_str(_598715), element(_598713, powerset(powerset(the_carrier(_598715)))), 10962 ^ _206269 : [(10963 ^ _206269) ^ [_599180, _599182] : [in(_599180, 10961 ^ [_598713, _598715, _599182]), 10966 ^ _206269 : [(10967 ^ _206269) ^ [] : [-(in(_599180, cartesian_product2(_598713, _599182)))], (10971 ^ _206269) ^ [] : [-(ordered_pair(10968 ^ [_598713, _598715, _599180, _599182], 10969 ^ [_598713, _598715, _599180, _599182]) = _599180)], (10973 ^ _206269) ^ [] : [-(in(10968 ^ [_598713, _598715, _599180, _599182], _598713))], (10975 ^ _206269) ^ [_599871] : [element(_599871, powerset(the_carrier(_598715))), _599871 = 10968 ^ [_598713, _598715, _599180, _599182], -(10969 ^ [_598713, _598715, _599180, _599182] = subset_complement(the_carrier(_598715), _599871))]]], (10985 ^ _206269) ^ [_600233, _600235] : [-(in(_600233, 10961 ^ [_598713, _598715, _600235])), in(_600233, cartesian_product2(_598713, _600235)), 10990 ^ _206269 : [(10991 ^ _206269) ^ [_600495, _600497] : [ordered_pair(_600497, _600495) = _600233, in(_600497, _598713), 10999 ^ _206269 : [(11000 ^ _206269) ^ [] : [-(element(10998 ^ [_598713, _598715, _600233, _600235, _600495, _600497], powerset(the_carrier(_598715))))], (11002 ^ _206269) ^ [] : [-(10998 ^ [_598713, _598715, _600233, _600235, _600495, _600497] = _600497)], (11004 ^ _206269) ^ [] : [_600495 = subset_complement(the_carrier(_598715), 10998 ^ [_598713, _598715, _600233, _600235, _600495, _600497])]]]]]]], (11008 ^ _206269) ^ [_601253, _601255, _601257] : [relation(_601255), relation(_601253), function(_601253), 11020 ^ _206269 : [(11021 ^ _206269) ^ [_601742] : [in(_601742, 11019 ^ [_601253, _601255, _601257]), 11024 ^ _206269 : [(11025 ^ _206269) ^ [] : [-(in(_601742, cartesian_product2(_601257, _601257)))], (11029 ^ _206269) ^ [] : [-(_601742 = ordered_pair(11026 ^ [_601253, _601255, _601257, _601742], 11027 ^ [_601253, _601255, _601257, _601742]))], (11031 ^ _206269) ^ [] : [-(in(ordered_pair(apply(_601253, 11026 ^ [_601253, _601255, _601257, _601742]), apply(_601253, 11027 ^ [_601253, _601255, _601257, _601742])), _601255))]]], (11033 ^ _206269) ^ [_602350] : [-(in(_602350, 11019 ^ [_601253, _601255, _601257])), in(_602350, cartesian_product2(_601257, _601257)), 11038 ^ _206269 : [(11039 ^ _206269) ^ [_602591, _602593] : [_602350 = ordered_pair(_602593, _602591), in(ordered_pair(apply(_601253, _602593), apply(_601253, _602591)), _601255)]]]]], (11048 ^ _206269) ^ [_603019, _603021] : [in(_603019, 11046 ^ [_603021]), 11051 ^ _206269 : [(11052 ^ _206269) ^ [] : [-(in(_603019, _603021))], (11054 ^ _206269) ^ [] : [-(ordinal(_603019))]]], (11056 ^ _206269) ^ [_603264, _603266] : [-(in(_603264, 11046 ^ [_603266])), in(_603264, _603266), ordinal(_603264)], (11066 ^ _206269) ^ [_603587, _603589, _603591] : [element(_603589, powerset(powerset(_603591))), relation(_603587), function(_603587), 11078 ^ _206269 : [(11079 ^ _206269) ^ [_604038] : [in(_604038, 11077 ^ [_603587, _603589, _603591]), 11082 ^ _206269 : [(11083 ^ _206269) ^ [] : [-(in(_604038, powerset(relation_dom(_603587))))], (11085 ^ _206269) ^ [] : [-(in(relation_image(_603587, _604038), _603589))]]], (11087 ^ _206269) ^ [_604329] : [-(in(_604329, 11077 ^ [_603587, _603589, _603591])), in(_604329, powerset(relation_dom(_603587))), in(relation_image(_603587, _604329), _603589)]]], (11097 ^ _206269) ^ [_604697, _604699] : [ordinal(_604697), 11101 ^ _206269 : [(11102 ^ _206269) ^ [_604970] : [in(_604970, 11100 ^ [_604697, _604699]), 11105 ^ _206269 : [(11106 ^ _206269) ^ [] : [-(in(_604970, succ(_604697)))], (11109 ^ _206269) ^ [] : [-(ordinal(11107 ^ [_604697, _604699, _604970]))], (11111 ^ _206269) ^ [] : [-(_604970 = 11107 ^ [_604697, _604699, _604970])], (11113 ^ _206269) ^ [] : [-(in(11107 ^ [_604697, _604699, _604970], _604699))]]], (11115 ^ _206269) ^ [_605479] : [-(in(_605479, 11100 ^ [_604697, _604699])), in(_605479, succ(_604697)), 11120 ^ _206269 : [(11121 ^ _206269) ^ [_605682] : [ordinal(_605682), _605479 = _605682, in(_605682, _604699)]]]]], (11133 ^ _206269) ^ [_606075, _606077] : [-(empty(_606077)), relation(_606075), 11190 ^ _206269 : [(11191 ^ _206269) ^ [] : [-(relation(11189 ^ [_606075, _606077]))], (11193 ^ _206269) ^ [] : [-(function(11189 ^ [_606075, _606077]))], (11195 ^ _206269) ^ [] : [-(relation_dom(11189 ^ [_606075, _606077]) = _606077)], (11197 ^ _206269) ^ [_609165] : [in(_609165, _606077), 11201 ^ _206269 : [(11202 ^ _206269) ^ [] : [-(_609165 = 11200 ^ [_606075, _606077, _609165])], (11204 ^ _206269) ^ [] : [-(in(apply(11189 ^ [_606075, _606077], _609165), 11200 ^ [_606075, _606077, _609165]))], (11206 ^ _206269) ^ [_609609] : [in(_609609, 11200 ^ [_606075, _606077, _609165]), -(in(ordered_pair(apply(11189 ^ [_606075, _606077], _609165), _609609), _606075))]]]], 11174 ^ _206269 : [(11175 ^ _206269) ^ [] : [-(in(11173 ^ [_606075, _606077], _606077))], (11177 ^ _206269) ^ [_608351, _608353] : [11173 ^ [_606075, _606077] = _608351, in(_608353, _608351), 11185 ^ _206269 : [(11186 ^ _206269) ^ [] : [-(in(11184 ^ [_606075, _606077, _608351, _608353], _608351))], (11188 ^ _206269) ^ [] : [in(ordered_pair(_608353, 11184 ^ [_606075, _606077, _608351, _608353]), _606075)]]]], 11147 ^ _206269 : [(11172 ^ _206269) ^ [] : [11145 ^ [_606075, _606077] = 11146 ^ [_606075, _606077]], (11148 ^ _206269) ^ [] : [-(in(11144 ^ [_606075, _606077], _606077))], (11151 ^ _206269) ^ [] : [-(11144 ^ [_606075, _606077] = 11149 ^ [_606075, _606077])], (11153 ^ _206269) ^ [] : [-(in(11145 ^ [_606075, _606077], 11149 ^ [_606075, _606077]))], (11155 ^ _206269) ^ [_607404] : [in(_607404, 11149 ^ [_606075, _606077]), -(in(ordered_pair(11145 ^ [_606075, _606077], _607404), _606075))], (11162 ^ _206269) ^ [] : [-(11144 ^ [_606075, _606077] = 11160 ^ [_606075, _606077])], (11164 ^ _206269) ^ [] : [-(in(11146 ^ [_606075, _606077], 11160 ^ [_606075, _606077]))], (11166 ^ _206269) ^ [_607880] : [in(_607880, 11160 ^ [_606075, _606077]), -(in(ordered_pair(11146 ^ [_606075, _606077], _607880), _606075))]]], (11212 ^ _206269) ^ [_609893] : [11218 ^ _206269 : [(11219 ^ _206269) ^ [] : [-(in(11215 ^ [_609893], _609893))], (11221 ^ _206269) ^ [] : [-(11216 ^ [_609893] = singleton(11215 ^ [_609893]))], (11223 ^ _206269) ^ [] : [-(11217 ^ [_609893] = singleton(11215 ^ [_609893]))], (11225 ^ _206269) ^ [] : [11216 ^ [_609893] = 11217 ^ [_609893]]], 11227 ^ _206269 : [(11228 ^ _206269) ^ [] : [-(in(11226 ^ [_609893], _609893))], (11230 ^ _206269) ^ [_610747] : [_610747 = singleton(11226 ^ [_609893])]], 11232 ^ _206269 : [(11233 ^ _206269) ^ [] : [-(relation(11231 ^ [_609893]))], (11235 ^ _206269) ^ [] : [-(function(11231 ^ [_609893]))], (11237 ^ _206269) ^ [] : [-(relation_dom(11231 ^ [_609893]) = _609893)], (11239 ^ _206269) ^ [_611119] : [in(_611119, _609893), -(apply(11231 ^ [_609893], _611119) = singleton(_611119))]]], (11245 ^ _206269) ^ [_611364, _611366] : [one_sorted_str(_611366), element(_611364, powerset(powerset(the_carrier(_611366)))), 11294 ^ _206269 : [(11295 ^ _206269) ^ [] : [-(relation(11293 ^ [_611364, _611366]))], (11297 ^ _206269) ^ [] : [-(function(11293 ^ [_611364, _611366]))], (11299 ^ _206269) ^ [] : [-(relation_dom(11293 ^ [_611364, _611366]) = complements_of_subsets(the_carrier(_611366), _611364))], (11301 ^ _206269) ^ [_613980] : [in(_613980, complements_of_subsets(the_carrier(_611366), _611364)), 11304 ^ _206269 : [(11305 ^ _206269) ^ [_614160] : [element(_614160, powerset(the_carrier(_611366))), _614160 = _613980, -(apply(11293 ^ [_611364, _611366], _613980) = subset_complement(the_carrier(_611366), _614160))]]]], 11284 ^ _206269 : [(11285 ^ _206269) ^ [] : [-(in(11283 ^ [_611364, _611366], complements_of_subsets(the_carrier(_611366), _611364)))], (11288 ^ _206269) ^ [_613396] : [-(element(11286 ^ [_611364, _611366, _613396], powerset(the_carrier(_611366))))], (11290 ^ _206269) ^ [_613477] : [-(11286 ^ [_611364, _611366, _613477] = 11283 ^ [_611364, _611366])], (11292 ^ _206269) ^ [_613540] : [_613540 = subset_complement(the_carrier(_611366), 11286 ^ [_611364, _611366, _613540])]], 11259 ^ _206269 : [(11282 ^ _206269) ^ [] : [11257 ^ [_611364, _611366] = 11258 ^ [_611364, _611366]], (11260 ^ _206269) ^ [] : [-(in(11256 ^ [_611364, _611366], complements_of_subsets(the_carrier(_611366), _611364)))], (11262 ^ _206269) ^ [_612432] : [element(_612432, powerset(the_carrier(_611366))), _612432 = 11256 ^ [_611364, _611366], -(11257 ^ [_611364, _611366] = subset_complement(the_carrier(_611366), _612432))], (11272 ^ _206269) ^ [_612757] : [element(_612757, powerset(the_carrier(_611366))), _612757 = 11256 ^ [_611364, _611366], -(11258 ^ [_611364, _611366] = subset_complement(the_carrier(_611366), _612757))]]], (11315 ^ _206269) ^ [_614545, _614547] : [one_sorted_str(_614547), element(_614545, powerset(powerset(the_carrier(_614547)))), 11364 ^ _206269 : [(11365 ^ _206269) ^ [] : [-(relation(11363 ^ [_614545, _614547]))], (11367 ^ _206269) ^ [] : [-(function(11363 ^ [_614545, _614547]))], (11369 ^ _206269) ^ [] : [-(relation_dom(11363 ^ [_614545, _614547]) = _614545)], (11371 ^ _206269) ^ [_617096] : [in(_617096, _614545), 11374 ^ _206269 : [(11375 ^ _206269) ^ [_617266] : [element(_617266, powerset(the_carrier(_614547))), _617266 = _617096, -(apply(11363 ^ [_614545, _614547], _617096) = subset_complement(the_carrier(_614547), _617266))]]]], 11354 ^ _206269 : [(11355 ^ _206269) ^ [] : [-(in(11353 ^ [_614545, _614547], _614545))], (11358 ^ _206269) ^ [_616527] : [-(element(11356 ^ [_614545, _614547, _616527], powerset(the_carrier(_614547))))], (11360 ^ _206269) ^ [_616608] : [-(11356 ^ [_614545, _614547, _616608] = 11353 ^ [_614545, _614547])], (11362 ^ _206269) ^ [_616671] : [_616671 = subset_complement(the_carrier(_614547), 11356 ^ [_614545, _614547, _616671])]], 11329 ^ _206269 : [(11352 ^ _206269) ^ [] : [11327 ^ [_614545, _614547] = 11328 ^ [_614545, _614547]], (11330 ^ _206269) ^ [] : [-(in(11326 ^ [_614545, _614547], _614545))], (11332 ^ _206269) ^ [_615573] : [element(_615573, powerset(the_carrier(_614547))), _615573 = 11326 ^ [_614545, _614547], -(11327 ^ [_614545, _614547] = subset_complement(the_carrier(_614547), _615573))], (11342 ^ _206269) ^ [_615898] : [element(_615898, powerset(the_carrier(_614547))), _615898 = 11326 ^ [_614545, _614547], -(11328 ^ [_614545, _614547] = subset_complement(the_carrier(_614547), _615898))]]], (11385 ^ _206269) ^ [] : [11440 ^ _206269 : [(11441 ^ _206269) ^ [_619639] : [ordinal(_619639), in(_619639, omega), 11448 ^ _206269 : [(11449 ^ _206269) ^ [_619895] : [element(_619895, powerset(powerset(_619639))), -(_619895 = empty_set), 11457 ^ _206269 : [(11458 ^ _206269) ^ [] : [-(in(11456 ^ [_619639, _619895], _619895))], (11460 ^ _206269) ^ [_620294] : [-(_620294 = 11456 ^ [_619639, _619895]), in(_620294, _619895), subset(11456 ^ [_619639, _619895], _620294)]]]]]], 11387 ^ _206269 : [(11388 ^ _206269) ^ [] : [-(ordinal(11386 ^ []))], (11423 ^ _206269) ^ [] : [-(in(11386 ^ [], omega))], (11426 ^ _206269) ^ [] : [-(element(11424 ^ [], powerset(powerset(11386 ^ []))))], (11428 ^ _206269) ^ [] : [11424 ^ [] = empty_set], (11430 ^ _206269) ^ [_619234] : [in(_619234, 11424 ^ []), 11434 ^ _206269 : [(11435 ^ _206269) ^ [] : [-(in(11433 ^ [_619234], 11424 ^ []))], (11437 ^ _206269) ^ [] : [-(subset(_619234, 11433 ^ [_619234]))], (11439 ^ _206269) ^ [] : [11433 ^ [_619234] = _619234]]], (11390 ^ _206269) ^ [_617926] : [ordinal(_617926), in(_617926, 11386 ^ []), in(_617926, omega), 11401 ^ _206269 : [(11402 ^ _206269) ^ [_618263] : [element(_618263, powerset(powerset(_617926))), -(_618263 = empty_set), 11410 ^ _206269 : [(11411 ^ _206269) ^ [] : [-(in(11409 ^ [_617926, _618263], _618263))], (11413 ^ _206269) ^ [_618662] : [-(_618662 = 11409 ^ [_617926, _618263]), in(_618662, _618263), subset(11409 ^ [_617926, _618263], _618662)]]]]]]], (11471 ^ _206269) ^ [_620725] : [-(relation(11469 ^ [_620725]))], (11473 ^ _206269) ^ [_620793] : [-(function(11469 ^ [_620793]))], (11475 ^ _206269) ^ [_620861] : [-(relation_dom(11469 ^ [_620861]) = _620861)], (11477 ^ _206269) ^ [_620941, _620943] : [in(_620941, _620943), -(apply(11469 ^ [_620943], _620941) = singleton(_620941))], (11483 ^ _206269) ^ [_621177, _621179] : [topological_space(_621179), top_str(_621179), element(_621177, powerset(the_carrier(_621179))), 11495 ^ _206269 : [(11496 ^ _206269) ^ [] : [-(element(11494 ^ [_621177, _621179], powerset(powerset(the_carrier(_621179)))))], (11498 ^ _206269) ^ [_621734] : [element(_621734, powerset(the_carrier(_621179))), 11501 ^ _206269 : [(11502 ^ _206269) ^ [] : [in(_621734, 11494 ^ [_621177, _621179]), 11506 ^ _206269 : [(11507 ^ _206269) ^ [] : [-(element(11505 ^ [_621177, _621179, _621734], powerset(the_carrier(_621179))))], (11509 ^ _206269) ^ [] : [-(11505 ^ [_621177, _621179, _621734] = _621734)], (11511 ^ _206269) ^ [] : [-(closed_subset(11505 ^ [_621177, _621179, _621734], _621179))], (11513 ^ _206269) ^ [] : [-(subset(_621177, _621734))]]], (11515 ^ _206269) ^ [] : [-(in(_621734, 11494 ^ [_621177, _621179])), 11516 ^ _206269 : [(11517 ^ _206269) ^ [_622436] : [element(_622436, powerset(the_carrier(_621179))), _622436 = _621734, closed_subset(_622436, _621179), subset(_621177, _621734)]]]]]]], (11533 ^ _206269) ^ [_622943, _622945] : [topological_space(_622945), top_str(_622945), element(_622943, powerset(powerset(the_carrier(_622945)))), 11545 ^ _206269 : [(11546 ^ _206269) ^ [] : [-(element(11544 ^ [_622943, _622945], powerset(powerset(the_carrier(_622945)))))], (11548 ^ _206269) ^ [_623460] : [element(_623460, powerset(the_carrier(_622945))), 11551 ^ _206269 : [(11552 ^ _206269) ^ [] : [in(_623460, 11544 ^ [_622943, _622945]), -(in(set_difference(cast_as_carrier_subset(_622945), _623460), _622943))], (11558 ^ _206269) ^ [] : [in(set_difference(cast_as_carrier_subset(_622945), _623460), _622943), -(in(_623460, 11544 ^ [_622943, _622945]))]]]]], (11564 ^ _206269) ^ [_623995, _623997] : [disjoint(_623997, _623995), -(disjoint(_623995, _623997))], (11570 ^ _206269) ^ [_624205, _624207] : [equipotent(_624207, _624205), -(equipotent(_624205, _624207))], (11576 ^ _206269) ^ [_624472, _624474, _624476, _624478] : [in(ordered_pair(_624478, _624476), cartesian_product2(_624474, _624472)), 11579 ^ _206269 : [(11580 ^ _206269) ^ [] : [-(in(_624478, _624474))], (11582 ^ _206269) ^ [] : [-(in(_624476, _624472))]]], (11584 ^ _206269) ^ [_624737, _624739, _624741, _624743] : [-(in(ordered_pair(_624743, _624741), cartesian_product2(_624739, _624737))), in(_624743, _624739), in(_624741, _624737)], (11594 ^ _206269) ^ [_625041] : [-(in(_625041, succ(_625041)))], (11596 ^ _206269) ^ [_625150, _625152] : [element(_625150, powerset(powerset(_625152))), 11599 ^ _206269 : [(11600 ^ _206269) ^ [] : [-(_625150 = empty_set), complements_of_subsets(_625152, _625150) = empty_set], (11606 ^ _206269) ^ [] : [-(complements_of_subsets(_625152, _625150) = empty_set), _625150 = empty_set]]], (11612 ^ _206269) ^ [_625669, _625671, _625673, _625675] : [unordered_pair(_625675, _625673) = unordered_pair(_625671, _625669), -(_625675 = _625671), -(_625675 = _625669)], (11622 ^ _206269) ^ [_626019, _626021, _626023] : [relation(_626019), 11625 ^ _206269 : [(11626 ^ _206269) ^ [] : [in(_626023, relation_rng(relation_rng_restriction(_626021, _626019))), 11629 ^ _206269 : [(11630 ^ _206269) ^ [] : [-(in(_626023, _626021))], (11632 ^ _206269) ^ [] : [-(in(_626023, relation_rng(_626019)))]]], (11634 ^ _206269) ^ [] : [-(in(_626023, relation_rng(relation_rng_restriction(_626021, _626019)))), in(_626023, _626021), in(_626023, relation_rng(_626019))]]], (11644 ^ _206269) ^ [_626678, _626680] : [relation(_626678), -(subset(relation_rng(relation_rng_restriction(_626680, _626678)), _626680))], (11650 ^ _206269) ^ [_626896, _626898] : [relation(_626896), -(subset(relation_rng_restriction(_626898, _626896), _626896))], (11656 ^ _206269) ^ [_627110, _627112] : [relation(_627110), -(subset(relation_rng(relation_rng_restriction(_627112, _627110)), relation_rng(_627110)))], (11662 ^ _206269) ^ [_627346, _627348, _627350] : [subset(_627350, _627348), 11665 ^ _206269 : [(11666 ^ _206269) ^ [] : [-(subset(cartesian_product2(_627350, _627346), cartesian_product2(_627348, _627346)))], (11668 ^ _206269) ^ [] : [-(subset(cartesian_product2(_627346, _627350), cartesian_product2(_627346, _627348)))]]], (11670 ^ _206269) ^ [_627663, _627665] : [relation(_627663), -(relation_rng(relation_rng_restriction(_627665, _627663)) = set_intersection2(relation_rng(_627663), _627665))], (11676 ^ _206269) ^ [_627919, _627921, _627923, _627925] : [-(subset(cartesian_product2(_627925, _627921), cartesian_product2(_627923, _627919))), subset(_627925, _627923), subset(_627921, _627919)], (11686 ^ _206269) ^ [_628250, _628252] : [element(_628250, powerset(powerset(_628252))), -(_628250 = empty_set), -(meet_of_subsets(_628252, complements_of_subsets(_628252, _628250)) = subset_complement(_628252, union_of_subsets(_628252, _628250)))], (11696 ^ _206269) ^ [_628570] : [one_sorted_str(_628570), -(cast_as_carrier_subset(_628570) = the_carrier(_628570))], (11702 ^ _206269) ^ [_628794, _628796, _628798] : [relation_of2_as_subset(_628794, _628798, _628796), 11705 ^ _206269 : [(11706 ^ _206269) ^ [] : [-(subset(relation_dom(_628794), _628798))], (11708 ^ _206269) ^ [] : [-(subset(relation_rng(_628794), _628796))]]], (11710 ^ _206269) ^ [_629097, _629099] : [element(_629097, powerset(powerset(_629099))), -(_629097 = empty_set), -(union_of_subsets(_629099, complements_of_subsets(_629099, _629097)) = subset_complement(_629099, meet_of_subsets(_629099, _629097)))], (11720 ^ _206269) ^ [_629431, _629433] : [subset(_629433, _629431), -(set_union2(_629433, _629431) = _629431)], (11727 ^ _206269) ^ [_629753] : [-(in(_629753, 11725 ^ [_629753]))], (11729 ^ _206269) ^ [_629865, _629867, _629869] : [-(in(_629865, 11725 ^ [_629869])), in(_629867, 11725 ^ [_629869]), subset(_629865, _629867)], (11739 ^ _206269) ^ [_630180, _630182] : [in(_630180, 11725 ^ [_630182]), -(in(powerset(_630180), 11725 ^ [_630182]))], (11745 ^ _206269) ^ [_630380, _630382] : [subset(_630380, 11725 ^ [_630382]), -(are_equipotent(_630380, 11725 ^ [_630382])), -(in(_630380, 11725 ^ [_630382]))], (11755 ^ _206269) ^ [_630706] : [-(empty_carrier(_630706)), topological_space(_630706), top_str(_630706), 11766 ^ _206269 : [(11785 ^ _206269) ^ [] : [11787 ^ _206269 : [(11788 ^ _206269) ^ [] : [-(element(11786 ^ [_630706], powerset(powerset(the_carrier(_630706)))))], (11790 ^ _206269) ^ [] : [-(centered(11786 ^ [_630706]))], (11792 ^ _206269) ^ [] : [-(closed_subsets(11786 ^ [_630706], _630706))], (11794 ^ _206269) ^ [] : [-(meet_of_subsets(the_carrier(_630706), 11786 ^ [_630706]) = empty_set)]], -(compact_top_space(_630706))], (11767 ^ _206269) ^ [] : [compact_top_space(_630706), 11770 ^ _206269 : [(11771 ^ _206269) ^ [_631138] : [element(_631138, powerset(powerset(the_carrier(_630706)))), centered(_631138), closed_subsets(_631138, _630706), meet_of_subsets(the_carrier(_630706), _631138) = empty_set]]]]], (11798 ^ _206269) ^ [_631988, _631990] : [-(finite(_631990)), subset(_631990, _631988), finite(_631988)], (11808 ^ _206269) ^ [_632269] : [one_sorted_str(_632269), 11811 ^ _206269 : [(11812 ^ _206269) ^ [_632415] : [element(_632415, powerset(powerset(the_carrier(_632269)))), 11815 ^ _206269 : [(11816 ^ _206269) ^ [] : [finite(complements_of_subsets(the_carrier(_632269), _632415)), -(finite(_632415))], (11822 ^ _206269) ^ [] : [finite(_632415), -(finite(complements_of_subsets(the_carrier(_632269), _632415)))]]]]], (11828 ^ _206269) ^ [_632917, _632919, _632921] : [relation(_632917), -(relation_dom_restriction(relation_rng_restriction(_632921, _632917), _632919) = relation_rng_restriction(_632921, relation_dom_restriction(_632917, _632919)))], (11834 ^ _206269) ^ [_633169, _633171, _633173] : [relation(_633169), 11837 ^ _206269 : [(11838 ^ _206269) ^ [] : [in(_633173, relation_image(_633169, _633171)), 11842 ^ _206269 : [(11843 ^ _206269) ^ [] : [-(in(11841 ^ [_633169, _633171, _633173], relation_dom(_633169)))], (11845 ^ _206269) ^ [] : [-(in(ordered_pair(11841 ^ [_633169, _633171, _633173], _633173), _633169))], (11847 ^ _206269) ^ [] : [-(in(11841 ^ [_633169, _633171, _633173], _633171))]]], (11849 ^ _206269) ^ [] : [-(in(_633173, relation_image(_633169, _633171))), 11850 ^ _206269 : [(11851 ^ _206269) ^ [_633770] : [in(_633770, relation_dom(_633169)), in(ordered_pair(_633770, _633173), _633169), in(_633770, _633171)]]]]], (11863 ^ _206269) ^ [_634167, _634169] : [relation(_634167), -(subset(relation_image(_634167, _634169), relation_rng(_634167)))], (11869 ^ _206269) ^ [_634385, _634387] : [-(subset(relation_image(_634385, relation_inverse_image(_634385, _634387)), _634387)), relation(_634385), function(_634385)], (11879 ^ _206269) ^ [_634692, _634694] : [relation(_634692), -(relation_image(_634692, _634694) = relation_image(_634692, set_intersection2(relation_dom(_634692), _634694)))], (11885 ^ _206269) ^ [_634922, _634924] : [relation(_634922), subset(_634924, relation_dom(_634922)), -(subset(_634924, relation_inverse_image(_634922, relation_image(_634922, _634924))))], (11895 ^ _206269) ^ [_635221] : [relation(_635221), -(relation_image(_635221, relation_dom(_635221)) = relation_rng(_635221))], (11901 ^ _206269) ^ [_635437, _635439] : [relation(_635437), function(_635437), subset(_635439, relation_rng(_635437)), -(relation_image(_635437, relation_inverse_image(_635437, _635439)) = _635439)], (11915 ^ _206269) ^ [_635867, _635869, _635871, _635873] : [relation_of2_as_subset(_635867, _635869, _635873), subset(relation_rng(_635867), _635871), -(relation_of2_as_subset(_635867, _635869, _635871))], (11925 ^ _206269) ^ [_636194, _636196] : [finite(_636196), -(finite(set_intersection2(_636196, _636194)))], (11931 ^ _206269) ^ [_636392] : [one_sorted_str(_636392), 11934 ^ _206269 : [(11935 ^ _206269) ^ [_636535] : [element(_636535, powerset(the_carrier(_636392))), -(subset_intersection2(the_carrier(_636392), _636535, cast_as_carrier_subset(_636392)) = _636535)]]], (11941 ^ _206269) ^ [_636762] : [relation(_636762), 11944 ^ _206269 : [(11945 ^ _206269) ^ [_636902] : [relation(_636902), -(relation_rng(relation_composition(_636762, _636902)) = relation_image(_636902, relation_rng(_636762)))]]], (11951 ^ _206269) ^ [_637151, _637153, _637155] : [relation(_637151), 11954 ^ _206269 : [(11955 ^ _206269) ^ [] : [in(_637155, relation_inverse_image(_637151, _637153)), 11959 ^ _206269 : [(11960 ^ _206269) ^ [] : [-(in(11958 ^ [_637151, _637153, _637155], relation_rng(_637151)))], (11962 ^ _206269) ^ [] : [-(in(ordered_pair(_637155, 11958 ^ [_637151, _637153, _637155]), _637151))], (11964 ^ _206269) ^ [] : [-(in(11958 ^ [_637151, _637153, _637155], _637153))]]], (11966 ^ _206269) ^ [] : [-(in(_637155, relation_inverse_image(_637151, _637153))), 11967 ^ _206269 : [(11968 ^ _206269) ^ [_637752] : [in(_637752, relation_rng(_637151)), in(ordered_pair(_637155, _637752), _637151), in(_637752, _637153)]]]]], (11980 ^ _206269) ^ [_638149, _638151] : [relation(_638149), -(subset(relation_inverse_image(_638149, _638151), relation_dom(_638149)))], (11986 ^ _206269) ^ [_638395, _638397, _638399, _638401] : [relation_of2_as_subset(_638395, _638397, _638401), subset(_638401, _638399), -(relation_of2_as_subset(_638395, _638397, _638399))], (11996 ^ _206269) ^ [_638704] : [top_str(_638704), 11999 ^ _206269 : [(12000 ^ _206269) ^ [_638852] : [element(_638852, powerset(powerset(the_carrier(_638704)))), 12003 ^ _206269 : [(12004 ^ _206269) ^ [] : [closed_subsets(_638852, _638704), -(open_subsets(complements_of_subsets(the_carrier(_638704), _638852), _638704))], (12010 ^ _206269) ^ [] : [open_subsets(complements_of_subsets(the_carrier(_638704), _638852), _638704), -(closed_subsets(_638852, _638704))]]]]], (12016 ^ _206269) ^ [_639360, _639362, _639364] : [relation(_639360), 12019 ^ _206269 : [(12020 ^ _206269) ^ [] : [in(_639364, relation_restriction(_639360, _639362)), 12023 ^ _206269 : [(12024 ^ _206269) ^ [] : [-(in(_639364, _639360))], (12026 ^ _206269) ^ [] : [-(in(_639364, cartesian_product2(_639362, _639362)))]]], (12028 ^ _206269) ^ [] : [-(in(_639364, relation_restriction(_639360, _639362))), in(_639364, _639360), in(_639364, cartesian_product2(_639362, _639362))]]], (12038 ^ _206269) ^ [_640016, _640018] : [relation(_640016), -(_640018 = empty_set), subset(_640018, relation_rng(_640016)), relation_inverse_image(_640016, _640018) = empty_set], (12052 ^ _206269) ^ [_640430, _640432, _640434] : [relation(_640430), subset(_640434, _640432), -(subset(relation_inverse_image(_640430, _640434), relation_inverse_image(_640430, _640432)))], (12062 ^ _206269) ^ [_640749, _640751] : [relation(_640749), function(_640749), finite(_640751), -(finite(relation_image(_640749, _640751)))], (12076 ^ _206269) ^ [_641123] : [one_sorted_str(_641123), 12079 ^ _206269 : [(12080 ^ _206269) ^ [_641271] : [element(_641271, powerset(the_carrier(_641123))), -(subset_complement(the_carrier(_641123), _641271) = subset_difference(the_carrier(_641123), cast_as_carrier_subset(_641123), _641271))]]], (12086 ^ _206269) ^ [_641508] : [top_str(_641508), 12089 ^ _206269 : [(12090 ^ _206269) ^ [_641656] : [element(_641656, powerset(powerset(the_carrier(_641508)))), 12093 ^ _206269 : [(12094 ^ _206269) ^ [] : [open_subsets(_641656, _641508), -(closed_subsets(complements_of_subsets(the_carrier(_641508), _641656), _641508))], (12100 ^ _206269) ^ [] : [closed_subsets(complements_of_subsets(the_carrier(_641508), _641656), _641508), -(open_subsets(_641656, _641508))]]]]], (12106 ^ _206269) ^ [_642150, _642152] : [relation(_642150), -(relation_restriction(_642150, _642152) = relation_dom_restriction(relation_rng_restriction(_642152, _642150), _642152))], (12112 ^ _206269) ^ [_642361, _642363] : [-(subset(set_intersection2(_642363, _642361), _642363))], (12114 ^ _206269) ^ [_642459] : [finite(_642459), 12117 ^ _206269 : [(12118 ^ _206269) ^ [_642634] : [element(_642634, powerset(powerset(_642459))), -(_642634 = empty_set), 12126 ^ _206269 : [(12127 ^ _206269) ^ [] : [-(in(12125 ^ [_642459, _642634], _642634))], (12129 ^ _206269) ^ [_643033] : [-(_643033 = 12125 ^ [_642459, _642634]), in(_643033, _642634), subset(12125 ^ [_642459, _642634], _643033)]]]]], (12139 ^ _206269) ^ [_643390, _643392] : [relation(_643390), -(relation_restriction(_643390, _643392) = relation_rng_restriction(_643392, relation_dom_restriction(_643390, _643392)))], (12145 ^ _206269) ^ [_643630, _643632, _643634] : [relation(_643630), in(_643634, relation_field(relation_restriction(_643630, _643632))), 12152 ^ _206269 : [(12153 ^ _206269) ^ [] : [-(in(_643634, relation_field(_643630)))], (12155 ^ _206269) ^ [] : [-(in(_643634, _643632))]]], (12157 ^ _206269) ^ [_644042, _644044, _644046] : [-(subset(_644046, set_intersection2(_644044, _644042))), subset(_644046, _644044), subset(_644046, _644042)], (12167 ^ _206269) ^ [_644328] : [-(set_union2(_644328, empty_set) = _644328)], (12169 ^ _206269) ^ [_644438, _644440] : [element(_644438, the_carrier(boole_lattice(_644440))), 12172 ^ _206269 : [(12173 ^ _206269) ^ [_644611] : [element(_644611, the_carrier(boole_lattice(_644440))), 12176 ^ _206269 : [(12177 ^ _206269) ^ [] : [-(join(boole_lattice(_644440), _644438, _644611) = set_union2(_644438, _644611))], (12179 ^ _206269) ^ [] : [-(meet(boole_lattice(_644440), _644438, _644611) = set_intersection2(_644438, _644611))]]]]], (12181 ^ _206269) ^ [_644957, _644959] : [in(_644959, _644957), -(element(_644959, _644957))], (12187 ^ _206269) ^ [_645181, _645183, _645185] : [-(subset(_645185, _645181)), subset(_645185, _645183), subset(_645183, _645181)], (12197 ^ _206269) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (12199 ^ _206269) ^ [_645557, _645559, _645561] : [relation(_645557), in(ordered_pair(_645561, _645559), _645557), 12206 ^ _206269 : [(12207 ^ _206269) ^ [] : [-(in(_645561, relation_dom(_645557)))], (12209 ^ _206269) ^ [] : [-(in(_645559, relation_rng(_645557)))]]], (12211 ^ _206269) ^ [_645955, _645957] : [relation(_645955), 12214 ^ _206269 : [(12215 ^ _206269) ^ [] : [-(subset(relation_field(relation_restriction(_645955, _645957)), relation_field(_645955)))], (12217 ^ _206269) ^ [] : [-(subset(relation_field(relation_restriction(_645955, _645957)), _645957))]]], (12219 ^ _206269) ^ [_646262, _646264] : [relation(_646262), function(_646262), 12226 ^ _206269 : [(12227 ^ _206269) ^ [_646512] : [relation(_646512), function(_646512), 12234 ^ _206269 : [(12235 ^ _206269) ^ [] : [in(_646264, relation_dom(relation_composition(_646512, _646262))), 12238 ^ _206269 : [(12239 ^ _206269) ^ [] : [-(in(_646264, relation_dom(_646512)))], (12241 ^ _206269) ^ [] : [-(in(apply(_646512, _646264), relation_dom(_646262)))]]], (12243 ^ _206269) ^ [] : [-(in(_646264, relation_dom(relation_composition(_646512, _646262)))), in(_646264, relation_dom(_646512)), in(apply(_646512, _646264), relation_dom(_646262))]]]]], (12253 ^ _206269) ^ [_647318, _647320, _647322, _647324] : [function(_647318), quasi_total(_647318, _647324, _647322), relation_of2_as_subset(_647318, _647324, _647322), 12264 ^ _206269 : [(12265 ^ _206269) ^ [_647687] : [relation(_647687), function(_647687), in(_647320, _647324), -(_647322 = empty_set), -(apply(relation_composition(_647318, _647687), _647320) = apply(_647687, apply(_647318, _647320)))]]], (12283 ^ _206269) ^ [_648244] : [epsilon_transitive(_648244), 12286 ^ _206269 : [(12287 ^ _206269) ^ [_648380] : [ordinal(_648380), proper_subset(_648244, _648380), -(in(_648244, _648380))]]], (12297 ^ _206269) ^ [_648670] : [relation(_648670), -(subset(_648670, cartesian_product2(relation_dom(_648670), relation_rng(_648670))))], (12303 ^ _206269) ^ [_648900, _648902, _648904] : [relation(_648900), -(subset(fiber(relation_restriction(_648900, _648904), _648902), fiber(_648900, _648902)))], (12309 ^ _206269) ^ [_649132, _649134] : [relation(_649132), function(_649132), 12316 ^ _206269 : [(12317 ^ _206269) ^ [_649381] : [relation(_649381), function(_649381), in(_649134, relation_dom(relation_composition(_649381, _649132))), -(apply(relation_composition(_649381, _649132), _649134) = apply(_649132, apply(_649381, _649134)))]]], (12331 ^ _206269) ^ [_649812] : [one_sorted_str(_649812), 12334 ^ _206269 : [(12335 ^ _206269) ^ [_649963] : [element(_649963, powerset(the_carrier(_649812))), -(subset_difference(the_carrier(_649812), cast_as_carrier_subset(_649812), subset_difference(the_carrier(_649812), cast_as_carrier_subset(_649812), _649963)) = _649963)]]], (12341 ^ _206269) ^ [_650234, _650236, _650238] : [relation_of2_as_subset(_650234, _650236, _650238), 12344 ^ _206269 : [(12345 ^ _206269) ^ [] : [12347 ^ _206269 : [(12348 ^ _206269) ^ [] : [-(in(12346 ^ [_650234, _650236, _650238], _650236))], (12350 ^ _206269) ^ [_650592] : [in(ordered_pair(12346 ^ [_650234, _650236, _650238], _650592), _650234)]], -(relation_dom_as_subset(_650236, _650238, _650234) = _650236)], (12354 ^ _206269) ^ [] : [relation_dom_as_subset(_650236, _650238, _650234) = _650236, 12357 ^ _206269 : [(12358 ^ _206269) ^ [_650829] : [in(_650829, _650236), -(in(ordered_pair(_650829, 12361 ^ [_650234, _650236, _650238, _650829]), _650234))]]]]], (12365 ^ _206269) ^ [_651151, _651153] : [relation(_651151), reflexive(_651151), -(reflexive(relation_restriction(_651151, _651153)))], (12375 ^ _206269) ^ [_651450, _651452] : [relation(_651450), function(_651450), 12382 ^ _206269 : [(12383 ^ _206269) ^ [_651696] : [relation(_651696), function(_651696), in(_651452, relation_dom(_651450)), -(apply(relation_composition(_651450, _651696), _651452) = apply(_651696, apply(_651450, _651452)))]]], (12397 ^ _206269) ^ [_652121] : [12412 ^ _206269 : [(12413 ^ _206269) ^ [_652524] : [element(_652524, the_carrier(_652121)), 12416 ^ _206269 : [(12417 ^ _206269) ^ [_652674] : [element(_652674, the_carrier(_652121)), -(below(_652121, meet_commut(_652121, _652524, _652674), _652524))]]]], -(empty_carrier(_652121)), meet_commutative(_652121), meet_absorbing(_652121), latt_str(_652121)], (12423 ^ _206269) ^ [_652918, _652920] : [ordinal(_652918), in(_652920, _652918), -(ordinal(_652920))], (12433 ^ _206269) ^ [_653227, _653229, _653231] : [relation_of2_as_subset(_653227, _653231, _653229), 12436 ^ _206269 : [(12437 ^ _206269) ^ [] : [12439 ^ _206269 : [(12440 ^ _206269) ^ [] : [-(in(12438 ^ [_653227, _653229, _653231], _653229))], (12442 ^ _206269) ^ [_653585] : [in(ordered_pair(_653585, 12438 ^ [_653227, _653229, _653231]), _653227)]], -(relation_rng_as_subset(_653231, _653229, _653227) = _653229)], (12446 ^ _206269) ^ [] : [relation_rng_as_subset(_653231, _653229, _653227) = _653229, 12449 ^ _206269 : [(12450 ^ _206269) ^ [_653822] : [in(_653822, _653229), -(in(ordered_pair(12453 ^ [_653227, _653229, _653231, _653822], _653822), _653227))]]]]], (12457 ^ _206269) ^ [_654144, _654146] : [relation(_654144), connected(_654144), -(connected(relation_restriction(_654144, _654146)))], (12467 ^ _206269) ^ [_654429] : [ordinal(_654429), 12470 ^ _206269 : [(12471 ^ _206269) ^ [_654579] : [ordinal(_654579), -(in(_654429, _654579)), -(_654429 = _654579), -(in(_654579, _654429))]]], (12485 ^ _206269) ^ [_654982, _654984] : [relation(_654982), transitive(_654982), -(transitive(relation_restriction(_654982, _654984)))], (12495 ^ _206269) ^ [_655267] : [antisymmetric_relstr(_655267), rel_str(_655267), 12502 ^ _206269 : [(12503 ^ _206269) ^ [_655510] : [element(_655510, the_carrier(_655267)), 12506 ^ _206269 : [(12507 ^ _206269) ^ [_655669] : [element(_655669, the_carrier(_655267)), -(_655510 = _655669), related(_655267, _655510, _655669), related(_655267, _655669, _655510)]]]]], (12521 ^ _206269) ^ [_656081] : [relation(_656081), 12524 ^ _206269 : [(12525 ^ _206269) ^ [_656231] : [relation(_656231), subset(_656081, _656231), 12532 ^ _206269 : [(12533 ^ _206269) ^ [] : [-(subset(relation_dom(_656081), relation_dom(_656231)))], (12535 ^ _206269) ^ [] : [-(subset(relation_rng(_656081), relation_rng(_656231)))]]]]], (12537 ^ _206269) ^ [_656626, _656628] : [relation(_656626), antisymmetric(_656626), -(antisymmetric(relation_restriction(_656626, _656628)))], (12547 ^ _206269) ^ [_656925, _656927] : [relation(_656925), well_orders(_656925, _656927), 12554 ^ _206269 : [(12555 ^ _206269) ^ [] : [-(relation_field(relation_restriction(_656925, _656927)) = _656927)], (12557 ^ _206269) ^ [] : [-(well_ordering(relation_restriction(_656925, _656927)))]]], (12559 ^ _206269) ^ [_657297] : [relation(_657297), function(_657297), finite(relation_dom(_657297)), -(finite(relation_rng(_657297)))], (12573 ^ _206269) ^ [_657659] : [-(empty_carrier(_657659)), join_commutative(_657659), join_semilatt_str(_657659), 12584 ^ _206269 : [(12585 ^ _206269) ^ [_657988] : [element(_657988, the_carrier(_657659)), 12588 ^ _206269 : [(12589 ^ _206269) ^ [_658147] : [element(_658147, the_carrier(_657659)), -(_657988 = _658147), below(_657659, _657988, _658147), below(_657659, _658147, _657988)]]]]], (12603 ^ _206269) ^ [_658561] : [transitive_relstr(_658561), rel_str(_658561), 12610 ^ _206269 : [(12611 ^ _206269) ^ [_658818] : [element(_658818, the_carrier(_658561)), 12614 ^ _206269 : [(12615 ^ _206269) ^ [_658991] : [element(_658991, the_carrier(_658561)), 12618 ^ _206269 : [(12619 ^ _206269) ^ [_659157] : [element(_659157, the_carrier(_658561)), -(related(_658561, _658818, _659157)), related(_658561, _658818, _658991), related(_658561, _658991, _659157)]]]]]]], (12634 ^ _206269) ^ [_659641] : [-(relation(12632 ^ [_659641]))], (12636 ^ _206269) ^ [_659689] : [-(well_orders(12632 ^ [_659689], _659689))], (12638 ^ _206269) ^ [_659817, _659819, _659821] : [subset(_659821, _659819), -(subset(set_intersection2(_659821, _659817), set_intersection2(_659819, _659817)))], (12644 ^ _206269) ^ [_660045, _660047] : [-(empty_carrier(_660045)), lattice(_660045), latt_str(_660045), 12655 ^ _206269 : [(12656 ^ _206269) ^ [_660372] : [element(_660372, the_carrier(_660045)), 12659 ^ _206269 : [(12660 ^ _206269) ^ [] : [latt_set_smaller(_660045, _660372, _660047), -(relstr_element_smaller(poset_of_lattice(_660045), _660047, cast_to_el_of_LattPOSet(_660045, _660372)))], (12666 ^ _206269) ^ [] : [relstr_element_smaller(poset_of_lattice(_660045), _660047, cast_to_el_of_LattPOSet(_660045, _660372)), -(latt_set_smaller(_660045, _660372, _660047))]]]]], (12672 ^ _206269) ^ [_660872] : [-(empty(_660872)), 12678 ^ _206269 : [(12679 ^ _206269) ^ [] : [-(in(12677 ^ [_660872], _660872))], (12681 ^ _206269) ^ [] : [-(12677 ^ [_660872] = empty_set)]], 12683 ^ _206269 : [(12684 ^ _206269) ^ [] : [-(relation(12682 ^ [_660872]))], (12686 ^ _206269) ^ [] : [-(function(12682 ^ [_660872]))], (12688 ^ _206269) ^ [] : [-(relation_dom(12682 ^ [_660872]) = _660872)], (12690 ^ _206269) ^ [_661540] : [in(_661540, _660872), -(in(apply(12682 ^ [_660872], _661540), _661540))]]], (12696 ^ _206269) ^ [_661784, _661786] : [subset(_661786, _661784), -(set_intersection2(_661786, _661784) = _661786)], (12702 ^ _206269) ^ [_662000, _662002] : [-(empty_carrier(_662000)), lattice(_662000), latt_str(_662000), 12713 ^ _206269 : [(12714 ^ _206269) ^ [_662329] : [element(_662329, the_carrier(poset_of_lattice(_662000))), 12717 ^ _206269 : [(12718 ^ _206269) ^ [] : [relstr_element_smaller(poset_of_lattice(_662000), _662002, _662329), -(latt_set_smaller(_662000, cast_to_el_of_lattice(_662000, _662329), _662002))], (12724 ^ _206269) ^ [] : [latt_set_smaller(_662000, cast_to_el_of_lattice(_662000, _662329), _662002), -(relstr_element_smaller(poset_of_lattice(_662000), _662002, _662329))]]]]], (12730 ^ _206269) ^ [_662833] : [top_str(_662833), 