%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU337+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n019.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 12:03:11 EDT 2023

% Result   : Theorem 183.29s 176.59s
% Output   : Proof 183.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU337+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 13:30:42 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 183.29/176.59  
% 183.29/176.59  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 183.29/176.59  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 183.29/176.59  %-----------------------------------------------------
% 183.29/176.59  ncf(matrix, plain, [(11501 ^ _684317) ^ [] : [11502 ^ _684317 : [(11503 ^ _684317) ^ [] : [-(open_subsets(11497 ^ [], 11494 ^ []))], (11505 ^ _684317) ^ [] : [closed_subsets(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), 11494 ^ [])]], 11506 ^ _684317 : [(11507 ^ _684317) ^ [] : [-(closed_subsets(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), 11494 ^ []))], (11509 ^ _684317) ^ [] : [open_subsets(11497 ^ [], 11494 ^ [])]]], (11499 ^ _684317) ^ [] : [-(element(11497 ^ [], powerset(powerset(the_carrier(11494 ^ [])))))], (11496 ^ _684317) ^ [] : [-(top_str(11494 ^ []))], !, (10200 ^ _257529) ^ [_633465, _633467] : [subset(_633467, _633465), -(set_difference(_633467, _633465) = empty_set)], (8670 ^ _257529) ^ [_580299, _580301] : [one_sorted_str(_580301), element(_580299, powerset(powerset(the_carrier(_580301)))), 8719 ^ _257529 : [(8720 ^ _257529) ^ [] : [-(relation(8718 ^ [_580299, _580301]))], (8726 ^ _257529) ^ [_582915] : [in(_582915, complements_of_subsets(the_carrier(_580301), _580299)), 8729 ^ _257529 : [(8730 ^ _257529) ^ [_583095] : [element(_583095, powerset(the_carrier(_580301))), _583095 = _582915, -(apply(8718 ^ [_580299, _580301], _582915) = subset_complement(the_carrier(_580301), _583095))]]], (8724 ^ _257529) ^ [] : [-(relation_dom(8718 ^ [_580299, _580301]) = complements_of_subsets(the_carrier(_580301), _580299))], (8722 ^ _257529) ^ [] : [-(function(8718 ^ [_580299, _580301]))]], 8709 ^ _257529 : [(8710 ^ _257529) ^ [] : [-(in(8708 ^ [_580299, _580301], complements_of_subsets(the_carrier(_580301), _580299)))], (8717 ^ _257529) ^ [_582475] : [_582475 = subset_complement(the_carrier(_580301), 8711 ^ [_580299, _580301, _582475])], (8715 ^ _257529) ^ [_582412] : [-(8711 ^ [_580299, _580301, _582412] = 8708 ^ [_580299, _580301])], (8713 ^ _257529) ^ [_582331] : [-(element(8711 ^ [_580299, _580301, _582331], powerset(the_carrier(_580301))))]], 8684 ^ _257529 : [(8707 ^ _257529) ^ [] : [8682 ^ [_580299, _580301] = 8683 ^ [_580299, _580301]], (8697 ^ _257529) ^ [_581692] : [element(_581692, powerset(the_carrier(_580301))), _581692 = 8681 ^ [_580299, _580301], -(8683 ^ [_580299, _580301] = subset_complement(the_carrier(_580301), _581692))], (8687 ^ _257529) ^ [_581367] : [element(_581367, powerset(the_carrier(_580301))), _581367 = 8681 ^ [_580299, _580301], -(8682 ^ [_580299, _580301] = subset_complement(the_carrier(_580301), _581367))], (8685 ^ _257529) ^ [] : [-(in(8681 ^ [_580299, _580301], complements_of_subsets(the_carrier(_580301), _580299)))]]], (4639 ^ _257529) ^ [] : [true___, -(true___)], (11417 ^ _257529) ^ [_673703, _673705] : [relation(_673703), -(subset(relation_rng(relation_dom_restriction(_673703, _673705)), relation_rng(_673703)))], (2926 ^ _257529) ^ [_358576, _358578] : [empty(_358578), 2929 ^ _257529 : [(2930 ^ _257529) ^ [] : [element(_358576, _358578), -(empty(_358576))], (2936 ^ _257529) ^ [] : [empty(_358576), -(element(_358576, _358578))]]], (5227 ^ _257529) ^ [_435990, _435992] : [v2_membered(_435992), 5230 ^ _257529 : [(5231 ^ _257529) ^ [] : [-(v1_membered(set_difference(_435992, _435990)))], (5233 ^ _257529) ^ [] : [-(v2_membered(set_difference(_435992, _435990)))]]], (592 ^ _257529) ^ [_275785, _275787, _275789, _275791] : [-(well_orders(_275789, _275785)), well_orders(_275791, _275787), _275791 = _275789, _275787 = _275785], (9152 ^ _257529) ^ [_598688] : [-(in(_598688, 9150 ^ [_598688]))], (11194 ^ _257529) ^ [_666303] : [ordinal(_666303), -(well_founded_relation(inclusion_relation(_666303)))], (724 ^ _257529) ^ [_279959, _279961, _279963, _279965] : [-(element(_279963, _279959)), element(_279965, _279961), _279965 = _279963, _279961 = _279959], (626 ^ _257529) ^ [_276791, _276793] : [-(function(_276791)), _276793 = _276791, function(_276793)], (672 ^ _257529) ^ [_278332, _278334, _278336, _278338] : [-(subset(_278336, _278332)), subset(_278338, _278334), _278338 = _278336, _278334 = _278332], (4 ^ _257529) ^ [_257760, _257762] : [_257762 = _257760, -(_257760 = _257762)], (4587 ^ _257529) ^ [] : [true___, -(true___)], (10634 ^ _257529) ^ [_648273, _648275] : [element(_648273, powerset(powerset(_648275))), -(_648273 = empty_set), -(union_of_subsets(_648275, complements_of_subsets(_648275, _648273)) = subset_difference(_648275, cast_to_subset(_648275), meet_of_subsets(_648275, _648273)))], (278 ^ _257529) ^ [_266121, _266123] : [-(meet_commutative(_266121)), _266123 = _266121, meet_commutative(_266123)], (11206 ^ _257529) ^ [_666739, _666741, _666743] : [relation(_666739), function(_666739), in(_666741, relation_dom(relation_dom_restriction(_666739, _666743))), -(apply(relation_dom_restriction(_666739, _666743), _666741) = apply(_666739, _666741))], (798 ^ _257529) ^ [_282793, _282795] : [_282795 = _282793, -(empty_carrier_subset(_282795) = empty_carrier_subset(_282793))], (5521 ^ _257529) ^ [_445285, _445287] : [element(_445285, powerset(powerset(_445287))), -(complements_of_subsets(_445287, complements_of_subsets(_445287, _445285)) = _445285)], (10699 ^ _257529) ^ [_650508] : [-(_650508 = empty_set), 10702 ^ _257529 : [(10703 ^ _257529) ^ [_650668] : [element(_650668, powerset(_650508)), 10706 ^ _257529 : [(10707 ^ _257529) ^ [_650822] : [element(_650822, _650508), -(in(_650822, _650668)), -(in(_650822, subset_complement(_650508, _650668)))]]]]], (11399 ^ _257529) ^ [_673037, _673039] : [relation(_673037), -(relation_dom(relation_dom_restriction(_673037, _673039)) = set_intersection2(relation_dom(_673037), _673039))], (10481 ^ _257529) ^ [_642981] : [relation(_642981), 10484 ^ _257529 : [(10485 ^ _257529) ^ [_643118] : [relation(_643118), -(subset(relation_rng(relation_composition(_642981, _643118)), relation_rng(_643118)))]]], (1270 ^ _257529) ^ [_300374] : [v1_membered(_300374), 1273 ^ _257529 : [(1274 ^ _257529) ^ [_300504] : [element(_300504, _300374), -(v1_xcmplx_0(_300504))]]], (11489 ^ _257529) ^ [_676301, _676303, _676305] : [singleton(_676305) = unordered_pair(_676303, _676301), -(_676303 = _676301)], (10717 ^ _257529) ^ [_651140] : [topological_space(_651140), top_str(_651140), 10724 ^ _257529 : [(10725 ^ _257529) ^ [_651361] : [element(_651361, powerset(the_carrier(_651140))), -(open_subset(interior(_651140, _651361), _651140))]]], (616 ^ _257529) ^ [_276496, _276498] : [-(relation(_276496)), _276498 = _276496, relation(_276498)], (2864 ^ _257529) ^ [_356481] : [one_sorted_str(_356481), -(empty_carrier_subset(_356481) = empty_set)], (4741 ^ _257529) ^ [_420123, _420125] : [element(_420123, powerset(powerset(_420125))), -(element(meet_of_subsets(_420125, _420123), powerset(_420125)))], (11303 ^ _257529) ^ [_670098, _670100, _670102] : [relation(_670098), 11306 ^ _257529 : [(11307 ^ _257529) ^ [] : [in(_670102, relation_dom(relation_dom_restriction(_670098, _670100))), 11310 ^ _257529 : [(11311 ^ _257529) ^ [] : [-(in(_670102, _670100))], (11313 ^ _257529) ^ [] : [-(in(_670102, relation_dom(_670098)))]]], (11315 ^ _257529) ^ [] : [-(in(_670102, relation_dom(relation_dom_restriction(_670098, _670100)))), in(_670102, _670100), in(_670102, relation_dom(_670098))]]], (9871 ^ _257529) ^ [_622631, _622633] : [relation(_622631), well_orders(_622631, _622633), 9878 ^ _257529 : [(9879 ^ _257529) ^ [] : [-(relation_field(relation_restriction(_622631, _622633)) = _622633)], (9881 ^ _257529) ^ [] : [-(well_ordering(relation_restriction(_622631, _622633)))]]], (2964 ^ _257529) ^ [_359801, _359803, _359805] : [-(_359801 = unordered_pair(_359805, _359803)), 2968 ^ _257529 : [(2973 ^ _257529) ^ [] : [2965 ^ [_359801, _359803, _359805] = _359803], (2971 ^ _257529) ^ [] : [2965 ^ [_359801, _359803, _359805] = _359805], (2969 ^ _257529) ^ [] : [-(in(2965 ^ [_359801, _359803, _359805], _359801))]], 2974 ^ _257529 : [(2981 ^ _257529) ^ [] : [in(2965 ^ [_359801, _359803, _359805], _359801)], (2975 ^ _257529) ^ [] : [-(2965 ^ [_359801, _359803, _359805] = _359805), -(2965 ^ [_359801, _359803, _359805] = _359803)]]], (2447 ^ _257529) ^ [_341686] : [relation(_341686), 2450 ^ _257529 : [(2451 ^ _257529) ^ [_341834] : [in(_341834, _341686), -(_341834 = ordered_pair(2454 ^ [_341686, _341834], 2455 ^ [_341686, _341834]))]]], (370 ^ _257529) ^ [_268944, _268946] : [-(being_limit_ordinal(_268944)), _268946 = _268944, being_limit_ordinal(_268946)], (2378 ^ _257529) ^ [_339215] : [-(succ(_339215) = set_union2(_339215, singleton(_339215)))], (4787 ^ _257529) ^ [_421641] : [top_str(_421641), -(one_sorted_str(_421641))], (5850 ^ _257529) ^ [] : [-(epsilon_transitive(5846 ^ []))], (6784 ^ _257529) ^ [_491037, _491039] : [-(empty(_491039)), relation(_491037), 6796 ^ _257529 : [(6810 ^ _257529) ^ [] : [-(in(6793 ^ [_491037, _491039], _491039))], (6823 ^ _257529) ^ [] : [6794 ^ [_491037, _491039] = 6795 ^ [_491037, _491039]], (6802 ^ _257529) ^ [] : [-(in(6794 ^ [_491037, _491039], 6798 ^ [_491037, _491039]))], (6804 ^ _257529) ^ [_492306] : [in(_492306, 6798 ^ [_491037, _491039]), -(in(ordered_pair(6794 ^ [_491037, _491039], _492306), _491037))], (6815 ^ _257529) ^ [] : [-(in(6795 ^ [_491037, _491039], 6811 ^ [_491037, _491039]))], (6800 ^ _257529) ^ [] : [-(6793 ^ [_491037, _491039] = 6798 ^ [_491037, _491039])], (6813 ^ _257529) ^ [] : [-(6793 ^ [_491037, _491039] = 6811 ^ [_491037, _491039])], (6817 ^ _257529) ^ [_492855] : [in(_492855, 6811 ^ [_491037, _491039]), -(in(ordered_pair(6795 ^ [_491037, _491039], _492855), _491037))], (6797 ^ _257529) ^ [] : [-(in(6793 ^ [_491037, _491039], _491039))]], 6825 ^ _257529 : [(6826 ^ _257529) ^ [_493283] : [in(_493283, 6824 ^ [_491037, _491039]), 6830 ^ _257529 : [(6831 ^ _257529) ^ [] : [-(in(6829 ^ [_491037, _491039, _493283], _491039))], (6833 ^ _257529) ^ [] : [-(in(6829 ^ [_491037, _491039, _493283], _491039))], (6840 ^ _257529) ^ [_493972] : [in(_493972, 6834 ^ [_491037, _491039, _493283]), -(in(ordered_pair(_493283, _493972), _491037))], (6838 ^ _257529) ^ [] : [-(in(_493283, 6834 ^ [_491037, _491039, _493283]))], (6836 ^ _257529) ^ [] : [-(6829 ^ [_491037, _491039, _493283] = 6834 ^ [_491037, _491039, _493283])]]], (6846 ^ _257529) ^ [_494189] : [-(in(_494189, 6824 ^ [_491037, _491039])), 6847 ^ _257529 : [(6848 ^ _257529) ^ [_494331] : [in(_494331, _491039), in(_494331, _491039), 6855 ^ _257529 : [(6856 ^ _257529) ^ [_494595] : [_494331 = _494595, in(_494189, _494595), 6864 ^ _257529 : [(6865 ^ _257529) ^ [] : [-(in(6863 ^ [_491037, _491039, _494189, _494331, _494595], _494595))], (6867 ^ _257529) ^ [] : [in(ordered_pair(_494189, 6863 ^ [_491037, _491039, _494189, _494331, _494595]), _491037)]]]]]]]]], (4633 ^ _257529) ^ [] : [true___, -(true___)], (3817 ^ _257529) ^ [_390127, _390129] : [element(_390127, powerset(_390129)), -(subset_complement(_390129, _390127) = set_difference(_390129, _390127))], (11164 ^ _257529) ^ [_665362] : [-(unordered_pair(_665362, _665362) = singleton(_665362))], (5895 ^ _257529) ^ [] : [-(ordinal(5889 ^ []))], (196 ^ _257529) ^ [_263593, _263595] : [-(natural(_263593)), _263595 = _263593, natural(_263595)], (4963 ^ _257529) ^ [_427233] : [-(cup_closed(powerset(_427233)))], (466 ^ _257529) ^ [_271916, _271918] : [-(empty_carrier(_271916)), _271918 = _271916, empty_carrier(_271918)], (5967 ^ _257529) ^ [] : [-(relation(5965 ^ []))], (10923 ^ _257529) ^ [_657805] : [relation(_657805), function(_657805), one_to_one(_657805), 10934 ^ _257529 : [(10935 ^ _257529) ^ [] : [-(relation_rng(_657805) = relation_dom(function_inverse(_657805)))], (10937 ^ _257529) ^ [] : [-(relation_dom(_657805) = relation_rng(function_inverse(_657805)))]]], (5904 ^ _257529) ^ [] : [-(being_limit_ordinal(5896 ^ []))], (5431 ^ _257529) ^ [] : [-(v5_membered(empty_set))], (9845 ^ _257529) ^ [_621787] : [relation(_621787), 9848 ^ _257529 : [(9849 ^ _257529) ^ [_621937] : [relation(_621937), subset(_621787, _621937), 9856 ^ _257529 : [(9857 ^ _257529) ^ [] : [-(subset(relation_dom(_621787), relation_dom(_621937)))], (9859 ^ _257529) ^ [] : [-(subset(relation_rng(_621787), relation_rng(_621937)))]]]]], (6061 ^ _257529) ^ [] : [-(relation(6059 ^ []))], (216 ^ _257529) ^ [_264183, _264185] : [-(relation_empty_yielding(_264183)), _264185 = _264183, relation_empty_yielding(_264185)], (5433 ^ _257529) ^ [_442434] : [empty(relation_rng(_442434)), -(empty(_442434)), relation(_442434)], (452 ^ _257529) ^ [_271500, _271502, _271504, _271506] : [-(open_subset(_271504, _271500)), open_subset(_271506, _271502), _271506 = _271504, _271502 = _271500], (9297 ^ _257529) ^ [_603534, _603536, _603538, _603540] : [relation_of2_as_subset(_603534, _603536, _603540), subset(relation_rng(_603534), _603538), -(relation_of2_as_subset(_603534, _603536, _603538))], (1964 ^ _257529) ^ [_324004] : [top_str(_324004), 1967 ^ _257529 : [(1968 ^ _257529) ^ [_324211] : [element(_324211, powerset(the_carrier(_324004))), 1971 ^ _257529 : [(1972 ^ _257529) ^ [_324419] : [element(_324419, powerset(the_carrier(_324004))), 1975 ^ _257529 : [(2015 ^ _257529) ^ [] : [-(_324419 = topstr_closure(_324004, _324211)), 2017 ^ _257529 : [(2018 ^ _257529) ^ [] : [-(in(2016 ^ [_324004, _324211, _324419], the_carrier(_324004)))], (2020 ^ _257529) ^ [] : [2021 ^ _257529 : [(2022 ^ _257529) ^ [] : [-(in(2016 ^ [_324004, _324211, _324419], _324419))], (2025 ^ _257529) ^ [] : [-(element(2023 ^ [_324004, _324211, _324419], powerset(the_carrier(_324004))))], (2031 ^ _257529) ^ [] : [-(disjoint(_324211, 2023 ^ [_324004, _324211, _324419]))], (2029 ^ _257529) ^ [] : [-(in(2016 ^ [_324004, _324211, _324419], 2023 ^ [_324004, _324211, _324419]))], (2027 ^ _257529) ^ [] : [-(open_subset(2023 ^ [_324004, _324211, _324419], _324004))]], 2032 ^ _257529 : [(2047 ^ _257529) ^ [] : [in(2016 ^ [_324004, _324211, _324419], _324419)], (2033 ^ _257529) ^ [_326682] : [element(_326682, powerset(the_carrier(_324004))), open_subset(_326682, _324004), in(2016 ^ [_324004, _324211, _324419], _326682), disjoint(_324211, _326682)]]]]], (1976 ^ _257529) ^ [] : [_324419 = topstr_closure(_324004, _324211), 1979 ^ _257529 : [(1980 ^ _257529) ^ [_324733] : [in(_324733, the_carrier(_324004)), 1983 ^ _257529 : [(2002 ^ _257529) ^ [] : [2004 ^ _257529 : [(2005 ^ _257529) ^ [] : [-(element(2003 ^ [_324004, _324211, _324419, _324733], powerset(the_carrier(_324004))))], (2011 ^ _257529) ^ [] : [-(disjoint(_324211, 2003 ^ [_324004, _324211, _324419, _324733]))], (2009 ^ _257529) ^ [] : [-(in(_324733, 2003 ^ [_324004, _324211, _324419, _324733]))], (2007 ^ _257529) ^ [] : [-(open_subset(2003 ^ [_324004, _324211, _324419, _324733], _324004))]], -(in(_324733, _324419))], (1984 ^ _257529) ^ [] : [in(_324733, _324419), 1987 ^ _257529 : [(1988 ^ _257529) ^ [_325028] : [element(_325028, powerset(the_carrier(_324004))), open_subset(_325028, _324004), in(_324733, _325028), disjoint(_324211, _325028)]]]]]]]]]]]]], (3228 ^ _257529) ^ [_369417] : [relation(_369417), 3231 ^ _257529 : [(3232 ^ _257529) ^ [_369575] : [relation(_369575), 3235 ^ _257529 : [(3246 ^ _257529) ^ [] : [3249 ^ _257529 : [(3250 ^ _257529) ^ [] : [-(in(ordered_pair(3247 ^ [_369417, _369575], 3248 ^ [_369417, _369575]), _369417))], (3252 ^ _257529) ^ [] : [in(ordered_pair(3247 ^ [_369417, _369575], 3248 ^ [_369417, _369575]), _369575)]], -(subset(_369417, _369575))], (3236 ^ _257529) ^ [] : [subset(_369417, _369575), 3239 ^ _257529 : [(3240 ^ _257529) ^ [_369851, _369853] : [in(ordered_pair(_369853, _369851), _369417), -(in(ordered_pair(_369853, _369851), _369575))]]]]]]], (11423 ^ _257529) ^ [_673896] : [-(union(powerset(_673896)) = _673896)], (11405 ^ _257529) ^ [_673265, _673267] : [in(_673267, _673265), -(subset(_673267, union(_673265)))], (11456 ^ _257529) ^ [_675133, _675135, _675137] : [-(in(_675133, 11452 ^ [_675137])), in(_675135, 11452 ^ [_675137]), subset(_675133, _675135)], (102 ^ _257529) ^ [_260817, _260819, _260821, _260823] : [-(is_reflexive_in(_260821, _260817)), is_reflexive_in(_260823, _260819), _260823 = _260821, _260819 = _260817], (11222 ^ _257529) ^ [_667206] : [-(relation_rng(identity_relation(_667206)) = _667206)], (4573 ^ _257529) ^ [_415321] : [-(element(cast_to_subset(_415321), powerset(_415321)))], (6063 ^ _257529) ^ [] : [-(relation_empty_yielding(6059 ^ []))], (5095 ^ _257529) ^ [] : [-(epsilon_connected(empty_set))], (5615 ^ _257529) ^ [_448635, _448637] : [in(_448637, _448635), -(subset(singleton(_448637), _448635))], (5041 ^ _257529) ^ [_429667, _429669] : [v1_membered(_429669), -(v1_membered(set_intersection2(_429669, _429667)))], (8740 ^ _257529) ^ [_583480, _583482] : [one_sorted_str(_583482), element(_583480, powerset(powerset(the_carrier(_583482)))), 8789 ^ _257529 : [(8790 ^ _257529) ^ [] : [-(relation(8788 ^ [_583480, _583482]))], (8796 ^ _257529) ^ [_586031] : [in(_586031, _583480), 8799 ^ _257529 : [(8800 ^ _257529) ^ [_586201] : [element(_586201, powerset(the_carrier(_583482))), _586201 = _586031, -(apply(8788 ^ [_583480, _583482], _586031) = subset_complement(the_carrier(_583482), _586201))]]], (8794 ^ _257529) ^ [] : [-(relation_dom(8788 ^ [_583480, _583482]) = _583480)], (8792 ^ _257529) ^ [] : [-(function(8788 ^ [_583480, _583482]))]], 8779 ^ _257529 : [(8780 ^ _257529) ^ [] : [-(in(8778 ^ [_583480, _583482], _583480))], (8787 ^ _257529) ^ [_585606] : [_585606 = subset_complement(the_carrier(_583482), 8781 ^ [_583480, _583482, _585606])], (8785 ^ _257529) ^ [_585543] : [-(8781 ^ [_583480, _583482, _585543] = 8778 ^ [_583480, _583482])], (8783 ^ _257529) ^ [_585462] : [-(element(8781 ^ [_583480, _583482, _585462], powerset(the_carrier(_583482))))]], 8754 ^ _257529 : [(8777 ^ _257529) ^ [] : [8752 ^ [_583480, _583482] = 8753 ^ [_583480, _583482]], (8767 ^ _257529) ^ [_584833] : [element(_584833, powerset(the_carrier(_583482))), _584833 = 8751 ^ [_583480, _583482], -(8753 ^ [_583480, _583482] = subset_complement(the_carrier(_583482), _584833))], (8757 ^ _257529) ^ [_584508] : [element(_584508, powerset(the_carrier(_583482))), _584508 = 8751 ^ [_583480, _583482], -(8752 ^ [_583480, _583482] = subset_complement(the_carrier(_583482), _584508))], (8755 ^ _257529) ^ [] : [-(in(8751 ^ [_583480, _583482], _583480))]]], (50 ^ _257529) ^ [_259162, _259164] : [-(v1_rat_1(_259162)), _259164 = _259162, v1_rat_1(_259164)], (6037 ^ _257529) ^ [] : [-(function(6033 ^ []))], (5802 ^ _257529) ^ [_454994, _454996, _454998, _455000] : [-(in(ordered_pair(_455000, _454998), cartesian_product2(_454996, _454994))), in(_455000, _454996), in(_454998, _454994)], (10438 ^ _257529) ^ [_641423] : [top_str(_641423), 10441 ^ _257529 : [(10442 ^ _257529) ^ [_641607] : [element(_641607, powerset(the_carrier(_641423))), 10445 ^ _257529 : [(10446 ^ _257529) ^ [_641792] : [in(_641792, the_carrier(_641423)), 10449 ^ _257529 : [(10468 ^ _257529) ^ [] : [10470 ^ _257529 : [(10471 ^ _257529) ^ [] : [-(element(10469 ^ [_641423, _641607, _641792], powerset(the_carrier(_641423))))], (10477 ^ _257529) ^ [] : [in(_641792, 10469 ^ [_641423, _641607, _641792])], (10475 ^ _257529) ^ [] : [-(subset(_641607, 10469 ^ [_641423, _641607, _641792]))], (10473 ^ _257529) ^ [] : [-(closed_subset(10469 ^ [_641423, _641607, _641792], _641423))]], -(in(_641792, topstr_closure(_641423, _641607)))], (10450 ^ _257529) ^ [] : [in(_641792, topstr_closure(_641423, _641607)), 10453 ^ _257529 : [(10454 ^ _257529) ^ [_642081] : [element(_642081, powerset(the_carrier(_641423))), -(in(_641792, _642081)), closed_subset(_642081, _641423), subset(_641607, _642081)]]]]]]]]], (394 ^ _257529) ^ [_269683, _269685] : [-(reflexive(_269683)), _269685 = _269683, reflexive(_269685)], (10352 ^ _257529) ^ [_638530] : [ordinal(_638530), 10355 ^ _257529 : [(10356 ^ _257529) ^ [] : [-(being_limit_ordinal(_638530)), 10360 ^ _257529 : [(10361 ^ _257529) ^ [] : [-(ordinal(10359 ^ [_638530]))], (10363 ^ _257529) ^ [] : [-(_638530 = succ(10359 ^ [_638530]))]]], (10365 ^ _257529) ^ [] : [being_limit_ordinal(_638530), 10366 ^ _257529 : [(10367 ^ _257529) ^ [_639001] : [ordinal(_639001), _638530 = succ(_639001)]]]]], (11095 ^ _257529) ^ [_663121] : [relation(_663121), 11098 ^ _257529 : [(11099 ^ _257529) ^ [] : [relation_dom(_663121) = empty_set, -(relation_rng(_663121) = empty_set)], (11105 ^ _257529) ^ [] : [relation_rng(_663121) = empty_set, -(relation_dom(_663121) = empty_set)]]], (8900 ^ _257529) ^ [_589796] : [-(relation_dom(8894 ^ [_589796]) = _589796)], (936 ^ _257529) ^ [_287997, _287999, _288001, _288003] : [-(fiber(_288003, _287999) = fiber(_288001, _287997)), _288003 = _288001, _287999 = _287997], (9009 ^ _257529) ^ [_593672, _593674, _593676, _593678] : [-(in(ordered_pair(_593678, _593676), cartesian_product2(_593674, _593672))), in(_593678, _593674), in(_593676, _593672)], (9190 ^ _257529) ^ [_599936] : [one_sorted_str(_599936), 9193 ^ _257529 : [(9194 ^ _257529) ^ [_600082] : [element(_600082, powerset(powerset(the_carrier(_599936)))), 9197 ^ _257529 : [(9198 ^ _257529) ^ [] : [finite(complements_of_subsets(the_carrier(_599936), _600082)), -(finite(_600082))], (9204 ^ _257529) ^ [] : [finite(_600082), -(finite(complements_of_subsets(the_carrier(_599936), _600082)))]]]]], (10644 ^ _257529) ^ [_648598, _648600] : [-(set_difference(_648600, set_difference(_648600, _648598)) = set_intersection2(_648600, _648598))], (4691 ^ _257529) ^ [] : [true___, -(true___)], (5864 ^ _257529) ^ [] : [-(relation(5862 ^ []))], (10755 ^ _257529) ^ [_652307] : [relation(_652307), 10758 ^ _257529 : [(10759 ^ _257529) ^ [_652503] : [relation(_652503), 10762 ^ _257529 : [(10763 ^ _257529) ^ [_652695] : [relation(_652695), function(_652695), relation_isomorphism(_652307, _652503, _652695), 10774 ^ _257529 : [(10775 ^ _257529) ^ [] : [reflexive(_652307), -(reflexive(_652503))], (10781 ^ _257529) ^ [] : [transitive(_652307), -(transitive(_652503))], (10799 ^ _257529) ^ [] : [well_founded_relation(_652307), -(well_founded_relation(_652503))], (10793 ^ _257529) ^ [] : [antisymmetric(_652307), -(antisymmetric(_652503))], (10787 ^ _257529) ^ [] : [connected(_652307), -(connected(_652503))]]]]]]], (5882 ^ _257529) ^ [] : [-(v2_membered(5876 ^ []))], (9127 ^ _257529) ^ [_597729, _597731, _597733] : [relation_of2_as_subset(_597729, _597733, _597731), 9130 ^ _257529 : [(9131 ^ _257529) ^ [] : [-(subset(relation_dom(_597729), _597733))], (9133 ^ _257529) ^ [] : [-(subset(relation_rng(_597729), _597731))]]], (4525 ^ _257529) ^ [_414022] : [4532 ^ _257529 : [(4533 ^ _257529) ^ [] : [-(relation(function_inverse(_414022)))], (4535 ^ _257529) ^ [] : [-(function(function_inverse(_414022)))]], relation(_414022), function(_414022)], (4775 ^ _257529) ^ [] : [true___, -(true___)], (6005 ^ _257529) ^ [_461689] : [6013 ^ _257529 : [(6018 ^ _257529) ^ [] : [-(closed_subset(6012 ^ [_461689], _461689))], (6016 ^ _257529) ^ [] : [-(open_subset(6012 ^ [_461689], _461689))], (6014 ^ _257529) ^ [] : [-(element(6012 ^ [_461689], powerset(the_carrier(_461689))))]], topological_space(_461689), top_str(_461689)], (2765 ^ _257529) ^ [_352791] : [-(in(2766 ^ [_352791], _352791)), -(_352791 = empty_set)], (11166 ^ _257529) ^ [_665460] : [empty(_665460), -(_665460 = empty_set)], (298 ^ _257529) ^ [_266711, _266713] : [-(latt_str(_266711)), _266713 = _266711, latt_str(_266713)], (2 ^ _257529) ^ [_257653] : [-(_257653 = _257653)], (10051 ^ _257529) ^ [_628542] : [-(ordinal(_628542)), 10053 ^ _257529 : [(10054 ^ _257529) ^ [] : [-(in(10052 ^ [_628542], _628542))], (10056 ^ _257529) ^ [] : [ordinal(10052 ^ [_628542]), subset(10052 ^ [_628542], _628542)]]], (4489 ^ _257529) ^ [] : [true___, -(true___)], (5087 ^ _257529) ^ [] : [-(function(empty_set))], (3877 ^ _257529) ^ [_392031] : [top_str(_392031), 3880 ^ _257529 : [(3881 ^ _257529) ^ [_392180] : [element(_392180, powerset(the_carrier(_392031))), 3884 ^ _257529 : [(3885 ^ _257529) ^ [] : [closed_subset(_392180, _392031), -(open_subset(subset_difference(the_carrier(_392031), cast_as_carrier_subset(_392031), _392180), _392031))], (3891 ^ _257529) ^ [] : [open_subset(subset_difference(the_carrier(_392031), cast_as_carrier_subset(_392031), _392180), _392031), -(closed_subset(_392180, _392031))]]]]], (4893 ^ _257529) ^ [_425039, _425041] : [4900 ^ _257529 : [(4901 ^ _257529) ^ [] : [-(empty(relation_composition(_425039, _425041)))], (4903 ^ _257529) ^ [] : [-(relation(relation_composition(_425039, _425041)))]], empty(_425041), relation(_425039)], (4593 ^ _257529) ^ [] : [true___, -(true___)], (2788 ^ _257529) ^ [_353603, _353605] : [-(_353603 = powerset(_353605)), 2792 ^ _257529 : [(2793 ^ _257529) ^ [] : [-(in(2789 ^ [_353603, _353605], _353603))], (2795 ^ _257529) ^ [] : [subset(2789 ^ [_353603, _353605], _353605)]], 2796 ^ _257529 : [(2797 ^ _257529) ^ [] : [-(subset(2789 ^ [_353603, _353605], _353605))], (2799 ^ _257529) ^ [] : [in(2789 ^ [_353603, _353605], _353603)]]], (6093 ^ _257529) ^ [_464588, _464590, _464592, _464594, _464596, _464598] : [-(apply_binary_as_element(_464598, _464596, _464594, _464592, _464590, _464588) = apply_binary(_464592, _464590, _464588)), -(empty(_464598)), -(empty(_464596)), function(_464592), quasi_total(_464592, cartesian_product2(_464598, _464596), _464594), relation_of2(_464592, cartesian_product2(_464598, _464596), _464594), element(_464590, _464598), element(_464588, _464596)], (5891 ^ _257529) ^ [] : [-(epsilon_transitive(5889 ^ []))], (4747 ^ _257529) ^ [_420365, _420367, _420369] : [-(element(subset_difference(_420369, _420367, _420365), powerset(_420369))), element(_420367, powerset(_420369)), element(_420365, powerset(_420369))], (5859 ^ _257529) ^ [] : [empty(5857 ^ [])], (10 ^ _257529) ^ [_257964, _257966, _257968] : [-(_257968 = _257964), _257968 = _257966, _257966 = _257964], (4931 ^ _257529) ^ [_426269, _426271] : [-(finite(relation_image(_426271, _426269))), relation(_426271), function(_426271), finite(_426269)], (6067 ^ _257529) ^ [_463679] : [6075 ^ _257529 : [(6076 ^ _257529) ^ [] : [-(element(6074 ^ [_463679], powerset(the_carrier(_463679))))], (6078 ^ _257529) ^ [] : [empty(6074 ^ [_463679])]], -(empty_carrier(_463679)), one_sorted_str(_463679)], (11172 ^ _257529) ^ [_665690, _665692, _665694, _665696] : [function(_665690), quasi_total(_665690, _665696, _665694), relation_of2_as_subset(_665690, _665696, _665694), in(_665692, _665696), -(_665694 = empty_set), -(in(apply(_665690, _665692), relation_rng(_665690)))], (8902 ^ _257529) ^ [_589876, _589878] : [in(_589876, _589878), -(apply(8894 ^ [_589878], _589876) = singleton(_589876))], (654 ^ _257529) ^ [_277751, _277753, _277755, _277757, _277759, _277761] : [-(relation_of2_as_subset(_277759, _277755, _277751)), relation_of2_as_subset(_277761, _277757, _277753), _277761 = _277759, _277757 = _277755, _277753 = _277751], (10218 ^ _257529) ^ [_634137, _634139, _634141] : [subset(unordered_pair(_634141, _634139), _634137), 10221 ^ _257529 : [(10222 ^ _257529) ^ [] : [-(in(_634141, _634137))], (10224 ^ _257529) ^ [] : [-(in(_634139, _634137))]]], (6565 ^ _257529) ^ [_483281] : [6566 ^ _257529 : [(6567 ^ _257529) ^ [_483402] : [ordinal(_483402), in(_483402, _483281)]], 6573 ^ _257529 : [(6578 ^ _257529) ^ [_483782] : [ordinal(_483782), in(_483782, _483281), -(ordinal_subset(6572 ^ [_483281], _483782))], (6576 ^ _257529) ^ [] : [-(in(6572 ^ [_483281], _483281))], (6574 ^ _257529) ^ [] : [-(ordinal(6572 ^ [_483281]))]]], (186 ^ _257529) ^ [_263298, _263300] : [-(v5_membered(_263298)), _263300 = _263298, v5_membered(_263300)], (9507 ^ _257529) ^ [_610669, _610671, _610673] : [relation(_610669), in(_610673, relation_field(relation_restriction(_610669, _610671))), 9514 ^ _257529 : [(9515 ^ _257529) ^ [] : [-(in(_610673, relation_field(_610669)))], (9517 ^ _257529) ^ [] : [-(in(_610673, _610671))]]], (8958 ^ _257529) ^ [_591878, _591880] : [topological_space(_591880), top_str(_591880), element(_591878, powerset(powerset(the_carrier(_591880)))), 8970 ^ _257529 : [(8971 ^ _257529) ^ [] : [-(element(8969 ^ [_591878, _591880], powerset(powerset(the_carrier(_591880)))))], (8973 ^ _257529) ^ [_592395] : [element(_592395, powerset(the_carrier(_591880))), 8976 ^ _257529 : [(8977 ^ _257529) ^ [] : [in(_592395, 8969 ^ [_591878, _591880]), -(in(set_difference(cast_as_carrier_subset(_591880), _592395), _591878))], (8983 ^ _257529) ^ [] : [in(set_difference(cast_as_carrier_subset(_591880), _592395), _591878), -(in(_592395, 8969 ^ [_591878, _591880]))]]]]], (1406 ^ _257529) ^ [_305083] : [ordinal(_305083), 1409 ^ _257529 : [(1410 ^ _257529) ^ [_305223] : [element(_305223, _305083), 1413 ^ _257529 : [(1418 ^ _257529) ^ [] : [-(ordinal(_305223))], (1416 ^ _257529) ^ [] : [-(epsilon_connected(_305223))], (1414 ^ _257529) ^ [] : [-(epsilon_transitive(_305223))]]]]], (380 ^ _257529) ^ [_269267, _269269, _269271, _269273] : [-(closed_subset(_269271, _269267)), closed_subset(_269273, _269269), _269273 = _269271, _269269 = _269267], (766 ^ _257529) ^ [_281679, _281681, _281683, _281685, _281687, _281689] : [-(unordered_triple(_281689, _281685, _281681) = unordered_triple(_281687, _281683, _281679)), _281689 = _281687, _281685 = _281683, _281681 = _281679], (9691 ^ _257529) ^ [_616754, _616756, _616758] : [relation_of2_as_subset(_616754, _616756, _616758), 9694 ^ _257529 : [(9695 ^ _257529) ^ [] : [9697 ^ _257529 : [(9698 ^ _257529) ^ [] : [-(in(9696 ^ [_616754, _616756, _616758], _616756))], (9700 ^ _257529) ^ [_617112] : [in(ordered_pair(9696 ^ [_616754, _616756, _616758], _617112), _616754)]], -(relation_dom_as_subset(_616756, _616758, _616754) = _616756)], (9704 ^ _257529) ^ [] : [relation_dom_as_subset(_616756, _616758, _616754) = _616756, 9707 ^ _257529 : [(9708 ^ _257529) ^ [_617349] : [in(_617349, _616756), -(in(ordered_pair(_617349, 9711 ^ [_616754, _616756, _616758, _617349]), _616754))]]]]], (2281 ^ _257529) ^ [_335701] : [2285 ^ _257529 : [(2290 ^ _257529) ^ [] : [2283 ^ [_335701] = 2284 ^ [_335701]], (2288 ^ _257529) ^ [] : [-(in(ordered_pair(2282 ^ [_335701], 2284 ^ [_335701]), _335701))], (2286 ^ _257529) ^ [] : [-(in(ordered_pair(2282 ^ [_335701], 2283 ^ [_335701]), _335701))]], -(function(_335701))], (4555 ^ _257529) ^ [] : [true___, -(true___)], (5527 ^ _257529) ^ [_445499, _445501] : [proper_subset(_445501, _445501)], (4781 ^ _257529) ^ [_421455] : [meet_semilatt_str(_421455), -(one_sorted_str(_421455))], (9261 ^ _257529) ^ [_602359, _602361] : [relation(_602359), -(relation_image(_602359, _602361) = relation_image(_602359, set_intersection2(relation_dom(_602359), _602361)))], (966 ^ _257529) ^ [_289118, _289120, _289122, _289124, _289126, _289128] : [-(meet_commut(_289128, _289124, _289120) = meet_commut(_289126, _289122, _289118)), _289128 = _289126, _289124 = _289122, _289120 = _289118], (9659 ^ _257529) ^ [_615652, _615654] : [relation(_615652), function(_615652), 9666 ^ _257529 : [(9667 ^ _257529) ^ [_615901] : [relation(_615901), function(_615901), in(_615654, relation_dom(relation_composition(_615901, _615652))), -(apply(relation_composition(_615901, _615652), _615654) = apply(_615652, apply(_615901, _615654)))]]], (5878 ^ _257529) ^ [] : [empty(5876 ^ [])], (5529 ^ _257529) ^ [_445594] : [relation(_445594), 5532 ^ _257529 : [(5543 ^ _257529) ^ [] : [5545 ^ _257529 : [(5546 ^ _257529) ^ [] : [-(in(5544 ^ [_445594], relation_field(_445594)))], (5548 ^ _257529) ^ [] : [in(ordered_pair(5544 ^ [_445594], 5544 ^ [_445594]), _445594)]], -(reflexive(_445594))], (5533 ^ _257529) ^ [] : [reflexive(_445594), 5536 ^ _257529 : [(5537 ^ _257529) ^ [_445838] : [in(_445838, relation_field(_445594)), -(in(ordered_pair(_445838, _445838), _445594))]]]]], (156 ^ _257529) ^ [_262413, _262415] : [-(v2_membered(_262413)), _262415 = _262413, v2_membered(_262415)], (7245 ^ _257529) ^ [_514406, _514408] : [topological_space(_514408), top_str(_514408), element(_514406, powerset(the_carrier(_514408))), 7261 ^ _257529 : [(7271 ^ _257529) ^ [] : [-(subset(_514406, 7259 ^ [_514406, _514408]))], (7284 ^ _257529) ^ [] : [7259 ^ [_514406, _514408] = 7260 ^ [_514406, _514408]], (7276 ^ _257529) ^ [] : [-(element(7274 ^ [_514406, _514408], powerset(the_carrier(_514408))))], (7282 ^ _257529) ^ [] : [-(subset(_514406, 7260 ^ [_514406, _514408]))], (7262 ^ _257529) ^ [] : [-(7258 ^ [_514406, _514408] = 7259 ^ [_514406, _514408])], (7278 ^ _257529) ^ [] : [-(7274 ^ [_514406, _514408] = 7260 ^ [_514406, _514408])], (7265 ^ _257529) ^ [] : [-(element(7263 ^ [_514406, _514408], powerset(the_carrier(_514408))))], (7280 ^ _257529) ^ [] : [-(closed_subset(7274 ^ [_514406, _514408], _514408))], (7273 ^ _257529) ^ [] : [-(7258 ^ [_514406, _514408] = 7260 ^ [_514406, _514408])], (7267 ^ _257529) ^ [] : [-(7263 ^ [_514406, _514408] = 7259 ^ [_514406, _514408])], (7269 ^ _257529) ^ [] : [-(closed_subset(7263 ^ [_514406, _514408], _514408))]], 7286 ^ _257529 : [(7287 ^ _257529) ^ [_516515] : [in(_516515, 7285 ^ [_514406, _514408]), 7291 ^ _257529 : [(7297 ^ _257529) ^ [] : [-(element(7295 ^ [_514406, _514408, _516515], powerset(the_carrier(_514408))))], (7292 ^ _257529) ^ [] : [-(in(7290 ^ [_514406, _514408, _516515], powerset(the_carrier(_514408))))], (7303 ^ _257529) ^ [] : [-(subset(_514406, _516515))], (7299 ^ _257529) ^ [] : [-(7295 ^ [_514406, _514408, _516515] = _516515)], (7301 ^ _257529) ^ [] : [-(closed_subset(7295 ^ [_514406, _514408, _516515], _514408))], (7294 ^ _257529) ^ [] : [-(7290 ^ [_514406, _514408, _516515] = _516515)]]], (7305 ^ _257529) ^ [_517316] : [-(in(_517316, 7285 ^ [_514406, _514408])), 7306 ^ _257529 : [(7307 ^ _257529) ^ [_517458] : [in(_517458, powerset(the_carrier(_514408))), _517458 = _517316, 7314 ^ _257529 : [(7315 ^ _257529) ^ [_517726] : [element(_517726, powerset(the_carrier(_514408))), _517726 = _517316, closed_subset(_517726, _514408), subset(_514406, _517316)]]]]]]], (4167 ^ _257529) ^ [_402407] : [one_sorted_str(_402407), 4170 ^ _257529 : [(4171 ^ _257529) ^ [_402557] : [element(_402557, powerset(powerset(the_carrier(_402407)))), 4174 ^ _257529 : [(4175 ^ _257529) ^ [] : [is_a_cover_of_carrier(_402407, _402557), -(cast_as_carrier_subset(_402407) = union_of_subsets(the_carrier(_402407), _402557))], (4181 ^ _257529) ^ [] : [cast_as_carrier_subset(_402407) = union_of_subsets(the_carrier(_402407), _402557), -(is_a_cover_of_carrier(_402407, _402557))]]]]], (1076 ^ _257529) ^ [_293087, _293089, _293091, _293093] : [-(subset_complement(_293093, _293089) = subset_complement(_293091, _293087)), _293093 = _293091, _293089 = _293087], (5960 ^ _257529) ^ [_460147] : [-(ordinal(5944 ^ [_460147]))], (9537 ^ _257529) ^ [_611701, _611703, _611705] : [-(subset(_611705, _611701)), subset(_611705, _611703), subset(_611703, _611701)], (476 ^ _257529) ^ [_272211, _272213] : [-(one_sorted_str(_272211)), _272213 = _272211, one_sorted_str(_272213)], (4627 ^ _257529) ^ [_416739, _416741] : [element(_416739, powerset(_416741)), -(element(subset_complement(_416741, _416739), powerset(_416741)))], (6042 ^ _257529) ^ [] : [empty(6040 ^ [])], (10017 ^ _257529) ^ [_627415] : [-(subset(empty_set, _627415))], (5996 ^ _257529) ^ [] : [empty(5994 ^ [])], (1306 ^ _257529) ^ [_301600] : [v4_membered(_301600), 1309 ^ _257529 : [(1310 ^ _257529) ^ [_301745] : [element(_301745, _301600), 1313 ^ _257529 : [(1314 ^ _257529) ^ [] : [-(v1_xcmplx_0(_301745))], (1320 ^ _257529) ^ [] : [-(v1_rat_1(_301745))], (1318 ^ _257529) ^ [] : [-(v1_int_1(_301745))], (1316 ^ _257529) ^ [] : [-(v1_xreal_0(_301745))]]]]], (11013 ^ _257529) ^ [_660722] : [-(empty_carrier(_660722)), one_sorted_str(_660722), 11020 ^ _257529 : [(11021 ^ _257529) ^ [_660953] : [element(_660953, powerset(powerset(the_carrier(_660722)))), is_a_cover_of_carrier(_660722, _660953), _660953 = empty_set]]], (9001 ^ _257529) ^ [_593407, _593409, _593411, _593413] : [in(ordered_pair(_593413, _593411), cartesian_product2(_593409, _593407)), 9004 ^ _257529 : [(9005 ^ _257529) ^ [] : [-(in(_593413, _593409))], (9007 ^ _257529) ^ [] : [-(in(_593411, _593407))]]], (9807 ^ _257529) ^ [_620664, _620666] : [relation(_620664), connected(_620664), -(connected(relation_restriction(_620664, _620666)))], (166 ^ _257529) ^ [_262708, _262710] : [-(v3_membered(_262708)), _262710 = _262708, v3_membered(_262710)], (4459 ^ _257529) ^ [] : [true___, -(true___)], (1520 ^ _257529) ^ [_308797] : [1531 ^ _257529 : [(1536 ^ _257529) ^ [] : [-(one_to_one(_308797))], (1534 ^ _257529) ^ [] : [-(function(_308797))], (1532 ^ _257529) ^ [] : [-(relation(_308797))]], relation(_308797), empty(_308797), function(_308797)], (11341 ^ _257529) ^ [_671282, _671284, _671286] : [relation(_671282), function(_671282), 11348 ^ _257529 : [(11349 ^ _257529) ^ [] : [in(ordered_pair(_671286, _671284), _671282), 11352 ^ _257529 : [(11353 ^ _257529) ^ [] : [-(in(_671286, relation_dom(_671282)))], (11355 ^ _257529) ^ [] : [-(_671284 = apply(_671282, _671286))]]], (11357 ^ _257529) ^ [] : [-(in(ordered_pair(_671286, _671284), _671282)), in(_671286, relation_dom(_671282)), _671284 = apply(_671282, _671286)]]], (11117 ^ _257529) ^ [_663777, _663779] : [-(in(_663777, _663779)), -(set_difference(_663779, singleton(_663777)) = _663779)], (4347 ^ _257529) ^ [_409433, _409435] : [-(proper_subset(_409435, _409433)), subset(_409435, _409433), -(_409435 = _409433)], (2459 ^ _257529) ^ [_342147] : [2461 ^ _257529 : [(2462 ^ _257529) ^ [] : [-(in(2460 ^ [_342147], _342147))], (2464 ^ _257529) ^ [_342384, _342386] : [2460 ^ [_342147] = ordered_pair(_342386, _342384)]], -(relation(_342147))], (10015 ^ _257529) ^ [_627336] : [-(reflexive(inclusion_relation(_627336)))], (4567 ^ _257529) ^ [] : [true___, -(true___)], (8260 ^ _257529) ^ [_562644, _562646] : [topological_space(_562646), top_str(_562646), element(_562644, powerset(powerset(the_carrier(_562646)))), 8272 ^ _257529 : [(8273 ^ _257529) ^ [_563087] : [in(_563087, 8271 ^ [_562644, _562646]), 8276 ^ _257529 : [(8277 ^ _257529) ^ [] : [-(in(_563087, powerset(the_carrier(_562646))))], (8279 ^ _257529) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_562646), _563087), _562644))]]], (8281 ^ _257529) ^ [_563368] : [-(in(_563368, 8271 ^ [_562644, _562646])), in(_563368, powerset(the_carrier(_562646))), in(set_difference(cast_as_carrier_subset(_562646), _563368), _562644)]]], (5978 ^ _257529) ^ [] : [-(one_to_one(5972 ^ []))], (1156 ^ _257529) ^ [_295972, _295974, _295976, _295978] : [-(set_union2(_295978, _295974) = set_union2(_295976, _295972)), _295978 = _295976, _295974 = _295972], (11224 ^ _257529) ^ [_667333, _667335, _667337] : [relation(_667333), function(_667333), in(_667335, _667337), -(apply(relation_dom_restriction(_667333, _667337), _667335) = apply(_667333, _667335))], (10497 ^ _257529) ^ [_643597, _643599, _643601, _643603] : [function(_643597), quasi_total(_643597, _643603, _643601), relation_of2_as_subset(_643597, _643603, _643601), -(_643601 = empty_set), 10512 ^ _257529 : [(10513 ^ _257529) ^ [_644075] : [in(_644075, relation_inverse_image(_643597, _643599)), 10516 ^ _257529 : [(10517 ^ _257529) ^ [] : [-(in(_644075, _643603))], (10519 ^ _257529) ^ [] : [-(in(apply(_643597, _644075), _643599))]]], (10521 ^ _257529) ^ [_644356] : [-(in(_644356, relation_inverse_image(_643597, _643599))), in(_644356, _643603), in(apply(_643597, _644356), _643599)]]], (7524 ^ _257529) ^ [_526971, _526973] : [one_sorted_str(_526973), element(_526971, powerset(powerset(the_carrier(_526973)))), 7531 ^ _257529 : [(7532 ^ _257529) ^ [_527455] : [7536 ^ _257529 : [(7555 ^ _257529) ^ [] : [-(7533 ^ [_526971, _526973, _527455] = 7535 ^ [_526971, _526973, _527455])], (7573 ^ _257529) ^ [] : [7534 ^ [_526971, _526973, _527455] = 7535 ^ [_526971, _526973, _527455]], (7543 ^ _257529) ^ [] : [-(in(7538 ^ [_526971, _526973, _527455], complements_of_subsets(the_carrier(_526973), _526971)))], (7545 ^ _257529) ^ [_528969] : [element(_528969, powerset(the_carrier(_526973))), _528969 = 7538 ^ [_526971, _526973, _527455], -(7539 ^ [_526971, _526973, _527455] = subset_complement(the_carrier(_526973), _528969))], (7561 ^ _257529) ^ [] : [-(in(7556 ^ [_526971, _526973, _527455], complements_of_subsets(the_carrier(_526973), _526971)))], (7541 ^ _257529) ^ [] : [-(ordered_pair(7538 ^ [_526971, _526973, _527455], 7539 ^ [_526971, _526973, _527455]) = 7534 ^ [_526971, _526973, _527455])], (7559 ^ _257529) ^ [] : [-(ordered_pair(7556 ^ [_526971, _526973, _527455], 7557 ^ [_526971, _526973, _527455]) = 7535 ^ [_526971, _526973, _527455])], (7563 ^ _257529) ^ [_529824] : [element(_529824, powerset(the_carrier(_526973))), _529824 = 7556 ^ [_526971, _526973, _527455], -(7557 ^ [_526971, _526973, _527455] = subset_complement(the_carrier(_526973), _529824))], (7537 ^ _257529) ^ [] : [-(7533 ^ [_526971, _526973, _527455] = 7534 ^ [_526971, _526973, _527455])]], 7575 ^ _257529 : [(7576 ^ _257529) ^ [_530420] : [in(_530420, 7574 ^ [_526971, _526973, _527455]), 7580 ^ _257529 : [(7581 ^ _257529) ^ [] : [-(in(7579 ^ [_526971, _526973, _527455, _530420], cartesian_product2(complements_of_subsets(the_carrier(_526973), _526971), _527455)))], (7583 ^ _257529) ^ [] : [-(7579 ^ [_526971, _526973, _527455, _530420] = _530420)], (7591 ^ _257529) ^ [_531375] : [element(_531375, powerset(the_carrier(_526973))), _531375 = 7584 ^ [_526971, _526973, _527455, _530420], -(7585 ^ [_526971, _526973, _527455, _530420] = subset_complement(the_carrier(_526973), _531375))], (7589 ^ _257529) ^ [] : [-(in(7584 ^ [_526971, _526973, _527455, _530420], complements_of_subsets(the_carrier(_526973), _526971)))], (7587 ^ _257529) ^ [] : [-(ordered_pair(7584 ^ [_526971, _526973, _527455, _530420], 7585 ^ [_526971, _526973, _527455, _530420]) = _530420)]]], (7601 ^ _257529) ^ [_531739] : [-(in(_531739, 7574 ^ [_526971, _526973, _527455])), 7602 ^ _257529 : [(7603 ^ _257529) ^ [_531920] : [in(_531920, cartesian_product2(complements_of_subsets(the_carrier(_526973), _526971), _527455)), _531920 = _531739, 7610 ^ _257529 : [(7611 ^ _257529) ^ [_532249, _532251] : [ordered_pair(_532251, _532249) = _531739, in(_532251, complements_of_subsets(the_carrier(_526973), _526971)), 7619 ^ _257529 : [(7624 ^ _257529) ^ [] : [_532249 = subset_complement(the_carrier(_526973), 7618 ^ [_526971, _526973, _527455, _531739, _531920, _532249, _532251])], (7622 ^ _257529) ^ [] : [-(7618 ^ [_526971, _526973, _527455, _531739, _531920, _532249, _532251] = _532251)], (7620 ^ _257529) ^ [] : [-(element(7618 ^ [_526971, _526973, _527455, _531739, _531920, _532249, _532251], powerset(the_carrier(_526973))))]]]]]]]]]]], (5089 ^ _257529) ^ [] : [-(one_to_one(empty_set))], (10236 ^ _257529) ^ [_634705, _634707] : [relation(_634705), -(relation_field(relation_restriction(_634705, _634707)) = _634707), well_ordering(_634705), subset(_634707, relation_field(_634705))], (10101 ^ _257529) ^ [_630165, _630167] : [relation(_630165), well_ordering(_630165), -(well_ordering(relation_restriction(_630165, _630167)))], (11383 ^ _257529) ^ [_672482, _672484, _672486] : [-(subset(set_union2(_672486, _672482), _672484)), subset(_672486, _672484), subset(_672482, _672484)], (8896 ^ _257529) ^ [_589660] : [-(relation(8894 ^ [_589660]))], (1616 ^ _257529) ^ [_311794, _311796, _311798] : [-(meet_commut(_311798, _311796, _311794) = meet_commut(_311798, _311794, _311796)), -(empty_carrier(_311798)), meet_commutative(_311798), meet_semilatt_str(_311798), element(_311796, the_carrier(_311798)), element(_311794, the_carrier(_311798))], (5141 ^ _257529) ^ [_432805, _432807] : [v2_membered(_432807), 5144 ^ _257529 : [(5145 ^ _257529) ^ [] : [-(v1_membered(set_intersection2(_432805, _432807)))], (5147 ^ _257529) ^ [] : [-(v2_membered(set_intersection2(_432805, _432807)))]]], (5911 ^ _257529) ^ [] : [-(one_to_one(5905 ^ []))], (4411 ^ _257529) ^ [_411022, _411024, _411026] : [-(element(join(_411026, _411024, _411022), the_carrier(_411026))), -(empty_carrier(_411026)), join_semilatt_str(_411026), element(_411024, the_carrier(_411026)), element(_411022, the_carrier(_411026))], (4870 ^ _257529) ^ [] : [-(one_sorted_str(4868 ^ []))], (2181 ^ _257529) ^ [_332227, _332229, _332231, _332233] : [_332227 = unordered_triple(_332233, _332231, _332229), 2184 ^ _257529 : [(2199 ^ _257529) ^ [_332829] : [2200 ^ _257529 : [(2205 ^ _257529) ^ [] : [_332829 = _332229], (2203 ^ _257529) ^ [] : [_332829 = _332231], (2201 ^ _257529) ^ [] : [_332829 = _332233]], -(in(_332829, _332227))], (2185 ^ _257529) ^ [_332429] : [in(_332429, _332227), -(_332429 = _332233), -(_332429 = _332231), -(_332429 = _332229)]]], (9773 ^ _257529) ^ [_619438, _619440] : [ordinal(_619438), in(_619440, _619438), -(ordinal(_619440))], (892 ^ _257529) ^ [_286432, _286434, _286436, _286438, _286440, _286442] : [-(subset_intersection2(_286442, _286438, _286434) = subset_intersection2(_286440, _286436, _286432)), _286442 = _286440, _286438 = _286436, _286434 = _286432], (3823 ^ _257529) ^ [_390338, _390340] : [-(ordered_pair(_390340, _390338) = unordered_pair(unordered_pair(_390340, _390338), singleton(_390340)))], (4133 ^ _257529) ^ [_401232] : [-(empty_carrier(_401232)), latt_str(_401232), 4140 ^ _257529 : [(4155 ^ _257529) ^ [] : [4157 ^ _257529 : [(4163 ^ _257529) ^ [] : [join(_401232, meet(_401232, 4156 ^ [_401232], 4159 ^ [_401232]), 4159 ^ [_401232]) = 4159 ^ [_401232]], (4161 ^ _257529) ^ [] : [-(element(4159 ^ [_401232], the_carrier(_401232)))], (4158 ^ _257529) ^ [] : [-(element(4156 ^ [_401232], the_carrier(_401232)))]], -(meet_absorbing(_401232))], (4141 ^ _257529) ^ [] : [meet_absorbing(_401232), 4144 ^ _257529 : [(4145 ^ _257529) ^ [_401580] : [element(_401580, the_carrier(_401232)), 4148 ^ _257529 : [(4149 ^ _257529) ^ [_401733] : [element(_401733, the_carrier(_401232)), -(join(_401232, meet(_401232, _401580, _401733), _401733) = _401733)]]]]]]], (6984 ^ _257529) ^ [_501901] : [6988 ^ _257529 : [(6989 ^ _257529) ^ [] : [-(in(6985 ^ [_501901], _501901))], (6991 ^ _257529) ^ [] : [-(6986 ^ [_501901] = singleton(6985 ^ [_501901]))], (6997 ^ _257529) ^ [] : [6986 ^ [_501901] = 6987 ^ [_501901]], (6995 ^ _257529) ^ [] : [-(6987 ^ [_501901] = singleton(6985 ^ [_501901]))], (6993 ^ _257529) ^ [] : [-(in(6985 ^ [_501901], _501901))]], 6999 ^ _257529 : [(7000 ^ _257529) ^ [_502787] : [in(_502787, 6998 ^ [_501901]), 7004 ^ _257529 : [(7009 ^ _257529) ^ [] : [-(_502787 = singleton(7003 ^ [_501901, _502787]))], (7007 ^ _257529) ^ [] : [-(in(7003 ^ [_501901, _502787], _501901))], (7005 ^ _257529) ^ [] : [-(in(7003 ^ [_501901, _502787], _501901))]]], (7011 ^ _257529) ^ [_503199] : [-(in(_503199, 6998 ^ [_501901])), 7012 ^ _257529 : [(7013 ^ _257529) ^ [_503306] : [in(_503306, _501901), in(_503306, _501901), _503199 = singleton(_503306)]]]]], (5091 ^ _257529) ^ [] : [-(empty(empty_set))], (2942 ^ _257529) ^ [_359076, _359078, _359080] : [_359076 = unordered_pair(_359080, _359078), 2945 ^ _257529 : [(2956 ^ _257529) ^ [_359536] : [2957 ^ _257529 : [(2958 ^ _257529) ^ [] : [_359536 = _359080], (2960 ^ _257529) ^ [] : [_359536 = _359078]], -(in(_359536, _359076))], (2946 ^ _257529) ^ [_359258] : [in(_359258, _359076), -(_359258 = _359080), -(_359258 = _359078)]]], (3275 ^ _257529) ^ [_371157] : [relation(_371157), 3278 ^ _257529 : [(3296 ^ _257529) ^ [_371960] : [-(is_well_founded_in(_371157, _371960)), 3298 ^ _257529 : [(3303 ^ _257529) ^ [_372302] : [in(_372302, 3297 ^ [_371157, _371960]), disjoint(fiber(_371157, _372302), 3297 ^ [_371157, _371960])], (3301 ^ _257529) ^ [] : [3297 ^ [_371157, _371960] = empty_set], (3299 ^ _257529) ^ [] : [-(subset(3297 ^ [_371157, _371960], _371960))]]], (3279 ^ _257529) ^ [_371354] : [is_well_founded_in(_371157, _371354), 3282 ^ _257529 : [(3283 ^ _257529) ^ [_371519] : [subset(_371519, _371354), -(_371519 = empty_set), 3291 ^ _257529 : [(3292 ^ _257529) ^ [] : [-(in(3290 ^ [_371157, _371354, _371519], _371519))], (3294 ^ _257529) ^ [] : [-(disjoint(fiber(_371157, 3290 ^ [_371157, _371354, _371519]), _371519))]]]]]]], (4357 ^ _257529) ^ [_409723] : [relation(_409723), function(_409723), one_to_one(_409723), -(function_inverse(_409723) = relation_inverse(_409723))], (60 ^ _257529) ^ [_259485, _259487, _259489, _259491] : [-(is_antisymmetric_in(_259489, _259485)), is_antisymmetric_in(_259491, _259487), _259491 = _259489, _259487 = _259485], (9368 ^ _257529) ^ [_606062, _606064, _606066, _606068] : [relation_of2_as_subset(_606062, _606064, _606068), subset(_606068, _606066), -(relation_of2_as_subset(_606062, _606064, _606066))], (3311 ^ _257529) ^ [_372660, _372662, _372664] : [_372660 = set_intersection2(_372664, _372662), 3314 ^ _257529 : [(3315 ^ _257529) ^ [_372842] : [in(_372842, _372660), 3318 ^ _257529 : [(3319 ^ _257529) ^ [] : [-(in(_372842, _372664))], (3321 ^ _257529) ^ [] : [-(in(_372842, _372662))]]], (3323 ^ _257529) ^ [_373101] : [-(in(_373101, _372660)), in(_373101, _372664), in(_373101, _372662)]]], (5969 ^ _257529) ^ [] : [-(empty(5965 ^ []))], (5181 ^ _257529) ^ [_434281, _434283] : [v4_membered(_434283), 5184 ^ _257529 : [(5185 ^ _257529) ^ [] : [-(v1_membered(set_intersection2(_434281, _434283)))], (5191 ^ _257529) ^ [] : [-(v4_membered(set_intersection2(_434281, _434283)))], (5189 ^ _257529) ^ [] : [-(v3_membered(set_intersection2(_434281, _434283)))], (5187 ^ _257529) ^ [] : [-(v2_membered(set_intersection2(_434281, _434283)))]]], (3951 ^ _257529) ^ [_394776] : [relation(_394776), 3954 ^ _257529 : [(3955 ^ _257529) ^ [_394936] : [relation(_394936), 3958 ^ _257529 : [(3975 ^ _257529) ^ [] : [-(_394936 = relation_inverse(_394776)), 3980 ^ _257529 : [(3981 ^ _257529) ^ [] : [-(in(ordered_pair(3976 ^ [_394776, _394936], 3977 ^ [_394776, _394936]), _394936))], (3983 ^ _257529) ^ [] : [in(ordered_pair(3977 ^ [_394776, _394936], 3976 ^ [_394776, _394936]), _394776)]], 3984 ^ _257529 : [(3985 ^ _257529) ^ [] : [-(in(ordered_pair(3977 ^ [_394776, _394936], 3976 ^ [_394776, _394936]), _394776))], (3987 ^ _257529) ^ [] : [in(ordered_pair(3976 ^ [_394776, _394936], 3977 ^ [_394776, _394936]), _394936)]]], (3959 ^ _257529) ^ [] : [_394936 = relation_inverse(_394776), 3962 ^ _257529 : [(3963 ^ _257529) ^ [_395245, _395247] : [in(ordered_pair(_395247, _395245), _394936), -(in(ordered_pair(_395245, _395247), _394776))], (3969 ^ _257529) ^ [_395435, _395437] : [in(ordered_pair(_395435, _395437), _394776), -(in(ordered_pair(_395437, _395435), _394936))]]]]]]], (5986 ^ _257529) ^ [] : [-(ordinal(5972 ^ []))], (11367 ^ _257529) ^ [_672023] : [relation(_672023), 11370 ^ _257529 : [(11371 ^ _257529) ^ [] : [well_orders(_672023, relation_field(_672023)), -(well_ordering(_672023))], (11377 ^ _257529) ^ [] : [well_ordering(_672023), -(well_orders(_672023, relation_field(_672023)))]]], (6173 ^ _257529) ^ [_466994, _466996, _466998] : [relation_of2(_466994, _466998, _466996), -(relation_rng_as_subset(_466998, _466996, _466994) = relation_rng(_466994))], (3637 ^ _257529) ^ [_383826, _383828, _383830] : [-(_383826 = set_difference(_383830, _383828)), 3649 ^ _257529 : [(3654 ^ _257529) ^ [] : [in(3638 ^ [_383826, _383828, _383830], _383826)], (3652 ^ _257529) ^ [] : [in(3638 ^ [_383826, _383828, _383830], _383828)], (3650 ^ _257529) ^ [] : [-(in(3638 ^ [_383826, _383828, _383830], _383830))]], 3641 ^ _257529 : [(3642 ^ _257529) ^ [] : [-(in(3638 ^ [_383826, _383828, _383830], _383826))], (3644 ^ _257529) ^ [] : [in(3638 ^ [_383826, _383828, _383830], _383830), -(in(3638 ^ [_383826, _383828, _383830], _383828))]]], (8637 ^ _257529) ^ [_578828] : [8643 ^ _257529 : [(8644 ^ _257529) ^ [] : [-(in(8640 ^ [_578828], _578828))], (8650 ^ _257529) ^ [] : [8641 ^ [_578828] = 8642 ^ [_578828]], (8648 ^ _257529) ^ [] : [-(8642 ^ [_578828] = singleton(8640 ^ [_578828]))], (8646 ^ _257529) ^ [] : [-(8641 ^ [_578828] = singleton(8640 ^ [_578828]))]], 8652 ^ _257529 : [(8653 ^ _257529) ^ [] : [-(in(8651 ^ [_578828], _578828))], (8655 ^ _257529) ^ [_579682] : [_579682 = singleton(8651 ^ [_578828])]], 8657 ^ _257529 : [(8658 ^ _257529) ^ [] : [-(relation(8656 ^ [_578828]))], (8664 ^ _257529) ^ [_580054] : [in(_580054, _578828), -(apply(8656 ^ [_578828], _580054) = singleton(_580054))], (8662 ^ _257529) ^ [] : [-(relation_dom(8656 ^ [_578828]) = _578828)], (8660 ^ _257529) ^ [] : [-(function(8656 ^ [_578828]))]]], (442 ^ _257529) ^ [_271177, _271179] : [-(topological_space(_271177)), _271179 = _271177, topological_space(_271179)], (5079 ^ _257529) ^ [_430944] : [-(relation(identity_relation(_430944)))], (10531 ^ _257529) ^ [_644706] : [topological_space(_644706), top_str(_644706), 10538 ^ _257529 : [(10539 ^ _257529) ^ [_644982] : [element(_644982, powerset(the_carrier(_644706))), 10543 ^ _257529 : [(10546 ^ _257529) ^ [_645373] : [element(_645373, powerset(the_carrier(_644706))), 10549 ^ _257529 : [(10550 ^ _257529) ^ [] : [in(_645373, 10542 ^ [_644706, _644982]), 10553 ^ _257529 : [(10554 ^ _257529) ^ [] : [-(closed_subset(_645373, _644706))], (10556 ^ _257529) ^ [] : [-(subset(_644982, _645373))]]], (10558 ^ _257529) ^ [] : [-(in(_645373, 10542 ^ [_644706, _644982])), closed_subset(_645373, _644706), subset(_644982, _645373)]]], (10568 ^ _257529) ^ [] : [-(topstr_closure(_644706, _644982) = meet_of_subsets(the_carrier(_644706), 10542 ^ [_644706, _644982]))], (10544 ^ _257529) ^ [] : [-(element(10542 ^ [_644706, _644982], powerset(powerset(the_carrier(_644706)))))]]]]], (9561 ^ _257529) ^ [_612475, _612477] : [relation(_612475), 9564 ^ _257529 : [(9565 ^ _257529) ^ [] : [-(subset(relation_field(relation_restriction(_612475, _612477)), relation_field(_612475)))], (9567 ^ _257529) ^ [] : [-(subset(relation_field(relation_restriction(_612475, _612477)), _612477))]]], (5159 ^ _257529) ^ [_433465, _433467] : [v3_membered(_433467), 5162 ^ _257529 : [(5167 ^ _257529) ^ [] : [-(v3_membered(set_intersection2(_433465, _433467)))], (5165 ^ _257529) ^ [] : [-(v2_membered(set_intersection2(_433465, _433467)))], (5163 ^ _257529) ^ [] : [-(v1_membered(set_intersection2(_433465, _433467)))]]], (1108 ^ _257529) ^ [_294213, _294215] : [_294215 = _294213, -(pair_second(_294215) = pair_second(_294213))], (5950 ^ _257529) ^ [_459807] : [-(relation(5944 ^ [_459807]))], (11047 ^ _257529) ^ [_661676] : [-(antisymmetric(inclusion_relation(_661676)))], (9897 ^ _257529) ^ [_623365] : [-(empty_carrier(_623365)), join_commutative(_623365), join_semilatt_str(_623365), 9908 ^ _257529 : [(9909 ^ _257529) ^ [_623694] : [element(_623694, the_carrier(_623365)), 9912 ^ _257529 : [(9913 ^ _257529) ^ [_623853] : [element(_623853, the_carrier(_623365)), -(_623694 = _623853), below(_623365, _623694, _623853), below(_623365, _623853, _623694)]]]]], (8103 ^ _257529) ^ [_556288, _556290, _556292] : [in(_556288, 8101 ^ [_556290, _556292]), 8106 ^ _257529 : [(8107 ^ _257529) ^ [] : [-(in(_556288, cartesian_product2(_556292, _556290)))], (8115 ^ _257529) ^ [] : [-(8109 ^ [_556288, _556290, _556292] = singleton(8108 ^ [_556288, _556290, _556292]))], (8113 ^ _257529) ^ [] : [-(in(8108 ^ [_556288, _556290, _556292], _556292))], (8111 ^ _257529) ^ [] : [-(ordered_pair(8108 ^ [_556288, _556290, _556292], 8109 ^ [_556288, _556290, _556292]) = _556288)]]], (9398 ^ _257529) ^ [_607027, _607029, _607031] : [relation(_607027), 9401 ^ _257529 : [(9402 ^ _257529) ^ [] : [in(_607031, relation_restriction(_607027, _607029)), 9405 ^ _257529 : [(9406 ^ _257529) ^ [] : [-(in(_607031, _607027))], (9408 ^ _257529) ^ [] : [-(in(_607031, cartesian_product2(_607029, _607029)))]]], (9410 ^ _257529) ^ [] : [-(in(_607031, relation_restriction(_607027, _607029))), in(_607031, _607027), in(_607031, cartesian_product2(_607029, _607029))]]], (4853 ^ _257529) ^ [_423575] : [join_semilatt_str(_423575), 4856 ^ _257529 : [(4861 ^ _257529) ^ [] : [-(relation_of2_as_subset(the_L_join(_423575), cartesian_product2(the_carrier(_423575), the_carrier(_423575)), the_carrier(_423575)))], (4859 ^ _257529) ^ [] : [-(quasi_total(the_L_join(_423575), cartesian_product2(the_carrier(_423575), the_carrier(_423575)), the_carrier(_423575)))], (4857 ^ _257529) ^ [] : [-(function(the_L_join(_423575)))]]], (1466 ^ _257529) ^ [_307065] : [v5_membered(_307065), 1469 ^ _257529 : [(1470 ^ _257529) ^ [_307217] : [element(_307217, powerset(_307065)), 1473 ^ _257529 : [(1474 ^ _257529) ^ [] : [-(v1_membered(_307217))], (1476 ^ _257529) ^ [] : [-(v2_membered(_307217))], (1482 ^ _257529) ^ [] : [-(v5_membered(_307217))], (1480 ^ _257529) ^ [] : [-(v4_membered(_307217))], (1478 ^ _257529) ^ [] : [-(v3_membered(_307217))]]]]], (2759 ^ _257529) ^ [_352612] : [_352612 = empty_set, 2762 ^ _257529 : [(2763 ^ _257529) ^ [_352725] : [in(_352725, _352612)]]], (4967 ^ _257529) ^ [_427343] : [-(preboolean(powerset(_427343)))], (3412 ^ _257529) ^ [_375880] : [relation(_375880), 3415 ^ _257529 : [(3433 ^ _257529) ^ [_376692] : [-(_376692 = relation_dom(_375880)), 3437 ^ _257529 : [(3438 ^ _257529) ^ [] : [-(in(3434 ^ [_375880, _376692], _376692))], (3440 ^ _257529) ^ [_376955] : [in(ordered_pair(3434 ^ [_375880, _376692], _376955), _375880)]], 3442 ^ _257529 : [(3443 ^ _257529) ^ [] : [-(in(ordered_pair(3434 ^ [_375880, _376692], 3441 ^ [_375880, _376692]), _375880))], (3445 ^ _257529) ^ [] : [in(3434 ^ [_375880, _376692], _376692)]]], (3416 ^ _257529) ^ [_376061] : [_376061 = relation_dom(_375880), 3419 ^ _257529 : [(3420 ^ _257529) ^ [_376241] : [in(_376241, _376061), -(in(ordered_pair(_376241, 3423 ^ [_375880, _376061, _376241]), _375880))], (3427 ^ _257529) ^ [_376485] : [3428 ^ _257529 : [(3429 ^ _257529) ^ [_376564] : [in(ordered_pair(_376485, _376564), _375880)]], -(in(_376485, _376061))]]]]], (10570 ^ _257529) ^ [_646109] : [relation(_646109), 10573 ^ _257529 : [(10574 ^ _257529) ^ [_646256] : [relation(_646256), subset(relation_rng(_646109), relation_dom(_646256)), -(relation_dom(relation_composition(_646109, _646256)) = relation_dom(_646109))]]], (10680 ^ _257529) ^ [_649824] : [ordinal(_649824), -(connected(inclusion_relation(_649824)))], (10064 ^ _257529) ^ [_628972, _628974] : [relation(_628972), well_founded_relation(_628972), -(well_founded_relation(relation_restriction(_628972, _628974)))], (6003 ^ _257529) ^ [_461590] : [-(empty(5999 ^ [_461590]))], (4387 ^ _257529) ^ [] : [true___, -(true___)], (1226 ^ _257529) ^ [_298498, _298500, _298502, _298504] : [-(unordered_pair(_298504, _298500) = unordered_pair(_298502, _298498)), _298504 = _298502, _298500 = _298498], (11059 ^ _257529) ^ [_662087] : [relation(_662087), function(_662087), one_to_one(_662087), -(one_to_one(function_inverse(_662087)))], (2051 ^ _257529) ^ [_327256] : [relation(_327256), 2054 ^ _257529 : [(2078 ^ _257529) ^ [_328369, _328371] : [-(_328369 = relation_image(_327256, _328371)), 2091 ^ _257529 : [(2096 ^ _257529) ^ [] : [in(2079 ^ [_327256, _328369, _328371], _328369)], (2094 ^ _257529) ^ [] : [-(in(2090 ^ [_327256, _328369, _328371], _328371))], (2092 ^ _257529) ^ [] : [-(in(ordered_pair(2090 ^ [_327256, _328369, _328371], 2079 ^ [_327256, _328369, _328371]), _327256))]], 2082 ^ _257529 : [(2083 ^ _257529) ^ [] : [-(in(2079 ^ [_327256, _328369, _328371], _328369))], (2085 ^ _257529) ^ [_328673] : [in(ordered_pair(_328673, 2079 ^ [_327256, _328369, _328371]), _327256), in(_328673, _328371)]]], (2055 ^ _257529) ^ [_327463, _327465] : [_327463 = relation_image(_327256, _327465), 2058 ^ _257529 : [(2059 ^ _257529) ^ [_327655] : [in(_327655, _327463), 2063 ^ _257529 : [(2064 ^ _257529) ^ [] : [-(in(ordered_pair(2062 ^ [_327256, _327463, _327465, _327655], _327655), _327256))], (2066 ^ _257529) ^ [] : [-(in(2062 ^ [_327256, _327463, _327465, _327655], _327465))]]], (2068 ^ _257529) ^ [_328009] : [-(in(_328009, _327463)), 2069 ^ _257529 : [(2070 ^ _257529) ^ [_328114] : [in(ordered_pair(_328114, _328009), _327256), in(_328114, _327465)]]]]]]], (5552 ^ _257529) ^ [_446303] : [singleton(_446303) = empty_set], (2910 ^ _257529) ^ [_358163, _358165] : [-(empty(_358165)), 2913 ^ _257529 : [(2914 ^ _257529) ^ [] : [element(_358163, _358165), -(in(_358163, _358165))], (2920 ^ _257529) ^ [] : [in(_358163, _358165), -(element(_358163, _358165))]]], (3658 ^ _257529) ^ [_384569] : [relation(_384569), function(_384569), 3665 ^ _257529 : [(3689 ^ _257529) ^ [_385723] : [-(_385723 = relation_rng(_384569)), 3702 ^ _257529 : [(3707 ^ _257529) ^ [] : [in(3690 ^ [_384569, _385723], _385723)], (3705 ^ _257529) ^ [] : [-(3690 ^ [_384569, _385723] = apply(_384569, 3701 ^ [_384569, _385723]))], (3703 ^ _257529) ^ [] : [-(in(3701 ^ [_384569, _385723], relation_dom(_384569)))]], 3693 ^ _257529 : [(3694 ^ _257529) ^ [] : [-(in(3690 ^ [_384569, _385723], _385723))], (3696 ^ _257529) ^ [_386018] : [in(_386018, relation_dom(_384569)), 