%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU386+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:03:22 EDT 2023

% Result   : Theorem 239.64s 231.42s
% Output   : Proof 239.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU386+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 13:53:28 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 239.64/231.42  
% 239.64/231.42  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 239.64/231.42  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 239.64/231.42  %-----------------------------------------------------
% 239.64/231.42  ncf(matrix, plain, [(20428 ^ _455504) ^ [] : [-(directed_relstr(20422 ^ []))], (20433 ^ _455504) ^ [] : [-(element(20431 ^ [], the_carrier(20415 ^ [])))], (20421 ^ _455504) ^ [] : [-(top_str(20415 ^ []))], (20426 ^ _455504) ^ [] : [-(transitive_relstr(20422 ^ []))], (20424 ^ _455504) ^ [] : [empty_carrier(20422 ^ [])], (20430 ^ _455504) ^ [] : [-(net_str(20422 ^ [], 20415 ^ []))], (20417 ^ _455504) ^ [] : [empty_carrier(20415 ^ [])], (20435 ^ _455504) ^ [] : [-(in(20431 ^ [], lim_points_of_net(20415 ^ [], 20422 ^ [])))], (20419 ^ _455504) ^ [] : [-(topological_space(20415 ^ []))], (20437 ^ _455504) ^ [] : [is_a_cluster_point_of_netstr(20415 ^ [], 20422 ^ [], 20431 ^ [])], !, (9643 ^ _115804) ^ [_263792, _263794, _263796] : [9650 ^ _115804 : [(9651 ^ _115804) ^ [] : [-(strict_net_str(preimage_subnetstr(_263796, _263794, _263792), _263796))], (9653 ^ _115804) ^ [] : [-(subnetstr(preimage_subnetstr(_263796, _263794, _263792), _263796, _263794))]], one_sorted_str(_263796), net_str(_263794, _263796)], (19703 ^ _115804) ^ [] : [-(relation_rng(empty_set) = empty_set)], (20332 ^ _115804) ^ [_439030, _439032] : [relation(_439030), -(relation_dom_restriction(_439030, _439032) = relation_composition(identity_relation(_439032), _439030))], (9443 ^ _115804) ^ [_260984, _260986, _260988] : [-(element(meet_commut(_260988, _260986, _260984), the_carrier(_260988))), -(empty_carrier(_260988)), meet_commutative(_260988), meet_semilatt_str(_260988), element(_260986, the_carrier(_260988)), element(_260984, the_carrier(_260988))], (10285 ^ _115804) ^ [_272392] : [-(join_associative(boole_lattice(_272392)))], (12155 ^ _115804) ^ [] : [-(join_absorbing(12137 ^ []))], (3342 ^ _115804) ^ [_163338] : [-(preboolean(_163338)), cup_closed(_163338), diff_closed(_163338)], (17483 ^ _115804) ^ [_394026] : [one_sorted_str(_394026), 17486 ^ _115804 : [(17487 ^ _115804) ^ [_394169] : [net_str(_394169, _394026), 17490 ^ _115804 : [(17491 ^ _115804) ^ [_394305] : [subnetstr(_394305, _394026, _394169), 17494 ^ _115804 : [(17495 ^ _115804) ^ [_394433] : [element(_394433, the_carrier(_394169)), 17498 ^ _115804 : [(17499 ^ _115804) ^ [_394552] : [element(_394552, the_carrier(_394169)), 17502 ^ _115804 : [(17503 ^ _115804) ^ [_394660] : [element(_394660, the_carrier(_394305)), 17506 ^ _115804 : [(17507 ^ _115804) ^ [_394757] : [element(_394757, the_carrier(_394305)), -(related(_394169, _394433, _394552)), _394433 = _394660, _394552 = _394757, related(_394305, _394660, _394757)]]]]]]]]]]]]], (12025 ^ _115804) ^ [_296103, _296105] : [in(_296105, _296103), -(subset(_296105, union(_296103)))], (13140 ^ _115804) ^ [_309490] : [-(k2_lattice3(_309490) = relation_of_lattice(_309490)), -(empty_carrier(_309490)), lattice(_309490), latt_str(_309490)], (1280 ^ _115804) ^ [_132940, _132942, _132944, _132946] : [-(disjoint(_132944, _132940)), disjoint(_132946, _132942), _132946 = _132944, _132942 = _132940], (9571 ^ _115804) ^ [_262733, _262735] : [element(_262733, powerset(powerset(_262735))), -(element(union_of_subsets(_262735, _262733), powerset(_262735)))], (12900 ^ _115804) ^ [] : [-(strict_rel_str(12894 ^ []))], (12507 ^ _115804) ^ [] : [empty_carrier(12503 ^ [])], (1042 ^ _115804) ^ [_129611, _129613, _129615, _129617] : [-(is_a_cover_of_carrier(_129615, _129611)), is_a_cover_of_carrier(_129617, _129613), _129617 = _129615, _129613 = _129611], (12286 ^ _115804) ^ [] : [-(relation(12284 ^ []))], (11047 ^ _115804) ^ [_282428] : [11062 ^ _115804 : [(11071 ^ _115804) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_282428)))], (11067 ^ _115804) ^ [] : [-(reflexive_relstr(poset_of_lattice(_282428)))], (11077 ^ _115804) ^ [] : [-(with_infima_relstr(poset_of_lattice(_282428)))], (11069 ^ _115804) ^ [] : [-(transitive_relstr(poset_of_lattice(_282428)))], (11065 ^ _115804) ^ [] : [-(strict_rel_str(poset_of_lattice(_282428)))], (11073 ^ _115804) ^ [] : [-(lower_bounded_relstr(poset_of_lattice(_282428)))], (11063 ^ _115804) ^ [] : [empty_carrier(poset_of_lattice(_282428))], (11075 ^ _115804) ^ [] : [-(with_suprema_relstr(poset_of_lattice(_282428)))]], -(empty_carrier(_282428)), lattice(_282428), lower_bounded_semilattstr(_282428), latt_str(_282428)], (12089 ^ _115804) ^ [] : [-(strict_latt_str(12083 ^ []))], (1140 ^ _115804) ^ [_130970, _130972] : [-(one_to_one(_130970)), _130972 = _130970, one_to_one(_130972)], (5767 ^ _115804) ^ [_201082] : [-(succ(_201082) = set_union2(_201082, singleton(_201082)))], (11299 ^ _115804) ^ [_285745] : [-(transitive_relstr(incl_POSet(_285745)))], (2380 ^ _115804) ^ [_150133, _150135, _150137, _150139] : [-(meet_of_subsets(_150139, _150135) = meet_of_subsets(_150137, _150133)), _150139 = _150137, _150135 = _150133], (10409 ^ _115804) ^ [_273911] : [-(reflexive_relstr(boole_POSet(_273911)))], (18766 ^ _115804) ^ [_414690] : [-(set_difference(_414690, empty_set) = _414690)], (890 ^ _115804) ^ [_127551, _127553, _127555, _127557, _127559, _127561] : [-(subnet(_127559, _127555, _127551)), subnet(_127561, _127557, _127553), _127561 = _127559, _127557 = _127555, _127553 = _127551], (15246 ^ _115804) ^ [_353022, _353024, _353026] : [relation(_353024), relation(_353022), function(_353022), 15262 ^ _115804 : [(15269 ^ _115804) ^ [] : [-(in(ordered_pair(apply(_353022, 15264 ^ [_353022, _353024, _353026]), apply(_353022, 15265 ^ [_353022, _353024, _353026])), _353024))], (15267 ^ _115804) ^ [] : [-(15260 ^ [_353022, _353024, _353026] = ordered_pair(15264 ^ [_353022, _353024, _353026], 15265 ^ [_353022, _353024, _353026]))], (15277 ^ _115804) ^ [] : [-(in(ordered_pair(apply(_353022, 15272 ^ [_353022, _353024, _353026]), apply(_353022, 15273 ^ [_353022, _353024, _353026])), _353024))], (15263 ^ _115804) ^ [] : [-(15259 ^ [_353022, _353024, _353026] = 15260 ^ [_353022, _353024, _353026])], (15271 ^ _115804) ^ [] : [-(15259 ^ [_353022, _353024, _353026] = 15261 ^ [_353022, _353024, _353026])], (15279 ^ _115804) ^ [] : [15260 ^ [_353022, _353024, _353026] = 15261 ^ [_353022, _353024, _353026]], (15275 ^ _115804) ^ [] : [-(15261 ^ [_353022, _353024, _353026] = ordered_pair(15272 ^ [_353022, _353024, _353026], 15273 ^ [_353022, _353024, _353026]))]], 15281 ^ _115804 : [(15282 ^ _115804) ^ [_353784] : [in(_353784, 15280 ^ [_353022, _353024, _353026]), 15286 ^ _115804 : [(15293 ^ _115804) ^ [] : [-(_353784 = ordered_pair(15290 ^ [_353022, _353024, _353026, _353784], 15291 ^ [_353022, _353024, _353026, _353784]))], (15287 ^ _115804) ^ [] : [-(in(15285 ^ [_353022, _353024, _353026, _353784], cartesian_product2(_353026, _353026)))], (15289 ^ _115804) ^ [] : [-(15285 ^ [_353022, _353024, _353026, _353784] = _353784)], (15295 ^ _115804) ^ [] : [-(in(ordered_pair(apply(_353022, 15290 ^ [_353022, _353024, _353026, _353784]), apply(_353022, 15291 ^ [_353022, _353024, _353026, _353784])), _353024))]]], (15297 ^ _115804) ^ [_354064] : [-(in(_354064, 15280 ^ [_353022, _353024, _353026])), 15298 ^ _115804 : [(15299 ^ _115804) ^ [_354154] : [in(_354154, cartesian_product2(_353026, _353026)), _354154 = _354064, 15306 ^ _115804 : [(15307 ^ _115804) ^ [_354302, _354304] : [_354064 = ordered_pair(_354304, _354302), in(ordered_pair(apply(_353022, _354304), apply(_353022, _354302)), _353024)]]]]]]], (12335 ^ _115804) ^ [] : [-(epsilon_connected(12331 ^ []))], (13506 ^ _115804) ^ [_314833, _314835, _314837] : [13525 ^ _115804 : [(13526 ^ _115804) ^ [] : [related_reflexive(_314837, _314835, _314833), -(related(_314837, _314835, _314833))], (13532 ^ _115804) ^ [] : [related(_314837, _314835, _314833), -(related_reflexive(_314837, _314835, _314833))]], -(empty_carrier(_314837)), reflexive_relstr(_314837), rel_str(_314837), element(_314835, the_carrier(_314837)), element(_314833, the_carrier(_314837))], (2234 ^ _115804) ^ [_147922, _147924, _147926, _147928] : [-(join_on_relstr(_147928, _147924) = join_on_relstr(_147926, _147922)), _147928 = _147926, _147924 = _147922], (14528 ^ _115804) ^ [_335728] : [ordinal(_335728), 14536 ^ _115804 : [(14572 ^ _115804) ^ [] : [-(ordinal(14570 ^ [_335728]))], (14537 ^ _115804) ^ [] : [-(14533 ^ [_335728] = 14534 ^ [_335728])], (14544 ^ _115804) ^ [] : [in(14538 ^ [_335728], omega), 14547 ^ _115804 : [(14548 ^ _115804) ^ [_336537] : [element(_336537, powerset(powerset(14538 ^ [_335728]))), -(_336537 = empty_set), 14556 ^ _115804 : [(14557 ^ _115804) ^ [] : [-(in(14555 ^ [_335728, _336537], _336537))], (14559 ^ _115804) ^ [_336749] : [-(_336749 = 14555 ^ [_335728, _336537]), in(_336749, _336537), subset(14555 ^ [_335728, _336537], _336749)]]]]], (14540 ^ _115804) ^ [] : [-(ordinal(14538 ^ [_335728]))], (14569 ^ _115804) ^ [] : [-(14533 ^ [_335728] = 14535 ^ [_335728])], (14542 ^ _115804) ^ [] : [-(14534 ^ [_335728] = 14538 ^ [_335728])], (14576 ^ _115804) ^ [] : [in(14570 ^ [_335728], omega), 14579 ^ _115804 : [(14580 ^ _115804) ^ [_337137] : [element(_337137, powerset(powerset(14570 ^ [_335728]))), -(_337137 = empty_set), 14588 ^ _115804 : [(14589 ^ _115804) ^ [] : [-(in(14587 ^ [_335728, _337137], _337137))], (14591 ^ _115804) ^ [_337349] : [-(_337349 = 14587 ^ [_335728, _337137]), in(_337349, _337137), subset(14587 ^ [_335728, _337137], _337349)]]]]], (14574 ^ _115804) ^ [] : [-(14535 ^ [_335728] = 14570 ^ [_335728])], (14601 ^ _115804) ^ [] : [14534 ^ [_335728] = 14535 ^ [_335728]]], 14603 ^ _115804 : [(14604 ^ _115804) ^ [_337688] : [in(_337688, 14602 ^ [_335728]), 14608 ^ _115804 : [(14618 ^ _115804) ^ [] : [in(14612 ^ [_335728, _337688], omega), 14621 ^ _115804 : [(14622 ^ _115804) ^ [_338182] : [element(_338182, powerset(powerset(14612 ^ [_335728, _337688]))), -(_338182 = empty_set), 14630 ^ _115804 : [(14631 ^ _115804) ^ [] : [-(in(14629 ^ [_335728, _337688, _338182], _338182))], (14633 ^ _115804) ^ [_338406] : [-(_338406 = 14629 ^ [_335728, _337688, _338182]), in(_338406, _338182), subset(14629 ^ [_335728, _337688, _338182], _338406)]]]]], (14616 ^ _115804) ^ [] : [-(_337688 = 14612 ^ [_335728, _337688])], (14614 ^ _115804) ^ [] : [-(ordinal(14612 ^ [_335728, _337688]))], (14609 ^ _115804) ^ [] : [-(in(14607 ^ [_335728, _337688], succ(_335728)))], (14611 ^ _115804) ^ [] : [-(14607 ^ [_335728, _337688] = _337688)]]], (14643 ^ _115804) ^ [_338599] : [-(in(_338599, 14602 ^ [_335728])), 14644 ^ _115804 : [(14645 ^ _115804) ^ [_338729] : [in(_338729, succ(_335728)), _338729 = _338599, 14652 ^ _115804 : [(14653 ^ _115804) ^ [_338916] : [ordinal(_338916), _338599 = _338916, 14660 ^ _115804 : [(14666 ^ _115804) ^ [] : [14662 ^ [_335728, _338599, _338729, _338916] = empty_set], (14661 ^ _115804) ^ [] : [-(in(_338916, omega))], (14664 ^ _115804) ^ [] : [-(element(14662 ^ [_335728, _338599, _338729, _338916], powerset(powerset(_338916))))], (14668 ^ _115804) ^ [_339235] : [in(_339235, 14662 ^ [_335728, _338599, _338729, _338916]), 14672 ^ _115804 : [(14673 ^ _115804) ^ [] : [-(in(14671 ^ [_335728, _338599, _338729, _338916, _339235], 14662 ^ [_335728, _338599, _338729, _338916]))], (14677 ^ _115804) ^ [] : [14671 ^ [_335728, _338599, _338729, _338916, _339235] = _339235], (14675 ^ _115804) ^ [] : [-(subset(_339235, 14671 ^ [_335728, _338599, _338729, _338916, _339235]))]]]]]]]]]]], (16208 ^ _115804) ^ [_372486] : [16214 ^ _115804 : [(16219 ^ _115804) ^ [] : [-(16213 ^ [_372486] = singleton(16211 ^ [_372486]))], (16215 ^ _115804) ^ [] : [-(in(16211 ^ [_372486], _372486))], (16217 ^ _115804) ^ [] : [-(16212 ^ [_372486] = singleton(16211 ^ [_372486]))], (16221 ^ _115804) ^ [] : [16212 ^ [_372486] = 16213 ^ [_372486]]], 16223 ^ _115804 : [(16224 ^ _115804) ^ [] : [-(in(16222 ^ [_372486], _372486))], (16226 ^ _115804) ^ [_372828] : [_372828 = singleton(16222 ^ [_372486])]], 16228 ^ _115804 : [(16233 ^ _115804) ^ [] : [-(relation_dom(16227 ^ [_372486]) = _372486)], (16229 ^ _115804) ^ [] : [-(relation(16227 ^ [_372486]))], (16231 ^ _115804) ^ [] : [-(function(16227 ^ [_372486]))], (16235 ^ _115804) ^ [_372983] : [in(_372983, _372486), -(apply(16227 ^ [_372486], _372983) = singleton(_372983))]]], (12109 ^ _115804) ^ [] : [-(lower_bounded_semilattstr(12083 ^ []))], (12039 ^ _115804) ^ [_296320, _296322, _296324, _296326] : [-(in(ordered_pair(_296326, _296324), cartesian_product2(_296322, _296320))), in(_296326, _296322), in(_296324, _296320)], (8987 ^ _115804) ^ [_254939, _254941, _254943] : [-(element(join(_254943, _254941, _254939), the_carrier(_254943))), -(empty_carrier(_254943)), join_semilatt_str(_254943), element(_254941, the_carrier(_254943)), element(_254939, the_carrier(_254943))], (16473 ^ _115804) ^ [_377994, _377996] : [in(_377994, _377996), -(apply(16465 ^ [_377996], _377994) = singleton(_377994))], (19749 ^ _115804) ^ [_430075] : [rel_str(_430075), 19752 ^ _115804 : [(19753 ^ _115804) ^ [_430228] : [full_subrelstr(_430228, _430075), subrelstr(_430228, _430075), 19760 ^ _115804 : [(19761 ^ _115804) ^ [_430420] : [element(_430420, the_carrier(_430075)), 19764 ^ _115804 : [(19765 ^ _115804) ^ [_430553] : [element(_430553, the_carrier(_430075)), 19768 ^ _115804 : [(19769 ^ _115804) ^ [_430675] : [element(_430675, the_carrier(_430228)), 19772 ^ _115804 : [(19773 ^ _115804) ^ [_430786] : [element(_430786, the_carrier(_430228)), -(related(_430228, _430675, _430786)), _430675 = _430420, _430786 = _430553, related(_430075, _430420, _430553), in(_430675, the_carrier(_430228)), in(_430786, the_carrier(_430228))]]]]]]]]]]], (12234 ^ _115804) ^ [] : [-(bounded_lattstr(12206 ^ []))], (20051 ^ _115804) ^ [_434886, _434888] : [in(_434888, _434886), empty(_434886)], (20410 ^ _115804) ^ [_440291, _440293, _440295] : [singleton(_440295) = unordered_pair(_440293, _440291), -(_440293 = _440291)], (122 ^ _115804) ^ [_117393, _117395, _117397, _117399] : [-(is_reflexive_in(_117397, _117393)), is_reflexive_in(_117399, _117395), _117399 = _117397, _117395 = _117393], (10145 ^ _115804) ^ [_270547, _270549] : [finite(_270549), -(finite(set_difference(_270549, _270547)))], (10329 ^ _115804) ^ [_272940] : [empty(succ(_272940))], (19705 ^ _115804) ^ [_429133, _429135] : [subset(_429135, _429133), proper_subset(_429133, _429135)], (12555 ^ _115804) ^ [_302072] : [-(ordinal(12539 ^ [_302072]))], (3078 ^ _115804) ^ [_160064] : [latt_str(_160064), 3093 ^ _115804 : [(3096 ^ _115804) ^ [] : [-(join_commutative(_160064))], (3112 ^ _115804) ^ [] : [-(upper_bounded_semilattstr(_160064))], (3106 ^ _115804) ^ [] : [-(join_absorbing(_160064))], (3098 ^ _115804) ^ [] : [-(join_associative(_160064))], (3108 ^ _115804) ^ [] : [-(lattice(_160064))], (3102 ^ _115804) ^ [] : [-(meet_associative(_160064))], (3100 ^ _115804) ^ [] : [-(meet_commutative(_160064))], (3110 ^ _115804) ^ [] : [-(lower_bounded_semilattstr(_160064))], (3104 ^ _115804) ^ [] : [-(meet_absorbing(_160064))], (3114 ^ _115804) ^ [] : [-(bounded_lattstr(_160064))], (3094 ^ _115804) ^ [] : [empty_carrier(_160064)]], -(empty_carrier(_160064)), lattice(_160064), complete_latt_str(_160064)], (12923 ^ _115804) ^ [] : [-(strict_latt_str(12917 ^ []))], (11297 ^ _115804) ^ [_285726] : [-(reflexive_relstr(incl_POSet(_285726)))], (11803 ^ _115804) ^ [_292937, _292939] : [-(in(_292939, _292937)), -(disjoint(singleton(_292939), _292937))], (1512 ^ _115804) ^ [_136106, _136108, _136110, _136112] : [-(subset(_136110, _136106)), subset(_136112, _136108), _136112 = _136110, _136108 = _136106], (11477 ^ _115804) ^ [_287942] : [-(distributive_relstr(boole_POSet(_287942)))], (10429 ^ _115804) ^ [_274146] : [-(heyting_relstr(boole_POSet(_274146)))], (18522 ^ _115804) ^ [_410950] : [-(empty_carrier(_410950)), one_sorted_str(_410950), 18529 ^ _115804 : [(18530 ^ _115804) ^ [_411105] : [18545 ^ _115804 : [(18546 ^ _115804) ^ [_411338, _411340] : [subnet(_411338, _410950, _411105), _411338 = preimage_subnetstr(_410950, _411105, _411340), -(is_eventually_in(_410950, _411338, _411340))]], -(empty_carrier(_411105)), transitive_relstr(_411105), directed_relstr(_411105), net_str(_411105, _410950)]]], (3126 ^ _115804) ^ [_160634] : [latt_str(_160634), 3137 ^ _115804 : [(3142 ^ _115804) ^ [] : [-(join_associative(_160634))], (3140 ^ _115804) ^ [] : [-(join_commutative(_160634))], (3148 ^ _115804) ^ [] : [-(meet_absorbing(_160634))], (3138 ^ _115804) ^ [] : [empty_carrier(_160634)], (3144 ^ _115804) ^ [] : [-(meet_commutative(_160634))], (3150 ^ _115804) ^ [] : [-(join_absorbing(_160634))], (3146 ^ _115804) ^ [] : [-(meet_associative(_160634))]], -(empty_carrier(_160634)), lattice(_160634)], (10547 ^ _115804) ^ [_275791, _275793] : [empty(unordered_pair(_275793, _275791))], (420 ^ _115804) ^ [_121260, _121262] : [-(complete_relstr(_121260)), _121262 = _121260, complete_relstr(_121262)], (18623 ^ _115804) ^ [_412475] : [-(empty_carrier(_412475)), lattice(_412475), complete_latt_str(_412475), latt_str(_412475), 18638 ^ _115804 : [(18639 ^ _115804) ^ [_412725] : [element(_412725, the_carrier(_412475)), 18642 ^ _115804 : [(18659 ^ _115804) ^ [_413092] : [-(_412725 = meet_of_latt_set(_412475, _413092)), latt_set_smaller(_412475, _412725, _413092), 18665 ^ _115804 : [(18666 ^ _115804) ^ [] : [-(element(18664 ^ [_412475, _412725, _413092], the_carrier(_412475)))], (18670 ^ _115804) ^ [] : [below_refl(_412475, 18664 ^ [_412475, _412725, _413092], _412725)], (18668 ^ _115804) ^ [] : [-(latt_set_smaller(_412475, 18664 ^ [_412475, _412725, _413092], _413092))]]], (18643 ^ _115804) ^ [_412835] : [_412725 = meet_of_latt_set(_412475, _412835), 18646 ^ _115804 : [(18647 ^ _115804) ^ [] : [-(latt_set_smaller(_412475, _412725, _412835))], (18649 ^ _115804) ^ [_412945] : [element(_412945, the_carrier(_412475)), latt_set_smaller(_412475, _412945, _412835), -(below_refl(_412475, _412945, _412725))]]]]]]], (6004 ^ _115804) ^ [_205001] : [top_str(_205001), 6007 ^ _115804 : [(6008 ^ _115804) ^ [_205080] : [element(_205080, powerset(the_carrier(_205001))), -(interior(_205001, _205080) = subset_complement(the_carrier(_205001), topstr_closure(_205001, subset_complement(the_carrier(_205001), _205080))))]]], (1854 ^ _115804) ^ [_141900, _141902, _141904, _141906, _141908, _141910] : [-(apply_binary(_141910, _141906, _141902) = apply_binary(_141908, _141904, _141900)), _141910 = _141908, _141906 = _141904, _141902 = _141900], (1810 ^ _115804) ^ [_141114, _141116, _141118, _141120, _141122, _141124, _141126, _141128] : [-(apply_on_structs(_141128, _141124, _141120, _141116) = apply_on_structs(_141126, _141122, _141118, _141114)), _141128 = _141126, _141124 = _141122, _141120 = _141118, _141116 = _141114], (12711 ^ _115804) ^ [] : [-(upper_bounded_relstr(12689 ^ []))], (13074 ^ _115804) ^ [_308471, _308473, _308475, _308477] : [-(apply_on_structs(_308477, _308475, _308473, _308471) = apply(_308473, _308471)), -(empty_carrier(_308477)), one_sorted_str(_308477), -(empty_carrier(_308475)), one_sorted_str(_308475), function(_308473), quasi_total(_308473, the_carrier(_308477), the_carrier(_308475)), relation_of2(_308473, the_carrier(_308477), the_carrier(_308475)), element(_308471, the_carrier(_308477))], (19222 ^ _115804) ^ [_421739] : [relation(_421739), 19225 ^ _115804 : [(19226 ^ _115804) ^ [_421822] : [relation(_421822), 19229 ^ _115804 : [(19230 ^ _115804) ^ [_421897] : [relation(_421897), function(_421897), relation_isomorphism(_421739, _421822, _421897), -(relation_isomorphism(_421822, _421739, function_inverse(_421897)))]]]]], (18823 ^ _115804) ^ [_415440] : [ordinal(_415440), 18826 ^ _115804 : [(18841 ^ _115804) ^ [] : [18843 ^ _115804 : [(18844 ^ _115804) ^ [] : [-(ordinal(18842 ^ [_415440]))], (18848 ^ _115804) ^ [] : [in(succ(18842 ^ [_415440]), _415440)], (18846 ^ _115804) ^ [] : [-(in(18842 ^ [_415440], _415440))]], -(being_limit_ordinal(_415440))], (18827 ^ _115804) ^ [] : [being_limit_ordinal(_415440), 18830 ^ _115804 : [(18831 ^ _115804) ^ [_415561] : [ordinal(_415561), in(_415561, _415440), -(in(succ(_415561), _415440))]]]]], (7641 ^ _115804) ^ [_231613, _231615] : [-(ordered_pair(_231615, _231613) = unordered_pair(unordered_pair(_231615, _231613), singleton(_231615)))], (12249 ^ _115804) ^ [] : [-(transitive_relstr(12239 ^ []))], (2550 ^ _115804) ^ [_152622, _152624] : [_152624 = _152622, -(relation_dom(_152624) = relation_dom(_152622))], (6159 ^ _115804) ^ [_207919, _207921] : [relation(_207919), 6162 ^ _115804 : [(6189 ^ _115804) ^ [] : [-(_207919 = inclusion_relation(_207921)), relation_field(_207919) = _207921, 6196 ^ _115804 : [(6197 ^ _115804) ^ [] : [-(in(6194 ^ [_207919, _207921], _207921))], (6201 ^ _115804) ^ [] : [6202 ^ _115804 : [(6203 ^ _115804) ^ [] : [-(in(ordered_pair(6194 ^ [_207919, _207921], 6195 ^ [_207919, _207921]), _207919))], (6205 ^ _115804) ^ [] : [subset(6194 ^ [_207919, _207921], 6195 ^ [_207919, _207921])]], 6206 ^ _115804 : [(6207 ^ _115804) ^ [] : [-(subset(6194 ^ [_207919, _207921], 6195 ^ [_207919, _207921]))], (6209 ^ _115804) ^ [] : [in(ordered_pair(6194 ^ [_207919, _207921], 6195 ^ [_207919, _207921]), _207919)]]], (6199 ^ _115804) ^ [] : [-(in(6195 ^ [_207919, _207921], _207921))]]], (6163 ^ _115804) ^ [] : [_207919 = inclusion_relation(_207921), 6166 ^ _115804 : [(6167 ^ _115804) ^ [] : [-(relation_field(_207919) = _207921)], (6169 ^ _115804) ^ [_208094, _208096] : [in(_208096, _207921), in(_208094, _207921), 6176 ^ _115804 : [(6177 ^ _115804) ^ [] : [in(ordered_pair(_208096, _208094), _207919), -(subset(_208096, _208094))], (6183 ^ _115804) ^ [] : [subset(_208096, _208094), -(in(ordered_pair(_208096, _208094), _207919))]]]]]]], (362 ^ _115804) ^ [_120491, _120493, _120495, _120497, _120499, _120501] : [-(bijective(_120499, _120495, _120491)), bijective(_120501, _120497, _120493), _120501 = _120499, _120497 = _120495, _120493 = _120491], (13262 ^ _115804) ^ [_311253, _311255, _311257] : [-(subset_union2(_311257, _311255, _311253) = set_union2(_311255, _311253)), element(_311255, powerset(_311257)), element(_311253, powerset(_311257))], (9117 ^ _115804) ^ [_256610] : [-(transitive(inclusion_order(_256610)))], (19997 ^ _115804) ^ [_434093, _434095, _434097] : [relation(_434093), function(_434093), in(_434095, relation_dom(relation_dom_restriction(_434093, _434097))), -(apply(relation_dom_restriction(_434093, _434097), _434095) = apply(_434093, _434095))], (2454 ^ _115804) ^ [_151218, _151220] : [_151220 = _151218, -(poset_of_lattice(_151220) = poset_of_lattice(_151218))], (1476 ^ _115804) ^ [_135568, _135570, _135572, _135574, _135576, _135578] : [-(quasi_total(_135576, _135572, _135568)), quasi_total(_135578, _135574, _135570), _135578 = _135576, _135574 = _135572, _135570 = _135568], (19904 ^ _115804) ^ [_432746] : [-(unordered_pair(_432746, _432746) = singleton(_432746))], (18160 ^ _115804) ^ [_405187] : [-(set_intersection2(_405187, empty_set) = empty_set)], (10415 ^ _115804) ^ [_273983] : [-(lower_bounded_relstr(boole_POSet(_273983)))], (12840 ^ _115804) ^ [] : [-(function(12834 ^ []))], (18182 ^ _115804) ^ [_405531, _405533] : [element(_405533, _405531), -(empty(_405531)), -(in(_405533, _405531))], (12938 ^ _115804) ^ [_306560, _306562] : [12946 ^ _115804 : [(12947 ^ _115804) ^ [] : [-(subnetstr(12945 ^ [_306560, _306562], _306562, _306560))], (12951 ^ _115804) ^ [] : [-(full_subnetstr(12945 ^ [_306560, _306562], _306562, _306560))], (12949 ^ _115804) ^ [] : [-(strict_net_str(12945 ^ [_306560, _306562], _306562))]], one_sorted_str(_306562), net_str(_306560, _306562)], (12667 ^ _115804) ^ [_303339] : [12679 ^ _115804 : [(12688 ^ _115804) ^ [] : [-(filtered_subset(12678 ^ [_303339], _303339))], (12686 ^ _115804) ^ [] : [-(directed_subset(12678 ^ [_303339], _303339))], (12684 ^ _115804) ^ [] : [-(finite(12678 ^ [_303339]))], (12680 ^ _115804) ^ [] : [-(element(12678 ^ [_303339], powerset(the_carrier(_303339))))], (12682 ^ _115804) ^ [] : [empty(12678 ^ [_303339])]], -(empty_carrier(_303339)), reflexive_relstr(_303339), rel_str(_303339)], (12141 ^ _115804) ^ [] : [empty_carrier(12137 ^ [])], (8238 ^ _115804) ^ [_242358] : [-(empty_carrier(_242358)), latt_str(_242358), 8245 ^ _115804 : [(8260 ^ _115804) ^ [] : [8262 ^ _115804 : [(8263 ^ _115804) ^ [] : [-(element(8261 ^ [_242358], the_carrier(_242358)))], (8268 ^ _115804) ^ [] : [join(_242358, meet(_242358, 8261 ^ [_242358], 8264 ^ [_242358]), 8264 ^ [_242358]) = 8264 ^ [_242358]], (8266 ^ _115804) ^ [] : [-(element(8264 ^ [_242358], the_carrier(_242358)))]], -(meet_absorbing(_242358))], (8246 ^ _115804) ^ [] : [meet_absorbing(_242358), 8249 ^ _115804 : [(8250 ^ _115804) ^ [_242546] : [element(_242546, the_carrier(_242358)), 8253 ^ _115804 : [(8254 ^ _115804) ^ [_242623] : [element(_242623, the_carrier(_242358)), -(join(_242358, meet(_242358, _242546, _242623), _242623) = _242623)]]]]]]], (18772 ^ _115804) ^ [_414764, _414766, _414768] : [in(_414768, _414766), in(_414766, _414764), in(_414764, _414768)], (18004 ^ _115804) ^ [_402810, _402812] : [-(empty_carrier(_402810)), lattice(_402810), latt_str(_402810), 18015 ^ _115804 : [(18016 ^ _115804) ^ [_402989] : [element(_402989, the_carrier(_402810)), 18019 ^ _115804 : [(18020 ^ _115804) ^ [] : [latt_set_smaller(_402810, _402989, _402812), -(relstr_element_smaller(poset_of_lattice(_402810), _402812, cast_to_el_of_LattPOSet(_402810, _402989)))], (18026 ^ _115804) ^ [] : [relstr_element_smaller(poset_of_lattice(_402810), _402812, cast_to_el_of_LattPOSet(_402810, _402989)), -(latt_set_smaller(_402810, _402989, _402812))]]]]], (18794 ^ _115804) ^ [_415071] : [-(transitive(inclusion_relation(_415071)))], (12577 ^ _115804) ^ [_302309] : [-(quasi_total(12567 ^ [_302309], _302309, _302309))], (12590 ^ _115804) ^ [] : [-(reflexive_relstr(12582 ^ []))], (10935 ^ _115804) ^ [_280842] : [-(complemented_lattstr(boole_lattice(_280842)))], (4599 ^ _115804) ^ [_180229] : [rel_str(_180229), -(bottom_of_relstr(_180229) = join_on_relstr(_180229, empty_set))], (10595 ^ _115804) ^ [_276425] : [10610 ^ _115804 : [(10619 ^ _115804) ^ [] : [-(v1_partfun1(the_InternalRel(_276425), the_carrier(_276425), the_carrier(_276425)))], (10617 ^ _115804) ^ [] : [-(transitive(the_InternalRel(_276425)))], (10615 ^ _115804) ^ [] : [-(antisymmetric(the_InternalRel(_276425)))], (10611 ^ _115804) ^ [] : [-(relation(the_InternalRel(_276425)))], (10613 ^ _115804) ^ [] : [-(reflexive(the_InternalRel(_276425)))]], reflexive_relstr(_276425), transitive_relstr(_276425), antisymmetric_relstr(_276425), rel_str(_276425)], (12811 ^ _115804) ^ [] : [empty_carrier(12807 ^ [])], (12163 ^ _115804) ^ [] : [-(bounded_lattstr(12137 ^ []))], (1892 ^ _115804) ^ [_142507, _142509, _142511, _142513, _142515, _142517] : [-(unordered_pair_as_carrier_subset(_142517, _142513, _142509) = unordered_pair_as_carrier_subset(_142515, _142511, _142507)), _142517 = _142515, _142513 = _142511, _142509 = _142507], (19493 ^ _115804) ^ [_426011, _426013, _426015] : [element(_426011, powerset(_426015)), in(_426013, subset_complement(_426015, _426011)), in(_426013, _426011)], (12274 ^ _115804) ^ [] : [-(epsilon_connected(12268 ^ []))], (20290 ^ _115804) ^ [_438394, _438396, _438398] : [-(subset(set_union2(_438398, _438394), _438396)), subset(_438398, _438396), subset(_438394, _438396)], (12226 ^ _115804) ^ [] : [-(lattice(12206 ^ []))], (7730 ^ _115804) ^ [_233024] : [rel_str(_233024), 7733 ^ _115804 : [(7734 ^ _115804) ^ [] : [antisymmetric_relstr(_233024), -(is_antisymmetric_in(the_InternalRel(_233024), the_carrier(_233024)))], (7740 ^ _115804) ^ [] : [is_antisymmetric_in(the_InternalRel(_233024), the_carrier(_233024)), -(antisymmetric_relstr(_233024))]]], (16985 ^ _115804) ^ [_385719] : [one_sorted_str(_385719), 16988 ^ _115804 : [(16989 ^ _115804) ^ [_385790] : [element(_385790, powerset(the_carrier(_385719))), -(subset_intersection2(the_carrier(_385719), _385790, cast_as_carrier_subset(_385719)) = _385790)]]], (19952 ^ _115804) ^ [_433384] : [-(empty_carrier(_433384)), topological_space(_433384), top_str(_433384), 19963 ^ _115804 : [(19964 ^ _115804) ^ [_433582] : [element(_433582, powerset(the_carrier(_433384))), 19967 ^ _115804 : [(19968 ^ _115804) ^ [_433678] : [element(_433678, the_carrier(_433384)), 19971 ^ _115804 : [(19982 ^ _115804) ^ [] : [19984 ^ _115804 : [(19985 ^ _115804) ^ [] : [-(point_neighbourhood(19983 ^ [_433384, _433582, _433678], _433384, _433678))], (19987 ^ _115804) ^ [] : [-(disjoint(19983 ^ [_433384, _433582, _433678], _433582))]], -(in(_433678, topstr_closure(_433384, _433582)))], (19972 ^ _115804) ^ [] : [in(_433678, topstr_closure(_433384, _433582)), 19975 ^ _115804 : [(19976 ^ _115804) ^ [_433817] : [point_neighbourhood(_433817, _433384, _433678), disjoint(_433817, _433582)]]]]]]]]], (3194 ^ _115804) ^ [_161463] : [3205 ^ _115804 : [(3206 ^ _115804) ^ [_161631] : [element(_161631, powerset(the_carrier(_161463))), 3209 ^ _115804 : [(3210 ^ _115804) ^ [] : [-(directed_subset(_161631, _161463))], (3212 ^ _115804) ^ [] : [-(filtered_subset(_161631, _161463))]]]], -(empty_carrier(_161463)), connected_relstr(_161463), rel_str(_161463)], (12281 ^ _115804) ^ [] : [empty(12279 ^ [])], (12253 ^ _115804) ^ [] : [-(with_suprema_relstr(12239 ^ []))], (12425 ^ _115804) ^ [] : [-(connected_relstr(12401 ^ []))], (9973 ^ _115804) ^ [_268366] : [rel_str(_268366), -(relation_of2_as_subset(the_InternalRel(_268366), the_carrier(_268366), the_carrier(_268366)))], (17270 ^ _115804) ^ [_390608] : [top_str(_390608), 17273 ^ _115804 : [(17274 ^ _115804) ^ [_390684] : [element(_390684, powerset(powerset(the_carrier(_390608)))), 17277 ^ _115804 : [(17278 ^ _115804) ^ [] : [open_subsets(_390684, _390608), -(closed_subsets(complements_of_subsets(the_carrier(_390608), _390684), _390608))], (17284 ^ _115804) ^ [] : [closed_subsets(complements_of_subsets(the_carrier(_390608), _390684), _390608), -(open_subsets(_390684, _390608))]]]]], (9357 ^ _115804) ^ [_259799, _259801, _259803] : [-(element(apply_netmap(_259803, _259801, _259799), the_carrier(_259803))), -(empty_carrier(_259803)), one_sorted_str(_259803), -(empty_carrier(_259801)), net_str(_259801, _259803), element(_259799, the_carrier(_259801))], (10157 ^ _115804) ^ [_270674, _270676] : [-(finite(relation_image(_270676, _270674))), relation(_270676), function(_270676), finite(_270674)], (10919 ^ _115804) ^ [_280690] : [-(meet_absorbing(boole_lattice(_280690)))], (548 ^ _115804) ^ [_122904, _122906] : [-(distributive_relstr(_122904)), _122906 = _122904, distributive_relstr(_122906)], (2508 ^ _115804) ^ [_152005, _152007, _152009, _152011] : [-(apply(_152011, _152007) = apply(_152009, _152005)), _152011 = _152009, _152007 = _152005], (12603 ^ _115804) ^ [] : [-(rel_str(12601 ^ []))], (16241 ^ _115804) ^ [_373092, _373094] : [one_sorted_str(_373094), element(_373092, powerset(powerset(the_carrier(_373094)))), 16290 ^ _115804 : [(16295 ^ _115804) ^ [] : [-(relation_dom(16289 ^ [_373092, _373094]) = complements_of_subsets(the_carrier(_373094), _373092))], (16291 ^ _115804) ^ [] : [-(relation(16289 ^ [_373092, _373094]))], (16293 ^ _115804) ^ [] : [-(function(16289 ^ [_373092, _373094]))], (16297 ^ _115804) ^ [_374427] : [in(_374427, complements_of_subsets(the_carrier(_373094), _373092)), 16300 ^ _115804 : [(16301 ^ _115804) ^ [_374527] : [element(_374527, powerset(the_carrier(_373094))), _374527 = _374427, -(apply(16289 ^ [_373092, _373094], _374427) = subset_complement(the_carrier(_373094), _374527))]]]], 16280 ^ _115804 : [(16286 ^ _115804) ^ [_374176] : [-(16282 ^ [_373092, _373094, _374176] = 16279 ^ [_373092, _373094])], (16281 ^ _115804) ^ [] : [-(in(16279 ^ [_373092, _373094], complements_of_subsets(the_carrier(_373094), _373092)))], (16284 ^ _115804) ^ [_374140] : [-(element(16282 ^ [_373092, _373094, _374140], powerset(the_carrier(_373094))))], (16288 ^ _115804) ^ [_374214] : [_374214 = subset_complement(the_carrier(_373094), 16282 ^ [_373092, _373094, _374214])]], 16255 ^ _115804 : [(16258 ^ _115804) ^ [_373632] : [element(_373632, powerset(the_carrier(_373094))), _373632 = 16252 ^ [_373092, _373094], -(16253 ^ [_373092, _373094] = subset_complement(the_carrier(_373094), _373632))], (16278 ^ _115804) ^ [] : [16253 ^ [_373092, _373094] = 16254 ^ [_373092, _373094]], (16256 ^ _115804) ^ [] : [-(in(16252 ^ [_373092, _373094], complements_of_subsets(the_carrier(_373094), _373092)))], (16268 ^ _115804) ^ [_373807] : [element(_373807, powerset(the_carrier(_373094))), _373807 = 16252 ^ [_373092, _373094], -(16254 ^ [_373092, _373094] = subset_complement(the_carrier(_373094), _373807))]]], (12255 ^ _115804) ^ [] : [-(with_infima_relstr(12239 ^ []))], (2676 ^ _115804) ^ [_154888, _154890] : [one_sorted_str(_154890), net_str(_154888, _154890), strict_net_str(_154888, _154890), -(_154888 = net_str_of(_154890, the_carrier(_154888), the_InternalRel(_154888), the_mapping(_154890, _154888)))], (19220 ^ _115804) ^ [_421705, _421707] : [-(set_difference(_421707, set_difference(_421707, _421705)) = set_intersection2(_421707, _421705))], (6492 ^ _115804) ^ [_213279] : [relation(_213279), 6495 ^ _115804 : [(6496 ^ _115804) ^ [_213365] : [relation(_213365), 6499 ^ _115804 : [(6516 ^ _115804) ^ [] : [-(_213279 = _213365), 6521 ^ _115804 : [(6522 ^ _115804) ^ [] : [-(in(ordered_pair(6517 ^ [_213279, _213365], 6518 ^ [_213279, _213365]), _213279))], (6524 ^ _115804) ^ [] : [in(ordered_pair(6517 ^ [_213279, _213365], 6518 ^ [_213279, _213365]), _213365)]], 6525 ^ _115804 : [(6526 ^ _115804) ^ [] : [-(in(ordered_pair(6517 ^ [_213279, _213365], 6518 ^ [_213279, _213365]), _213365))], (6528 ^ _115804) ^ [] : [in(ordered_pair(6517 ^ [_213279, _213365], 6518 ^ [_213279, _213365]), _213279)]]], (6500 ^ _115804) ^ [] : [_213279 = _213365, 6503 ^ _115804 : [(6504 ^ _115804) ^ [_213511, _213513] : [in(ordered_pair(_213513, _213511), _213279), -(in(ordered_pair(_213513, _213511), _213365))], (6510 ^ _115804) ^ [_213600, _213602] : [in(ordered_pair(_213602, _213600), _213365), -(in(ordered_pair(_213602, _213600), _213279))]]]]]]], (2498 ^ _115804) ^ [_151856, _151858, _151860, _151862] : [-(ordered_pair(_151862, _151858) = ordered_pair(_151860, _151856)), _151862 = _151860, _151858 = _151856], (5592 ^ _115804) ^ [_198020] : [-(finite(_198020)), 5593 ^ _115804 : [(5594 ^ _115804) ^ [_198071] : [relation(_198071), function(_198071), relation_rng(_198071) = _198020, in(relation_dom(_198071), omega)]]], (9011 ^ _115804) ^ [] : [true___, -(true___)], (14960 ^ _115804) ^ [_345092, _345094] : [one_sorted_str(_345094), element(_345092, powerset(powerset(the_carrier(_345094)))), 14967 ^ _115804 : [(14968 ^ _115804) ^ [_345465] : [14972 ^ _115804 : [(14995 ^ _115804) ^ [] : [-(ordered_pair(14992 ^ [_345092, _345094, _345465], 14993 ^ [_345092, _345094, _345465]) = 14971 ^ [_345092, _345094, _345465])], (14973 ^ _115804) ^ [] : [-(14969 ^ [_345092, _345094, _345465] = 14970 ^ [_345092, _345094, _345465])], (14981 ^ _115804) ^ [_346138] : [element(_346138, powerset(the_carrier(_345094))), _346138 = 14974 ^ [_345092, _345094, _345465], -(14975 ^ [_345092, _345094, _345465] = subset_complement(the_carrier(_345094), _346138))], (14977 ^ _115804) ^ [] : [-(ordered_pair(14974 ^ [_345092, _345094, _345465], 14975 ^ [_345092, _345094, _345465]) = 14970 ^ [_345092, _345094, _345465])], (14991 ^ _115804) ^ [] : [-(14969 ^ [_345092, _345094, _345465] = 14971 ^ [_345092, _345094, _345465])], (14979 ^ _115804) ^ [] : [-(in(14974 ^ [_345092, _345094, _345465], complements_of_subsets(the_carrier(_345094), _345092)))], (14999 ^ _115804) ^ [_346525] : [element(_346525, powerset(the_carrier(_345094))), _346525 = 14992 ^ [_345092, _345094, _345465], -(14993 ^ [_345092, _345094, _345465] = subset_complement(the_carrier(_345094), _346525))], (14997 ^ _115804) ^ [] : [-(in(14992 ^ [_345092, _345094, _345465], complements_of_subsets(the_carrier(_345094), _345092)))], (15009 ^ _115804) ^ [] : [14970 ^ [_345092, _345094, _345465] = 14971 ^ [_345092, _345094, _345465]]], 15011 ^ _115804 : [(15012 ^ _115804) ^ [_346879] : [in(_346879, 15010 ^ [_345092, _345094, _345465]), 15016 ^ _115804 : [(15027 ^ _115804) ^ [_347346] : [element(_347346, powerset(the_carrier(_345094))), _347346 = 15020 ^ [_345092, _345094, _345465, _346879], -(15021 ^ [_345092, _345094, _345465, _346879] = subset_complement(the_carrier(_345094), _347346))], (15025 ^ _115804) ^ [] : [-(in(15020 ^ [_345092, _345094, _345465, _346879], complements_of_subsets(the_carrier(_345094), _345092)))], (15023 ^ _115804) ^ [] : [-(ordered_pair(15020 ^ [_345092, _345094, _345465, _346879], 15021 ^ [_345092, _345094, _345465, _346879]) = _346879)], (15017 ^ _115804) ^ [] : [-(in(15015 ^ [_345092, _345094, _345465, _346879], cartesian_product2(complements_of_subsets(the_carrier(_345094), _345092), _345465)))], (15019 ^ _115804) ^ [] : [-(15015 ^ [_345092, _345094, _345465, _346879] = _346879)]]], (15037 ^ _115804) ^ [_347557] : [-(in(_347557, 15010 ^ [_345092, _345094, _345465])), 15038 ^ _115804 : [(15039 ^ _115804) ^ [_347680] : [in(_347680, cartesian_product2(complements_of_subsets(the_carrier(_345094), _345092), _345465)), _347680 = _347557, 15046 ^ _115804 : [(15047 ^ _115804) ^ [_347866, _347868] : [ordered_pair(_347868, _347866) = _347557, in(_347868, complements_of_subsets(the_carrier(_345094), _345092)), 15055 ^ _115804 : [(15056 ^ _115804) ^ [] : [-(element(15054 ^ [_345092, _345094, _345465, _347557, _347680, _347866, _347868], powerset(the_carrier(_345094))))], (15060 ^ _115804) ^ [] : [_347866 = subset_complement(the_carrier(_345094), 15054 ^ [_345092, _345094, _345465, _347557, _347680, _347866, _347868])], (15058 ^ _115804) ^ [] : [-(15054 ^ [_345092, _345094, _345465, _347557, _347680, _347866, _347868] = _347868)]]]]]]]]]]], (11726 ^ _115804) ^ [_291796, _291798, _291800] : [-(subset_union2(_291800, _291798, _291798) = _291798), element(_291798, powerset(_291800)), element(_291796, powerset(_291800))], (12609 ^ _115804) ^ [] : [-(reflexive_relstr(12601 ^ []))], (10381 ^ _115804) ^ [_273590] : [-(reflexive_relstr(boole_POSet(_273590)))], (9267 ^ _115804) ^ [_258671, _258673] : [relation(_258673), -(relation(relation_restriction(_258673, _258671)))], (17381 ^ _115804) ^ [_392469, _392471] : [in(_392471, _392469), -(element(_392471, _392469))], (1570 ^ _115804) ^ [_136867, _136869] : [-(transitive_relstr(_136867)), _136869 = _136867, transitive_relstr(_136869)], (12912 ^ _115804) ^ [] : [-(upper_bounded_relstr(12894 ^ []))], (11021 ^ _115804) ^ [_282076, _282078] : [empty(unordered_pair(_282078, _282076))], (2630 ^ _115804) ^ [_153816, _153818, _153820, _153822] : [-(unordered_pair(_153822, _153818) = unordered_pair(_153820, _153816)), _153822 = _153820, _153818 = _153816], (13422 ^ _115804) ^ [_313701, _313703, _313705] : [relation_of2_as_subset(_313701, _313705, _313703), -(relation_of2(_313701, _313705, _313703))], (390 ^ _115804) ^ [_120885, _120887] : [-(join_complete_relstr(_120885)), _120887 = _120885, join_complete_relstr(_120887)], (10585 ^ _115804) ^ [_276307] : [-(meet_commutative(boole_lattice(_276307)))], (18582 ^ _115804) ^ [_411869, _411871, _411873, _411875] : [ordered_pair(_411875, _411873) = ordered_pair(_411871, _411869), 18585 ^ _115804 : [(18586 ^ _115804) ^ [] : [-(_411875 = _411871)], (18588 ^ _115804) ^ [] : [-(_411873 = _411869)]]], (18423 ^ _115804) ^ [_409375] : [-(empty_carrier(_409375)), one_sorted_str(_409375), 18430 ^ _115804 : [(18431 ^ _115804) ^ [_409519] : [18446 ^ _115804 : [(18447 ^ _115804) ^ [_409741] : [is_often_in(_409375, _409519, _409741), -(subnet(preimage_subnetstr(_409375, _409519, _409741), _409375, _409519))]], -(empty_carrier(_409519)), transitive_relstr(_409519), directed_relstr(_409519), net_str(_409519, _409375)]]], (5957 ^ _115804) ^ [_204310] : [one_sorted_str(_204310), 5960 ^ _115804 : [(5961 ^ _115804) ^ [] : [empty_carrier(_204310), -(empty(the_carrier(_204310)))], (5967 ^ _115804) ^ [] : [empty(the_carrier(_204310)), -(empty_carrier(_204310))]]], (19277 ^ _115804) ^ [_422510] : [-(boole_POSet(_422510) = incl_POSet(powerset(_422510)))], (10437 ^ _115804) ^ [_274222] : [-(with_infima_relstr(boole_POSet(_274222)))], (1294 ^ _115804) ^ [_133133, _133135, _133137, _133139, _133141, _133143] : [-(is_eventually_in(_133141, _133137, _133133)), is_eventually_in(_133143, _133139, _133135), _133143 = _133141, _133139 = _133137, _133135 = _133133], (16590 ^ _115804) ^ [_379949] : [-(in(_379949, succ(_379949)))], (12436 ^ _115804) ^ [] : [-(strict_rel_str(12430 ^ []))], (12573 ^ _115804) ^ [_302265] : [-(function(12567 ^ [_302265]))], (12497 ^ _115804) ^ [] : [-(with_suprema_relstr(12465 ^ []))], (3830 ^ _115804) ^ [_169389, _169391] : [-(empty(_169389)), 3833 ^ _115804 : [(3834 ^ _115804) ^ [_169475] : [relation_of2(_169475, _169391, _169389), 3845 ^ _115804 : [(3846 ^ _115804) ^ [] : [-(function(_169475))], (3850 ^ _115804) ^ [] : [-(quasi_total(_169475, _169391, _169389))], (3848 ^ _115804) ^ [] : [-(v1_partfun1(_169475, _169391, _169389))]], function(_169475), quasi_total(_169475, _169391, _169389)]]], (12752 ^ _115804) ^ [] : [-(upper_bounded_relstr(12732 ^ []))], (9705 ^ _115804) ^ [_264723, _264725] : [element(_264723, powerset(powerset(_264725))), -(element(complements_of_subsets(_264725, _264723), powerset(powerset(_264725))))], (1122 ^ _115804) ^ [_130701, _130703, _130705, _130707, _130709, _130711] : [-(related(_130709, _130705, _130701)), related(_130711, _130707, _130703), _130711 = _130709, _130707 = _130705, _130703 = _130701], (4890 ^ _115804) ^ [_186075] : [relation(_186075), function(_186075), 4897 ^ _115804 : [(4920 ^ _115804) ^ [_186583, _186585] : [-(_186583 = relation_inverse_image(_186075, _186585)), 4932 ^ _115804 : [(4933 ^ _115804) ^ [] : [-(in(4921 ^ [_186075, _186583, _186585], relation_dom(_186075)))], (4937 ^ _115804) ^ [] : [in(4921 ^ [_186075, _186583, _186585], _186583)], (4935 ^ _115804) ^ [] : [-(in(apply(_186075, 4921 ^ [_186075, _186583, _186585]), _186585))]], 4924 ^ _115804 : [(4925 ^ _115804) ^ [] : [-(in(4921 ^ [_186075, _186583, _186585], _186583))], (4927 ^ _115804) ^ [] : [in(4921 ^ [_186075, _186583, _186585], relation_dom(_186075)), in(apply(_186075, 4921 ^ [_186075, _186583, _186585]), _186585)]]], (4898 ^ _115804) ^ [_186227, _186229] : [_186227 = relation_inverse_image(_186075, _186229), 4901 ^ _115804 : [(4902 ^ _115804) ^ [_186321] : [in(_186321, _186227), 4905 ^ _115804 : [(4906 ^ _115804) ^ [] : [-(in(_186321, relation_dom(_186075)))], (4908 ^ _115804) ^ [] : [-(in(apply(_186075, _186321), _186229))]]], (4910 ^ _115804) ^ [_186434] : [-(in(_186434, _186227)), in(_186434, relation_dom(_186075)), in(apply(_186075, _186434), _186229)]]]]], (12085 ^ _115804) ^ [] : [-(latt_str(12083 ^ []))], (10 ^ _115804) ^ [_115927, _115929, _115931] : [-(_115931 = _115927), _115931 = _115929, _115929 = _115927], (12631 ^ _115804) ^ [_302862, _302864] : [-(relation_of2(12629 ^ [_302862, _302864], _302864, _302862))], (1150 ^ _115804) ^ [_131095, _131097] : [-(well_founded_relation(_131095)), _131097 = _131095, well_founded_relation(_131097)], (11161 ^ _115804) ^ [_283981] : [ordinal(_283981), 11164 ^ _115804 : [(11165 ^ _115804) ^ [] : [-(epsilon_transitive(union(_283981)))], (11169 ^ _115804) ^ [] : [-(ordinal(union(_283981)))], (11167 ^ _115804) ^ [] : [-(epsilon_connected(union(_283981)))]]], (3188 ^ _115804) ^ [_161376, _161378, _161380] : [element(_161376, powerset(cartesian_product2(_161380, _161378))), -(relation(_161376))], (166 ^ _115804) ^ [_117961, _117963, _117965, _117967] : [-(v1_binop_1(_117965, _117961)), v1_binop_1(_117967, _117963), _117967 = _117965, _117963 = _117961], (10907 ^ _115804) ^ [_280575] : [empty_carrier(boole_lattice(_280575))], (15790 ^ _115804) ^ [_363813, _363815] : [ordinal(_363815), element(_363813, powerset(powerset(succ(_363815)))), 15798 ^ _115804 : [(15799 ^ _115804) ^ [_364018] : [in(_364018, 15797 ^ [_363813, _363815]), 15802 ^ _115804 : [(15803 ^ _115804) ^ [] : [-(in(_364018, powerset(_363815)))], (15808 ^ _115804) ^ [] : [-(_364018 = set_difference(15804 ^ [_363813, _363815, _364018], singleton(_363815)))], (15806 ^ _115804) ^ [] : [-(in(15804 ^ [_363813, _363815, _364018], _363813))]]], (15810 ^ _115804) ^ [_364194] : [-(in(_364194, 15797 ^ [_363813, _363815])), in(_364194, powerset(_363815)), 15815 ^ _115804 : [(15816 ^ _115804) ^ [_364304] : [in(_364304, _363813), _364194 = set_difference(_364304, singleton(_363815))]]]]], (14319 ^ _115804) ^ [_331816, _331818, _331820] : [-(empty_carrier(_331820)), transitive_relstr(_331820), rel_str(_331820), element(_331818, powerset(the_carrier(_331820))), finite(_331816), element(_331816, powerset(_331818)), 14347 ^ _115804 : [(14351 ^ _115804) ^ [] : [-(14349 ^ [_331816, _331818, _331820] = 14345 ^ [_331816, _331818, _331820])], (14370 ^ _115804) ^ [] : [-(relstr_set_smaller(_331820, 14361 ^ [_331816, _331818, _331820], 14364 ^ [_331816, _331818, _331820]))], (14363 ^ _115804) ^ [] : [-(14361 ^ [_331816, _331818, _331820] = 14346 ^ [_331816, _331818, _331820])], (14354 ^ _115804) ^ [] : [-(element(14352 ^ [_331816, _331818, _331820], the_carrier(_331820)))], (14366 ^ _115804) ^ [] : [-(element(14364 ^ [_331816, _331818, _331820], the_carrier(_331820)))], (14358 ^ _115804) ^ [] : [-(relstr_set_smaller(_331820, 14349 ^ [_331816, _331818, _331820], 14352 ^ [_331816, _331818, _331820]))], (14356 ^ _115804) ^ [] : [-(in(14352 ^ [_331816, _331818, _331820], _331818))], (14368 ^ _115804) ^ [] : [-(in(14364 ^ [_331816, _331818, _331820], _331818))], (14360 ^ _115804) ^ [] : [-(14344 ^ [_331816, _331818, _331820] = 14346 ^ [_331816, _331818, _331820])], (14372 ^ _115804) ^ [] : [14345 ^ [_331816, _331818, _331820] = 14346 ^ [_331816, _331818, _331820]], (14348 ^ _115804) ^ [] : [-(14344 ^ [_331816, _331818, _331820] = 14345 ^ [_331816, _331818, _331820])]], 14374 ^ _115804 : [(14375 ^ _115804) ^ [_332843] : [in(_332843, 14373 ^ [_331816, _331818, _331820]), 14379 ^ _115804 : [(14385 ^ _115804) ^ [] : [-(14383 ^ [_331816, _331818, _331820, _332843] = _332843)], (14382 ^ _115804) ^ [] : [-(14378 ^ [_331816, _331818, _331820, _332843] = _332843)], (14390 ^ _115804) ^ [] : [-(in(14386 ^ [_331816, _331818, _331820, _332843], _331818))], (14392 ^ _115804) ^ [] : [-(relstr_set_smaller(_331820, 14383 ^ [_331816, _331818, _331820, _332843], 14386 ^ [_331816, _331818, _331820, _332843]))], (14380 ^ _115804) ^ [] : [-(in(14378 ^ [_331816, _331818, _331820, _332843], powerset(_331816)))], (14388 ^ _115804) ^ [] : [-(element(14386 ^ [_331816, _331818, _331820, _332843], the_carrier(_331820)))]]], (14394 ^ _115804) ^ [_333162] : [-(in(_333162, 14373 ^ [_331816, _331818, _331820])), 14395 ^ _115804 : [(14396 ^ _115804) ^ [_333254] : [in(_333254, powerset(_331816)), _333254 = _333162, 14403 ^ _115804 : [(14404 ^ _115804) ^ [_333403] : [_333403 = _333162, 14407 ^ _115804 : [(14408 ^ _115804) ^ [_333483] : [element(_333483, the_carrier(_331820)), in(_333483, _331818), relstr_set_smaller(_331820, _333403, _333483)]]]]]]]]], (12454 ^ _115804) ^ [] : [-(with_suprema_relstr(12430 ^ []))], (12265 ^ _115804) ^ [] : [-(up_complete_relstr(12239 ^ []))], (12744 ^ _115804) ^ [] : [-(with_suprema_relstr(12732 ^ []))], (18714 ^ _115804) ^ [_413983, _413985, _413987] : [subset(unordered_pair(_413987, _413985), _413983), 18717 ^ _115804 : [(18718 ^ _115804) ^ [] : [-(in(_413987, _413983))], (18720 ^ _115804) ^ [] : [-(in(_413985, _413983))]]], (12638 ^ _115804) ^ [] : [empty(12636 ^ [])], (13416 ^ _115804) ^ [_313584, _313586, _313588, _313590] : [relation_of2(_313586, _313590, _313588), -(relation_dom_restr_as_relation_of(_313590, _313588, _313586, _313584) = relation_dom_restriction(_313586, _313584))], (14461 ^ _115804) ^ [_334413, _334415] : [14465 ^ _115804 : [(14482 ^ _115804) ^ [] : [-(in(14477 ^ [_334413, _334415], _334415))], (14470 ^ _115804) ^ [] : [-(ordered_pair(14467 ^ [_334413, _334415], 14468 ^ [_334413, _334415]) = 14463 ^ [_334413, _334415])], (14476 ^ _115804) ^ [] : [-(14462 ^ [_334413, _334415] = 14464 ^ [_334413, _334415])], (14472 ^ _115804) ^ [] : [-(in(14467 ^ [_334413, _334415], _334415))], (14480 ^ _115804) ^ [] : [-(ordered_pair(14477 ^ [_334413, _334415], 14478 ^ [_334413, _334415]) = 14464 ^ [_334413, _334415])], (14474 ^ _115804) ^ [] : [-(14468 ^ [_334413, _334415] = singleton(14467 ^ [_334413, _334415]))], (14486 ^ _115804) ^ [] : [14463 ^ [_334413, _334415] = 14464 ^ [_334413, _334415]], (14484 ^ _115804) ^ [] : [-(14478 ^ [_334413, _334415] = singleton(14477 ^ [_334413, _334415]))], (14466 ^ _115804) ^ [] : [-(14462 ^ [_334413, _334415] = 14463 ^ [_334413, _334415])]], 14488 ^ _115804 : [(14489 ^ _115804) ^ [_335016] : [in(_335016, 14487 ^ [_334413, _334415]), 14493 ^ _115804 : [(14504 ^ _115804) ^ [] : [-(14498 ^ [_334413, _334415, _335016] = singleton(14497 ^ [_334413, _334415, _335016]))], (14502 ^ _115804) ^ [] : [-(in(14497 ^ [_334413, _334415, _335016], _334415))], (14500 ^ _115804) ^ [] : [-(ordered_pair(14497 ^ [_334413, _334415, _335016], 14498 ^ [_334413, _334415, _335016]) = _335016)], (14494 ^ _115804) ^ [] : [-(in(14492 ^ [_334413, _334415, _335016], cartesian_product2(_334415, _334413)))], (14496 ^ _115804) ^ [] : [-(14492 ^ [_334413, _334415, _335016] = _335016)]]], (14506 ^ _115804) ^ [_335297] : [-(in(_335297, 14487 ^ [_334413, _334415])), 14507 ^ _115804 : [(14508 ^ _115804) ^ [_335382] : [in(_335382, cartesian_product2(_334415, _334413)), _335382 = _335297, 14515 ^ _115804 : [(14516 ^ _115804) ^ [_335525, _335527] : [ordered_pair(_335527, _335525) = _335297, in(_335527, _334415), _335525 = singleton(_335527)]]]]]]], (2292 ^ _115804) ^ [_148827, _148829, _148831, _148833] : [-(meet_of_latt_set(_148833, _148829) = meet_of_latt_set(_148831, _148827)), _148833 = _148831, _148829 = _148827], (2476 ^ _115804) ^ [_151537, _151539] : [_151539 = _151537, -(pair_second(_151539) = pair_second(_151537))], (19857 ^ _115804) ^ [_431992, _431994] : [-(in(_431992, _431994)), -(set_difference(_431994, singleton(_431992)) = _431994)], (17154 ^ _115804) ^ [_388718, _388720, _388722] : [relation(_388718), 17157 ^ _115804 : [(17158 ^ _115804) ^ [] : [in(_388722, relation_restriction(_388718, _388720)), 17161 ^ _115804 : [(17162 ^ _115804) ^ [] : [-(in(_388722, _388718))], (17164 ^ _115804) ^ [] : [-(in(_388722, cartesian_product2(_388720, _388720)))]]], (17166 ^ _115804) ^ [] : [-(in(_388722, relation_restriction(_388718, _388720))), in(_388722, _388718), in(_388722, cartesian_product2(_388720, _388720))]]], (15409 ^ _115804) ^ [_356139, _356141] : [ordinal(_356139), 15417 ^ _115804 : [(15432 ^ _115804) ^ [] : [-(15416 ^ [_356139, _356141] = 15428 ^ [_356139, _356141])], (15421 ^ _115804) ^ [] : [-(ordinal(15419 ^ [_356139, _356141]))], (15427 ^ _115804) ^ [] : [-(15414 ^ [_356139, _356141] = 15416 ^ [_356139, _356141])], (15423 ^ _115804) ^ [] : [-(15415 ^ [_356139, _356141] = 15419 ^ [_356139, _356141])], (15430 ^ _115804) ^ [] : [-(ordinal(15428 ^ [_356139, _356141]))], (15425 ^ _115804) ^ [] : [-(in(15419 ^ [_356139, _356141], _356141))], (15436 ^ _115804) ^ [] : [15415 ^ [_356139, _356141] = 15416 ^ [_356139, _356141]], (15434 ^ _115804) ^ [] : [-(in(15428 ^ [_356139, _356141], _356141))], (15418 ^ _115804) ^ [] : [-(15414 ^ [_356139, _356141] = 15415 ^ [_356139, _356141])]], 15438 ^ _115804 : [(15439 ^ _115804) ^ [_356704] : [in(_356704, 15437 ^ [_356139, _356141]), 15443 ^ _115804 : [(15453 ^ _115804) ^ [] : [-(in(15447 ^ [_356139, _356141, _356704], _356141))], (15451 ^ _115804) ^ [] : [-(_356704 = 15447 ^ [_356139, _356141, _356704])], (15449 ^ _115804) ^ [] : [-(ordinal(15447 ^ [_356139, _356141, _356704]))], (15444 ^ _115804) ^ [] : [-(in(15442 ^ [_356139, _356141, _356704], succ(_356139)))], (15446 ^ _115804) ^ [] : [-(15442 ^ [_356139, _356141, _356704] = _356704)]]], (15455 ^ _115804) ^ [_356948] : [-(in(_356948, 15437 ^ [_356139, _356141])), 15456 ^ _115804 : [(15457 ^ _115804) ^ [_357021] : [in(_357021, succ(_356139)), _357021 = _356948, 15464 ^ _115804 : [(15465 ^ _115804) ^ [_357151] : [ordinal(_357151), _356948 = _357151, in(_357151, _356141)]]]]]]], (5743 ^ _115804) ^ [_200628] : [5744 ^ _115804 : [(5745 ^ _115804) ^ [_200708, _200710] : [_200628 = ordered_pair(_200710, _200708)]], 5746 ^ _115804 : [(5757 ^ _115804) ^ [_200911] : [5760 ^ _115804 : [(5761 ^ _115804) ^ [] : [-(_200628 = ordered_pair(5758 ^ [_200628, _200911], 5759 ^ [_200628, _200911]))], (5763 ^ _115804) ^ [] : [_200911 = 5758 ^ [_200628, _200911]]], -(_200911 = pair_first(_200628))], (5747 ^ _115804) ^ [_200749] : [_200749 = pair_first(_200628), 5750 ^ _115804 : [(5751 ^ _115804) ^ [_200824, _200826] : [_200628 = ordered_pair(_200826, _200824), -(_200749 = _200826)]]]]], (1160 ^ _115804) ^ [_131220, _131222, _131224, _131226, _131228, _131230] : [-(relstr_set_smaller(_131228, _131224, _131220)), relstr_set_smaller(_131230, _131226, _131222), _131230 = _131228, _131226 = _131224, _131222 = _131220], (12491 ^ _115804) ^ [] : [-(heyting_relstr(12465 ^ []))], (10971 ^ _115804) ^ [_281397, _281399] : [10990 ^ _115804 : [(10995 ^ _115804) ^ [] : [-(transitive_relstr(rel_str_of(_281399, _281397)))], (10991 ^ _115804) ^ [] : [-(strict_rel_str(rel_str_of(_281399, _281397)))], (10993 ^ _115804) ^ [] : [-(reflexive_relstr(rel_str_of(_281399, _281397)))], (10997 ^ _115804) ^ [] : [-(antisymmetric_relstr(rel_str_of(_281399, _281397)))]], reflexive(_281397), antisymmetric(_281397), transitive(_281397), v1_partfun1(_281397, _281399, _281399), relation_of2(_281397, _281399, _281399)], (18231 ^ _115804) ^ [_406220, _406222] : [-(empty_carrier(_406220)), lattice(_406220), latt_str(_406220), 18242 ^ _115804 : [(18243 ^ _115804) ^ [_406399] : [element(_406399, the_carrier(_406220)), 18246 ^ _115804 : [(18247 ^ _115804) ^ [] : [latt_element_smaller(_406220, _406399, _406222), -(relstr_set_smaller(poset_of_lattice(_406220), _406222, cast_to_el_of_LattPOSet(_406220, _406399)))], (18253 ^ _115804) ^ [] : [relstr_set_smaller(poset_of_lattice(_406220), _406222, cast_to_el_of_LattPOSet(_406220, _406399)), -(latt_element_smaller(_406220, _406399, _406222))]]]]], (11175 ^ _115804) ^ [_284142, _284144] : [empty(cartesian_product2(_284144, _284142)), -(empty(_284144)), -(empty(_284142))], (6532 ^ _115804) ^ [_213990, _213992] : [-(empty(_213992)), 6535 ^ _115804 : [(6536 ^ _115804) ^ [] : [element(_213990, _213992), -(in(_213990, _213992))], (6542 ^ _115804) ^ [] : [in(_213990, _213992), -(element(_213990, _213992))]]], (15356 ^ _115804) ^ [_355138, _355140, _355142] : [element(_355140, powerset(powerset(_355142))), relation(_355138), function(_355138), 15372 ^ _115804 : [(15381 ^ _115804) ^ [] : [15370 ^ [_355138, _355140, _355142] = 15371 ^ [_355138, _355140, _355142]], (15379 ^ _115804) ^ [] : [-(in(relation_image(_355138, 15371 ^ [_355138, _355140, _355142]), _355140))], (15377 ^ _115804) ^ [] : [-(15369 ^ [_355138, _355140, _355142] = 15371 ^ [_355138, _355140, _355142])], (15373 ^ _115804) ^ [] : [-(15369 ^ [_355138, _355140, _355142] = 15370 ^ [_355138, _355140, _355142])], (15375 ^ _115804) ^ [] : [-(in(relation_image(_355138, 15370 ^ [_355138, _355140, _355142]), _355140))]], 15383 ^ _115804 : [(15384 ^ _115804) ^ [_355682] : [in(_355682, 15382 ^ [_355138, _355140, _355142]), 15388 ^ _115804 : [(15389 ^ _115804) ^ [] : [-(in(15387 ^ [_355138, _355140, _355142, _355682], powerset(relation_dom(_355138))))], (15393 ^ _115804) ^ [] : [-(in(relation_image(_355138, _355682), _355140))], (15391 ^ _115804) ^ [] : [-(15387 ^ [_355138, _355140, _355142, _355682] = _355682)]]], (15395 ^ _115804) ^ [_355868] : [-(in(_355868, 15382 ^ [_355138, _355140, _355142])), 15396 ^ _115804 : [(15397 ^ _115804) ^ [_355934] : [in(_355934, powerset(relation_dom(_355138))), _355934 = _355868, in(relation_image(_355138, _355868), _355140)]]]]], (1380 ^ _115804) ^ [_134296, _134298, _134300, _134302] : [-(filtered_subset(_134300, _134296)), filtered_subset(_134302, _134298), _134302 = _134300, _134298 = _134296], (18768 ^ _115804) ^ [_414714] : [-(lower_bounded_semilattstr(boole_lattice(_414714)))], (10929 ^ _115804) ^ [_280785] : [-(lower_bounded_semilattstr(boole_lattice(_280785)))], (10793 ^ _115804) ^ [_278995, _278997] : [v4_membered(_278997), 10796 ^ _115804 : [(10801 ^ _115804) ^ [] : [-(v3_membered(set_intersection2(_278997, _278995)))], (10797 ^ _115804) ^ [] : [-(v1_membered(set_intersection2(_278997, _278995)))], (10799 ^ _115804) ^ [] : [-(v2_membered(set_intersection2(_278997, _278995)))], (10803 ^ _115804) ^ [] : [-(v4_membered(set_intersection2(_278997, _278995)))]]], (1312 ^ _115804) ^ [_133402, _133404, _133406, _133408, _133410, _133412] : [-(is_often_in(_133410, _133406, _133402)), is_often_in(_133412, _133408, _133404), _133412 = _133410, _133408 = _133406, _133404 = _133402], (6374 ^ _115804) ^ [_211354] : [centered(_211354), 6377 ^ _115804 : [(6378 ^ _115804) ^ [] : [_211354 = empty_set], (6380 ^ _115804) ^ [_211463] : [-(_211463 = empty_set), subset(_211463, _211354), finite(_211463), set_meet(_211463) = empty_set]]], (5769 ^ _115804) ^ [_201112] : [top_str(_201112), 5772 ^ _115804 : [(5807 ^ _115804) ^ [] : [-(topological_space(_201112)), in(the_carrier(_201112), the_topology(_201112)), 5815 ^ _115804 : [(5816 ^ _115804) ^ [] : [-(element(5814 ^ [_201112], powerset(powerset(the_carrier(_201112)))))], (5820 ^ _115804) ^ [] : [in(union_of_subsets(the_carrier(_201112), 5814 ^ [_201112]), the_topology(_201112))], (5818 ^ _115804) ^ [] : [-(subset(5814 ^ [_201112], the_topology(_201112)))]], 5822 ^ _115804 : [(5832 ^ _115804) ^ [] : [in(subset_intersection2(the_carrier(_201112), 5821 ^ [_201112], 5824 ^ [_201112]), the_topology(_201112))], (5830 ^ _115804) ^ [] : [-(in(5824 ^ [_201112], the_topology(_201112)))], (5828 ^ _115804) ^ [] : [-(in(5821 ^ [_201112], the_topology(_201112)))], (5823 ^ _115804) ^ [] : [-(element(5821 ^ [_201112], powerset(the_carrier(_201112))))], (5826 ^ _115804) ^ [] : [-(element(5824 ^ [_201112], powerset(the_carrier(_201112))))]]], (5773 ^ _115804) ^ [] : [topological_space(_201112), 5776 ^ _115804 : [(5777 ^ _115804) ^ [] : [-(in(the_carrier(_201112), the_topology(_201112)))], (5789 ^ _115804) ^ [_201501] : [element(_201501, powerset(the_carrier(_201112))), 5792 ^ _115804 : [(5793 ^ _115804) ^ [_201600] : [element(_201600, powerset(the_carrier(_201112))), -(in(subset_intersection2(the_carrier(_201112), _201501, _201600), the_topology(_201112))), in(_201501, the_topology(_201112)), in(_201600, the_topology(_201112))]]], (5779 ^ _115804) ^ [_201346] : [element(_201346, powerset(powerset(the_carrier(_201112)))), subset(_201346, the_topology(_201112)), -(in(union_of_subsets(the_carrier(_201112), _201346), the_topology(_201112)))]]]]], (12031 ^ _115804) ^ [_296205, _296207, _296209, _296211] : [in(ordered_pair(_296211, _296209), cartesian_product2(_296207, _296205)), 12034 ^ _115804 : [(12035 ^ _115804) ^ [] : [-(in(_296211, _296207))], (12037 ^ _115804) ^ [] : [-(in(_296209, _296205))]]], (10335 ^ _115804) ^ [] : [-(ordinal(omega))], (12295 ^ _115804) ^ [_299252, _299254] : [-(function(12289 ^ [_299252, _299254]))], (18032 ^ _115804) ^ [_403234] : [-(empty(_403234)), 18038 ^ _115804 : [(18039 ^ _115804) ^ [] : [-(in(18037 ^ [_403234], _403234))], (18041 ^ _115804) ^ [] : [-(18037 ^ [_403234] = empty_set)]], 18043 ^ _115804 : [(18048 ^ _115804) ^ [] : [-(relation_dom(18042 ^ [_403234]) = _403234)], (18044 ^ _115804) ^ [] : [-(relation(18042 ^ [_403234]))], (18046 ^ _115804) ^ [] : [-(function(18042 ^ [_403234]))], (18050 ^ _115804) ^ [_403520] : [in(_403520, _403234), -(in(apply(18042 ^ [_403234], _403520), _403520))]]], (18372 ^ _115804) ^ [_408628, _408630] : [-(empty_carrier(_408628)), lattice(_408628), latt_str(_408628), 18383 ^ _115804 : [(18384 ^ _115804) ^ [_408809] : [element(_408809, the_carrier(poset_of_lattice(_408628))), 18387 ^ _115804 : [(18388 ^ _115804) ^ [] : [relstr_set_smaller(poset_of_lattice(_408628), _408630, _408809), -(latt_element_smaller(_408628, cast_to_el_of_lattice(_408628, _408809), _408630))], (18394 ^ _115804) ^ [] : [latt_element_smaller(_408628, cast_to_el_of_lattice(_408628, _408809), _408630), -(relstr_set_smaller(poset_of_lattice(_408628), _408630, _408809))]]]]], (13604 ^ _115804) ^ [_316156, _316158] : [-(empty(_316158)), relation(_316156), 13616 ^ _115804 : [(13633 ^ _115804) ^ [] : [-(13613 ^ [_316156, _316158] = 13631 ^ [_316156, _316158])], (13617 ^ _115804) ^ [] : [-(in(13613 ^ [_316156, _316158], _316158))], (13624 ^ _115804) ^ [_316759] : [in(_316759, 13618 ^ [_316156, _316158]), -(in(ordered_pair(13614 ^ [_316156, _316158], _316759), _316156))], (13620 ^ _115804) ^ [] : [-(13613 ^ [_316156, _316158] = 13618 ^ [_316156, _316158])], (13630 ^ _115804) ^ [] : [-(in(13613 ^ [_316156, _316158], _316158))], (13622 ^ _115804) ^ [] : [-(in(13614 ^ [_316156, _316158], 13618 ^ [_316156, _316158]))], (13637 ^ _115804) ^ [_317017] : [in(_317017, 13631 ^ [_316156, _316158]), -(in(ordered_pair(13615 ^ [_316156, _316158], _317017), _316156))], (13635 ^ _115804) ^ [] : [-(in(13615 ^ [_316156, _316158], 13631 ^ [_316156, _316158]))], (13643 ^ _115804) ^ [] : [13614 ^ [_316156, _316158] = 13615 ^ [_316156, _316158]]], 13645 ^ _115804 : [(13650 ^ _115804) ^ [_317327, _317329] : [in(ordered_pair(_317329, _317327), 13644 ^ [_316156, _316158]), 13653 ^ _115804 : [(13663 ^ _115804) ^ [_317587] : [in(_317587, 13657 ^ [_316156, _316158, _317327, _317329]), -(in(ordered_pair(_317327, _317587), _316156))], (13661 ^ _115804) ^ [] : [-(in(_317327, 13657 ^ [_316156, _316158, _317327, _317329]))], (13659 ^ _115804) ^ [] : [-(_317329 = 13657 ^ [_316156, _316158, _317327, _317329])], (13654 ^ _115804) ^ [] : [-(in(_317329, _316158))], (13656 ^ _115804) ^ [] : [-(in(_317329, _316158))]]], (13646 ^ _115804) ^ [] : [-(relation(13644 ^ [_316156, _316158]))], (13648 ^ _115804) ^ [] : [-(function(13644 ^ [_316156, _316158]))], (13669 ^ _115804) ^ [_317706, _317708] : [-(in(ordered_pair(_317708, _317706), 13644 ^ [_316156, _316158])), in(_317708, _316158), in(_317708, _316158), 13678 ^ _115804 : [(13679 ^ _115804) ^ [_317888] : [_317708 = _317888, in(_317706, _317888), 13687 ^ _115804 : [(13688 ^ _115804) ^ [] : [-(in(13686 ^ [_316156, _316158, _317706, _317708, _317888], _317888))], (13690 ^ _115804) ^ [] : [in(ordered_pair(_317706, 13686 ^ [_316156, _316158, _317706, _317708, _317888]), _316156)]]]]]]], (1234 ^ _115804) ^ [_132277, _132279, _132281, _132283, _132285, _132287] : [-(below_refl(_132285, _132281, _132277)), below_refl(_132287, _132283, _132279), _132287 = _132285, _132283 = _132281, _132279 = _132277], (10435 ^ _115804) ^ [_274203] : [-(with_suprema_relstr(boole_POSet(_274203)))], (20013 ^ _115804) ^ [_434328] : [-(relation_rng(identity_relation(_434328)) = _434328)], (14681 ^ _115804) ^ [_339543, _339545] : [topological_space(_339545), top_str(_339545), element(_339543, powerset(the_carrier(_339545))), 14697 ^ _115804 : [(14701 ^ _115804) ^ [] : [-(element(14699 ^ [_339543, _339545], powerset(the_carrier(_339545))))], (14718 ^ _115804) ^ [] : [-(subset(_339543, 14696 ^ [_339543, _339545]))], (14712 ^ _115804) ^ [] : [-(element(14710 ^ [_339543, _339545], powerset(the_carrier(_339545))))], (14703 ^ _115804) ^ [] : [-(14699 ^ [_339543, _339545] = 14695 ^ [_339543, _339545])], (14714 ^ _115804) ^ [] : [-(14710 ^ [_339543, _339545] = 14696 ^ [_339543, _339545])], (14707 ^ _115804) ^ [] : [-(subset(_339543, 14695 ^ [_339543, _339545]))], (14705 ^ _115804) ^ [] : [-(closed_subset(14699 ^ [_339543, _339545], _339545))], (14716 ^ _115804) ^ [] : [-(closed_subset(14710 ^ [_339543, _339545], _339545))], (14709 ^ _115804) ^ [] : [-(14694 ^ [_339543, _339545] = 14696 ^ [_339543, _339545])], (14720 ^ _115804) ^ [] : [14695 ^ [_339543, _339545] = 14696 ^ [_339543, _339545]], (14698 ^ _115804) ^ [] : [-(14694 ^ [_339543, _339545] = 14695 ^ [_339543, _339545])]], 14722 ^ _115804 : [(14723 ^ _115804) ^ [_340330] : [in(_340330, 14721 ^ [_339543, _339545]), 14727 ^ _115804 : [(14733 ^ _115804) ^ [] : [-(element(14731 ^ [_339543, _339545, _340330], powerset(the_carrier(_339545))))], (14730 ^ _115804) ^ [] : [-(14726 ^ [_339543, _339545, _340330] = _340330)], (14737 ^ _115804) ^ [] : [-(closed_subset(14731 ^ [_339543, _339545, _340330], _339545))], (14739 ^ _115804) ^ [] : [-(subset(_339543, _340330))], (14728 ^ _115804) ^ [] : [-(in(14726 ^ [_339543, _339545, _340330], powerset(the_carrier(_339545))))], (14735 ^ _115804) ^ [] : [-(14731 ^ [_339543, _339545, _340330] = _340330)]]], (14741 ^ _115804) ^ [_340612] : [-(in(_340612, 14721 ^ [_339543, _339545])), 14742 ^ _115804 : [(14743 ^ _115804) ^ [_340698] : [in(_340698, powerset(the_carrier(_339545))), _340698 = _340612, 14750 ^ _115804 : [(14751 ^ _115804) ^ [_340843] : [element(_340843, powerset(the_carrier(_339545))), _340843 = _340612, closed_subset(_340843, _339545), subset(_339543, _340612)]]]]]]], (11469 ^ _115804) ^ [_287866] : [-(upper_bounded_relstr(boole_POSet(_287866)))], (18062 ^ _115804) ^ [_403710] : [-(empty_carrier(_403710)), one_sorted_str(_403710), 18069 ^ _115804 : [(18070 ^ _115804) ^ [_403850] : [18085 ^ _115804 : [(18086 ^ _115804) ^ [_404068] : [is_eventually_in(_403710, _403850, _404068), -(is_often_in(_403710, _403850, _404068))]], -(empty_carrier(_403850)), transitive_relstr(_403850), directed_relstr(_403850), net_str(_403850, _403710)]]], (14882 ^ _115804) ^ [_343238, _343240] : [one_sorted_str(_343240), element(_343238, powerset(powerset(the_carrier(_343240)))), 14894 ^ _115804 : [(14909 ^ _115804) ^ [_343933] : [element(_343933, powerset(the_carrier(_343240))), _343933 = 14891 ^ [_343238, _343240], -(14893 ^ [_343238, _343240] = subset_complement(the_carrier(_343240), _343933))], (14907 ^ _115804) ^ [] : [-(in(14891 ^ [_343238, _343240], complements_of_subsets(the_carrier(_343240), _343238)))], (14897 ^ _115804) ^ [_343725] : [element(_343725, powerset(the_carrier(_343240))), _343725 = 14891 ^ [_343238, _343240], -(14892 ^ [_343238, _343240] = subset_complement(the_carrier(_343240), _343725))], (14919 ^ _115804) ^ [] : [14892 ^ [_343238, _343240] = 14893 ^ [_343238, _343240]], (14895 ^ _115804) ^ [] : [-(in(14891 ^ [_343238, _343240], complements_of_subsets(the_carrier(_343240), _343238)))]], 14921 ^ _115804 : [(14922 ^ _115804) ^ [_344233] : [in(_344233, 14920 ^ [_343238, _343240]), 14926 ^ _115804 : [(14927 ^ _115804) ^ [] : [-(in(14925 ^ [_343238, _343240, _344233], complements_of_subsets(the_carrier(_343240), _343238)))], (14931 ^ _115804) ^ [_344476] : [element(_344476, powerset(the_carrier(_343240))), _344476 = 14925 ^ [_343238, _343240, _344233], -(_344233 = subset_complement(the_carrier(_343240), _344476))], (14929 ^ _115804) ^ [] : [-(in(14925 ^ [_343238, _343240, _344233], complements_of_subsets(the_carrier(_343240), _343238)))]]], (14941 ^ _115804) ^ [_344653] : [-(in(_344653, 14920 ^ [_343238, _343240])), 14942 ^ _115804 : [(14943 ^ _115804) ^ [_344744] : [in(_344744, complements_of_subsets(the_carrier(_343240), _343238)), in(_344744, complements_of_subsets(the_carrier(_343240), _343238)), 14951 ^ _115804 : [(14952 ^ _115804) ^ [] : [-(element(14950 ^ [_343238, _343240, _344653, _344744], powerset(the_carrier(_343240))))], (14956 ^ _115804) ^ [] : [_344653 = subset_complement(the_carrier(_343240), 14950 ^ [_343238, _343240, _344653, _344744])], (14954 ^ _115804) ^ [] : [-(14950 ^ [_343238, _343240, _344653, _344744] = _344744)]]]]]]], (19823 ^ _115804) ^ [_431515] : [relation(_431515), 19828 ^ _115804 : [(19829 ^ _115804) ^ [] : [relation_dom(_431515) = empty_set], (19831 ^ _115804) ^ [] : [relation_rng(_431515) = empty_set]], -(_431515 = empty_set)], (12452 ^ _115804) ^ [] : [-(join_complete_relstr(12430 ^ []))], (10019 ^ _115804) ^ [] : [-(rel_str(10017 ^ []))], (16852 ^ _115804) ^ [_383781, _383783] : [-(finite(_383783)), subset(_383783, _383781), finite(_383781)], (18674 ^ _115804) ^ [_413373, _413375] : [in(_413373, _413375), -(apply(identity_relation(_413375), _413373) = _413373)], (11965 ^ _115804) ^ [_295242] : [relation(_295242), 11968 ^ _115804 : [(11991 ^ _115804) ^ [] : [11994 ^ _115804 : [(12003 ^ _115804) ^ [] : [in(ordered_pair(11993 ^ [_295242], 11992 ^ [_295242]), _295242)], (12001 ^ _115804) ^ [] : [in(ordered_pair(11992 ^ [_295242], 11993 ^ [_295242]), _295242)], (11999 ^ _115804) ^ [] : [11992 ^ [_295242] = 11993 ^ [_295242]], (11995 ^ _115804) ^ [] : [-(in(11992 ^ [_295242], relation_field(_295242)))], (11997 ^ _115804) ^ [] : [-(in(11993 ^ [_295242], relation_field(_295242)))]], -(connected(_295242))], (11969 ^ _115804) ^ [] : [connected(_295242), 11972 ^ _115804 : [(11973 ^ _115804) ^ [_295397, _295399] : [in(_295399, relation_field(_295242)), in(_295397, relation_field(_295242)), -(_295399 = _295397), -(in(ordered_pair(_295399, _295397), _295242)), -(in(ordered_pair(_295397, _295399), _295242))]]]]], (12293 ^ _115804) ^ [_299226, _299228] : [-(relation(12289 ^ [_299226, _299228]))], (10805 ^ _115804) ^ [_279160, _279162] : [v4_membered(_279162), 10808 ^ _115804 : [(10813 ^ _115804) ^ [] : [-(v3_membered(set_intersection2(_279160, _279162)))], (10809 ^ _115804) ^ [] : [-(v1_membered(set_intersection2(_279160, _279162)))], (10811 ^ _115804) ^ [] : [-(v2_membered(set_intersection2(_279160, _279162)))], (10815 ^ _115804) ^ [] : [-(v4_membered(set_intersection2(_279160, _279162)))]]], (12635 ^ _115804) ^ [_302918, _302920] : [-(function(12629 ^ [_302918, _302920]))], (9907 ^ _115804) ^ [_267401, _267403] : [one_sorted_str(_267403), net_str(_267401, _267403), 9914 ^ _115804 : [(9915 ^ _115804) ^ [_267515] : [subnetstr(_267515, _267403, _267401), -(net_str(_267515, _267403))]]], (6735 ^ _115804) ^ [_216958] : [rel_str(_216958), 6738 ^ _115804 : [(6765 ^ _115804) ^ [] : [6767 ^ _115804 : [(6774 ^ _115804) ^ [] : [-(element(6772 ^ [_216958], the_carrier(_216958)))], (6771 ^ _115804) ^ [] : [-(element(6769 ^ [_216958], the_carrier(_216958)))], (6778 ^ _115804) ^ [] : [-(related(_216958, 6769 ^ [_216958], 6772 ^ [_216958]))], (6780 ^ _115804) ^ [] : [related(_216958, 6766 ^ [_216958], 6772 ^ [_216958])], (6768 ^ _115804) ^ [] : [-(element(6766 ^ [_216958], the_carrier(_216958)))], (6776 ^ _115804) ^ [] : [-(related(_216958, 6766 ^ [_216958], 6769 ^ [_216958]))]], -(transitive_relstr(_216958))], (6739 ^ _115804) ^ [] : [transitive_relstr(_216958), 6742 ^ _115804 : [(6743 ^ _115804) ^ [_217115] : [element(_217115, the_carrier(_216958)), 6746 ^ _115804 : [(6747 ^ _115804) ^ [_217212] : [element(_217212, the_carrier(_216958)), 6750 ^ _115804 : [(6751 ^ _115804) ^ [_217298] : [element(_217298, the_carrier(_216958)), -(related(_216958, _217115, _217298)), related(_216958, _217115, _217212), related(_216958, _217212, _217298)]]]]]]]]], (2374 ^ _115804) ^ [_150048, _150050] : [_150050 = _150048, -(cast_to_subset(_150050) = cast_to_subset(_150048))], (4326 ^ _115804) ^ [_175651, _175653] : [-(set_intersection2(_175653, _175651) = set_intersection2(_175651, _175653))], (11688 ^ _115804) ^ [_291192, _291194, _291196] : [11711 ^ _115804 : [(11712 ^ _115804) ^ [_291585, _291587, _291589] : [latt_str_of(_291196, _291194, _291192) = latt_str_of(_291589, _291587, _291585), 11715 ^ _115804 : [(11716 ^ _115804) ^ [] : [-(_291196 = _291589)], (11720 ^ _115804) ^ [] : [-(_291192 = _291585)], (11718 ^ _115804) ^ [] : [-(_291194 = _291587)]]]], function(_291194), quasi_total(_291194, cartesian_product2(_291196, _291196), _291196), relation_of2(_291194, cartesian_product2(_291196, _291196), _291196), function(_291192), quasi_total(_291192, cartesian_product2(_291196, _291196), _291196), relation_of2(_291192, cartesian_product2(_291196, _291196), _291196)], (156 ^ _115804) ^ [_117836, _117838] : [-(preboolean(_117836)), _117838 = _117836, preboolean(_117838)], (7173 ^ _115804) ^ [_224289] : [ordinal(_224289), 7176 ^ _115804 : [(7177 ^ _115804) ^ [] : [-(epsilon_transitive(_224289))], (7179 ^ _115804) ^ [] : [-(epsilon_connected(_224289))]]], (2986 ^ _115804) ^ [_158822] : [v2_membered(_158822), 2989 ^ _115804 : [(2990 ^ _115804) ^ [_158887] : [element(_158887, powerset(_158822)), 2993 ^ _115804 : [(2994 ^ _115804) ^ [] : [-(v1_membered(_158887))], (2996 ^ _115804) ^ [] : [-(v2_membered(_158887))]]]]], (10733 ^ _115804) ^ [_278196] : [10748 ^ _115804 : [(10757 ^ _115804) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_278196)))], (10753 ^ _115804) ^ [] : [-(reflexive_relstr(poset_of_lattice(_278196)))], (10763 ^ _115804) ^ [] : [-(with_infima_relstr(poset_of_lattice(_278196)))], (10755 ^ _115804) ^ [] : [-(transitive_relstr(poset_of_lattice(_278196)))], (10751 ^ _115804) ^ [] : [-(strict_rel_str(poset_of_lattice(_278196)))], (10759 ^ _115804) ^ [] : [-(upper_bounded_relstr(poset_of_lattice(_278196)))], (10749 ^ _115804) ^ [] : [empty_carrier(poset_of_lattice(_278196))], (10761 ^ _115804) ^ [] : [-(with_suprema_relstr(poset_of_lattice(_278196)))]], -(empty_carrier(_278196)), lattice(_278196), upper_bounded_semilattstr(_278196), latt_str(_278196)], (10551 ^ _115804) ^ [_275843] : [-(relation(identity_relation(_275843)))], (9809 ^ _115804) ^ [] : [true___, -(true___)], (4551 ^ _115804) ^ [_179226] : [-(empty_carrier(_179226)), one_sorted_str(_179226), 4558 ^ _115804 : [(4559 ^ _115804) ^ [_179392] : [-(empty_carrier(_179392)), net_str(_179392, _179226), 4566 ^ _115804 : [(4584 ^ _115804) ^ [_179892] : [-(is_eventually_in(_179226, _179392, _179892)), 4585 ^ _115804 : [(4586 ^ _115804) ^ [_179961] : [element(_179961, the_carrier(_179392)), 4590 ^ _115804 : [(4591 ^ _115804) ^ [] : [-(element(4589 ^ [_179226, _179392, _179892, _179961], the_carrier(_179392)))], (4595 ^ _115804) ^ [] : [in(apply_netmap(_179226, _179392, 4589 ^ [_179226, _179392, _179892, _179961]), _179892)], (4593 ^ _115804) ^ [] : [-(related(_179392, _179961, 4589 ^ [_179226, _179392, _179892, _179961]))]]]]], (4567 ^ _115804) ^ [_179558] : [is_eventually_in(_179226, _179392, _179558), 4571 ^ _115804 : [(4572 ^ _115804) ^ [] : [-(element(4570 ^ [_179226, _179392, _179558], the_carrier(_179392)))], (4574 ^ _115804) ^ [_179721] : [element(_179721, the_carrier(_179392)), related(_179392, 4570 ^ [_179226, _179392, _179558], _179721), -(in(apply_netmap(_179226, _179392, _179721), _179558))]]]]]]], (9815 ^ _115804) ^ [_266253] : [meet_semilatt_str(_266253), -(one_sorted_str(_266253))], (3370 ^ _115804) ^ [_163670, _163672, _163674] : [relation_of2(_163670, _163674, _163672), 3385 ^ _115804 : [(3390 ^ _115804) ^ [] : [-(quasi_total(_163670, _163674, _163672))], (3386 ^ _115804) ^ [] : [-(function(_163670))], (3388 ^ _115804) ^ [] : [-(one_to_one(_163670))], (3392 ^ _115804) ^ [] : [-(onto(_163670, _163674, _163672))]], function(_163670), quasi_total(_163670, _163674, _163672), bijective(_163670, _163674, _163672)], (478 ^ _115804) ^ [_122029, _122031] : [-(bounded_relstr(_122029)), _122031 = _122029, bounded_relstr(_122031)], (12423 ^ _115804) ^ [] : [-(bounded_relstr(12401 ^ []))], (12528 ^ _115804) ^ [] : [empty_carrier(12524 ^ [])], (18722 ^ _115804) ^ [_414090, _414092, _414094] : [-(subset(unordered_pair(_414094, _414092), _414090)), in(_414094, _414090), in(_414092, _414090)], (19589 ^ _115804) ^ [_427519, _427521] : [relation(_427519), function(_427519), 19604 ^ _115804 : [(19605 ^ _115804) ^ [] : [-(_427521 = apply(_427519, apply(function_inverse(_427519), _427521)))], (19607 ^ _115804) ^ [] : [-(_427521 = apply(relation_composition(function_inverse(_427519), _427519), _427521))]], one_to_one(_427519), in(_427521, relation_rng(_427519))], (12415 ^ _115804) ^ [] : [-(with_infima_relstr(12401 ^ []))], (11105 ^ _115804) ^ [_283202, _283204] : [11112 ^ _115804 : [(11113 ^ _115804) ^ [] : [-(relation(relation_dom_restriction(_283204, _283202)))], (11115 ^ _115804) ^ [] : [-(function(relation_dom_restriction(_283204, _283202)))]], relation(_283204), function(_283204)], (7191 ^ _115804) ^ [_224501] : [relation(_224501), 7194 ^ _115804 : [(7212 ^ _115804) ^ [_224875] : [-(_224875 = relation_dom(_224501)), 7216 ^ _115804 : [(7217 ^ _115804) ^ [] : [-(in(7213 ^ [_224501, _224875], _224875))], (7219 ^ _115804) ^ [_225009] : [in(ordered_pair(7213 ^ [_224501, _224875], _225009), _224501)]], 7221 ^ _115804 : [(7222 ^ _115804) ^ [] : [-(in(ordered_pair(7213 ^ [_224501, _224875], 7220 ^ [_224501, _224875]), _224501))], (7224 ^ _115804) ^ [] : [in(7213 ^ [_224501, _224875], _224875)]]], (7195 ^ _115804) ^ [_224593] : [_224593 = relation_dom(_224501), 7198 ^ _115804 : [(7199 ^ _115804) ^ [_224680] : [in(_224680, _224593), -(in(ordered_pair(_224680, 7202 ^ [_224501, _224593, _224680]), _224501))], (7206 ^ _115804) ^ [_224775] : [7207 ^ _115804 : [(7208 ^ _115804) ^ [_224819] : [in(ordered_pair(_224775, _224819), _224501)]], -(in(_224775, _224593))]]]]], (19639 ^ _115804) ^ [_428289, _428291, _428293] : [in(_428293, _428291), element(_428291, powerset(_428289)), empty(_428289)], (12103 ^ _115804) ^ [] : [-(lattice(12083 ^ []))], (12575 ^ _115804) ^ [_302287] : [-(one_to_one(12567 ^ [_302287]))], (10337 ^ _115804) ^ [] : [empty(omega)], (13272 ^ _115804) ^ [_311408, _311410, _311412, _311414] : [-(function_invverse_img_as_carrier_subset(_311414, _311412, _311410, _311408) = relation_inverse_image(_311410, _311408)), one_sorted_str(_311414), one_sorted_str(_311412), function(_311410), quasi_total(_311410, the_carrier(_311414), the_carrier(_311412)), relation_of2(_311410, the_carrier(_311414), the_carrier(_311412))], (12624 ^ _115804) ^ [] : [-(epsilon_transitive(12614 ^ []))], (10659 ^ _115804) ^ [_277141, _277143] : [-(relation(set_union2(_277143, _277141))), relation(_277143), relation(_277141)], (10925 ^ _115804) ^ [_280747] : [-(distributive_lattstr(boole_lattice(_280747)))], (6014 ^ _115804) ^ [_205201] : [top_str(_205201), 6017 ^ _115804 : [(6018 ^ _115804) ^ [_205293] : [element(_205293, powerset(powerset(the_carrier(_205201)))), 6021 ^ _115804 : [(6036 ^ _115804) ^ [] : [6038 ^ _115804 : [(6039 ^ _115804) ^ [] : [-(element(6037 ^ [_205201, _205293], powerset(the_carrier(_205201))))], (6043 ^ _115804) ^ [] : [open_subset(6037 ^ [_205201, _205293], _205201)], (6041 ^ _115804) ^ [] : [-(in(6037 ^ [_205201, _205293], _205293))]], -(open_subsets(_205293, _205201))], (6022 ^ _115804) ^ [] : [open_subsets(_205293, _205201), 6025 ^ _115804 : [(6026 ^ _115804) ^ [_205437] : [element(_205437, powerset(the_carrier(_205201))), in(_205437, _205293), -(open_subset(_205437, _205201))]]]]]]], (12793 ^ _115804) ^ [_304815] : [-(reflexive(12787 ^ [_304815]))], (12768 ^ _115804) ^ [] : [-(relation(12766 ^ []))], (4010 ^ _115804) ^ [_171679] : [latt_str(_171679), 4029 ^ _115804 : [(4030 ^ _115804) ^ [] : [empty_carrier(_171679)], (4032 ^ _115804) ^ [] : [-(boolean_lattstr(_171679))]], -(empty_carrier(_171679)), distributive_lattstr(_171679), bounded_lattstr(_171679), complemented_lattstr(_171679)], (16646 ^ _115804) ^ [_380716, _380718] : [relation(_380716), -(subset(relation_rng_restriction(_380718, _380716), _380716))], (264 ^ _115804) ^ [_119222, _119224] : [-(v2_membered(_119222)), _119224 = _119222, v2_membered(_119224)], (12186 ^ _115804) ^ [] : [-(lower_bounded_semilattstr(12164 ^ []))], (146 ^ _115804) ^ [_117711, _117713] : [-(diff_closed(_117711)), _117713 = _117711, diff_closed(_117713)], (468 ^ _115804) ^ [_121904, _121906] : [-(relation_empty_yielding(_121904)), _121906 = _121904, relation_empty_yielding(_121906)], (12750 ^ _115804) ^ [] : [-(lower_bounded_relstr(12732 ^ []))], (10773 ^ _115804) ^ [_278721, _278723] : [v3_membered(_278723), 10776 ^ _115804 : [(10777 ^ _115804) ^ [] : [-(v1_membered(set_intersection2(_278723, _278721)))], (10781 ^ _115804) ^ [] : [-(v3_membered(set_intersection2(_278723, _278721)))], (10779 ^ _115804) ^ [] : [-(v2_membered(set_intersection2(_278723, _278721)))]]], (5973 ^ _115804) ^ [_204524, _204526] : [_204524 = singleton(_204526), 5976 ^ _115804 : [(5977 ^ _115804) ^ [_204603] : [in(_204603, _204524), -(_204603 = _204526)], (5983 ^ _115804) ^ [_204678] : [_204678 = _204526, -(in(_204678, _204524))]]], (20114 ^ _115804) ^ [_435897, _435899] : [disjoint(_435899, _435897), -(set_difference(_435899, _435897) = _435899)], (6411 ^ _115804) ^ [_211914] : [-(poset_of_lattice(_211914) = rel_str_of(the_carrier(_211914), k2_lattice3(_211914))), -(empty_carrier(_211914)), lattice(_211914), latt_str(_211914)], (5552 ^ _115804) ^ [_197408, _197410, _197412, _197414] : [-(_197408 = unordered_triple(_197414, _197412, _197410)), 5556 ^ _115804 : [(5561 ^ _115804) ^ [] : [5553 ^ [_197408, _197410, _197412, _197414] = _197412], (5557 ^ _115804) ^ [] : [-(in(5553 ^ [_197408, _197410, _197412, _197414], _197408))], (5559 ^ _115804) ^ [] : [5553 ^ [_197408, _197410, _197412, _197414] = _197414], (5563 ^ _115804) ^ [] : [5553 ^ [_197408, _197410, _197412, _197414] = _197410]], 5564 ^ _115804 : [(5575 ^ _115804) ^ [] : [in(5553 ^ [_197408, _197410, _197412, _197414], _197408)], (5565 ^ _115804) ^ [] : [-(5553 ^ [_197408, _197410, _197412, _197414] = _197414), -(5553 ^ [_197408, _197410, _197412, _197414] = _197412), -(5553 ^ [_197408, _197410, _197412, _197414] = _197410)]]], (80 ^ _115804) ^ [_116814, _116816, _116818, _116820] : [-(is_antisymmetric_in(_116818, _116814)), is_antisymmetric_in(_116820, _116816), _116820 = _116818, _116816 = _116814], (12391 ^ _115804) ^ [_300261] : [rel_str(_300261), 12395 ^ _115804 : [(12396 ^ _115804) ^ [] : [-(element(12394 ^ [_300261], powerset(the_carrier(_300261))))], (12400 ^ _115804) ^ [] : [-(filtered_subset(12394 ^ [_300261], _300261))], (12398 ^ _115804) ^ [] : [-(directed_subset(12394 ^ [_300261], _300261))]]], (10195 ^ _115804) ^ [_271176, _271178] : [-(finite(cartesian_product2(_271178, _271176))), finite(_271178), finite(_271176)], (11467 ^ _115804) ^ [_287847] : [-(lower_bounded_relstr(boole_POSet(_287847)))], (10249 ^ _115804) ^ [_271939] : [-(finite(singleton(_271939)))], (1422 ^ _115804) ^ [_134875, _134877, _134879, _134881] : [-(well_orders(_134879, _134875)), well_orders(_134881, _134877), _134881 = _134879, _134877 = _134875], (17459 ^ _115804) ^ [_393681] : [-(the_InternalRel(incl_POSet(_393681)) = inclusion_order(_393681))], (10279 ^ _115804) ^ [_272334] : [empty_carrier(boole_lattice(_272334))], (17475 ^ _115804) ^ [_393901, _393903] : [relation(_393901), 17478 ^ _115804 : [(17479 ^ _115804) ^ [] : [-(subset(relation_field(relation_restriction(_393901, _393903)), relation_field(_393901)))], (17481 ^ _115804) ^ [] : [-(subset(relation_field(relation_restriction(_393901, _393903)), _393903))]]], (11173 ^ _115804) ^ [] : [-(relation(empty_set))], (18852 ^ _115804) ^ [_415847] : [-(empty_carrier(_415847)), topological_space(_415847), top_str(_415847), 18863 ^ _115804 : [(18864 ^ _115804) ^ [_416040] : [18879 ^ _115804 : [(18880 ^ _115804) ^ [_416263] : [subnet(_416263, _415847, _416040), -(subset(lim_points_of_net(_415847, _416040), lim_points_of_net(_415847, _416263)))]], -(empty_carrier(_416040)), transitive_relstr(_416040), directed_relstr(_416040), net_str(_416040, _415847)]]], (9019 ^ _115804) ^ [_255346] : [one_sorted_str(_255346), -(element(empty_carrier_subset(_255346), powerset(the_carrier(_255346))))], (1252 ^ _115804) ^ [_132546, _132548, _132550, _132552, _132554, _132556] : [-(related_reflexive(_132554, _132550, _132546)), related_reflexive(_132556, _132552, _132548), _132556 = _132554, _132552 = _132550, _132548 = _132546], (1370 ^ _115804) ^ [_134171, _134173] : [-(empty(_134171)), _134173 = _134171, empty(_134173)], (12726 ^ _115804) ^ [_304082] : [empty(12722 ^ [_304082])], (11413 ^ _115804) ^ [_287217] : [-(transitive_relstr(boole_POSet(_287217)))], (13294 ^ _115804) ^ [_311743, _311745, _311747] : [relation_of2(_311743, _311747, _311745), -(relation_rng_as_subset(_311747, _311745, _311743) = relation_rng(_311743))], (17845 ^ _115804) ^ [_400363, _400365] : [relation(_400363), transitive(_400363), -(transitive(relation_restriction(_400363, _400365)))], (12208 ^ _115804) ^ [] : [-(latt_str(12206 ^ []))], (12220 ^ _115804) ^ [] : [-(meet_associative(12206 ^ []))], (7832 ^ _115804) ^ [_234672] : [relation(_234672), 7835 ^ _115804 : [(7836 ^ _115804) ^ [_234760] : [relation(_234760), 7839 ^ _115804 : [(7856 ^ _115804) ^ [] : [-(_234760 = relation_inverse(_234672)), 7861 ^ _115804 : [(7862 ^ _115804) ^ [] : [-(in(ordered_pair(7857 ^ [_234672, _234760], 7858 ^ [_234672, _234760]), _234760))], (7864 ^ _115804) ^ [] : [in(ordered_pair(7858 ^ [_234672, _234760], 7857 ^ [_234672, _234760]), _234672)]], 7865 ^ _115804 : [(7866 ^ _115804) ^ [] : [-(in(ordered_pair(7858 ^ [_234672, _234760], 7857 ^ [_234672, _234760]), _234672))], (7868 ^ _115804) ^ [] : [in(ordered_pair(7857 ^ [_234672, _234760], 7858 ^ [_234672, _234760]), _234760)]]], (7840 ^ _115804) ^ [] : [_234760 = relation_inverse(_234672), 7843 ^ _115804 : [(7844 ^ _115804) ^ [_234910, _234912] : [in(ordered_pair(_234912, _234910), _234760), -(in(ordered_pair(_234910, _234912), _234672))], (7850 ^ _115804) ^ [_234999, _235001] : [in(ordered_pair(_234999, _235001), _234672), -(in(ordered_pair(_235001, _234999), _234760))]]]]]]], (12224 ^ _115804) ^ [] : [-(join_absorbing(12206 ^ []))], (17290 ^ _115804) ^ [_390922, _390924] : [relation(_390922), -(relation_restriction(_390922, _390924) = relation_dom_restriction(relation_rng_restriction(_390924, _390922), _390924))], (13256 ^ _115804) ^ [_311160, _311162, _311164] : [relation_of2(_311160, _311164, _311162), -(relation_dom_as_subset(_311164, _311162, _311160) = relation_dom(_311160))], (12203 ^ _115804) ^ [] : [-(antisymmetric_relstr(12193 ^ []))], (10171 ^ _115804) ^ [_270853, _270855] : [10178 ^ _115804 : [(10179 ^ _115804) ^ [] : [-(relation(relation_dom_restriction(_270855, _270853)))], (10181 ^ _115804) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_270855, _270853)))]], relation(_270855), relation_empty_yielding(_270855)], (9099 ^ _115804) ^ [_256406] : [-(relation(inclusion_relation(_256406)))], (10379 ^ _115804) ^ [_273571] : [-(strict_rel_str(boole_POSet(_273571)))], (2928 ^ _115804) ^ [_158104] : [rel_str(_158104), 2951 ^ _115804 : [(2960 ^ _115804) ^ [] : [-(upper_bounded_relstr(_158104))], (2958 ^ _115804) ^ [] : [-(with_suprema_relstr(_158104))], (2956 ^ _115804) ^ [] : [-(antisymmetric_relstr(_158104))], (2952 ^ _115804) ^ [] : [empty_carrier(_158104)], (2954 ^ _115804) ^ [] : [-(reflexive_relstr(_158104))]], -(empty_carrier(_158104)), reflexive_relstr(_158104), antisymmetric_relstr(_158104), upper_bounded_relstr(_158104), join_complete_relstr(_158104)], (12493 ^ _115804) ^ [] : [-(complemented_relstr(12465 ^ []))], (17051 ^ _115804) ^ [_386941, _386943, _386945] : [relation(_386941), 17054 ^ _115804 : [(17055 ^ _115804) ^ [] : [in(_386945, relation_inverse_image(_386941, _386943)), 17059 ^ _115804 : [(17060 ^ _115804) ^ [] : [-(in(17058 ^ [_386941, _386943, _386945], relation_rng(_386941)))], (17064 ^ _115804) ^ [] : [-(in(17058 ^ [_386941, _386943, _386945], _386943))], (17062 ^ _115804) ^ [] : [-(in(ordered_pair(_386945, 17058 ^ [_386941, _386943, _386945]), _386941))]]], (17066 ^ _115804) ^ [] : [-(in(_386945, relation_inverse_image(_386941, _386943))), 17067 ^ _115804 : [(17068 ^ _115804) ^ [_387196] : [in(_387196, relation_rng(_386941)), in(ordered_pair(_386945, _387196), _386941), in(_387196, _386943)]]]]], (12349 ^ _115804) ^ [] : [-(relation(12347 ^ []))], (19906 ^ _115804) ^ [_432774] : [empty(_432774), -(_432774 = empty_set)], (5637 ^ _115804) ^ [_198732, _198734, _198736] : [relation_of2_as_subset(_198732, _198736, _198734), 5640 ^ _115804 : [(5641 ^ _115804) ^ [] : [5642 ^ _115804 : [(5643 ^ _115804) ^ [] : [-(_198734 = empty_set)], (5645 ^ _115804) ^ [] : [_198736 = empty_set]], 5646 ^ _115804 : [(5647 ^ _115804) ^ [] : [quasi_total(_198732, _198736, _198734), -(_198736 = relation_dom_as_subset(_198736, _198734, _198732))], (5653 ^ _115804) ^ [] : [_198736 = relation_dom_as_subset(_198736, _198734, _198732), -(quasi_total(_198732, _198736, _198734))]]], (5659 ^ _115804) ^ [] : [_198734 = empty_set, -(_198736 = empty_set), 5666 ^ _115804 : [(5667 ^ _115804) ^ [] : [quasi_total(_198732, _198736, _198734), -(_198732 = empty_set)], (5673 ^ _115804) ^ [] : [_198732 = empty_set, -(quasi_total(_198732, _198736, _198734))]]]]], (9921 ^ _115804) ^ [_267602, _267604, _267606] : [relation_of2_as_subset(_267602, _267606, _267604), -(element(_267602, powerset(cartesian_product2(_267606, _267604))))], (7357 ^ _115804) ^ [_227147, _227149] : [equipotent(_227149, _227147), 7361 ^ _115804 : [(7370 ^ _115804) ^ [] : [-(relation_rng(7360 ^ [_227147, _227149]) = _227147)], (7368 ^ _115804) ^ [] : [-(relation_dom(7360 ^ [_227147, _227149]) = _227149)], (7366 ^ _115804) ^ [] : [-(one_to_one(7360 ^ [_227147, _227149]))], (7362 ^ _115804) ^ [] : [-(relation(7360 ^ [_227147, _227149]))], (7364 ^ _115804) ^ [] : [-(function(7360 ^ [_227147, _227149]))]]], (10553 ^ _115804) ^ [_275864] : [-(function(identity_relation(_275864)))], (16311 ^ _115804) ^ [_374720, _374722] : [one_sorted_str(_374722), element(_374720, powerset(powerset(the_carrier(_374722)))), 16360 ^ _115804 : [(16365 ^ _115804) ^ [] : [-(relation_dom(16359 ^ [_374720, _374722]) = _374720)], (16361 ^ _115804) ^ [] : [-(relation(16359 ^ [_374720, _374722]))], (16363 ^ _115804) ^ [] : [-(function(16359 ^ [_374720, _374722]))], (16367 ^ _115804) ^ [_376004] : [in(_376004, _374720), 16370 ^ _115804 : [(16371 ^ _115804) ^ [_376094] : [element(_376094, powerset(the_carrier(_374722))), _376094 = _376004, -(apply(16359 ^ [_374720, _374722], _376004) = subset_complement(the_carrier(_374722), _376094))]]]], 16350 ^ _115804 : [(16356 ^ _115804) ^ [_375768] : [-(16352 ^ [_374720, _374722, _375768] = 16349 ^ [_374720, _374722])], (16351 ^ _115804) ^ [] : [-(in(16349 ^ [_374720, _374722], _374720))], (16354 ^ _115804) ^ [_375732] : [-(element(16352 ^ [_374720, _374722, _375732], powerset(the_carrier(_374722))))], (16358 ^ _115804) ^ [_375806] : [_375806 = subset_complement(the_carrier(_374722), 16352 ^ [_374720, _374722, _375806])]], 16325 ^ _115804 : [(16328 ^ _115804) ^ [_375230] : [element(_375230, powerset(the_carrier(_374722))), _375230 = 16322 ^ [_374720, _374722], -(16323 ^ [_374720, _374722] = subset_complement(the_carrier(_374722), _375230))], (16348 ^ _115804) ^ [] : [16323 ^ [_374720, _374722] = 16324 ^ [_374720, _374722]], (16326 ^ _115804) ^ [] : [-(in(16322 ^ [_374720, _374722], _374720))], (16338 ^ _115804) ^ [_375405] : [element(_375405, powerset(the_carrier(_374722))), _375405 = 16322 ^ [_374720, _374722], -(16324 ^ [_374720, _374722] = subset_complement(the_carrier(_374722), _375405))]]], (11311 ^ _115804) ^ [] : [-(v4_membered(empty_set))], (5268 ^ _115804) ^ [_192637] : [-(empty_carrier(_192637)), latt_str(_192637), 5275 ^ _115804 : [(5276 ^ _115804) ^ [_192781] : [element(_192781, the_carrier(_192637)), 5279 ^ _115804 : [(5294 ^ _115804) ^ [_193100] : [5296 ^ _115804 : [(5297 ^ _115804) ^ [] : [-(element(5295 ^ [_192637, _192781, _193100], the_carrier(_192637)))], (5301 ^ _115804) ^ [] : [below(_192637, _192781, 5295 ^ [_192637, _192781, _193100])], (5299 ^ _115804) ^ [] : [-(in(5295 ^ [_192637, _192781, _193100], _193100))]], -(latt_set_smaller(_192637, _192781, _193100))], (5280 ^ _115804) ^ [_192881] : [latt_set_smaller(_192637, _192781, _192881), 5283 ^ _115804 : [(5284 ^ _115804) ^ [_192957] : [element(_192957, the_carrier(_192637)), in(_192957, _192881), -(below(_192637, _192781, _192957))]]]]]]], (6443 ^ _115804) ^ [_212467] : [6444 ^ _115804 : [(6445 ^ _115804) ^ [_212547, _212549] : [_212467 = ordered_pair(_212549, _212547)]], 6446 ^ _115804 : [(6457 ^ _115804) ^ [_212750] : [6460 ^ _115804 : [(6461 ^ _115804) ^ [] : [-(_212467 = ordered_pair(6458 ^ [_212467, _212750], 6459 ^ [_212467, _212750]))], (6463 ^ _115804) ^ [] : [_212750 = 6459 ^ [_212467, _212750]]], -(_212750 = pair_second(_212467))], (6447 ^ _115804) ^ [_212588] : [_212588 = pair_second(_212467), 6450 ^ _115804 : [(6451 ^ _115804) ^ [_212663, _212665] : [_212467 = ordered_pair(_212665, _212663), -(_212588 = _212663)]]]]], (9193 ^ _115804) ^ [_257675, _257677, _257679] : [-(element(meet(_257679, _257677, _257675), the_carrier(_257679))), -(empty_carrier(_257679)), meet_semilatt_str(_257679), element(_257677, the_carrier(_257679)), element(_257675, the_carrier(_257679))], (1714 ^ _115804) ^ [_139610, _139612, _139614, _139616] : [-(a_2_2_lattice3(_139616, _139612) = a_2_2_lattice3(_139614, _139610)), _139616 = _139614, _139612 = _139610], (3182 ^ _115804) ^ [_161305] : [empty(_161305), -(relation(_161305))], (2962 ^ _115804) ^ [_158518] : [empty(_158518), 2965 ^ _115804 : [(2974 ^ _115804) ^ [] : [-(v5_membered(_158518))], (2972 ^ _115804) ^ [] : [-(v4_membered(_158518))], (2970 ^ _115804) ^ [] : [-(v3_membered(_158518))], (2966 ^ _115804) ^ [] : [-(v1_membered(_158518))], (2968 ^ _115804) ^ [] : [-(v2_membered(_158518))]]], (12143 ^ _115804) ^ [] : [-(strict_latt_str(12137 ^ []))], (11399 ^ _115804) ^ [_287046] : [empty(_287046), 11402 ^ _115804 : [(11403 ^ _115804) ^ [] : [-(empty(relation_rng(_287046)))], (11405 ^ _115804) ^ [] : [-(relation(relation_rng(_287046)))]]], (7027 ^ _115804) ^ [_221873, _221875] : [7029 ^ _115804 : [(7030 ^ _115804) ^ [] : [-(in(7028 ^ [_221873, _221875], _221875))], (7032 ^ _115804) ^ [] : [in(7028 ^ [_221873, _221875], _221873)]], -(subset(_221875, _221873))], (6623 ^ _115804) ^ [_215209] : [top_str(_215209), 6626 ^ _115804 : [(6627 ^ _115804) ^ [_215301] : [element(_215301, powerset(powerset(the_carrier(_215209)))), 6630 ^ _115804 : [(6645 ^ _115804) ^ [] : [6647 ^ _115804 : [(6648 ^ _115804) ^ [] : [-(element(6646 ^ [_215209, _215301], powerset(the_carrier(_215209))))], (6652 ^ _115804) ^ [] : [closed_subset(6646 ^ [_215209, _215301], _215209)], (6650 ^ _115804) ^ [] : [-(in(6646 ^ [_215209, _215301], _215301))]], -(closed_subsets(_215301, _215209))], (6631 ^ _115804) ^ [] : [closed_subsets(_215301, _215209), 6634 ^ _115804 : [(6635 ^ _115804) ^ [_215445] : [element(_215445, powerset(the_carrier(_215209))), in(_215445, _215301), -(closed_subset(_215445, _215209))]]]]]]], (12543 ^ _115804) ^ [_301940] : [-(empty(12539 ^ [_301940]))], (12099 ^ _115804) ^ [] : [-(meet_absorbing(12083 ^ []))], (16469 ^ _115804) ^ [_377941] : [-(function(16465 ^ [_377941]))], (12607 ^ _115804) ^ [] : [-(strict_rel_str(12601 ^ []))], (4786 ^ _115804) ^ [_183604] : [-(empty_carrier(_183604)), one_sorted_str(_183604), 4793 ^ _115804 : [(4794 ^ _115804) ^ [_183876] : [-(empty_carrier(_183876)), transitive_relstr(_183876), directed_relstr(_183876), net_str(_183876, _183604), 4809 ^ _115804 : [(4810 ^ _115804) ^ [_184226] : [-(empty_carrier(_184226)), transitive_relstr(_184226), directed_relstr(_184226), net_str(_184226, _183604), 4825 ^ _115804 : [(4826 ^ _115804) ^ [] : [subnet(_184226, _183604, _183876), 4830 ^ _115804 : [(4839 ^ _115804) ^ [_184872] : [element(_184872, the_carrier(_183876)), 4843 ^ _115804 : [(4844 ^ _115804) ^ [] : [-(element(4842 ^ [_183604, _183876, _184226, _184872], the_carrier(_184226)))], (4846 ^ _115804) ^ [_185069] : [element(_185069, the_carrier(_184226)), related(_184226, 4842 ^ [_183604, _183876, _184226, _184872], _185069), -(related(_183876, _184872, apply_on_set_and_struct(the_carrier(_184226), _183876, 4829 ^ [_183604, _183876, _184226], _185069)))]]], (4837 ^ _115804) ^ [] : [-(the_mapping(_183604, _184226) = function_of_composition(the_carrier(_184226), the_carrier(_183876), the_carrier(_183604), 4829 ^ [_183604, _183876, _184226], the_mapping(_183604, _183876)))], (4835 ^ _115804) ^ [] : [-(relation_of2_as_subset(4829 ^ [_183604, _183876, _184226], the_carrier(_184226), the_carrier(_183876)))], (4831 ^ _115804) ^ [] : [-(function(4829 ^ [_183604, _183876, _184226]))], (4833 ^ _115804) ^ [] : [-(quasi_total(4829 ^ [_183604, _183876, _184226], the_carrier(_184226), the_carrier(_183876)))]]], (4856 ^ _115804) ^ [] : [-(subnet(_184226, _183604, _183876)), 4857 ^ _115804 : [(4858 ^ _115804) ^ [_185309] : [function(_185309), quasi_total(_185309, the_carrier(_184226), the_carrier(_183876)), relation_of2_as_subset(_185309, the_carrier(_184226), the_carrier(_183876)), the_mapping(_183604, _184226) = function_of_composition(the_carrier(_184226), the_carrier(_183876), the_carrier(_183604), _185309, the_mapping(_183604, _183876)), 4874 ^ _115804 : [(4875 ^ _115804) ^ [] : [-(element(4873 ^ [_183604, _183876, _184226, _185309], the_carrier(_183876)))], (4877 ^ _115804) ^ [_185726] : [element(_185726, the_carrier(_184226)), 4881 ^ _115804 : [(4882 ^ _115804) ^ [] : [-(element(4880 ^ [_183604, _183876, _184226, _185309, _185726], the_carrier(_184226)))], (4886 ^ _115804) ^ [] : [related(_183876, 4873 ^ [_183604, _183876, _184226, _185309], apply_on_set_and_struct(the_carrier(_184226), _183876, _185309, 4880 ^ [_183604, _183876, _184226, _185309, _185726]))], (4884 ^ _115804) ^ [] : [-(related(_184226, _185726, 4880 ^ [_183604, _183876, _184226, _185309, _185726]))]]]]]]]]]]]]], (9789 ^ _115804) ^ [_265925, _265927, _265929, _265931] : [relation_of2(_265927, _265931, _265929), -(relation_of2_as_subset(relation_dom_restr_as_relation_of(_265931, _265929, _265927, _265925), _265931, _265929))], (8272 ^ _115804) ^ [_242946] : [one_sorted_str(_242946), 8275 ^ _115804 : [(8276 ^ _115804) ^ [_243024] : [element(_243024, powerset(powerset(the_carrier(_242946)))), 8279 ^ _115804 : [(8280 ^ _115804) ^ [] : [is_a_cover_of_carrier(_242946, _243024), -(cast_as_carrier_subset(_242946) = union_of_subsets(the_carrier(_242946), _243024))], (8286 ^ _115804) ^ [] : [cast_as_carrier_subset(_242946) = union_of_subsets(the_carrier(_242946), _243024), -(is_a_cover_of_carrier(_242946, _243024))]]]]], (18512 ^ _115804) ^ [_410821, _410823] : [relation(_410821), well_ordering(_410821), -(well_ordering(relation_restriction(_410821, _410823)))], (16774 ^ _115804) ^ [_382625, _382627] : [subset(_382627, _382625), -(set_union2(_382627, _382625) = _382625)], (12731 ^ _115804) ^ [] : [empty(12729 ^ [])], (12549 ^ _115804) ^ [_302006] : [-(one_to_one(12539 ^ [_302006]))], (12367 ^ _115804) ^ [] : [-(relation(12363 ^ []))], (11439 ^ _115804) ^ [_287525, _287527] : [11446 ^ _115804 : [(11447 ^ _115804) ^ [] : [-(empty(relation_composition(_287527, _287525)))], (11449 ^ _115804) ^ [] : [-(relation(relation_composition(_287527, _287525)))]], empty(_287527), relation(_287525)], (12691 ^ _115804) ^ [] : [-(rel_str(12689 ^ []))], (12151 ^ _115804) ^ [] : [-(meet_associative(12137 ^ []))], (1920 ^ _115804) ^ [_142949, _142951, _142953, _142955, _142957, _142959, _142961, _142963] : [-(apply_on_set_and_struct(_142963, _142959, _142955, _142951) = apply_on_set_and_struct(_142961, _142957, _142953, _142949)), _142963 = _142961, _142959 = _142957, _142955 = _142953, _142951 = _142949], (12579 ^ _115804) ^ [_302333] : [-(onto(12567 ^ [_302333], _302333, _302333))], (12358 ^ _115804) ^ [] : [-(relation(12356 ^ []))], (4360 ^ _115804) ^ [_176155, _176157, _176159] : [-(subset_intersection2(_176159, _176157, _176155) = subset_intersection2(_176159, _176155, _176157)), element(_176157, powerset(_176159)), element(_176155, powerset(_176159))], (12113 ^ _115804) ^ [_297274] : [12129 ^ _115804 : [(12134 ^ _115804) ^ [] : [-(filtered_subset(12128 ^ [_297274], _297274))], (12130 ^ _115804) ^ [] : [-(element(12128 ^ [_297274], powerset(the_carrier(_297274))))], (12132 ^ _115804) ^ [] : [empty(12128 ^ [_297274])], (12136 ^ _115804) ^ [] : [-(upper_relstr_subset(12128 ^ [_297274], _297274))]], -(empty_carrier(_297274)), reflexive_relstr(_297274), transitive_relstr(_297274), rel_str(_297274)], (10303 ^ _115804) ^ [_272563] : [-(upper_bounded_semilattstr(boole_lattice(_272563)))], (16021 ^ _115804) ^ [_368756, _368758] : [ordinal(_368756), 16025 ^ _115804 : [(16026 ^ _115804) ^ [_368897] : [in(_368897, 16024 ^ [_368756, _368758]), 16029 ^ _115804 : [(16035 ^ _115804) ^ [] : [-(_368897 = 16031 ^ [_368756, _368758, _368897])], (16030 ^ _115804) ^ [] : [-(in(_368897, succ(_368756)))], (16033 ^ _115804) ^ [] : [-(ordinal(16031 ^ [_368756, _368758, _368897]))], (16037 ^ _115804) ^ [] : [-(in(16031 ^ [_368756, _368758, _368897], _368758))]]], (16039 ^ _115804) ^ [_369094] : [-(in(_369094, 16024 ^ [_368756, _368758])), in(_369094, succ(_368756)), 16044 ^ _115804 : [(16045 ^ _115804) ^ [_369204] : [ordinal(_369204), _369094 = _369204, in(_369204, _368758)]]]]], (7460 ^ _115804) ^ [_228732] : [relation(_228732), function(_228732), 7467 ^ _115804 : [(7491 ^ _115804) ^ [_229276] : [-(_229276 = relation_rng(_228732)), 7504 ^ _115804 : [(7505 ^ _115804) ^ [] : [-(in(7503 ^ [_228732, _229276], relation_dom(_228732)))], (7509 ^ _115804) ^ [] : [in(7492 ^ [_228732, _229276], _229276)], (7507 ^ _115804) ^ [] : [-(7492 ^ [_228732, _229276] = apply(_228732, 7503 ^ [_228732, _229276]))]], 7495 ^ _115804 : [(7496 ^ _115804) ^ [] : [-(in(7492 ^ [_228732, _229276], _229276))], (7498 ^ _115804) ^ [_229419] : [in(_229419, relation_dom(_228732)), 7492 ^ [_228732, _229276] = apply(_228732, _229419)]]], (7468 ^ _115804) ^ [_228880] : [_228880 = relation_rng(_228732), 7471 ^ _115804 : [(7472 ^ _115804) ^ [_228975] : [in(_228975, _228880), 7476 ^ _115804 : [(7477 ^ _115804) ^ [] : [-(in(7475 ^ [_228732, _228880, _228975], relation_dom(_228732)))], (7479 ^ _115804) ^ [] : [-(_228975 = apply(_228732, 7475 ^ [_228732, _228880, _228975]))]]], (7481 ^ _115804) ^ [_229109] : [-(in(_229109, _228880)), 7482 ^ _115804 : [(7483 ^ _115804) ^ [_229156] : [in(_229156, relation_dom(_228732)), _229109 = apply(_228732, _229156)]]]]]]], (10921 ^ _115804) ^ [_280709] : [-(join_absorbing(boole_lattice(_280709)))], (7295 ^ _115804) ^ [_226318, _226320] : [-(_226318 = union(_226320)), 7308 ^ _115804 : [(7309 ^ _115804) ^ [] : [-(in(7296 ^ [_226318, _226320], 7307 ^ [_226318, _226320]))], (7313 ^ _115804) ^ [] : [in(7296 ^ [_226318, _226320], _226318)], (7311 ^ _115804) ^ [] : [-(in(7307 ^ [_226318, _226320], _226320))]], 7299 ^ _115804 : [(7300 ^ _115804) ^ [] : [-(in(7296 ^ [_226318, _226320], _226318))], (7302 ^ _115804) ^ [_226451] : [in(7296 ^ [_226318, _226320], _226451), in(_226451, _226320)]]], (15980 ^ _115804) ^ [_368066, _368068] : [-(in(_368066, 15970 ^ [_368068])), in(_368066, _368068), ordinal(_368066)], (1000 ^ _115804) ^ [_129024, _129026] : [-(connected(_129024)), _129026 = _129024, connected(_129026)], (20338 ^ _115804) ^ [_439121, _439123] : [relation(_439121), -(subset(relation_rng(relation_dom_restriction(_439121, _439123)), relation_rng(_439121)))], (9391 ^ _115804) ^ [_260248] : [-(strict_rel_str(boole_POSet(_260248)))], (10411 ^ _115804) ^ [_273935] : [-(transitive_relstr(boole_POSet(_273935)))], (12880 ^ _115804) ^ [] : [-(boolean_relstr(12850 ^ []))], (10131 ^ _115804) ^ [_270365, _270367] : [finite(_270367), -(finite(set_intersection2(_270367, _270365)))], (908 ^ _115804) ^ [_127820, _127822] : [-(being_limit_ordinal(_127820)), _127822 = _127820, being_limit_ordinal(_127822)], (11887 ^ _115804) ^ [_294116, _294118] : [element(_294116, powerset(_294118)), 11890 ^ _115804 : [(11891 ^ _115804) ^ [_294183] : [in(_294183, _294116), -(in(_294183, _294118))]]], (14206 ^ _115804) ^ [_328406, _328408] : [-(empty(_328408)), relation(_328406), 14213 ^ _115804 : [(14214 ^ _115804) ^ [_328763] : [14218 ^ _115804 : [(14238 ^ _115804) ^ [] : [-(14215 ^ [_328406, _328408, _328763] = 14217 ^ [_328406, _328408, _328763])], (14228 ^ _115804) ^ [] : [-(14220 ^ [_328406, _328408, _328763] = 14226 ^ [_328406, _328408, _328763])], (14242 ^ _115804) ^ [] : [-(ordered_pair(14239 ^ [_328406, _328408, _328763], 14240 ^ [_328406, _328408, _328763]) = 14217 ^ [_328406, _328408, _328763])], (14223 ^ _115804) ^ [] : [-(ordered_pair(14220 ^ [_328406, _328408, _328763], 14221 ^ [_328406, _328408, _328763]) = 14216 ^ [_328406, _328408, _328763])], (14247 ^ _115804) ^ [] : [-(14239 ^ [_328406, _328408, _328763] = 14245 ^ [_328406, _328408, _328763])], (14225 ^ _115804) ^ [] : [-(in(14220 ^ [_328406, _328408, _328763], _328408))], (14249 ^ _115804) ^ [] : [-(in(14240 ^ [_328406, _328408, _328763], 14245 ^ [_328406, _328408, _328763]))], (14232 ^ _115804) ^ [_329558] : [in(_329558, 14226 ^ [_328406, _328408, _328763]), -(in(ordered_pair(14221 ^ [_328406, _328408, _328763], _329558), _328406))], (14244 ^ _115804) ^ [] : [-(in(14239 ^ [_328406, _328408, _328763], _328408))], (14251 ^ _115804) ^ [_330008] : [in(_330008, 14245 ^ [_328406, _328408, _328763]), -(in(ordered_pair(14240 ^ [_328406, _328408, _328763], _330008), _328406))], (14230 ^ _115804) ^ [] : [-(in(14221 ^ [_328406, _328408, _328763], 14226 ^ [_328406, _328408, _328763]))], (14219 ^ _115804) ^ [] : [-(14215 ^ [_328406, _328408, _328763] = 14216 ^ [_328406, _328408, _328763])], (14257 ^ _115804) ^ [] : [14216 ^ [_328406, _328408, _328763] = 14217 ^ [_328406, _328408, _328763]]], 14259 ^ _115804 : [(14260 ^ _115804) ^ [_330297] : [in(_330297, 14258 ^ [_328406, _328408, _328763]), 14264 ^ _115804 : [(14271 ^ _115804) ^ [] : [-(ordered_pair(14268 ^ [_328406, _328408, _328763, _330297], 14269 ^ [_328406, _328408, _328763, _330297]) = _330297)], (14267 ^ _115804) ^ [] : [-(14263 ^ [_328406, _328408, _328763, _330297] = _330297)], (14278 ^ _115804) ^ [] : [-(in(14269 ^ [_328406, _328408, _328763, _330297], 14274 ^ [_328406, _328408, _328763, _330297]))], (14265 ^ _115804) ^ [] : [-(in(14263 ^ [_328406, _328408, _328763, _330297], cartesian_product2(_328408, _328763)))], (14273 ^ _115804) ^ [] : [-(in(14268 ^ [_328406, _328408, _328763, _330297], _328408))], (14280 ^ _115804) ^ [_330895] : [in(_330895, 14274 ^ [_328406, _328408, _328763, _330297]), -(in(ordered_pair(14269 ^ [_328406, _328408, _328763, _330297], _330895), _328406))], (14276 ^ _115804) ^ [] : [-(14268 ^ [_328406, _328408, _328763, _330297] = 14274 ^ [_328406, _328408, _328763, _330297])]]], (14286 ^ _115804) ^ [_331040] : [-(in(_331040, 14258 ^ [_328406, _328408, _328763])), 14287 ^ _115804 : [(14288 ^ _115804) ^ [_331158] : [in(_331158, cartesian_product2(_328408, _328763)), _331158 = _331040, 14295 ^ _115804 : [(14296 ^ _115804) ^ [_331334, _331336] : [ordered_pair(_331336, _331334) = _331040, in(_331336, _328408), 14303 ^ _115804 : [(14304 ^ _115804) ^ [_331493] : [_331336 = _331493, in(_331334, _331493), 14312 ^ _115804 : [(14313 ^ _115804) ^ [] : [-(in(14311 ^ [_328406, _328408, _328763, _331040, _331158, _331334, _331336, _331493], _331493))], (14315 ^ _115804) ^ [] : [in(ordered_pair(_331334, 14311 ^ [_328406, _328408, _328763, _331040, _331158, _331334, _331336, _331493]), _328406)]]]]]]]]]]]]], (12297 ^ _115804) ^ [_299280, _299282] : [-(quasi_total(12289 ^ [_299280, _299282], _299282, _299280))], (10251 ^ _115804) ^ [_271975] : [empty(powerset(_271975))], (10443 ^ _115804) ^ [_274319, _274321] : [relation_of2(_274319, singleton(_274321), singleton(_274321)), 10446 ^ _115804 : [(10447 ^ _115804) ^ [] : [empty_carrier(rel_str_of(singleton(_274321), _274319))], (10451 ^ _115804) ^ [] : [-(trivial_carrier(rel_str_of(singleton(_274321), _274319)))], (10449 ^ _115804) ^ [] : [-(strict_rel_str(rel_str_of(singleton(_274321), _274319)))]]], (19246 ^ _115804) ^ [_422124, _422126, _422128] : [-(element(_422128, _422124)), in(_422128, _422126), element(_422126, powerset(_422124))], (12519 ^ _115804) ^ [] : [-(with_infima_relstr(12503 ^ []))], (9385 ^ _115804) ^ [_260169] : [rel_str(_260169), -(element(bottom_of_relstr(_260169), the_carrier(_260169)))], (9627 ^ _115804) ^ [_263544, _263546] : [element(_263544, powerset(powerset(_263546))), -(element(meet_of_subsets(_263546, _263544), powerset(_263546)))], (11897 ^ _115804) ^ [_294266] : [relation(_294266), 11900 ^ _115804 : [(11915 ^ _115804) ^ [] : [11918 ^ _115804 : [(11919 ^ _115804) ^ [] : [-(in(ordered_pair(11916 ^ [_294266], 11917 ^ [_294266]), _294266))], (11923 ^ _115804) ^ [] : [11916 ^ [_294266] = 11917 ^ [_294266]], (11921 ^ _115804) ^ [] : [-(in(ordered_pair(11917 ^ [_294266], 11916 ^ [_294266]), _294266))]], -(antisymmetric(_294266))], (11901 ^ _115804) ^ [] : [antisymmetric(_294266), 11904 ^ _115804 : [(11905 ^ _115804) ^ [_294397, _294399] : [-(_294399 = _294397), in(ordered_pair(_294399, _294397), _294266), in(ordered_pair(_294397, _294399), _294266)]]]]], (528 ^ _115804) ^ [_122654, _122656] : [-(with_infima_relstr(_122654)), _122656 = _122654, with_infima_relstr(_122656)], (1800 ^ _115804) ^ [_140965, _140967, _140969, _140971] : [-(relation_restriction_as_relation_of(_140971, _140967) = relation_restriction_as_relation_of(_140969, _140965)), _140971 = _140969, _140967 = _140965], (17461 ^ _115804) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (12270 ^ _115804) ^ [] : [empty(12268 ^ [])], (12856 ^ _115804) ^ [] : [-(strict_rel_str(12850 ^ []))], (10403 ^ _115804) ^ [_273801] : [-(distributive_relstr(boole_POSet(_273801)))], (10859 ^ _115804) ^ [_279899, _279901] : [v3_membered(_279901), 10862 ^ _115804 : [(10863 ^ _115804) ^ [] : [-(v1_membered(set_difference(_279901, _279899)))], (10867 ^ _115804) ^ [] : [-(v3_membered(set_difference(_279901, _279899)))], (10865 ^ _115804) ^ [] : [-(v2_membered(set_difference(_279901, _279899)))]]], (2244 ^ _115804) ^ [_148071, _148073, _148075, _148077] : [-(cast_to_el_of_lattice(_148077, _148073) = cast_to_el_of_lattice(_148075, _148071)), _148077 = _148075, _148073 = _148071], (12263 ^ _115804) ^ [] : [-(bounded_relstr(12239 ^ []))], (20190 ^ _115804) ^ [_436938] : [-(empty_carrier(_436938)), one_sorted_str(_436938), 20197 ^ _115804 : [(20198 ^ _115804) ^ [_437093] : [-(empty_carrier(_437093)), net_str(_437093, _436938), 20205 ^ _115804 : [(20206 ^ _115804) ^ [_437236, _437238] : [subset(_437238, _437236), 20209 ^ _115804 : [(20210 ^ _115804) ^ [] : [is_eventually_in(_436938, _437093, _437238), -(is_eventually_in(_436938, _437093, _437236))], (20216 ^ _115804) ^ [] : [is_often_in(_436938, _437093, _437238), -(is_often_in(_436938, _437093, _437236))]]]]]]], (194 ^ _115804) ^ [_118347, _118349] : [-(modular_lattstr(_118347)), _118349 = _118347, modular_lattstr(_118349)], (11463 ^ _115804) ^ [_287809] : [-(with_infima_relstr(boole_POSet(_287809)))], (13000 ^ _115804) ^ [] : [-(join_commutative(12992 ^ []))], (684 ^ _115804) ^ [_124684, _124686, _124688, _124690] : [-(open_subsets(_124688, _124684)), open_subsets(_124690, _124686), _124690 = _124688, _124686 = _124684], (14820 ^ _115804) ^ [_342080, _342082] : [ordinal(_342082), element(_342080, powerset(powerset(succ(_342082)))), 14832 ^ _115804 : [(14838 ^ _115804) ^ [] : [-(14830 ^ [_342080, _342082] = set_difference(14834 ^ [_342080, _342082], singleton(_342082)))], (14836 ^ _115804) ^ [] : [-(in(14834 ^ [_342080, _342082], _342080))], (14845 ^ _115804) ^ [] : [-(14831 ^ [_342080, _342082] = set_difference(14841 ^ [_342080, _342082], singleton(_342082)))], (14833 ^ _115804) ^ [] : [-(14829 ^ [_342080, _342082] = 14830 ^ [_342080, _342082])], (14840 ^ _115804) ^ [] : [-(14829 ^ [_342080, _342082] = 14831 ^ [_342080, _342082])], (14847 ^ _115804) ^ [] : [14830 ^ [_342080, _342082] = 14831 ^ [_342080, _342082]], (14843 ^ _115804) ^ [] : [-(in(14841 ^ [_342080, _342082], _342080))]], 14849 ^ _115804 : [(14850 ^ _115804) ^ [_342667] : [in(_342667, 14848 ^ [_342080, _342082]), 14854 ^ _115804 : [(14860 ^ _115804) ^ [] : [-(in(14858 ^ [_342080, _342082, _342667], _342080))], (14855 ^ _115804) ^ [] : [-(in(14853 ^ [_342080, _342082, _342667], powerset(_342082)))], (14857 ^ _115804) ^ [] : [-(14853 ^ [_342080, _342082, _342667] = _342667)], (14862 ^ _115804) ^ [] : [-(_342667 = set_difference(14858 ^ [_342080, _342082, _342667], singleton(_342082)))]]], (14864 ^ _115804) ^ [_342890] : [-(in(_342890, 14848 ^ [_342080, _342082])), 14865 ^ _115804 : [(14866 ^ _115804) ^ [_342963] : [in(_342963, powerset(_342082)), _342963 = _342890, 14873 ^ _115804 : [(14874 ^ _115804) ^ [_343093] : [in(_343093, _342080), _342890 = set_difference(_343093, singleton(_342082))]]]]]]], (12586 ^ _115804) ^ [] : [empty_carrier(12582 ^ [])], (736 ^ _115804) ^ [_125388, _125390, _125392, _125394, _125396, _125398] : [-(full_subnetstr(_125396, _125392, _125388)), full_subnetstr(_125398, _125394, _125390), _125398 = _125396, _125394 = _125392, _125390 = _125388], (12306 ^ _115804) ^ [] : [-(reflexive_relstr(12298 ^ []))], (15972 ^ _115804) ^ [_367959, _367961] : [in(_367959, 15970 ^ [_367961]), 15975 ^ _115804 : [(15976 ^ _115804) ^ [] : [-(in(_367959, _367961))], (15978 ^ _115804) ^ [] : [-(ordinal(_367959))]]], (16783 ^ _115804) ^ [_382820, _382822, _382824] : [-(in(_382820, 16779 ^ [_382824])), in(_382822, 16779 ^ [_382824]), subset(_382820, _382822)], (9287 ^ _115804) ^ [_258913] : [-(rel_str(incl_POSet(_258913)))], (9351 ^ _115804) ^ [] : [true___, -(true___)], (17855 ^ _115804) ^ [_400492] : [antisymmetric_relstr(_400492), rel_str(_400492), 17862 ^ _115804 : [(17863 ^ _115804) ^ [_400628] : [element(_400628, the_carrier(_400492)), 17866 ^ _115804 : [(17867 ^ _115804) ^ [_400711] : [element(_400711, the_carrier(_400492)), -(_400628 = _400711), related(_400492, _400628, _400711), related(_400492, _400711, _400628)]]]]], (18209 ^ _115804) ^ [_405879] : [-(subset(empty_set, _405879))], (11285 ^ _115804) ^ [_285582] : [empty(relation_dom(_285582)), -(empty(_285582)), relation(_285582)], (9113 ^ _115804) ^ [_256572] : [-(reflexive(inclusion_order(_256572)))], (9711 ^ _115804) ^ [_264822, _264824, _264826, _264828] : [-(element(apply_on_set_and_struct2(_264828, _264826, _264824, _264822), the_carrier(_264826))), -(empty(_264828)), -(empty_carrier(_264826)), one_sorted_str(_264826), function(_264824), quasi_total(_264824, _264828, the_carrier(_264826)), relation_of2(_264824, _264828, the_carrier(_264826)), element(_264822, _264828)], (2590 ^ _115804) ^ [_153242, _153244] : [_153244 = _153242, -(identity_relation(_153244) = identity_relation(_153242))], (17343 ^ _115804) ^ [_391812, _391814, _391816] : [-(subset(_391816, set_intersection2(_391814, _391812))), subset(_391816, _391814), subset(_391816, _391812)], (12898 ^ _115804) ^ [] : [empty_carrier(12894 ^ [])], (16682 ^ _115804) ^ [_381259, _381261] : [element(_381259, powerset(powerset(_381261))), -(_381259 = empty_set), -(meet_of_subsets(_381261, complements_of_subsets(_381261, _381259)) = subset_complement(_381261, union_of_subsets(_381261, _381259)))], (12650 ^ _115804) ^ [_303108] : [proper_element(12646 ^ [_303108], powerset(_303108))], (4124 ^ _115804) ^ [_173073] : [rel_str(_173073), 4135 ^ _115804 : [(4136 ^ _115804) ^ [] : [empty_carrier(_173073)], (4138 ^ _115804) ^ [] : [-(upper_bounded_relstr(_173073))]], -(empty_carrier(_173073)), heyting_relstr(_173073)], (2224 ^ _115804) ^ [_147773, _147775, _147777, _147779] : [-(meet_on_relstr(_147779, _147775) = meet_on_relstr(_147777, _147773)), _147779 = _147777, _147775 = _147773], (13014 ^ _115804) ^ [_307599, _307601, _307603, _307605] : [-(k10_filter_1(_307605, _307603, _307601, _307599) = ordered_pair(_307601, _307599)), -(empty_carrier(_307605)), lattice(_307605), latt_str(_307605), -(empty_carrier(_307603)), lattice(_307603), latt_str(_307603), element(_307601, the_carrier(_307605)), element(_307599, the_carrier(_307603))], (3708 ^ _115804) ^ [_167874] : [latt_str(_167874), 3719 ^ _115804 : [(3720 ^ _115804) ^ [] : [empty_carrier(_167874)], (3724 ^ _115804) ^ [] : [-(upper_bounded_semilattstr(_167874))], (3722 ^ _115804) ^ [] : [-(lower_bounded_semilattstr(_167874))]], -(empty_carrier(_167874)), bounded_lattstr(_167874)], (12505 ^ _115804) ^ [] : [-(rel_str(12503 ^ []))], (12972 ^ _115804) ^ [_307048, _307050] : [12984 ^ _115804 : [(12989 ^ _115804) ^ [] : [-(strict_net_str(12983 ^ [_307048, _307050], _307050))], (12985 ^ _115804) ^ [] : [-(subnetstr(12983 ^ [_307048, _307050], _307050, _307048))], (12987 ^ _115804) ^ [] : [empty_carrier(12983 ^ [_307048, _307050])], (12991 ^ _115804) ^ [] : [-(full_subnetstr(12983 ^ [_307048, _307050], _307050, _307048))]], one_sorted_str(_307050), -(empty_carrier(_307048)), net_str(_307048, _307050)], (2574 ^ _115804) ^ [_153008, _153010] : [_153010 = _153008, -(identity_on_carrier(_153010) = identity_on_carrier(_153008))], (10205 ^ _115804) ^ [_271305, _271307] : [10220 ^ _115804 : [(10225 ^ _115804) ^ [] : [-(function(the_mapping(_271307, _271305)))], (10221 ^ _115804) ^ [] : [empty(the_mapping(_271307, _271305))], (10223 ^ _115804) ^ [] : [-(relation(the_mapping(_271307, _271305)))], (10227 ^ _115804) ^ [] : [-(quasi_total(the_mapping(_271307, _271305), the_carrier(_271305), the_carrier(_271307)))]], -(empty_carrier(_271307)), one_sorted_str(_271307), -(empty_carrier(_271305)), net_str(_271305, _271307)], (19073 ^ _115804) ^ [_419308, _419310, _419312, _419314] : [function(_419308), quasi_total(_419308, _419314, _419312), relation_of2_as_subset(_419308, _419314, _419312), -(_419312 = empty_set), 19088 ^ _115804 : [(19089 ^ _115804) ^ [_419570] : [in(_419570, relation_inverse_image(_419308, _419310)), 19092 ^ _115804 : [(19093 ^ _115804) ^ [] : [-(in(_419570, _419314))], (19095 ^ _115804) ^ [] : [-(in(apply(_419308, _419570), _419310))]]], (19097 ^ _115804) ^ [_419687] : [-(in(_419687, relation_inverse_image(_419308, _419310))), in(_419687, _419314), in(apply(_419308, _419687), _419310)]]], (5892 ^ _115804) ^ [_203302, _203304] : [-(_203304 = empty_set), 5895 ^ _115804 : [(5919 ^ _115804) ^ [] : [-(_203302 = set_meet(_203304)), 5923 ^ _115804 : [(5924 ^ _115804) ^ [] : [-(in(5920 ^ [_203302, _203304], _203302))], (5929 ^ _115804) ^ [] : [in(5920 ^ [_203302, _203304], 5925 ^ [_203302, _203304])], (5927 ^ _115804) ^ [] : [-(in(5925 ^ [_203302, _203304], _203304))]], 5930 ^ _115804 : [(5937 ^ _115804) ^ [] : [in(5920 ^ [_203302, _203304], _203302)], (5931 ^ _115804) ^ [_203939] : [in(_203939, _203304), -(in(5920 ^ [_203302, _203304], _203939))]]], (5896 ^ _115804) ^ [] : [_203302 = set_meet(_203304), 5899 ^ _115804 : [(5910 ^ _115804) ^ [_203595] : [5912 ^ _115804 : [(5913 ^ _115804) ^ [] : [-(in(5911 ^ [_203302, _203304, _203595], _203304))], (5915 ^ _115804) ^ [] : [in(_203595, 5911 ^ [_203302, _203304, _203595])]], -(in(_203595, _203302))], (5900 ^ _115804) ^ [_203449] : [in(_203449, _203302), 5903 ^ _115804 : [(5904 ^ _115804) ^ [_203514] : [in(_203514, _203304), -(in(_203449, _203514))]]]]]]], (2530 ^ _115804) ^ [_152324, _152326, _152328, _152330] : [-(set_union2(_152330, _152326) = set_union2(_152328, _152324)), _152330 = _152328, _152326 = _152324], (19323 ^ _115804) ^ [_423137] : [topological_space(_423137), top_str(_423137), 19330 ^ _115804 : [(19331 ^ _115804) ^ [_423251] : [element(_423251, powerset(the_carrier(_423137))), -(open_subset(interior(_423137, _423251), _423137))]]], (8165 ^ _115804) ^ [_241206] : [relation(_241206), function(_241206), 8172 ^ _115804 : [(8191 ^ _115804) ^ [] : [8194 ^ _115804 : [(8199 ^ _115804) ^ [] : [-(apply(_241206, 8192 ^ [_241206]) = apply(_241206, 8193 ^ [_241206]))], (8195 ^ _115804) ^ [] : [-(in(8192 ^ [_241206], relation_dom(_241206)))], (8197 ^ _115804) ^ [] : [-(in(8193 ^ [_241206], relation_dom(_241206)))], (8201 ^ _115804) ^ [] : [8192 ^ [_241206] = 8193 ^ [_241206]]], -(one_to_one(_241206))], (8173 ^ _115804) ^ [] : [one_to_one(_241206), 8176 ^ _115804 : [(8177 ^ _115804) ^ [_241395, _241397] : [-(_241397 = _241395), in(_241397, relation_dom(_241206)), in(_241395, relation_dom(_241206)), apply(_241206, _241397) = apply(_241206, _241395)]]]]], (12330 ^ _115804) ^ [] : [-(strict_rel_str(12326 ^ []))], (19683 ^ _115804) ^ [_428874] : [relation(_428874), 19686 ^ _115804 : [(19687 ^ _115804) ^ [] : [well_founded_relation(_428874), -(is_well_founded_in(_428874, relation_field(_428874)))], (19693 ^ _115804) ^ [] : [is_well_founded_in(_428874, relation_field(_428874)), -(well_founded_relation(_428874))]]], (11419 ^ _115804) ^ [_287274] : [-(upper_bounded_relstr(boole_POSet(_287274)))], (7598 ^ _115804) ^ [_230865] : [relation(_230865), 7601 ^ _115804 : [(7619 ^ _115804) ^ [_231239] : [-(_231239 = relation_rng(_230865)), 7623 ^ _115804 : [(7624 ^ _115804) ^ [] : [-(in(7620 ^ [_230865, _231239], _231239))], (7626 ^ _115804) ^ [_231373] : [in(ordered_pair(_231373, 7620 ^ [_230865, _231239]), _230865)]], 7628 ^ _115804 : [(7629 ^ _115804) ^ [] : [-(in(ordered_pair(7627 ^ [_230865, _231239], 7620 ^ [_230865, _231239]), _230865))], (7631 ^ _115804) ^ [] : [in(7620 ^ [_230865, _231239], _231239)]]], (7602 ^ _115804) ^ [_230957] : [_230957 = relation_rng(_230865), 7605 ^ _115804 : [(7606 ^ _115804) ^ [_231044] : [in(_231044, _230957), -(in(ordered_pair(7609 ^ [_230865, _230957, _231044], _231044), _230865))], (7613 ^ _115804) ^ [_231139] : [7614 ^ _115804 : [(7615 ^ _115804) ^ [_231183] : [in(ordered_pair(_231183, _231139), _230865)]], -(in(_231139, _230957))]]]]], (12748 ^ _115804) ^ [] : [-(complete_relstr(12732 ^ []))], (12523 ^ _115804) ^ [] : [-(trivial_carrier(12503 ^ []))], (10727 ^ _115804) ^ [_278117, _278119] : [-(empty(_278119)), empty(set_union2(_278119, _278117))], (12444 ^ _115804) ^ [] : [-(lower_bounded_relstr(12430 ^ []))], (2402 ^ _115804) ^ [_150452, _150454] : [_150454 = _150452, -(bottom_of_semilattstr(_150454) = bottom_of_semilattstr(_150452))], (7752 ^ _115804) ^ [_233317] : [_233317 = union(_233317), -(being_limit_ordinal(_233317))], (9101 ^ _115804) ^ [] : [true___, -(true___)], (956 ^ _115804) ^ [_128456, _128458] : [-(lower_bounded_semilattstr(_128456)), _128458 = _128456, lower_bounded_semilattstr(_128458)], (18949 ^ _115804) ^ [_417226] : [topological_space(_417226), top_str(_417226), 18956 ^ _115804 : [(18957 ^ _115804) ^ [_417371] : [element(_417371, powerset(powerset(the_carrier(_417226)))), 18963 ^ _115804 : [(18964 ^ _115804) ^ [] : [-(element(18962 ^ [_417226, _417371], powerset(the_carrier(_417226))))], (18968 ^ _115804) ^ [] : [closed_subset(18962 ^ [_417226, _417371], _417226)], (18966 ^ _115804) ^ [] : [-(in(18962 ^ [_417226, _417371], _417371))]], -(closed_subset(meet_of_subsets(the_carrier(_417226), _417371), _417226))]]], (2254 ^ _115804) ^ [_148220, _148222, _148224, _148226, _148228, _148230, _148232, _148234] : [-(ordered_pair_as_product_element(_148234, _148230, _148226, _148222) = ordered_pair_as_product_element(_148232, _148228, _148224, _148220)), _148234 = _148232, _148230 = _148228, _148226 = _148224, _148222 = _148220], (10783 ^ _115804) ^ [_278858, _278860] : [v3_membered(_278860), 10786 ^ _115804 : [(10787 ^ _115804) ^ [] : [-(v1_membered(set_intersection2(_278858, _278860)))], (10791 ^ _115804) ^ [] : [-(v3_membered(set_intersection2(_278858, _278860)))], (10789 ^ _115804) ^ [] : [-(v2_membered(set_intersection2(_278858, _278860)))]]], (12139 ^ _115804) ^ [] : [-(latt_str(12137 ^ []))], (2428 ^ _115804) ^ [_150835, _150837, _150839, _150841] : [-(interior(_150841, _150837) = interior(_150839, _150835)), _150841 = _150839, _150837 = _150835], (18805 ^ _115804) ^ [_415184, _415186] : [disjoint(_415186, _415184), 18806 ^ _115804 : [(18807 ^ _115804) ^ [_415224] : [in(_415224, _415186), in(_415224, _415184)]]], (40 ^ _115804) ^ [_116314, _116316] : [-(v1_int_1(_116314)), _116316 = _116314, v1_int_1(_116316)], (9783 ^ _115804) ^ [_265846, _265848] : [relation(_265846), -(relation(relation_rng_restriction(_265848, _265846)))], (17559 ^ _115804) ^ [_395582, _395584, _395586, _395588] : [function(_395582), quasi_total(_395582, _395588, _395586), relation_of2_as_subset(_395582, _395588, _395586), 17570 ^ _115804 : [(17571 ^ _115804) ^ [_395791] : [relation(_395791), function(_395791), in(_395584, _395588), -(_395586 = empty_set), -(apply(relation_composition(_395582, _395791), _395584) = apply(_395791, apply(_395582, _395584)))]]], (12998 ^ _115804) ^ [] : [-(strict_latt_str(12992 ^ []))], (10401 ^ _115804) ^ [_273780] : [-(join_complete_relstr(boole_POSet(_273780)))], (8474 ^ _115804) ^ [_246650, _246652] : [-(proper_subset(_246652, _246650)), subset(_246652, _246650), -(_246652 = _246650)], (10629 ^ _115804) ^ [] : [-(empty(empty_set))], (12908 ^ _115804) ^ [] : [-(with_suprema_relstr(12894 ^ []))], (20057 ^ _115804) ^ [_434960] : [-(empty_carrier(_434960)), lattice(_434960), latt_str(_434960), 20068 ^ _115804 : [(20069 ^ _115804) ^ [_435149] : [element(_435149, the_carrier(_434960)), 20072 ^ _115804 : [(20073 ^ _115804) ^ [_435234] : [element(_435234, the_carrier(_434960)), 20076 ^ _115804 : [(20077 ^ _115804) ^ [] : [below_refl(_434960, _435149, _435234), -(related_reflexive(poset_of_lattice(_434960), cast_to_el_of_LattPOSet(_434960, _435149), cast_to_el_of_LattPOSet(_434960, _435234)))], (20083 ^ _115804) ^ [] : [related_reflexive(poset_of_lattice(_434960), cast_to_el_of_LattPOSet(_434960, _435149), cast_to_el_of_LattPOSet(_434960, _435234)), -(below_refl(_434960, _435149, _435234))]]]]]]], (11423 ^ _115804) ^ [_287312] : [-(with_suprema_relstr(boole_POSet(_287312)))], (10583 ^ _115804) ^ [_276288] : [-(join_associative(boole_lattice(_276288)))], (11475 ^ _115804) ^ [_287923] : [-(join_complete_relstr(boole_POSet(_287923)))], (3678 ^ _115804) ^ [_167487, _167489] : [relation_of2(_167487, _167489, _167489), 3697 ^ _115804 : [(3706 ^ _115804) ^ [] : [-(bijective(_167487, _167489, _167489))], (3704 ^ _115804) ^ [] : [-(onto(_167487, _167489, _167489))], (3702 ^ _115804) ^ [] : [-(quasi_total(_167487, _167489, _167489))], (3698 ^ _115804) ^ [] : [-(function(_167487))], (3700 ^ _115804) ^ [] : [-(one_to_one(_167487))]], function(_167487), v1_partfun1(_167487, _167489, _167489), reflexive(_167487), quasi_total(_167487, _167489, _167489)], (10063 ^ _115804) ^ [_269495] : [-(element(10061 ^ [_269495], _269495))], (15634 ^ _115804) ^ [_360600] : [ordinal(_360600), 15638 ^ _115804 : [(15675 ^ _115804) ^ [_361628] : [-(in(_361628, 15637 ^ [_360600])), in(_361628, succ(_360600)), 15680 ^ _115804 : [(15681 ^ _115804) ^ [_361793] : [ordinal(_361793), _361628 = _361793, 15688 ^ _115804 : [(15694 ^ _115804) ^ [] : [15690 ^ [_360600, _361628, _361793] = empty_set], (15689 ^ _115804) ^ [] : [-(in(_361793, omega))], (15692 ^ _115804) ^ [] : [-(element(15690 ^ [_360600, _361628, _361793], powerset(powerset(_361793))))], (15696 ^ _115804) ^ [_362102] : [in(_362102, 15690 ^ [_360600, _361628, _361793]), 15700 ^ _115804 : [(15701 ^ _115804) ^ [] : [-(in(15699 ^ [_360600, _361628, _361793, _362102], 15690 ^ [_360600, _361628, _361793]))], (15705 ^ _115804) ^ [] : [15699 ^ [_360600, _361628, _361793, _362102] = _362102], (15703 ^ _115804) ^ [] : [-(subset(_362102, 15699 ^ [_360600, _361628, _361793, _362102]))]]]]]]], (15639 ^ _115804) ^ [_360859] : [in(_360859, 15637 ^ [_360600]), 15642 ^ _115804 : [(15648 ^ _115804) ^ [] : [-(_360859 = 15644 ^ [_360600, _360859])], (15643 ^ _115804) ^ [] : [-(in(_360859, succ(_360600)))], (15646 ^ _115804) ^ [] : [-(ordinal(15644 ^ [_360600, _360859]))], (15650 ^ _115804) ^ [] : [in(15644 ^ [_360600, _360859], omega), 15653 ^ _115804 : [(15654 ^ _115804) ^ [_361213] : [element(_361213, powerset(powerset(15644 ^ [_360600, _360859]))), -(_361213 = empty_set), 15662 ^ _115804 : [(15663 ^ _115804) ^ [] : [-(in(15661 ^ [_360600, _360859, _361213], _361213))], (15665 ^ _115804) ^ [_361437] : [-(_361437 = 15661 ^ [_360600, _360859, _361213]), in(_361437, _361213), subset(15661 ^ [_360600, _360859, _361213], _361437)]]]]]]]]], (6047 ^ _115804) ^ [_205750] : [rel_str(_205750), 6050 ^ _115804 : [(6051 ^ _115804) ^ [_205888] : [element(_205888, powerset(the_carrier(_205750))), 6054 ^ _115804 : [(6084 ^ _115804) ^ [] : [-(directed_subset(_205888, _205750)), 6086 ^ _115804 : [(6096 ^ _115804) ^ [_206800] : [element(_206800, the_carrier(_205750)), in(_206800, _205888), related(_205750, 6085 ^ [_205750, _205888], _206800), related(_205750, 6088 ^ [_205750, _205888], _206800)], (6094 ^ _115804) ^ [] : [-(in(6088 ^ [_205750, _205888], _205888))], (6092 ^ _115804) ^ [] : [-(in(6085 ^ [_205750, _205888], _205888))], (6087 ^ _115804) ^ [] : [-(element(6085 ^ [_205750, _205888], the_carrier(_205750)))], (6090 ^ _115804) ^ [] : [-(element(6088 ^ [_205750, _205888], the_carrier(_205750)))]]], (6055 ^ _115804) ^ [] : [directed_subset(_205888, _205750), 6058 ^ _115804 : [(6059 ^ _115804) ^ [_206076] : [element(_206076, the_carrier(_205750)), 6062 ^ _115804 : [(6063 ^ _115804) ^ [_206190] : [element(_206190, the_carrier(_205750)), in(_206076, _205888), in(_206190, _205888), 6075 ^ _115804 : [(6080 ^ _115804) ^ [] : [-(related(_205750, _206076, 6074 ^ [_205750, _205888, _206076, _206190]))], (6076 ^ _115804) ^ [] : [-(element(6074 ^ [_205750, _205888, _206076, _206190], the_carrier(_205750)))], (6078 ^ _115804) ^ [] : [-(in(6074 ^ [_205750, _205888, _206076, _206190], _205888))], (6082 ^ _115804) ^ [] : [-(related(_205750, _206190, 6074 ^ [_205750, _205888, _206076, _206190]))]]]]]]]]]]], (1056 ^ _115804) ^ [_129804, _129806, _129808, _129810] : [-(is_well_founded_in(_129808, _129804)), is_well_founded_in(_129810, _129806), _129810 = _129808, _129806 = _129804], (15538 ^ _115804) ^ [_358849, _358851, _358853] : [-(empty_carrier(_358853)), transitive_relstr(_358853), rel_str(_358853), element(_358851, powerset(the_carrier(_358853))), finite(_358849), element(_358849, powerset(_358851)), 15562 ^ _115804 : [(15563 ^ _115804) ^ [_359303] : [in(_359303, 15561 ^ [_358849, _358851, _358853]), 15566 ^ _115804 : [(15577 ^ _115804) ^ [] : [-(relstr_set_smaller(_358853, 15568 ^ [_358849, _358851, _358853, _359303], 15571 ^ [_358849, _358851, _358853, _359303]))], (15575 ^ _115804) ^ [] : [-(in(15571 ^ [_358849, _358851, _358853, _359303], _358851))], (15573 ^ _115804) ^ [] : [-(element(15571 ^ [_358849, _358851, _358853, _359303], the_carrier(_358853)))], (15567 ^ _115804) ^ [] : [-(in(_359303, powerset(_358849)))], (15570 ^ _115804) ^ [] : [-(15568 ^ [_358849, _358851, _358853, _359303] = _359303)]]], (15579 ^ _115804) ^ [_359571] : [-(in(_359571, 15561 ^ [_358849, _358851, _358853])), in(_359571, powerset(_358849)), 15584 ^ _115804 : [(15585 ^ _115804) ^ [_359702] : [_359702 = _359571, 15588 ^ _115804 : [(15589 ^ _115804) ^ [_359780] : [element(_359780, the_carrier(_358853)), in(_359780, _358851), relstr_set_smaller(_358853, _359702, _359780)]]]]]]], (11367 ^ _115804) ^ [_286632] : [-(empty(_286632)), 11370 ^ _115804 : [(11379 ^ _115804) ^ [] : [-(antisymmetric_relstr(incl_POSet(_286632)))], (11377 ^ _115804) ^ [] : [-(transitive_relstr(incl_POSet(_286632)))], (11375 ^ _115804) ^ [] : [-(reflexive_relstr(incl_POSet(_286632)))], (11371 ^ _115804) ^ [] : [empty_carrier(incl_POSet(_286632))], (11373 ^ _115804) ^ [] : [-(strict_rel_str(incl_POSet(_286632)))]]], (12784 ^ _115804) ^ [] : [-(epsilon_connected(12778 ^ []))], (17329 ^ _115804) ^ [_391614] : [-(bottom_of_relstr(boole_POSet(_391614)) = empty_set)], (12210 ^ _115804) ^ [] : [empty_carrier(12206 ^ [])], (11481 ^ _115804) ^ [_288015, _288017] : [-(empty_carrier(_288015)), lattice(_288015), latt_str(_288015), 11492 ^ _115804 : [(11493 ^ _115804) ^ [] : [in(_288017, a_1_0_filter_1(_288015)), 11498 ^ _115804 : [(11503 ^ _115804) ^ [] : [-(_288017 = ordered_pair_as_product_element(the_carrier(_288015), the_carrier(_288015), 11496 ^ [_288015, _288017], 11497 ^ [_288015, _288017]))], (11499 ^ _115804) ^ [] : [-(element(11496 ^ [_288015, _288017], the_carrier(_288015)))], (11501 ^ _115804) ^ [] : [-(element(11497 ^ [_288015, _288017], the_carrier(_288015)))], (11505 ^ _115804) ^ [] : [-(below_refl(_288015, 11496 ^ [_288015, _288017], 11497 ^ [_288015, _288017]))]]], (11507 ^ _115804) ^ [] : [-(in(_288017, a_1_0_filter_1(_288015))), 11508 ^ _115804 : [(11509 ^ _115804) ^ [_288427, _288429] : [element(_288429, the_carrier(_288015)), element(_288427, the_carrier(_288015)), _288017 = ordered_pair_as_product_element(the_carrier(_288015), the_carrier(_288015), _288429, _288427), below_refl(_288015, _288429, _288427)]]]]], (1702 ^ _115804) ^ [_139440, _139442] : [_139442 = _139440, -(the_L_meet(_139442) = the_L_meet(_139440))], (19529 ^ _115804) ^ [_426560] : [relation(_426560), function(_426560), one_to_one(_426560), 19540 ^ _115804 : [(19541 ^ _115804) ^ [] : [-(relation_rng(_426560) = relation_dom(function_inverse(_426560)))], (19543 ^ _115804) ^ [] : [-(relation_dom(_426560) = relation_rng(function_inverse(_426560)))]]], (6112 ^ _115804) ^ [_207070] : [relation(_207070), 6115 ^ _115804 : [(6138 ^ _115804) ^ [_207535, _207537] : [-(_207535 = fiber(_207070, _207537)), 6150 ^ _115804 : [(6151 ^ _115804) ^ [] : [6139 ^ [_207070, _207535, _207537] = _207537], (6155 ^ _115804) ^ [] : [in(6139 ^ [_207070, _207535, _207537], _207535)], (6153 ^ _115804) ^ [] : [-(in(ordered_pair(6139 ^ [_207070, _207535, _207537], _207537), _207070))]], 6142 ^ _115804 : [(6143 ^ _115804) ^ [] : [-(in(6139 ^ [_207070, _207535, _207537], _207535))], (6145 ^ _115804) ^ [] : [-(6139 ^ [_207070, _207535, _207537] = _207537), in(ordered_pair(6139 ^ [_207070, _207535, _207537], _207537), _207070)]]], (6116 ^ _115804) ^ [_207174, _207176] : [_207174 = fiber(_207070, _207176), 6119 ^ _115804 : [(6120 ^ _115804) ^ [_207268] : [in(_207268, _207174), 6123 ^ _115804 : [(6124 ^ _115804) ^ [] : [_207268 = _207176], (6126 ^ _115804) ^ [] : [-(in(ordered_pair(_207268, _207176), _207070))]]], (6128 ^ _115804) ^ [_207387] : [-(in(_207387, _207174)), -(_207387 = _207176), in(ordered_pair(_207387, _207176), _207070)]]]]], (918 ^ _115804) ^ [_127945, _127947, _127949, _127951] : [-(ex_sup_of_relstr_set(_127949, _127945)), ex_sup_of_relstr_set(_127951, _127947), _127951 = _127949, _127947 = _127945], (11525 ^ _115804) ^ [_288687, _288689, _288691] : [-(empty_carrier(_288689)), latt_str(_288689), 11532 ^ _115804 : [(11533 ^ _115804) ^ [] : [in(_288691, a_2_2_lattice3(_288689, _288687)), 11537 ^ _115804 : [(11538 ^ _115804) ^ [] : [-(element(11536 ^ [_288687, _288689, _288691], the_carrier(_288689)))], (11542 ^ _115804) ^ [] : [-(latt_set_smaller(_288689, 11536 ^ [_288687, _288689, _288691], _288687))], (11540 ^ _115804) ^ [] : [-(_288691 = 11536 ^ [_288687, _288689, _288691])]]], (11544 ^ _115804) ^ [] : [-(in(_288691, a_2_2_lattice3(_288689, _288687))), 11545 ^ _115804 : [(11546 ^ _115804) ^ [_288993] : [element(_288993, the_carrier(_288689)), _288691 = _288993, latt_set_smaller(_288689, _288993, _288687)]]]]], (16752 ^ _115804) ^ [_382242] : [-(empty_carrier(_382242)), one_sorted_str(_382242), 16759 ^ _115804 : [(16760 ^ _115804) ^ [_382382] : [-(empty_carrier(_382382)), net_str(_382382, _382242), 16767 ^ _115804 : [(16768 ^ _115804) ^ [_382510] : [element(_382510, the_carrier(_382382)), -(the_carrier(netstr_restr_to_element(_382242, _382382, _382510)) = a_3_0_waybel_9(_382242, _382382, _382510))]]]]], (11736 ^ _115804) ^ [_291945, _291947, _291949] : [-(subset_intersection2(_291949, _291947, _291947) = _291947), element(_291947, powerset(_291949)), element(_291945, powerset(_291949))], (10291 ^ _115804) ^ [_272449] : [-(meet_absorbing(boole_lattice(_272449)))], (2 ^ _115804) ^ [_115831] : [-(_115831 = _115831)], (11305 ^ _115804) ^ [] : [-(v1_membered(empty_set))], (1762 ^ _115804) ^ [_140358, _140360, _140362, _140364, _140366, _140368] : [-(latt_str_of(_140368, _140364, _140360) = latt_str_of(_140366, _140362, _140358)), _140368 = _140366, _140364 = _140362, _140360 = _140358], (10433 ^ _115804) ^ [_274184] : [-(boolean_relstr(boole_POSet(_274184)))], (11927 ^ _115804) ^ [_294712, _294714, _294716] : [subset(_294716, _294714), -(in(_294712, _294716)), -(subset(_294716, set_difference(_294714, singleton(_294712))))], (17463 ^ _115804) ^ [_393730, _393732, _393734] : [relation(_393730), in(ordered_pair(_393734, _393732), _393730), 17470 ^ _115804 : [(17471 ^ _115804) ^ [] : [-(in(_393734, relation_dom(_393730)))], (17473 ^ _115804) ^ [] : [-(in(_393732, relation_rng(_393730)))]]], (11451 ^ _115804) ^ [_287694] : [empty_carrier(boole_POSet(_287694))], (13454 ^ _115804) ^ [_314137, _314139] : [equipotent(_314139, _314137), -(are_equipotent(_314139, _314137))], (8805 ^ _115804) ^ [_252447, _252449, _252451, _252453] : [8824 ^ _115804 : [(8825 ^ _115804) ^ [] : [-(strict_net_str(net_str_of(_252453, _252451, _252449, _252447), _252453))], (8827 ^ _115804) ^ [] : [-(net_str(net_str_of(_252453, _252451, _252449, _252447), _252453))]], one_sorted_str(_252453), relation_of2(_252449, _252451, _252451), function(_252447), quasi_total(_252447, _252451, the_carrier(_252453)), relation_of2(_252447, _252451, the_carrier(_252453))], (16923 ^ _115804) ^ [_384836, _384838] : [-(subset(relation_image(_384836, relation_inverse_image(_384836, _384838)), _384838)), relation(_384836), function(_384836)], (9395 ^ _115804) ^ [_260295, _260297, _260299, _260301] : [-(element(apply_on_set_and_struct(_260301, _260299, _260297, _260295), the_carrier(_260299))), -(empty(_260301)), -(empty_carrier(_260299)), rel_str(_260299), function(_260297), quasi_total(_260297, _260301, the_carrier(_260299)), relation_of2(_260297, _260301, the_carrier(_260299)), element(_260295, _260301)], (4605 ^ _115804) ^ [_180312] : [relation(_180312), function(_180312), 4612 ^ _115804 : [(4642 ^ _115804) ^ [_180990, _180992] : [-(_180990 = relation_image(_180312, _180992)), 4659 ^ _115804 : [(4664 ^ _115804) ^ [] : [-(4643 ^ [_180312, _180990, _180992] = apply(_180312, 4658 ^ [_180312, _180990, _180992]))], (4660 ^ _115804) ^ [] : [-(in(4658 ^ [_180312, _180990, _180992], relation_dom(_180312)))], (4662 ^ _115804) ^ [] : [-(in(4658 ^ [_180312, _180990, _180992], _180992))], (4666 ^ _115804) ^ [] : [in(4643 ^ [_180312, _180990, _180992], _180990)]], 4646 ^ _115804 : [(4647 ^ _115804) ^ [] : [-(in(4643 ^ [_180312, _180990, _180992], _180990))], (4649 ^ _115804) ^ [_181154] : [in(_181154, relation_dom(_180312)), in(_181154, _180992), 4643 ^ [_180312, _180990, _180992] = apply(_180312, _181154)]]], (4613 ^ _115804) ^ [_180475, _180477] : [_180475 = relation_image(_180312, _180477), 4616 ^ _115804 : [(4617 ^ _115804) ^ [_180580] : [in(_180580, _180475), 4621 ^ _115804 : [(4622 ^ _115804) ^ [] : [-(in(4620 ^ [_180312, _180475, _180477, _180580], relation_dom(_180312)))], (4626 ^ _115804) ^ [] : [-(_180580 = apply(_180312, 4620 ^ [_180312, _180475, _180477, _180580]))], (4624 ^ _115804) ^ [] : [-(in(4620 ^ [_180312, _180475, _180477, _180580], _180477))]]], (4628 ^ _115804) ^ [_180755] : [-(in(_180755, _180475)), 4629 ^ _115804 : [(4630 ^ _115804) ^ [_180810] : [in(_180810, relation_dom(_180312)), in(_180810, _180477), _180755 = apply(_180312, _180810)]]]]]]], (10299 ^ _115804) ^ [_272525] : [-(modular_lattstr(boole_lattice(_272525)))], (18271 ^ _115804) ^ [_406816] : [top_str(_406816), 18274 ^ _115804 : [(18275 ^ _115804) ^ [_406890] : [element(_406890, powerset(the_carrier(_406816))), 18278 ^ _115804 : [(18279 ^ _115804) ^ [] : [open_subset(_406890, _406816), -(closed_subset(subset_complement(the_carrier(_406816), _406890), _406816))], (18285 ^ _115804) ^ [] : [closed_subset(subset_complement(the_carrier(_406816), _406890), _406816), -(open_subset(_406890, _406816))]]]]], (9795 ^ _115804) ^ [_266020] : [-(relation(relation_of_lattice(_266020))), -(empty_carrier(_266020)), lattice(_266020), latt_str(_266020)], (6244 ^ _115804) ^ [_209185, _209187] : [-(_209185 = powerset(_209187)), 6248 ^ _115804 : [(6249 ^ _115804) ^ [] : [-(in(6245 ^ [_209185, _209187], _209185))], (6251 ^ _115804) ^ [] : [subset(6245 ^ [_209185, _209187], _209187)]], 6252 ^ _115804 : [(6253 ^ _115804) ^ [] : [-(subset(6245 ^ [_209185, _209187], _209187))], (6255 ^ _115804) ^ [] : [in(6245 ^ [_209185, _209187], _209185)]]], (450 ^ _115804) ^ [_121635, _121637, _121639, _121641, _121643, _121645] : [-(v1_partfun1(_121643, _121639, _121635)), v1_partfun1(_121645, _121641, _121637), _121645 = _121643, _121641 = _121639, _121637 = _121635], (12149 ^ _115804) ^ [] : [-(meet_commutative(12137 ^ []))], (2580 ^ _115804) ^ [_153093, _153095, _153097, _153099] : [-(relation_composition(_153099, _153095) = relation_composition(_153097, _153093)), _153099 = _153097, _153095 = _153093], (518 ^ _115804) ^ [_122529, _122531] : [-(with_suprema_relstr(_122529)), _122531 = _122529, with_suprema_relstr(_122531)], (12721 ^ _115804) ^ [] : [-(v3_waybel_3(12689 ^ []))], (18992 ^ _115804) ^ [_417961] : [19007 ^ _115804 : [(19008 ^ _115804) ^ [_418172] : [element(_418172, the_carrier(_417961)), -(related(_417961, bottom_of_relstr(_417961), _418172))]], -(empty_carrier(_417961)), antisymmetric_relstr(_417961), lower_bounded_relstr(_417961), rel_str(_417961)], (10593 ^ _115804) ^ [_276385] : [-(lattice(boole_lattice(_276385)))], (19361 ^ _115804) ^ [_423727] : [relation(_423727), 19364 ^ _115804 : [(19365 ^ _115804) ^ [_423851] : [relation(_423851), 19368 ^ _115804 : [(19369 ^ _115804) ^ [_423967] : [relation(_423967), function(_423967), relation_isomorphism(_423727, _423851, _423967), 19380 ^ _115804 : [(19405 ^ _115804) ^ [] : [well_founded_relation(_423727), -(well_founded_relation(_423851))], (19399 ^ _115804) ^ [] : [antisymmetric(_423727), -(antisymmetric(_423851))], (19393 ^ _115804) ^ [] : [connected(_423727), -(connected(_423851))], (19381 ^ _115804) ^ [] : [reflexive(_423727), -(reflexive(_423851))], (19387 ^ _115804) ^ [] : [transitive(_423727), -(transitive(_423851))]]]]]]], (12566 ^ _115804) ^ [] : [-(function(12560 ^ []))], (12882 ^ _115804) ^ [_305883] : [12890 ^ _115804 : [(12891 ^ _115804) ^ [] : [-(element(12889 ^ [_305883], powerset(the_carrier(_305883))))], (12893 ^ _115804) ^ [] : [empty(12889 ^ [_305883])]], -(empty_carrier(_305883)), one_sorted_str(_305883)], (12842 ^ _115804) ^ [_305450] : [one_sorted_str(_305450), 12846 ^ _115804 : [(12847 ^ _115804) ^ [] : [-(net_str(12845 ^ [_305450], _305450))], (12849 ^ _115804) ^ [] : [-(strict_net_str(12845 ^ [_305450], _305450))]]], (1224 ^ _115804) ^ [_132152, _132154] : [-(latt_str(_132152)), _132154 = _132152, latt_str(_132154)], (11295 ^ _115804) ^ [_285707] : [-(strict_rel_str(incl_POSet(_285707)))], (10287 ^ _115804) ^ [_272411] : [-(meet_commutative(boole_lattice(_272411)))], (4432 ^ _115804) ^ [_177241, _177243] : [_177243 = _177241, 4435 ^ _115804 : [(4436 ^ _115804) ^ [] : [-(subset(_177243, _177241))], (4438 ^ _115804) ^ [] : [-(subset(_177241, _177243))]]], (13550 ^ _115804) ^ [_315423, _315425] : [-(equipotent(_315425, _315425))], (2396 ^ _115804) ^ [_150367, _150369] : [_150369 = _150367, -(incl_POSet(_150369) = incl_POSet(_150367))], (12709 ^ _115804) ^ [] : [-(lower_bounded_relstr(12689 ^ []))], (8059 ^ _115804) ^ [_239096, _239098] : [disjoint(_239098, _239096), -(set_intersection2(_239098, _239096) = empty_set)], (2318 ^ _115804) ^ [_149210, _149212] : [_149212 = _149210, -(boole_lattice(_149212) = boole_lattice(_149210))], (11275 ^ _115804) ^ [_285457] : [-(closed_subset(cast_as_carrier_subset(_285457), _285457)), topological_space(_285457), top_str(_285457)], (17296 ^ _115804) ^ [_391015, _391017] : [-(subset(set_intersection2(_391017, _391015), _391017))], (12317 ^ _115804) ^ [] : [-(v1_membered(12313 ^ []))], (4050 ^ _115804) ^ [_172183] : [rel_str(_172183), 4077 ^ _115804 : [(4082 ^ _115804) ^ [] : [-(transitive_relstr(_172183))], (4080 ^ _115804) ^ [] : [-(reflexive_relstr(_172183))], (4086 ^ _115804) ^ [] : [-(connected_relstr(_172183))], (4088 ^ _115804) ^ [] : [-(v2_waybel_3(_172183))], (4078 ^ _115804) ^ [] : [empty_carrier(_172183)], (4084 ^ _115804) ^ [] : [-(antisymmetric_relstr(_172183))]], -(empty_carrier(_172183)), reflexive_relstr(_172183), transitive_relstr(_172183), antisymmetric_relstr(_172183), complete_relstr(_172183), connected_relstr(_172183)], (9863 ^ _115804) ^ [_266828, _266830] : [9878 ^ _115804 : [(9879 ^ _115804) ^ [_267053] : [point_neighbourhood(_267053, _266830, _266828), -(element(_267053, powerset(the_carrier(_266830))))]], -(empty_carrier(_266830)), topological_space(_266830), top_str(_266830), element(_266828, the_carrier(_266830))], (11815 ^ _115804) ^ [_293064] : [relation(_293064), 11818 ^ _115804 : [(11833 ^ _115804) ^ [] : [11837 ^ _115804 : [(11838 ^ _115804) ^ [] : [-(in(ordered_pair(11834 ^ [_293064], 11835 ^ [_293064]), _293064))], (11842 ^ _115804) ^ [] : [in(ordered_pair(11834 ^ [_293064], 11836 ^ [_293064]), _293064)], (11840 ^ _115804) ^ [] : [-(in(ordered_pair(11835 ^ [_293064], 11836 ^ [_293064]), _293064))]], -(transitive(_293064))], (11819 ^ _115804) ^ [] : [transitive(_293064), 11822 ^ _115804 : [(11823 ^ _115804) ^ [_293203, _293205, _293207] : [-(in(ordered_pair(_293207, _293203), _293064)), in(ordered_pair(_293207, _293205), _293064), in(ordered_pair(_293205, _293203), _293064)]]]]], (12910 ^ _115804) ^ [] : [-(with_infima_relstr(12894 ^ []))], (3624 ^ _115804) ^ [_166800] : [rel_str(_166800), 3639 ^ _115804 : [(3640 ^ _115804) ^ [] : [empty_carrier(_166800)], (3644 ^ _115804) ^ [] : [-(v2_waybel_3(_166800))], (3642 ^ _115804) ^ [] : [-(reflexive_relstr(_166800))]], -(empty_carrier(_166800)), trivial_carrier(_166800), reflexive_relstr(_166800)], (17260 ^ _115804) ^ [_390417] : [one_sorted_str(_390417), 17263 ^ _115804 : [(17264 ^ _115804) ^ [_390493] : [element(_390493, powerset(the_carrier(_390417))), -(subset_complement(the_carrier(_390417), _390493) = subset_difference(the_carrier(_390417), cast_as_carrier_subset(_390417), _390493))]]], (6816 ^ _115804) ^ [_218475, _218477, _218479] : [-(_218475 = cartesian_product2(_218479, _218477)), 6834 ^ _115804 : [(6839 ^ _115804) ^ [] : [-(6817 ^ [_218475, _218477, _218479] = ordered_pair(6832 ^ [_218475, _218477, _218479], 6833 ^ [_218475, _218477, _218479]))], (6835 ^ _115804) ^ [] : [-(in(6832 ^ [_218475, _218477, _218479], _218479))], (6837 ^ _115804) ^ [] : [-(in(6833 ^ [_218475, _218477, _218479], _218477))], (6841 ^ _115804) ^ [] : [in(6817 ^ [_218475, _218477, _218479], _218475)]], 6820 ^ _115804 : [(6821 ^ _115804) ^ [] : [-(in(6817 ^ [_218475, _218477, _218479], _218475))], (6823 ^ _115804) ^ [_218645, _218647] : [in(_218647, _218479), in(_218645, _218477), 6817 ^ [_218475, _218477, _218479] = ordered_pair(_218647, _218645)]]], (12346 ^ _115804) ^ [] : [-(being_limit_ordinal(12338 ^ []))], (12247 ^ _115804) ^ [] : [-(reflexive_relstr(12239 ^ []))], (9339 ^ _115804) ^ [] : [true___, -(true___)], (12746 ^ _115804) ^ [] : [-(with_infima_relstr(12732 ^ []))], (9991 ^ _115804) ^ [_268601, _268603] : [9998 ^ _115804 : [(9999 ^ _115804) ^ [] : [-(function(the_mapping(_268603, _268601)))], (10003 ^ _115804) ^ [] : [-(relation_of2_as_subset(the_mapping(_268603, _268601), the_carrier(_268601), the_carrier(_268603)))], (10001 ^ _115804) ^ [] : [-(quasi_total(the_mapping(_268603, _268601), the_carrier(_268601), the_carrier(_268603)))]], one_sorted_str(_268603), net_str(_268601, _268603)], (11309 ^ _115804) ^ [] : [-(v3_membered(empty_set))], (9217 ^ _115804) ^ [_257994, _257996, _257998, _258000] : [9224 ^ _115804 : [(9225 ^ _115804) ^ [] : [-(function(partfun_dom_restriction(_258000, _257998, _257996, _257994)))], (9227 ^ _115804) ^ [] : [-(relation_of2_as_subset(partfun_dom_restriction(_258000, _257998, _257996, _257994), _258000, _257998))]], function(_257996), relation_of2(_257996, _258000, _257998)], (8897 ^ _115804) ^ [_253777, _253779] : [-(element(lim_points_of_net(_253779, _253777), powerset(the_carrier(_253779)))), -(empty_carrier(_253779)), topological_space(_253779), top_str(_253779), -(empty_carrier(_253777)), transitive_relstr(_253777), directed_relstr(_253777), net_str(_253777, _253779)], (12996 ^ _115804) ^ [] : [empty_carrier(12992 ^ [])], (2656 ^ _115804) ^ [_154612] : [rel_str(_154612), strict_rel_str(_154612), -(_154612 = rel_str_of(the_carrier(_154612), the_InternalRel(_154612)))], (11459 ^ _115804) ^ [_287771] : [-(antisymmetric_relstr(boole_POSet(_287771)))], (12809 ^ _115804) ^ [] : [-(one_sorted_str(12807 ^ []))], (10627 ^ _115804) ^ [] : [-(one_to_one(empty_set))], (20015 ^ _115804) ^ [_434357, _434359, _434361] : [relation(_434357), function(_434357), in(_434359, _434361), -(apply(relation_dom_restriction(_434357, _434361), _434359) = apply(_434357, _434359))], (9345 ^ _115804) ^ [_259649, _259651] : [element(_259649, powerset(_259651)), -(element(subset_complement(_259651, _259649), powerset(_259651)))], (10413 ^ _115804) ^ [_273959] : [-(antisymmetric_relstr(boole_POSet(_273959)))], (10577 ^ _115804) ^ [_276230] : [empty_carrier(boole_lattice(_276230))], (5679 ^ _115804) ^ [_199327, _199329] : [strict_latt_str(_199327), latt_str(_199327), 5686 ^ _115804 : [(5687 ^ _115804) ^ [] : [_199327 = boole_lattice(_199329), 5690 ^ _115804 : [(5691 ^ _115804) ^ [] : [-(the_carrier(_199327) = powerset(_199329))], (5693 ^ _115804) ^ [_199577] : [element(_199577, powerset(_199329)), 5696 ^ _115804 : [(5697 ^ _115804) ^ [_199674] : [element(_199674, powerset(_199329)), 5700 ^ _115804 : [(5701 ^ _115804) ^ [] : [-(apply_binary(the_L_join(_199327), _199577, _199674) = subset_union2(_199329, _199577, _199674))], (5703 ^ _115804) ^ [] : [-(apply_binary(the_L_meet(_199327), _199577, _199674) = subset_intersection2(_199329, _199577, _199674))]]]]]]], (5705 ^ _115804) ^ [] : [-(_199327 = boole_lattice(_199329)), the_carrier(_199327) = powerset(_199329), 5711 ^ _115804 : [(5712 ^ _115804) ^ [] : [-(element(5710 ^ [_199327, _199329], powerset(_199329)))], (5717 ^ _115804) ^ [] : [apply_binary(the_L_join(_199327), 5710 ^ [_199327, _199329], 5713 ^ [_199327, _199329]) = subset_union2(_199329, 5710 ^ [_199327, _199329], 5713 ^ [_199327, _199329]), apply_binary(the_L_meet(_199327), 5710 ^ [_199327, _199329], 5713 ^ [_199327, _199329]) = subset_intersection2(_199329, 5710 ^ [_199327, _199329], 5713 ^ [_199327, _199329])], (5715 ^ _115804) ^ [] : [-(element(5713 ^ [_199327, _199329], powerset(_199329)))]]]]], (12245 ^ _115804) ^ [] : [-(strict_rel_str(12239 ^ []))], (12854 ^ _115804) ^ [] : [empty_carrier(12850 ^ [])], (13318 ^ _115804) ^ [_312113, _312115] : [element(_312113, powerset(powerset(_312115))), -(meet_of_subsets(_312115, _312113) = set_meet(_312113))], (12192 ^ _115804) ^ [] : [-(complemented_lattstr(12164 ^ []))], (11391 ^ _115804) ^ [_286955] : [-(strict_rel_str(boole_POSet(_286955)))], (20312 ^ _115804) ^ [_438717] : [-(empty_carrier(_438717)), one_sorted_str(_438717), 20319 ^ _115804 : [(20320 ^ _115804) ^ [_438840] : [element(_438840, the_carrier(_438717)), -(apply_as_element(the_carrier(_438717), the_carrier(_438717), identity_on_carrier(_438717), _438840) = _438840)]]], (9285 ^ _115804) ^ [_258892] : [-(strict_rel_str(incl_POSet(_258892)))], (10385 ^ _115804) ^ [_273628] : [-(antisymmetric_relstr(boole_POSet(_273628)))], (13324 ^ _115804) ^ [_312208, _312210, _312212] : [-(subset_difference(_312212, _312210, _312208) = set_difference(_312210, _312208)), element(_312210, powerset(_312212)), element(_312208, powerset(_312212))], (6259 ^ _115804) ^ [_209427] : [rel_str(_209427), 6262 ^ _115804 : [(6263 ^ _115804) ^ [_209535] : [element(_209535, powerset(the_carrier(_209427))), 6266 ^ _115804 : [(6289 ^ _115804) ^ [] : [6291 ^ _115804 : [(6301 ^ _115804) ^ [] : [in(6293 ^ [_209427, _209535], _209535)], (6299 ^ _115804) ^ [] : [-(related(_209427, 6290 ^ [_209427, _209535], 6293 ^ [_209427, _209535]))], (6297 ^ _115804) ^ [] : [-(in(6290 ^ [_209427, _209535], _209535))], (6292 ^ _115804) ^ [] : [-(element(6290 ^ [_209427, _209535], the_carrier(_209427)))], (6295 ^ _115804) ^ [] : [-(element(6293 ^ [_209427, _209535], the_carrier(_209427)))]], -(upper_relstr_subset(_209535, _209427))], (6267 ^ _115804) ^ [] : [upper_relstr_subset(_209535, _209427), 6270 ^ _115804 : [(6271 ^ _115804) ^ [_209693] : [element(_209693, the_carrier(_209427)), 6274 ^ _115804 : [(6275 ^ _115804) ^ [_209777] : [element(_209777, the_carrier(_209427)), -(in(_209777, _209535)), in(_209693, _209535), related(_209427, _209693, _209777)]]]]]]]]], (5725 ^ _115804) ^ [_200265] : [-(empty_carrier(_200265)), join_semilatt_str(_200265), 5732 ^ _115804 : [(5733 ^ _115804) ^ [_200409] : [element(_200409, the_carrier(_200265)), 5736 ^ _115804 : [(5737 ^ _115804) ^ [_200497] : [element(_200497, the_carrier(_200265)), -(join(_200265, _200409, _200497) = apply_binary_as_element(the_carrier(_200265), the_carrier(_200265), the_carrier(_200265), the_L_join(_200265), _200409, _200497))]]]]], (11746 ^ _115804) ^ [_292094, _292096] : [element(_292094, powerset(_292096)), -(subset_complement(_292096, subset_complement(_292096, _292094)) = _292094)], (10297 ^ _115804) ^ [_272506] : [-(distributive_lattstr(boole_lattice(_272506)))], (640 ^ _115804) ^ [_124116, _124118] : [-(join_absorbing(_124116)), _124118 = _124116, join_absorbing(_124118)], (11722 ^ _115804) ^ [_291740, _291742] : [-(set_union2(_291742, _291742) = _291742)], (12545 ^ _115804) ^ [_301962] : [-(relation(12539 ^ [_301962]))], (8797 ^ _115804) ^ [_252334, _252336] : [relation_of2(_252334, _252336, _252336), 8800 ^ _115804 : [(8801 ^ _115804) ^ [] : [-(strict_rel_str(rel_str_of(_252336, _252334)))], (8803 ^ _115804) ^ [] : [-(rel_str(rel_str_of(_252336, _252334)))]]], (18680 ^ _115804) ^ [_413460, _413462] : [-(subset(set_difference(_413462, _413460), _413462))], (16572 ^ _115804) ^ [_379683, _379685, _379687, _379689] : [in(ordered_pair(_379689, _379687), cartesian_product2(_379685, _379683)), 16575 ^ _115804 : [(16576 ^ _115804) ^ [] : [-(in(_379689, _379685))], (16578 ^ _115804) ^ [] : [-(in(_379687, _379683))]]], (12333 ^ _115804) ^ [] : [-(epsilon_transitive(12331 ^ []))], (3352 ^ _115804) ^ [_163457] : [3363 ^ _115804 : [(3364 ^ _115804) ^ [] : [-(relation(_163457))], (3368 ^ _115804) ^ [] : [-(one_to_one(_163457))], (3366 ^ _115804) ^ [] : [-(function(_163457))]], relation(_163457), empty(_163457), function(_163457)], (10643 ^ _115804) ^ [_276940] : [-(symmetric(identity_relation(_276940)))], (4384 ^ _115804) ^ [_176452, _176454] : [relation(_176452), 4387 ^ _115804 : [(4410 ^ _115804) ^ [] : [-(_176452 = identity_relation(_176454)), 4423 ^ _115804 : [(4424 ^ _115804) ^ [] : [-(in(4411 ^ [_176452, _176454], _176454))], (4428 ^ _115804) ^ [] : [in(ordered_pair(4411 ^ [_176452, _176454], 4412 ^ [_176452, _176454]), _176452)], (4426 ^ _115804) ^ [] : [-(4411 ^ [_176452, _176454] = 4412 ^ [_176452, _176454])]], 4415 ^ _115804 : [(4416 ^ _115804) ^ [] : [-(in(ordered_pair(4411 ^ [_176452, _176454], 4412 ^ [_176452, _176454]), _176452))], (4418 ^ _115804) ^ [] : [in(4411 ^ [_176452, _176454], _176454), 4411 ^ [_176452, _176454] = 4412 ^ [_176452, _176454]]]], (4388 ^ _115804) ^ [] : [_176452 = identity_relation(_176454), 4391 ^ _115804 : [(4392 ^ _115804) ^ [_176605, _176607] : [in(ordered_pair(_176607, _176605), _176452), 4395 ^ _115804 : [(4396 ^ _115804) ^ [] : [-(in(_176607, _176454))], (4398 ^ _115804) ^ [] : [-(_176607 = _176605)]]], (4400 ^ _115804) ^ [_176714, _176716] : [-(in(ordered_pair(_176716, _176714), _176452)), in(_176716, _176454), _176716 = _176714]]]]], (12571 ^ _115804) ^ [_302243] : [-(relation(12567 ^ [_302243]))], (12487 ^ _115804) ^ [] : [v1_yellow_3(12465 ^ [])], (19503 ^ _115804) ^ [_426155] : [relation(_426155), 19506 ^ _115804 : [(19507 ^ _115804) ^ [_426239] : [relation(_426239), 19510 ^ _115804 : [(19511 ^ _115804) ^ [_426315] : [relation(_426315), function(_426315), -(well_ordering(_426239)), well_ordering(_426155), relation_isomorphism(_426155, _426239, _426315)]]]]], (3446 ^ _115804) ^ [_164624] : [-(ordinal(_164624)), epsilon_transitive(_164624), epsilon_connected(_164624)], (1952 ^ _115804) ^ [_143471, _143473, _143475, _143477, _143479, _143481, _143483, _143485] : [-(function_invverse_img_as_carrier_subset(_143485, _143481, _143477, _143473) = function_invverse_img_as_carrier_subset(_143483, _143479, _143475, _143471)), _143485 = _143483, _143481 = _143479, _143477 = _143475, _143473 = _143471], (12442 ^ _115804) ^ [] : [-(antisymmetric_relstr(12430 ^ []))], (9211 ^ _115804) ^ [] : [true___, -(true___)], (10119 ^ _115804) ^ [_270206, _270208] : [10126 ^ _115804 : [(10127 ^ _115804) ^ [] : [-(empty(relation_composition(_270206, _270208)))], (10129 ^ _115804) ^ [] : [-(relation(relation_composition(_270206, _270208)))]], empty(_270208), relation(_270206)], (12176 ^ _115804) ^ [] : [-(meet_commutative(12164 ^ []))], (12276 ^ _115804) ^ [] : [-(ordinal(12268 ^ []))], (8564 ^ _115804) ^ [_248550] : [one_sorted_str(_248550), 8567 ^ _115804 : [(8568 ^ _115804) ^ [_248650] : [net_str(_248650, _248550), 8571 ^ _115804 : [(8572 ^ _115804) ^ [_248743] : [net_str(_248743, _248550), 8575 ^ _115804 : [(8576 ^ _115804) ^ [] : [subnetstr(_248743, _248550, _248650), 8579 ^ _115804 : [(8580 ^ _115804) ^ [] : [-(subrelstr(_248743, _248650))], (8582 ^ _115804) ^ [] : [-(the_mapping(_248550, _248743) = relation_dom_restr_as_relation_of(the_carrier(_248650), the_carrier(_248550), the_mapping(_248550, _248650), the_carrier(_248743)))]]], (8584 ^ _115804) ^ [] : [-(subnetstr(_248743, _248550, _248650)), subrelstr(_248743, _248650), the_mapping(_248550, _248743) = relation_dom_restr_as_relation_of(the_carrier(_248650), the_carrier(_248550), the_mapping(_248550, _248650), the_carrier(_248743))]]]]]]], (10257 ^ _115804) ^ [_272035] : [-(preboolean(powerset(_272035)))], (9317 ^ _115804) ^ [_259278, _259280, _259282] : [-(element(join_commut(_259282, _259280, _259278), the_carrier(_259282))), -(empty_carrier(_259282)), join_commutative(_259282), join_semilatt_str(_259282), element(_259280, the_carrier(_259282)), element(_259278, the_carrier(_259282))], (11313 ^ _115804) ^ [] : [-(v5_membered(empty_set))], (12251 ^ _115804) ^ [] : [-(antisymmetric_relstr(12239 ^ []))], (12921 ^ _115804) ^ [] : [empty_carrier(12917 ^ [])], (12864 ^ _115804) ^ [] : [-(with_suprema_relstr(12850 ^ []))], (12502 ^ _115804) ^ [] : [-(empty(12500 ^ []))], (20148 ^ _115804) ^ [_436367, _436369] : [relation(_436367), -(subset(relation_dom_restriction(_436367, _436369), _436367))], (558 ^ _115804) ^ [_123029, _123031] : [-(heyting_relstr(_123029)), _123031 = _123029, heyting_relstr(_123031)], (6786 ^ _115804) ^ [_217942, _217944, _217946] : [_217942 = cartesian_product2(_217946, _217944), 6789 ^ _115804 : [(6790 ^ _115804) ^ [_218050] : [in(_218050, _217942), 6795 ^ _115804 : [(6796 ^ _115804) ^ [] : [-(in(6793 ^ [_217942, _217944, _217946, _218050], _217946))], (6800 ^ _115804) ^ [] : [-(_218050 = ordered_pair(6793 ^ [_217942, _217944, _217946, _218050], 6794 ^ [_217942, _217944, _217946, _218050]))], (6798 ^ _115804) ^ [] : [-(in(6794 ^ [_217942, _217944, _217946, _218050], _217944))]]], (6802 ^ _115804) ^ [_218237] : [-(in(_218237, _217942)), 6803 ^ _115804 : [(6804 ^ _115804) ^ [_218295, _218297] : [in(_218297, _217946), in(_218295, _217944), _218237 = ordered_pair(_218297, _218295)]]]]], (12953 ^ _115804) ^ [_306767] : [12965 ^ _115804 : [(12966 ^ _115804) ^ [] : [-(element(12964 ^ [_306767], powerset(the_carrier(_306767))))], (12970 ^ _115804) ^ [] : [-(closed_subset(12964 ^ [_306767], _306767))], (12968 ^ _115804) ^ [] : [empty(12964 ^ [_306767])]], -(empty_carrier(_306767)), topological_space(_306767), top_str(_306767)], (12738 ^ _115804) ^ [] : [-(reflexive_relstr(12732 ^ []))], (17447 ^ _115804) ^ [_393526, _393528, _393530] : [-(subset(_393530, _393526)), subset(_393530, _393528), subset(_393528, _393526)], (12874 ^ _115804) ^ [] : [-(distributive_relstr(12850 ^ []))], (18413 ^ _115804) ^ [_409246, _409248] : [relation(_409246), well_founded_relation(_409246), -(well_founded_relation(relation_restriction(_409246, _409248)))], (2116 ^ _115804) ^ [_146115, _146117, _146119, _146121, _146123, _146125] : [-(join(_146125, _146121, _146117) = join(_146123, _146119, _146115)), _146125 = _146123, _146121 = _146119, _146117 = _146115], (12477 ^ _115804) ^ [] : [-(transitive_relstr(12465 ^ []))], (1744 ^ _115804) ^ [_140057, _140059, _140061, _140063, _140065, _140067, _140069, _140071] : [-(net_str_of(_140071, _140067, _140063, _140059) = net_str_of(_140069, _140065, _140061, _140057)), _140071 = _140069, _140067 = _140065, _140063 = _140061, _140059 = _140057], (16781 ^ _115804) ^ [_382792] : [-(in(_382792, 16779 ^ [_382792]))], (3048 ^ _115804) ^ [_159683] : [preboolean(_159683), 3051 ^ _115804 : [(3052 ^ _115804) ^ [] : [-(cup_closed(_159683))], (3054 ^ _115804) ^ [] : [-(diff_closed(_159683))]]], (12919 ^ _115804) ^ [] : [-(latt_str(12917 ^ []))], (3562 ^ _115804) ^ [_166011, _166013, _166015] : [relation_of2(_166011, _166015, _166013), 3581 ^ _115804 : [(3582 ^ _115804) ^ [] : [-(function(_166011))], (3586 ^ _115804) ^ [] : [-(bijective(_166011, _166015, _166013))], (3584 ^ _115804) ^ [] : [-(quasi_total(_166011, _166015, _166013))]], function(_166011), one_to_one(_166011), quasi_total(_166011, _166015, _166013), onto(_166011, _166015, _166013)], (12770 ^ _115804) ^ [] : [-(function(12766 ^ []))], (9159 ^ _115804) ^ [_257220] : [9166 ^ _115804 : [(9167 ^ _115804) ^ [] : [-(relation(function_inverse(_257220)))], (9169 ^ _115804) ^ [] : [-(function(function_inverse(_257220)))]], relation(_257220), function(_257220)], (10311 ^ _115804) ^ [_272641] : [-(complete_latt_str(boole_lattice(_272641)))], (15932 ^ _115804) ^ [_367137, _367139, _367141] : [relation(_367139), relation(_367137), function(_367137), 15944 ^ _115804 : [(15945 ^ _115804) ^ [_367412] : [in(_367412, 15943 ^ [_367137, _367139, _367141]), 15948 ^ _115804 : [(15949 ^ _115804) ^ [] : [-(in(_367412, cartesian_product2(_367141, _367141)))], (15955 ^ _115804) ^ [] : [-(in(ordered_pair(apply(_367137, 15950 ^ [_367137, _367139, _367141, _367412]), apply(_367137, 15951 ^ [_367137, _367139, _367141, _367412])), _367139))], (15953 ^ _115804) ^ [] : [-(_367412 = ordered_pair(15950 ^ [_367137, _367139, _367141, _367412], 15951 ^ [_367137, _367139, _367141, _367412]))]]], (15957 ^ _115804) ^ [_367641] : [-(in(_367641, 15943 ^ [_367137, _367139, _367141])), in(_367641, cartesian_product2(_367141, _367141)), 15962 ^ _115804 : [(15963 ^ _115804) ^ [_367771, _367773] : [_367641 = ordered_pair(_367773, _367771), in(ordered_pair(apply(_367137, _367773), apply(_367137, _367771)), _367139)]]]]], (17041 ^ _115804) ^ [_386774] : [relation(_386774), 17044 ^ _115804 : [(17045 ^ _115804) ^ [_386842] : [relation(_386842), -(relation_rng(relation_composition(_386774, _386842)) = relation_image(_386842, relation_rng(_386774)))]]], (13900 ^ _115804) ^ [_322476] : [13901 ^ _115804 : [(13902 ^ _115804) ^ [_322545] : [ordinal(_322545), in(_322545, _322476)]], 13908 ^ _115804 : [(13909 ^ _115804) ^ [] : [-(ordinal(13907 ^ [_322476]))], (13913 ^ _115804) ^ [_322702] : [ordinal(_322702), in(_322702, _322476), -(ordinal_subset(13907 ^ [_322476], _322702))], (13911 ^ _115804) ^ [] : [-(in(13907 ^ [_322476], _322476))]]], (9821 ^ _115804) ^ [_266324] : [rel_str(_266324), -(one_sorted_str(_266324))], (19258 ^ _115804) ^ [_422290] : [ordinal(_422290), -(connected(inclusion_relation(_422290)))], (10923 ^ _115804) ^ [_280728] : [-(lattice(boole_lattice(_280728)))], (10421 ^ _115804) ^ [_274055] : [-(up_complete_relstr(boole_POSet(_274055)))], (19940 ^ _115804) ^ [_433200] : [rel_str(_433200), 19943 ^ _115804 : [(19944 ^ _115804) ^ [_433269] : [element(_433269, the_carrier(_433200)), 19947 ^ _115804 : [(19948 ^ _115804) ^ [] : [-(relstr_set_smaller(_433200, empty_set, _433269))], (19950 ^ _115804) ^ [] : [-(relstr_element_smaller(_433200, empty_set, _433269))]]]]], (9555 ^ _115804) ^ [_262511, _262513] : [-(relation(relation_composition(_262513, _262511))), relation(_262513), relation(_262511)], (12218 ^ _115804) ^ [] : [-(meet_commutative(12206 ^ []))], (12600 ^ _115804) ^ [] : [-(complete_relstr(12582 ^ []))], (9741 ^ _115804) ^ [_265263, _265265] : [9756 ^ _115804 : [(9757 ^ _115804) ^ [] : [-(strict_latt_str(k8_filter_1(_265265, _265263)))], (9759 ^ _115804) ^ [] : [-(latt_str(k8_filter_1(_265265, _265263)))]], -(empty_carrier(_265265)), latt_str(_265265), -(empty_carrier(_265263)), latt_str(_265263)], (1776 ^ _115804) ^ [_140579, _140581, _140583, _140585, _140587, _140589, _140591, _140593] : [-(k10_filter_1(_140593, _140589, _140585, _140581) = k10_filter_1(_140591, _140587, _140583, _140579)), _140593 = _140591, _140589 = _140587, _140585 = _140583, _140581 = _140579], (9379 ^ _115804) ^ [] : [true___, -(true___)], (11395 ^ _115804) ^ [_286993] : [-(transitive_relstr(boole_POSet(_286993)))], (19835 ^ _115804) ^ [_431684] : [relation(_431684), 19838 ^ _115804 : [(19839 ^ _115804) ^ [] : [relation_dom(_431684) = empty_set, -(relation_rng(_431684) = empty_set)], (19845 ^ _115804) ^ [] : [relation_rng(_431684) = empty_set, -(relation_dom(_431684) = empty_set)]]], (12742 ^ _115804) ^ [] : [-(antisymmetric_relstr(12732 ^ []))], (12007 ^ _115804) ^ [_295884, _295886] : [subset(_295886, singleton(_295884)), -(_295886 = empty_set), -(_295886 = singleton(_295884))], (12521 ^ _115804) ^ [] : [-(complete_relstr(12503 ^ []))], (2004 ^ _115804) ^ [_144331, _144333, _144335, _144337, _144339, _144341, _144343, _144345] : [-(apply_on_set_and_struct2(_144345, _144341, _144337, _144333) = apply_on_set_and_struct2(_144343, _144339, _144335, _144331)), _144345 = _144343, _144341 = _144339, _144337 = _144335, _144333 = _144331], (11644 ^ _115804) ^ [_290456, _290458] : [relation_of2(_290456, _290458, _290458), 11647 ^ _115804 : [(11648 ^ _115804) ^ [_290538, _290540] : [rel_str_of(_290458, _290456) = rel_str_of(_290540, _290538), 11651 ^ _115804 : [(11652 ^ _115804) ^ [] : [-(_290458 = _290540)], (11654 ^ _115804) ^ [] : [-(_290456 = _290538)]]]]], (10591 ^ _115804) ^ [_276364] : [-(join_absorbing(boole_lattice(_276364)))], (304 ^ _115804) ^ [_119722, _119724] : [-(connected_relstr(_119722)), _119724 = _119722, connected_relstr(_119724)], (9235 ^ _115804) ^ [] : [true___, -(true___)], (2640 ^ _115804) ^ [_153965, _153967] : [_153967 = _153965, -(the_carrier(_153967) = the_carrier(_153965))], (2460 ^ _115804) ^ [_151303, _151305, _151307, _151309] : [-(cast_to_el_of_LattPOSet(_151309, _151305) = cast_to_el_of_LattPOSet(_151307, _151303)), _151309 = _151307, _151305 = _151303], (12530 ^ _115804) ^ [] : [-(strict_rel_str(12524 ^ []))], (1394 ^ _115804) ^ [_134489, _134491, _134493, _134495] : [-(upper_relstr_subset(_134493, _134489)), upper_relstr_subset(_134495, _134491), _134495 = _134493, _134491 = _134489], (5117 ^ _115804) ^ [_190133] : [rel_str(_190133), 5120 ^ _115804 : [(5121 ^ _115804) ^ [_190211] : [rel_str(_190211), 5124 ^ _115804 : [(5125 ^ _115804) ^ [] : [subrelstr(_190211, _190133), 5128 ^ _115804 : [(5129 ^ _115804) ^ [] : [-(subset(the_carrier(_190211), the_carrier(_190133)))], (5131 ^ _115804) ^ [] : [-(subset(the_InternalRel(_190211), the_InternalRel(_190133)))]]], (5133 ^ _115804) ^ [] : [-(subrelstr(_190211, _190133)), subset(the_carrier(_190211), the_carrier(_190133)), subset(the_InternalRel(_190211), the_InternalRel(_190133))]]]]], (10939 ^ _115804) ^ [_280917, _280919, _280921] : [10966 ^ _115804 : [(10967 ^ _115804) ^ [] : [empty_carrier(latt_str_of(_280921, _280919, _280917))], (10969 ^ _115804) ^ [] : [-(strict_latt_str(latt_str_of(_280921, _280919, _280917)))]], -(empty(_280921)), function(_280919), quasi_total(_280919, cartesian_product2(_280921, _280921), _280921), relation_of2(_280919, cartesian_product2(_280921, _280921), _280921), function(_280917), quasi_total(_280917, cartesian_product2(_280921, _280921), _280921), relation_of2(_280917, cartesian_product2(_280921, _280921), _280921)], (6548 ^ _115804) ^ [_214190, _214192] : [empty(_214192), 6551 ^ _115804 : [(6552 ^ _115804) ^ [] : [element(_214190, _214192), -(empty(_214190))], (6558 ^ _115804) ^ [] : [empty(_214190), -(element(_214190, _214192))]]], (18192 ^ _115804) ^ [_405619, _405621] : [-(_405621 = _405619), 18196 ^ _115804 : [(18197 ^ _115804) ^ [] : [-(in(18193 ^ [_405619, _405621], _405621))], (18199 ^ _115804) ^ [] : [in(18193 ^ [_405619, _405621], _405619)]], 18200 ^ _115804 : [(18201 ^ _115804) ^ [] : [-(in(18193 ^ [_405619, _405621], _405619))], (18203 ^ _115804) ^ [] : [in(18193 ^ [_405619, _405621], _405621)]]], (2340 ^ _115804) ^ [_149529, _149531, _149533, _149535] : [-(union_of_subsets(_149535, _149531) = union_of_subsets(_149533, _149529)), _149535 = _149533, _149531 = _149529], (1080 ^ _115804) ^ [_130122, _130124, _130126, _130128] : [-(proper_subset(_130126, _130122)), proper_subset(_130128, _130124), _130128 = _130126, _130124 = _130122], (17996 ^ _115804) ^ [_402689] : [-(well_orders(17992 ^ [_402689], _402689))], (10339 ^ _115804) ^ [_273045] : [one_sorted_str(_273045), 10342 ^ _115804 : [(10347 ^ _115804) ^ [] : [-(v2_membered(empty_carrier_subset(_273045)))], (10345 ^ _115804) ^ [] : [-(v1_membered(empty_carrier_subset(_273045)))], (10351 ^ _115804) ^ [] : [-(v4_membered(empty_carrier_subset(_273045)))], (10353 ^ _115804) ^ [] : [-(v5_membered(empty_carrier_subset(_273045)))], (10343 ^ _115804) ^ [] : [-(empty(empty_carrier_subset(_273045)))], (10349 ^ _115804) ^ [] : [-(v3_membered(empty_carrier_subset(_273045)))]]], (11301 ^ _115804) ^ [_285766] : [-(antisymmetric_relstr(incl_POSet(_285766)))], (4328 ^ _115804) ^ [_175682, _175684, _175686] : [-(meet_commut(_175686, _175684, _175682) = meet_commut(_175686, _175682, _175684)), -(empty_carrier(_175686)), meet_commutative(_175686), meet_semilatt_str(_175686), element(_175684, the_carrier(_175686)), element(_175682, the_carrier(_175686))], (10377 ^ _115804) ^ [_273551] : [empty_carrier(boole_POSet(_273551))], (13164 ^ _115804) ^ [_309823, _309825, _309827] : [-(unordered_pair_as_carrier_subset(_309827, _309825, _309823) = unordered_pair(_309825, _309823)), -(empty_carrier(_309827)), one_sorted_str(_309827), element(_309825, the_carrier(_309827)), element(_309823, the_carrier(_309827))], (10911 ^ _115804) ^ [_280614] : [-(join_commutative(boole_lattice(_280614)))], (3756 ^ _115804) ^ [_168467] : [rel_str(_168467), 3787 ^ _115804 : [(3816 ^ _115804) ^ [] : [-(complete_relstr(_168467))], (3790 ^ _115804) ^ [] : [-(reflexive_relstr(_168467))], (3796 ^ _115804) ^ [] : [-(lower_bounded_relstr(_168467))], (3798 ^ _115804) ^ [] : [-(upper_bounded_relstr(_168467))], (3804 ^ _115804) ^ [] : [-(join_complete_relstr(_168467))], (3808 ^ _115804) ^ [] : [-(v1_waybel_2(_168467))], (3792 ^ _115804) ^ [] : [-(transitive_relstr(_168467))], (3806 ^ _115804) ^ [] : [v1_yellow_3(_168467)], (3812 ^ _115804) ^ [] : [-(with_suprema_relstr(_168467))], (3800 ^ _115804) ^ [] : [-(bounded_relstr(_168467))], (3810 ^ _115804) ^ [] : [-(v2_waybel_2(_168467))], (3788 ^ _115804) ^ [] : [empty_carrier(_168467)], (3794 ^ _115804) ^ [] : [-(antisymmetric_relstr(_168467))], (3814 ^ _115804) ^ [] : [-(with_infima_relstr(_168467))], (3802 ^ _115804) ^ [] : [-(up_complete_relstr(_168467))]], reflexive_relstr(_168467), transitive_relstr(_168467), antisymmetric_relstr(_168467), lower_bounded_relstr(_168467), v3_waybel_3(_168467), with_suprema_relstr(_168467), with_infima_relstr(_168467)], (17086 ^ _115804) ^ [_387464, _387466, _387468, _387470] : [relation_of2_as_subset(_387464, _387466, _387470), subset(_387470, _387468), -(relation_of2_as_subset(_387464, _387466, _387468))], (9689 ^ _115804) ^ [_264491] : [one_sorted_str(_264491), 9692 ^ _115804 : [(9693 ^ _115804) ^ [] : [-(function(identity_on_carrier(_264491)))], (9697 ^ _115804) ^ [] : [-(relation_of2_as_subset(identity_on_carrier(_264491), the_carrier(_264491), the_carrier(_264491)))], (9695 ^ _115804) ^ [] : [-(quasi_total(identity_on_carrier(_264491), the_carrier(_264491), the_carrier(_264491)))]]], (12257 ^ _115804) ^ [] : [-(complete_relstr(12239 ^ []))], (11411 ^ _115804) ^ [_287198] : [-(reflexive_relstr(boole_POSet(_287198)))], (5941 ^ _115804) ^ [_204095, _204097] : [_204097 = empty_set, 5944 ^ _115804 : [(5945 ^ _115804) ^ [] : [_204095 = set_meet(_204097), -(_204095 = empty_set)], (5951 ^ _115804) ^ [] : [_204095 = empty_set, -(_204095 = set_meet(_204097))]]], (12509 ^ _115804) ^ [] : [-(strict_rel_str(12503 ^ []))], (7228 ^ _115804) ^ [_225156] : [relation(_225156), 7231 ^ _115804 : [(7254 ^ _115804) ^ [_225620] : [7257 ^ _115804 : [(7266 ^ _115804) ^ [] : [7255 ^ [_225156, _225620] = 7256 ^ [_225156, _225620]], (7264 ^ _115804) ^ [] : [-(in(ordered_pair(7256 ^ [_225156, _225620], 7255 ^ [_225156, _225620]), _225156))], (7262 ^ _115804) ^ [] : [-(in(ordered_pair(7255 ^ [_225156, _225620], 7256 ^ [_225156, _225620]), _225156))], (7258 ^ _115804) ^ [] : [-(in(7255 ^ [_225156, _225620], _225620))], (7260 ^ _115804) ^ [] : [-(in(7256 ^ [_225156, _225620], _225620))]], -(is_antisymmetric_in(_225156, _225620))], (7232 ^ _115804) ^ [_225267] : [is_antisymmetric_in(_225156, _225267), 7235 ^ _115804 : [(7236 ^ _115804) ^ [_225359, _225361] : [-(_225361 = _225359), in(_225361, _225267), in(_225359, _225267), in(ordered_pair(_225361, _225359), _225156), in(ordered_pair(_225359, _225361), _225156)]]]]], (17222 ^ _115804) ^ [_389900, _389902] : [relation(_389900), -(_389902 = empty_set), subset(_389902, relation_rng(_389900)), relation_inverse_image(_389900, _389902) = empty_set], (10333 ^ _115804) ^ [] : [-(epsilon_connected(omega))], (12471 ^ _115804) ^ [] : [trivial_carrier(12465 ^ [])], (11409 ^ _115804) ^ [_287179] : [-(strict_rel_str(boole_POSet(_287179)))], (9017 ^ _115804) ^ [_255317] : [-(element(k1_pcomps_1(_255317), powerset(powerset(_255317))))], (10419 ^ _115804) ^ [_274031] : [-(bounded_relstr(boole_POSet(_274031)))], (726 ^ _115804) ^ [_125263, _125265] : [-(epsilon_transitive(_125263)), _125265 = _125263, epsilon_transitive(_125265)], (2040 ^ _115804) ^ [_144933, _144935, _144937, _144939, _144941, _144943] : [-(a_3_0_waybel_9(_144943, _144939, _144935) = a_3_0_waybel_9(_144941, _144937, _144933)), _144943 = _144941, _144939 = _144937, _144935 = _144933], (10365 ^ _115804) ^ [_273381] : [empty(the_carrier(_273381)), -(empty_carrier(_273381)), one_sorted_str(_273381)], (10933 ^ _115804) ^ [_280823] : [-(bounded_lattstr(boole_lattice(_280823)))], (204 ^ _115804) ^ [_118472, _118474] : [-(distributive_lattstr(_118472)), _118474 = _118472, distributive_lattstr(_118474)], (1214 ^ _115804) ^ [_132027, _132029] : [-(lattice(_132027)), _132029 = _132027, lattice(_132029)], (12868 ^ _115804) ^ [] : [-(lower_bounded_relstr(12850 ^ []))], (12310 ^ _115804) ^ [] : [-(antisymmetric_relstr(12298 ^ []))], (12526 ^ _115804) ^ [] : [-(rel_str(12524 ^ []))], (2712 ^ _115804) ^ [_155386] : [rel_str(_155386), 2727 ^ _115804 : [(2732 ^ _115804) ^ [] : [-(up_complete_relstr(_155386))], (2728 ^ _115804) ^ [] : [empty_carrier(_155386)], (2730 ^ _115804) ^ [] : [-(reflexive_relstr(_155386))], (2734 ^ _115804) ^ [] : [-(join_complete_relstr(_155386))]], -(empty_carrier(_155386)), reflexive_relstr(_155386), complete_relstr(_155386)], (16129 ^ _115804) ^ [_370588, _370590] : [-(empty(_370590)), relation(_370588), 16186 ^ _115804 : [(16191 ^ _115804) ^ [] : [-(relation_dom(16185 ^ [_370588, _370590]) = _370590)], (16187 ^ _115804) ^ [] : [-(relation(16185 ^ [_370588, _370590]))], (16189 ^ _115804) ^ [] : [-(function(16185 ^ [_370588, _370590]))], (16193 ^ _115804) ^ [_372110] : [in(_372110, _370590), 16197 ^ _115804 : [(16198 ^ _115804) ^ [] : [-(_372110 = 16196 ^ [_370588, _370590, _372110])], (16202 ^ _115804) ^ [_372339] : [in(_372339, 16196 ^ [_370588, _370590, _372110]), -(in(ordered_pair(apply(16185 ^ [_370588, _370590], _372110), _372339), _370588))], (16200 ^ _115804) ^ [] : [-(in(apply(16185 ^ [_370588, _370590], _372110), 16196 ^ [_370588, _370590, _372110]))]]]], 16170 ^ _115804 : [(16171 ^ _115804) ^ [] : [-(in(16169 ^ [_370588, _370590], _370590))], (16173 ^ _115804) ^ [_371711, _371713] : [16169 ^ [_370588, _370590] = _371711, in(_371713, _371711), 16181 ^ _115804 : [(16182 ^ _115804) ^ [] : [-(in(16180 ^ [_370588, _370590, _371711, _371713], _371711))], (16184 ^ _115804) ^ [] : [in(ordered_pair(_371713, 16180 ^ [_370588, _370590, _371711, _371713]), _370588)]]]], 16143 ^ _115804 : [(16151 ^ _115804) ^ [_371244] : [in(_371244, 16145 ^ [_370588, _370590]), -(in(ordered_pair(16141 ^ [_370588, _370590], _371244), _370588))], (16147 ^ _115804) ^ [] : [-(16140 ^ [_370588, _370590] = 16145 ^ [_370588, _370590])], (16162 ^ _115804) ^ [_371474] : [in(_371474, 16156 ^ [_370588, _370590]), -(in(ordered_pair(16142 ^ [_370588, _370590], _371474), _370588))], (16149 ^ _115804) ^ [] : [-(in(16141 ^ [_370588, _370590], 16145 ^ [_370588, _370590]))], (16144 ^ _115804) ^ [] : [-(in(16140 ^ [_370588, _370590], _370590))], (16158 ^ _115804) ^ [] : [-(16140 ^ [_370588, _370590] = 16156 ^ [_370588, _370590])], (16168 ^ _115804) ^ [] : [16141 ^ [_370588, _370590] = 16142 ^ [_370588, _370590]], (16160 ^ _115804) ^ [] : [-(in(16142 ^ [_370588, _370590], 16156 ^ [_370588, _370590]))]]], (12105 ^ _115804) ^ [] : [-(distributive_lattstr(12083 ^ []))], (9963 ^ _115804) ^ [_268193] : [meet_semilatt_str(_268193), 9966 ^ _115804 : [(9967 ^ _115804) ^ [] : [-(function(the_L_meet(_268193)))], (9971 ^ _115804) ^ [] : [-(relation_of2_as_subset(the_L_meet(_268193), cartesian_product2(the_carrier(_268193), the_carrier(_268193)), the_carrier(_268193)))], (9969 ^ _115804) ^ [] : [-(quasi_total(the_L_meet(_268193), cartesian_product2(the_carrier(_268193), the_carrier(_268193)), the_carrier(_268193)))]]], (20112 ^ _115804) ^ [_435854, _435856] : [-(subset(_435856, set_union2(_435856, _435854)))], (11117 ^ _115804) ^ [_283361] : [11128 ^ _115804 : [(11137 ^ _115804) ^ [] : [-(v1_partfun1(the_L_meet(_283361), cartesian_product2(the_carrier(_283361), the_carrier(_283361)), the_carrier(_283361)))], (11135 ^ _115804) ^ [] : [-(v1_binop_1(the_L_meet(_283361), the_carrier(_283361)))], (11133 ^ _115804) ^ [] : [-(quasi_total(the_L_meet(_283361), cartesian_product2(the_carrier(_283361), the_carrier(_283361)), the_carrier(_283361)))], (11129 ^ _115804) ^ [] : [-(relation(the_L_meet(_283361)))], (11131 ^ _115804) ^ [] : [-(function(the_L_meet(_283361)))]], -(empty_carrier(_283361)), meet_commutative(_283361), meet_semilatt_str(_283361)], (698 ^ _115804) ^ [_124877, _124879, _124881, _124883] : [-(closed_subsets(_124881, _124877)), closed_subsets(_124883, _124879), _124883 = _124881, _124879 = _124877], (2156 ^ _115804) ^ [_146727, _146729, _146731, _146733] : [-(cartesian_product2(_146733, _146729) = cartesian_product2(_146731, _146727)), _146733 = _146731, _146729 = _146727], (3968 ^ _115804) ^ [_171129] : [rel_str(_171129), -(bounded_relstr(_171129)), lower_bounded_relstr(_171129), upper_bounded_relstr(_171129)], (7784 ^ _115804) ^ [_233807] : [relation(_233807), 7787 ^ _115804 : [(7810 ^ _115804) ^ [_234207] : [7813 ^ _115804 : [(7822 ^ _115804) ^ [] : [in(ordered_pair(7812 ^ [_233807, _234207], 7811 ^ [_233807, _234207]), _233807)], (7820 ^ _115804) ^ [] : [in(ordered_pair(7811 ^ [_233807, _234207], 7812 ^ [_233807, _234207]), _233807)], (7818 ^ _115804) ^ [] : [7811 ^ [_233807, _234207] = 7812 ^ [_233807, _234207]], (7814 ^ _115804) ^ [] : [-(in(7811 ^ [_233807, _234207], _234207))], (7816 ^ _115804) ^ [] : [-(in(7812 ^ [_233807, _234207], _234207))]], -(is_connected_in(_233807, _234207))], (7788 ^ _115804) ^ [_233926] : [is_connected_in(_233807, _233926), 7791 ^ _115804 : [(7792 ^ _115804) ^ [_234026, _234028] : [in(_234028, _233926), in(_234026, _233926), -(_234028 = _234026), -(in(ordered_pair(_234028, _234026), _233807)), -(in(ordered_pair(_234026, _234028), _233807))]]]]], (12786 ^ _115804) ^ [] : [-(ordinal(12778 ^ []))], (334 ^ _115804) ^ [_120097, _120099] : [-(natural(_120097)), _120099 = _120097, natural(_120099)], (9527 ^ _115804) ^ [] : [true___, -(true___)], (16618 ^ _115804) ^ [_380325, _380327, _380329] : [relation(_380325), 16621 ^ _115804 : [(16622 ^ _115804) ^ [] : [in(_380329, relation_rng(relation_rng_restriction(_380327, _380325))), 16625 ^ _115804 : [(16626 ^ _115804) ^ [] : [-(in(_380329, _380327))], (16628 ^ _115804) ^ [] : [-(in(_380329, relation_rng(_380325)))]]], (16630 ^ _115804) ^ [] : [-(in(_380329, relation_rng(relation_rng_restriction(_380327, _380325)))), in(_380329, _380327), in(_380329, relation_rng(_380325))]]], (9487 ^ _115804) ^ [] : [true___, -(true___)], (7372 ^ _115804) ^ [_227360, _227362] : [-(equipotent(_227362, _227360)), 7373 ^ _115804 : [(7374 ^ _115804) ^ [_227419] : [relation(_227419), function(_227419), one_to_one(_227419), relation_dom(_227419) = _227362, relation_rng(_227419) = _227360]]], (5068 ^ _115804) ^ [_189226] : [relation(_189226), 5071 ^ _115804 : [(5095 ^ _115804) ^ [_189731, _189733] : [-(_189731 = relation_image(_189226, _189733)), 5108 ^ _115804 : [(5109 ^ _115804) ^ [] : [-(in(ordered_pair(5107 ^ [_189226, _189731, _189733], 5096 ^ [_189226, _189731, _189733]), _189226))], (5113 ^ _115804) ^ [] : [in(5096 ^ [_189226, _189731, _189733], _189731)], (5111 ^ _115804) ^ [] : [-(in(5107 ^ [_189226, _189731, _189733], _189733))]], 5099 ^ _115804 : [(5100 ^ _115804) ^ [] : [-(in(5096 ^ [_189226, _189731, _189733], _189731))], (5102 ^ _115804) ^ [_189879] : [in(ordered_pair(_189879, 5096 ^ [_189226, _189731, _189733]), _189226), in(_189879, _189733)]]], (5072 ^ _115804) ^ [_189333, _189335] : [_189333 = relation_image(_189226, _189335), 5075 ^ _115804 : [(5076 ^ _115804) ^ [_189430] : [in(_189430, _189333), 5080 ^ _115804 : [(5081 ^ _115804) ^ [] : [-(in(ordered_pair(5079 ^ [_189226, _189333, _189335, _189430], _189430), _189226))], (5083 ^ _115804) ^ [] : [-(in(5079 ^ [_189226, _189333, _189335, _189430], _189335))]]], (5085 ^ _115804) ^ [_189566] : [-(in(_189566, _189333)), 5086 ^ _115804 : [(5087 ^ _115804) ^ [_189613] : [in(ordered_pair(_189613, _189566), _189226), in(_189613, _189335)]]]]]]], (12342 ^ _115804) ^ [] : [-(epsilon_connected(12338 ^ []))], (17615 ^ _115804) ^ [_396410] : [one_sorted_str(_396410), 17618 ^ _115804 : [(17619 ^ _115804) ^ [_396574] : [-(empty_carrier(_396574)), net_str(_396574, _396410), 17626 ^ _115804 : [(17627 ^ _115804) ^ [_396777] : [-(empty_carrier(_396777)), full_subnetstr(_396777, _396410, _396574), subnetstr(_396777, _396410, _396574), 17638 ^ _115804 : [(17639 ^ _115804) ^ [_397016] : [element(_397016, the_carrier(_396574)), 17642 ^ _115804 : [(17643 ^ _115804) ^ [_397135] : [element(_397135, the_carrier(_396574)), 17646 ^ _115804 : [(17647 ^ _115804) ^ [_397243] : [element(_397243, the_carrier(_396777)), 17650 ^ _115804 : [(17651 ^ _115804) ^ [_397340] : [element(_397340, the_carrier(_396777)), -(related(_396777, _397243, _397340)), _397016 = _397243, _397135 = _397340, related(_396574, _397016, _397135)]]]]]]]]]]]]], (294 ^ _115804) ^ [_119597, _119599] : [-(v5_membered(_119597)), _119599 = _119597, v5_membered(_119599)], (1708 ^ _115804) ^ [_139525, _139527] : [_139527 = _139525, -(a_1_0_filter_1(_139527) = a_1_0_filter_1(_139525))], (12199 ^ _115804) ^ [] : [-(reflexive_relstr(12193 ^ []))], (19190 ^ _115804) ^ [_421284, _421286] : [element(_421284, powerset(powerset(_421286))), -(_421284 = empty_set), -(subset_difference(_421286, cast_to_subset(_421286), union_of_subsets(_421286, _421284)) = meet_of_subsets(_421286, complements_of_subsets(_421286, _421284)))], (13006 ^ _115804) ^ [] : [-(meet_associative(12992 ^ []))], (12862 ^ _115804) ^ [] : [-(antisymmetric_relstr(12850 ^ []))], (13552 ^ _115804) ^ [_315448, _315450, _315452] : [-(below_refl(_315452, _315450, _315450)), -(empty_carrier(_315452)), meet_commutative(_315452), meet_absorbing(_315452), join_absorbing(_315452), latt_str(_315452), element(_315450, the_carrier(_315452)), element(_315448, the_carrier(_315452))], (2054 ^ _115804) ^ [_145154, _145156, _145158, _145160, _145162, _145164] : [-(subset_intersection2(_145164, _145160, _145156) = subset_intersection2(_145162, _145158, _145154)), _145164 = _145162, _145160 = _145158, _145156 = _145154], (10671 ^ _115804) ^ [_277303, _277305] : [-(closed_subset(topstr_closure(_277305, _277303), _277305)), topological_space(_277305), top_str(_277305), element(_277303, powerset(the_carrier(_277305)))], (2166 ^ _115804) ^ [_146876, _146878, _146880, _146882] : [-(fiber(_146882, _146878) = fiber(_146880, _146876)), _146882 = _146880, _146878 = _146876], (18120 ^ _115804) ^ [_404592] : [top_str(_404592), 18123 ^ _115804 : [(18124 ^ _115804) ^ [_404666] : [element(_404666, powerset(the_carrier(_404592))), 18127 ^ _115804 : [(18128 ^ _115804) ^ [] : [closed_subset(_404666, _404592), -(open_subset(subset_complement(the_carrier(_404592), _404666), _404592))], (18134 ^ _115804) ^ [] : [open_subset(subset_complement(the_carrier(_404592), _404666), _404592), -(closed_subset(_404666, _404592))]]]]], (12613 ^ _115804) ^ [] : [-(antisymmetric_relstr(12601 ^ []))], (12378 ^ _115804) ^ [_300091] : [12386 ^ _115804 : [(12387 ^ _115804) ^ [] : [-(element(12385 ^ [_300091], powerset(the_carrier(_300091))))], (12389 ^ _115804) ^ [] : [-(open_subset(12385 ^ [_300091], _300091))]], topological_space(_300091), top_str(_300091)], (12740 ^ _115804) ^ [] : [-(transitive_relstr(12732 ^ []))], (10399 ^ _115804) ^ [_273761] : [-(up_complete_relstr(boole_POSet(_273761)))], (11558 ^ _115804) ^ [_289174, _289176, _289178] : [-(empty_carrier(_289176)), lattice(_289176), complete_latt_str(_289176), latt_str(_289176), 11573 ^ _115804 : [(11574 ^ _115804) ^ [] : [in(_289178, a_2_3_lattice3(_289176, _289174)), 11578 ^ _115804 : [(11579 ^ _115804) ^ [] : [-(element(11577 ^ [_289174, _289176, _289178], the_carrier(_289176)))], (11583 ^ _115804) ^ [] : [-(latt_set_smaller(_289176, 11577 ^ [_289174, _289176, _289178], _289174))], (11581 ^ _115804) ^ [] : [-(_289178 = 11577 ^ [_289174, _289176, _289178])]]], (11585 ^ _115804) ^ [] : [-(in(_289178, a_2_3_lattice3(_289176, _289174))), 11586 ^ _115804 : [(11587 ^ _115804) ^ [_289584] : [element(_289584, the_carrier(_289176)), _289178 = _289584, latt_set_smaller(_289176, _289584, _289174)]]]]], (19067 ^ _115804) ^ [_419219, _419221] : [subset(_419221, _419219), -(_419219 = set_union2(_419221, set_difference(_419219, _419221)))], (840 ^ _115804) ^ [_126820, _126822, _126824, _126826, _126828, _126830] : [-(latt_element_smaller(_126828, _126824, _126820)), latt_element_smaller(_126830, _126826, _126822), _126830 = _126828, _126826 = _126824, _126822 = _126820], (12238 ^ _115804) ^ [] : [-(boolean_lattstr(12206 ^ []))], (8857 ^ _115804) ^ [_253223, _253225, _253227, _253229] : [-(element(k10_filter_1(_253229, _253227, _253225, _253223), the_carrier(k8_filter_1(_253229, _253227)))), -(empty_carrier(_253229)), lattice(_253229), latt_str(_253229), -(empty_carrier(_253227)), lattice(_253227), latt_str(_253227), element(_253225, the_carrier(_253229)), element(_253223, the_carrier(_253227))], (12626 ^ _115804) ^ [] : [-(epsilon_connected(12614 ^ []))], (1650 ^ _115804) ^ [_138666, _138668, _138670, _138672, _138674, _138676] : [-(unordered_triple(_138676, _138672, _138668) = unordered_triple(_138674, _138670, _138666)), _138676 = _138674, _138672 = _138670, _138668 = _138666], (10405 ^ _115804) ^ [_273863] : [empty_carrier(boole_POSet(_273863))], (11393 ^ _115804) ^ [_286974] : [-(reflexive_relstr(boole_POSet(_286974)))], (4350 ^ _115804) ^ [_175998, _176000, _176002] : [-(subset_union2(_176002, _176000, _175998) = subset_union2(_176002, _175998, _176000)), element(_176000, powerset(_176002)), element(_175998, powerset(_176002))], (612 ^ _115804) ^ [_123722, _123724] : [-(meet_semilatt_str(_123722)), _123724 = _123722, meet_semilatt_str(_123724)], (802 ^ _115804) ^ [_126301, _126303] : [-(join_commutative(_126301)), _126303 = _126301, join_commutative(_126303)], (12701 ^ _115804) ^ [] : [-(antisymmetric_relstr(12689 ^ []))], (9123 ^ _115804) ^ [] : [true___, -(true___)], (8953 ^ _115804) ^ [_254509, _254511, _254513, _254515] : [-(element(ordered_pair_as_product_element(_254515, _254513, _254511, _254509), cartesian_product2(_254515, _254513))), -(empty(_254515)), -(empty(_254513)), element(_254511, _254515), element(_254509, _254513)], (12513 ^ _115804) ^ [] : [-(transitive_relstr(12503 ^ []))], (224 ^ _115804) ^ [_118722, _118724] : [-(bounded_lattstr(_118722)), _118724 = _118722, bounded_lattstr(_118724)], (12159 ^ _115804) ^ [] : [-(lower_bounded_semilattstr(12137 ^ []))], (12775 ^ _115804) ^ [] : [-(latt_str(12773 ^ []))], (9273 ^ _115804) ^ [] : [true___, -(true___)], (12534 ^ _115804) ^ [] : [-(transitive_relstr(12524 ^ []))], (18682 ^ _115804) ^ [_413488] : [relation(_413488), 18685 ^ _115804 : [(18686 ^ _115804) ^ [] : [-(relation_rng(_413488) = relation_dom(relation_inverse(_413488)))], (18688 ^ _115804) ^ [] : [-(relation_dom(_413488) = relation_rng(relation_inverse(_413488)))]]], (6486 ^ _115804) ^ [_213202] : [one_sorted_str(_213202), -(empty_carrier_subset(_213202) = empty_set)], (20387 ^ _115804) ^ [_439924, _439926] : [in(_439924, 20373 ^ [_439926]), 20391 ^ _115804 : [(20392 ^ _115804) ^ [] : [-(in(20390 ^ [_439924, _439926], 20373 ^ [_439926]))], (20394 ^ _115804) ^ [_440070] : [subset(_440070, _439924), -(in(_440070, 20390 ^ [_439924, _439926]))]]], (17353 ^ _115804) ^ [_391951] : [one_sorted_str(_391951), 17356 ^ _115804 : [(17357 ^ _115804) ^ [_392026] : [net_str(_392026, _391951), 17360 ^ _115804 : [(17361 ^ _115804) ^ [_392094] : [subnetstr(_392094, _391951, _392026), -(subset(the_carrier(_392094), the_carrier(_392026)))]]]]], (16479 ^ _115804) ^ [_378097, _378099] : [topological_space(_378099), top_str(_378099), element(_378097, powerset(the_carrier(_378099))), 16491 ^ _115804 : [(16492 ^ _115804) ^ [] : [-(element(16490 ^ [_378097, _378099], powerset(powerset(the_carrier(_378099)))))], (16494 ^ _115804) ^ [_378416] : [element(_378416, powerset(the_carrier(_378099))), 16497 ^ _115804 : [(16498 ^ _115804) ^ [] : [in(_378416, 16490 ^ [_378097, _378099]), 16502 ^ _115804 : [(16507 ^ _115804) ^ [] : [-(closed_subset(16501 ^ [_378097, _378099, _378416], _378099))], (16503 ^ _115804) ^ [] : [-(element(16501 ^ [_378097, _378099, _378416], powerset(the_carrier(_378099))))], (16505 ^ _115804) ^ [] : [-(16501 ^ [_378097, _378099, _378416] = _378416)], (16509 ^ _115804) ^ [] : [-(subset(_378097, _378416))]]], (16511 ^ _115804) ^ [] : [-(in(_378416, 16490 ^ [_378097, _378099])), 16512 ^ _115804 : [(16513 ^ _115804) ^ [_378711] : [element(_378711, powerset(the_carrier(_378099))), _378711 = _378416, closed_subset(_378711, _378099), subset(_378097, _378416)]]]]]]], (7416 ^ _115804) ^ [_228053, _228055, _228057] : [-(_228053 = set_difference(_228057, _228055)), 7428 ^ _115804 : [(7429 ^ _115804) ^ [] : [-(in(7417 ^ [_228053, _228055, _228057], _228057))], (7433 ^ _115804) ^ [] : [in(7417 ^ [_228053, _228055, _228057], _228053)], (7431 ^ _115804) ^ [] : [in(7417 ^ [_228053, _228055, _228057], _228055)]], 7420 ^ _115804 : [(7421 ^ _115804) ^ [] : [-(in(7417 ^ [_228053, _228055, _228057], _228053))], (7423 ^ _115804) ^ [] : [in(7417 ^ [_228053, _228055, _228057], _228057), -(in(7417 ^ [_228053, _228055, _228057], _228055))]]], (12772 ^ _115804) ^ [] : [-(one_to_one(12766 ^ []))], (3898 ^ _115804) ^ [_170286] : [rel_str(_170286), 3909 ^ _115804 : [(3914 ^ _115804) ^ [] : [-(transitive_relstr(_170286))], (3912 ^ _115804) ^ [] : [-(reflexive_relstr(_170286))], (3918 ^ _115804) ^ [] : [-(with_suprema_relstr(_170286))], (3920 ^ _115804) ^ [] : [-(with_infima_relstr(_170286))], (3910 ^ _115804) ^ [] : [empty_carrier(_170286)], (3916 ^ _115804) ^ [] : [-(antisymmetric_relstr(_170286))]], -(empty_carrier(_170286)), heyting_relstr(_170286)], (20377 ^ _115804) ^ [_439771, _439773, _439775] : [-(in(_439771, 20373 ^ [_439775])), in(_439773, 20373 ^ [_439775]), subset(_439771, _439773)], (12594 ^ _115804) ^ [] : [-(antisymmetric_relstr(12582 ^ []))], (10633 ^ _115804) ^ [] : [-(epsilon_connected(empty_set))], (16467 ^ _115804) ^ [_377914] : [-(relation(16465 ^ [_377914]))], (7635 ^ _115804) ^ [_231520, _231522] : [element(_231520, powerset(_231522)), -(subset_complement(_231522, _231520) = set_difference(_231522, _231520))], (19545 ^ _115804) ^ [_426781] : [topological_space(_426781), top_str(_426781), 19552 ^ _115804 : [(19553 ^ _115804) ^ [_426941] : [top_str(_426941), 19556 ^ _115804 : [(19557 ^ _115804) ^ [_427045] : [element(_427045, powerset(the_carrier(_426781))), 19560 ^ _115804 : [(19561 ^ _115804) ^ [_427146] : [element(_427146, powerset(the_carrier(_426941))), 19564 ^ _115804 : [(19565 ^ _115804) ^ [] : [open_subset(_427146, _426941), -(interior(_426941, _427146) = _427146)], (19571 ^ _115804) ^ [] : [interior(_426781, _427045) = _427045, -(open_subset(_427045, _426781))]]]]]]]]], (12097 ^ _115804) ^ [] : [-(meet_associative(12083 ^ []))], (7826 ^ _115804) ^ [_234572] : [relation(_234572), 7829 ^ _115804 : [(7830 ^ _115804) ^ [_234636] : [-(relation_restriction(_234572, _234636) = set_intersection2(_234572, cartesian_product2(_234636, _234636)))]]], (12261 ^ _115804) ^ [] : [-(upper_bounded_relstr(12239 ^ []))], (2736 ^ _115804) ^ [_155682] : [rel_str(_155682), 2747 ^ _115804 : [(2760 ^ _115804) ^ [] : [-(upper_bounded_relstr(_155682))], (2750 ^ _115804) ^ [] : [-(reflexive_relstr(_155682))], (2756 ^ _115804) ^ [] : [-(with_suprema_relstr(_155682))], (2752 ^ _115804) ^ [] : [-(transitive_relstr(_155682))], (2758 ^ _115804) ^ [] : [-(with_infima_relstr(_155682))], (2754 ^ _115804) ^ [] : [-(antisymmetric_relstr(_155682))], (2764 ^ _115804) ^ [] : [-(heyting_relstr(_155682))], (2762 ^ _115804) ^ [] : [-(distributive_relstr(_155682))], (2748 ^ _115804) ^ [] : [empty_carrier(_155682)]], -(empty_carrier(_155682)), boolean_relstr(_155682)], (10038 ^ _115804) ^ [] : [-(latt_str(10036 ^ []))], (9393 ^ _115804) ^ [_260269] : [-(rel_str(boole_POSet(_260269)))], (18982 ^ _115804) ^ [_417800] : [top_str(_417800), 18985 ^ _115804 : [(18986 ^ _115804) ^ [_417866] : [element(_417866, powerset(the_carrier(_417800))), -(subset(interior(_417800, _417866), _417866))]]], (10255 ^ _115804) ^ [_272014] : [-(diff_closed(powerset(_272014)))], (13334 ^ _115804) ^ [_312363, _312365, _312367, _312369, _312371] : [-(function_of_composition(_312371, _312369, _312367, _312365, _312363) = relation_composition(_312365, _312363)), -(empty(_312369)), function(_312365), quasi_total(_312365, _312371, _312369), relation_of2(_312365, _312371, _312369), function(_312363), quasi_total(_312363, _312369, _312367), relation_of2(_312363, _312369, _312367)], (932 ^ _115804) ^ [_128138, _128140, _128142, _128144] : [-(ex_inf_of_relstr_set(_128142, _128138)), ex_inf_of_relstr_set(_128144, _128140), _128144 = _128142, _128140 = _128138], (12178 ^ _115804) ^ [] : [-(meet_associative(12164 ^ []))], (19256 ^ _115804) ^ [_422261] : [-(the_carrier(boole_POSet(_422261)) = powerset(_422261))], (6967 ^ _115804) ^ [_220848] : [6970 ^ _115804 : [(6979 ^ _115804) ^ [] : [in(6969 ^ [_220848], 6968 ^ [_220848])], (6977 ^ _115804) ^ [] : [6968 ^ [_220848] = 6969 ^ [_220848]], (6975 ^ _115804) ^ [] : [in(6968 ^ [_220848], 6969 ^ [_220848])], (6971 ^ _115804) ^ [] : [-(in(6968 ^ [_220848], _220848))], (6973 ^ _115804) ^ [] : [-(in(6969 ^ [_220848], _220848))]], -(epsilon_connected(_220848))], (3152 ^ _115804) ^ [_160948] : [v5_membered(_160948), -(v4_membered(_160948))], (10631 ^ _115804) ^ [] : [-(epsilon_transitive(empty_set))], (13582 ^ _115804) ^ [_315854, _315856, _315858] : [-(related_reflexive(_315858, _315856, _315856)), -(empty_carrier(_315858)), reflexive_relstr(_315858), rel_str(_315858), element(_315856, the_carrier(_315858)), element(_315854, the_carrier(_315858))], (20346 ^ _115804) ^ [_439237, _439239, _439241, _439243] : [function(_439237), quasi_total(_439237, _439243, _439241), relation_of2_as_subset(_439237, _439243, _439241), subset(_439241, _439239), 20363 ^ _115804 : [(20364 ^ _115804) ^ [] : [-(_439241 = empty_set)], (20366 ^ _115804) ^ [] : [_439243 = empty_set]], 20367 ^ _115804 : [(20368 ^ _115804) ^ [] : [-(function(_439237))], (20372 ^ _115804) ^ [] : [-(relation_of2_as_subset(_439237, _439243, _439239))], (20370 ^ _115804) ^ [] : [-(quasi_total(_439237, _439243, _439239))]]], (16652 ^ _115804) ^ [_380797, _380799] : [relation(_380797), -(subset(relation_rng(relation_rng_restriction(_380799, _380797)), relation_rng(_380797)))], (980 ^ _115804) ^ [_128774, _128776] : [-(reflexive(_128774)), _128776 = _128774, reflexive(_128776)], (7758 ^ _115804) ^ [_233396] : [top_str(_233396), 7761 ^ _115804 : [(7762 ^ _115804) ^ [_233473] : [element(_233473, powerset(the_carrier(_233396))), 7765 ^ _115804 : [(7766 ^ _115804) ^ [] : [closed_subset(_233473, _233396), -(open_subset(subset_difference(the_carrier(_233396), cast_as_carrier_subset(_233396), _233473), _233396))], (7772 ^ _115804) ^ [] : [open_subset(subset_difference(the_carrier(_233396), cast_as_carrier_subset(_233396), _233473), _233396), -(closed_subset(_233473, _233396))]]]]], (12214 ^ _115804) ^ [] : [-(join_commutative(12206 ^ []))], (12272 ^ _115804) ^ [] : [-(epsilon_transitive(12268 ^ []))], (12622 ^ _115804) ^ [] : [-(empty(12614 ^ []))], (5482 ^ _115804) ^ [_196333] : [5489 ^ _115804 : [(5490 ^ _115804) ^ [_196451, _196453] : [-(apply_binary(_196333, _196453, _196451) = apply(_196333, ordered_pair(_196453, _196451)))]], relation(_196333), function(_196333)], (1938 ^ _115804) ^ [_143250, _143252, _143254, _143256, _143258, _143260] : [-(subset_union2(_143260, _143256, _143252) = subset_union2(_143258, _143254, _143250)), _143260 = _143258, _143256 = _143254, _143252 = _143250], (17387 ^ _115804) ^ [_392546] : [-(empty_carrier(_392546)), transitive_relstr(_392546), rel_str(_392546), 17398 ^ _115804 : [(17399 ^ _115804) ^ [_392759] : [element(_392759, powerset(the_carrier(_392546))), 17402 ^ _115804 : [(17426 ^ _115804) ^ [] : [17442 ^ _115804 : [(17443 ^ _115804) ^ [] : [empty(_392759)], (17445 ^ _115804) ^ [] : [-(directed_subset(_392759, _392546))]], 17428 ^ _115804 : [(17429 ^ _115804) ^ [] : [-(finite(17427 ^ [_392546, _392759]))], (17433 ^ _115804) ^ [_393301] : [element(_393301, the_carrier(_392546)), in(_393301, _392759), relstr_set_smaller(_392546, 17427 ^ [_392546, _392759], _393301)], (17431 ^ _115804) ^ [] : [-(element(17427 ^ [_392546, _392759], powerset(_392759)))]]], (17403 ^ _115804) ^ [] : [-(empty(_392759)), directed_subset(_392759, _392546), 17410 ^ _115804 : [(17411 ^ _115804) ^ [_392969] : [17419 ^ _115804 : [(17420 ^ _115804) ^ [] : [-(element(17418 ^ [_392546, _392759, _392969], the_carrier(_392546)))], (17424 ^ _115804) ^ [] : [-(relstr_set_smaller(_392546, _392969, 17418 ^ [_392546, _392759, _392969]))], (17422 ^ _115804) ^ [] : [-(in(17418 ^ [_392546, _392759, _392969], _392759))]], finite(_392969), element(_392969, powerset(_392759))]]]]]]], (16979 ^ _115804) ^ [_385640, _385642] : [finite(_385642), -(finite(set_intersection2(_385642, _385640)))], (12197 ^ _115804) ^ [] : [empty_carrier(12193 ^ [])], (12328 ^ _115804) ^ [] : [-(rel_str(12326 ^ []))], (20375 ^ _115804) ^ [_439743] : [-(in(_439743, 20373 ^ [_439743]))], (1456 ^ _115804) ^ [_135318, _135320] : [-(relation(_135318)), _135320 = _135318, relation(_135320)], (10999 ^ _115804) ^ [_281770] : [ordinal(_281770), 11002 ^ _115804 : [(11007 ^ _115804) ^ [] : [-(epsilon_connected(succ(_281770)))], (11003 ^ _115804) ^ [] : [empty(succ(_281770))], (11005 ^ _115804) ^ [] : [-(epsilon_transitive(succ(_281770)))], (11009 ^ _115804) ^ [] : [-(ordinal(succ(_281770)))]]], (15602 ^ _115804) ^ [_360054, _360056, _360058] : [in(_360054, 15600 ^ [_360056, _360058]), 15605 ^ _115804 : [(15612 ^ _115804) ^ [] : [-(in(15607 ^ [_360054, _360056, _360058], _360058))], (15606 ^ _115804) ^ [] : [-(in(_360054, cartesian_product2(_360058, _360056)))], (15610 ^ _115804) ^ [] : [-(ordered_pair(15607 ^ [_360054, _360056, _360058], 15608 ^ [_360054, _360056, _360058]) = _360054)], (15614 ^ _115804) ^ [] : [-(15608 ^ [_360054, _360056, _360058] = singleton(15607 ^ [_360054, _360056, _360058]))]]], (19176 ^ _115804) ^ [_421056] : [relation(_421056), 19179 ^ _115804 : [(19180 ^ _115804) ^ [_421131] : [relation(_421131), subset(relation_dom(_421056), relation_rng(_421131)), -(relation_rng(relation_composition(_421131, _421056)) = relation_rng(_421056))]]], (2524 ^ _115804) ^ [_152239, _152241] : [_152241 = _152239, -(relation_field(_152241) = relation_field(_152239))], (3514 ^ _115804) ^ [_165429] : [rel_str(_165429), 3529 ^ _115804 : [(3538 ^ _115804) ^ [] : [-(complete_relstr(_165429))], (3536 ^ _115804) ^ [] : [-(antisymmetric_relstr(_165429))], (3534 ^ _115804) ^ [] : [-(transitive_relstr(_165429))], (3530 ^ _115804) ^ [] : [empty_carrier(_165429)], (3532 ^ _115804) ^ [] : [-(reflexive_relstr(_165429))]], -(empty_carrier(_165429)), reflexive_relstr(_165429), trivial_carrier(_165429)], (2800 ^ _115804) ^ [_156480] : [v3_membered(_156480), 2803 ^ _115804 : [(2804 ^ _115804) ^ [_156548] : [element(_156548, _156480), 2807 ^ _115804 : [(2808 ^ _115804) ^ [] : [-(v1_xcmplx_0(_156548))], (2812 ^ _115804) ^ [] : [-(v1_rat_1(_156548))], (2810 ^ _115804) ^ [] : [-(v1_xreal_0(_156548))]]]]], (11417 ^ _115804) ^ [_287255] : [-(lower_bounded_relstr(boole_POSet(_287255)))], (10509 ^ _115804) ^ [_275272, _275274] : [v1_membered(_275274), -(v1_membered(set_intersection2(_275274, _275272)))], (314 ^ _115804) ^ [_119847, _119849] : [-(trivial_carrier(_119847)), _119849 = _119847, trivial_carrier(_119849)], (19649 ^ _115804) ^ [_428423, _428425] : [element(_428423, powerset(_428425)), 19652 ^ _115804 : [(19653 ^ _115804) ^ [] : [proper_element(_428423, powerset(_428425)), _428423 = _428425], (19659 ^ _115804) ^ [] : [-(_428423 = _428425), -(proper_element(_428423, powerset(_428425)))]]], (19813 ^ _115804) ^ [_431382, _431384, _431386] : [-(disjoint(_431386, _431382)), subset(_431386, _431384), disjoint(_431384, _431382)], (11381 ^ _115804) ^ [_286822] : [empty(_286822), 11384 ^ _115804 : [(11385 ^ _115804) ^ [] : [-(empty(relation_dom(_286822)))], (11387 ^ _115804) ^ [] : [-(relation(relation_dom(_286822)))]]], (19244 ^ _115804) ^ [_422098] : [-(set_difference(empty_set, _422098) = empty_set)], (12797 ^ _115804) ^ [_304859] : [-(antisymmetric(12787 ^ [_304859]))], (10027 ^ _115804) ^ [_269083] : [one_sorted_str(_269083), -(net_str(10030 ^ [_269083], _269083))], (7072 ^ _115804) ^ [_222711, _222713, _222715] : [_222711 = set_intersection2(_222715, _222713), 7075 ^ _115804 : [(7076 ^ _115804) ^ [_222800] : [in(_222800, _222711), 7079 ^ _115804 : [(7080 ^ _115804) ^ [] : [-(in(_222800, _222715))], (7082 ^ _115804) ^ [] : [-(in(_222800, _222713))]]], (7084 ^ _115804) ^ [_222903] : [-(in(_222903, _222711)), in(_222903, _222715), in(_222903, _222713)]]], (12325 ^ _115804) ^ [] : [-(v5_membered(12313 ^ []))], (12914 ^ _115804) ^ [] : [-(distributive_relstr(12894 ^ []))], (10587 ^ _115804) ^ [_276326] : [-(meet_associative(boole_lattice(_276326)))], (2444 ^ _115804) ^ [_151069, _151071, _151073, _151075] : [-(topstr_closure(_151075, _151071) = topstr_closure(_151073, _151069)), _151075 = _151073, _151071 = _151069], (12184 ^ _115804) ^ [] : [-(lattice(12164 ^ []))], (13002 ^ _115804) ^ [] : [-(join_associative(12992 ^ []))], (17367 ^ _115804) ^ [_392191] : [-(set_union2(_392191, empty_set) = _392191)], (10307 ^ _115804) ^ [_272601] : [-(complemented_lattstr(boole_lattice(_272601)))], (16969 ^ _115804) ^ [_385495, _385497, _385499, _385501] : [relation_of2_as_subset(_385495, _385497, _385501), subset(relation_rng(_385495), _385499), -(relation_of2_as_subset(_385495, _385497, _385499))], (12462 ^ _115804) ^ [] : [-(v2_waybel_3(12430 ^ []))], (12407 ^ _115804) ^ [] : [-(reflexive_relstr(12401 ^ []))], (12093 ^ _115804) ^ [] : [-(join_associative(12083 ^ []))], (12824 ^ _115804) ^ [_305219] : [-(empty(_305219)), 12828 ^ _115804 : [(12829 ^ _115804) ^ [] : [-(element(12827 ^ [_305219], powerset(_305219)))], (12833 ^ _115804) ^ [] : [-(finite(12827 ^ [_305219]))], (12831 ^ _115804) ^ [] : [empty(12827 ^ [_305219])]]], (16949 ^ _115804) ^ [_385213] : [relation(_385213), -(relation_image(_385213, relation_dom(_385213)) = relation_rng(_385213))], (13548 ^ _115804) ^ [_315398, _315400] : [-(subset(_315400, _315400))], (12483 ^ _115804) ^ [] : [-(upper_bounded_relstr(12465 ^ []))], (12866 ^ _115804) ^ [] : [-(with_infima_relstr(12850 ^ []))], (4722 ^ _115804) ^ [_182438] : [relation(_182438), 4725 ^ _115804 : [(4726 ^ _115804) ^ [] : [antisymmetric(_182438), -(is_antisymmetric_in(_182438, relation_field(_182438)))], (4732 ^ _115804) ^ [] : [is_antisymmetric_in(_182438, relation_field(_182438)), -(antisymmetric(_182438))]]], (11041 ^ _115804) ^ [_282349, _282351] : [-(empty(_282351)), empty(set_union2(_282349, _282351))], (9493 ^ _115804) ^ [] : [true___, -(true___)], (344 ^ _115804) ^ [_120222, _120224, _120226, _120228, _120230, _120232] : [-(onto(_120230, _120226, _120222)), onto(_120232, _120228, _120224), _120232 = _120230, _120228 = _120226, _120224 = _120222], (9037 ^ _115804) ^ [] : [true___, -(true___)], (10649 ^ _115804) ^ [_277014] : [empty(cast_as_carrier_subset(_277014)), -(empty_carrier(_277014)), one_sorted_str(_277014)], (1828 ^ _115804) ^ [_141415, _141417, _141419, _141421, _141423, _141425, _141427, _141429, _141431, _141433, _141435, _141437] : [-(apply_binary_as_element(_141437, _141433, _141429, _141425, _141421, _141417) = apply_binary_as_element(_141435, _141431, _141427, _141423, _141419, _141415)), _141437 = _141435, _141433 = _141431, _141429 = _141427, _141425 = _141423, _141421 = _141419, _141417 = _141415], (16608 ^ _115804) ^ [_380215, _380217, _380219, _380221] : [unordered_pair(_380221, _380219) = unordered_pair(_380217, _380215), -(_380221 = _380217), -(_380221 = _380215)], (13182 ^ _115804) ^ [_310085, _310087, _310089] : [-(join_commut(_310089, _310087, _310085) = join(_310089, _310087, _310085)), -(empty_carrier(_310089)), join_commutative(_310089), join_semilatt_str(_310089), element(_310087, the_carrier(_310089)), element(_310085, the_carrier(_310089))], (12369 ^ _115804) ^ [_299958] : [-(empty(_299958)), 12373 ^ _115804 : [(12374 ^ _115804) ^ [] : [-(element(12372 ^ [_299958], powerset(_299958)))], (12376 ^ _115804) ^ [] : [empty(12372 ^ [_299958])]]], (12017 ^ _115804) ^ [_295978, _295980] : [12018 ^ _115804 : [(12019 ^ _115804) ^ [] : [_295980 = empty_set], (12021 ^ _115804) ^ [] : [_295980 = singleton(_295978)]], -(subset(_295980, singleton(_295978)))], (3232 ^ _115804) ^ [_161972] : [rel_str(_161972), 3263 ^ _115804 : [(3266 ^ _115804) ^ [] : [-(reflexive_relstr(_161972))], (3284 ^ _115804) ^ [] : [-(with_infima_relstr(_161972))], (3270 ^ _115804) ^ [] : [-(antisymmetric_relstr(_161972))], (3280 ^ _115804) ^ [] : [-(join_complete_relstr(_161972))], (3286 ^ _115804) ^ [] : [-(complete_relstr(_161972))], (3282 ^ _115804) ^ [] : [-(with_suprema_relstr(_161972))], (3274 ^ _115804) ^ [] : [-(upper_bounded_relstr(_161972))], (3268 ^ _115804) ^ [] : [-(transitive_relstr(_161972))], (3264 ^ _115804) ^ [] : [empty_carrier(_161972)], (3276 ^ _115804) ^ [] : [-(bounded_relstr(_161972))], (3272 ^ _115804) ^ [] : [-(lower_bounded_relstr(_161972))], (3278 ^ _115804) ^ [] : [-(up_complete_relstr(_161972))]], -(empty_carrier(_161972)), reflexive_relstr(_161972), transitive_relstr(_161972), antisymmetric_relstr(_161972), upper_bounded_relstr(_161972), up_complete_relstr(_161972), join_complete_relstr(_161972)], (19146 ^ _115804) ^ [_420594] : [relation(_420594), 19149 ^ _115804 : [(19150 ^ _115804) ^ [_420669] : [relation(_420669), subset(relation_rng(_420594), relation_dom(_420669)), -(relation_dom(relation_composition(_420594, _420669)) = relation_dom(_420594))]]], (2278 ^ _115804) ^ [_148606, _148608, _148610, _148612, _148614, _148616] : [-(preimage_subnetstr(_148616, _148612, _148608) = preimage_subnetstr(_148614, _148610, _148606)), _148616 = _148614, _148612 = _148610, _148608 = _148606], (12870 ^ _115804) ^ [] : [-(upper_bounded_relstr(12850 ^ []))], (18207 ^ _115804) ^ [_405855] : [-(reflexive(inclusion_relation(_405855)))], (12693 ^ _115804) ^ [] : [empty_carrier(12689 ^ [])], (12440 ^ _115804) ^ [] : [-(transitive_relstr(12430 ^ []))], (10113 ^ _115804) ^ [_270127, _270129] : [finite(_270127), -(finite(set_intersection2(_270129, _270127)))], (10427 ^ _115804) ^ [_274127] : [-(distributive_relstr(boole_POSet(_274127)))], (17331 ^ _115804) ^ [_391641, _391643, _391645] : [relation(_391641), in(_391645, relation_field(relation_restriction(_391641, _391643))), 17338 ^ _115804 : [(17339 ^ _115804) ^ [] : [-(in(_391645, relation_field(_391641)))], (17341 ^ _115804) ^ [] : [-(in(_391645, _391643))]]], (12182 ^ _115804) ^ [] : [-(join_absorbing(12164 ^ []))], (2624 ^ _115804) ^ [_153731, _153733] : [_153733 = _153731, -(singleton(_153733) = singleton(_153731))], (772 ^ _115804) ^ [_125926, _125928] : [-(meet_commutative(_125926)), _125928 = _125926, meet_commutative(_125928)], (8681 ^ _115804) ^ [_250443] : [-(empty_carrier(_250443)), topological_space(_250443), top_str(_250443), 8692 ^ _115804 : [(8693 ^ _115804) ^ [_250641] : [-(empty_carrier(_250641)), net_str(_250641, _250443), 8700 ^ _115804 : [(8701 ^ _115804) ^ [_250779] : [element(_250779, the_carrier(_250443)), 8704 ^ _115804 : [(8715 ^ _115804) ^ [] : [8717 ^ _115804 : [(8718 ^ _115804) ^ [] : [-(point_neighbourhood(8716 ^ [_250443, _250641, _250779], _250443, _250779))], (8720 ^ _115804) ^ [] : [is_often_in(_250443, _250641, 8716 ^ [_250443, _250641, _250779])]], -(is_a_cluster_point_of_netstr(_250443, _250641, _250779))], (8705 ^ _115804) ^ [] : [is_a_cluster_point_of_netstr(_250443, _250641, _250779), 8708 ^ _115804 : [(8709 ^ _115804) ^ [_250913] : [point_neighbourhood(_250913, _250443, _250779), -(is_often_in(_250443, _250641, _250913))]]]]]]]]], (19264 ^ _115804) ^ [_422371, _422373] : [-(disjoint(_422373, _422371)), -(in(19267 ^ [_422371, _422373], set_intersection2(_422373, _422371)))], (9517 ^ _115804) ^ [_261983] : [-(element(bottom_of_semilattstr(_261983), the_carrier(_261983))), -(empty_carrier(_261983)), meet_semilatt_str(_261983)], (8767 ^ _115804) ^ [_251873] : [one_sorted_str(_251873), 8770 ^ _115804 : [(8771 ^ _115804) ^ [_251957] : [net_str(_251957, _251873), 8774 ^ _115804 : [(8775 ^ _115804) ^ [_252034] : [subnetstr(_252034, _251873, _251957), 8778 ^ _115804 : [(8779 ^ _115804) ^ [] : [full_subnetstr(_252034, _251873, _251957), 8782 ^ _115804 : [(8783 ^ _115804) ^ [] : [-(full_subrelstr(_252034, _251957))], (8785 ^ _115804) ^ [] : [-(subrelstr(_252034, _251957))]]], (8787 ^ _115804) ^ [] : [-(full_subnetstr(_252034, _251873, _251957)), full_subrelstr(_252034, _251957), subrelstr(_252034, _251957)]]]]]]], (12705 ^ _115804) ^ [] : [-(with_infima_relstr(12689 ^ []))], (11079 ^ _115804) ^ [_282844, _282846] : [v4_membered(_282846), 11082 ^ _115804 : [(11087 ^ _115804) ^ [] : [-(v3_membered(set_difference(_282846, _282844)))], (11083 ^ _115804) ^ [] : [-(v1_membered(set_difference(_282846, _282844)))], (11085 ^ _115804) ^ [] : [-(v2_membered(set_difference(_282846, _282844)))], (11089 ^ _115804) ^ [] : [-(v4_membered(set_difference(_282846, _282844)))]]], (9885 ^ _115804) ^ [] : [true___, -(true___)], (8891 ^ _115804) ^ [] : [true___, -(true___)], (12756 ^ _115804) ^ [_304406] : [-(empty(_304406)), 12760 ^ _115804 : [(12761 ^ _115804) ^ [] : [-(element(12759 ^ [_304406], powerset(_304406)))], (12765 ^ _115804) ^ [] : [-(finite(12759 ^ [_304406]))], (12763 ^ _115804) ^ [] : [empty(12759 ^ [_304406])]]], (9031 ^ _115804) ^ [] : [true___, -(true___)], (2482 ^ _115804) ^ [_151622, _151624] : [_151624 = _151622, -(inclusion_relation(_151624) = inclusion_relation(_151622))], (12596 ^ _115804) ^ [] : [-(with_suprema_relstr(12582 ^ []))], (9025 ^ _115804) ^ [] : [true___, -(true___)], (1580 ^ _115804) ^ [_136992, _136994] : [-(directed_relstr(_136992)), _136994 = _136992, directed_relstr(_136994)], (12168 ^ _115804) ^ [] : [empty_carrier(12164 ^ [])], (10927 ^ _115804) ^ [_280766] : [-(modular_lattstr(boole_lattice(_280766)))], (20164 ^ _115804) ^ [_436575, _436577, _436579] : [relation(_436575), function(_436575), 20171 ^ _115804 : [(20172 ^ _115804) ^ [] : [in(ordered_pair(_436579, _436577), _436575), 20175 ^ _115804 : [(20176 ^ _115804) ^ [] : [-(in(_436579, relation_dom(_436575)))], (20178 ^ _115804) ^ [] : [-(_436577 = apply(_436575, _436579))]]], (20180 ^ _115804) ^ [] : [-(in(ordered_pair(_436579, _436577), _436575)), in(_436579, relation_dom(_436575)), _436577 = apply(_436575, _436579)]]], (19170 ^ _115804) ^ [_420969, _420971] : [in(_420971, _420969), -(set_union2(singleton(_420971), _420969) = _420969)], (10313 ^ _115804) ^ [_272707] : [empty_carrier(boole_lattice(_272707))], (2910 ^ _115804) ^ [_157857] : [v5_membered(_157857), 2913 ^ _115804 : [(2914 ^ _115804) ^ [_157935] : [element(_157935, _157857), 2917 ^ _115804 : [(2926 ^ _115804) ^ [] : [-(v1_rat_1(_157935))], (2924 ^ _115804) ^ [] : [-(v1_int_1(_157935))], (2922 ^ _115804) ^ [] : [-(v1_xreal_0(_157935))], (2918 ^ _115804) ^ [] : [-(v1_xcmplx_0(_157935))], (2920 ^ _115804) ^ [] : [-(natural(_157935))]]]]], (17701 ^ _115804) ^ [_398214, _398216, _398218] : [relation_of2_as_subset(_398214, _398216, _398218), 17704 ^ _115804 : [(17705 ^ _115804) ^ [] : [17707 ^ _115804 : [(17708 ^ _115804) ^ [] : [-(in(17706 ^ [_398214, _398216, _398218], _398216))], (17710 ^ _115804) ^ [_398394] : [in(ordered_pair(17706 ^ [_398214, _398216, _398218], _398394), _398214)]], -(relation_dom_as_subset(_398216, _398218, _398214) = _398216)], (17714 ^ _115804) ^ [] : [relation_dom_as_subset(_398216, _398218, _398214) = _398216, 17717 ^ _115804 : [(17718 ^ _115804) ^ [_398509] : [in(_398509, _398216), -(in(ordered_pair(_398509, 17721 ^ [_398214, _398216, _398218, _398509]), _398214))]]]]], (9699 ^ _115804) ^ [_264644, _264646] : [relation(_264646), -(relation(relation_dom_restriction(_264646, _264644)))], (7115 ^ _115804) ^ [_223396] : [relation(_223396), function(_223396), 7122 ^ _115804 : [(7123 ^ _115804) ^ [_223556, _223558] : [in(_223558, relation_dom(_223396)), 7126 ^ _115804 : [(7127 ^ _115804) ^ [] : [_223556 = apply(_223396, _223558), -(in(ordered_pair(_223558, _223556), _223396))], (7133 ^ _115804) ^ [] : [in(ordered_pair(_223558, _223556), _223396), -(_223556 = apply(_223396, _223558))]]], (7139 ^ _115804) ^ [_223786, _223788] : [-(in(_223788, relation_dom(_223396))), 7142 ^ _115804 : [(7143 ^ _115804) ^ [] : [_223786 = apply(_223396, _223788), -(_223786 = empty_set)], (7149 ^ _115804) ^ [] : [_223786 = empty_set, -(_223786 = apply(_223396, _223788))]]]]], (3332 ^ _115804) ^ [_163195] : [finite(_163195), 3335 ^ _115804 : [(3336 ^ _115804) ^ [_163255] : [element(_163255, powerset(_163195)), -(finite(_163255))]]], (9613 ^ _115804) ^ [_263343] : [-(relation_of2_as_subset(identity_as_relation_of(_263343), _263343, _263343))], (9577 ^ _115804) ^ [_262828, _262830, _262832] : [-(element(subset_intersection2(_262832, _262830, _262828), powerset(_262832))), element(_262830, powerset(_262832)), element(_262828, powerset(_262832))], (18140 ^ _115804) ^ [_404900] : [18155 ^ _115804 : [(18156 ^ _115804) ^ [_405122] : [-(join_of_latt_set(_404900, _405122) = join_on_relstr(poset_of_lattice(_404900), _405122))], (18158 ^ _115804) ^ [_405150] : [-(meet_of_latt_set(_404900, _405150) = meet_on_relstr(poset_of_lattice(_404900), _405150))]], -(empty_carrier(_404900)), lattice(_404900), complete_latt_str(_404900), latt_str(_404900)], (440 ^ _115804) ^ [_121510, _121512] : [-(symmetric(_121510)), _121512 = _121510, symmetric(_121512)], (12469 ^ _115804) ^ [] : [empty_carrier(12465 ^ [])], (16640 ^ _115804) ^ [_380631, _380633] : [relation(_380631), -(subset(relation_rng(relation_rng_restriction(_380633, _380631)), _380633))], (2618 ^ _115804) ^ [_153646, _153648] : [_153648 = _153646, -(powerset(_153648) = powerset(_153646))], (12236 ^ _115804) ^ [] : [-(complemented_lattstr(12206 ^ []))], (17897 ^ _115804) ^ [_401167, _401169] : [relation(_401167), antisymmetric(_401167), -(antisymmetric(relation_restriction(_401167, _401169)))], (9471 ^ _115804) ^ [_261371, _261373, _261375] : [relation_of2(_261371, _261375, _261373), -(element(relation_dom_as_subset(_261375, _261373, _261371), powerset(_261375)))], (2646 ^ _115804) ^ [_154046, _154048, _154050, _154052] : [-(lim_points_of_net(_154052, _154048) = lim_points_of_net(_154050, _154046)), _154052 = _154050, _154048 = _154046], (254 ^ _115804) ^ [_119097, _119099] : [-(v1_membered(_119097)), _119099 = _119097, v1_membered(_119099)], (12212 ^ _115804) ^ [] : [-(strict_latt_str(12206 ^ []))], (12569 ^ _115804) ^ [_302219] : [-(relation_of2(12567 ^ [_302219], _302219, _302219))], (10183 ^ _115804) ^ [_271012] : [10190 ^ _115804 : [(10191 ^ _115804) ^ [] : [empty(the_InternalRel(_271012))], (10193 ^ _115804) ^ [] : [-(relation(the_InternalRel(_271012)))]], -(v1_yellow_3(_271012)), rel_str(_271012)], (10040 ^ _115804) ^ [_269214, _269216] : [-(point_neighbourhood(10055 ^ [_269214, _269216], _269216, _269214)), -(empty_carrier(_269216)), topological_space(_269216), top_str(_269216), element(_269214, the_carrier(_269216))], (14767 ^ _115804) ^ [_341104, _341106] : [topological_space(_341106), top_str(_341106), element(_341104, powerset(powerset(the_carrier(_341106)))), 14783 ^ _115804 : [(14792 ^ _115804) ^ [] : [14781 ^ [_341104, _341106] = 14782 ^ [_341104, _341106]], (14790 ^ _115804) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_341106), 14782 ^ [_341104, _341106]), _341104))], (14788 ^ _115804) ^ [] : [-(14780 ^ [_341104, _341106] = 14782 ^ [_341104, _341106])], (14784 ^ _115804) ^ [] : [-(14780 ^ [_341104, _341106] = 14781 ^ [_341104, _341106])], (14786 ^ _115804) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_341106), 14781 ^ [_341104, _341106]), _341104))]], 14794 ^ _115804 : [(14795 ^ _115804) ^ [_341633] : [in(_341633, 14793 ^ [_341104, _341106]), 14799 ^ _115804 : [(14800 ^ _115804) ^ [] : [-(in(14798 ^ [_341104, _341106, _341633], powerset(the_carrier(_341106))))], (14804 ^ _115804) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_341106), _341633), _341104))], (14802 ^ _115804) ^ [] : [-(14798 ^ [_341104, _341106, _341633] = _341633)]]], (14806 ^ _115804) ^ [_341813] : [-(in(_341813, 14793 ^ [_341104, _341106])), 14807 ^ _115804 : [(14808 ^ _115804) ^ [_341877] : [in(_341877, powerset(the_carrier(_341106))), _341877 = _341813, in(set_difference(cast_as_carrier_subset(_341106), _341813), _341104)]]]]], (12858 ^ _115804) ^ [] : [-(reflexive_relstr(12850 ^ []))], (3214 ^ _115804) ^ [_161746] : [rel_str(_161746), 3225 ^ _115804 : [(3226 ^ _115804) ^ [] : [empty_carrier(_161746)], (3230 ^ _115804) ^ [] : [-(with_infima_relstr(_161746))], (3228 ^ _115804) ^ [] : [-(with_suprema_relstr(_161746))]], -(empty_carrier(_161746)), complete_relstr(_161746)], (8927 ^ _115804) ^ [_254174, _254176] : [-(element(join_of_latt_set(_254176, _254174), the_carrier(_254176))), -(empty_carrier(_254176)), latt_str(_254176)], (12403 ^ _115804) ^ [] : [-(rel_str(12401 ^ []))], (3288 ^ _115804) ^ [_162636] : [rel_str(_162636), empty_carrier(_162636), -(v1_yellow_3(_162636))], (19851 ^ _115804) ^ [_431910, _431912] : [set_difference(_431912, singleton(_431910)) = _431912, in(_431910, _431912)], (12538 ^ _115804) ^ [] : [v1_yellow_3(12524 ^ [])], (3646 ^ _115804) ^ [_167074] : [rel_str(_167074), 3657 ^ _115804 : [(3658 ^ _115804) ^ [] : [empty_carrier(_167074)], (3660 ^ _115804) ^ [] : [-(bounded_relstr(_167074))]], -(empty_carrier(_167074)), complete_relstr(_167074)], (20126 ^ _115804) ^ [_436061, _436063, _436065] : [relation(_436061), 20129 ^ _115804 : [(20130 ^ _115804) ^ [] : [in(_436065, relation_dom(relation_dom_restriction(_436061, _436063))), 20133 ^ _115804 : [(20134 ^ _115804) ^ [] : [-(in(_436065, _436063))], (20136 ^ _115804) ^ [] : [-(in(_436065, relation_dom(_436061)))]]], (20138 ^ _115804) ^ [] : [-(in(_436065, relation_dom(relation_dom_restriction(_436061, _436063)))), in(_436065, _436063), in(_436065, relation_dom(_436061))]]], (20300 ^ _115804) ^ [_438533, _438535, _438537] : [singleton(_438537) = unordered_pair(_438535, _438533), -(_438537 = _438535)], (10153 ^ _115804) ^ [] : [-(relation(empty_set))], (3012 ^ _115804) ^ [_159193] : [v4_membered(_159193), 3015 ^ _115804 : [(3016 ^ _115804) ^ [_159268] : [element(_159268, powerset(_159193)), 3019 ^ _115804 : [(3024 ^ _115804) ^ [] : [-(v3_membered(_159268))], (3020 ^ _115804) ^ [] : [-(v1_membered(_159268))], (3022 ^ _115804) ^ [] : [-(v2_membered(_159268))], (3026 ^ _115804) ^ [] : [-(v4_membered(_159268))]]]]], (12446 ^ _115804) ^ [] : [-(upper_bounded_relstr(12430 ^ []))], (7437 ^ _115804) ^ [_228419] : [rel_str(_228419), 7440 ^ _115804 : [(7441 ^ _115804) ^ [] : [lower_bounded_relstr(_228419), 7445 ^ _115804 : [(7446 ^ _115804) ^ [] : [-(element(7444 ^ [_228419], the_carrier(_228419)))], (7448 ^ _115804) ^ [] : [-(relstr_element_smaller(_228419, the_carrier(_228419), 7444 ^ [_228419]))]]], (7450 ^ _115804) ^ [] : [-(lower_bounded_relstr(_228419)), 7451 ^ _115804 : [(7452 ^ _115804) ^ [_228613] : [element(_228613, the_carrier(_228419)), relstr_element_smaller(_228419, the_carrier(_228419), _228613)]]]]], (13538 ^ _115804) ^ [_315273, _315275] : [-(ordinal_subset(_315275, _315275)), ordinal(_315275), ordinal(_315273)], (18556 ^ _115804) ^ [_411497] : [ordinal(_411497), 18559 ^ _115804 : [(18560 ^ _115804) ^ [_411563] : [ordinal(_411563), 18563 ^ _115804 : [(18564 ^ _115804) ^ [] : [in(_411497, _411563), -(ordinal_subset(succ(_411497), _411563))], (18570 ^ _115804) ^ [] : [ordinal_subset(succ(_411497), _411563), -(in(_411497, _411563))]]]]], (16658 ^ _115804) ^ [_380886, _380888, _380890] : [subset(_380890, _380888), 16661 ^ _115804 : [(16662 ^ _115804) ^ [] : [-(subset(cartesian_product2(_380890, _380886), cartesian_product2(_380888, _380886)))], (16664 ^ _115804) ^ [] : [-(subset(cartesian_product2(_380886, _380890), cartesian_product2(_380886, _380888)))]]], (12111 ^ _115804) ^ [] : [-(upper_bounded_semilattstr(12083 ^ []))], (8151 ^ _115804) ^ [_241026] : [-(relation_of_lattice(_241026) = a_1_0_filter_1(_241026)), -(empty_carrier(_241026)), lattice(_241026), latt_str(_241026)], (17236 ^ _115804) ^ [_390093, _390095, _390097] : [relation(_390093), subset(_390097, _390095), -(subset(relation_inverse_image(_390093, _390097), relation_inverse_image(_390093, _390095)))], (12791 ^ _115804) ^ [_304793] : [-(relation(12787 ^ [_304793]))], (10521 ^ _115804) ^ [_275430, _275432] : [v2_membered(_275432), 10524 ^ _115804 : [(10525 ^ _115804) ^ [] : [-(v1_membered(set_intersection2(_275432, _275430)))], (10527 ^ _115804) ^ [] : [-(v2_membered(set_intersection2(_275432, _275430)))]]], (13694 ^ _115804) ^ [_318176] : [13698 ^ _115804 : [(13707 ^ _115804) ^ [] : [13696 ^ [_318176] = 13697 ^ [_318176]], (13705 ^ _115804) ^ [] : [-(13697 ^ [_318176] = singleton(13695 ^ [_318176]))], (13703 ^ _115804) ^ [] : [-(in(13695 ^ [_318176], _318176))], (13699 ^ _115804) ^ [] : [-(in(13695 ^ [_318176], _318176))], (13701 ^ _115804) ^ [] : [-(13696 ^ [_318176] = singleton(13695 ^ [_318176]))]], 13709 ^ _115804 : [(13714 ^ _115804) ^ [_318574, _318576] : [in(ordered_pair(_318576, _318574), 13708 ^ [_318176]), 13717 ^ _115804 : [(13718 ^ _115804) ^ [] : [-(in(_318576, _318176))], (13722 ^ _115804) ^ [] : [-(_318574 = singleton(_318576))], (13720 ^ _115804) ^ [] : [-(in(_318576, _318176))]]], (13710 ^ _115804) ^ [] : [-(relation(13708 ^ [_318176]))], (13712 ^ _115804) ^ [] : [-(function(13708 ^ [_318176]))], (13724 ^ _115804) ^ [_318719, _318721] : [-(in(ordered_pair(_318721, _318719), 13708 ^ [_318176])), in(_318721, _318176), in(_318721, _318176), _318719 = singleton(_318721)]]], (12481 ^ _115804) ^ [] : [-(lower_bounded_relstr(12465 ^ []))], (12801 ^ _115804) ^ [_304905] : [-(v1_partfun1(12787 ^ [_304905], _304905, _304905))], (180 ^ _115804) ^ [_118154, _118156, _118158, _118160] : [-(v2_binop_1(_118158, _118154)), v2_binop_1(_118160, _118156), _118160 = _118158, _118156 = _118154], (1330 ^ _115804) ^ [_133671, _133673] : [-(reflexive_relstr(_133671)), _133673 = _133671, reflexive_relstr(_133673)], (12337 ^ _115804) ^ [] : [-(ordinal(12331 ^ []))], (8977 ^ _115804) ^ [] : [true___, -(true___)], (10086 ^ _115804) ^ [_269780, _269782] : [-(subnet(10109 ^ [_269780, _269782], _269782, _269780)), -(empty_carrier(_269782)), one_sorted_str(_269782), -(empty_carrier(_269780)), transitive_relstr(_269780), directed_relstr(_269780), net_str(_269780, _269782)], (3852 ^ _115804) ^ [_169720] : [latt_str(_169720), 3863 ^ _115804 : [(3868 ^ _115804) ^ [] : [-(lower_bounded_semilattstr(_169720))], (3866 ^ _115804) ^ [] : [-(distributive_lattstr(_169720))], (3872 ^ _115804) ^ [] : [-(bounded_lattstr(_169720))], (3874 ^ _115804) ^ [] : [-(complemented_lattstr(_169720))], (3864 ^ _115804) ^ [] : [empty_carrier(_169720)], (3870 ^ _115804) ^ [] : [-(upper_bounded_semilattstr(_169720))]], -(empty_carrier(_169720)), boolean_lattstr(_169720)], (19991 ^ _115804) ^ [_434008, _434010] : [subset(singleton(_434010), singleton(_434008)), -(_434010 = _434008)], (3042 ^ _115804) ^ [_159612] : [empty(_159612), -(finite(_159612))], (3588 ^ _115804) ^ [_166360] : [latt_str(_166360), 3603 ^ _115804 : [(3604 ^ _115804) ^ [] : [empty_carrier(_166360)], (3606 ^ _115804) ^ [] : [-(bounded_lattstr(_166360))]], -(empty_carrier(_166360)), lower_bounded_semilattstr(_166360), upper_bounded_semilattstr(_166360)], (12180 ^ _115804) ^ [] : [-(meet_absorbing(12164 ^ []))], (19799 ^ _115804) ^ [_431209] : [relation(_431209), function(_431209), one_to_one(_431209), -(one_to_one(function_inverse(_431209)))], (9107 ^ _115804) ^ [_256489, _256491] : [rel_str(_256491), -(element(join_on_relstr(_256491, _256489), the_carrier(_256491)))], (12456 ^ _115804) ^ [] : [-(with_infima_relstr(12430 ^ []))], (17963 ^ _115804) ^ [_402117] : [transitive_relstr(_402117), rel_str(_402117), 17970 ^ _115804 : [(17971 ^ _115804) ^ [_402267] : [element(_402267, the_carrier(_402117)), 17974 ^ _115804 : [(17975 ^ _115804) ^ [_402364] : [element(_402364, the_carrier(_402117)), 17978 ^ _115804 : [(17979 ^ _115804) ^ [_402450] : [element(_402450, the_carrier(_402117)), -(related(_402117, _402267, _402450)), related(_402117, _402267, _402364), related(_402117, _402364, _402450)]]]]]]], (12101 ^ _115804) ^ [] : [-(join_absorbing(12083 ^ []))], (10065 ^ _115804) ^ [_269523] : [rel_str(_269523), -(subrelstr(10068 ^ [_269523], _269523))], (18340 ^ _115804) ^ [_408105] : [-(empty_carrier(_408105)), one_sorted_str(_408105), 18347 ^ _115804 : [(18348 ^ _115804) ^ [_408258] : [18363 ^ _115804 : [(18364 ^ _115804) ^ [_408489] : [is_often_in(_408105, _408258, _408489), 18367 ^ _115804 : [(18368 ^ _115804) ^ [] : [empty_carrier(preimage_subnetstr(_408105, _408258, _408489))], (18370 ^ _115804) ^ [] : [-(directed_relstr(preimage_subnetstr(_408105, _408258, _408489)))]]]], -(empty_carrier(_408258)), transitive_relstr(_408258), directed_relstr(_408258), net_str(_408258, _408105)]]], (17907 ^ _115804) ^ [_401296, _401298] : [relation(_401296), well_orders(_401296, _401298), 17914 ^ _115804 : [(17915 ^ _115804) ^ [] : [-(relation_field(relation_restriction(_401296, _401298)) = _401298)], (17917 ^ _115804) ^ [] : [-(well_ordering(relation_restriction(_401296, _401298)))]]], (70 ^ _115804) ^ [_116689, _116691] : [-(v2_waybel_2(_116689)), _116691 = _116689, v2_waybel_2(_116691)], (11303 ^ _115804) ^ [] : [-(empty(empty_set))], (4450 ^ _115804) ^ [_177471] : [rel_str(_177471), 4453 ^ _115804 : [(4454 ^ _115804) ^ [_177580, _177582] : [element(_177580, the_carrier(_177471)), ex_inf_of_relstr_set(_177471, _177582), 4461 ^ _115804 : [(4478 ^ _115804) ^ [] : [-(_177580 = meet_on_relstr(_177471, _177582)), relstr_element_smaller(_177471, _177582, _177580), 4484 ^ _115804 : [(4485 ^ _115804) ^ [] : [-(element(4483 ^ [_177471, _177580, _177582], the_carrier(_177471)))], (4489 ^ _115804) ^ [] : [related(_177471, 4483 ^ [_177471, _177580, _177582], _177580)], (4487 ^ _115804) ^ [] : [-(relstr_element_smaller(_177471, _177582, 4483 ^ [_177471, _177580, _177582]))]]], (4462 ^ _115804) ^ [] : [_177580 = meet_on_relstr(_177471, _177582), 4465 ^ _115804 : [(4466 ^ _115804) ^ [] : [-(relstr_element_smaller(_177471, _177582, _177580))], (4468 ^ _115804) ^ [_177807] : [element(_177807, the_carrier(_177471)), relstr_element_smaller(_177471, _177582, _177807), -(related(_177471, _177807, _177580))]]]]]]], (17096 ^ _115804) ^ [_387605] : [top_str(_387605), 17099 ^ _115804 : [(17100 ^ _115804) ^ [_387681] : [element(_387681, powerset(powerset(the_carrier(_387605)))), 17103 ^ _115804 : [(17104 ^ _115804) ^ [] : [closed_subsets(_387681, _387605), -(open_subsets(complements_of_subsets(the_carrier(_387605), _387681), _387605))], (17110 ^ _115804) ^ [] : [open_subsets(complements_of_subsets(the_carrier(_387605), _387681), _387605), -(closed_subsets(_387681, _387605))]]]]], (15824 ^ _115804) ^ [_364439, _364441] : [one_sorted_str(_364441), element(_364439, powerset(powerset(the_carrier(_364441)))), 15832 ^ _115804 : [(15833 ^ _115804) ^ [_364744, _364746] : [in(_364744, 15831 ^ [_364439, _364441, _364746]), 15836 ^ _115804 : [(15843 ^ _115804) ^ [] : [-(in(15838 ^ [_364439, _364441, _364744, _364746], complements_of_subsets(the_carrier(_364441), _364439)))], (15837 ^ _115804) ^ [] : [-(in(_364744, cartesian_product2(complements_of_subsets(the_carrier(_364441), _364439), _364746)))], (15841 ^ _115804) ^ [] : [-(ordered_pair(15838 ^ [_364439, _364441, _364744, _364746], 15839 ^ [_364439, _364441, _364744, _364746]) = _364744)], (15845 ^ _115804) ^ [_365078] : [element(_365078, powerset(the_carrier(_364441))), _365078 = 15838 ^ [_364439, _364441, _364744, _364746], -(15839 ^ [_364439, _364441, _364744, _364746] = subset_complement(the_carrier(_364441), _365078))]]], (15855 ^ _115804) ^ [_365287, _365289] : [-(in(_365287, 15831 ^ [_364439, _364441, _365289])), in(_365287, cartesian_product2(complements_of_subsets(the_carrier(_364441), _364439), _365289)), 15860 ^ _115804 : [(15861 ^ _115804) ^ [_365455, _365457] : [ordered_pair(_365457, _365455) = _365287, in(_365457, complements_of_subsets(the_carrier(_364441), _364439)), 15869 ^ _115804 : [(15870 ^ _115804) ^ [] : [-(element(15868 ^ [_364439, _364441, _365287, _365289, _365455, _365457], powerset(the_carrier(_364441))))], (15874 ^ _115804) ^ [] : [_365455 = subset_complement(the_carrier(_364441), 15868 ^ [_364439, _364441, _365287, _365289, _365455, _365457])], (15872 ^ _115804) ^ [] : [-(15868 ^ [_364439, _364441, _365287, _365289, _365455, _365457] = _365457)]]]]]]], (1494 ^ _115804) ^ [_135837, _135839, _135841, _135843, _135845, _135847] : [-(relation_of2_as_subset(_135845, _135841, _135837)), relation_of2_as_subset(_135847, _135843, _135839), _135847 = _135845, _135843 = _135841, _135839 = _135837], (11479 ^ _115804) ^ [_287963] : [-(complemented_relstr(boole_POSet(_287963)))], (19699 ^ _115804) ^ [_429076] : [-(antisymmetric(inclusion_relation(_429076)))], (12640 ^ _115804) ^ [] : [-(relation(12636 ^ []))], (10831 ^ _115804) ^ [_279518, _279520] : [v5_membered(_279520), 10834 ^ _115804 : [(10843 ^ _115804) ^ [] : [-(v5_membered(set_intersection2(_279518, _279520)))], (10841 ^ _115804) ^ [] : [-(v4_membered(set_intersection2(_279518, _279520)))], (10839 ^ _115804) ^ [] : [-(v3_membered(set_intersection2(_279518, _279520)))], (10835 ^ _115804) ^ [] : [-(v1_membered(set_intersection2(_279518, _279520)))], (10837 ^ _115804) ^ [] : [-(v2_membered(set_intersection2(_279518, _279520)))]]], (3982 ^ _115804) ^ [_171295, _171297] : [-(empty(_171297)), -(empty(_171295)), 3989 ^ _115804 : [(3990 ^ _115804) ^ [_171394] : [relation_of2(_171394, _171297, _171295), 4001 ^ _115804 : [(4006 ^ _115804) ^ [] : [-(v1_partfun1(_171394, _171297, _171295))], (4002 ^ _115804) ^ [] : [-(function(_171394))], (4004 ^ _115804) ^ [] : [empty(_171394)], (4008 ^ _115804) ^ [] : [-(quasi_total(_171394, _171297, _171295))]], function(_171394), quasi_total(_171394, _171297, _171295)]]], (10355 ^ _115804) ^ [_273252, _273254] : [-(relation(set_intersection2(_273254, _273252))), relation(_273254), relation(_273252)], (568 ^ _115804) ^ [_123154, _123156, _123158, _123160] : [-(strict_net_str(_123158, _123154)), strict_net_str(_123160, _123156), _123160 = _123158, _123156 = _123154], (10151 ^ _115804) ^ [] : [-(empty(empty_set))], (15709 ^ _115804) ^ [_362384, _362386] : [topological_space(_362386), top_str(_362386), element(_362384, powerset(the_carrier(_362386))), 15721 ^ _115804 : [(15722 ^ _115804) ^ [_362661] : [in(_362661, 15720 ^ [_362384, _362386]), 15725 ^ _115804 : [(15735 ^ _115804) ^ [] : [-(subset(_362384, _362661))], (15733 ^ _115804) ^ [] : [-(closed_subset(15727 ^ [_362384, _362386, _362661], _362386))], (15731 ^ _115804) ^ [] : [-(15727 ^ [_362384, _362386, _362661] = _362661)], (15726 ^ _115804) ^ [] : [-(in(_362661, powerset(the_carrier(_362386))))], (15729 ^ _115804) ^ [] : [-(element(15727 ^ [_362384, _362386, _362661], powerset(the_carrier(_362386))))]]], (15737 ^ _115804) ^ [_362896] : [-(in(_362896, 15720 ^ [_362384, _362386])), in(_362896, powerset(the_carrier(_362386))), 15742 ^ _115804 : [(15743 ^ _115804) ^ [_363021] : [element(_363021, powerset(the_carrier(_362386))), _363021 = _362896, closed_subset(_363021, _362386), subset(_362384, _362896)]]]]], (12872 ^ _115804) ^ [] : [-(bounded_relstr(12850 ^ []))], (12170 ^ _115804) ^ [] : [-(strict_latt_str(12164 ^ []))], (19057 ^ _115804) ^ [_419061] : [relation(_419061), 19060 ^ _115804 : [(19061 ^ _115804) ^ [_419126] : [relation(_419126), -(subset(relation_rng(relation_composition(_419061, _419126)), relation_rng(_419126)))]]], (966 ^ _115804) ^ [_128581, _128583, _128585, _128587] : [-(closed_subset(_128585, _128581)), closed_subset(_128587, _128583), _128587 = _128585, _128583 = _128581], (10581 ^ _115804) ^ [_276269] : [-(join_commutative(boole_lattice(_276269)))], (12145 ^ _115804) ^ [] : [-(join_commutative(12137 ^ []))], (11339 ^ _115804) ^ [_286207, _286209, _286211, _286213] : [11362 ^ _115804 : [(11363 ^ _115804) ^ [] : [empty_carrier(net_str_of(_286213, _286211, _286209, _286207))], (11365 ^ _115804) ^ [] : [-(strict_net_str(net_str_of(_286213, _286211, _286209, _286207), _286213))]], one_sorted_str(_286213), -(empty(_286211)), relation_of2(_286209, _286211, _286211), function(_286207), quasi_total(_286207, _286211, the_carrier(_286213)), relation_of2(_286207, _286211, the_carrier(_286213))], (9261 ^ _115804) ^ [] : [true___, -(true___)], (10885 ^ _115804) ^ [_280235] : [10896 ^ _115804 : [(10905 ^ _115804) ^ [] : [-(v1_partfun1(the_L_join(_280235), cartesian_product2(the_carrier(_280235), the_carrier(_280235)), the_carrier(_280235)))], (10903 ^ _115804) ^ [] : [-(v2_binop_1(the_L_join(_280235), the_carrier(_280235)))], (10901 ^ _115804) ^ [] : [-(quasi_total(the_L_join(_280235), cartesian_product2(the_carrier(_280235), the_carrier(_280235)), the_carrier(_280235)))], (10897 ^ _115804) ^ [] : [-(relation(the_L_join(_280235)))], (10899 ^ _115804) ^ [] : [-(function(the_L_join(_280235)))]], -(empty_carrier(_280235)), join_associative(_280235), join_semilatt_str(_280235)], (15477 ^ _115804) ^ [_357340, _357342] : [-(empty(_357342)), relation(_357340), 15485 ^ _115804 : [(15486 ^ _115804) ^ [_357624, _357626] : [in(_357624, 15484 ^ [_357340, _357342, _357626]), 15489 ^ _115804 : [(15496 ^ _115804) ^ [] : [-(in(15491 ^ [_357340, _357342, _357624, _357626], _357342))], (15494 ^ _115804) ^ [] : [-(ordered_pair(15491 ^ [_357340, _357342, _357624, _357626], 15492 ^ [_357340, _357342, _357624, _357626]) = _357624)], (15501 ^ _115804) ^ [] : [-(in(15492 ^ [_357340, _357342, _357624, _357626], 15497 ^ [_357340, _357342, _357624, _357626]))], (15503 ^ _115804) ^ [_358090] : [in(_358090, 15497 ^ [_357340, _357342, _357624, _357626]), -(in(ordered_pair(15492 ^ [_357340, _357342, _357624, _357626], _358090), _357340))], (15490 ^ _115804) ^ [] : [-(in(_357624, cartesian_product2(_357342, _357626)))], (15499 ^ _115804) ^ [] : [-(15491 ^ [_357340, _357342, _357624, _357626] = 15497 ^ [_357340, _357342, _357624, _357626])]]], (15509 ^ _115804) ^ [_358233, _358235] : [-(in(_358233, 15484 ^ [_357340, _357342, _358235])), in(_358233, cartesian_product2(_357342, _358235)), 15514 ^ _115804 : [(15515 ^ _115804) ^ [_358391, _358393] : [ordered_pair(_358393, _358391) = _358233, in(_358393, _357342), 15522 ^ _115804 : [(15523 ^ _115804) ^ [_358546] : [_358393 = _358546, in(_358391, _358546), 15531 ^ _115804 : [(15532 ^ _115804) ^ [] : [-(in(15530 ^ [_357340, _357342, _358233, _358235, _358391, _358393, _358546], _358546))], (15534 ^ _115804) ^ [] : [in(ordered_pair(_358391, 15530 ^ [_357340, _357342, _358233, _358235, _358391, _358393, _358546]), _357340)]]]]]]]]], (5886 ^ _115804) ^ [_203205, _203207, _203209] : [subset(_203205, cartesian_product2(_203209, _203207)), -(relation_of2(_203205, _203209, _203207))], (3456 ^ _115804) ^ [_164743] : [rel_str(_164743), 3487 ^ _115804 : [(3502 ^ _115804) ^ [] : [-(lower_bounded_relstr(_164743))], (3496 ^ _115804) ^ [] : [-(with_suprema_relstr(_164743))], (3504 ^ _115804) ^ [] : [-(upper_bounded_relstr(_164743))], (3492 ^ _115804) ^ [] : [-(transitive_relstr(_164743))], (3508 ^ _115804) ^ [] : [-(connected_relstr(_164743))], (3494 ^ _115804) ^ [] : [-(antisymmetric_relstr(_164743))], (3510 ^ _115804) ^ [] : [-(up_complete_relstr(_164743))], (3500 ^ _115804) ^ [] : [-(complete_relstr(_164743))], (3506 ^ _115804) ^ [] : [-(bounded_relstr(_164743))], (3512 ^ _115804) ^ [] : [-(join_complete_relstr(_164743))], (3498 ^ _115804) ^ [] : [-(with_infima_relstr(_164743))], (3490 ^ _115804) ^ [] : [-(reflexive_relstr(_164743))], (3488 ^ _115804) ^ [] : [empty_carrier(_164743)]], -(empty_carrier(_164743)), reflexive_relstr(_164743), transitive_relstr(_164743), antisymmetric_relstr(_164743), lower_bounded_relstr(_164743), connected_relstr(_164743), up_complete_relstr(_164743)], (9625 ^ _115804) ^ [_263520] : [-(relation(identity_relation(_263520)))], (12754 ^ _115804) ^ [] : [-(bounded_relstr(12732 ^ []))], (18746 ^ _115804) ^ [_414422, _414424] : [-(set_union2(_414424, set_difference(_414422, _414424)) = set_union2(_414424, _414422))], (10641 ^ _115804) ^ [_276921] : [-(reflexive(identity_relation(_276921)))], (2866 ^ _115804) ^ [_157293] : [v4_membered(_157293), 2869 ^ _115804 : [(2870 ^ _115804) ^ [_157366] : [element(_157366, _157293), 2873 ^ _115804 : [(2878 ^ _115804) ^ [] : [-(v1_int_1(_157366))], (2874 ^ _115804) ^ [] : [-(v1_xcmplx_0(_157366))], (2876 ^ _115804) ^ [] : [-(v1_xreal_0(_157366))], (2880 ^ _115804) ^ [] : [-(v1_rat_1(_157366))]]]]], (12813 ^ _115804) ^ [_305038] : [one_sorted_str(_305038), 12817 ^ _115804 : [(12818 ^ _115804) ^ [] : [-(element(12816 ^ [_305038], powerset(powerset(the_carrier(_305038)))))], (12822 ^ _115804) ^ [] : [-(finite(12816 ^ [_305038]))], (12820 ^ _115804) ^ [] : [empty(12816 ^ [_305038])]]], (19863 ^ _115804) ^ [_432035, _432037] : [relation(_432035), function(_432035), 19870 ^ _115804 : [(19871 ^ _115804) ^ [_432191] : [relation(_432191), function(_432191), 19878 ^ _115804 : [(19879 ^ _115804) ^ [] : [_432035 = relation_dom_restriction(_432191, _432037), 19882 ^ _115804 : [(19883 ^ _115804) ^ [] : [-(relation_dom(_432035) = set_intersection2(relation_dom(_432191), _432037))], (19885 ^ _115804) ^ [_432422] : [in(_432422, relation_dom(_432035)), -(apply(_432035, _432422) = apply(_432191, _432422))]]], (19891 ^ _115804) ^ [] : [-(_432035 = relation_dom_restriction(_432191, _432037)), relation_dom(_432035) = set_intersection2(relation_dom(_432191), _432037), 19897 ^ _115804 : [(19898 ^ _115804) ^ [] : [-(in(19896 ^ [_432035, _432037, _432191], relation_dom(_432035)))], (19900 ^ _115804) ^ [] : [apply(_432035, 19896 ^ [_432035, _432037, _432191]) = apply(_432191, 19896 ^ [_432035, _432037, _432191])]]]]]]], (3158 ^ _115804) ^ [_161019] : [ordinal(_161019), 3161 ^ _115804 : [(3162 ^ _115804) ^ [] : [-(epsilon_transitive(_161019))], (3164 ^ _115804) ^ [] : [-(epsilon_connected(_161019))]]], (2106 ^ _115804) ^ [_145966, _145968, _145970, _145972] : [-(relation_rng_restriction(_145972, _145968) = relation_rng_restriction(_145970, _145966)), _145972 = _145970, _145968 = _145966], (4304 ^ _115804) ^ [_175335, _175337, _175339] : [-(join_commut(_175339, _175337, _175335) = join_commut(_175339, _175335, _175337)), -(empty_carrier(_175339)), join_commutative(_175339), join_semilatt_str(_175339), element(_175337, the_carrier(_175339)), element(_175335, the_carrier(_175339))], (11415 ^ _115804) ^ [_287236] : [-(antisymmetric_relstr(boole_POSet(_287236)))], (18909 ^ _115804) ^ [_416668] : [18924 ^ _115804 : [(18925 ^ _115804) ^ [] : [-(ex_sup_of_relstr_set(_416668, empty_set))], (18927 ^ _115804) ^ [] : [-(ex_inf_of_relstr_set(_416668, the_carrier(_416668)))]], -(empty_carrier(_416668)), antisymmetric_relstr(_416668), lower_bounded_relstr(_416668), rel_str(_416668)], (3614 ^ _115804) ^ [_166683] : [empty(_166683), 3617 ^ _115804 : [(3618 ^ _115804) ^ [] : [-(epsilon_transitive(_166683))], (3622 ^ _115804) ^ [] : [-(ordinal(_166683))], (3620 ^ _115804) ^ [] : [-(epsilon_connected(_166683))]]], (1466 ^ _115804) ^ [_135443, _135445] : [-(function(_135443)), _135445 = _135443, function(_135445)], (12458 ^ _115804) ^ [] : [-(complete_relstr(12430 ^ []))], (17881 ^ _115804) ^ [_400916] : [relation(_400916), 17884 ^ _115804 : [(17885 ^ _115804) ^ [_400994] : [relation(_400994), subset(_400916, _400994), 17892 ^ _115804 : [(17893 ^ _115804) ^ [] : [-(subset(relation_dom(_400916), relation_dom(_400994)))], (17895 ^ _115804) ^ [] : [-(subset(relation_rng(_400916), relation_rng(_400994)))]]]]], (1680 ^ _115804) ^ [_139121, _139123, _139125, _139127] : [-(the_mapping(_139127, _139123) = the_mapping(_139125, _139121)), _139127 = _139125, _139123 = _139121], (2606 ^ _115804) ^ [_153476, _153478] : [_153478 = _153476, -(relation_rng(_153478) = relation_rng(_153476))], (18485 ^ _115804) ^ [_410385, _410387] : [ordinal(_410385), subset(_410387, _410385), -(_410387 = empty_set), 18497 ^ _115804 : [(18498 ^ _115804) ^ [] : [-(ordinal(18496 ^ [_410385, _410387]))], (18502 ^ _115804) ^ [_410664] : [ordinal(_410664), in(_410664, _410387), -(ordinal_subset(18496 ^ [_410385, _410387], _410664))], (18500 ^ _115804) ^ [] : [-(in(18496 ^ [_410385, _410387], _410387))]]], (12536 ^ _115804) ^ [] : [-(antisymmetric_relstr(12524 ^ []))], (11397 ^ _115804) ^ [_287014] : [-(antisymmetric_relstr(boole_POSet(_287014)))], (12499 ^ _115804) ^ [] : [-(with_infima_relstr(12465 ^ []))], (6219 ^ _115804) ^ [_208864] : [-(in(6220 ^ [_208864], _208864)), -(_208864 = empty_set)], (2150 ^ _115804) ^ [_146642, _146644] : [_146644 = _146642, -(inclusion_order(_146644) = inclusion_order(_146642))], (13010 ^ _115804) ^ [] : [-(join_absorbing(12992 ^ []))], (1540 ^ _115804) ^ [_136492, _136494] : [-(topological_space(_136492)), _136494 = _136492, topological_space(_136494)], (1794 ^ _115804) ^ [_140880, _140882] : [_140882 = _140880, -(k1_pcomps_1(_140882) = k1_pcomps_1(_140880))], (18886 ^ _115804) ^ [_416368] : [ordinal(_416368), 18889 ^ _115804 : [(18890 ^ _115804) ^ [] : [-(being_limit_ordinal(_416368)), 18894 ^ _115804 : [(18895 ^ _115804) ^ [] : [-(ordinal(18893 ^ [_416368]))], (18897 ^ _115804) ^ [] : [-(_416368 = succ(18893 ^ [_416368]))]]], (18899 ^ _115804) ^ [] : [being_limit_ordinal(_416368), 18900 ^ _115804 : [(18901 ^ _115804) ^ [_416558] : [ordinal(_416558), _416368 = succ(_416558)]]]]], (11752 ^ _115804) ^ [_292187] : [relation(_292187), -(relation_inverse(relation_inverse(_292187)) = _292187)], (9565 ^ _115804) ^ [_262640, _262642, _262644] : [relation_of2(_262640, _262644, _262642), -(element(relation_rng_as_subset(_262644, _262642, _262640), powerset(_262642)))], (15616 ^ _115804) ^ [_360288, _360290, _360292] : [-(in(_360288, 15600 ^ [_360290, _360292])), in(_360288, cartesian_product2(_360292, _360290)), 15621 ^ _115804 : [(15622 ^ _115804) ^ [_360411, _360413] : [ordered_pair(_360413, _360411) = _360288, in(_360413, _360292), _360411 = singleton(_360413)]]], (12547 ^ _115804) ^ [_301984] : [-(function(12539 ^ [_301984]))], (872 ^ _115804) ^ [_127282, _127284, _127286, _127288, _127290, _127292] : [-(latt_set_smaller(_127290, _127286, _127282)), latt_set_smaller(_127292, _127288, _127284), _127292 = _127290, _127288 = _127286, _127284 = _127282], (12475 ^ _115804) ^ [] : [-(reflexive_relstr(12465 ^ []))], (11185 ^ _115804) ^ [_284227, _284229] : [-(closed_subset(subset_complement(the_carrier(_284229), _284227), _284229)), topological_space(_284229), top_str(_284229), open_subset(_284227, _284229), element(_284227, powerset(the_carrier(_284229)))], (7778 ^ _115804) ^ [_233716] : [relation(_233716), -(relation_field(_233716) = set_union2(relation_dom(_233716), relation_rng(_233716)))], (10423 ^ _115804) ^ [_274079] : [-(join_complete_relstr(boole_POSet(_274079)))], (3540 ^ _115804) ^ [_165747] : [rel_str(_165747), -(v1_yellow_3(_165747)), empty_carrier(_165747)], (16793 ^ _115804) ^ [_382973, _382975] : [in(_382973, 16779 ^ [_382975]), -(in(powerset(_382973), 16779 ^ [_382975]))], (19912 ^ _115804) ^ [_432847, _432849, _432851, _432853] : [function(_432847), quasi_total(_432847, _432853, _432851), relation_of2_as_subset(_432847, _432853, _432851), in(_432849, _432853), -(_432851 = empty_set), -(in(apply(_432847, _432849), relation_rng(_432847)))], (18758 ^ _115804) ^ [_414565, _414567] : [18759 ^ _115804 : [(18760 ^ _115804) ^ [] : [_414567 = empty_set], (18762 ^ _115804) ^ [] : [_414567 = singleton(_414565)]], -(subset(_414567, singleton(_414565)))], (12323 ^ _115804) ^ [] : [-(v4_membered(12313 ^ []))], (2182 ^ _115804) ^ [_147110, _147112, _147114, _147116, _147118, _147120] : [-(relation_dom_as_subset(_147120, _147116, _147112) = relation_dom_as_subset(_147118, _147114, _147110)), _147120 = _147118, _147116 = _147114, _147112 = _147110], (12438 ^ _115804) ^ [] : [-(reflexive_relstr(12430 ^ []))], (10084 ^ _115804) ^ [_269747, _269749] : [-(relation_of2_as_subset(10082 ^ [_269747, _269749], _269749, _269747))], (3394 ^ _115804) ^ [_163989] : [rel_str(_163989), with_infima_relstr(_163989), empty_carrier(_163989)], (12362 ^ _115804) ^ [] : [-(function(12356 ^ []))], (1970 ^ _115804) ^ [_143772, _143774] : [_143774 = _143772, -(identity_as_relation_of(_143774) = identity_as_relation_of(_143772))], (12467 ^ _115804) ^ [] : [-(rel_str(12465 ^ []))], (10247 ^ _115804) ^ [_271917] : [empty(singleton(_271917))], (9891 ^ _115804) ^ [] : [true___, -(true___)], (12860 ^ _115804) ^ [] : [-(transitive_relstr(12850 ^ []))], (11325 ^ _115804) ^ [_286016, _286018] : [-(open_subset(interior(_286018, _286016), _286018)), topological_space(_286018), top_str(_286018), element(_286016, powerset(the_carrier(_286018)))], (7094 ^ _115804) ^ [_223042, _223044, _223046] : [-(_223042 = set_intersection2(_223046, _223044)), 7106 ^ _115804 : [(7107 ^ _115804) ^ [] : [-(in(7095 ^ [_223042, _223044, _223046], _223046))], (7111 ^ _115804) ^ [] : [in(7095 ^ [_223042, _223044, _223046], _223042)], (7109 ^ _115804) ^ [] : [-(in(7095 ^ [_223042, _223044, _223046], _223044))]], 7098 ^ _115804 : [(7099 ^ _115804) ^ [] : [-(in(7095 ^ [_223042, _223044, _223046], _223042))], (7101 ^ _115804) ^ [] : [in(7095 ^ [_223042, _223044, _223046], _223046), in(7095 ^ [_223042, _223044, _223046], _223044)]]], (12283 ^ _115804) ^ [] : [-(finite(12279 ^ []))], (622 ^ _115804) ^ [_123847, _123849, _123851, _123853, _123855, _123857] : [-(relation_of2(_123855, _123851, _123847)), relation_of2(_123857, _123853, _123849), _123857 = _123855, _123853 = _123851, _123849 = _123847], (18782 ^ _115804) ^ [_414911, _414913] : [element(_414913, powerset(_414911)), -(subset(_414913, _414911))], (11809 ^ _115804) ^ [_292975, _292977] : [relation(_292975), -(subset(relation_dom(relation_rng_restriction(_292977, _292975)), relation_dom(_292975)))], (8484 ^ _115804) ^ [_246784] : [rel_str(_246784), 8487 ^ _115804 : [(8526 ^ _115804) ^ [_247739] : [-(ex_inf_of_relstr_set(_246784, _247739)), 8527 ^ _115804 : [(8528 ^ _115804) ^ [_247862] : [element(_247862, the_carrier(_246784)), relstr_element_smaller(_246784, _247739, _247862), 8538 ^ _115804 : [(8539 ^ _115804) ^ [] : [-(element(8537 ^ [_246784, _247739, _247862], the_carrier(_246784)))], (8543 ^ _115804) ^ [] : [related(_246784, 8537 ^ [_246784, _247739, _247862], _247862)], (8541 ^ _115804) ^ [] : [-(relstr_element_smaller(_246784, _247739, 8537 ^ [_246784, _247739, _247862]))]], 8545 ^ _115804 : [(8548 ^ _115804) ^ [] : [-(relstr_element_smaller(_246784, _247739, 8544 ^ [_246784, _247739, _247862]))], (8546 ^ _115804) ^ [] : [-(element(8544 ^ [_246784, _247739, _247862], the_carrier(_246784)))], (8560 ^ _115804) ^ [] : [8544 ^ [_246784, _247739, _247862] = _247862], (8550 ^ _115804) ^ [_248310] : [element(_248310, the_carrier(_246784)), relstr_element_smaller(_246784, _247739, _248310), -(related(_246784, _248310, 8544 ^ [_246784, _247739, _247862]))]]]]], (8488 ^ _115804) ^ [_246949] : [ex_inf_of_relstr_set(_246784, _246949), 8492 ^ _115804 : [(8497 ^ _115804) ^ [_247251] : [element(_247251, the_carrier(_246784)), relstr_element_smaller(_246784, _246949, _247251), -(related(_246784, _247251, 8491 ^ [_246784, _246949]))], (8493 ^ _115804) ^ [] : [-(element(8491 ^ [_246784, _246949], the_carrier(_246784)))], (8495 ^ _115804) ^ [] : [-(relstr_element_smaller(_246784, _246949, 8491 ^ [_246784, _246949]))], (8507 ^ _115804) ^ [_247402] : [element(_247402, the_carrier(_246784)), -(_247402 = 8491 ^ [_246784, _246949]), relstr_element_smaller(_246784, _246949, _247402), 8517 ^ _115804 : [(8518 ^ _115804) ^ [] : [-(element(8516 ^ [_246784, _246949, _247402], the_carrier(_246784)))], (8522 ^ _115804) ^ [] : [related(_246784, 8516 ^ [_246784, _246949, _247402], _247402)], (8520 ^ _115804) ^ [] : [-(relstr_element_smaller(_246784, _246949, 8516 ^ [_246784, _246949, _247402]))]]]]]]], (18291 ^ _115804) ^ [_407124] : [antisymmetric_relstr(_407124), rel_str(_407124), 18298 ^ _115804 : [(18299 ^ _115804) ^ [_407330] : [element(_407330, the_carrier(_407124)), 18302 ^ _115804 : [(18323 ^ _115804) ^ [_407802] : [18335 ^ _115804 : [(18336 ^ _115804) ^ [] : [-(_407330 = join_on_relstr(_407124, _407802))], (18338 ^ _115804) ^ [] : [-(ex_sup_of_relstr_set(_407124, _407802))]], relstr_set_smaller(_407124, _407802, _407330), 18329 ^ _115804 : [(18330 ^ _115804) ^ [] : [-(element(18328 ^ [_407124, _407330, _407802], the_carrier(_407124)))], (18334 ^ _115804) ^ [] : [related(_407124, _407330, 18328 ^ [_407124, _407330, _407802])], (18332 ^ _115804) ^ [] : [-(relstr_set_smaller(_407124, _407802, 18328 ^ [_407124, _407330, _407802]))]]], (18303 ^ _115804) ^ [_407489] : [_407330 = join_on_relstr(_407124, _407489), ex_sup_of_relstr_set(_407124, _407489), 18310 ^ _115804 : [(18311 ^ _115804) ^ [] : [-(relstr_set_smaller(_407124, _407489, _407330))], (18313 ^ _115804) ^ [_407653] : [element(_407653, the_carrier(_407124)), relstr_set_smaller(_407124, _407489, _407653), -(related(_407124, _407330, _407653))]]]]]]], (10555 ^ _115804) ^ [_275890] : [10566 ^ _115804 : [(10575 ^ _115804) ^ [] : [-(v1_partfun1(the_L_join(_275890), cartesian_product2(the_carrier(_275890), the_carrier(_275890)), the_carrier(_275890)))], (10573 ^ _115804) ^ [] : [-(v1_binop_1(the_L_join(_275890), the_carrier(_275890)))], (10571 ^ _115804) ^ [] : [-(quasi_total(the_L_join(_275890), cartesian_product2(the_carrier(_275890), the_carrier(_275890)), the_carrier(_275890)))], (10567 ^ _115804) ^ [] : [-(relation(the_L_join(_275890)))], (10569 ^ _115804) ^ [] : [-(function(the_L_join(_275890)))]], -(empty_carrier(_275890)), join_commutative(_275890), join_semilatt_str(_275890)], (8466 ^ _115804) ^ [_246543, _246545] : [proper_subset(_246545, _246543), 8469 ^ _115804 : [(8470 ^ _115804) ^ [] : [-(subset(_246545, _246543))], (8472 ^ _115804) ^ [] : [_246545 = _246543]]], (11253 ^ _115804) ^ [_285127] : [11264 ^ _115804 : [(11273 ^ _115804) ^ [] : [-(v1_partfun1(the_L_meet(_285127), cartesian_product2(the_carrier(_285127), the_carrier(_285127)), the_carrier(_285127)))], (11271 ^ _115804) ^ [] : [-(v2_binop_1(the_L_meet(_285127), the_carrier(_285127)))], (11269 ^ _115804) ^ [] : [-(quasi_total(the_L_meet(_285127), cartesian_product2(the_carrier(_285127), the_carrier(_285127)), the_carrier(_285127)))], (11265 ^ _115804) ^ [] : [-(relation(the_L_meet(_285127)))], (11267 ^ _115804) ^ [] : [-(function(the_L_meet(_285127)))]], -(empty_carrier(_285127)), meet_associative(_285127), meet_semilatt_str(_285127)], (17603 ^ _115804) ^ [_396228] : [relation(_396228), -(subset(_396228, cartesian_product2(relation_dom(_396228), relation_rng(_396228))))], (15064 ^ _115804) ^ [_348256, _348258] : [one_sorted_str(_348258), element(_348256, powerset(powerset(the_carrier(_348258)))), 15076 ^ _115804 : [(15091 ^ _115804) ^ [_348911] : [element(_348911, powerset(the_carrier(_348258))), _348911 = 15073 ^ [_348256, _348258], -(15075 ^ [_348256, _348258] = subset_complement(the_carrier(_348258), _348911))], (15089 ^ _115804) ^ [] : [-(in(15073 ^ [_348256, _348258], _348256))], (15079 ^ _115804) ^ [_348708] : [element(_348708, powerset(the_carrier(_348258))), _348708 = 15073 ^ [_348256, _348258], -(15074 ^ [_348256, _348258] = subset_complement(the_carrier(_348258), _348708))], (15101 ^ _115804) ^ [] : [15074 ^ [_348256, _348258] = 15075 ^ [_348256, _348258]], (15077 ^ _115804) ^ [] : [-(in(15073 ^ [_348256, _348258], _348256))]], 15103 ^ _115804 : [(15104 ^ _115804) ^ [_349201] : [in(_349201, 15102 ^ [_348256, _348258]), 15108 ^ _115804 : [(15109 ^ _115804) ^ [] : [-(in(15107 ^ [_348256, _348258, _349201], _348256))], (15113 ^ _115804) ^ [_349418] : [element(_349418, powerset(the_carrier(_348258))), _349418 = 15107 ^ [_348256, _348258, _349201], -(_349201 = subset_complement(the_carrier(_348258), _349418))], (15111 ^ _115804) ^ [] : [-(in(15107 ^ [_348256, _348258, _349201], _348256))]]], (15123 ^ _115804) ^ [_349595] : [-(in(_349595, 15102 ^ [_348256, _348258])), 15124 ^ _115804 : [(15125 ^ _115804) ^ [_349676] : [in(_349676, _348256), in(_349676, _348256), 15133 ^ _115804 : [(15134 ^ _115804) ^ [] : [-(element(15132 ^ [_348256, _348258, _349595, _349676], powerset(the_carrier(_348258))))], (15138 ^ _115804) ^ [] : [_349595 = subset_complement(the_carrier(_348258), 15132 ^ [_348256, _348258, _349595, _349676])], (15136 ^ _115804) ^ [] : [-(15132 ^ [_348256, _348258, _349595, _349676] = _349676)]]]]]]], (18796 ^ _115804) ^ [_415101, _415103] : [-(disjoint(_415103, _415101)), 18800 ^ _115804 : [(18801 ^ _115804) ^ [] : [-(in(18799 ^ [_415101, _415103], _415103))], (18803 ^ _115804) ^ [] : [-(in(18799 ^ [_415101, _415103], _415101))]]], (18259 ^ _115804) ^ [_406645, _406647, _406649] : [relation(_406645), in(ordered_pair(_406649, _406647), _406645), 18266 ^ _115804 : [(18267 ^ _115804) ^ [] : [-(in(_406649, relation_field(_406645)))], (18269 ^ _115804) ^ [] : [-(in(_406647, relation_field(_406645)))]]], (234 ^ _115804) ^ [_118847, _118849] : [-(complemented_lattstr(_118847)), _118849 = _118847, complemented_lattstr(_118849)], (17323 ^ _115804) ^ [_391521, _391523] : [relation(_391521), -(relation_restriction(_391521, _391523) = relation_rng_restriction(_391523, relation_dom_restriction(_391521, _391523)))], (6989 ^ _115804) ^ [_221243] : [relation(_221243), 6992 ^ _115804 : [(6993 ^ _115804) ^ [_221329] : [relation(_221329), 6996 ^ _115804 : [(7007 ^ _115804) ^ [] : [7010 ^ _115804 : [(7011 ^ _115804) ^ [] : [-(in(ordered_pair(7008 ^ [_221243, _221329], 7009 ^ [_221243, _221329]), _221243))], (7013 ^ _115804) ^ [] : [in(ordered_pair(7008 ^ [_221243, _221329], 7009 ^ [_221243, _221329]), _221329)]], -(subset(_221243, _221329))], (6997 ^ _115804) ^ [] : [subset(_221243, _221329), 7000 ^ _115804 : [(7001 ^ _115804) ^ [_221460, _221462] : [in(ordered_pair(_221462, _221460), _221243), -(in(ordered_pair(_221462, _221460), _221329))]]]]]]], (712 ^ _115804) ^ [_125070, _125072, _125074, _125076] : [-(directed_subset(_125074, _125070)), directed_subset(_125076, _125072), _125076 = _125074, _125072 = _125070], (1590 ^ _115804) ^ [_137117, _137119, _137121, _137123] : [-(net_str(_137121, _137117)), net_str(_137123, _137119), _137123 = _137121, _137119 = _137117], (12230 ^ _115804) ^ [] : [-(lower_bounded_semilattstr(12206 ^ []))], (15990 ^ _115804) ^ [_368205, _368207, _368209] : [element(_368207, powerset(powerset(_368209))), relation(_368205), function(_368205), 16002 ^ _115804 : [(16003 ^ _115804) ^ [_368442] : [in(_368442, 16001 ^ [_368205, _368207, _368209]), 16006 ^ _115804 : [(16007 ^ _115804) ^ [] : [-(in(_368442, powerset(relation_dom(_368205))))], (16009 ^ _115804) ^ [] : [-(in(relation_image(_368205, _368442), _368207))]]], (16011 ^ _115804) ^ [_368577] : [-(in(_368577, 16001 ^ [_368205, _368207, _368209])), in(_368577, powerset(relation_dom(_368205))), in(relation_image(_368205, _368577), _368207)]]], (822 ^ _115804) ^ [_126551, _126553, _126555, _126557, _126559, _126561] : [-(below(_126559, _126555, _126551)), below(_126561, _126557, _126553), _126561 = _126559, _126557 = _126555, _126553 = _126551], (16742 ^ _115804) ^ [_382118, _382120] : [element(_382118, powerset(powerset(_382120))), -(_382118 = empty_set), -(union_of_subsets(_382120, complements_of_subsets(_382120, _382118)) = subset_complement(_382120, meet_of_subsets(_382120, _382118)))], (20344 ^ _115804) ^ [_439210] : [-(union(powerset(_439210)) = _439210)], (10913 ^ _115804) ^ [_280633] : [-(join_associative(boole_lattice(_280633)))], (11455 ^ _115804) ^ [_287733] : [-(reflexive_relstr(boole_POSet(_287733)))], (11656 ^ _115804) ^ [_290661, _290663, _290665, _290667] : [11675 ^ _115804 : [(11676 ^ _115804) ^ [_291005, _291007, _291009, _291011] : [net_str_of(_290667, _290665, _290663, _290661) = net_str_of(_291011, _291009, _291007, _291005), 11679 ^ _115804 : [(11684 ^ _115804) ^ [] : [-(_290663 = _291007)], (11680 ^ _115804) ^ [] : [-(_290667 = _291011)], (11682 ^ _115804) ^ [] : [-(_290665 = _291009)], (11686 ^ _115804) ^ [] : [-(_290661 = _291005)]]]], one_sorted_str(_290667), relation_of2(_290663, _290665, _290665), function(_290661), quasi_total(_290661, _290665, the_carrier(_290667)), relation_of2(_290661, _290665, the_carrier(_290667))], (13234 ^ _115804) ^ [_310844, _310846, _310848] : [-(meet_commut(_310848, _310846, _310844) = meet(_310848, _310846, _310844)), -(empty_carrier(_310848)), meet_commutative(_310848), meet_semilatt_str(_310848), element(_310846, the_carrier(_310848)), element(_310844, the_carrier(_310848))], (12450 ^ _115804) ^ [] : [-(up_complete_relstr(12430 ^ []))], (11315 ^ _115804) ^ [_285889] : [empty(relation_rng(_285889)), -(empty(_285889)), relation(_285889)], (17817 ^ _115804) ^ [_400043, _400045] : [relation(_400043), connected(_400043), -(connected(relation_restriction(_400043, _400045)))], (10253 ^ _115804) ^ [_271995] : [-(cup_closed(powerset(_271995)))], (244 ^ _115804) ^ [_118972, _118974] : [-(boolean_lattstr(_118972)), _118974 = _118972, boolean_lattstr(_118974)], (15878 ^ _115804) ^ [_365823, _365825] : [one_sorted_str(_365825), element(_365823, powerset(powerset(the_carrier(_365825)))), 15886 ^ _115804 : [(15887 ^ _115804) ^ [_366108, _366110] : [in(_366108, 15885 ^ [_365823, _365825, _366110]), 15890 ^ _115804 : [(15897 ^ _115804) ^ [] : [-(in(15892 ^ [_365823, _365825, _366108, _366110], _365823))], (15891 ^ _115804) ^ [] : [-(in(_366108, cartesian_product2(_365823, _366110)))], (15895 ^ _115804) ^ [] : [-(ordered_pair(15892 ^ [_365823, _365825, _366108, _366110], 15893 ^ [_365823, _365825, _366108, _366110]) = _366108)], (15899 ^ _115804) ^ [_366417] : [element(_366417, powerset(the_carrier(_365825))), _366417 = 15892 ^ [_365823, _365825, _366108, _366110], -(15893 ^ [_365823, _365825, _366108, _366110] = subset_complement(the_carrier(_365825), _366417))]]], (15909 ^ _115804) ^ [_366626, _366628] : [-(in(_366626, 15885 ^ [_365823, _365825, _366628])), in(_366626, cartesian_product2(_365823, _366628)), 15914 ^ _115804 : [(15915 ^ _115804) ^ [_366779, _366781] : [ordered_pair(_366781, _366779) = _366626, in(_366781, _365823), 15923 ^ _115804 : [(15924 ^ _115804) ^ [] : [-(element(15922 ^ [_365823, _365825, _366626, _366628, _366779, _366781], powerset(the_carrier(_365825))))], (15928 ^ _115804) ^ [] : [_366779 = subset_complement(the_carrier(_365825), 15922 ^ [_365823, _365825, _366626, _366628, _366779, _366781])], (15926 ^ _115804) ^ [] : [-(15922 ^ [_365823, _365825, _366626, _366628, _366779, _366781] = _366781)]]]]]]], (9655 ^ _115804) ^ [_263967, _263969, _263971, _263973, _263975] : [9682 ^ _115804 : [(9683 ^ _115804) ^ [] : [-(function(function_of_composition(_263975, _263973, _263971, _263969, _263967)))], (9687 ^ _115804) ^ [] : [-(relation_of2_as_subset(function_of_composition(_263975, _263973, _263971, _263969, _263967), _263975, _263971))], (9685 ^ _115804) ^ [] : [-(quasi_total(function_of_composition(_263975, _263973, _263971, _263969, _263967), _263975, _263971))]], -(empty(_263973)), function(_263969), quasi_total(_263969, _263975, _263973), relation_of2(_263969, _263975, _263973), function(_263967), quasi_total(_263967, _263973, _263971), relation_of2(_263967, _263973, _263971)], (2998 ^ _115804) ^ [_158994] : [v3_membered(_158994), 3001 ^ _115804 : [(3002 ^ _115804) ^ [_159064] : [element(_159064, powerset(_158994)), 3005 ^ _115804 : [(3006 ^ _115804) ^ [] : [-(v1_membered(_159064))], (3010 ^ _115804) ^ [] : [-(v3_membered(_159064))], (3008 ^ _115804) ^ [] : [-(v2_membered(_159064))]]]]], (4941 ^ _115804) ^ [_186963] : [-(empty_carrier(_186963)), meet_semilatt_str(_186963), 4948 ^ _115804 : [(4949 ^ _115804) ^ [] : [lower_bounded_semilattstr(_186963), 4953 ^ _115804 : [(4954 ^ _115804) ^ [] : [-(element(4952 ^ [_186963], the_carrier(_186963)))], (4956 ^ _115804) ^ [_187222] : [element(_187222, the_carrier(_186963)), 4959 ^ _115804 : [(4960 ^ _115804) ^ [] : [-(meet(_186963, 4952 ^ [_186963], _187222) = 4952 ^ [_186963])], (4962 ^ _115804) ^ [] : [-(meet(_186963, _187222, 4952 ^ [_186963]) = 4952 ^ [_186963])]]]]], (4964 ^ _115804) ^ [] : [-(lower_bounded_semilattstr(_186963)), 4965 ^ _115804 : [(4966 ^ _115804) ^ [_187406] : [element(_187406, the_carrier(_186963)), 4970 ^ _115804 : [(4971 ^ _115804) ^ [] : [-(element(4969 ^ [_186963, _187406], the_carrier(_186963)))], (4973 ^ _115804) ^ [] : [meet(_186963, _187406, 4969 ^ [_186963, _187406]) = _187406, meet(_186963, 4969 ^ [_186963, _187406], _187406) = _187406]]]]]]], (12087 ^ _115804) ^ [] : [empty_carrier(12083 ^ [])], (12304 ^ _115804) ^ [] : [-(strict_rel_str(12298 ^ []))], (12713 ^ _115804) ^ [] : [-(bounded_relstr(12689 ^ []))], (16529 ^ _115804) ^ [_378962, _378964] : [topological_space(_378964), top_str(_378964), element(_378962, powerset(powerset(the_carrier(_378964)))), 16541 ^ _115804 : [(16542 ^ _115804) ^ [] : [-(element(16540 ^ [_378962, _378964], powerset(powerset(the_carrier(_378964)))))], (16544 ^ _115804) ^ [_379241] : [element(_379241, powerset(the_carrier(_378964))), 16547 ^ _115804 : [(16548 ^ _115804) ^ [] : [in(_379241, 16540 ^ [_378962, _378964]), -(in(set_difference(cast_as_carrier_subset(_378964), _379241), _378962))], (16554 ^ _115804) ^ [] : [in(set_difference(cast_as_carrier_subset(_378964), _379241), _378962), -(in(_379241, 16540 ^ [_378962, _378964]))]]]]], (2696 ^ _115804) ^ [_155171, _155173] : [proper_subset(_155173, _155171), proper_subset(_155171, _155173)], (12190 ^ _115804) ^ [] : [-(bounded_lattstr(12164 ^ []))], (11797 ^ _115804) ^ [_292861, _292863] : [disjoint(singleton(_292863), _292861), in(_292863, _292861)], (19411 ^ _115804) ^ [_424537] : [relation(_424537), function(_424537), one_to_one(_424537), 19422 ^ _115804 : [(19423 ^ _115804) ^ [_424784] : [relation(_424784), function(_424784), 19430 ^ _115804 : [(19461 ^ _115804) ^ [] : [-(_424784 = function_inverse(_424537)), relation_dom(_424784) = relation_rng(_424537), 19470 ^ _115804 : [(19471 ^ _115804) ^ [] : [-(in(19466 ^ [_424537, _424784], relation_rng(_424537)))], (19475 ^ _115804) ^ [] : [in(19467 ^ [_424537, _424784], relation_dom(_424537)), 19466 ^ [_424537, _424784] = apply(_424537, 19467 ^ [_424537, _424784])], (19473 ^ _115804) ^ [] : [-(19467 ^ [_424537, _424784] = apply(_424784, 19466 ^ [_424537, _424784]))]], 19480 ^ _115804 : [(19481 ^ _115804) ^ [] : [-(in(19467 ^ [_424537, _424784], relation_dom(_424537)))], (19485 ^ _115804) ^ [] : [in(19466 ^ [_424537, _424784], relation_rng(_424537)), 19467 ^ [_424537, _424784] = apply(_424784, 19466 ^ [_424537, _424784])], (19483 ^ _115804) ^ [] : [-(19466 ^ [_424537, _424784] = apply(_424537, 19467 ^ [_424537, _424784]))]]], (19431 ^ _115804) ^ [] : [_424784 = function_inverse(_424537), 19434 ^ _115804 : [(19435 ^ _115804) ^ [] : [-(relation_dom(_424784) = relation_rng(_424537))], (19449 ^ _115804) ^ [_425243, _425245] : [19456 ^ _115804 : [(19457 ^ _115804) ^ [] : [-(in(_425245, relation_rng(_424537)))], (19459 ^ _115804) ^ [] : [-(_425243 = apply(_424784, _425245))]], in(_425243, relation_dom(_424537)), _425245 = apply(_424537, _425243)], (19437 ^ _115804) ^ [_425064, _425066] : [19444 ^ _115804 : [(19445 ^ _115804) ^ [] : [-(in(_425064, relation_dom(_424537)))], (19447 ^ _115804) ^ [] : [-(_425066 = apply(_424537, _425064))]], in(_425066, relation_rng(_424537)), _425064 = apply(_424784, _425066)]]]]]]], (2360 ^ _115804) ^ [_149827, _149829, _149831, _149833, _149835, _149837] : [-(subset_difference(_149837, _149833, _149829) = subset_difference(_149835, _149831, _149827)), _149837 = _149835, _149833 = _149831, _149829 = _149827], (12495 ^ _115804) ^ [] : [-(boolean_relstr(12465 ^ []))], (2308 ^ _115804) ^ [_149061, _149063, _149065, _149067] : [-(relation_restriction(_149067, _149063) = relation_restriction(_149065, _149061)), _149067 = _149065, _149063 = _149061], (10315 ^ _115804) ^ [_272729] : [-(strict_latt_str(boole_lattice(_272729)))], (17298 ^ _115804) ^ [_391043] : [finite(_391043), 17301 ^ _115804 : [(17302 ^ _115804) ^ [_391146] : [element(_391146, powerset(powerset(_391043))), -(_391146 = empty_set), 17310 ^ _115804 : [(17311 ^ _115804) ^ [] : [-(in(17309 ^ [_391043, _391146], _391146))], (17313 ^ _115804) ^ [_391348] : [-(_391348 = 17309 ^ [_391043, _391146]), in(_391348, _391146), subset(17309 ^ [_391043, _391146], _391348)]]]]], (380 ^ _115804) ^ [_120760, _120762] : [-(up_complete_relstr(_120760)), _120762 = _120760, up_complete_relstr(_120762)], (12515 ^ _115804) ^ [] : [-(antisymmetric_relstr(12503 ^ []))], (11471 ^ _115804) ^ [_287885] : [-(bounded_relstr(boole_POSet(_287885)))], (2518 ^ _115804) ^ [_152154, _152156] : [_152156 = _152154, -(bottom_of_relstr(_152156) = bottom_of_relstr(_152154))], (12485 ^ _115804) ^ [] : [-(bounded_relstr(12465 ^ []))], (13394 ^ _115804) ^ [_313260, _313262, _313264, _313266] : [-(apply_as_element(_313266, _313264, _313262, _313260) = apply(_313262, _313260)), -(empty(_313266)), function(_313262), quasi_total(_313262, _313266, _313264), relation_of2(_313262, _313266, _313264), element(_313260, _313266)], (9093 ^ _115804) ^ [] : [true___, -(true___)], (4738 ^ _115804) ^ [_182640] : [-(empty_carrier(_182640)), one_sorted_str(_182640), 4745 ^ _115804 : [(4746 ^ _115804) ^ [_182806] : [-(empty_carrier(_182806)), net_str(_182806, _182640), 4753 ^ _115804 : [(4754 ^ _115804) ^ [_182972] : [is_often_in(_182640, _182806, _182972), 4757 ^ _115804 : [(4758 ^ _115804) ^ [_183065] : [element(_183065, the_carrier(_182806)), 4762 ^ _115804 : [(4763 ^ _115804) ^ [] : [-(element(4761 ^ [_182640, _182806, _182972, _183065], the_carrier(_182806)))], (4767 ^ _115804) ^ [] : [-(in(apply_netmap(_182640, _182806, 4761 ^ [_182640, _182806, _182972, _183065]), _182972))], (4765 ^ _115804) ^ [] : [-(related(_182806, _183065, 4761 ^ [_182640, _182806, _182972, _183065]))]]]]], (4769 ^ _115804) ^ [_183252] : [-(is_often_in(_182640, _182806, _183252)), 4771 ^ _115804 : [(4772 ^ _115804) ^ [] : [-(element(4770 ^ [_182640, _182806, _183252], the_carrier(_182806)))], (4774 ^ _115804) ^ [_183391] : [element(_183391, the_carrier(_182806)), related(_182806, 4770 ^ [_182640, _182806, _183252], _183391), in(apply_netmap(_182640, _182806, _183391), _183252)]]]]]]], (13008 ^ _115804) ^ [] : [-(meet_absorbing(12992 ^ []))], (4090 ^ _115804) ^ [_172667] : [latt_str(_172667), 4105 ^ _115804 : [(4118 ^ _115804) ^ [] : [-(join_absorbing(_172667))], (4108 ^ _115804) ^ [] : [-(join_commutative(_172667))], (4114 ^ _115804) ^ [] : [-(meet_associative(_172667))], (4110 ^ _115804) ^ [] : [-(join_associative(_172667))], (4116 ^ _115804) ^ [] : [-(meet_absorbing(_172667))], (4112 ^ _115804) ^ [] : [-(meet_commutative(_172667))], (4122 ^ _115804) ^ [] : [-(modular_lattstr(_172667))], (4120 ^ _115804) ^ [] : [-(lattice(_172667))], (4106 ^ _115804) ^ [] : [empty_carrier(_172667)]], -(empty_carrier(_172667)), lattice(_172667), distributive_lattstr(_172667)], (10645 ^ _115804) ^ [_276959] : [-(antisymmetric(identity_relation(_276959)))], (19200 ^ _115804) ^ [_421414] : [top_str(_421414), 19203 ^ _115804 : [(19204 ^ _115804) ^ [_421480] : [element(_421480, powerset(the_carrier(_421414))), -(subset(_421480, topstr_closure(_421414, _421480)))]]], (7872 ^ _115804) ^ [_235383] : [-(empty_carrier(_235383)), one_sorted_str(_235383), 7879 ^ _115804 : [(7880 ^ _115804) ^ [_235611] : [-(empty_carrier(_235611)), net_str(_235611, _235383), 7887 ^ _115804 : [(7888 ^ _115804) ^ [_235827] : [element(_235827, the_carrier(_235611)), 7891 ^ _115804 : [(7892 ^ _115804) ^ [_235983] : [strict_net_str(_235983, _235383), net_str(_235983, _235383), 7899 ^ _115804 : [(7933 ^ _115804) ^ [] : [-(_235983 = netstr_restr_to_element(_235383, _235611, _235827)), the_InternalRel(_235983) = relation_restriction_as_relation_of(the_InternalRel(_235611), the_carrier(_235983)), the_mapping(_235383, _235983) = partfun_dom_restriction(the_carrier(_235611), the_carrier(_235383), the_mapping(_235383, _235611), the_carrier(_235983)), 7952 ^ _115804 : [(7957 ^ _115804) ^ [] : [-(related(_235611, _235827, 7951 ^ [_235383, _235611, _235827, _235983]))], (7953 ^ _115804) ^ [] : [-(element(7951 ^ [_235383, _235611, _235827, _235983], the_carrier(_235611)))], (7955 ^ _115804) ^ [] : [-(7951 ^ [_235383, _235611, _235827, _235983] = 7936 ^ [_235383, _235611, _235827, _235983])], (7959 ^ _115804) ^ [] : [in(7936 ^ [_235383, _235611, _235827, _235983], the_carrier(_235983))]], 7939 ^ _115804 : [(7940 ^ _115804) ^ [] : [-(in(7936 ^ [_235383, _235611, _235827, _235983], the_carrier(_235983)))], (7942 ^ _115804) ^ [_236896] : [element(_236896, the_carrier(_235611)), _236896 = 7936 ^ [_235383, _235611, _235827, _235983], related(_235611, _235827, _236896)]]], (7900 ^ _115804) ^ [] : [_235983 = netstr_restr_to_element(_235383, _235611, _235827), 7903 ^ _115804 : [(7904 ^ _115804) ^ [_236252] : [in(_236252, the_carrier(_235983)), 7908 ^ _115804 : [(7909 ^ _115804) ^ [] : [-(element(7907 ^ [_235383, _235611, _235827, _235983, _236252], the_carrier(_235611)))], (7913 ^ _115804) ^ [] : [-(related(_235611, _235827, 7907 ^ [_235383, _235611, _235827, _235983, _236252]))], (7911 ^ _115804) ^ [] : [-(7907 ^ [_235383, _235611, _235827, _235983, _236252] = _236252)]]], (7929 ^ _115804) ^ [] : [-(the_InternalRel(_235983) = relation_restriction_as_relation_of(the_InternalRel(_235611), the_carrier(_235983)))], (7931 ^ _115804) ^ [] : [-(the_mapping(_235383, _235983) = partfun_dom_restriction(the_carrier(_235611), the_carrier(_235383), the_mapping(_235383, _235611), the_carrier(_235983)))], (7915 ^ _115804) ^ [_236435] : [-(in(_236435, the_carrier(_235983))), 7916 ^ _115804 : [(7917 ^ _115804) ^ [_236492] : [element(_236492, the_carrier(_235611)), _236492 = _236435, related(_235611, _235827, _236492)]]]]]]]]]]]]], (12448 ^ _115804) ^ [] : [-(bounded_relstr(12430 ^ []))], (16799 ^ _115804) ^ [_383070, _383072] : [subset(_383070, 16779 ^ [_383072]), -(are_equipotent(_383070, 16779 ^ [_383072])), -(in(_383070, 16779 ^ [_383072]))], (16592 ^ _115804) ^ [_379974, _379976] : [element(_379974, powerset(powerset(_379976))), 16595 ^ _115804 : [(16596 ^ _115804) ^ [] : [-(_379974 = empty_set), complements_of_subsets(_379976, _379974) = empty_set], (16602 ^ _115804) ^ [] : [-(complements_of_subsets(_379976, _379974) = empty_set), _379974 = empty_set]]], (12232 ^ _115804) ^ [] : [-(upper_bounded_semilattstr(12206 ^ []))], (11858 ^ _115804) ^ [_293709, _293711] : [relation(_293709), well_ordering(_293709), equipotent(_293711, relation_field(_293709)), 11870 ^ _115804 : [(11871 ^ _115804) ^ [] : [-(relation(11869 ^ [_293709, _293711]))], (11873 ^ _115804) ^ [] : [-(well_orders(11869 ^ [_293709, _293711], _293711))]]], (7969 ^ _115804) ^ [_237377] : [relation(_237377), 7972 ^ _115804 : [(7973 ^ _115804) ^ [_237526] : [relation(_237526), 7976 ^ _115804 : [(7977 ^ _115804) ^ [_237667] : [relation(_237667), function(_237667), 7984 ^ _115804 : [(8019 ^ _115804) ^ [] : [-(relation_isomorphism(_237377, _237526, _237667)), relation_dom(_237667) = relation_field(_237377), relation_rng(_237667) = relation_field(_237526), one_to_one(_237667), 8048 ^ _115804 : [(8053 ^ _115804) ^ [] : [-(in(ordered_pair(apply(_237667, 8032 ^ [_237377, _237526, _237667]), apply(_237667, 8033 ^ [_237377, _237526, _237667])), _237526))], (8049 ^ _115804) ^ [] : [-(in(8032 ^ [_237377, _237526, _237667], relation_field(_237377)))], (8051 ^ _115804) ^ [] : [-(in(8033 ^ [_237377, _237526, _237667], relation_field(_237377)))], (8055 ^ _115804) ^ [] : [in(ordered_pair(8032 ^ [_237377, _237526, _237667], 8033 ^ [_237377, _237526, _237667]), _237377)]], 8036 ^ _115804 : [(8037 ^ _115804) ^ [] : [-(in(ordered_pair(8032 ^ [_237377, _237526, _237667], 8033 ^ [_237377, _237526, _237667]), _237377))], (8039 ^ _115804) ^ [] : [in(8032 ^ [_237377, _237526, _237667], relation_field(_237377)), in(8033 ^ [_237377, _237526, _237667], relation_field(_237377)), in(ordered_pair(apply(_237667, 8032 ^ [_237377, _237526, _237667]), apply(_237667, 8033 ^ [_237377, _237526, _237667])), _237526)]]], (7985 ^ _115804) ^ [] : [relation_isomorphism(_237377, _237526, _237667), 7988 ^ _115804 : [(8005 ^ _115804) ^ [_238150, _238152] : [-(in(ordered_pair(_238152, _238150), _237377)), in(_238152, relation_field(_237377)), in(_238150, relation_field(_237377)), in(ordered_pair(apply(_237667, _238152), apply(_237667, _238150)), _237526)], (7995 ^ _115804) ^ [_237989, _237991] : [in(ordered_pair(_237991, _237989), _237377), 7998 ^ _115804 : [(7999 ^ _115804) ^ [] : [-(in(_237991, relation_field(_237377)))], (8003 ^ _115804) ^ [] : [-(in(ordered_pair(apply(_237667, _237991), apply(_237667, _237989)), _237526))], (8001 ^ _115804) ^ [] : [-(in(_237989, relation_field(_237377)))]]], (7993 ^ _115804) ^ [] : [-(one_to_one(_237667))], (7989 ^ _115804) ^ [] : [-(relation_dom(_237667) = relation_field(_237377))], (7991 ^ _115804) ^ [] : [-(relation_rng(_237667) = relation_field(_237526))]]]]]]]]], (5248 ^ _115804) ^ [_192325] : [rel_str(_192325), 5251 ^ _115804 : [(5252 ^ _115804) ^ [_192399] : [subrelstr(_192399, _192325), 5255 ^ _115804 : [(5256 ^ _115804) ^ [] : [full_subrelstr(_192399, _192325), -(the_InternalRel(_192399) = relation_restriction_as_relation_of(the_InternalRel(_192325), the_carrier(_192399)))], (5262 ^ _115804) ^ [] : [the_InternalRel(_192399) = relation_restriction_as_relation_of(the_InternalRel(_192325), the_carrier(_192399)), -(full_subrelstr(_192399, _192325))]]]]], (2766 ^ _115804) ^ [_156040] : [v2_membered(_156040), 2769 ^ _115804 : [(2770 ^ _115804) ^ [_156103] : [element(_156103, _156040), 2773 ^ _115804 : [(2774 ^ _115804) ^ [] : [-(v1_xcmplx_0(_156103))], (2776 ^ _115804) ^ [] : [-(v1_xreal_0(_156103))]]]]], (3818 ^ _115804) ^ [_169247] : [rel_str(_169247), bounded_relstr(_169247), 3825 ^ _115804 : [(3826 ^ _115804) ^ [] : [-(lower_bounded_relstr(_169247))], (3828 ^ _115804) ^ [] : [-(upper_bounded_relstr(_169247))]]], (12628 ^ _115804) ^ [] : [-(ordinal(12614 ^ []))], (14119 ^ _115804) ^ [_326367, _326369] : [-(empty(_326369)), relation(_326367), 14131 ^ _115804 : [(14148 ^ _115804) ^ [] : [-(14128 ^ [_326367, _326369] = 14146 ^ [_326367, _326369])], (14132 ^ _115804) ^ [] : [-(in(14128 ^ [_326367, _326369], _326369))], (14139 ^ _115804) ^ [_326957] : [in(_326957, 14133 ^ [_326367, _326369]), -(in(ordered_pair(14129 ^ [_326367, _326369], _326957), _326367))], (14135 ^ _115804) ^ [] : [-(14128 ^ [_326367, _326369] = 14133 ^ [_326367, _326369])], (14145 ^ _115804) ^ [] : [-(in(14128 ^ [_326367, _326369], _326369))], (14137 ^ _115804) ^ [] : [-(in(14129 ^ [_326367, _326369], 14133 ^ [_326367, _326369]))], (14152 ^ _115804) ^ [_327215] : [in(_327215, 14146 ^ [_326367, _326369]), -(in(ordered_pair(14130 ^ [_326367, _326369], _327215), _326367))], (14150 ^ _115804) ^ [] : [-(in(14130 ^ [_326367, _326369], 14146 ^ [_326367, _326369]))], (14158 ^ _115804) ^ [] : [14129 ^ [_326367, _326369] = 14130 ^ [_326367, _326369]]], 14160 ^ _115804 : [(14161 ^ _115804) ^ [_327452] : [in(_327452, 14159 ^ [_326367, _326369]), 14165 ^ _115804 : [(14175 ^ _115804) ^ [_327783] : [in(_327783, 14169 ^ [_326367, _326369, _327452]), -(in(ordered_pair(_327452, _327783), _326367))], (14173 ^ _115804) ^ [] : [-(in(_327452, 14169 ^ [_326367, _326369, _327452]))], (14171 ^ _115804) ^ [] : [-(14164 ^ [_326367, _326369, _327452] = 14169 ^ [_326367, _326369, _327452])], (14166 ^ _115804) ^ [] : [-(in(14164 ^ [_326367, _326369, _327452], _326369))], (14168 ^ _115804) ^ [] : [-(in(14164 ^ [_326367, _326369, _327452], _326369))]]], (14181 ^ _115804) ^ [_327896] : [-(in(_327896, 14159 ^ [_326367, _326369])), 14182 ^ _115804 : [(14183 ^ _115804) ^ [_327982] : [in(_327982, _326369), in(_327982, _326369), 14190 ^ _115804 : [(14191 ^ _115804) ^ [_328123] : [_327982 = _328123, in(_327896, _328123), 14199 ^ _115804 : [(14200 ^ _115804) ^ [] : [-(in(14198 ^ [_326367, _326369, _327896, _327982, _328123], _328123))], (14202 ^ _115804) ^ [] : [in(ordered_pair(_327896, 14198 ^ [_326367, _326369, _327896, _327982, _328123]), _326367)]]]]]]]]], (3116 ^ _115804) ^ [_160514] : [rel_str(_160514), with_suprema_relstr(_160514), empty_carrier(_160514)], (18400 ^ _115804) ^ [_409059] : [-(ordinal(_409059)), 18402 ^ _115804 : [(18403 ^ _115804) ^ [] : [-(in(18401 ^ [_409059], _409059))], (18405 ^ _115804) ^ [] : [ordinal(18401 ^ [_409059]), subset(18401 ^ [_409059], _409059)]]], (9059 ^ _115804) ^ [_255840, _255842, _255844, _255846] : [-(element(apply_on_structs(_255846, _255844, _255842, _255840), the_carrier(_255844))), -(empty_carrier(_255846)), one_sorted_str(_255846), -(empty_carrier(_255844)), one_sorted_str(_255844), function(_255842), quasi_total(_255842, the_carrier(_255846), the_carrier(_255844)), relation_of2(_255842, the_carrier(_255846), the_carrier(_255844)), element(_255840, the_carrier(_255846))], (10016 ^ _115804) ^ [] : [-(meet_semilatt_str(10014 ^ []))], (17609 ^ _115804) ^ [_396315, _396317, _396319] : [relation(_396315), -(subset(fiber(relation_restriction(_396315, _396319), _396317), fiber(_396315, _396317)))], (10005 ^ _115804) ^ [_268814] : [join_semilatt_str(_268814), 10008 ^ _115804 : [(10009 ^ _115804) ^ [] : [-(function(the_L_join(_268814)))], (10013 ^ _115804) ^ [] : [-(relation_of2_as_subset(the_L_join(_268814), cartesian_product2(the_carrier(_268814), the_carrier(_268814)), the_carrier(_268814)))], (10011 ^ _115804) ^ [] : [-(quasi_total(the_L_join(_268814), cartesian_product2(the_carrier(_268814), the_carrier(_268814)), the_carrier(_268814)))]]], (284 ^ _115804) ^ [_119472, _119474] : [-(v4_membered(_119472)), _119474 = _119472, v4_membered(_119474)], (11846 ^ _115804) ^ [_293549, _293551] : [subset(singleton(_293551), _293549), -(in(_293551, _293549))], (12147 ^ _115804) ^ [] : [-(join_associative(12137 ^ []))], (2976 ^ _115804) ^ [_158679] : [v1_membered(_158679), 2979 ^ _115804 : [(2980 ^ _115804) ^ [_158739] : [element(_158739, powerset(_158679)), -(v1_membered(_158739))]]], (2488 ^ _115804) ^ [_151707, _151709, _151711, _151713] : [-(set_difference(_151713, _151709) = set_difference(_151711, _151707)), _151713 = _151711, _151709 = _151707], (19337 ^ _115804) ^ [_423348] : [top_str(_423348), 19340 ^ _115804 : [(19341 ^ _115804) ^ [_423440] : [element(_423440, powerset(the_carrier(_423348))), 19344 ^ _115804 : [(19345 ^ _115804) ^ [] : [closed_subset(_423440, _423348), -(topstr_closure(_423348, _423440) = _423440)], (19351 ^ _115804) ^ [] : [-(closed_subset(_423440, _423348)), topological_space(_423348), topstr_closure(_423348, _423440) = _423440]]]]], (94 ^ _115804) ^ [_117007, _117009, _117011, _117013] : [-(is_connected_in(_117011, _117007)), is_connected_in(_117013, _117009), _117013 = _117011, _117009 = _117007], (17669 ^ _115804) ^ [_397651, _397653] : [relation(_397651), function(_397651), 17676 ^ _115804 : [(17677 ^ _115804) ^ [_397789] : [relation(_397789), function(_397789), in(_397653, relation_dom(relation_composition(_397789, _397651))), -(apply(relation_composition(_397789, _397651), _397653) = apply(_397651, apply(_397789, _397653)))]]], (13300 ^ _115804) ^ [_311836, _311838] : [element(_311836, powerset(powerset(_311838))), -(union_of_subsets(_311838, _311836) = union(_311836))], (20274 ^ _115804) ^ [_438192] : [relation(_438192), 20277 ^ _115804 : [(20278 ^ _115804) ^ [] : [well_orders(_438192, relation_field(_438192)), -(well_ordering(_438192))], (20284 ^ _115804) ^ [] : [well_ordering(_438192), -(well_orders(_438192, relation_field(_438192)))]]], (6305 ^ _115804) ^ [_210276] : [-(empty_carrier(_210276)), latt_str(_210276), -(empty_carrier(_210276)), lattice(_210276), complete_latt_str(_210276), latt_str(_210276), 6328 ^ _115804 : [(6329 ^ _115804) ^ [_210623, _210625] : [element(_210623, the_carrier(_210276)), 6332 ^ _115804 : [(6349 ^ _115804) ^ [] : [-(_210623 = join_of_latt_set(_210276, _210625)), latt_element_smaller(_210276, _210623, _210625), 6355 ^ _115804 : [(6356 ^ _115804) ^ [] : [-(element(6354 ^ [_210276, _210623, _210625], the_carrier(_210276)))], (6360 ^ _115804) ^ [] : [below(_210276, _210623, 6354 ^ [_210276, _210623, _210625])], (6358 ^ _115804) ^ [] : [-(latt_element_smaller(_210276, 6354 ^ [_210276, _210623, _210625], _210625))]]], (6333 ^ _115804) ^ [] : [_210623 = join_of_latt_set(_210276, _210625), 6336 ^ _115804 : [(6337 ^ _115804) ^ [] : [-(latt_element_smaller(_210276, _210623, _210625))], (6339 ^ _115804) ^ [_210798] : [element(_210798, the_carrier(_210276)), latt_element_smaller(_210276, _210798, _210625), -(below(_210276, _210623, _210798))]]]]]]], (6983 ^ _115804) ^ [_221162] : [one_sorted_str(_221162), -(cast_as_carrier_subset(_221162) = the_carrier(_221162))], (20 ^ _115804) ^ [_116064, _116066] : [-(v1_xcmplx_0(_116064)), _116066 = _116064, v1_xcmplx_0(_116066)], (12308 ^ _115804) ^ [] : [-(transitive_relstr(12298 ^ []))], (1724 ^ _115804) ^ [_139759, _139761, _139763, _139765] : [-(a_2_3_lattice3(_139765, _139761) = a_2_3_lattice3(_139763, _139759)), _139765 = _139763, _139761 = _139759], (4 ^ _115804) ^ [_115854, _115856] : [_115856 = _115854, -(_115854 = _115856)], (10407 ^ _115804) ^ [_273887] : [-(strict_rel_str(boole_POSet(_273887)))], (10317 ^ _115804) ^ [_272755, _272757] : [10324 ^ _115804 : [(10325 ^ _115804) ^ [] : [empty_carrier(rel_str_of(_272757, _272755))], (10327 ^ _115804) ^ [] : [-(strict_rel_str(rel_str_of(_272757, _272755)))]], -(empty(_272757)), relation_of2(_272755, _272757, _272757)], (9897 ^ _115804) ^ [_267264] : [rel_str(_267264), 9900 ^ _115804 : [(9901 ^ _115804) ^ [_267322] : [subrelstr(_267322, _267264), -(rel_str(_267322))]]], (4194 ^ _115804) ^ [_173956] : [rel_str(_173956), 4209 ^ _115804 : [(4214 ^ _115804) ^ [] : [-(with_suprema_relstr(_173956))], (4210 ^ _115804) ^ [] : [empty_carrier(_173956)], (4212 ^ _115804) ^ [] : [-(reflexive_relstr(_173956))], (4216 ^ _115804) ^ [] : [-(upper_bounded_relstr(_173956))]], reflexive_relstr(_173956), with_suprema_relstr(_173956), up_complete_relstr(_173956)], (10137 ^ _115804) ^ [_270444] : [empty(_270444), 10140 ^ _115804 : [(10141 ^ _115804) ^ [] : [-(empty(relation_inverse(_270444)))], (10143 ^ _115804) ^ [] : [-(relation(relation_inverse(_270444)))]]], (18092 ^ _115804) ^ [_404161, _404163] : [-(empty_carrier(_404161)), lattice(_404161), latt_str(_404161), 18103 ^ _115804 : [(18104 ^ _115804) ^ [_404342] : [element(_404342, the_carrier(poset_of_lattice(_404161))), 18107 ^ _115804 : [(18108 ^ _115804) ^ [] : [relstr_element_smaller(poset_of_lattice(_404161), _404163, _404342), -(latt_set_smaller(_404161, cast_to_el_of_lattice(_404161, _404342), _404163))], (18114 ^ _115804) ^ [] : [latt_set_smaller(_404161, cast_to_el_of_lattice(_404161, _404342), _404163), -(relstr_element_smaller(poset_of_lattice(_404161), _404163, _404342))]]]]], (18770 ^ _115804) ^ [_414735] : [-(bottom_of_semilattstr(boole_lattice(_414735)) = empty_set)], (2408 ^ _115804) ^ [_150537, _150539, _150541, _150543] : [-(join_of_latt_set(_150543, _150539) = join_of_latt_set(_150541, _150537)), _150543 = _150541, _150539 = _150537], (19210 ^ _115804) ^ [_421575, _421577] : [element(_421575, powerset(powerset(_421577))), -(_421575 = empty_set), -(union_of_subsets(_421577, complements_of_subsets(_421577, _421575)) = subset_difference(_421577, cast_to_subset(_421577), meet_of_subsets(_421577, _421575)))], (9425 ^ _115804) ^ [_260736, _260738] : [-(element(cast_to_el_of_LattPOSet(_260738, _260736), the_carrier(poset_of_lattice(_260738)))), -(empty_carrier(_260738)), lattice(_260738), latt_str(_260738), element(_260736, the_carrier(_260738))], (12095 ^ _115804) ^ [] : [-(meet_commutative(12083 ^ []))], (16933 ^ _115804) ^ [_384973, _384975] : [relation(_384973), -(relation_image(_384973, _384975) = relation_image(_384973, set_intersection2(relation_dom(_384973), _384975)))], (18690 ^ _115804) ^ [_413626, _413628] : [set_difference(_413628, _413626) = empty_set, -(subset(_413628, _413626))], (10431 ^ _115804) ^ [_274165] : [-(complemented_relstr(boole_POSet(_274165)))], (5848 ^ _115804) ^ [_202529] : [5850 ^ _115804 : [(5851 ^ _115804) ^ [] : [-(in(5849 ^ [_202529], _202529))], (5853 ^ _115804) ^ [_202642, _202644] : [5849 ^ [_202529] = ordered_pair(_202644, _202642)]], -(relation(_202529))], (10331 ^ _115804) ^ [] : [-(epsilon_transitive(omega))], (12319 ^ _115804) ^ [] : [-(v2_membered(12313 ^ []))], (18972 ^ _115804) ^ [_417642] : [relation(_417642), 18975 ^ _115804 : [(18976 ^ _115804) ^ [_417707] : [relation(_417707), -(subset(relation_dom(relation_composition(_417642, _417707)), relation_dom(_417642)))]]], (17757 ^ _115804) ^ [_399107] : [17772 ^ _115804 : [(17773 ^ _115804) ^ [_399333] : [element(_399333, the_carrier(_399107)), 17776 ^ _115804 : [(17777 ^ _115804) ^ [_399407] : [element(_399407, the_carrier(_399107)), -(below(_399107, meet_commut(_399107, _399333, _399407), _399333))]]]], -(empty_carrier(_399107)), meet_commutative(_399107), meet_absorbing(_399107), latt_str(_399107)], (12616 ^ _115804) ^ [] : [-(relation(12614 ^ []))], (12058 ^ _115804) ^ [_296615, _296617, _296619] : [relation(_296615), function(_296615), 12065 ^ _115804 : [(12066 ^ _115804) ^ [] : [in(_296617, relation_dom(relation_dom_restriction(_296615, _296619))), 12069 ^ _115804 : [(12070 ^ _115804) ^ [] : [-(in(_296617, relation_dom(_296615)))], (12072 ^ _115804) ^ [] : [-(in(_296617, _296619))]]], (12074 ^ _115804) ^ [] : [-(in(_296617, relation_dom(relation_dom_restriction(_296615, _296619)))), in(_296617, relation_dom(_296615)), in(_296617, _296619)]]], (11241 ^ _115804) ^ [_284968, _284970] : [11248 ^ _115804 : [(11249 ^ _115804) ^ [] : [-(relation(relation_rng_restriction(_284970, _284968)))], (11251 ^ _115804) ^ [] : [-(function(relation_rng_restriction(_284970, _284968)))]], relation(_284968), function(_284968)], (11139 ^ _115804) ^ [_283691] : [11150 ^ _115804 : [(11159 ^ _115804) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_283691)))], (11157 ^ _115804) ^ [] : [-(transitive_relstr(poset_of_lattice(_283691)))], (11155 ^ _115804) ^ [] : [-(reflexive_relstr(poset_of_lattice(_283691)))], (11151 ^ _115804) ^ [] : [empty_carrier(poset_of_lattice(_283691))], (11153 ^ _115804) ^ [] : [-(strict_rel_str(poset_of_lattice(_283691)))]], -(empty_carrier(_283691)), lattice(_283691), latt_str(_283691)], (12780 ^ _115804) ^ [] : [empty(12778 ^ [])], (6226 ^ _115804) ^ [_208905] : [-(incl_POSet(_208905) = rel_str_of(_208905, inclusion_order(_208905)))], (9587 ^ _115804) ^ [_262981, _262983, _262985] : [9606 ^ _115804 : [(9607 ^ _115804) ^ [] : [-(strict_net_str(netstr_restr_to_element(_262985, _262983, _262981), _262985))], (9609 ^ _115804) ^ [] : [-(net_str(netstr_restr_to_element(_262985, _262983, _262981), _262985))]], -(empty_carrier(_262985)), one_sorted_str(_262985), -(empty_carrier(_262983)), net_str(_262983, _262985), element(_262981, the_carrier(_262983))], (6899 ^ _115804) ^ [_219869] : [6910 ^ _115804 : [(6911 ^ _115804) ^ [_220032] : [element(_220032, the_carrier(_219869)), -(cast_to_el_of_LattPOSet(_219869, _220032) = _220032)]], -(empty_carrier(_219869)), lattice(_219869), latt_str(_219869)], (19609 ^ _115804) ^ [_427810] : [-(empty_carrier(_427810)), topological_space(_427810), top_str(_427810), 19620 ^ _115804 : [(19621 ^ _115804) ^ [_427998] : [element(_427998, powerset(the_carrier(_427810))), 19624 ^ _115804 : [(19625 ^ _115804) ^ [_428084] : [element(_428084, the_carrier(_427810)), -(point_neighbourhood(_427998, _427810, _428084)), open_subset(_427998, _427810), in(_428084, _427998)]]]]], (12724 ^ _115804) ^ [_304046] : [-(element(12722 ^ [_304046], powerset(powerset(_304046))))], (10425 ^ _115804) ^ [_274107] : [v1_yellow_3(boole_POSet(_274107))], (19279 ^ _115804) ^ [_422539] : [19294 ^ _115804 : [(19303 ^ _115804) ^ [] : [-(bottom_of_semilattstr(_422539) = join_of_latt_set(_422539, empty_set))], (19301 ^ _115804) ^ [] : [-(latt_str(_422539))], (19299 ^ _115804) ^ [] : [-(lower_bounded_semilattstr(_422539))], (19295 ^ _115804) ^ [] : [empty_carrier(_422539)], (19297 ^ _115804) ^ [] : [-(lattice(_422539))]], -(empty_carrier(_422539)), lattice(_422539), complete_latt_str(_422539), latt_str(_422539)], (10453 ^ _115804) ^ [_274490] : [10464 ^ _115804 : [(10469 ^ _115804) ^ [] : [-(reflexive_relstr(poset_of_lattice(_274490)))], (10467 ^ _115804) ^ [] : [-(strict_rel_str(poset_of_lattice(_274490)))], (10475 ^ _115804) ^ [] : [-(with_suprema_relstr(poset_of_lattice(_274490)))], (10465 ^ _115804) ^ [] : [empty_carrier(poset_of_lattice(_274490))], (10471 ^ _115804) ^ [] : [-(transitive_relstr(poset_of_lattice(_274490)))], (10477 ^ _115804) ^ [] : [-(with_infima_relstr(poset_of_lattice(_274490)))], (10473 ^ _115804) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_274490)))]], -(empty_carrier(_274490)), lattice(_274490), latt_str(_274490)], (10579 ^ _115804) ^ [_276250] : [-(strict_latt_str(boole_lattice(_276250)))], (7155 ^ _115804) ^ [_224017] : [7166 ^ _115804 : [(7167 ^ _115804) ^ [_224182] : [element(_224182, the_carrier(poset_of_lattice(_224017))), -(cast_to_el_of_lattice(_224017, _224182) = _224182)]], -(empty_carrier(_224017)), lattice(_224017), latt_str(_224017)], (6945 ^ _115804) ^ [_220593] : [epsilon_connected(_220593), 6948 ^ _115804 : [(6949 ^ _115804) ^ [_220683, _220685] : [in(_220685, _220593), in(_220683, _220593), -(in(_220685, _220683)), -(_220685 = _220683), -(in(_220683, _220685))]]], (6564 ^ _115804) ^ [_214412, _214414, _214416] : [_214412 = unordered_pair(_214416, _214414), 6567 ^ _115804 : [(6578 ^ _115804) ^ [_214591] : [6579 ^ _115804 : [(6580 ^ _115804) ^ [] : [_214591 = _214416], (6582 ^ _115804) ^ [] : [_214591 = _214414]], -(in(_214591, _214412))], (6568 ^ _115804) ^ [_214501] : [in(_214501, _214412), -(_214501 = _214416), -(_214501 = _214414)]]], (6228 ^ _115804) ^ [_208950, _208952] : [_208950 = powerset(_208952), 6231 ^ _115804 : [(6232 ^ _115804) ^ [_209029] : [in(_209029, _208950), -(subset(_209029, _208952))], (6238 ^ _115804) ^ [_209104] : [subset(_209104, _208952), -(in(_209104, _208950))]]], (17080 ^ _115804) ^ [_387379, _387381] : [relation(_387379), -(subset(relation_inverse_image(_387379, _387381), relation_dom(_387379)))], (12460 ^ _115804) ^ [] : [-(distributive_relstr(12430 ^ []))], (2176 ^ _115804) ^ [_147025, _147027] : [_147027 = _147025, -(cast_as_carrier_subset(_147027) = cast_as_carrier_subset(_147025))], (5989 ^ _115804) ^ [_204759, _204761] : [-(_204759 = singleton(_204761)), 5993 ^ _115804 : [(5994 ^ _115804) ^ [] : [-(in(5990 ^ [_204759, _204761], _204759))], (5996 ^ _115804) ^ [] : [5990 ^ [_204759, _204761] = _204761]], 5997 ^ _115804 : [(5998 ^ _115804) ^ [] : [-(5990 ^ [_204759, _204761] = _204761)], (6000 ^ _115804) ^ [] : [in(5990 ^ [_204759, _204761], _204759)]]], (3876 ^ _115804) ^ [_170012] : [rel_str(_170012), 3891 ^ _115804 : [(3892 ^ _115804) ^ [] : [empty_carrier(_170012)], (3896 ^ _115804) ^ [] : [-(connected_relstr(_170012))], (3894 ^ _115804) ^ [] : [-(reflexive_relstr(_170012))]], -(empty_carrier(_170012)), reflexive_relstr(_170012), trivial_carrier(_170012)], (17919 ^ _115804) ^ [_401463] : [relation(_401463), function(_401463), finite(relation_dom(_401463)), -(finite(relation_rng(_401463)))], (10639 ^ _115804) ^ [_276902] : [-(function(identity_relation(_276902)))], (3166 ^ _115804) ^ [_161114] : [3177 ^ _115804 : [(3178 ^ _115804) ^ [] : [-(relation(_161114))], (3180 ^ _115804) ^ [] : [-(reflexive(_161114))]], relation(_161114), symmetric(_161114), transitive(_161114)], (12427 ^ _115804) ^ [] : [-(up_complete_relstr(12401 ^ []))], (7317 ^ _115804) ^ [_226677] : [relation(_226677), 7320 ^ _115804 : [(7321 ^ _115804) ^ [] : [well_ordering(_226677), 7324 ^ _115804 : [(7333 ^ _115804) ^ [] : [-(well_founded_relation(_226677))], (7331 ^ _115804) ^ [] : [-(connected(_226677))], (7329 ^ _115804) ^ [] : [-(antisymmetric(_226677))], (7325 ^ _115804) ^ [] : [-(reflexive(_226677))], (7327 ^ _115804) ^ [] : [-(transitive(_226677))]]], (7335 ^ _115804) ^ [] : [-(well_ordering(_226677)), reflexive(_226677), transitive(_226677), antisymmetric(_226677), connected(_226677), well_founded_relation(_226677)]]], (13316 ^ _115804) ^ [_312086] : [-(identity_as_relation_of(_312086) = identity_relation(_312086))], (7017 ^ _115804) ^ [_221731, _221733] : [subset(_221733, _221731), 7020 ^ _115804 : [(7021 ^ _115804) ^ [_221794] : [in(_221794, _221733), -(in(_221794, _221731))]]], (16888 ^ _115804) ^ [_384313, _384315, _384317] : [relation(_384313), 16891 ^ _115804 : [(16892 ^ _115804) ^ [] : [in(_384317, relation_image(_384313, _384315)), 16896 ^ _115804 : [(16897 ^ _115804) ^ [] : [-(in(16895 ^ [_384313, _384315, _384317], relation_dom(_384313)))], (16901 ^ _115804) ^ [] : [-(in(16895 ^ [_384313, _384315, _384317], _384315))], (16899 ^ _115804) ^ [] : [-(in(ordered_pair(16895 ^ [_384313, _384315, _384317], _384317), _384313))]]], (16903 ^ _115804) ^ [] : [-(in(_384317, relation_image(_384313, _384315))), 16904 ^ _115804 : [(16905 ^ _115804) ^ [_384568] : [in(_384568, relation_dom(_384313)), in(ordered_pair(_384568, _384317), _384313), in(_384568, _384315)]]]]], (10155 ^ _115804) ^ [] : [-(relation_empty_yielding(empty_set))], (5362 ^ _115804) ^ [_194193] : [-(empty_carrier(_194193)), latt_str(_194193), 5369 ^ _115804 : [(5370 ^ _115804) ^ [_194337] : [element(_194337, the_carrier(_194193)), 5373 ^ _115804 : [(5388 ^ _115804) ^ [_194656] : [5390 ^ _115804 : [(5391 ^ _115804) ^ [] : [-(element(5389 ^ [_194193, _194337, _194656], the_carrier(_194193)))], (5395 ^ _115804) ^ [] : [below(_194193, 5389 ^ [_194193, _194337, _194656], _194337)], (5393 ^ _115804) ^ [] : [-(in(5389 ^ [_194193, _194337, _194656], _194656))]], -(latt_element_smaller(_194193, _194337, _194656))], (5374 ^ _115804) ^ [_194437] : [latt_element_smaller(_194193, _194337, _194437), 5377 ^ _115804 : [(5378 ^ _115804) ^ [_194513] : [element(_194513, the_carrier(_194193)), in(_194513, _194437), -(below(_194193, _194513, _194337))]]]]]]], (17827 ^ _115804) ^ [_400172] : [ordinal(_400172), 17830 ^ _115804 : [(17831 ^ _115804) ^ [_400250] : [ordinal(_400250), -(in(_400172, _400250)), -(_400172 = _400250), -(in(_400250, _400172))]]], (20326 ^ _115804) ^ [_438949, _438951] : [in(_438951, _438949), -(subset(_438951, union(_438949)))], (11307 ^ _115804) ^ [] : [-(v2_membered(empty_set))], (12288 ^ _115804) ^ [] : [-(function(12284 ^ []))], (1526 ^ _115804) ^ [_136299, _136301, _136303, _136305] : [-(are_equipotent(_136303, _136299)), are_equipotent(_136305, _136301), _136305 = _136303, _136301 = _136299], (3062 ^ _115804) ^ [_159849, _159851, _159853] : [relation_of2(_159849, _159853, _159851), 3073 ^ _115804 : [(3074 ^ _115804) ^ [] : [-(function(_159849))], (3076 ^ _115804) ^ [] : [-(quasi_total(_159849, _159853, _159851))]], function(_159849), v1_partfun1(_159849, _159853, _159851)], (12300 ^ _115804) ^ [] : [-(rel_str(12298 ^ []))], (19305 ^ _115804) ^ [_422868] : [-(_422868 = empty_set), 19308 ^ _115804 : [(19309 ^ _115804) ^ [_422951] : [element(_422951, powerset(_422868)), 19312 ^ _115804 : [(19313 ^ _115804) ^ [_423029] : [element(_423029, _422868), -(in(_423029, _422951)), -(in(_423029, subset_complement(_422868, _422951)))]]]]], (12413 ^ _115804) ^ [] : [-(with_suprema_relstr(12401 ^ []))], (7270 ^ _115804) ^ [_225912] : [-(cast_to_subset(_225912) = _225912)], (12479 ^ _115804) ^ [] : [-(antisymmetric_relstr(12465 ^ []))], (946 ^ _115804) ^ [_128331, _128333] : [-(complete_latt_str(_128331)), _128333 = _128331, complete_latt_str(_128333)], (18788 ^ _115804) ^ [_414988, _414990] : [subset(_414990, _414988), -(element(_414990, powerset(_414988)))], (20222 ^ _115804) ^ [_437481] : [-(empty_carrier(_437481)), reflexive_relstr(_437481), transitive_relstr(_437481), antisymmetric_relstr(_437481), lower_bounded_relstr(_437481), rel_str(_437481), 20245 ^ _115804 : [(20246 ^ _115804) ^ [_437820] : [-(empty(_437820)), filtered_subset(_437820, _437481), upper_relstr_subset(_437820, _437481), element(_437820, powerset(the_carrier(_437481))), 20261 ^ _115804 : [(20262 ^ _115804) ^ [] : [proper_element(_437820, powerset(the_carrier(_437481))), in(bottom_of_relstr(_437481), _437820)], (20268 ^ _115804) ^ [] : [-(in(bottom_of_relstr(_437481), _437820)), -(proper_element(_437820, powerset(the_carrier(_437481))))]]]]], (8350 ^ _115804) ^ [_244452] : [relation(_244452), 8353 ^ _115804 : [(8380 ^ _115804) ^ [_245016] : [8384 ^ _115804 : [(8389 ^ _115804) ^ [] : [-(in(8383 ^ [_244452, _245016], _245016))], (8387 ^ _115804) ^ [] : [-(in(8382 ^ [_244452, _245016], _245016))], (8393 ^ _115804) ^ [] : [-(in(ordered_pair(8382 ^ [_244452, _245016], 8383 ^ [_244452, _245016]), _244452))], (8395 ^ _115804) ^ [] : [in(ordered_pair(8381 ^ [_244452, _245016], 8383 ^ [_244452, _245016]), _244452)], (8385 ^ _115804) ^ [] : [-(in(8381 ^ [_244452, _245016], _245016))], (8391 ^ _115804) ^ [] : [-(in(ordered_pair(8381 ^ [_244452, _245016], 8382 ^ [_244452, _245016]), _244452))]], -(is_transitive_in(_244452, _245016))], (8354 ^ _115804) ^ [_244577] : [is_transitive_in(_244452, _244577), 8357 ^ _115804 : [(8358 ^ _115804) ^ [_244683, _244685, _244687] : [-(in(ordered_pair(_244687, _244683), _244452)), in(_244687, _244577), in(_244685, _244577), in(_244683, _244577), in(ordered_pair(_244687, _244685), _244452), in(ordered_pair(_244685, _244683), _244452)]]]]], (8641 ^ _115804) ^ [_249831] : [rel_str(_249831), 8644 ^ _115804 : [(8645 ^ _115804) ^ [_249917] : [element(_249917, the_carrier(_249831)), 8648 ^ _115804 : [(8649 ^ _115804) ^ [_249998] : [element(_249998, the_carrier(_249831)), 8652 ^ _115804 : [(8653 ^ _115804) ^ [] : [related(_249831, _249917, _249998), -(in(ordered_pair(_249917, _249998), the_InternalRel(_249831)))], (8659 ^ _115804) ^ [] : [in(ordered_pair(_249917, _249998), the_InternalRel(_249831)), -(related(_249831, _249917, _249998))]]]]]]], (12836 ^ _115804) ^ [] : [-(relation(12834 ^ []))], (8983 ^ _115804) ^ [_254892] : [-(strict_latt_str(boole_lattice(_254892)))], (1906 ^ _115804) ^ [_142728, _142730, _142732, _142734, _142736, _142738] : [-(join_commut(_142738, _142734, _142730) = join_commut(_142736, _142732, _142728)), _142738 = _142736, _142734 = _142732, _142730 = _142728], (13923 ^ _115804) ^ [] : [14050 ^ _115804 : [(14051 ^ _115804) ^ [_325107] : [ordinal(_325107), in(_325107, omega), 14058 ^ _115804 : [(14059 ^ _115804) ^ [_325258] : [element(_325258, powerset(powerset(_325107))), -(_325258 = empty_set), 14067 ^ _115804 : [(14068 ^ _115804) ^ [] : [-(in(14066 ^ [_325107, _325258], _325258))], (14070 ^ _115804) ^ [_325460] : [-(_325460 = 14066 ^ [_325107, _325258]), in(_325460, _325258), subset(14066 ^ [_325107, _325258], _325460)]]]]]], 13926 ^ _115804 : [(13932 ^ _115804) ^ [] : [13928 ^ [] = empty_set], (13927 ^ _115804) ^ [] : [-(in(empty_set, omega))], (13930 ^ _115804) ^ [] : [-(element(13928 ^ [], powerset(powerset(empty_set))))], (13934 ^ _115804) ^ [_322993] : [in(_322993, 13928 ^ []), 13938 ^ _115804 : [(13939 ^ _115804) ^ [] : [-(in(13937 ^ [_322993], 13928 ^ []))], (13943 ^ _115804) ^ [] : [13937 ^ [_322993] = _322993], (13941 ^ _115804) ^ [] : [-(subset(_322993, 13937 ^ [_322993]))]]]], 13947 ^ _115804 : [(13978 ^ _115804) ^ [] : [-(element(13976 ^ [], powerset(powerset(succ(13946 ^ [])))))], (13975 ^ _115804) ^ [] : [-(in(succ(13946 ^ []), omega))], (13982 ^ _115804) ^ [_323833] : [in(_323833, 13976 ^ []), 13986 ^ _115804 : [(13987 ^ _115804) ^ [] : [-(in(13985 ^ [_323833], 13976 ^ []))], (13991 ^ _115804) ^ [] : [13985 ^ [_323833] = _323833], (13989 ^ _115804) ^ [] : [-(subset(_323833, 13985 ^ [_323833]))]]], (13950 ^ _115804) ^ [] : [in(13946 ^ [], omega), 13953 ^ _115804 : [(13954 ^ _115804) ^ [_323380] : [element(_323380, powerset(powerset(13946 ^ []))), -(_323380 = empty_set), 13962 ^ _115804 : [(13963 ^ _115804) ^ [] : [-(in(13961 ^ [_323380], _323380))], (13965 ^ _115804) ^ [_323566] : [-(_323566 = 13961 ^ [_323380]), in(_323566, _323380), subset(13961 ^ [_323380], _323566)]]]]], (13948 ^ _115804) ^ [] : [-(ordinal(13946 ^ []))], (13980 ^ _115804) ^ [] : [13976 ^ [] = empty_set]], 13993 ^ _115804 : [(14038 ^ _115804) ^ [] : [14034 ^ [] = empty_set], (14033 ^ _115804) ^ [] : [-(in(13992 ^ [], omega))], (13998 ^ _115804) ^ [_324211] : [ordinal(_324211), in(_324211, 13992 ^ []), in(_324211, omega), 14009 ^ _115804 : [(14010 ^ _115804) ^ [_324410] : [element(_324410, powerset(powerset(_324211))), -(_324410 = empty_set), 14018 ^ _115804 : [(14019 ^ _115804) ^ [] : [-(in(14017 ^ [_324211, _324410], _324410))], (14021 ^ _115804) ^ [_324612] : [-(_324612 = 14017 ^ [_324211, _324410]), in(_324612, _324410), subset(14017 ^ [_324211, _324410], _324612)]]]]], (14036 ^ _115804) ^ [] : [-(element(14034 ^ [], powerset(powerset(13992 ^ []))))], (14031 ^ _115804) ^ [] : [13992 ^ [] = empty_set], (14040 ^ _115804) ^ [_324921] : [in(_324921, 14034 ^ []), 14044 ^ _115804 : [(14045 ^ _115804) ^ [] : [-(in(14043 ^ [_324921], 14034 ^ []))], (14049 ^ _115804) ^ [] : [14043 ^ [_324921] = _324921], (14047 ^ _115804) ^ [] : [-(subset(_324921, 14043 ^ [_324921]))]]], (13994 ^ _115804) ^ [] : [-(ordinal(13992 ^ []))], (13996 ^ _115804) ^ [] : [-(being_limit_ordinal(13992 ^ []))]]], (19701 ^ _115804) ^ [] : [-(relation_dom(empty_set) = empty_set)], (5492 ^ _115804) ^ [_196490] : [-(empty_carrier(_196490)), topological_space(_196490), top_str(_196490), 5503 ^ _115804 : [(5504 ^ _115804) ^ [_196675] : [element(_196675, the_carrier(_196490)), 5507 ^ _115804 : [(5508 ^ _115804) ^ [_196756] : [element(_196756, powerset(the_carrier(_196490))), 5511 ^ _115804 : [(5512 ^ _115804) ^ [] : [point_neighbourhood(_196756, _196490, _196675), -(in(_196675, interior(_196490, _196756)))], (5518 ^ _115804) ^ [] : [in(_196675, interior(_196490, _196756)), -(point_neighbourhood(_196756, _196490, _196675))]]]]]]], (11724 ^ _115804) ^ [_291768, _291770] : [-(set_intersection2(_291770, _291770) = _291770)], (12719 ^ _115804) ^ [] : [-(v2_waybel_3(12689 ^ []))], (50 ^ _115804) ^ [_116439, _116441] : [-(v1_rat_1(_116439)), _116441 = _116439, v1_rat_1(_116441)], (592 ^ _115804) ^ [_123472, _123474] : [-(join_associative(_123472)), _123474 = _123472, join_associative(_123474)], (108 ^ _115804) ^ [_117200, _117202, _117204, _117206] : [-(is_transitive_in(_117204, _117200)), is_transitive_in(_117206, _117202), _117206 = _117204, _117202 = _117200], (10589 ^ _115804) ^ [_276345] : [-(meet_absorbing(boole_lattice(_276345)))], (12611 ^ _115804) ^ [] : [-(transitive_relstr(12601 ^ []))], (12592 ^ _115804) ^ [] : [-(transitive_relstr(12582 ^ []))], (12557 ^ _115804) ^ [_302094] : [-(natural(12539 ^ [_302094]))], (11791 ^ _115804) ^ [_292774, _292776] : [in(_292776, _292774), -(set_union2(singleton(_292776), _292774) = _292774)], (16471 ^ _115804) ^ [_377968] : [-(relation_dom(16465 ^ [_377968]) = _377968)], (3550 ^ _115804) ^ [_165870] : [element(_165870, omega), 3553 ^ _115804 : [(3558 ^ _115804) ^ [] : [-(ordinal(_165870))], (3554 ^ _115804) ^ [] : [-(epsilon_transitive(_165870))], (3556 ^ _115804) ^ [] : [-(epsilon_connected(_165870))], (3560 ^ _115804) ^ [] : [-(natural(_165870))]]], (12321 ^ _115804) ^ [] : [-(v3_membered(12313 ^ []))], (1868 ^ _115804) ^ [_142121, _142123] : [_142123 = _142121, -(k2_lattice3(_142123) = k2_lattice3(_142121))], (12222 ^ _115804) ^ [] : [-(meet_absorbing(12206 ^ []))], (400 ^ _115804) ^ [_121010, _121012] : [-(v2_waybel_3(_121010)), _121012 = _121010, v2_waybel_3(_121012)], (12695 ^ _115804) ^ [] : [-(strict_rel_str(12689 ^ []))], (10765 ^ _115804) ^ [_278612, _278614] : [v2_membered(_278614), 10768 ^ _115804 : [(10769 ^ _115804) ^ [] : [-(v1_membered(set_intersection2(_278612, _278614)))], (10771 ^ _115804) ^ [] : [-(v2_membered(set_intersection2(_278612, _278614)))]]], (4218 ^ _115804) ^ [_174249] : [rel_str(_174249), 4257 ^ _115804 : [(4260 ^ _115804) ^ [] : [-(reflexive_relstr(_174249))], (4278 ^ _115804) ^ [] : [-(complemented_relstr(_174249))], (4264 ^ _115804) ^ [] : [-(antisymmetric_relstr(_174249))], (4274 ^ _115804) ^ [] : [-(bounded_relstr(_174249))], (4280 ^ _115804) ^ [] : [-(boolean_relstr(_174249))], (4276 ^ _115804) ^ [] : [-(distributive_relstr(_174249))], (4268 ^ _115804) ^ [] : [-(with_infima_relstr(_174249))], (4262 ^ _115804) ^ [] : [-(transitive_relstr(_174249))], (4258 ^ _115804) ^ [] : [empty_carrier(_174249)], (4270 ^ _115804) ^ [] : [-(lower_bounded_relstr(_174249))], (4266 ^ _115804) ^ [] : [-(with_suprema_relstr(_174249))], (4272 ^ _115804) ^ [] : [-(upper_bounded_relstr(_174249))]], -(empty_carrier(_174249)), reflexive_relstr(_174249), transitive_relstr(_174249), antisymmetric_relstr(_174249), with_suprema_relstr(_174249), with_infima_relstr(_174249), bounded_relstr(_174249), distributive_relstr(_174249), complemented_relstr(_174249)], (12421 ^ _115804) ^ [] : [-(upper_bounded_relstr(12401 ^ []))], (12351 ^ _115804) ^ [] : [-(function(12347 ^ []))], (12804 ^ _115804) ^ [] : [-(relation(12802 ^ []))], (4160 ^ _115804) ^ [_173554] : [rel_str(_173554), 4171 ^ _115804 : [(4174 ^ _115804) ^ [] : [-(reflexive_relstr(_173554))], (4190 ^ _115804) ^ [] : [-(distributive_relstr(_173554))], (4184 ^ _115804) ^ [] : [-(lower_bounded_relstr(_173554))], (4176 ^ _115804) ^ [] : [-(transitive_relstr(_173554))], (4186 ^ _115804) ^ [] : [-(upper_bounded_relstr(_173554))], (4180 ^ _115804) ^ [] : [-(with_suprema_relstr(_173554))], (4178 ^ _115804) ^ [] : [-(antisymmetric_relstr(_173554))], (4188 ^ _115804) ^ [] : [-(bounded_relstr(_173554))], (4182 ^ _115804) ^ [] : [-(with_infima_relstr(_173554))], (4192 ^ _115804) ^ [] : [-(complemented_relstr(_173554))], (4172 ^ _115804) ^ [] : [empty_carrier(_173554)]], -(empty_carrier(_173554)), boolean_relstr(_173554)], (16728 ^ _115804) ^ [_381922] : [one_sorted_str(_381922), -(cast_as_carrier_subset(_381922) = the_carrier(_381922))], (12315 ^ _115804) ^ [] : [empty(12313 ^ [])], (12806 ^ _115804) ^ [] : [-(relation_empty_yielding(12802 ^ []))], (19107 ^ _115804) ^ [_419852] : [topological_space(_419852), top_str(_419852), 19114 ^ _115804 : [(19115 ^ _115804) ^ [_420021] : [element(_420021, powerset(the_carrier(_419852))), 19119 ^ _115804 : [(19120 ^ _115804) ^ [] : [-(element(19118 ^ [_419852, _420021], powerset(powerset(the_carrier(_419852)))))], (19122 ^ _115804) ^ [_420230] : [element(_420230, powerset(the_carrier(_419852))), 19125 ^ _115804 : [(19126 ^ _115804) ^ [] : [in(_420230, 19118 ^ [_419852, _420021]), 19129 ^ _115804 : [(19130 ^ _115804) ^ [] : [-(closed_subset(_420230, _419852))], (19132 ^ _115804) ^ [] : [-(subset(_420021, _420230))]]], (19134 ^ _115804) ^ [] : [-(in(_420230, 19118 ^ [_419852, _420021])), closed_subset(_420230, _419852), subset(_420021, _420230)]]], (19144 ^ _115804) ^ [] : [-(topstr_closure(_419852, _420021) = meet_of_subsets(the_carrier(_419852), 19118 ^ [_419852, _420021]))]]]]], (12228 ^ _115804) ^ [] : [-(distributive_lattstr(12206 ^ []))], (10549 ^ _115804) ^ [_275816, _275818] : [-(finite(unordered_pair(_275818, _275816)))], (10625 ^ _115804) ^ [] : [-(function(empty_set))], (9043 ^ _115804) ^ [_255608, _255610] : [relation(_255610), -(relation_of2_as_subset(relation_restriction_as_relation_of(_255610, _255608), _255608, _255608))], (12161 ^ _115804) ^ [] : [-(upper_bounded_semilattstr(12137 ^ []))], (13460 ^ _115804) ^ [_314210, _314212] : [are_equipotent(_314212, _314210), -(equipotent(_314212, _314210))], (20029 ^ _115804) ^ [_434560, _434562, _434564, _434566] : [relation(_434560), 20032 ^ _115804 : [(20033 ^ _115804) ^ [] : [in(ordered_pair(_434566, _434564), relation_composition(identity_relation(_434562), _434560)), 20036 ^ _115804 : [(20037 ^ _115804) ^ [] : [-(in(_434566, _434562))], (20039 ^ _115804) ^ [] : [-(in(ordered_pair(_434566, _434564), _434560))]]], (20041 ^ _115804) ^ [] : [-(in(ordered_pair(_434566, _434564), relation_composition(identity_relation(_434562), _434560))), in(_434566, _434562), in(ordered_pair(_434566, _434564), _434560)]]], (7036 ^ _115804) ^ [_222015] : [relation(_222015), 7039 ^ _115804 : [(7057 ^ _115804) ^ [_222380] : [-(is_well_founded_in(_222015, _222380)), 7059 ^ _115804 : [(7060 ^ _115804) ^ [] : [-(subset(7058 ^ [_222015, _222380], _222380))], (7064 ^ _115804) ^ [_222543] : [in(_222543, 7058 ^ [_222015, _222380]), disjoint(fiber(_222015, _222543), 7058 ^ [_222015, _222380])], (7062 ^ _115804) ^ [] : [7058 ^ [_222015, _222380] = empty_set]]], (7040 ^ _115804) ^ [_222123] : [is_well_founded_in(_222015, _222123), 7043 ^ _115804 : [(7044 ^ _115804) ^ [_222212] : [subset(_222212, _222123), -(_222212 = empty_set), 7052 ^ _115804 : [(7053 ^ _115804) ^ [] : [-(in(7051 ^ [_222015, _222123, _222212], _222212))], (7055 ^ _115804) ^ [] : [-(disjoint(fiber(_222015, 7051 ^ [_222015, _222123, _222212]), _222212))]]]]]]], (18696 ^ _115804) ^ [_413705, _413707] : [subset(_413707, _413705), -(set_difference(_413707, _413705) = empty_set)], (12896 ^ _115804) ^ [] : [-(rel_str(12894 ^ []))], (19160 ^ _115804) ^ [_420822, _420824] : [element(_420822, powerset(powerset(_420824))), -(_420822 = empty_set), complements_of_subsets(_420824, _420822) = empty_set], (2702 ^ _115804) ^ [_155249] : [v1_membered(_155249), 2705 ^ _115804 : [(2706 ^ _115804) ^ [_155307] : [element(_155307, _155249), -(v1_xcmplx_0(_155307))]]], (9499 ^ _115804) ^ [_261735, _261737] : [-(element(cast_to_el_of_lattice(_261737, _261735), the_carrier(_261737))), -(empty_carrier(_261737)), lattice(_261737), latt_str(_261737), element(_261735, the_carrier(poset_of_lattice(_261737)))], (3662 ^ _115804) ^ [_167278] : [rel_str(_167278), 3673 ^ _115804 : [(3674 ^ _115804) ^ [] : [empty_carrier(_167278)], (3676 ^ _115804) ^ [] : [v1_yellow_3(_167278)]], -(empty_carrier(_167278)), reflexive_relstr(_167278)], (13428 ^ _115804) ^ [_313780, _313782, _313784] : [relation_of2(_313780, _313784, _313782), -(relation_of2_as_subset(_313780, _313784, _313782))], (9049 ^ _115804) ^ [_255691, _255693] : [-(element(interior(_255693, _255691), powerset(the_carrier(_255693)))), top_str(_255693), element(_255691, powerset(the_carrier(_255693)))], (12172 ^ _115804) ^ [] : [-(join_commutative(12164 ^ []))], (4282 ^ _115804) ^ [_175009, _175011, _175013] : [-(unordered_pair_as_carrier_subset(_175013, _175011, _175009) = unordered_pair_as_carrier_subset(_175013, _175009, _175011)), -(empty_carrier(_175013)), one_sorted_str(_175013), element(_175011, the_carrier(_175013)), element(_175009, the_carrier(_175013))], (6607 ^ _115804) ^ [_215034, _215036] : [element(_215034, _215036), 6610 ^ _115804 : [(6611 ^ _115804) ^ [] : [proper_element(_215034, _215036), _215034 = union(_215036)], (6617 ^ _115804) ^ [] : [-(_215034 = union(_215036)), -(proper_element(_215034, _215036))]]], (12419 ^ _115804) ^ [] : [-(lower_bounded_relstr(12401 ^ []))], (1270 ^ _115804) ^ [_132815, _132817] : [-(ordinal(_132815)), _132817 = _132815, ordinal(_132817)], (10293 ^ _115804) ^ [_272468] : [-(join_absorbing(boole_lattice(_272468)))], (17369 ^ _115804) ^ [_392217, _392219] : [element(_392217, the_carrier(boole_lattice(_392219))), 17372 ^ _115804 : [(17373 ^ _115804) ^ [_392316] : [element(_392316, the_carrier(boole_lattice(_392219))), 17376 ^ _115804 : [(17377 ^ _115804) ^ [] : [-(join(boole_lattice(_392219), _392217, _392316) = set_union2(_392217, _392316))], (17379 ^ _115804) ^ [] : [-(meet(boole_lattice(_392219), _392217, _392316) = set_intersection2(_392217, _392316))]]]]], (18590 ^ _115804) ^ [_411988, _411990] : [relation(_411988), function(_411988), 18597 ^ _115804 : [(18598 ^ _115804) ^ [] : [_411988 = identity_relation(_411990), 18601 ^ _115804 : [(18602 ^ _115804) ^ [] : [-(relation_dom(_411988) = _411990)], (18604 ^ _115804) ^ [_412196] : [in(_412196, _411990), -(apply(_411988, _412196) = _412196)]]], (18610 ^ _115804) ^ [] : [-(_411988 = identity_relation(_411990)), relation_dom(_411988) = _411990, 18616 ^ _115804 : [(18617 ^ _115804) ^ [] : [-(in(18615 ^ [_411988, _411990], _411990))], (18619 ^ _115804) ^ [] : [apply(_411988, 18615 ^ [_411988, _411990]) = 18615 ^ [_411988, _411990]]]]]], (11461 ^ _115804) ^ [_287790] : [-(with_suprema_relstr(boole_POSet(_287790)))], (12473 ^ _115804) ^ [] : [-(strict_rel_str(12465 ^ []))], (9129 ^ _115804) ^ [_256745, _256747, _256749, _256751, _256753, _256755] : [-(element(apply_binary_as_element(_256755, _256753, _256751, _256749, _256747, _256745), _256751)), -(empty(_256755)), -(empty(_256753)), function(_256749), quasi_total(_256749, cartesian_product2(_256755, _256753), _256751), relation_of2(_256749, cartesian_product2(_256755, _256753), _256751), element(_256747, _256755), element(_256745, _256753)], (12584 ^ _115804) ^ [] : [-(rel_str(12582 ^ []))], (792 ^ _115804) ^ [_126176, _126178] : [-(finite(_126176)), _126178 = _126176, finite(_126178)], (4370 ^ _115804) ^ [_176312, _176314] : [ordinal(_176314), ordinal(_176312), -(ordinal_subset(_176314, _176312)), -(ordinal_subset(_176312, _176314))], (12411 ^ _115804) ^ [] : [-(antisymmetric_relstr(12401 ^ []))], (16917 ^ _115804) ^ [_384751, _384753] : [relation(_384751), -(subset(relation_image(_384751, _384753), relation_rng(_384751)))], (1982 ^ _115804) ^ [_143942, _143944, _143946, _143948, _143950, _143952, _143954, _143956, _143958, _143960] : [-(function_of_composition(_143960, _143956, _143952, _143948, _143944) = function_of_composition(_143958, _143954, _143950, _143946, _143942)), _143960 = _143958, _143956 = _143954, _143952 = _143950, _143948 = _143946, _143944 = _143942], (2556 ^ _115804) ^ [_152707, _152709, _152711, _152713, _152715, _152717, _152719, _152721] : [-(apply_as_element(_152721, _152717, _152713, _152709) = apply_as_element(_152719, _152715, _152711, _152707)), _152721 = _152719, _152717 = _152715, _152713 = _152711, _152709 = _152707], (16939 ^ _115804) ^ [_385070, _385072] : [relation(_385070), subset(_385072, relation_dom(_385070)), -(subset(_385072, relation_inverse_image(_385070, relation_image(_385070, _385072))))], (10283 ^ _115804) ^ [_272373] : [-(join_commutative(boole_lattice(_272373)))], (10647 ^ _115804) ^ [_276980] : [-(transitive(identity_relation(_276980)))], (12312 ^ _115804) ^ [] : [-(complete_relstr(12298 ^ []))], (12562 ^ _115804) ^ [] : [-(relation(12560 ^ []))], (12878 ^ _115804) ^ [] : [-(complemented_relstr(12850 ^ []))], (12699 ^ _115804) ^ [] : [-(transitive_relstr(12689 ^ []))], (10845 ^ _115804) ^ [_279711, _279713] : [v1_membered(_279713), -(v1_membered(set_difference(_279713, _279711)))], (11789 ^ _115804) ^ [_292749] : [singleton(_292749) = empty_set], (1874 ^ _115804) ^ [_142206, _142208, _142210, _142212, _142214, _142216, _142218, _142220] : [-(partfun_dom_restriction(_142220, _142216, _142212, _142208) = partfun_dom_restriction(_142218, _142214, _142210, _142206)), _142220 = _142218, _142216 = _142214, _142212 = _142210, _142208 = _142206], (1976 ^ _115804) ^ [_143857, _143859] : [_143859 = _143857, -(set_meet(_143859) = set_meet(_143857))], (12405 ^ _115804) ^ [] : [empty_carrier(12401 ^ [])], (2196 ^ _115804) ^ [_147331, _147333, _147335, _147337, _147339, _147341] : [-(meet_commut(_147341, _147337, _147333) = meet_commut(_147339, _147335, _147331)), _147341 = _147339, _147337 = _147335, _147333 = _147331], (5183 ^ _115804) ^ [_191216] : [relation(_191216), 5186 ^ _115804 : [(5210 ^ _115804) ^ [_191721, _191723] : [-(_191721 = relation_inverse_image(_191216, _191723)), 5223 ^ _115804 : [(5224 ^ _115804) ^ [] : [-(in(ordered_pair(5211 ^ [_191216, _191721, _191723], 5222 ^ [_191216, _191721, _191723]), _191216))], (5228 ^ _115804) ^ [] : [in(5211 ^ [_191216, _191721, _191723], _191721)], (5226 ^ _115804) ^ [] : [-(in(5222 ^ [_191216, _191721, _191723], _191723))]], 5214 ^ _115804 : [(5215 ^ _115804) ^ [] : [-(in(5211 ^ [_191216, _191721, _191723], _191721))], (5217 ^ _115804) ^ [_191869] : [in(ordered_pair(5211 ^ [_191216, _191721, _191723], _191869), _191216), in(_191869, _191723)]]], (5187 ^ _115804) ^ [_191323, _191325] : [_191323 = relation_inverse_image(_191216, _191325), 5190 ^ _115804 : [(5191 ^ _115804) ^ [_191420] : [in(_191420, _191323), 5195 ^ _115804 : [(5196 ^ _115804) ^ [] : [-(in(ordered_pair(_191420, 5194 ^ [_191216, _191323, _191325, _191420]), _191216))], (5198 ^ _115804) ^ [] : [-(in(5194 ^ [_191216, _191323, _191325, _191420], _191325))]]], (5200 ^ _115804) ^ [_191556] : [-(in(_191556, _191323)), 5201 ^ _115804 : [(5202 ^ _115804) ^ [_191603] : [in(ordered_pair(_191556, _191603), _191216), in(_191603, _191325)]]]]]]], (8608 ^ _115804) ^ [_249271] : [rel_str(_249271), 8611 ^ _115804 : [(8612 ^ _115804) ^ [_249364, _249366] : [element(_249364, the_carrier(_249271)), 8615 ^ _115804 : [(8630 ^ _115804) ^ [] : [8632 ^ _115804 : [(8633 ^ _115804) ^ [] : [-(element(8631 ^ [_249271, _249364, _249366], the_carrier(_249271)))], (8637 ^ _115804) ^ [] : [related(_249271, 8631 ^ [_249271, _249364, _249366], _249364)], (8635 ^ _115804) ^ [] : [-(in(8631 ^ [_249271, _249364, _249366], _249366))]], -(relstr_set_smaller(_249271, _249366, _249364))], (8616 ^ _115804) ^ [] : [relstr_set_smaller(_249271, _249366, _249364), 8619 ^ _115804 : [(8620 ^ _115804) ^ [_249505] : [element(_249505, the_carrier(_249271)), in(_249505, _249366), -(related(_249271, _249505, _249364))]]]]]]], (274 ^ _115804) ^ [_119347, _119349] : [-(v3_membered(_119347)), _119349 = _119347, v3_membered(_119349)], (12153 ^ _115804) ^ [] : [-(meet_absorbing(12137 ^ []))], (19934 ^ _115804) ^ [_433125] : [ordinal(_433125), -(well_founded_relation(inclusion_relation(_433125)))], (12429 ^ _115804) ^ [] : [-(join_complete_relstr(12401 ^ []))], (1340 ^ _115804) ^ [_133796, _133798] : [-(antisymmetric_relstr(_133796)), _133798 = _133796, antisymmetric_relstr(_133798)], (12734 ^ _115804) ^ [] : [-(rel_str(12732 ^ []))], (1604 ^ _115804) ^ [_137310, _137312, _137314, _137316] : [-(element(_137314, _137310)), element(_137316, _137312), _137316 = _137314, _137312 = _137310], (5579 ^ _115804) ^ [_197848] : [finite(_197848), 5583 ^ _115804 : [(5588 ^ _115804) ^ [] : [-(relation_rng(5582 ^ [_197848]) = _197848)], (5584 ^ _115804) ^ [] : [-(relation(5582 ^ [_197848]))], (5586 ^ _115804) ^ [] : [-(function(5582 ^ [_197848]))], (5590 ^ _115804) ^ [] : [-(in(relation_dom(5582 ^ [_197848]), omega))]]], (2272 ^ _115804) ^ [_148521, _148523] : [_148523 = _148521, -(relation_of_lattice(_148523) = relation_of_lattice(_148521))], (12166 ^ _115804) ^ [] : [-(latt_str(12164 ^ []))], (9985 ^ _115804) ^ [] : [true___, -(true___)], (11937 ^ _115804) ^ [_294814] : [-(empty_carrier(_294814)), one_sorted_str(_294814), 11944 ^ _115804 : [(11945 ^ _115804) ^ [_294954] : [element(_294954, powerset(the_carrier(_294814))), 11948 ^ _115804 : [(11949 ^ _115804) ^ [_295040] : [element(_295040, the_carrier(_294814)), 11952 ^ _115804 : [(11953 ^ _115804) ^ [] : [in(_295040, subset_complement(the_carrier(_294814), _294954)), in(_295040, _294954)], (11959 ^ _115804) ^ [] : [-(in(_295040, _294954)), -(in(_295040, subset_complement(the_carrier(_294814), _294954)))]]]]]]], (16882 ^ _115804) ^ [_384212, _384214, _384216] : [relation(_384212), -(relation_dom_restriction(relation_rng_restriction(_384216, _384212), _384214) = relation_rng_restriction(_384216, relation_dom_restriction(_384212, _384214)))], (11425 ^ _115804) ^ [_287331] : [-(with_infima_relstr(boole_POSet(_287331)))], (11457 ^ _115804) ^ [_287752] : [-(transitive_relstr(boole_POSet(_287752)))], (12107 ^ _115804) ^ [] : [-(modular_lattstr(12083 ^ []))], (1070 ^ _115804) ^ [_129997, _129999] : [-(antisymmetric(_129997)), _129999 = _129997, antisymmetric(_129999)], (8065 ^ _115804) ^ [_239175, _239177] : [set_intersection2(_239177, _239175) = empty_set, -(disjoint(_239177, _239175))], (12464 ^ _115804) ^ [] : [-(v3_waybel_3(12430 ^ []))], (11407 ^ _115804) ^ [_287159] : [empty_carrier(boole_POSet(_287159))], (7272 ^ _115804) ^ [_225952, _225954] : [_225952 = union(_225954), 7275 ^ _115804 : [(7276 ^ _115804) ^ [_226042] : [in(_226042, _225952), 7280 ^ _115804 : [(7281 ^ _115804) ^ [] : [-(in(_226042, 7279 ^ [_225952, _225954, _226042]))], (7283 ^ _115804) ^ [] : [-(in(7279 ^ [_225952, _225954, _226042], _225954))]]], (7285 ^ _115804) ^ [_226166] : [-(in(_226166, _225952)), 7286 ^ _115804 : [(7287 ^ _115804) ^ [_226208] : [in(_226166, _226208), in(_226208, _225954)]]]]], (10301 ^ _115804) ^ [_272544] : [-(lower_bounded_semilattstr(boole_lattice(_272544)))], (12652 ^ _115804) ^ [_303140] : [12660 ^ _115804 : [(12661 ^ _115804) ^ [] : [-(element(12659 ^ [_303140], powerset(the_carrier(_303140))))], (12665 ^ _115804) ^ [] : [-(closed_subset(12659 ^ [_303140], _303140))], (12663 ^ _115804) ^ [] : [-(open_subset(12659 ^ [_303140], _303140))]], topological_space(_303140), top_str(_303140)], (2144 ^ _115804) ^ [_146557, _146559] : [_146559 = _146557, -(the_InternalRel(_146559) = the_InternalRel(_146557))], (9115 ^ _115804) ^ [_256591] : [-(antisymmetric(inclusion_order(_256591)))], (12241 ^ _115804) ^ [] : [-(rel_str(12239 ^ []))], (7529 ^ _115804) ^ [_229886] : [_229886 = omega, 7532 ^ _115804 : [(7537 ^ _115804) ^ [] : [-(ordinal(_229886))], (7533 ^ _115804) ^ [] : [-(in(empty_set, _229886))], (7535 ^ _115804) ^ [] : [-(being_limit_ordinal(_229886))], (7539 ^ _115804) ^ [_230034] : [ordinal(_230034), -(subset(_229886, _230034)), in(empty_set, _230034), being_limit_ordinal(_230034)]]], (16666 ^ _115804) ^ [_381015, _381017] : [relation(_381015), -(relation_rng(relation_rng_restriction(_381017, _381015)) = set_intersection2(relation_rng(_381015), _381017))], (2814 ^ _115804) ^ [_156673] : [rel_str(_156673), 2845 ^ _115804 : [(2856 ^ _115804) ^ [] : [-(with_infima_relstr(_156673))], (2860 ^ _115804) ^ [] : [-(lower_bounded_relstr(_156673))], (2850 ^ _115804) ^ [] : [-(transitive_relstr(_156673))], (2854 ^ _115804) ^ [] : [-(with_suprema_relstr(_156673))], (2852 ^ _115804) ^ [] : [-(antisymmetric_relstr(_156673))], (2858 ^ _115804) ^ [] : [-(complete_relstr(_156673))], (2846 ^ _115804) ^ [] : [empty_carrier(_156673)], (2862 ^ _115804) ^ [] : [-(upper_bounded_relstr(_156673))], (2848 ^ _115804) ^ [] : [-(reflexive_relstr(_156673))], (2864 ^ _115804) ^ [] : [-(bounded_relstr(_156673))]], -(empty_carrier(_156673)), reflexive_relstr(_156673), transitive_relstr(_156673), antisymmetric_relstr(_156673), with_suprema_relstr(_156673), lower_bounded_relstr(_156673), up_complete_relstr(_156673)], (11091 ^ _115804) ^ [_283009, _283011] : [v5_membered(_283011), 11094 ^ _115804 : [(11103 ^ _115804) ^ [] : [-(v5_membered(set_difference(_283011, _283009)))], (11101 ^ _115804) ^ [] : [-(v4_membered(set_difference(_283011, _283009)))], (11099 ^ _115804) ^ [] : [-(v3_membered(set_difference(_283011, _283009)))], (11095 ^ _115804) ^ [] : [-(v1_membered(set_difference(_283011, _283009)))], (11097 ^ _115804) ^ [] : [-(v2_membered(set_difference(_283011, _283009)))]]], (12091 ^ _115804) ^ [] : [-(join_commutative(12083 ^ []))], (19577 ^ _115804) ^ [_427405] : [relation(_427405), -(in(ordered_pair(19582 ^ [_427405], 19583 ^ [_427405]), _427405)), -(_427405 = empty_set)], (10817 ^ _115804) ^ [_279325, _279327] : [v5_membered(_279327), 10820 ^ _115804 : [(10829 ^ _115804) ^ [] : [-(v5_membered(set_intersection2(_279327, _279325)))], (10827 ^ _115804) ^ [] : [-(v4_membered(set_intersection2(_279327, _279325)))], (10825 ^ _115804) ^ [] : [-(v3_membered(set_intersection2(_279327, _279325)))], (10821 ^ _115804) ^ [] : [-(v1_membered(set_intersection2(_279327, _279325)))], (10823 ^ _115804) ^ [] : [-(v2_membered(set_intersection2(_279327, _279325)))]]], (12799 ^ _115804) ^ [_304881] : [-(transitive(12787 ^ [_304881]))], (60 ^ _115804) ^ [_116564, _116566] : [-(v1_waybel_2(_116564)), _116566 = _116564, v1_waybel_2(_116566)], (4440 ^ _115804) ^ [_177340, _177342] : [-(_177342 = _177340), subset(_177342, _177340), subset(_177340, _177342)], (3440 ^ _115804) ^ [_164553] : [v4_membered(_164553), -(v3_membered(_164553))], (9241 ^ _115804) ^ [_258321, _258323, _258325] : [-(element(unordered_pair_as_carrier_subset(_258325, _258323, _258321), powerset(the_carrier(_258325)))), -(empty_carrier(_258325)), one_sorted_str(_258325), element(_258323, the_carrier(_258325)), element(_258321, the_carrier(_258325))], (9289 ^ _115804) ^ [] : [true___, -(true___)], (12559 ^ _115804) ^ [_302118] : [-(finite(12539 ^ [_302118]))], (1550 ^ _115804) ^ [_136617, _136619] : [-(top_str(_136617)), _136619 = _136617, top_str(_136619)], (10072 ^ _115804) ^ [_269606, _269608] : [-(subnetstr(10079 ^ [_269606, _269608], _269608, _269606)), one_sorted_str(_269608), net_str(_269606, _269608)], (17116 ^ _115804) ^ [_387919] : [-(empty_carrier(_387919)), one_sorted_str(_387919), 17123 ^ _115804 : [(17124 ^ _115804) ^ [_388102] : [-(empty_carrier(_388102)), directed_relstr(_388102), net_str(_388102, _387919), 17135 ^ _115804 : [(17136 ^ _115804) ^ [_388318] : [element(_388318, the_carrier(_388102)), 17139 ^ _115804 : [(17140 ^ _115804) ^ [_388424] : [element(_388424, the_carrier(_388102)), 17143 ^ _115804 : [(17144 ^ _115804) ^ [_388519] : [element(_388519, the_carrier(netstr_restr_to_element(_387919, _388102, _388318))), _388424 = _388519, -(apply_netmap(_387919, _388102, _388424) = apply_netmap(_387919, netstr_restr_to_element(_387919, _388102, _388318), _388519))]]]]]]]]], (12409 ^ _115804) ^ [] : [-(transitive_relstr(12401 ^ []))], (10259 ^ _115804) ^ [_272065, _272067] : [10274 ^ _115804 : [(10275 ^ _115804) ^ [] : [-(relation(relation_composition(_272067, _272065)))], (10277 ^ _115804) ^ [] : [-(function(relation_composition(_272067, _272065)))]], relation(_272067), function(_272067), relation(_272065), function(_272065)], (10383 ^ _115804) ^ [_273609] : [-(transitive_relstr(boole_POSet(_273609)))], (12201 ^ _115804) ^ [] : [-(transitive_relstr(12193 ^ []))], (650 ^ _115804) ^ [_124241, _124243, _124245, _124247] : [-(equipotent(_124245, _124241)), equipotent(_124247, _124243), _124247 = _124245, _124243 = _124241], (8829 ^ _115804) ^ [_252808, _252810, _252812] : [8852 ^ _115804 : [(8853 ^ _115804) ^ [] : [-(strict_latt_str(latt_str_of(_252812, _252810, _252808)))], (8855 ^ _115804) ^ [] : [-(latt_str(latt_str_of(_252812, _252810, _252808)))]], function(_252810), quasi_total(_252810, cartesian_product2(_252812, _252812), _252812), relation_of2(_252810, cartesian_product2(_252812, _252812), _252812), function(_252808), quasi_total(_252808, cartesian_product2(_252812, _252812), _252812), relation_of2(_252808, cartesian_product2(_252812, _252812), _252812)], (8205 ^ _115804) ^ [_241798] : [rel_str(_241798), 8208 ^ _115804 : [(8209 ^ _115804) ^ [_241891, _241893] : [element(_241891, the_carrier(_241798)), 8212 ^ _115804 : [(8227 ^ _115804) ^ [] : [8229 ^ _115804 : [(8230 ^ _115804) ^ [] : [-(element(8228 ^ [_241798, _241891, _241893], the_carrier(_241798)))], (8234 ^ _115804) ^ [] : [related(_241798, _241891, 8228 ^ [_241798, _241891, _241893])], (8232 ^ _115804) ^ [] : [-(in(8228 ^ [_241798, _241891, _241893], _241893))]], -(relstr_element_smaller(_241798, _241893, _241891))], (8213 ^ _115804) ^ [] : [relstr_element_smaller(_241798, _241893, _241891), 8216 ^ _115804 : [(8217 ^ _115804) ^ [_242032] : [element(_242032, the_carrier(_241798)), in(_242032, _241893), -(related(_241798, _241891, _242032))]]]]]]], (10635 ^ _115804) ^ [] : [-(ordinal(empty_set))], (2324 ^ _115804) ^ [_149295, _149297] : [_149297 = _149295, -(succ(_149297) = succ(_149295))], (1010 ^ _115804) ^ [_129149, _129151, _129153, _129155, _129157, _129159] : [-(relation_isomorphism(_129157, _129153, _129149)), relation_isomorphism(_129159, _129155, _129151), _129159 = _129157, _129155 = _129153, _129151 = _129149], (4034 ^ _115804) ^ [_171979] : [rel_str(_171979), 4045 ^ _115804 : [(4046 ^ _115804) ^ [] : [empty_carrier(_171979)], (4048 ^ _115804) ^ [] : [-(distributive_relstr(_171979))]], -(empty_carrier(_171979)), heyting_relstr(_171979)], (12205 ^ _115804) ^ [] : [-(connected_relstr(12193 ^ []))], (14420 ^ _115804) ^ [_333704] : [14424 ^ _115804 : [(14433 ^ _115804) ^ [] : [14422 ^ [_333704] = 14423 ^ [_333704]], (14431 ^ _115804) ^ [] : [-(14423 ^ [_333704] = singleton(14421 ^ [_333704]))], (14429 ^ _115804) ^ [] : [-(in(14421 ^ [_333704], _333704))], (14425 ^ _115804) ^ [] : [-(in(14421 ^ [_333704], _333704))], (14427 ^ _115804) ^ [] : [-(14422 ^ [_333704] = singleton(14421 ^ [_333704]))]], 14435 ^ _115804 : [(14436 ^ _115804) ^ [_334020] : [in(_334020, 14434 ^ [_333704]), 14440 ^ _115804 : [(14441 ^ _115804) ^ [] : [-(in(14439 ^ [_333704, _334020], _333704))], (14445 ^ _115804) ^ [] : [-(_334020 = singleton(14439 ^ [_333704, _334020]))], (14443 ^ _115804) ^ [] : [-(in(14439 ^ [_333704, _334020], _333704))]]], (14447 ^ _115804) ^ [_334183] : [-(in(_334183, 14434 ^ [_333704])), 14448 ^ _115804 : [(14449 ^ _115804) ^ [_334236] : [in(_334236, _333704), in(_334236, _333704), _334183 = singleton(_334236)]]]]], (20306 ^ _115804) ^ [_438622, _438624] : [relation(_438622), -(relation_dom(relation_dom_restriction(_438622, _438624)) = set_intersection2(relation_dom(_438622), _438624))], (812 ^ _115804) ^ [_126426, _126428] : [-(join_semilatt_str(_126426)), _126428 = _126426, join_semilatt_str(_126428)], (10397 ^ _115804) ^ [_273742] : [-(bounded_relstr(boole_POSet(_273742)))], (10281 ^ _115804) ^ [_272354] : [-(strict_latt_str(boole_lattice(_272354)))], (2068 ^ _115804) ^ [_145375, _145377, _145379, _145381, _145383, _145385] : [-(apply_netmap(_145385, _145381, _145377) = apply_netmap(_145383, _145379, _145375)), _145385 = _145383, _145381 = _145379, _145377 = _145375], (11758 ^ _115804) ^ [_292268, _292270] : [element(_292268, powerset(powerset(_292270))), -(complements_of_subsets(_292270, complements_of_subsets(_292270, _292268)) = _292268)], (10915 ^ _115804) ^ [_280652] : [-(meet_commutative(boole_lattice(_280652)))], (16955 ^ _115804) ^ [_385300, _385302] : [relation(_385300), function(_385300), subset(_385302, relation_rng(_385300)), -(relation_image(_385300, relation_inverse_image(_385300, _385302)) = _385302)], (10909 ^ _115804) ^ [_280595] : [-(strict_latt_str(boole_lattice(_280595)))], (12906 ^ _115804) ^ [] : [-(antisymmetric_relstr(12894 ^ []))], (6586 ^ _115804) ^ [_214712, _214714, _214716] : [-(_214712 = unordered_pair(_214716, _214714)), 6590 ^ _115804 : [(6591 ^ _115804) ^ [] : [-(in(6587 ^ [_214712, _214714, _214716], _214712))], (6595 ^ _115804) ^ [] : [6587 ^ [_214712, _214714, _214716] = _214714], (6593 ^ _115804) ^ [] : [6587 ^ [_214712, _214714, _214716] = _214716]], 6596 ^ _115804 : [(6603 ^ _115804) ^ [] : [in(6587 ^ [_214712, _214714, _214716], _214712)], (6597 ^ _115804) ^ [] : [-(6587 ^ [_214712, _214714, _214716] = _214716), -(6587 ^ [_214712, _214714, _214716] = _214714)]]], (582 ^ _115804) ^ [_123347, _123349] : [-(strict_latt_str(_123347)), _123349 = _123347, strict_latt_str(_123349)], (17735 ^ _115804) ^ [_398753, _398755] : [relation(_398753), function(_398753), 17742 ^ _115804 : [(17743 ^ _115804) ^ [_398888] : [relation(_398888), function(_398888), in(_398755, relation_dom(_398753)), -(apply(relation_composition(_398753, _398888), _398755) = apply(_398888, apply(_398753, _398755)))]]], (20400 ^ _115804) ^ [_440165, _440167] : [subset(_440165, 20373 ^ [_440167]), -(are_equipotent(_440165, 20373 ^ [_440167])), -(in(_440165, 20373 ^ [_440167]))], (12697 ^ _115804) ^ [] : [-(reflexive_relstr(12689 ^ []))], (858 ^ _115804) ^ [_127089, _127091, _127093, _127095] : [-(ordinal_subset(_127093, _127089)), ordinal_subset(_127095, _127091), _127095 = _127093, _127091 = _127089], (10289 ^ _115804) ^ [_272430] : [-(meet_associative(boole_lattice(_272430)))], (13004 ^ _115804) ^ [] : [-(meet_commutative(12992 ^ []))], (2540 ^ _115804) ^ [_152473, _152475, _152477, _152479] : [-(set_intersection2(_152479, _152475) = set_intersection2(_152477, _152473)), _152479 = _152477, _152475 = _152473], (11453 ^ _115804) ^ [_287714] : [-(strict_rel_str(boole_POSet(_287714)))], (9611 ^ _115804) ^ [_263320] : [-(v1_partfun1(identity_as_relation_of(_263320), _263320, _263320))], (12902 ^ _115804) ^ [] : [-(reflexive_relstr(12894 ^ []))], (12648 ^ _115804) ^ [_303079] : [-(element(12646 ^ [_303079], powerset(_303079)))], (2082 ^ _115804) ^ [_145596, _145598, _145600, _145602, _145604, _145606] : [-(netstr_restr_to_element(_145606, _145602, _145598) = netstr_restr_to_element(_145604, _145600, _145596)), _145606 = _145604, _145602 = _145600, _145598 = _145596], (14080 ^ _115804) ^ [_325639, _325641, _325643] : [relation(_325641), relation(_325639), function(_325639), 14092 ^ _115804 : [(14093 ^ _115804) ^ [] : [-(relation(14091 ^ [_325639, _325641, _325643]))], (14105 ^ _115804) ^ [_326114, _326116] : [-(in(ordered_pair(_326116, _326114), 14091 ^ [_325639, _325641, _325643])), in(_326116, _325643), in(_326114, _325643), in(ordered_pair(apply(_325639, _326116), apply(_325639, _326114)), _325641)], (14095 ^ _115804) ^ [_325943, _325945] : [in(ordered_pair(_325945, _325943), 14091 ^ [_325639, _325641, _325643]), 14098 ^ _115804 : [(14099 ^ _115804) ^ [] : [-(in(_325945, _325643))], (14103 ^ _115804) ^ [] : [-(in(ordered_pair(apply(_325639, _325945), apply(_325639, _325943)), _325641))], (14101 ^ _115804) ^ [] : [-(in(_325943, _325643))]]]]], (12517 ^ _115804) ^ [] : [-(with_suprema_relstr(12503 ^ []))], (13066 ^ _115804) ^ [_308357] : [-(k1_pcomps_1(_308357) = powerset(_308357))], (18162 ^ _115804) ^ [_405213, _405215] : [element(_405213, the_carrier(boole_lattice(_405215))), 18165 ^ _115804 : [(18166 ^ _115804) ^ [_405297] : [element(_405297, the_carrier(boole_lattice(_405215))), 18169 ^ _115804 : [(18170 ^ _115804) ^ [] : [below(boole_lattice(_405215), _405213, _405297), -(subset(_405213, _405297))], (18176 ^ _115804) ^ [] : [subset(_405213, _405297), -(below(boole_lattice(_405215), _405213, _405297))]]]]], (2882 ^ _115804) ^ [_157513] : [rel_str(_157513), 2901 ^ _115804 : [(2906 ^ _115804) ^ [] : [-(antisymmetric_relstr(_157513))], (2902 ^ _115804) ^ [] : [empty_carrier(_157513)], (2904 ^ _115804) ^ [] : [-(reflexive_relstr(_157513))], (2908 ^ _115804) ^ [] : [-(with_infima_relstr(_157513))]], -(empty_carrier(_157513)), reflexive_relstr(_157513), antisymmetric_relstr(_157513), join_complete_relstr(_157513)], (13110 ^ _115804) ^ [_309007, _309009, _309011, _309013, _309015, _309017] : [-(apply_binary_as_element(_309017, _309015, _309013, _309011, _309009, _309007) = apply_binary(_309011, _309009, _309007)), -(empty(_309017)), -(empty(_309015)), function(_309011), quasi_total(_309011, cartesian_product2(_309017, _309015), _309013), relation_of2(_309011, cartesian_product2(_309017, _309015), _309013), element(_309009, _309017), element(_309007, _309015)], (16381 ^ _115804) ^ [] : [16436 ^ _115804 : [(16437 ^ _115804) ^ [_377337] : [ordinal(_377337), in(_377337, omega), 16444 ^ _115804 : [(16445 ^ _115804) ^ [_377488] : [element(_377488, powerset(powerset(_377337))), -(_377488 = empty_set), 16453 ^ _115804 : [(16454 ^ _115804) ^ [] : [-(in(16452 ^ [_377337, _377488], _377488))], (16456 ^ _115804) ^ [_377690] : [-(_377690 = 16452 ^ [_377337, _377488]), in(_377690, _377488), subset(16452 ^ [_377337, _377488], _377690)]]]]]], 16383 ^ _115804 : [(16422 ^ _115804) ^ [] : [-(element(16420 ^ [], powerset(powerset(16382 ^ []))))], (16419 ^ _115804) ^ [] : [-(in(16382 ^ [], omega))], (16426 ^ _115804) ^ [_377163] : [in(_377163, 16420 ^ []), 16430 ^ _115804 : [(16431 ^ _115804) ^ [] : [-(in(16429 ^ [_377163], 16420 ^ []))], (16435 ^ _115804) ^ [] : [16429 ^ [_377163] = _377163], (16433 ^ _115804) ^ [] : [-(subset(_377163, 16429 ^ [_377163]))]]], (16386 ^ _115804) ^ [_376479] : [ordinal(_376479), in(_376479, 16382 ^ []), in(_376479, omega), 16397 ^ _115804 : [(16398 ^ _115804) ^ [_376678] : [element(_376678, powerset(powerset(_376479))), -(_376678 = empty_set), 16406 ^ _115804 : [(16407 ^ _115804) ^ [] : [-(in(16405 ^ [_376479, _376678], _376678))], (16409 ^ _115804) ^ [_376880] : [-(_376880 = 16405 ^ [_376479, _376678]), in(_376880, _376678), subset(16405 ^ [_376479, _376678], _376880)]]]]], (16384 ^ _115804) ^ [] : [-(ordinal(16382 ^ []))], (16424 ^ _115804) ^ [] : [16420 ^ [] = empty_set]]], (9295 ^ _115804) ^ [_258998] : [9306 ^ _115804 : [(9315 ^ _115804) ^ [] : [-(rel_str(poset_of_lattice(_258998)))], (9313 ^ _115804) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_258998)))], (9311 ^ _115804) ^ [] : [-(transitive_relstr(poset_of_lattice(_258998)))], (9307 ^ _115804) ^ [] : [-(strict_rel_str(poset_of_lattice(_258998)))], (9309 ^ _115804) ^ [] : [-(reflexive_relstr(poset_of_lattice(_258998)))]], -(empty_carrier(_258998)), lattice(_258998), latt_str(_258998)], (1618 ^ _115804) ^ [_137503, _137505, _137507, _137509] : [-(in(_137507, _137503)), in(_137509, _137505), _137509 = _137507, _137505 = _137503], (19271 ^ _115804) ^ [_422413, _422415] : [19272 ^ _115804 : [(19273 ^ _115804) ^ [_422455] : [in(_422455, set_intersection2(_422415, _422413))]], disjoint(_422415, _422413)], (12789 ^ _115804) ^ [_304769] : [-(relation_of2(12787 ^ [_304769], _304769, _304769))], (20120 ^ _115804) ^ [_435976, _435978] : [set_difference(_435978, _435976) = _435978, -(disjoint(_435978, _435976))], (10931 ^ _115804) ^ [_280804] : [-(upper_bounded_semilattstr(boole_lattice(_280804)))], (8937 ^ _115804) ^ [_254312, _254314] : [-(element(meet_of_latt_set(_254314, _254312), the_carrier(_254314))), -(empty_carrier(_254314)), latt_str(_254314)], (12216 ^ _115804) ^ [] : [-(join_associative(12206 ^ []))], (16692 ^ _115804) ^ [_381383, _381385] : [element(_381383, powerset(the_carrier(boole_POSet(_381385)))), 16695 ^ _115804 : [(16714 ^ _115804) ^ [] : [16717 ^ _115804 : [(16722 ^ _115804) ^ [] : [-(in(16715 ^ [_381383, _381385], _381383))], (16718 ^ _115804) ^ [] : [-(subset(16715 ^ [_381383, _381385], 16716 ^ [_381383, _381385]))], (16720 ^ _115804) ^ [] : [-(subset(16716 ^ [_381383, _381385], _381385))], (16724 ^ _115804) ^ [] : [in(16716 ^ [_381383, _381385], _381383)]], -(upper_relstr_subset(_381383, boole_POSet(_381385)))], (16696 ^ _115804) ^ [] : [upper_relstr_subset(_381383, boole_POSet(_381385)), 16699 ^ _115804 : [(16700 ^ _115804) ^ [_381538, _381540] : [-(in(_381538, _381383)), subset(_381540, _381538), subset(_381538, _381385), in(_381540, _381383)]]]]], (9927 ^ _115804) ^ [_267693, _267695] : [9950 ^ _115804 : [(9951 ^ _115804) ^ [_268030] : [subnet(_268030, _267695, _267693), 9954 ^ _115804 : [(9959 ^ _115804) ^ [] : [-(directed_relstr(_268030))], (9955 ^ _115804) ^ [] : [empty_carrier(_268030)], (9957 ^ _115804) ^ [] : [-(transitive_relstr(_268030))], (9961 ^ _115804) ^ [] : [-(net_str(_268030, _267695))]]]], -(empty_carrier(_267695)), one_sorted_str(_267695), -(empty_carrier(_267693)), transitive_relstr(_267693), directed_relstr(_267693), net_str(_267693, _267695)], (9121 ^ _115804) ^ [_256652] : [-(relation_of2_as_subset(inclusion_order(_256652), _256652, _256652))], (20093 ^ _115804) ^ [_435550, _435552] : [in(_435552, _435550), 20097 ^ _115804 : [(20098 ^ _115804) ^ [] : [-(in(20096 ^ [_435550, _435552], _435550))], (20100 ^ _115804) ^ [_435681] : [in(_435681, _435550), in(_435681, 20096 ^ [_435550, _435552])]]], (10395 ^ _115804) ^ [_273723] : [-(upper_bounded_relstr(boole_POSet(_273723)))], (1690 ^ _115804) ^ [_139270, _139272] : [_139272 = _139270, -(empty_carrier_subset(_139272) = empty_carrier_subset(_139270))], (12353 ^ _115804) ^ [] : [-(one_to_one(12347 ^ []))], (19711 ^ _115804) ^ [_429209] : [rel_str(_429209), 19714 ^ _115804 : [(19715 ^ _115804) ^ [_429340] : [subrelstr(_429340, _429209), 19718 ^ _115804 : [(19719 ^ _115804) ^ [_429464] : [element(_429464, the_carrier(_429209)), 19722 ^ _115804 : [(19723 ^ _115804) ^ [_429581] : [element(_429581, the_carrier(_429209)), 19726 ^ _115804 : [(19727 ^ _115804) ^ [_429687] : [element(_429687, the_carrier(_429340)), 19730 ^ _115804 : [(19731 ^ _115804) ^ [_429782] : [element(_429782, the_carrier(_429340)), -(related(_429209, _429464, _429581)), _429687 = _429464, _429782 = _429581, related(_429340, _429687, _429782)]]]]]]]]]]], (12605 ^ _115804) ^ [] : [empty_carrier(12601 ^ [])], (2390 ^ _115804) ^ [_150282, _150284] : [_150284 = _150282, -(boole_POSet(_150284) = boole_POSet(_150282))], (1408 ^ _115804) ^ [_134682, _134684, _134686, _134688] : [-(proper_element(_134686, _134682)), proper_element(_134688, _134684), _134688 = _134686, _134684 = _134682], (9761 ^ _115804) ^ [_265528, _265530, _265532, _265534] : [-(element(apply_as_element(_265534, _265532, _265530, _265528), _265532)), -(empty(_265534)), function(_265530), quasi_total(_265530, _265534, _265532), relation_of2(_265530, _265534, _265532), element(_265528, _265534)], (1436 ^ _115804) ^ [_135068, _135070] : [-(well_ordering(_135068)), _135070 = _135068, well_ordering(_135070)], (10917 ^ _115804) ^ [_280671] : [-(meet_associative(boole_lattice(_280671)))], (664 ^ _115804) ^ [_124434, _124436] : [-(compact_top_space(_124434)), _124436 = _124434, compact_top_space(_124436)], (12728 ^ _115804) ^ [_304107] : [-(finite(12722 ^ [_304107]))], (18815 ^ _115804) ^ [_415331] : [subset(_415331, empty_set), -(_415331 = empty_set)], (7394 ^ _115804) ^ [_227709, _227711, _227713] : [_227709 = set_difference(_227713, _227711), 7397 ^ _115804 : [(7398 ^ _115804) ^ [_227800] : [in(_227800, _227709), 7401 ^ _115804 : [(7402 ^ _115804) ^ [] : [-(in(_227800, _227713))], (7404 ^ _115804) ^ [] : [in(_227800, _227711)]]], (7406 ^ _115804) ^ [_227911] : [-(in(_227911, _227709)), in(_227911, _227713), -(in(_227911, _227711))]]], (17176 ^ _115804) ^ [_389021] : [antisymmetric_relstr(_389021), rel_str(_389021), 17183 ^ _115804 : [(17184 ^ _115804) ^ [_389181] : [ex_inf_of_relstr_set(_389021, _389181), 17188 ^ _115804 : [(17189 ^ _115804) ^ [] : [-(element(17187 ^ [_389021, _389181], the_carrier(_389021)))], (17193 ^ _115804) ^ [_389373] : [element(_389373, the_carrier(_389021)), relstr_element_smaller(_389021, _389181, _389373), -(related(_389021, _389373, 17187 ^ [_389021, _389181]))], (17191 ^ _115804) ^ [] : [-(relstr_element_smaller(_389021, _389181, 17187 ^ [_389021, _389181]))]]], (17203 ^ _115804) ^ [_389532] : [-(ex_inf_of_relstr_set(_389021, _389532)), 17204 ^ _115804 : [(17205 ^ _115804) ^ [_389602] : [element(_389602, the_carrier(_389021)), relstr_element_smaller(_389021, _389532, _389602), 17213 ^ _115804 : [(17214 ^ _115804) ^ [] : [-(element(17212 ^ [_389021, _389532, _389602], the_carrier(_389021)))], (17218 ^ _115804) ^ [] : [related(_389021, 17212 ^ [_389021, _389532, _389602], _389602)], (17216 ^ _115804) ^ [] : [-(relstr_element_smaller(_389021, _389532, 17212 ^ [_389021, _389532, _389602]))]]]]]]], (5836 ^ _115804) ^ [_202344] : [relation(_202344), 5839 ^ _115804 : [(5840 ^ _115804) ^ [_202420] : [in(_202420, _202344), -(_202420 = ordered_pair(5843 ^ [_202344, _202420], 5844 ^ [_202344, _202420]))]]], (17691 ^ _115804) ^ [_398014] : [one_sorted_str(_398014), 17694 ^ _115804 : [(17695 ^ _115804) ^ [_398093] : [element(_398093, powerset(the_carrier(_398014))), -(subset_difference(the_carrier(_398014), cast_as_carrier_subset(_398014), subset_difference(the_carrier(_398014), cast_as_carrier_subset(_398014), _398093)) = _398093)]]], (12195 ^ _115804) ^ [] : [-(rel_str(12193 ^ []))], (13204 ^ _115804) ^ [_310401, _310403, _310405, _310407] : [-(apply_on_set_and_struct(_310407, _310405, _310403, _310401) = apply(_310403, _310401)), -(empty(_310407)), -(empty_carrier(_310405)), rel_str(_310405), function(_310403), quasi_total(_310403, _310407, the_carrier(_310405)), relation_of2(_310403, _310407, the_carrier(_310405)), element(_310401, _310407)], (8444 ^ _115804) ^ [_246137] : [-(empty_carrier(_246137)), one_sorted_str(_246137), 8451 ^ _115804 : [(8452 ^ _115804) ^ [_246279] : [-(empty_carrier(_246279)), net_str(_246279, _246137), 8459 ^ _115804 : [(8460 ^ _115804) ^ [_246409] : [element(_246409, the_carrier(_246279)), -(apply_netmap(_246137, _246279, _246409) = apply_on_structs(_246279, _246137, the_mapping(_246137, _246279), _246409))]]]]], (11023 ^ _115804) ^ [_282103, _282105] : [-(open_subset(subset_complement(the_carrier(_282105), _282103), _282105)), topological_space(_282105), top_str(_282105), closed_subset(_282103, _282105), element(_282103, powerset(the_carrier(_282105)))], (10060 ^ _115804) ^ [_269462, _269464] : [-(relation_of2(10058 ^ [_269462, _269464], _269464, _269462))], (8985 ^ _115804) ^ [_254913] : [-(latt_str(boole_lattice(_254913)))], (11881 ^ _115804) ^ [_294031, _294033] : [subset(_294033, _294031), -(set_difference(_294033, _294031) = empty_set)], (12360 ^ _115804) ^ [] : [-(relation_empty_yielding(12356 ^ []))], (2210 ^ _115804) ^ [_147552, _147554, _147556, _147558, _147560, _147562] : [-(relation_rng_as_subset(_147562, _147558, _147554) = relation_rng_as_subset(_147560, _147556, _147552)), _147562 = _147560, _147558 = _147556, _147554 = _147552], (2596 ^ _115804) ^ [_153327, _153329, _153331, _153333] : [-(relation_dom_restriction(_153333, _153329) = relation_dom_restriction(_153331, _153327)), _153333 = _153331, _153329 = _153327], (1734 ^ _115804) ^ [_139908, _139910, _139912, _139914] : [-(rel_str_of(_139914, _139910) = rel_str_of(_139912, _139908)), _139914 = _139912, _139910 = _139908], (4302 ^ _115804) ^ [_175304, _175306] : [-(set_union2(_175306, _175304) = set_union2(_175304, _175306))], (10035 ^ _115804) ^ [] : [-(join_semilatt_str(10033 ^ []))], (1108 ^ _115804) ^ [_130508, _130510, _130512, _130514] : [-(subrelstr(_130512, _130508)), subrelstr(_130514, _130510), _130514 = _130512, _130510 = _130508], (10309 ^ _115804) ^ [_272620] : [-(boolean_lattstr(boole_lattice(_272620)))], (12581 ^ _115804) ^ [_302359] : [-(bijective(12567 ^ [_302359], _302359, _302359))], (12541 ^ _115804) ^ [_301915] : [-(element(12539 ^ [_301915], powerset(_301915)))], (12434 ^ _115804) ^ [] : [empty_carrier(12430 ^ [])], (12620 ^ _115804) ^ [] : [-(one_to_one(12614 ^ []))], (13364 ^ _115804) ^ [_312817, _312819, _312821, _312823] : [-(apply_on_set_and_struct2(_312823, _312821, _312819, _312817) = apply(_312819, _312817)), -(empty(_312823)), -(empty_carrier(_312821)), one_sorted_str(_312821), function(_312819), quasi_total(_312819, _312823, the_carrier(_312821)), relation_of2(_312819, _312823, the_carrier(_312821)), element(_312817, _312823)], (11011 ^ _115804) ^ [_281935, _281937] : [-(relation(set_difference(_281937, _281935))), relation(_281937), relation(_281935)], (5524 ^ _115804) ^ [_197022, _197024, _197026, _197028] : [_197022 = unordered_triple(_197028, _197026, _197024), 5527 ^ _115804 : [(5542 ^ _115804) ^ [_197242] : [5543 ^ _115804 : [(5544 ^ _115804) ^ [] : [_197242 = _197028], (5548 ^ _115804) ^ [] : [_197242 = _197024], (5546 ^ _115804) ^ [] : [_197242 = _197026]], -(in(_197242, _197022))], (5528 ^ _115804) ^ [_197129] : [in(_197129, _197022), -(_197129 = _197028), -(_197129 = _197026), -(_197129 = _197024)]]], (16580 ^ _115804) ^ [_379798, _379800, _379802, _379804] : [-(in(ordered_pair(_379804, _379802), cartesian_product2(_379800, _379798))), in(_379804, _379800), in(_379802, _379798)], (12302 ^ _115804) ^ [] : [empty_carrier(12298 ^ [])], (10937 ^ _115804) ^ [_280863] : [-(boolean_lattstr(boole_lattice(_280863)))], (11766 ^ _115804) ^ [_292402] : [relation(_292402), 11769 ^ _115804 : [(11780 ^ _115804) ^ [] : [11782 ^ _115804 : [(11783 ^ _115804) ^ [] : [-(in(11781 ^ [_292402], relation_field(_292402)))], (11785 ^ _115804) ^ [] : [in(ordered_pair(11781 ^ [_292402], 11781 ^ [_292402]), _292402)]], -(reflexive(_292402))], (11770 ^ _115804) ^ [] : [reflexive(_292402), 11773 ^ _115804 : [(11774 ^ _115804) ^ [_292521] : [in(_292521, relation_field(_292402)), -(in(ordered_pair(_292521, _292521), _292402))]]]]], (2418 ^ _115804) ^ [_150686, _150688, _150690, _150692] : [-(subset_complement(_150692, _150688) = subset_complement(_150690, _150686)), _150692 = _150690, _150688 = _150686], (12432 ^ _115804) ^ [] : [-(rel_str(12430 ^ []))], (602 ^ _115804) ^ [_123597, _123599] : [-(meet_associative(_123597)), _123599 = _123597, meet_associative(_123599)], (4300 ^ _115804) ^ [_175273, _175275] : [-(unordered_pair(_175275, _175273) = unordered_pair(_175273, _175275))], (17589 ^ _115804) ^ [_396033] : [epsilon_transitive(_396033), 17592 ^ _115804 : [(17593 ^ _115804) ^ [_396097] : [ordinal(_396097), proper_subset(_396033, _396097), -(in(_396033, _396097))]]], (20091 ^ _115804) ^ [_435518, _435520] : [-(pair_second(ordered_pair(_435520, _435518)) = _435518)], (9615 ^ _115804) ^ [_263371, _263373] : [-(element(topstr_closure(_263373, _263371), powerset(the_carrier(_263373)))), top_str(_263373), element(_263371, powerset(the_carrier(_263373)))], (10439 ^ _115804) ^ [_274243] : [-(complete_relstr(boole_POSet(_274243)))], (1560 ^ _115804) ^ [_136742, _136744] : [-(empty_carrier(_136742)), _136744 = _136742, empty_carrier(_136744)], (17933 ^ _115804) ^ [_401640] : [-(empty_carrier(_401640)), join_commutative(_401640), join_semilatt_str(_401640), 17944 ^ _115804 : [(17945 ^ _115804) ^ [_401827] : [element(_401827, the_carrier(_401640)), 17948 ^ _115804 : [(17949 ^ _115804) ^ [_401910] : [element(_401910, the_carrier(_401640)), -(_401827 = _401910), below(_401640, _401827, _401910), below(_401640, _401910, _401827)]]]]], (12795 ^ _115804) ^ [_304837] : [-(symmetric(12787 ^ [_304837]))], (18929 ^ _115804) ^ [_416918, _416920] : [element(_416918, powerset(_416920)), 18932 ^ _115804 : [(18933 ^ _115804) ^ [_416996] : [element(_416996, powerset(_416920)), 18936 ^ _115804 : [(18937 ^ _115804) ^ [] : [disjoint(_416918, _416996), -(subset(_416918, subset_complement(_416920, _416996)))], (18943 ^ _115804) ^ [] : [subset(_416918, subset_complement(_416920, _416996)), -(disjoint(_416918, _416996))]]]]], (11171 ^ _115804) ^ [] : [-(empty(empty_set))], (12259 ^ _115804) ^ [] : [-(lower_bounded_relstr(12239 ^ []))], (12553 ^ _115804) ^ [_302050] : [-(epsilon_connected(12539 ^ [_302050]))], (9119 ^ _115804) ^ [_256629] : [-(v1_partfun1(inclusion_order(_256629), _256629, _256629))], (12904 ^ _115804) ^ [] : [-(transitive_relstr(12894 ^ []))], (6714 ^ _115804) ^ [_216636, _216638, _216640] : [-(_216636 = set_union2(_216640, _216638)), 6718 ^ _115804 : [(6719 ^ _115804) ^ [] : [-(in(6715 ^ [_216636, _216638, _216640], _216636))], (6723 ^ _115804) ^ [] : [in(6715 ^ [_216636, _216638, _216640], _216638)], (6721 ^ _115804) ^ [] : [in(6715 ^ [_216636, _216638, _216640], _216640)]], 6724 ^ _115804 : [(6731 ^ _115804) ^ [] : [in(6715 ^ [_216636, _216638, _216640], _216636)], (6725 ^ _115804) ^ [] : [-(in(6715 ^ [_216636, _216638, _216640], _216640)), -(in(6715 ^ [_216636, _216638, _216640], _216638))]]], (7513 ^ _115804) ^ [_229666] : [rel_str(_229666), 7516 ^ _115804 : [(7517 ^ _115804) ^ [] : [transitive_relstr(_229666), -(is_transitive_in(the_InternalRel(_229666), the_carrier(_229666)))], (7523 ^ _115804) ^ [] : [is_transitive_in(the_InternalRel(_229666), the_carrier(_229666)), -(transitive_relstr(_229666))]]], (20106 ^ _115804) ^ [_435779] : [ordinal(_435779), -(well_ordering(inclusion_relation(_435779)))], (12551 ^ _115804) ^ [_302028] : [-(epsilon_transitive(12539 ^ [_302028]))], (5232 ^ _115804) ^ [_192123] : [relation(_192123), 5235 ^ _115804 : [(5236 ^ _115804) ^ [] : [connected(_192123), -(is_connected_in(_192123, relation_field(_192123)))], (5242 ^ _115804) ^ [] : [is_connected_in(_192123, relation_field(_192123)), -(connected(_192123))]]], (10305 ^ _115804) ^ [_272582] : [-(bounded_lattstr(boole_lattice(_272582)))], (11389 ^ _115804) ^ [_286935] : [empty_carrier(boole_POSet(_286935))], (17793 ^ _115804) ^ [_399633, _399635, _399637] : [relation_of2_as_subset(_399633, _399637, _399635), 17796 ^ _115804 : [(17797 ^ _115804) ^ [] : [17799 ^ _115804 : [(17800 ^ _115804) ^ [] : [-(in(17798 ^ [_399633, _399635, _399637], _399635))], (17802 ^ _115804) ^ [_399813] : [in(ordered_pair(_399813, 17798 ^ [_399633, _399635, _399637]), _399633)]], -(relation_rng_as_subset(_399637, _399635, _399633) = _399635)], (17806 ^ _115804) ^ [] : [relation_rng_as_subset(_399637, _399635, _399633) = _399635, 17809 ^ _115804 : [(17810 ^ _115804) ^ [_399928] : [in(_399928, _399635), -(in(ordered_pair(17813 ^ [_399633, _399635, _399637, _399928], _399928), _399633))]]]]], (10389 ^ _115804) ^ [_273666] : [-(with_infima_relstr(boole_POSet(_273666)))], (2778 ^ _115804) ^ [_156206] : [rel_str(_156206), 2793 ^ _115804 : [(2794 ^ _115804) ^ [] : [empty_carrier(_156206)], (2798 ^ _115804) ^ [] : [-(lower_bounded_relstr(_156206))], (2796 ^ _115804) ^ [] : [-(reflexive_relstr(_156206))]], -(empty_carrier(_156206)), reflexive_relstr(_156206), join_complete_relstr(_156206)], (11852 ^ _115804) ^ [_293626, _293628] : [in(_293628, _293626), -(subset(singleton(_293628), _293626))], (10621 ^ _115804) ^ [] : [-(relation(empty_set))], (5399 ^ _115804) ^ [_194870] : [-(empty_carrier(_194870)), topological_space(_194870), top_str(_194870), 5410 ^ _115804 : [(5411 ^ _115804) ^ [_195101] : [-(empty_carrier(_195101)), transitive_relstr(_195101), directed_relstr(_195101), net_str(_195101, _194870), 5426 ^ _115804 : [(5427 ^ _115804) ^ [_195362] : [element(_195362, powerset(the_carrier(_194870))), 5430 ^ _115804 : [(5458 ^ _115804) ^ [] : [-(_195362 = lim_points_of_net(_194870, _195101)), 5460 ^ _115804 : [(5461 ^ _115804) ^ [] : [-(element(5459 ^ [_194870, _195101, _195362], the_carrier(_194870)))], (5463 ^ _115804) ^ [] : [5464 ^ _115804 : [(5465 ^ _115804) ^ [] : [-(in(5459 ^ [_194870, _195101, _195362], _195362))], (5470 ^ _115804) ^ [] : [is_eventually_in(_194870, _195101, 5466 ^ [_194870, _195101, _195362])], (5468 ^ _115804) ^ [] : [-(point_neighbourhood(5466 ^ [_194870, _195101, _195362], _194870, 5459 ^ [_194870, _195101, _195362]))]], 5471 ^ _115804 : [(5478 ^ _115804) ^ [] : [in(5459 ^ [_194870, _195101, _195362], _195362)], (5472 ^ _115804) ^ [_196138] : [point_neighbourhood(_196138, _194870, 5459 ^ [_194870, _195101, _195362]), -(is_eventually_in(_194870, _195101, _196138))]]]]], (5431 ^ _115804) ^ [] : [_195362 = lim_points_of_net(_194870, _195101), 5434 ^ _115804 : [(5435 ^ _115804) ^ [_195523] : [element(_195523, the_carrier(_194870)), 5438 ^ _115804 : [(5449 ^ _115804) ^ [] : [5451 ^ _115804 : [(5452 ^ _115804) ^ [] : [-(point_neighbourhood(5450 ^ [_194870, _195101, _195362, _195523], _194870, _195523))], (5454 ^ _115804) ^ [] : [is_eventually_in(_194870, _195101, 5450 ^ [_194870, _195101, _195362, _195523])]], -(in(_195523, _195362))], (5439 ^ _115804) ^ [] : [in(_195523, _195362), 5442 ^ _115804 : [(5443 ^ _115804) ^ [_195659] : [point_neighbourhood(_195659, _194870, _195523), -(is_eventually_in(_194870, _195101, _195659))]]]]]]]]]]]]], (30 ^ _115804) ^ [_116189, _116191] : [-(v1_xreal_0(_116189)), _116191 = _116189, v1_xreal_0(_116191)], (7578 ^ _115804) ^ [_230569] : [top_str(_230569), 7581 ^ _115804 : [(7582 ^ _115804) ^ [_230640] : [element(_230640, powerset(the_carrier(_230569))), 7585 ^ _115804 : [(7586 ^ _115804) ^ [] : [open_subset(_230640, _230569), -(in(_230640, the_topology(_230569)))], (7592 ^ _115804) ^ [] : [in(_230640, the_topology(_230569)), -(open_subset(_230640, _230569))]]]]], (5610 ^ _115804) ^ [_198296] : [function(_198296), 5613 ^ _115804 : [(5614 ^ _115804) ^ [_198377, _198379, _198381] : [-(_198379 = _198377), in(ordered_pair(_198381, _198379), _198296), in(ordered_pair(_198381, _198377), _198296)]]], (5857 ^ _115804) ^ [_202706] : [relation(_202706), 5860 ^ _115804 : [(5871 ^ _115804) ^ [_202942] : [5873 ^ _115804 : [(5874 ^ _115804) ^ [] : [-(in(5872 ^ [_202706, _202942], _202942))], (5876 ^ _115804) ^ [] : [in(ordered_pair(5872 ^ [_202706, _202942], 5872 ^ [_202706, _202942]), _202706)]], -(is_reflexive_in(_202706, _202942))], (5861 ^ _115804) ^ [_202791] : [is_reflexive_in(_202706, _202791), 5864 ^ _115804 : [(5865 ^ _115804) ^ [_202857] : [in(_202857, _202791), -(in(ordered_pair(_202857, _202857), _202706))]]]]], (12782 ^ _115804) ^ [] : [-(epsilon_transitive(12778 ^ []))], (17994 ^ _115804) ^ [_402665] : [-(relation(17992 ^ [_402665]))], (13154 ^ _115804) ^ [_309670, _309672, _309674, _309676] : [-(partfun_dom_restriction(_309676, _309674, _309672, _309670) = relation_dom_restriction(_309672, _309670)), function(_309672), relation_of2(_309672, _309676, _309674)], (11764 ^ _115804) ^ [_292377, _292379] : [proper_subset(_292379, _292379)], (10685 ^ _115804) ^ [_277493] : [-(empty(_277493)), 10688 ^ _115804 : [(10693 ^ _115804) ^ [] : [-(strict_rel_str(boole_POSet(_277493)))], (10709 ^ _115804) ^ [] : [-(join_complete_relstr(boole_POSet(_277493)))], (10719 ^ _115804) ^ [] : [-(boolean_relstr(boole_POSet(_277493)))], (10697 ^ _115804) ^ [] : [-(transitive_relstr(boole_POSet(_277493)))], (10711 ^ _115804) ^ [] : [v1_yellow_3(boole_POSet(_277493))], (10707 ^ _115804) ^ [] : [-(up_complete_relstr(boole_POSet(_277493)))], (10691 ^ _115804) ^ [] : [trivial_carrier(boole_POSet(_277493))], (10721 ^ _115804) ^ [] : [-(with_suprema_relstr(boole_POSet(_277493)))], (10695 ^ _115804) ^ [] : [-(reflexive_relstr(boole_POSet(_277493)))], (10717 ^ _115804) ^ [] : [-(complemented_relstr(boole_POSet(_277493)))], (10699 ^ _115804) ^ [] : [-(antisymmetric_relstr(boole_POSet(_277493)))], (10723 ^ _115804) ^ [] : [-(with_infima_relstr(boole_POSet(_277493)))], (10725 ^ _115804) ^ [] : [-(complete_relstr(boole_POSet(_277493)))], (10715 ^ _115804) ^ [] : [-(heyting_relstr(boole_POSet(_277493)))], (10701 ^ _115804) ^ [] : [-(lower_bounded_relstr(boole_POSet(_277493)))], (10705 ^ _115804) ^ [] : [-(bounded_relstr(boole_POSet(_277493)))], (10689 ^ _115804) ^ [] : [empty_carrier(boole_POSet(_277493))], (10703 ^ _115804) ^ [] : [-(upper_bounded_relstr(boole_POSet(_277493)))], (10713 ^ _115804) ^ [] : [-(distributive_relstr(boole_POSet(_277493)))]]], (4670 ^ _115804) ^ [_181501, _181503] : [relation(_181501), 4673 ^ _115804 : [(4674 ^ _115804) ^ [_181598] : [relation(_181598), 4677 ^ _115804 : [(4700 ^ _115804) ^ [] : [-(_181598 = relation_rng_restriction(_181503, _181501)), 4713 ^ _115804 : [(4714 ^ _115804) ^ [] : [-(in(4702 ^ [_181501, _181503, _181598], _181503))], (4718 ^ _115804) ^ [] : [in(ordered_pair(4701 ^ [_181501, _181503, _181598], 4702 ^ [_181501, _181503, _181598]), _181598)], (4716 ^ _115804) ^ [] : [-(in(ordered_pair(4701 ^ [_181501, _181503, _181598], 4702 ^ [_181501, _181503, _181598]), _181501))]], 4705 ^ _115804 : [(4706 ^ _115804) ^ [] : [-(in(ordered_pair(4701 ^ [_181501, _181503, _181598], 4702 ^ [_181501, _181503, _181598]), _181598))], (4708 ^ _115804) ^ [] : [in(4702 ^ [_181501, _181503, _181598], _181503), in(ordered_pair(4701 ^ [_181501, _181503, _181598], 4702 ^ [_181501, _181503, _181598]), _181501)]]], (4678 ^ _115804) ^ [] : [_181598 = relation_rng_restriction(_181503, _181501), 4681 ^ _115804 : [(4682 ^ _115804) ^ [_181760, _181762] : [in(ordered_pair(_181762, _181760), _181598), 4685 ^ _115804 : [(4686 ^ _115804) ^ [] : [-(in(_181760, _181503))], (4688 ^ _115804) ^ [] : [-(in(ordered_pair(_181762, _181760), _181501))]]], (4690 ^ _115804) ^ [_181877, _181879] : [-(in(ordered_pair(_181879, _181877), _181598)), in(_181877, _181503), in(ordered_pair(_181879, _181877), _181501)]]]]]]], (1350 ^ _115804) ^ [_133921, _133923] : [-(lower_bounded_relstr(_133921)), _133923 = _133921, lower_bounded_relstr(_133923)], (18056 ^ _115804) ^ [_403627, _403629] : [subset(_403629, _403627), -(set_intersection2(_403629, _403627) = _403629)], (9229 ^ _115804) ^ [_258177] : [one_sorted_str(_258177), -(element(cast_as_carrier_subset(_258177), powerset(the_carrier(_258177))))], (17998 ^ _115804) ^ [_402719, _402721, _402723] : [subset(_402723, _402721), -(subset(set_intersection2(_402723, _402719), set_intersection2(_402721, _402719)))], (13108 ^ _115804) ^ [_308980] : [-(inclusion_order(_308980) = inclusion_relation(_308980))], (10851 ^ _115804) ^ [_279790, _279792] : [v2_membered(_279792), 10854 ^ _115804 : [(10855 ^ _115804) ^ [] : [-(v1_membered(set_difference(_279792, _279790)))], (10857 ^ _115804) ^ [] : [-(v2_membered(set_difference(_279792, _279790)))]]], (11599 ^ _115804) ^ [_289769, _289771, _289773, _289775] : [-(empty_carrier(_289773)), one_sorted_str(_289773), -(empty_carrier(_289771)), net_str(_289771, _289773), element(_289769, the_carrier(_289771)), 11618 ^ _115804 : [(11619 ^ _115804) ^ [] : [in(_289775, a_3_0_waybel_9(_289773, _289771, _289769)), 11623 ^ _115804 : [(11624 ^ _115804) ^ [] : [-(element(11622 ^ [_289769, _289771, _289773, _289775], the_carrier(_289771)))], (11628 ^ _115804) ^ [] : [-(related(_289771, _289769, 11622 ^ [_289769, _289771, _289773, _289775]))], (11626 ^ _115804) ^ [] : [-(_289775 = 11622 ^ [_289769, _289771, _289773, _289775])]]], (11630 ^ _115804) ^ [] : [-(in(_289775, a_3_0_waybel_9(_289773, _289771, _289769))), 11631 ^ _115804 : [(11632 ^ _115804) ^ [_290264] : [element(_290264, the_carrier(_289771)), _289775 = _290264, related(_289771, _289769, _290264)]]]]], (1696 ^ _115804) ^ [_139355, _139357] : [_139357 = _139355, -(the_L_join(_139357) = the_L_join(_139355))], (10623 ^ _115804) ^ [] : [-(relation_empty_yielding(empty_set))], (13048 ^ _115804) ^ [_308090, _308092, _308094, _308096] : [-(ordered_pair_as_product_element(_308096, _308094, _308092, _308090) = ordered_pair(_308092, _308090)), -(empty(_308096)), -(empty(_308094)), element(_308092, _308096), element(_308090, _308094)], (9465 ^ _115804) ^ [_261296] : [relation(_261296), -(relation(relation_inverse(_261296)))], (9533 ^ _115804) ^ [_262174, _262176, _262178, _262180] : [-(element(function_invverse_img_as_carrier_subset(_262180, _262178, _262176, _262174), powerset(the_carrier(_262180)))), one_sorted_str(_262180), one_sorted_str(_262178), function(_262176), quasi_total(_262176, the_carrier(_262180), the_carrier(_262178)), relation_of2(_262176, the_carrier(_262180), the_carrier(_262178))], (12267 ^ _115804) ^ [] : [-(join_complete_relstr(12239 ^ []))], (12994 ^ _115804) ^ [] : [-(latt_str(12992 ^ []))], (8665 ^ _115804) ^ [_250241] : [relation(_250241), 8668 ^ _115804 : [(8669 ^ _115804) ^ [] : [reflexive(_250241), -(is_reflexive_in(_250241, relation_field(_250241)))], (8675 ^ _115804) ^ [] : [is_reflexive_in(_250241, relation_field(_250241)), -(reflexive(_250241))]]], (12777 ^ _115804) ^ [] : [-(strict_latt_str(12773 ^ []))], (3298 ^ _115804) ^ [_162755] : [v5_membered(_162755), 3301 ^ _115804 : [(3302 ^ _115804) ^ [_162835] : [element(_162835, powerset(_162755)), 3305 ^ _115804 : [(3314 ^ _115804) ^ [] : [-(v5_membered(_162835))], (3312 ^ _115804) ^ [] : [-(v4_membered(_162835))], (3310 ^ _115804) ^ [] : [-(v3_membered(_162835))], (3306 ^ _115804) ^ [] : [-(v1_membered(_162835))], (3308 ^ _115804) ^ [] : [-(v2_membered(_162835))]]]]], (10391 ^ _115804) ^ [_273685] : [-(complete_relstr(boole_POSet(_273685)))], (508 ^ _115804) ^ [_122404, _122406] : [-(strict_rel_str(_122404)), _122406 = _122404, strict_rel_str(_122406)], (538 ^ _115804) ^ [_122779, _122781] : [-(upper_bounded_relstr(_122779)), _122781 = _122779, upper_bounded_relstr(_122781)], (4493 ^ _115804) ^ [_178192] : [one_sorted_str(_178192), -(identity_on_carrier(_178192) = identity_as_relation_of(the_carrier(_178192)))], (214 ^ _115804) ^ [_118597, _118599] : [-(upper_bounded_semilattstr(_118597)), _118599 = _118597, upper_bounded_semilattstr(_118599)], (17246 ^ _115804) ^ [_390236, _390238] : [relation(_390236), function(_390236), finite(_390238), -(finite(relation_image(_390236, _390238)))], (8594 ^ _115804) ^ [_249092] : [relation(_249092), function(_249092), one_to_one(_249092), -(function_inverse(_249092) = relation_inverse(_249092))], (13738 ^ _115804) ^ [_318938, _318940] : [one_sorted_str(_318940), element(_318938, powerset(powerset(the_carrier(_318940)))), 13750 ^ _115804 : [(13765 ^ _115804) ^ [_319646] : [element(_319646, powerset(the_carrier(_318940))), _319646 = 13747 ^ [_318938, _318940], -(13749 ^ [_318938, _318940] = subset_complement(the_carrier(_318940), _319646))], (13763 ^ _115804) ^ [] : [-(in(13747 ^ [_318938, _318940], complements_of_subsets(the_carrier(_318940), _318938)))], (13753 ^ _115804) ^ [_319438] : [element(_319438, powerset(the_carrier(_318940))), _319438 = 13747 ^ [_318938, _318940], -(13748 ^ [_318938, _318940] = subset_complement(the_carrier(_318940), _319438))], (13775 ^ _115804) ^ [] : [13748 ^ [_318938, _318940] = 13749 ^ [_318938, _318940]], (13751 ^ _115804) ^ [] : [-(in(13747 ^ [_318938, _318940], complements_of_subsets(the_carrier(_318940), _318938)))]], 13777 ^ _115804 : [(13782 ^ _115804) ^ [_320019, _320021] : [in(ordered_pair(_320021, _320019), 13776 ^ [_318938, _318940]), 13785 ^ _115804 : [(13786 ^ _115804) ^ [] : [-(in(_320021, complements_of_subsets(the_carrier(_318940), _318938)))], (13790 ^ _115804) ^ [_320195] : [element(_320195, powerset(the_carrier(_318940))), _320195 = _320021, -(_320019 = subset_complement(the_carrier(_318940), _320195))], (13788 ^ _115804) ^ [] : [-(in(_320021, complements_of_subsets(the_carrier(_318940), _318938)))]]], (13778 ^ _115804) ^ [] : [-(relation(13776 ^ [_318938, _318940]))], (13780 ^ _115804) ^ [] : [-(function(13776 ^ [_318938, _318940]))], (13800 ^ _115804) ^ [_320358, _320360] : [-(in(ordered_pair(_320360, _320358), 13776 ^ [_318938, _318940])), in(_320360, complements_of_subsets(the_carrier(_318940), _318938)), in(_320360, complements_of_subsets(the_carrier(_318940), _318938)), 13810 ^ _115804 : [(13811 ^ _115804) ^ [] : [-(element(13809 ^ [_318938, _318940, _320358, _320360], powerset(the_carrier(_318940))))], (13815 ^ _115804) ^ [] : [_320358 = subset_complement(the_carrier(_318940), 13809 ^ [_318938, _318940, _320358, _320360])], (13813 ^ _115804) ^ [] : [-(13809 ^ [_318938, _318940, _320358, _320360] = _320360)]]]]], (4499 ^ _115804) ^ [_178277] : [relation(_178277), 4502 ^ _115804 : [(4503 ^ _115804) ^ [_178377, _178379] : [relation(_178377), 4506 ^ _115804 : [(4529 ^ _115804) ^ [] : [-(_178377 = relation_dom_restriction(_178277, _178379)), 4542 ^ _115804 : [(4543 ^ _115804) ^ [] : [-(in(4530 ^ [_178277, _178377, _178379], _178379))], (4547 ^ _115804) ^ [] : [in(ordered_pair(4530 ^ [_178277, _178377, _178379], 4531 ^ [_178277, _178377, _178379]), _178377)], (4545 ^ _115804) ^ [] : [-(in(ordered_pair(4530 ^ [_178277, _178377, _178379], 4531 ^ [_178277, _178377, _178379]), _178277))]], 4534 ^ _115804 : [(4535 ^ _115804) ^ [] : [-(in(ordered_pair(4530 ^ [_178277, _178377, _178379], 4531 ^ [_178277, _178377, _178379]), _178377))], (4537 ^ _115804) ^ [] : [in(4530 ^ [_178277, _178377, _178379], _178379), in(ordered_pair(4530 ^ [_178277, _178377, _178379], 4531 ^ [_178277, _178377, _178379]), _178277)]]], (4507 ^ _115804) ^ [] : [_178377 = relation_dom_restriction(_178277, _178379), 4510 ^ _115804 : [(4511 ^ _115804) ^ [_178539, _178541] : [in(ordered_pair(_178541, _178539), _178377), 4514 ^ _115804 : [(4515 ^ _115804) ^ [] : [-(in(_178541, _178379))], (4517 ^ _115804) ^ [] : [-(in(ordered_pair(_178541, _178539), _178277))]]], (4519 ^ _115804) ^ [_178656, _178658] : [-(in(ordered_pair(_178658, _178656), _178377)), in(_178658, _178379), in(ordered_pair(_178658, _178656), _178277)]]]]]]], (15759 ^ _115804) ^ [_363268, _363270] : [topological_space(_363270), top_str(_363270), element(_363268, powerset(powerset(the_carrier(_363270)))), 15771 ^ _115804 : [(15772 ^ _115804) ^ [_363505] : [in(_363505, 15770 ^ [_363268, _363270]), 15775 ^ _115804 : [(15776 ^ _115804) ^ [] : [-(in(_363505, powerset(the_carrier(_363270))))], (15778 ^ _115804) ^ [] : [-(in(set_difference(cast_as_carrier_subset(_363270), _363505), _363268))]]], (15780 ^ _115804) ^ [_363638] : [-(in(_363638, 15770 ^ [_363268, _363270])), in(_363638, powerset(the_carrier(_363270))), in(set_difference(cast_as_carrier_subset(_363270), _363638), _363268)]]], (15315 ^ _115804) ^ [_354469] : [15319 ^ _115804 : [(15328 ^ _115804) ^ [] : [15317 ^ [_354469] = 15318 ^ [_354469]], (15326 ^ _115804) ^ [] : [-(ordinal(15318 ^ [_354469]))], (15324 ^ _115804) ^ [] : [-(15316 ^ [_354469] = 15318 ^ [_354469])], (15320 ^ _115804) ^ [] : [-(15316 ^ [_354469] = 15317 ^ [_354469])], (15322 ^ _115804) ^ [] : [-(ordinal(15317 ^ [_354469]))]], 15330 ^ _115804 : [(15331 ^ _115804) ^ [_354767] : [in(_354767, 15329 ^ [_354469]), 15335 ^ _115804 : [(15336 ^ _115804) ^ [] : [-(in(15334 ^ [_354469, _354767], _354469))], (15340 ^ _115804) ^ [] : [-(ordinal(_354767))], (15338 ^ _115804) ^ [] : [-(15334 ^ [_354469, _354767] = _354767)]]], (15342 ^ _115804) ^ [_354917] : [-(in(_354917, 15329 ^ [_354469])), 15343 ^ _115804 : [(15344 ^ _115804) ^ [_354967] : [in(_354967, _354469), _354967 = _354917, ordinal(_354917)]]]]], (12633 ^ _115804) ^ [_302890, _302892] : [-(relation(12629 ^ [_302890, _302892]))], (6656 ^ _115804) ^ [_215758] : [relation(_215758), 6659 ^ _115804 : [(6677 ^ _115804) ^ [] : [-(well_founded_relation(_215758)), 6679 ^ _115804 : [(6680 ^ _115804) ^ [] : [-(subset(6678 ^ [_215758], relation_field(_215758)))], (6684 ^ _115804) ^ [_216179] : [in(_216179, 6678 ^ [_215758]), disjoint(fiber(_215758, _216179), 6678 ^ [_215758])], (6682 ^ _115804) ^ [] : [6678 ^ [_215758] = empty_set]]], (6660 ^ _115804) ^ [] : [well_founded_relation(_215758), 6663 ^ _115804 : [(6664 ^ _115804) ^ [_215900] : [subset(_215900, relation_field(_215758)), -(_215900 = empty_set), 6672 ^ _115804 : [(6673 ^ _115804) ^ [] : [-(in(6671 ^ [_215758, _215900], _215900))], (6675 ^ _115804) ^ [] : [-(disjoint(fiber(_215758, 6671 ^ [_215758, _215900]), _215900))]]]]]]], (10295 ^ _115804) ^ [_272487] : [-(lattice(boole_lattice(_272487)))], (2302 ^ _115804) ^ [_148976, _148978] : [_148978 = _148976, -(relation_inverse(_148978) = relation_inverse(_148976))], (754 ^ _115804) ^ [_125657, _125659, _125661, _125663, _125665, _125667] : [-(subnetstr(_125665, _125661, _125657)), subnetstr(_125667, _125663, _125659), _125667 = _125665, _125663 = _125661, _125659 = _125657], (12049 ^ _115804) ^ [_296471, _296473] : [12051 ^ _115804 : [(12052 ^ _115804) ^ [] : [-(in(12050 ^ [_296471, _296473], _296473))], (12054 ^ _115804) ^ [] : [in(12050 ^ [_296471, _296473], _296471)]], -(element(_296473, powerset(_296471)))], (10375 ^ _115804) ^ [_273517] : [empty(powerset(_273517))], (3732 ^ _115804) ^ [_168171] : [rel_str(_168171), 3747 ^ _115804 : [(3752 ^ _115804) ^ [] : [-(up_complete_relstr(_168171))], (3748 ^ _115804) ^ [] : [empty_carrier(_168171)], (3750 ^ _115804) ^ [] : [-(reflexive_relstr(_168171))], (3754 ^ _115804) ^ [] : [-(v2_waybel_3(_168171))]], -(empty_carrier(_168171)), reflexive_relstr(_168171), v3_waybel_3(_168171)], (1632 ^ _115804) ^ [_137692, _137694, _137696, _137698, _137700, _137702] : [-(is_a_cluster_point_of_netstr(_137700, _137696, _137692)), is_a_cluster_point_of_netstr(_137702, _137698, _137694), _137702 = _137700, _137698 = _137696, _137694 = _137692], (1664 ^ _115804) ^ [_138887, _138889, _138891, _138893] : [-(k8_filter_1(_138893, _138889) = k8_filter_1(_138891, _138887)), _138893 = _138891, _138889 = _138887], (8071 ^ _115804) ^ [_239260] : [rel_str(_239260), 8074 ^ _115804 : [(8113 ^ _115804) ^ [_240215] : [-(ex_sup_of_relstr_set(_239260, _240215)), 8114 ^ _115804 : [(8115 ^ _115804) ^ [_240338] : [element(_240338, the_carrier(_239260)), relstr_set_smaller(_239260, _240215, _240338), 8125 ^ _115804 : [(8126 ^ _115804) ^ [] : [-(element(8124 ^ [_239260, _240215, _240338], the_carrier(_239260)))], (8130 ^ _115804) ^ [] : [related(_239260, _240338, 8124 ^ [_239260, _240215, _240338])], (8128 ^ _115804) ^ [] : [-(relstr_set_smaller(_239260, _240215, 8124 ^ [_239260, _240215, _240338]))]], 8132 ^ _115804 : [(8135 ^ _115804) ^ [] : [-(relstr_set_smaller(_239260, _240215, 8131 ^ [_239260, _240215, _240338]))], (8133 ^ _115804) ^ [] : [-(element(8131 ^ [_239260, _240215, _240338], the_carrier(_239260)))], (8147 ^ _115804) ^ [] : [8131 ^ [_239260, _240215, _240338] = _240338], (8137 ^ _115804) ^ [_240786] : [element(_240786, the_carrier(_239260)), relstr_set_smaller(_239260, _240215, _240786), -(related(_239260, 8131 ^ [_239260, _240215, _240338], _240786))]]]]], (8075 ^ _115804) ^ [_239425] : [ex_sup_of_relstr_set(_239260, _239425), 8079 ^ _115804 : [(8084 ^ _115804) ^ [_239727] : [element(_239727, the_carrier(_239260)), relstr_set_smaller(_239260, _239425, _239727), -(related(_239260, 8078 ^ [_239260, _239425], _239727))], (8080 ^ _115804) ^ [] : [-(element(8078 ^ [_239260, _239425], the_carrier(_239260)))], (8082 ^ _115804) ^ [] : [-(relstr_set_smaller(_239260, _239425, 8078 ^ [_239260, _239425]))], (8094 ^ _115804) ^ [_239878] : [element(_239878, the_carrier(_239260)), -(_239878 = 8078 ^ [_239260, _239425]), relstr_set_smaller(_239260, _239425, _239878), 8104 ^ _115804 : [(8105 ^ _115804) ^ [] : [-(element(8103 ^ [_239260, _239425, _239878], the_carrier(_239260)))], (8109 ^ _115804) ^ [] : [related(_239260, _239878, 8103 ^ [_239260, _239425, _239878])], (8107 ^ _115804) ^ [] : [-(relstr_set_smaller(_239260, _239425, 8103 ^ [_239260, _239425, _239878]))]]]]]]], (10669 ^ _115804) ^ [_277279] : [empty(singleton(_277279))], (12157 ^ _115804) ^ [] : [-(lattice(12137 ^ []))], (18211 ^ _115804) ^ [_405902, _405904] : [element(_405902, the_carrier(boole_POSet(_405904))), 18214 ^ _115804 : [(18215 ^ _115804) ^ [_405986] : [element(_405986, the_carrier(boole_POSet(_405904))), 18218 ^ _115804 : [(18219 ^ _115804) ^ [] : [related_reflexive(boole_POSet(_405904), _405902, _405986), -(subset(_405902, _405986))], (18225 ^ _115804) ^ [] : [subset(_405902, _405986), -(related_reflexive(boole_POSet(_405904), _405902, _405986))]]]]], (9633 ^ _115804) ^ [_263639, _263641, _263643] : [-(element(subset_difference(_263643, _263641, _263639), powerset(_263643))), element(_263641, powerset(_263643)), element(_263639, powerset(_263643))], (6394 ^ _115804) ^ [_211645] : [-(centered(_211645)), -(_211645 = empty_set), 6400 ^ _115804 : [(6405 ^ _115804) ^ [] : [-(finite(6399 ^ [_211645]))], (6401 ^ _115804) ^ [] : [6399 ^ [_211645] = empty_set], (6403 ^ _115804) ^ [] : [-(subset(6399 ^ [_211645], _211645))], (6407 ^ _115804) ^ [] : [-(set_meet(6399 ^ [_211645]) = empty_set)]]], (16995 ^ _115804) ^ [_385895] : [antisymmetric_relstr(_385895), rel_str(_385895), 17002 ^ _115804 : [(17003 ^ _115804) ^ [_386055] : [ex_sup_of_relstr_set(_385895, _386055), 17007 ^ _115804 : [(17008 ^ _115804) ^ [] : [-(element(17006 ^ [_385895, _386055], the_carrier(_385895)))], (17012 ^ _115804) ^ [_386247] : [element(_386247, the_carrier(_385895)), relstr_set_smaller(_385895, _386055, _386247), -(related(_385895, 17006 ^ [_385895, _386055], _386247))], (17010 ^ _115804) ^ [] : [-(relstr_set_smaller(_385895, _386055, 17006 ^ [_385895, _386055]))]]], (17022 ^ _115804) ^ [_386406] : [-(ex_sup_of_relstr_set(_385895, _386406)), 17023 ^ _115804 : [(17024 ^ _115804) ^ [_386476] : [element(_386476, the_carrier(_385895)), relstr_set_smaller(_385895, _386406, _386476), 17032 ^ _115804 : [(17033 ^ _115804) ^ [] : [-(element(17031 ^ [_385895, _386406, _386476], the_carrier(_385895)))], (17037 ^ _115804) ^ [] : [related(_385895, _386476, 17031 ^ [_385895, _386406, _386476])], (17035 ^ _115804) ^ [] : [-(relstr_set_smaller(_385895, _386406, 17031 ^ [_385895, _386406, _386476]))]]]]]]], (5624 ^ _115804) ^ [_198526] : [5628 ^ _115804 : [(5629 ^ _115804) ^ [] : [-(in(ordered_pair(5625 ^ [_198526], 5626 ^ [_198526]), _198526))], (5633 ^ _115804) ^ [] : [5626 ^ [_198526] = 5627 ^ [_198526]], (5631 ^ _115804) ^ [] : [-(in(ordered_pair(5625 ^ [_198526], 5627 ^ [_198526]), _198526))]], -(function(_198526))], (6784 ^ _115804) ^ [_217895] : [-(boole_POSet(_217895) = poset_of_lattice(boole_lattice(_217895)))], (9477 ^ _115804) ^ [_261464, _261466, _261468] : [-(element(subset_union2(_261468, _261466, _261464), powerset(_261468))), element(_261466, powerset(_261468)), element(_261464, powerset(_261468))], (10869 ^ _115804) ^ [_280036] : [10880 ^ _115804 : [(10881 ^ _115804) ^ [] : [-(relation(relation_inverse(_280036)))], (10883 ^ _115804) ^ [] : [-(function(relation_inverse(_280036)))]], relation(_280036), function(_280036), one_to_one(_280036)], (2470 ^ _115804) ^ [_151452, _151454] : [_151454 = _151452, -(pair_first(_151454) = pair_first(_151452))], (674 ^ _115804) ^ [_124559, _124561] : [-(centered(_124559)), _124561 = _124559, centered(_124561)], (12532 ^ _115804) ^ [] : [-(reflexive_relstr(12524 ^ []))], (9979 ^ _115804) ^ [_268453] : [top_str(_268453), -(element(the_topology(_268453), powerset(powerset(the_carrier(_268453)))))], (12417 ^ _115804) ^ [] : [-(complete_relstr(12401 ^ []))], (6425 ^ _115804) ^ [_212104] : [-(empty_carrier(_212104)), meet_semilatt_str(_212104), 6432 ^ _115804 : [(6433 ^ _115804) ^ [_212248] : [element(_212248, the_carrier(_212104)), 6436 ^ _115804 : [(6437 ^ _115804) ^ [_212336] : [element(_212336, the_carrier(_212104)), -(meet(_212104, _212248, _212336) = apply_binary_as_element(the_carrier(_212104), the_carrier(_212104), the_carrier(_212104), the_L_meet(_212104), _212248, _212336))]]]]], (1446 ^ _115804) ^ [_135193, _135195] : [-(one_sorted_str(_135193)), _135195 = _135193, one_sorted_str(_135195)], (17457 ^ _115804) ^ [_393657] : [-(the_carrier(incl_POSet(_393657)) = _393657)], (10479 ^ _115804) ^ [_274844, _274846] : [empty(ordered_pair(_274846, _274844))], (12243 ^ _115804) ^ [] : [empty_carrier(12239 ^ [])], (12365 ^ _115804) ^ [] : [-(empty(12363 ^ []))], (2096 ^ _115804) ^ [_145817, _145819, _145821, _145823] : [-(relation_image(_145823, _145819) = relation_image(_145821, _145817)), _145823 = _145821, _145819 = _145817], (12916 ^ _115804) ^ [] : [-(heyting_relstr(12894 ^ []))], (13012 ^ _115804) ^ [] : [-(lattice(12992 ^ []))], (4981 ^ _115804) ^ [_187676] : [top_str(_187676), 4984 ^ _115804 : [(4985 ^ _115804) ^ [_187811] : [element(_187811, powerset(the_carrier(_187676))), 4988 ^ _115804 : [(4989 ^ _115804) ^ [_187943] : [element(_187943, powerset(the_carrier(_187676))), 4992 ^ _115804 : [(5032 ^ _115804) ^ [] : [-(_187943 = topstr_closure(_187676, _187811)), 5034 ^ _115804 : [(5035 ^ _115804) ^ [] : [-(in(5033 ^ [_187676, _187811, _187943], the_carrier(_187676)))], (5037 ^ _115804) ^ [] : [5038 ^ _115804 : [(5048 ^ _115804) ^ [] : [-(disjoint(_187811, 5040 ^ [_187676, _187811, _187943]))], (5046 ^ _115804) ^ [] : [-(in(5033 ^ [_187676, _187811, _187943], 5040 ^ [_187676, _187811, _187943]))], (5044 ^ _115804) ^ [] : [-(open_subset(5040 ^ [_187676, _187811, _187943], _187676))], (5039 ^ _115804) ^ [] : [-(in(5033 ^ [_187676, _187811, _187943], _187943))], (5042 ^ _115804) ^ [] : [-(element(5040 ^ [_187676, _187811, _187943], powerset(the_carrier(_187676))))]], 5049 ^ _115804 : [(5064 ^ _115804) ^ [] : [in(5033 ^ [_187676, _187811, _187943], _187943)], (5050 ^ _115804) ^ [_188924] : [element(_188924, powerset(the_carrier(_187676))), open_subset(_188924, _187676), in(5033 ^ [_187676, _187811, _187943], _188924), disjoint(_187811, _188924)]]]]], (4993 ^ _115804) ^ [] : [_187943 = topstr_closure(_187676, _187811), 4996 ^ _115804 : [(4997 ^ _115804) ^ [_188120] : [in(_188120, the_carrier(_187676)), 5000 ^ _115804 : [(5019 ^ _115804) ^ [] : [5021 ^ _115804 : [(5026 ^ _115804) ^ [] : [-(in(_188120, 5020 ^ [_187676, _187811, _187943, _188120]))], (5022 ^ _115804) ^ [] : [-(element(5020 ^ [_187676, _187811, _187943, _188120], powerset(the_carrier(_187676))))], (5024 ^ _115804) ^ [] : [-(open_subset(5020 ^ [_187676, _187811, _187943, _188120], _187676))], (5028 ^ _115804) ^ [] : [-(disjoint(_187811, 5020 ^ [_187676, _187811, _187943, _188120]))]], -(in(_188120, _187943))], (5001 ^ _115804) ^ [] : [in(_188120, _187943), 5004 ^ _115804 : [(5005 ^ _115804) ^ [_188272] : [element(_188272, powerset(the_carrier(_187676))), open_subset(_188272, _187676), in(_188120, _188272), disjoint(_187811, _188272)]]]]]]]]]]]]], (498 ^ _115804) ^ [_122279, _122281] : [-(boolean_relstr(_122279)), _122281 = _122279, boolean_relstr(_122281)], (13068 ^ _115804) ^ [_308384, _308386] : [relation(_308386), -(relation_restriction_as_relation_of(_308386, _308384) = relation_restriction(_308386, _308384))], (12564 ^ _115804) ^ [] : [-(empty(12560 ^ []))], (7746 ^ _115804) ^ [_233244] : [being_limit_ordinal(_233244), -(_233244 = union(_233244))], (12876 ^ _115804) ^ [] : [-(heyting_relstr(12850 ^ []))], (17783 ^ _115804) ^ [_399508, _399510] : [ordinal(_399508), in(_399510, _399508), -(ordinal(_399510))], (12852 ^ _115804) ^ [] : [-(rel_str(12850 ^ []))], (19665 ^ _115804) ^ [_428602] : [-(empty_carrier(_428602)), one_sorted_str(_428602), 19672 ^ _115804 : [(19673 ^ _115804) ^ [_428726] : [element(_428726, powerset(powerset(the_carrier(_428602)))), is_a_cover_of_carrier(_428602, _428726), _428726 = empty_set]]], (3608 ^ _115804) ^ [_166612] : [v3_membered(_166612), -(v2_membered(_166612))], (6364 ^ _115804) ^ [_211191] : [6371 ^ _115804 : [(6372 ^ _115804) ^ [_211306] : [-(meet_of_latt_set(_211191, _211306) = join_of_latt_set(_211191, a_2_2_lattice3(_211191, _211306)))]], -(empty_carrier(_211191)), latt_str(_211191)], (12717 ^ _115804) ^ [] : [-(join_complete_relstr(12689 ^ []))], (13466 ^ _115804) ^ [_314289, _314291, _314293] : [13493 ^ _115804 : [(13494 ^ _115804) ^ [] : [below_refl(_314293, _314291, _314289), -(below(_314293, _314291, _314289))], (13500 ^ _115804) ^ [] : [below(_314293, _314291, _314289), -(below_refl(_314293, _314291, _314289))]], -(empty_carrier(_314293)), meet_commutative(_314293), meet_absorbing(_314293), join_absorbing(_314293), latt_str(_314293), element(_314291, the_carrier(_314293)), element(_314289, the_carrier(_314293))], (11465 ^ _115804) ^ [_287828] : [-(complete_relstr(boole_POSet(_287828)))], (16672 ^ _115804) ^ [_381110, _381112, _381114, _381116] : [-(subset(cartesian_product2(_381116, _381112), cartesian_product2(_381114, _381110))), subset(_381116, _381114), subset(_381112, _381110)], (5346 ^ _115804) ^ [_193991] : [relation(_193991), 5349 ^ _115804 : [(5350 ^ _115804) ^ [] : [transitive(_193991), -(is_transitive_in(_193991, relation_field(_193991)))], (5356 ^ _115804) ^ [] : [is_transitive_in(_193991, relation_field(_193991)), -(transitive(_193991))]]], (20154 ^ _115804) ^ [_436448, _436450] : [empty(_436450), -(_436450 = _436448), empty(_436448)], (12736 ^ _115804) ^ [] : [empty_carrier(12732 ^ [])], (10229 ^ _115804) ^ [_271650, _271652, _271654] : [10240 ^ _115804 : [(10241 ^ _115804) ^ [] : [-(transitive_relstr(preimage_subnetstr(_271654, _271652, _271650)))], (10245 ^ _115804) ^ [] : [-(full_subnetstr(preimage_subnetstr(_271654, _271652, _271650), _271654, _271652))], (10243 ^ _115804) ^ [] : [-(strict_net_str(preimage_subnetstr(_271654, _271652, _271650), _271654))]], one_sorted_str(_271654), transitive_relstr(_271652), net_str(_271652, _271654)], (12707 ^ _115804) ^ [] : [-(complete_relstr(12689 ^ []))], (9833 ^ _115804) ^ [] : [true___, -(true___)], (12511 ^ _115804) ^ [] : [-(reflexive_relstr(12503 ^ []))], (18702 ^ _115804) ^ [_413805, _413807] : [subset(singleton(_413807), _413805), -(in(_413807, _413805))], (13306 ^ _115804) ^ [_311931, _311933, _311935] : [-(subset_intersection2(_311935, _311933, _311931) = set_intersection2(_311933, _311931)), element(_311933, powerset(_311935)), element(_311931, powerset(_311935))], (5143 ^ _115804) ^ [_190516] : [one_sorted_str(_190516), 5146 ^ _115804 : [(5147 ^ _115804) ^ [_190630] : [net_str(_190630, _190516), 5150 ^ _115804 : [(5151 ^ _115804) ^ [_190737, _190739] : [strict_net_str(_190737, _190516), subnetstr(_190737, _190516, _190630), 5158 ^ _115804 : [(5159 ^ _115804) ^ [] : [_190737 = preimage_subnetstr(_190516, _190630, _190739), 5162 ^ _115804 : [(5163 ^ _115804) ^ [] : [-(full_subrelstr(_190737, _190630))], (5167 ^ _115804) ^ [] : [-(the_carrier(_190737) = function_invverse_img_as_carrier_subset(_190630, _190516, the_mapping(_190516, _190630), _190739))], (5165 ^ _115804) ^ [] : [-(subrelstr(_190737, _190630))]]], (5169 ^ _115804) ^ [] : [-(_190737 = preimage_subnetstr(_190516, _190630, _190739)), full_subrelstr(_190737, _190630), subrelstr(_190737, _190630), the_carrier(_190737) = function_invverse_img_as_carrier_subset(_190630, _190516, the_mapping(_190516, _190630), _190739)]]]]]]], (2330 ^ _115804) ^ [_149380, _149382, _149384, _149386] : [-(relation_inverse_image(_149386, _149382) = relation_inverse_image(_149384, _149380)), _149386 = _149384, _149382 = _149380], (20089 ^ _115804) ^ [_435491, _435493] : [-(pair_first(ordered_pair(_435493, _435491)) = _435493)], (12618 ^ _115804) ^ [] : [-(function(12614 ^ []))], (2612 ^ _115804) ^ [_153561, _153563] : [_153563 = _153561, -(union(_153563) = union(_153561))], (12645 ^ _115804) ^ [_303031] : [-(empty(12641 ^ [_303031]))], (9855 ^ _115804) ^ [_266733] : [latt_str(_266733), 9858 ^ _115804 : [(9859 ^ _115804) ^ [] : [-(meet_semilatt_str(_266733))], (9861 ^ _115804) ^ [] : [-(join_semilatt_str(_266733))]]], (9279 ^ _115804) ^ [_258809, _258811] : [rel_str(_258811), -(element(meet_on_relstr(_258811, _258809), the_carrier(_258811)))], (18732 ^ _115804) ^ [_414231, _414233] : [relation(_414231), -(relation_field(relation_restriction(_414231, _414233)) = _414233), well_ordering(_414231), subset(_414233, relation_field(_414231))], (2022 ^ _115804) ^ [_144632, _144634, _144636, _144638, _144640, _144642, _144644, _144646] : [-(relation_dom_restr_as_relation_of(_144646, _144642, _144638, _144634) = relation_dom_restr_as_relation_of(_144644, _144640, _144636, _144632)), _144646 = _144644, _144642 = _144640, _144638 = _144636, _144634 = _144632], (12838 ^ _115804) ^ [] : [-(relation_empty_yielding(12834 ^ []))], (9171 ^ _115804) ^ [_257371] : [9182 ^ _115804 : [(9191 ^ _115804) ^ [] : [-(relation_of2_as_subset(k2_lattice3(_257371), the_carrier(_257371), the_carrier(_257371)))], (9189 ^ _115804) ^ [] : [-(v1_partfun1(k2_lattice3(_257371), the_carrier(_257371), the_carrier(_257371)))], (9187 ^ _115804) ^ [] : [-(transitive(k2_lattice3(_257371)))], (9183 ^ _115804) ^ [] : [-(reflexive(k2_lattice3(_257371)))], (9185 ^ _115804) ^ [] : [-(antisymmetric(k2_lattice3(_257371)))]], -(empty_carrier(_257371)), lattice(_257371), latt_str(_257371)], (9259 ^ _115804) ^ [_258585] : [-(element(cast_to_subset(_258585), powerset(_258585)))], (488 ^ _115804) ^ [_122154, _122156] : [-(complemented_relstr(_122154)), _122156 = _122154, complemented_relstr(_122156)], (3316 ^ _115804) ^ [_163008] : [3323 ^ _115804 : [(3328 ^ _115804) ^ [] : [-(ordinal(_163008))], (3324 ^ _115804) ^ [] : [-(epsilon_transitive(_163008))], (3326 ^ _115804) ^ [] : [-(epsilon_connected(_163008))], (3330 ^ _115804) ^ [] : [-(natural(_163008))]], empty(_163008), ordinal(_163008)], (1028 ^ _115804) ^ [_129418, _129420, _129422, _129424] : [-(open_subset(_129422, _129418)), open_subset(_129424, _129420), _129424 = _129422, _129420 = _129418], (6845 ^ _115804) ^ [_218993] : [top_str(_218993), 6848 ^ _115804 : [(6849 ^ _115804) ^ [] : [compact_top_space(_218993), 6852 ^ _115804 : [(6853 ^ _115804) ^ [_219157] : [element(_219157, powerset(powerset(the_carrier(_218993)))), is_a_cover_of_carrier(_218993, _219157), open_subsets(_219157, _218993), 6865 ^ _115804 : [(6870 ^ _115804) ^ [] : [-(is_a_cover_of_carrier(_218993, 6864 ^ [_218993, _219157]))], (6866 ^ _115804) ^ [] : [-(element(6864 ^ [_218993, _219157], powerset(powerset(the_carrier(_218993)))))], (6868 ^ _115804) ^ [] : [-(subset(6864 ^ [_218993, _219157], _219157))], (6872 ^ _115804) ^ [] : [-(finite(6864 ^ [_218993, _219157]))]]]]], (6874 ^ _115804) ^ [] : [-(compact_top_space(_218993)), 6876 ^ _115804 : [(6881 ^ _115804) ^ [] : [-(open_subsets(6875 ^ [_218993], _218993))], (6877 ^ _115804) ^ [] : [-(element(6875 ^ [_218993], powerset(powerset(the_carrier(_218993)))))], (6879 ^ _115804) ^ [] : [-(is_a_cover_of_carrier(_218993, 6875 ^ [_218993]))], (6883 ^ _115804) ^ [_219628] : [element(_219628, powerset(powerset(the_carrier(_218993)))), subset(_219628, 6875 ^ [_218993]), is_a_cover_of_carrier(_218993, _219628), finite(_219628)]]]]], (12291 ^ _115804) ^ [_299198, _299200] : [-(relation_of2(12289 ^ [_299198, _299200], _299200, _299198))], (782 ^ _115804) ^ [_126051, _126053] : [-(meet_absorbing(_126051)), _126053 = _126051, meet_absorbing(_126053)], (10515 ^ _115804) ^ [_275351, _275353] : [v1_membered(_275353), -(v1_membered(set_intersection2(_275351, _275353)))], (8724 ^ _115804) ^ [_251152] : [rel_str(_251152), 8727 ^ _115804 : [(8728 ^ _115804) ^ [_251261, _251263] : [element(_251261, the_carrier(_251152)), ex_sup_of_relstr_set(_251152, _251263), 8735 ^ _115804 : [(8752 ^ _115804) ^ [] : [-(_251261 = join_on_relstr(_251152, _251263)), relstr_set_smaller(_251152, _251263, _251261), 8758 ^ _115804 : [(8759 ^ _115804) ^ [] : [-(element(8757 ^ [_251152, _251261, _251263], the_carrier(_251152)))], (8763 ^ _115804) ^ [] : [related(_251152, _251261, 8757 ^ [_251152, _251261, _251263])], (8761 ^ _115804) ^ [] : [-(relstr_set_smaller(_251152, _251263, 8757 ^ [_251152, _251261, _251263]))]]], (8736 ^ _115804) ^ [] : [_251261 = join_on_relstr(_251152, _251263), 8739 ^ _115804 : [(8740 ^ _115804) ^ [] : [-(relstr_set_smaller(_251152, _251263, _251261))], (8742 ^ _115804) ^ [_251488] : [element(_251488, the_carrier(_251152)), relstr_set_smaller(_251152, _251263, _251488), -(related(_251152, _251261, _251488))]]]]]]], (12643 ^ _115804) ^ [_303004] : [-(element(12641 ^ [_303004], powerset(_303004)))], (990 ^ _115804) ^ [_128899, _128901] : [-(transitive(_128899)), _128901 = _128899, transitive(_128901)], (12489 ^ _115804) ^ [] : [-(distributive_relstr(12465 ^ []))], (10637 ^ _115804) ^ [_276883] : [-(relation(identity_relation(_276883)))], (13434 ^ _115804) ^ [_313865, _313867] : [ordinal(_313867), ordinal(_313865), 13441 ^ _115804 : [(13442 ^ _115804) ^ [] : [ordinal_subset(_313867, _313865), -(subset(_313867, _313865))], (13448 ^ _115804) ^ [] : [subset(_313867, _313865), -(ordinal_subset(_313867, _313865))]]], (8292 ^ _115804) ^ [_243268] : [relation(_243268), 8295 ^ _115804 : [(8296 ^ _115804) ^ [_243381] : [relation(_243381), 8299 ^ _115804 : [(8300 ^ _115804) ^ [_243486] : [relation(_243486), 8303 ^ _115804 : [(8327 ^ _115804) ^ [] : [-(_243486 = relation_composition(_243268, _243381)), 8341 ^ _115804 : [(8342 ^ _115804) ^ [] : [-(in(ordered_pair(8328 ^ [_243268, _243381, _243486], 8340 ^ [_243268, _243381, _243486]), _243268))], (8346 ^ _115804) ^ [] : [in(ordered_pair(8328 ^ [_243268, _243381, _243486], 8329 ^ [_243268, _243381, _243486]), _243486)], (8344 ^ _115804) ^ [] : [-(in(ordered_pair(8340 ^ [_243268, _243381, _243486], 8329 ^ [_243268, _243381, _243486]), _243381))]], 8332 ^ _115804 : [(8333 ^ _115804) ^ [] : [-(in(ordered_pair(8328 ^ [_243268, _243381, _243486], 8329 ^ [_243268, _243381, _243486]), _243486))], (8335 ^ _115804) ^ [_244142] : [in(ordered_pair(8328 ^ [_243268, _243381, _243486], _244142), _243268), in(ordered_pair(_244142, 8329 ^ [_243268, _243381, _243486]), _243381)]]], (8304 ^ _115804) ^ [] : [_243486 = relation_composition(_243268, _243381), 8307 ^ _115804 : [(8308 ^ _115804) ^ [_243656, _243658] : [in(ordered_pair(_243658, _243656), _243486), 8312 ^ _115804 : [(8313 ^ _115804) ^ [] : [-(in(ordered_pair(_243658, 8311 ^ [_243268, _243381, _243486, _243656, _243658]), _243268))], (8315 ^ _115804) ^ [] : [-(in(ordered_pair(8311 ^ [_243268, _243381, _243486, _243656, _243658], _243656), _243381))]]], (8317 ^ _115804) ^ [_243810, _243812] : [-(in(ordered_pair(_243812, _243810), _243486)), 8318 ^ _115804 : [(8319 ^ _115804) ^ [_243865] : [in(ordered_pair(_243812, _243865), _243268), in(ordered_pair(_243865, _243810), _243381)]]]]]]]]]]], (8971 ^ _115804) ^ [] : [true___, -(true___)], (11427 ^ _115804) ^ [_287352] : [-(complete_relstr(boole_POSet(_287352)))], (7643 ^ _115804) ^ [_231649] : [relation(_231649), 7646 ^ _115804 : [(7647 ^ _115804) ^ [_231744] : [well_orders(_231649, _231744), 7650 ^ _115804 : [(7659 ^ _115804) ^ [] : [-(is_well_founded_in(_231649, _231744))], (7657 ^ _115804) ^ [] : [-(is_connected_in(_231649, _231744))], (7655 ^ _115804) ^ [] : [-(is_antisymmetric_in(_231649, _231744))], (7651 ^ _115804) ^ [] : [-(is_reflexive_in(_231649, _231744))], (7653 ^ _115804) ^ [] : [-(is_transitive_in(_231649, _231744))]]], (7661 ^ _115804) ^ [_231915] : [-(well_orders(_231649, _231915)), is_reflexive_in(_231649, _231915), is_transitive_in(_231649, _231915), is_antisymmetric_in(_231649, _231915), is_connected_in(_231649, _231915), is_well_founded_in(_231649, _231915)]]], (3056 ^ _115804) ^ [_159778] : [empty(_159778), -(function(_159778))], (1178 ^ _115804) ^ [_131489, _131491, _131493, _131495, _131497, _131499] : [-(relstr_element_smaller(_131497, _131493, _131489)), relstr_element_smaller(_131499, _131495, _131491), _131499 = _131497, _131495 = _131493, _131491 = _131489], (8399 ^ _115804) ^ [_245355, _245357] : [element(_245355, powerset(powerset(_245357))), 8402 ^ _115804 : [(8403 ^ _115804) ^ [_245461] : [element(_245461, powerset(powerset(_245357))), 8406 ^ _115804 : [(8427 ^ _115804) ^ [] : [-(_245461 = complements_of_subsets(_245357, _245355)), 8429 ^ _115804 : [(8430 ^ _115804) ^ [] : [-(element(8428 ^ [_245355, _245357, _245461], powerset(_245357)))], (8432 ^ _115804) ^ [] : [8433 ^ _115804 : [(8434 ^ _115804) ^ [] : [-(in(8428 ^ [_245355, _245357, _245461], _245461))], (8436 ^ _115804) ^ [] : [in(subset_complement(_245357, 8428 ^ [_245355, _245357, _245461]), _245355)]], 8437 ^ _115804 : [(8438 ^ _115804) ^ [] : [-(in(subset_complement(_245357, 8428 ^ [_245355, _245357, _245461]), _245355))], (8440 ^ _115804) ^ [] : [in(8428 ^ [_245355, _245357, _245461], _245461)]]]]], (8407 ^ _115804) ^ [] : [_245461 = complements_of_subsets(_245357, _245355), 8410 ^ _115804 : [(8411 ^ _115804) ^ [_245612] : [element(_245612, powerset(_245357)), 8414 ^ _115804 : [(8415 ^ _115804) ^ [] : [in(_245612, _245461), -(in(subset_complement(_245357, _245612), _245355))], (8421 ^ _115804) ^ [] : [in(subset_complement(_245357, _245612), _245355), -(in(_245612, _245461))]]]]]]]]], (1196 ^ _115804) ^ [_131758, _131760, _131762, _131764, _131766, _131768] : [-(point_neighbourhood(_131766, _131762, _131758)), point_neighbourhood(_131768, _131764, _131760), _131768 = _131766, _131764 = _131762, _131760 = _131758], (3726 ^ _115804) ^ [_168100] : [v2_membered(_168100), -(v1_membered(_168100))], (10441 ^ _115804) ^ [] : [-(empty(empty_set))], (7553 ^ _115804) ^ [_230217] : [-(_230217 = omega), in(empty_set, _230217), being_limit_ordinal(_230217), ordinal(_230217), 7567 ^ _115804 : [(7572 ^ _115804) ^ [] : [-(being_limit_ordinal(7566 ^ [_230217]))], (7568 ^ _115804) ^ [] : [-(ordinal(7566 ^ [_230217]))], (7570 ^ _115804) ^ [] : [-(in(empty_set, 7566 ^ [_230217]))], (7574 ^ _115804) ^ [] : [subset(_230217, 7566 ^ [_230217])]]], (430 ^ _115804) ^ [_121385, _121387] : [-(epsilon_connected(_121385)), _121387 = _121385, epsilon_connected(_121387)], (12598 ^ _115804) ^ [] : [-(with_infima_relstr(12582 ^ []))], (2350 ^ _115804) ^ [_149678, _149680, _149682, _149684] : [-(complements_of_subsets(_149684, _149680) = complements_of_subsets(_149682, _149678)), _149684 = _149682, _149680 = _149678], (16560 ^ _115804) ^ [_379508, _379510] : [disjoint(_379510, _379508), -(disjoint(_379508, _379510))], (12355 ^ _115804) ^ [] : [-(empty(12347 ^ []))], (11429 ^ _115804) ^ [_287396, _287398] : [-(finite(set_union2(_287398, _287396))), finite(_287398), finite(_287396)], (3028 ^ _115804) ^ [_159419] : [ordinal(_159419), 3031 ^ _115804 : [(3032 ^ _115804) ^ [_159487] : [element(_159487, _159419), 3035 ^ _115804 : [(3036 ^ _115804) ^ [] : [-(epsilon_transitive(_159487))], (3040 ^ _115804) ^ [] : [-(ordinal(_159487))], (3038 ^ _115804) ^ [] : [-(epsilon_connected(_159487))]]]]], (10025 ^ _115804) ^ [] : [-(one_sorted_str(10023 ^ []))], (19014 ^ _115804) ^ [_418263] : [top_str(_418263), 19017 ^ _115804 : [(19018 ^ _115804) ^ [_418375] : [element(_418375, powerset(the_carrier(_418263))), 19021 ^ _115804 : [(19022 ^ _115804) ^ [_418484] : [in(_418484, the_carrier(_418263)), 19025 ^ _115804 : [(19044 ^ _115804) ^ [] : [19046 ^ _115804 : [(19051 ^ _115804) ^ [] : [-(subset(_418375, 19045 ^ [_418263, _418375, _418484]))], (19047 ^ _115804) ^ [] : [-(element(19045 ^ [_418263, _418375, _418484], powerset(the_carrier(_418263))))], (19049 ^ _115804) ^ [] : [-(closed_subset(19045 ^ [_418263, _418375, _418484], _418263))], (19053 ^ _115804) ^ [] : [in(_418484, 19045 ^ [_418263, _418375, _418484])]], -(in(_418484, topstr_closure(_418263, _418375)))], (19026 ^ _115804) ^ [] : [in(_418484, topstr_closure(_418263, _418375)), 19029 ^ _115804 : [(19030 ^ _115804) ^ [_418636] : [element(_418636, powerset(the_carrier(_418263))), -(in(_418484, _418636)), closed_subset(_418636, _418263), subset(_418375, _418636)]]]]]]]]], (1674 ^ _115804) ^ [_139036, _139038] : [_139038 = _139036, -(the_topology(_139038) = the_topology(_139036))], (17725 ^ _115804) ^ [_398624, _398626] : [relation(_398624), reflexive(_398624), -(reflexive(relation_restriction(_398624, _398626)))], (11203 ^ _115804) ^ [_284474] : [11218 ^ _115804 : [(11221 ^ _115804) ^ [] : [-(strict_rel_str(poset_of_lattice(_284474)))], (11237 ^ _115804) ^ [] : [-(with_infima_relstr(poset_of_lattice(_284474)))], (11231 ^ _115804) ^ [] : [-(upper_bounded_relstr(poset_of_lattice(_284474)))], (11223 ^ _115804) ^ [] : [-(reflexive_relstr(poset_of_lattice(_284474)))], (11233 ^ _115804) ^ [] : [-(bounded_relstr(poset_of_lattice(_284474)))], (11227 ^ _115804) ^ [] : [-(antisymmetric_relstr(poset_of_lattice(_284474)))], (11225 ^ _115804) ^ [] : [-(transitive_relstr(poset_of_lattice(_284474)))], (11235 ^ _115804) ^ [] : [-(with_suprema_relstr(poset_of_lattice(_284474)))], (11229 ^ _115804) ^ [] : [-(lower_bounded_relstr(poset_of_lattice(_284474)))], (11239 ^ _115804) ^ [] : [-(complete_relstr(poset_of_lattice(_284474)))], (11219 ^ _115804) ^ [] : [empty_carrier(poset_of_lattice(_284474))]], -(empty_carrier(_284474)), lattice(_284474), complete_latt_str(_284474), latt_str(_284474)], (12278 ^ _115804) ^ [] : [-(natural(12268 ^ []))], (6477 ^ _115804) ^ [_213069] : [6479 ^ _115804 : [(6480 ^ _115804) ^ [] : [-(in(6478 ^ [_213069], _213069))], (6482 ^ _115804) ^ [] : [subset(6478 ^ [_213069], _213069)]], -(epsilon_transitive(_213069))], (9827 ^ _115804) ^ [_266395] : [top_str(_266395), -(one_sorted_str(_266395))], (324 ^ _115804) ^ [_119972, _119974] : [-(v1_yellow_3(_119972)), _119974 = _119972, v1_yellow_3(_119974)], (12174 ^ _115804) ^ [] : [-(join_associative(12164 ^ []))], (16862 ^ _115804) ^ [_383906] : [one_sorted_str(_383906), 16865 ^ _115804 : [(16866 ^ _115804) ^ [_383980] : [element(_383980, powerset(powerset(the_carrier(_383906)))), 16869 ^ _115804 : [(16870 ^ _115804) ^ [] : [finite(complements_of_subsets(the_carrier(_383906), _383980)), -(finite(_383980))], (16876 ^ _115804) ^ [] : [finite(_383980), -(finite(complements_of_subsets(the_carrier(_383906), _383980)))]]]]], (2666 ^ _115804) ^ [_154747] : [latt_str(_154747), strict_latt_str(_154747), -(_154747 = latt_str_of(the_carrier(_154747), the_L_join(_154747), the_L_meet(_154747)))], (16566 ^ _115804) ^ [_379585, _379587] : [equipotent(_379587, _379585), -(equipotent(_379585, _379587))], (6692 ^ _115804) ^ [_216336, _216338, _216340] : [_216336 = set_union2(_216340, _216338), 6695 ^ _115804 : [(6706 ^ _115804) ^ [_216515] : [6707 ^ _115804 : [(6708 ^ _115804) ^ [] : [in(_216515, _216340)], (6710 ^ _115804) ^ [] : [in(_216515, _216338)]], -(in(_216515, _216336))], (6696 ^ _115804) ^ [_216425] : [in(_216425, _216336), -(in(_216425, _216340)), -(in(_216425, _216338))]]], (410 ^ _115804) ^ [_121135, _121137] : [-(v3_waybel_3(_121135)), _121137 = _121135, v3_waybel_3(_121137)], (16734 ^ _115804) ^ [_382003, _382005, _382007] : [relation_of2_as_subset(_382003, _382007, _382005), 16737 ^ _115804 : [(16738 ^ _115804) ^ [] : [-(subset(relation_dom(_382003), _382007))], (16740 ^ _115804) ^ [] : [-(subset(relation_rng(_382003), _382005))]]], (7683 ^ _115804) ^ [_232206] : [-(empty_carrier(_232206)), rel_str(_232206), 7690 ^ _115804 : [(7691 ^ _115804) ^ [] : [directed_relstr(_232206), 7694 ^ _115804 : [(7695 ^ _115804) ^ [_232407] : [element(_232407, the_carrier(_232206)), 7698 ^ _115804 : [(7699 ^ _115804) ^ [_232497] : [element(_232497, the_carrier(_232206)), 7703 ^ _115804 : [(7704 ^ _115804) ^ [] : [-(element(7702 ^ [_232206, _232407, _232497], the_carrier(_232206)))], (7708 ^ _115804) ^ [] : [-(related(_232206, _232497, 7702 ^ [_232206, _232407, _232497]))], (7706 ^ _115804) ^ [] : [-(related(_232206, _232407, 7702 ^ [_232206, _232407, _232497]))]]]]]]], (7710 ^ _115804) ^ [] : [-(directed_relstr(_232206)), 7712 ^ _115804 : [(7713 ^ _115804) ^ [] : [-(element(7711 ^ [_232206], the_carrier(_232206)))], (7718 ^ _115804) ^ [_232829] : [element(_232829, the_carrier(_232206)), related(_232206, 7711 ^ [_232206], _232829), related(_232206, 7714 ^ [_232206], _232829)], (7716 ^ _115804) ^ [] : [-(element(7714 ^ [_232206], the_carrier(_232206)))]]]]], (10393 ^ _115804) ^ [_273704] : [-(lower_bounded_relstr(boole_POSet(_273704)))], (6213 ^ _115804) ^ [_208782] : [_208782 = empty_set, 6216 ^ _115804 : [(6217 ^ _115804) ^ [_208843] : [in(_208843, _208782)]]], (9849 ^ _115804) ^ [_266662] : [join_semilatt_str(_266662), -(one_sorted_str(_266662))], (18821 ^ _115804) ^ [_415406, _415408] : [-(set_difference(set_union2(_415408, _415406), _415406) = set_difference(_415408, _415406))], (11875 ^ _115804) ^ [_293952, _293954] : [set_difference(_293954, _293952) = empty_set, -(subset(_293954, _293952))], (12188 ^ _115804) ^ [] : [-(upper_bounded_semilattstr(12164 ^ []))], (3922 ^ _115804) ^ [_170578] : [rel_str(_170578), 3953 ^ _115804 : [(3958 ^ _115804) ^ [] : [-(transitive_relstr(_170578))], (3956 ^ _115804) ^ [] : [-(reflexive_relstr(_170578))], (3964 ^ _115804) ^ [] : [-(lower_bounded_relstr(_170578))], (3954 ^ _115804) ^ [] : [empty_carrier(_170578)], (3960 ^ _115804) ^ [] : [-(antisymmetric_relstr(_170578))], (3966 ^ _115804) ^ [] : [-(v3_waybel_3(_170578))], (3962 ^ _115804) ^ [] : [-(with_suprema_relstr(_170578))]], reflexive_relstr(_170578), transitive_relstr(_170578), antisymmetric_relstr(_170578), with_suprema_relstr(_170578), lower_bounded_relstr(_170578), up_complete_relstr(_170578), v2_waybel_3(_170578)], (2130 ^ _115804) ^ [_146336, _146338, _146340, _146342, _146344, _146346] : [-(meet(_146346, _146342, _146338) = meet(_146344, _146340, _146336)), _146346 = _146344, _146342 = _146340, _146338 = _146336], (9839 ^ _115804) ^ [_266525] : [one_sorted_str(_266525), 9842 ^ _115804 : [(9843 ^ _115804) ^ [_266583] : [net_str(_266583, _266525), -(rel_str(_266583))]]], (12925 ^ _115804) ^ [_306390] : [12933 ^ _115804 : [(12934 ^ _115804) ^ [] : [-(element(12932 ^ [_306390], powerset(the_carrier(_306390))))], (12936 ^ _115804) ^ [] : [-(closed_subset(12932 ^ [_306390], _306390))]], topological_space(_306390), top_str(_306390)], (10022 ^ _115804) ^ [] : [-(top_str(10020 ^ []))], (6917 ^ _115804) ^ [_220123] : [-(empty_carrier(_220123)), join_semilatt_str(_220123), 6924 ^ _115804 : [(6925 ^ _115804) ^ [_220259] : [element(_220259, the_carrier(_220123)), 6928 ^ _115804 : [(6929 ^ _115804) ^ [_220339] : [element(_220339, the_carrier(_220123)), 6932 ^ _115804 : [(6933 ^ _115804) ^ [] : [below(_220123, _220259, _220339), -(join(_220123, _220259, _220339) = _220339)], (6939 ^ _115804) ^ [] : [join(_220123, _220259, _220339) = _220339, -(below(_220123, _220259, _220339))]]]]]]], (18708 ^ _115804) ^ [_413882, _413884] : [in(_413884, _413882), -(subset(singleton(_413884), _413882))], (12588 ^ _115804) ^ [] : [-(strict_rel_str(12582 ^ []))], (12715 ^ _115804) ^ [] : [-(up_complete_relstr(12689 ^ []))], (18576 ^ _115804) ^ [_411778, _411780, _411782] : [subset(_411782, _411780), -(subset(set_difference(_411782, _411778), set_difference(_411780, _411778)))], (11421 ^ _115804) ^ [_287293] : [-(bounded_relstr(boole_POSet(_287293)))], (136 ^ _115804) ^ [_117586, _117588] : [-(cup_closed(_117586)), _117588 = _117586, cup_closed(_117588)], (5880 ^ _115804) ^ [_203122, _203124, _203126] : [relation_of2(_203122, _203126, _203124), -(subset(_203122, cartesian_product2(_203126, _203124)))], (11473 ^ _115804) ^ [_287904] : [-(up_complete_relstr(boole_POSet(_287904)))], (1094 ^ _115804) ^ [_130315, _130317, _130319, _130321] : [-(full_subrelstr(_130319, _130315)), full_subrelstr(_130321, _130317), _130321 = _130319, _130317 = _130315], (18748 ^ _115804) ^ [_414471, _414473] : [subset(_414473, singleton(_414471)), -(_414473 = empty_set), -(_414473 = singleton(_414471))], (1360 ^ _115804) ^ [_134046, _134048] : [-(rel_str(_134046)), _134048 = _134046, rel_str(_134048)], (2438 ^ _115804) ^ [_150984, _150986] : [_150986 = _150984, -(function_inverse(_150986) = function_inverse(_150984))], (4140 ^ _115804) ^ [_173277] : [transitive_relstr(_173277), rel_str(_173277), 4147 ^ _115804 : [(4148 ^ _115804) ^ [_173395] : [subrelstr(_173395, _173277), full_subrelstr(_173395, _173277), 4155 ^ _115804 : [(4156 ^ _115804) ^ [] : [-(transitive_relstr(_173395))], (4158 ^ _115804) ^ [] : [-(full_subrelstr(_173395, _173277))]]]]], (17525 ^ _115804) ^ [_395062, _395064] : [relation(_395062), function(_395062), 17532 ^ _115804 : [(17533 ^ _115804) ^ [_395201] : [relation(_395201), function(_395201), 17540 ^ _115804 : [(17541 ^ _115804) ^ [] : [in(_395064, relation_dom(relation_composition(_395201, _395062))), 17544 ^ _115804 : [(17545 ^ _115804) ^ [] : [-(in(_395064, relation_dom(_395201)))], (17547 ^ _115804) ^ [] : [-(in(apply(_395201, _395064), relation_dom(_395062)))]]], (17549 ^ _115804) ^ [] : [-(in(_395064, relation_dom(relation_composition(_395201, _395062)))), in(_395064, relation_dom(_395201)), in(apply(_395201, _395064), relation_dom(_395062))]]]]], (10387 ^ _115804) ^ [_273647] : [-(with_suprema_relstr(boole_POSet(_273647)))], (12344 ^ _115804) ^ [] : [-(ordinal(12338 ^ []))], (5305 ^ _115804) ^ [_193314] : [-(empty_carrier(_193314)), meet_semilatt_str(_193314), lower_bounded_semilattstr(_193314), 5316 ^ _115804 : [(5317 ^ _115804) ^ [_193507] : [element(_193507, the_carrier(_193314)), 5320 ^ _115804 : [(5321 ^ _115804) ^ [] : [_193507 = bottom_of_semilattstr(_193314), 5324 ^ _115804 : [(5325 ^ _115804) ^ [_193653] : [element(_193653, the_carrier(_193314)), 5328 ^ _115804 : [(5329 ^ _115804) ^ [] : [-(meet(_193314, _193507, _193653) = _193507)], (5331 ^ _115804) ^ [] : [-(meet(_193314, _193653, _193507) = _193507)]]]]], (5333 ^ _115804) ^ [] : [-(_193507 = bottom_of_semilattstr(_193314)), 5335 ^ _115804 : [(5336 ^ _115804) ^ [] : [-(element(5334 ^ [_193314, _193507], the_carrier(_193314)))], (5338 ^ _115804) ^ [] : [meet(_193314, _193507, 5334 ^ [_193314, _193507]) = _193507, meet(_193314, 5334 ^ [_193314, _193507], _193507) = _193507]]]]]]], (16809 ^ _115804) ^ [_383200] : [-(empty_carrier(_383200)), topological_space(_383200), top_str(_383200), 16820 ^ _115804 : [(16839 ^ _115804) ^ [] : [16841 ^ _115804 : [(16846 ^ _115804) ^ [] : [-(closed_subsets(16840 ^ [_383200], _383200))], (16842 ^ _115804) ^ [] : [-(element(16840 ^ [_383200], powerset(powerset(the_carrier(_383200)))))], (16844 ^ _115804) ^ [] : [-(centered(16840 ^ [_383200]))], (16848 ^ _115804) ^ [] : [-(meet_of_subsets(the_carrier(_383200), 16840 ^ [_383200]) = empty_set)]], -(compact_top_space(_383200))], (16821 ^ _115804) ^ [] : [compact_top_space(_383200), 16824 ^ _115804 : [(16825 ^ _115804) ^ [_383437] : [element(_383437, powerset(powerset(the_carrier(_383200)))), centered(_383437), closed_subsets(_383437, _383200), meet_of_subsets(the_carrier(_383200), _383437) = empty_set]]]]], (6467 ^ _115804) ^ [_212933] : [epsilon_transitive(_212933), 6470 ^ _115804 : [(6471 ^ _115804) ^ [_212992] : [in(_212992, _212933), -(subset(_212992, _212933))]]], (13819 ^ _115804) ^ [_320752, _320754] : [one_sorted_str(_320754), element(_320752, powerset(powerset(the_carrier(_320754)))), 13831 ^ _115804 : [(13846 ^ _115804) ^ [_321420] : [element(_321420, powerset(the_carrier(_320754))), _321420 = 13828 ^ [_320752, _320754], -(13830 ^ [_320752, _320754] = subset_complement(the_carrier(_320754), _321420))], (13844 ^ _115804) ^ [] : [-(in(13828 ^ [_320752, _320754], _320752))], (13834 ^ _115804) ^ [_321217] : [element(_321217, powerset(the_carrier(_320754))), _321217 = 13828 ^ [_320752, _320754], -(13829 ^ [_320752, _320754] = subset_complement(the_carrier(_320754), _321217))], (13856 ^ _115804) ^ [] : [13829 ^ [_320752, _320754] = 13830 ^ [_320752, _320754]], (13832 ^ _115804) ^ [] : [-(in(13828 ^ [_320752, _320754], _320752))]], 13858 ^ _115804 : [(13863 ^ _115804) ^ [_321783, _321785] : [in(ordered_pair(_321785, _321783), 13857 ^ [_320752, _320754]), 13866 ^ _115804 : [(13867 ^ _115804) ^ [] : [-(in(_321785, _320752))], (13871 ^ _115804) ^ [_321939] : [element(_321939, powerset(the_carrier(_320754))), _321939 = _321785, -(_321783 = subset_complement(the_carrier(_320754), _321939))], (13869 ^ _115804) ^ [] : [-(in(_321785, _320752))]]], (13859 ^ _115804) ^ [] : [-(relation(13857 ^ [_320752, _320754]))], (13861 ^ _115804) ^ [] : [-(function(13857 ^ [_320752, _320754]))], (13881 ^ _115804) ^ [_322102, _322104] : [-(in(ordered_pair(_322104, _322102), 13857 ^ [_320752, _320754])), in(_322104, _320752), in(_322104, _320752), 13891 ^ _115804 : [(13892 ^ _115804) ^ [] : [-(element(13890 ^ [_320752, _320754, _322102, _322104], powerset(the_carrier(_320754))))], (13896 ^ _115804) ^ [] : [_322102 = subset_complement(the_carrier(_320754), 13890 ^ [_320752, _320754, _322102, _322104])], (13894 ^ _115804) ^ [] : [-(13890 ^ [_320752, _320754, _322102, _322104] = _322104)]]]]], (10417 ^ _115804) ^ [_274007] : [-(upper_bounded_relstr(boole_POSet(_274007)))], (15142 ^ _115804) ^ [_350004, _350006] : [one_sorted_str(_350006), element(_350004, powerset(powerset(the_carrier(_350006)))), 15149 ^ _115804 : [(15150 ^ _115804) ^ [_350357] : [15154 ^ _115804 : [(15177 ^ _115804) ^ [] : [-(ordered_pair(15174 ^ [_350004, _350006, _350357], 15175 ^ [_350004, _350006, _350357]) = 15153 ^ [_350004, _350006, _350357])], (15155 ^ _115804) ^ [] : [-(15151 ^ [_350004, _350006, _350357] = 15152 ^ [_350004, _350006, _350357])], (15163 ^ _115804) ^ [_350990] : [element(_350990, powerset(the_carrier(_350006))), _350990 = 15156 ^ [_350004, _350006, _350357], -(15157 ^ [_350004, _350006, _350357] = subset_complement(the_carrier(_350006), _350990))], (15159 ^ _115804) ^ [] : [-(ordered_pair(15156 ^ [_350004, _350006, _350357], 15157 ^ [_350004, _350006, _350357]) = 15152 ^ [_350004, _350006, _350357])], (15173 ^ _115804) ^ [] : [-(15151 ^ [_350004, _350006, _350357] = 15153 ^ [_350004, _350006, _350357])], (15161 ^ _115804) ^ [] : [-(in(15156 ^ [_350004, _350006, _350357], _350004))], (15181 ^ _115804) ^ [_351367] : [element(_351367, powerset(the_carrier(_350006))), _351367 = 15174 ^ [_350004, _350006, _350357], -(15175 ^ [_350004, _350006, _350357] = subset_complement(the_carrier(_350006), _351367))], (15179 ^ _115804) ^ [] : [-(in(15174 ^ [_350004, _350006, _350357], _350004))], (15191 ^ _115804) ^ [] : [15152 ^ [_350004, _350006, _350357] = 15153 ^ [_350004, _350006, _350357]]], 15193 ^ _115804 : [(15194 ^ _115804) ^ [_351711] : [in(_351711, 15192 ^ [_350004, _350006, _350357]), 15198 ^ _115804 : [(15209 ^ _115804) ^ [_352147] : [element(_352147, powerset(the_carrier(_350006))), _352147 = 15202 ^ [_350004, _350006, _350357, _351711], -(15203 ^ [_350004, _350006, _350357, _351711] = subset_complement(the_carrier(_350006), _352147))], (15207 ^ _115804) ^ [] : [-(in(15202 ^ [_350004, _350006, _350357, _351711], _350004))], (15205 ^ _115804) ^ [] : [-(ordered_pair(15202 ^ [_350004, _350006, _350357, _351711], 15203 ^ [_350004, _350006, _350357, _351711]) = _351711)], (15199 ^ _115804) ^ [] : [-(in(15197 ^ [_350004, _350006, _350357, _351711], cartesian_product2(_350004, _350357)))], (15201 ^ _115804) ^ [] : [-(15197 ^ [_350004, _350006, _350357, _351711] = _351711)]]], (15219 ^ _115804) ^ [_352358] : [-(in(_352358, 15192 ^ [_350004, _350006, _350357])), 15220 ^ _115804 : [(15221 ^ _115804) ^ [_352471] : [in(_352471, cartesian_product2(_350004, _350357)), _352471 = _352358, 15228 ^ _115804 : [(15229 ^ _115804) ^ [_352642, _352644] : [ordered_pair(_352644, _352642) = _352358, in(_352644, _350004), 15237 ^ _115804 : [(15238 ^ _115804) ^ [] : [-(element(15236 ^ [_350004, _350006, _350357, _352358, _352471, _352642, _352644], powerset(the_carrier(_350006))))], (15242 ^ _115804) ^ [] : [_352642 = subset_complement(the_carrier(_350006), 15236 ^ [_350004, _350006, _350357, _352358, _352471, _352642, _352644])], (15240 ^ _115804) ^ [] : [-(15236 ^ [_350004, _350006, _350357, _352358, _352471, _352642, _352644] = _352644)]]]]]]]]]]], (18453 ^ _115804) ^ [_409842] : [-(empty_carrier(_409842)), lattice(_409842), latt_str(_409842), 18464 ^ _115804 : [(18465 ^ _115804) ^ [_410033] : [element(_410033, the_carrier(_409842)), 18468 ^ _115804 : [(18469 ^ _115804) ^ [_410120] : [element(_410120, the_carrier(_409842)), 18472 ^ _115804 : [(18473 ^ _115804) ^ [] : [in(ordered_pair_as_product_element(the_carrier(_409842), the_carrier(_409842), _410033, _410120), relation_of_lattice(_409842)), -(below_refl(_409842, _410033, _410120))], (18479 ^ _115804) ^ [] : [below_refl(_409842, _410033, _410120), -(in(ordered_pair_as_product_element(the_carrier(_409842), the_carrier(_409842), _410033, _410120), relation_of_lattice(_409842)))]]]]]]], (2690 ^ _115804) ^ [_155093, _155095] : [in(_155095, _155093), in(_155093, _155095)], (20011 ^ _115804) ^ [_434304] : [-(relation_dom(identity_relation(_434304)) = _434304)], (3404 ^ _115804) ^ [_164109] : [latt_str(_164109), 3435 ^ _115804 : [(3436 ^ _115804) ^ [] : [empty_carrier(_164109)], (3438 ^ _115804) ^ [] : [-(lattice(_164109))]], -(empty_carrier(_164109)), join_commutative(_164109), join_associative(_164109), meet_commutative(_164109), meet_associative(_164109), meet_absorbing(_164109), join_absorbing(_164109)], (12340 ^ _115804) ^ [] : [-(epsilon_transitive(12338 ^ []))], (12703 ^ _115804) ^ [] : [-(with_suprema_relstr(12689 ^ []))], (9005 ^ _115804) ^ [] : [true___, -(true___)], (16057 ^ _115804) ^ [_369381, _369383, _369385] : [-(empty_carrier(_369385)), transitive_relstr(_369385), rel_str(_369385), element(_369383, powerset(the_carrier(_369385))), finite(_369381), element(_369381, powerset(_369383)), 16122 ^ _115804 : [(16123 ^ _115804) ^ [] : [-(element(16121 ^ [_369381, _369383, _369385], the_carrier(_369385)))], (16127 ^ _115804) ^ [] : [-(relstr_set_smaller(_369385, _369381, 16121 ^ [_369381, _369383, _369385]))], (16125 ^ _115804) ^ [] : [-(in(16121 ^ [_369381, _369383, _369385], _369383))]], finite(_369381), 16088 ^ _115804 : [(16089 ^ _115804) ^ [_369933] : [element(_369933, the_carrier(_369385)), in(_369933, _369383), relstr_set_smaller(_369385, empty_set, _369933)]], 16100 ^ _115804 : [(16106 ^ _115804) ^ [] : [-(element(16104 ^ [_369381, _369383, _369385], the_carrier(_369385)))], (16103 ^ _115804) ^ [] : [-(subset(16099 ^ [_369381, _369383, _369385], _369381))], (16110 ^ _115804) ^ [] : [-(relstr_set_smaller(_369385, 16099 ^ [_369381, _369383, _369385], 16104 ^ [_369381, _369383, _369385]))], (16112 ^ _115804) ^ [_370276] : [element(_370276, the_carrier(_369385)), in(_370276, _369383), relstr_set_smaller(_369385, set_union2(16099 ^ [_369381, _369383, _369385], singleton(16098 ^ [_369381, _369383, _369385])), _370276)], (16101 ^ _115804) ^ [] : [-(in(16098 ^ [_369381, _369383, _369385], _369381))], (16108 ^ _115804) ^ [] : [-(in(16104 ^ [_369381, _369383, _369385], _369383))]]], (10529 ^ _115804) ^ [_275539] : [10536 ^ _115804 : [(10545 ^ _115804) ^ [] : [-(natural(succ(_275539)))], (10543 ^ _115804) ^ [] : [-(ordinal(succ(_275539)))], (10541 ^ _115804) ^ [] : [-(epsilon_connected(succ(_275539)))], (10537 ^ _115804) ^ [] : [empty(succ(_275539))], (10539 ^ _115804) ^ [] : [-(epsilon_transitive(succ(_275539)))]], ordinal(_275539), natural(_275539)], (7181 ^ _115804) ^ [_224380] : [-(ordinal(_224380)), epsilon_transitive(_224380), epsilon_connected(_224380)], (8947 ^ _115804) ^ [] : [true___, -(true___)], (10481 ^ _115804) ^ [_274871, _274873, _274875] : [10504 ^ _115804 : [(10505 ^ _115804) ^ [] : [empty_carrier(netstr_restr_to_element(_274875, _274873, _274871))], (10507 ^ _115804) ^ [] : [-(strict_net_str(netstr_restr_to_element(_274875, _274873, _274871), _274875))]], -(empty_carrier(_274875)), one_sorted_str(_274875), -(empty_carrier(_274873)), directed_relstr(_274873), net_str(_274873, _274875), element(_274871, the_carrier(_274873))]], input).
% 239.64/231.42  ncf('1',plain,[-(directed_relstr(20422 ^ []))],start(20428 ^ 0)).
% 239.64/231.42  ncf('1.1',plain,[directed_relstr(20422 ^ []), 18086 : is_eventually_in(20415 ^ [], 20422 ^ [], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []]), 18086 : -(is_often_in(20415 ^ [], 20422 ^ [], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []])), 18086 : -(empty_carrier(20422 ^ [])), 18086 : transitive_relstr(20422 ^ []), 18086 : net_str(20422 ^ [], 20415 ^ []), 18070 : -(empty_carrier(20415 ^ [])), 18070 : one_sorted_str(20415 ^ [])],extension(18062 ^ 1,bind([[_403710, _403850, _404068], [20415 ^ [], 20422 ^ [], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []]]]))).
% 239.64/231.42  ncf('1.1.1',plain,[-(is_eventually_in(20415 ^ [], 20422 ^ [], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []])), 5443 : point_neighbourhood(8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []], 20415 ^ [], 20431 ^ []), 5443 : in(20431 ^ [], lim_points_of_net(20415 ^ [], 20422 ^ [])), 5439 : element(20431 ^ [], the_carrier(20415 ^ [])), 5435 : lim_points_of_net(20415 ^ [], 20422 ^ []) = lim_points_of_net(20415 ^ [], 20422 ^ []), 5431 : element(lim_points_of_net(20415 ^ [], 20422 ^ []), powerset(the_carrier(20415 ^ []))), 5427 : -(empty_carrier(20422 ^ [])), 5427 : transitive_relstr(20422 ^ []), 5427 : directed_relstr(20422 ^ []), 5427 : net_str(20422 ^ [], 20415 ^ []), 5411 : -(empty_carrier(20415 ^ [])), 5411 : topological_space(20415 ^ []), 5411 : top_str(20415 ^ [])],extension(5399 ^ 6,bind([[_194870, _195101, _195362, _195523, _195659], [20415 ^ [], 20422 ^ [], lim_points_of_net(20415 ^ [], 20422 ^ []), 20431 ^ [], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []]]]))).
% 239.64/231.42  ncf('1.1.1.1',plain,[-(point_neighbourhood(8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []], 20415 ^ [], 20431 ^ [])), 8715 : -(is_a_cluster_point_of_netstr(20415 ^ [], 20422 ^ [], 20431 ^ [])), 8715 : element(20431 ^ [], the_carrier(20415 ^ [])), 8701 : -(empty_carrier(20422 ^ [])), 8701 : net_str(20422 ^ [], 20415 ^ []), 8693 : -(empty_carrier(20415 ^ [])), 8693 : topological_space(20415 ^ []), 8693 : top_str(20415 ^ [])],extension(8681 ^ 19,bind([[_250443, _250641, _250779], [20415 ^ [], 20422 ^ [], 20431 ^ []]]))).
% 239.64/231.42  ncf('1.1.1.1.1',plain,[is_a_cluster_point_of_netstr(20415 ^ [], 20422 ^ [], 20431 ^ [])],extension(20437 ^ 26)).
% 239.64/231.42  ncf('1.1.1.1.2',plain,[-(element(20431 ^ [], the_carrier(20415 ^ [])))],extension(20433 ^ 24)).
% 239.64/231.42  ncf('1.1.1.1.3',plain,[empty_carrier(20422 ^ [])],extension(20424 ^ 22)).
% 239.64/231.42  ncf('1.1.1.1.4',plain,[-(net_str(20422 ^ [], 20415 ^ []))],extension(20430 ^ 22)).
% 239.64/231.42  ncf('1.1.1.1.5',plain,[empty_carrier(20415 ^ [])],extension(20417 ^ 20)).
% 239.64/231.42  ncf('1.1.1.1.6',plain,[-(topological_space(20415 ^ []))],extension(20419 ^ 20)).
% 239.64/231.42  ncf('1.1.1.1.7',plain,[-(top_str(20415 ^ []))],extension(20421 ^ 20)).
% 239.64/231.42  ncf('1.1.1.2',plain,[-(in(20431 ^ [], lim_points_of_net(20415 ^ [], 20422 ^ [])))],extension(20435 ^ 17)).
% 239.64/231.42  ncf('1.1.1.3',plain,[-(element(20431 ^ [], the_carrier(20415 ^ [])))],extension(20433 ^ 15)).
% 239.64/231.42  ncf('1.1.1.4',plain,[-(lim_points_of_net(20415 ^ [], 20422 ^ []) = lim_points_of_net(20415 ^ [], 20422 ^ []))],extension(2 ^ 13,bind([[_115831], [lim_points_of_net(20415 ^ [], 20422 ^ [])]]))).
% 239.64/231.42  ncf('1.1.1.5',plain,[-(element(lim_points_of_net(20415 ^ [], 20422 ^ []), powerset(the_carrier(20415 ^ [])))), -(empty_carrier(20415 ^ [])), topological_space(20415 ^ []), top_str(20415 ^ []), -(empty_carrier(20422 ^ [])), transitive_relstr(20422 ^ []), directed_relstr(20422 ^ []), net_str(20422 ^ [], 20415 ^ [])],extension(8897 ^ 11,bind([[_253777, _253779], [20422 ^ [], 20415 ^ []]]))).
% 239.64/231.42  ncf('1.1.1.5.1',plain,[empty_carrier(20415 ^ [])],extension(20417 ^ 12)).
% 239.64/231.42  ncf('1.1.1.5.2',plain,[-(topological_space(20415 ^ []))],extension(20419 ^ 12)).
% 239.64/231.42  ncf('1.1.1.5.3',plain,[-(top_str(20415 ^ []))],extension(20421 ^ 12)).
% 239.64/231.42  ncf('1.1.1.5.4',plain,[empty_carrier(20422 ^ [])],extension(20424 ^ 12)).
% 239.64/231.42  ncf('1.1.1.5.5',plain,[-(transitive_relstr(20422 ^ []))],extension(20426 ^ 12)).
% 239.64/231.42  ncf('1.1.1.5.6',plain,[-(directed_relstr(20422 ^ []))],reduction('1')).
% 239.64/231.42  ncf('1.1.1.5.7',plain,[-(net_str(20422 ^ [], 20415 ^ []))],extension(20430 ^ 12)).
% 239.64/231.42  ncf('1.1.1.6',plain,[empty_carrier(20422 ^ [])],extension(20424 ^ 9)).
% 239.64/231.42  ncf('1.1.1.7',plain,[-(transitive_relstr(20422 ^ []))],extension(20426 ^ 9)).
% 239.64/231.42  ncf('1.1.1.8',plain,[-(directed_relstr(20422 ^ []))],reduction('1')).
% 239.64/231.42  ncf('1.1.1.9',plain,[-(net_str(20422 ^ [], 20415 ^ []))],extension(20430 ^ 9)).
% 239.64/231.42  ncf('1.1.1.10',plain,[empty_carrier(20415 ^ [])],extension(20417 ^ 7)).
% 239.64/231.42  ncf('1.1.1.11',plain,[-(topological_space(20415 ^ []))],extension(20419 ^ 7)).
% 239.64/231.42  ncf('1.1.1.12',plain,[-(top_str(20415 ^ []))],extension(20421 ^ 7)).
% 239.64/231.42  ncf('1.1.2',plain,[is_often_in(20415 ^ [], 20422 ^ [], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []]), -(is_often_in(20415 ^ [], 20422 ^ [], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []])), 20415 ^ [] = 20415 ^ [], 20422 ^ [] = 20422 ^ [], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []] = 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []]],extension(1312 ^ 6,bind([[_133402, _133404, _133406, _133408, _133410, _133412], [8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []], 20422 ^ [], 20422 ^ [], 20415 ^ [], 20415 ^ []]]))).
% 239.64/231.42  ncf('1.1.2.1',plain,[is_often_in(20415 ^ [], 20422 ^ [], 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []]), 8715 : -(is_a_cluster_point_of_netstr(20415 ^ [], 20422 ^ [], 20431 ^ [])), 8715 : element(20431 ^ [], the_carrier(20415 ^ [])), 8701 : -(empty_carrier(20422 ^ [])), 8701 : net_str(20422 ^ [], 20415 ^ []), 8693 : -(empty_carrier(20415 ^ [])), 8693 : topological_space(20415 ^ []), 8693 : top_str(20415 ^ [])],extension(8681 ^ 7,bind([[_250443, _250641, _250779], [20415 ^ [], 20422 ^ [], 20431 ^ []]]))).
% 239.64/231.42  ncf('1.1.2.1.1',plain,[is_a_cluster_point_of_netstr(20415 ^ [], 20422 ^ [], 20431 ^ [])],extension(20437 ^ 14)).
% 239.64/231.42  ncf('1.1.2.1.2',plain,[-(element(20431 ^ [], the_carrier(20415 ^ [])))],extension(20433 ^ 12)).
% 239.64/231.42  ncf('1.1.2.1.3',plain,[empty_carrier(20422 ^ [])],extension(20424 ^ 10)).
% 239.64/231.42  ncf('1.1.2.1.4',plain,[-(net_str(20422 ^ [], 20415 ^ []))],extension(20430 ^ 10)).
% 239.64/231.42  ncf('1.1.2.1.5',plain,[empty_carrier(20415 ^ [])],extension(20417 ^ 8)).
% 239.64/231.42  ncf('1.1.2.1.6',plain,[-(topological_space(20415 ^ []))],extension(20419 ^ 8)).
% 239.64/231.42  ncf('1.1.2.1.7',plain,[-(top_str(20415 ^ []))],extension(20421 ^ 8)).
% 239.64/231.42  ncf('1.1.2.2',plain,[-(20415 ^ [] = 20415 ^ [])],extension(2 ^ 7,bind([[_115831], [20415 ^ []]]))).
% 239.64/231.42  ncf('1.1.2.3',plain,[-(20422 ^ [] = 20422 ^ [])],extension(2 ^ 7,bind([[_115831], [20422 ^ []]]))).
% 239.64/231.42  ncf('1.1.2.4',plain,[-(8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []] = 8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []])],extension(2 ^ 7,bind([[_115831], [8716 ^ [20415 ^ [], 20422 ^ [], 20431 ^ []]]]))).
% 239.64/231.42  ncf('1.1.3',plain,[empty_carrier(20422 ^ [])],extension(20424 ^ 4)).
% 239.64/231.42  ncf('1.1.4',plain,[-(transitive_relstr(20422 ^ []))],extension(20426 ^ 4)).
% 239.64/231.42  ncf('1.1.5',plain,[-(net_str(20422 ^ [], 20415 ^ []))],extension(20430 ^ 4)).
% 239.64/231.42  ncf('1.1.6',plain,[empty_carrier(20415 ^ [])],extension(20417 ^ 2)).
% 239.64/231.42  ncf('1.1.7',plain,[-(one_sorted_str(20415 ^ [])), top_str(20415 ^ [])],extension(9827 ^ 2,bind([[_266395], [20415 ^ []]]))).
% 239.64/231.42  ncf('1.1.7.1',plain,[-(top_str(20415 ^ []))],extension(20421 ^ 3)).
% 239.64/231.42  %-----------------------------------------------------
% 239.64/231.42  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------