12733 ^ _206269 : [(12734 ^ _206269) ^ [_662979] : [element(_662979, powerset(the_carrier(_662833))), 12737 ^ _206269 : [(12738 ^ _206269) ^ [] : [closed_subset(_662979, _662833), -(open_subset(subset_complement(the_carrier(_662833), _662979), _662833))], (12744 ^ _206269) ^ [] : [open_subset(subset_complement(the_carrier(_662833), _662979), _662833), -(closed_subset(_662979, _662833))]]]]], (12750 ^ _206269) ^ [_663440] : [-(set_intersection2(_663440, empty_set) = empty_set)], (12752 ^ _206269) ^ [_663550, _663552] : [element(_663550, the_carrier(boole_lattice(_663552))), 12755 ^ _206269 : [(12756 ^ _206269) ^ [_663708] : [element(_663708, the_carrier(boole_lattice(_663552))), 12759 ^ _206269 : [(12760 ^ _206269) ^ [] : [below(boole_lattice(_663552), _663550, _663708), -(subset(_663550, _663708))], (12766 ^ _206269) ^ [] : [subset(_663550, _663708), -(below(boole_lattice(_663552), _663550, _663708))]]]]], (12772 ^ _206269) ^ [_664210, _664212] : [element(_664212, _664210), -(empty(_664210)), -(in(_664212, _664210))], (12782 ^ _206269) ^ [_664508, _664510] : [-(_664510 = _664508), 12786 ^ _206269 : [(12787 ^ _206269) ^ [] : [-(in(12783 ^ [_664508, _664510], _664510))], (12789 ^ _206269) ^ [] : [in(12783 ^ [_664508, _664510], _664508)]], 12790 ^ _206269 : [(12791 ^ _206269) ^ [] : [-(in(12783 ^ [_664508, _664510], _664508))], (12793 ^ _206269) ^ [] : [in(12783 ^ [_664508, _664510], _664510)]]], (12797 ^ _206269) ^ [_665009] : [-(reflexive(inclusion_relation(_665009)))], (12799 ^ _206269) ^ [_665088] : [-(subset(empty_set, _665088))], (12801 ^ _206269) ^ [_665195, _665197] : [-(empty_carrier(_665195)), lattice(_665195), latt_str(_665195), 12812 ^ _206269 : [(12813 ^ _206269) ^ [_665522] : [element(_665522, the_carrier(_665195)), 12816 ^ _206269 : [(12817 ^ _206269) ^ [] : [latt_element_smaller(_665195, _665522, _665197), -(relstr_set_smaller(poset_of_lattice(_665195), _665197, cast_to_el_of_LattPOSet(_665195, _665522)))], (12823 ^ _206269) ^ [] : [relstr_set_smaller(poset_of_lattice(_665195), _665197, cast_to_el_of_LattPOSet(_665195, _665522)), -(latt_element_smaller(_665195, _665522, _665197))]]]]], (12829 ^ _206269) ^ [_666050, _666052, _666054] : [relation(_666050), in(ordered_pair(_666054, _666052), _666050), 12836 ^ _206269 : [(12837 ^ _206269) ^ [] : [-(in(_666054, relation_field(_666050)))], (12839 ^ _206269) ^ [] : [-(in(_666052, relation_field(_666050)))]]], (12841 ^ _206269) ^ [_666434] : [top_str(_666434), 12844 ^ _206269 : [(12845 ^ _206269) ^ [_666580] : [element(_666580, powerset(the_carrier(_666434))), 12848 ^ _206269 : [(12849 ^ _206269) ^ [] : [open_subset(_666580, _666434), -(closed_subset(subset_complement(the_carrier(_666434), _666580), _666434))], (12855 ^ _206269) ^ [] : [closed_subset(subset_complement(the_carrier(_666434), _666580), _666434), -(open_subset(_666580, _666434))]]]]], (12861 ^ _206269) ^ [_667070, _667072] : [-(empty_carrier(_667070)), lattice(_667070), latt_str(_667070), 12872 ^ _206269 : [(12873 ^ _206269) ^ [_667399] : [element(_667399, the_carrier(poset_of_lattice(_667070))), 12876 ^ _206269 : [(12877 ^ _206269) ^ [] : [relstr_set_smaller(poset_of_lattice(_667070), _667072, _667399), -(latt_element_smaller(_667070, cast_to_el_of_lattice(_667070, _667399), _667072))], (12883 ^ _206269) ^ [] : [latt_element_smaller(_667070, cast_to_el_of_lattice(_667070, _667399), _667072), -(relstr_set_smaller(poset_of_lattice(_667070), _667072, _667399))]]]]], (12889 ^ _206269) ^ [_667903] : [-(ordinal(_667903)), 12891 ^ _206269 : [(12892 ^ _206269) ^ [] : [-(in(12890 ^ [_667903], _667903))], (12894 ^ _206269) ^ [] : [ordinal(12890 ^ [_667903]), subset(12890 ^ [_667903], _667903)]]], (12902 ^ _206269) ^ [_668333, _668335] : [relation(_668333), well_founded_relation(_668333), -(well_founded_relation(relation_restriction(_668333, _668335)))], (12912 ^ _206269) ^ [_668618] : [-(empty_carrier(_668618)), lattice(_668618), latt_str(_668618), 12923 ^ _206269 : [(12924 ^ _206269) ^ [_668951] : [element(_668951, the_carrier(_668618)), 12927 ^ _206269 : [(12928 ^ _206269) ^ [_669114] : [element(_669114, the_carrier(_668618)), 12931 ^ _206269 : [(12932 ^ _206269) ^ [] : [in(ordered_pair_as_product_element(the_carrier(_668618), the_carrier(_668618), _668951, _669114), relation_of_lattice(_668618)), -(below_refl(_668618, _668951, _669114))], (12938 ^ _206269) ^ [] : [below_refl(_668618, _668951, _669114), -(in(ordered_pair_as_product_element(the_carrier(_668618), the_carrier(_668618), _668951, _669114), relation_of_lattice(_668618)))]]]]]]], (12944 ^ _206269) ^ [_669648, _669650] : [ordinal(_669648), subset(_669650, _669648), -(_669650 = empty_set), 12956 ^ _206269 : [(12957 ^ _206269) ^ [] : [-(ordinal(12955 ^ [_669648, _669650]))], (12959 ^ _206269) ^ [] : [-(in(12955 ^ [_669648, _669650], _669650))], (12961 ^ _206269) ^ [_670200] : [ordinal(_670200), in(_670200, _669650), -(ordinal_subset(12955 ^ [_669648, _669650], _670200))]]], (12971 ^ _206269) ^ [_670542, _670544] : [relation(_670542), well_ordering(_670542), -(well_ordering(relation_restriction(_670542, _670544)))], (12981 ^ _206269) ^ [_670827] : [ordinal(_670827), 12984 ^ _206269 : [(12985 ^ _206269) ^ [_670965] : [ordinal(_670965), 12988 ^ _206269 : [(12989 ^ _206269) ^ [] : [in(_670827, _670965), -(ordinal_subset(succ(_670827), _670965))], (12995 ^ _206269) ^ [] : [ordinal_subset(succ(_670827), _670965), -(in(_670827, _670965))]]]]], (13001 ^ _206269) ^ [_671450, _671452, _671454] : [subset(_671454, _671452), -(subset(set_difference(_671454, _671450), set_difference(_671452, _671450)))], (13007 ^ _206269) ^ [_671706, _671708, _671710, _671712] : [ordered_pair(_671712, _671710) = ordered_pair(_671708, _671706), 13010 ^ _206269 : [(13011 ^ _206269) ^ [] : [-(_671712 = _671708)], (13013 ^ _206269) ^ [] : [-(_671710 = _671706)]]], (13015 ^ _206269) ^ [_672019, _672021] : [relation(_672019), function(_672019), 13022 ^ _206269 : [(13023 ^ _206269) ^ [] : [_672019 = identity_relation(_672021), 13026 ^ _206269 : [(13027 ^ _206269) ^ [] : [-(relation_dom(_672019) = _672021)], (13029 ^ _206269) ^ [_672438] : [in(_672438, _672021), -(apply(_672019, _672438) = _672438)]]], (13035 ^ _206269) ^ [] : [-(_672019 = identity_relation(_672021)), relation_dom(_672019) = _672021, 13041 ^ _206269 : [(13042 ^ _206269) ^ [] : [-(in(13040 ^ [_672019, _672021], _672021))], (13044 ^ _206269) ^ [] : [apply(_672019, 13040 ^ [_672019, _672021]) = 13040 ^ [_672019, _672021]]]]]], (13048 ^ _206269) ^ [_673029] : [-(empty_carrier(_673029)), lattice(_673029), complete_latt_str(_673029), latt_str(_673029), 13063 ^ _206269 : [(13064 ^ _206269) ^ [_673456] : [element(_673456, the_carrier(_673029)), 13067 ^ _206269 : [(13084 ^ _206269) ^ [_674188] : [-(_673456 = meet_of_latt_set(_673029, _674188)), latt_set_smaller(_673029, _673456, _674188), 13090 ^ _206269 : [(13091 ^ _206269) ^ [] : [-(element(13089 ^ [_673029, _673456, _674188], the_carrier(_673029)))], (13093 ^ _206269) ^ [] : [-(latt_set_smaller(_673029, 13089 ^ [_673029, _673456, _674188], _674188))], (13095 ^ _206269) ^ [] : [below_refl(_673029, 13089 ^ [_673029, _673456, _674188], _673456)]]], (13068 ^ _206269) ^ [_673659] : [_673456 = meet_of_latt_set(_673029, _673659), 13071 ^ _206269 : [(13072 ^ _206269) ^ [] : [-(latt_set_smaller(_673029, _673456, _673659))], (13074 ^ _206269) ^ [_673896] : [element(_673896, the_carrier(_673029)), latt_set_smaller(_673029, _673896, _673659), -(below_refl(_673029, _673896, _673456))]]]]]]], (13099 ^ _206269) ^ [_674785, _674787] : [in(_674785, _674787), -(apply(identity_relation(_674787), _674785) = _674785)], (13105 ^ _206269) ^ [_674990, _674992] : [-(subset(set_difference(_674992, _674990), _674992))], (13107 ^ _206269) ^ [_675088] : [relation(_675088), 13110 ^ _206269 : [(13111 ^ _206269) ^ [] : [-(relation_rng(_675088) = relation_dom(relation_inverse(_675088)))], (13113 ^ _206269) ^ [] : [-(relation_dom(_675088) = relation_rng(relation_inverse(_675088)))]]], (13115 ^ _206269) ^ [_675416, _675418] : [set_difference(_675418, _675416) = empty_set, -(subset(_675418, _675416))], (13121 ^ _206269) ^ [_675584, _675586] : [subset(_675586, _675584), -(set_difference(_675586, _675584) = empty_set)], (13127 ^ _206269) ^ [_675831, _675833] : [subset(singleton(_675833), _675831), -(in(_675833, _675831))], (13133 ^ _206269) ^ [_675997, _675999] : [in(_675999, _675997), -(subset(singleton(_675999), _675997))], (13139 ^ _206269) ^ [_676256, _676258, _676260] : [subset(unordered_pair(_676260, _676258), _676256), 13142 ^ _206269 : [(13143 ^ _206269) ^ [] : [-(in(_676260, _676256))], (13145 ^ _206269) ^ [] : [-(in(_676258, _676256))]]], (13147 ^ _206269) ^ [_676507, _676509, _676511] : [-(subset(unordered_pair(_676511, _676509), _676507)), in(_676511, _676507), in(_676509, _676507)], (13157 ^ _206269) ^ [_676824, _676826] : [relation(_676824), -(relation_field(relation_restriction(_676824, _676826)) = _676826), well_ordering(_676824), subset(_676826, relation_field(_676824))], (13171 ^ _206269) ^ [_677207, _677209] : [-(set_union2(_677209, set_difference(_677207, _677209)) = set_union2(_677209, _677207))], (13183 ^ _206269) ^ [_677614, _677616] : [13184 ^ _206269 : [(13185 ^ _206269) ^ [] : [_677616 = empty_set], (13187 ^ _206269) ^ [] : [_677616 = singleton(_677614)]], -(subset(_677616, singleton(_677614)))], (13173 ^ _206269) ^ [_677354, _677356] : [subset(_677356, singleton(_677354)), -(_677356 = empty_set), -(_677356 = singleton(_677354))], (13191 ^ _206269) ^ [_677879] : [-(set_difference(_677879, empty_set) = _677879)], (13193 ^ _206269) ^ [_677980] : [-(lower_bounded_semilattstr(boole_lattice(_677980)))], (13195 ^ _206269) ^ [_678025] : [-(bottom_of_semilattstr(boole_lattice(_678025)) = empty_set)], (13197 ^ _206269) ^ [_678152, _678154, _678156] : [in(_678156, _678154), in(_678154, _678152), in(_678152, _678156)], (13207 ^ _206269) ^ [_678489, _678491] : [element(_678491, powerset(_678489)), -(subset(_678491, _678489))], (13213 ^ _206269) ^ [_678655, _678657] : [subset(_678657, _678655), -(element(_678657, powerset(_678655)))], (13219 ^ _206269) ^ [_678842] : [-(transitive(inclusion_relation(_678842)))], (13221 ^ _206269) ^ [_678970, _678972] : [-(disjoint(_678972, _678970)), 13225 ^ _206269 : [(13226 ^ _206269) ^ [] : [-(in(13224 ^ [_678970, _678972], _678972))], (13228 ^ _206269) ^ [] : [-(in(13224 ^ [_678970, _678972], _678970))]]], (13230 ^ _206269) ^ [_679284, _679286] : [disjoint(_679286, _679284), 13231 ^ _206269 : [(13232 ^ _206269) ^ [_679376] : [in(_679376, _679286), in(_679376, _679284)]]], (13240 ^ _206269) ^ [_679633] : [subset(_679633, empty_set), -(_679633 = empty_set)], (13246 ^ _206269) ^ [_679822, _679824] : [-(set_difference(set_union2(_679824, _679822), _679822) = set_difference(_679824, _679822))], (13248 ^ _206269) ^ [_679926] : [ordinal(_679926), 13251 ^ _206269 : [(13266 ^ _206269) ^ [] : [13268 ^ _206269 : [(13269 ^ _206269) ^ [] : [-(ordinal(13267 ^ [_679926]))], (13271 ^ _206269) ^ [] : [-(in(13267 ^ [_679926], _679926))], (13273 ^ _206269) ^ [] : [in(succ(13267 ^ [_679926]), _679926)]], -(being_limit_ordinal(_679926))], (13252 ^ _206269) ^ [] : [being_limit_ordinal(_679926), 13255 ^ _206269 : [(13256 ^ _206269) ^ [_680172] : [ordinal(_680172), in(_680172, _679926), -(in(succ(_680172), _679926))]]]]], (13277 ^ _206269) ^ [_680798] : [ordinal(_680798), 13280 ^ _206269 : [(13281 ^ _206269) ^ [] : [-(being_limit_ordinal(_680798)), 13285 ^ _206269 : [(13286 ^ _206269) ^ [] : [-(ordinal(13284 ^ [_680798]))], (13288 ^ _206269) ^ [] : [-(_680798 = succ(13284 ^ [_680798]))]]], (13290 ^ _206269) ^ [] : [being_limit_ordinal(_680798), 13291 ^ _206269 : [(13292 ^ _206269) ^ [_681269] : [ordinal(_681269), _680798 = succ(_681269)]]]]], (13300 ^ _206269) ^ [_681536, _681538] : [element(_681536, powerset(_681538)), 13303 ^ _206269 : [(13304 ^ _206269) ^ [_681688] : [element(_681688, powerset(_681538)), 13307 ^ _206269 : [(13308 ^ _206269) ^ [] : [disjoint(_681536, _681688), -(subset(_681536, subset_complement(_681538, _681688)))], (13314 ^ _206269) ^ [] : [subset(_681536, subset_complement(_681538, _681688)), -(disjoint(_681536, _681688))]]]]], (13320 ^ _206269) ^ [_682172] : [topological_space(_682172), top_str(_682172), 13327 ^ _206269 : [(13328 ^ _206269) ^ [_682424] : [element(_682424, powerset(powerset(the_carrier(_682172)))), 13334 ^ _206269 : [(13335 ^ _206269) ^ [] : [-(element(13333 ^ [_682172, _682424], powerset(the_carrier(_682172))))], (13337 ^ _206269) ^ [] : [-(in(13333 ^ [_682172, _682424], _682424))], (13339 ^ _206269) ^ [] : [closed_subset(13333 ^ [_682172, _682424], _682172)]], -(closed_subset(meet_of_subsets(the_carrier(_682172), _682424), _682172))]]], (13343 ^ _206269) ^ [_682984] : [relation(_682984), 13346 ^ _206269 : [(13347 ^ _206269) ^ [_683121] : [relation(_683121), -(subset(relation_dom(relation_composition(_682984, _683121)), relation_dom(_682984)))]]], (13353 ^ _206269) ^ [_683336] : [top_str(_683336), 13356 ^ _206269 : [(13357 ^ _206269) ^ [_683474] : [element(_683474, powerset(the_carrier(_683336))), -(subset(interior(_683336, _683474), _683474))]]], (13363 ^ _206269) ^ [_683691] : [top_str(_683691), 13366 ^ _206269 : [(13367 ^ _206269) ^ [_683875] : [element(_683875, powerset(the_carrier(_683691))), 13370 ^ _206269 : [(13371 ^ _206269) ^ [_684060] : [in(_684060, the_carrier(_683691)), 13374 ^ _206269 : [(13393 ^ _206269) ^ [] : [13395 ^ _206269 : [(13396 ^ _206269) ^ [] : [-(element(13394 ^ [_683691, _683875, _684060], powerset(the_carrier(_683691))))], (13398 ^ _206269) ^ [] : [-(closed_subset(13394 ^ [_683691, _683875, _684060], _683691))], (13400 ^ _206269) ^ [] : [-(subset(_683875, 13394 ^ [_683691, _683875, _684060]))], (13402 ^ _206269) ^ [] : [in(_684060, 13394 ^ [_683691, _683875, _684060])]], -(in(_684060, topstr_closure(_683691, _683875)))], (13375 ^ _206269) ^ [] : [in(_684060, topstr_closure(_683691, _683875)), 13378 ^ _206269 : [(13379 ^ _206269) ^ [_684349] : [element(_684349, powerset(the_carrier(_683691))), -(in(_684060, _684349)), closed_subset(_684349, _683691), subset(_683875, _684349)]]]]]]]]], (13406 ^ _206269) ^ [_685249] : [relation(_685249), 13409 ^ _206269 : [(13410 ^ _206269) ^ [_685386] : [relation(_685386), -(subset(relation_rng(relation_composition(_685249, _685386)), relation_rng(_685386)))]]], (13416 ^ _206269) ^ [_685615, _685617] : [subset(_685617, _685615), -(_685615 = set_union2(_685617, set_difference(_685615, _685617)))], (13422 ^ _206269) ^ [_685865, _685867, _685869, _685871] : [function(_685865), quasi_total(_685865, _685871, _685869), relation_of2_as_subset(_685865, _685871, _685869), -(_685869 = empty_set), 13437 ^ _206269 : [(13438 ^ _206269) ^ [_686343] : [in(_686343, relation_inverse_image(_685865, _685867)), 13441 ^ _206269 : [(13442 ^ _206269) ^ [] : [-(in(_686343, _685871))], (13444 ^ _206269) ^ [] : [-(in(apply(_685865, _686343), _685867))]]], (13446 ^ _206269) ^ [_686624] : [-(in(_686624, relation_inverse_image(_685865, _685867))), in(_686624, _685871), in(apply(_685865, _686624), _685867)]]], (13456 ^ _206269) ^ [_686974] : [topological_space(_686974), top_str(_686974), 13463 ^ _206269 : [(13464 ^ _206269) ^ [_687250] : [element(_687250, powerset(the_carrier(_686974))), 13468 ^ _206269 : [(13469 ^ _206269) ^ [] : [-(element(13467 ^ [_686974, _687250], powerset(powerset(the_carrier(_686974)))))], (13493 ^ _206269) ^ [] : [-(topstr_closure(_686974, _687250) = meet_of_subsets(the_carrier(_686974), 13467 ^ [_686974, _687250]))], (13471 ^ _206269) ^ [_687641] : [element(_687641, powerset(the_carrier(_686974))), 13474 ^ _206269 : [(13475 ^ _206269) ^ [] : [in(_687641, 13467 ^ [_686974, _687250]), 13478 ^ _206269 : [(13479 ^ _206269) ^ [] : [-(closed_subset(_687641, _686974))], (13481 ^ _206269) ^ [] : [-(subset(_687250, _687641))]]], (13483 ^ _206269) ^ [] : [-(in(_687641, 13467 ^ [_686974, _687250])), closed_subset(_687641, _686974), subset(_687250, _687641)]]]]]]], (13495 ^ _206269) ^ [_688377] : [relation(_688377), 13498 ^ _206269 : [(13499 ^ _206269) ^ [_688524] : [relation(_688524), subset(relation_rng(_688377), relation_dom(_688524)), -(relation_dom(relation_composition(_688377, _688524)) = relation_dom(_688377))]]], (13509 ^ _206269) ^ [_688850, _688852] : [element(_688850, powerset(powerset(_688852))), -(_688850 = empty_set), complements_of_subsets(_688852, _688850) = empty_set], (13519 ^ _206269) ^ [_689167, _689169] : [in(_689169, _689167), -(set_union2(singleton(_689169), _689167) = _689167)], (13525 ^ _206269) ^ [_689373] : [relation(_689373), 13528 ^ _206269 : [(13529 ^ _206269) ^ [_689520] : [relation(_689520), subset(relation_dom(_689373), relation_rng(_689520)), -(relation_rng(relation_composition(_689520, _689373)) = relation_rng(_689373))]]], (13539 ^ _206269) ^ [_689846, _689848] : [element(_689846, powerset(powerset(_689848))), -(_689846 = empty_set), -(subset_difference(_689848, cast_to_subset(_689848), union_of_subsets(_689848, _689846)) = meet_of_subsets(_689848, complements_of_subsets(_689848, _689846)))], (13549 ^ _206269) ^ [_690172] : [top_str(_690172), 13552 ^ _206269 : [(13553 ^ _206269) ^ [_690310] : [element(_690310, powerset(the_carrier(_690172))), -(subset(_690310, topstr_closure(_690172, _690310)))]]], (13559 ^ _206269) ^ [_690541, _690543] : [element(_690541, powerset(powerset(_690543))), -(_690541 = empty_set), -(union_of_subsets(_690543, complements_of_subsets(_690543, _690541)) = subset_difference(_690543, cast_to_subset(_690543), meet_of_subsets(_690543, _690541)))], (13569 ^ _206269) ^ [_690866, _690868] : [-(set_difference(_690868, set_difference(_690868, _690866)) = set_intersection2(_690868, _690866))], (13571 ^ _206269) ^ [_690970] : [relation(_690970), 13574 ^ _206269 : [(13575 ^ _206269) ^ [_691125] : [relation(_691125), 13578 ^ _206269 : [(13579 ^ _206269) ^ [_691276] : [relation(_691276), function(_691276), relation_isomorphism(_690970, _691125, _691276), -(relation_isomorphism(_691125, _690970, function_inverse(_691276)))]]]]], (13593 ^ _206269) ^ [_691669] : [-(set_difference(empty_set, _691669) = empty_set)], (13595 ^ _206269) ^ [_691793, _691795, _691797] : [-(element(_691797, _691793)), in(_691797, _691795), element(_691795, powerset(_691793))], (13605 ^ _206269) ^ [_692092] : [ordinal(_692092), -(connected(inclusion_relation(_692092)))], (13611 ^ _206269) ^ [_692316, _692318] : [-(disjoint(_692318, _692316)), -(in(13614 ^ [_692316, _692318], set_intersection2(_692318, _692316)))], (13618 ^ _206269) ^ [_692551, _692553] : [13619 ^ _206269 : [(13620 ^ _206269) ^ [_692624] : [in(_692624, set_intersection2(_692553, _692551))]], disjoint(_692553, _692551)], (13624 ^ _206269) ^ [_692776] : [13639 ^ _206269 : [(13640 ^ _206269) ^ [] : [empty_carrier(_692776)], (13642 ^ _206269) ^ [] : [-(lattice(_692776))], (13644 ^ _206269) ^ [] : [-(lower_bounded_semilattstr(_692776))], (13646 ^ _206269) ^ [] : [-(latt_str(_692776))], (13648 ^ _206269) ^ [] : [-(bottom_of_semilattstr(_692776) = join_of_latt_set(_692776, empty_set))]], -(empty_carrier(_692776)), lattice(_692776), complete_latt_str(_692776), latt_str(_692776)], (13650 ^ _206269) ^ [_693508] : [-(_693508 = empty_set), 13653 ^ _206269 : [(13654 ^ _206269) ^ [_693668] : [element(_693668, powerset(_693508)), 13657 ^ _206269 : [(13658 ^ _206269) ^ [_693822] : [element(_693822, _693508), -(in(_693822, _693668)), -(in(_693822, subset_complement(_693508, _693668)))]]]]], (13668 ^ _206269) ^ [_694140] : [topological_space(_694140), top_str(_694140), 13675 ^ _206269 : [(13676 ^ _206269) ^ [_694361] : [element(_694361, powerset(the_carrier(_694140))), -(open_subset(interior(_694140, _694361), _694140))]]], (13682 ^ _206269) ^ [_694580] : [top_str(_694580), 13685 ^ _206269 : [(13686 ^ _206269) ^ [_694744] : [element(_694744, powerset(the_carrier(_694580))), 13689 ^ _206269 : [(13690 ^ _206269) ^ [] : [closed_subset(_694744, _694580), -(topstr_closure(_694580, _694744) = _694744)], (13696 ^ _206269) ^ [] : [-(closed_subset(_694744, _694580)), topological_space(_694580), topstr_closure(_694580, _694744) = _694744]]]]], (13706 ^ _206269) ^ [_695307] : [relation(_695307), 13709 ^ _206269 : [(13710 ^ _206269) ^ [_695503] : [relation(_695503), 13713 ^ _206269 : [(13714 ^ _206269) ^ [_695695] : [relation(_695695), function(_695695), relation_isomorphism(_695307, _695503, _695695), 13725 ^ _206269 : [(13726 ^ _206269) ^ [] : [reflexive(_695307), -(reflexive(_695503))], (13732 ^ _206269) ^ [] : [transitive(_695307), -(transitive(_695503))], (13738 ^ _206269) ^ [] : [connected(_695307), -(connected(_695503))], (13744 ^ _206269) ^ [] : [antisymmetric(_695307), -(antisymmetric(_695503))], (13750 ^ _206269) ^ [] : [well_founded_relation(_695307), -(well_founded_relation(_695503))]]]]]]], (13756 ^ _206269) ^ [_696847] : [relation(_696847), function(_696847), one_to_one(_696847), 13767 ^ _206269 : [(13768 ^ _206269) ^ [_697234] : [relation(_697234), function(_697234), 13775 ^ _206269 : [(13806 ^ _206269) ^ [] : [-(_697234 = function_inverse(_696847)), relation_dom(_697234) = relation_rng(_696847), 13815 ^ _206269 : [(13816 ^ _206269) ^ [] : [-(in(13811 ^ [_696847, _697234], relation_rng(_696847)))], (13818 ^ _206269) ^ [] : [-(13812 ^ [_696847, _697234] = apply(_697234, 13811 ^ [_696847, _697234]))], (13820 ^ _206269) ^ [] : [in(13812 ^ [_696847, _697234], relation_dom(_696847)), 13811 ^ [_696847, _697234] = apply(_696847, 13812 ^ [_696847, _697234])]], 13825 ^ _206269 : [(13826 ^ _206269) ^ [] : [-(in(13812 ^ [_696847, _697234], relation_dom(_696847)))], (13828 ^ _206269) ^ [] : [-(13811 ^ [_696847, _697234] = apply(_696847, 13812 ^ [_696847, _697234]))], (13830 ^ _206269) ^ [] : [in(13811 ^ [_696847, _697234], relation_rng(_696847)), 13812 ^ [_696847, _697234] = apply(_697234, 13811 ^ [_696847, _697234])]]], (13776 ^ _206269) ^ [] : [_697234 = function_inverse(_696847), 13779 ^ _206269 : [(13780 ^ _206269) ^ [] : [-(relation_dom(_697234) = relation_rng(_696847))], (13782 ^ _206269) ^ [_697751, _697753] : [13789 ^ _206269 : [(13790 ^ _206269) ^ [] : [-(in(_697751, relation_dom(_696847)))], (13792 ^ _206269) ^ [] : [-(_697753 = apply(_696847, _697751))]], in(_697753, relation_rng(_696847)), _697751 = apply(_697234, _697753)], (13794 ^ _206269) ^ [_698125, _698127] : [13801 ^ _206269 : [(13802 ^ _206269) ^ [] : [-(in(_698127, relation_rng(_696847)))], (13804 ^ _206269) ^ [] : [-(_698125 = apply(_697234, _698127))]], in(_698125, relation_dom(_696847)), _698127 = apply(_696847, _698125)]]]]]]], (13838 ^ _206269) ^ [_699700, _699702, _699704] : [element(_699700, powerset(_699704)), in(_699702, subset_complement(_699704, _699700)), in(_699702, _699700)], (13848 ^ _206269) ^ [_700006] : [relation(_700006), 13851 ^ _206269 : [(13852 ^ _206269) ^ [_700162] : [relation(_700162), 13855 ^ _206269 : [(13856 ^ _206269) ^ [_700314] : [relation(_700314), function(_700314), -(well_ordering(_700162)), well_ordering(_700006), relation_isomorphism(_700006, _700162, _700314)]]]]], (13874 ^ _206269) ^ [_700805] : [relation(_700805), function(_700805), one_to_one(_700805), 13885 ^ _206269 : [(13886 ^ _206269) ^ [] : [-(relation_rng(_700805) = relation_dom(function_inverse(_700805)))], (13888 ^ _206269) ^ [] : [-(relation_dom(_700805) = relation_rng(function_inverse(_700805)))]]], (13890 ^ _206269) ^ [_701258] : [topological_space(_701258), top_str(_701258), 13897 ^ _206269 : [(13898 ^ _206269) ^ [_701525] : [top_str(_701525), 13901 ^ _206269 : [(13902 ^ _206269) ^ [_701705] : [element(_701705, powerset(the_carrier(_701258))), 13905 ^ _206269 : [(13906 ^ _206269) ^ [_701886] : [element(_701886, powerset(the_carrier(_701525))), 13909 ^ _206269 : [(13910 ^ _206269) ^ [] : [open_subset(_701886, _701525), -(interior(_701525, _701886) = _701886)], (13916 ^ _206269) ^ [] : [interior(_701258, _701705) = _701705, -(open_subset(_701705, _701258))]]]]]]]]], (13922 ^ _206269) ^ [_702410] : [relation(_702410), -(in(ordered_pair(13927 ^ [_702410], 13928 ^ [_702410]), _702410)), -(_702410 = empty_set)], (13934 ^ _206269) ^ [_702828, _702830] : [relation(_702828), function(_702828), 13949 ^ _206269 : [(13950 ^ _206269) ^ [] : [-(_702830 = apply(_702828, apply(function_inverse(_702828), _702830)))], (13952 ^ _206269) ^ [] : [-(_702830 = apply(relation_composition(function_inverse(_702828), _702828), _702830))]], one_to_one(_702828), in(_702830, relation_rng(_702828))], (13954 ^ _206269) ^ [_703398] : [-(empty_carrier(_703398)), topological_space(_703398), top_str(_703398), 13965 ^ _206269 : [(13966 ^ _206269) ^ [_703728] : [element(_703728, powerset(the_carrier(_703398))), 13969 ^ _206269 : [(13970 ^ _206269) ^ [_703890] : [element(_703890, the_carrier(_703398)), -(point_neighbourhood(_703728, _703398, _703890)), open_subset(_703728, _703398), in(_703890, _703728)]]]]], (13984 ^ _206269) ^ [_704330, _704332, _704334] : [in(_704334, _704332), element(_704332, powerset(_704330)), empty(_704330)], (13994 ^ _206269) ^ [_704640, _704642] : [element(_704640, powerset(_704642)), 13997 ^ _206269 : [(13998 ^ _206269) ^ [] : [proper_element(_704640, powerset(_704642)), _704640 = _704642], (14004 ^ _206269) ^ [] : [-(_704640 = _704642), -(proper_element(_704640, powerset(_704642)))]]], (14010 ^ _206269) ^ [_705098] : [-(empty_carrier(_705098)), one_sorted_str(_705098), 14017 ^ _206269 : [(14018 ^ _206269) ^ [_705329] : [element(_705329, powerset(powerset(the_carrier(_705098)))), is_a_cover_of_carrier(_705098, _705329), _705329 = empty_set]]], (14028 ^ _206269) ^ [_705636] : [relation(_705636), 14031 ^ _206269 : [(14032 ^ _206269) ^ [] : [well_founded_relation(_705636), -(is_well_founded_in(_705636, relation_field(_705636)))], (14038 ^ _206269) ^ [] : [is_well_founded_in(_705636, relation_field(_705636)), -(well_founded_relation(_705636))]]], (14044 ^ _206269) ^ [_706052] : [-(antisymmetric(inclusion_relation(_706052)))], (14046 ^ _206269) ^ [] : [-(relation_dom(empty_set) = empty_set)], (14048 ^ _206269) ^ [] : [-(relation_rng(empty_set) = empty_set)], (14050 ^ _206269) ^ [_706268, _706270] : [subset(_706270, _706268), proper_subset(_706268, _706270)], (14056 ^ _206269) ^ [_706463] : [relation(_706463), function(_706463), one_to_one(_706463), -(one_to_one(function_inverse(_706463)))], (14070 ^ _206269) ^ [_706849, _706851, _706853] : [-(disjoint(_706853, _706849)), subset(_706853, _706851), disjoint(_706851, _706849)], (14080 ^ _206269) ^ [_707144] : [relation(_707144), 14085 ^ _206269 : [(14086 ^ _206269) ^ [] : [relation_dom(_707144) = empty_set], (14088 ^ _206269) ^ [] : [relation_rng(_707144) = empty_set]], -(_707144 = empty_set)], (14092 ^ _206269) ^ [_707497] : [relation(_707497), 14095 ^ _206269 : [(14096 ^ _206269) ^ [] : [relation_dom(_707497) = empty_set, -(relation_rng(_707497) = empty_set)], (14102 ^ _206269) ^ [] : [relation_rng(_707497) = empty_set, -(relation_dom(_707497) = empty_set)]]], (14108 ^ _206269) ^ [_707980, _707982] : [set_difference(_707982, singleton(_707980)) = _707982, in(_707980, _707982)], (14114 ^ _206269) ^ [_708153, _708155] : [-(in(_708153, _708155)), -(set_difference(_708155, singleton(_708153)) = _708155)], (14120 ^ _206269) ^ [_708378, _708380] : [relation(_708378), function(_708378), 14127 ^ _206269 : [(14128 ^ _206269) ^ [_708645] : [relation(_708645), function(_708645), 14135 ^ _206269 : [(14136 ^ _206269) ^ [] : [_708378 = relation_dom_restriction(_708645, _708380), 14139 ^ _206269 : [(14140 ^ _206269) ^ [] : [-(relation_dom(_708378) = set_intersection2(relation_dom(_708645), _708380))], (14142 ^ _206269) ^ [_709099] : [in(_709099, relation_dom(_708378)), -(apply(_708378, _709099) = apply(_708645, _709099))]]], (14148 ^ _206269) ^ [] : [-(_708378 = relation_dom_restriction(_708645, _708380)), relation_dom(_708378) = set_intersection2(relation_dom(_708645), _708380), 14154 ^ _206269 : [(14155 ^ _206269) ^ [] : [-(in(14153 ^ [_708378, _708380, _708645], relation_dom(_708378)))], (14157 ^ _206269) ^ [] : [apply(_708378, 14153 ^ [_708378, _708380, _708645]) = apply(_708645, 14153 ^ [_708378, _708380, _708645])]]]]]]], (14161 ^ _206269) ^ [_709738] : [-(unordered_pair(_709738, _709738) = singleton(_709738))], (14163 ^ _206269) ^ [_709836] : [empty(_709836), -(_709836 = empty_set)], (14169 ^ _206269) ^ [_710066, _710068, _710070, _710072] : [function(_710066), quasi_total(_710066, _710072, _710070), relation_of2_as_subset(_710066, _710072, _710070), in(_710068, _710072), -(_710070 = empty_set), -(in(apply(_710066, _710068), relation_rng(_710066)))], (14191 ^ _206269) ^ [_710679] : [ordinal(_710679), -(well_founded_relation(inclusion_relation(_710679)))], (14197 ^ _206269) ^ [_710883, _710885] : [subset(singleton(_710885), singleton(_710883)), -(_710885 = _710883)], (14203 ^ _206269) ^ [_711115, _711117, _711119] : [relation(_711115), function(_711115), in(_711117, relation_dom(relation_dom_restriction(_711115, _711119))), -(apply(relation_dom_restriction(_711115, _711119), _711117) = apply(_711115, _711117))], (14217 ^ _206269) ^ [_711534] : [-(relation_dom(identity_relation(_711534)) = _711534)], (14219 ^ _206269) ^ [_711582] : [-(relation_rng(identity_relation(_711582)) = _711582)], (14221 ^ _206269) ^ [_711709, _711711, _711713] : [relation(_711709), function(_711709), in(_711711, _711713), -(apply(relation_dom_restriction(_711709, _711713), _711711) = apply(_711709, _711711))], (14235 ^ _206269) ^ [_712155, _712157, _712159, _712161] : [relation(_712155), 14238 ^ _206269 : [(14239 ^ _206269) ^ [] : [in(ordered_pair(_712161, _712159), relation_composition(identity_relation(_712157), _712155)), 14242 ^ _206269 : [(14243 ^ _206269) ^ [] : [-(in(_712161, _712157))], (14245 ^ _206269) ^ [] : [-(in(ordered_pair(_712161, _712159), _712155))]]], (14247 ^ _206269) ^ [] : [-(in(ordered_pair(_712161, _712159), relation_composition(identity_relation(_712157), _712155))), in(_712161, _712157), in(ordered_pair(_712161, _712159), _712155)]]], (14257 ^ _206269) ^ [_712848, _712850] : [in(_712850, _712848), empty(_712848)], (14263 ^ _206269) ^ [_713041] : [-(empty_carrier(_713041)), lattice(_713041), latt_str(_713041), 14274 ^ _206269 : [(14275 ^ _206269) ^ [_713372] : [element(_713372, the_carrier(_713041)), 14278 ^ _206269 : [(14279 ^ _206269) ^ [_713533] : [element(_713533, the_carrier(_713041)), 14282 ^ _206269 : [(14283 ^ _206269) ^ [] : [below_refl(_713041, _713372, _713533), -(related_reflexive(poset_of_lattice(_713041), cast_to_el_of_LattPOSet(_713041, _713372), cast_to_el_of_LattPOSet(_713041, _713533)))], (14289 ^ _206269) ^ [] : [related_reflexive(poset_of_lattice(_713041), cast_to_el_of_LattPOSet(_713041, _713372), cast_to_el_of_LattPOSet(_713041, _713533)), -(below_refl(_713041, _713372, _713533))]]]]]]], (14295 ^ _206269) ^ [_714066, _714068] : [-(pair_first(ordered_pair(_714068, _714066)) = _714068)], (14297 ^ _206269) ^ [_714117, _714119] : [-(pair_second(ordered_pair(_714119, _714117)) = _714117)], (14299 ^ _206269) ^ [_714233, _714235] : [in(_714235, _714233), 14303 ^ _206269 : [(14304 ^ _206269) ^ [] : [-(in(14302 ^ [_714233, _714235], _714233))], (14306 ^ _206269) ^ [_714524] : [in(_714524, _714233), in(_714524, 14302 ^ [_714233, _714235])]]], (14312 ^ _206269) ^ [_714750] : [ordinal(_714750), -(well_ordering(inclusion_relation(_714750)))], (14318 ^ _206269) ^ [_714939, _714941] : [-(subset(_714941, set_union2(_714941, _714939)))], (14320 ^ _206269) ^ [_715080, _715082] : [disjoint(_715082, _715080), -(set_difference(_715082, _715080) = _715082)], (14326 ^ _206269) ^ [_715248, _715250] : [set_difference(_715250, _715248) = _715250, -(disjoint(_715250, _715248))], (14332 ^ _206269) ^ [_715480, _715482, _715484] : [relation(_715480), 14335 ^ _206269 : [(14336 ^ _206269) ^ [] : [in(_715484, relation_dom(relation_dom_restriction(_715480, _715482))), 14339 ^ _206269 : [(14340 ^ _206269) ^ [] : [-(in(_715484, _715482))], (14342 ^ _206269) ^ [] : [-(in(_715484, relation_dom(_715480)))]]], (14344 ^ _206269) ^ [] : [-(in(_715484, relation_dom(relation_dom_restriction(_715480, _715482)))), in(_715484, _715482), in(_715484, relation_dom(_715480))]]], (14354 ^ _206269) ^ [_716139, _716141] : [relation(_716139), -(subset(relation_dom_restriction(_716139, _716141), _716139))], (14360 ^ _206269) ^ [_716353, _716355] : [empty(_716355), -(_716355 = _716353), empty(_716353)], (14370 ^ _206269) ^ [_716664, _716666, _716668] : [relation(_716664), function(_716664), 14377 ^ _206269 : [(14378 ^ _206269) ^ [] : [in(ordered_pair(_716668, _716666), _716664), 14381 ^ _206269 : [(14382 ^ _206269) ^ [] : [-(in(_716668, relation_dom(_716664)))], (14384 ^ _206269) ^ [] : [-(_716666 = apply(_716664, _716668))]]], (14386 ^ _206269) ^ [] : [-(in(ordered_pair(_716668, _716666), _716664)), in(_716668, relation_dom(_716664)), _716666 = apply(_716664, _716668)]]], (14396 ^ _206269) ^ [_717405] : [relation(_717405), 14399 ^ _206269 : [(14400 ^ _206269) ^ [] : [well_orders(_717405, relation_field(_717405)), -(well_ordering(_717405))], (14406 ^ _206269) ^ [] : [well_ordering(_717405), -(well_orders(_717405, relation_field(_717405)))]]], (14412 ^ _206269) ^ [_717864, _717866, _717868] : [-(subset(set_union2(_717868, _717864), _717866)), subset(_717868, _717866), subset(_717864, _717866)], (14422 ^ _206269) ^ [_718193, _718195, _718197] : [singleton(_718197) = unordered_pair(_718195, _718193), -(_718197 = _718195)], (14428 ^ _206269) ^ [_718419, _718421] : [relation(_718419), -(relation_dom(relation_dom_restriction(_718419, _718421)) = set_intersection2(relation_dom(_718419), _718421))], (14434 ^ _206269) ^ [_718633] : [-(empty_carrier(_718633)), one_sorted_str(_718633), 14441 ^ _206269 : [(14442 ^ _206269) ^ [_718863] : [element(_718863, the_carrier(_718633)), -(apply_as_element(the_carrier(_718633), the_carrier(_718633), identity_on_carrier(_718633), _718863) = _718863)]]], (14448 ^ _206269) ^ [_719108, _719110] : [in(_719110, _719108), -(subset(_719110, union(_719108)))], (14454 ^ _206269) ^ [_719322, _719324] : [relation(_719322), -(relation_dom_restriction(_719322, _719324) = relation_composition(identity_relation(_719324), _719322))], (14460 ^ _206269) ^ [_719546, _719548] : [relation(_719546), -(subset(relation_rng(relation_dom_restriction(_719546, _719548)), relation_rng(_719546)))], (14466 ^ _206269) ^ [_719739] : [-(union(powerset(_719739)) = _719739)], (14468 ^ _206269) ^ [_719878, _719880, _719882, _719884] : [function(_719878), quasi_total(_719878, _719884, _719882), relation_of2_as_subset(_719878, _719884, _719882), subset(_719882, _719880), 14485 ^ _206269 : [(14486 ^ _206269) ^ [] : [-(_719882 = empty_set)], (14488 ^ _206269) ^ [] : [_719884 = empty_set]], 14489 ^ _206269 : [(14490 ^ _206269) ^ [] : [-(function(_719878))], (14492 ^ _206269) ^ [] : [-(quasi_total(_719878, _719884, _719880))], (14494 ^ _206269) ^ [] : [-(relation_of2_as_subset(_719878, _719884, _719880))]]], (14532 ^ _206269) ^ [_722144, _722146, _722148] : [singleton(_722148) = unordered_pair(_722146, _722144), -(_722146 = _722144)], (14497 ^ _206269) ^ [_720864] : [-(in(_720864, 14495 ^ [_720864]))], (14499 ^ _206269) ^ [_720976, _720978, _720980] : [-(in(_720976, 14495 ^ [_720980])), in(_720978, 14495 ^ [_720980]), subset(_720976, _720978)], (14509 ^ _206269) ^ [_721291, _721293] : [in(_721291, 14495 ^ [_721293]), 14513 ^ _206269 : [(14514 ^ _206269) ^ [] : [-(in(14512 ^ [_721291, _721293], 14495 ^ [_721293]))], (14516 ^ _206269) ^ [_721603] : [subset(_721603, _721291), -(in(_721603, 14512 ^ [_721291, _721293]))]]], (14522 ^ _206269) ^ [_721810, _721812] : [subset(_721810, 14495 ^ [_721812]), -(are_equipotent(_721810, 14495 ^ [_721812])), -(in(_721810, 14495 ^ [_721812]))]], input).
% 5.81/6.58  ncf('1',plain,[relstr_set_smaller(14537 ^ [], empty_set, 14540 ^ []), relstr_element_smaller(14537 ^ [], empty_set, 14540 ^ [])],start(14544 ^ 0)).
% 5.81/6.58  ncf('1.1',plain,[-(relstr_set_smaller(14537 ^ [], empty_set, 14540 ^ [])), 5818 : -(in(5814 ^ [14537 ^ [], 14540 ^ [], empty_set], empty_set)), 5813 : element(14540 ^ [], the_carrier(14537 ^ [])), 5795 : rel_str(14537 ^ [])],extension(5791 ^ 1,bind([[_405412, _405591, _405593], [14537 ^ [], 14540 ^ [], empty_set]]))).
% 5.81/6.58  ncf('1.1.1',plain,[in(5814 ^ [14537 ^ [], 14540 ^ [], empty_set], empty_set), empty(empty_set)],extension(14257 ^ 8,bind([[_712848, _712850], [empty_set, 5814 ^ [14537 ^ [], 14540 ^ [], empty_set]]]))).
% 5.81/6.58  ncf('1.1.1.1',plain,[-(empty(empty_set))],extension(6742 ^ 9)).
% 5.81/6.58  ncf('1.1.2',plain,[-(element(14540 ^ [], the_carrier(14537 ^ [])))],extension(14542 ^ 4)).
% 5.81/6.58  ncf('1.1.3',plain,[-(rel_str(14537 ^ []))],extension(14539 ^ 2)).
% 5.81/6.58  ncf('1.2',plain,[-(relstr_element_smaller(14537 ^ [], empty_set, 14540 ^ [])), 5547 : -(in(5543 ^ [14537 ^ [], 14540 ^ [], empty_set], empty_set)), 5542 : element(14540 ^ [], the_carrier(14537 ^ [])), 5524 : rel_str(14537 ^ [])],extension(5520 ^ 1,bind([[_395397, _395576, _395578], [14537 ^ [], 14540 ^ [], empty_set]]))).
% 5.81/6.58  ncf('1.2.1',plain,[in(5543 ^ [14537 ^ [], 14540 ^ [], empty_set], empty_set), empty(empty_set)],extension(14257 ^ 8,bind([[_712848, _712850], [empty_set, 5543 ^ [14537 ^ [], 14540 ^ [], empty_set]]]))).
% 5.81/6.58  ncf('1.2.1.1',plain,[-(empty(empty_set))],extension(6742 ^ 9)).
% 5.81/6.58  ncf('1.2.2',plain,[-(element(14540 ^ [], the_carrier(14537 ^ [])))],extension(14542 ^ 4)).
% 5.81/6.58  ncf('1.2.3',plain,[-(rel_str(14537 ^ []))],extension(14539 ^ 2)).
% 5.81/6.58  %-----------------------------------------------------
% 5.81/6.58  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------