3690 ^ [_384569, _385723] = apply(_384569, _386018)]]], (3666 ^ _257529) ^ [_384841] : [_384841 = relation_rng(_384569), 3669 ^ _257529 : [(3670 ^ _257529) ^ [_385029] : [in(_385029, _384841), 3674 ^ _257529 : [(3675 ^ _257529) ^ [] : [-(in(3673 ^ [_384569, _384841, _385029], relation_dom(_384569)))], (3677 ^ _257529) ^ [] : [-(_385029 = apply(_384569, 3673 ^ [_384569, _384841, _385029]))]]], (3679 ^ _257529) ^ [_385371] : [-(in(_385371, _384841)), 3680 ^ _257529 : [(3681 ^ _257529) ^ [_385474] : [in(_385474, relation_dom(_384569)), _385371 = apply(_384569, _385474)]]]]]]], (1718 ^ _257529) ^ [_315055, _315057] : [-(_315057 = _315055), subset(_315057, _315055), subset(_315055, _315057)], (1662 ^ _257529) ^ [_313137, _313139] : [relation(_313137), 1665 ^ _257529 : [(1688 ^ _257529) ^ [] : [-(_313137 = identity_relation(_313139)), 1701 ^ _257529 : [(1706 ^ _257529) ^ [] : [in(ordered_pair(1689 ^ [_313137, _313139], 1690 ^ [_313137, _313139]), _313137)], (1704 ^ _257529) ^ [] : [-(1689 ^ [_313137, _313139] = 1690 ^ [_313137, _313139])], (1702 ^ _257529) ^ [] : [-(in(1689 ^ [_313137, _313139], _313139))]], 1693 ^ _257529 : [(1694 ^ _257529) ^ [] : [-(in(ordered_pair(1689 ^ [_313137, _313139], 1690 ^ [_313137, _313139]), _313137))], (1696 ^ _257529) ^ [] : [in(1689 ^ [_313137, _313139], _313139), 1689 ^ [_313137, _313139] = 1690 ^ [_313137, _313139]]]], (1666 ^ _257529) ^ [] : [_313137 = identity_relation(_313139), 1669 ^ _257529 : [(1670 ^ _257529) ^ [_313447, _313449] : [in(ordered_pair(_313449, _313447), _313137), 1673 ^ _257529 : [(1674 ^ _257529) ^ [] : [-(in(_313449, _313139))], (1676 ^ _257529) ^ [] : [-(_313449 = _313447)]]], (1678 ^ _257529) ^ [_313710, _313712] : [-(in(ordered_pair(_313712, _313710), _313137)), in(_313712, _313139), _313712 = _313710]]]]], (4885 ^ _257529) ^ [_424710, _424712] : [-(relation_of2_as_subset(4883 ^ [_424710, _424712], _424712, _424710))], (1214 ^ _257529) ^ [_298034, _298036] : [_298036 = _298034, -(union(_298036) = union(_298034))], (5644 ^ _257529) ^ [_449584, _449586] : [subset(_449586, _449584), -(set_difference(_449586, _449584) = empty_set)], (11053 ^ _257529) ^ [_661892, _661894] : [subset(_661894, _661892), proper_subset(_661892, _661894)], (8379 ^ _257529) ^ [_567648, _567650] : [one_sorted_str(_567650), element(_567648, powerset(powerset(the_carrier(_567650)))), 8387 ^ _257529 : [(8388 ^ _257529) ^ [_568115, _568117] : [in(_568115, 8386 ^ [_567648, _567650, _568117]), 8391 ^ _257529 : [(8392 ^ _257529) ^ [] : [-(in(_568115, cartesian_product2(_567648, _568117)))], (8400 ^ _257529) ^ [_568806] : [element(_568806, powerset(the_carrier(_567650))), _568806 = 8393 ^ [_567648, _567650, _568115, _568117], -(8394 ^ [_567648, _567650, _568115, _568117] = subset_complement(the_carrier(_567650), _568806))], (8398 ^ _257529) ^ [] : [-(in(8393 ^ [_567648, _567650, _568115, _568117], _567648))], (8396 ^ _257529) ^ [] : [-(ordered_pair(8393 ^ [_567648, _567650, _568115, _568117], 8394 ^ [_567648, _567650, _568115, _568117]) = _568115)]]], (8410 ^ _257529) ^ [_569168, _569170] : [-(in(_569168, 8386 ^ [_567648, _567650, _569170])), in(_569168, cartesian_product2(_567648, _569170)), 8415 ^ _257529 : [(8416 ^ _257529) ^ [_569430, _569432] : [ordered_pair(_569432, _569430) = _569168, in(_569432, _567648), 8424 ^ _257529 : [(8429 ^ _257529) ^ [] : [_569430 = subset_complement(the_carrier(_567650), 8423 ^ [_567648, _567650, _569168, _569170, _569430, _569432])], (8427 ^ _257529) ^ [] : [-(8423 ^ [_567648, _567650, _569168, _569170, _569430, _569432] = _569432)], (8425 ^ _257529) ^ [] : [-(element(8423 ^ [_567648, _567650, _569168, _569170, _569430, _569432], powerset(the_carrier(_567650))))]]]]]]], (2985 ^ _257529) ^ [_360538] : [top_str(_360538), 2988 ^ _257529 : [(2989 ^ _257529) ^ [_360702] : [element(_360702, powerset(powerset(the_carrier(_360538)))), 2992 ^ _257529 : [(3007 ^ _257529) ^ [] : [3009 ^ _257529 : [(3014 ^ _257529) ^ [] : [closed_subset(3008 ^ [_360538, _360702], _360538)], (3012 ^ _257529) ^ [] : [-(in(3008 ^ [_360538, _360702], _360702))], (3010 ^ _257529) ^ [] : [-(element(3008 ^ [_360538, _360702], powerset(the_carrier(_360538))))]], -(closed_subsets(_360702, _360538))], (2993 ^ _257529) ^ [] : [closed_subsets(_360702, _360538), 2996 ^ _257529 : [(2997 ^ _257529) ^ [_360977] : [element(_360977, powerset(the_carrier(_360538))), in(_360977, _360702), -(closed_subset(_360977, _360538))]]]]]]], (4882 ^ _257529) ^ [_424571] : [-(element(4880 ^ [_424571], _424571))], (9075 ^ _257529) ^ [_595831, _595833] : [relation(_595831), -(subset(relation_rng_restriction(_595833, _595831), _595831))], (5321 ^ _257529) ^ [_439043, _439045] : [v5_membered(_439045), 5324 ^ _257529 : [(5325 ^ _257529) ^ [] : [-(v1_membered(set_difference(_439045, _439043)))], (5327 ^ _257529) ^ [] : [-(v2_membered(set_difference(_439045, _439043)))], (5333 ^ _257529) ^ [] : [-(v5_membered(set_difference(_439045, _439043)))], (5331 ^ _257529) ^ [] : [-(v4_membered(set_difference(_439045, _439043)))], (5329 ^ _257529) ^ [] : [-(v3_membered(set_difference(_439045, _439043)))]]], (30 ^ _257529) ^ [_258572, _258574] : [-(v1_xreal_0(_258572)), _258574 = _258572, v1_xreal_0(_258574)], (2149 ^ _257529) ^ [_331294] : [relation(_331294), 2152 ^ _257529 : [(2153 ^ _257529) ^ [] : [connected(_331294), -(is_connected_in(_331294, relation_field(_331294)))], (2159 ^ _257529) ^ [] : [is_connected_in(_331294, relation_field(_331294)), -(connected(_331294))]]], (5499 ^ _257529) ^ [_444538, _444540, _444542] : [-(subset_intersection2(_444542, _444540, _444540) = _444540), element(_444540, powerset(_444542)), element(_444538, powerset(_444542))], (9647 ^ _257529) ^ [_615190] : [relation(_615190), -(subset(_615190, cartesian_product2(relation_dom(_615190), relation_rng(_615190))))], (11325 ^ _257529) ^ [_670757, _670759] : [relation(_670757), -(subset(relation_dom_restriction(_670757, _670759), _670757))], (10321 ^ _257529) ^ [_637554, _637556] : [-(set_difference(set_union2(_637556, _637554), _637554) = set_difference(_637556, _637554))], (1590 ^ _257529) ^ [_310942, _310944] : [-(set_union2(_310944, _310942) = set_union2(_310942, _310944))], (2615 ^ _257529) ^ [_347560] : [top_str(_347560), 2618 ^ _257529 : [(2619 ^ _257529) ^ [_347711] : [element(_347711, powerset(the_carrier(_347560))), -(interior(_347560, _347711) = subset_complement(the_carrier(_347560), topstr_closure(_347560, subset_complement(the_carrier(_347560), _347711))))]]], (10294 ^ _257529) ^ [_636574] : [-(transitive(inclusion_relation(_636574)))], (858 ^ _257529) ^ [_285182, _285184, _285186, _285188, _285190, _285192] : [-(join(_285192, _285188, _285184) = join(_285190, _285186, _285182)), _285192 = _285190, _285188 = _285186, _285184 = _285182], (9101 ^ _257529) ^ [_596854, _596856, _596858, _596860] : [-(subset(cartesian_product2(_596860, _596856), cartesian_product2(_596858, _596854))), subset(_596860, _596858), subset(_596856, _596854)], (4294 ^ _257529) ^ [_407604, _407606] : [element(_407604, powerset(powerset(_407606))), 4297 ^ _257529 : [(4298 ^ _257529) ^ [_407784] : [element(_407784, powerset(powerset(_407606))), 4301 ^ _257529 : [(4322 ^ _257529) ^ [] : [-(_407784 = complements_of_subsets(_407606, _407604)), 4324 ^ _257529 : [(4325 ^ _257529) ^ [] : [-(element(4323 ^ [_407604, _407606, _407784], powerset(_407606)))], (4327 ^ _257529) ^ [] : [4328 ^ _257529 : [(4329 ^ _257529) ^ [] : [-(in(4323 ^ [_407604, _407606, _407784], _407784))], (4331 ^ _257529) ^ [] : [in(subset_complement(_407606, 4323 ^ [_407604, _407606, _407784]), _407604)]], 4332 ^ _257529 : [(4333 ^ _257529) ^ [] : [-(in(subset_complement(_407606, 4323 ^ [_407604, _407606, _407784]), _407604))], (4335 ^ _257529) ^ [] : [in(4323 ^ [_407604, _407606, _407784], _407784)]]]]], (4302 ^ _257529) ^ [] : [_407784 = complements_of_subsets(_407606, _407604), 4305 ^ _257529 : [(4306 ^ _257529) ^ [_408072] : [element(_408072, powerset(_407606)), 4309 ^ _257529 : [(4310 ^ _257529) ^ [] : [in(_408072, _407784), -(in(subset_complement(_407606, _408072), _407604))], (4316 ^ _257529) ^ [] : [in(subset_complement(_407606, _408072), _407604), -(in(_408072, _407784))]]]]]]]]], (176 ^ _257529) ^ [_263003, _263005] : [-(v4_membered(_263003)), _263005 = _263003, v4_membered(_263005)], (10897 ^ _257529) ^ [_657006] : [relation(_657006), 10900 ^ _257529 : [(10901 ^ _257529) ^ [_657162] : [relation(_657162), 10904 ^ _257529 : [(10905 ^ _257529) ^ [_657314] : [relation(_657314), function(_657314), -(well_ordering(_657162)), well_ordering(_657006), relation_isomorphism(_657006, _657162, _657314)]]]]], (5875 ^ _257529) ^ [_457343, _457345] : [-(quasi_total(5867 ^ [_457343, _457345], _457345, _457343))], (10323 ^ _257529) ^ [_637658] : [ordinal(_637658), 10326 ^ _257529 : [(10341 ^ _257529) ^ [] : [10343 ^ _257529 : [(10348 ^ _257529) ^ [] : [in(succ(10342 ^ [_637658]), _637658)], (10346 ^ _257529) ^ [] : [-(in(10342 ^ [_637658], _637658))], (10344 ^ _257529) ^ [] : [-(ordinal(10342 ^ [_637658]))]], -(being_limit_ordinal(_637658))], (10327 ^ _257529) ^ [] : [being_limit_ordinal(_637658), 10330 ^ _257529 : [(10331 ^ _257529) ^ [_637904] : [ordinal(_637904), in(_637904, _637658), -(in(succ(_637904), _637658))]]]]], (6039 ^ _257529) ^ [] : [-(one_to_one(6033 ^ []))], (10624 ^ _257529) ^ [_647904] : [top_str(_647904), 10627 ^ _257529 : [(10628 ^ _257529) ^ [_648042] : [element(_648042, powerset(the_carrier(_647904))), -(subset(_648042, topstr_closure(_647904, _648042)))]]], (5974 ^ _257529) ^ [] : [-(relation(5972 ^ []))], (4679 ^ _257529) ^ [] : [true___, -(true___)], (5109 ^ _257529) ^ [_431814, _431816] : [-(relation(set_union2(_431816, _431814))), relation(_431816), relation(_431814)], (10206 ^ _257529) ^ [_633712, _633714] : [subset(singleton(_633714), _633712), -(in(_633714, _633712))], (4621 ^ _257529) ^ [] : [true___, -(true___)], (6359 ^ _257529) ^ [_474394] : [6363 ^ _257529 : [(6364 ^ _257529) ^ [] : [-(in(6360 ^ [_474394], _474394))], (6366 ^ _257529) ^ [] : [-(6361 ^ [_474394] = singleton(6360 ^ [_474394]))], (6372 ^ _257529) ^ [] : [6361 ^ [_474394] = 6362 ^ [_474394]], (6370 ^ _257529) ^ [] : [-(6362 ^ [_474394] = singleton(6360 ^ [_474394]))], (6368 ^ _257529) ^ [] : [-(in(6360 ^ [_474394], _474394))]], 6374 ^ _257529 : [(6375 ^ _257529) ^ [] : [-(relation(6373 ^ [_474394]))], (6389 ^ _257529) ^ [_475799, _475801] : [-(in(ordered_pair(_475801, _475799), 6373 ^ [_474394])), in(_475801, _474394), in(_475801, _474394), _475799 = singleton(_475801)], (6379 ^ _257529) ^ [_475456, _475458] : [in(ordered_pair(_475458, _475456), 6373 ^ [_474394]), 6382 ^ _257529 : [(6387 ^ _257529) ^ [] : [-(_475456 = singleton(_475458))], (6385 ^ _257529) ^ [] : [-(in(_475458, _474394))], (6383 ^ _257529) ^ [] : [-(in(_475458, _474394))]]], (6377 ^ _257529) ^ [] : [-(function(6373 ^ [_474394]))]]], (9313 ^ _257529) ^ [_604059] : [one_sorted_str(_604059), 9316 ^ _257529 : [(9317 ^ _257529) ^ [_604202] : [element(_604202, powerset(the_carrier(_604059))), -(subset_intersection2(the_carrier(_604059), _604202, cast_as_carrier_subset(_604059)) = _604202)]]], (500 ^ _257529) ^ [_272978, _272980, _272982, _272984] : [-(is_well_founded_in(_272982, _272978)), is_well_founded_in(_272984, _272980), _272984 = _272982, _272980 = _272978], (10315 ^ _257529) ^ [_637365] : [subset(_637365, empty_set), -(_637365 = empty_set)], (5097 ^ _257529) ^ [] : [-(ordinal(empty_set))], (5900 ^ _257529) ^ [] : [-(epsilon_connected(5896 ^ []))], (6871 ^ _257529) ^ [_495198, _495200] : [-(empty(_495200)), relation(_495198), 6878 ^ _257529 : [(6879 ^ _257529) ^ [_495666] : [6883 ^ _257529 : [(6914 ^ _257529) ^ [] : [-(in(6905 ^ [_495198, _495200, _495666], 6910 ^ [_495198, _495200, _495666]))], (6912 ^ _257529) ^ [] : [-(6904 ^ [_495198, _495200, _495666] = 6910 ^ [_495198, _495200, _495666])], (6909 ^ _257529) ^ [] : [-(in(6904 ^ [_495198, _495200, _495666], _495200))], (6897 ^ _257529) ^ [_497444] : [in(_497444, 6891 ^ [_495198, _495200, _495666]), -(in(ordered_pair(6886 ^ [_495198, _495200, _495666], _497444), _495198))], (6907 ^ _257529) ^ [] : [-(ordered_pair(6904 ^ [_495198, _495200, _495666], 6905 ^ [_495198, _495200, _495666]) = 6882 ^ [_495198, _495200, _495666])], (6884 ^ _257529) ^ [] : [-(6880 ^ [_495198, _495200, _495666] = 6881 ^ [_495198, _495200, _495666])], (6916 ^ _257529) ^ [_498463] : [in(_498463, 6910 ^ [_495198, _495200, _495666]), -(in(ordered_pair(6905 ^ [_495198, _495200, _495666], _498463), _495198))], (6903 ^ _257529) ^ [] : [-(6880 ^ [_495198, _495200, _495666] = 6882 ^ [_495198, _495200, _495666])], (6895 ^ _257529) ^ [] : [-(in(6886 ^ [_495198, _495200, _495666], 6891 ^ [_495198, _495200, _495666]))], (6890 ^ _257529) ^ [] : [-(in(6885 ^ [_495198, _495200, _495666], _495200))], (6888 ^ _257529) ^ [] : [-(ordered_pair(6885 ^ [_495198, _495200, _495666], 6886 ^ [_495198, _495200, _495666]) = 6881 ^ [_495198, _495200, _495666])], (6893 ^ _257529) ^ [] : [-(6885 ^ [_495198, _495200, _495666] = 6891 ^ [_495198, _495200, _495666])], (6922 ^ _257529) ^ [] : [6881 ^ [_495198, _495200, _495666] = 6882 ^ [_495198, _495200, _495666]]], 6924 ^ _257529 : [(6925 ^ _257529) ^ [_498953] : [in(_498953, 6923 ^ [_495198, _495200, _495666]), 6929 ^ _257529 : [(6932 ^ _257529) ^ [] : [-(6928 ^ [_495198, _495200, _495666, _498953] = _498953)], (6943 ^ _257529) ^ [] : [-(in(6934 ^ [_495198, _495200, _495666, _498953], 6939 ^ [_495198, _495200, _495666, _498953]))], (6945 ^ _257529) ^ [_500184] : [in(_500184, 6939 ^ [_495198, _495200, _495666, _498953]), -(in(ordered_pair(6934 ^ [_495198, _495200, _495666, _498953], _500184), _495198))], (6938 ^ _257529) ^ [] : [-(in(6933 ^ [_495198, _495200, _495666, _498953], _495200))], (6930 ^ _257529) ^ [] : [-(in(6928 ^ [_495198, _495200, _495666, _498953], cartesian_product2(_495200, _495666)))], (6936 ^ _257529) ^ [] : [-(ordered_pair(6933 ^ [_495198, _495200, _495666, _498953], 6934 ^ [_495198, _495200, _495666, _498953]) = _498953)], (6941 ^ _257529) ^ [] : [-(6933 ^ [_495198, _495200, _495666, _498953] = 6939 ^ [_495198, _495200, _495666, _498953])]]], (6951 ^ _257529) ^ [_500439] : [-(in(_500439, 6923 ^ [_495198, _495200, _495666])), 6952 ^ _257529 : [(6953 ^ _257529) ^ [_500615] : [in(_500615, cartesian_product2(_495200, _495666)), _500615 = _500439, 6960 ^ _257529 : [(6961 ^ _257529) ^ [_500934, _500936] : [ordered_pair(_500936, _500934) = _500439, in(_500936, _495200), 6968 ^ _257529 : [(6969 ^ _257529) ^ [_501232] : [_500936 = _501232, in(_500934, _501232), 6977 ^ _257529 : [(6978 ^ _257529) ^ [] : [-(in(6976 ^ [_495198, _495200, _495666, _500439, _500615, _500934, _500936, _501232], _501232))], (6980 ^ _257529) ^ [] : [in(ordered_pair(_500934, 6976 ^ [_495198, _495200, _495666, _500439, _500615, _500934, _500936, _501232]), _495198)]]]]]]]]]]]]], (5285 ^ _257529) ^ [_437889, _437891] : [-(open_subset(subset_complement(the_carrier(_437891), _437889), _437891)), topological_space(_437891), top_str(_437891), closed_subset(_437889, _437891), element(_437889, powerset(the_carrier(_437891)))], (5389 ^ _257529) ^ [_441190, _441192] : [5396 ^ _257529 : [(5397 ^ _257529) ^ [] : [-(relation(relation_rng_restriction(_441192, _441190)))], (5399 ^ _257529) ^ [] : [-(function(relation_rng_restriction(_441192, _441190)))]], relation(_441190), function(_441190)], (10111 ^ _257529) ^ [_630450] : [ordinal(_630450), 10114 ^ _257529 : [(10115 ^ _257529) ^ [_630588] : [ordinal(_630588), 10118 ^ _257529 : [(10119 ^ _257529) ^ [] : [in(_630450, _630588), -(ordinal_subset(succ(_630450), _630588))], (10125 ^ _257529) ^ [] : [ordinal_subset(succ(_630450), _630588), -(in(_630450, _630588))]]]]], (5149 ^ _257529) ^ [_433096, _433098] : [v3_membered(_433098), 5152 ^ _257529 : [(5157 ^ _257529) ^ [] : [-(v3_membered(set_intersection2(_433098, _433096)))], (5155 ^ _257529) ^ [] : [-(v2_membered(set_intersection2(_433098, _433096)))], (5153 ^ _257529) ^ [] : [-(v1_membered(set_intersection2(_433098, _433096)))]]], (5913 ^ _257529) ^ [] : [-(empty(5905 ^ []))], (9817 ^ _257529) ^ [_620949] : [ordinal(_620949), 9820 ^ _257529 : [(9821 ^ _257529) ^ [_621099] : [ordinal(_621099), -(in(_620949, _621099)), -(_620949 = _621099), -(in(_621099, _620949))]]], (3897 ^ _257529) ^ [_392665] : [relation(_392665), -(relation_field(_392665) = set_union2(relation_dom(_392665), relation_rng(_392665)))], (1192 ^ _257529) ^ [_297239, _297241] : [_297241 = _297239, -(identity_relation(_297241) = identity_relation(_297239))], (5423 ^ _257529) ^ [] : [-(v1_membered(empty_set))], (5465 ^ _257529) ^ [_443374] : [empty(_443374), 5468 ^ _257529 : [(5469 ^ _257529) ^ [] : [-(empty(relation_rng(_443374)))], (5471 ^ _257529) ^ [] : [-(relation(relation_rng(_443374)))]]], (10600 ^ _257529) ^ [_647105] : [relation(_647105), 10603 ^ _257529 : [(10604 ^ _257529) ^ [_647252] : [relation(_647252), subset(relation_dom(_647105), relation_rng(_647252)), -(relation_rng(relation_composition(_647252, _647105)) = relation_rng(_647105))]]], (5884 ^ _257529) ^ [] : [-(v3_membered(5876 ^ []))], (9681 ^ _257529) ^ [_616332] : [one_sorted_str(_616332), 9684 ^ _257529 : [(9685 ^ _257529) ^ [_616483] : [element(_616483, powerset(the_carrier(_616332))), -(subset_difference(the_carrier(_616332), cast_as_carrier_subset(_616332), subset_difference(the_carrier(_616332), cast_as_carrier_subset(_616332), _616483)) = _616483)]]], (10418 ^ _257529) ^ [_640716] : [relation(_640716), 10421 ^ _257529 : [(10422 ^ _257529) ^ [_640853] : [relation(_640853), -(subset(relation_dom(relation_composition(_640716, _640853)), relation_dom(_640716)))]]], (5788 ^ _257529) ^ [_454458, _454460] : [in(_454460, _454458), -(subset(_454460, union(_454458)))], (1340 ^ _257529) ^ [_302803] : [empty(_302803), 1343 ^ _257529 : [(1344 ^ _257529) ^ [] : [-(v1_membered(_302803))], (1346 ^ _257529) ^ [] : [-(v2_membered(_302803))], (1352 ^ _257529) ^ [] : [-(v5_membered(_302803))], (1350 ^ _257529) ^ [] : [-(v4_membered(_302803))], (1348 ^ _257529) ^ [] : [-(v3_membered(_302803))]]], (10686 ^ _257529) ^ [_650048, _650050] : [-(disjoint(_650050, _650048)), -(in(10689 ^ [_650048, _650050], set_intersection2(_650050, _650048)))], (6001 ^ _257529) ^ [_461539] : [-(element(5999 ^ [_461539], powerset(_461539)))], (9111 ^ _257529) ^ [_597185, _597187] : [element(_597185, powerset(powerset(_597187))), -(_597185 = empty_set), -(meet_of_subsets(_597187, complements_of_subsets(_597187, _597185)) = subset_complement(_597187, union_of_subsets(_597187, _597185)))], (3493 ^ _257529) ^ [_379081, _379083] : [_379081 = union(_379083), 3496 ^ _257529 : [(3497 ^ _257529) ^ [_379262] : [in(_379262, _379081), 3501 ^ _257529 : [(3502 ^ _257529) ^ [] : [-(in(_379262, 3500 ^ [_379081, _379083, _379262]))], (3504 ^ _257529) ^ [] : [-(in(3500 ^ [_379081, _379083, _379262], _379083))]]], (3506 ^ _257529) ^ [_379589] : [-(in(_379589, _379081)), 3507 ^ _257529 : [(3508 ^ _257529) ^ [_379687] : [in(_379589, _379687), in(_379687, _379083)]]]]], (1102 ^ _257529) ^ [_293995, _293997] : [_293997 = _293995, -(pair_first(_293997) = pair_first(_293995))], (4475 ^ _257529) ^ [] : [true___, -(true___)], (4831 ^ _257529) ^ [_422869] : [meet_semilatt_str(_422869), 4834 ^ _257529 : [(4839 ^ _257529) ^ [] : [-(relation_of2_as_subset(the_L_meet(_422869), cartesian_product2(the_carrier(_422869), the_carrier(_422869)), the_carrier(_422869)))], (4837 ^ _257529) ^ [] : [-(quasi_total(the_L_meet(_422869), cartesian_product2(the_carrier(_422869), the_carrier(_422869)), the_carrier(_422869)))], (4835 ^ _257529) ^ [] : [-(function(the_L_meet(_422869)))]]], (9549 ^ _257529) ^ [_612077, _612079, _612081] : [relation(_612077), in(ordered_pair(_612081, _612079), _612077), 9556 ^ _257529 : [(9557 ^ _257529) ^ [] : [-(in(_612081, relation_dom(_612077)))], (9559 ^ _257529) ^ [] : [-(in(_612079, relation_rng(_612077)))]]], (9938 ^ _257529) ^ [_624706] : [-(empty(_624706)), 9944 ^ _257529 : [(9945 ^ _257529) ^ [] : [-(in(9943 ^ [_624706], _624706))], (9947 ^ _257529) ^ [] : [-(9943 ^ [_624706] = empty_set)]], 9949 ^ _257529 : [(9950 ^ _257529) ^ [] : [-(relation(9948 ^ [_624706]))], (9956 ^ _257529) ^ [_625374] : [in(_625374, _624706), -(in(apply(9948 ^ [_624706], _625374), _625374))], (9954 ^ _257529) ^ [] : [-(relation_dom(9948 ^ [_624706]) = _624706)], (9952 ^ _257529) ^ [] : [-(function(9948 ^ [_624706]))]]], (10428 ^ _257529) ^ [_641068] : [top_str(_641068), 10431 ^ _257529 : [(10432 ^ _257529) ^ [_641206] : [element(_641206, powerset(the_carrier(_641068))), -(subset(interior(_641068, _641206), _641206))]]], (1120 ^ _257529) ^ [_294677, _294679, _294681, _294683] : [-(set_difference(_294683, _294679) = set_difference(_294681, _294677)), _294683 = _294681, _294679 = _294677], (5085 ^ _257529) ^ [] : [-(relation_empty_yielding(empty_set))], (9021 ^ _257529) ^ [_594085, _594087] : [element(_594085, powerset(powerset(_594087))), 9024 ^ _257529 : [(9025 ^ _257529) ^ [] : [-(_594085 = empty_set), complements_of_subsets(_594087, _594085) = empty_set], (9031 ^ _257529) ^ [] : [-(complements_of_subsets(_594087, _594085) = empty_set), _594085 = empty_set]]], (10296 ^ _257529) ^ [_636702, _636704] : [-(disjoint(_636704, _636702)), 10300 ^ _257529 : [(10301 ^ _257529) ^ [] : [-(in(10299 ^ [_636702, _636704], _636704))], (10303 ^ _257529) ^ [] : [-(in(10299 ^ [_636702, _636704], _636702))]]], (4707 ^ _257529) ^ [_418924, _418926, _418928] : [relation_of2(_418924, _418928, _418926), -(element(relation_rng_as_subset(_418928, _418926, _418924), powerset(_418926)))], (9154 ^ _257529) ^ [_598800, _598802, _598804] : [-(in(_598800, 9150 ^ [_598804])), in(_598802, 9150 ^ [_598804]), subset(_598800, _598802)], (5956 ^ _257529) ^ [_460011] : [-(epsilon_transitive(5944 ^ [_460011]))], (3222 ^ _257529) ^ [_369221] : [one_sorted_str(_369221), -(cast_as_carrier_subset(_369221) = the_carrier(_369221))], (6403 ^ _257529) ^ [_476235, _476237] : [one_sorted_str(_476237), element(_476235, powerset(powerset(the_carrier(_476237)))), 6415 ^ _257529 : [(6440 ^ _257529) ^ [] : [6413 ^ [_476235, _476237] = 6414 ^ [_476235, _476237]], (6416 ^ _257529) ^ [] : [-(in(6412 ^ [_476235, _476237], complements_of_subsets(the_carrier(_476237), _476235)))], (6430 ^ _257529) ^ [_477682] : [element(_477682, powerset(the_carrier(_476237))), _477682 = 6412 ^ [_476235, _476237], -(6414 ^ [_476235, _476237] = subset_complement(the_carrier(_476237), _477682))], (6428 ^ _257529) ^ [] : [-(in(6412 ^ [_476235, _476237], complements_of_subsets(the_carrier(_476237), _476235)))], (6418 ^ _257529) ^ [_477279] : [element(_477279, powerset(the_carrier(_476237))), _477279 = 6412 ^ [_476235, _476237], -(6413 ^ [_476235, _476237] = subset_complement(the_carrier(_476237), _477279))]], 6442 ^ _257529 : [(6443 ^ _257529) ^ [] : [-(relation(6441 ^ [_476235, _476237]))], (6465 ^ _257529) ^ [_479055, _479057] : [-(in(ordered_pair(_479057, _479055), 6441 ^ [_476235, _476237])), in(_479057, complements_of_subsets(the_carrier(_476237), _476235)), in(_479057, complements_of_subsets(the_carrier(_476237), _476235)), 6475 ^ _257529 : [(6480 ^ _257529) ^ [] : [_479055 = subset_complement(the_carrier(_476237), 6474 ^ [_476235, _476237, _479055, _479057])], (6478 ^ _257529) ^ [] : [-(6474 ^ [_476235, _476237, _479055, _479057] = _479057)], (6476 ^ _257529) ^ [] : [-(element(6474 ^ [_476235, _476237, _479055, _479057], powerset(the_carrier(_476237))))]]], (6447 ^ _257529) ^ [_478383, _478385] : [in(ordered_pair(_478385, _478383), 6441 ^ [_476235, _476237]), 6450 ^ _257529 : [(6455 ^ _257529) ^ [_478739] : [element(_478739, powerset(the_carrier(_476237))), _478739 = _478385, -(_478383 = subset_complement(the_carrier(_476237), _478739))], (6453 ^ _257529) ^ [] : [-(in(_478385, complements_of_subsets(the_carrier(_476237), _476235)))], (6451 ^ _257529) ^ [] : [-(in(_478385, complements_of_subsets(the_carrier(_476237), _476235)))]]], (6445 ^ _257529) ^ [] : [-(function(6441 ^ [_476235, _476237]))]]], (4673 ^ _257529) ^ [_418024, _418026, _418028] : [relation_of2(_418024, _418028, _418026), -(element(relation_dom_as_subset(_418028, _418026, _418024), powerset(_418028)))], (2625 ^ _257529) ^ [_347954] : [top_str(_347954), 2628 ^ _257529 : [(2629 ^ _257529) ^ [_348118] : [element(_348118, powerset(powerset(the_carrier(_347954)))), 2632 ^ _257529 : [(2647 ^ _257529) ^ [] : [2649 ^ _257529 : [(2654 ^ _257529) ^ [] : [open_subset(2648 ^ [_347954, _348118], _347954)], (2652 ^ _257529) ^ [] : [-(in(2648 ^ [_347954, _348118], _348118))], (2650 ^ _257529) ^ [] : [-(element(2648 ^ [_347954, _348118], powerset(the_carrier(_347954))))]], -(open_subsets(_348118, _347954))], (2633 ^ _257529) ^ [] : [open_subsets(_348118, _347954), 2636 ^ _257529 : [(2637 ^ _257529) ^ [_348393] : [element(_348393, powerset(the_carrier(_347954))), in(_348393, _348118), -(open_subset(_348393, _347954))]]]]]]], (4393 ^ _257529) ^ [] : [true___, -(true___)], (1440 ^ _257529) ^ [_306198] : [v5_membered(_306198), -(v4_membered(_306198))], (10270 ^ _257529) ^ [_635760] : [-(set_difference(_635760, empty_set) = _635760)], (1364 ^ _257529) ^ [_303607] : [v2_membered(_303607), 1367 ^ _257529 : [(1368 ^ _257529) ^ [_303744] : [element(_303744, powerset(_303607)), 1371 ^ _257529 : [(1372 ^ _257529) ^ [] : [-(v1_membered(_303744))], (1374 ^ _257529) ^ [] : [-(v2_membered(_303744))]]]]], (11425 ^ _257529) ^ [_674035, _674037, _674039, _674041] : [function(_674035), quasi_total(_674035, _674041, _674039), relation_of2_as_subset(_674035, _674041, _674039), subset(_674039, _674037), 11442 ^ _257529 : [(11443 ^ _257529) ^ [] : [-(_674039 = empty_set)], (11445 ^ _257529) ^ [] : [_674041 = empty_set]], 11446 ^ _257529 : [(11451 ^ _257529) ^ [] : [-(relation_of2_as_subset(_674035, _674041, _674037))], (11449 ^ _257529) ^ [] : [-(quasi_total(_674035, _674041, _674037))], (11447 ^ _257529) ^ [] : [-(function(_674035))]]], (3903 ^ _257529) ^ [_392871] : [relation(_392871), 3906 ^ _257529 : [(3929 ^ _257529) ^ [_393763] : [3932 ^ _257529 : [(3933 ^ _257529) ^ [] : [-(in(3930 ^ [_392871, _393763], _393763))], (3935 ^ _257529) ^ [] : [-(in(3931 ^ [_392871, _393763], _393763))], (3941 ^ _257529) ^ [] : [in(ordered_pair(3931 ^ [_392871, _393763], 3930 ^ [_392871, _393763]), _392871)], (3939 ^ _257529) ^ [] : [in(ordered_pair(3930 ^ [_392871, _393763], 3931 ^ [_392871, _393763]), _392871)], (3937 ^ _257529) ^ [] : [3930 ^ [_392871, _393763] = 3931 ^ [_392871, _393763]]], -(is_connected_in(_392871, _393763))], (3907 ^ _257529) ^ [_393079] : [is_connected_in(_392871, _393079), 3910 ^ _257529 : [(3911 ^ _257529) ^ [_393269, _393271] : [in(_393271, _393079), in(_393269, _393079), -(_393271 = _393269), -(in(ordered_pair(_393271, _393269), _392871)), -(in(ordered_pair(_393269, _393271), _392871))]]]]], (1566 ^ _257529) ^ [_310144] : [v3_membered(_310144), -(v2_membered(_310144))], (738 ^ _257529) ^ [_280403, _280405, _280407, _280409] : [-(open_subsets(_280407, _280403)), open_subsets(_280409, _280405), _280409 = _280407, _280405 = _280403], (4719 ^ _257529) ^ [_419396, _419398, _419400] : [-(element(subset_intersection2(_419400, _419398, _419396), powerset(_419400))), element(_419398, powerset(_419400)), element(_419396, powerset(_419400))], (1140 ^ _257529) ^ [_295395, _295397, _295399, _295401] : [-(apply(_295401, _295397) = apply(_295399, _295395)), _295401 = _295399, _295397 = _295395], (4483 ^ _257529) ^ [] : [true___, -(true___)], (1845 ^ _257529) ^ [_319843, _319845] : [relation(_319843), 1848 ^ _257529 : [(1849 ^ _257529) ^ [_320014] : [relation(_320014), 1852 ^ _257529 : [(1875 ^ _257529) ^ [] : [-(_320014 = relation_rng_restriction(_319845, _319843)), 1888 ^ _257529 : [(1893 ^ _257529) ^ [] : [in(ordered_pair(1876 ^ [_319843, _319845, _320014], 1877 ^ [_319843, _319845, _320014]), _320014)], (1891 ^ _257529) ^ [] : [-(in(ordered_pair(1876 ^ [_319843, _319845, _320014], 1877 ^ [_319843, _319845, _320014]), _319843))], (1889 ^ _257529) ^ [] : [-(in(1877 ^ [_319843, _319845, _320014], _319845))]], 1880 ^ _257529 : [(1881 ^ _257529) ^ [] : [-(in(ordered_pair(1876 ^ [_319843, _319845, _320014], 1877 ^ [_319843, _319845, _320014]), _320014))], (1883 ^ _257529) ^ [] : [in(1877 ^ [_319843, _319845, _320014], _319845), in(ordered_pair(1876 ^ [_319843, _319845, _320014], 1877 ^ [_319843, _319845, _320014]), _319843)]]], (1853 ^ _257529) ^ [] : [_320014 = relation_rng_restriction(_319845, _319843), 1856 ^ _257529 : [(1857 ^ _257529) ^ [_320341, _320343] : [in(ordered_pair(_320343, _320341), _320014), 1860 ^ _257529 : [(1861 ^ _257529) ^ [] : [-(in(_320341, _319845))], (1863 ^ _257529) ^ [] : [-(in(ordered_pair(_320343, _320341), _319843))]]], (1865 ^ _257529) ^ [_320620, _320622] : [-(in(ordered_pair(_320622, _320620), _320014)), in(_320620, _319845), in(ordered_pair(_320622, _320620), _319843)]]]]]]], (6745 ^ _257529) ^ [_489584, _489586, _489588] : [relation(_489586), relation(_489584), function(_489584), 6757 ^ _257529 : [(6770 ^ _257529) ^ [_490546, _490548] : [-(in(ordered_pair(_490548, _490546), 6756 ^ [_489584, _489586, _489588])), in(_490548, _489588), in(_490546, _489588), in(ordered_pair(apply(_489584, _490548), apply(_489584, _490546)), _489586)], (6760 ^ _257529) ^ [_490157, _490159] : [in(ordered_pair(_490159, _490157), 6756 ^ [_489584, _489586, _489588]), 6763 ^ _257529 : [(6768 ^ _257529) ^ [] : [-(in(ordered_pair(apply(_489584, _490159), apply(_489584, _490157)), _489586))], (6766 ^ _257529) ^ [] : [-(in(_490157, _489588))], (6764 ^ _257529) ^ [] : [-(in(_490159, _489588))]]], (6758 ^ _257529) ^ [] : [-(relation(6756 ^ [_489584, _489586, _489588]))]]], (1056 ^ _257529) ^ [_292369, _292371, _292373, _292375] : [-(meet_of_subsets(_292375, _292371) = meet_of_subsets(_292373, _292369)), _292375 = _292373, _292371 = _292369], (5245 ^ _257529) ^ [_436636] : [5256 ^ _257529 : [(5257 ^ _257529) ^ [] : [-(relation(relation_inverse(_436636)))], (5259 ^ _257529) ^ [] : [-(function(relation_inverse(_436636)))]], relation(_436636), function(_436636), one_to_one(_436636)], (11411 ^ _257529) ^ [_673479, _673481] : [relation(_673479), -(relation_dom_restriction(_673479, _673481) = relation_composition(identity_relation(_673481), _673479))], (6185 ^ _257529) ^ [_467466, _467468, _467470] : [-(subset_intersection2(_467470, _467468, _467466) = set_intersection2(_467468, _467466)), element(_467468, powerset(_467470)), element(_467466, powerset(_467470))], (3266 ^ _257529) ^ [_370814, _370816] : [3268 ^ _257529 : [(3269 ^ _257529) ^ [] : [-(in(3267 ^ [_370814, _370816], _370816))], (3271 ^ _257529) ^ [] : [in(3267 ^ [_370814, _370816], _370814)]], -(subset(_370816, _370814))], (4399 ^ _257529) ^ [] : [true___, -(true___)], (5638 ^ _257529) ^ [_449416, _449418] : [set_difference(_449418, _449416) = empty_set, -(subset(_449418, _449416))], (8522 ^ _257529) ^ [_573632, _573634] : [ordinal(_573632), 8526 ^ _257529 : [(8527 ^ _257529) ^ [_573905] : [in(_573905, 8525 ^ [_573632, _573634]), 8530 ^ _257529 : [(8531 ^ _257529) ^ [] : [-(in(_573905, succ(_573632)))], (8538 ^ _257529) ^ [] : [-(in(8532 ^ [_573632, _573634, _573905], _573634))], (8536 ^ _257529) ^ [] : [-(_573905 = 8532 ^ [_573632, _573634, _573905])], (8534 ^ _257529) ^ [] : [-(ordinal(8532 ^ [_573632, _573634, _573905]))]]], (8540 ^ _257529) ^ [_574414] : [-(in(_574414, 8525 ^ [_573632, _573634])), in(_574414, succ(_573632)), 8545 ^ _257529 : [(8546 ^ _257529) ^ [_574617] : [ordinal(_574617), _574414 = _574617, in(_574617, _573634)]]]]], (5473 ^ _257529) ^ [_443653, _443655] : [-(finite(set_union2(_443655, _443653))), finite(_443655), finite(_443653)], (6179 ^ _257529) ^ [_467224, _467226] : [element(_467224, powerset(powerset(_467226))), -(union_of_subsets(_467226, _467224) = union(_467224))], (5039 ^ _257529) ^ [_429556, _429558] : [empty(ordered_pair(_429558, _429556))], (5856 ^ _257529) ^ [] : [-(natural(5846 ^ []))], (1897 ^ _257529) ^ [_321766] : [relation(_321766), 1900 ^ _257529 : [(1901 ^ _257529) ^ [] : [antisymmetric(_321766), -(is_antisymmetric_in(_321766, relation_field(_321766)))], (1907 ^ _257529) ^ [] : [is_antisymmetric_in(_321766, relation_field(_321766)), -(antisymmetric(_321766))]]], (7331 ^ _257529) ^ [_518256, _518258] : [topological_space(_518258), top_str(_518258), element(_518256, powerset(powerset(the_carrier(_518258)))), 7347 ^ _257529 : [(7348 ^ _257529) ^ [] : [-(7344 ^ [_518256, _518258] = 7345 ^ [_518256, _518258])], (7350 ^ _257529) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_518258), 7345 ^ [_518256, _518258]), _518256))], (7356 ^ _257529) ^ [] : [7345 ^ [_518256, _518258] = 7346 ^ [_518256, _518258]], (7354 ^ _257529) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_518258), 7346 ^ [_518256, _518258]), _518256))], (7352 ^ _257529) ^ [] : [-(7344 ^ [_518256, _518258] = 7346 ^ [_518256, _518258])]], 7358 ^ _257529 : [(7359 ^ _257529) ^ [_519500] : [in(_519500, 7357 ^ [_518256, _518258]), 7363 ^ _257529 : [(7368 ^ _257529) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_518258), _519500), _518256))], (7366 ^ _257529) ^ [] : [-(7362 ^ [_518256, _518258, _519500] = _519500)], (7364 ^ _257529) ^ [] : [-(in(7362 ^ [_518256, _518258, _519500], powerset(the_carrier(_518258))))]]], (7370 ^ _257529) ^ [_519950] : [-(in(_519950, 7357 ^ [_518256, _518258])), 7371 ^ _257529 : [(7372 ^ _257529) ^ [_520070] : [in(_520070, powerset(the_carrier(_518258))), _520070 = _519950, in(set_difference(cast_as_carrier_subset(_518258), _519950), _518256)]]]]], (5193 ^ _257529) ^ [_434728, _434730] : [v5_membered(_434730), 5196 ^ _257529 : [(5197 ^ _257529) ^ [] : [-(v1_membered(set_intersection2(_434730, _434728)))], (5199 ^ _257529) ^ [] : [-(v2_membered(set_intersection2(_434730, _434728)))], (5205 ^ _257529) ^ [] : [-(v5_membered(set_intersection2(_434730, _434728)))], (5203 ^ _257529) ^ [] : [-(v4_membered(set_intersection2(_434730, _434728)))], (5201 ^ _257529) ^ [] : [-(v3_membered(set_intersection2(_434730, _434728)))]]], (10250 ^ _257529) ^ [_635088, _635090] : [-(set_union2(_635090, set_difference(_635088, _635090)) = set_union2(_635090, _635088))], (318 ^ _257529) ^ [_267301, _267303] : [-(join_commutative(_267301)), _267303 = _267301, join_commutative(_267303)], (9968 ^ _257529) ^ [_625820] : [top_str(_625820), 9971 ^ _257529 : [(9972 ^ _257529) ^ [_625966] : [element(_625966, powerset(the_carrier(_625820))), 9975 ^ _257529 : [(9976 ^ _257529) ^ [] : [closed_subset(_625966, _625820), -(open_subset(subset_complement(the_carrier(_625820), _625966), _625820))], (9982 ^ _257529) ^ [] : [open_subset(subset_complement(the_carrier(_625820), _625966), _625820), -(closed_subset(_625966, _625820))]]]]], (9476 ^ _257529) ^ [_609498] : [finite(_609498), 9479 ^ _257529 : [(9480 ^ _257529) ^ [_609673] : [element(_609673, powerset(powerset(_609498))), -(_609673 = empty_set), 9488 ^ _257529 : [(9489 ^ _257529) ^ [] : [-(in(9487 ^ [_609498, _609673], _609673))], (9491 ^ _257529) ^ [_610072] : [-(_610072 = 9487 ^ [_609498, _609673]), in(_610072, _609673), subset(9487 ^ [_609498, _609673], _610072)]]]]], (9164 ^ _257529) ^ [_599115, _599117] : [in(_599115, 9150 ^ [_599117]), -(in(powerset(_599115), 9150 ^ [_599117]))], (5982 ^ _257529) ^ [] : [-(epsilon_transitive(5972 ^ []))], (7628 ^ _257529) ^ [_533040, _533042] : [one_sorted_str(_533042), element(_533040, powerset(powerset(the_carrier(_533042)))), 7640 ^ _257529 : [(7665 ^ _257529) ^ [] : [7638 ^ [_533040, _533042] = 7639 ^ [_533040, _533042]], (7641 ^ _257529) ^ [] : [-(in(7637 ^ [_533040, _533042], _533040))], (7655 ^ _257529) ^ [_534414] : [element(_534414, powerset(the_carrier(_533042))), _534414 = 7637 ^ [_533040, _533042], -(7639 ^ [_533040, _533042] = subset_complement(the_carrier(_533042), _534414))], (7653 ^ _257529) ^ [] : [-(in(7637 ^ [_533040, _533042], _533040))], (7643 ^ _257529) ^ [_534016] : [element(_534016, powerset(the_carrier(_533042))), _534016 = 7637 ^ [_533040, _533042], -(7638 ^ [_533040, _533042] = subset_complement(the_carrier(_533042), _534016))]], 7667 ^ _257529 : [(7668 ^ _257529) ^ [_534934] : [in(_534934, 7666 ^ [_533040, _533042]), 7672 ^ _257529 : [(7677 ^ _257529) ^ [_535366] : [element(_535366, powerset(the_carrier(_533042))), _535366 = 7671 ^ [_533040, _533042, _534934], -(_534934 = subset_complement(the_carrier(_533042), _535366))], (7675 ^ _257529) ^ [] : [-(in(7671 ^ [_533040, _533042, _534934], _533040))], (7673 ^ _257529) ^ [] : [-(in(7671 ^ [_533040, _533042, _534934], _533040))]]], (7687 ^ _257529) ^ [_535688] : [-(in(_535688, 7666 ^ [_533040, _533042])), 7688 ^ _257529 : [(7689 ^ _257529) ^ [_535825] : [in(_535825, _533040), in(_535825, _533040), 7697 ^ _257529 : [(7702 ^ _257529) ^ [] : [_535688 = subset_complement(the_carrier(_533042), 7696 ^ [_533040, _533042, _535688, _535825])], (7700 ^ _257529) ^ [] : [-(7696 ^ [_533040, _533042, _535688, _535825] = _535825)], (7698 ^ _257529) ^ [] : [-(element(7696 ^ [_533040, _533042, _535688, _535825], powerset(the_carrier(_533042))))]]]]]]], (2236 ^ _257529) ^ [_334208] : [finite(_334208), 2240 ^ _257529 : [(2241 ^ _257529) ^ [] : [-(relation(2239 ^ [_334208]))], (2247 ^ _257529) ^ [] : [-(in(relation_dom(2239 ^ [_334208]), omega))], (2245 ^ _257529) ^ [] : [-(relation_rng(2239 ^ [_334208]) = _334208)], (2243 ^ _257529) ^ [] : [-(function(2239 ^ [_334208]))]]], (10305 ^ _257529) ^ [_637016, _637018] : [disjoint(_637018, _637016), 10306 ^ _257529 : [(10307 ^ _257529) ^ [_637108] : [in(_637108, _637018), in(_637108, _637016)]]], (4991 ^ _257529) ^ [] : [-(epsilon_transitive(omega))], (9019 ^ _257529) ^ [_593976] : [-(in(_593976, succ(_593976)))], (1426 ^ _257529) ^ [_305755] : [preboolean(_305755), 1429 ^ _257529 : [(1430 ^ _257529) ^ [] : [-(cup_closed(_305755))], (1432 ^ _257529) ^ [] : [-(diff_closed(_305755))]]], (10614 ^ _257529) ^ [_647578, _647580] : [element(_647578, powerset(powerset(_647580))), -(_647578 = empty_set), -(subset_difference(_647580, cast_to_subset(_647580), union_of_subsets(_647580, _647578)) = meet_of_subsets(_647580, complements_of_subsets(_647580, _647578)))], (1086 ^ _257529) ^ [_293446, _293448, _293450, _293452] : [-(interior(_293452, _293448) = interior(_293450, _293446)), _293452 = _293450, _293448 = _293446], (9251 ^ _257529) ^ [_602052, _602054] : [-(subset(relation_image(_602052, relation_inverse_image(_602052, _602054)), _602054)), relation(_602052), function(_602052)], (10226 ^ _257529) ^ [_634388, _634390, _634392] : [-(subset(unordered_pair(_634392, _634390), _634388)), in(_634392, _634388), in(_634390, _634388)], (6056 ^ _257529) ^ [] : [-(one_sorted_str(6054 ^ []))], (2568 ^ _257529) ^ [_346046] : [one_sorted_str(_346046), 2571 ^ _257529 : [(2572 ^ _257529) ^ [] : [empty_carrier(_346046), -(empty(the_carrier(_346046)))], (2578 ^ _257529) ^ [] : [empty(the_carrier(_346046)), -(empty_carrier(_346046))]]], (5980 ^ _257529) ^ [] : [-(empty(5972 ^ []))], (5361 ^ _257529) ^ [_440393, _440395] : [empty(cartesian_product2(_440395, _440393)), -(empty(_440395)), -(empty(_440393))], (11123 ^ _257529) ^ [_664002, _664004] : [relation(_664002), function(_664002), 11130 ^ _257529 : [(11131 ^ _257529) ^ [_664269] : [relation(_664269), function(_664269), 11138 ^ _257529 : [(11139 ^ _257529) ^ [] : [_664002 = relation_dom_restriction(_664269, _664004), 11142 ^ _257529 : [(11143 ^ _257529) ^ [] : [-(relation_dom(_664002) = set_intersection2(relation_dom(_664269), _664004))], (11145 ^ _257529) ^ [_664723] : [in(_664723, relation_dom(_664002)), -(apply(_664002, _664723) = apply(_664269, _664723))]]], (11151 ^ _257529) ^ [] : [-(_664002 = relation_dom_restriction(_664269, _664004)), relation_dom(_664002) = set_intersection2(relation_dom(_664269), _664004), 11157 ^ _257529 : [(11158 ^ _257529) ^ [] : [-(in(11156 ^ [_664002, _664004, _664269], relation_dom(_664002)))], (11160 ^ _257529) ^ [] : [apply(_664002, 11156 ^ [_664002, _664004, _664269]) = apply(_664269, 11156 ^ [_664002, _664004, _664269])]]]]]]], (11479 ^ _257529) ^ [_675967, _675969] : [subset(_675967, 11452 ^ [_675969]), -(are_equipotent(_675967, 11452 ^ [_675969])), -(in(_675967, 11452 ^ [_675969]))], (11266 ^ _257529) ^ [_668684, _668686] : [-(pair_first(ordered_pair(_668686, _668684)) = _668686)], (2294 ^ _257529) ^ [_336345, _336347, _336349] : [relation_of2_as_subset(_336345, _336349, _336347), 2297 ^ _257529 : [(2298 ^ _257529) ^ [] : [2299 ^ _257529 : [(2300 ^ _257529) ^ [] : [-(_336347 = empty_set)], (2302 ^ _257529) ^ [] : [_336349 = empty_set]], 2303 ^ _257529 : [(2304 ^ _257529) ^ [] : [quasi_total(_336345, _336349, _336347), -(_336349 = relation_dom_as_subset(_336349, _336347, _336345))], (2310 ^ _257529) ^ [] : [_336349 = relation_dom_as_subset(_336349, _336347, _336345), -(quasi_total(_336345, _336349, _336347))]]], (2316 ^ _257529) ^ [] : [_336347 = empty_set, -(_336349 = empty_set), 2323 ^ _257529 : [(2324 ^ _257529) ^ [] : [quasi_total(_336345, _336349, _336347), -(_336345 = empty_set)], (2330 ^ _257529) ^ [] : [_336345 = empty_set, -(quasi_total(_336345, _336349, _336347))]]]]], (10145 ^ _257529) ^ [_631642, _631644] : [relation(_631642), function(_631642), 10152 ^ _257529 : [(10153 ^ _257529) ^ [] : [_631642 = identity_relation(_631644), 10156 ^ _257529 : [(10157 ^ _257529) ^ [] : [-(relation_dom(_631642) = _631644)], (10159 ^ _257529) ^ [_632061] : [in(_632061, _631644), -(apply(_631642, _632061) = _632061)]]], (10165 ^ _257529) ^ [] : [-(_631642 = identity_relation(_631644)), relation_dom(_631642) = _631644, 10171 ^ _257529 : [(10172 ^ _257529) ^ [] : [-(in(10170 ^ [_631642, _631644], _631644))], (10174 ^ _257529) ^ [] : [apply(_631642, 10170 ^ [_631642, _631644]) = 10170 ^ [_631642, _631644]]]]]], (10031 ^ _257529) ^ [_627920] : [top_str(_627920), 10034 ^ _257529 : [(10035 ^ _257529) ^ [_628066] : [element(_628066, powerset(the_carrier(_627920))), 10038 ^ _257529 : [(10039 ^ _257529) ^ [] : [open_subset(_628066, _627920), -(closed_subset(subset_complement(the_carrier(_627920), _628066), _627920))], (10045 ^ _257529) ^ [] : [closed_subset(subset_complement(the_carrier(_627920), _628066), _627920), -(open_subset(_628066, _627920))]]]]], (792 ^ _257529) ^ [_282575, _282577] : [_282577 = _282575, -(the_L_join(_282577) = the_L_join(_282575))], (254 ^ _257529) ^ [_265410, _265412, _265414, _265416] : [-(equipotent(_265414, _265410)), equipotent(_265416, _265412), _265416 = _265414, _265412 = _265410], (6080 ^ _257529) ^ [_464100] : [6088 ^ _257529 : [(6089 ^ _257529) ^ [] : [-(element(6087 ^ [_464100], powerset(the_carrier(_464100))))], (6091 ^ _257529) ^ [] : [-(closed_subset(6087 ^ [_464100], _464100))]], topological_space(_464100), top_str(_464100)], (5457 ^ _257529) ^ [_443109] : [empty(_443109), 5460 ^ _257529 : [(5461 ^ _257529) ^ [] : [-(empty(relation_dom(_443109)))], (5463 ^ _257529) ^ [] : [-(relation(relation_dom(_443109)))]]], (980 ^ _257529) ^ [_289634, _289636, _289638, _289640, _289642, _289644] : [-(relation_rng_as_subset(_289644, _289640, _289636) = relation_rng_as_subset(_289642, _289638, _289634)), _289644 = _289642, _289640 = _289638, _289636 = _289634], (636 ^ _257529) ^ [_277142, _277144, _277146, _277148, _277150, _277152] : [-(quasi_total(_277150, _277146, _277142)), quasi_total(_277152, _277148, _277144), _277152 = _277150, _277148 = _277146, _277144 = _277142], (5566 ^ _257529) ^ [_446845, _446847] : [-(in(_446847, _446845)), -(disjoint(singleton(_446847), _446845))], (424 ^ _257529) ^ [_270624, _270626, _270628, _270630, _270632, _270634] : [-(relation_isomorphism(_270632, _270628, _270624)), relation_isomorphism(_270634, _270630, _270626), _270634 = _270632, _270630 = _270628, _270626 = _270624], (10491 ^ _257529) ^ [_643347, _643349] : [subset(_643349, _643347), -(_643347 = set_union2(_643349, set_difference(_643347, _643349)))], (872 ^ _257529) ^ [_285698, _285700, _285702, _285704, _285706, _285708] : [-(meet(_285708, _285704, _285700) = meet(_285706, _285702, _285698)), _285708 = _285706, _285704 = _285702, _285700 = _285698], (1376 ^ _257529) ^ [_304022] : [v3_membered(_304022), 1379 ^ _257529 : [(1380 ^ _257529) ^ [_304164] : [element(_304164, powerset(_304022)), 1383 ^ _257529 : [(1388 ^ _257529) ^ [] : [-(v3_membered(_304164))], (1386 ^ _257529) ^ [] : [-(v2_membered(_304164))], (1384 ^ _257529) ^ [] : [-(v1_membered(_304164))]]]]], (4537 ^ _257529) ^ [_414398, _414400, _414402] : [-(element(meet(_414402, _414400, _414398), the_carrier(_414402))), -(empty_carrier(_414402)), meet_semilatt_str(_414402), element(_414400, the_carrier(_414402)), element(_414398, the_carrier(_414402))], (5015 ^ _257529) ^ [_428865, _428867] : [-(relation(set_intersection2(_428867, _428865))), relation(_428867), relation(_428865)], (5902 ^ _257529) ^ [] : [-(ordinal(5896 ^ []))], (4864 ^ _257529) ^ [] : [-(meet_semilatt_str(4862 ^ []))], (1236 ^ _257529) ^ [_298829, _298831] : [_298831 = _298829, -(powerset(_298831) = powerset(_298829))], (1500 ^ _257529) ^ [_308191] : [finite(_308191), 1503 ^ _257529 : [(1504 ^ _257529) ^ [_308323] : [element(_308323, powerset(_308191)), -(finite(_308323))]]], (548 ^ _257529) ^ [_274428, _274430] : [-(well_founded_relation(_274428)), _274430 = _274428, well_founded_relation(_274430)], (1390 ^ _257529) ^ [_304514] : [v4_membered(_304514), 1393 ^ _257529 : [(1394 ^ _257529) ^ [_304661] : [element(_304661, powerset(_304514)), 1397 ^ _257529 : [(1398 ^ _257529) ^ [] : [-(v1_membered(_304661))], (1404 ^ _257529) ^ [] : [-(v4_membered(_304661))], (1402 ^ _257529) ^ [] : [-(v3_membered(_304661))], (1400 ^ _257529) ^ [] : [-(v2_membered(_304661))]]]]], (994 ^ _257529) ^ [_290094, _290096] : [_290096 = _290094, -(relation_inverse(_290096) = relation_inverse(_290094))], (11289 ^ _257529) ^ [_669557, _669559] : [-(subset(_669559, set_union2(_669559, _669557)))], (8291 ^ _257529) ^ [_563724, _563726] : [ordinal(_563726), element(_563724, powerset(powerset(succ(_563726)))), 8299 ^ _257529 : [(8300 ^ _257529) ^ [_564098] : [in(_564098, 8298 ^ [_563724, _563726]), 8303 ^ _257529 : [(8309 ^ _257529) ^ [] : [-(_564098 = set_difference(8305 ^ [_563724, _563726, _564098], singleton(_563726)))], (8307 ^ _257529) ^ [] : [-(in(8305 ^ [_563724, _563726, _564098], _563724))], (8304 ^ _257529) ^ [] : [-(in(_564098, powerset(_563726)))]]], (8311 ^ _257529) ^ [_564534] : [-(in(_564534, 8298 ^ [_563724, _563726])), in(_564534, powerset(_563726)), 8316 ^ _257529 : [(8317 ^ _257529) ^ [_564737] : [in(_564737, _563724), _564534 = set_difference(_564737, singleton(_563726))]]]]], (9170 ^ _257529) ^ [_599315, _599317] : [subset(_599315, 9150 ^ [_599317]), -(are_equipotent(_599315, 9150 ^ [_599317])), -(in(_599315, 9150 ^ [_599317]))], (2491 ^ _257529) ^ [_343463, _343465, _343467] : [relation_of2(_343463, _343467, _343465), -(subset(_343463, cartesian_product2(_343467, _343465)))], (2584 ^ _257529) ^ [_346517, _346519] : [_346517 = singleton(_346519), 2587 ^ _257529 : [(2588 ^ _257529) ^ [_346687] : [in(_346687, _346517), -(_346687 = _346519)], (2594 ^ _257529) ^ [_346859] : [_346859 = _346519, -(in(_346859, _346517))]]], (8558 ^ _257529) ^ [_575010, _575012] : [-(empty(_575012)), relation(_575010), 8615 ^ _257529 : [(8616 ^ _257529) ^ [] : [-(relation(8614 ^ [_575010, _575012]))], (8622 ^ _257529) ^ [_578100] : [in(_578100, _575012), 8626 ^ _257529 : [(8631 ^ _257529) ^ [_578544] : [in(_578544, 8625 ^ [_575010, _575012, _578100]), -(in(ordered_pair(apply(8614 ^ [_575010, _575012], _578100), _578544), _575010))], (8629 ^ _257529) ^ [] : [-(in(apply(8614 ^ [_575010, _575012], _578100), 8625 ^ [_575010, _575012, _578100]))], (8627 ^ _257529) ^ [] : [-(_578100 = 8625 ^ [_575010, _575012, _578100])]]], (8620 ^ _257529) ^ [] : [-(relation_dom(8614 ^ [_575010, _575012]) = _575012)], (8618 ^ _257529) ^ [] : [-(function(8614 ^ [_575010, _575012]))]], 8599 ^ _257529 : [(8600 ^ _257529) ^ [] : [-(in(8598 ^ [_575010, _575012], _575012))], (8602 ^ _257529) ^ [_577286, _577288] : [8598 ^ [_575010, _575012] = _577286, in(_577288, _577286), 8610 ^ _257529 : [(8611 ^ _257529) ^ [] : [-(in(8609 ^ [_575010, _575012, _577286, _577288], _577286))], (8613 ^ _257529) ^ [] : [in(ordered_pair(_577288, 8609 ^ [_575010, _575012, _577286, _577288]), _575010)]]]], 8572 ^ _257529 : [(8573 ^ _257529) ^ [] : [-(in(8569 ^ [_575010, _575012], _575012))], (8589 ^ _257529) ^ [] : [-(in(8571 ^ [_575010, _575012], 8585 ^ [_575010, _575012]))], (8597 ^ _257529) ^ [] : [8570 ^ [_575010, _575012] = 8571 ^ [_575010, _575012]], (8591 ^ _257529) ^ [_576815] : [in(_576815, 8585 ^ [_575010, _575012]), -(in(ordered_pair(8571 ^ [_575010, _575012], _576815), _575010))], (8578 ^ _257529) ^ [] : [-(in(8570 ^ [_575010, _575012], 8574 ^ [_575010, _575012]))], (8587 ^ _257529) ^ [] : [-(8569 ^ [_575010, _575012] = 8585 ^ [_575010, _575012])], (8580 ^ _257529) ^ [_576339] : [in(_576339, 8574 ^ [_575010, _575012]), -(in(ordered_pair(8570 ^ [_575010, _575012], _576339), _575010))], (8576 ^ _257529) ^ [] : [-(8569 ^ [_575010, _575012] = 8574 ^ [_575010, _575012])]]], (2209 ^ _257529) ^ [_333191, _333193, _333195, _333197] : [-(_333191 = unordered_triple(_333197, _333195, _333193)), 2213 ^ _257529 : [(2214 ^ _257529) ^ [] : [-(in(2210 ^ [_333191, _333193, _333195, _333197], _333191))], (2220 ^ _257529) ^ [] : [2210 ^ [_333191, _333193, _333195, _333197] = _333193], (2218 ^ _257529) ^ [] : [2210 ^ [_333191, _333193, _333195, _333197] = _333195], (2216 ^ _257529) ^ [] : [2210 ^ [_333191, _333193, _333195, _333197] = _333197]], 2221 ^ _257529 : [(2232 ^ _257529) ^ [] : [in(2210 ^ [_333191, _333193, _333195, _333197], _333191)], (2222 ^ _257529) ^ [] : [-(2210 ^ [_333191, _333193, _333195, _333197] = _333197), -(2210 ^ [_333191, _333193, _333195, _333197] = _333195), -(2210 ^ [_333191, _333193, _333195, _333197] = _333193)]]], (9095 ^ _257529) ^ [_596598, _596600] : [relation(_596598), -(relation_rng(relation_rng_restriction(_596600, _596598)) = set_intersection2(relation_rng(_596598), _596600))], (6267 ^ _257529) ^ [_470131, _470133] : [-(equipotent(_470133, _470133))], (9180 ^ _257529) ^ [_599655, _599657] : [-(finite(_599657)), subset(_599657, _599655), finite(_599655)], (7973 ^ _257529) ^ [_550145, _550147] : [ordinal(_550145), 7981 ^ _257529 : [(7994 ^ _257529) ^ [] : [-(ordinal(7992 ^ [_550145, _550147]))], (7982 ^ _257529) ^ [] : [-(7978 ^ [_550145, _550147] = 7979 ^ [_550145, _550147])], (7989 ^ _257529) ^ [] : [-(in(7983 ^ [_550145, _550147], _550147))], (7991 ^ _257529) ^ [] : [-(7978 ^ [_550145, _550147] = 7980 ^ [_550145, _550147])], (7998 ^ _257529) ^ [] : [-(in(7992 ^ [_550145, _550147], _550147))], (7987 ^ _257529) ^ [] : [-(7979 ^ [_550145, _550147] = 7983 ^ [_550145, _550147])], (7996 ^ _257529) ^ [] : [-(7980 ^ [_550145, _550147] = 7992 ^ [_550145, _550147])], (8000 ^ _257529) ^ [] : [7979 ^ [_550145, _550147] = 7980 ^ [_550145, _550147]], (7985 ^ _257529) ^ [] : [-(ordinal(7983 ^ [_550145, _550147]))]], 8002 ^ _257529 : [(8003 ^ _257529) ^ [_551747] : [in(_551747, 8001 ^ [_550145, _550147]), 8007 ^ _257529 : [(8008 ^ _257529) ^ [] : [-(in(8006 ^ [_550145, _550147, _551747], succ(_550145)))], (8010 ^ _257529) ^ [] : [-(8006 ^ [_550145, _550147, _551747] = _551747)], (8017 ^ _257529) ^ [] : [-(in(8011 ^ [_550145, _550147, _551747], _550147))], (8015 ^ _257529) ^ [] : [-(_551747 = 8011 ^ [_550145, _550147, _551747])], (8013 ^ _257529) ^ [] : [-(ordinal(8011 ^ [_550145, _550147, _551747]))]]], (8019 ^ _257529) ^ [_552434] : [-(in(_552434, 8001 ^ [_550145, _550147])), 8020 ^ _257529 : [(8021 ^ _257529) ^ [_552563] : [in(_552563, succ(_550145)), _552563 = _552434, 8028 ^ _257529 : [(8029 ^ _257529) ^ [_552816] : [ordinal(_552816), _552434 = _552816, in(_552816, _550147)]]]]]]], (5880 ^ _257529) ^ [] : [-(v1_membered(5876 ^ []))], (11031 ^ _257529) ^ [_661260] : [relation(_661260), 11034 ^ _257529 : [(11035 ^ _257529) ^ [] : [well_founded_relation(_661260), -(is_well_founded_in(_661260, relation_field(_661260)))], (11041 ^ _257529) ^ [] : [is_well_founded_in(_661260, relation_field(_661260)), -(well_founded_relation(_661260))]]], (5821 ^ _257529) ^ [_455700, _455702, _455704] : [relation(_455700), function(_455700), 5828 ^ _257529 : [(5829 ^ _257529) ^ [] : [in(_455702, relation_dom(relation_dom_restriction(_455700, _455704))), 5832 ^ _257529 : [(5833 ^ _257529) ^ [] : [-(in(_455702, relation_dom(_455700)))], (5835 ^ _257529) ^ [] : [-(in(_455702, _455704))]]], (5837 ^ _257529) ^ [] : [-(in(_455702, relation_dom(relation_dom_restriction(_455700, _455704)))), in(_455702, relation_dom(_455700)), in(_455702, _455704)]]], (1264 ^ _257529) ^ [_300177, _300179] : [proper_subset(_300179, _300177), proper_subset(_300177, _300179)], (8210 ^ _257529) ^ [_560829, _560831] : [topological_space(_560831), top_str(_560831), element(_560829, powerset(the_carrier(_560831))), 8222 ^ _257529 : [(8223 ^ _257529) ^ [_561312] : [in(_561312, 8221 ^ [_560829, _560831]), 8226 ^ _257529 : [(8227 ^ _257529) ^ [] : [-(in(_561312, powerset(the_carrier(_560831))))], (8230 ^ _257529) ^ [] : [-(element(8228 ^ [_560829, _560831, _561312], powerset(the_carrier(_560831))))], (8236 ^ _257529) ^ [] : [-(subset(_560829, _561312))], (8234 ^ _257529) ^ [] : [-(closed_subset(8228 ^ [_560829, _560831, _561312], _560831))], (8232 ^ _257529) ^ [] : [-(8228 ^ [_560829, _560831, _561312] = _561312)]]], (8238 ^ _257529) ^ [_561922] : [-(in(_561922, 8221 ^ [_560829, _560831])), in(_561922, powerset(the_carrier(_560831))), 8243 ^ _257529 : [(8244 ^ _257529) ^ [_562140] : [element(_562140, powerset(the_carrier(_560831))), _562140 = _561922, closed_subset(_562140, _560831), subset(_560829, _561922)]]]]], (5621 ^ _257529) ^ [_448851, _448853] : [relation(_448851), well_ordering(_448851), equipotent(_448853, relation_field(_448851)), 5633 ^ _257529 : [(5634 ^ _257529) ^ [] : [-(relation(5632 ^ [_448851, _448853]))], (5636 ^ _257529) ^ [] : [-(well_orders(5632 ^ [_448851, _448853], _448853))]]], (1544 ^ _257529) ^ [_309476] : [-(ordinal(_309476)), epsilon_transitive(_309476), epsilon_connected(_309476)], (786 ^ _257529) ^ [_282357, _282359] : [_282359 = _282357, -(the_topology(_282359) = the_topology(_282357))], (5443 ^ _257529) ^ [_442725, _442727] : [-(open_subset(interior(_442727, _442725), _442727)), topological_space(_442727), top_str(_442727), element(_442725, powerset(the_carrier(_442727)))], (844 ^ _257529) ^ [_284666, _284668, _284670, _284672, _284674, _284676] : [-(join_commut(_284676, _284672, _284668) = join_commut(_284674, _284670, _284666)), _284676 = _284674, _284672 = _284670, _284668 = _284666], (4847 ^ _257529) ^ [] : [true___, -(true___)], (5119 ^ _257529) ^ [_432083] : [empty(singleton(_432083))], (952 ^ _257529) ^ [_288602, _288604, _288606, _288608, _288610, _288612] : [-(relation_dom_as_subset(_288612, _288608, _288604) = relation_dom_as_subset(_288610, _288606, _288602)), _288612 = _288610, _288608 = _288606, _288604 = _288602], (6167 ^ _257529) ^ [_466750, _466752, _466754] : [relation_of2(_466750, _466754, _466752), -(relation_dom_as_subset(_466754, _466752, _466750) = relation_dom(_466750))], (74 ^ _257529) ^ [_259929, _259931, _259933, _259935] : [-(is_connected_in(_259933, _259929)), is_connected_in(_259935, _259931), _259935 = _259933, _259931 = _259929], (2705 ^ _257529) ^ [_350797, _350799] : [relation(_350797), 2708 ^ _257529 : [(2735 ^ _257529) ^ [] : [-(_350797 = inclusion_relation(_350799)), relation_field(_350797) = _350799, 2742 ^ _257529 : [(2747 ^ _257529) ^ [] : [2748 ^ _257529 : [(2749 ^ _257529) ^ [] : [-(in(ordered_pair(2740 ^ [_350797, _350799], 2741 ^ [_350797, _350799]), _350797))], (2751 ^ _257529) ^ [] : [subset(2740 ^ [_350797, _350799], 2741 ^ [_350797, _350799])]], 2752 ^ _257529 : [(2753 ^ _257529) ^ [] : [-(subset(2740 ^ [_350797, _350799], 2741 ^ [_350797, _350799]))], (2755 ^ _257529) ^ [] : [in(ordered_pair(2740 ^ [_350797, _350799], 2741 ^ [_350797, _350799]), _350797)]]], (2745 ^ _257529) ^ [] : [-(in(2741 ^ [_350797, _350799], _350799))], (2743 ^ _257529) ^ [] : [-(in(2740 ^ [_350797, _350799], _350799))]]], (2709 ^ _257529) ^ [] : [_350797 = inclusion_relation(_350799), 2712 ^ _257529 : [(2713 ^ _257529) ^ [] : [-(relation_field(_350797) = _350799)], (2715 ^ _257529) ^ [_351160, _351162] : [in(_351162, _350799), in(_351160, _350799), 2722 ^ _257529 : [(2723 ^ _257529) ^ [] : [in(ordered_pair(_351162, _351160), _350797), -(subset(_351162, _351160))], (2729 ^ _257529) ^ [] : [subset(_351162, _351160), -(in(ordered_pair(_351162, _351160), _350797))]]]]]]], (10212 ^ _257529) ^ [_633878, _633880] : [in(_633880, _633878), -(subset(singleton(_633880), _633878))], (5918 ^ _257529) ^ [] : [-(relation(5914 ^ []))], (1454 ^ _257529) ^ [_306641] : [empty(_306641), -(relation(_306641))], (5866 ^ _257529) ^ [] : [-(function(5862 ^ []))], (4873 ^ _257529) ^ [] : [-(join_semilatt_str(4871 ^ []))], (9307 ^ _257529) ^ [_603861, _603863] : [finite(_603863), -(finite(set_intersection2(_603863, _603861)))], (3991 ^ _257529) ^ [_396240] : [relation(_396240), 3994 ^ _257529 : [(3995 ^ _257529) ^ [_396461] : [relation(_396461), 3998 ^ _257529 : [(3999 ^ _257529) ^ [_396678] : [relation(_396678), function(_396678), 4006 ^ _257529 : [(4041 ^ _257529) ^ [] : [-(relation_isomorphism(_396240, _396461, _396678)), relation_dom(_396678) = relation_field(_396240), relation_rng(_396678) = relation_field(_396461), one_to_one(_396678), 4070 ^ _257529 : [(4071 ^ _257529) ^ [] : [-(in(4054 ^ [_396240, _396461, _396678], relation_field(_396240)))], (4077 ^ _257529) ^ [] : [in(ordered_pair(4054 ^ [_396240, _396461, _396678], 4055 ^ [_396240, _396461, _396678]), _396240)], (4075 ^ _257529) ^ [] : [-(in(ordered_pair(apply(_396678, 4054 ^ [_396240, _396461, _396678]), apply(_396678, 4055 ^ [_396240, _396461, _396678])), _396461))], (4073 ^ _257529) ^ [] : [-(in(4055 ^ [_396240, _396461, _396678], relation_field(_396240)))]], 4058 ^ _257529 : [(4059 ^ _257529) ^ [] : [-(in(ordered_pair(4054 ^ [_396240, _396461, _396678], 4055 ^ [_396240, _396461, _396678]), _396240))], (4061 ^ _257529) ^ [] : [in(4054 ^ [_396240, _396461, _396678], relation_field(_396240)), in(4055 ^ [_396240, _396461, _396678], relation_field(_396240)), in(ordered_pair(apply(_396678, 4054 ^ [_396240, _396461, _396678]), apply(_396678, 4055 ^ [_396240, _396461, _396678])), _396461)]]], (4007 ^ _257529) ^ [] : [relation_isomorphism(_396240, _396461, _396678), 4010 ^ _257529 : [(4011 ^ _257529) ^ [] : [-(relation_dom(_396678) = relation_field(_396240))], (4013 ^ _257529) ^ [] : [-(relation_rng(_396678) = relation_field(_396461))], (4027 ^ _257529) ^ [_397723, _397725] : [-(in(ordered_pair(_397725, _397723), _396240)), in(_397725, relation_field(_396240)), in(_397723, relation_field(_396240)), in(ordered_pair(apply(_396678, _397725), apply(_396678, _397723)), _396461)], (4017 ^ _257529) ^ [_397344, _397346] : [in(ordered_pair(_397346, _397344), _396240), 4020 ^ _257529 : [(4025 ^ _257529) ^ [] : [-(in(ordered_pair(apply(_396678, _397346), apply(_396678, _397344)), _396461))], (4023 ^ _257529) ^ [] : [-(in(_397344, relation_field(_396240)))], (4021 ^ _257529) ^ [] : [-(in(_397346, relation_field(_396240)))]]], (4015 ^ _257529) ^ [] : [-(one_to_one(_396678))]]]]]]]]], (714 ^ _257529) ^ [_279636, _279638] : [-(top_str(_279636)), _279638 = _279636, top_str(_279638)], (926 ^ _257529) ^ [_287638, _287640, _287642, _287644] : [-(cartesian_product2(_287644, _287640) = cartesian_product2(_287642, _287638)), _287644 = _287642, _287640 = _287638], (3711 ^ _257529) ^ [_386624] : [_386624 = omega, 3714 ^ _257529 : [(3715 ^ _257529) ^ [] : [-(in(empty_set, _386624))], (3721 ^ _257529) ^ [_386973] : [ordinal(_386973), -(subset(_386624, _386973)), in(empty_set, _386973), being_limit_ordinal(_386973)], (3719 ^ _257529) ^ [] : [-(ordinal(_386624))], (3717 ^ _257529) ^ [] : [-(being_limit_ordinal(_386624))]]], (5427 ^ _257529) ^ [] : [-(v3_membered(empty_set))], (11200 ^ _257529) ^ [_666507, _666509] : [subset(singleton(_666509), singleton(_666507)), -(_666509 = _666507)], (700 ^ _257529) ^ [_279220, _279222, _279224, _279226] : [-(in(_279224, _279220)), in(_279226, _279222), _279226 = _279224, _279222 = _279220], (404 ^ _257529) ^ [_269978, _269980] : [-(transitive(_269978)), _269980 = _269978, transitive(_269980)], (9547 ^ _257529) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (5871 ^ _257529) ^ [_457219, _457221] : [-(relation(5867 ^ [_457219, _457221]))], (10939 ^ _257529) ^ [_658258] : [topological_space(_658258), top_str(_658258), 10946 ^ _257529 : [(10947 ^ _257529) ^ [_658525] : [top_str(_658525), 10950 ^ _257529 : [(10951 ^ _257529) ^ [_658705] : [element(_658705, powerset(the_carrier(_658258))), 10954 ^ _257529 : [(10955 ^ _257529) ^ [_658886] : [element(_658886, powerset(the_carrier(_658525))), 10958 ^ _257529 : [(10959 ^ _257529) ^ [] : [open_subset(_658886, _658525), -(interior(_658525, _658886) = _658886)], (10965 ^ _257529) ^ [] : [interior(_658258, _658705) = _658705, -(open_subset(_658705, _658258))]]]]]]]]], (9747 ^ _257529) ^ [_618641] : [9762 ^ _257529 : [(9763 ^ _257529) ^ [_619044] : [element(_619044, the_carrier(_618641)), 9766 ^ _257529 : [(9767 ^ _257529) ^ [_619194] : [element(_619194, the_carrier(_618641)), -(below(_618641, meet_commut(_618641, _619044, _619194), _619044))]]]], -(empty_carrier(_618641)), meet_commutative(_618641), meet_absorbing(_618641), latt_str(_618641)], (11049 ^ _257529) ^ [] : [-(relation_dom(empty_set) = empty_set)], (136 ^ _257529) ^ [_261823, _261825] : [-(preboolean(_261823)), _261825 = _261823, preboolean(_261825)], (6021 ^ _257529) ^ [] : [empty(6019 ^ [])], (5916 ^ _257529) ^ [] : [-(empty(5914 ^ []))], (5948 ^ _257529) ^ [_459739] : [-(empty(5944 ^ [_459739]))], (9835 ^ _257529) ^ [_621502, _621504] : [relation(_621502), transitive(_621502), -(transitive(relation_restriction(_621502, _621504)))], (6145 ^ _257529) ^ [_466127, _466129, _466131] : [-(meet_commut(_466131, _466129, _466127) = meet(_466131, _466129, _466127)), -(empty_carrier(_466131)), meet_commutative(_466131), meet_semilatt_str(_466131), element(_466129, the_carrier(_466131)), element(_466127, the_carrier(_466131))], (4081 ^ _257529) ^ [_399550, _399552] : [disjoint(_399552, _399550), -(set_intersection2(_399552, _399550) = empty_set)], (10731 ^ _257529) ^ [_651580] : [top_str(_651580), 10734 ^ _257529 : [(10735 ^ _257529) ^ [_651744] : [element(_651744, powerset(the_carrier(_651580))), 10738 ^ _257529 : [(10739 ^ _257529) ^ [] : [closed_subset(_651744, _651580), -(topstr_closure(_651580, _651744) = _651744)], (10745 ^ _257529) ^ [] : [-(closed_subset(_651744, _651580)), topological_space(_651580), topstr_closure(_651580, _651744) = _651744]]]]], (4989 ^ _257529) ^ [_427979] : [empty(succ(_427979))], (4969 ^ _257529) ^ [_427457, _427459] : [4984 ^ _257529 : [(4985 ^ _257529) ^ [] : [-(relation(relation_composition(_427459, _427457)))], (4987 ^ _257529) ^ [] : [-(function(relation_composition(_427459, _427457)))]], relation(_427459), function(_427459), relation(_427457), function(_427457)], (9121 ^ _257529) ^ [_597505] : [one_sorted_str(_597505), -(cast_as_carrier_subset(_597505) = the_carrier(_597505))], (4825 ^ _257529) ^ [_422655, _422657, _422659] : [relation_of2_as_subset(_422655, _422659, _422657), -(element(_422655, powerset(cartesian_product2(_422659, _422657))))], (946 ^ _257529) ^ [_288328, _288330] : [_288330 = _288328, -(cast_as_carrier_subset(_288330) = cast_as_carrier_subset(_288328))], (1096 ^ _257529) ^ [_293777, _293779] : [_293779 = _293777, -(function_inverse(_293779) = function_inverse(_293777))], (9468 ^ _257529) ^ [_609189, _609191] : [relation(_609189), -(relation_restriction(_609189, _609191) = relation_dom_restriction(relation_rng_restriction(_609191, _609189), _609191))], (5852 ^ _257529) ^ [] : [-(epsilon_connected(5846 ^ []))], (4561 ^ _257529) ^ [_415017] : [one_sorted_str(_415017), -(element(cast_as_carrier_subset(_415017), powerset(the_carrier(_415017))))], (88 ^ _257529) ^ [_260373, _260375, _260377, _260379] : [-(is_transitive_in(_260377, _260373)), is_transitive_in(_260379, _260375), _260379 = _260377, _260375 = _260373], (4713 ^ _257529) ^ [_419154, _419156] : [element(_419154, powerset(powerset(_419156))), -(element(union_of_subsets(_419156, _419154), powerset(_419156)))], (268 ^ _257529) ^ [_265826, _265828] : [-(epsilon_transitive(_265826)), _265828 = _265826, epsilon_transitive(_265828)], (1036 ^ _257529) ^ [_291663, _291665, _291667, _291669, _291671, _291673] : [-(subset_difference(_291673, _291669, _291665) = subset_difference(_291671, _291667, _291663)), _291673 = _291671, _291669 = _291667, _291665 = _291663], (5509 ^ _257529) ^ [_444863, _444865] : [element(_444863, powerset(_444865)), -(subset_complement(_444865, subset_complement(_444865, _444863)) = _444863)], (4959 ^ _257529) ^ [_427068] : [-(finite(singleton(_427068)))], (582 ^ _257529) ^ [_275462, _275464] : [-(empty(_275462)), _275464 = _275462, empty(_275464)], (1322 ^ _257529) ^ [_302163] : [v5_membered(_302163), 1325 ^ _257529 : [(1326 ^ _257529) ^ [_302313] : [element(_302313, _302163), 1329 ^ _257529 : [(1330 ^ _257529) ^ [] : [-(v1_xcmplx_0(_302313))], (1332 ^ _257529) ^ [] : [-(natural(_302313))], (1338 ^ _257529) ^ [] : [-(v1_rat_1(_302313))], (1336 ^ _257529) ^ [] : [-(v1_int_1(_302313))], (1334 ^ _257529) ^ [] : [-(v1_xreal_0(_302313))]]]]], (7446 ^ _257529) ^ [_523371, _523373] : [one_sorted_str(_523373), element(_523371, powerset(powerset(the_carrier(_523373)))), 7458 ^ _257529 : [(7483 ^ _257529) ^ [] : [7456 ^ [_523371, _523373] = 7457 ^ [_523371, _523373]], (7459 ^ _257529) ^ [] : [-(in(7455 ^ [_523371, _523373], complements_of_subsets(the_carrier(_523373), _523371)))], (7473 ^ _257529) ^ [_524805] : [element(_524805, powerset(the_carrier(_523373))), _524805 = 7455 ^ [_523371, _523373], -(7457 ^ [_523371, _523373] = subset_complement(the_carrier(_523373), _524805))], (7471 ^ _257529) ^ [] : [-(in(7455 ^ [_523371, _523373], complements_of_subsets(the_carrier(_523373), _523371)))], (7461 ^ _257529) ^ [_524402] : [element(_524402, powerset(the_carrier(_523373))), _524402 = 7455 ^ [_523371, _523373], -(7456 ^ [_523371, _523373] = subset_complement(the_carrier(_523373), _524402))]], 7485 ^ _257529 : [(7486 ^ _257529) ^ [_525335] : [in(_525335, 7484 ^ [_523371, _523373]), 7490 ^ _257529 : [(7495 ^ _257529) ^ [_525797] : [element(_525797, powerset(the_carrier(_523373))), _525797 = 7489 ^ [_523371, _523373, _525335], -(_525335 = subset_complement(the_carrier(_523373), _525797))], (7493 ^ _257529) ^ [] : [-(in(7489 ^ [_523371, _523373, _525335], complements_of_subsets(the_carrier(_523373), _523371)))], (7491 ^ _257529) ^ [] : [-(in(7489 ^ [_523371, _523373, _525335], complements_of_subsets(the_carrier(_523373), _523371)))]]], (7505 ^ _257529) ^ [_526119] : [-(in(_526119, 7484 ^ [_523371, _523373])), 7506 ^ _257529 : [(7507 ^ _257529) ^ [_526266] : [in(_526266, complements_of_subsets(the_carrier(_523373), _523371)), in(_526266, complements_of_subsets(the_carrier(_523373), _523371)), 7515 ^ _257529 : [(7520 ^ _257529) ^ [] : [_526119 = subset_complement(the_carrier(_523373), 7514 ^ [_523371, _523373, _526119, _526266])], (7518 ^ _257529) ^ [] : [-(7514 ^ [_523371, _523373, _526119, _526266] = _526266)], (7516 ^ _257529) ^ [] : [-(element(7514 ^ [_523371, _523373, _526119, _526266], powerset(the_carrier(_523373))))]]]]]]], (3735 ^ _257529) ^ [_387322] : [-(_387322 = omega), in(empty_set, _387322), being_limit_ordinal(_387322), ordinal(_387322), 3749 ^ _257529 : [(3750 ^ _257529) ^ [] : [-(ordinal(3748 ^ [_387322]))], (3756 ^ _257529) ^ [] : [subset(_387322, 3748 ^ [_387322])], (3754 ^ _257529) ^ [] : [-(being_limit_ordinal(3748 ^ [_387322]))], (3752 ^ _257529) ^ [] : [-(in(empty_set, 3748 ^ [_387322]))]]], (1728 ^ _257529) ^ [_315342] : [relation(_315342), 1731 ^ _257529 : [(1732 ^ _257529) ^ [_315528, _315530] : [relation(_315528), 1735 ^ _257529 : [(1758 ^ _257529) ^ [] : [-(_315528 = relation_dom_restriction(_315342, _315530)), 1771 ^ _257529 : [(1776 ^ _257529) ^ [] : [in(ordered_pair(1759 ^ [_315342, _315528, _315530], 1760 ^ [_315342, _315528, _315530]), _315528)], (1774 ^ _257529) ^ [] : [-(in(ordered_pair(1759 ^ [_315342, _315528, _315530], 1760 ^ [_315342, _315528, _315530]), _315342))], (1772 ^ _257529) ^ [] : [-(in(1759 ^ [_315342, _315528, _315530], _315530))]], 1763 ^ _257529 : [(1764 ^ _257529) ^ [] : [-(in(ordered_pair(1759 ^ [_315342, _315528, _315530], 1760 ^ [_315342, _315528, _315530]), _315528))], (1766 ^ _257529) ^ [] : [in(1759 ^ [_315342, _315528, _315530], _315530), in(ordered_pair(1759 ^ [_315342, _315528, _315530], 1760 ^ [_315342, _315528, _315530]), _315342)]]], (1736 ^ _257529) ^ [] : [_315528 = relation_dom_restriction(_315342, _315530), 1739 ^ _257529 : [(1740 ^ _257529) ^ [_315853, _315855] : [in(ordered_pair(_315855, _315853), _315528), 1743 ^ _257529 : [(1744 ^ _257529) ^ [] : [-(in(_315855, _315530))], (1746 ^ _257529) ^ [] : [-(in(ordered_pair(_315855, _315853), _315342))]]], (1748 ^ _257529) ^ [_316132, _316134] : [-(in(ordered_pair(_316134, _316132), _315528)), in(_316134, _315530), in(ordered_pair(_316134, _316132), _315342)]]]]]]], (5121 ^ _257529) ^ [_432191, _432193] : [-(closed_subset(topstr_closure(_432193, _432191), _432193)), topological_space(_432193), top_str(_432193), element(_432191, powerset(the_carrier(_432193)))], (5952 ^ _257529) ^ [_459875] : [-(function(5944 ^ [_459875]))], (4245 ^ _257529) ^ [_405545] : [relation(_405545), 4248 ^ _257529 : [(4275 ^ _257529) ^ [_406580] : [4279 ^ _257529 : [(4284 ^ _257529) ^ [] : [-(in(4278 ^ [_405545, _406580], _406580))], (4280 ^ _257529) ^ [] : [-(in(4276 ^ [_405545, _406580], _406580))], (4290 ^ _257529) ^ [] : [in(ordered_pair(4276 ^ [_405545, _406580], 4278 ^ [_405545, _406580]), _405545)], (4286 ^ _257529) ^ [] : [-(in(ordered_pair(4276 ^ [_405545, _406580], 4277 ^ [_405545, _406580]), _405545))], (4288 ^ _257529) ^ [] : [-(in(ordered_pair(4277 ^ [_405545, _406580], 4278 ^ [_405545, _406580]), _405545))], (4282 ^ _257529) ^ [] : [-(in(4277 ^ [_405545, _406580], _406580))]], -(is_transitive_in(_405545, _406580))], (4249 ^ _257529) ^ [_405759] : [is_transitive_in(_405545, _405759), 4252 ^ _257529 : [(4253 ^ _257529) ^ [_405969, _405971, _405973] : [-(in(ordered_pair(_405973, _405969), _405545)), in(_405973, _405759), in(_405971, _405759), in(_405969, _405759), in(ordered_pair(_405973, _405971), _405545), in(ordered_pair(_405971, _405969), _405545)]]]]], (5888 ^ _257529) ^ [] : [-(v5_membered(5876 ^ []))], (236 ^ _257529) ^ [_264829, _264831, _264833, _264835, _264837, _264839] : [-(relation_of2(_264837, _264833, _264829)), relation_of2(_264839, _264835, _264831), _264839 = _264837, _264835 = _264833, _264831 = _264829], (1252 ^ _257529) ^ [_299386, _299388] : [_299388 = _299386, -(the_carrier(_299388) = the_carrier(_299386))], (1176 ^ _257529) ^ [_296662, _296664] : [_296664 = _296662, -(relation_dom(_296664) = relation_dom(_296662))], (5560 ^ _257529) ^ [_446632, _446634] : [disjoint(singleton(_446634), _446632), in(_446634, _446632)], (5335 ^ _257529) ^ [_439568, _439570] : [5342 ^ _257529 : [(5343 ^ _257529) ^ [] : [-(relation(relation_dom_restriction(_439570, _439568)))], (5345 ^ _257529) ^ [] : [-(function(relation_dom_restriction(_439570, _439568)))]], relation(_439570), function(_439570)], (916 ^ _257529) ^ [_287279, _287281, _287283, _287285] : [-(relation_rng_restriction(_287285, _287281) = relation_rng_restriction(_287283, _287279)), _287285 = _287283, _287281 = _287279], (4905 ^ _257529) ^ [_425417, _425419] : [finite(_425419), -(finite(set_intersection2(_425419, _425417)))], (9277 ^ _257529) ^ [_602888] : [relation(_602888), -(relation_image(_602888, relation_dom(_602888)) = relation_rng(_602888))], (6048 ^ _257529) ^ [] : [-(ordinal(6040 ^ []))], (9501 ^ _257529) ^ [_610429, _610431] : [relation(_610429), -(relation_restriction(_610429, _610431) = relation_rng_restriction(_610431, relation_dom_restriction(_610429, _610431)))], (9519 ^ _257529) ^ [_611081, _611083, _611085] : [-(subset(_611085, set_intersection2(_611083, _611081))), subset(_611085, _611083), subset(_611085, _611081)], (10983 ^ _257529) ^ [_659828, _659830] : [relation(_659828), function(_659828), 10998 ^ _257529 : [(10999 ^ _257529) ^ [] : [-(_659830 = apply(_659828, apply(function_inverse(_659828), _659830)))], (11001 ^ _257529) ^ [] : [-(_659830 = apply(relation_composition(function_inverse(_659828), _659828), _659830))]], one_to_one(_659828), in(_659830, relation_rng(_659828))], (11454 ^ _257529) ^ [_675021] : [-(in(_675021, 11452 ^ [_675021]))], (5047 ^ _257529) ^ [_429879, _429881] : [v1_membered(_429881), -(v1_membered(set_intersection2(_429879, _429881)))], (9047 ^ _257529) ^ [_594954, _594956, _594958] : [relation(_594954), 9050 ^ _257529 : [(9051 ^ _257529) ^ [] : [in(_594958, relation_rng(relation_rng_restriction(_594956, _594954))), 9054 ^ _257529 : [(9055 ^ _257529) ^ [] : [-(in(_594958, _594956))], (9057 ^ _257529) ^ [] : [-(in(_594958, relation_rng(_594954)))]]], (9059 ^ _257529) ^ [] : [-(in(_594958, relation_rng(relation_rng_restriction(_594956, _594954)))), in(_594958, _594956), in(_594958, relation_rng(_594954))]]], (8995 ^ _257529) ^ [_593140, _593142] : [equipotent(_593142, _593140), -(equipotent(_593140, _593142))], (5283 ^ _257529) ^ [_437778, _437780] : [empty(unordered_pair(_437780, _437778))], (7092 ^ _257529) ^ [_507239] : [ordinal(_507239), 7100 ^ _257529 : [(7133 ^ _257529) ^ [] : [-(7097 ^ [_507239] = 7099 ^ [_507239])], (7165 ^ _257529) ^ [] : [7098 ^ [_507239] = 7099 ^ [_507239]], (7106 ^ _257529) ^ [] : [-(7098 ^ [_507239] = 7102 ^ [_507239])], (7108 ^ _257529) ^ [] : [in(7102 ^ [_507239], omega), 7111 ^ _257529 : [(7112 ^ _257529) ^ [_508863] : [element(_508863, powerset(powerset(7102 ^ [_507239]))), -(_508863 = empty_set), 7120 ^ _257529 : [(7121 ^ _257529) ^ [] : [-(in(7119 ^ [_507239, _508863], _508863))], (7123 ^ _257529) ^ [_509272] : [-(_509272 = 7119 ^ [_507239, _508863]), in(_509272, _508863), subset(7119 ^ [_507239, _508863], _509272)]]]]], (7138 ^ _257529) ^ [] : [-(7099 ^ [_507239] = 7134 ^ [_507239])], (7104 ^ _257529) ^ [] : [-(ordinal(7102 ^ [_507239]))], (7136 ^ _257529) ^ [] : [-(ordinal(7134 ^ [_507239]))], (7140 ^ _257529) ^ [] : [in(7134 ^ [_507239], omega), 7143 ^ _257529 : [(7144 ^ _257529) ^ [_510013] : [element(_510013, powerset(powerset(7134 ^ [_507239]))), -(_510013 = empty_set), 7152 ^ _257529 : [(7153 ^ _257529) ^ [] : [-(in(7151 ^ [_507239, _510013], _510013))], (7155 ^ _257529) ^ [_510422] : [-(_510422 = 7151 ^ [_507239, _510013]), in(_510422, _510013), subset(7151 ^ [_507239, _510013], _510422)]]]]], (7101 ^ _257529) ^ [] : [-(7097 ^ [_507239] = 7098 ^ [_507239])]], 7167 ^ _257529 : [(7168 ^ _257529) ^ [_510991] : [in(_510991, 7166 ^ [_507239]), 7172 ^ _257529 : [(7173 ^ _257529) ^ [] : [-(in(7171 ^ [_507239, _510991], succ(_507239)))], (7175 ^ _257529) ^ [] : [-(7171 ^ [_507239, _510991] = _510991)], (7182 ^ _257529) ^ [] : [in(7176 ^ [_507239, _510991], omega), 7185 ^ _257529 : [(7186 ^ _257529) ^ [_511857] : [element(_511857, powerset(powerset(7176 ^ [_507239, _510991]))), -(_511857 = empty_set), 7194 ^ _257529 : [(7195 ^ _257529) ^ [] : [-(in(7193 ^ [_507239, _510991, _511857], _511857))], (7197 ^ _257529) ^ [_512288] : [-(_512288 = 7193 ^ [_507239, _510991, _511857]), in(_512288, _511857), subset(7193 ^ [_507239, _510991, _511857], _512288)]]]]], (7180 ^ _257529) ^ [] : [-(_510991 = 7176 ^ [_507239, _510991])], (7178 ^ _257529) ^ [] : [-(ordinal(7176 ^ [_507239, _510991]))]]], (7207 ^ _257529) ^ [_512630] : [-(in(_512630, 7166 ^ [_507239])), 7208 ^ _257529 : [(7209 ^ _257529) ^ [_512814] : [in(_512814, succ(_507239)), _512814 = _512630, 7216 ^ _257529 : [(7217 ^ _257529) ^ [_513118] : [ordinal(_513118), _512630 = _513118, 7224 ^ _257529 : [(7225 ^ _257529) ^ [] : [-(in(_513118, omega))], (7232 ^ _257529) ^ [_513748] : [in(_513748, 7226 ^ [_507239, _512630, _512814, _513118]), 7236 ^ _257529 : [(7241 ^ _257529) ^ [] : [7235 ^ [_507239, _512630, _512814, _513118, _513748] = _513748], (7239 ^ _257529) ^ [] : [-(subset(_513748, 7235 ^ [_507239, _512630, _512814, _513118, _513748]))], (7237 ^ _257529) ^ [] : [-(in(7235 ^ [_507239, _512630, _512814, _513118, _513748], 7226 ^ [_507239, _512630, _512814, _513118]))]]], (7230 ^ _257529) ^ [] : [7226 ^ [_507239, _512630, _512814, _513118] = empty_set], (7228 ^ _257529) ^ [] : [-(element(7226 ^ [_507239, _512630, _512814, _513118], powerset(powerset(_513118))))]]]]]]]]], (10584 ^ _257529) ^ [_646582, _646584] : [element(_646582, powerset(powerset(_646584))), -(_646582 = empty_set), complements_of_subsets(_646584, _646582) = empty_set], (1538 ^ _257529) ^ [_309290] : [v4_membered(_309290), -(v3_membered(_309290))], (2845 ^ _257529) ^ [_355856] : [epsilon_transitive(_355856), 2848 ^ _257529 : [(2849 ^ _257529) ^ [_355987] : [in(_355987, _355856), -(subset(_355987, _355856))]]], (3394 ^ _257529) ^ [_375386] : [ordinal(_375386), 3397 ^ _257529 : [(3398 ^ _257529) ^ [] : [-(epsilon_transitive(_375386))], (3400 ^ _257529) ^ [] : [-(epsilon_connected(_375386))]]], (414 ^ _257529) ^ [_270273, _270275] : [-(connected(_270273)), _270275 = _270273, connected(_270275)], (1130 ^ _257529) ^ [_295036, _295038, _295040, _295042] : [-(ordered_pair(_295042, _295038) = ordered_pair(_295040, _295036)), _295042 = _295040, _295038 = _295036], (1016 ^ _257529) ^ [_290917, _290919, _290921, _290923] : [-(relation_inverse_image(_290923, _290919) = relation_inverse_image(_290921, _290917)), _290923 = _290921, _290919 = _290917], (9145 ^ _257529) ^ [_598366, _598368] : [subset(_598368, _598366), -(set_union2(_598368, _598366) = _598366)], (5873 ^ _257529) ^ [_457291, _457293] : [-(function(5867 ^ [_457291, _457293]))], (5848 ^ _257529) ^ [] : [empty(5846 ^ [])], (116 ^ _257529) ^ [_261233, _261235] : [-(cup_closed(_261233)), _261235 = _261233, cup_closed(_261235)], (4339 ^ _257529) ^ [_409195, _409197] : [proper_subset(_409197, _409195), 4342 ^ _257529 : [(4343 ^ _257529) ^ [] : [-(subset(_409197, _409195))], (4345 ^ _257529) ^ [] : [_409197 = _409195]]], (4911 ^ _257529) ^ [_425615] : [empty(_425615), 4914 ^ _257529 : [(4915 ^ _257529) ^ [] : [-(empty(relation_inverse(_425615)))], (4917 ^ _257529) ^ [] : [-(relation(relation_inverse(_425615)))]]], (1588 ^ _257529) ^ [_310842, _310844] : [-(unordered_pair(_310844, _310842) = unordered_pair(_310842, _310844))], (11260 ^ _257529) ^ [_668472, _668474] : [in(_668474, _668472), empty(_668472)], (3945 ^ _257529) ^ [_394548] : [relation(_394548), 3948 ^ _257529 : [(3949 ^ _257529) ^ [_394667] : [-(relation_restriction(_394548, _394667) = set_intersection2(_394548, cartesian_product2(_394667, _394667)))]]], (9420 ^ _257529) ^ [_607683, _607685] : [relation(_607683), -(_607685 = empty_set), subset(_607685, relation_rng(_607683)), relation_inverse_image(_607683, _607685) = empty_set], (4965 ^ _257529) ^ [_427298] : [-(diff_closed(powerset(_427298)))], (5497 ^ _257529) ^ [_444412, _444414] : [-(set_intersection2(_444414, _444414) = _444414)], (1638 ^ _257529) ^ [_312417, _312419, _312421] : [-(subset_intersection2(_312421, _312419, _312417) = subset_intersection2(_312421, _312417, _312419)), element(_312419, powerset(_312421)), element(_312417, powerset(_312421))], (3354 ^ _257529) ^ [_374124] : [relation(_374124), function(_374124), 3361 ^ _257529 : [(3362 ^ _257529) ^ [_374416, _374418] : [in(_374418, relation_dom(_374124)), 3365 ^ _257529 : [(3366 ^ _257529) ^ [] : [_374416 = apply(_374124, _374418), -(in(ordered_pair(_374418, _374416), _374124))], (3372 ^ _257529) ^ [] : [in(ordered_pair(_374418, _374416), _374124), -(_374416 = apply(_374124, _374418))]]], (3378 ^ _257529) ^ [_374868, _374870] : [-(in(_374870, relation_dom(_374124))), 3381 ^ _257529 : [(3382 ^ _257529) ^ [] : [_374868 = apply(_374124, _374870), -(_374868 = empty_set)], (3388 ^ _257529) ^ [] : [_374868 = empty_set, -(_374868 = apply(_374124, _374870))]]]]], (5861 ^ _257529) ^ [] : [-(finite(5857 ^ []))], (6243 ^ _257529) ^ [_469383, _469385] : [equipotent(_469385, _469383), -(are_equipotent(_469385, _469383))], (9928 ^ _257529) ^ [_624316] : [-(relation(9926 ^ [_624316]))], (4739 ^ _257529) ^ [_420015] : [-(relation(identity_relation(_420015)))], (10000 ^ _257529) ^ [_626835, _626837] : [-(_626837 = _626835), 10004 ^ _257529 : [(10005 ^ _257529) ^ [] : [-(in(10001 ^ [_626835, _626837], _626837))], (10007 ^ _257529) ^ [] : [in(10001 ^ [_626835, _626837], _626835)]], 10008 ^ _257529 : [(10009 ^ _257529) ^ [] : [-(in(10001 ^ [_626835, _626837], _626835))], (10011 ^ _257529) ^ [] : [in(10001 ^ [_626835, _626837], _626837)]]], (3097 ^ _257529) ^ [_364461, _364463, _364465] : [_364461 = cartesian_product2(_364465, _364463), 3100 ^ _257529 : [(3101 ^ _257529) ^ [_364662] : [in(_364662, _364461), 3106 ^ _257529 : [(3111 ^ _257529) ^ [] : [-(_364662 = ordered_pair(3104 ^ [_364461, _364463, _364465, _364662], 3105 ^ [_364461, _364463, _364465, _364662]))], (3109 ^ _257529) ^ [] : [-(in(3105 ^ [_364461, _364463, _364465, _364662], _364463))], (3107 ^ _257529) ^ [] : [-(in(3104 ^ [_364461, _364463, _364465, _364662], _364465))]]], (3113 ^ _257529) ^ [_365222] : [-(in(_365222, _364461)), 3114 ^ _257529 : [(3115 ^ _257529) ^ [_365352, _365354] : [in(_365354, _364465), in(_365352, _364463), _365222 = ordered_pair(_365354, _365352)]]]]], (1710 ^ _257529) ^ [_314818, _314820] : [_314820 = _314818, 1713 ^ _257529 : [(1714 ^ _257529) ^ [] : [-(subset(_314820, _314818))], (1716 ^ _257529) ^ [] : [-(subset(_314818, _314820))]]], (308 ^ _257529) ^ [_267006, _267008] : [-(finite(_267006)), _267008 = _267006, finite(_267008)], (4481 ^ _257529) ^ [_412740] : [-(relation(inclusion_relation(_412740)))], (4945 ^ _257529) ^ [_426655, _426657] : [4952 ^ _257529 : [(4953 ^ _257529) ^ [] : [-(relation(relation_dom_restriction(_426657, _426655)))], (4955 ^ _257529) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_426657, _426655)))]], relation(_426657), relation_empty_yielding(_426657)], (11220 ^ _257529) ^ [_667158] : [-(relation_dom(identity_relation(_667158)) = _667158)], (4187 ^ _257529) ^ [_403043] : [relation(_403043), 4190 ^ _257529 : [(4191 ^ _257529) ^ [_403228] : [relation(_403228), 4194 ^ _257529 : [(4195 ^ _257529) ^ [_403409] : [relation(_403409), 4198 ^ _257529 : [(4222 ^ _257529) ^ [] : [-(_403409 = relation_composition(_403043, _403228)), 4236 ^ _257529 : [(4241 ^ _257529) ^ [] : [in(ordered_pair(4223 ^ [_403043, _403228, _403409], 4224 ^ [_403043, _403228, _403409]), _403409)], (4239 ^ _257529) ^ [] : [-(in(ordered_pair(4235 ^ [_403043, _403228, _403409], 4224 ^ [_403043, _403228, _403409]), _403228))], (4237 ^ _257529) ^ [] : [-(in(ordered_pair(4223 ^ [_403043, _403228, _403409], 4235 ^ [_403043, _403228, _403409]), _403043))]], 4227 ^ _257529 : [(4228 ^ _257529) ^ [] : [-(in(ordered_pair(4223 ^ [_403043, _403228, _403409], 4224 ^ [_403043, _403228, _403409]), _403409))], (4230 ^ _257529) ^ [_404873] : [in(ordered_pair(4223 ^ [_403043, _403228, _403409], _404873), _403043), in(ordered_pair(_404873, 4224 ^ [_403043, _403228, _403409]), _403228)]]], (4199 ^ _257529) ^ [] : [_403409 = relation_composition(_403043, _403228), 4202 ^ _257529 : [(4203 ^ _257529) ^ [_403744, _403746] : [in(ordered_pair(_403746, _403744), _403409), 4207 ^ _257529 : [(4208 ^ _257529) ^ [] : [-(in(ordered_pair(_403746, 4206 ^ [_403043, _403228, _403409, _403744, _403746]), _403043))], (4210 ^ _257529) ^ [] : [-(in(ordered_pair(4206 ^ [_403043, _403228, _403409, _403744, _403746], _403744), _403228))]]], (4212 ^ _257529) ^ [_404129, _404131] : [-(in(ordered_pair(_404131, _404129), _403409)), 4213 ^ _257529 : [(4214 ^ _257529) ^ [_404242] : [in(ordered_pair(_404131, _404242), _403043), in(ordered_pair(_404242, _404129), _403228)]]]]]]]]]]], (5690 ^ _257529) ^ [_451204, _451206, _451208] : [subset(_451208, _451206), -(in(_451204, _451208)), -(subset(_451208, set_difference(_451206, singleton(_451204))))], (5893 ^ _257529) ^ [] : [-(epsilon_connected(5889 ^ []))], (5728 ^ _257529) ^ [_452418] : [relation(_452418), 5731 ^ _257529 : [(5754 ^ _257529) ^ [] : [5757 ^ _257529 : [(5758 ^ _257529) ^ [] : [-(in(5755 ^ [_452418], relation_field(_452418)))], (5760 ^ _257529) ^ [] : [-(in(5756 ^ [_452418], relation_field(_452418)))], (5766 ^ _257529) ^ [] : [in(ordered_pair(5756 ^ [_452418], 5755 ^ [_452418]), _452418)], (5764 ^ _257529) ^ [] : [in(ordered_pair(5755 ^ [_452418], 5756 ^ [_452418]), _452418)], (5762 ^ _257529) ^ [] : [5755 ^ [_452418] = 5756 ^ [_452418]]], -(connected(_452418))], (5732 ^ _257529) ^ [] : [connected(_452418), 5735 ^ _257529 : [(5736 ^ _257529) ^ [_452712, _452714] : [in(_452714, relation_field(_452418)), in(_452712, relation_field(_452418)), -(_452714 = _452712), -(in(ordered_pair(_452714, _452712), _452418)), -(in(ordered_pair(_452712, _452714), _452418))]]]]], (3184 ^ _257529) ^ [_367877] : [epsilon_connected(_367877), 3187 ^ _257529 : [(3188 ^ _257529) ^ [_368053, _368055] : [in(_368055, _367877), in(_368053, _367877), -(in(_368055, _368053)), -(_368055 = _368053), -(in(_368053, _368055))]]], (5794 ^ _257529) ^ [_454729, _454731, _454733, _454735] : [in(ordered_pair(_454735, _454733), cartesian_product2(_454731, _454729)), 5797 ^ _257529 : [(5798 ^ _257529) ^ [] : [-(in(_454735, _454731))], (5800 ^ _257529) ^ [] : [-(in(_454733, _454729))]]], (5035 ^ _257529) ^ [_429411] : [empty(powerset(_429411))], (8491 ^ _257529) ^ [_572522, _572524, _572526] : [element(_572524, powerset(powerset(_572526))), relation(_572522), function(_572522), 8503 ^ _257529 : [(8504 ^ _257529) ^ [_572973] : [in(_572973, 8502 ^ [_572522, _572524, _572526]), 8507 ^ _257529 : [(8508 ^ _257529) ^ [] : [-(in(_572973, powerset(relation_dom(_572522))))], (8510 ^ _257529) ^ [] : [-(in(relation_image(_572522, _572973), _572524))]]], (8512 ^ _257529) ^ [_573264] : [-(in(_573264, 8502 ^ [_572522, _572524, _572526])), in(_573264, powerset(relation_dom(_572522))), in(relation_image(_572522, _573264), _572524)]]], (5943 ^ _257529) ^ [] : [-(empty(5941 ^ []))], (1434 ^ _257529) ^ [_306012] : [empty(_306012), -(function(_306012))], (11238 ^ _257529) ^ [_667779, _667781, _667783, _667785] : [relation(_667779), 11241 ^ _257529 : [(11242 ^ _257529) ^ [] : [in(ordered_pair(_667785, _667783), relation_composition(identity_relation(_667781), _667779)), 11245 ^ _257529 : [(11246 ^ _257529) ^ [] : [-(in(_667785, _667781))], (11248 ^ _257529) ^ [] : [-(in(ordered_pair(_667785, _667783), _667779))]]], (11250 ^ _257529) ^ [] : [-(in(ordered_pair(_667785, _667783), relation_composition(identity_relation(_667781), _667779))), in(_667785, _667781), in(ordered_pair(_667785, _667783), _667779)]]], (5770 ^ _257529) ^ [_453904, _453906] : [subset(_453906, singleton(_453904)), -(_453906 = empty_set), -(_453906 = singleton(_453904))], (6265 ^ _257529) ^ [_470037, _470039] : [-(subset(_470039, _470039))], (9444 ^ _257529) ^ [_608416, _608418] : [relation(_608416), function(_608416), finite(_608418), -(finite(relation_image(_608416, _608418)))], (4645 ^ _257529) ^ [_417215, _417217, _417219] : [-(element(meet_commut(_417219, _417217, _417215), the_carrier(_417219))), -(empty_carrier(_417219)), meet_commutative(_417219), meet_semilatt_str(_417219), element(_417217, the_carrier(_417219)), element(_417215, the_carrier(_417219))], (4371 ^ _257529) ^ [_410087] : [relation(_410087), 4374 ^ _257529 : [(4375 ^ _257529) ^ [] : [reflexive(_410087), -(is_reflexive_in(_410087, relation_field(_410087)))], (4381 ^ _257529) ^ [] : [is_reflexive_in(_410087, relation_field(_410087)), -(reflexive(_410087))]]], (9962 ^ _257529) ^ [_625618, _625620] : [subset(_625620, _625618), -(set_intersection2(_625620, _625618) = _625620)], (11466 ^ _257529) ^ [_675448, _675450] : [in(_675448, 11452 ^ [_675450]), 11470 ^ _257529 : [(11471 ^ _257529) ^ [] : [-(in(11469 ^ [_675448, _675450], 11452 ^ [_675450]))], (11473 ^ _257529) ^ [_675760] : [subset(_675760, _675448), -(in(_675760, 11469 ^ [_675448, _675450]))]]], (5946 ^ _257529) ^ [_459668] : [-(element(5944 ^ [_459668], powerset(_459668)))], (6123 ^ _257529) ^ [_465504, _465506, _465508] : [-(join_commut(_465508, _465506, _465504) = join(_465508, _465506, _465504)), -(empty_carrier(_465508)), join_commutative(_465508), join_semilatt_str(_465508), element(_465506, the_carrier(_465508)), element(_465504, the_carrier(_465508))], (1182 ^ _257529) ^ [_296908, _296910, _296912, _296914] : [-(relation_composition(_296914, _296910) = relation_composition(_296912, _296908)), _296914 = _296912, _296910 = _296908], (486 ^ _257529) ^ [_272534, _272536, _272538, _272540] : [-(is_a_cover_of_carrier(_272538, _272534)), is_a_cover_of_carrier(_272540, _272536), _272540 = _272538, _272536 = _272534], (6269 ^ _257529) ^ [_470240, _470242] : [-(empty(_470242)), relation(_470240), 6281 ^ _257529 : [(6295 ^ _257529) ^ [] : [-(in(6278 ^ [_470240, _470242], _470242))], (6308 ^ _257529) ^ [] : [6279 ^ [_470240, _470242] = 6280 ^ [_470240, _470242]], (6287 ^ _257529) ^ [] : [-(in(6279 ^ [_470240, _470242], 6283 ^ [_470240, _470242]))], (6289 ^ _257529) ^ [_471522] : [in(_471522, 6283 ^ [_470240, _470242]), -(in(ordered_pair(6279 ^ [_470240, _470242], _471522), _470240))], (6300 ^ _257529) ^ [] : [-(in(6280 ^ [_470240, _470242], 6296 ^ [_470240, _470242]))], (6285 ^ _257529) ^ [] : [-(6278 ^ [_470240, _470242] = 6283 ^ [_470240, _470242])], (6298 ^ _257529) ^ [] : [-(6278 ^ [_470240, _470242] = 6296 ^ [_470240, _470242])], (6302 ^ _257529) ^ [_472071] : [in(_472071, 6296 ^ [_470240, _470242]), -(in(ordered_pair(6280 ^ [_470240, _470242], _472071), _470240))], (6282 ^ _257529) ^ [] : [-(in(6278 ^ [_470240, _470242], _470242))]], 6310 ^ _257529 : [(6311 ^ _257529) ^ [] : [-(relation(6309 ^ [_470240, _470242]))], (6334 ^ _257529) ^ [_473481, _473483] : [-(in(ordered_pair(_473483, _473481), 6309 ^ [_470240, _470242])), in(_473483, _470242), in(_473483, _470242), 6343 ^ _257529 : [(6344 ^ _257529) ^ [_473797] : [_473483 = _473797, in(_473481, _473797), 6352 ^ _257529 : [(6353 ^ _257529) ^ [] : [-(in(6351 ^ [_470240, _470242, _473481, _473483, _473797], _473797))], (6355 ^ _257529) ^ [] : [in(ordered_pair(_473481, 6351 ^ [_470240, _470242, _473481, _473483, _473797]), _470240)]]]]], (6315 ^ _257529) ^ [_472670, _472672] : [in(ordered_pair(_472672, _472670), 6309 ^ [_470240, _470242]), 6318 ^ _257529 : [(6319 ^ _257529) ^ [] : [-(in(_472672, _470242))], (6321 ^ _257529) ^ [] : [-(in(_472672, _470242))], (6328 ^ _257529) ^ [_473252] : [in(_473252, 6322 ^ [_470240, _470242, _472670, _472672]), -(in(ordered_pair(_472670, _473252), _470240))], (6326 ^ _257529) ^ [] : [-(in(_472670, 6322 ^ [_470240, _470242, _472670, _472672]))], (6324 ^ _257529) ^ [] : [-(_472672 = 6322 ^ [_470240, _470242, _472670, _472672])]]], (6313 ^ _257529) ^ [] : [-(function(6309 ^ [_470240, _470242]))]]], (5660 ^ _257529) ^ [_450154] : [relation(_450154), 5663 ^ _257529 : [(5678 ^ _257529) ^ [] : [5681 ^ _257529 : [(5686 ^ _257529) ^ [] : [5679 ^ [_450154] = 5680 ^ [_450154]], (5684 ^ _257529) ^ [] : [-(in(ordered_pair(5680 ^ [_450154], 5679 ^ [_450154]), _450154))], (5682 ^ _257529) ^ [] : [-(in(ordered_pair(5679 ^ [_450154], 5680 ^ [_450154]), _450154))]], -(antisymmetric(_450154))], (5664 ^ _257529) ^ [] : [antisymmetric(_450154), 5667 ^ _257529 : [(5668 ^ _257529) ^ [_450424, _450426] : [-(_450426 = _450424), in(ordered_pair(_450426, _450424), _450154), in(ordered_pair(_450424, _450426), _450154)]]]]], (1242 ^ _257529) ^ [_299075, _299077, _299079, _299081] : [-(complements_of_subsets(_299081, _299077) = complements_of_subsets(_299079, _299075)), _299081 = _299079, _299077 = _299075], (5554 ^ _257529) ^ [_446412, _446414] : [in(_446414, _446412), -(set_union2(singleton(_446414), _446412) = _446412)], (4927 ^ _257529) ^ [] : [-(relation(empty_set))], (5780 ^ _257529) ^ [_454164, _454166] : [5781 ^ _257529 : [(5782 ^ _257529) ^ [] : [_454166 = empty_set], (5784 ^ _257529) ^ [] : [_454166 = singleton(_454164)]], -(subset(_454166, singleton(_454164)))], (8481 ^ _257529) ^ [_572199, _572201] : [-(in(_572199, 8471 ^ [_572201])), in(_572199, _572201), ordinal(_572199)], (3615 ^ _257529) ^ [_383095, _383097, _383099] : [_383095 = set_difference(_383099, _383097), 3618 ^ _257529 : [(3619 ^ _257529) ^ [_383279] : [in(_383279, _383095), 3622 ^ _257529 : [(3623 ^ _257529) ^ [] : [-(in(_383279, _383099))], (3625 ^ _257529) ^ [] : [in(_383279, _383097)]]], (3627 ^ _257529) ^ [_383539] : [-(in(_383539, _383095)), in(_383539, _383099), -(in(_383539, _383097))]]], (4769 ^ _257529) ^ [_421138, _421140] : [relation(_421138), -(relation(relation_rng_restriction(_421140, _421138)))], (5854 ^ _257529) ^ [] : [-(ordinal(5846 ^ []))], (10282 ^ _257529) ^ [_636221, _636223] : [element(_636223, powerset(_636221)), -(subset(_636223, _636221))], (5061 ^ _257529) ^ [_430368] : [5068 ^ _257529 : [(5069 ^ _257529) ^ [] : [empty(succ(_430368))], (5071 ^ _257529) ^ [] : [-(epsilon_transitive(succ(_430368)))], (5077 ^ _257529) ^ [] : [-(natural(succ(_430368)))], (5075 ^ _257529) ^ [] : [-(ordinal(succ(_430368)))], (5073 ^ _257529) ^ [] : [-(epsilon_connected(succ(_430368)))]], ordinal(_430368), natural(_430368)], (1026 ^ _257529) ^ [_291276, _291278, _291280, _291282] : [-(union_of_subsets(_291282, _291278) = union_of_subsets(_291280, _291276)), _291282 = _291280, _291278 = _291276], (4819 ^ _257529) ^ [] : [true___, -(true___)], (5989 ^ _257529) ^ [_461107, _461109] : [-(relation_of2(5987 ^ [_461107, _461109], _461109, _461107))], (5221 ^ _257529) ^ [_435778, _435780] : [v1_membered(_435780), -(v1_membered(set_difference(_435780, _435778)))], (2100 ^ _257529) ^ [_329275] : [relation(_329275), 2103 ^ _257529 : [(2127 ^ _257529) ^ [_330388, _330390] : [-(_330388 = relation_inverse_image(_329275, _330390)), 2140 ^ _257529 : [(2145 ^ _257529) ^ [] : [in(2128 ^ [_329275, _330388, _330390], _330388)], (2143 ^ _257529) ^ [] : [-(in(2139 ^ [_329275, _330388, _330390], _330390))], (2141 ^ _257529) ^ [] : [-(in(ordered_pair(2128 ^ [_329275, _330388, _330390], 2139 ^ [_329275, _330388, _330390]), _329275))]], 2131 ^ _257529 : [(2132 ^ _257529) ^ [] : [-(in(2128 ^ [_329275, _330388, _330390], _330388))], (2134 ^ _257529) ^ [_330692] : [in(ordered_pair(2128 ^ [_329275, _330388, _330390], _330692), _329275), in(_330692, _330390)]]], (2104 ^ _257529) ^ [_329482, _329484] : [_329482 = relation_inverse_image(_329275, _329484), 2107 ^ _257529 : [(2108 ^ _257529) ^ [_329674] : [in(_329674, _329482), 2112 ^ _257529 : [(2113 ^ _257529) ^ [] : [-(in(ordered_pair(_329674, 2111 ^ [_329275, _329482, _329484, _329674]), _329275))], (2115 ^ _257529) ^ [] : [-(in(2111 ^ [_329275, _329482, _329484, _329674], _329484))]]], (2117 ^ _257529) ^ [_330028] : [-(in(_330028, _329482)), 2118 ^ _257529 : [(2119 ^ _257529) ^ [_330133] : [in(ordered_pair(_330028, _330133), _329275), in(_330133, _329484)]]]]]]], (8908 ^ _257529) ^ [_590112, _590114] : [topological_space(_590114), top_str(_590114), element(_590112, powerset(the_carrier(_590114))), 8920 ^ _257529 : [(8921 ^ _257529) ^ [] : [-(element(8919 ^ [_590112, _590114], powerset(powerset(the_carrier(_590114)))))], (8923 ^ _257529) ^ [_590669] : [element(_590669, powerset(the_carrier(_590114))), 8926 ^ _257529 : [(8927 ^ _257529) ^ [] : [in(_590669, 8919 ^ [_590112, _590114]), 8931 ^ _257529 : [(8932 ^ _257529) ^ [] : [-(element(8930 ^ [_590112, _590114, _590669], powerset(the_carrier(_590114))))], (8938 ^ _257529) ^ [] : [-(subset(_590112, _590669))], (8936 ^ _257529) ^ [] : [-(closed_subset(8930 ^ [_590112, _590114, _590669], _590114))], (8934 ^ _257529) ^ [] : [-(8930 ^ [_590112, _590114, _590669] = _590669)]]], (8940 ^ _257529) ^ [] : [-(in(_590669, 8919 ^ [_590112, _590114])), 8941 ^ _257529 : [(8942 ^ _257529) ^ [_591371] : [element(_591371, powerset(the_carrier(_590114))), _591371 = _590669, closed_subset(_591371, _590114), subset(_590112, _590669)]]]]]]], (4995 ^ _257529) ^ [] : [-(ordinal(omega))], (3593 ^ _257529) ^ [_382388, _382390] : [-(equipotent(_382390, _382388)), 3594 ^ _257529 : [(3595 ^ _257529) ^ [_382499] : [relation(_382499), function(_382499), one_to_one(_382499), relation_dom(_382499) = _382390, relation_rng(_382499) = _382388]]], (10375 ^ _257529) ^ [_639268, _639270] : [element(_639268, powerset(_639270)), 10378 ^ _257529 : [(10379 ^ _257529) ^ [_639420] : [element(_639420, powerset(_639270)), 10382 ^ _257529 : [(10383 ^ _257529) ^ [] : [disjoint(_639268, _639420), -(subset(_639268, subset_complement(_639270, _639420)))], (10389 ^ _257529) ^ [] : [subset(_639268, subset_complement(_639270, _639420)), -(disjoint(_639268, _639420))]]]]], (5169 ^ _257529) ^ [_433834, _433836] : [v4_membered(_433836), 5172 ^ _257529 : [(5173 ^ _257529) ^ [] : [-(v1_membered(set_intersection2(_433836, _433834)))], (5179 ^ _257529) ^ [] : [-(v4_membered(set_intersection2(_433836, _433834)))], (5177 ^ _257529) ^ [] : [-(v3_membered(set_intersection2(_433836, _433834)))], (5175 ^ _257529) ^ [] : [-(v2_membered(set_intersection2(_433836, _433834)))]]], (9210 ^ _257529) ^ [_600584, _600586, _600588] : [relation(_600584), -(relation_dom_restriction(relation_rng_restriction(_600588, _600584), _600586) = relation_rng_restriction(_600588, relation_dom_restriction(_600584, _600586)))], (5993 ^ _257529) ^ [_461233, _461235] : [-(function(5987 ^ [_461233, _461235]))], (10693 ^ _257529) ^ [_650283, _650285] : [10694 ^ _257529 : [(10695 ^ _257529) ^ [_650356] : [in(_650356, set_intersection2(_650285, _650283))]], disjoint(_650285, _650283)], (5411 ^ _257529) ^ [_441829] : [empty(relation_dom(_441829)), -(empty(_441829)), relation(_441829)], (9474 ^ _257529) ^ [_609400, _609402] : [-(subset(set_intersection2(_609402, _609400), _609402))], (1050 ^ _257529) ^ [_292123, _292125] : [_292125 = _292123, -(cast_to_subset(_292125) = cast_to_subset(_292123))], (10272 ^ _257529) ^ [_635884, _635886, _635888] : [in(_635888, _635886), in(_635886, _635884), in(_635884, _635888)], (8325 ^ _257529) ^ [_565047, _565049] : [one_sorted_str(_565049), element(_565047, powerset(powerset(the_carrier(_565049)))), 8333 ^ _257529 : [(8334 ^ _257529) ^ [_565534, _565536] : [in(_565534, 8332 ^ [_565047, _565049, _565536]), 8337 ^ _257529 : [(8338 ^ _257529) ^ [] : [-(in(_565534, cartesian_product2(complements_of_subsets(the_carrier(_565049), _565047), _565536)))], (8346 ^ _257529) ^ [_566255] : [element(_566255, powerset(the_carrier(_565049))), _566255 = 8339 ^ [_565047, _565049, _565534, _565536], -(8340 ^ [_565047, _565049, _565534, _565536] = subset_complement(the_carrier(_565049), _566255))], (8344 ^ _257529) ^ [] : [-(in(8339 ^ [_565047, _565049, _565534, _565536], complements_of_subsets(the_carrier(_565049), _565047)))], (8342 ^ _257529) ^ [] : [-(ordered_pair(8339 ^ [_565047, _565049, _565534, _565536], 8340 ^ [_565047, _565049, _565534, _565536]) = _565534)]]], (8356 ^ _257529) ^ [_566617, _566619] : [-(in(_566617, 8332 ^ [_565047, _565049, _566619])), in(_566617, cartesian_product2(complements_of_subsets(the_carrier(_565049), _565047), _566619)), 8361 ^ _257529 : [(8362 ^ _257529) ^ [_566894, _566896] : [ordered_pair(_566896, _566894) = _566617, in(_566896, complements_of_subsets(the_carrier(_565049), _565047)), 8370 ^ _257529 : [(8375 ^ _257529) ^ [] : [_566894 = subset_complement(the_carrier(_565049), 8369 ^ [_565047, _565049, _566617, _566619, _566894, _566896])], (8373 ^ _257529) ^ [] : [-(8369 ^ [_565047, _565049, _566617, _566619, _566894, _566896] = _566896)], (8371 ^ _257529) ^ [] : [-(element(8369 ^ [_565047, _565049, _566617, _566619, _566894, _566896], powerset(the_carrier(_565049))))]]]]]]], (6484 ^ _257529) ^ [_479820, _479822] : [one_sorted_str(_479822), element(_479820, powerset(powerset(the_carrier(_479822)))), 6496 ^ _257529 : [(6521 ^ _257529) ^ [] : [6494 ^ [_479820, _479822] = 6495 ^ [_479820, _479822]], (6497 ^ _257529) ^ [] : [-(in(6493 ^ [_479820, _479822], _479820))], (6511 ^ _257529) ^ [_481207] : [element(_481207, powerset(the_carrier(_479822))), _481207 = 6493 ^ [_479820, _479822], -(6495 ^ [_479820, _479822] = subset_complement(the_carrier(_479822), _481207))], (6509 ^ _257529) ^ [] : [-(in(6493 ^ [_479820, _479822], _479820))], (6499 ^ _257529) ^ [_480809] : [element(_480809, powerset(the_carrier(_479822))), _480809 = 6493 ^ [_479820, _479822], -(6494 ^ [_479820, _479822] = subset_complement(the_carrier(_479822), _480809))]], 6523 ^ _257529 : [(6524 ^ _257529) ^ [] : [-(relation(6522 ^ [_479820, _479822]))], (6546 ^ _257529) ^ [_482550, _482552] : [-(in(ordered_pair(_482552, _482550), 6522 ^ [_479820, _479822])), in(_482552, _479820), in(_482552, _479820), 6556 ^ _257529 : [(6561 ^ _257529) ^ [] : [_482550 = subset_complement(the_carrier(_479822), 6555 ^ [_479820, _479822, _482550, _482552])], (6559 ^ _257529) ^ [] : [-(6555 ^ [_479820, _479822, _482550, _482552] = _482552)], (6557 ^ _257529) ^ [] : [-(element(6555 ^ [_479820, _479822, _482550, _482552], powerset(the_carrier(_479822))))]]], (6528 ^ _257529) ^ [_481898, _481900] : [in(ordered_pair(_481900, _481898), 6522 ^ [_479820, _479822]), 6531 ^ _257529 : [(6536 ^ _257529) ^ [_482234] : [element(_482234, powerset(the_carrier(_479822))), _482234 = _481900, -(_481898 = subset_complement(the_carrier(_479822), _482234))], (6534 ^ _257529) ^ [] : [-(in(_481900, _479820))], (6532 ^ _257529) ^ [] : [-(in(_481900, _479820))]]], (6526 ^ _257529) ^ [] : [-(function(6522 ^ [_479820, _479822]))]]], (7384 ^ _257529) ^ [_520488, _520490] : [ordinal(_520490), element(_520488, powerset(powerset(succ(_520490)))), 7396 ^ _257529 : [(7400 ^ _257529) ^ [] : [-(in(7398 ^ [_520488, _520490], _520488))], (7409 ^ _257529) ^ [] : [-(7395 ^ [_520488, _520490] = set_difference(7405 ^ [_520488, _520490], singleton(_520490)))], (7411 ^ _257529) ^ [] : [7394 ^ [_520488, _520490] = 7395 ^ [_520488, _520490]], (7404 ^ _257529) ^ [] : [-(7393 ^ [_520488, _520490] = 7395 ^ [_520488, _520490])], (7397 ^ _257529) ^ [] : [-(7393 ^ [_520488, _520490] = 7394 ^ [_520488, _520490])], (7402 ^ _257529) ^ [] : [-(7394 ^ [_520488, _520490] = set_difference(7398 ^ [_520488, _520490], singleton(_520490)))], (7407 ^ _257529) ^ [] : [-(in(7405 ^ [_520488, _520490], _520488))]], 7413 ^ _257529 : [(7414 ^ _257529) ^ [_522047] : [in(_522047, 7412 ^ [_520488, _520490]), 7418 ^ _257529 : [(7419 ^ _257529) ^ [] : [-(in(7417 ^ [_520488, _520490, _522047], powerset(_520490)))], (7426 ^ _257529) ^ [] : [-(_522047 = set_difference(7422 ^ [_520488, _520490, _522047], singleton(_520490)))], (7424 ^ _257529) ^ [] : [-(in(7422 ^ [_520488, _520490, _522047], _520488))], (7421 ^ _257529) ^ [] : [-(7417 ^ [_520488, _520490, _522047] = _522047)]]], (7428 ^ _257529) ^ [_522661] : [-(in(_522661, 7412 ^ [_520488, _520490])), 7429 ^ _257529 : [(7430 ^ _257529) ^ [_522790] : [in(_522790, powerset(_520490)), _522790 = _522661, 7437 ^ _257529 : [(7438 ^ _257529) ^ [_523043] : [in(_523043, _520488), _522661 = set_difference(_523043, singleton(_520490))]]]]]]], (1510 ^ _257529) ^ [_308528] : [-(preboolean(_308528)), cup_closed(_308528), diff_closed(_308528)], (5429 ^ _257529) ^ [] : [-(v4_membered(empty_set))], (5495 ^ _257529) ^ [_444315, _444317] : [-(set_union2(_444317, _444317) = _444317)], (126 ^ _257529) ^ [_261528, _261530] : [-(diff_closed(_261528)), _261530 = _261528, diff_closed(_261530)], (5929 ^ _257529) ^ [_459070] : [5937 ^ _257529 : [(5938 ^ _257529) ^ [] : [-(element(5936 ^ [_459070], powerset(the_carrier(_459070))))], (5940 ^ _257529) ^ [] : [-(open_subset(5936 ^ [_459070], _459070))]], topological_space(_459070), top_str(_459070)], (5962 ^ _257529) ^ [_460215] : [-(natural(5944 ^ [_460215]))], (11003 ^ _257529) ^ [_660426, _660428, _660430] : [in(_660430, _660428), element(_660428, powerset(_660426)), empty(_660426)], (906 ^ _257529) ^ [_286920, _286922, _286924, _286926] : [-(relation_image(_286926, _286922) = relation_image(_286924, _286920)), _286926 = _286924, _286922 = _286920], (1614 ^ _257529) ^ [_311665, _311667] : [-(set_intersection2(_311667, _311665) = set_intersection2(_311665, _311667))], (9362 ^ _257529) ^ [_605816, _605818] : [relation(_605816), -(subset(relation_inverse_image(_605816, _605818), relation_dom(_605816)))], (5359 ^ _257529) ^ [] : [-(relation(empty_set))], (5869 ^ _257529) ^ [_457145, _457147] : [-(relation_of2(5867 ^ [_457145, _457147], _457147, _457145))], (4435 ^ _257529) ^ [] : [true___, -(true___)], (5099 ^ _257529) ^ [_431523] : [empty(cast_as_carrier_subset(_431523)), -(empty_carrier(_431523)), one_sorted_str(_431523)], (1446 ^ _257529) ^ [_306384] : [ordinal(_306384), 1449 ^ _257529 : [(1450 ^ _257529) ^ [] : [-(epsilon_transitive(_306384))], (1452 ^ _257529) ^ [] : [-(epsilon_connected(_306384))]]], (5650 ^ _257529) ^ [_449802, _449804] : [element(_449802, powerset(_449804)), 5653 ^ _257529 : [(5654 ^ _257529) ^ [_449943] : [in(_449943, _449802), -(in(_449943, _449804))]]], (524 ^ _257529) ^ [_273717, _273719, _273721, _273723] : [-(proper_subset(_273721, _273717)), proper_subset(_273723, _273719), _273723 = _273721, _273719 = _273717], (4447 ^ _257529) ^ [] : [true___, -(true___)], (3018 ^ _257529) ^ [_361653] : [relation(_361653), 3021 ^ _257529 : [(3039 ^ _257529) ^ [] : [-(well_founded_relation(_361653)), 3041 ^ _257529 : [(3046 ^ _257529) ^ [_362603] : [in(_362603, 3040 ^ [_361653]), disjoint(fiber(_361653, _362603), 3040 ^ [_361653])], (3044 ^ _257529) ^ [] : [3040 ^ [_361653] = empty_set], (3042 ^ _257529) ^ [] : [-(subset(3040 ^ [_361653], relation_field(_361653)))]]], (3022 ^ _257529) ^ [] : [well_founded_relation(_361653), 3025 ^ _257529 : [(3026 ^ _257529) ^ [_361920] : [subset(_361920, relation_field(_361653)), -(_361920 = empty_set), 3034 ^ _257529 : [(3035 ^ _257529) ^ [] : [-(in(3033 ^ [_361653, _361920], _361920))], (3037 ^ _257529) ^ [] : [-(disjoint(fiber(_361653, 3033 ^ [_361653, _361920]), _361920))]]]]]]], (4799 ^ _257529) ^ [_421946] : [join_semilatt_str(_421946), -(one_sorted_str(_421946))], (10594 ^ _257529) ^ [_646899, _646901] : [in(_646901, _646899), -(set_union2(singleton(_646901), _646899) = _646899)], (9283 ^ _257529) ^ [_603104, _603106] : [relation(_603104), function(_603104), subset(_603106, relation_rng(_603104)), -(relation_image(_603104, relation_inverse_image(_603104, _603106)) = _603106)], (5958 ^ _257529) ^ [_460079] : [-(epsilon_connected(5944 ^ [_460079]))], (1166 ^ _257529) ^ [_296331, _296333, _296335, _296337] : [-(set_intersection2(_296337, _296333) = set_intersection2(_296335, _296331)), _296337 = _296335, _296333 = _296331], (9725 ^ _257529) ^ [_617970, _617972] : [relation(_617970), function(_617970), 9732 ^ _257529 : [(9733 ^ _257529) ^ [_618216] : [relation(_618216), function(_618216), in(_617972, relation_dom(_617970)), -(apply(relation_composition(_617970, _618216), _617972) = apply(_618216, apply(_617970, _617972)))]]], (9135 ^ _257529) ^ [_598032, _598034] : [element(_598032, powerset(powerset(_598034))), -(_598032 = empty_set), -(union_of_subsets(_598034, complements_of_subsets(_598034, _598032)) = subset_complement(_598034, meet_of_subsets(_598034, _598032)))], (10887 ^ _257529) ^ [_656700, _656702, _656704] : [element(_656700, powerset(_656704)), in(_656702, subset_complement(_656704, _656700)), in(_656702, _656700)], (9245 ^ _257529) ^ [_601834, _601836] : [relation(_601834), -(subset(relation_image(_601834, _601836), relation_rng(_601834)))], (3333 ^ _257529) ^ [_373385, _373387, _373389] : [-(_373385 = set_intersection2(_373389, _373387)), 3345 ^ _257529 : [(3350 ^ _257529) ^ [] : [in(3334 ^ [_373385, _373387, _373389], _373385)], (3348 ^ _257529) ^ [] : [-(in(3334 ^ [_373385, _373387, _373389], _373387))], (3346 ^ _257529) ^ [] : [-(in(3334 ^ [_373385, _373387, _373389], _373389))]], 3337 ^ _257529 : [(3338 ^ _257529) ^ [] : [-(in(3334 ^ [_373385, _373387, _373389], _373385))], (3340 ^ _257529) ^ [] : [in(3334 ^ [_373385, _373387, _373389], _373389), in(3334 ^ [_373385, _373387, _373389], _373387)]]], (2165 ^ _257529) ^ [_331725] : [relation(_331725), 2168 ^ _257529 : [(2169 ^ _257529) ^ [] : [transitive(_331725), -(is_transitive_in(_331725, relation_field(_331725)))], (2175 ^ _257529) ^ [] : [is_transitive_in(_331725, relation_field(_331725)), -(transitive(_331725))]]], (4793 ^ _257529) ^ [] : [true___, -(true___)], (20 ^ _257529) ^ [_258277, _258279] : [-(v1_xcmplx_0(_258277)), _258279 = _258277, v1_xcmplx_0(_258279)], (11297 ^ _257529) ^ [_669866, _669868] : [set_difference(_669868, _669866) = _669868, -(disjoint(_669868, _669866))], (4876 ^ _257529) ^ [] : [-(latt_str(4874 ^ []))], (5700 ^ _257529) ^ [_451510] : [-(empty_carrier(_451510)), one_sorted_str(_451510), 5707 ^ _257529 : [(5708 ^ _257529) ^ [_451757] : [element(_451757, powerset(the_carrier(_451510))), 5711 ^ _257529 : [(5712 ^ _257529) ^ [_451919] : [element(_451919, the_carrier(_451510)), 5715 ^ _257529 : [(5716 ^ _257529) ^ [] : [in(_451919, subset_complement(the_carrier(_451510), _451757)), in(_451919, _451757)], (5722 ^ _257529) ^ [] : [-(in(_451919, _451757)), -(in(_451919, subset_complement(the_carrier(_451510), _451757)))]]]]]]], (4405 ^ _257529) ^ [] : [true___, -(true___)], (5303 ^ _257529) ^ [_438380, _438382] : [-(empty(_438382)), empty(set_union2(_438380, _438382))], (10194 ^ _257529) ^ [_633297, _633299] : [set_difference(_633299, _633297) = empty_set, -(subset(_633299, _633297))], (3449 ^ _257529) ^ [_377321] : [relation(_377321), 3452 ^ _257529 : [(3475 ^ _257529) ^ [_378189] : [3478 ^ _257529 : [(3479 ^ _257529) ^ [] : [-(in(3476 ^ [_377321, _378189], _378189))], (3481 ^ _257529) ^ [] : [-(in(3477 ^ [_377321, _378189], _378189))], (3487 ^ _257529) ^ [] : [3476 ^ [_377321, _378189] = 3477 ^ [_377321, _378189]], (3485 ^ _257529) ^ [] : [-(in(ordered_pair(3477 ^ [_377321, _378189], 3476 ^ [_377321, _378189]), _377321))], (3483 ^ _257529) ^ [] : [-(in(ordered_pair(3476 ^ [_377321, _378189], 3477 ^ [_377321, _378189]), _377321))]], -(is_antisymmetric_in(_377321, _378189))], (3453 ^ _257529) ^ [_377521] : [is_antisymmetric_in(_377321, _377521), 3456 ^ _257529 : [(3457 ^ _257529) ^ [_377703, _377705] : [-(_377705 = _377703), in(_377705, _377521), in(_377703, _377521), in(ordered_pair(_377705, _377703), _377321), in(ordered_pair(_377703, _377705), _377321)]]]]], (2658 ^ _257529) ^ [_349069] : [relation(_349069), 2661 ^ _257529 : [(2684 ^ _257529) ^ [_350021, _350023] : [-(_350021 = fiber(_349069, _350023)), 2696 ^ _257529 : [(2701 ^ _257529) ^ [] : [in(2685 ^ [_349069, _350021, _350023], _350021)], (2699 ^ _257529) ^ [] : [-(in(ordered_pair(2685 ^ [_349069, _350021, _350023], _350023), _349069))], (2697 ^ _257529) ^ [] : [2685 ^ [_349069, _350021, _350023] = _350023]], 2688 ^ _257529 : [(2689 ^ _257529) ^ [] : [-(in(2685 ^ [_349069, _350021, _350023], _350021))], (2691 ^ _257529) ^ [] : [-(2685 ^ [_349069, _350021, _350023] = _350023), in(ordered_pair(2685 ^ [_349069, _350021, _350023], _350023), _349069)]]], (2662 ^ _257529) ^ [_349273, _349275] : [_349273 = fiber(_349069, _349275), 2665 ^ _257529 : [(2666 ^ _257529) ^ [_349462] : [in(_349462, _349273), 2669 ^ _257529 : [(2670 ^ _257529) ^ [] : [_349462 = _349275], (2672 ^ _257529) ^ [] : [-(in(ordered_pair(_349462, _349275), _349069))]]], (2674 ^ _257529) ^ [_349728] : [-(in(_349728, _349273)), -(_349728 = _349275), in(ordered_pair(_349728, _349275), _349069)]]]]], (226 ^ _257529) ^ [_264478, _264480] : [-(meet_semilatt_str(_264478)), _264480 = _264478, meet_semilatt_str(_264480)], (9990 ^ _257529) ^ [_626537, _626539] : [element(_626539, _626537), -(empty(_626537)), -(in(_626539, _626537))], (6053 ^ _257529) ^ [] : [-(relation_empty_yielding(6049 ^ []))], (2821 ^ _257529) ^ [_354800] : [2822 ^ _257529 : [(2823 ^ _257529) ^ [_354922, _354924] : [_354800 = ordered_pair(_354924, _354922)]], 2824 ^ _257529 : [(2835 ^ _257529) ^ [_355385] : [2838 ^ _257529 : [(2839 ^ _257529) ^ [] : [-(_354800 = ordered_pair(2836 ^ [_354800, _355385], 2837 ^ [_354800, _355385]))], (2841 ^ _257529) ^ [] : [_355385 = 2837 ^ [_354800, _355385]]], -(_355385 = pair_second(_354800))], (2825 ^ _257529) ^ [_355031] : [_355031 = pair_second(_354800), 2828 ^ _257529 : [(2829 ^ _257529) ^ [_355196, _355198] : [_354800 = ordered_pair(_355198, _355196), -(_355031 = _355196)]]]]], (538 ^ _257529) ^ [_274133, _274135] : [-(one_to_one(_274133)), _274135 = _274133, one_to_one(_274135)], (1354 ^ _257529) ^ [_303270] : [v1_membered(_303270), 1357 ^ _257529 : [(1358 ^ _257529) ^ [_303402] : [element(_303402, powerset(_303270)), -(v1_membered(_303402))]]], (5025 ^ _257529) ^ [_429150] : [empty(the_carrier(_429150)), -(empty_carrier(_429150)), one_sorted_str(_429150)], (2855 ^ _257529) ^ [_356156] : [2857 ^ _257529 : [(2858 ^ _257529) ^ [] : [-(in(2856 ^ [_356156], _356156))], (2860 ^ _257529) ^ [] : [subset(2856 ^ [_356156], _356156)]], -(epsilon_transitive(_356156))], (9988 ^ _257529) ^ [_626427] : [-(set_intersection2(_626427, empty_set) = empty_set)], (7879 ^ _257529) ^ [_546114] : [7883 ^ _257529 : [(7884 ^ _257529) ^ [] : [-(7880 ^ [_546114] = 7881 ^ [_546114])], (7886 ^ _257529) ^ [] : [-(ordinal(7881 ^ [_546114]))], (7892 ^ _257529) ^ [] : [7881 ^ [_546114] = 7882 ^ [_546114]], (7890 ^ _257529) ^ [] : [-(ordinal(7882 ^ [_546114]))], (7888 ^ _257529) ^ [] : [-(7880 ^ [_546114] = 7882 ^ [_546114])]], 7894 ^ _257529 : [(7895 ^ _257529) ^ [_546949] : [in(_546949, 7893 ^ [_546114]), 7899 ^ _257529 : [(7904 ^ _257529) ^ [] : [-(ordinal(_546949))], (7902 ^ _257529) ^ [] : [-(7898 ^ [_546114, _546949] = _546949)], (7900 ^ _257529) ^ [] : [-(in(7898 ^ [_546114, _546949], _546114))]]], (7906 ^ _257529) ^ [_547345] : [-(in(_547345, 7893 ^ [_546114])), 7907 ^ _257529 : [(7908 ^ _257529) ^ [_547449] : [in(_547449, _546114), _547449 = _547345, ordinal(_547345)]]]]], (8473 ^ _257529) ^ [_571954, _571956] : [in(_571954, 8471 ^ [_571956]), 8476 ^ _257529 : [(8477 ^ _257529) ^ [] : [-(in(_571954, _571956))], (8479 ^ _257529) ^ [] : [-(ordinal(_571954))]]], (9323 ^ _257529) ^ [_604429] : [relation(_604429), 9326 ^ _257529 : [(9327 ^ _257529) ^ [_604569] : [relation(_604569), -(relation_rng(relation_composition(_604429, _604569)) = relation_image(_604569, relation_rng(_604429)))]]], (2503 ^ _257529) ^ [_343885, _343887] : [-(_343887 = empty_set), 2506 ^ _257529 : [(2530 ^ _257529) ^ [] : [-(_343885 = set_meet(_343887)), 2534 ^ _257529 : [(2540 ^ _257529) ^ [] : [in(2531 ^ [_343885, _343887], 2536 ^ [_343885, _343887])], (2538 ^ _257529) ^ [] : [-(in(2536 ^ [_343885, _343887], _343887))], (2535 ^ _257529) ^ [] : [-(in(2531 ^ [_343885, _343887], _343885))]], 2541 ^ _257529 : [(2548 ^ _257529) ^ [] : [in(2531 ^ [_343885, _343887], _343885)], (2542 ^ _257529) ^ [_345287] : [in(_345287, _343887), -(in(2531 ^ [_343885, _343887], _345287))]]], (2507 ^ _257529) ^ [] : [_343885 = set_meet(_343887), 2510 ^ _257529 : [(2521 ^ _257529) ^ [_344513] : [2523 ^ _257529 : [(2524 ^ _257529) ^ [] : [-(in(2522 ^ [_343885, _343887, _344513], _343887))], (2526 ^ _257529) ^ [] : [in(_344513, 2522 ^ [_343885, _343887, _344513])]], -(in(_344513, _343885))], (2511 ^ _257529) ^ [_344183] : [in(_344183, _343885), 2514 ^ _257529 : [(2515 ^ _257529) ^ [_344328] : [in(_344328, _343887), -(in(_344183, _344328))]]]]]]], (5998 ^ _257529) ^ [] : [-(relation(5994 ^ []))], (338 ^ _257529) ^ [_267947, _267949, _267951, _267953, _267955, _267957] : [-(below(_267955, _267951, _267947)), below(_267957, _267953, _267949), _267957 = _267955, _267953 = _267951, _267949 = _267947], (1066 ^ _257529) ^ [_292728, _292730, _292732, _292734] : [-(topstr_closure(_292734, _292730) = topstr_closure(_292732, _292728)), _292734 = _292732, _292730 = _292728], (3780 ^ _257529) ^ [_388672] : [relation(_388672), 3783 ^ _257529 : [(3801 ^ _257529) ^ [_389484] : [-(_389484 = relation_rng(_388672)), 3805 ^ _257529 : [(3806 ^ _257529) ^ [] : [-(in(3802 ^ [_388672, _389484], _389484))], (3808 ^ _257529) ^ [_389747] : [in(ordered_pair(_389747, 3802 ^ [_388672, _389484]), _388672)]], 3810 ^ _257529 : [(3811 ^ _257529) ^ [] : [-(in(ordered_pair(3809 ^ [_388672, _389484], 3802 ^ [_388672, _389484]), _388672))], (3813 ^ _257529) ^ [] : [in(3802 ^ [_388672, _389484], _389484)]]], (3784 ^ _257529) ^ [_388853] : [_388853 = relation_rng(_388672), 3787 ^ _257529 : [(3788 ^ _257529) ^ [_389033] : [in(_389033, _388853), -(in(ordered_pair(3791 ^ [_388672, _388853, _389033], _389033), _388672))], (3795 ^ _257529) ^ [_389277] : [3796 ^ _257529 : [(3797 ^ _257529) ^ [_389356] : [in(ordered_pair(_389356, _389277), _388672)]], -(in(_389277, _388853))]]]]], (6023 ^ _257529) ^ [_462280] : [-(empty(_462280)), 6027 ^ _257529 : [(6032 ^ _257529) ^ [] : [-(finite(6026 ^ [_462280]))], (6030 ^ _257529) ^ [] : [empty(6026 ^ [_462280])], (6028 ^ _257529) ^ [] : [-(element(6026 ^ [_462280], powerset(_462280)))]]], (6051 ^ _257529) ^ [] : [-(relation(6049 ^ []))], (6035 ^ _257529) ^ [] : [-(relation(6033 ^ []))], (4997 ^ _257529) ^ [] : [empty(omega)], (2497 ^ _257529) ^ [_343639, _343641, _343643] : [subset(_343639, cartesian_product2(_343643, _343641)), -(relation_of2(_343639, _343643, _343641))], (6217 ^ _257529) ^ [_468585, _468587, _468589] : [relation_of2(_468585, _468589, _468587), -(relation_of2_as_subset(_468585, _468589, _468587))], (6195 ^ _257529) ^ [_467797, _467799] : [element(_467797, powerset(powerset(_467799))), -(meet_of_subsets(_467799, _467797) = set_meet(_467797))], (10252 ^ _257529) ^ [_635235, _635237] : [subset(_635237, singleton(_635235)), -(_635237 = empty_set), -(_635237 = singleton(_635235))], (11270 ^ _257529) ^ [_668851, _668853] : [in(_668853, _668851), 11274 ^ _257529 : [(11275 ^ _257529) ^ [] : [-(in(11273 ^ [_668851, _668853], _668851))], (11277 ^ _257529) ^ [_669142] : [in(_669142, _668851), in(_669142, 11273 ^ [_668851, _668853])]]], (9069 ^ _257529) ^ [_595613, _595615] : [relation(_595613), -(subset(relation_rng(relation_rng_restriction(_595615, _595613)), _595615))], (9883 ^ _257529) ^ [_623003] : [relation(_623003), function(_623003), finite(relation_dom(_623003)), -(finite(relation_rng(_623003)))], (7025 ^ _257529) ^ [_503686, _503688] : [7029 ^ _257529 : [(7044 ^ _257529) ^ [] : [-(ordered_pair(7041 ^ [_503686, _503688], 7042 ^ [_503686, _503688]) = 7028 ^ [_503686, _503688])], (7030 ^ _257529) ^ [] : [-(7026 ^ [_503686, _503688] = 7027 ^ [_503686, _503688])], (7038 ^ _257529) ^ [] : [-(7032 ^ [_503686, _503688] = singleton(7031 ^ [_503686, _503688]))], (7040 ^ _257529) ^ [] : [-(7026 ^ [_503686, _503688] = 7028 ^ [_503686, _503688])], (7048 ^ _257529) ^ [] : [-(7042 ^ [_503686, _503688] = singleton(7041 ^ [_503686, _503688]))], (7036 ^ _257529) ^ [] : [-(in(7031 ^ [_503686, _503688], _503688))], (7046 ^ _257529) ^ [] : [-(in(7041 ^ [_503686, _503688], _503688))], (7050 ^ _257529) ^ [] : [7027 ^ [_503686, _503688] = 7028 ^ [_503686, _503688]], (7034 ^ _257529) ^ [] : [-(ordered_pair(7031 ^ [_503686, _503688], 7032 ^ [_503686, _503688]) = 7027 ^ [_503686, _503688])]], 7052 ^ _257529 : [(7053 ^ _257529) ^ [_505559] : [in(_505559, 7051 ^ [_503686, _503688]), 7057 ^ _257529 : [(7058 ^ _257529) ^ [] : [-(in(7056 ^ [_503686, _503688, _505559], cartesian_product2(_503688, _503686)))], (7060 ^ _257529) ^ [] : [-(7056 ^ [_503686, _503688, _505559] = _505559)], (7068 ^ _257529) ^ [] : [-(7062 ^ [_503686, _503688, _505559] = singleton(7061 ^ [_503686, _503688, _505559]))], (7066 ^ _257529) ^ [] : [-(in(7061 ^ [_503686, _503688, _505559], _503688))], (7064 ^ _257529) ^ [] : [-(ordered_pair(7061 ^ [_503686, _503688, _505559], 7062 ^ [_503686, _503688, _505559]) = _505559)]]], (7070 ^ _257529) ^ [_506399] : [-(in(_506399, 7051 ^ [_503686, _503688])), 7071 ^ _257529 : [(7072 ^ _257529) ^ [_506540] : [in(_506540, cartesian_product2(_503688, _503686)), _506540 = _506399, 7079 ^ _257529 : [(7080 ^ _257529) ^ [_506820, _506822] : [ordered_pair(_506822, _506820) = _506399, in(_506822, _503688), _506820 = singleton(_506822)]]]]]]], (5425 ^ _257529) ^ [] : [-(v2_membered(empty_set))], (6065 ^ _257529) ^ [] : [-(function(6059 ^ []))], (11083 ^ _257529) ^ [_662768] : [relation(_662768), 11088 ^ _257529 : [(11089 ^ _257529) ^ [] : [relation_dom(_662768) = empty_set], (11091 ^ _257529) ^ [] : [relation_rng(_662768) = empty_set]], -(_662768 = empty_set)], (2870 ^ _257529) ^ [_356673] : [relation(_356673), 2873 ^ _257529 : [(2874 ^ _257529) ^ [_356831] : [relation(_356831), 2877 ^ _257529 : [(2894 ^ _257529) ^ [] : [-(_356673 = _356831), 2899 ^ _257529 : [(2900 ^ _257529) ^ [] : [-(in(ordered_pair(2895 ^ [_356673, _356831], 2896 ^ [_356673, _356831]), _356673))], (2902 ^ _257529) ^ [] : [in(ordered_pair(2895 ^ [_356673, _356831], 2896 ^ [_356673, _356831]), _356831)]], 2903 ^ _257529 : [(2904 ^ _257529) ^ [] : [-(in(ordered_pair(2895 ^ [_356673, _356831], 2896 ^ [_356673, _356831]), _356831))], (2906 ^ _257529) ^ [] : [in(ordered_pair(2895 ^ [_356673, _356831], 2896 ^ [_356673, _356831]), _356673)]]], (2878 ^ _257529) ^ [] : [_356673 = _356831, 2881 ^ _257529 : [(2882 ^ _257529) ^ [_357136, _357138] : [in(ordered_pair(_357138, _357136), _356673), -(in(ordered_pair(_357138, _357136), _356831))], (2888 ^ _257529) ^ [_357326, _357328] : [in(ordered_pair(_357328, _357326), _356831), -(in(ordered_pair(_357328, _357326), _356673))]]]]]]], (2803 ^ _257529) ^ [_354125] : [-(empty_carrier(_354125)), meet_semilatt_str(_354125), 2810 ^ _257529 : [(2811 ^ _257529) ^ [_354376] : [element(_354376, the_carrier(_354125)), 2814 ^ _257529 : [(2815 ^ _257529) ^ [_354540] : [element(_354540, the_carrier(_354125)), -(meet(_354125, _354376, _354540) = apply_binary_as_element(the_carrier(_354125), the_carrier(_354125), the_carrier(_354125), the_L_meet(_354125), _354376, _354540))]]]]], (2336 ^ _257529) ^ [_337521] : [-(empty_carrier(_337521)), join_semilatt_str(_337521), 2343 ^ _257529 : [(2344 ^ _257529) ^ [_337772] : [element(_337772, the_carrier(_337521)), 2347 ^ _257529 : [(2348 ^ _257529) ^ [_337936] : [element(_337936, the_carrier(_337521)), -(join(_337521, _337772, _337936) = apply_binary_as_element(the_carrier(_337521), the_carrier(_337521), the_carrier(_337521), the_L_join(_337521), _337772, _337936))]]]]], (4957 ^ _257529) ^ [_427023] : [empty(singleton(_427023))], (5578 ^ _257529) ^ [_447270] : [relation(_447270), 5581 ^ _257529 : [(5596 ^ _257529) ^ [] : [5600 ^ _257529 : [(5605 ^ _257529) ^ [] : [in(ordered_pair(5597 ^ [_447270], 5599 ^ [_447270]), _447270)], (5603 ^ _257529) ^ [] : [-(in(ordered_pair(5598 ^ [_447270], 5599 ^ [_447270]), _447270))], (5601 ^ _257529) ^ [] : [-(in(ordered_pair(5597 ^ [_447270], 5598 ^ [_447270]), _447270))]], -(transitive(_447270))], (5582 ^ _257529) ^ [] : [transitive(_447270), 5585 ^ _257529 : [(5586 ^ _257529) ^ [_447562, _447564, _447566] : [-(in(ordered_pair(_447566, _447562), _447270)), in(ordered_pair(_447566, _447564), _447270), in(ordered_pair(_447564, _447562), _447270)]]]]], (8810 ^ _257529) ^ [] : [8865 ^ _257529 : [(8866 ^ _257529) ^ [_588574] : [ordinal(_588574), in(_588574, omega), 8873 ^ _257529 : [(8874 ^ _257529) ^ [_588830] : [element(_588830, powerset(powerset(_588574))), -(_588830 = empty_set), 8882 ^ _257529 : [(8883 ^ _257529) ^ [] : [-(in(8881 ^ [_588574, _588830], _588830))], (8885 ^ _257529) ^ [_589229] : [-(_589229 = 8881 ^ [_588574, _588830]), in(_589229, _588830), subset(8881 ^ [_588574, _588830], _589229)]]]]]], 8812 ^ _257529 : [(8851 ^ _257529) ^ [] : [-(element(8849 ^ [], powerset(powerset(8811 ^ []))))], (8813 ^ _257529) ^ [] : [-(ordinal(8811 ^ []))], (8815 ^ _257529) ^ [_586861] : [ordinal(_586861), in(_586861, 8811 ^ []), in(_586861, omega), 8826 ^ _257529 : [(8827 ^ _257529) ^ [_587198] : [element(_587198, powerset(powerset(_586861))), -(_587198 = empty_set), 8835 ^ _257529 : [(8836 ^ _257529) ^ [] : [-(in(8834 ^ [_586861, _587198], _587198))], (8838 ^ _257529) ^ [_587597] : [-(_587597 = 8834 ^ [_586861, _587198]), in(_587597, _587198), subset(8834 ^ [_586861, _587198], _587597)]]]]], (8853 ^ _257529) ^ [] : [8849 ^ [] = empty_set], (8855 ^ _257529) ^ [_588169] : [in(_588169, 8849 ^ []), 8859 ^ _257529 : [(8864 ^ _257529) ^ [] : [8858 ^ [_588169] = _588169], (8862 ^ _257529) ^ [] : [-(subset(_588169, 8858 ^ [_588169]))], (8860 ^ _257529) ^ [] : [-(in(8858 ^ [_588169], 8849 ^ []))]]], (8848 ^ _257529) ^ [] : [-(in(8811 ^ [], omega))]]], (2772 ^ _257529) ^ [_353082, _353084] : [_353082 = powerset(_353084), 2775 ^ _257529 : [(2776 ^ _257529) ^ [_353252] : [in(_353252, _353082), -(subset(_353252, _353084))], (2782 ^ _257529) ^ [_353424] : [subset(_353424, _353084), -(in(_353424, _353082))]]], (11268 ^ _257529) ^ [_668735, _668737] : [-(pair_second(ordered_pair(_668737, _668735)) = _668735)], (4763 ^ _257529) ^ [_420906, _420908] : [element(_420906, powerset(powerset(_420908))), -(element(complements_of_subsets(_420908, _420906), powerset(powerset(_420908))))], (5135 ^ _257529) ^ [_432589, _432591] : [-(empty(_432591)), empty(set_union2(_432591, _432589))], (4887 ^ _257529) ^ [_424827, _424829] : [finite(_424827), -(finite(set_intersection2(_424829, _424827)))], (6201 ^ _257529) ^ [_468039, _468041, _468043] : [-(subset_difference(_468043, _468041, _468039) = set_difference(_468041, _468039)), element(_468041, powerset(_468043)), element(_468039, powerset(_468043))], (11073 ^ _257529) ^ [_662473, _662475, _662477] : [-(disjoint(_662477, _662473)), subset(_662477, _662475), disjoint(_662475, _662473)], (2468 ^ _257529) ^ [_342541] : [relation(_342541), 2471 ^ _257529 : [(2482 ^ _257529) ^ [_343040] : [2484 ^ _257529 : [(2485 ^ _257529) ^ [] : [-(in(2483 ^ [_342541, _343040], _343040))], (2487 ^ _257529) ^ [] : [in(ordered_pair(2483 ^ [_342541, _343040], 2483 ^ [_342541, _343040]), _342541)]], -(is_reflexive_in(_342541, _343040))], (2472 ^ _257529) ^ [_342715] : [is_reflexive_in(_342541, _342715), 2475 ^ _257529 : [(2476 ^ _257529) ^ [_342857] : [in(_342857, _342715), -(in(ordered_pair(_342857, _342857), _342541))]]]]], (10670 ^ _257529) ^ [_649525, _649527, _649529] : [-(element(_649529, _649525)), in(_649529, _649527), element(_649527, powerset(_649525))], (3491 ^ _257529) ^ [_378943] : [-(cast_to_subset(_378943) = _378943)], (9932 ^ _257529) ^ [_624492, _624494, _624496] : [subset(_624496, _624494), -(subset(set_intersection2(_624496, _624492), set_intersection2(_624494, _624492)))], (5976 ^ _257529) ^ [] : [-(function(5972 ^ []))], (606 ^ _257529) ^ [_276201, _276203] : [-(well_ordering(_276201)), _276203 = _276201, well_ordering(_276203)], (328 ^ _257529) ^ [_267596, _267598] : [-(join_semilatt_str(_267596)), _267598 = _267596, join_semilatt_str(_267598)], (6044 ^ _257529) ^ [] : [-(epsilon_transitive(6040 ^ []))], (5971 ^ _257529) ^ [] : [-(function(5965 ^ []))], (5515 ^ _257529) ^ [_445075] : [relation(_445075), -(relation_inverse(relation_inverse(_445075)) = _445075)], (4813 ^ _257529) ^ [] : [true___, -(true___)], (1010 ^ _257529) ^ [_290671, _290673] : [_290673 = _290671, -(succ(_290673) = succ(_290671))], (1292 ^ _257529) ^ [_301114] : [v3_membered(_301114), 1295 ^ _257529 : [(1296 ^ _257529) ^ [_301254] : [element(_301254, _301114), 1299 ^ _257529 : [(1304 ^ _257529) ^ [] : [-(v1_rat_1(_301254))], (1302 ^ _257529) ^ [] : [-(v1_xreal_0(_301254))], (1300 ^ _257529) ^ [] : [-(v1_xcmplx_0(_301254))]]]]], (1420 ^ _257529) ^ [_305569] : [empty(_305569), -(finite(_305569))], (3578 ^ _257529) ^ [_381817, _381819] : [equipotent(_381819, _381817), 3582 ^ _257529 : [(3583 ^ _257529) ^ [] : [-(relation(3581 ^ [_381817, _381819]))], (3585 ^ _257529) ^ [] : [-(function(3581 ^ [_381817, _381819]))], (3591 ^ _257529) ^ [] : [-(relation_rng(3581 ^ [_381817, _381819]) = _381817)], (3589 ^ _257529) ^ [] : [-(relation_dom(3581 ^ [_381817, _381819]) = _381819)], (3587 ^ _257529) ^ [] : [-(one_to_one(3581 ^ [_381817, _381819]))]]], (4805 ^ _257529) ^ [_422132] : [latt_str(_422132), 4808 ^ _257529 : [(4809 ^ _257529) ^ [] : [-(meet_semilatt_str(_422132))], (4811 ^ _257529) ^ [] : [-(join_semilatt_str(_422132))]]], (5886 ^ _257529) ^ [] : [-(v4_membered(5876 ^ []))], (10186 ^ _257529) ^ [_632969] : [relation(_632969), 10189 ^ _257529 : [(10190 ^ _257529) ^ [] : [-(relation_rng(_632969) = relation_dom(relation_inverse(_632969)))], (10192 ^ _257529) ^ [] : [-(relation_dom(_632969) = relation_rng(relation_inverse(_632969)))]]], (7706 ^ _257529) ^ [_536510, _536512] : [one_sorted_str(_536512), element(_536510, powerset(powerset(the_carrier(_536512)))), 7713 ^ _257529 : [(7714 ^ _257529) ^ [_536974] : [7718 ^ _257529 : [(7737 ^ _257529) ^ [] : [-(7715 ^ [_536510, _536512, _536974] = 7717 ^ [_536510, _536512, _536974])], (7755 ^ _257529) ^ [] : [7716 ^ [_536510, _536512, _536974] = 7717 ^ [_536510, _536512, _536974]], (7725 ^ _257529) ^ [] : [-(in(7720 ^ [_536510, _536512, _536974], _536510))], (7727 ^ _257529) ^ [_538423] : [element(_538423, powerset(the_carrier(_536512))), _538423 = 7720 ^ [_536510, _536512, _536974], -(7721 ^ [_536510, _536512, _536974] = subset_complement(the_carrier(_536512), _538423))], (7743 ^ _257529) ^ [] : [-(in(7738 ^ [_536510, _536512, _536974], _536510))], (7723 ^ _257529) ^ [] : [-(ordered_pair(7720 ^ [_536510, _536512, _536974], 7721 ^ [_536510, _536512, _536974]) = 7716 ^ [_536510, _536512, _536974])], (7741 ^ _257529) ^ [] : [-(ordered_pair(7738 ^ [_536510, _536512, _536974], 7739 ^ [_536510, _536512, _536974]) = 7717 ^ [_536510, _536512, _536974])], (7745 ^ _257529) ^ [_539263] : [element(_539263, powerset(the_carrier(_536512))), _539263 = 7738 ^ [_536510, _536512, _536974], -(7739 ^ [_536510, _536512, _536974] = subset_complement(the_carrier(_536512), _539263))], (7719 ^ _257529) ^ [] : [-(7715 ^ [_536510, _536512, _536974] = 7716 ^ [_536510, _536512, _536974])]], 7757 ^ _257529 : [(7758 ^ _257529) ^ [_539849] : [in(_539849, 7756 ^ [_536510, _536512, _536974]), 7762 ^ _257529 : [(7763 ^ _257529) ^ [] : [-(in(7761 ^ [_536510, _536512, _536974, _539849], cartesian_product2(_536510, _536974)))], (7765 ^ _257529) ^ [] : [-(7761 ^ [_536510, _536512, _536974, _539849] = _539849)], (7773 ^ _257529) ^ [_540764] : [element(_540764, powerset(the_carrier(_536512))), _540764 = 7766 ^ [_536510, _536512, _536974, _539849], -(7767 ^ [_536510, _536512, _536974, _539849] = subset_complement(the_carrier(_536512), _540764))], (7771 ^ _257529) ^ [] : [-(in(7766 ^ [_536510, _536512, _536974, _539849], _536510))], (7769 ^ _257529) ^ [] : [-(ordered_pair(7766 ^ [_536510, _536512, _536974, _539849], 7767 ^ [_536510, _536512, _536974, _539849]) = _539849)]]], (7783 ^ _257529) ^ [_541128] : [-(in(_541128, 7756 ^ [_536510, _536512, _536974])), 7784 ^ _257529 : [(7785 ^ _257529) ^ [_541299] : [in(_541299, cartesian_product2(_536510, _536974)), _541299 = _541128, 7792 ^ _257529 : [(7793 ^ _257529) ^ [_541613, _541615] : [ordered_pair(_541615, _541613) = _541128, in(_541615, _536510), 7801 ^ _257529 : [(7806 ^ _257529) ^ [] : [_541613 = subset_complement(the_carrier(_536512), 7800 ^ [_536510, _536512, _536974, _541128, _541299, _541613, _541615])], (7804 ^ _257529) ^ [] : [-(7800 ^ [_536510, _536512, _536974, _541128, _541299, _541613, _541615] = _541615)], (7802 ^ _257529) ^ [] : [-(element(7800 ^ [_536510, _536512, _536974, _541128, _541299, _541613, _541615], powerset(the_carrier(_536512))))]]]]]]]]]]], (1198 ^ _257529) ^ [_297485, _297487, _297489, _297491] : [-(relation_dom_restriction(_297491, _297487) = relation_dom_restriction(_297489, _297485)), _297491 = _297489, _297487 = _297485], (9531 ^ _257529) ^ [_611477, _611479] : [in(_611479, _611477), -(element(_611479, _611477))], (10019 ^ _257529) ^ [_627536, _627538, _627540] : [relation(_627536), in(ordered_pair(_627540, _627538), _627536), 10026 ^ _257529 : [(10027 ^ _257529) ^ [] : [-(in(_627540, relation_field(_627536)))], (10029 ^ _257529) ^ [] : [-(in(_627538, relation_field(_627536)))]]], (7810 ^ _257529) ^ [_542408, _542410, _542412] : [relation(_542410), relation(_542408), function(_542408), 7826 ^ _257529 : [(7831 ^ _257529) ^ [] : [-(7824 ^ [_542408, _542410, _542412] = ordered_pair(7828 ^ [_542408, _542410, _542412], 7829 ^ [_542408, _542410, _542412]))], (7841 ^ _257529) ^ [] : [-(in(ordered_pair(apply(_542408, 7836 ^ [_542408, _542410, _542412]), apply(_542408, 7837 ^ [_542408, _542410, _542412])), _542410))], (7843 ^ _257529) ^ [] : [7824 ^ [_542408, _542410, _542412] = 7825 ^ [_542408, _542410, _542412]], (7835 ^ _257529) ^ [] : [-(7823 ^ [_542408, _542410, _542412] = 7825 ^ [_542408, _542410, _542412])], (7827 ^ _257529) ^ [] : [-(7823 ^ [_542408, _542410, _542412] = 7824 ^ [_542408, _542410, _542412])], (7833 ^ _257529) ^ [] : [-(in(ordered_pair(apply(_542408, 7828 ^ [_542408, _542410, _542412]), apply(_542408, 7829 ^ [_542408, _542410, _542412])), _542410))], (7839 ^ _257529) ^ [] : [-(7825 ^ [_542408, _542410, _542412] = ordered_pair(7836 ^ [_542408, _542410, _542412], 7837 ^ [_542408, _542410, _542412]))]], 7845 ^ _257529 : [(7846 ^ _257529) ^ [_544518] : [in(_544518, 7844 ^ [_542408, _542410, _542412]), 7850 ^ _257529 : [(7851 ^ _257529) ^ [] : [-(in(7849 ^ [_542408, _542410, _542412, _544518], cartesian_product2(_542412, _542412)))], (7859 ^ _257529) ^ [] : [-(in(ordered_pair(apply(_542408, 7854 ^ [_542408, _542410, _542412, _544518]), apply(_542408, 7855 ^ [_542408, _542410, _542412, _544518])), _542410))], (7857 ^ _257529) ^ [] : [-(_544518 = ordered_pair(7854 ^ [_542408, _542410, _542412, _544518], 7855 ^ [_542408, _542410, _542412, _544518]))], (7853 ^ _257529) ^ [] : [-(7849 ^ [_542408, _542410, _542412, _544518] = _544518)]]], (7861 ^ _257529) ^ [_545327] : [-(in(_545327, 7844 ^ [_542408, _542410, _542412])), 7862 ^ _257529 : [(7863 ^ _257529) ^ [_545475] : [in(_545475, cartesian_product2(_542412, _542412)), _545475 = _545327, 7870 ^ _257529 : [(7871 ^ _257529) ^ [_545766, _545768] : [_545327 = ordered_pair(_545768, _545766), in(ordered_pair(apply(_542408, _545768), apply(_542408, _545766)), _542410)]]]]]]], (4495 ^ _257529) ^ [_413142, _413144, _413146, _413148, _413150, _413152] : [-(element(apply_binary_as_element(_413152, _413150, _413148, _413146, _413144, _413142), _413148)), -(empty(_413152)), -(empty(_413150)), function(_413146), quasi_total(_413146, cartesian_product2(_413152, _413150), _413148), relation_of2(_413146, cartesian_product2(_413152, _413150), _413148), element(_413144, _413152), element(_413142, _413150)], (4685 ^ _257529) ^ [] : [true___, -(true___)], (5991 ^ _257529) ^ [_461181, _461183] : [-(relation(5987 ^ [_461181, _461183]))], (3054 ^ _257529) ^ [_362942, _362944, _362946] : [_362942 = set_union2(_362946, _362944), 3057 ^ _257529 : [(3068 ^ _257529) ^ [_363402] : [3069 ^ _257529 : [(3070 ^ _257529) ^ [] : [in(_363402, _362946)], (3072 ^ _257529) ^ [] : [in(_363402, _362944)]], -(in(_363402, _362942))], (3058 ^ _257529) ^ [_363124] : [in(_363124, _362942), -(in(_363124, _362946)), -(in(_363124, _362944))]]], (5909 ^ _257529) ^ [] : [-(function(5905 ^ []))], (1208 ^ _257529) ^ [_297816, _297818] : [_297818 = _297816, -(relation_rng(_297818) = relation_rng(_297816))], (568 ^ _257529) ^ [_275046, _275048, _275050, _275052] : [-(disjoint(_275050, _275046)), disjoint(_275052, _275048), _275052 = _275050, _275048 = _275046], (5812 ^ _257529) ^ [_455327, _455329] : [5814 ^ _257529 : [(5815 ^ _257529) ^ [] : [-(in(5813 ^ [_455327, _455329], _455329))], (5817 ^ _257529) ^ [] : [in(5813 ^ [_455327, _455329], _455327)]], -(element(_455329, powerset(_455327)))], (10805 ^ _257529) ^ [_653847] : [relation(_653847), function(_653847), one_to_one(_653847), 10816 ^ _257529 : [(10817 ^ _257529) ^ [_654234] : [relation(_654234), function(_654234), 10824 ^ _257529 : [(10855 ^ _257529) ^ [] : [-(_654234 = function_inverse(_653847)), relation_dom(_654234) = relation_rng(_653847), 10864 ^ _257529 : [(10869 ^ _257529) ^ [] : [in(10861 ^ [_653847, _654234], relation_dom(_653847)), 10860 ^ [_653847, _654234] = apply(_653847, 10861 ^ [_653847, _654234])], (10867 ^ _257529) ^ [] : [-(10861 ^ [_653847, _654234] = apply(_654234, 10860 ^ [_653847, _654234]))], (10865 ^ _257529) ^ [] : [-(in(10860 ^ [_653847, _654234], relation_rng(_653847)))]], 10874 ^ _257529 : [(10879 ^ _257529) ^ [] : [in(10860 ^ [_653847, _654234], relation_rng(_653847)), 10861 ^ [_653847, _654234] = apply(_654234, 10860 ^ [_653847, _654234])], (10877 ^ _257529) ^ [] : [-(10860 ^ [_653847, _654234] = apply(_653847, 10861 ^ [_653847, _654234]))], (10875 ^ _257529) ^ [] : [-(in(10861 ^ [_653847, _654234], relation_dom(_653847)))]]], (10825 ^ _257529) ^ [] : [_654234 = function_inverse(_653847), 10828 ^ _257529 : [(10843 ^ _257529) ^ [_655125, _655127] : [10850 ^ _257529 : [(10851 ^ _257529) ^ [] : [-(in(_655127, relation_rng(_653847)))], (10853 ^ _257529) ^ [] : [-(_655125 = apply(_654234, _655127))]], in(_655125, relation_dom(_653847)), _655127 = apply(_653847, _655125)], (10831 ^ _257529) ^ [_654751, _654753] : [10838 ^ _257529 : [(10839 ^ _257529) ^ [] : [-(in(_654751, relation_dom(_653847)))], (10841 ^ _257529) ^ [] : [-(_654753 = apply(_653847, _654751))]], in(_654753, relation_rng(_653847)), _654751 = apply(_654234, _654753)], (10829 ^ _257529) ^ [] : [-(relation_dom(_654234) = relation_rng(_653847))]]]]]]], (4929 ^ _257529) ^ [] : [-(relation_empty_yielding(empty_set))], (5483 ^ _257529) ^ [_443952, _443954] : [5490 ^ _257529 : [(5491 ^ _257529) ^ [] : [-(empty(relation_composition(_443954, _443952)))], (5493 ^ _257529) ^ [] : [-(relation(relation_composition(_443954, _443952)))]], empty(_443954), relation(_443952)], (5037 ^ _257529) ^ [] : [-(empty(empty_set))], (3538 ^ _257529) ^ [_380759] : [relation(_380759), 3541 ^ _257529 : [(3542 ^ _257529) ^ [] : [well_ordering(_380759), 3545 ^ _257529 : [(3546 ^ _257529) ^ [] : [-(reflexive(_380759))], (3548 ^ _257529) ^ [] : [-(transitive(_380759))], (3554 ^ _257529) ^ [] : [-(well_founded_relation(_380759))], (3552 ^ _257529) ^ [] : [-(connected(_380759))], (3550 ^ _257529) ^ [] : [-(antisymmetric(_380759))]]], (3556 ^ _257529) ^ [] : [-(well_ordering(_380759)), reflexive(_380759), transitive(_380759), antisymmetric(_380759), connected(_380759), well_founded_relation(_380759)]]], (4993 ^ _257529) ^ [] : [-(epsilon_connected(omega))], (2267 ^ _257529) ^ [_335230] : [function(_335230), 2270 ^ _257529 : [(2271 ^ _257529) ^ [_335411, _335413, _335415] : [-(_335413 = _335411), in(ordered_pair(_335415, _335413), _335230), in(ordered_pair(_335415, _335411), _335230)]]], (3402 ^ _257529) ^ [_375609] : [-(ordinal(_375609)), epsilon_transitive(_375609), epsilon_connected(_375609)], (146 ^ _257529) ^ [_262118, _262120] : [-(v1_membered(_262118)), _262120 = _262118, v1_membered(_262120)], (8117 ^ _257529) ^ [_556934, _556936, _556938] : [-(in(_556934, 8101 ^ [_556936, _556938])), in(_556934, cartesian_product2(_556938, _556936)), 8122 ^ _257529 : [(8123 ^ _257529) ^ [_557160, _557162] : [ordered_pair(_557162, _557160) = _556934, in(_557162, _556938), _557160 = singleton(_557162)]]], (4087 ^ _257529) ^ [_399718, _399720] : [set_intersection2(_399720, _399718) = empty_set, -(disjoint(_399720, _399718))], (1572 ^ _257529) ^ [_310330] : [empty(_310330), 1575 ^ _257529 : [(1580 ^ _257529) ^ [] : [-(ordinal(_310330))], (1578 ^ _257529) ^ [] : [-(epsilon_connected(_310330))], (1576 ^ _257529) ^ [] : [-(epsilon_transitive(_310330))]]], (558 ^ _257529) ^ [_274723, _274725] : [-(ordinal(_274723)), _274725 = _274723, ordinal(_274725)], (10137 ^ _257529) ^ [_631329, _631331, _631333, _631335] : [ordered_pair(_631335, _631333) = ordered_pair(_631331, _631329), 10140 ^ _257529 : [(10141 ^ _257529) ^ [] : [-(_631335 = _631331)], (10143 ^ _257529) ^ [] : [-(_631333 = _631329)]]], (4729 ^ _257529) ^ [_419725, _419727] : [-(element(topstr_closure(_419727, _419725), powerset(the_carrier(_419727)))), top_str(_419727), element(_419725, powerset(the_carrier(_419727)))], (11393 ^ _257529) ^ [_672811, _672813, _672815] : [singleton(_672815) = unordered_pair(_672813, _672811), -(_672815 = _672813)], (4919 ^ _257529) ^ [_425894, _425896] : [finite(_425896), -(finite(set_difference(_425896, _425894)))], (5357 ^ _257529) ^ [] : [-(empty(empty_set))], (3760 ^ _257529) ^ [_388062] : [top_str(_388062), 3763 ^ _257529 : [(3764 ^ _257529) ^ [_388205] : [element(_388205, powerset(the_carrier(_388062))), 3767 ^ _257529 : [(3768 ^ _257529) ^ [] : [open_subset(_388205, _388062), -(in(_388205, the_topology(_388062)))], (3774 ^ _257529) ^ [] : [in(_388205, the_topology(_388062)), -(open_subset(_388205, _388062))]]]]], (1592 ^ _257529) ^ [_311071, _311073, _311075] : [-(join_commut(_311075, _311073, _311071) = join_commut(_311075, _311071, _311073)), -(empty_carrier(_311075)), join_commutative(_311075), join_semilatt_str(_311075), element(_311073, the_carrier(_311075)), element(_311071, the_carrier(_311075))], (8898 ^ _257529) ^ [_589728] : [-(function(8894 ^ [_589728]))], (6588 ^ _257529) ^ [] : [6715 ^ _257529 : [(6716 ^ _257529) ^ [_488549] : [ordinal(_488549), in(_488549, omega), 6723 ^ _257529 : [(6724 ^ _257529) ^ [_488805] : [element(_488805, powerset(powerset(_488549))), -(_488805 = empty_set), 6732 ^ _257529 : [(6733 ^ _257529) ^ [] : [-(in(6731 ^ [_488549, _488805], _488805))], (6735 ^ _257529) ^ [_489204] : [-(_489204 = 6731 ^ [_488549, _488805]), in(_489204, _488805), subset(6731 ^ [_488549, _488805], _489204)]]]]]], 6591 ^ _257529 : [(6592 ^ _257529) ^ [] : [-(in(empty_set, omega))], (6599 ^ _257529) ^ [_484388] : [in(_484388, 6593 ^ []), 6603 ^ _257529 : [(6608 ^ _257529) ^ [] : [6602 ^ [_484388] = _484388], (6606 ^ _257529) ^ [] : [-(subset(_484388, 6602 ^ [_484388]))], (6604 ^ _257529) ^ [] : [-(in(6602 ^ [_484388], 6593 ^ []))]]], (6597 ^ _257529) ^ [] : [6593 ^ [] = empty_set], (6595 ^ _257529) ^ [] : [-(element(6593 ^ [], powerset(powerset(empty_set))))]], 6612 ^ _257529 : [(6643 ^ _257529) ^ [] : [-(element(6641 ^ [], powerset(powerset(succ(6611 ^ [])))))], (6613 ^ _257529) ^ [] : [-(ordinal(6611 ^ []))], (6615 ^ _257529) ^ [] : [in(6611 ^ [], omega), 6618 ^ _257529 : [(6619 ^ _257529) ^ [_485122] : [element(_485122, powerset(powerset(6611 ^ []))), -(_485122 = empty_set), 6627 ^ _257529 : [(6628 ^ _257529) ^ [] : [-(in(6626 ^ [_485122], _485122))], (6630 ^ _257529) ^ [_485495] : [-(_485495 = 6626 ^ [_485122]), in(_485495, _485122), subset(6626 ^ [_485122], _485495)]]]]], (6645 ^ _257529) ^ [] : [6641 ^ [] = empty_set], (6647 ^ _257529) ^ [_486039] : [in(_486039, 6641 ^ []), 6651 ^ _257529 : [(6656 ^ _257529) ^ [] : [6650 ^ [_486039] = _486039], (6654 ^ _257529) ^ [] : [-(subset(_486039, 6650 ^ [_486039]))], (6652 ^ _257529) ^ [] : [-(in(6650 ^ [_486039], 6641 ^ []))]]], (6640 ^ _257529) ^ [] : [-(in(succ(6611 ^ []), omega))]], 6658 ^ _257529 : [(6696 ^ _257529) ^ [] : [6657 ^ [] = empty_set], (6661 ^ _257529) ^ [] : [-(being_limit_ordinal(6657 ^ []))], (6659 ^ _257529) ^ [] : [-(ordinal(6657 ^ []))], (6663 ^ _257529) ^ [_486767] : [ordinal(_486767), in(_486767, 6657 ^ []), in(_486767, omega), 6674 ^ _257529 : [(6675 ^ _257529) ^ [_487104] : [element(_487104, powerset(powerset(_486767))), -(_487104 = empty_set), 6683 ^ _257529 : [(6684 ^ _257529) ^ [] : [-(in(6682 ^ [_486767, _487104], _487104))], (6686 ^ _257529) ^ [_487503] : [-(_487503 = 6682 ^ [_486767, _487104]), in(_487503, _487104), subset(6682 ^ [_486767, _487104], _487503)]]]]], (6701 ^ _257529) ^ [] : [-(element(6699 ^ [], powerset(powerset(6657 ^ []))))], (6705 ^ _257529) ^ [_488129] : [in(_488129, 6699 ^ []), 6709 ^ _257529 : [(6714 ^ _257529) ^ [] : [6708 ^ [_488129] = _488129], (6712 ^ _257529) ^ [] : [-(subset(_488129, 6708 ^ [_488129]))], (6710 ^ _257529) ^ [] : [-(in(6708 ^ [_488129], 6699 ^ []))]]], (6703 ^ _257529) ^ [] : [6699 ^ [] = empty_set], (6698 ^ _257529) ^ [] : [-(in(6657 ^ [], omega))]]], (4441 ^ _257529) ^ [_411760] : [one_sorted_str(_411760), -(element(empty_carrier_subset(_411760), powerset(the_carrier(_411760))))], (4867 ^ _257529) ^ [] : [-(top_str(4865 ^ []))], (4453 ^ _257529) ^ [] : [true___, -(true___)], (1150 ^ _257529) ^ [_295726, _295728] : [_295728 = _295726, -(relation_field(_295728) = relation_field(_295726))], (5053 ^ _257529) ^ [_430091, _430093] : [v2_membered(_430093), 5056 ^ _257529 : [(5057 ^ _257529) ^ [] : [-(v1_membered(set_intersection2(_430093, _430091)))], (5059 ^ _257529) ^ [] : [-(v2_membered(set_intersection2(_430093, _430091)))]]], (4841 ^ _257529) ^ [_423252] : [top_str(_423252), -(element(the_topology(_423252), powerset(powerset(the_carrier(_423252)))))], (9267 ^ _257529) ^ [_602589, _602591] : [relation(_602589), subset(_602591, relation_dom(_602589)), -(subset(_602591, relation_inverse_image(_602589, relation_image(_602589, _602591))))], (1280 ^ _257529) ^ [_300705] : [v2_membered(_300705), 1283 ^ _257529 : [(1284 ^ _257529) ^ [_300840] : [element(_300840, _300705), 1287 ^ _257529 : [(1288 ^ _257529) ^ [] : [-(v1_xcmplx_0(_300840))], (1290 ^ _257529) ^ [] : [-(v1_xreal_0(_300840))]]]]], (1114 ^ _257529) ^ [_294431, _294433] : [_294433 = _294431, -(inclusion_relation(_294433) = inclusion_relation(_294431))], (9715 ^ _257529) ^ [_617671, _617673] : [relation(_617671), reflexive(_617671), -(reflexive(relation_restriction(_617671, _617673)))], (2249 ^ _257529) ^ [_334669] : [-(finite(_334669)), 2250 ^ _257529 : [(2251 ^ _257529) ^ [_334772] : [relation(_334772), function(_334772), relation_rng(_334772) = _334669, in(relation_dom(_334772), omega)]]], (9378 ^ _257529) ^ [_606371] : [top_str(_606371), 9381 ^ _257529 : [(9382 ^ _257529) ^ [_606519] : [element(_606519, powerset(powerset(the_carrier(_606371)))), 9385 ^ _257529 : [(9386 ^ _257529) ^ [] : [closed_subsets(_606519, _606371), -(open_subsets(complements_of_subsets(the_carrier(_606371), _606519), _606371))], (9392 ^ _257529) ^ [] : [open_subsets(complements_of_subsets(the_carrier(_606371), _606519), _606371), -(closed_subsets(_606519, _606371))]]]]], (4757 ^ _257529) ^ [_420694, _420696] : [relation(_420696), -(relation(relation_dom_restriction(_420696, _420694)))], (9216 ^ _257529) ^ [_600836, _600838, _600840] : [relation(_600836), 9219 ^ _257529 : [(9220 ^ _257529) ^ [] : [in(_600840, relation_image(_600836, _600838)), 9224 ^ _257529 : [(9229 ^ _257529) ^ [] : [-(in(9223 ^ [_600836, _600838, _600840], _600838))], (9227 ^ _257529) ^ [] : [-(in(ordered_pair(9223 ^ [_600836, _600838, _600840], _600840), _600836))], (9225 ^ _257529) ^ [] : [-(in(9223 ^ [_600836, _600838, _600840], relation_dom(_600836)))]]], (9231 ^ _257529) ^ [] : [-(in(_600840, relation_image(_600836, _600838))), 9232 ^ _257529 : [(9233 ^ _257529) ^ [_601437] : [in(_601437, relation_dom(_600836)), in(ordered_pair(_601437, _600840), _600836), in(_601437, _600838)]]]]], (5984 ^ _257529) ^ [] : [-(epsilon_connected(5972 ^ []))], (9037 ^ _257529) ^ [_594604, _594606, _594608, _594610] : [unordered_pair(_594610, _594608) = unordered_pair(_594606, _594604), -(_594610 = _594606), -(_594610 = _594604)], (4581 ^ _257529) ^ [_415551, _415553] : [relation(_415553), -(relation(relation_restriction(_415553, _415551)))], (9861 ^ _257529) ^ [_622332, _622334] : [relation(_622332), antisymmetric(_622332), -(antisymmetric(relation_restriction(_622332, _622334)))], (3871 ^ _257529) ^ [_391837] : [_391837 = union(_391837), -(being_limit_ordinal(_391837))], (2552 ^ _257529) ^ [_345592, _345594] : [_345594 = empty_set, 2555 ^ _257529 : [(2556 ^ _257529) ^ [] : [_345592 = set_meet(_345594), -(_345592 = empty_set)], (2562 ^ _257529) ^ [] : [_345592 = empty_set, -(_345592 = set_meet(_345594))]]], (10184 ^ _257529) ^ [_632871, _632873] : [-(subset(set_difference(_632873, _632871), _632873))], (6211 ^ _257529) ^ [_468413, _468415, _468417] : [relation_of2_as_subset(_468413, _468417, _468415), -(relation_of2(_468413, _468417, _468415))], (10178 ^ _257529) ^ [_632666, _632668] : [in(_632666, _632668), -(apply(identity_relation(_632668), _632666) = _632666)], (1258 ^ _257529) ^ [_299966, _299968] : [in(_299968, _299966), in(_299966, _299968)], (5207 ^ _257529) ^ [_435253, _435255] : [v5_membered(_435255), 5210 ^ _257529 : [(5211 ^ _257529) ^ [] : [-(v1_membered(set_intersection2(_435253, _435255)))], (5213 ^ _257529) ^ [] : [-(v2_membered(set_intersection2(_435253, _435255)))], (5219 ^ _257529) ^ [] : [-(v5_membered(set_intersection2(_435253, _435255)))], (5217 ^ _257529) ^ [] : [-(v4_membered(set_intersection2(_435253, _435255)))], (5215 ^ _257529) ^ [] : [-(v3_membered(set_intersection2(_435253, _435255)))]]], (1648 ^ _257529) ^ [_312750, _312752] : [ordinal(_312752), ordinal(_312750), -(ordinal_subset(_312752, _312750)), -(ordinal_subset(_312750, _312752))], (9633 ^ _257529) ^ [_614764] : [epsilon_transitive(_614764), 9636 ^ _257529 : [(9637 ^ _257529) ^ [_614900] : [ordinal(_614900), proper_subset(_614764, _614900), -(in(_614764, _614900))]]], (5371 ^ _257529) ^ [_440699, _440701] : [-(closed_subset(subset_complement(the_carrier(_440701), _440699), _440701)), topological_space(_440701), top_str(_440701), open_subset(_440699, _440701), element(_440699, powerset(the_carrier(_440701)))], (4961 ^ _257529) ^ [_427168] : [empty(powerset(_427168))], (9653 ^ _257529) ^ [_615420, _615422, _615424] : [relation(_615420), -(subset(fiber(relation_restriction(_615420, _615424), _615422), fiber(_615420, _615422)))], (3076 ^ _257529) ^ [_363667, _363669, _363671] : [-(_363667 = set_union2(_363671, _363669)), 3080 ^ _257529 : [(3085 ^ _257529) ^ [] : [in(3077 ^ [_363667, _363669, _363671], _363669)], (3083 ^ _257529) ^ [] : [in(3077 ^ [_363667, _363669, _363671], _363671)], (3081 ^ _257529) ^ [] : [-(in(3077 ^ [_363667, _363669, _363671], _363667))]], 3086 ^ _257529 : [(3093 ^ _257529) ^ [] : [in(3077 ^ [_363667, _363669, _363671], _363667)], (3087 ^ _257529) ^ [] : [-(in(3077 ^ [_363667, _363669, _363671], _363671)), -(in(3077 ^ [_363667, _363669, _363671], _363669))]]], (686 ^ _257529) ^ [_278776, _278778, _278780, _278782] : [-(are_equipotent(_278780, _278776)), are_equipotent(_278782, _278778), _278782 = _278780, _278778 = _278776], (356 ^ _257529) ^ [_268528, _268530, _268532, _268534] : [-(ordinal_subset(_268532, _268528)), ordinal_subset(_268534, _268530), _268534 = _268532, _268530 = _268528], (1460 ^ _257529) ^ [_306855, _306857, _306859] : [element(_306855, powerset(cartesian_product2(_306859, _306857))), -(relation(_306855))], (9603 ^ _257529) ^ [_613838, _613840, _613842, _613844] : [function(_613838), quasi_total(_613838, _613844, _613842), relation_of2_as_subset(_613838, _613844, _613842), 9614 ^ _257529 : [(9615 ^ _257529) ^ [_614207] : [relation(_614207), function(_614207), in(_613840, _613844), -(_613842 = empty_set), -(apply(relation_composition(_613838, _614207), _613840) = apply(_614207, apply(_613838, _613840)))]]], (5081 ^ _257529) ^ [_430989] : [-(function(identity_relation(_430989)))], (886 ^ _257529) ^ [_286158, _286160] : [_286160 = _286158, -(set_meet(_286160) = set_meet(_286158))], (6249 ^ _257529) ^ [_469545, _469547] : [are_equipotent(_469547, _469545), -(equipotent(_469547, _469545))], (11291 ^ _257529) ^ [_669698, _669700] : [disjoint(_669700, _669698), -(set_difference(_669700, _669698) = _669700)], (3127 ^ _257529) ^ [_365718, _365720, _365722] : [-(_365718 = cartesian_product2(_365722, _365720)), 3145 ^ _257529 : [(3146 ^ _257529) ^ [] : [-(in(3143 ^ [_365718, _365720, _365722], _365722))], (3152 ^ _257529) ^ [] : [in(3128 ^ [_365718, _365720, _365722], _365718)], (3150 ^ _257529) ^ [] : [-(3128 ^ [_365718, _365720, _365722] = ordered_pair(3143 ^ [_365718, _365720, _365722], 3144 ^ [_365718, _365720, _365722]))], (3148 ^ _257529) ^ [] : [-(in(3144 ^ [_365718, _365720, _365722], _365720))]], 3131 ^ _257529 : [(3132 ^ _257529) ^ [] : [-(in(3128 ^ [_365718, _365720, _365722], _365718))], (3134 ^ _257529) ^ [_366056, _366058] : [in(_366058, _365722), in(_366056, _365720), 3128 ^ [_365718, _365720, _365722] = ordered_pair(_366058, _366056)]]], (1484 ^ _257529) ^ [_307711] : [1491 ^ _257529 : [(1492 ^ _257529) ^ [] : [-(epsilon_transitive(_307711))], (1498 ^ _257529) ^ [] : [-(natural(_307711))], (1496 ^ _257529) ^ [] : [-(ordinal(_307711))], (1494 ^ _257529) ^ [] : [-(epsilon_connected(_307711))]], empty(_307711), ordinal(_307711)], (6046 ^ _257529) ^ [] : [-(epsilon_connected(6040 ^ []))], (206 ^ _257529) ^ [_263888, _263890] : [-(epsilon_connected(_263888)), _263890 = _263888, epsilon_connected(_263890)], (5609 ^ _257529) ^ [_448469, _448471] : [subset(singleton(_448471), _448469), -(in(_448471, _448469))], (10262 ^ _257529) ^ [_635495, _635497] : [10263 ^ _257529 : [(10264 ^ _257529) ^ [] : [_635497 = empty_set], (10266 ^ _257529) ^ [] : [_635497 = singleton(_635495)]], -(subset(_635497, singleton(_635495)))], (804 ^ _257529) ^ [_283151, _283153, _283155, _283157, _283159, _283161, _283163, _283165, _283167, _283169, _283171, _283173] : [-(apply_binary_as_element(_283173, _283169, _283165, _283161, _283157, _283153) = apply_binary_as_element(_283171, _283167, _283163, _283159, _283155, _283151)), _283173 = _283171, _283169 = _283167, _283165 = _283163, _283161 = _283159, _283157 = _283155, _283153 = _283151], (11111 ^ _257529) ^ [_663604, _663606] : [set_difference(_663606, singleton(_663604)) = _663606, in(_663604, _663606)], (5347 ^ _257529) ^ [_439932] : [ordinal(_439932), 5350 ^ _257529 : [(5355 ^ _257529) ^ [] : [-(ordinal(union(_439932)))], (5353 ^ _257529) ^ [] : [-(epsilon_connected(union(_439932)))], (5351 ^ _257529) ^ [] : [-(epsilon_transitive(union(_439932)))]]], (4999 ^ _257529) ^ [_428290] : [one_sorted_str(_428290), 5002 ^ _257529 : [(5007 ^ _257529) ^ [] : [-(v2_membered(empty_carrier_subset(_428290)))], (5003 ^ _257529) ^ [] : [-(empty(empty_carrier_subset(_428290)))], (5013 ^ _257529) ^ [] : [-(v5_membered(empty_carrier_subset(_428290)))], (5009 ^ _257529) ^ [] : [-(v3_membered(empty_carrier_subset(_428290)))], (5011 ^ _257529) ^ [] : [-(v4_membered(empty_carrier_subset(_428290)))], (5005 ^ _257529) ^ [] : [-(v1_membered(empty_carrier_subset(_428290)))]]], (10646 ^ _257529) ^ [_648702] : [relation(_648702), 10649 ^ _257529 : [(10650 ^ _257529) ^ [_648857] : [relation(_648857), 10653 ^ _257529 : [(10654 ^ _257529) ^ [_649008] : [relation(_649008), function(_649008), relation_isomorphism(_648702, _648857, _649008), -(relation_isomorphism(_648857, _648702, function_inverse(_649008)))]]]]], (4599 ^ _257529) ^ [_416015, _416017, _416019] : [-(element(join_commut(_416019, _416017, _416015), the_carrier(_416019))), -(empty_carrier(_416019)), join_commutative(_416019), join_semilatt_str(_416019), element(_416017, the_carrier(_416019)), element(_416015, the_carrier(_416019))], (752 ^ _257529) ^ [_280827, _280829, _280831, _280833] : [-(closed_subsets(_280831, _280827)), closed_subsets(_280833, _280829), _280833 = _280831, _280829 = _280827], (7920 ^ _257529) ^ [_547837, _547839, _547841] : [element(_547839, powerset(powerset(_547841))), relation(_547837), function(_547837), 7936 ^ _257529 : [(7937 ^ _257529) ^ [] : [-(7933 ^ [_547837, _547839, _547841] = 7934 ^ [_547837, _547839, _547841])], (7939 ^ _257529) ^ [] : [-(in(relation_image(_547837, 7934 ^ [_547837, _547839, _547841]), _547839))], (7945 ^ _257529) ^ [] : [7934 ^ [_547837, _547839, _547841] = 7935 ^ [_547837, _547839, _547841]], (7943 ^ _257529) ^ [] : [-(in(relation_image(_547837, 7935 ^ [_547837, _547839, _547841]), _547839))], (7941 ^ _257529) ^ [] : [-(7933 ^ [_547837, _547839, _547841] = 7935 ^ [_547837, _547839, _547841])]], 7947 ^ _257529 : [(7948 ^ _257529) ^ [_549123] : [in(_549123, 7946 ^ [_547837, _547839, _547841]), 7952 ^ _257529 : [(7957 ^ _257529) ^ [] : [-(in(relation_image(_547837, _549123), _547839))], (7955 ^ _257529) ^ [] : [-(7951 ^ [_547837, _547839, _547841, _549123] = _549123)], (7953 ^ _257529) ^ [] : [-(in(7951 ^ [_547837, _547839, _547841, _549123], powerset(relation_dom(_547837))))]]], (7959 ^ _257529) ^ [_549591] : [-(in(_549591, 7946 ^ [_547837, _547839, _547841])), 7960 ^ _257529 : [(7961 ^ _257529) ^ [_549715] : [in(_549715, powerset(relation_dom(_547837))), _549715 = _549591, in(relation_image(_547837, _549591), _547839)]]]]], (10074 ^ _257529) ^ [_629271, _629273] : [ordinal(_629271), subset(_629273, _629271), -(_629273 = empty_set), 10086 ^ _257529 : [(10091 ^ _257529) ^ [_629823] : [ordinal(_629823), in(_629823, _629273), -(ordinal_subset(10085 ^ [_629271, _629273], _629823))], (10089 ^ _257529) ^ [] : [-(in(10085 ^ [_629271, _629273], _629273))], (10087 ^ _257529) ^ [] : [-(ordinal(10085 ^ [_629271, _629273]))]]], (3865 ^ _257529) ^ [_391679] : [being_limit_ordinal(_391679), -(_391679 = union(_391679))], (2600 ^ _257529) ^ [_347038, _347040] : [-(_347038 = singleton(_347040)), 2604 ^ _257529 : [(2605 ^ _257529) ^ [] : [-(in(2601 ^ [_347038, _347040], _347038))], (2607 ^ _257529) ^ [] : [2601 ^ [_347038, _347040] = _347040]], 2608 ^ _257529 : [(2609 ^ _257529) ^ [] : [-(2601 ^ [_347038, _347040] = _347040)], (2611 ^ _257529) ^ [] : [in(2601 ^ [_347038, _347040], _347038)]]], (5309 ^ _257529) ^ [_438596, _438598] : [v4_membered(_438598), 5312 ^ _257529 : [(5313 ^ _257529) ^ [] : [-(v1_membered(set_difference(_438598, _438596)))], (5319 ^ _257529) ^ [] : [-(v4_membered(set_difference(_438598, _438596)))], (5317 ^ _257529) ^ [] : [-(v3_membered(set_difference(_438598, _438596)))], (5315 ^ _257529) ^ [] : [-(v2_membered(set_difference(_438598, _438596)))]]], (514 ^ _257529) ^ [_273394, _273396] : [-(antisymmetric(_273394)), _273396 = _273394, antisymmetric(_273396)], (6255 ^ _257529) ^ [_469757, _469759] : [-(ordinal_subset(_469759, _469759)), ordinal(_469759), ordinal(_469757)], (4093 ^ _257529) ^ [_399922] : [relation(_399922), function(_399922), 4100 ^ _257529 : [(4119 ^ _257529) ^ [] : [4122 ^ _257529 : [(4123 ^ _257529) ^ [] : [-(in(4120 ^ [_399922], relation_dom(_399922)))], (4129 ^ _257529) ^ [] : [4120 ^ [_399922] = 4121 ^ [_399922]], (4127 ^ _257529) ^ [] : [-(apply(_399922, 4120 ^ [_399922]) = apply(_399922, 4121 ^ [_399922]))], (4125 ^ _257529) ^ [] : [-(in(4121 ^ [_399922], relation_dom(_399922)))]], -(one_to_one(_399922))], (4101 ^ _257529) ^ [] : [one_to_one(_399922), 4104 ^ _257529 : [(4105 ^ _257529) ^ [_400285, _400287] : [-(_400287 = _400285), in(_400287, relation_dom(_399922)), in(_400285, relation_dom(_399922)), apply(_399922, _400287) = apply(_399922, _400285)]]]]], (9930 ^ _257529) ^ [_624364] : [-(well_orders(9926 ^ [_624364], _624364))], (1582 ^ _257529) ^ [_310657] : [v2_membered(_310657), -(v1_membered(_310657))], (3825 ^ _257529) ^ [_390444] : [relation(_390444), 3828 ^ _257529 : [(3829 ^ _257529) ^ [_390628] : [well_orders(_390444, _390628), 3832 ^ _257529 : [(3833 ^ _257529) ^ [] : [-(is_reflexive_in(_390444, _390628))], (3835 ^ _257529) ^ [] : [-(is_transitive_in(_390444, _390628))], (3841 ^ _257529) ^ [] : [-(is_well_founded_in(_390444, _390628))], (3839 ^ _257529) ^ [] : [-(is_connected_in(_390444, _390628))], (3837 ^ _257529) ^ [] : [-(is_antisymmetric_in(_390444, _390628))]]], (3843 ^ _257529) ^ [_391089] : [-(well_orders(_390444, _391089)), is_reflexive_in(_390444, _391089), is_transitive_in(_390444, _391089), is_antisymmetric_in(_390444, _391089), is_connected_in(_390444, _391089), is_well_founded_in(_390444, _391089)]]], (5093 ^ _257529) ^ [] : [-(epsilon_transitive(empty_set))], (10288 ^ _257529) ^ [_636387, _636389] : [subset(_636389, _636387), -(element(_636389, powerset(_636387)))], (10395 ^ _257529) ^ [_639904] : [topological_space(_639904), top_str(_639904), 10402 ^ _257529 : [(10403 ^ _257529) ^ [_640156] : [element(_640156, powerset(powerset(the_carrier(_639904)))), 10409 ^ _257529 : [(10414 ^ _257529) ^ [] : [closed_subset(10408 ^ [_639904, _640156], _639904)], (10412 ^ _257529) ^ [] : [-(in(10408 ^ [_639904, _640156], _640156))], (10410 ^ _257529) ^ [] : [-(element(10408 ^ [_639904, _640156], powerset(the_carrier(_639904))))]], -(closed_subset(meet_of_subsets(the_carrier(_639904), _640156), _639904))]]], (10131 ^ _257529) ^ [_631073, _631075, _631077] : [subset(_631077, _631075), -(subset(set_difference(_631077, _631073), set_difference(_631075, _631073)))], (10971 ^ _257529) ^ [_659410] : [relation(_659410), -(in(ordered_pair(10976 ^ [_659410], 10977 ^ [_659410]), _659410)), -(_659410 = empty_set)], (5261 ^ _257529) ^ [_437067] : [ordinal(_437067), 5264 ^ _257529 : [(5265 ^ _257529) ^ [] : [empty(succ(_437067))], (5271 ^ _257529) ^ [] : [-(ordinal(succ(_437067)))], (5269 ^ _257529) ^ [] : [-(epsilon_connected(succ(_437067)))], (5267 ^ _257529) ^ [] : [-(epsilon_transitive(succ(_437067)))]]], (9081 ^ _257529) ^ [_596045, _596047] : [relation(_596045), -(subset(relation_rng(relation_rng_restriction(_596047, _596045)), relation_rng(_596045)))], (9333 ^ _257529) ^ [_604818, _604820, _604822] : [relation(_604818), 9336 ^ _257529 : [(9337 ^ _257529) ^ [] : [in(_604822, relation_inverse_image(_604818, _604820)), 9341 ^ _257529 : [(9346 ^ _257529) ^ [] : [-(in(9340 ^ [_604818, _604820, _604822], _604820))], (9344 ^ _257529) ^ [] : [-(in(ordered_pair(_604822, 9340 ^ [_604818, _604820, _604822]), _604818))], (9342 ^ _257529) ^ [] : [-(in(9340 ^ [_604818, _604820, _604822], relation_rng(_604818)))]]], (9348 ^ _257529) ^ [] : [-(in(_604822, relation_inverse_image(_604818, _604820))), 9349 ^ _257529 : [(9350 ^ _257529) ^ [_605419] : [in(_605419, relation_rng(_604818)), in(ordered_pair(_604822, _605419), _604818), in(_605419, _604820)]]]]], (780 ^ _257529) ^ [_282139, _282141] : [_282141 = _282139, -(the_L_meet(_282141) = the_L_meet(_282139))], (1000 ^ _257529) ^ [_290340, _290342, _290344, _290346] : [-(relation_restriction(_290346, _290342) = relation_restriction(_290344, _290340)), _290346 = _290344, _290342 = _290340], (2380 ^ _257529) ^ [_339315] : [top_str(_339315), 2383 ^ _257529 : [(2418 ^ _257529) ^ [] : [-(topological_space(_339315)), in(the_carrier(_339315), the_topology(_339315)), 2426 ^ _257529 : [(2431 ^ _257529) ^ [] : [in(union_of_subsets(the_carrier(_339315), 2425 ^ [_339315]), the_topology(_339315))], (2429 ^ _257529) ^ [] : [-(subset(2425 ^ [_339315], the_topology(_339315)))], (2427 ^ _257529) ^ [] : [-(element(2425 ^ [_339315], powerset(powerset(the_carrier(_339315)))))]], 2433 ^ _257529 : [(2434 ^ _257529) ^ [] : [-(element(2432 ^ [_339315], powerset(the_carrier(_339315))))], (2437 ^ _257529) ^ [] : [-(element(2435 ^ [_339315], powerset(the_carrier(_339315))))], (2443 ^ _257529) ^ [] : [in(subset_intersection2(the_carrier(_339315), 2432 ^ [_339315], 2435 ^ [_339315]), the_topology(_339315))], (2441 ^ _257529) ^ [] : [-(in(2435 ^ [_339315], the_topology(_339315)))], (2439 ^ _257529) ^ [] : [-(in(2432 ^ [_339315], the_topology(_339315)))]]], (2384 ^ _257529) ^ [] : [topological_space(_339315), 2387 ^ _257529 : [(2400 ^ _257529) ^ [_340030] : [element(_340030, powerset(the_carrier(_339315))), 2403 ^ _257529 : [(2404 ^ _257529) ^ [_340205] : [element(_340205, powerset(the_carrier(_339315))), -(in(subset_intersection2(the_carrier(_339315), _340030, _340205), the_topology(_339315))), in(_340030, the_topology(_339315)), in(_340205, the_topology(_339315))]]], (2390 ^ _257529) ^ [_339733] : [element(_339733, powerset(powerset(the_carrier(_339315)))), subset(_339733, the_topology(_339315)), -(in(union_of_subsets(the_carrier(_339315), _339733), the_topology(_339315)))], (2388 ^ _257529) ^ [] : [-(in(the_carrier(_339315), the_topology(_339315)))]]]]], (5273 ^ _257529) ^ [_437495, _437497] : [-(relation(set_difference(_437497, _437495))), relation(_437497), relation(_437495)], (5898 ^ _257529) ^ [] : [-(epsilon_transitive(5896 ^ []))], (8135 ^ _257529) ^ [_557556] : [ordinal(_557556), 8139 ^ _257529 : [(8176 ^ _257529) ^ [_559353] : [-(in(_559353, 8138 ^ [_557556])), in(_559353, succ(_557556)), 8181 ^ _257529 : [(8182 ^ _257529) ^ [_559607] : [ordinal(_559607), _559353 = _559607, 8189 ^ _257529 : [(8190 ^ _257529) ^ [] : [-(in(_559607, omega))], (8197 ^ _257529) ^ [_560213] : [in(_560213, 8191 ^ [_557556, _559353, _559607]), 8201 ^ _257529 : [(8206 ^ _257529) ^ [] : [8200 ^ [_557556, _559353, _559607, _560213] = _560213], (8204 ^ _257529) ^ [] : [-(subset(_560213, 8200 ^ [_557556, _559353, _559607, _560213]))], (8202 ^ _257529) ^ [] : [-(in(8200 ^ [_557556, _559353, _559607, _560213], 8191 ^ [_557556, _559353, _559607]))]]], (8195 ^ _257529) ^ [] : [8191 ^ [_557556, _559353, _559607] = empty_set], (8193 ^ _257529) ^ [] : [-(element(8191 ^ [_557556, _559353, _559607], powerset(powerset(_559607))))]]]]], (8140 ^ _257529) ^ [_557943] : [in(_557943, 8138 ^ [_557556]), 8143 ^ _257529 : [(8144 ^ _257529) ^ [] : [-(in(_557943, succ(_557556)))], (8151 ^ _257529) ^ [] : [in(8145 ^ [_557556, _557943], omega), 8154 ^ _257529 : [(8155 ^ _257529) ^ [_558582] : [element(_558582, powerset(powerset(8145 ^ [_557556, _557943]))), -(_558582 = empty_set), 8163 ^ _257529 : [(8164 ^ _257529) ^ [] : [-(in(8162 ^ [_557556, _557943, _558582], _558582))], (8166 ^ _257529) ^ [_559013] : [-(_559013 = 8162 ^ [_557556, _557943, _558582]), in(_559013, _558582), subset(8162 ^ [_557556, _557943, _558582], _559013)]]]]], (8149 ^ _257529) ^ [] : [-(_557943 = 8145 ^ [_557556, _557943])], (8147 ^ _257529) ^ [] : [-(ordinal(8145 ^ [_557556, _557943]))]]]]], (1554 ^ _257529) ^ [_309745] : [element(_309745, omega), 1557 ^ _257529 : [(1558 ^ _257529) ^ [] : [-(epsilon_transitive(_309745))], (1564 ^ _257529) ^ [] : [-(natural(_309745))], (1562 ^ _257529) ^ [] : [-(ordinal(_309745))], (1560 ^ _257529) ^ [] : [-(epsilon_connected(_309745))]]], (5907 ^ _257529) ^ [] : [-(relation(5905 ^ []))], (9087 ^ _257529) ^ [_596281, _596283, _596285] : [subset(_596285, _596283), 9090 ^ _257529 : [(9091 ^ _257529) ^ [] : [-(subset(cartesian_product2(_596285, _596281), cartesian_product2(_596283, _596281)))], (9093 ^ _257529) ^ [] : [-(subset(cartesian_product2(_596281, _596285), cartesian_product2(_596281, _596283)))]]], (9783 ^ _257529) ^ [_619747, _619749, _619751] : [relation_of2_as_subset(_619747, _619751, _619749), 9786 ^ _257529 : [(9787 ^ _257529) ^ [] : [9789 ^ _257529 : [(9790 ^ _257529) ^ [] : [-(in(9788 ^ [_619747, _619749, _619751], _619749))], (9792 ^ _257529) ^ [_620105] : [in(ordered_pair(_620105, 9788 ^ [_619747, _619749, _619751]), _619747)]], -(relation_rng_as_subset(_619751, _619749, _619747) = _619749)], (9796 ^ _257529) ^ [] : [relation_rng_as_subset(_619751, _619749, _619747) = _619749, 9799 ^ _257529 : [(9800 ^ _257529) ^ [_620342] : [in(_620342, _619749), -(in(ordered_pair(9803 ^ [_619747, _619749, _619751, _620342], _620342), _619747))]]]]], (3156 ^ _257529) ^ [_366952] : [-(empty_carrier(_366952)), join_semilatt_str(_366952), 3163 ^ _257529 : [(3164 ^ _257529) ^ [_367195] : [element(_367195, the_carrier(_366952)), 3167 ^ _257529 : [(3168 ^ _257529) ^ [_367351] : [element(_367351, the_carrier(_366952)), 3171 ^ _257529 : [(3172 ^ _257529) ^ [] : [below(_366952, _367195, _367351), -(join(_366952, _367195, _367351) = _367351)], (3178 ^ _257529) ^ [] : [join(_366952, _367195, _367351) = _367351, -(below(_366952, _367195, _367351))]]]]]]], (10668 ^ _257529) ^ [_649401] : [-(set_difference(empty_set, _649401) = empty_set)], (9569 ^ _257529) ^ [_612782, _612784] : [relation(_612782), function(_612782), 9576 ^ _257529 : [(9577 ^ _257529) ^ [_613032] : [relation(_613032), function(_613032), 9584 ^ _257529 : [(9585 ^ _257529) ^ [] : [in(_612784, relation_dom(relation_composition(_613032, _612782))), 9588 ^ _257529 : [(9589 ^ _257529) ^ [] : [-(in(_612784, relation_dom(_613032)))], (9591 ^ _257529) ^ [] : [-(in(apply(_613032, _612784), relation_dom(_612782)))]]], (9593 ^ _257529) ^ [] : [-(in(_612784, relation_dom(relation_composition(_613032, _612782)))), in(_612784, relation_dom(_613032)), in(apply(_613032, _612784), relation_dom(_612782))]]]]], (4429 ^ _257529) ^ [] : [true___, -(true___)], (6058 ^ _257529) ^ [] : [empty_carrier(6054 ^ [])], (4879 ^ _257529) ^ [_424444, _424446] : [-(relation_of2(4877 ^ [_424444, _424446], _424446, _424444))], (2354 ^ _257529) ^ [_338196] : [2355 ^ _257529 : [(2356 ^ _257529) ^ [_338318, _338320] : [_338196 = ordered_pair(_338320, _338318)]], 2357 ^ _257529 : [(2368 ^ _257529) ^ [_338781] : [2371 ^ _257529 : [(2372 ^ _257529) ^ [] : [-(_338196 = ordered_pair(2369 ^ [_338196, _338781], 2370 ^ [_338196, _338781]))], (2374 ^ _257529) ^ [] : [_338781 = 2369 ^ [_338196, _338781]]], -(_338781 = pair_first(_338196))], (2358 ^ _257529) ^ [_338427] : [_338427 = pair_first(_338196), 2361 ^ _257529 : [(2362 ^ _257529) ^ [_338592, _338594] : [_338196 = ordered_pair(_338594, _338592), -(_338427 = _338594)]]]]], (5401 ^ _257529) ^ [_441554] : [-(closed_subset(cast_as_carrier_subset(_441554), _441554)), topological_space(_441554), top_str(_441554)], (11283 ^ _257529) ^ [_669368] : [ordinal(_669368), -(well_ordering(inclusion_relation(_669368)))], (288 ^ _257529) ^ [_266416, _266418] : [-(meet_absorbing(_266416)), _266418 = _266416, meet_absorbing(_266418)], (3206 ^ _257529) ^ [_368515] : [3209 ^ _257529 : [(3210 ^ _257529) ^ [] : [-(in(3207 ^ [_368515], _368515))], (3212 ^ _257529) ^ [] : [-(in(3208 ^ [_368515], _368515))], (3218 ^ _257529) ^ [] : [in(3208 ^ [_368515], 3207 ^ [_368515])], (3216 ^ _257529) ^ [] : [3207 ^ [_368515] = 3208 ^ [_368515]], (3214 ^ _257529) ^ [] : [in(3207 ^ [_368515], 3208 ^ [_368515])]], -(epsilon_connected(_368515))], (1780 ^ _257529) ^ [_317287] : [relation(_317287), function(_317287), 1787 ^ _257529 : [(1817 ^ _257529) ^ [_318713, _318715] : [-(_318713 = relation_image(_317287, _318715)), 1834 ^ _257529 : [(1835 ^ _257529) ^ [] : [-(in(1833 ^ [_317287, _318713, _318715], relation_dom(_317287)))], (1841 ^ _257529) ^ [] : [in(1818 ^ [_317287, _318713, _318715], _318713)], (1839 ^ _257529) ^ [] : [-(1818 ^ [_317287, _318713, _318715] = apply(_317287, 1833 ^ [_317287, _318713, _318715]))], (1837 ^ _257529) ^ [] : [-(in(1833 ^ [_317287, _318713, _318715], _318715))]], 1821 ^ _257529 : [(1822 ^ _257529) ^ [] : [-(in(1818 ^ [_317287, _318713, _318715], _318713))], (1824 ^ _257529) ^ [_319033] : [in(_319033, relation_dom(_317287)), in(_319033, _318715), 1818 ^ [_317287, _318713, _318715] = apply(_317287, _319033)]]], (1788 ^ _257529) ^ [_317585, _317587] : [_317585 = relation_image(_317287, _317587), 1791 ^ _257529 : [(1792 ^ _257529) ^ [_317785] : [in(_317785, _317585), 1796 ^ _257529 : [(1801 ^ _257529) ^ [] : [-(_317785 = apply(_317287, 1795 ^ [_317287, _317585, _317587, _317785]))], (1799 ^ _257529) ^ [] : [-(in(1795 ^ [_317287, _317585, _317587, _317785], _317587))], (1797 ^ _257529) ^ [] : [-(in(1795 ^ [_317287, _317585, _317587, _317785], relation_dom(_317287)))]]], (1803 ^ _257529) ^ [_318240] : [-(in(_318240, _317585)), 1804 ^ _257529 : [(1805 ^ _257529) ^ [_318353] : [in(_318353, relation_dom(_317287)), in(_318353, _317587), _318240 = apply(_317287, _318353)]]]]]]], (3256 ^ _257529) ^ [_370500, _370502] : [subset(_370502, _370500), 3259 ^ _257529 : [(3260 ^ _257529) ^ [_370637] : [in(_370637, _370502), -(in(_370637, _370500))]]], (8041 ^ _257529) ^ [_553231, _553233] : [-(empty(_553233)), relation(_553231), 8049 ^ _257529 : [(8050 ^ _257529) ^ [_553697, _553699] : [in(_553697, 8048 ^ [_553231, _553233, _553699]), 8053 ^ _257529 : [(8060 ^ _257529) ^ [] : [-(in(8055 ^ [_553231, _553233, _553697, _553699], _553233))], (8054 ^ _257529) ^ [] : [-(in(_553697, cartesian_product2(_553233, _553699)))], (8067 ^ _257529) ^ [_554699] : [in(_554699, 8061 ^ [_553231, _553233, _553697, _553699]), -(in(ordered_pair(8056 ^ [_553231, _553233, _553697, _553699], _554699), _553231))], (8063 ^ _257529) ^ [] : [-(8055 ^ [_553231, _553233, _553697, _553699] = 8061 ^ [_553231, _553233, _553697, _553699])], (8065 ^ _257529) ^ [] : [-(in(8056 ^ [_553231, _553233, _553697, _553699], 8061 ^ [_553231, _553233, _553697, _553699]))], (8058 ^ _257529) ^ [] : [-(ordered_pair(8055 ^ [_553231, _553233, _553697, _553699], 8056 ^ [_553231, _553233, _553697, _553699]) = _553697)]]], (8073 ^ _257529) ^ [_554952, _554954] : [-(in(_554952, 8048 ^ [_553231, _553233, _554954])), in(_554952, cartesian_product2(_553233, _554954)), 8078 ^ _257529 : [(8079 ^ _257529) ^ [_555219, _555221] : [ordered_pair(_555221, _555219) = _554952, in(_555221, _553233), 8086 ^ _257529 : [(8087 ^ _257529) ^ [_555507] : [_555221 = _555507, in(_555219, _555507), 8095 ^ _257529 : [(8096 ^ _257529) ^ [] : [-(in(8094 ^ [_553231, _553233, _554952, _554954, _555219, _555221, _555507], _555507))], (8098 ^ _257529) ^ [] : [in(ordered_pair(_555219, 8094 ^ [_553231, _553233, _554952, _554954, _555219, _555221, _555507]), _553231)]]]]]]]]], (8989 ^ _257529) ^ [_592930, _592932] : [disjoint(_592932, _592930), -(disjoint(_592930, _592932))], (9458 ^ _257529) ^ [_608790] : [one_sorted_str(_608790), 9461 ^ _257529 : [(9462 ^ _257529) ^ [_608938] : [element(_608938, powerset(the_carrier(_608790))), -(subset_complement(the_carrier(_608790), _608938) = subset_difference(the_carrier(_608790), cast_as_carrier_subset(_608790), _608938))]]], (4925 ^ _257529) ^ [] : [-(empty(empty_set))], (5421 ^ _257529) ^ [] : [-(empty(empty_set))], (11051 ^ _257529) ^ [] : [-(relation_rng(empty_set) = empty_set)], (4667 ^ _257529) ^ [_417806] : [relation(_417806), -(relation(relation_inverse(_417806)))], (1913 ^ _257529) ^ [_322197] : [relation(_322197), function(_322197), 1920 ^ _257529 : [(1943 ^ _257529) ^ [_323236, _323238] : [-(_323236 = relation_inverse_image(_322197, _323238)), 1955 ^ _257529 : [(1960 ^ _257529) ^ [] : [in(1944 ^ [_322197, _323236, _323238], _323236)], (1958 ^ _257529) ^ [] : [-(in(apply(_322197, 1944 ^ [_322197, _323236, _323238]), _323238))], (1956 ^ _257529) ^ [] : [-(in(1944 ^ [_322197, _323236, _323238], relation_dom(_322197)))]], 1947 ^ _257529 : [(1948 ^ _257529) ^ [] : [-(in(1944 ^ [_322197, _323236, _323238], _323236))], (1950 ^ _257529) ^ [] : [in(1944 ^ [_322197, _323236, _323238], relation_dom(_322197)), in(apply(_322197, 1944 ^ [_322197, _323236, _323238]), _323238)]]], (1921 ^ _257529) ^ [_322484, _322486] : [_322484 = relation_inverse_image(_322197, _322486), 1924 ^ _257529 : [(1925 ^ _257529) ^ [_322673] : [in(_322673, _322484), 1928 ^ _257529 : [(1929 ^ _257529) ^ [] : [-(in(_322673, relation_dom(_322197)))], (1931 ^ _257529) ^ [] : [-(in(apply(_322197, _322673), _322486))]]], (1933 ^ _257529) ^ [_322942] : [-(in(_322942, _322484)), in(_322942, relation_dom(_322197)), in(apply(_322197, _322942), _322486)]]]]], (5964 ^ _257529) ^ [_460263] : [-(finite(5944 ^ [_460263]))], (5572 ^ _257529) ^ [_447062, _447064] : [relation(_447062), -(subset(relation_dom(relation_rng_restriction(_447064, _447062)), relation_dom(_447062)))], (8433 ^ _257529) ^ [_570188, _570190, _570192] : [relation(_570190), relation(_570188), function(_570188), 8445 ^ _257529 : [(8446 ^ _257529) ^ [_570677] : [in(_570677, 8444 ^ [_570188, _570190, _570192]), 8449 ^ _257529 : [(8456 ^ _257529) ^ [] : [-(in(ordered_pair(apply(_570188, 8451 ^ [_570188, _570190, _570192, _570677]), apply(_570188, 8452 ^ [_570188, _570190, _570192, _570677])), _570190))], (8454 ^ _257529) ^ [] : [-(_570677 = ordered_pair(8451 ^ [_570188, _570190, _570192, _570677], 8452 ^ [_570188, _570190, _570192, _570677]))], (8450 ^ _257529) ^ [] : [-(in(_570677, cartesian_product2(_570192, _570192)))]]], (8458 ^ _257529) ^ [_571285] : [-(in(_571285, 8444 ^ [_570188, _570190, _570192])), in(_571285, cartesian_product2(_570192, _570192)), 8463 ^ _257529 : [(8464 ^ _257529) ^ [_571526, _571528] : [_571285 = ordered_pair(_571528, _571526), in(ordered_pair(apply(_570188, _571528), apply(_570188, _571526)), _570190)]]]]], (11331 ^ _257529) ^ [_670971, _670973] : [empty(_670973), -(_670973 = _670971), empty(_670971)], (5235 ^ _257529) ^ [_436281, _436283] : [v3_membered(_436283), 5238 ^ _257529 : [(5243 ^ _257529) ^ [] : [-(v3_membered(set_difference(_436283, _436281)))], (5241 ^ _257529) ^ [] : [-(v2_membered(set_difference(_436283, _436281)))], (5239 ^ _257529) ^ [] : [-(v1_membered(set_difference(_436283, _436281)))]]], (5920 ^ _257529) ^ [_458738] : [-(empty(_458738)), 5924 ^ _257529 : [(5925 ^ _257529) ^ [] : [-(element(5923 ^ [_458738], powerset(_458738)))], (5927 ^ _257529) ^ [] : [empty(5923 ^ [_458738])]]], (4575 ^ _257529) ^ [] : [true___, -(true___)], (5954 ^ _257529) ^ [_459943] : [-(one_to_one(5944 ^ [_459943]))], (6223 ^ _257529) ^ [_468807, _468809] : [ordinal(_468809), ordinal(_468807), 6230 ^ _257529 : [(6231 ^ _257529) ^ [] : [ordinal_subset(_468809, _468807), -(subset(_468809, _468807))], (6237 ^ _257529) ^ [] : [subset(_468809, _468807), -(ordinal_subset(_468809, _468807))]]], (1220 ^ _257529) ^ [_298252, _298254] : [_298254 = _298252, -(singleton(_298254) = singleton(_298252))], (40 ^ _257529) ^ [_258867, _258869] : [-(v1_int_1(_258867)), _258869 = _258867, v1_int_1(_258869)], (3516 ^ _257529) ^ [_379926, _379928] : [-(_379926 = union(_379928)), 3529 ^ _257529 : [(3534 ^ _257529) ^ [] : [in(3517 ^ [_379926, _379928], _379926)], (3532 ^ _257529) ^ [] : [-(in(3528 ^ [_379926, _379928], _379928))], (3530 ^ _257529) ^ [] : [-(in(3517 ^ [_379926, _379928], 3528 ^ [_379926, _379928]))]], 3520 ^ _257529 : [(3521 ^ _257529) ^ [] : [-(in(3517 ^ [_379926, _379928], _379926))], (3523 ^ _257529) ^ [_380209] : [in(3517 ^ [_379926, _379928], _380209), in(_380209, _379928)]]], (4465 ^ _257529) ^ [_412331, _412333] : [-(element(interior(_412333, _412331), powerset(the_carrier(_412333)))), top_str(_412333), element(_412331, powerset(the_carrier(_412333)))], (4697 ^ _257529) ^ [_418611, _418613] : [-(relation(relation_composition(_418613, _418611))), relation(_418613), relation(_418611)], (9434 ^ _257529) ^ [_608097, _608099, _608101] : [relation(_608097), subset(_608101, _608099), -(subset(relation_inverse_image(_608097, _608101), relation_inverse_image(_608097, _608099)))], (9529 ^ _257529) ^ [_611367] : [-(set_union2(_611367, empty_set) = _611367)], (830 ^ _257529) ^ [_284150, _284152, _284154, _284156, _284158, _284160] : [-(apply_binary(_284160, _284156, _284152) = apply_binary(_284158, _284154, _284150)), _284160 = _284158, _284156 = _284154, _284152 = _284150], (5083 ^ _257529) ^ [] : [-(relation(empty_set))]], input).
% 183.29/176.60  ncf('1',plain,[11503 : -(open_subsets(11497 ^ [], 11494 ^ [])), 11507 : -(closed_subsets(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), 11494 ^ []))],start(11501 ^ 0)).
% 183.29/176.60  ncf('1.1',plain,[open_subsets(11497 ^ [], 11494 ^ []), -(open_subsets(complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])), 11494 ^ [])), 11497 ^ [] = complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])), 11494 ^ [] = 11494 ^ []],extension(738 ^ 3,bind([[_280403, _280405, _280407, _280409], [11494 ^ [], 11494 ^ [], complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])), 11497 ^ []]]))).
% 183.29/176.60  ncf('1.1.1',plain,[open_subsets(complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])), 11494 ^ []), 9392 : -(closed_subsets(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), 11494 ^ [])), 9392 : element(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), powerset(powerset(the_carrier(11494 ^ [])))), 9382 : top_str(11494 ^ [])],extension(9378 ^ 4,bind([[_606371, _606519], [11494 ^ [], complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])]]))).
% 183.29/176.60  ncf('1.1.1.1',plain,[closed_subsets(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), 11494 ^ [])],extension(11505 ^ 9)).
% 183.29/176.60  ncf('1.1.1.2',plain,[-(element(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), powerset(powerset(the_carrier(11494 ^ []))))), element(11497 ^ [], powerset(powerset(the_carrier(11494 ^ []))))],extension(4763 ^ 7,bind([[_420906, _420908], [11497 ^ [], the_carrier(11494 ^ [])]]))).
% 183.29/176.60  ncf('1.1.1.2.1',plain,[-(element(11497 ^ [], powerset(powerset(the_carrier(11494 ^ [])))))],extension(11499 ^ 8)).
% 183.29/176.60  ncf('1.1.1.3',plain,[-(top_str(11494 ^ []))],extension(11496 ^ 5)).
% 183.29/176.60  ncf('1.1.2',plain,[-(11497 ^ [] = complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []))), complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])) = 11497 ^ []],extension(4 ^ 4,bind([[_257760, _257762], [11497 ^ [], complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []))]]))).
% 183.29/176.60  ncf('1.1.2.1',plain,[-(complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])) = 11497 ^ []), element(11497 ^ [], powerset(powerset(the_carrier(11494 ^ []))))],extension(5521 ^ 5,bind([[_445285, _445287], [11497 ^ [], the_carrier(11494 ^ [])]]))).
% 183.29/176.60  ncf('1.1.2.1.1',plain,[-(element(11497 ^ [], powerset(powerset(the_carrier(11494 ^ [])))))],extension(11499 ^ 6)).
% 183.29/176.60  ncf('1.1.3',plain,[-(11494 ^ [] = 11494 ^ [])],extension(2 ^ 4,bind([[_257653], [11494 ^ []]]))).
% 183.29/176.60  ncf('1.2',plain,[closed_subsets(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), 11494 ^ []), 9386 : -(open_subsets(complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])), 11494 ^ [])), 9386 : element(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), powerset(powerset(the_carrier(11494 ^ [])))), 9382 : top_str(11494 ^ [])],extension(9378 ^ 3,bind([[_606371, _606519], [11494 ^ [], complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])]]))).
% 183.29/176.60  ncf('1.2.1',plain,[open_subsets(complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])), 11494 ^ []), -(open_subsets(11497 ^ [], 11494 ^ [])), complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])) = 11497 ^ [], 11494 ^ [] = 11494 ^ []],extension(738 ^ 8,bind([[_280403, _280405, _280407, _280409], [11494 ^ [], 11494 ^ [], 11497 ^ [], complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []))]]))).
% 183.29/176.60  ncf('1.2.1.1',plain,[open_subsets(11497 ^ [], 11494 ^ [])],extension(11509 ^ 9)).
% 183.29/176.60  ncf('1.2.1.2',plain,[-(complements_of_subsets(the_carrier(11494 ^ []), complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ [])) = 11497 ^ []), element(11497 ^ [], powerset(powerset(the_carrier(11494 ^ []))))],extension(5521 ^ 9,bind([[_445285, _445287], [11497 ^ [], the_carrier(11494 ^ [])]]))).
% 183.29/176.60  ncf('1.2.1.2.1',plain,[-(element(11497 ^ [], powerset(powerset(the_carrier(11494 ^ [])))))],extension(11499 ^ 10)).
% 183.29/176.60  ncf('1.2.1.3',plain,[-(11494 ^ [] = 11494 ^ [])],extension(2 ^ 9,bind([[_257653], [11494 ^ []]]))).
% 183.29/176.60  ncf('1.2.2',plain,[-(element(complements_of_subsets(the_carrier(11494 ^ []), 11497 ^ []), powerset(powerset(the_carrier(11494 ^ []))))), element(11497 ^ [], powerset(powerset(the_carrier(11494 ^ []))))],extension(4763 ^ 6,bind([[_420906, _420908], [11497 ^ [], the_carrier(11494 ^ [])]]))).
% 183.29/176.60  ncf('1.2.2.1',plain,[-(element(11497 ^ [], powerset(powerset(the_carrier(11494 ^ [])))))],extension(11499 ^ 7)).
% 183.29/176.60  ncf('1.2.3',plain,[-(top_str(11494 ^ []))],extension(11496 ^ 4)).
% 183.29/176.60  %-----------------------------------------------------
% 183.29/176.60  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------