%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU320+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 12:03:08 EDT 2023

% Result   : Theorem 199.48s 192.22s
% Output   : Proof 199.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU320+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 13:50:29 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 199.48/192.22  
% 199.48/192.22  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 199.48/192.22  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 199.48/192.22  %-----------------------------------------------------
% 199.48/192.22  ncf(matrix, plain, [(10253 ^ _457920) ^ [] : [10254 ^ _457920 : [(10257 ^ _457920) ^ [] : [closed_subset(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), 10246 ^ [])], (10255 ^ _457920) ^ [] : [-(open_subset(10249 ^ [], 10246 ^ []))]], 10258 ^ _457920 : [(10261 ^ _457920) ^ [] : [open_subset(10249 ^ [], 10246 ^ [])], (10259 ^ _457920) ^ [] : [-(closed_subset(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), 10246 ^ []))]]], (10251 ^ _457920) ^ [] : [-(element(10249 ^ [], powerset(the_carrier(10246 ^ []))))], (10248 ^ _457920) ^ [] : [-(top_str(10246 ^ []))], !, (7941 ^ _84654) ^ [_373989] : [-(in(_373989, succ(_373989)))], (10012 ^ _84654) ^ [_442971, _442973] : [in(_442973, _442971), empty(_442971)], (5733 ^ _84654) ^ [] : [-(function(5729 ^ []))], (8493 ^ _84654) ^ [_392796] : [relation(_392796), -(subset(_392796, cartesian_product2(relation_dom(_392796), relation_rng(_392796))))], (1530 ^ _84654) ^ [_136056] : [v2_membered(_136056), -(v1_membered(_136056))], (10206 ^ _84654) ^ [_449520] : [-(in(_449520, 10204 ^ [_449520]))], (9502 ^ _84654) ^ [_426677, _426679] : [-(disjoint(_426679, _426677)), -(in(9505 ^ [_426677, _426679], set_intersection2(_426679, _426677)))], (5189 ^ _84654) ^ [] : [-(v1_membered(empty_set))], (2439 ^ _84654) ^ [_168862, _168864, _168866] : [relation_of2(_168862, _168866, _168864), -(subset(_168862, cartesian_product2(_168866, _168864)))], (4289 ^ _84654) ^ [] : [true___, -(true___)], (9974 ^ _84654) ^ [_441705] : [-(relation_rng(identity_relation(_441705)) = _441705)], (5595 ^ _84654) ^ [_275648, _275650] : [-(relation(5591 ^ [_275648, _275650]))], (2815 ^ _84654) ^ [_182038, _182040] : [empty(_182040), 2818 ^ _84654 : [(2825 ^ _84654) ^ [] : [empty(_182038), -(element(_182038, _182040))], (2819 ^ _84654) ^ [] : [element(_182038, _182040), -(empty(_182038))]]], (8189 ^ _84654) ^ [_382663] : [relation(_382663), 8192 ^ _84654 : [(8193 ^ _84654) ^ [_382803] : [relation(_382803), -(relation_rng(relation_composition(_382663, _382803)) = relation_image(_382803, relation_rng(_382663)))]]], (8836 ^ _84654) ^ [_404143, _404145] : [element(_404145, _404143), -(empty(_404143)), -(in(_404145, _404143))], (8784 ^ _84654) ^ [_402312] : [-(empty(_402312)), 8790 ^ _84654 : [(8793 ^ _84654) ^ [] : [-(8789 ^ [_402312] = empty_set)], (8791 ^ _84654) ^ [] : [-(in(8789 ^ [_402312], _402312))]], 8795 ^ _84654 : [(8802 ^ _84654) ^ [_402980] : [in(_402980, _402312), -(in(apply(8794 ^ [_402312], _402980), _402980))], (8796 ^ _84654) ^ [] : [-(relation(8794 ^ [_402312]))], (8800 ^ _84654) ^ [] : [-(relation_dom(8794 ^ [_402312]) = _402312)], (8798 ^ _84654) ^ [] : [-(function(8794 ^ [_402312]))]]], (5141 ^ _84654) ^ [] : [-(empty(empty_set))], (5105 ^ _84654) ^ [_259269, _259271] : [v5_membered(_259271), 5108 ^ _84654 : [(5111 ^ _84654) ^ [] : [-(v2_membered(set_difference(_259271, _259269)))], (5113 ^ _84654) ^ [] : [-(v3_membered(set_difference(_259271, _259269)))], (5115 ^ _84654) ^ [] : [-(v4_membered(set_difference(_259271, _259269)))], (5117 ^ _84654) ^ [] : [-(v5_membered(set_difference(_259271, _259269)))], (5109 ^ _84654) ^ [] : [-(v1_membered(set_difference(_259271, _259269)))]]], (864 ^ _84654) ^ [_112691, _112693, _112695, _112697] : [-(relation_image(_112697, _112693) = relation_image(_112695, _112691)), _112697 = _112695, _112693 = _112691], (4321 ^ _84654) ^ [_234534, _234536, _234538, _234540, _234542, _234544] : [-(element(apply_binary_as_element(_234544, _234542, _234540, _234538, _234536, _234534), _234540)), -(empty(_234544)), -(empty(_234542)), function(_234538), quasi_total(_234538, cartesian_product2(_234544, _234542), _234540), relation_of2(_234538, cartesian_product2(_234544, _234542), _234540), element(_234536, _234544), element(_234534, _234542)], (9783 ^ _84654) ^ [_435759] : [relation(_435759), 9786 ^ _84654 : [(9793 ^ _84654) ^ [] : [is_well_founded_in(_435759, relation_field(_435759)), -(well_founded_relation(_435759))], (9787 ^ _84654) ^ [] : [well_founded_relation(_435759), -(is_well_founded_in(_435759, relation_field(_435759)))]]], (2215 ^ _84654) ^ [_160629] : [function(_160629), 2218 ^ _84654 : [(2219 ^ _84654) ^ [_160810, _160812, _160814] : [-(_160812 = _160810), in(ordered_pair(_160814, _160812), _160629), in(ordered_pair(_160814, _160810), _160629)]]], (9307 ^ _84654) ^ [_419976, _419978] : [subset(_419978, _419976), -(_419976 = set_union2(_419978, set_difference(_419976, _419978)))], (7380 ^ _84654) ^ [_352256, _352258] : [topological_space(_352258), top_str(_352258), element(_352256, powerset(the_carrier(_352258))), 7392 ^ _84654 : [(7408 ^ _84654) ^ [_353349] : [-(in(_353349, 7391 ^ [_352256, _352258])), in(_353349, powerset(the_carrier(_352258))), 7413 ^ _84654 : [(7414 ^ _84654) ^ [_353567] : [element(_353567, powerset(the_carrier(_352258))), _353567 = _353349, closed_subset(_353567, _352258), subset(_352256, _353349)]]], (7393 ^ _84654) ^ [_352739] : [in(_352739, 7391 ^ [_352256, _352258]), 7396 ^ _84654 : [(7400 ^ _84654) ^ [] : [-(element(7398 ^ [_352256, _352258, _352739], powerset(the_carrier(_352258))))], (7402 ^ _84654) ^ [] : [-(7398 ^ [_352256, _352258, _352739] = _352739)], (7404 ^ _84654) ^ [] : [-(closed_subset(7398 ^ [_352256, _352258, _352739], _352258))], (7406 ^ _84654) ^ [] : [-(subset(_352256, _352739))], (7397 ^ _84654) ^ [] : [-(in(_352739, powerset(the_carrier(_352258))))]]]]], (5373 ^ _84654) ^ [_268188, _268190] : [relation(_268188), well_ordering(_268188), equipotent(_268190, relation_field(_268188)), 5385 ^ _84654 : [(5388 ^ _84654) ^ [] : [-(well_orders(5384 ^ [_268188, _268190], _268190))], (5386 ^ _84654) ^ [] : [-(relation(5384 ^ [_268188, _268190]))]]], (8290 ^ _84654) ^ [_386022, _386024] : [relation(_386022), function(_386022), finite(_386024), -(finite(relation_image(_386022, _386024)))], (8173 ^ _84654) ^ [_382095, _382097] : [finite(_382097), -(finite(set_intersection2(_382097, _382095)))], (136 ^ _84654) ^ [_88948, _88950] : [-(preboolean(_88948)), _88950 = _88948, preboolean(_88950)], (1408 ^ _84654) ^ [_132254, _132256, _132258] : [element(_132254, powerset(cartesian_product2(_132258, _132256))), -(relation(_132254))], (5119 ^ _84654) ^ [_259794, _259796] : [5126 ^ _84654 : [(5129 ^ _84654) ^ [] : [-(function(relation_dom_restriction(_259796, _259794)))], (5127 ^ _84654) ^ [] : [-(relation(relation_dom_restriction(_259796, _259794)))]], relation(_259796), function(_259796)], (10 ^ _84654) ^ [_85089, _85091, _85093] : [-(_85093 = _85089), _85093 = _85091, _85091 = _85089], (844 ^ _84654) ^ [_111929, _111931] : [_111931 = _111929, -(set_meet(_111931) = set_meet(_111929))], (4499 ^ _84654) ^ [_239416, _239418, _239420] : [relation_of2(_239416, _239420, _239418), -(element(relation_dom_as_subset(_239420, _239418, _239416), powerset(_239420)))], (7273 ^ _84654) ^ [_347715, _347717, _347719] : [in(_347715, 7271 ^ [_347717, _347719]), 7276 ^ _84654 : [(7285 ^ _84654) ^ [] : [-(7279 ^ [_347715, _347717, _347719] = singleton(7278 ^ [_347715, _347717, _347719]))], (7277 ^ _84654) ^ [] : [-(in(_347715, cartesian_product2(_347719, _347717)))], (7283 ^ _84654) ^ [] : [-(in(7278 ^ [_347715, _347717, _347719], _347719))], (7281 ^ _84654) ^ [] : [-(ordered_pair(7278 ^ [_347715, _347717, _347719], 7279 ^ [_347715, _347717, _347719]) = _347715)]]], (2407 ^ _84654) ^ [_167546] : [2409 ^ _84654 : [(2412 ^ _84654) ^ [_167783, _167785] : [2408 ^ [_167546] = ordered_pair(_167785, _167783)], (2410 ^ _84654) ^ [] : [-(in(2408 ^ [_167546], _167546))]], -(relation(_167546))], (1502 ^ _84654) ^ [_135144] : [element(_135144, omega), 1505 ^ _84654 : [(1512 ^ _84654) ^ [] : [-(natural(_135144))], (1506 ^ _84654) ^ [] : [-(epsilon_transitive(_135144))], (1510 ^ _84654) ^ [] : [-(ordinal(_135144))], (1508 ^ _84654) ^ [] : [-(epsilon_connected(_135144))]]], (8365 ^ _84654) ^ [_388687, _388689, _388691] : [-(subset(_388691, set_intersection2(_388689, _388687))), subset(_388691, _388689), subset(_388691, _388687)], (4925 ^ _84654) ^ [_252929, _252931] : [-(relation(set_union2(_252931, _252929))), relation(_252931), relation(_252929)], (2302 ^ _84654) ^ [_163595] : [2303 ^ _84654 : [(2304 ^ _84654) ^ [_163717, _163719] : [_163595 = ordered_pair(_163719, _163717)]], 2305 ^ _84654 : [(2306 ^ _84654) ^ [_163826] : [_163826 = pair_first(_163595), 2309 ^ _84654 : [(2310 ^ _84654) ^ [_163991, _163993] : [_163595 = ordered_pair(_163993, _163991), -(_163826 = _163993)]]], (2316 ^ _84654) ^ [_164180] : [2319 ^ _84654 : [(2322 ^ _84654) ^ [] : [_164180 = 2317 ^ [_163595, _164180]], (2320 ^ _84654) ^ [] : [-(_163595 = ordered_pair(2317 ^ [_163595, _164180], 2318 ^ [_163595, _164180]))]], -(_164180 = pair_first(_163595))]]], (9400 ^ _84654) ^ [_423211, _423213] : [element(_423211, powerset(powerset(_423213))), -(_423211 = empty_set), complements_of_subsets(_423213, _423211) = empty_set], (1432 ^ _84654) ^ [_133110] : [1439 ^ _84654 : [(1446 ^ _84654) ^ [] : [-(natural(_133110))], (1440 ^ _84654) ^ [] : [-(epsilon_transitive(_133110))], (1444 ^ _84654) ^ [] : [-(ordinal(_133110))], (1442 ^ _84654) ^ [] : [-(epsilon_connected(_133110))]], empty(_133110), ordinal(_133110)], (4619 ^ _84654) ^ [] : [true___, -(true___)], (5545 ^ _84654) ^ [_274129, _274131, _274133] : [relation(_274129), function(_274129), 5552 ^ _84654 : [(5561 ^ _84654) ^ [] : [-(in(_274131, relation_dom(relation_dom_restriction(_274129, _274133)))), in(_274131, relation_dom(_274129)), in(_274131, _274133)], (5553 ^ _84654) ^ [] : [in(_274131, relation_dom(relation_dom_restriction(_274129, _274133))), 5556 ^ _84654 : [(5559 ^ _84654) ^ [] : [-(in(_274131, _274133))], (5557 ^ _84654) ^ [] : [-(in(_274131, relation_dom(_274129)))]]]]], (8117 ^ _84654) ^ [_380286, _380288] : [-(subset(relation_image(_380286, relation_inverse_image(_380286, _380288)), _380288)), relation(_380286), function(_380286)], (102 ^ _84654) ^ [_87942, _87944, _87946, _87948] : [-(is_reflexive_in(_87946, _87942)), is_reflexive_in(_87948, _87944), _87948 = _87946, _87944 = _87942], (8865 ^ _84654) ^ [_405142, _405144, _405146] : [relation(_405142), in(ordered_pair(_405146, _405144), _405142), 8872 ^ _84654 : [(8875 ^ _84654) ^ [] : [-(in(_405144, relation_field(_405142)))], (8873 ^ _84654) ^ [] : [-(in(_405146, relation_field(_405142)))]]], (10018 ^ _84654) ^ [_443183, _443185] : [-(pair_first(ordered_pair(_443185, _443183)) = _443185)], (5075 ^ _84654) ^ [_258212, _258214] : [-(relation(set_difference(_258214, _258212))), relation(_258214), relation(_258212)], (5330 ^ _84654) ^ [_266607] : [relation(_266607), 5333 ^ _84654 : [(5334 ^ _84654) ^ [] : [transitive(_266607), 5337 ^ _84654 : [(5338 ^ _84654) ^ [_266899, _266901, _266903] : [-(in(ordered_pair(_266903, _266899), _266607)), in(ordered_pair(_266903, _266901), _266607), in(ordered_pair(_266901, _266899), _266607)]]], (5348 ^ _84654) ^ [] : [5352 ^ _84654 : [(5357 ^ _84654) ^ [] : [in(ordered_pair(5349 ^ [_266607], 5351 ^ [_266607]), _266607)], (5355 ^ _84654) ^ [] : [-(in(ordered_pair(5350 ^ [_266607], 5351 ^ [_266607]), _266607))], (5353 ^ _84654) ^ [] : [-(in(ordered_pair(5349 ^ [_266607], 5350 ^ [_266607]), _266607))]], -(transitive(_266607))]]], (5714 ^ _84654) ^ [_279601] : [-(empty(5710 ^ [_279601]))], (2734 ^ _84654) ^ [_179318] : [epsilon_transitive(_179318), 2737 ^ _84654 : [(2738 ^ _84654) ^ [_179449] : [in(_179449, _179318), -(subset(_179449, _179318))]]], (5624 ^ _84654) ^ [] : [-(epsilon_connected(5620 ^ []))], (5628 ^ _84654) ^ [] : [-(being_limit_ordinal(5620 ^ []))], (994 ^ _84654) ^ [_117406, _117408, _117410, _117412] : [-(complements_of_subsets(_117412, _117408) = complements_of_subsets(_117410, _117406)), _117412 = _117410, _117408 = _117406], (1486 ^ _84654) ^ [_134689] : [v4_membered(_134689), -(v3_membered(_134689))], (4815 ^ _84654) ^ [_249371] : [empty(succ(_249371))], (268 ^ _84654) ^ [_92951, _92953] : [-(epsilon_transitive(_92951)), _92953 = _92951, epsilon_transitive(_92953)], (1536 ^ _84654) ^ [_136241, _136243] : [-(unordered_pair(_136243, _136241) = unordered_pair(_136241, _136243))], (4589 ^ _84654) ^ [_242298, _242300] : [element(_242298, powerset(powerset(_242300))), -(element(complements_of_subsets(_242300, _242298), powerset(powerset(_242300))))], (400 ^ _84654) ^ [_96954, _96956] : [-(topological_space(_96954)), _96956 = _96954, topological_space(_96956)], (8774 ^ _84654) ^ [_401922] : [-(relation(8772 ^ [_401922]))], (3084 ^ _84654) ^ [_191764] : [relation(_191764), 3087 ^ _84654 : [(3088 ^ _84654) ^ [_191922] : [relation(_191922), 3091 ^ _84654 : [(3092 ^ _84654) ^ [] : [subset(_191764, _191922), 3095 ^ _84654 : [(3096 ^ _84654) ^ [_192198, _192200] : [in(ordered_pair(_192200, _192198), _191764), -(in(ordered_pair(_192200, _192198), _191922))]]], (3102 ^ _84654) ^ [] : [3105 ^ _84654 : [(3108 ^ _84654) ^ [] : [in(ordered_pair(3103 ^ [_191764, _191922], 3104 ^ [_191764, _191922]), _191922)], (3106 ^ _84654) ^ [] : [-(in(ordered_pair(3103 ^ [_191764, _191922], 3104 ^ [_191764, _191922]), _191764))]], -(subset(_191764, _191922))]]]]], (5197 ^ _84654) ^ [] : [-(v5_membered(empty_set))], (4459 ^ _84654) ^ [] : [true___, -(true___)], (5919 ^ _84654) ^ [_286317, _286319] : [ordinal(_286319), ordinal(_286317), 5926 ^ _84654 : [(5933 ^ _84654) ^ [] : [subset(_286319, _286317), -(ordinal_subset(_286319, _286317))], (5927 ^ _84654) ^ [] : [ordinal_subset(_286319, _286317), -(subset(_286319, _286317))]]], (4789 ^ _84654) ^ [_248625] : [-(cup_closed(powerset(_248625)))], (8707 ^ _84654) ^ [_399938, _399940] : [relation(_399938), antisymmetric(_399938), -(antisymmetric(relation_restriction(_399938, _399940)))], (5047 ^ _84654) ^ [_257353] : [5058 ^ _84654 : [(5061 ^ _84654) ^ [] : [-(function(relation_inverse(_257353)))], (5059 ^ _84654) ^ [] : [-(relation(relation_inverse(_257353)))]], relation(_257353), function(_257353), one_to_one(_257353)], (3258 ^ _84654) ^ [_197956] : [-(ordinal(_197956)), epsilon_transitive(_197956), epsilon_connected(_197956)], (9114 ^ _84654) ^ [_413371, _413373] : [subset(_413373, _413371), -(element(_413373, powerset(_413371)))], (5759 ^ _84654) ^ [] : [-(relation_empty_yielding(5755 ^ []))], (6518 ^ _84654) ^ [_312351] : [6522 ^ _84654 : [(6525 ^ _84654) ^ [] : [-(6520 ^ [_312351] = singleton(6519 ^ [_312351]))], (6527 ^ _84654) ^ [] : [-(in(6519 ^ [_312351], _312351))], (6529 ^ _84654) ^ [] : [-(6521 ^ [_312351] = singleton(6519 ^ [_312351]))], (6531 ^ _84654) ^ [] : [6520 ^ [_312351] = 6521 ^ [_312351]], (6523 ^ _84654) ^ [] : [-(in(6519 ^ [_312351], _312351))]], 6533 ^ _84654 : [(6545 ^ _84654) ^ [_313649] : [-(in(_313649, 6532 ^ [_312351])), 6546 ^ _84654 : [(6547 ^ _84654) ^ [_313756] : [in(_313756, _312351), in(_313756, _312351), _313649 = singleton(_313756)]]], (6534 ^ _84654) ^ [_313237] : [in(_313237, 6532 ^ [_312351]), 6538 ^ _84654 : [(6543 ^ _84654) ^ [] : [-(_313237 = singleton(6537 ^ [_312351, _313237]))], (6541 ^ _84654) ^ [] : [-(in(6537 ^ [_312351, _313237], _312351))], (6539 ^ _84654) ^ [] : [-(in(6537 ^ [_312351, _313237], _312351))]]]]], (644 ^ _84654) ^ [_104569, _104571, _104573, _104575] : [-(are_equipotent(_104573, _104569)), are_equipotent(_104575, _104571), _104575 = _104573, _104571 = _104569], (7620 ^ _84654) ^ [_361310, _361312] : [-(empty(_361312)), relation(_361310), 7677 ^ _84654 : [(7684 ^ _84654) ^ [_364400] : [in(_364400, _361312), 7688 ^ _84654 : [(7693 ^ _84654) ^ [_364844] : [in(_364844, 7687 ^ [_361310, _361312, _364400]), -(in(ordered_pair(apply(7676 ^ [_361310, _361312], _364400), _364844), _361310))], (7691 ^ _84654) ^ [] : [-(in(apply(7676 ^ [_361310, _361312], _364400), 7687 ^ [_361310, _361312, _364400]))], (7689 ^ _84654) ^ [] : [-(_364400 = 7687 ^ [_361310, _361312, _364400])]]], (7678 ^ _84654) ^ [] : [-(relation(7676 ^ [_361310, _361312]))], (7682 ^ _84654) ^ [] : [-(relation_dom(7676 ^ [_361310, _361312]) = _361312)], (7680 ^ _84654) ^ [] : [-(function(7676 ^ [_361310, _361312]))]], 7661 ^ _84654 : [(7664 ^ _84654) ^ [_363586, _363588] : [7660 ^ [_361310, _361312] = _363586, in(_363588, _363586), 7672 ^ _84654 : [(7675 ^ _84654) ^ [] : [in(ordered_pair(_363588, 7671 ^ [_361310, _361312, _363586, _363588]), _361310)], (7673 ^ _84654) ^ [] : [-(in(7671 ^ [_361310, _361312, _363586, _363588], _363586))]]], (7662 ^ _84654) ^ [] : [-(in(7660 ^ [_361310, _361312], _361312))]], 7634 ^ _84654 : [(7640 ^ _84654) ^ [] : [-(in(7632 ^ [_361310, _361312], 7636 ^ [_361310, _361312]))], (7649 ^ _84654) ^ [] : [-(7631 ^ [_361310, _361312] = 7647 ^ [_361310, _361312])], (7642 ^ _84654) ^ [_362639] : [in(_362639, 7636 ^ [_361310, _361312]), -(in(ordered_pair(7632 ^ [_361310, _361312], _362639), _361310))], (7651 ^ _84654) ^ [] : [-(in(7633 ^ [_361310, _361312], 7647 ^ [_361310, _361312]))], (7635 ^ _84654) ^ [] : [-(in(7631 ^ [_361310, _361312], _361312))], (7659 ^ _84654) ^ [] : [7632 ^ [_361310, _361312] = 7633 ^ [_361310, _361312]], (7638 ^ _84654) ^ [] : [-(7631 ^ [_361310, _361312] = 7636 ^ [_361310, _361312])], (7653 ^ _84654) ^ [_363115] : [in(_363115, 7647 ^ [_361310, _361312]), -(in(ordered_pair(7633 ^ [_361310, _361312], _363115), _361310))]]], (5869 ^ _84654) ^ [_284504, _284506, _284508] : [relation_of2(_284504, _284508, _284506), -(relation_rng_as_subset(_284508, _284506, _284504) = relation_rng(_284504))], (4419 ^ _84654) ^ [] : [true___, -(true___)], (7943 ^ _84654) ^ [_374126, _374128, _374130, _374132] : [unordered_pair(_374132, _374130) = unordered_pair(_374128, _374126), -(_374132 = _374128), -(_374132 = _374126)], (496 ^ _84654) ^ [_99926, _99928] : [-(one_to_one(_99926)), _99928 = _99926, one_to_one(_99928)], (7287 ^ _84654) ^ [_348361, _348363, _348365] : [-(in(_348361, 7271 ^ [_348363, _348365])), in(_348361, cartesian_product2(_348365, _348363)), 7292 ^ _84654 : [(7293 ^ _84654) ^ [_348587, _348589] : [ordered_pair(_348589, _348587) = _348361, in(_348589, _348365), _348587 = singleton(_348589)]]], (9741 ^ _84654) ^ [_434447] : [relation(_434447), -(in(ordered_pair(9746 ^ [_434447], 9747 ^ [_434447]), _434447)), -(_434447 = empty_set)], (6559 ^ _84654) ^ [_314136, _314138] : [6563 ^ _84654 : [(6574 ^ _84654) ^ [] : [-(6560 ^ [_314136, _314138] = 6562 ^ [_314136, _314138])], (6584 ^ _84654) ^ [] : [6561 ^ [_314136, _314138] = 6562 ^ [_314136, _314138]], (6582 ^ _84654) ^ [] : [-(6576 ^ [_314136, _314138] = singleton(6575 ^ [_314136, _314138]))], (6578 ^ _84654) ^ [] : [-(ordered_pair(6575 ^ [_314136, _314138], 6576 ^ [_314136, _314138]) = 6562 ^ [_314136, _314138])], (6564 ^ _84654) ^ [] : [-(6560 ^ [_314136, _314138] = 6561 ^ [_314136, _314138])], (6572 ^ _84654) ^ [] : [-(6566 ^ [_314136, _314138] = singleton(6565 ^ [_314136, _314138]))], (6568 ^ _84654) ^ [] : [-(ordered_pair(6565 ^ [_314136, _314138], 6566 ^ [_314136, _314138]) = 6561 ^ [_314136, _314138])], (6570 ^ _84654) ^ [] : [-(in(6565 ^ [_314136, _314138], _314138))], (6580 ^ _84654) ^ [] : [-(in(6575 ^ [_314136, _314138], _314138))]], 6586 ^ _84654 : [(6604 ^ _84654) ^ [_316849] : [-(in(_316849, 6585 ^ [_314136, _314138])), 6605 ^ _84654 : [(6606 ^ _84654) ^ [_316990] : [in(_316990, cartesian_product2(_314138, _314136)), _316990 = _316849, 6613 ^ _84654 : [(6614 ^ _84654) ^ [_317270, _317272] : [ordered_pair(_317272, _317270) = _316849, in(_317272, _314138), _317270 = singleton(_317272)]]]]], (6587 ^ _84654) ^ [_316009] : [in(_316009, 6585 ^ [_314136, _314138]), 6591 ^ _84654 : [(6594 ^ _84654) ^ [] : [-(6590 ^ [_314136, _314138, _316009] = _316009)], (6598 ^ _84654) ^ [] : [-(ordered_pair(6595 ^ [_314136, _314138, _316009], 6596 ^ [_314136, _314138, _316009]) = _316009)], (6600 ^ _84654) ^ [] : [-(in(6595 ^ [_314136, _314138, _316009], _314138))], (6602 ^ _84654) ^ [] : [-(6596 ^ [_314136, _314138, _316009] = singleton(6595 ^ [_314136, _314138, _316009]))], (6592 ^ _84654) ^ [] : [-(in(6590 ^ [_314136, _314138, _316009], cartesian_product2(_314138, _314136)))]]]]], (9916 ^ _84654) ^ [_439861] : [-(unordered_pair(_439861, _439861) = singleton(_439861))], (4817 ^ _84654) ^ [] : [-(epsilon_transitive(omega))], (2416 ^ _84654) ^ [_167940] : [relation(_167940), 2419 ^ _84654 : [(2420 ^ _84654) ^ [_168114] : [is_reflexive_in(_167940, _168114), 2423 ^ _84654 : [(2424 ^ _84654) ^ [_168256] : [in(_168256, _168114), -(in(ordered_pair(_168256, _168256), _167940))]]], (2430 ^ _84654) ^ [_168439] : [2432 ^ _84654 : [(2435 ^ _84654) ^ [] : [in(ordered_pair(2431 ^ [_167940, _168439], 2431 ^ [_167940, _168439]), _167940)], (2433 ^ _84654) ^ [] : [-(in(2431 ^ [_167940, _168439], _168439))]], -(is_reflexive_in(_167940, _168439))]]], (5661 ^ _84654) ^ [_277818] : [-(relation(5655 ^ [_277818]))], (9244 ^ _84654) ^ [_417700] : [relation(_417700), 9247 ^ _84654 : [(9248 ^ _84654) ^ [_417837] : [relation(_417837), -(subset(relation_dom(relation_composition(_417700, _417837)), relation_dom(_417700)))]]], (4951 ^ _84654) ^ [_253813, _253815] : [v3_membered(_253815), 4954 ^ _84654 : [(4959 ^ _84654) ^ [] : [-(v3_membered(set_intersection2(_253815, _253813)))], (4957 ^ _84654) ^ [] : [-(v2_membered(set_intersection2(_253815, _253813)))], (4955 ^ _84654) ^ [] : [-(v1_membered(set_intersection2(_253815, _253813)))]]], (5671 ^ _84654) ^ [_278158] : [-(ordinal(5655 ^ [_278158]))], (5306 ^ _84654) ^ [_265749, _265751] : [in(_265751, _265749), -(set_union2(singleton(_265751), _265749) = _265749)], (5009 ^ _84654) ^ [_255970, _255972] : [v5_membered(_255972), 5012 ^ _84654 : [(5015 ^ _84654) ^ [] : [-(v2_membered(set_intersection2(_255970, _255972)))], (5017 ^ _84654) ^ [] : [-(v3_membered(set_intersection2(_255970, _255972)))], (5019 ^ _84654) ^ [] : [-(v4_membered(set_intersection2(_255970, _255972)))], (5021 ^ _84654) ^ [] : [-(v5_membered(set_intersection2(_255970, _255972)))], (5013 ^ _84654) ^ [] : [-(v1_membered(set_intersection2(_255970, _255972)))]]], (1793 ^ _84654) ^ [_145242, _145244] : [relation(_145242), 1796 ^ _84654 : [(1797 ^ _84654) ^ [_145413] : [relation(_145413), 1800 ^ _84654 : [(1801 ^ _84654) ^ [] : [_145413 = relation_rng_restriction(_145244, _145242), 1804 ^ _84654 : [(1813 ^ _84654) ^ [_146019, _146021] : [-(in(ordered_pair(_146021, _146019), _145413)), in(_146019, _145244), in(ordered_pair(_146021, _146019), _145242)], (1805 ^ _84654) ^ [_145740, _145742] : [in(ordered_pair(_145742, _145740), _145413), 1808 ^ _84654 : [(1811 ^ _84654) ^ [] : [-(in(ordered_pair(_145742, _145740), _145242))], (1809 ^ _84654) ^ [] : [-(in(_145740, _145244))]]]]], (1823 ^ _84654) ^ [] : [-(_145413 = relation_rng_restriction(_145244, _145242)), 1836 ^ _84654 : [(1841 ^ _84654) ^ [] : [in(ordered_pair(1824 ^ [_145242, _145244, _145413], 1825 ^ [_145242, _145244, _145413]), _145413)], (1839 ^ _84654) ^ [] : [-(in(ordered_pair(1824 ^ [_145242, _145244, _145413], 1825 ^ [_145242, _145244, _145413]), _145242))], (1837 ^ _84654) ^ [] : [-(in(1825 ^ [_145242, _145244, _145413], _145244))]], 1828 ^ _84654 : [(1831 ^ _84654) ^ [] : [in(1825 ^ [_145242, _145244, _145413], _145244), in(ordered_pair(1824 ^ [_145242, _145244, _145413], 1825 ^ [_145242, _145244, _145413]), _145242)], (1829 ^ _84654) ^ [] : [-(in(ordered_pair(1824 ^ [_145242, _145244, _145413], 1825 ^ [_145242, _145244, _145413]), _145413))]]]]]]], (4863 ^ _84654) ^ [] : [-(empty(empty_set))], (9044 ^ _84654) ^ [_411121, _411123, _411125] : [subset(unordered_pair(_411125, _411123), _411121), 9047 ^ _84654 : [(9050 ^ _84654) ^ [] : [-(in(_411123, _411121))], (9048 ^ _84654) ^ [] : [-(in(_411125, _411121))]]], (696 ^ _84654) ^ [_106196, _106198, _106200, _106202] : [-(open_subset(_106200, _106196)), open_subset(_106202, _106198), _106202 = _106200, _106198 = _106196], (9946 ^ _84654) ^ [_440802] : [ordinal(_440802), -(well_founded_relation(inclusion_relation(_440802)))], (9410 ^ _84654) ^ [_423528, _423530] : [in(_423530, _423528), -(set_union2(singleton(_423530), _423528) = _423528)], (5678 ^ _84654) ^ [] : [-(relation(5676 ^ []))], (4657 ^ _84654) ^ [_244261] : [meet_semilatt_str(_244261), 4660 ^ _84654 : [(4665 ^ _84654) ^ [] : [-(relation_of2_as_subset(the_L_meet(_244261), cartesian_product2(the_carrier(_244261), the_carrier(_244261)), the_carrier(_244261)))], (4663 ^ _84654) ^ [] : [-(quasi_total(the_L_meet(_244261), cartesian_product2(the_carrier(_244261), the_carrier(_244261)), the_carrier(_244261)))], (4661 ^ _84654) ^ [] : [-(function(the_L_meet(_244261)))]]], (6405 ^ _84654) ^ [_305648, _305650] : [-(empty(_305650)), relation(_305648), 6412 ^ _84654 : [(6413 ^ _84654) ^ [_306116] : [6417 ^ _84654 : [(6446 ^ _84654) ^ [] : [-(6438 ^ [_305648, _305650, _306116] = 6444 ^ [_305648, _305650, _306116])], (6427 ^ _84654) ^ [] : [-(6419 ^ [_305648, _305650, _306116] = 6425 ^ [_305648, _305650, _306116])], (6418 ^ _84654) ^ [] : [-(6414 ^ [_305648, _305650, _306116] = 6415 ^ [_305648, _305650, _306116])], (6431 ^ _84654) ^ [_307894] : [in(_307894, 6425 ^ [_305648, _305650, _306116]), -(in(ordered_pair(6420 ^ [_305648, _305650, _306116], _307894), _305648))], (6422 ^ _84654) ^ [] : [-(ordered_pair(6419 ^ [_305648, _305650, _306116], 6420 ^ [_305648, _305650, _306116]) = 6415 ^ [_305648, _305650, _306116])], (6441 ^ _84654) ^ [] : [-(ordered_pair(6438 ^ [_305648, _305650, _306116], 6439 ^ [_305648, _305650, _306116]) = 6416 ^ [_305648, _305650, _306116])], (6448 ^ _84654) ^ [] : [-(in(6439 ^ [_305648, _305650, _306116], 6444 ^ [_305648, _305650, _306116]))], (6443 ^ _84654) ^ [] : [-(in(6438 ^ [_305648, _305650, _306116], _305650))], (6429 ^ _84654) ^ [] : [-(in(6420 ^ [_305648, _305650, _306116], 6425 ^ [_305648, _305650, _306116]))], (6450 ^ _84654) ^ [_308913] : [in(_308913, 6444 ^ [_305648, _305650, _306116]), -(in(ordered_pair(6439 ^ [_305648, _305650, _306116], _308913), _305648))], (6456 ^ _84654) ^ [] : [6415 ^ [_305648, _305650, _306116] = 6416 ^ [_305648, _305650, _306116]], (6437 ^ _84654) ^ [] : [-(6414 ^ [_305648, _305650, _306116] = 6416 ^ [_305648, _305650, _306116])], (6424 ^ _84654) ^ [] : [-(in(6419 ^ [_305648, _305650, _306116], _305650))]], 6458 ^ _84654 : [(6485 ^ _84654) ^ [_310889] : [-(in(_310889, 6457 ^ [_305648, _305650, _306116])), 6486 ^ _84654 : [(6487 ^ _84654) ^ [_311065] : [in(_311065, cartesian_product2(_305650, _306116)), _311065 = _310889, 6494 ^ _84654 : [(6495 ^ _84654) ^ [_311384, _311386] : [ordered_pair(_311386, _311384) = _310889, in(_311386, _305650), 6502 ^ _84654 : [(6503 ^ _84654) ^ [_311682] : [_311386 = _311682, in(_311384, _311682), 6511 ^ _84654 : [(6514 ^ _84654) ^ [] : [in(ordered_pair(_311384, 6510 ^ [_305648, _305650, _306116, _310889, _311065, _311384, _311386, _311682]), _305648)], (6512 ^ _84654) ^ [] : [-(in(6510 ^ [_305648, _305650, _306116, _310889, _311065, _311384, _311386, _311682], _311682))]]]]]]]]], (6459 ^ _84654) ^ [_309403] : [in(_309403, 6457 ^ [_305648, _305650, _306116]), 6463 ^ _84654 : [(6475 ^ _84654) ^ [] : [-(6467 ^ [_305648, _305650, _306116, _309403] = 6473 ^ [_305648, _305650, _306116, _309403])], (6466 ^ _84654) ^ [] : [-(6462 ^ [_305648, _305650, _306116, _309403] = _309403)], (6464 ^ _84654) ^ [] : [-(in(6462 ^ [_305648, _305650, _306116, _309403], cartesian_product2(_305650, _306116)))], (6470 ^ _84654) ^ [] : [-(ordered_pair(6467 ^ [_305648, _305650, _306116, _309403], 6468 ^ [_305648, _305650, _306116, _309403]) = _309403)], (6477 ^ _84654) ^ [] : [-(in(6468 ^ [_305648, _305650, _306116, _309403], 6473 ^ [_305648, _305650, _306116, _309403]))], (6479 ^ _84654) ^ [_310634] : [in(_310634, 6473 ^ [_305648, _305650, _306116, _309403]), -(in(ordered_pair(6468 ^ [_305648, _305650, _306116, _309403], _310634), _305648))], (6472 ^ _84654) ^ [] : [-(in(6467 ^ [_305648, _305650, _306116, _309403], _305650))]]]]]]], (9918 ^ _84654) ^ [_439959] : [empty(_439959), -(_439959 = empty_set)], (5504 ^ _84654) ^ [_272593, _272595] : [5505 ^ _84654 : [(5508 ^ _84654) ^ [] : [_272595 = singleton(_272593)], (5506 ^ _84654) ^ [] : [_272595 = empty_set]], -(subset(_272595, singleton(_272593)))], (7584 ^ _84654) ^ [_359932, _359934] : [ordinal(_359932), 7588 ^ _84654 : [(7602 ^ _84654) ^ [_360714] : [-(in(_360714, 7587 ^ [_359932, _359934])), in(_360714, succ(_359932)), 7607 ^ _84654 : [(7608 ^ _84654) ^ [_360917] : [ordinal(_360917), _360714 = _360917, in(_360917, _359934)]]], (7589 ^ _84654) ^ [_360205] : [in(_360205, 7587 ^ [_359932, _359934]), 7592 ^ _84654 : [(7600 ^ _84654) ^ [] : [-(in(7594 ^ [_359932, _359934, _360205], _359934))], (7593 ^ _84654) ^ [] : [-(in(_360205, succ(_359932)))], (7598 ^ _84654) ^ [] : [-(_360205 = 7594 ^ [_359932, _359934, _360205])], (7596 ^ _84654) ^ [] : [-(ordinal(7594 ^ [_359932, _359934, _360205]))]]]]], (10218 ^ _84654) ^ [_449947, _449949] : [in(_449947, 10204 ^ [_449949]), 10222 ^ _84654 : [(10225 ^ _84654) ^ [_450259] : [subset(_450259, _449947), -(in(_450259, 10221 ^ [_449947, _449949]))], (10223 ^ _84654) ^ [] : [-(in(10221 ^ [_449947, _449949], 10204 ^ [_449949]))]]], (9801 ^ _84654) ^ [] : [-(relation_dom(empty_set) = empty_set)], (9773 ^ _84654) ^ [_435463, _435465, _435467] : [in(_435467, _435465), element(_435465, powerset(_435463)), empty(_435463)], (3636 ^ _84654) ^ [_211019] : [relation(_211019), 3639 ^ _84654 : [(3640 ^ _84654) ^ [_211200] : [_211200 = relation_rng(_211019), 3643 ^ _84654 : [(3651 ^ _84654) ^ [_211624] : [3652 ^ _84654 : [(3653 ^ _84654) ^ [_211703] : [in(ordered_pair(_211703, _211624), _211019)]], -(in(_211624, _211200))], (3644 ^ _84654) ^ [_211380] : [in(_211380, _211200), -(in(ordered_pair(3647 ^ [_211019, _211200, _211380], _211380), _211019))]]], (3657 ^ _84654) ^ [_211831] : [-(_211831 = relation_rng(_211019)), 3661 ^ _84654 : [(3664 ^ _84654) ^ [_212094] : [in(ordered_pair(_212094, 3658 ^ [_211019, _211831]), _211019)], (3662 ^ _84654) ^ [] : [-(in(3658 ^ [_211019, _211831], _211831))]], 3666 ^ _84654 : [(3669 ^ _84654) ^ [] : [in(3658 ^ [_211019, _211831], _211831)], (3667 ^ _84654) ^ [] : [-(in(ordered_pair(3665 ^ [_211019, _211831], 3658 ^ [_211019, _211831]), _211019))]]]]], (4207 ^ _84654) ^ [_231798] : [relation(_231798), 4210 ^ _84654 : [(4217 ^ _84654) ^ [] : [is_reflexive_in(_231798, relation_field(_231798)), -(reflexive(_231798))], (4211 ^ _84654) ^ [] : [reflexive(_231798), -(is_reflexive_in(_231798, relation_field(_231798)))]]], (5572 ^ _84654) ^ [] : [empty(5570 ^ [])], (4081 ^ _84654) ^ [_227256] : [relation(_227256), 4084 ^ _84654 : [(4085 ^ _84654) ^ [_227470] : [is_transitive_in(_227256, _227470), 4088 ^ _84654 : [(4089 ^ _84654) ^ [_227680, _227682, _227684] : [-(in(ordered_pair(_227684, _227680), _227256)), in(_227684, _227470), in(_227682, _227470), in(_227680, _227470), in(ordered_pair(_227684, _227682), _227256), in(ordered_pair(_227682, _227680), _227256)]]], (4111 ^ _84654) ^ [_228291] : [4115 ^ _84654 : [(4124 ^ _84654) ^ [] : [-(in(ordered_pair(4113 ^ [_227256, _228291], 4114 ^ [_227256, _228291]), _227256))], (4122 ^ _84654) ^ [] : [-(in(ordered_pair(4112 ^ [_227256, _228291], 4113 ^ [_227256, _228291]), _227256))], (4126 ^ _84654) ^ [] : [in(ordered_pair(4112 ^ [_227256, _228291], 4114 ^ [_227256, _228291]), _227256)], (4116 ^ _84654) ^ [] : [-(in(4112 ^ [_227256, _228291], _228291))], (4118 ^ _84654) ^ [] : [-(in(4113 ^ [_227256, _228291], _228291))], (4120 ^ _84654) ^ [] : [-(in(4114 ^ [_227256, _228291], _228291))]], -(is_transitive_in(_227256, _228291))]]], (1104 ^ _84654) ^ [_121384, _121386, _121388, _121390] : [-(set_union2(_121390, _121386) = set_union2(_121388, _121384)), _121390 = _121388, _121386 = _121384], (3673 ^ _84654) ^ [_212474, _212476] : [element(_212474, powerset(_212476)), -(subset_complement(_212476, _212474) = set_difference(_212476, _212474))], (4401 ^ _84654) ^ [] : [true___, -(true___)], (1288 ^ _84654) ^ [_128202] : [empty(_128202), 1291 ^ _84654 : [(1294 ^ _84654) ^ [] : [-(v2_membered(_128202))], (1296 ^ _84654) ^ [] : [-(v3_membered(_128202))], (1298 ^ _84654) ^ [] : [-(v4_membered(_128202))], (1300 ^ _84654) ^ [] : [-(v5_membered(_128202))], (1292 ^ _84654) ^ [] : [-(v1_membered(_128202))]]], (5606 ^ _84654) ^ [] : [-(v2_membered(5600 ^ []))], (1098 ^ _84654) ^ [_121138, _121140] : [_121140 = _121138, -(relation_field(_121140) = relation_field(_121138))], (1162 ^ _84654) ^ [_123446, _123448] : [_123448 = _123446, -(union(_123448) = union(_123446))], (8383 ^ _84654) ^ [_389307, _389309, _389311] : [-(subset(_389311, _389307)), subset(_389311, _389309), subset(_389309, _389307)], (7430 ^ _84654) ^ [_354071, _354073] : [topological_space(_354073), top_str(_354073), element(_354071, powerset(powerset(the_carrier(_354073)))), 7442 ^ _84654 : [(7451 ^ _84654) ^ [_354795] : [-(in(_354795, 7441 ^ [_354071, _354073])), in(_354795, powerset(the_carrier(_354073))), in(set_difference(cast_as_carrier_subset(_354073), _354795), _354071)], (7443 ^ _84654) ^ [_354514] : [in(_354514, 7441 ^ [_354071, _354073]), 7446 ^ _84654 : [(7449 ^ _84654) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_354073), _354514), _354071))], (7447 ^ _84654) ^ [] : [-(in(_354514, powerset(the_carrier(_354073))))]]]]], (8304 ^ _84654) ^ [_386396] : [one_sorted_str(_386396), 8307 ^ _84654 : [(8308 ^ _84654) ^ [_386544] : [element(_386544, powerset(the_carrier(_386396))), -(subset_complement(the_carrier(_386396), _386544) = subset_difference(the_carrier(_386396), cast_as_carrier_subset(_386396), _386544))]]], (2129 ^ _84654) ^ [_157626, _157628, _157630, _157632] : [_157626 = unordered_triple(_157632, _157630, _157628), 2132 ^ _84654 : [(2133 ^ _84654) ^ [_157828] : [in(_157828, _157626), -(_157828 = _157632), -(_157828 = _157630), -(_157828 = _157628)], (2147 ^ _84654) ^ [_158228] : [2148 ^ _84654 : [(2153 ^ _84654) ^ [] : [_158228 = _157628], (2151 ^ _84654) ^ [] : [_158228 = _157630], (2149 ^ _84654) ^ [] : [_158228 = _157632]], -(in(_158228, _157626))]]], (10157 ^ _84654) ^ [_447764, _447766] : [in(_447766, _447764), -(subset(_447766, union(_447764)))], (2048 ^ _84654) ^ [_154674] : [relation(_154674), 2051 ^ _84654 : [(2052 ^ _84654) ^ [_154881, _154883] : [_154881 = relation_inverse_image(_154674, _154883), 2055 ^ _84654 : [(2065 ^ _84654) ^ [_155427] : [-(in(_155427, _154881)), 2066 ^ _84654 : [(2067 ^ _84654) ^ [_155532] : [in(ordered_pair(_155427, _155532), _154674), in(_155532, _154883)]]], (2056 ^ _84654) ^ [_155073] : [in(_155073, _154881), 2060 ^ _84654 : [(2063 ^ _84654) ^ [] : [-(in(2059 ^ [_154674, _154881, _154883, _155073], _154883))], (2061 ^ _84654) ^ [] : [-(in(ordered_pair(_155073, 2059 ^ [_154674, _154881, _154883, _155073]), _154674))]]]]], (2075 ^ _84654) ^ [_155787, _155789] : [-(_155787 = relation_inverse_image(_154674, _155789)), 2088 ^ _84654 : [(2093 ^ _84654) ^ [] : [in(2076 ^ [_154674, _155787, _155789], _155787)], (2091 ^ _84654) ^ [] : [-(in(2087 ^ [_154674, _155787, _155789], _155789))], (2089 ^ _84654) ^ [] : [-(in(ordered_pair(2076 ^ [_154674, _155787, _155789], 2087 ^ [_154674, _155787, _155789]), _154674))]], 2079 ^ _84654 : [(2082 ^ _84654) ^ [_156091] : [in(ordered_pair(2076 ^ [_154674, _155787, _155789], _156091), _154674), in(_156091, _155789)], (2080 ^ _84654) ^ [] : [-(in(2076 ^ [_154674, _155787, _155789], _155787))]]]]], (5719 ^ _84654) ^ [_279790] : [-(empty(_279790)), 5723 ^ _84654 : [(5728 ^ _84654) ^ [] : [-(finite(5722 ^ [_279790]))], (5726 ^ _84654) ^ [] : [empty(5722 ^ [_279790])], (5724 ^ _84654) ^ [] : [-(element(5722 ^ [_279790], powerset(_279790)))]]], (1999 ^ _84654) ^ [_152655] : [relation(_152655), 2002 ^ _84654 : [(2003 ^ _84654) ^ [_152862, _152864] : [_152862 = relation_image(_152655, _152864), 2006 ^ _84654 : [(2016 ^ _84654) ^ [_153408] : [-(in(_153408, _152862)), 2017 ^ _84654 : [(2018 ^ _84654) ^ [_153513] : [in(ordered_pair(_153513, _153408), _152655), in(_153513, _152864)]]], (2007 ^ _84654) ^ [_153054] : [in(_153054, _152862), 2011 ^ _84654 : [(2014 ^ _84654) ^ [] : [-(in(2010 ^ [_152655, _152862, _152864, _153054], _152864))], (2012 ^ _84654) ^ [] : [-(in(ordered_pair(2010 ^ [_152655, _152862, _152864, _153054], _153054), _152655))]]]]], (2026 ^ _84654) ^ [_153768, _153770] : [-(_153768 = relation_image(_152655, _153770)), 2039 ^ _84654 : [(2044 ^ _84654) ^ [] : [in(2027 ^ [_152655, _153768, _153770], _153768)], (2042 ^ _84654) ^ [] : [-(in(2038 ^ [_152655, _153768, _153770], _153770))], (2040 ^ _84654) ^ [] : [-(in(ordered_pair(2038 ^ [_152655, _153768, _153770], 2027 ^ [_152655, _153768, _153770]), _152655))]], 2030 ^ _84654 : [(2033 ^ _84654) ^ [_154072] : [in(ordered_pair(_154072, 2027 ^ [_152655, _153768, _153770]), _152655), in(_154072, _153770)], (2031 ^ _84654) ^ [] : [-(in(2027 ^ [_152655, _153768, _153770], _153768))]]]]], (5599 ^ _84654) ^ [_275772, _275774] : [-(quasi_total(5591 ^ [_275772, _275774], _275774, _275772))], (2648 ^ _84654) ^ [_176074] : [_176074 = empty_set, 2651 ^ _84654 : [(2652 ^ _84654) ^ [_176187] : [in(_176187, _176074)]]], (8347 ^ _84654) ^ [_388035, _388037] : [relation(_388035), -(relation_restriction(_388035, _388037) = relation_rng_restriction(_388037, relation_dom_restriction(_388035, _388037)))], (5631 ^ _84654) ^ [] : [-(relation(5629 ^ []))], (8963 ^ _84654) ^ [_408313, _408315, _408317, _408319] : [ordered_pair(_408319, _408317) = ordered_pair(_408315, _408313), 8966 ^ _84654 : [(8969 ^ _84654) ^ [] : [-(_408317 = _408313)], (8967 ^ _84654) ^ [] : [-(_408319 = _408315)]]], (7880 ^ _84654) ^ [_371891, _371893] : [topological_space(_371893), top_str(_371893), element(_371891, powerset(powerset(the_carrier(_371893)))), 7892 ^ _84654 : [(7895 ^ _84654) ^ [_372408] : [element(_372408, powerset(the_carrier(_371893))), 7898 ^ _84654 : [(7905 ^ _84654) ^ [] : [in(set_difference(cast_as_carrier_subset(_371893), _372408), _371891), -(in(_372408, 7891 ^ [_371891, _371893]))], (7899 ^ _84654) ^ [] : [in(_372408, 7891 ^ [_371891, _371893]), -(in(set_difference(cast_as_carrier_subset(_371893), _372408), _371891))]]], (7893 ^ _84654) ^ [] : [-(element(7891 ^ [_371891, _371893], powerset(powerset(the_carrier(_371893)))))]]], (4505 ^ _84654) ^ [] : [true___, -(true___)], (440 ^ _84654) ^ [_98190, _98192, _98194, _98196, _98198, _98200] : [-(relation_isomorphism(_98198, _98194, _98190)), relation_isomorphism(_98200, _98196, _98192), _98200 = _98198, _98196 = _98194, _98192 = _98190], (5217 ^ _84654) ^ [_262711] : [empty(_262711), 5220 ^ _84654 : [(5223 ^ _84654) ^ [] : [-(relation(relation_rng(_262711)))], (5221 ^ _84654) ^ [] : [-(empty(relation_rng(_262711)))]]], (5361 ^ _84654) ^ [_267806, _267808] : [subset(singleton(_267808), _267806), -(in(_267808, _267806))], (472 ^ _84654) ^ [_99187, _99189] : [-(antisymmetric(_99187)), _99189 = _99187, antisymmetric(_99189)], (5281 ^ _84654) ^ [_264931] : [relation(_264931), 5284 ^ _84654 : [(5285 ^ _84654) ^ [] : [reflexive(_264931), 5288 ^ _84654 : [(5289 ^ _84654) ^ [_265175] : [in(_265175, relation_field(_264931)), -(in(ordered_pair(_265175, _265175), _264931))]]], (5295 ^ _84654) ^ [] : [5297 ^ _84654 : [(5300 ^ _84654) ^ [] : [in(ordered_pair(5296 ^ [_264931], 5296 ^ [_264931]), _264931)], (5298 ^ _84654) ^ [] : [-(in(5296 ^ [_264931], relation_field(_264931)))]], -(reflexive(_264931))]]], (5602 ^ _84654) ^ [] : [empty(5600 ^ [])], (3847 ^ _84654) ^ [_218587] : [relation(_218587), 3850 ^ _84654 : [(3851 ^ _84654) ^ [_218808] : [relation(_218808), 3854 ^ _84654 : [(3855 ^ _84654) ^ [_219025] : [relation(_219025), function(_219025), 3862 ^ _84654 : [(3863 ^ _84654) ^ [] : [relation_isomorphism(_218587, _218808, _219025), 3866 ^ _84654 : [(3869 ^ _84654) ^ [] : [-(relation_rng(_219025) = relation_field(_218808))], (3871 ^ _84654) ^ [] : [-(one_to_one(_219025))], (3873 ^ _84654) ^ [_219691, _219693] : [in(ordered_pair(_219693, _219691), _218587), 3876 ^ _84654 : [(3881 ^ _84654) ^ [] : [-(in(ordered_pair(apply(_219025, _219693), apply(_219025, _219691)), _218808))], (3879 ^ _84654) ^ [] : [-(in(_219691, relation_field(_218587)))], (3877 ^ _84654) ^ [] : [-(in(_219693, relation_field(_218587)))]]], (3883 ^ _84654) ^ [_220070, _220072] : [-(in(ordered_pair(_220072, _220070), _218587)), in(_220072, relation_field(_218587)), in(_220070, relation_field(_218587)), in(ordered_pair(apply(_219025, _220072), apply(_219025, _220070)), _218808)], (3867 ^ _84654) ^ [] : [-(relation_dom(_219025) = relation_field(_218587))]]], (3897 ^ _84654) ^ [] : [-(relation_isomorphism(_218587, _218808, _219025)), relation_dom(_219025) = relation_field(_218587), relation_rng(_219025) = relation_field(_218808), one_to_one(_219025), 3926 ^ _84654 : [(3933 ^ _84654) ^ [] : [in(ordered_pair(3910 ^ [_218587, _218808, _219025], 3911 ^ [_218587, _218808, _219025]), _218587)], (3927 ^ _84654) ^ [] : [-(in(3910 ^ [_218587, _218808, _219025], relation_field(_218587)))], (3931 ^ _84654) ^ [] : [-(in(ordered_pair(apply(_219025, 3910 ^ [_218587, _218808, _219025]), apply(_219025, 3911 ^ [_218587, _218808, _219025])), _218808))], (3929 ^ _84654) ^ [] : [-(in(3911 ^ [_218587, _218808, _219025], relation_field(_218587)))]], 3914 ^ _84654 : [(3917 ^ _84654) ^ [] : [in(3910 ^ [_218587, _218808, _219025], relation_field(_218587)), in(3911 ^ [_218587, _218808, _219025], relation_field(_218587)), in(ordered_pair(apply(_219025, 3910 ^ [_218587, _218808, _219025]), apply(_219025, 3911 ^ [_218587, _218808, _219025])), _218808)], (3915 ^ _84654) ^ [] : [-(in(ordered_pair(3910 ^ [_218587, _218808, _219025], 3911 ^ [_218587, _218808, _219025]), _218587))]]]]]]]]], (884 ^ _84654) ^ [_113409, _113411, _113413, _113415] : [-(cartesian_product2(_113415, _113411) = cartesian_product2(_113413, _113409)), _113415 = _113413, _113411 = _113409], (3591 ^ _84654) ^ [_209669] : [-(_209669 = omega), in(empty_set, _209669), being_limit_ordinal(_209669), ordinal(_209669), 3605 ^ _84654 : [(3612 ^ _84654) ^ [] : [subset(_209669, 3604 ^ [_209669])], (3606 ^ _84654) ^ [] : [-(ordinal(3604 ^ [_209669]))], (3610 ^ _84654) ^ [] : [-(being_limit_ordinal(3604 ^ [_209669]))], (3608 ^ _84654) ^ [] : [-(in(empty_set, 3604 ^ [_209669]))]]], (8353 ^ _84654) ^ [_388275, _388277, _388279] : [relation(_388275), in(_388279, relation_field(relation_restriction(_388275, _388277))), 8360 ^ _84654 : [(8363 ^ _84654) ^ [] : [-(in(_388279, _388277))], (8361 ^ _84654) ^ [] : [-(in(_388279, relation_field(_388275)))]]], (5093 ^ _84654) ^ [_258822, _258824] : [v4_membered(_258824), 5096 ^ _84654 : [(5103 ^ _84654) ^ [] : [-(v4_membered(set_difference(_258824, _258822)))], (5097 ^ _84654) ^ [] : [-(v1_membered(set_difference(_258824, _258822)))], (5101 ^ _84654) ^ [] : [-(v3_membered(set_difference(_258824, _258822)))], (5099 ^ _84654) ^ [] : [-(v2_membered(set_difference(_258824, _258822)))]]], (952 ^ _84654) ^ [_115865, _115867] : [_115867 = _115865, -(relation_inverse(_115867) = relation_inverse(_115865))], (8890 ^ _84654) ^ [_405956, _405958] : [relation(_405956), well_founded_relation(_405956), -(well_founded_relation(relation_restriction(_405956, _405958)))], (8322 ^ _84654) ^ [_387104] : [finite(_387104), 8325 ^ _84654 : [(8326 ^ _84654) ^ [_387279] : [element(_387279, powerset(powerset(_387104))), -(_387279 = empty_set), 8334 ^ _84654 : [(8337 ^ _84654) ^ [_387678] : [-(_387678 = 8333 ^ [_387104, _387279]), in(_387678, _387279), subset(8333 ^ [_387104, _387279], _387678)], (8335 ^ _84654) ^ [] : [-(in(8333 ^ [_387104, _387279], _387279))]]]]], (4309 ^ _84654) ^ [] : [true___, -(true___)], (2759 ^ _84654) ^ [_180135] : [relation(_180135), 2762 ^ _84654 : [(2763 ^ _84654) ^ [_180293] : [relation(_180293), 2766 ^ _84654 : [(2767 ^ _84654) ^ [] : [_180135 = _180293, 2770 ^ _84654 : [(2777 ^ _84654) ^ [_180788, _180790] : [in(ordered_pair(_180790, _180788), _180293), -(in(ordered_pair(_180790, _180788), _180135))], (2771 ^ _84654) ^ [_180598, _180600] : [in(ordered_pair(_180600, _180598), _180135), -(in(ordered_pair(_180600, _180598), _180293))]]], (2783 ^ _84654) ^ [] : [-(_180135 = _180293), 2788 ^ _84654 : [(2791 ^ _84654) ^ [] : [in(ordered_pair(2784 ^ [_180135, _180293], 2785 ^ [_180135, _180293]), _180293)], (2789 ^ _84654) ^ [] : [-(in(ordered_pair(2784 ^ [_180135, _180293], 2785 ^ [_180135, _180293]), _180135))]], 2792 ^ _84654 : [(2795 ^ _84654) ^ [] : [in(ordered_pair(2784 ^ [_180135, _180293], 2785 ^ [_180135, _180293]), _180135)], (2793 ^ _84654) ^ [] : [-(in(ordered_pair(2784 ^ [_180135, _180293], 2785 ^ [_180135, _180293]), _180293))]]]]]]], (8653 ^ _84654) ^ [_398270, _398272] : [relation(_398270), connected(_398270), -(connected(relation_restriction(_398270, _398272)))], (5518 ^ _84654) ^ [_273158, _273160, _273162, _273164] : [in(ordered_pair(_273164, _273162), cartesian_product2(_273160, _273158)), 5521 ^ _84654 : [(5524 ^ _84654) ^ [] : [-(in(_273162, _273158))], (5522 ^ _84654) ^ [] : [-(in(_273164, _273160))]]], (5390 ^ _84654) ^ [_268753, _268755] : [set_difference(_268755, _268753) = empty_set, -(subset(_268755, _268753))], (1068 ^ _84654) ^ [_120089, _120091, _120093, _120095] : [-(set_difference(_120095, _120091) = set_difference(_120093, _120089)), _120095 = _120093, _120091 = _120089], (4971 ^ _84654) ^ [_254551, _254553] : [v4_membered(_254553), 4974 ^ _84654 : [(4981 ^ _84654) ^ [] : [-(v4_membered(set_intersection2(_254553, _254551)))], (4975 ^ _84654) ^ [] : [-(v1_membered(set_intersection2(_254553, _254551)))], (4979 ^ _84654) ^ [] : [-(v3_membered(set_intersection2(_254553, _254551)))], (4977 ^ _84654) ^ [] : [-(v2_membered(set_intersection2(_254553, _254551)))]]], (5612 ^ _84654) ^ [] : [-(v5_membered(5600 ^ []))], (4283 ^ _84654) ^ [] : [true___, -(true___)], (2516 ^ _84654) ^ [_171488, _171490] : [_171488 = singleton(_171490), 2519 ^ _84654 : [(2526 ^ _84654) ^ [_171830] : [_171830 = _171490, -(in(_171830, _171488))], (2520 ^ _84654) ^ [_171658] : [in(_171658, _171488), -(_171658 = _171490)]]], (6122 ^ _84654) ^ [] : [6249 ^ _84654 : [(6250 ^ _84654) ^ [_298999] : [ordinal(_298999), in(_298999, omega), 6257 ^ _84654 : [(6258 ^ _84654) ^ [_299255] : [element(_299255, powerset(powerset(_298999))), -(_299255 = empty_set), 6266 ^ _84654 : [(6269 ^ _84654) ^ [_299654] : [-(_299654 = 6265 ^ [_298999, _299255]), in(_299654, _299255), subset(6265 ^ [_298999, _299255], _299654)], (6267 ^ _84654) ^ [] : [-(in(6265 ^ [_298999, _299255], _299255))]]]]]], 6125 ^ _84654 : [(6133 ^ _84654) ^ [_294838] : [in(_294838, 6127 ^ []), 6137 ^ _84654 : [(6142 ^ _84654) ^ [] : [6136 ^ [_294838] = _294838], (6140 ^ _84654) ^ [] : [-(subset(_294838, 6136 ^ [_294838]))], (6138 ^ _84654) ^ [] : [-(in(6136 ^ [_294838], 6127 ^ []))]]], (6126 ^ _84654) ^ [] : [-(in(empty_set, omega))], (6131 ^ _84654) ^ [] : [6127 ^ [] = empty_set], (6129 ^ _84654) ^ [] : [-(element(6127 ^ [], powerset(powerset(empty_set))))]], 6146 ^ _84654 : [(6181 ^ _84654) ^ [_296489] : [in(_296489, 6175 ^ []), 6185 ^ _84654 : [(6190 ^ _84654) ^ [] : [6184 ^ [_296489] = _296489], (6188 ^ _84654) ^ [] : [-(subset(_296489, 6184 ^ [_296489]))], (6186 ^ _84654) ^ [] : [-(in(6184 ^ [_296489], 6175 ^ []))]]], (6179 ^ _84654) ^ [] : [6175 ^ [] = empty_set], (6149 ^ _84654) ^ [] : [in(6145 ^ [], omega), 6152 ^ _84654 : [(6153 ^ _84654) ^ [_295572] : [element(_295572, powerset(powerset(6145 ^ []))), -(_295572 = empty_set), 6161 ^ _84654 : [(6164 ^ _84654) ^ [_295945] : [-(_295945 = 6160 ^ [_295572]), in(_295945, _295572), subset(6160 ^ [_295572], _295945)], (6162 ^ _84654) ^ [] : [-(in(6160 ^ [_295572], _295572))]]]]], (6147 ^ _84654) ^ [] : [-(ordinal(6145 ^ []))], (6174 ^ _84654) ^ [] : [-(in(succ(6145 ^ []), omega))], (6177 ^ _84654) ^ [] : [-(element(6175 ^ [], powerset(powerset(succ(6145 ^ [])))))]], 6192 ^ _84654 : [(6235 ^ _84654) ^ [] : [-(element(6233 ^ [], powerset(powerset(6191 ^ []))))], (6239 ^ _84654) ^ [_298579] : [in(_298579, 6233 ^ []), 6243 ^ _84654 : [(6248 ^ _84654) ^ [] : [6242 ^ [_298579] = _298579], (6246 ^ _84654) ^ [] : [-(subset(_298579, 6242 ^ [_298579]))], (6244 ^ _84654) ^ [] : [-(in(6242 ^ [_298579], 6233 ^ []))]]], (6237 ^ _84654) ^ [] : [6233 ^ [] = empty_set], (6195 ^ _84654) ^ [] : [-(being_limit_ordinal(6191 ^ []))], (6230 ^ _84654) ^ [] : [6191 ^ [] = empty_set], (6193 ^ _84654) ^ [] : [-(ordinal(6191 ^ []))], (6232 ^ _84654) ^ [] : [-(in(6191 ^ [], omega))], (6197 ^ _84654) ^ [_297217] : [ordinal(_297217), in(_297217, 6191 ^ []), in(_297217, omega), 6208 ^ _84654 : [(6209 ^ _84654) ^ [_297554] : [element(_297554, powerset(powerset(_297217))), -(_297554 = empty_set), 6217 ^ _84654 : [(6220 ^ _84654) ^ [_297953] : [-(_297953 = 6216 ^ [_297217, _297554]), in(_297953, _297554), subset(6216 ^ [_297217, _297554], _297953)], (6218 ^ _84654) ^ [] : [-(in(6216 ^ [_297217, _297554], _297554))]]]]]]], (390 ^ _84654) ^ [_96659, _96661] : [-(being_limit_ordinal(_96659)), _96661 = _96659, being_limit_ordinal(_96661)], (1156 ^ _84654) ^ [_123228, _123230] : [_123230 = _123228, -(relation_rng(_123230) = relation_rng(_123228))], (226 ^ _84654) ^ [_91603, _91605] : [-(meet_semilatt_str(_91603)), _91605 = _91603, meet_semilatt_str(_91605)], (4917 ^ _84654) ^ [] : [-(empty(empty_set))], (5087 ^ _84654) ^ [_258606, _258608] : [-(empty(_258608)), empty(set_union2(_258606, _258608))], (4821 ^ _84654) ^ [] : [-(ordinal(omega))], (984 ^ _84654) ^ [_117047, _117049, _117051, _117053] : [-(union_of_subsets(_117053, _117049) = union_of_subsets(_117051, _117047)), _117053 = _117051, _117049 = _117047], (5412 ^ _84654) ^ [_269491] : [relation(_269491), 5415 ^ _84654 : [(5416 ^ _84654) ^ [] : [antisymmetric(_269491), 5419 ^ _84654 : [(5420 ^ _84654) ^ [_269761, _269763] : [-(_269763 = _269761), in(ordered_pair(_269763, _269761), _269491), in(ordered_pair(_269761, _269763), _269491)]]], (5430 ^ _84654) ^ [] : [5433 ^ _84654 : [(5438 ^ _84654) ^ [] : [5431 ^ [_269491] = 5432 ^ [_269491]], (5436 ^ _84654) ^ [] : [-(in(ordered_pair(5432 ^ [_269491], 5431 ^ [_269491]), _269491))], (5434 ^ _84654) ^ [] : [-(in(ordered_pair(5431 ^ [_269491], 5432 ^ [_269491]), _269491))]], -(antisymmetric(_269491))]]], (8957 ^ _84654) ^ [_408057, _408059, _408061] : [subset(_408061, _408059), -(subset(set_difference(_408061, _408057), set_difference(_408059, _408057)))], (166 ^ _84654) ^ [_89833, _89835] : [-(v3_membered(_89833)), _89835 = _89833, v3_membered(_89835)], (5597 ^ _84654) ^ [_275720, _275722] : [-(function(5591 ^ [_275720, _275722]))], (8814 ^ _84654) ^ [_403426] : [top_str(_403426), 8817 ^ _84654 : [(8818 ^ _84654) ^ [_403572] : [element(_403572, powerset(the_carrier(_403426))), 8821 ^ _84654 : [(8828 ^ _84654) ^ [] : [open_subset(subset_complement(the_carrier(_403426), _403572), _403426), -(closed_subset(_403572, _403426))], (8822 ^ _84654) ^ [] : [closed_subset(_403572, _403426), -(open_subset(subset_complement(the_carrier(_403426), _403572), _403426))]]]]], (4523 ^ _84654) ^ [_240003, _240005] : [-(relation(relation_composition(_240005, _240003))), relation(_240005), relation(_240003)], (20 ^ _84654) ^ [_85402, _85404] : [-(v1_xcmplx_0(_85402)), _85404 = _85402, v1_xcmplx_0(_85404)], (4399 ^ _84654) ^ [_236713] : [-(element(cast_to_subset(_236713), powerset(_236713)))], (4943 ^ _84654) ^ [_253522, _253524] : [v2_membered(_253524), 4946 ^ _84654 : [(4949 ^ _84654) ^ [] : [-(v2_membered(set_intersection2(_253522, _253524)))], (4947 ^ _84654) ^ [] : [-(v1_membered(set_intersection2(_253522, _253524)))]]], (7822 ^ _84654) ^ [_369809] : [-(relation_dom(7816 ^ [_369809]) = _369809)], (7553 ^ _84654) ^ [_358822, _358824, _358826] : [element(_358824, powerset(powerset(_358826))), relation(_358822), function(_358822), 7565 ^ _84654 : [(7574 ^ _84654) ^ [_359564] : [-(in(_359564, 7564 ^ [_358822, _358824, _358826])), in(_359564, powerset(relation_dom(_358822))), in(relation_image(_358822, _359564), _358824)], (7566 ^ _84654) ^ [_359273] : [in(_359273, 7564 ^ [_358822, _358824, _358826]), 7569 ^ _84654 : [(7572 ^ _84654) ^ [] : [-(in(relation_image(_358822, _359273), _358824))], (7570 ^ _84654) ^ [] : [-(in(_359273, powerset(relation_dom(_358822))))]]]]], (9825 ^ _84654) ^ [_436972, _436974, _436976] : [-(disjoint(_436976, _436972)), subset(_436976, _436974), disjoint(_436974, _436972)], (8038 ^ _84654) ^ [_377542] : [-(in(_377542, 8036 ^ [_377542]))], (9076 ^ _84654) ^ [_412072, _412074] : [-(set_union2(_412074, set_difference(_412072, _412074)) = set_union2(_412074, _412072))], (9799 ^ _84654) ^ [_436175] : [-(antisymmetric(inclusion_relation(_436175)))], (10151 ^ _84654) ^ [_447536, _447538] : [relation(_447536), -(relation_dom(relation_dom_restriction(_447536, _447538)) = set_intersection2(relation_dom(_447536), _447538))], (1402 ^ _84654) ^ [_132040] : [empty(_132040), -(relation(_132040))], (5145 ^ _84654) ^ [_260619, _260621] : [empty(cartesian_product2(_260621, _260619)), -(empty(_260621)), -(empty(_260619))], (9972 ^ _84654) ^ [_441657] : [-(relation_dom(identity_relation(_441657)) = _441657)], (5604 ^ _84654) ^ [] : [-(v1_membered(5600 ^ []))], (5875 ^ _84654) ^ [_284734, _284736] : [element(_284734, powerset(powerset(_284736))), -(union_of_subsets(_284736, _284734) = union(_284734))], (9078 ^ _84654) ^ [_412219, _412221] : [subset(_412221, singleton(_412219)), -(_412221 = empty_set), -(_412221 = singleton(_412219))], (4791 ^ _84654) ^ [_248690] : [-(diff_closed(powerset(_248690)))], (8179 ^ _84654) ^ [_382293] : [one_sorted_str(_382293), 8182 ^ _84654 : [(8183 ^ _84654) ^ [_382436] : [element(_382436, powerset(the_carrier(_382293))), -(subset_intersection2(the_carrier(_382293), _382436, cast_as_carrier_subset(_382293)) = _382436)]]], (762 ^ _84654) ^ [_108922, _108924, _108926, _108928, _108930, _108932, _108934, _108936, _108938, _108940, _108942, _108944] : [-(apply_binary_as_element(_108944, _108940, _108936, _108932, _108928, _108924) = apply_binary_as_element(_108942, _108938, _108934, _108930, _108926, _108922)), _108944 = _108942, _108940 = _108938, _108936 = _108934, _108932 = _108930, _108928 = _108926, _108924 = _108922], (9811 ^ _84654) ^ [_436586] : [relation(_436586), function(_436586), one_to_one(_436586), -(one_to_one(function_inverse(_436586)))], (1520 ^ _84654) ^ [_135729] : [empty(_135729), 1523 ^ _84654 : [(1528 ^ _84654) ^ [] : [-(ordinal(_135729))], (1526 ^ _84654) ^ [] : [-(epsilon_connected(_135729))], (1524 ^ _84654) ^ [] : [-(epsilon_transitive(_135729))]]], (8143 ^ _84654) ^ [_381122] : [relation(_381122), -(relation_image(_381122, relation_dom(_381122)) = relation_rng(_381122))], (1056 ^ _84654) ^ [_119625, _119627] : [_119627 = _119625, -(pair_second(_119627) = pair_second(_119625))], (2197 ^ _84654) ^ [_160068] : [-(finite(_160068)), 2198 ^ _84654 : [(2199 ^ _84654) ^ [_160171] : [relation(_160171), function(_160171), relation_rng(_160171) = _160068, in(relation_dom(_160171), omega)]]], (5891 ^ _84654) ^ [_285307, _285309] : [element(_285307, powerset(powerset(_285309))), -(meet_of_subsets(_285309, _285307) = set_meet(_285307))], (6099 ^ _84654) ^ [_293731] : [6100 ^ _84654 : [(6101 ^ _84654) ^ [_293852] : [ordinal(_293852), in(_293852, _293731)]], 6107 ^ _84654 : [(6112 ^ _84654) ^ [_294232] : [ordinal(_294232), in(_294232, _293731), -(ordinal_subset(6106 ^ [_293731], _294232))], (6110 ^ _84654) ^ [] : [-(in(6106 ^ [_293731], _293731))], (6108 ^ _84654) ^ [] : [-(ordinal(6106 ^ [_293731]))]]], (9416 ^ _84654) ^ [_423734] : [relation(_423734), 9419 ^ _84654 : [(9420 ^ _84654) ^ [_423881] : [relation(_423881), subset(relation_dom(_423734), relation_rng(_423881)), -(relation_rng(relation_composition(_423881, _423734)) = relation_rng(_423734))]]], (1140 ^ _84654) ^ [_122651, _122653] : [_122653 = _122651, -(identity_relation(_122653) = identity_relation(_122651))], (4607 ^ _84654) ^ [_242847] : [meet_semilatt_str(_242847), -(one_sorted_str(_242847))], (506 ^ _84654) ^ [_100221, _100223] : [-(well_founded_relation(_100221)), _100223 = _100221, well_founded_relation(_100223)], (974 ^ _84654) ^ [_116688, _116690, _116692, _116694] : [-(relation_inverse_image(_116694, _116690) = relation_inverse_image(_116692, _116688)), _116694 = _116692, _116690 = _116688], (1212 ^ _84654) ^ [_125576, _125578] : [proper_subset(_125578, _125576), proper_subset(_125576, _125578)], (7535 ^ _84654) ^ [_358254, _358256] : [in(_358254, 7533 ^ [_358256]), 7538 ^ _84654 : [(7541 ^ _84654) ^ [] : [-(ordinal(_358254))], (7539 ^ _84654) ^ [] : [-(in(_358254, _358256))]]], (958 ^ _84654) ^ [_116111, _116113, _116115, _116117] : [-(relation_restriction(_116117, _116113) = relation_restriction(_116115, _116111)), _116117 = _116115, _116113 = _116111], (8280 ^ _84654) ^ [_385703, _385705, _385707] : [relation(_385703), subset(_385707, _385705), -(subset(relation_inverse_image(_385703, _385707), relation_inverse_image(_385703, _385705)))], (8266 ^ _84654) ^ [_385289, _385291] : [relation(_385289), -(_385291 = empty_set), subset(_385291, relation_rng(_385289)), relation_inverse_image(_385289, _385291) = empty_set], (9958 ^ _84654) ^ [_441238, _441240, _441242] : [relation(_441238), function(_441238), in(_441240, relation_dom(relation_dom_restriction(_441238, _441242))), -(apply(relation_dom_restriction(_441238, _441242), _441240) = apply(_441238, _441240))], (420 ^ _84654) ^ [_97544, _97546] : [-(transitive(_97544)), _97546 = _97544, transitive(_97546)], (7495 ^ _84654) ^ [_356488, _356490, _356492] : [relation(_356490), relation(_356488), function(_356488), 7507 ^ _84654 : [(7520 ^ _84654) ^ [_357585] : [-(in(_357585, 7506 ^ [_356488, _356490, _356492])), in(_357585, cartesian_product2(_356492, _356492)), 7525 ^ _84654 : [(7526 ^ _84654) ^ [_357826, _357828] : [_357585 = ordered_pair(_357828, _357826), in(ordered_pair(apply(_356488, _357828), apply(_356488, _357826)), _356490)]]], (7508 ^ _84654) ^ [_356977] : [in(_356977, 7506 ^ [_356488, _356490, _356492]), 7511 ^ _84654 : [(7518 ^ _84654) ^ [] : [-(in(ordered_pair(apply(_356488, 7513 ^ [_356488, _356490, _356492, _356977]), apply(_356488, 7514 ^ [_356488, _356490, _356492, _356977])), _356490))], (7516 ^ _84654) ^ [] : [-(_356977 = ordered_pair(7513 ^ [_356488, _356490, _356492, _356977], 7514 ^ [_356488, _356490, _356492, _356977]))], (7512 ^ _84654) ^ [] : [-(in(_356977, cartesian_product2(_356492, _356492)))]]]]], (4937 ^ _84654) ^ [_253306, _253308] : [-(empty(_253308)), empty(set_union2(_253308, _253306))], (4023 ^ _84654) ^ [_224754] : [relation(_224754), 4026 ^ _84654 : [(4027 ^ _84654) ^ [_224939] : [relation(_224939), 4030 ^ _84654 : [(4031 ^ _84654) ^ [_225120] : [relation(_225120), 4034 ^ _84654 : [(4035 ^ _84654) ^ [] : [_225120 = relation_composition(_224754, _224939), 4038 ^ _84654 : [(4048 ^ _84654) ^ [_225840, _225842] : [-(in(ordered_pair(_225842, _225840), _225120)), 4049 ^ _84654 : [(4050 ^ _84654) ^ [_225953] : [in(ordered_pair(_225842, _225953), _224754), in(ordered_pair(_225953, _225840), _224939)]]], (4039 ^ _84654) ^ [_225455, _225457] : [in(ordered_pair(_225457, _225455), _225120), 4043 ^ _84654 : [(4046 ^ _84654) ^ [] : [-(in(ordered_pair(4042 ^ [_224754, _224939, _225120, _225455, _225457], _225455), _224939))], (4044 ^ _84654) ^ [] : [-(in(ordered_pair(_225457, 4042 ^ [_224754, _224939, _225120, _225455, _225457]), _224754))]]]]], (4058 ^ _84654) ^ [] : [-(_225120 = relation_composition(_224754, _224939)), 4072 ^ _84654 : [(4077 ^ _84654) ^ [] : [in(ordered_pair(4059 ^ [_224754, _224939, _225120], 4060 ^ [_224754, _224939, _225120]), _225120)], (4075 ^ _84654) ^ [] : [-(in(ordered_pair(4071 ^ [_224754, _224939, _225120], 4060 ^ [_224754, _224939, _225120]), _224939))], (4073 ^ _84654) ^ [] : [-(in(ordered_pair(4059 ^ [_224754, _224939, _225120], 4071 ^ [_224754, _224939, _225120]), _224754))]], 4063 ^ _84654 : [(4066 ^ _84654) ^ [_226584] : [in(ordered_pair(4059 ^ [_224754, _224939, _225120], _226584), _224754), in(ordered_pair(_226584, 4060 ^ [_224754, _224939, _225120]), _224939)], (4064 ^ _84654) ^ [] : [-(in(ordered_pair(4059 ^ [_224754, _224939, _225120], 4060 ^ [_224754, _224939, _225120]), _225120))]]]]]]]]], (1024 ^ _84654) ^ [_118499, _118501, _118503, _118505] : [-(meet_of_subsets(_118505, _118501) = meet_of_subsets(_118503, _118499)), _118505 = _118503, _118501 = _118499], (9924 ^ _84654) ^ [_440189, _440191, _440193, _440195] : [function(_440189), quasi_total(_440189, _440195, _440193), relation_of2_as_subset(_440189, _440195, _440193), in(_440191, _440195), -(_440193 = empty_set), -(in(apply(_440189, _440191), relation_rng(_440189)))], (5617 ^ _84654) ^ [] : [-(epsilon_connected(5613 ^ []))], (4690 ^ _84654) ^ [] : [-(meet_semilatt_str(4688 ^ []))], (5249 ^ _84654) ^ [_263749, _263751] : [-(set_intersection2(_263751, _263751) = _263751)], (1861 ^ _84654) ^ [_147596] : [relation(_147596), function(_147596), 1868 ^ _84654 : [(1869 ^ _84654) ^ [_147883, _147885] : [_147883 = relation_inverse_image(_147596, _147885), 1872 ^ _84654 : [(1881 ^ _84654) ^ [_148341] : [-(in(_148341, _147883)), in(_148341, relation_dom(_147596)), in(apply(_147596, _148341), _147885)], (1873 ^ _84654) ^ [_148072] : [in(_148072, _147883), 1876 ^ _84654 : [(1879 ^ _84654) ^ [] : [-(in(apply(_147596, _148072), _147885))], (1877 ^ _84654) ^ [] : [-(in(_148072, relation_dom(_147596)))]]]]], (1891 ^ _84654) ^ [_148635, _148637] : [-(_148635 = relation_inverse_image(_147596, _148637)), 1903 ^ _84654 : [(1908 ^ _84654) ^ [] : [in(1892 ^ [_147596, _148635, _148637], _148635)], (1906 ^ _84654) ^ [] : [-(in(apply(_147596, 1892 ^ [_147596, _148635, _148637]), _148637))], (1904 ^ _84654) ^ [] : [-(in(1892 ^ [_147596, _148635, _148637], relation_dom(_147596)))]], 1895 ^ _84654 : [(1898 ^ _84654) ^ [] : [in(1892 ^ [_147596, _148635, _148637], relation_dom(_147596)), in(apply(_147596, 1892 ^ [_147596, _148635, _148637]), _148637)], (1896 ^ _84654) ^ [] : [-(in(1892 ^ [_147596, _148635, _148637], _148635))]]]]], (8031 ^ _84654) ^ [_377220, _377222] : [subset(_377222, _377220), -(set_union2(_377222, _377220) = _377220)], (6318 ^ _84654) ^ [_301487, _301489] : [-(empty(_301489)), relation(_301487), 6330 ^ _84654 : [(6338 ^ _84654) ^ [_302756] : [in(_302756, 6332 ^ [_301487, _301489]), -(in(ordered_pair(6328 ^ [_301487, _301489], _302756), _301487))], (6351 ^ _84654) ^ [_303305] : [in(_303305, 6345 ^ [_301487, _301489]), -(in(ordered_pair(6329 ^ [_301487, _301489], _303305), _301487))], (6349 ^ _84654) ^ [] : [-(in(6329 ^ [_301487, _301489], 6345 ^ [_301487, _301489]))], (6344 ^ _84654) ^ [] : [-(in(6327 ^ [_301487, _301489], _301489))], (6357 ^ _84654) ^ [] : [6328 ^ [_301487, _301489] = 6329 ^ [_301487, _301489]], (6336 ^ _84654) ^ [] : [-(in(6328 ^ [_301487, _301489], 6332 ^ [_301487, _301489]))], (6331 ^ _84654) ^ [] : [-(in(6327 ^ [_301487, _301489], _301489))], (6334 ^ _84654) ^ [] : [-(6327 ^ [_301487, _301489] = 6332 ^ [_301487, _301489])], (6347 ^ _84654) ^ [] : [-(6327 ^ [_301487, _301489] = 6345 ^ [_301487, _301489])]], 6359 ^ _84654 : [(6380 ^ _84654) ^ [_304639] : [-(in(_304639, 6358 ^ [_301487, _301489])), 6381 ^ _84654 : [(6382 ^ _84654) ^ [_304781] : [in(_304781, _301489), in(_304781, _301489), 6389 ^ _84654 : [(6390 ^ _84654) ^ [_305045] : [_304781 = _305045, in(_304639, _305045), 6398 ^ _84654 : [(6401 ^ _84654) ^ [] : [in(ordered_pair(_304639, 6397 ^ [_301487, _301489, _304639, _304781, _305045]), _301487)], (6399 ^ _84654) ^ [] : [-(in(6397 ^ [_301487, _301489, _304639, _304781, _305045], _305045))]]]]]]], (6360 ^ _84654) ^ [_303733] : [in(_303733, 6358 ^ [_301487, _301489]), 6364 ^ _84654 : [(6367 ^ _84654) ^ [] : [-(in(6363 ^ [_301487, _301489, _303733], _301489))], (6370 ^ _84654) ^ [] : [-(6363 ^ [_301487, _301489, _303733] = 6368 ^ [_301487, _301489, _303733])], (6372 ^ _84654) ^ [] : [-(in(_303733, 6368 ^ [_301487, _301489, _303733]))], (6374 ^ _84654) ^ [_304422] : [in(_304422, 6368 ^ [_301487, _301489, _303733]), -(in(ordered_pair(_303733, _304422), _301487))], (6365 ^ _84654) ^ [] : [-(in(6363 ^ [_301487, _301489, _303733], _301489))]]]]], (8537 ^ _84654) ^ [_394360, _394362, _394364] : [relation_of2_as_subset(_394360, _394362, _394364), 8540 ^ _84654 : [(8550 ^ _84654) ^ [] : [relation_dom_as_subset(_394362, _394364, _394360) = _394362, 8553 ^ _84654 : [(8554 ^ _84654) ^ [_394955] : [in(_394955, _394362), -(in(ordered_pair(_394955, 8557 ^ [_394360, _394362, _394364, _394955]), _394360))]]], (8541 ^ _84654) ^ [] : [8543 ^ _84654 : [(8546 ^ _84654) ^ [_394718] : [in(ordered_pair(8542 ^ [_394360, _394362, _394364], _394718), _394360)], (8544 ^ _84654) ^ [] : [-(in(8542 ^ [_394360, _394362, _394364], _394362))]], -(relation_dom_as_subset(_394362, _394364, _394360) = _394362)]]], (8377 ^ _84654) ^ [_389083, _389085] : [in(_389085, _389083), -(element(_389085, _389083))], (1114 ^ _84654) ^ [_121743, _121745, _121747, _121749] : [-(set_intersection2(_121749, _121745) = set_intersection2(_121747, _121743)), _121749 = _121747, _121745 = _121743], (10049 ^ _84654) ^ [_444365, _444367] : [set_difference(_444367, _444365) = _444367, -(disjoint(_444367, _444365))], (4539 ^ _84654) ^ [_240546, _240548] : [element(_240546, powerset(powerset(_240548))), -(element(union_of_subsets(_240548, _240546), powerset(_240548)))], (4873 ^ _84654) ^ [_251271, _251273] : [v1_membered(_251273), -(v1_membered(set_intersection2(_251271, _251273)))], (5155 ^ _84654) ^ [_260925, _260927] : [5162 ^ _84654 : [(5165 ^ _84654) ^ [] : [-(function(relation_rng_restriction(_260927, _260925)))], (5163 ^ _84654) ^ [] : [-(relation(relation_rng_restriction(_260927, _260925)))]], relation(_260925), function(_260925)], (5763 ^ _84654) ^ [_281189] : [5771 ^ _84654 : [(5774 ^ _84654) ^ [] : [empty(5770 ^ [_281189])], (5772 ^ _84654) ^ [] : [-(element(5770 ^ [_281189], powerset(the_carrier(_281189))))]], -(empty_carrier(_281189)), one_sorted_str(_281189)], (1414 ^ _84654) ^ [_132464] : [v5_membered(_132464), 1417 ^ _84654 : [(1418 ^ _84654) ^ [_132616] : [element(_132616, powerset(_132464)), 1421 ^ _84654 : [(1424 ^ _84654) ^ [] : [-(v2_membered(_132616))], (1426 ^ _84654) ^ [] : [-(v3_membered(_132616))], (1428 ^ _84654) ^ [] : [-(v4_membered(_132616))], (1430 ^ _84654) ^ [] : [-(v5_membered(_132616))], (1422 ^ _84654) ^ [] : [-(v1_membered(_132616))]]]]], (206 ^ _84654) ^ [_91013, _91015] : [-(epsilon_connected(_91013)), _91015 = _91013, epsilon_connected(_91015)], (5615 ^ _84654) ^ [] : [-(epsilon_transitive(5613 ^ []))], (6779 ^ _84654) ^ [_324856, _324858] : [topological_space(_324858), top_str(_324858), element(_324856, powerset(the_carrier(_324858))), 6795 ^ _84654 : [(6812 ^ _84654) ^ [] : [-(6808 ^ [_324856, _324858] = 6794 ^ [_324856, _324858])], (6807 ^ _84654) ^ [] : [-(6792 ^ [_324856, _324858] = 6794 ^ [_324856, _324858])], (6816 ^ _84654) ^ [] : [-(subset(_324856, 6794 ^ [_324856, _324858]))], (6810 ^ _84654) ^ [] : [-(element(6808 ^ [_324856, _324858], powerset(the_carrier(_324858))))], (6818 ^ _84654) ^ [] : [6793 ^ [_324856, _324858] = 6794 ^ [_324856, _324858]], (6805 ^ _84654) ^ [] : [-(subset(_324856, 6793 ^ [_324856, _324858]))], (6814 ^ _84654) ^ [] : [-(closed_subset(6808 ^ [_324856, _324858], _324858))], (6799 ^ _84654) ^ [] : [-(element(6797 ^ [_324856, _324858], powerset(the_carrier(_324858))))], (6796 ^ _84654) ^ [] : [-(6792 ^ [_324856, _324858] = 6793 ^ [_324856, _324858])], (6801 ^ _84654) ^ [] : [-(6797 ^ [_324856, _324858] = 6793 ^ [_324856, _324858])], (6803 ^ _84654) ^ [] : [-(closed_subset(6797 ^ [_324856, _324858], _324858))]], 6820 ^ _84654 : [(6839 ^ _84654) ^ [_327766] : [-(in(_327766, 6819 ^ [_324856, _324858])), 6840 ^ _84654 : [(6841 ^ _84654) ^ [_327908] : [in(_327908, powerset(the_carrier(_324858))), _327908 = _327766, 6848 ^ _84654 : [(6849 ^ _84654) ^ [_328176] : [element(_328176, powerset(the_carrier(_324858))), _328176 = _327766, closed_subset(_328176, _324858), subset(_324856, _327766)]]]]], (6821 ^ _84654) ^ [_326965] : [in(_326965, 6819 ^ [_324856, _324858]), 6825 ^ _84654 : [(6835 ^ _84654) ^ [] : [-(closed_subset(6829 ^ [_324856, _324858, _326965], _324858))], (6833 ^ _84654) ^ [] : [-(6829 ^ [_324856, _324858, _326965] = _326965)], (6837 ^ _84654) ^ [] : [-(subset(_324856, _326965))], (6826 ^ _84654) ^ [] : [-(in(6824 ^ [_324856, _324858, _326965], powerset(the_carrier(_324858))))], (6828 ^ _84654) ^ [] : [-(6824 ^ [_324856, _324858, _326965] = _326965)], (6831 ^ _84654) ^ [] : [-(element(6829 ^ [_324856, _324858, _326965], powerset(the_carrier(_324858))))]]]]], (3210 ^ _84654) ^ [_196471] : [relation(_196471), function(_196471), 3217 ^ _84654 : [(3234 ^ _84654) ^ [_197215, _197217] : [-(in(_197217, relation_dom(_196471))), 3237 ^ _84654 : [(3244 ^ _84654) ^ [] : [_197215 = empty_set, -(_197215 = apply(_196471, _197217))], (3238 ^ _84654) ^ [] : [_197215 = apply(_196471, _197217), -(_197215 = empty_set)]]], (3218 ^ _84654) ^ [_196763, _196765] : [in(_196765, relation_dom(_196471)), 3221 ^ _84654 : [(3228 ^ _84654) ^ [] : [in(ordered_pair(_196765, _196763), _196471), -(_196763 = apply(_196471, _196765))], (3222 ^ _84654) ^ [] : [_196763 = apply(_196471, _196765), -(in(ordered_pair(_196765, _196763), _196471))]]]]], (3449 ^ _84654) ^ [_204735, _204737] : [-(equipotent(_204737, _204735)), 3450 ^ _84654 : [(3451 ^ _84654) ^ [_204846] : [relation(_204846), function(_204846), one_to_one(_204846), relation_dom(_204846) = _204737, relation_rng(_204846) = _204735]]], (5789 ^ _84654) ^ [_282098, _282100, _282102, _282104, _282106, _282108] : [-(apply_binary_as_element(_282108, _282106, _282104, _282102, _282100, _282098) = apply_binary(_282102, _282100, _282098)), -(empty(_282108)), -(empty(_282106)), function(_282102), quasi_total(_282102, cartesian_product2(_282108, _282106), _282104), relation_of2(_282102, cartesian_product2(_282108, _282106), _282104), element(_282100, _282108), element(_282098, _282106)], (9835 ^ _84654) ^ [_437267] : [relation(_437267), 9840 ^ _84654 : [(9843 ^ _84654) ^ [] : [relation_rng(_437267) = empty_set], (9841 ^ _84654) ^ [] : [relation_dom(_437267) = empty_set]], -(_437267 = empty_set)], (10022 ^ _84654) ^ [_443350, _443352] : [in(_443352, _443350), 10026 ^ _84654 : [(10029 ^ _84654) ^ [_443641] : [in(_443641, _443350), in(_443641, 10025 ^ [_443350, _443352])], (10027 ^ _84654) ^ [] : [-(in(10025 ^ [_443350, _443352], _443350))]]], (5754 ^ _84654) ^ [] : [empty_carrier(5750 ^ [])], (3801 ^ _84654) ^ [_216895] : [relation(_216895), 3804 ^ _84654 : [(3805 ^ _84654) ^ [_217014] : [-(relation_restriction(_216895, _217014) = set_intersection2(_216895, cartesian_product2(_217014, _217014)))]]], (10041 ^ _84654) ^ [_444056, _444058] : [-(subset(_444058, set_union2(_444058, _444056)))], (4673 ^ _84654) ^ [] : [true___, -(true___)], (5279 ^ _84654) ^ [_264836, _264838] : [proper_subset(_264838, _264838)], (8527 ^ _84654) ^ [_393938] : [one_sorted_str(_393938), 8530 ^ _84654 : [(8531 ^ _84654) ^ [_394089] : [element(_394089, powerset(the_carrier(_393938))), -(subset_difference(the_carrier(_393938), cast_as_carrier_subset(_393938), subset_difference(the_carrier(_393938), cast_as_carrier_subset(_393938), _394089)) = _394089)]]], (5576 ^ _84654) ^ [] : [-(epsilon_connected(5570 ^ []))], (3349 ^ _84654) ^ [_201428, _201430] : [_201428 = union(_201430), 3352 ^ _84654 : [(3362 ^ _84654) ^ [_201936] : [-(in(_201936, _201428)), 3363 ^ _84654 : [(3364 ^ _84654) ^ [_202034] : [in(_201936, _202034), in(_202034, _201430)]]], (3353 ^ _84654) ^ [_201609] : [in(_201609, _201428), 3357 ^ _84654 : [(3360 ^ _84654) ^ [] : [-(in(3356 ^ [_201428, _201430, _201609], _201430))], (3358 ^ _84654) ^ [] : [-(in(_201609, 3356 ^ [_201428, _201430, _201609]))]]]]], (10020 ^ _84654) ^ [_443234, _443236] : [-(pair_second(ordered_pair(_443236, _443234)) = _443234)], (4271 ^ _84654) ^ [] : [true___, -(true___)], (2983 ^ _84654) ^ [_188065, _188067, _188069] : [-(_188065 = cartesian_product2(_188069, _188067)), 3001 ^ _84654 : [(3008 ^ _84654) ^ [] : [in(2984 ^ [_188065, _188067, _188069], _188065)], (3002 ^ _84654) ^ [] : [-(in(2999 ^ [_188065, _188067, _188069], _188069))], (3006 ^ _84654) ^ [] : [-(2984 ^ [_188065, _188067, _188069] = ordered_pair(2999 ^ [_188065, _188067, _188069], 3000 ^ [_188065, _188067, _188069]))], (3004 ^ _84654) ^ [] : [-(in(3000 ^ [_188065, _188067, _188069], _188067))]], 2987 ^ _84654 : [(2990 ^ _84654) ^ [_188403, _188405] : [in(_188405, _188069), in(_188403, _188067), 2984 ^ [_188065, _188067, _188069] = ordered_pair(_188405, _188403)], (2988 ^ _84654) ^ [] : [-(in(2984 ^ [_188065, _188067, _188069], _188065))]]], (9607 ^ _84654) ^ [_430036] : [relation(_430036), function(_430036), one_to_one(_430036), 9618 ^ _84654 : [(9619 ^ _84654) ^ [_430423] : [relation(_430423), function(_430423), 9626 ^ _84654 : [(9627 ^ _84654) ^ [] : [_430423 = function_inverse(_430036), 9630 ^ _84654 : [(9645 ^ _84654) ^ [_431314, _431316] : [9652 ^ _84654 : [(9655 ^ _84654) ^ [] : [-(_431314 = apply(_430423, _431316))], (9653 ^ _84654) ^ [] : [-(in(_431316, relation_rng(_430036)))]], in(_431314, relation_dom(_430036)), _431316 = apply(_430036, _431314)], (9633 ^ _84654) ^ [_430940, _430942] : [9640 ^ _84654 : [(9643 ^ _84654) ^ [] : [-(_430942 = apply(_430036, _430940))], (9641 ^ _84654) ^ [] : [-(in(_430940, relation_dom(_430036)))]], in(_430942, relation_rng(_430036)), _430940 = apply(_430423, _430942)], (9631 ^ _84654) ^ [] : [-(relation_dom(_430423) = relation_rng(_430036))]]], (9657 ^ _84654) ^ [] : [-(_430423 = function_inverse(_430036)), relation_dom(_430423) = relation_rng(_430036), 9666 ^ _84654 : [(9671 ^ _84654) ^ [] : [in(9663 ^ [_430036, _430423], relation_dom(_430036)), 9662 ^ [_430036, _430423] = apply(_430036, 9663 ^ [_430036, _430423])], (9669 ^ _84654) ^ [] : [-(9663 ^ [_430036, _430423] = apply(_430423, 9662 ^ [_430036, _430423]))], (9667 ^ _84654) ^ [] : [-(in(9662 ^ [_430036, _430423], relation_rng(_430036)))]], 9676 ^ _84654 : [(9681 ^ _84654) ^ [] : [in(9662 ^ [_430036, _430423], relation_rng(_430036)), 9663 ^ [_430036, _430423] = apply(_430423, 9662 ^ [_430036, _430423])], (9679 ^ _84654) ^ [] : [-(9662 ^ [_430036, _430423] = apply(_430036, 9663 ^ [_430036, _430423]))], (9677 ^ _84654) ^ [] : [-(in(9663 ^ [_430036, _430423], relation_dom(_430036)))]]]]]]], (5143 ^ _84654) ^ [] : [-(relation(empty_set))], (3305 ^ _84654) ^ [_199668] : [relation(_199668), 3308 ^ _84654 : [(3309 ^ _84654) ^ [_199868] : [is_antisymmetric_in(_199668, _199868), 3312 ^ _84654 : [(3313 ^ _84654) ^ [_200050, _200052] : [-(_200052 = _200050), in(_200052, _199868), in(_200050, _199868), in(ordered_pair(_200052, _200050), _199668), in(ordered_pair(_200050, _200052), _199668)]]], (3331 ^ _84654) ^ [_200536] : [3334 ^ _84654 : [(3337 ^ _84654) ^ [] : [-(in(3333 ^ [_199668, _200536], _200536))], (3339 ^ _84654) ^ [] : [-(in(ordered_pair(3332 ^ [_199668, _200536], 3333 ^ [_199668, _200536]), _199668))], (3341 ^ _84654) ^ [] : [-(in(ordered_pair(3333 ^ [_199668, _200536], 3332 ^ [_199668, _200536]), _199668))], (3343 ^ _84654) ^ [] : [3332 ^ [_199668, _200536] = 3333 ^ [_199668, _200536]], (3335 ^ _84654) ^ [] : [-(in(3332 ^ [_199668, _200536], _200536))]], -(is_antisymmetric_in(_199668, _200536))]]], (8056 ^ _84654) ^ [_378169, _378171] : [subset(_378169, 8036 ^ [_378171]), -(are_equipotent(_378169, 8036 ^ [_378171])), -(in(_378169, 8036 ^ [_378171]))], (5752 ^ _84654) ^ [] : [-(one_sorted_str(5750 ^ []))], (40 ^ _84654) ^ [_85992, _85994] : [-(v1_int_1(_85992)), _85994 = _85992, v1_int_1(_85994)], (9254 ^ _84654) ^ [_418052] : [top_str(_418052), 9257 ^ _84654 : [(9258 ^ _84654) ^ [_418236] : [element(_418236, powerset(the_carrier(_418052))), 9261 ^ _84654 : [(9262 ^ _84654) ^ [_418421] : [in(_418421, the_carrier(_418052)), 9265 ^ _84654 : [(9266 ^ _84654) ^ [] : [in(_418421, topstr_closure(_418052, _418236)), 9269 ^ _84654 : [(9270 ^ _84654) ^ [_418710] : [element(_418710, powerset(the_carrier(_418052))), -(in(_418421, _418710)), closed_subset(_418710, _418052), subset(_418236, _418710)]]], (9284 ^ _84654) ^ [] : [9286 ^ _84654 : [(9293 ^ _84654) ^ [] : [in(_418421, 9285 ^ [_418052, _418236, _418421])], (9287 ^ _84654) ^ [] : [-(element(9285 ^ [_418052, _418236, _418421], powerset(the_carrier(_418052))))], (9291 ^ _84654) ^ [] : [-(subset(_418236, 9285 ^ [_418052, _418236, _418421]))], (9289 ^ _84654) ^ [] : [-(closed_subset(9285 ^ [_418052, _418236, _418421], _418052))]], -(in(_418421, topstr_closure(_418052, _418236)))]]]]]]], (5640 ^ _84654) ^ [] : [-(empty(5638 ^ []))], (2229 ^ _84654) ^ [_161100] : [2233 ^ _84654 : [(2238 ^ _84654) ^ [] : [2231 ^ [_161100] = 2232 ^ [_161100]], (2236 ^ _84654) ^ [] : [-(in(ordered_pair(2230 ^ [_161100], 2232 ^ [_161100]), _161100))], (2234 ^ _84654) ^ [] : [-(in(ordered_pair(2230 ^ [_161100], 2231 ^ [_161100]), _161100))]], -(function(_161100))], (4679 ^ _84654) ^ [_244967] : [join_semilatt_str(_244967), 4682 ^ _84654 : [(4687 ^ _84654) ^ [] : [-(relation_of2_as_subset(the_L_join(_244967), cartesian_product2(the_carrier(_244967), the_carrier(_244967)), the_carrier(_244967)))], (4685 ^ _84654) ^ [] : [-(quasi_total(the_L_join(_244967), cartesian_product2(the_carrier(_244967), the_carrier(_244967)), the_carrier(_244967)))], (4683 ^ _84654) ^ [] : [-(function(the_L_join(_244967)))]]], (5131 ^ _84654) ^ [_260158] : [ordinal(_260158), 5134 ^ _84654 : [(5139 ^ _84654) ^ [] : [-(ordinal(union(_260158)))], (5137 ^ _84654) ^ [] : [-(epsilon_connected(union(_260158)))], (5135 ^ _84654) ^ [] : [-(epsilon_transitive(union(_260158)))]]], (672 ^ _84654) ^ [_105429, _105431] : [-(top_str(_105429)), _105431 = _105429, top_str(_105431)], (9805 ^ _84654) ^ [_436391, _436393] : [subset(_436393, _436391), proper_subset(_436391, _436393)], (4755 ^ _84654) ^ [] : [-(relation_empty_yielding(empty_set))], (4731 ^ _84654) ^ [_246809, _246811] : [finite(_246811), -(finite(set_intersection2(_246811, _246809)))], (5644 ^ _84654) ^ [_277167] : [-(empty(_277167)), 5648 ^ _84654 : [(5651 ^ _84654) ^ [] : [empty(5647 ^ [_277167])], (5649 ^ _84654) ^ [] : [-(element(5647 ^ [_277167], powerset(_277167)))]]], (874 ^ _84654) ^ [_113050, _113052, _113054, _113056] : [-(relation_rng_restriction(_113056, _113052) = relation_rng_restriction(_113054, _113050)), _113056 = _113054, _113052 = _113050], (5619 ^ _84654) ^ [] : [-(ordinal(5613 ^ []))], (4229 ^ _84654) ^ [] : [true___, -(true___)], (5881 ^ _84654) ^ [_284976, _284978, _284980] : [-(subset_intersection2(_284980, _284978, _284976) = set_intersection2(_284978, _284976)), element(_284978, powerset(_284980)), element(_284976, powerset(_284980))], (2799 ^ _84654) ^ [_181625, _181627] : [-(empty(_181627)), 2802 ^ _84654 : [(2809 ^ _84654) ^ [] : [in(_181625, _181627), -(element(_181625, _181627))], (2803 ^ _84654) ^ [] : [element(_181625, _181627), -(in(_181625, _181627))]]], (5608 ^ _84654) ^ [] : [-(v3_membered(5600 ^ []))], (4819 ^ _84654) ^ [] : [-(epsilon_connected(omega))], (1130 ^ _84654) ^ [_122320, _122322, _122324, _122326] : [-(relation_composition(_122326, _122322) = relation_composition(_122324, _122320)), _122326 = _122324, _122322 = _122320], (5367 ^ _84654) ^ [_267972, _267974] : [in(_267974, _267972), -(subset(singleton(_267974), _267972))], (5863 ^ _84654) ^ [_284260, _284262, _284264] : [relation_of2(_284260, _284264, _284262), -(relation_dom_as_subset(_284264, _284262, _284260) = relation_dom(_284260))], (8593 ^ _84654) ^ [_396247] : [8608 ^ _84654 : [(8609 ^ _84654) ^ [_396650] : [element(_396650, the_carrier(_396247)), 8612 ^ _84654 : [(8613 ^ _84654) ^ [_396800] : [element(_396800, the_carrier(_396247)), -(below(_396247, meet_commut(_396247, _396650, _396800), _396650))]]]], -(empty_carrier(_396247)), meet_commutative(_396247), meet_absorbing(_396247), latt_str(_396247)], (5735 ^ _84654) ^ [] : [-(one_to_one(5729 ^ []))], (4699 ^ _84654) ^ [] : [-(join_semilatt_str(4697 ^ []))], (8244 ^ _84654) ^ [_384633, _384635, _384637] : [relation(_384633), 8247 ^ _84654 : [(8256 ^ _84654) ^ [] : [-(in(_384637, relation_restriction(_384633, _384635))), in(_384637, _384633), in(_384637, cartesian_product2(_384635, _384635))], (8248 ^ _84654) ^ [] : [in(_384637, relation_restriction(_384633, _384635)), 8251 ^ _84654 : [(8254 ^ _84654) ^ [] : [-(in(_384637, cartesian_product2(_384635, _384635)))], (8252 ^ _84654) ^ [] : [-(in(_384637, _384633))]]]]], (9026 ^ _84654) ^ [_410449, _410451] : [subset(_410451, _410449), -(set_difference(_410451, _410449) = empty_set)], (4407 ^ _84654) ^ [_236943, _236945] : [relation(_236945), -(relation(relation_restriction(_236945, _236943)))], (2451 ^ _84654) ^ [_169284, _169286] : [-(_169286 = empty_set), 2454 ^ _84654 : [(2455 ^ _84654) ^ [] : [_169284 = set_meet(_169286), 2458 ^ _84654 : [(2459 ^ _84654) ^ [_169582] : [in(_169582, _169284), 2462 ^ _84654 : [(2463 ^ _84654) ^ [_169727] : [in(_169727, _169286), -(in(_169582, _169727))]]], (2469 ^ _84654) ^ [_169912] : [2471 ^ _84654 : [(2474 ^ _84654) ^ [] : [in(_169912, 2470 ^ [_169284, _169286, _169912])], (2472 ^ _84654) ^ [] : [-(in(2470 ^ [_169284, _169286, _169912], _169286))]], -(in(_169912, _169284))]]], (2478 ^ _84654) ^ [] : [-(_169284 = set_meet(_169286)), 2482 ^ _84654 : [(2488 ^ _84654) ^ [] : [in(2479 ^ [_169284, _169286], 2484 ^ [_169284, _169286])], (2486 ^ _84654) ^ [] : [-(in(2484 ^ [_169284, _169286], _169286))], (2483 ^ _84654) ^ [] : [-(in(2479 ^ [_169284, _169286], _169284))]], 2489 ^ _84654 : [(2490 ^ _84654) ^ [_170686] : [in(_170686, _169286), -(in(2479 ^ [_169284, _169286], _170686))], (2496 ^ _84654) ^ [] : [in(2479 ^ [_169284, _169286], _169284)]]]]], (658 ^ _84654) ^ [_105013, _105015, _105017, _105019] : [-(in(_105017, _105013)), in(_105019, _105015), _105019 = _105017, _105015 = _105013], (4645 ^ _84654) ^ [] : [true___, -(true___)], (594 ^ _84654) ^ [_102935, _102937, _102939, _102941, _102943, _102945] : [-(quasi_total(_102943, _102939, _102935)), quasi_total(_102945, _102941, _102937), _102945 = _102943, _102941 = _102939, _102937 = _102935], (5742 ^ _84654) ^ [] : [-(epsilon_connected(5736 ^ []))], (4567 ^ _84654) ^ [_241515, _241517] : [element(_241515, powerset(powerset(_241517))), -(element(meet_of_subsets(_241517, _241515), powerset(_241517)))], (4183 ^ _84654) ^ [_231144, _231146] : [-(proper_subset(_231146, _231144)), subset(_231146, _231144), -(_231146 = _231144)], (3989 ^ _84654) ^ [_223579] : [-(empty_carrier(_223579)), latt_str(_223579), 3996 ^ _84654 : [(3997 ^ _84654) ^ [] : [meet_absorbing(_223579), 4000 ^ _84654 : [(4001 ^ _84654) ^ [_223927] : [element(_223927, the_carrier(_223579)), 4004 ^ _84654 : [(4005 ^ _84654) ^ [_224080] : [element(_224080, the_carrier(_223579)), -(join(_223579, meet(_223579, _223927, _224080), _224080) = _224080)]]]]], (4011 ^ _84654) ^ [] : [4013 ^ _84654 : [(4019 ^ _84654) ^ [] : [join(_223579, meet(_223579, 4012 ^ [_223579], 4015 ^ [_223579]), 4015 ^ [_223579]) = 4015 ^ [_223579]], (4017 ^ _84654) ^ [] : [-(element(4015 ^ [_223579], the_carrier(_223579)))], (4014 ^ _84654) ^ [] : [-(element(4012 ^ [_223579], the_carrier(_223579)))]], -(meet_absorbing(_223579))]]], (2744 ^ _84654) ^ [_179618] : [2746 ^ _84654 : [(2749 ^ _84654) ^ [] : [subset(2745 ^ [_179618], _179618)], (2747 ^ _84654) ^ [] : [-(in(2745 ^ [_179618], _179618))]], -(epsilon_transitive(_179618))], (5897 ^ _84654) ^ [_285549, _285551, _285553] : [-(subset_difference(_285553, _285551, _285549) = set_difference(_285551, _285549)), element(_285551, powerset(_285553)), element(_285549, powerset(_285553))], (4757 ^ _84654) ^ [_247661, _247663] : [-(finite(relation_image(_247663, _247661))), relation(_247663), function(_247663), finite(_247661)], (5744 ^ _84654) ^ [] : [-(ordinal(5736 ^ []))], (5235 ^ _84654) ^ [_263289, _263291] : [5242 ^ _84654 : [(5245 ^ _84654) ^ [] : [-(relation(relation_composition(_263291, _263289)))], (5243 ^ _84654) ^ [] : [-(empty(relation_composition(_263291, _263289)))]], empty(_263291), relation(_263289)], (8808 ^ _84654) ^ [_403224, _403226] : [subset(_403226, _403224), -(set_intersection2(_403226, _403224) = _403226)], (9803 ^ _84654) ^ [] : [-(relation_rng(empty_set) = empty_set)], (1254 ^ _84654) ^ [_126999] : [v4_membered(_126999), 1257 ^ _84654 : [(1258 ^ _84654) ^ [_127144] : [element(_127144, _126999), 1261 ^ _84654 : [(1268 ^ _84654) ^ [] : [-(v1_rat_1(_127144))], (1262 ^ _84654) ^ [] : [-(v1_xcmplx_0(_127144))], (1266 ^ _84654) ^ [] : [-(v1_int_1(_127144))], (1264 ^ _84654) ^ [] : [-(v1_xreal_0(_127144))]]]]], (8834 ^ _84654) ^ [_404033] : [-(set_intersection2(_404033, empty_set) = empty_set)], (9725 ^ _84654) ^ [_433994] : [relation(_433994), function(_433994), one_to_one(_433994), 9736 ^ _84654 : [(9739 ^ _84654) ^ [] : [-(relation_dom(_433994) = relation_rng(function_inverse(_433994)))], (9737 ^ _84654) ^ [] : [-(relation_rng(_433994) = relation_dom(function_inverse(_433994)))]]], (9976 ^ _84654) ^ [_441832, _441834, _441836] : [relation(_441832), function(_441832), in(_441834, _441836), -(apply(relation_dom_restriction(_441832, _441836), _441834) = apply(_441832, _441834))], (4555 ^ _84654) ^ [_241117, _241119] : [-(element(topstr_closure(_241119, _241117), powerset(the_carrier(_241119)))), top_str(_241119), element(_241117, powerset(the_carrier(_241119)))], (5965 ^ _84654) ^ [_287750, _287752] : [-(empty(_287752)), relation(_287750), 5977 ^ _84654 : [(5985 ^ _84654) ^ [_289032] : [in(_289032, 5979 ^ [_287750, _287752]), -(in(ordered_pair(5975 ^ [_287750, _287752], _289032), _287750))], (5998 ^ _84654) ^ [_289581] : [in(_289581, 5992 ^ [_287750, _287752]), -(in(ordered_pair(5976 ^ [_287750, _287752], _289581), _287750))], (5996 ^ _84654) ^ [] : [-(in(5976 ^ [_287750, _287752], 5992 ^ [_287750, _287752]))], (5991 ^ _84654) ^ [] : [-(in(5974 ^ [_287750, _287752], _287752))], (6004 ^ _84654) ^ [] : [5975 ^ [_287750, _287752] = 5976 ^ [_287750, _287752]], (5983 ^ _84654) ^ [] : [-(in(5975 ^ [_287750, _287752], 5979 ^ [_287750, _287752]))], (5978 ^ _84654) ^ [] : [-(in(5974 ^ [_287750, _287752], _287752))], (5981 ^ _84654) ^ [] : [-(5974 ^ [_287750, _287752] = 5979 ^ [_287750, _287752])], (5994 ^ _84654) ^ [] : [-(5974 ^ [_287750, _287752] = 5992 ^ [_287750, _287752])]], 6006 ^ _84654 : [(6030 ^ _84654) ^ [_290991, _290993] : [-(in(ordered_pair(_290993, _290991), 6005 ^ [_287750, _287752])), in(_290993, _287752), in(_290993, _287752), 6039 ^ _84654 : [(6040 ^ _84654) ^ [_291307] : [_290993 = _291307, in(_290991, _291307), 6048 ^ _84654 : [(6051 ^ _84654) ^ [] : [in(ordered_pair(_290991, 6047 ^ [_287750, _287752, _290991, _290993, _291307]), _287750)], (6049 ^ _84654) ^ [] : [-(in(6047 ^ [_287750, _287752, _290991, _290993, _291307], _291307))]]]]], (6007 ^ _84654) ^ [] : [-(relation(6005 ^ [_287750, _287752]))], (6011 ^ _84654) ^ [_290180, _290182] : [in(ordered_pair(_290182, _290180), 6005 ^ [_287750, _287752]), 6014 ^ _84654 : [(6017 ^ _84654) ^ [] : [-(in(_290182, _287752))], (6020 ^ _84654) ^ [] : [-(_290182 = 6018 ^ [_287750, _287752, _290180, _290182])], (6022 ^ _84654) ^ [] : [-(in(_290180, 6018 ^ [_287750, _287752, _290180, _290182]))], (6024 ^ _84654) ^ [_290762] : [in(_290762, 6018 ^ [_287750, _287752, _290180, _290182]), -(in(ordered_pair(_290180, _290762), _287750))], (6015 ^ _84654) ^ [] : [-(in(_290182, _287752))]]], (6009 ^ _84654) ^ [] : [-(function(6005 ^ [_287750, _287752]))]]], (3012 ^ _84654) ^ [_189299] : [-(empty_carrier(_189299)), join_semilatt_str(_189299), 3019 ^ _84654 : [(3020 ^ _84654) ^ [_189542] : [element(_189542, the_carrier(_189299)), 3023 ^ _84654 : [(3024 ^ _84654) ^ [_189698] : [element(_189698, the_carrier(_189299)), 3027 ^ _84654 : [(3034 ^ _84654) ^ [] : [join(_189299, _189542, _189698) = _189698, -(below(_189299, _189542, _189698))], (3028 ^ _84654) ^ [] : [below(_189299, _189542, _189698), -(join(_189299, _189542, _189698) = _189698)]]]]]]], (1374 ^ _84654) ^ [_131154] : [preboolean(_131154), 1377 ^ _84654 : [(1380 ^ _84654) ^ [] : [-(diff_closed(_131154))], (1378 ^ _84654) ^ [] : [-(cup_closed(_131154))]]], (2910 ^ _84654) ^ [_185289, _185291, _185293] : [_185289 = set_union2(_185293, _185291), 2913 ^ _84654 : [(2914 ^ _84654) ^ [_185471] : [in(_185471, _185289), -(in(_185471, _185293)), -(in(_185471, _185291))], (2924 ^ _84654) ^ [_185749] : [2925 ^ _84654 : [(2928 ^ _84654) ^ [] : [in(_185749, _185291)], (2926 ^ _84654) ^ [] : [in(_185749, _185293)]], -(in(_185749, _185289))]]], (1368 ^ _84654) ^ [_130968] : [empty(_130968), -(finite(_130968))], (10169 ^ _84654) ^ [_448202, _448204] : [relation(_448202), -(subset(relation_rng(relation_dom_restriction(_448202, _448204)), relation_rng(_448202)))], (4241 ^ _84654) ^ [] : [true___, -(true___)], (308 ^ _84654) ^ [_94131, _94133] : [-(latt_str(_94131)), _94133 = _94131, latt_str(_94133)], (176 ^ _84654) ^ [_90128, _90130] : [-(v4_membered(_90128)), _90130 = _90128, v4_membered(_90130)], (612 ^ _84654) ^ [_103544, _103546, _103548, _103550, _103552, _103554] : [-(relation_of2_as_subset(_103552, _103548, _103544)), relation_of2_as_subset(_103554, _103550, _103546), _103554 = _103552, _103550 = _103548, _103546 = _103544], (7830 ^ _84654) ^ [_370125, _370127] : [topological_space(_370127), top_str(_370127), element(_370125, powerset(the_carrier(_370127))), 7842 ^ _84654 : [(7845 ^ _84654) ^ [_370682] : [element(_370682, powerset(the_carrier(_370127))), 7848 ^ _84654 : [(7862 ^ _84654) ^ [] : [-(in(_370682, 7841 ^ [_370125, _370127])), 7863 ^ _84654 : [(7864 ^ _84654) ^ [_371384] : [element(_371384, powerset(the_carrier(_370127))), _371384 = _370682, closed_subset(_371384, _370127), subset(_370125, _370682)]]], (7849 ^ _84654) ^ [] : [in(_370682, 7841 ^ [_370125, _370127]), 7853 ^ _84654 : [(7860 ^ _84654) ^ [] : [-(subset(_370125, _370682))], (7854 ^ _84654) ^ [] : [-(element(7852 ^ [_370125, _370127, _370682], powerset(the_carrier(_370127))))], (7858 ^ _84654) ^ [] : [-(closed_subset(7852 ^ [_370125, _370127, _370682], _370127))], (7856 ^ _84654) ^ [] : [-(7852 ^ [_370125, _370127, _370682] = _370682)]]]]], (7843 ^ _84654) ^ [] : [-(element(7841 ^ [_370125, _370127], powerset(powerset(the_carrier(_370127)))))]]], (4865 ^ _84654) ^ [_250948, _250950] : [empty(ordered_pair(_250950, _250948))], (10083 ^ _84654) ^ [_445470, _445472] : [empty(_445472), -(_445472 = _445470), empty(_445470)], (430 ^ _84654) ^ [_97839, _97841] : [-(connected(_97839)), _97841 = _97839, connected(_97841)], (5749 ^ _84654) ^ [] : [-(relation_empty_yielding(5745 ^ []))], (8111 ^ _84654) ^ [_380068, _380070] : [relation(_380068), -(subset(relation_image(_380068, _380070), relation_rng(_380068)))], (2753 ^ _84654) ^ [_179943] : [one_sorted_str(_179943), -(empty_carrier_subset(_179943) = empty_set)], (5199 ^ _84654) ^ [_262169] : [empty(relation_rng(_262169)), -(empty(_262169)), relation(_262169)], (9098 ^ _84654) ^ [_412868, _412870, _412872] : [in(_412872, _412870), in(_412870, _412868), in(_412868, _412872)], (9486 ^ _84654) ^ [_426154, _426156, _426158] : [-(element(_426158, _426154)), in(_426158, _426156), element(_426156, powerset(_426154))], (1564 ^ _84654) ^ [_137193, _137195, _137197] : [-(meet_commut(_137197, _137195, _137193) = meet_commut(_137197, _137193, _137195)), -(empty_carrier(_137197)), meet_commutative(_137197), meet_semilatt_str(_137197), element(_137195, the_carrier(_137197)), element(_137193, the_carrier(_137197))], (8066 ^ _84654) ^ [_378509, _378511] : [-(finite(_378511)), subset(_378511, _378509), finite(_378509)], (910 ^ _84654) ^ [_114373, _114375, _114377, _114379, _114381, _114383] : [-(relation_dom_as_subset(_114383, _114379, _114375) = relation_dom_as_subset(_114381, _114377, _114373)), _114383 = _114381, _114379 = _114377, _114375 = _114373], (4631 ^ _84654) ^ [_243524] : [latt_str(_243524), 4634 ^ _84654 : [(4637 ^ _84654) ^ [] : [-(join_semilatt_str(_243524))], (4635 ^ _84654) ^ [] : [-(meet_semilatt_str(_243524))]]], (584 ^ _84654) ^ [_102584, _102586] : [-(function(_102584)), _102586 = _102584, function(_102586)], (5442 ^ _84654) ^ [_270541, _270543, _270545] : [subset(_270545, _270543), -(in(_270541, _270545)), -(subset(_270545, set_difference(_270543, singleton(_270541))))], (1338 ^ _84654) ^ [_129913] : [v4_membered(_129913), 1341 ^ _84654 : [(1342 ^ _84654) ^ [_130060] : [element(_130060, powerset(_129913)), 1345 ^ _84654 : [(1352 ^ _84654) ^ [] : [-(v4_membered(_130060))], (1346 ^ _84654) ^ [] : [-(v1_membered(_130060))], (1350 ^ _84654) ^ [] : [-(v3_membered(_130060))], (1348 ^ _84654) ^ [] : [-(v2_membered(_130060))]]]]], (9149 ^ _84654) ^ [_414642] : [ordinal(_414642), 9152 ^ _84654 : [(9153 ^ _84654) ^ [] : [being_limit_ordinal(_414642), 9156 ^ _84654 : [(9157 ^ _84654) ^ [_414888] : [ordinal(_414888), in(_414888, _414642), -(in(succ(_414888), _414642))]]], (9167 ^ _84654) ^ [] : [9169 ^ _84654 : [(9174 ^ _84654) ^ [] : [in(succ(9168 ^ [_414642]), _414642)], (9172 ^ _84654) ^ [] : [-(in(9168 ^ [_414642], _414642))], (9170 ^ _84654) ^ [] : [-(ordinal(9168 ^ [_414642]))]], -(being_limit_ordinal(_414642))]]], (10119 ^ _84654) ^ [_446522] : [relation(_446522), 10122 ^ _84654 : [(10129 ^ _84654) ^ [] : [well_ordering(_446522), -(well_orders(_446522, relation_field(_446522)))], (10123 ^ _84654) ^ [] : [well_orders(_446522, relation_field(_446522)), -(well_ordering(_446522))]]], (4713 ^ _84654) ^ [_246219, _246221] : [finite(_246219), -(finite(set_intersection2(_246221, _246219)))], (802 ^ _84654) ^ [_110437, _110439, _110441, _110443, _110445, _110447] : [-(join_commut(_110447, _110443, _110439) = join_commut(_110445, _110441, _110437)), _110447 = _110445, _110443 = _110441, _110439 = _110437], (516 ^ _84654) ^ [_100516, _100518] : [-(ordinal(_100516)), _100518 = _100516, ordinal(_100518)], (5225 ^ _84654) ^ [_262990, _262992] : [-(finite(set_union2(_262992, _262990))), finite(_262992), finite(_262990)], (5691 ^ _84654) ^ [] : [-(empty(5683 ^ []))], (5731 ^ _84654) ^ [] : [-(relation(5729 ^ []))], (5578 ^ _84654) ^ [] : [-(ordinal(5570 ^ []))], (8007 ^ _84654) ^ [_376376, _376378, _376380, _376382] : [-(subset(cartesian_product2(_376382, _376378), cartesian_product2(_376380, _376376))), subset(_376382, _376380), subset(_376378, _376376)], (682 ^ _84654) ^ [_105752, _105754, _105756, _105758] : [-(element(_105756, _105752)), element(_105758, _105754), _105758 = _105756, _105754 = _105752], (9131 ^ _84654) ^ [_414000, _414002] : [disjoint(_414002, _414000), 9132 ^ _84654 : [(9133 ^ _84654) ^ [_414092] : [in(_414092, _414002), in(_414092, _414000)]]], (156 ^ _84654) ^ [_89538, _89540] : [-(v2_membered(_89538)), _89540 = _89538, v2_membered(_89540)], (3268 ^ _84654) ^ [_198227] : [relation(_198227), 3271 ^ _84654 : [(3272 ^ _84654) ^ [_198408] : [_198408 = relation_dom(_198227), 3275 ^ _84654 : [(3283 ^ _84654) ^ [_198832] : [3284 ^ _84654 : [(3285 ^ _84654) ^ [_198911] : [in(ordered_pair(_198832, _198911), _198227)]], -(in(_198832, _198408))], (3276 ^ _84654) ^ [_198588] : [in(_198588, _198408), -(in(ordered_pair(_198588, 3279 ^ [_198227, _198408, _198588]), _198227))]]], (3289 ^ _84654) ^ [_199039] : [-(_199039 = relation_dom(_198227)), 3293 ^ _84654 : [(3296 ^ _84654) ^ [_199302] : [in(ordered_pair(3290 ^ [_198227, _199039], _199302), _198227)], (3294 ^ _84654) ^ [] : [-(in(3290 ^ [_198227, _199039], _199039))]], 3298 ^ _84654 : [(3301 ^ _84654) ^ [] : [in(3290 ^ [_198227, _199039], _199039)], (3299 ^ _84654) ^ [] : [-(in(ordered_pair(3290 ^ [_198227, _199039], 3297 ^ [_198227, _199039]), _198227))]]]]], (5702 ^ _84654) ^ [_279192, _279194] : [-(relation(5698 ^ [_279192, _279194]))], (5657 ^ _84654) ^ [_277679] : [-(element(5655 ^ [_277679], powerset(_277679)))], (4702 ^ _84654) ^ [] : [-(latt_str(4700 ^ []))], (5324 ^ _84654) ^ [_266399, _266401] : [relation(_266399), -(subset(relation_dom(relation_rng_restriction(_266401, _266399)), relation_dom(_266399)))], (5642 ^ _84654) ^ [] : [-(relation(5638 ^ []))], (4693 ^ _84654) ^ [] : [-(top_str(4691 ^ []))], (116 ^ _84654) ^ [_88358, _88360] : [-(cup_closed(_88358)), _88360 = _88358, cup_closed(_88360)], (278 ^ _84654) ^ [_93246, _93248] : [-(one_sorted_str(_93246)), _93248 = _93246, one_sorted_str(_93248)], (9297 ^ _84654) ^ [_419610] : [relation(_419610), 9300 ^ _84654 : [(9301 ^ _84654) ^ [_419747] : [relation(_419747), -(subset(relation_rng(relation_composition(_419610, _419747)), relation_rng(_419747)))]]], (60 ^ _84654) ^ [_86610, _86612, _86614, _86616] : [-(is_antisymmetric_in(_86614, _86610)), is_antisymmetric_in(_86616, _86612), _86616 = _86614, _86612 = _86610], (1538 ^ _84654) ^ [_136341, _136343] : [-(set_union2(_136343, _136341) = set_union2(_136341, _136343))], (10055 ^ _84654) ^ [_444597, _444599, _444601] : [relation(_444597), 10058 ^ _84654 : [(10067 ^ _84654) ^ [] : [-(in(_444601, relation_dom(relation_dom_restriction(_444597, _444599)))), in(_444601, _444599), in(_444601, relation_dom(_444597))], (10059 ^ _84654) ^ [] : [in(_444601, relation_dom(relation_dom_restriction(_444597, _444599))), 10062 ^ _84654 : [(10065 ^ _84654) ^ [] : [-(in(_444601, relation_dom(_444597)))], (10063 ^ _84654) ^ [] : [-(in(_444601, _444599))]]]]], (8449 ^ _84654) ^ [_391444, _391446, _391448, _391450] : [function(_391444), quasi_total(_391444, _391450, _391448), relation_of2_as_subset(_391444, _391450, _391448), 8460 ^ _84654 : [(8461 ^ _84654) ^ [_391813] : [relation(_391813), function(_391813), in(_391446, _391450), -(_391448 = empty_set), -(apply(relation_composition(_391444, _391813), _391446) = apply(_391813, apply(_391444, _391446)))]]], (2547 ^ _84654) ^ [_172531] : [relation(_172531), 2550 ^ _84654 : [(2551 ^ _84654) ^ [_172735, _172737] : [_172735 = fiber(_172531, _172737), 2554 ^ _84654 : [(2563 ^ _84654) ^ [_173190] : [-(in(_173190, _172735)), -(_173190 = _172737), in(ordered_pair(_173190, _172737), _172531)], (2555 ^ _84654) ^ [_172924] : [in(_172924, _172735), 2558 ^ _84654 : [(2561 ^ _84654) ^ [] : [-(in(ordered_pair(_172924, _172737), _172531))], (2559 ^ _84654) ^ [] : [_172924 = _172737]]]]], (2573 ^ _84654) ^ [_173483, _173485] : [-(_173483 = fiber(_172531, _173485)), 2585 ^ _84654 : [(2590 ^ _84654) ^ [] : [in(2574 ^ [_172531, _173483, _173485], _173483)], (2588 ^ _84654) ^ [] : [-(in(ordered_pair(2574 ^ [_172531, _173483, _173485], _173485), _172531))], (2586 ^ _84654) ^ [] : [2574 ^ [_172531, _173483, _173485] = _173485]], 2577 ^ _84654 : [(2580 ^ _84654) ^ [] : [-(2574 ^ [_172531, _173483, _173485] = _173485), in(ordered_pair(2574 ^ [_172531, _173483, _173485], _173485), _172531)], (2578 ^ _84654) ^ [] : [-(in(2574 ^ [_172531, _173483, _173485], _173483))]]]]], (3679 ^ _84654) ^ [_212685, _212687] : [-(ordered_pair(_212687, _212685) = unordered_pair(unordered_pair(_212687, _212685), singleton(_212687)))], (4453 ^ _84654) ^ [_238131, _238133] : [element(_238131, powerset(_238133)), -(element(subset_complement(_238133, _238131), powerset(_238133)))], (3949 ^ _84654) ^ [_222269] : [relation(_222269), function(_222269), 3956 ^ _84654 : [(3957 ^ _84654) ^ [] : [one_to_one(_222269), 3960 ^ _84654 : [(3961 ^ _84654) ^ [_222632, _222634] : [-(_222634 = _222632), in(_222634, relation_dom(_222269)), in(_222632, relation_dom(_222269)), apply(_222269, _222634) = apply(_222269, _222632)]]], (3975 ^ _84654) ^ [] : [3978 ^ _84654 : [(3985 ^ _84654) ^ [] : [3976 ^ [_222269] = 3977 ^ [_222269]], (3979 ^ _84654) ^ [] : [-(in(3976 ^ [_222269], relation_dom(_222269)))], (3983 ^ _84654) ^ [] : [-(apply(_222269, 3976 ^ [_222269]) = apply(_222269, 3977 ^ [_222269]))], (3981 ^ _84654) ^ [] : [-(in(3977 ^ [_222269], relation_dom(_222269)))]], -(one_to_one(_222269))]]], (7953 ^ _84654) ^ [_374476, _374478, _374480] : [relation(_374476), 7956 ^ _84654 : [(7965 ^ _84654) ^ [] : [-(in(_374480, relation_rng(relation_rng_restriction(_374478, _374476)))), in(_374480, _374478), in(_374480, relation_rng(_374476))], (7957 ^ _84654) ^ [] : [in(_374480, relation_rng(relation_rng_restriction(_374478, _374476))), 7960 ^ _84654 : [(7963 ^ _84654) ^ [] : [-(in(_374480, relation_rng(_374476)))], (7961 ^ _84654) ^ [] : [-(in(_374480, _374478))]]]]], (298 ^ _84654) ^ [_93836, _93838] : [-(meet_absorbing(_93836)), _93838 = _93836, meet_absorbing(_93838)], (3122 ^ _84654) ^ [_193161, _193163] : [3124 ^ _84654 : [(3127 ^ _84654) ^ [] : [in(3123 ^ [_193161, _193163], _193161)], (3125 ^ _84654) ^ [] : [-(in(3123 ^ [_193161, _193163], _193163))]], -(subset(_193163, _193161))], (1845 ^ _84654) ^ [_147165] : [relation(_147165), 1848 ^ _84654 : [(1855 ^ _84654) ^ [] : [is_antisymmetric_in(_147165, relation_field(_147165)), -(antisymmetric(_147165))], (1849 ^ _84654) ^ [] : [antisymmetric(_147165), -(is_antisymmetric_in(_147165, relation_field(_147165)))]]], (1302 ^ _84654) ^ [_128669] : [v1_membered(_128669), 1305 ^ _84654 : [(1306 ^ _84654) ^ [_128801] : [element(_128801, powerset(_128669)), -(v1_membered(_128801))]]], (5029 ^ _84654) ^ [_256707, _256709] : [v2_membered(_256709), 5032 ^ _84654 : [(5035 ^ _84654) ^ [] : [-(v2_membered(set_difference(_256709, _256707)))], (5033 ^ _84654) ^ [] : [-(v1_membered(set_difference(_256709, _256707)))]]], (126 ^ _84654) ^ [_88653, _88655] : [-(diff_closed(_88653)), _88655 = _88653, diff_closed(_88655)], (8729 ^ _84654) ^ [_400609] : [relation(_400609), function(_400609), finite(relation_dom(_400609)), -(finite(relation_rng(_400609)))], (8001 ^ _84654) ^ [_376120, _376122] : [relation(_376120), -(relation_rng(relation_rng_restriction(_376122, _376120)) = set_intersection2(relation_rng(_376120), _376122))], (1728 ^ _84654) ^ [_142686] : [relation(_142686), function(_142686), 1735 ^ _84654 : [(1736 ^ _84654) ^ [_142984, _142986] : [_142984 = relation_image(_142686, _142986), 1739 ^ _84654 : [(1751 ^ _84654) ^ [_143639] : [-(in(_143639, _142984)), 1752 ^ _84654 : [(1753 ^ _84654) ^ [_143752] : [in(_143752, relation_dom(_142686)), in(_143752, _142986), _143639 = apply(_142686, _143752)]]], (1740 ^ _84654) ^ [_143184] : [in(_143184, _142984), 1744 ^ _84654 : [(1749 ^ _84654) ^ [] : [-(_143184 = apply(_142686, 1743 ^ [_142686, _142984, _142986, _143184]))], (1747 ^ _84654) ^ [] : [-(in(1743 ^ [_142686, _142984, _142986, _143184], _142986))], (1745 ^ _84654) ^ [] : [-(in(1743 ^ [_142686, _142984, _142986, _143184], relation_dom(_142686)))]]]]], (1765 ^ _84654) ^ [_144112, _144114] : [-(_144112 = relation_image(_142686, _144114)), 1782 ^ _84654 : [(1789 ^ _84654) ^ [] : [in(1766 ^ [_142686, _144112, _144114], _144112)], (1783 ^ _84654) ^ [] : [-(in(1781 ^ [_142686, _144112, _144114], relation_dom(_142686)))], (1787 ^ _84654) ^ [] : [-(1766 ^ [_142686, _144112, _144114] = apply(_142686, 1781 ^ [_142686, _144112, _144114]))], (1785 ^ _84654) ^ [] : [-(in(1781 ^ [_142686, _144112, _144114], _144114))]], 1769 ^ _84654 : [(1772 ^ _84654) ^ [_144432] : [in(_144432, relation_dom(_142686)), in(_144432, _144114), 1766 ^ [_142686, _144112, _144114] = apply(_142686, _144432)], (1770 ^ _84654) ^ [] : [-(in(1766 ^ [_142686, _144112, _144114], _144112))]]]]], (8149 ^ _84654) ^ [_381338, _381340] : [relation(_381338), function(_381338), subset(_381340, relation_rng(_381338)), -(relation_image(_381338, relation_inverse_image(_381338, _381340)) = _381340)], (5452 ^ _84654) ^ [_270847] : [relation(_270847), 5455 ^ _84654 : [(5456 ^ _84654) ^ [] : [connected(_270847), 5459 ^ _84654 : [(5460 ^ _84654) ^ [_271141, _271143] : [in(_271143, relation_field(_270847)), in(_271141, relation_field(_270847)), -(_271143 = _271141), -(in(ordered_pair(_271143, _271141), _270847)), -(in(ordered_pair(_271141, _271143), _270847))]]], (5478 ^ _84654) ^ [] : [5481 ^ _84654 : [(5484 ^ _84654) ^ [] : [-(in(5480 ^ [_270847], relation_field(_270847)))], (5486 ^ _84654) ^ [] : [5479 ^ [_270847] = 5480 ^ [_270847]], (5488 ^ _84654) ^ [] : [in(ordered_pair(5479 ^ [_270847], 5480 ^ [_270847]), _270847)], (5490 ^ _84654) ^ [] : [in(ordered_pair(5480 ^ [_270847], 5479 ^ [_270847]), _270847)], (5482 ^ _84654) ^ [] : [-(in(5479 ^ [_270847], relation_field(_270847)))]], -(connected(_270847))]]], (5667 ^ _84654) ^ [_278022] : [-(epsilon_transitive(5655 ^ [_278022]))], (8499 ^ _84654) ^ [_393026, _393028, _393030] : [relation(_393026), -(subset(fiber(relation_restriction(_393026, _393030), _393028), fiber(_393026, _393028)))], (5402 ^ _84654) ^ [_269139, _269141] : [element(_269139, powerset(_269141)), 5405 ^ _84654 : [(5406 ^ _84654) ^ [_269280] : [in(_269280, _269139), -(in(_269280, _269141))]]], (4447 ^ _84654) ^ [] : [true___, -(true___)], (5580 ^ _84654) ^ [] : [-(natural(5570 ^ []))], (1540 ^ _84654) ^ [_136470, _136472, _136474] : [-(join_commut(_136474, _136472, _136470) = join_commut(_136474, _136470, _136472)), -(empty_carrier(_136474)), join_commutative(_136474), join_semilatt_str(_136474), element(_136472, the_carrier(_136474)), element(_136470, the_carrier(_136474))], (3062 ^ _84654) ^ [_190862] : [3065 ^ _84654 : [(3068 ^ _84654) ^ [] : [-(in(3064 ^ [_190862], _190862))], (3070 ^ _84654) ^ [] : [in(3063 ^ [_190862], 3064 ^ [_190862])], (3072 ^ _84654) ^ [] : [3063 ^ [_190862] = 3064 ^ [_190862]], (3074 ^ _84654) ^ [] : [in(3064 ^ [_190862], 3063 ^ [_190862])], (3066 ^ _84654) ^ [] : [-(in(3063 ^ [_190862], _190862))]], -(epsilon_connected(_190862))], (1088 ^ _84654) ^ [_120807, _120809, _120811, _120813] : [-(apply(_120813, _120809) = apply(_120811, _120807)), _120813 = _120811, _120809 = _120807], (9753 ^ _84654) ^ [_434865, _434867] : [relation(_434865), function(_434865), 9768 ^ _84654 : [(9771 ^ _84654) ^ [] : [-(_434867 = apply(relation_composition(function_inverse(_434865), _434865), _434867))], (9769 ^ _84654) ^ [] : [-(_434867 = apply(_434865, apply(function_inverse(_434865), _434867)))]], one_to_one(_434865), in(_434867, relation_rng(_434865))], (8023 ^ _84654) ^ [_376917, _376919, _376921] : [relation_of2_as_subset(_376917, _376921, _376919), 8026 ^ _84654 : [(8029 ^ _84654) ^ [] : [-(subset(relation_rng(_376917), _376919))], (8027 ^ _84654) ^ [] : [-(subset(relation_dom(_376917), _376921))]]], (3078 ^ _84654) ^ [_191568] : [one_sorted_str(_191568), -(cast_as_carrier_subset(_191568) = the_carrier(_191568))], (482 ^ _84654) ^ [_99510, _99512, _99514, _99516] : [-(proper_subset(_99514, _99510)), proper_subset(_99516, _99512), _99516 = _99514, _99512 = _99510], (4471 ^ _84654) ^ [_238607, _238609, _238611] : [-(element(meet_commut(_238611, _238609, _238607), the_carrier(_238611))), -(empty_carrier(_238611)), meet_commutative(_238611), meet_semilatt_str(_238611), element(_238609, the_carrier(_238611)), element(_238607, the_carrier(_238611))], (9430 ^ _84654) ^ [_424207, _424209] : [element(_424207, powerset(powerset(_424209))), -(_424207 = empty_set), -(subset_difference(_424209, cast_to_subset(_424209), union_of_subsets(_424209, _424207)) = meet_of_subsets(_424209, complements_of_subsets(_424209, _424207)))], (4393 ^ _84654) ^ [] : [true___, -(true___)], (9201 ^ _84654) ^ [_416252, _416254] : [element(_416252, powerset(_416254)), 9204 ^ _84654 : [(9205 ^ _84654) ^ [_416404] : [element(_416404, powerset(_416254)), 9208 ^ _84654 : [(9215 ^ _84654) ^ [] : [subset(_416252, subset_complement(_416254, _416404)), -(disjoint(_416252, _416404))], (9209 ^ _84654) ^ [] : [disjoint(_416252, _416404), -(subset(_416252, subset_complement(_416254, _416404)))]]]]], (5669 ^ _84654) ^ [_278090] : [-(epsilon_connected(5655 ^ [_278090]))], (4387 ^ _84654) ^ [_236409] : [one_sorted_str(_236409), -(element(cast_as_carrier_subset(_236409), powerset(the_carrier(_236409))))], (328 ^ _84654) ^ [_94721, _94723] : [-(empty_carrier(_94721)), _94723 = _94721, empty_carrier(_94723)], (8877 ^ _84654) ^ [_405526] : [-(ordinal(_405526)), 8879 ^ _84654 : [(8882 ^ _84654) ^ [] : [ordinal(8878 ^ [_405526]), subset(8878 ^ [_405526], _405526)], (8880 ^ _84654) ^ [] : [-(in(8878 ^ [_405526], _405526))]]], (5187 ^ _84654) ^ [] : [-(empty(empty_set))], (5907 ^ _84654) ^ [_285923, _285925, _285927] : [relation_of2_as_subset(_285923, _285927, _285925), -(relation_of2(_285923, _285927, _285925))], (5663 ^ _84654) ^ [_277886] : [-(function(5655 ^ [_277886]))], (410 ^ _84654) ^ [_97249, _97251] : [-(reflexive(_97249)), _97251 = _97249, reflexive(_97251)], (5585 ^ _84654) ^ [] : [-(finite(5581 ^ []))], (4651 ^ _84654) ^ [_244047, _244049, _244051] : [relation_of2_as_subset(_244047, _244051, _244049), -(element(_244047, powerset(cartesian_product2(_244051, _244049))))], (1146 ^ _84654) ^ [_122897, _122899, _122901, _122903] : [-(relation_dom_restriction(_122903, _122899) = relation_dom_restriction(_122901, _122897)), _122903 = _122901, _122899 = _122897], (5195 ^ _84654) ^ [] : [-(v4_membered(empty_set))], (5951 ^ _84654) ^ [_287267, _287269] : [-(ordinal_subset(_287269, _287269)), ordinal(_287269), ordinal(_287267)], (4823 ^ _84654) ^ [] : [empty(omega)], (5675 ^ _84654) ^ [_278274] : [-(finite(5655 ^ [_278274]))], (7211 ^ _84654) ^ [_344658, _344660] : [-(empty(_344660)), relation(_344658), 7219 ^ _84654 : [(7243 ^ _84654) ^ [_346379, _346381] : [-(in(_346379, 7218 ^ [_344658, _344660, _346381])), in(_346379, cartesian_product2(_344660, _346381)), 7248 ^ _84654 : [(7249 ^ _84654) ^ [_346646, _346648] : [ordered_pair(_346648, _346646) = _346379, in(_346648, _344660), 7256 ^ _84654 : [(7257 ^ _84654) ^ [_346934] : [_346648 = _346934, in(_346646, _346934), 7265 ^ _84654 : [(7268 ^ _84654) ^ [] : [in(ordered_pair(_346646, 7264 ^ [_344658, _344660, _346379, _346381, _346646, _346648, _346934]), _344658)], (7266 ^ _84654) ^ [] : [-(in(7264 ^ [_344658, _344660, _346379, _346381, _346646, _346648, _346934], _346934))]]]]]]], (7220 ^ _84654) ^ [_345124, _345126] : [in(_345124, 7218 ^ [_344658, _344660, _345126]), 7223 ^ _84654 : [(7235 ^ _84654) ^ [] : [-(in(7226 ^ [_344658, _344660, _345124, _345126], 7231 ^ [_344658, _344660, _345124, _345126]))], (7233 ^ _84654) ^ [] : [-(7225 ^ [_344658, _344660, _345124, _345126] = 7231 ^ [_344658, _344660, _345124, _345126])], (7237 ^ _84654) ^ [_346126] : [in(_346126, 7231 ^ [_344658, _344660, _345124, _345126]), -(in(ordered_pair(7226 ^ [_344658, _344660, _345124, _345126], _346126), _344658))], (7224 ^ _84654) ^ [] : [-(in(_345124, cartesian_product2(_344660, _345126)))], (7228 ^ _84654) ^ [] : [-(ordered_pair(7225 ^ [_344658, _344660, _345124, _345126], 7226 ^ [_344658, _344660, _345124, _345126]) = _345124)], (7230 ^ _84654) ^ [] : [-(in(7225 ^ [_344658, _344660, _345124, _345126], _344660))]]]]], (2500 ^ _84654) ^ [_170991, _170993] : [_170993 = empty_set, 2503 ^ _84654 : [(2510 ^ _84654) ^ [] : [_170991 = empty_set, -(_170991 = set_meet(_170993))], (2504 ^ _84654) ^ [] : [_170991 = set_meet(_170993), -(_170991 = empty_set)]]], (9052 ^ _84654) ^ [_411372, _411374, _411376] : [-(subset(unordered_pair(_411376, _411374), _411372)), in(_411376, _411372), in(_411374, _411372)], (4911 ^ _84654) ^ [] : [-(relation_empty_yielding(empty_set))], (924 ^ _84654) ^ [_114889, _114891, _114893, _114895, _114897, _114899] : [-(meet_commut(_114899, _114895, _114891) = meet_commut(_114897, _114893, _114889)), _114899 = _114897, _114895 = _114893, _114891 = _114889], (4595 ^ _84654) ^ [_242530, _242532] : [relation(_242530), -(relation(relation_rng_restriction(_242532, _242530)))], (2710 ^ _84654) ^ [_178262] : [2711 ^ _84654 : [(2712 ^ _84654) ^ [_178384, _178386] : [_178262 = ordered_pair(_178386, _178384)]], 2713 ^ _84654 : [(2714 ^ _84654) ^ [_178493] : [_178493 = pair_second(_178262), 2717 ^ _84654 : [(2718 ^ _84654) ^ [_178658, _178660] : [_178262 = ordered_pair(_178660, _178658), -(_178493 = _178658)]]], (2724 ^ _84654) ^ [_178847] : [2727 ^ _84654 : [(2730 ^ _84654) ^ [] : [_178847 = 2726 ^ [_178262, _178847]], (2728 ^ _84654) ^ [] : [-(_178262 = ordered_pair(2725 ^ [_178262, _178847], 2726 ^ [_178262, _178847]))]], -(_178847 = pair_second(_178262))]]], (5574 ^ _84654) ^ [] : [-(epsilon_transitive(5570 ^ []))], (5635 ^ _84654) ^ [] : [-(one_to_one(5629 ^ []))], (5583 ^ _84654) ^ [] : [empty(5581 ^ [])], (5261 ^ _84654) ^ [_264200, _264202] : [element(_264200, powerset(_264202)), -(subset_complement(_264202, subset_complement(_264202, _264200)) = _264200)], (4783 ^ _84654) ^ [_248415] : [empty(singleton(_248415))], (458 ^ _84654) ^ [_98771, _98773, _98775, _98777] : [-(is_well_founded_in(_98775, _98771)), is_well_founded_in(_98777, _98773), _98777 = _98775, _98773 = _98771], (376 ^ _84654) ^ [_96243, _96245, _96247, _96249] : [-(ordinal_subset(_96247, _96243)), ordinal_subset(_96249, _96245), _96249 = _96247, _96245 = _96243], (5963 ^ _84654) ^ [_287641, _287643] : [-(equipotent(_287643, _287643))], (2326 ^ _84654) ^ [_164614] : [-(succ(_164614) = set_union2(_164614, singleton(_164614)))], (10145 ^ _84654) ^ [_447310, _447312, _447314] : [singleton(_447314) = unordered_pair(_447312, _447310), -(_447314 = _447312)], (4351 ^ _84654) ^ [_235414] : [4358 ^ _84654 : [(4361 ^ _84654) ^ [] : [-(function(function_inverse(_235414)))], (4359 ^ _84654) ^ [] : [-(relation(function_inverse(_235414)))]], relation(_235414), function(_235414)], (9450 ^ _84654) ^ [_424902, _424904] : [element(_424902, powerset(powerset(_424904))), -(_424902 = empty_set), -(union_of_subsets(_424904, complements_of_subsets(_424904, _424902)) = subset_difference(_424904, cast_to_subset(_424904), meet_of_subsets(_424904, _424902)))], (4705 ^ _84654) ^ [_245836, _245838] : [-(relation_of2(4703 ^ [_245836, _245838], _245838, _245836))], (1004 ^ _84654) ^ [_117793, _117795, _117797, _117799, _117801, _117803] : [-(subset_difference(_117803, _117799, _117795) = subset_difference(_117801, _117797, _117793)), _117803 = _117801, _117799 = _117797, _117795 = _117793], (10077 ^ _84654) ^ [_445256, _445258] : [relation(_445256), -(subset(relation_dom_restriction(_445256, _445258), _445256))], (5961 ^ _84654) ^ [_287547, _287549] : [-(subset(_287549, _287549))], (5913 ^ _84654) ^ [_286095, _286097, _286099] : [relation_of2(_286095, _286099, _286097), -(relation_of2_as_subset(_286095, _286099, _286097))], (5697 ^ _84654) ^ [] : [-(ordinal(5683 ^ []))], (338 ^ _84654) ^ [_95016, _95018] : [-(join_commutative(_95016)), _95018 = _95016, join_commutative(_95018)], (1228 ^ _84654) ^ [_126104] : [v2_membered(_126104), 1231 ^ _84654 : [(1232 ^ _84654) ^ [_126239] : [element(_126239, _126104), 1235 ^ _84654 : [(1238 ^ _84654) ^ [] : [-(v1_xreal_0(_126239))], (1236 ^ _84654) ^ [] : [-(v1_xcmplx_0(_126239))]]]]], (1044 ^ _84654) ^ [_119189, _119191] : [_119191 = _119189, -(function_inverse(_119191) = function_inverse(_119189))], (5536 ^ _84654) ^ [_273756, _273758] : [5538 ^ _84654 : [(5541 ^ _84654) ^ [] : [in(5537 ^ [_273756, _273758], _273756)], (5539 ^ _84654) ^ [] : [-(in(5537 ^ [_273756, _273758], _273758))]], -(element(_273758, powerset(_273756)))], (4265 ^ _84654) ^ [] : [true___, -(true___)], (5494 ^ _84654) ^ [_272333, _272335] : [subset(_272335, singleton(_272333)), -(_272335 = empty_set), -(_272335 = singleton(_272333))], (5273 ^ _84654) ^ [_264622, _264624] : [element(_264622, powerset(powerset(_264624))), -(complements_of_subsets(_264624, complements_of_subsets(_264624, _264622)) = _264622)], (9863 ^ _84654) ^ [_438103, _438105] : [set_difference(_438105, singleton(_438103)) = _438105, in(_438103, _438105)], (5659 ^ _84654) ^ [_277750] : [-(empty(5655 ^ [_277750]))], (4545 ^ _84654) ^ [_240788, _240790, _240792] : [-(element(subset_intersection2(_240792, _240790, _240788), powerset(_240792))), element(_240790, powerset(_240792)), element(_240788, powerset(_240792))], (8050 ^ _84654) ^ [_377969, _377971] : [in(_377969, 8036 ^ [_377971]), -(in(powerset(_377969), 8036 ^ [_377971]))], (9221 ^ _84654) ^ [_416888] : [topological_space(_416888), top_str(_416888), 9228 ^ _84654 : [(9229 ^ _84654) ^ [_417140] : [element(_417140, powerset(powerset(the_carrier(_416888)))), 9235 ^ _84654 : [(9240 ^ _84654) ^ [] : [closed_subset(9234 ^ [_416888, _417140], _416888)], (9238 ^ _84654) ^ [] : [-(in(9234 ^ [_416888, _417140], _417140))], (9236 ^ _84654) ^ [] : [-(element(9234 ^ [_416888, _417140], powerset(the_carrier(_416888))))]], -(closed_subset(meet_of_subsets(the_carrier(_416888), _417140), _416888))]]], (5267 ^ _84654) ^ [_264412] : [relation(_264412), -(relation_inverse(relation_inverse(_264412)) = _264412)], (1050 ^ _84654) ^ [_119407, _119409] : [_119409 = _119407, -(pair_first(_119409) = pair_first(_119407))], (3721 ^ _84654) ^ [_214026] : [being_limit_ordinal(_214026), -(_214026 = union(_214026))], (5757 ^ _84654) ^ [] : [-(relation(5755 ^ []))], (8861 ^ _84654) ^ [_404942] : [-(reflexive(inclusion_relation(_404942)))], (8127 ^ _84654) ^ [_380593, _380595] : [relation(_380593), -(relation_image(_380593, _380595) = relation_image(_380593, set_intersection2(relation_dom(_380593), _380595)))], (1610 ^ _84654) ^ [_138536, _138538] : [relation(_138536), 1613 ^ _84654 : [(1614 ^ _84654) ^ [] : [_138536 = identity_relation(_138538), 1617 ^ _84654 : [(1626 ^ _84654) ^ [_139109, _139111] : [-(in(ordered_pair(_139111, _139109), _138536)), in(_139111, _138538), _139111 = _139109], (1618 ^ _84654) ^ [_138846, _138848] : [in(ordered_pair(_138848, _138846), _138536), 1621 ^ _84654 : [(1624 ^ _84654) ^ [] : [-(_138848 = _138846)], (1622 ^ _84654) ^ [] : [-(in(_138848, _138538))]]]]], (1636 ^ _84654) ^ [] : [-(_138536 = identity_relation(_138538)), 1649 ^ _84654 : [(1654 ^ _84654) ^ [] : [in(ordered_pair(1637 ^ [_138536, _138538], 1638 ^ [_138536, _138538]), _138536)], (1652 ^ _84654) ^ [] : [-(1637 ^ [_138536, _138538] = 1638 ^ [_138536, _138538])], (1650 ^ _84654) ^ [] : [-(in(1637 ^ [_138536, _138538], _138538))]], 1641 ^ _84654 : [(1644 ^ _84654) ^ [] : [in(1637 ^ [_138536, _138538], _138538), 1637 ^ [_138536, _138538] = 1638 ^ [_138536, _138538]], (1642 ^ _84654) ^ [] : [-(in(ordered_pair(1637 ^ [_138536, _138538], 1638 ^ [_138536, _138538]), _138536))]]]]], (1018 ^ _84654) ^ [_118253, _118255] : [_118255 = _118253, -(cast_to_subset(_118255) = cast_to_subset(_118253))], (5318 ^ _84654) ^ [_266182, _266184] : [-(in(_266184, _266182)), -(disjoint(singleton(_266184), _266182))], (8776 ^ _84654) ^ [_401970] : [-(well_orders(8772 ^ [_401970], _401970))], (7305 ^ _84654) ^ [_348983] : [ordinal(_348983), 7309 ^ _84654 : [(7310 ^ _84654) ^ [_349370] : [in(_349370, 7308 ^ [_348983]), 7313 ^ _84654 : [(7321 ^ _84654) ^ [] : [in(7315 ^ [_348983, _349370], omega), 7324 ^ _84654 : [(7325 ^ _84654) ^ [_350009] : [element(_350009, powerset(powerset(7315 ^ [_348983, _349370]))), -(_350009 = empty_set), 7333 ^ _84654 : [(7336 ^ _84654) ^ [_350440] : [-(_350440 = 7332 ^ [_348983, _349370, _350009]), in(_350440, _350009), subset(7332 ^ [_348983, _349370, _350009], _350440)], (7334 ^ _84654) ^ [] : [-(in(7332 ^ [_348983, _349370, _350009], _350009))]]]]], (7314 ^ _84654) ^ [] : [-(in(_349370, succ(_348983)))], (7319 ^ _84654) ^ [] : [-(_349370 = 7315 ^ [_348983, _349370])], (7317 ^ _84654) ^ [] : [-(ordinal(7315 ^ [_348983, _349370]))]]], (7346 ^ _84654) ^ [_350780] : [-(in(_350780, 7308 ^ [_348983])), in(_350780, succ(_348983)), 7351 ^ _84654 : [(7352 ^ _84654) ^ [_351034] : [ordinal(_351034), _350780 = _351034, 7359 ^ _84654 : [(7367 ^ _84654) ^ [_351640] : [in(_351640, 7361 ^ [_348983, _350780, _351034]), 7371 ^ _84654 : [(7376 ^ _84654) ^ [] : [7370 ^ [_348983, _350780, _351034, _351640] = _351640], (7374 ^ _84654) ^ [] : [-(subset(_351640, 7370 ^ [_348983, _350780, _351034, _351640]))], (7372 ^ _84654) ^ [] : [-(in(7370 ^ [_348983, _350780, _351034, _351640], 7361 ^ [_348983, _350780, _351034]))]]], (7360 ^ _84654) ^ [] : [-(in(_351034, omega))], (7365 ^ _84654) ^ [] : [7361 ^ [_348983, _350780, _351034] = empty_set], (7363 ^ _84654) ^ [] : [-(element(7361 ^ [_348983, _350780, _351034], powerset(powerset(_351034))))]]]]]]], (5526 ^ _84654) ^ [_273423, _273425, _273427, _273429] : [-(in(ordered_pair(_273429, _273427), cartesian_product2(_273425, _273423))), in(_273429, _273425), in(_273427, _273423)], (4793 ^ _84654) ^ [_248735] : [-(preboolean(powerset(_248735)))], (5712 ^ _84654) ^ [_279550] : [-(element(5710 ^ [_279550], powerset(_279550)))], (7461 ^ _84654) ^ [_355151, _355153] : [ordinal(_355153), element(_355151, powerset(powerset(succ(_355153)))), 7469 ^ _84654 : [(7481 ^ _84654) ^ [_355961] : [-(in(_355961, 7468 ^ [_355151, _355153])), in(_355961, powerset(_355153)), 7486 ^ _84654 : [(7487 ^ _84654) ^ [_356164] : [in(_356164, _355151), _355961 = set_difference(_356164, singleton(_355153))]]], (7470 ^ _84654) ^ [_355525] : [in(_355525, 7468 ^ [_355151, _355153]), 7473 ^ _84654 : [(7479 ^ _84654) ^ [] : [-(_355525 = set_difference(7475 ^ [_355151, _355153, _355525], singleton(_355153)))], (7477 ^ _84654) ^ [] : [-(in(7475 ^ [_355151, _355153, _355525], _355151))], (7474 ^ _84654) ^ [] : [-(in(_355525, powerset(_355153)))]]]]], (1912 ^ _84654) ^ [_149403] : [top_str(_149403), 1915 ^ _84654 : [(1916 ^ _84654) ^ [_149610] : [element(_149610, powerset(the_carrier(_149403))), 1919 ^ _84654 : [(1920 ^ _84654) ^ [_149818] : [element(_149818, powerset(the_carrier(_149403))), 1923 ^ _84654 : [(1924 ^ _84654) ^ [] : [_149818 = topstr_closure(_149403, _149610), 1927 ^ _84654 : [(1928 ^ _84654) ^ [_150132] : [in(_150132, the_carrier(_149403)), 1931 ^ _84654 : [(1932 ^ _84654) ^ [] : [in(_150132, _149818), 1935 ^ _84654 : [(1936 ^ _84654) ^ [_150427] : [element(_150427, powerset(the_carrier(_149403))), open_subset(_150427, _149403), in(_150132, _150427), disjoint(_149610, _150427)]]], (1950 ^ _84654) ^ [] : [1952 ^ _84654 : [(1959 ^ _84654) ^ [] : [-(disjoint(_149610, 1951 ^ [_149403, _149610, _149818, _150132]))], (1953 ^ _84654) ^ [] : [-(element(1951 ^ [_149403, _149610, _149818, _150132], powerset(the_carrier(_149403))))], (1957 ^ _84654) ^ [] : [-(in(_150132, 1951 ^ [_149403, _149610, _149818, _150132]))], (1955 ^ _84654) ^ [] : [-(open_subset(1951 ^ [_149403, _149610, _149818, _150132], _149403))]], -(in(_150132, _149818))]]]]], (1963 ^ _84654) ^ [] : [-(_149818 = topstr_closure(_149403, _149610)), 1965 ^ _84654 : [(1968 ^ _84654) ^ [] : [1969 ^ _84654 : [(1973 ^ _84654) ^ [] : [-(element(1971 ^ [_149403, _149610, _149818], powerset(the_carrier(_149403))))], (1975 ^ _84654) ^ [] : [-(open_subset(1971 ^ [_149403, _149610, _149818], _149403))], (1977 ^ _84654) ^ [] : [-(in(1964 ^ [_149403, _149610, _149818], 1971 ^ [_149403, _149610, _149818]))], (1979 ^ _84654) ^ [] : [-(disjoint(_149610, 1971 ^ [_149403, _149610, _149818]))], (1970 ^ _84654) ^ [] : [-(in(1964 ^ [_149403, _149610, _149818], _149818))]], 1980 ^ _84654 : [(1981 ^ _84654) ^ [_152081] : [element(_152081, powerset(the_carrier(_149403))), open_subset(_152081, _149403), in(1964 ^ [_149403, _149610, _149818], _152081), disjoint(_149610, _152081)], (1995 ^ _84654) ^ [] : [in(1964 ^ [_149403, _149610, _149818], _149818)]]], (1966 ^ _84654) ^ [] : [-(in(1964 ^ [_149403, _149610, _149818], the_carrier(_149403)))]]]]]]]]], (5685 ^ _84654) ^ [] : [-(relation(5683 ^ []))], (3434 ^ _84654) ^ [_204164, _204166] : [equipotent(_204166, _204164), 3438 ^ _84654 : [(3441 ^ _84654) ^ [] : [-(function(3437 ^ [_204164, _204166]))], (3443 ^ _84654) ^ [] : [-(one_to_one(3437 ^ [_204164, _204166]))], (3445 ^ _84654) ^ [] : [-(relation_dom(3437 ^ [_204164, _204166]) = _204166)], (3447 ^ _84654) ^ [] : [-(relation_rng(3437 ^ [_204164, _204166]) = _204164)], (3439 ^ _84654) ^ [] : [-(relation(3437 ^ [_204164, _204166]))]]], (4625 ^ _84654) ^ [_243338] : [join_semilatt_str(_243338), -(one_sorted_str(_243338))], (1658 ^ _84654) ^ [_140217, _140219] : [_140219 = _140217, 1661 ^ _84654 : [(1664 ^ _84654) ^ [] : [-(subset(_140217, _140219))], (1662 ^ _84654) ^ [] : [-(subset(_140219, _140217))]]], (4861 ^ _84654) ^ [_250803] : [empty(powerset(_250803))], (9484 ^ _84654) ^ [_426030] : [-(set_difference(empty_set, _426030) = empty_set)], (216 ^ _84654) ^ [_91308, _91310] : [-(relation_empty_yielding(_91308)), _91310 = _91308, relation_empty_yielding(_91310)], (4961 ^ _84654) ^ [_254182, _254184] : [v3_membered(_254184), 4964 ^ _84654 : [(4969 ^ _84654) ^ [] : [-(v3_membered(set_intersection2(_254182, _254184)))], (4967 ^ _84654) ^ [] : [-(v2_membered(set_intersection2(_254182, _254184)))], (4965 ^ _84654) ^ [] : [-(v1_membered(set_intersection2(_254182, _254184)))]]], (4381 ^ _84654) ^ [] : [true___, -(true___)], (7993 ^ _84654) ^ [_375803, _375805, _375807] : [subset(_375807, _375805), 7996 ^ _84654 : [(7999 ^ _84654) ^ [] : [-(subset(cartesian_product2(_375803, _375807), cartesian_product2(_375803, _375805)))], (7997 ^ _84654) ^ [] : [-(subset(cartesian_product2(_375807, _375803), cartesian_product2(_375805, _375803)))]]], (5680 ^ _84654) ^ [] : [-(empty(5676 ^ []))], (9847 ^ _84654) ^ [_437620] : [relation(_437620), 9850 ^ _84654 : [(9857 ^ _84654) ^ [] : [relation_rng(_437620) = empty_set, -(relation_dom(_437620) = empty_set)], (9851 ^ _84654) ^ [] : [relation_dom(_437620) = empty_set, -(relation_rng(_437620) = empty_set)]]], (4517 ^ _84654) ^ [] : [true___, -(true___)], (5761 ^ _84654) ^ [] : [-(function(5755 ^ []))], (318 ^ _84654) ^ [_94426, _94428] : [-(finite(_94426)), _94428 = _94426, finite(_94428)], (4 ^ _84654) ^ [_84885, _84887] : [_84887 = _84885, -(_84885 = _84887)], (5841 ^ _84654) ^ [_283637, _283639, _283641] : [-(meet_commut(_283641, _283639, _283637) = meet(_283641, _283639, _283637)), -(empty_carrier(_283641)), meet_commutative(_283641), meet_semilatt_str(_283641), element(_283639, the_carrier(_283641)), element(_283637, the_carrier(_283641))], (10177 ^ _84654) ^ [_448534, _448536, _448538, _448540] : [function(_448534), quasi_total(_448534, _448540, _448538), relation_of2_as_subset(_448534, _448540, _448538), subset(_448538, _448536), 10194 ^ _84654 : [(10197 ^ _84654) ^ [] : [_448540 = empty_set], (10195 ^ _84654) ^ [] : [-(_448538 = empty_set)]], 10198 ^ _84654 : [(10203 ^ _84654) ^ [] : [-(relation_of2_as_subset(_448534, _448540, _448536))], (10201 ^ _84654) ^ [] : [-(quasi_total(_448534, _448540, _448536))], (10199 ^ _84654) ^ [] : [-(function(_448534))]]], (5704 ^ _84654) ^ [_279244, _279246] : [-(function(5698 ^ [_279244, _279246]))], (8691 ^ _84654) ^ [_399393] : [relation(_399393), 8694 ^ _84654 : [(8695 ^ _84654) ^ [_399543] : [relation(_399543), subset(_399393, _399543), 8702 ^ _84654 : [(8705 ^ _84654) ^ [] : [-(subset(relation_rng(_399393), relation_rng(_399543)))], (8703 ^ _84654) ^ [] : [-(subset(relation_dom(_399393), relation_dom(_399543)))]]]]], (4573 ^ _84654) ^ [_241757, _241759, _241761] : [-(element(subset_difference(_241761, _241759, _241757), powerset(_241761))), element(_241759, powerset(_241761)), element(_241757, powerset(_241761))], (816 ^ _84654) ^ [_110953, _110955, _110957, _110959, _110961, _110963] : [-(join(_110963, _110959, _110955) = join(_110961, _110957, _110953)), _110963 = _110961, _110959 = _110957, _110955 = _110953], (4919 ^ _84654) ^ [] : [-(epsilon_transitive(empty_set))], (4511 ^ _84654) ^ [] : [true___, -(true___)], (5610 ^ _84654) ^ [] : [-(v4_membered(5600 ^ []))], (50 ^ _84654) ^ [_86287, _86289] : [-(v1_rat_1(_86287)), _86289 = _86287, v1_rat_1(_86289)], (10043 ^ _84654) ^ [_444197, _444199] : [disjoint(_444199, _444197), -(set_difference(_444199, _444197) = _444199)], (3471 ^ _84654) ^ [_205442, _205444, _205446] : [_205442 = set_difference(_205446, _205444), 3474 ^ _84654 : [(3483 ^ _84654) ^ [_205886] : [-(in(_205886, _205442)), in(_205886, _205446), -(in(_205886, _205444))], (3475 ^ _84654) ^ [_205626] : [in(_205626, _205442), 3478 ^ _84654 : [(3481 ^ _84654) ^ [] : [in(_205626, _205444)], (3479 ^ _84654) ^ [] : [-(in(_205626, _205446))]]]]], (4307 ^ _84654) ^ [_234132] : [-(relation(inclusion_relation(_234132)))], (4413 ^ _84654) ^ [] : [true___, -(true___)], (9689 ^ _84654) ^ [_432889, _432891, _432893] : [element(_432889, powerset(_432893)), in(_432891, subset_complement(_432893, _432889)), in(_432891, _432889)], (6626 ^ _84654) ^ [_317689] : [ordinal(_317689), 6634 ^ _84654 : [(6642 ^ _84654) ^ [] : [in(6636 ^ [_317689], omega), 6645 ^ _84654 : [(6646 ^ _84654) ^ [_319313] : [element(_319313, powerset(powerset(6636 ^ [_317689]))), -(_319313 = empty_set), 6654 ^ _84654 : [(6657 ^ _84654) ^ [_319722] : [-(_319722 = 6653 ^ [_317689, _319313]), in(_319722, _319313), subset(6653 ^ [_317689, _319313], _319722)], (6655 ^ _84654) ^ [] : [-(in(6653 ^ [_317689, _319313], _319313))]]]]], (6674 ^ _84654) ^ [] : [in(6668 ^ [_317689], omega), 6677 ^ _84654 : [(6678 ^ _84654) ^ [_320463] : [element(_320463, powerset(powerset(6668 ^ [_317689]))), -(_320463 = empty_set), 6686 ^ _84654 : [(6689 ^ _84654) ^ [_320872] : [-(_320872 = 6685 ^ [_317689, _320463]), in(_320872, _320463), subset(6685 ^ [_317689, _320463], _320872)], (6687 ^ _84654) ^ [] : [-(in(6685 ^ [_317689, _320463], _320463))]]]]], (6672 ^ _84654) ^ [] : [-(6633 ^ [_317689] = 6668 ^ [_317689])], (6667 ^ _84654) ^ [] : [-(6631 ^ [_317689] = 6633 ^ [_317689])], (6699 ^ _84654) ^ [] : [6632 ^ [_317689] = 6633 ^ [_317689]], (6640 ^ _84654) ^ [] : [-(6632 ^ [_317689] = 6636 ^ [_317689])], (6635 ^ _84654) ^ [] : [-(6631 ^ [_317689] = 6632 ^ [_317689])], (6638 ^ _84654) ^ [] : [-(ordinal(6636 ^ [_317689]))], (6670 ^ _84654) ^ [] : [-(ordinal(6668 ^ [_317689]))]], 6701 ^ _84654 : [(6741 ^ _84654) ^ [_323080] : [-(in(_323080, 6700 ^ [_317689])), 6742 ^ _84654 : [(6743 ^ _84654) ^ [_323264] : [in(_323264, succ(_317689)), _323264 = _323080, 6750 ^ _84654 : [(6751 ^ _84654) ^ [_323568] : [ordinal(_323568), _323080 = _323568, 6758 ^ _84654 : [(6766 ^ _84654) ^ [_324198] : [in(_324198, 6760 ^ [_317689, _323080, _323264, _323568]), 6770 ^ _84654 : [(6775 ^ _84654) ^ [] : [6769 ^ [_317689, _323080, _323264, _323568, _324198] = _324198], (6773 ^ _84654) ^ [] : [-(subset(_324198, 6769 ^ [_317689, _323080, _323264, _323568, _324198]))], (6771 ^ _84654) ^ [] : [-(in(6769 ^ [_317689, _323080, _323264, _323568, _324198], 6760 ^ [_317689, _323080, _323264, _323568]))]]], (6759 ^ _84654) ^ [] : [-(in(_323568, omega))], (6764 ^ _84654) ^ [] : [6760 ^ [_317689, _323080, _323264, _323568] = empty_set], (6762 ^ _84654) ^ [] : [-(element(6760 ^ [_317689, _323080, _323264, _323568], powerset(powerset(_323568))))]]]]]]], (6702 ^ _84654) ^ [_321441] : [in(_321441, 6700 ^ [_317689]), 6706 ^ _84654 : [(6709 ^ _84654) ^ [] : [-(6705 ^ [_317689, _321441] = _321441)], (6712 ^ _84654) ^ [] : [-(ordinal(6710 ^ [_317689, _321441]))], (6714 ^ _84654) ^ [] : [-(_321441 = 6710 ^ [_317689, _321441])], (6716 ^ _84654) ^ [] : [in(6710 ^ [_317689, _321441], omega), 6719 ^ _84654 : [(6720 ^ _84654) ^ [_322307] : [element(_322307, powerset(powerset(6710 ^ [_317689, _321441]))), -(_322307 = empty_set), 6728 ^ _84654 : [(6731 ^ _84654) ^ [_322738] : [-(_322738 = 6727 ^ [_317689, _321441, _322307]), in(_322738, _322307), subset(6727 ^ [_317689, _321441, _322307], _322738)], (6729 ^ _84654) ^ [] : [-(in(6727 ^ [_317689, _321441, _322307], _322307))]]]]], (6707 ^ _84654) ^ [] : [-(in(6705 ^ [_317689, _321441], succ(_317689)))]]]]], (4983 ^ _84654) ^ [_254998, _255000] : [v4_membered(_255000), 4986 ^ _84654 : [(4993 ^ _84654) ^ [] : [-(v4_membered(set_intersection2(_254998, _255000)))], (4987 ^ _84654) ^ [] : [-(v1_membered(set_intersection2(_254998, _255000)))], (4991 ^ _84654) ^ [] : [-(v3_membered(set_intersection2(_254998, _255000)))], (4989 ^ _84654) ^ [] : [-(v2_membered(set_intersection2(_254998, _255000)))]]], (6055 ^ _84654) ^ [_291904] : [6059 ^ _84654 : [(6062 ^ _84654) ^ [] : [-(6057 ^ [_291904] = singleton(6056 ^ [_291904]))], (6064 ^ _84654) ^ [] : [-(in(6056 ^ [_291904], _291904))], (6066 ^ _84654) ^ [] : [-(6058 ^ [_291904] = singleton(6056 ^ [_291904]))], (6068 ^ _84654) ^ [] : [6057 ^ [_291904] = 6058 ^ [_291904]], (6060 ^ _84654) ^ [] : [-(in(6056 ^ [_291904], _291904))]], 6070 ^ _84654 : [(6085 ^ _84654) ^ [_293309, _293311] : [-(in(ordered_pair(_293311, _293309), 6069 ^ [_291904])), in(_293311, _291904), in(_293311, _291904), _293309 = singleton(_293311)], (6071 ^ _84654) ^ [] : [-(relation(6069 ^ [_291904]))], (6075 ^ _84654) ^ [_292966, _292968] : [in(ordered_pair(_292968, _292966), 6069 ^ [_291904]), 6078 ^ _84654 : [(6083 ^ _84654) ^ [] : [-(_292966 = singleton(_292968))], (6081 ^ _84654) ^ [] : [-(in(_292968, _291904))], (6079 ^ _84654) ^ [] : [-(in(_292968, _291904))]]], (6073 ^ _84654) ^ [] : [-(function(6069 ^ [_291904]))]]], (5626 ^ _84654) ^ [] : [-(ordinal(5620 ^ []))], (5717 ^ _84654) ^ [] : [empty(5715 ^ [])], (9533 ^ _84654) ^ [_427769] : [top_str(_427769), 9536 ^ _84654 : [(9537 ^ _84654) ^ [_427933] : [element(_427933, powerset(the_carrier(_427769))), 9540 ^ _84654 : [(9547 ^ _84654) ^ [] : [-(closed_subset(_427933, _427769)), topological_space(_427769), topstr_closure(_427769, _427933) = _427933], (9541 ^ _84654) ^ [] : [closed_subset(_427933, _427769), -(topstr_closure(_427769, _427933) = _427933)]]]]], (4223 ^ _84654) ^ [] : [true___, -(true___)], (2157 ^ _84654) ^ [_158590, _158592, _158594, _158596] : [-(_158590 = unordered_triple(_158596, _158594, _158592)), 2161 ^ _84654 : [(2168 ^ _84654) ^ [] : [2158 ^ [_158590, _158592, _158594, _158596] = _158592], (2162 ^ _84654) ^ [] : [-(in(2158 ^ [_158590, _158592, _158594, _158596], _158590))], (2166 ^ _84654) ^ [] : [2158 ^ [_158590, _158592, _158594, _158596] = _158594], (2164 ^ _84654) ^ [] : [2158 ^ [_158590, _158592, _158594, _158596] = _158596]], 2169 ^ _84654 : [(2170 ^ _84654) ^ [] : [-(2158 ^ [_158590, _158592, _158594, _158596] = _158596), -(2158 ^ [_158590, _158592, _158594, _158596] = _158594), -(2158 ^ [_158590, _158592, _158594, _158596] = _158592)], (2180 ^ _84654) ^ [] : [in(2158 ^ [_158590, _158592, _158594, _158596], _158590)]]], (4277 ^ _84654) ^ [_233471] : [one_sorted_str(_233471), -(element(empty_carrier_subset(_233471), powerset(the_carrier(_233471))))], (2395 ^ _84654) ^ [_167085] : [relation(_167085), 2398 ^ _84654 : [(2399 ^ _84654) ^ [_167233] : [in(_167233, _167085), -(_167233 = ordered_pair(2402 ^ [_167085, _167233], 2403 ^ [_167085, _167233]))]]], (9313 ^ _84654) ^ [_420226, _420228, _420230, _420232] : [function(_420226), quasi_total(_420226, _420232, _420230), relation_of2_as_subset(_420226, _420232, _420230), -(_420230 = empty_set), 9328 ^ _84654 : [(9337 ^ _84654) ^ [_420985] : [-(in(_420985, relation_inverse_image(_420226, _420228))), in(_420985, _420232), in(apply(_420226, _420985), _420228)], (9329 ^ _84654) ^ [_420704] : [in(_420704, relation_inverse_image(_420226, _420228)), 9332 ^ _84654 : [(9335 ^ _84654) ^ [] : [-(in(apply(_420226, _420704), _420228))], (9333 ^ _84654) ^ [] : [-(in(_420704, _420232))]]]]], (1184 ^ _84654) ^ [_124241, _124243] : [_124243 = _124241, -(powerset(_124243) = powerset(_124241))], (4737 ^ _84654) ^ [_247007] : [empty(_247007), 4740 ^ _84654 : [(4743 ^ _84654) ^ [] : [-(relation(relation_inverse(_247007)))], (4741 ^ _84654) ^ [] : [-(empty(relation_inverse(_247007)))]]], (7917 ^ _84654) ^ [_373153, _373155] : [equipotent(_373155, _373153), -(equipotent(_373153, _373155))], (9088 ^ _84654) ^ [_412479, _412481] : [9089 ^ _84654 : [(9092 ^ _84654) ^ [] : [_412481 = singleton(_412479)], (9090 ^ _84654) ^ [] : [_412481 = empty_set]], -(subset(_412481, singleton(_412479)))], (8778 ^ _84654) ^ [_402098, _402100, _402102] : [subset(_402102, _402100), -(subset(set_intersection2(_402102, _402098), set_intersection2(_402100, _402098)))], (4719 ^ _84654) ^ [_246431, _246433] : [4726 ^ _84654 : [(4729 ^ _84654) ^ [] : [-(relation(relation_composition(_246431, _246433)))], (4727 ^ _84654) ^ [] : [-(empty(relation_composition(_246431, _246433)))]], empty(_246433), relation(_246431)], (74 ^ _84654) ^ [_87054, _87056, _87058, _87060] : [-(is_connected_in(_87058, _87054)), is_connected_in(_87060, _87056), _87060 = _87058, _87056 = _87054], (5622 ^ _84654) ^ [] : [-(epsilon_transitive(5620 ^ []))], (3347 ^ _84654) ^ [_201290] : [-(cast_to_subset(_201290) = _201290)], (850 ^ _84654) ^ [_112203, _112205, _112207, _112209, _112211, _112213] : [-(subset_intersection2(_112213, _112209, _112205) = subset_intersection2(_112211, _112207, _112203)), _112213 = _112211, _112209 = _112207, _112205 = _112203], (8375 ^ _84654) ^ [_388973] : [-(set_union2(_388973, empty_set) = _388973)], (5747 ^ _84654) ^ [] : [-(relation(5745 ^ []))], (6865 ^ _84654) ^ [_328706, _328708] : [topological_space(_328708), top_str(_328708), element(_328706, powerset(powerset(the_carrier(_328708)))), 6881 ^ _84654 : [(6884 ^ _84654) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_328708), 6879 ^ [_328706, _328708]), _328706))], (6886 ^ _84654) ^ [] : [-(6878 ^ [_328706, _328708] = 6880 ^ [_328706, _328708])], (6888 ^ _84654) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_328708), 6880 ^ [_328706, _328708]), _328706))], (6890 ^ _84654) ^ [] : [6879 ^ [_328706, _328708] = 6880 ^ [_328706, _328708]], (6882 ^ _84654) ^ [] : [-(6878 ^ [_328706, _328708] = 6879 ^ [_328706, _328708])]], 6892 ^ _84654 : [(6904 ^ _84654) ^ [_330400] : [-(in(_330400, 6891 ^ [_328706, _328708])), 6905 ^ _84654 : [(6906 ^ _84654) ^ [_330520] : [in(_330520, powerset(the_carrier(_328708))), _330520 = _330400, in(set_difference(cast_as_carrier_subset(_328708), _330400), _328706)]]], (6893 ^ _84654) ^ [_329950] : [in(_329950, 6891 ^ [_328706, _328708]), 6897 ^ _84654 : [(6902 ^ _84654) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_328708), _329950), _328706))], (6900 ^ _84654) ^ [] : [-(6896 ^ [_328706, _328708, _329950] = _329950)], (6898 ^ _84654) ^ [] : [-(in(6896 ^ [_328706, _328708, _329950], powerset(the_carrier(_328708))))]]]]], (1240 ^ _84654) ^ [_126513] : [v3_membered(_126513), 1243 ^ _84654 : [(1244 ^ _84654) ^ [_126653] : [element(_126653, _126513), 1247 ^ _84654 : [(1252 ^ _84654) ^ [] : [-(v1_rat_1(_126653))], (1250 ^ _84654) ^ [] : [-(v1_xreal_0(_126653))], (1248 ^ _84654) ^ [] : [-(v1_xcmplx_0(_126653))]]]]], (5396 ^ _84654) ^ [_268921, _268923] : [subset(_268923, _268921), -(set_difference(_268923, _268921) = empty_set)], (1174 ^ _84654) ^ [_123910, _123912, _123914, _123916] : [-(unordered_pair(_123916, _123912) = unordered_pair(_123914, _123910)), _123916 = _123914, _123912 = _123910], (1124 ^ _84654) ^ [_122074, _122076] : [_122076 = _122074, -(relation_dom(_122076) = relation_dom(_122074))], (3937 ^ _84654) ^ [_221897, _221899] : [disjoint(_221899, _221897), -(set_intersection2(_221899, _221897) = empty_set)], (3372 ^ _84654) ^ [_202273, _202275] : [-(_202273 = union(_202275)), 3385 ^ _84654 : [(3390 ^ _84654) ^ [] : [in(3373 ^ [_202273, _202275], _202273)], (3388 ^ _84654) ^ [] : [-(in(3384 ^ [_202273, _202275], _202275))], (3386 ^ _84654) ^ [] : [-(in(3373 ^ [_202273, _202275], 3384 ^ [_202273, _202275]))]], 3376 ^ _84654 : [(3379 ^ _84654) ^ [_202556] : [in(3373 ^ [_202273, _202275], _202556), in(_202556, _202275)], (3377 ^ _84654) ^ [] : [-(in(3373 ^ [_202273, _202275], _202273))]]], (6980 ^ _84654) ^ [_333835, _333837, _333839] : [relation(_333837), relation(_333835), function(_333835), 6996 ^ _84654 : [(7009 ^ _84654) ^ [] : [-(6995 ^ [_333835, _333837, _333839] = ordered_pair(7006 ^ [_333835, _333837, _333839], 7007 ^ [_333835, _333837, _333839]))], (7001 ^ _84654) ^ [] : [-(6994 ^ [_333835, _333837, _333839] = ordered_pair(6998 ^ [_333835, _333837, _333839], 6999 ^ [_333835, _333837, _333839]))], (6997 ^ _84654) ^ [] : [-(6993 ^ [_333835, _333837, _333839] = 6994 ^ [_333835, _333837, _333839])], (7003 ^ _84654) ^ [] : [-(in(ordered_pair(apply(_333835, 6998 ^ [_333835, _333837, _333839]), apply(_333835, 6999 ^ [_333835, _333837, _333839])), _333837))], (7011 ^ _84654) ^ [] : [-(in(ordered_pair(apply(_333835, 7006 ^ [_333835, _333837, _333839]), apply(_333835, 7007 ^ [_333835, _333837, _333839])), _333837))], (7013 ^ _84654) ^ [] : [6994 ^ [_333835, _333837, _333839] = 6995 ^ [_333835, _333837, _333839]], (7005 ^ _84654) ^ [] : [-(6993 ^ [_333835, _333837, _333839] = 6995 ^ [_333835, _333837, _333839])]], 7015 ^ _84654 : [(7031 ^ _84654) ^ [_336754] : [-(in(_336754, 7014 ^ [_333835, _333837, _333839])), 7032 ^ _84654 : [(7033 ^ _84654) ^ [_336902] : [in(_336902, cartesian_product2(_333839, _333839)), _336902 = _336754, 7040 ^ _84654 : [(7041 ^ _84654) ^ [_337193, _337195] : [_336754 = ordered_pair(_337195, _337193), in(ordered_pair(apply(_333835, _337195), apply(_333835, _337193)), _333837)]]]]], (7016 ^ _84654) ^ [_335945] : [in(_335945, 7014 ^ [_333835, _333837, _333839]), 7020 ^ _84654 : [(7029 ^ _84654) ^ [] : [-(in(ordered_pair(apply(_333835, 7024 ^ [_333835, _333837, _333839, _335945]), apply(_333835, 7025 ^ [_333835, _333837, _333839, _335945])), _333837))], (7021 ^ _84654) ^ [] : [-(in(7019 ^ [_333835, _333837, _333839, _335945], cartesian_product2(_333839, _333839)))], (7027 ^ _84654) ^ [] : [-(_335945 = ordered_pair(7024 ^ [_333835, _333837, _333839, _335945], 7025 ^ [_333835, _333837, _333839, _335945]))], (7023 ^ _84654) ^ [] : [-(7019 ^ [_333835, _333837, _333839, _335945] = _335945)]]]]], (2328 ^ _84654) ^ [_164714] : [top_str(_164714), 2331 ^ _84654 : [(2332 ^ _84654) ^ [] : [topological_space(_164714), 2335 ^ _84654 : [(2348 ^ _84654) ^ [_165429] : [element(_165429, powerset(the_carrier(_164714))), 2351 ^ _84654 : [(2352 ^ _84654) ^ [_165604] : [element(_165604, powerset(the_carrier(_164714))), -(in(subset_intersection2(the_carrier(_164714), _165429, _165604), the_topology(_164714))), in(_165429, the_topology(_164714)), in(_165604, the_topology(_164714))]]], (2338 ^ _84654) ^ [_165132] : [element(_165132, powerset(powerset(the_carrier(_164714)))), subset(_165132, the_topology(_164714)), -(in(union_of_subsets(the_carrier(_164714), _165132), the_topology(_164714)))], (2336 ^ _84654) ^ [] : [-(in(the_carrier(_164714), the_topology(_164714)))]]], (2366 ^ _84654) ^ [] : [-(topological_space(_164714)), in(the_carrier(_164714), the_topology(_164714)), 2374 ^ _84654 : [(2379 ^ _84654) ^ [] : [in(union_of_subsets(the_carrier(_164714), 2373 ^ [_164714]), the_topology(_164714))], (2377 ^ _84654) ^ [] : [-(subset(2373 ^ [_164714], the_topology(_164714)))], (2375 ^ _84654) ^ [] : [-(element(2373 ^ [_164714], powerset(powerset(the_carrier(_164714)))))]], 2381 ^ _84654 : [(2385 ^ _84654) ^ [] : [-(element(2383 ^ [_164714], powerset(the_carrier(_164714))))], (2387 ^ _84654) ^ [] : [-(in(2380 ^ [_164714], the_topology(_164714)))], (2389 ^ _84654) ^ [] : [-(in(2383 ^ [_164714], the_topology(_164714)))], (2391 ^ _84654) ^ [] : [in(subset_intersection2(the_carrier(_164714), 2380 ^ [_164714], 2383 ^ [_164714]), the_topology(_164714))], (2382 ^ _84654) ^ [] : [-(element(2380 ^ [_164714], powerset(the_carrier(_164714))))]]]]], (2654 ^ _84654) ^ [_176253] : [-(in(2655 ^ [_176253], _176253)), -(_176253 = empty_set)], (2 ^ _84654) ^ [_84778] : [-(_84778 = _84778)], (8743 ^ _84654) ^ [_400971] : [-(empty_carrier(_400971)), join_commutative(_400971), join_semilatt_str(_400971), 8754 ^ _84654 : [(8755 ^ _84654) ^ [_401300] : [element(_401300, the_carrier(_400971)), 8758 ^ _84654 : [(8759 ^ _84654) ^ [_401459] : [element(_401459, the_carrier(_400971)), -(_401300 = _401459), below(_400971, _401300, _401459), below(_400971, _401459, _401300)]]]]], (8320 ^ _84654) ^ [_387006, _387008] : [-(subset(set_intersection2(_387008, _387006), _387008))], (1206 ^ _84654) ^ [_125365, _125367] : [in(_125367, _125365), in(_125365, _125367)], (9096 ^ _84654) ^ [_412744] : [-(set_difference(_412744, empty_set) = _412744)], (756 ^ _84654) ^ [_108564, _108566] : [_108566 = _108564, -(empty_carrier_subset(_108566) = empty_carrier_subset(_108564))], (9557 ^ _84654) ^ [_428496] : [relation(_428496), 9560 ^ _84654 : [(9561 ^ _84654) ^ [_428692] : [relation(_428692), 9564 ^ _84654 : [(9565 ^ _84654) ^ [_428884] : [relation(_428884), function(_428884), relation_isomorphism(_428496, _428692, _428884), 9576 ^ _84654 : [(9583 ^ _84654) ^ [] : [transitive(_428496), -(transitive(_428692))], (9589 ^ _84654) ^ [] : [connected(_428496), -(connected(_428692))], (9595 ^ _84654) ^ [] : [antisymmetric(_428496), -(antisymmetric(_428692))], (9601 ^ _84654) ^ [] : [well_founded_relation(_428496), -(well_founded_relation(_428692))], (9577 ^ _84654) ^ [] : [reflexive(_428496), -(reflexive(_428692))]]]]]]], (7543 ^ _84654) ^ [_358499, _358501] : [-(in(_358499, 7533 ^ [_358501])), in(_358499, _358501), ordinal(_358499)], (1562 ^ _84654) ^ [_137064, _137066] : [-(set_intersection2(_137066, _137064) = set_intersection2(_137064, _137066))], (3131 ^ _84654) ^ [_193504] : [relation(_193504), 3134 ^ _84654 : [(3135 ^ _84654) ^ [_193701] : [is_well_founded_in(_193504, _193701), 3138 ^ _84654 : [(3139 ^ _84654) ^ [_193866] : [subset(_193866, _193701), -(_193866 = empty_set), 3147 ^ _84654 : [(3150 ^ _84654) ^ [] : [-(disjoint(fiber(_193504, 3146 ^ [_193504, _193701, _193866]), _193866))], (3148 ^ _84654) ^ [] : [-(in(3146 ^ [_193504, _193701, _193866], _193866))]]]]], (3152 ^ _84654) ^ [_194307] : [-(is_well_founded_in(_193504, _194307)), 3154 ^ _84654 : [(3159 ^ _84654) ^ [_194649] : [in(_194649, 3153 ^ [_193504, _194307]), disjoint(fiber(_193504, _194649), 3153 ^ [_193504, _194307])], (3157 ^ _84654) ^ [] : [3153 ^ [_193504, _194307] = empty_set], (3155 ^ _84654) ^ [] : [-(subset(3153 ^ [_193504, _194307], _194307))]]]]], (9004 ^ _84654) ^ [_409650, _409652] : [in(_409650, _409652), -(apply(identity_relation(_409652), _409650) = _409650)], (5193 ^ _84654) ^ [] : [-(v3_membered(empty_set))], (5665 ^ _84654) ^ [_277954] : [-(one_to_one(5655 ^ [_277954]))], (4907 ^ _84654) ^ [_252381] : [-(function(identity_relation(_252381)))], (1034 ^ _84654) ^ [_118858, _118860, _118862, _118864] : [-(topstr_closure(_118864, _118860) = topstr_closure(_118862, _118858)), _118864 = _118862, _118860 = _118858], (1218 ^ _84654) ^ [_125773] : [v1_membered(_125773), 1221 ^ _84654 : [(1222 ^ _84654) ^ [_125903] : [element(_125903, _125773), -(v1_xcmplx_0(_125903))]]], (1168 ^ _84654) ^ [_123664, _123666] : [_123666 = _123664, -(singleton(_123666) = singleton(_123664))], (3753 ^ _84654) ^ [_215012] : [relation(_215012), -(relation_field(_215012) = set_union2(relation_dom(_215012), relation_rng(_215012)))], (8717 ^ _84654) ^ [_400237, _400239] : [relation(_400237), well_orders(_400237, _400239), 8724 ^ _84654 : [(8727 ^ _84654) ^ [] : [-(well_ordering(relation_restriction(_400237, _400239)))], (8725 ^ _84654) ^ [] : [-(relation_field(relation_restriction(_400237, _400239)) = _400239)]]], (5700 ^ _84654) ^ [_279118, _279120] : [-(relation_of2(5698 ^ [_279118, _279120], _279120, _279118))], (9178 ^ _84654) ^ [_415514] : [ordinal(_415514), 9181 ^ _84654 : [(9191 ^ _84654) ^ [] : [being_limit_ordinal(_415514), 9192 ^ _84654 : [(9193 ^ _84654) ^ [_415985] : [ordinal(_415985), _415514 = succ(_415985)]]], (9182 ^ _84654) ^ [] : [-(being_limit_ordinal(_415514)), 9186 ^ _84654 : [(9189 ^ _84654) ^ [] : [-(_415514 = succ(9185 ^ [_415514]))], (9187 ^ _84654) ^ [] : [-(ordinal(9185 ^ [_415514]))]]]]], (4787 ^ _84654) ^ [_248560] : [empty(powerset(_248560))], (5945 ^ _84654) ^ [_287055, _287057] : [are_equipotent(_287057, _287055), -(equipotent(_287057, _287055))], (904 ^ _84654) ^ [_114099, _114101] : [_114101 = _114099, -(cast_as_carrier_subset(_114101) = cast_as_carrier_subset(_114099))], (5247 ^ _84654) ^ [_263652, _263654] : [-(set_union2(_263654, _263654) = _263654)], (3167 ^ _84654) ^ [_195007, _195009, _195011] : [_195007 = set_intersection2(_195011, _195009), 3170 ^ _84654 : [(3179 ^ _84654) ^ [_195448] : [-(in(_195448, _195007)), in(_195448, _195011), in(_195448, _195009)], (3171 ^ _84654) ^ [_195189] : [in(_195189, _195007), 3174 ^ _84654 : [(3177 ^ _84654) ^ [] : [-(in(_195189, _195009))], (3175 ^ _84654) ^ [] : [-(in(_195189, _195011))]]]]], (10163 ^ _84654) ^ [_447978, _447980] : [relation(_447978), -(relation_dom_restriction(_447978, _447980) = relation_composition(identity_relation(_447980), _447978))], (3807 ^ _84654) ^ [_217123] : [relation(_217123), 3810 ^ _84654 : [(3811 ^ _84654) ^ [_217283] : [relation(_217283), 3814 ^ _84654 : [(3815 ^ _84654) ^ [] : [_217283 = relation_inverse(_217123), 3818 ^ _84654 : [(3825 ^ _84654) ^ [_217782, _217784] : [in(ordered_pair(_217782, _217784), _217123), -(in(ordered_pair(_217784, _217782), _217283))], (3819 ^ _84654) ^ [_217592, _217594] : [in(ordered_pair(_217594, _217592), _217283), -(in(ordered_pair(_217592, _217594), _217123))]]], (3831 ^ _84654) ^ [] : [-(_217283 = relation_inverse(_217123)), 3836 ^ _84654 : [(3839 ^ _84654) ^ [] : [in(ordered_pair(3833 ^ [_217123, _217283], 3832 ^ [_217123, _217283]), _217123)], (3837 ^ _84654) ^ [] : [-(in(ordered_pair(3832 ^ [_217123, _217283], 3833 ^ [_217123, _217283]), _217283))]], 3840 ^ _84654 : [(3843 ^ _84654) ^ [] : [in(ordered_pair(3832 ^ [_217123, _217283], 3833 ^ [_217123, _217283]), _217283)], (3841 ^ _84654) ^ [] : [-(in(ordered_pair(3833 ^ [_217123, _217283], 3832 ^ [_217123, _217283]), _217123))]]]]]]], (3727 ^ _84654) ^ [_214184] : [_214184 = union(_214184), -(being_limit_ordinal(_214184))], (1200 ^ _84654) ^ [_124798, _124800] : [_124800 = _124798, -(the_carrier(_124800) = the_carrier(_124798))], (1492 ^ _84654) ^ [_134875] : [-(ordinal(_134875)), epsilon_transitive(_134875), epsilon_connected(_134875)], (5654 ^ _84654) ^ [] : [-(empty(5652 ^ []))], (4130 ^ _84654) ^ [_229315, _229317] : [element(_229315, powerset(powerset(_229317))), 4133 ^ _84654 : [(4134 ^ _84654) ^ [_229495] : [element(_229495, powerset(powerset(_229317))), 4137 ^ _84654 : [(4138 ^ _84654) ^ [] : [_229495 = complements_of_subsets(_229317, _229315), 4141 ^ _84654 : [(4142 ^ _84654) ^ [_229783] : [element(_229783, powerset(_229317)), 4145 ^ _84654 : [(4152 ^ _84654) ^ [] : [in(subset_complement(_229317, _229783), _229315), -(in(_229783, _229495))], (4146 ^ _84654) ^ [] : [in(_229783, _229495), -(in(subset_complement(_229317, _229783), _229315))]]]]], (4158 ^ _84654) ^ [] : [-(_229495 = complements_of_subsets(_229317, _229315)), 4160 ^ _84654 : [(4163 ^ _84654) ^ [] : [4164 ^ _84654 : [(4167 ^ _84654) ^ [] : [in(subset_complement(_229317, 4159 ^ [_229315, _229317, _229495]), _229315)], (4165 ^ _84654) ^ [] : [-(in(4159 ^ [_229315, _229317, _229495], _229495))]], 4168 ^ _84654 : [(4171 ^ _84654) ^ [] : [in(4159 ^ [_229315, _229317, _229495], _229495)], (4169 ^ _84654) ^ [] : [-(in(subset_complement(_229317, 4159 ^ [_229315, _229317, _229495]), _229315))]]], (4161 ^ _84654) ^ [] : [-(element(4159 ^ [_229315, _229317, _229495], powerset(_229317)))]]]]]]], (4913 ^ _84654) ^ [] : [-(function(empty_set))], (7732 ^ _84654) ^ [] : [7787 ^ _84654 : [(7788 ^ _84654) ^ [_368587] : [ordinal(_368587), in(_368587, omega), 7795 ^ _84654 : [(7796 ^ _84654) ^ [_368843] : [element(_368843, powerset(powerset(_368587))), -(_368843 = empty_set), 7804 ^ _84654 : [(7807 ^ _84654) ^ [_369242] : [-(_369242 = 7803 ^ [_368587, _368843]), in(_369242, _368843), subset(7803 ^ [_368587, _368843], _369242)], (7805 ^ _84654) ^ [] : [-(in(7803 ^ [_368587, _368843], _368843))]]]]]], 7734 ^ _84654 : [(7777 ^ _84654) ^ [_368182] : [in(_368182, 7771 ^ []), 7781 ^ _84654 : [(7786 ^ _84654) ^ [] : [7780 ^ [_368182] = _368182], (7784 ^ _84654) ^ [] : [-(subset(_368182, 7780 ^ [_368182]))], (7782 ^ _84654) ^ [] : [-(in(7780 ^ [_368182], 7771 ^ []))]]], (7775 ^ _84654) ^ [] : [7771 ^ [] = empty_set], (7737 ^ _84654) ^ [_366874] : [ordinal(_366874), in(_366874, 7733 ^ []), in(_366874, omega), 7748 ^ _84654 : [(7749 ^ _84654) ^ [_367211] : [element(_367211, powerset(powerset(_366874))), -(_367211 = empty_set), 7757 ^ _84654 : [(7760 ^ _84654) ^ [_367610] : [-(_367610 = 7756 ^ [_366874, _367211]), in(_367610, _367211), subset(7756 ^ [_366874, _367211], _367610)], (7758 ^ _84654) ^ [] : [-(in(7756 ^ [_366874, _367211], _367211))]]]]], (7735 ^ _84654) ^ [] : [-(ordinal(7733 ^ []))], (7770 ^ _84654) ^ [] : [-(in(7733 ^ [], omega))], (7773 ^ _84654) ^ [] : [-(element(7771 ^ [], powerset(powerset(7733 ^ []))))]]], (4601 ^ _84654) ^ [] : [true___, -(true___)], (8900 ^ _84654) ^ [_406255, _406257] : [ordinal(_406255), subset(_406257, _406255), -(_406257 = empty_set), 8912 ^ _84654 : [(8917 ^ _84654) ^ [_406807] : [ordinal(_406807), in(_406807, _406257), -(ordinal_subset(8911 ^ [_406255, _406257], _406807))], (8915 ^ _84654) ^ [] : [-(in(8911 ^ [_406255, _406257], _406257))], (8913 ^ _84654) ^ [] : [-(ordinal(8911 ^ [_406255, _406257]))]]], (2932 ^ _84654) ^ [_186014, _186016, _186018] : [-(_186014 = set_union2(_186018, _186016)), 2936 ^ _84654 : [(2941 ^ _84654) ^ [] : [in(2933 ^ [_186014, _186016, _186018], _186016)], (2939 ^ _84654) ^ [] : [in(2933 ^ [_186014, _186016, _186018], _186018)], (2937 ^ _84654) ^ [] : [-(in(2933 ^ [_186014, _186016, _186018], _186014))]], 2942 ^ _84654 : [(2943 ^ _84654) ^ [] : [-(in(2933 ^ [_186014, _186016, _186018], _186018)), -(in(2933 ^ [_186014, _186016, _186018], _186016))], (2949 ^ _84654) ^ [] : [in(2933 ^ [_186014, _186016, _186018], _186014)]]], (9875 ^ _84654) ^ [_438501, _438503] : [relation(_438501), function(_438501), 9882 ^ _84654 : [(9883 ^ _84654) ^ [_438768] : [relation(_438768), function(_438768), 9890 ^ _84654 : [(9903 ^ _84654) ^ [] : [-(_438501 = relation_dom_restriction(_438768, _438503)), relation_dom(_438501) = set_intersection2(relation_dom(_438768), _438503), 9909 ^ _84654 : [(9912 ^ _84654) ^ [] : [apply(_438501, 9908 ^ [_438501, _438503, _438768]) = apply(_438768, 9908 ^ [_438501, _438503, _438768])], (9910 ^ _84654) ^ [] : [-(in(9908 ^ [_438501, _438503, _438768], relation_dom(_438501)))]]], (9891 ^ _84654) ^ [] : [_438501 = relation_dom_restriction(_438768, _438503), 9894 ^ _84654 : [(9897 ^ _84654) ^ [_439222] : [in(_439222, relation_dom(_438501)), -(apply(_438501, _439222) = apply(_438768, _439222))], (9895 ^ _84654) ^ [] : [-(relation_dom(_438501) = set_intersection2(relation_dom(_438768), _438503))]]]]]]], (9141 ^ _84654) ^ [_414349] : [subset(_414349, empty_set), -(_414349 = empty_set)], (830 ^ _84654) ^ [_111469, _111471, _111473, _111475, _111477, _111479] : [-(meet(_111479, _111475, _111471) = meet(_111477, _111473, _111469)), _111479 = _111477, _111475 = _111473, _111471 = _111469], (9460 ^ _84654) ^ [_425227, _425229] : [-(set_difference(_425229, set_difference(_425229, _425227)) = set_intersection2(_425229, _425227))], (8571 ^ _84654) ^ [_395576, _395578] : [relation(_395576), function(_395576), 8578 ^ _84654 : [(8579 ^ _84654) ^ [_395822] : [relation(_395822), function(_395822), in(_395578, relation_dom(_395576)), -(apply(relation_composition(_395576, _395822), _395578) = apply(_395822, apply(_395576, _395578)))]]], (1382 ^ _84654) ^ [_131411] : [empty(_131411), -(function(_131411))], (10241 ^ _84654) ^ [_450800, _450802, _450804] : [singleton(_450804) = unordered_pair(_450802, _450800), -(_450802 = _450800)], (3250 ^ _84654) ^ [_197733] : [ordinal(_197733), 3253 ^ _84654 : [(3256 ^ _84654) ^ [] : [-(epsilon_connected(_197733))], (3254 ^ _84654) ^ [] : [-(epsilon_transitive(_197733))]]], (4751 ^ _84654) ^ [] : [-(empty(empty_set))], (5776 ^ _84654) ^ [_281610] : [5784 ^ _84654 : [(5787 ^ _84654) ^ [] : [-(closed_subset(5783 ^ [_281610], _281610))], (5785 ^ _84654) ^ [] : [-(element(5783 ^ [_281610], powerset(the_carrier(_281610))))]], topological_space(_281610), top_str(_281610)], (3514 ^ _84654) ^ [_206916] : [relation(_206916), function(_206916), 3521 ^ _84654 : [(3522 ^ _84654) ^ [_207188] : [_207188 = relation_rng(_206916), 3525 ^ _84654 : [(3535 ^ _84654) ^ [_207718] : [-(in(_207718, _207188)), 3536 ^ _84654 : [(3537 ^ _84654) ^ [_207821] : [in(_207821, relation_dom(_206916)), _207718 = apply(_206916, _207821)]]], (3526 ^ _84654) ^ [_207376] : [in(_207376, _207188), 3530 ^ _84654 : [(3533 ^ _84654) ^ [] : [-(_207376 = apply(_206916, 3529 ^ [_206916, _207188, _207376]))], (3531 ^ _84654) ^ [] : [-(in(3529 ^ [_206916, _207188, _207376], relation_dom(_206916)))]]]]], (3545 ^ _84654) ^ [_208070] : [-(_208070 = relation_rng(_206916)), 3558 ^ _84654 : [(3563 ^ _84654) ^ [] : [in(3546 ^ [_206916, _208070], _208070)], (3561 ^ _84654) ^ [] : [-(3546 ^ [_206916, _208070] = apply(_206916, 3557 ^ [_206916, _208070]))], (3559 ^ _84654) ^ [] : [-(in(3557 ^ [_206916, _208070], relation_dom(_206916)))]], 3549 ^ _84654 : [(3552 ^ _84654) ^ [_208365] : [in(_208365, relation_dom(_206916)), 3546 ^ [_206916, _208070] = apply(_206916, _208365)], (3550 ^ _84654) ^ [] : [-(in(3546 ^ [_206916, _208070], _208070))]]]]], (5819 ^ _84654) ^ [_283014, _283016, _283018] : [-(join_commut(_283018, _283016, _283014) = join(_283018, _283016, _283014)), -(empty_carrier(_283018)), join_commutative(_283018), join_semilatt_str(_283018), element(_283016, the_carrier(_283018)), element(_283014, the_carrier(_283018))], (938 ^ _84654) ^ [_115405, _115407, _115409, _115411, _115413, _115415] : [-(relation_rng_as_subset(_115415, _115411, _115407) = relation_rng_as_subset(_115413, _115409, _115405)), _115415 = _115413, _115411 = _115409, _115407 = _115405], (6918 ^ _84654) ^ [_330938, _330940] : [ordinal(_330940), element(_330938, powerset(powerset(succ(_330940)))), 6930 ^ _84654 : [(6941 ^ _84654) ^ [] : [-(in(6939 ^ [_330938, _330940], _330938))], (6934 ^ _84654) ^ [] : [-(in(6932 ^ [_330938, _330940], _330938))], (6931 ^ _84654) ^ [] : [-(6927 ^ [_330938, _330940] = 6928 ^ [_330938, _330940])], (6936 ^ _84654) ^ [] : [-(6928 ^ [_330938, _330940] = set_difference(6932 ^ [_330938, _330940], singleton(_330940)))], (6943 ^ _84654) ^ [] : [-(6929 ^ [_330938, _330940] = set_difference(6939 ^ [_330938, _330940], singleton(_330940)))], (6945 ^ _84654) ^ [] : [6928 ^ [_330938, _330940] = 6929 ^ [_330938, _330940]], (6938 ^ _84654) ^ [] : [-(6927 ^ [_330938, _330940] = 6929 ^ [_330938, _330940])]], 6947 ^ _84654 : [(6962 ^ _84654) ^ [_333111] : [-(in(_333111, 6946 ^ [_330938, _330940])), 6963 ^ _84654 : [(6964 ^ _84654) ^ [_333240] : [in(_333240, powerset(_330940)), _333240 = _333111, 6971 ^ _84654 : [(6972 ^ _84654) ^ [_333493] : [in(_333493, _330938), _333111 = set_difference(_333493, singleton(_330940))]]]]], (6948 ^ _84654) ^ [_332497] : [in(_332497, 6946 ^ [_330938, _330940]), 6952 ^ _84654 : [(6960 ^ _84654) ^ [] : [-(_332497 = set_difference(6956 ^ [_330938, _330940, _332497], singleton(_330940)))], (6953 ^ _84654) ^ [] : [-(in(6951 ^ [_330938, _330940, _332497], powerset(_330940)))], (6958 ^ _84654) ^ [] : [-(in(6956 ^ [_330938, _330940, _332497], _330938))], (6955 ^ _84654) ^ [] : [-(6951 ^ [_330938, _330940, _332497] = _332497)]]]]], (7818 ^ _84654) ^ [_369673] : [-(relation(7816 ^ [_369673]))], (5673 ^ _84654) ^ [_278226] : [-(natural(5655 ^ [_278226]))], (3733 ^ _84654) ^ [_214378] : [top_str(_214378), 3736 ^ _84654 : [(3737 ^ _84654) ^ [_214527] : [element(_214527, powerset(the_carrier(_214378))), 3740 ^ _84654 : [(3747 ^ _84654) ^ [] : [open_subset(subset_difference(the_carrier(_214378), cast_as_carrier_subset(_214378), _214527), _214378), -(closed_subset(_214527, _214378))], (3741 ^ _84654) ^ [] : [closed_subset(_214527, _214378), -(open_subset(subset_difference(the_carrier(_214378), cast_as_carrier_subset(_214378), _214527), _214378))]]]]], (186 ^ _84654) ^ [_90423, _90425] : [-(v5_membered(_90423)), _90425 = _90423, v5_membered(_90425)], (2831 ^ _84654) ^ [_182538, _182540, _182542] : [_182538 = unordered_pair(_182542, _182540), 2834 ^ _84654 : [(2835 ^ _84654) ^ [_182720] : [in(_182720, _182538), -(_182720 = _182542), -(_182720 = _182540)], (2845 ^ _84654) ^ [_182998] : [2846 ^ _84654 : [(2849 ^ _84654) ^ [] : [_182998 = _182540], (2847 ^ _84654) ^ [] : [_182998 = _182542]], -(in(_182998, _182538))]]], (3681 ^ _84654) ^ [_212791] : [relation(_212791), 3684 ^ _84654 : [(3699 ^ _84654) ^ [_213436] : [-(well_orders(_212791, _213436)), is_reflexive_in(_212791, _213436), is_transitive_in(_212791, _213436), is_antisymmetric_in(_212791, _213436), is_connected_in(_212791, _213436), is_well_founded_in(_212791, _213436)], (3685 ^ _84654) ^ [_212975] : [well_orders(_212791, _212975), 3688 ^ _84654 : [(3691 ^ _84654) ^ [] : [-(is_transitive_in(_212791, _212975))], (3693 ^ _84654) ^ [] : [-(is_antisymmetric_in(_212791, _212975))], (3695 ^ _84654) ^ [] : [-(is_connected_in(_212791, _212975))], (3697 ^ _84654) ^ [] : [-(is_well_founded_in(_212791, _212975))], (3689 ^ _84654) ^ [] : [-(is_reflexive_in(_212791, _212975))]]]]], (4909 ^ _84654) ^ [] : [-(relation(empty_set))], (4639 ^ _84654) ^ [] : [true___, -(true___)], (574 ^ _84654) ^ [_102289, _102291] : [-(relation(_102289)), _102291 = _102289, relation(_102291)], (7987 ^ _84654) ^ [_375567, _375569] : [relation(_375567), -(subset(relation_rng(relation_rng_restriction(_375569, _375567)), relation_rng(_375567)))], (2242 ^ _84654) ^ [_161744, _161746, _161748] : [relation_of2_as_subset(_161744, _161748, _161746), 2245 ^ _84654 : [(2264 ^ _84654) ^ [] : [_161746 = empty_set, -(_161748 = empty_set), 2271 ^ _84654 : [(2278 ^ _84654) ^ [] : [_161744 = empty_set, -(quasi_total(_161744, _161748, _161746))], (2272 ^ _84654) ^ [] : [quasi_total(_161744, _161748, _161746), -(_161744 = empty_set)]]], (2246 ^ _84654) ^ [] : [2247 ^ _84654 : [(2250 ^ _84654) ^ [] : [_161748 = empty_set], (2248 ^ _84654) ^ [] : [-(_161746 = empty_set)]], 2251 ^ _84654 : [(2258 ^ _84654) ^ [] : [_161748 = relation_dom_as_subset(_161748, _161746, _161744), -(quasi_total(_161744, _161748, _161746))], (2252 ^ _84654) ^ [] : [quasi_total(_161744, _161748, _161746), -(_161748 = relation_dom_as_subset(_161748, _161746, _161744))]]]]], (3493 ^ _84654) ^ [_206173, _206175, _206177] : [-(_206173 = set_difference(_206177, _206175)), 3505 ^ _84654 : [(3510 ^ _84654) ^ [] : [in(3494 ^ [_206173, _206175, _206177], _206173)], (3508 ^ _84654) ^ [] : [in(3494 ^ [_206173, _206175, _206177], _206175)], (3506 ^ _84654) ^ [] : [-(in(3494 ^ [_206173, _206175, _206177], _206177))]], 3497 ^ _84654 : [(3500 ^ _84654) ^ [] : [in(3494 ^ [_206173, _206175, _206177], _206177), -(in(3494 ^ [_206173, _206175, _206177], _206175))], (3498 ^ _84654) ^ [] : [-(in(3494 ^ [_206173, _206175, _206177], _206173))]]], (9120 ^ _84654) ^ [_413558] : [-(transitive(inclusion_relation(_413558)))], (1270 ^ _84654) ^ [_127562] : [v5_membered(_127562), 1273 ^ _84654 : [(1274 ^ _84654) ^ [_127712] : [element(_127712, _127562), 1277 ^ _84654 : [(1280 ^ _84654) ^ [] : [-(natural(_127712))], (1282 ^ _84654) ^ [] : [-(v1_xreal_0(_127712))], (1284 ^ _84654) ^ [] : [-(v1_int_1(_127712))], (1286 ^ _84654) ^ [] : [-(v1_rat_1(_127712))], (1278 ^ _84654) ^ [] : [-(v1_xcmplx_0(_127712))]]]]], (9012 ^ _84654) ^ [_409953] : [relation(_409953), 9015 ^ _84654 : [(9018 ^ _84654) ^ [] : [-(relation_dom(_409953) = relation_rng(relation_inverse(_409953)))], (9016 ^ _84654) ^ [] : [-(relation_rng(_409953) = relation_dom(relation_inverse(_409953)))]]], (7981 ^ _84654) ^ [_375353, _375355] : [relation(_375353), -(subset(relation_rng_restriction(_375355, _375353), _375353))], (9032 ^ _84654) ^ [_410696, _410698] : [subset(singleton(_410698), _410696), -(in(_410698, _410696))], (4493 ^ _84654) ^ [_239198] : [relation(_239198), -(relation(relation_inverse(_239198)))], (2532 ^ _84654) ^ [_172009, _172011] : [-(_172009 = singleton(_172011)), 2536 ^ _84654 : [(2539 ^ _84654) ^ [] : [2533 ^ [_172009, _172011] = _172011], (2537 ^ _84654) ^ [] : [-(in(2533 ^ [_172009, _172011], _172009))]], 2540 ^ _84654 : [(2543 ^ _84654) ^ [] : [in(2533 ^ [_172009, _172011], _172009)], (2541 ^ _84654) ^ [] : [-(2533 ^ [_172009, _172011] = _172011)]]], (8076 ^ _84654) ^ [_378818, _378820, _378822] : [relation(_378818), -(relation_dom_restriction(relation_rng_restriction(_378822, _378818), _378820) = relation_rng_restriction(_378822, relation_dom_restriction(_378818, _378820)))], (5588 ^ _84654) ^ [] : [-(relation(5586 ^ []))], (5709 ^ _84654) ^ [] : [-(relation(5705 ^ []))], (1596 ^ _84654) ^ [_138149, _138151] : [ordinal(_138151), ordinal(_138149), -(ordinal_subset(_138151, _138149)), -(ordinal_subset(_138149, _138151))], (3112 ^ _84654) ^ [_192847, _192849] : [subset(_192849, _192847), 3115 ^ _84654 : [(3116 ^ _84654) ^ [_192984] : [in(_192984, _192849), -(in(_192984, _192847))]]], (894 ^ _84654) ^ [_113768, _113770, _113772, _113774] : [-(fiber(_113774, _113770) = fiber(_113772, _113768)), _113774 = _113772, _113770 = _113768], (1666 ^ _84654) ^ [_140454, _140456] : [-(_140456 = _140454), subset(_140456, _140454), subset(_140454, _140456)], (2184 ^ _84654) ^ [_159607] : [finite(_159607), 2188 ^ _84654 : [(2195 ^ _84654) ^ [] : [-(in(relation_dom(2187 ^ [_159607]), omega))], (2189 ^ _84654) ^ [] : [-(relation(2187 ^ [_159607]))], (2193 ^ _84654) ^ [] : [-(relation_rng(2187 ^ [_159607]) = _159607)], (2191 ^ _84654) ^ [] : [-(function(2187 ^ [_159607]))]]], (9020 ^ _84654) ^ [_410281, _410283] : [set_difference(_410283, _410281) = empty_set, -(subset(_410283, _410281))], (2953 ^ _84654) ^ [_186808, _186810, _186812] : [_186808 = cartesian_product2(_186812, _186810), 2956 ^ _84654 : [(2969 ^ _84654) ^ [_187569] : [-(in(_187569, _186808)), 2970 ^ _84654 : [(2971 ^ _84654) ^ [_187699, _187701] : [in(_187701, _186812), in(_187699, _186810), _187569 = ordered_pair(_187701, _187699)]]], (2957 ^ _84654) ^ [_187009] : [in(_187009, _186808), 2962 ^ _84654 : [(2967 ^ _84654) ^ [] : [-(_187009 = ordered_pair(2960 ^ [_186808, _186810, _186812, _187009], 2961 ^ [_186808, _186810, _186812, _187009]))], (2965 ^ _84654) ^ [] : [-(in(2961 ^ [_186808, _186810, _186812, _187009], _186810))], (2963 ^ _84654) ^ [] : [-(in(2960 ^ [_186808, _186810, _186812, _187009], _186812))]]]]], (564 ^ _84654) ^ [_101994, _101996] : [-(well_ordering(_101994)), _101996 = _101994, well_ordering(_101996)], (4887 ^ _84654) ^ [_251760] : [4894 ^ _84654 : [(4897 ^ _84654) ^ [] : [-(epsilon_transitive(succ(_251760)))], (4899 ^ _84654) ^ [] : [-(epsilon_connected(succ(_251760)))], (4901 ^ _84654) ^ [] : [-(ordinal(succ(_251760)))], (4903 ^ _84654) ^ [] : [-(natural(succ(_251760)))], (4895 ^ _84654) ^ [] : [empty(succ(_251760))]], ordinal(_251760), natural(_251760)], (4785 ^ _84654) ^ [_248460] : [-(finite(singleton(_248460)))], (5512 ^ _84654) ^ [_272887, _272889] : [in(_272889, _272887), -(subset(_272889, union(_272887)))], (4915 ^ _84654) ^ [] : [-(one_to_one(empty_set))], (1448 ^ _84654) ^ [_133590] : [finite(_133590), 1451 ^ _84654 : [(1452 ^ _84654) ^ [_133722] : [element(_133722, powerset(_133590)), -(finite(_133722))]]], (10135 ^ _84654) ^ [_446981, _446983, _446985] : [-(subset(set_union2(_446985, _446981), _446983)), subset(_446985, _446983), subset(_446981, _446983)], (630 ^ _84654) ^ [_104125, _104127, _104129, _104131] : [-(subset(_104129, _104125)), subset(_104131, _104127), _104131 = _104129, _104127 = _104125], (5167 ^ _84654) ^ [_261289] : [-(closed_subset(cast_as_carrier_subset(_261289), _261289)), topological_space(_261289), top_str(_261289)], (4175 ^ _84654) ^ [_230906, _230908] : [proper_subset(_230908, _230906), 4178 ^ _84654 : [(4181 ^ _84654) ^ [] : [_230908 = _230906], (4179 ^ _84654) ^ [] : [-(subset(_230908, _230906))]]], (9010 ^ _84654) ^ [_409855, _409857] : [-(subset(set_difference(_409857, _409855), _409857))], (738 ^ _84654) ^ [_107910, _107912] : [_107912 = _107910, -(the_L_meet(_107912) = the_L_meet(_107910))], (8663 ^ _84654) ^ [_398555] : [ordinal(_398555), 8666 ^ _84654 : [(8667 ^ _84654) ^ [_398705] : [ordinal(_398705), -(in(_398555, _398705)), -(_398555 = _398705), -(in(_398705, _398555))]]], (8846 ^ _84654) ^ [_404441, _404443] : [-(_404443 = _404441), 8850 ^ _84654 : [(8853 ^ _84654) ^ [] : [in(8847 ^ [_404441, _404443], _404441)], (8851 ^ _84654) ^ [] : [-(in(8847 ^ [_404441, _404443], _404443))]], 8854 ^ _84654 : [(8857 ^ _84654) ^ [] : [in(8847 ^ [_404441, _404443], _404443)], (8855 ^ _84654) ^ [] : [-(in(8847 ^ [_404441, _404443], _404441))]]], (10231 ^ _84654) ^ [_450466, _450468] : [subset(_450466, 10204 ^ [_450468]), -(are_equipotent(_450466, 10204 ^ [_450468])), -(in(_450466, 10204 ^ [_450468]))], (9440 ^ _84654) ^ [_424533] : [top_str(_424533), 9443 ^ _84654 : [(9444 ^ _84654) ^ [_424671] : [element(_424671, powerset(the_carrier(_424533))), -(subset(_424671, topstr_closure(_424533, _424671)))]]], (8228 ^ _84654) ^ [_384050, _384052] : [relation(_384050), -(subset(relation_inverse_image(_384050, _384052), relation_dom(_384050)))], (7931 ^ _84654) ^ [_373685, _373687, _373689, _373691] : [-(in(ordered_pair(_373691, _373689), cartesian_product2(_373687, _373685))), in(_373691, _373687), in(_373689, _373685)], (710 ^ _84654) ^ [_106620, _106622, _106624, _106626] : [-(closed_subset(_106624, _106620)), closed_subset(_106626, _106622), _106626 = _106624, _106622 = _106620], (3189 ^ _84654) ^ [_195732, _195734, _195736] : [-(_195732 = set_intersection2(_195736, _195734)), 3201 ^ _84654 : [(3206 ^ _84654) ^ [] : [in(3190 ^ [_195732, _195734, _195736], _195732)], (3204 ^ _84654) ^ [] : [-(in(3190 ^ [_195732, _195734, _195736], _195734))], (3202 ^ _84654) ^ [] : [-(in(3190 ^ [_195732, _195734, _195736], _195736))]], 3193 ^ _84654 : [(3196 ^ _84654) ^ [] : [in(3190 ^ [_195732, _195734, _195736], _195736), in(3190 ^ [_195732, _195734, _195736], _195734)], (3194 ^ _84654) ^ [] : [-(in(3190 ^ [_195732, _195734, _195736], _195732))]]], (1354 ^ _84654) ^ [_130482] : [ordinal(_130482), 1357 ^ _84654 : [(1358 ^ _84654) ^ [_130622] : [element(_130622, _130482), 1361 ^ _84654 : [(1366 ^ _84654) ^ [] : [-(ordinal(_130622))], (1364 ^ _84654) ^ [] : [-(epsilon_connected(_130622))], (1362 ^ _84654) ^ [] : [-(epsilon_transitive(_130622))]]]]], (968 ^ _84654) ^ [_116442, _116444] : [_116444 = _116442, -(succ(_116444) = succ(_116442))], (3759 ^ _84654) ^ [_215218] : [relation(_215218), 3762 ^ _84654 : [(3763 ^ _84654) ^ [_215426] : [is_connected_in(_215218, _215426), 3766 ^ _84654 : [(3767 ^ _84654) ^ [_215616, _215618] : [in(_215618, _215426), in(_215616, _215426), -(_215618 = _215616), -(in(ordered_pair(_215618, _215616), _215218)), -(in(ordered_pair(_215616, _215618), _215218))]]], (3785 ^ _84654) ^ [_216110] : [3788 ^ _84654 : [(3791 ^ _84654) ^ [] : [-(in(3787 ^ [_215218, _216110], _216110))], (3793 ^ _84654) ^ [] : [3786 ^ [_215218, _216110] = 3787 ^ [_215218, _216110]], (3795 ^ _84654) ^ [] : [in(ordered_pair(3786 ^ [_215218, _216110], 3787 ^ [_215218, _216110]), _215218)], (3797 ^ _84654) ^ [] : [in(ordered_pair(3787 ^ [_215218, _216110], 3786 ^ [_215218, _216110]), _215218)], (3789 ^ _84654) ^ [] : [-(in(3786 ^ [_215218, _216110], _216110))]], -(is_connected_in(_215218, _216110))]]], (7820 ^ _84654) ^ [_369741] : [-(function(7816 ^ [_369741]))], (8407 ^ _84654) ^ [_390081, _390083] : [relation(_390081), 8410 ^ _84654 : [(8413 ^ _84654) ^ [] : [-(subset(relation_field(relation_restriction(_390081, _390083)), _390083))], (8411 ^ _84654) ^ [] : [-(subset(relation_field(relation_restriction(_390081, _390083)), relation_field(_390081)))]]], (5689 ^ _84654) ^ [] : [-(one_to_one(5683 ^ []))], (5251 ^ _84654) ^ [_263875, _263877, _263879] : [-(subset_intersection2(_263879, _263877, _263877) = _263877), element(_263877, powerset(_263879)), element(_263875, powerset(_263879))], (236 ^ _84654) ^ [_91954, _91956, _91958, _91960, _91962, _91964] : [-(relation_of2(_91962, _91958, _91954)), relation_of2(_91964, _91960, _91956), _91964 = _91962, _91960 = _91958, _91956 = _91954], (7143 ^ _84654) ^ [_341572, _341574] : [ordinal(_341572), 7151 ^ _84654 : [(7161 ^ _84654) ^ [] : [-(7148 ^ [_341572, _341574] = 7150 ^ [_341572, _341574])], (7170 ^ _84654) ^ [] : [7149 ^ [_341572, _341574] = 7150 ^ [_341572, _341574]], (7168 ^ _84654) ^ [] : [-(in(7162 ^ [_341572, _341574], _341574))], (7164 ^ _84654) ^ [] : [-(ordinal(7162 ^ [_341572, _341574]))], (7152 ^ _84654) ^ [] : [-(7148 ^ [_341572, _341574] = 7149 ^ [_341572, _341574])], (7159 ^ _84654) ^ [] : [-(in(7153 ^ [_341572, _341574], _341574))], (7155 ^ _84654) ^ [] : [-(ordinal(7153 ^ [_341572, _341574]))], (7157 ^ _84654) ^ [] : [-(7149 ^ [_341572, _341574] = 7153 ^ [_341572, _341574])], (7166 ^ _84654) ^ [] : [-(7150 ^ [_341572, _341574] = 7162 ^ [_341572, _341574])]], 7172 ^ _84654 : [(7189 ^ _84654) ^ [_343861] : [-(in(_343861, 7171 ^ [_341572, _341574])), 7190 ^ _84654 : [(7191 ^ _84654) ^ [_343990] : [in(_343990, succ(_341572)), _343990 = _343861, 7198 ^ _84654 : [(7199 ^ _84654) ^ [_344243] : [ordinal(_344243), _343861 = _344243, in(_344243, _341574)]]]]], (7173 ^ _84654) ^ [_343174] : [in(_343174, 7171 ^ [_341572, _341574]), 7177 ^ _84654 : [(7180 ^ _84654) ^ [] : [-(7176 ^ [_341572, _341574, _343174] = _343174)], (7183 ^ _84654) ^ [] : [-(ordinal(7181 ^ [_341572, _341574, _343174]))], (7185 ^ _84654) ^ [] : [-(_343174 = 7181 ^ [_341572, _341574, _343174])], (7187 ^ _84654) ^ [] : [-(in(7181 ^ [_341572, _341574, _343174], _341574))], (7178 ^ _84654) ^ [] : [-(in(7176 ^ [_341572, _341574, _343174], succ(_341572)))]]]]], (1312 ^ _84654) ^ [_129006] : [v2_membered(_129006), 1315 ^ _84654 : [(1316 ^ _84654) ^ [_129143] : [element(_129143, powerset(_129006)), 1319 ^ _84654 : [(1322 ^ _84654) ^ [] : [-(v2_membered(_129143))], (1320 ^ _84654) ^ [] : [-(v1_membered(_129143))]]]]], (5633 ^ _84654) ^ [] : [-(function(5629 ^ []))], (2661 ^ _84654) ^ [_176544, _176546] : [_176544 = powerset(_176546), 2664 ^ _84654 : [(2671 ^ _84654) ^ [_176886] : [subset(_176886, _176546), -(in(_176886, _176544))], (2665 ^ _84654) ^ [_176714] : [in(_176714, _176544), -(subset(_176714, _176546))]]], (4923 ^ _84654) ^ [] : [-(ordinal(empty_set))], (4247 ^ _84654) ^ [_232733, _232735, _232737] : [-(element(join(_232737, _232735, _232733), the_carrier(_232737))), -(empty_carrier(_232737)), join_semilatt_str(_232737), element(_232735, the_carrier(_232737)), element(_232733, the_carrier(_232737))], (9108 ^ _84654) ^ [_413205, _413207] : [element(_413207, powerset(_413205)), -(subset(_413207, _413205))], (7824 ^ _84654) ^ [_369889, _369891] : [in(_369889, _369891), -(apply(7816 ^ [_369891], _369889) = singleton(_369889))], (9062 ^ _84654) ^ [_411689, _411691] : [relation(_411689), -(relation_field(relation_restriction(_411689, _411691)) = _411691), well_ordering(_411689), subset(_411691, relation_field(_411689))], (4613 ^ _84654) ^ [_243033] : [top_str(_243033), -(one_sorted_str(_243033))], (1324 ^ _84654) ^ [_129421] : [v3_membered(_129421), 1327 ^ _84654 : [(1328 ^ _84654) ^ [_129563] : [element(_129563, powerset(_129421)), 1331 ^ _84654 : [(1336 ^ _84654) ^ [] : [-(v3_membered(_129563))], (1334 ^ _84654) ^ [] : [-(v2_membered(_129563))], (1332 ^ _84654) ^ [] : [-(v1_membered(_129563))]]]]], (2445 ^ _84654) ^ [_169038, _169040, _169042] : [subset(_169038, cartesian_product2(_169042, _169040)), -(relation_of2(_169038, _169042, _169040))], (10035 ^ _84654) ^ [_443867] : [ordinal(_443867), -(well_ordering(inclusion_relation(_443867)))], (4795 ^ _84654) ^ [_248849, _248851] : [4810 ^ _84654 : [(4813 ^ _84654) ^ [] : [-(function(relation_composition(_248851, _248849)))], (4811 ^ _84654) ^ [] : [-(relation(relation_composition(_248851, _248849)))]], relation(_248851), function(_248851), relation(_248849), function(_248849)], (6279 ^ _84654) ^ [_300034, _300036, _300038] : [relation(_300036), relation(_300034), function(_300034), 6291 ^ _84654 : [(6304 ^ _84654) ^ [_300996, _300998] : [-(in(ordered_pair(_300998, _300996), 6290 ^ [_300034, _300036, _300038])), in(_300998, _300038), in(_300996, _300038), in(ordered_pair(apply(_300034, _300998), apply(_300034, _300996)), _300036)], (6294 ^ _84654) ^ [_300607, _300609] : [in(ordered_pair(_300609, _300607), 6290 ^ [_300034, _300036, _300038]), 6297 ^ _84654 : [(6302 ^ _84654) ^ [] : [-(in(ordered_pair(apply(_300034, _300609), apply(_300034, _300607)), _300036))], (6300 ^ _84654) ^ [] : [-(in(_300607, _300038))], (6298 ^ _84654) ^ [] : [-(in(_300609, _300038))]]], (6292 ^ _84654) ^ [] : [-(relation(6290 ^ [_300034, _300036, _300038]))]]], (348 ^ _84654) ^ [_95311, _95313] : [-(join_semilatt_str(_95311)), _95313 = _95311, join_semilatt_str(_95313)], (8395 ^ _84654) ^ [_389683, _389685, _389687] : [relation(_389683), in(ordered_pair(_389687, _389685), _389683), 8402 ^ _84654 : [(8405 ^ _84654) ^ [] : [-(in(_389685, relation_rng(_389683)))], (8403 ^ _84654) ^ [] : [-(in(_389687, relation_dom(_389683)))]]], (750 ^ _84654) ^ [_108346, _108348] : [_108348 = _108346, -(the_L_join(_108348) = the_L_join(_108346))], (8082 ^ _84654) ^ [_379070, _379072, _379074] : [relation(_379070), 8085 ^ _84654 : [(8097 ^ _84654) ^ [] : [-(in(_379074, relation_image(_379070, _379072))), 8098 ^ _84654 : [(8099 ^ _84654) ^ [_379671] : [in(_379671, relation_dom(_379070)), in(ordered_pair(_379671, _379074), _379070), in(_379671, _379072)]]], (8086 ^ _84654) ^ [] : [in(_379074, relation_image(_379070, _379072)), 8090 ^ _84654 : [(8095 ^ _84654) ^ [] : [-(in(8089 ^ [_379070, _379072, _379074], _379072))], (8093 ^ _84654) ^ [] : [-(in(ordered_pair(8089 ^ [_379070, _379072, _379074], _379074), _379070))], (8091 ^ _84654) ^ [] : [-(in(8089 ^ [_379070, _379072, _379074], relation_dom(_379070)))]]]]], (254 ^ _84654) ^ [_92535, _92537, _92539, _92541] : [-(equipotent(_92539, _92535)), equipotent(_92541, _92537), _92541 = _92539, _92537 = _92535], (1062 ^ _84654) ^ [_119843, _119845] : [_119845 = _119843, -(inclusion_relation(_119845) = inclusion_relation(_119843))], (4425 ^ _84654) ^ [_237407, _237409, _237411] : [-(element(join_commut(_237411, _237409, _237407), the_carrier(_237411))), -(empty_carrier(_237411)), join_commutative(_237411), join_semilatt_str(_237411), element(_237409, the_carrier(_237411)), element(_237407, the_carrier(_237411))], (5637 ^ _84654) ^ [] : [-(empty(5629 ^ []))], (5037 ^ _84654) ^ [_256998, _257000] : [v3_membered(_257000), 5040 ^ _84654 : [(5045 ^ _84654) ^ [] : [-(v3_membered(set_difference(_257000, _256998)))], (5043 ^ _84654) ^ [] : [-(v2_membered(set_difference(_257000, _256998)))], (5041 ^ _84654) ^ [] : [-(v1_membered(set_difference(_257000, _256998)))]]], (2677 ^ _84654) ^ [_177065, _177067] : [-(_177065 = powerset(_177067)), 2681 ^ _84654 : [(2684 ^ _84654) ^ [] : [subset(2678 ^ [_177065, _177067], _177067)], (2682 ^ _84654) ^ [] : [-(in(2678 ^ [_177065, _177067], _177065))]], 2685 ^ _84654 : [(2688 ^ _84654) ^ [] : [in(2678 ^ [_177065, _177067], _177065)], (2686 ^ _84654) ^ [] : [-(subset(2678 ^ [_177065, _177067], _177067))]]], (1394 ^ _84654) ^ [_131783] : [ordinal(_131783), 1397 ^ _84654 : [(1400 ^ _84654) ^ [] : [-(epsilon_connected(_131783))], (1398 ^ _84654) ^ [] : [-(epsilon_transitive(_131783))]]], (9122 ^ _84654) ^ [_413686, _413688] : [-(disjoint(_413688, _413686)), 9126 ^ _84654 : [(9129 ^ _84654) ^ [] : [-(in(9125 ^ [_413686, _413688], _413686))], (9127 ^ _84654) ^ [] : [-(in(9125 ^ [_413686, _413688], _413688))]]], (4921 ^ _84654) ^ [] : [-(epsilon_connected(empty_set))], (4745 ^ _84654) ^ [_247286, _247288] : [finite(_247288), -(finite(set_difference(_247288, _247286)))], (4841 ^ _84654) ^ [_250257, _250259] : [-(relation(set_intersection2(_250259, _250257))), relation(_250259), relation(_250257)], (4851 ^ _84654) ^ [_250542] : [empty(the_carrier(_250542)), -(empty_carrier(_250542)), one_sorted_str(_250542)], (8314 ^ _84654) ^ [_386795, _386797] : [relation(_386795), -(relation_restriction(_386795, _386797) = relation_dom_restriction(relation_rng_restriction(_386797, _386795), _386797))], (8971 ^ _84654) ^ [_408626, _408628] : [relation(_408626), function(_408626), 8978 ^ _84654 : [(8991 ^ _84654) ^ [] : [-(_408626 = identity_relation(_408628)), relation_dom(_408626) = _408628, 8997 ^ _84654 : [(9000 ^ _84654) ^ [] : [apply(_408626, 8996 ^ [_408626, _408628]) = 8996 ^ [_408626, _408628]], (8998 ^ _84654) ^ [] : [-(in(8996 ^ [_408626, _408628], _408628))]]], (8979 ^ _84654) ^ [] : [_408626 = identity_relation(_408628), 8982 ^ _84654 : [(8985 ^ _84654) ^ [_409045] : [in(_409045, _408628), -(apply(_408626, _409045) = _409045)], (8983 ^ _84654) ^ [] : [-(relation_dom(_408626) = _408628)]]]]], (4565 ^ _84654) ^ [_241407] : [-(relation(identity_relation(_241407)))], (2874 ^ _84654) ^ [_184000] : [relation(_184000), 2877 ^ _84654 : [(2878 ^ _84654) ^ [] : [well_founded_relation(_184000), 2881 ^ _84654 : [(2882 ^ _84654) ^ [_184267] : [subset(_184267, relation_field(_184000)), -(_184267 = empty_set), 2890 ^ _84654 : [(2893 ^ _84654) ^ [] : [-(disjoint(fiber(_184000, 2889 ^ [_184000, _184267]), _184267))], (2891 ^ _84654) ^ [] : [-(in(2889 ^ [_184000, _184267], _184267))]]]]], (2895 ^ _84654) ^ [] : [-(well_founded_relation(_184000)), 2897 ^ _84654 : [(2902 ^ _84654) ^ [_184950] : [in(_184950, 2896 ^ [_184000]), disjoint(fiber(_184000, _184950), 2896 ^ [_184000])], (2900 ^ _84654) ^ [] : [2896 ^ [_184000] = empty_set], (2898 ^ _84654) ^ [] : [-(subset(2896 ^ [_184000], relation_field(_184000)))]]]]], (5740 ^ _84654) ^ [] : [-(epsilon_transitive(5736 ^ []))], (8937 ^ _84654) ^ [_407434] : [ordinal(_407434), 8940 ^ _84654 : [(8941 ^ _84654) ^ [_407572] : [ordinal(_407572), 8944 ^ _84654 : [(8951 ^ _84654) ^ [] : [ordinal_subset(succ(_407434), _407572), -(in(_407434, _407572))], (8945 ^ _84654) ^ [] : [in(_407434, _407572), -(ordinal_subset(succ(_407434), _407572))]]]]], (30 ^ _84654) ^ [_85697, _85699] : [-(v1_xreal_0(_85697)), _85699 = _85697, v1_xreal_0(_85699)], (4995 ^ _84654) ^ [_255445, _255447] : [v5_membered(_255447), 4998 ^ _84654 : [(5001 ^ _84654) ^ [] : [-(v2_membered(set_intersection2(_255447, _255445)))], (5003 ^ _84654) ^ [] : [-(v3_membered(set_intersection2(_255447, _255445)))], (5005 ^ _84654) ^ [] : [-(v4_membered(set_intersection2(_255447, _255445)))], (5007 ^ _84654) ^ [] : [-(v5_membered(set_intersection2(_255447, _255445)))], (4999 ^ _84654) ^ [] : [-(v1_membered(set_intersection2(_255447, _255445)))]]], (8163 ^ _84654) ^ [_381768, _381770, _381772, _381774] : [relation_of2_as_subset(_381768, _381770, _381774), subset(relation_rng(_381768), _381772), -(relation_of2_as_subset(_381768, _381770, _381772))], (3567 ^ _84654) ^ [_208971] : [_208971 = omega, 3570 ^ _84654 : [(3577 ^ _84654) ^ [_209320] : [ordinal(_209320), -(subset(_208971, _209320)), in(empty_set, _209320), being_limit_ordinal(_209320)], (3571 ^ _84654) ^ [] : [-(in(empty_set, _208971))], (3575 ^ _84654) ^ [] : [-(ordinal(_208971))], (3573 ^ _84654) ^ [] : [-(being_limit_ordinal(_208971))]]], (5939 ^ _84654) ^ [_286893, _286895] : [equipotent(_286895, _286893), -(are_equipotent(_286895, _286893))], (4935 ^ _84654) ^ [_253198] : [empty(singleton(_253198))], (2113 ^ _84654) ^ [_157124] : [relation(_157124), 2116 ^ _84654 : [(2123 ^ _84654) ^ [] : [is_transitive_in(_157124, relation_field(_157124)), -(transitive(_157124))], (2117 ^ _84654) ^ [] : [transitive(_157124), -(is_transitive_in(_157124, relation_field(_157124)))]]], (9699 ^ _84654) ^ [_433195] : [relation(_433195), 9702 ^ _84654 : [(9703 ^ _84654) ^ [_433351] : [relation(_433351), 9706 ^ _84654 : [(9707 ^ _84654) ^ [_433503] : [relation(_433503), function(_433503), -(well_ordering(_433351)), well_ordering(_433195), relation_isomorphism(_433195, _433351, _433503)]]]]], (5085 ^ _84654) ^ [_258495, _258497] : [empty(unordered_pair(_258497, _258495))], (4295 ^ _84654) ^ [] : [true___, -(true___)], (5191 ^ _84654) ^ [] : [-(v2_membered(empty_set))], (1676 ^ _84654) ^ [_140741] : [relation(_140741), 1679 ^ _84654 : [(1680 ^ _84654) ^ [_140927, _140929] : [relation(_140927), 1683 ^ _84654 : [(1684 ^ _84654) ^ [] : [_140927 = relation_dom_restriction(_140741, _140929), 1687 ^ _84654 : [(1696 ^ _84654) ^ [_141531, _141533] : [-(in(ordered_pair(_141533, _141531), _140927)), in(_141533, _140929), in(ordered_pair(_141533, _141531), _140741)], (1688 ^ _84654) ^ [_141252, _141254] : [in(ordered_pair(_141254, _141252), _140927), 1691 ^ _84654 : [(1694 ^ _84654) ^ [] : [-(in(ordered_pair(_141254, _141252), _140741))], (1692 ^ _84654) ^ [] : [-(in(_141254, _140929))]]]]], (1706 ^ _84654) ^ [] : [-(_140927 = relation_dom_restriction(_140741, _140929)), 1719 ^ _84654 : [(1724 ^ _84654) ^ [] : [in(ordered_pair(1707 ^ [_140741, _140927, _140929], 1708 ^ [_140741, _140927, _140929]), _140927)], (1722 ^ _84654) ^ [] : [-(in(ordered_pair(1707 ^ [_140741, _140927, _140929], 1708 ^ [_140741, _140927, _140929]), _140741))], (1720 ^ _84654) ^ [] : [-(in(1707 ^ [_140741, _140927, _140929], _140929))]], 1711 ^ _84654 : [(1714 ^ _84654) ^ [] : [in(1707 ^ [_140741, _140927, _140929], _140929), in(ordered_pair(1707 ^ [_140741, _140927, _140929], 1708 ^ [_140741, _140927, _140929]), _140741)], (1712 ^ _84654) ^ [] : [-(in(ordered_pair(1707 ^ [_140741, _140927, _140929], 1708 ^ [_140741, _140927, _140929]), _140927))]]]]]]], (9869 ^ _84654) ^ [_438276, _438278] : [-(in(_438276, _438278)), -(set_difference(_438278, singleton(_438276)) = _438278)], (3394 ^ _84654) ^ [_203106] : [relation(_203106), 3397 ^ _84654 : [(3412 ^ _84654) ^ [] : [-(well_ordering(_203106)), reflexive(_203106), transitive(_203106), antisymmetric(_203106), connected(_203106), well_founded_relation(_203106)], (3398 ^ _84654) ^ [] : [well_ordering(_203106), 3401 ^ _84654 : [(3404 ^ _84654) ^ [] : [-(transitive(_203106))], (3406 ^ _84654) ^ [] : [-(antisymmetric(_203106))], (3408 ^ _84654) ^ [] : [-(connected(_203106))], (3410 ^ _84654) ^ [] : [-(well_founded_relation(_203106))], (3402 ^ _84654) ^ [] : [-(reflexive(_203106))]]]]], (9038 ^ _84654) ^ [_410862, _410864] : [in(_410864, _410862), -(subset(singleton(_410864), _410862))], (8505 ^ _84654) ^ [_393258, _393260] : [relation(_393258), function(_393258), 8512 ^ _84654 : [(8513 ^ _84654) ^ [_393507] : [relation(_393507), function(_393507), in(_393260, relation_dom(relation_composition(_393507, _393258))), -(apply(relation_composition(_393507, _393258), _393260) = apply(_393258, apply(_393507, _393260)))]]], (526 ^ _84654) ^ [_100839, _100841, _100843, _100845] : [-(disjoint(_100843, _100839)), disjoint(_100845, _100841), _100845 = _100843, _100841 = _100839], (8199 ^ _84654) ^ [_383052, _383054, _383056] : [relation(_383052), 8202 ^ _84654 : [(8214 ^ _84654) ^ [] : [-(in(_383056, relation_inverse_image(_383052, _383054))), 8215 ^ _84654 : [(8216 ^ _84654) ^ [_383653] : [in(_383653, relation_rng(_383052)), in(ordered_pair(_383056, _383653), _383052), in(_383653, _383054)]]], (8203 ^ _84654) ^ [] : [in(_383056, relation_inverse_image(_383052, _383054)), 8207 ^ _84654 : [(8212 ^ _84654) ^ [] : [-(in(8206 ^ [_383052, _383054, _383056], _383054))], (8210 ^ _84654) ^ [] : [-(in(ordered_pair(_383056, 8206 ^ [_383052, _383054, _383056]), _383052))], (8208 ^ _84654) ^ [] : [-(in(8206 ^ [_383052, _383054, _383056], relation_rng(_383052)))]]]]], (4301 ^ _84654) ^ [] : [true___, -(true___)], (5738 ^ _84654) ^ [] : [empty(5736 ^ [])], (8415 ^ _84654) ^ [_390388, _390390] : [relation(_390388), function(_390388), 8422 ^ _84654 : [(8423 ^ _84654) ^ [_390638] : [relation(_390638), function(_390638), 8430 ^ _84654 : [(8439 ^ _84654) ^ [] : [-(in(_390390, relation_dom(relation_composition(_390638, _390388)))), in(_390390, relation_dom(_390638)), in(apply(_390638, _390390), relation_dom(_390388))], (8431 ^ _84654) ^ [] : [in(_390390, relation_dom(relation_composition(_390638, _390388))), 8434 ^ _84654 : [(8437 ^ _84654) ^ [] : [-(in(apply(_390638, _390390), relation_dom(_390388)))], (8435 ^ _84654) ^ [] : [-(in(_390390, relation_dom(_390638)))]]]]]]], (146 ^ _84654) ^ [_89243, _89245] : [-(v1_membered(_89243)), _89245 = _89243, v1_membered(_89245)], (8681 ^ _84654) ^ [_399108, _399110] : [relation(_399108), transitive(_399108), -(transitive(relation_restriction(_399108, _399110)))], (4583 ^ _84654) ^ [_242086, _242088] : [relation(_242088), -(relation(relation_dom_restriction(_242088, _242086)))], (8619 ^ _84654) ^ [_397044, _397046] : [ordinal(_397044), in(_397046, _397044), -(ordinal(_397046))], (9147 ^ _84654) ^ [_414538, _414540] : [-(set_difference(set_union2(_414540, _414538), _414538) = set_difference(_414540, _414538))], (10208 ^ _84654) ^ [_449632, _449634, _449636] : [-(in(_449632, 10204 ^ [_449636])), in(_449634, 10204 ^ [_449636]), subset(_449632, _449634)], (4465 ^ _84654) ^ [] : [true___, -(true___)], (288 ^ _84654) ^ [_93541, _93543] : [-(meet_commutative(_93541)), _93543 = _93541, meet_commutative(_93543)], (9952 ^ _84654) ^ [_441006, _441008] : [subset(singleton(_441008), singleton(_441006)), -(_441008 = _441006)], (1078 ^ _84654) ^ [_120448, _120450, _120452, _120454] : [-(ordered_pair(_120454, _120450) = ordered_pair(_120452, _120448)), _120454 = _120452, _120450 = _120448], (5590 ^ _84654) ^ [] : [-(function(5586 ^ []))], (9515 ^ _84654) ^ [_427137] : [-(_427137 = empty_set), 9518 ^ _84654 : [(9519 ^ _84654) ^ [_427297] : [element(_427297, powerset(_427137)), 9522 ^ _84654 : [(9523 ^ _84654) ^ [_427451] : [element(_427451, _427137), -(in(_427451, _427297)), -(in(_427451, subset_complement(_427137, _427297)))]]]]], (8234 ^ _84654) ^ [_384296, _384298, _384300, _384302] : [relation_of2_as_subset(_384296, _384298, _384302), subset(_384302, _384300), -(relation_of2_as_subset(_384296, _384298, _384300))], (8393 ^ _84654) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (2284 ^ _84654) ^ [_162920] : [-(empty_carrier(_162920)), join_semilatt_str(_162920), 2291 ^ _84654 : [(2292 ^ _84654) ^ [_163171] : [element(_163171, the_carrier(_162920)), 2295 ^ _84654 : [(2296 ^ _84654) ^ [_163335] : [element(_163335, the_carrier(_162920)), -(join(_162920, _163171, _163335) = apply_binary_as_element(the_carrier(_162920), the_carrier(_162920), the_carrier(_162920), the_L_join(_162920), _163171, _163335))]]]]], (1388 ^ _84654) ^ [_131597] : [v5_membered(_131597), -(v4_membered(_131597))], (10093 ^ _84654) ^ [_445781, _445783, _445785] : [relation(_445781), function(_445781), 10100 ^ _84654 : [(10109 ^ _84654) ^ [] : [-(in(ordered_pair(_445785, _445783), _445781)), in(_445785, relation_dom(_445781)), _445783 = apply(_445781, _445785)], (10101 ^ _84654) ^ [] : [in(ordered_pair(_445785, _445783), _445781), 10104 ^ _84654 : [(10107 ^ _84654) ^ [] : [-(_445783 = apply(_445781, _445785))], (10105 ^ _84654) ^ [] : [-(in(_445785, relation_dom(_445781)))]]]]], (540 ^ _84654) ^ [_101255, _101257] : [-(empty(_101255)), _101257 = _101255, empty(_101257)], (196 ^ _84654) ^ [_90718, _90720] : [-(natural(_90718)), _90720 = _90718, natural(_90720)], (8629 ^ _84654) ^ [_397353, _397355, _397357] : [relation_of2_as_subset(_397353, _397357, _397355), 8632 ^ _84654 : [(8642 ^ _84654) ^ [] : [relation_rng_as_subset(_397357, _397355, _397353) = _397355, 8645 ^ _84654 : [(8646 ^ _84654) ^ [_397948] : [in(_397948, _397355), -(in(ordered_pair(8649 ^ [_397353, _397355, _397357, _397948], _397948), _397353))]]], (8633 ^ _84654) ^ [] : [8635 ^ _84654 : [(8638 ^ _84654) ^ [_397711] : [in(ordered_pair(_397711, 8634 ^ [_397353, _397355, _397357]), _397353)], (8636 ^ _84654) ^ [] : [-(in(8634 ^ [_397353, _397355, _397357], _397355))]], -(relation_rng_as_subset(_397357, _397355, _397353) = _397355)]]], (5023 ^ _84654) ^ [_256495, _256497] : [v1_membered(_256497), -(v1_membered(set_difference(_256497, _256495)))], (7923 ^ _84654) ^ [_373420, _373422, _373424, _373426] : [in(ordered_pair(_373426, _373424), cartesian_product2(_373422, _373420)), 7926 ^ _84654 : [(7929 ^ _84654) ^ [] : [-(in(_373424, _373420))], (7927 ^ _84654) ^ [] : [-(in(_373426, _373422))]]], (4193 ^ _84654) ^ [_231434] : [relation(_231434), function(_231434), one_to_one(_231434), -(function_inverse(_231434) = relation_inverse(_231434))], (9462 ^ _84654) ^ [_425331] : [relation(_425331), 9465 ^ _84654 : [(9466 ^ _84654) ^ [_425486] : [relation(_425486), 9469 ^ _84654 : [(9470 ^ _84654) ^ [_425637] : [relation(_425637), function(_425637), relation_isomorphism(_425331, _425486, _425637), -(relation_isomorphism(_425486, _425331, function_inverse(_425637)))]]]]], (5063 ^ _84654) ^ [_257784] : [ordinal(_257784), 5066 ^ _84654 : [(5073 ^ _84654) ^ [] : [-(ordinal(succ(_257784)))], (5067 ^ _84654) ^ [] : [empty(succ(_257784))], (5071 ^ _84654) ^ [] : [-(epsilon_connected(succ(_257784)))], (5069 ^ _84654) ^ [] : [-(epsilon_transitive(succ(_257784)))]]], (7049 ^ _84654) ^ [_337541] : [7053 ^ _84654 : [(7056 ^ _84654) ^ [] : [-(ordinal(7051 ^ [_337541]))], (7058 ^ _84654) ^ [] : [-(7050 ^ [_337541] = 7052 ^ [_337541])], (7060 ^ _84654) ^ [] : [-(ordinal(7052 ^ [_337541]))], (7062 ^ _84654) ^ [] : [7051 ^ [_337541] = 7052 ^ [_337541]], (7054 ^ _84654) ^ [] : [-(7050 ^ [_337541] = 7051 ^ [_337541])]], 7064 ^ _84654 : [(7076 ^ _84654) ^ [_338772] : [-(in(_338772, 7063 ^ [_337541])), 7077 ^ _84654 : [(7078 ^ _84654) ^ [_338876] : [in(_338876, _337541), _338876 = _338772, ordinal(_338772)]]], (7065 ^ _84654) ^ [_338376] : [in(_338376, 7063 ^ [_337541]), 7069 ^ _84654 : [(7074 ^ _84654) ^ [] : [-(ordinal(_338376))], (7072 ^ _84654) ^ [] : [-(7068 ^ [_337541, _338376] = _338376)], (7070 ^ _84654) ^ [] : [-(in(7068 ^ [_337541, _338376], _337541))]]]]], (5312 ^ _84654) ^ [_265969, _265971] : [disjoint(singleton(_265971), _265969), in(_265971, _265969)], (8927 ^ _84654) ^ [_407149, _407151] : [relation(_407149), well_ordering(_407149), -(well_ordering(relation_restriction(_407149, _407151)))], (4696 ^ _84654) ^ [] : [-(one_sorted_str(4694 ^ []))], (788 ^ _84654) ^ [_109921, _109923, _109925, _109927, _109929, _109931] : [-(apply_binary(_109931, _109927, _109923) = apply_binary(_109929, _109925, _109921)), _109931 = _109929, _109927 = _109925, _109923 = _109921], (1458 ^ _84654) ^ [_133927] : [-(preboolean(_133927)), cup_closed(_133927), diff_closed(_133927)], (4825 ^ _84654) ^ [_249682] : [one_sorted_str(_249682), 4828 ^ _84654 : [(4837 ^ _84654) ^ [] : [-(v4_membered(empty_carrier_subset(_249682)))], (4835 ^ _84654) ^ [] : [-(v3_membered(empty_carrier_subset(_249682)))], (4839 ^ _84654) ^ [] : [-(v5_membered(empty_carrier_subset(_249682)))], (4829 ^ _84654) ^ [] : [-(empty(empty_carrier_subset(_249682)))], (4831 ^ _84654) ^ [] : [-(v1_membered(empty_carrier_subset(_249682)))], (4833 ^ _84654) ^ [] : [-(v2_membered(empty_carrier_subset(_249682)))]]], (9509 ^ _84654) ^ [_426912, _426914] : [9510 ^ _84654 : [(9511 ^ _84654) ^ [_426985] : [in(_426985, set_intersection2(_426914, _426912))]], disjoint(_426914, _426912)], (5593 ^ _84654) ^ [_275574, _275576] : [-(relation_of2(5591 ^ [_275574, _275576], _275576, _275574))], (4711 ^ _84654) ^ [_246102, _246104] : [-(relation_of2_as_subset(4709 ^ [_246102, _246104], _246104, _246102))], (5695 ^ _84654) ^ [] : [-(epsilon_connected(5683 ^ []))], (4879 ^ _84654) ^ [_251483, _251485] : [v2_membered(_251485), 4882 ^ _84654 : [(4885 ^ _84654) ^ [] : [-(v2_membered(set_intersection2(_251485, _251483)))], (4883 ^ _84654) ^ [] : [-(v1_membered(set_intersection2(_251485, _251483)))]]], (358 ^ _84654) ^ [_95662, _95664, _95666, _95668, _95670, _95672] : [-(below(_95670, _95666, _95662)), below(_95672, _95668, _95664), _95672 = _95670, _95668 = _95666, _95664 = _95662], (8017 ^ _84654) ^ [_376693] : [one_sorted_str(_376693), -(cast_as_carrier_subset(_376693) = the_carrier(_376693))], (2853 ^ _84654) ^ [_183263, _183265, _183267] : [-(_183263 = unordered_pair(_183267, _183265)), 2857 ^ _84654 : [(2862 ^ _84654) ^ [] : [2854 ^ [_183263, _183265, _183267] = _183265], (2860 ^ _84654) ^ [] : [2854 ^ [_183263, _183265, _183267] = _183267], (2858 ^ _84654) ^ [] : [-(in(2854 ^ [_183263, _183265, _183267], _183263))]], 2863 ^ _84654 : [(2864 ^ _84654) ^ [] : [-(2854 ^ [_183263, _183265, _183267] = _183267), -(2854 ^ [_183263, _183265, _183267] = _183265)], (2870 ^ _84654) ^ [] : [in(2854 ^ [_183263, _183265, _183267], _183263)]]], (4533 ^ _84654) ^ [_240316, _240318, _240320] : [relation_of2(_240316, _240320, _240318), -(element(relation_rng_as_subset(_240320, _240318, _240316), powerset(_240318)))], (4708 ^ _84654) ^ [_245963] : [-(element(4706 ^ [_245963], _245963))], (4667 ^ _84654) ^ [_244644] : [top_str(_244644), -(element(the_topology(_244644), powerset(powerset(the_carrier(_244644)))))], (4235 ^ _84654) ^ [] : [true___, -(true___)], (8863 ^ _84654) ^ [_405021] : [-(subset(empty_set, _405021))], (4905 ^ _84654) ^ [_252336] : [-(relation(identity_relation(_252336)))], (4363 ^ _84654) ^ [_235790, _235792, _235794] : [-(element(meet(_235794, _235792, _235790), the_carrier(_235794))), -(empty_carrier(_235794)), meet_semilatt_str(_235794), element(_235792, the_carrier(_235794)), element(_235790, the_carrier(_235794))], (1468 ^ _84654) ^ [_134196] : [1479 ^ _84654 : [(1484 ^ _84654) ^ [] : [-(one_to_one(_134196))], (1482 ^ _84654) ^ [] : [-(function(_134196))], (1480 ^ _84654) ^ [] : [-(relation(_134196))]], relation(_134196), empty(_134196), function(_134196)], (8133 ^ _84654) ^ [_380823, _380825] : [relation(_380823), subset(_380825, relation_dom(_380823)), -(subset(_380825, relation_inverse_image(_380823, relation_image(_380823, _380825))))], (4867 ^ _84654) ^ [_251059, _251061] : [v1_membered(_251061), -(v1_membered(set_intersection2(_251061, _251059)))], (5687 ^ _84654) ^ [] : [-(function(5683 ^ []))], (2594 ^ _84654) ^ [_174259, _174261] : [relation(_174259), 2597 ^ _84654 : [(2598 ^ _84654) ^ [] : [_174259 = inclusion_relation(_174261), 2601 ^ _84654 : [(2604 ^ _84654) ^ [_174622, _174624] : [in(_174624, _174261), in(_174622, _174261), 2611 ^ _84654 : [(2618 ^ _84654) ^ [] : [subset(_174624, _174622), -(in(ordered_pair(_174624, _174622), _174259))], (2612 ^ _84654) ^ [] : [in(ordered_pair(_174624, _174622), _174259), -(subset(_174624, _174622))]]], (2602 ^ _84654) ^ [] : [-(relation_field(_174259) = _174261)]]], (2624 ^ _84654) ^ [] : [-(_174259 = inclusion_relation(_174261)), relation_field(_174259) = _174261, 2631 ^ _84654 : [(2636 ^ _84654) ^ [] : [2637 ^ _84654 : [(2640 ^ _84654) ^ [] : [subset(2629 ^ [_174259, _174261], 2630 ^ [_174259, _174261])], (2638 ^ _84654) ^ [] : [-(in(ordered_pair(2629 ^ [_174259, _174261], 2630 ^ [_174259, _174261]), _174259))]], 2641 ^ _84654 : [(2644 ^ _84654) ^ [] : [in(ordered_pair(2629 ^ [_174259, _174261], 2630 ^ [_174259, _174261]), _174259)], (2642 ^ _84654) ^ [] : [-(subset(2629 ^ [_174259, _174261], 2630 ^ [_174259, _174261]))]]], (2634 ^ _84654) ^ [] : [-(in(2630 ^ [_174259, _174261], _174261))], (2632 ^ _84654) ^ [] : [-(in(2629 ^ [_174259, _174261], _174261))]]]]], (88 ^ _84654) ^ [_87498, _87500, _87502, _87504] : [-(is_transitive_in(_87502, _87498)), is_transitive_in(_87504, _87500), _87504 = _87502, _87500 = _87498], (4753 ^ _84654) ^ [] : [-(relation(empty_set))], (1514 ^ _84654) ^ [_135543] : [v3_membered(_135543), -(v2_membered(_135543))], (2692 ^ _84654) ^ [_177587] : [-(empty_carrier(_177587)), meet_semilatt_str(_177587), 2699 ^ _84654 : [(2700 ^ _84654) ^ [_177838] : [element(_177838, the_carrier(_177587)), 2703 ^ _84654 : [(2704 ^ _84654) ^ [_178002] : [element(_178002, the_carrier(_177587)), -(meet(_177587, _177838, _178002) = apply_binary_as_element(the_carrier(_177587), the_carrier(_177587), the_carrier(_177587), the_L_meet(_177587), _177838, _178002))]]]]], (5177 ^ _84654) ^ [_261564] : [empty(relation_dom(_261564)), -(empty(_261564)), relation(_261564)], (7090 ^ _84654) ^ [_339264, _339266, _339268] : [element(_339266, powerset(powerset(_339268))), relation(_339264), function(_339264), 7106 ^ _84654 : [(7109 ^ _84654) ^ [] : [-(in(relation_image(_339264, 7104 ^ [_339264, _339266, _339268]), _339266))], (7111 ^ _84654) ^ [] : [-(7103 ^ [_339264, _339266, _339268] = 7105 ^ [_339264, _339266, _339268])], (7113 ^ _84654) ^ [] : [-(in(relation_image(_339264, 7105 ^ [_339264, _339266, _339268]), _339266))], (7115 ^ _84654) ^ [] : [7104 ^ [_339264, _339266, _339268] = 7105 ^ [_339264, _339266, _339268]], (7107 ^ _84654) ^ [] : [-(7103 ^ [_339264, _339266, _339268] = 7104 ^ [_339264, _339266, _339268])]], 7117 ^ _84654 : [(7129 ^ _84654) ^ [_341018] : [-(in(_341018, 7116 ^ [_339264, _339266, _339268])), 7130 ^ _84654 : [(7131 ^ _84654) ^ [_341142] : [in(_341142, powerset(relation_dom(_339264))), _341142 = _341018, in(relation_image(_339264, _341018), _339266)]]], (7118 ^ _84654) ^ [_340550] : [in(_340550, 7116 ^ [_339264, _339266, _339268]), 7122 ^ _84654 : [(7127 ^ _84654) ^ [] : [-(in(relation_image(_339264, _340550), _339266))], (7125 ^ _84654) ^ [] : [-(7121 ^ [_339264, _339266, _339268, _340550] = _340550)], (7123 ^ _84654) ^ [] : [-(in(7121 ^ [_339264, _339266, _339268, _340550], powerset(relation_dom(_339264))))]]]]], (3040 ^ _84654) ^ [_190224] : [epsilon_connected(_190224), 3043 ^ _84654 : [(3044 ^ _84654) ^ [_190400, _190402] : [in(_190402, _190224), in(_190400, _190224), -(in(_190402, _190400)), -(_190402 = _190400), -(in(_190400, _190402))]]], (5707 ^ _84654) ^ [] : [empty(5705 ^ [])], (744 ^ _84654) ^ [_108128, _108130] : [_108130 = _108128, -(the_topology(_108130) = the_topology(_108128))], (9347 ^ _84654) ^ [_421335] : [topological_space(_421335), top_str(_421335), 9354 ^ _84654 : [(9355 ^ _84654) ^ [_421611] : [element(_421611, powerset(the_carrier(_421335))), 9359 ^ _84654 : [(9362 ^ _84654) ^ [_422002] : [element(_422002, powerset(the_carrier(_421335))), 9365 ^ _84654 : [(9374 ^ _84654) ^ [] : [-(in(_422002, 9358 ^ [_421335, _421611])), closed_subset(_422002, _421335), subset(_421611, _422002)], (9366 ^ _84654) ^ [] : [in(_422002, 9358 ^ [_421335, _421611]), 9369 ^ _84654 : [(9372 ^ _84654) ^ [] : [-(subset(_421611, _422002))], (9370 ^ _84654) ^ [] : [-(closed_subset(_422002, _421335))]]]]], (9384 ^ _84654) ^ [] : [-(topstr_closure(_421335, _421611) = meet_of_subsets(the_carrier(_421335), 9358 ^ [_421335, _421611]))], (9360 ^ _84654) ^ [] : [-(element(9358 ^ [_421335, _421611], powerset(powerset(the_carrier(_421335)))))]]]]], (9496 ^ _84654) ^ [_426453] : [ordinal(_426453), -(connected(inclusion_relation(_426453)))], (7975 ^ _84654) ^ [_375135, _375137] : [relation(_375135), -(subset(relation_rng(relation_rng_restriction(_375137, _375135)), _375137))], (4315 ^ _84654) ^ [] : [true___, -(true___)], (2097 ^ _84654) ^ [_156693] : [relation(_156693), 2100 ^ _84654 : [(2107 ^ _84654) ^ [] : [is_connected_in(_156693, relation_field(_156693)), -(connected(_156693))], (2101 ^ _84654) ^ [] : [connected(_156693), -(is_connected_in(_156693, relation_field(_156693)))]]], (9386 ^ _84654) ^ [_422738] : [relation(_422738), 9389 ^ _84654 : [(9390 ^ _84654) ^ [_422885] : [relation(_422885), subset(relation_rng(_422738), relation_dom(_422885)), -(relation_dom(relation_composition(_422738, _422885)) = relation_dom(_422738))]]], (8561 ^ _84654) ^ [_395277, _395279] : [relation(_395277), reflexive(_395277), -(reflexive(relation_restriction(_395277, _395279)))], (7699 ^ _84654) ^ [_365128] : [7705 ^ _84654 : [(7712 ^ _84654) ^ [] : [7703 ^ [_365128] = 7704 ^ [_365128]], (7706 ^ _84654) ^ [] : [-(in(7702 ^ [_365128], _365128))], (7710 ^ _84654) ^ [] : [-(7704 ^ [_365128] = singleton(7702 ^ [_365128]))], (7708 ^ _84654) ^ [] : [-(7703 ^ [_365128] = singleton(7702 ^ [_365128]))]], 7714 ^ _84654 : [(7717 ^ _84654) ^ [_365982] : [_365982 = singleton(7713 ^ [_365128])], (7715 ^ _84654) ^ [] : [-(in(7713 ^ [_365128], _365128))]], 7719 ^ _84654 : [(7726 ^ _84654) ^ [_366354] : [in(_366354, _365128), -(apply(7718 ^ [_365128], _366354) = singleton(_366354))], (7720 ^ _84654) ^ [] : [-(relation(7718 ^ [_365128]))], (7724 ^ _84654) ^ [] : [-(relation_dom(7718 ^ [_365128]) = _365128)], (7722 ^ _84654) ^ [] : [-(function(7718 ^ [_365128]))]]], (724 ^ _84654) ^ [_107450, _107452, _107454, _107456, _107458, _107460] : [-(unordered_triple(_107460, _107456, _107452) = unordered_triple(_107458, _107454, _107450)), _107460 = _107458, _107456 = _107454, _107452 = _107450], (5682 ^ _84654) ^ [] : [-(function(5676 ^ []))], (1586 ^ _84654) ^ [_137816, _137818, _137820] : [-(subset_intersection2(_137820, _137818, _137816) = subset_intersection2(_137820, _137816, _137818)), element(_137818, powerset(_137820)), element(_137816, powerset(_137820))], (10175 ^ _84654) ^ [_448395] : [-(union(powerset(_448395)) = _448395)], (3616 ^ _84654) ^ [_210409] : [top_str(_210409), 3619 ^ _84654 : [(3620 ^ _84654) ^ [_210552] : [element(_210552, powerset(the_carrier(_210409))), 3623 ^ _84654 : [(3630 ^ _84654) ^ [] : [in(_210552, the_topology(_210409)), -(open_subset(_210552, _210409))], (3624 ^ _84654) ^ [] : [open_subset(_210552, _210409), -(in(_210552, the_topology(_210409)))]]]]], (7911 ^ _84654) ^ [_372943, _372945] : [disjoint(_372945, _372943), -(disjoint(_372943, _372945))], (9990 ^ _84654) ^ [_442278, _442280, _442282, _442284] : [relation(_442278), 9993 ^ _84654 : [(10002 ^ _84654) ^ [] : [-(in(ordered_pair(_442284, _442282), relation_composition(identity_relation(_442280), _442278))), in(_442284, _442280), in(ordered_pair(_442284, _442282), _442278)], (9994 ^ _84654) ^ [] : [in(ordered_pair(_442284, _442282), relation_composition(identity_relation(_442280), _442278)), 9997 ^ _84654 : [(10000 ^ _84654) ^ [] : [-(in(ordered_pair(_442284, _442282), _442278))], (9998 ^ _84654) ^ [] : [-(in(_442284, _442280))]]]]], (1190 ^ _84654) ^ [_124487, _124489, _124491, _124493] : [-(subset_complement(_124493, _124489) = subset_complement(_124491, _124487)), _124493 = _124491, _124489 = _124487], (8479 ^ _84654) ^ [_392370] : [epsilon_transitive(_392370), 8482 ^ _84654 : [(8483 ^ _84654) ^ [_392506] : [ordinal(_392506), proper_subset(_392370, _392506), -(in(_392370, _392506))]]], (550 ^ _84654) ^ [_101578, _101580, _101582, _101584] : [-(well_orders(_101582, _101578)), well_orders(_101584, _101580), _101584 = _101582, _101580 = _101578], (5304 ^ _84654) ^ [_265640] : [singleton(_265640) = empty_set], (5209 ^ _84654) ^ [_262446] : [empty(_262446), 5212 ^ _84654 : [(5215 ^ _84654) ^ [] : [-(relation(relation_dom(_262446)))], (5213 ^ _84654) ^ [] : [-(empty(relation_dom(_262446)))]]], (5693 ^ _84654) ^ [] : [-(epsilon_transitive(5683 ^ []))], (4771 ^ _84654) ^ [_248047, _248049] : [4778 ^ _84654 : [(4781 ^ _84654) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_248049, _248047)))], (4779 ^ _84654) ^ [] : [-(relation(relation_dom_restriction(_248049, _248047)))]], relation(_248049), relation_empty_yielding(_248049)], (3943 ^ _84654) ^ [_222065, _222067] : [set_intersection2(_222067, _222065) = empty_set, -(disjoint(_222067, _222065))], (8040 ^ _84654) ^ [_377654, _377656, _377658] : [-(in(_377654, 8036 ^ [_377658])), in(_377656, 8036 ^ [_377658]), subset(_377654, _377656)]], input).
% 199.48/192.22  ncf('1',plain,[10255 : -(open_subset(10249 ^ [], 10246 ^ [])), 10261 : open_subset(10249 ^ [], 10246 ^ [])],start(10253 ^ 0)).
% 199.48/192.22  ncf('1.1',plain,[open_subset(10249 ^ [], 10246 ^ []), -(open_subset(subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])), 10246 ^ [])), 10249 ^ [] = subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])), 10246 ^ [] = 10246 ^ []],extension(696 ^ 3,bind([[_106196, _106198, _106200, _106202], [10246 ^ [], 10246 ^ [], subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])), 10249 ^ []]]))).
% 199.48/192.22  ncf('1.1.1',plain,[open_subset(subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])), 10246 ^ []), 8828 : -(closed_subset(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), 10246 ^ [])), 8828 : element(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), powerset(the_carrier(10246 ^ []))), 8818 : top_str(10246 ^ [])],extension(8814 ^ 4,bind([[_403426, _403572], [10246 ^ [], subset_complement(the_carrier(10246 ^ []), 10249 ^ [])]]))).
% 199.48/192.22  ncf('1.1.1.1',plain,[closed_subset(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), 10246 ^ [])],extension(10257 ^ 9)).
% 199.48/192.22  ncf('1.1.1.2',plain,[-(element(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), powerset(the_carrier(10246 ^ [])))), element(10249 ^ [], powerset(the_carrier(10246 ^ [])))],extension(4453 ^ 7,bind([[_238131, _238133], [10249 ^ [], the_carrier(10246 ^ [])]]))).
% 199.48/192.22  ncf('1.1.1.2.1',plain,[-(element(10249 ^ [], powerset(the_carrier(10246 ^ []))))],extension(10251 ^ 8)).
% 199.48/192.22  ncf('1.1.1.3',plain,[-(top_str(10246 ^ []))],extension(10248 ^ 5)).
% 199.48/192.22  ncf('1.1.2',plain,[-(10249 ^ [] = subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ []))), subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])) = 10249 ^ []],extension(4 ^ 4,bind([[_84885, _84887], [10249 ^ [], subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ []))]]))).
% 199.48/192.22  ncf('1.1.2.1',plain,[-(subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])) = 10249 ^ []), element(10249 ^ [], powerset(the_carrier(10246 ^ [])))],extension(5261 ^ 5,bind([[_264200, _264202], [10249 ^ [], the_carrier(10246 ^ [])]]))).
% 199.48/192.22  ncf('1.1.2.1.1',plain,[-(element(10249 ^ [], powerset(the_carrier(10246 ^ []))))],extension(10251 ^ 6)).
% 199.48/192.22  ncf('1.1.3',plain,[-(10246 ^ [] = 10246 ^ []), unordered_pair(10246 ^ [], 10246 ^ []) = unordered_pair(10246 ^ [], 10246 ^ []), -(10246 ^ [] = 10246 ^ [])],extension(7943 ^ 4,bind([[_374126, _374128, _374130, _374132], [10246 ^ [], 10246 ^ [], 10246 ^ [], 10246 ^ []]]))).
% 199.48/192.22  ncf('1.1.3.1',plain,[-(unordered_pair(10246 ^ [], 10246 ^ []) = unordered_pair(10246 ^ [], 10246 ^ []))],extension(1536 ^ 5,bind([[_136241, _136243], [10246 ^ [], 10246 ^ []]]))).
% 199.48/192.22  ncf('1.1.3.2',plain,[10246 ^ [] = 10246 ^ []],reduction('1.1')).
% 199.48/192.22  ncf('1.2',plain,[-(open_subset(10249 ^ [], 10246 ^ [])), open_subset(subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])), 10246 ^ []), subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])) = 10249 ^ [], 10246 ^ [] = 10246 ^ []],extension(696 ^ 3,bind([[_106196, _106198, _106200, _106202], [10246 ^ [], 10246 ^ [], 10249 ^ [], subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ []))]]))).
% 199.48/192.22  ncf('1.2.1',plain,[-(open_subset(subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])), 10246 ^ [])), 8822 : closed_subset(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), 10246 ^ []), 8822 : element(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), powerset(the_carrier(10246 ^ []))), 8818 : top_str(10246 ^ [])],extension(8814 ^ 4,bind([[_403426, _403572], [10246 ^ [], subset_complement(the_carrier(10246 ^ []), 10249 ^ [])]]))).
% 199.48/192.22  ncf('1.2.1.1',plain,[-(closed_subset(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), 10246 ^ []))],extension(10259 ^ 9)).
% 199.48/192.22  ncf('1.2.1.2',plain,[-(element(subset_complement(the_carrier(10246 ^ []), 10249 ^ []), powerset(the_carrier(10246 ^ [])))), element(10249 ^ [], powerset(the_carrier(10246 ^ [])))],extension(4453 ^ 7,bind([[_238131, _238133], [10249 ^ [], the_carrier(10246 ^ [])]]))).
% 199.48/192.22  ncf('1.2.1.2.1',plain,[-(element(10249 ^ [], powerset(the_carrier(10246 ^ []))))],extension(10251 ^ 8)).
% 199.48/192.22  ncf('1.2.1.3',plain,[-(top_str(10246 ^ []))],extension(10248 ^ 5)).
% 199.48/192.22  ncf('1.2.2',plain,[-(subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])) = 10249 ^ []), subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])) = 10249 ^ [], 10249 ^ [] = 10249 ^ []],extension(10 ^ 4,bind([[_85089, _85091, _85093], [10249 ^ [], 10249 ^ [], subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ []))]]))).
% 199.48/192.22  ncf('1.2.2.1',plain,[-(subset_complement(the_carrier(10246 ^ []), subset_complement(the_carrier(10246 ^ []), 10249 ^ [])) = 10249 ^ []), element(10249 ^ [], powerset(the_carrier(10246 ^ [])))],extension(5261 ^ 5,bind([[_264200, _264202], [10249 ^ [], the_carrier(10246 ^ [])]]))).
% 199.48/192.22  ncf('1.2.2.1.1',plain,[-(element(10249 ^ [], powerset(the_carrier(10246 ^ []))))],extension(10251 ^ 6)).
% 199.48/192.22  ncf('1.2.2.2',plain,[-(10249 ^ [] = 10249 ^ [])],extension(2 ^ 5,bind([[_84778], [10249 ^ []]]))).
% 199.48/192.22  ncf('1.2.3',plain,[-(10246 ^ [] = 10246 ^ []), unordered_pair(10246 ^ [], 10246 ^ []) = unordered_pair(10246 ^ [], 10246 ^ []), -(10246 ^ [] = 10246 ^ [])],extension(7943 ^ 4,bind([[_374126, _374128, _374130, _374132], [10246 ^ [], 10246 ^ [], 10246 ^ [], 10246 ^ []]]))).
% 199.48/192.22  ncf('1.2.3.1',plain,[-(unordered_pair(10246 ^ [], 10246 ^ []) = unordered_pair(10246 ^ [], 10246 ^ []))],extension(1536 ^ 5,bind([[_136241, _136243], [10246 ^ [], 10246 ^ []]]))).
% 199.48/192.22  ncf('1.2.3.2',plain,[10246 ^ [] = 10246 ^ []],reduction('1.2')).
% 199.48/192.22  %-----------------------------------------------------
% 199.48/192.22  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------