%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU261+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n032.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 12:02:55 EDT 2023

% Result   : Theorem 145.72s 141.51s
% Output   : Proof 145.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem  : SEU261+2 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.09  % Command  : nanocop.sh %s %d
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 300
% 0.09/0.28  % DateTime : Thu May 18 13:06:19 EDT 2023
% 0.09/0.28  % CPUTime  : 
% 145.72/141.51  
% 145.72/141.51  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 145.72/141.51  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 145.72/141.51  %-----------------------------------------------------
% 145.72/141.51  ncf(matrix, plain, [(4739 ^ _24642) ^ [] : [-(relation(4737 ^ []))], (4742 ^ _24642) ^ [] : [-(relation(4740 ^ []))], (4745 ^ _24642) ^ [] : [-(relation(4743 ^ []))], (4747 ^ _24642) ^ [] : [-(function(4743 ^ []))], (4749 ^ _24642) ^ [] : [-(well_ordering(4737 ^ []))], (4751 ^ _24642) ^ [] : [-(relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []))], (4753 ^ _24642) ^ [] : [well_ordering(4740 ^ [])], (2 ^ _24642) ^ [_24662, _24664] : [in(_24664, _24662), in(_24662, _24664)], (8 ^ _24642) ^ [_24740, _24742] : [proper_subset(_24742, _24740), proper_subset(_24740, _24742)], (14 ^ _24642) ^ [_24818] : [empty(_24818), -(function(_24818))], (20 ^ _24642) ^ [_24889] : [ordinal(_24889), 23 ^ _24642 : [(24 ^ _24642) ^ [] : [-(epsilon_transitive(_24889))], (26 ^ _24642) ^ [] : [-(epsilon_connected(_24889))]]], (28 ^ _24642) ^ [_24984] : [empty(_24984), -(relation(_24984))], (34 ^ _24642) ^ [_25055] : [45 ^ _24642 : [(46 ^ _24642) ^ [] : [-(relation(_25055))], (48 ^ _24642) ^ [] : [-(function(_25055))], (50 ^ _24642) ^ [] : [-(one_to_one(_25055))]], relation(_25055), empty(_25055), function(_25055)], (52 ^ _24642) ^ [_25268] : [-(ordinal(_25268)), epsilon_transitive(_25268), epsilon_connected(_25268)], (62 ^ _24642) ^ [_25387] : [empty(_25387), 65 ^ _24642 : [(66 ^ _24642) ^ [] : [-(epsilon_transitive(_25387))], (68 ^ _24642) ^ [] : [-(epsilon_connected(_25387))], (70 ^ _24642) ^ [] : [-(ordinal(_25387))]]], (72 ^ _24642) ^ [_25504, _25506] : [-(unordered_pair(_25506, _25504) = unordered_pair(_25504, _25506))], (74 ^ _24642) ^ [_25535, _25537] : [-(set_union2(_25537, _25535) = set_union2(_25535, _25537))], (76 ^ _24642) ^ [_25566, _25568] : [-(set_intersection2(_25568, _25566) = set_intersection2(_25566, _25568))], (78 ^ _24642) ^ [_25662, _25664] : [ordinal(_25664), ordinal(_25662), -(ordinal_subset(_25664, _25662)), -(ordinal_subset(_25662, _25664))], (92 ^ _24642) ^ [_26049, _26051] : [relation(_26049), 95 ^ _24642 : [(118 ^ _24642) ^ [] : [-(_26049 = identity_relation(_26051)), 131 ^ _24642 : [(132 ^ _24642) ^ [] : [-(in(119 ^ [_26049, _26051], _26051))], (134 ^ _24642) ^ [] : [-(119 ^ [_26049, _26051] = 120 ^ [_26049, _26051])], (136 ^ _24642) ^ [] : [in(ordered_pair(119 ^ [_26049, _26051], 120 ^ [_26049, _26051]), _26049)]], 123 ^ _24642 : [(124 ^ _24642) ^ [] : [-(in(ordered_pair(119 ^ [_26049, _26051], 120 ^ [_26049, _26051]), _26049))], (126 ^ _24642) ^ [] : [in(119 ^ [_26049, _26051], _26051), 119 ^ [_26049, _26051] = 120 ^ [_26049, _26051]]]], (96 ^ _24642) ^ [] : [_26049 = identity_relation(_26051), 99 ^ _24642 : [(100 ^ _24642) ^ [_26359, _26361] : [in(ordered_pair(_26361, _26359), _26049), 103 ^ _24642 : [(104 ^ _24642) ^ [] : [-(in(_26361, _26051))], (106 ^ _24642) ^ [] : [-(_26361 = _26359)]]], (108 ^ _24642) ^ [_26622, _26624] : [-(in(ordered_pair(_26624, _26622), _26049)), in(_26624, _26051), _26624 = _26622]]]]], (140 ^ _24642) ^ [_27730, _27732] : [_27732 = _27730, 143 ^ _24642 : [(144 ^ _24642) ^ [] : [-(subset(_27732, _27730))], (146 ^ _24642) ^ [] : [-(subset(_27730, _27732))]]], (148 ^ _24642) ^ [_27967, _27969] : [-(_27969 = _27967), subset(_27969, _27967), subset(_27967, _27969)], (158 ^ _24642) ^ [_28254] : [relation(_28254), 161 ^ _24642 : [(162 ^ _24642) ^ [_28440, _28442] : [relation(_28440), 165 ^ _24642 : [(188 ^ _24642) ^ [] : [-(_28440 = relation_dom_restriction(_28254, _28442)), 201 ^ _24642 : [(202 ^ _24642) ^ [] : [-(in(189 ^ [_28254, _28440, _28442], _28442))], (204 ^ _24642) ^ [] : [-(in(ordered_pair(189 ^ [_28254, _28440, _28442], 190 ^ [_28254, _28440, _28442]), _28254))], (206 ^ _24642) ^ [] : [in(ordered_pair(189 ^ [_28254, _28440, _28442], 190 ^ [_28254, _28440, _28442]), _28440)]], 193 ^ _24642 : [(194 ^ _24642) ^ [] : [-(in(ordered_pair(189 ^ [_28254, _28440, _28442], 190 ^ [_28254, _28440, _28442]), _28440))], (196 ^ _24642) ^ [] : [in(189 ^ [_28254, _28440, _28442], _28442), in(ordered_pair(189 ^ [_28254, _28440, _28442], 190 ^ [_28254, _28440, _28442]), _28254)]]], (166 ^ _24642) ^ [] : [_28440 = relation_dom_restriction(_28254, _28442), 169 ^ _24642 : [(170 ^ _24642) ^ [_28765, _28767] : [in(ordered_pair(_28767, _28765), _28440), 173 ^ _24642 : [(174 ^ _24642) ^ [] : [-(in(_28767, _28442))], (176 ^ _24642) ^ [] : [-(in(ordered_pair(_28767, _28765), _28254))]]], (178 ^ _24642) ^ [_29044, _29046] : [-(in(ordered_pair(_29046, _29044), _28440)), in(_29046, _28442), in(ordered_pair(_29046, _29044), _28254)]]]]]]], (210 ^ _24642) ^ [_30199] : [relation(_30199), function(_30199), 217 ^ _24642 : [(247 ^ _24642) ^ [_31625, _31627] : [-(_31625 = relation_image(_30199, _31627)), 264 ^ _24642 : [(265 ^ _24642) ^ [] : [-(in(263 ^ [_30199, _31625, _31627], relation_dom(_30199)))], (267 ^ _24642) ^ [] : [-(in(263 ^ [_30199, _31625, _31627], _31627))], (269 ^ _24642) ^ [] : [-(248 ^ [_30199, _31625, _31627] = apply(_30199, 263 ^ [_30199, _31625, _31627]))], (271 ^ _24642) ^ [] : [in(248 ^ [_30199, _31625, _31627], _31625)]], 251 ^ _24642 : [(252 ^ _24642) ^ [] : [-(in(248 ^ [_30199, _31625, _31627], _31625))], (254 ^ _24642) ^ [_31945] : [in(_31945, relation_dom(_30199)), in(_31945, _31627), 248 ^ [_30199, _31625, _31627] = apply(_30199, _31945)]]], (218 ^ _24642) ^ [_30497, _30499] : [_30497 = relation_image(_30199, _30499), 221 ^ _24642 : [(222 ^ _24642) ^ [_30697] : [in(_30697, _30497), 226 ^ _24642 : [(227 ^ _24642) ^ [] : [-(in(225 ^ [_30199, _30497, _30499, _30697], relation_dom(_30199)))], (229 ^ _24642) ^ [] : [-(in(225 ^ [_30199, _30497, _30499, _30697], _30499))], (231 ^ _24642) ^ [] : [-(_30697 = apply(_30199, 225 ^ [_30199, _30497, _30499, _30697]))]]], (233 ^ _24642) ^ [_31152] : [-(in(_31152, _30497)), 234 ^ _24642 : [(235 ^ _24642) ^ [_31265] : [in(_31265, relation_dom(_30199)), in(_31265, _30499), _31152 = apply(_30199, _31265)]]]]]]], (275 ^ _24642) ^ [_32755, _32757] : [relation(_32755), 278 ^ _24642 : [(279 ^ _24642) ^ [_32926] : [relation(_32926), 282 ^ _24642 : [(305 ^ _24642) ^ [] : [-(_32926 = relation_rng_restriction(_32757, _32755)), 318 ^ _24642 : [(319 ^ _24642) ^ [] : [-(in(307 ^ [_32755, _32757, _32926], _32757))], (321 ^ _24642) ^ [] : [-(in(ordered_pair(306 ^ [_32755, _32757, _32926], 307 ^ [_32755, _32757, _32926]), _32755))], (323 ^ _24642) ^ [] : [in(ordered_pair(306 ^ [_32755, _32757, _32926], 307 ^ [_32755, _32757, _32926]), _32926)]], 310 ^ _24642 : [(311 ^ _24642) ^ [] : [-(in(ordered_pair(306 ^ [_32755, _32757, _32926], 307 ^ [_32755, _32757, _32926]), _32926))], (313 ^ _24642) ^ [] : [in(307 ^ [_32755, _32757, _32926], _32757), in(ordered_pair(306 ^ [_32755, _32757, _32926], 307 ^ [_32755, _32757, _32926]), _32755)]]], (283 ^ _24642) ^ [] : [_32926 = relation_rng_restriction(_32757, _32755), 286 ^ _24642 : [(287 ^ _24642) ^ [_33253, _33255] : [in(ordered_pair(_33255, _33253), _32926), 290 ^ _24642 : [(291 ^ _24642) ^ [] : [-(in(_33253, _32757))], (293 ^ _24642) ^ [] : [-(in(ordered_pair(_33255, _33253), _32755))]]], (295 ^ _24642) ^ [_33532, _33534] : [-(in(ordered_pair(_33534, _33532), _32926)), in(_33532, _32757), in(ordered_pair(_33534, _33532), _32755)]]]]]]], (327 ^ _24642) ^ [_34678] : [relation(_34678), 330 ^ _24642 : [(331 ^ _24642) ^ [] : [antisymmetric(_34678), -(is_antisymmetric_in(_34678, relation_field(_34678)))], (337 ^ _24642) ^ [] : [is_antisymmetric_in(_34678, relation_field(_34678)), -(antisymmetric(_34678))]]], (343 ^ _24642) ^ [_35109] : [relation(_35109), function(_35109), 350 ^ _24642 : [(373 ^ _24642) ^ [_36148, _36150] : [-(_36148 = relation_inverse_image(_35109, _36150)), 385 ^ _24642 : [(386 ^ _24642) ^ [] : [-(in(374 ^ [_35109, _36148, _36150], relation_dom(_35109)))], (388 ^ _24642) ^ [] : [-(in(apply(_35109, 374 ^ [_35109, _36148, _36150]), _36150))], (390 ^ _24642) ^ [] : [in(374 ^ [_35109, _36148, _36150], _36148)]], 377 ^ _24642 : [(378 ^ _24642) ^ [] : [-(in(374 ^ [_35109, _36148, _36150], _36148))], (380 ^ _24642) ^ [] : [in(374 ^ [_35109, _36148, _36150], relation_dom(_35109)), in(apply(_35109, 374 ^ [_35109, _36148, _36150]), _36150)]]], (351 ^ _24642) ^ [_35396, _35398] : [_35396 = relation_inverse_image(_35109, _35398), 354 ^ _24642 : [(355 ^ _24642) ^ [_35585] : [in(_35585, _35396), 358 ^ _24642 : [(359 ^ _24642) ^ [] : [-(in(_35585, relation_dom(_35109)))], (361 ^ _24642) ^ [] : [-(in(apply(_35109, _35585), _35398))]]], (363 ^ _24642) ^ [_35854] : [-(in(_35854, _35396)), in(_35854, relation_dom(_35109)), in(apply(_35109, _35854), _35398)]]]]], (394 ^ _24642) ^ [_36916] : [relation(_36916), 397 ^ _24642 : [(421 ^ _24642) ^ [_38029, _38031] : [-(_38029 = relation_image(_36916, _38031)), 434 ^ _24642 : [(435 ^ _24642) ^ [] : [-(in(ordered_pair(433 ^ [_36916, _38029, _38031], 422 ^ [_36916, _38029, _38031]), _36916))], (437 ^ _24642) ^ [] : [-(in(433 ^ [_36916, _38029, _38031], _38031))], (439 ^ _24642) ^ [] : [in(422 ^ [_36916, _38029, _38031], _38029)]], 425 ^ _24642 : [(426 ^ _24642) ^ [] : [-(in(422 ^ [_36916, _38029, _38031], _38029))], (428 ^ _24642) ^ [_38333] : [in(ordered_pair(_38333, 422 ^ [_36916, _38029, _38031]), _36916), in(_38333, _38031)]]], (398 ^ _24642) ^ [_37123, _37125] : [_37123 = relation_image(_36916, _37125), 401 ^ _24642 : [(402 ^ _24642) ^ [_37315] : [in(_37315, _37123), 406 ^ _24642 : [(407 ^ _24642) ^ [] : [-(in(ordered_pair(405 ^ [_36916, _37123, _37125, _37315], _37315), _36916))], (409 ^ _24642) ^ [] : [-(in(405 ^ [_36916, _37123, _37125, _37315], _37125))]]], (411 ^ _24642) ^ [_37669] : [-(in(_37669, _37123)), 412 ^ _24642 : [(413 ^ _24642) ^ [_37774] : [in(ordered_pair(_37774, _37669), _36916), in(_37774, _37125)]]]]]]], (443 ^ _24642) ^ [_38935] : [relation(_38935), 446 ^ _24642 : [(470 ^ _24642) ^ [_40048, _40050] : [-(_40048 = relation_inverse_image(_38935, _40050)), 483 ^ _24642 : [(484 ^ _24642) ^ [] : [-(in(ordered_pair(471 ^ [_38935, _40048, _40050], 482 ^ [_38935, _40048, _40050]), _38935))], (486 ^ _24642) ^ [] : [-(in(482 ^ [_38935, _40048, _40050], _40050))], (488 ^ _24642) ^ [] : [in(471 ^ [_38935, _40048, _40050], _40048)]], 474 ^ _24642 : [(475 ^ _24642) ^ [] : [-(in(471 ^ [_38935, _40048, _40050], _40048))], (477 ^ _24642) ^ [_40352] : [in(ordered_pair(471 ^ [_38935, _40048, _40050], _40352), _38935), in(_40352, _40050)]]], (447 ^ _24642) ^ [_39142, _39144] : [_39142 = relation_inverse_image(_38935, _39144), 450 ^ _24642 : [(451 ^ _24642) ^ [_39334] : [in(_39334, _39142), 455 ^ _24642 : [(456 ^ _24642) ^ [] : [-(in(ordered_pair(_39334, 454 ^ [_38935, _39142, _39144, _39334]), _38935))], (458 ^ _24642) ^ [] : [-(in(454 ^ [_38935, _39142, _39144, _39334], _39144))]]], (460 ^ _24642) ^ [_39688] : [-(in(_39688, _39142)), 461 ^ _24642 : [(462 ^ _24642) ^ [_39793] : [in(ordered_pair(_39688, _39793), _38935), in(_39793, _39144)]]]]]]], (492 ^ _24642) ^ [_40954] : [relation(_40954), 495 ^ _24642 : [(496 ^ _24642) ^ [] : [connected(_40954), -(is_connected_in(_40954, relation_field(_40954)))], (502 ^ _24642) ^ [] : [is_connected_in(_40954, relation_field(_40954)), -(connected(_40954))]]], (508 ^ _24642) ^ [_41385] : [relation(_41385), 511 ^ _24642 : [(512 ^ _24642) ^ [] : [transitive(_41385), -(is_transitive_in(_41385, relation_field(_41385)))], (518 ^ _24642) ^ [] : [is_transitive_in(_41385, relation_field(_41385)), -(transitive(_41385))]]], (552 ^ _24642) ^ [_42851, _42853, _42855, _42857] : [-(_42851 = unordered_triple(_42857, _42855, _42853)), 556 ^ _24642 : [(557 ^ _24642) ^ [] : [-(in(553 ^ [_42851, _42853, _42855, _42857], _42851))], (559 ^ _24642) ^ [] : [553 ^ [_42851, _42853, _42855, _42857] = _42857], (561 ^ _24642) ^ [] : [553 ^ [_42851, _42853, _42855, _42857] = _42855], (563 ^ _24642) ^ [] : [553 ^ [_42851, _42853, _42855, _42857] = _42853]], 564 ^ _24642 : [(575 ^ _24642) ^ [] : [in(553 ^ [_42851, _42853, _42855, _42857], _42851)], (565 ^ _24642) ^ [] : [-(553 ^ [_42851, _42853, _42855, _42857] = _42857), -(553 ^ [_42851, _42853, _42855, _42857] = _42855), -(553 ^ [_42851, _42853, _42855, _42857] = _42853)]]], (524 ^ _24642) ^ [_41887, _41889, _41891, _41893] : [_41887 = unordered_triple(_41893, _41891, _41889), 527 ^ _24642 : [(542 ^ _24642) ^ [_42489] : [543 ^ _24642 : [(544 ^ _24642) ^ [] : [_42489 = _41893], (546 ^ _24642) ^ [] : [_42489 = _41891], (548 ^ _24642) ^ [] : [_42489 = _41889]], -(in(_42489, _41887))], (528 ^ _24642) ^ [_42089] : [in(_42089, _41887), -(_42089 = _41893), -(_42089 = _41891), -(_42089 = _41889)]]], (579 ^ _24642) ^ [_43824] : [-(succ(_43824) = set_union2(_43824, singleton(_43824)))], (593 ^ _24642) ^ [_44414] : [595 ^ _24642 : [(596 ^ _24642) ^ [] : [-(in(594 ^ [_44414], _44414))], (598 ^ _24642) ^ [_44651, _44653] : [594 ^ [_44414] = ordered_pair(_44653, _44651)]], -(relation(_44414))], (581 ^ _24642) ^ [_43953] : [relation(_43953), 584 ^ _24642 : [(585 ^ _24642) ^ [_44101] : [in(_44101, _43953), -(_44101 = ordered_pair(588 ^ [_43953, _44101], 589 ^ [_43953, _44101]))]]], (602 ^ _24642) ^ [_44808] : [relation(_44808), 605 ^ _24642 : [(616 ^ _24642) ^ [_45307] : [618 ^ _24642 : [(619 ^ _24642) ^ [] : [-(in(617 ^ [_44808, _45307], _45307))], (621 ^ _24642) ^ [] : [in(ordered_pair(617 ^ [_44808, _45307], 617 ^ [_44808, _45307]), _44808)]], -(is_reflexive_in(_44808, _45307))], (606 ^ _24642) ^ [_44982] : [is_reflexive_in(_44808, _44982), 609 ^ _24642 : [(610 ^ _24642) ^ [_45124] : [in(_45124, _44982), -(in(ordered_pair(_45124, _45124), _44808))]]]]], (674 ^ _24642) ^ [_47414, _47416] : [_47416 = empty_set, 677 ^ _24642 : [(678 ^ _24642) ^ [] : [_47414 = set_meet(_47416), -(_47414 = empty_set)], (684 ^ _24642) ^ [] : [_47414 = empty_set, -(_47414 = set_meet(_47416))]]], (625 ^ _24642) ^ [_45707, _45709] : [-(_45709 = empty_set), 628 ^ _24642 : [(652 ^ _24642) ^ [] : [-(_45707 = set_meet(_45709)), 656 ^ _24642 : [(657 ^ _24642) ^ [] : [-(in(653 ^ [_45707, _45709], _45707))], (660 ^ _24642) ^ [] : [-(in(658 ^ [_45707, _45709], _45709))], (662 ^ _24642) ^ [] : [in(653 ^ [_45707, _45709], 658 ^ [_45707, _45709])]], 663 ^ _24642 : [(670 ^ _24642) ^ [] : [in(653 ^ [_45707, _45709], _45707)], (664 ^ _24642) ^ [_47109] : [in(_47109, _45709), -(in(653 ^ [_45707, _45709], _47109))]]], (629 ^ _24642) ^ [] : [_45707 = set_meet(_45709), 632 ^ _24642 : [(643 ^ _24642) ^ [_46335] : [645 ^ _24642 : [(646 ^ _24642) ^ [] : [-(in(644 ^ [_45707, _45709, _46335], _45709))], (648 ^ _24642) ^ [] : [in(_46335, 644 ^ [_45707, _45709, _46335])]], -(in(_46335, _45707))], (633 ^ _24642) ^ [_46005] : [in(_46005, _45707), 636 ^ _24642 : [(637 ^ _24642) ^ [_46150] : [in(_46150, _45709), -(in(_46005, _46150))]]]]]]], (706 ^ _24642) ^ [_48432, _48434] : [-(_48432 = singleton(_48434)), 710 ^ _24642 : [(711 ^ _24642) ^ [] : [-(in(707 ^ [_48432, _48434], _48432))], (713 ^ _24642) ^ [] : [707 ^ [_48432, _48434] = _48434]], 714 ^ _24642 : [(715 ^ _24642) ^ [] : [-(707 ^ [_48432, _48434] = _48434)], (717 ^ _24642) ^ [] : [in(707 ^ [_48432, _48434], _48432)]]], (690 ^ _24642) ^ [_47911, _47913] : [_47911 = singleton(_47913), 693 ^ _24642 : [(694 ^ _24642) ^ [_48081] : [in(_48081, _47911), -(_48081 = _47913)], (700 ^ _24642) ^ [_48253] : [_48253 = _47913, -(in(_48253, _47911))]]], (721 ^ _24642) ^ [_48954] : [relation(_48954), 724 ^ _24642 : [(747 ^ _24642) ^ [_49906, _49908] : [-(_49906 = fiber(_48954, _49908)), 759 ^ _24642 : [(760 ^ _24642) ^ [] : [748 ^ [_48954, _49906, _49908] = _49908], (762 ^ _24642) ^ [] : [-(in(ordered_pair(748 ^ [_48954, _49906, _49908], _49908), _48954))], (764 ^ _24642) ^ [] : [in(748 ^ [_48954, _49906, _49908], _49906)]], 751 ^ _24642 : [(752 ^ _24642) ^ [] : [-(in(748 ^ [_48954, _49906, _49908], _49906))], (754 ^ _24642) ^ [] : [-(748 ^ [_48954, _49906, _49908] = _49908), in(ordered_pair(748 ^ [_48954, _49906, _49908], _49908), _48954)]]], (725 ^ _24642) ^ [_49158, _49160] : [_49158 = fiber(_48954, _49160), 728 ^ _24642 : [(729 ^ _24642) ^ [_49347] : [in(_49347, _49158), 732 ^ _24642 : [(733 ^ _24642) ^ [] : [_49347 = _49160], (735 ^ _24642) ^ [] : [-(in(ordered_pair(_49347, _49160), _48954))]]], (737 ^ _24642) ^ [_49613] : [-(in(_49613, _49158)), -(_49613 = _49160), in(ordered_pair(_49613, _49160), _48954)]]]]], (768 ^ _24642) ^ [_50697] : [_50697 = empty_set, 771 ^ _24642 : [(772 ^ _24642) ^ [_50810] : [in(_50810, _50697)]]], (774 ^ _24642) ^ [_50876] : [-(in(775 ^ [_50876], _50876)), -(_50876 = empty_set)], (797 ^ _24642) ^ [_51688, _51690] : [-(_51688 = powerset(_51690)), 801 ^ _24642 : [(802 ^ _24642) ^ [] : [-(in(798 ^ [_51688, _51690], _51688))], (804 ^ _24642) ^ [] : [subset(798 ^ [_51688, _51690], _51690)]], 805 ^ _24642 : [(806 ^ _24642) ^ [] : [-(subset(798 ^ [_51688, _51690], _51690))], (808 ^ _24642) ^ [] : [in(798 ^ [_51688, _51690], _51688)]]], (781 ^ _24642) ^ [_51167, _51169] : [_51167 = powerset(_51169), 784 ^ _24642 : [(785 ^ _24642) ^ [_51337] : [in(_51337, _51167), -(subset(_51337, _51169))], (791 ^ _24642) ^ [_51509] : [subset(_51509, _51169), -(in(_51509, _51167))]]], (822 ^ _24642) ^ [_52539] : [824 ^ _24642 : [(825 ^ _24642) ^ [] : [-(in(823 ^ [_52539], _52539))], (827 ^ _24642) ^ [] : [subset(823 ^ [_52539], _52539)]], -(epsilon_transitive(_52539))], (812 ^ _24642) ^ [_52239] : [epsilon_transitive(_52239), 815 ^ _24642 : [(816 ^ _24642) ^ [_52370] : [in(_52370, _52239), -(subset(_52370, _52239))]]], (831 ^ _24642) ^ [_52864] : [relation(_52864), 834 ^ _24642 : [(835 ^ _24642) ^ [_53022] : [relation(_53022), 838 ^ _24642 : [(855 ^ _24642) ^ [] : [-(_52864 = _53022), 860 ^ _24642 : [(861 ^ _24642) ^ [] : [-(in(ordered_pair(856 ^ [_52864, _53022], 857 ^ [_52864, _53022]), _52864))], (863 ^ _24642) ^ [] : [in(ordered_pair(856 ^ [_52864, _53022], 857 ^ [_52864, _53022]), _53022)]], 864 ^ _24642 : [(865 ^ _24642) ^ [] : [-(in(ordered_pair(856 ^ [_52864, _53022], 857 ^ [_52864, _53022]), _53022))], (867 ^ _24642) ^ [] : [in(ordered_pair(856 ^ [_52864, _53022], 857 ^ [_52864, _53022]), _52864)]]], (839 ^ _24642) ^ [] : [_52864 = _53022, 842 ^ _24642 : [(843 ^ _24642) ^ [_53327, _53329] : [in(ordered_pair(_53329, _53327), _52864), -(in(ordered_pair(_53329, _53327), _53022))], (849 ^ _24642) ^ [_53517, _53519] : [in(ordered_pair(_53519, _53517), _53022), -(in(ordered_pair(_53519, _53517), _52864))]]]]]]], (871 ^ _24642) ^ [_54354, _54356] : [-(empty(_54356)), 874 ^ _24642 : [(875 ^ _24642) ^ [] : [element(_54354, _54356), -(in(_54354, _54356))], (881 ^ _24642) ^ [] : [in(_54354, _54356), -(element(_54354, _54356))]]], (887 ^ _24642) ^ [_54767, _54769] : [empty(_54769), 890 ^ _24642 : [(891 ^ _24642) ^ [] : [element(_54767, _54769), -(empty(_54767))], (897 ^ _24642) ^ [] : [empty(_54767), -(element(_54767, _54769))]]], (925 ^ _24642) ^ [_55992, _55994, _55996] : [-(_55992 = unordered_pair(_55996, _55994)), 929 ^ _24642 : [(930 ^ _24642) ^ [] : [-(in(926 ^ [_55992, _55994, _55996], _55992))], (932 ^ _24642) ^ [] : [926 ^ [_55992, _55994, _55996] = _55996], (934 ^ _24642) ^ [] : [926 ^ [_55992, _55994, _55996] = _55994]], 935 ^ _24642 : [(942 ^ _24642) ^ [] : [in(926 ^ [_55992, _55994, _55996], _55992)], (936 ^ _24642) ^ [] : [-(926 ^ [_55992, _55994, _55996] = _55996), -(926 ^ [_55992, _55994, _55996] = _55994)]]], (903 ^ _24642) ^ [_55267, _55269, _55271] : [_55267 = unordered_pair(_55271, _55269), 906 ^ _24642 : [(917 ^ _24642) ^ [_55727] : [918 ^ _24642 : [(919 ^ _24642) ^ [] : [_55727 = _55271], (921 ^ _24642) ^ [] : [_55727 = _55269]], -(in(_55727, _55267))], (907 ^ _24642) ^ [_55449] : [in(_55449, _55267), -(_55449 = _55271), -(_55449 = _55269)]]], (946 ^ _24642) ^ [_56729] : [relation(_56729), 949 ^ _24642 : [(967 ^ _24642) ^ [] : [-(well_founded_relation(_56729)), 969 ^ _24642 : [(970 ^ _24642) ^ [] : [-(subset(968 ^ [_56729], relation_field(_56729)))], (972 ^ _24642) ^ [] : [968 ^ [_56729] = empty_set], (974 ^ _24642) ^ [_57679] : [in(_57679, 968 ^ [_56729]), disjoint(fiber(_56729, _57679), 968 ^ [_56729])]]], (950 ^ _24642) ^ [] : [well_founded_relation(_56729), 953 ^ _24642 : [(954 ^ _24642) ^ [_56996] : [subset(_56996, relation_field(_56729)), -(_56996 = empty_set), 962 ^ _24642 : [(963 ^ _24642) ^ [] : [-(in(961 ^ [_56729, _56996], _56996))], (965 ^ _24642) ^ [] : [-(disjoint(fiber(_56729, 961 ^ [_56729, _56996]), _56996))]]]]]]], (1004 ^ _24642) ^ [_58743, _58745, _58747] : [-(_58743 = set_union2(_58747, _58745)), 1008 ^ _24642 : [(1009 ^ _24642) ^ [] : [-(in(1005 ^ [_58743, _58745, _58747], _58743))], (1011 ^ _24642) ^ [] : [in(1005 ^ [_58743, _58745, _58747], _58747)], (1013 ^ _24642) ^ [] : [in(1005 ^ [_58743, _58745, _58747], _58745)]], 1014 ^ _24642 : [(1021 ^ _24642) ^ [] : [in(1005 ^ [_58743, _58745, _58747], _58743)], (1015 ^ _24642) ^ [] : [-(in(1005 ^ [_58743, _58745, _58747], _58747)), -(in(1005 ^ [_58743, _58745, _58747], _58745))]]], (982 ^ _24642) ^ [_58018, _58020, _58022] : [_58018 = set_union2(_58022, _58020), 985 ^ _24642 : [(996 ^ _24642) ^ [_58478] : [997 ^ _24642 : [(998 ^ _24642) ^ [] : [in(_58478, _58022)], (1000 ^ _24642) ^ [] : [in(_58478, _58020)]], -(in(_58478, _58018))], (986 ^ _24642) ^ [_58200] : [in(_58200, _58018), -(in(_58200, _58022)), -(in(_58200, _58020))]]], (1055 ^ _24642) ^ [_60794, _60796, _60798] : [-(_60794 = cartesian_product2(_60798, _60796)), 1073 ^ _24642 : [(1074 ^ _24642) ^ [] : [-(in(1071 ^ [_60794, _60796, _60798], _60798))], (1076 ^ _24642) ^ [] : [-(in(1072 ^ [_60794, _60796, _60798], _60796))], (1078 ^ _24642) ^ [] : [-(1056 ^ [_60794, _60796, _60798] = ordered_pair(1071 ^ [_60794, _60796, _60798], 1072 ^ [_60794, _60796, _60798]))], (1080 ^ _24642) ^ [] : [in(1056 ^ [_60794, _60796, _60798], _60794)]], 1059 ^ _24642 : [(1060 ^ _24642) ^ [] : [-(in(1056 ^ [_60794, _60796, _60798], _60794))], (1062 ^ _24642) ^ [_61132, _61134] : [in(_61134, _60798), in(_61132, _60796), 1056 ^ [_60794, _60796, _60798] = ordered_pair(_61134, _61132)]]], (1025 ^ _24642) ^ [_59537, _59539, _59541] : [_59537 = cartesian_product2(_59541, _59539), 1028 ^ _24642 : [(1029 ^ _24642) ^ [_59738] : [in(_59738, _59537), 1034 ^ _24642 : [(1035 ^ _24642) ^ [] : [-(in(1032 ^ [_59537, _59539, _59541, _59738], _59541))], (1037 ^ _24642) ^ [] : [-(in(1033 ^ [_59537, _59539, _59541, _59738], _59539))], (1039 ^ _24642) ^ [] : [-(_59738 = ordered_pair(1032 ^ [_59537, _59539, _59541, _59738], 1033 ^ [_59537, _59539, _59541, _59738]))]]], (1041 ^ _24642) ^ [_60298] : [-(in(_60298, _59537)), 1042 ^ _24642 : [(1043 ^ _24642) ^ [_60428, _60430] : [in(_60430, _59541), in(_60428, _59539), _60298 = ordered_pair(_60430, _60428)]]]]], (1106 ^ _24642) ^ [_62695] : [1109 ^ _24642 : [(1110 ^ _24642) ^ [] : [-(in(1107 ^ [_62695], _62695))], (1112 ^ _24642) ^ [] : [-(in(1108 ^ [_62695], _62695))], (1114 ^ _24642) ^ [] : [in(1107 ^ [_62695], 1108 ^ [_62695])], (1116 ^ _24642) ^ [] : [1107 ^ [_62695] = 1108 ^ [_62695]], (1118 ^ _24642) ^ [] : [in(1108 ^ [_62695], 1107 ^ [_62695])]], -(epsilon_connected(_62695))], (1084 ^ _24642) ^ [_62057] : [epsilon_connected(_62057), 1087 ^ _24642 : [(1088 ^ _24642) ^ [_62233, _62235] : [in(_62235, _62057), in(_62233, _62057), -(in(_62235, _62233)), -(_62235 = _62233), -(in(_62233, _62235))]]], (1122 ^ _24642) ^ [_63401] : [relation(_63401), 1125 ^ _24642 : [(1126 ^ _24642) ^ [_63559] : [relation(_63559), 1129 ^ _24642 : [(1140 ^ _24642) ^ [] : [1143 ^ _24642 : [(1144 ^ _24642) ^ [] : [-(in(ordered_pair(1141 ^ [_63401, _63559], 1142 ^ [_63401, _63559]), _63401))], (1146 ^ _24642) ^ [] : [in(ordered_pair(1141 ^ [_63401, _63559], 1142 ^ [_63401, _63559]), _63559)]], -(subset(_63401, _63559))], (1130 ^ _24642) ^ [] : [subset(_63401, _63559), 1133 ^ _24642 : [(1134 ^ _24642) ^ [_63835, _63837] : [in(ordered_pair(_63837, _63835), _63401), -(in(ordered_pair(_63837, _63835), _63559))]]]]]]], (1160 ^ _24642) ^ [_64798, _64800] : [1162 ^ _24642 : [(1163 ^ _24642) ^ [] : [-(in(1161 ^ [_64798, _64800], _64800))], (1165 ^ _24642) ^ [] : [in(1161 ^ [_64798, _64800], _64798)]], -(subset(_64800, _64798))], (1150 ^ _24642) ^ [_64484, _64486] : [subset(_64486, _64484), 1153 ^ _24642 : [(1154 ^ _24642) ^ [_64621] : [in(_64621, _64486), -(in(_64621, _64484))]]], (1169 ^ _24642) ^ [_65141] : [relation(_65141), 1172 ^ _24642 : [(1190 ^ _24642) ^ [_65944] : [-(is_well_founded_in(_65141, _65944)), 1192 ^ _24642 : [(1193 ^ _24642) ^ [] : [-(subset(1191 ^ [_65141, _65944], _65944))], (1195 ^ _24642) ^ [] : [1191 ^ [_65141, _65944] = empty_set], (1197 ^ _24642) ^ [_66286] : [in(_66286, 1191 ^ [_65141, _65944]), disjoint(fiber(_65141, _66286), 1191 ^ [_65141, _65944])]]], (1173 ^ _24642) ^ [_65338] : [is_well_founded_in(_65141, _65338), 1176 ^ _24642 : [(1177 ^ _24642) ^ [_65503] : [subset(_65503, _65338), -(_65503 = empty_set), 1185 ^ _24642 : [(1186 ^ _24642) ^ [] : [-(in(1184 ^ [_65141, _65338, _65503], _65503))], (1188 ^ _24642) ^ [] : [-(disjoint(fiber(_65141, 1184 ^ [_65141, _65338, _65503]), _65503))]]]]]]], (1227 ^ _24642) ^ [_67369, _67371, _67373] : [-(_67369 = set_intersection2(_67373, _67371)), 1239 ^ _24642 : [(1240 ^ _24642) ^ [] : [-(in(1228 ^ [_67369, _67371, _67373], _67373))], (1242 ^ _24642) ^ [] : [-(in(1228 ^ [_67369, _67371, _67373], _67371))], (1244 ^ _24642) ^ [] : [in(1228 ^ [_67369, _67371, _67373], _67369)]], 1231 ^ _24642 : [(1232 ^ _24642) ^ [] : [-(in(1228 ^ [_67369, _67371, _67373], _67369))], (1234 ^ _24642) ^ [] : [in(1228 ^ [_67369, _67371, _67373], _67373), in(1228 ^ [_67369, _67371, _67373], _67371)]]], (1205 ^ _24642) ^ [_66644, _66646, _66648] : [_66644 = set_intersection2(_66648, _66646), 1208 ^ _24642 : [(1209 ^ _24642) ^ [_66826] : [in(_66826, _66644), 1212 ^ _24642 : [(1213 ^ _24642) ^ [] : [-(in(_66826, _66648))], (1215 ^ _24642) ^ [] : [-(in(_66826, _66646))]]], (1217 ^ _24642) ^ [_67085] : [-(in(_67085, _66644)), in(_67085, _66648), in(_67085, _66646)]]], (1248 ^ _24642) ^ [_68108] : [relation(_68108), function(_68108), 1255 ^ _24642 : [(1256 ^ _24642) ^ [_68400, _68402] : [in(_68402, relation_dom(_68108)), 1259 ^ _24642 : [(1260 ^ _24642) ^ [] : [_68400 = apply(_68108, _68402), -(in(ordered_pair(_68402, _68400), _68108))], (1266 ^ _24642) ^ [] : [in(ordered_pair(_68402, _68400), _68108), -(_68400 = apply(_68108, _68402))]]], (1272 ^ _24642) ^ [_68852, _68854] : [-(in(_68854, relation_dom(_68108))), 1275 ^ _24642 : [(1276 ^ _24642) ^ [] : [_68852 = apply(_68108, _68854), -(_68852 = empty_set)], (1282 ^ _24642) ^ [] : [_68852 = empty_set, -(_68852 = apply(_68108, _68854))]]]]], (1288 ^ _24642) ^ [_69370] : [ordinal(_69370), 1291 ^ _24642 : [(1292 ^ _24642) ^ [] : [-(epsilon_transitive(_69370))], (1294 ^ _24642) ^ [] : [-(epsilon_connected(_69370))]]], (1296 ^ _24642) ^ [_69593] : [-(ordinal(_69593)), epsilon_transitive(_69593), epsilon_connected(_69593)], (1306 ^ _24642) ^ [_69864] : [relation(_69864), 1309 ^ _24642 : [(1327 ^ _24642) ^ [_70676] : [-(_70676 = relation_dom(_69864)), 1331 ^ _24642 : [(1332 ^ _24642) ^ [] : [-(in(1328 ^ [_69864, _70676], _70676))], (1334 ^ _24642) ^ [_70939] : [in(ordered_pair(1328 ^ [_69864, _70676], _70939), _69864)]], 1336 ^ _24642 : [(1337 ^ _24642) ^ [] : [-(in(ordered_pair(1328 ^ [_69864, _70676], 1335 ^ [_69864, _70676]), _69864))], (1339 ^ _24642) ^ [] : [in(1328 ^ [_69864, _70676], _70676)]]], (1310 ^ _24642) ^ [_70045] : [_70045 = relation_dom(_69864), 1313 ^ _24642 : [(1314 ^ _24642) ^ [_70225] : [in(_70225, _70045), -(in(ordered_pair(_70225, 1317 ^ [_69864, _70045, _70225]), _69864))], (1321 ^ _24642) ^ [_70469] : [1322 ^ _24642 : [(1323 ^ _24642) ^ [_70548] : [in(ordered_pair(_70469, _70548), _69864)]], -(in(_70469, _70045))]]]]], (1343 ^ _24642) ^ [_71305] : [relation(_71305), 1346 ^ _24642 : [(1369 ^ _24642) ^ [_72173] : [1372 ^ _24642 : [(1373 ^ _24642) ^ [] : [-(in(1370 ^ [_71305, _72173], _72173))], (1375 ^ _24642) ^ [] : [-(in(1371 ^ [_71305, _72173], _72173))], (1377 ^ _24642) ^ [] : [-(in(ordered_pair(1370 ^ [_71305, _72173], 1371 ^ [_71305, _72173]), _71305))], (1379 ^ _24642) ^ [] : [-(in(ordered_pair(1371 ^ [_71305, _72173], 1370 ^ [_71305, _72173]), _71305))], (1381 ^ _24642) ^ [] : [1370 ^ [_71305, _72173] = 1371 ^ [_71305, _72173]]], -(is_antisymmetric_in(_71305, _72173))], (1347 ^ _24642) ^ [_71505] : [is_antisymmetric_in(_71305, _71505), 1350 ^ _24642 : [(1351 ^ _24642) ^ [_71687, _71689] : [-(_71689 = _71687), in(_71689, _71505), in(_71687, _71505), in(ordered_pair(_71689, _71687), _71305), in(ordered_pair(_71687, _71689), _71305)]]]]], (1385 ^ _24642) ^ [_72927] : [-(cast_to_subset(_72927) = _72927)], (1410 ^ _24642) ^ [_73910, _73912] : [-(_73910 = union(_73912)), 1423 ^ _24642 : [(1424 ^ _24642) ^ [] : [-(in(1411 ^ [_73910, _73912], 1422 ^ [_73910, _73912]))], (1426 ^ _24642) ^ [] : [-(in(1422 ^ [_73910, _73912], _73912))], (1428 ^ _24642) ^ [] : [in(1411 ^ [_73910, _73912], _73910)]], 1414 ^ _24642 : [(1415 ^ _24642) ^ [] : [-(in(1411 ^ [_73910, _73912], _73910))], (1417 ^ _24642) ^ [_74193] : [in(1411 ^ [_73910, _73912], _74193), in(_74193, _73912)]]], (1387 ^ _24642) ^ [_73065, _73067] : [_73065 = union(_73067), 1390 ^ _24642 : [(1391 ^ _24642) ^ [_73246] : [in(_73246, _73065), 1395 ^ _24642 : [(1396 ^ _24642) ^ [] : [-(in(_73246, 1394 ^ [_73065, _73067, _73246]))], (1398 ^ _24642) ^ [] : [-(in(1394 ^ [_73065, _73067, _73246], _73067))]]], (1400 ^ _24642) ^ [_73573] : [-(in(_73573, _73065)), 1401 ^ _24642 : [(1402 ^ _24642) ^ [_73671] : [in(_73573, _73671), in(_73671, _73067)]]]]], (1432 ^ _24642) ^ [_74743] : [relation(_74743), 1435 ^ _24642 : [(1436 ^ _24642) ^ [] : [well_ordering(_74743), 1439 ^ _24642 : [(1440 ^ _24642) ^ [] : [-(reflexive(_74743))], (1442 ^ _24642) ^ [] : [-(transitive(_74743))], (1444 ^ _24642) ^ [] : [-(antisymmetric(_74743))], (1446 ^ _24642) ^ [] : [-(connected(_74743))], (1448 ^ _24642) ^ [] : [-(well_founded_relation(_74743))]]], (1450 ^ _24642) ^ [] : [-(well_ordering(_74743)), reflexive(_74743), transitive(_74743), antisymmetric(_74743), connected(_74743), well_founded_relation(_74743)]]], (1494 ^ _24642) ^ [_76546, _76548, _76550] : [-(_76546 = set_difference(_76550, _76548)), 1506 ^ _24642 : [(1507 ^ _24642) ^ [] : [-(in(1495 ^ [_76546, _76548, _76550], _76550))], (1509 ^ _24642) ^ [] : [in(1495 ^ [_76546, _76548, _76550], _76548)], (1511 ^ _24642) ^ [] : [in(1495 ^ [_76546, _76548, _76550], _76546)]], 1498 ^ _24642 : [(1499 ^ _24642) ^ [] : [-(in(1495 ^ [_76546, _76548, _76550], _76546))], (1501 ^ _24642) ^ [] : [in(1495 ^ [_76546, _76548, _76550], _76550), -(in(1495 ^ [_76546, _76548, _76550], _76548))]]], (1472 ^ _24642) ^ [_75815, _75817, _75819] : [_75815 = set_difference(_75819, _75817), 1475 ^ _24642 : [(1476 ^ _24642) ^ [_75999] : [in(_75999, _75815), 1479 ^ _24642 : [(1480 ^ _24642) ^ [] : [-(in(_75999, _75819))], (1482 ^ _24642) ^ [] : [in(_75999, _75817)]]], (1484 ^ _24642) ^ [_76259] : [-(in(_76259, _75815)), in(_76259, _75819), -(in(_76259, _75817))]]], (1515 ^ _24642) ^ [_77289] : [relation(_77289), function(_77289), 1522 ^ _24642 : [(1546 ^ _24642) ^ [_78443] : [-(_78443 = relation_rng(_77289)), 1559 ^ _24642 : [(1560 ^ _24642) ^ [] : [-(in(1558 ^ [_77289, _78443], relation_dom(_77289)))], (1562 ^ _24642) ^ [] : [-(1547 ^ [_77289, _78443] = apply(_77289, 1558 ^ [_77289, _78443]))], (1564 ^ _24642) ^ [] : [in(1547 ^ [_77289, _78443], _78443)]], 1550 ^ _24642 : [(1551 ^ _24642) ^ [] : [-(in(1547 ^ [_77289, _78443], _78443))], (1553 ^ _24642) ^ [_78738] : [in(_78738, relation_dom(_77289)), 1547 ^ [_77289, _78443] = apply(_77289, _78738)]]], (1523 ^ _24642) ^ [_77561] : [_77561 = relation_rng(_77289), 1526 ^ _24642 : [(1527 ^ _24642) ^ [_77749] : [in(_77749, _77561), 1531 ^ _24642 : [(1532 ^ _24642) ^ [] : [-(in(1530 ^ [_77289, _77561, _77749], relation_dom(_77289)))], (1534 ^ _24642) ^ [] : [-(_77749 = apply(_77289, 1530 ^ [_77289, _77561, _77749]))]]], (1536 ^ _24642) ^ [_78091] : [-(in(_78091, _77561)), 1537 ^ _24642 : [(1538 ^ _24642) ^ [_78194] : [in(_78194, relation_dom(_77289)), _78091 = apply(_77289, _78194)]]]]]]], (1568 ^ _24642) ^ [_79315] : [relation(_79315), 1571 ^ _24642 : [(1589 ^ _24642) ^ [_80127] : [-(_80127 = relation_rng(_79315)), 1593 ^ _24642 : [(1594 ^ _24642) ^ [] : [-(in(1590 ^ [_79315, _80127], _80127))], (1596 ^ _24642) ^ [_80390] : [in(ordered_pair(_80390, 1590 ^ [_79315, _80127]), _79315)]], 1598 ^ _24642 : [(1599 ^ _24642) ^ [] : [-(in(ordered_pair(1597 ^ [_79315, _80127], 1590 ^ [_79315, _80127]), _79315))], (1601 ^ _24642) ^ [] : [in(1590 ^ [_79315, _80127], _80127)]]], (1572 ^ _24642) ^ [_79496] : [_79496 = relation_rng(_79315), 1575 ^ _24642 : [(1576 ^ _24642) ^ [_79676] : [in(_79676, _79496), -(in(ordered_pair(1579 ^ [_79315, _79496, _79676], _79676), _79315))], (1583 ^ _24642) ^ [_79920] : [1584 ^ _24642 : [(1585 ^ _24642) ^ [_79999] : [in(ordered_pair(_79999, _79920), _79315)]], -(in(_79920, _79496))]]]]], (1605 ^ _24642) ^ [_80770, _80772] : [element(_80770, powerset(_80772)), -(subset_complement(_80772, _80770) = set_difference(_80772, _80770))], (1611 ^ _24642) ^ [_80981, _80983] : [-(ordered_pair(_80983, _80981) = unordered_pair(unordered_pair(_80983, _80981), singleton(_80983)))], (1613 ^ _24642) ^ [_81087] : [relation(_81087), 1616 ^ _24642 : [(1617 ^ _24642) ^ [_81271] : [well_orders(_81087, _81271), 1620 ^ _24642 : [(1621 ^ _24642) ^ [] : [-(is_reflexive_in(_81087, _81271))], (1623 ^ _24642) ^ [] : [-(is_transitive_in(_81087, _81271))], (1625 ^ _24642) ^ [] : [-(is_antisymmetric_in(_81087, _81271))], (1627 ^ _24642) ^ [] : [-(is_connected_in(_81087, _81271))], (1629 ^ _24642) ^ [] : [-(is_well_founded_in(_81087, _81271))]]], (1631 ^ _24642) ^ [_81732] : [-(well_orders(_81087, _81732)), is_reflexive_in(_81087, _81732), is_transitive_in(_81087, _81732), is_antisymmetric_in(_81087, _81732), is_connected_in(_81087, _81732), is_well_founded_in(_81087, _81732)]]], (1653 ^ _24642) ^ [_82322] : [being_limit_ordinal(_82322), -(_82322 = union(_82322))], (1659 ^ _24642) ^ [_82480] : [_82480 = union(_82480), -(being_limit_ordinal(_82480))], (1665 ^ _24642) ^ [_82674] : [relation(_82674), -(relation_field(_82674) = set_union2(relation_dom(_82674), relation_rng(_82674)))], (1671 ^ _24642) ^ [_82880] : [relation(_82880), 1674 ^ _24642 : [(1697 ^ _24642) ^ [_83772] : [1700 ^ _24642 : [(1701 ^ _24642) ^ [] : [-(in(1698 ^ [_82880, _83772], _83772))], (1703 ^ _24642) ^ [] : [-(in(1699 ^ [_82880, _83772], _83772))], (1705 ^ _24642) ^ [] : [1698 ^ [_82880, _83772] = 1699 ^ [_82880, _83772]], (1707 ^ _24642) ^ [] : [in(ordered_pair(1698 ^ [_82880, _83772], 1699 ^ [_82880, _83772]), _82880)], (1709 ^ _24642) ^ [] : [in(ordered_pair(1699 ^ [_82880, _83772], 1698 ^ [_82880, _83772]), _82880)]], -(is_connected_in(_82880, _83772))], (1675 ^ _24642) ^ [_83088] : [is_connected_in(_82880, _83088), 1678 ^ _24642 : [(1679 ^ _24642) ^ [_83278, _83280] : [in(_83280, _83088), in(_83278, _83088), -(_83280 = _83278), -(in(ordered_pair(_83280, _83278), _82880)), -(in(ordered_pair(_83278, _83280), _82880))]]]]], (1713 ^ _24642) ^ [_84557] : [relation(_84557), 1716 ^ _24642 : [(1717 ^ _24642) ^ [_84676] : [-(relation_restriction(_84557, _84676) = set_intersection2(_84557, cartesian_product2(_84676, _84676)))]]], (1719 ^ _24642) ^ [_84785] : [relation(_84785), 1722 ^ _24642 : [(1723 ^ _24642) ^ [_84945] : [relation(_84945), 1726 ^ _24642 : [(1743 ^ _24642) ^ [] : [-(_84945 = relation_inverse(_84785)), 1748 ^ _24642 : [(1749 ^ _24642) ^ [] : [-(in(ordered_pair(1744 ^ [_84785, _84945], 1745 ^ [_84785, _84945]), _84945))], (1751 ^ _24642) ^ [] : [in(ordered_pair(1745 ^ [_84785, _84945], 1744 ^ [_84785, _84945]), _84785)]], 1752 ^ _24642 : [(1753 ^ _24642) ^ [] : [-(in(ordered_pair(1745 ^ [_84785, _84945], 1744 ^ [_84785, _84945]), _84785))], (1755 ^ _24642) ^ [] : [in(ordered_pair(1744 ^ [_84785, _84945], 1745 ^ [_84785, _84945]), _84945)]]], (1727 ^ _24642) ^ [] : [_84945 = relation_inverse(_84785), 1730 ^ _24642 : [(1731 ^ _24642) ^ [_85254, _85256] : [in(ordered_pair(_85256, _85254), _84945), -(in(ordered_pair(_85254, _85256), _84785))], (1737 ^ _24642) ^ [_85444, _85446] : [in(ordered_pair(_85444, _85446), _84785), -(in(ordered_pair(_85446, _85444), _84945))]]]]]]], (1759 ^ _24642) ^ [_86249] : [relation(_86249), 1762 ^ _24642 : [(1763 ^ _24642) ^ [_86470] : [relation(_86470), 1766 ^ _24642 : [(1767 ^ _24642) ^ [_86687] : [relation(_86687), function(_86687), 1774 ^ _24642 : [(1809 ^ _24642) ^ [] : [-(relation_isomorphism(_86249, _86470, _86687)), relation_dom(_86687) = relation_field(_86249), relation_rng(_86687) = relation_field(_86470), one_to_one(_86687), 1838 ^ _24642 : [(1839 ^ _24642) ^ [] : [-(in(1822 ^ [_86249, _86470, _86687], relation_field(_86249)))], (1841 ^ _24642) ^ [] : [-(in(1823 ^ [_86249, _86470, _86687], relation_field(_86249)))], (1843 ^ _24642) ^ [] : [-(in(ordered_pair(apply(_86687, 1822 ^ [_86249, _86470, _86687]), apply(_86687, 1823 ^ [_86249, _86470, _86687])), _86470))], (1845 ^ _24642) ^ [] : [in(ordered_pair(1822 ^ [_86249, _86470, _86687], 1823 ^ [_86249, _86470, _86687]), _86249)]], 1826 ^ _24642 : [(1827 ^ _24642) ^ [] : [-(in(ordered_pair(1822 ^ [_86249, _86470, _86687], 1823 ^ [_86249, _86470, _86687]), _86249))], (1829 ^ _24642) ^ [] : [in(1822 ^ [_86249, _86470, _86687], relation_field(_86249)), in(1823 ^ [_86249, _86470, _86687], relation_field(_86249)), in(ordered_pair(apply(_86687, 1822 ^ [_86249, _86470, _86687]), apply(_86687, 1823 ^ [_86249, _86470, _86687])), _86470)]]], (1775 ^ _24642) ^ [] : [relation_isomorphism(_86249, _86470, _86687), 1778 ^ _24642 : [(1779 ^ _24642) ^ [] : [-(relation_dom(_86687) = relation_field(_86249))], (1781 ^ _24642) ^ [] : [-(relation_rng(_86687) = relation_field(_86470))], (1783 ^ _24642) ^ [] : [-(one_to_one(_86687))], (1785 ^ _24642) ^ [_87353, _87355] : [in(ordered_pair(_87355, _87353), _86249), 1788 ^ _24642 : [(1789 ^ _24642) ^ [] : [-(in(_87355, relation_field(_86249)))], (1791 ^ _24642) ^ [] : [-(in(_87353, relation_field(_86249)))], (1793 ^ _24642) ^ [] : [-(in(ordered_pair(apply(_86687, _87355), apply(_86687, _87353)), _86470))]]], (1795 ^ _24642) ^ [_87732, _87734] : [-(in(ordered_pair(_87734, _87732), _86249)), in(_87734, relation_field(_86249)), in(_87732, relation_field(_86249)), in(ordered_pair(apply(_86687, _87734), apply(_86687, _87732)), _86470)]]]]]]]]], (1849 ^ _24642) ^ [_89559, _89561] : [disjoint(_89561, _89559), -(set_intersection2(_89561, _89559) = empty_set)], (1855 ^ _24642) ^ [_89727, _89729] : [set_intersection2(_89729, _89727) = empty_set, -(disjoint(_89729, _89727))], (1861 ^ _24642) ^ [_89931] : [relation(_89931), function(_89931), 1868 ^ _24642 : [(1887 ^ _24642) ^ [] : [1890 ^ _24642 : [(1891 ^ _24642) ^ [] : [-(in(1888 ^ [_89931], relation_dom(_89931)))], (1893 ^ _24642) ^ [] : [-(in(1889 ^ [_89931], relation_dom(_89931)))], (1895 ^ _24642) ^ [] : [-(apply(_89931, 1888 ^ [_89931]) = apply(_89931, 1889 ^ [_89931]))], (1897 ^ _24642) ^ [] : [1888 ^ [_89931] = 1889 ^ [_89931]]], -(one_to_one(_89931))], (1869 ^ _24642) ^ [] : [one_to_one(_89931), 1872 ^ _24642 : [(1873 ^ _24642) ^ [_90294, _90296] : [-(_90296 = _90294), in(_90296, relation_dom(_89931)), in(_90294, relation_dom(_89931)), apply(_89931, _90296) = apply(_89931, _90294)]]]]], (1901 ^ _24642) ^ [_91241] : [relation(_91241), 1904 ^ _24642 : [(1905 ^ _24642) ^ [_91426] : [relation(_91426), 1908 ^ _24642 : [(1909 ^ _24642) ^ [_91607] : [relation(_91607), 1912 ^ _24642 : [(1936 ^ _24642) ^ [] : [-(_91607 = relation_composition(_91241, _91426)), 1950 ^ _24642 : [(1951 ^ _24642) ^ [] : [-(in(ordered_pair(1937 ^ [_91241, _91426, _91607], 1949 ^ [_91241, _91426, _91607]), _91241))], (1953 ^ _24642) ^ [] : [-(in(ordered_pair(1949 ^ [_91241, _91426, _91607], 1938 ^ [_91241, _91426, _91607]), _91426))], (1955 ^ _24642) ^ [] : [in(ordered_pair(1937 ^ [_91241, _91426, _91607], 1938 ^ [_91241, _91426, _91607]), _91607)]], 1941 ^ _24642 : [(1942 ^ _24642) ^ [] : [-(in(ordered_pair(1937 ^ [_91241, _91426, _91607], 1938 ^ [_91241, _91426, _91607]), _91607))], (1944 ^ _24642) ^ [_93071] : [in(ordered_pair(1937 ^ [_91241, _91426, _91607], _93071), _91241), in(ordered_pair(_93071, 1938 ^ [_91241, _91426, _91607]), _91426)]]], (1913 ^ _24642) ^ [] : [_91607 = relation_composition(_91241, _91426), 1916 ^ _24642 : [(1917 ^ _24642) ^ [_91942, _91944] : [in(ordered_pair(_91944, _91942), _91607), 1921 ^ _24642 : [(1922 ^ _24642) ^ [] : [-(in(ordered_pair(_91944, 1920 ^ [_91241, _91426, _91607, _91942, _91944]), _91241))], (1924 ^ _24642) ^ [] : [-(in(ordered_pair(1920 ^ [_91241, _91426, _91607, _91942, _91944], _91942), _91426))]]], (1926 ^ _24642) ^ [_92327, _92329] : [-(in(ordered_pair(_92329, _92327), _91607)), 1927 ^ _24642 : [(1928 ^ _24642) ^ [_92440] : [in(ordered_pair(_92329, _92440), _91241), in(ordered_pair(_92440, _92327), _91426)]]]]]]]]]]], (1959 ^ _24642) ^ [_93743] : [relation(_93743), 1962 ^ _24642 : [(1989 ^ _24642) ^ [_94778] : [1993 ^ _24642 : [(1994 ^ _24642) ^ [] : [-(in(1990 ^ [_93743, _94778], _94778))], (1996 ^ _24642) ^ [] : [-(in(1991 ^ [_93743, _94778], _94778))], (1998 ^ _24642) ^ [] : [-(in(1992 ^ [_93743, _94778], _94778))], (2000 ^ _24642) ^ [] : [-(in(ordered_pair(1990 ^ [_93743, _94778], 1991 ^ [_93743, _94778]), _93743))], (2002 ^ _24642) ^ [] : [-(in(ordered_pair(1991 ^ [_93743, _94778], 1992 ^ [_93743, _94778]), _93743))], (2004 ^ _24642) ^ [] : [in(ordered_pair(1990 ^ [_93743, _94778], 1992 ^ [_93743, _94778]), _93743)]], -(is_transitive_in(_93743, _94778))], (1963 ^ _24642) ^ [_93957] : [is_transitive_in(_93743, _93957), 1966 ^ _24642 : [(1967 ^ _24642) ^ [_94167, _94169, _94171] : [-(in(ordered_pair(_94171, _94167), _93743)), in(_94171, _93957), in(_94169, _93957), in(_94167, _93957), in(ordered_pair(_94171, _94169), _93743), in(ordered_pair(_94169, _94167), _93743)]]]]], (2008 ^ _24642) ^ [_95802, _95804] : [element(_95802, powerset(powerset(_95804))), 2011 ^ _24642 : [(2012 ^ _24642) ^ [_95982] : [element(_95982, powerset(powerset(_95804))), 2015 ^ _24642 : [(2036 ^ _24642) ^ [] : [-(_95982 = complements_of_subsets(_95804, _95802)), 2038 ^ _24642 : [(2039 ^ _24642) ^ [] : [-(element(2037 ^ [_95802, _95804, _95982], powerset(_95804)))], (2041 ^ _24642) ^ [] : [2042 ^ _24642 : [(2043 ^ _24642) ^ [] : [-(in(2037 ^ [_95802, _95804, _95982], _95982))], (2045 ^ _24642) ^ [] : [in(subset_complement(_95804, 2037 ^ [_95802, _95804, _95982]), _95802)]], 2046 ^ _24642 : [(2047 ^ _24642) ^ [] : [-(in(subset_complement(_95804, 2037 ^ [_95802, _95804, _95982]), _95802))], (2049 ^ _24642) ^ [] : [in(2037 ^ [_95802, _95804, _95982], _95982)]]]]], (2016 ^ _24642) ^ [] : [_95982 = complements_of_subsets(_95804, _95802), 2019 ^ _24642 : [(2020 ^ _24642) ^ [_96270] : [element(_96270, powerset(_95804)), 2023 ^ _24642 : [(2024 ^ _24642) ^ [] : [in(_96270, _95982), -(in(subset_complement(_95804, _96270), _95802))], (2030 ^ _24642) ^ [] : [in(subset_complement(_95804, _96270), _95802), -(in(_96270, _95982))]]]]]]]]], (2053 ^ _24642) ^ [_97393, _97395] : [proper_subset(_97395, _97393), 2056 ^ _24642 : [(2057 ^ _24642) ^ [] : [-(subset(_97395, _97393))], (2059 ^ _24642) ^ [] : [_97395 = _97393]]], (2061 ^ _24642) ^ [_97631, _97633] : [-(proper_subset(_97633, _97631)), subset(_97633, _97631), -(_97633 = _97631)], (2071 ^ _24642) ^ [_97921] : [relation(_97921), function(_97921), one_to_one(_97921), -(function_inverse(_97921) = relation_inverse(_97921))], (2085 ^ _24642) ^ [_98285] : [relation(_98285), 2088 ^ _24642 : [(2089 ^ _24642) ^ [] : [reflexive(_98285), -(is_reflexive_in(_98285, relation_field(_98285)))], (2095 ^ _24642) ^ [] : [is_reflexive_in(_98285, relation_field(_98285)), -(reflexive(_98285))]]], (2101 ^ _24642) ^ [] : [true___, -(true___)], (2107 ^ _24642) ^ [] : [true___, -(true___)], (2113 ^ _24642) ^ [] : [true___, -(true___)], (2119 ^ _24642) ^ [] : [true___, -(true___)], (2125 ^ _24642) ^ [] : [true___, -(true___)], (2131 ^ _24642) ^ [] : [true___, -(true___)], (2137 ^ _24642) ^ [] : [true___, -(true___)], (2143 ^ _24642) ^ [] : [true___, -(true___)], (2149 ^ _24642) ^ [] : [true___, -(true___)], (2155 ^ _24642) ^ [] : [true___, -(true___)], (2161 ^ _24642) ^ [_99906] : [2168 ^ _24642 : [(2169 ^ _24642) ^ [] : [-(relation(function_inverse(_99906)))], (2171 ^ _24642) ^ [] : [-(function(function_inverse(_99906)))]], relation(_99906), function(_99906)], (2173 ^ _24642) ^ [] : [true___, -(true___)], (2179 ^ _24642) ^ [_100358] : [-(element(cast_to_subset(_100358), powerset(_100358)))], (2181 ^ _24642) ^ [] : [true___, -(true___)], (2187 ^ _24642) ^ [_100588, _100590] : [relation(_100590), -(relation(relation_restriction(_100590, _100588)))], (2193 ^ _24642) ^ [] : [true___, -(true___)], (2199 ^ _24642) ^ [] : [true___, -(true___)], (2205 ^ _24642) ^ [] : [true___, -(true___)], (2211 ^ _24642) ^ [_101157, _101159] : [element(_101157, powerset(_101159)), -(element(subset_complement(_101159, _101157), powerset(_101159)))], (2217 ^ _24642) ^ [] : [true___, -(true___)], (2223 ^ _24642) ^ [] : [true___, -(true___)], (2229 ^ _24642) ^ [_101605] : [relation(_101605), -(relation(relation_inverse(_101605)))], (2235 ^ _24642) ^ [] : [true___, -(true___)], (2241 ^ _24642) ^ [] : [true___, -(true___)], (2247 ^ _24642) ^ [_102047, _102049] : [-(relation(relation_composition(_102049, _102047))), relation(_102049), relation(_102047)], (2257 ^ _24642) ^ [_102346, _102348] : [element(_102346, powerset(powerset(_102348))), -(element(union_of_subsets(_102348, _102346), powerset(_102348)))], (2263 ^ _24642) ^ [_102545] : [-(relation(identity_relation(_102545)))], (2265 ^ _24642) ^ [_102653, _102655] : [element(_102653, powerset(powerset(_102655))), -(element(meet_of_subsets(_102655, _102653), powerset(_102655)))], (2271 ^ _24642) ^ [_102895, _102897, _102899] : [-(element(subset_difference(_102899, _102897, _102895), powerset(_102899))), element(_102897, powerset(_102899)), element(_102895, powerset(_102899))], (2281 ^ _24642) ^ [_103224, _103226] : [relation(_103226), -(relation(relation_dom_restriction(_103226, _103224)))], (2287 ^ _24642) ^ [_103436, _103438] : [element(_103436, powerset(powerset(_103438))), -(element(complements_of_subsets(_103438, _103436), powerset(powerset(_103438))))], (2293 ^ _24642) ^ [_103668, _103670] : [relation(_103668), -(relation(relation_rng_restriction(_103670, _103668)))], (2299 ^ _24642) ^ [] : [true___, -(true___)], (2305 ^ _24642) ^ [] : [true___, -(true___)], (2312 ^ _24642) ^ [_104128] : [-(element(2310 ^ [_104128], _104128))], (2314 ^ _24642) ^ [_104240, _104242] : [2321 ^ _24642 : [(2322 ^ _24642) ^ [] : [-(empty(relation_composition(_104240, _104242)))], (2324 ^ _24642) ^ [] : [-(relation(relation_composition(_104240, _104242)))]], empty(_104242), relation(_104240)], (2326 ^ _24642) ^ [_104604] : [empty(_104604), 2329 ^ _24642 : [(2330 ^ _24642) ^ [] : [-(empty(relation_inverse(_104604)))], (2332 ^ _24642) ^ [] : [-(relation(relation_inverse(_104604)))]]], (2334 ^ _24642) ^ [] : [-(empty(empty_set))], (2336 ^ _24642) ^ [] : [-(relation(empty_set))], (2338 ^ _24642) ^ [] : [-(relation_empty_yielding(empty_set))], (2340 ^ _24642) ^ [_105046, _105048] : [2347 ^ _24642 : [(2348 ^ _24642) ^ [] : [-(relation(relation_dom_restriction(_105048, _105046)))], (2350 ^ _24642) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_105048, _105046)))]], relation(_105048), relation_empty_yielding(_105048)], (2352 ^ _24642) ^ [_105424, _105426] : [2367 ^ _24642 : [(2368 ^ _24642) ^ [] : [-(relation(relation_composition(_105426, _105424)))], (2370 ^ _24642) ^ [] : [-(function(relation_composition(_105426, _105424)))]], relation(_105426), function(_105426), relation(_105424), function(_105424)], (2372 ^ _24642) ^ [_105946] : [empty(succ(_105946))], (2374 ^ _24642) ^ [_106054, _106056] : [-(relation(set_intersection2(_106056, _106054))), relation(_106056), relation(_106054)], (2384 ^ _24642) ^ [_106323] : [empty(powerset(_106323))], (2386 ^ _24642) ^ [] : [-(empty(empty_set))], (2388 ^ _24642) ^ [_106468, _106470] : [empty(ordered_pair(_106470, _106468))], (2390 ^ _24642) ^ [_106570] : [-(relation(identity_relation(_106570)))], (2392 ^ _24642) ^ [_106615] : [-(function(identity_relation(_106615)))], (2394 ^ _24642) ^ [] : [-(relation(empty_set))], (2396 ^ _24642) ^ [] : [-(relation_empty_yielding(empty_set))], (2398 ^ _24642) ^ [] : [-(function(empty_set))], (2400 ^ _24642) ^ [] : [-(one_to_one(empty_set))], (2402 ^ _24642) ^ [] : [-(empty(empty_set))], (2404 ^ _24642) ^ [] : [-(epsilon_transitive(empty_set))], (2406 ^ _24642) ^ [] : [-(epsilon_connected(empty_set))], (2408 ^ _24642) ^ [] : [-(ordinal(empty_set))], (2410 ^ _24642) ^ [_107163, _107165] : [-(relation(set_union2(_107165, _107163))), relation(_107165), relation(_107163)], (2420 ^ _24642) ^ [_107432] : [empty(singleton(_107432))], (2422 ^ _24642) ^ [_107540, _107542] : [-(empty(_107542)), empty(set_union2(_107542, _107540))], (2428 ^ _24642) ^ [_107742] : [2439 ^ _24642 : [(2440 ^ _24642) ^ [] : [-(relation(relation_inverse(_107742)))], (2442 ^ _24642) ^ [] : [-(function(relation_inverse(_107742)))]], relation(_107742), function(_107742), one_to_one(_107742)], (2444 ^ _24642) ^ [_108173] : [ordinal(_108173), 2447 ^ _24642 : [(2448 ^ _24642) ^ [] : [empty(succ(_108173))], (2450 ^ _24642) ^ [] : [-(epsilon_transitive(succ(_108173)))], (2452 ^ _24642) ^ [] : [-(epsilon_connected(succ(_108173)))], (2454 ^ _24642) ^ [] : [-(ordinal(succ(_108173)))]]], (2456 ^ _24642) ^ [_108601, _108603] : [-(relation(set_difference(_108603, _108601))), relation(_108603), relation(_108601)], (2466 ^ _24642) ^ [_108884, _108886] : [empty(unordered_pair(_108886, _108884))], (2468 ^ _24642) ^ [_108995, _108997] : [-(empty(_108997)), empty(set_union2(_108995, _108997))], (2474 ^ _24642) ^ [_109211, _109213] : [2481 ^ _24642 : [(2482 ^ _24642) ^ [] : [-(relation(relation_dom_restriction(_109213, _109211)))], (2484 ^ _24642) ^ [] : [-(function(relation_dom_restriction(_109213, _109211)))]], relation(_109213), function(_109213)], (2486 ^ _24642) ^ [_109575] : [ordinal(_109575), 2489 ^ _24642 : [(2490 ^ _24642) ^ [] : [-(epsilon_transitive(union(_109575)))], (2492 ^ _24642) ^ [] : [-(epsilon_connected(union(_109575)))], (2494 ^ _24642) ^ [] : [-(ordinal(union(_109575)))]]], (2496 ^ _24642) ^ [] : [-(empty(empty_set))], (2498 ^ _24642) ^ [] : [-(relation(empty_set))], (2500 ^ _24642) ^ [_110036, _110038] : [empty(cartesian_product2(_110038, _110036)), -(empty(_110038)), -(empty(_110036))], (2510 ^ _24642) ^ [_110342, _110344] : [2517 ^ _24642 : [(2518 ^ _24642) ^ [] : [-(relation(relation_rng_restriction(_110344, _110342)))], (2520 ^ _24642) ^ [] : [-(function(relation_rng_restriction(_110344, _110342)))]], relation(_110342), function(_110342)], (2522 ^ _24642) ^ [_110706] : [empty(relation_dom(_110706)), -(empty(_110706)), relation(_110706)], (2532 ^ _24642) ^ [_110983] : [empty(relation_rng(_110983)), -(empty(_110983)), relation(_110983)], (2542 ^ _24642) ^ [_111260] : [empty(_111260), 2545 ^ _24642 : [(2546 ^ _24642) ^ [] : [-(empty(relation_dom(_111260)))], (2548 ^ _24642) ^ [] : [-(relation(relation_dom(_111260)))]]], (2550 ^ _24642) ^ [_111525] : [empty(_111525), 2553 ^ _24642 : [(2554 ^ _24642) ^ [] : [-(empty(relation_rng(_111525)))], (2556 ^ _24642) ^ [] : [-(relation(relation_rng(_111525)))]]], (2558 ^ _24642) ^ [_111804, _111806] : [2565 ^ _24642 : [(2566 ^ _24642) ^ [] : [-(empty(relation_composition(_111806, _111804)))], (2568 ^ _24642) ^ [] : [-(relation(relation_composition(_111806, _111804)))]], empty(_111806), relation(_111804)], (2570 ^ _24642) ^ [_112167, _112169] : [-(set_union2(_112169, _112169) = _112169)], (2572 ^ _24642) ^ [_112264, _112266] : [-(set_intersection2(_112266, _112266) = _112266)], (2574 ^ _24642) ^ [_112376, _112378] : [element(_112376, powerset(_112378)), -(subset_complement(_112378, subset_complement(_112378, _112376)) = _112376)], (2580 ^ _24642) ^ [_112588] : [relation(_112588), -(relation_inverse(relation_inverse(_112588)) = _112588)], (2586 ^ _24642) ^ [_112798, _112800] : [element(_112798, powerset(powerset(_112800))), -(complements_of_subsets(_112800, complements_of_subsets(_112800, _112798)) = _112798)], (2592 ^ _24642) ^ [_113012, _113014] : [proper_subset(_113014, _113014)], (2594 ^ _24642) ^ [_113107] : [relation(_113107), 2597 ^ _24642 : [(2608 ^ _24642) ^ [] : [2610 ^ _24642 : [(2611 ^ _24642) ^ [] : [-(in(2609 ^ [_113107], relation_field(_113107)))], (2613 ^ _24642) ^ [] : [in(ordered_pair(2609 ^ [_113107], 2609 ^ [_113107]), _113107)]], -(reflexive(_113107))], (2598 ^ _24642) ^ [] : [reflexive(_113107), 2601 ^ _24642 : [(2602 ^ _24642) ^ [_113351] : [in(_113351, relation_field(_113107)), -(in(ordered_pair(_113351, _113351), _113107))]]]]], (2617 ^ _24642) ^ [_113816] : [singleton(_113816) = empty_set], (2619 ^ _24642) ^ [_113925, _113927] : [in(_113927, _113925), -(set_union2(singleton(_113927), _113925) = _113925)], (2625 ^ _24642) ^ [_114145, _114147] : [disjoint(singleton(_114147), _114145), in(_114147, _114145)], (2631 ^ _24642) ^ [_114358, _114360] : [-(in(_114360, _114358)), -(disjoint(singleton(_114360), _114358))], (2637 ^ _24642) ^ [_114575, _114577] : [relation(_114575), -(subset(relation_dom(relation_rng_restriction(_114577, _114575)), relation_dom(_114575)))], (2643 ^ _24642) ^ [_114783] : [relation(_114783), 2646 ^ _24642 : [(2661 ^ _24642) ^ [] : [2665 ^ _24642 : [(2666 ^ _24642) ^ [] : [-(in(ordered_pair(2662 ^ [_114783], 2663 ^ [_114783]), _114783))], (2668 ^ _24642) ^ [] : [-(in(ordered_pair(2663 ^ [_114783], 2664 ^ [_114783]), _114783))], (2670 ^ _24642) ^ [] : [in(ordered_pair(2662 ^ [_114783], 2664 ^ [_114783]), _114783)]], -(transitive(_114783))], (2647 ^ _24642) ^ [] : [transitive(_114783), 2650 ^ _24642 : [(2651 ^ _24642) ^ [_115075, _115077, _115079] : [-(in(ordered_pair(_115079, _115075), _114783)), in(ordered_pair(_115079, _115077), _114783), in(ordered_pair(_115077, _115075), _114783)]]]]], (2674 ^ _24642) ^ [_115982, _115984] : [subset(singleton(_115984), _115982), -(in(_115984, _115982))], (2680 ^ _24642) ^ [_116148, _116150] : [in(_116150, _116148), -(subset(singleton(_116150), _116148))], (2686 ^ _24642) ^ [_116393, _116395] : [set_difference(_116395, _116393) = empty_set, -(subset(_116395, _116393))], (2692 ^ _24642) ^ [_116561, _116563] : [subset(_116563, _116561), -(set_difference(_116563, _116561) = empty_set)], (2698 ^ _24642) ^ [_116779, _116781] : [element(_116779, powerset(_116781)), 2701 ^ _24642 : [(2702 ^ _24642) ^ [_116920] : [in(_116920, _116779), -(in(_116920, _116781))]]], (2708 ^ _24642) ^ [_117131] : [relation(_117131), 2711 ^ _24642 : [(2726 ^ _24642) ^ [] : [2729 ^ _24642 : [(2730 ^ _24642) ^ [] : [-(in(ordered_pair(2727 ^ [_117131], 2728 ^ [_117131]), _117131))], (2732 ^ _24642) ^ [] : [-(in(ordered_pair(2728 ^ [_117131], 2727 ^ [_117131]), _117131))], (2734 ^ _24642) ^ [] : [2727 ^ [_117131] = 2728 ^ [_117131]]], -(antisymmetric(_117131))], (2712 ^ _24642) ^ [] : [antisymmetric(_117131), 2715 ^ _24642 : [(2716 ^ _24642) ^ [_117401, _117403] : [-(_117403 = _117401), in(ordered_pair(_117403, _117401), _117131), in(ordered_pair(_117401, _117403), _117131)]]]]], (2738 ^ _24642) ^ [_118181, _118183, _118185] : [subset(_118185, _118183), -(in(_118181, _118185)), -(subset(_118185, set_difference(_118183, singleton(_118181))))], (2748 ^ _24642) ^ [_118487] : [relation(_118487), 2751 ^ _24642 : [(2774 ^ _24642) ^ [] : [2777 ^ _24642 : [(2778 ^ _24642) ^ [] : [-(in(2775 ^ [_118487], relation_field(_118487)))], (2780 ^ _24642) ^ [] : [-(in(2776 ^ [_118487], relation_field(_118487)))], (2782 ^ _24642) ^ [] : [2775 ^ [_118487] = 2776 ^ [_118487]], (2784 ^ _24642) ^ [] : [in(ordered_pair(2775 ^ [_118487], 2776 ^ [_118487]), _118487)], (2786 ^ _24642) ^ [] : [in(ordered_pair(2776 ^ [_118487], 2775 ^ [_118487]), _118487)]], -(connected(_118487))], (2752 ^ _24642) ^ [] : [connected(_118487), 2755 ^ _24642 : [(2756 ^ _24642) ^ [_118781, _118783] : [in(_118783, relation_field(_118487)), in(_118781, relation_field(_118487)), -(_118783 = _118781), -(in(ordered_pair(_118783, _118781), _118487)), -(in(ordered_pair(_118781, _118783), _118487))]]]]], (2800 ^ _24642) ^ [_120233, _120235] : [2801 ^ _24642 : [(2802 ^ _24642) ^ [] : [_120235 = empty_set], (2804 ^ _24642) ^ [] : [_120235 = singleton(_120233)]], -(subset(_120235, singleton(_120233)))], (2790 ^ _24642) ^ [_119973, _119975] : [subset(_119975, singleton(_119973)), -(_119975 = empty_set), -(_119975 = singleton(_119973))], (2808 ^ _24642) ^ [_120527, _120529] : [in(_120529, _120527), -(subset(_120529, union(_120527)))], (2814 ^ _24642) ^ [_120798, _120800, _120802, _120804] : [in(ordered_pair(_120804, _120802), cartesian_product2(_120800, _120798)), 2817 ^ _24642 : [(2818 ^ _24642) ^ [] : [-(in(_120804, _120800))], (2820 ^ _24642) ^ [] : [-(in(_120802, _120798))]]], (2822 ^ _24642) ^ [_121063, _121065, _121067, _121069] : [-(in(ordered_pair(_121069, _121067), cartesian_product2(_121065, _121063))), in(_121069, _121065), in(_121067, _121063)], (2832 ^ _24642) ^ [_121396, _121398] : [2834 ^ _24642 : [(2835 ^ _24642) ^ [] : [-(in(2833 ^ [_121396, _121398], _121398))], (2837 ^ _24642) ^ [] : [in(2833 ^ [_121396, _121398], _121396)]], -(element(_121398, powerset(_121396)))], (2841 ^ _24642) ^ [_121769, _121771, _121773] : [relation(_121769), function(_121769), 2848 ^ _24642 : [(2849 ^ _24642) ^ [] : [in(_121771, relation_dom(relation_dom_restriction(_121769, _121773))), 2852 ^ _24642 : [(2853 ^ _24642) ^ [] : [-(in(_121771, relation_dom(_121769)))], (2855 ^ _24642) ^ [] : [-(in(_121771, _121773))]]], (2857 ^ _24642) ^ [] : [-(in(_121771, relation_dom(relation_dom_restriction(_121769, _121773)))), in(_121771, relation_dom(_121769)), in(_121771, _121773)]]], (2868 ^ _24642) ^ [] : [-(relation(2866 ^ []))], (2870 ^ _24642) ^ [] : [-(function(2866 ^ []))], (2873 ^ _24642) ^ [] : [-(epsilon_transitive(2871 ^ []))], (2875 ^ _24642) ^ [] : [-(epsilon_connected(2871 ^ []))], (2877 ^ _24642) ^ [] : [-(ordinal(2871 ^ []))], (2880 ^ _24642) ^ [] : [-(empty(2878 ^ []))], (2882 ^ _24642) ^ [] : [-(relation(2878 ^ []))], (2884 ^ _24642) ^ [_123014] : [-(empty(_123014)), 2888 ^ _24642 : [(2889 ^ _24642) ^ [] : [-(element(2887 ^ [_123014], powerset(_123014)))], (2891 ^ _24642) ^ [] : [empty(2887 ^ [_123014])]]], (2894 ^ _24642) ^ [] : [-(empty(2892 ^ []))], (2897 ^ _24642) ^ [] : [-(relation(2895 ^ []))], (2899 ^ _24642) ^ [] : [-(empty(2895 ^ []))], (2901 ^ _24642) ^ [] : [-(function(2895 ^ []))], (2904 ^ _24642) ^ [] : [-(relation(2902 ^ []))], (2906 ^ _24642) ^ [] : [-(function(2902 ^ []))], (2908 ^ _24642) ^ [] : [-(one_to_one(2902 ^ []))], (2910 ^ _24642) ^ [] : [-(empty(2902 ^ []))], (2912 ^ _24642) ^ [] : [-(epsilon_transitive(2902 ^ []))], (2914 ^ _24642) ^ [] : [-(epsilon_connected(2902 ^ []))], (2916 ^ _24642) ^ [] : [-(ordinal(2902 ^ []))], (2919 ^ _24642) ^ [] : [empty(2917 ^ [])], (2921 ^ _24642) ^ [] : [-(relation(2917 ^ []))], (2924 ^ _24642) ^ [_124294] : [-(element(2922 ^ [_124294], powerset(_124294)))], (2926 ^ _24642) ^ [_124345] : [-(empty(2922 ^ [_124345]))], (2929 ^ _24642) ^ [] : [empty(2927 ^ [])], (2932 ^ _24642) ^ [] : [-(relation(2930 ^ []))], (2934 ^ _24642) ^ [] : [-(function(2930 ^ []))], (2936 ^ _24642) ^ [] : [-(one_to_one(2930 ^ []))], (2939 ^ _24642) ^ [] : [empty(2937 ^ [])], (2941 ^ _24642) ^ [] : [-(epsilon_transitive(2937 ^ []))], (2943 ^ _24642) ^ [] : [-(epsilon_connected(2937 ^ []))], (2945 ^ _24642) ^ [] : [-(ordinal(2937 ^ []))], (2948 ^ _24642) ^ [] : [-(relation(2946 ^ []))], (2950 ^ _24642) ^ [] : [-(relation_empty_yielding(2946 ^ []))], (2953 ^ _24642) ^ [] : [-(relation(2951 ^ []))], (2955 ^ _24642) ^ [] : [-(relation_empty_yielding(2951 ^ []))], (2957 ^ _24642) ^ [] : [-(function(2951 ^ []))], (2959 ^ _24642) ^ [_125385, _125387] : [element(_125385, powerset(powerset(_125387))), -(union_of_subsets(_125387, _125385) = union(_125385))], (2965 ^ _24642) ^ [_125613, _125615] : [element(_125613, powerset(powerset(_125615))), -(meet_of_subsets(_125615, _125613) = set_meet(_125613))], (2971 ^ _24642) ^ [_125855, _125857, _125859] : [-(subset_difference(_125859, _125857, _125855) = set_difference(_125857, _125855)), element(_125857, powerset(_125859)), element(_125855, powerset(_125859))], (2981 ^ _24642) ^ [_126186, _126188] : [ordinal(_126188), ordinal(_126186), 2988 ^ _24642 : [(2989 ^ _24642) ^ [] : [ordinal_subset(_126188, _126186), -(subset(_126188, _126186))], (2995 ^ _24642) ^ [] : [subset(_126188, _126186), -(ordinal_subset(_126188, _126186))]]], (3001 ^ _24642) ^ [_126733, _126735] : [-(ordinal_subset(_126735, _126735)), ordinal(_126735), ordinal(_126733)], (3011 ^ _24642) ^ [_127013, _127015] : [-(subset(_127015, _127015))], (3013 ^ _24642) ^ [_127122, _127124] : [disjoint(_127124, _127122), -(disjoint(_127122, _127124))], (3019 ^ _24642) ^ [_127389, _127391, _127393, _127395] : [in(ordered_pair(_127395, _127393), cartesian_product2(_127391, _127389)), 3022 ^ _24642 : [(3023 ^ _24642) ^ [] : [-(in(_127395, _127391))], (3025 ^ _24642) ^ [] : [-(in(_127393, _127389))]]], (3027 ^ _24642) ^ [_127654, _127656, _127658, _127660] : [-(in(ordered_pair(_127660, _127658), cartesian_product2(_127656, _127654))), in(_127660, _127656), in(_127658, _127654)], (3037 ^ _24642) ^ [_127958] : [-(in(_127958, succ(_127958)))], (3039 ^ _24642) ^ [_128095, _128097, _128099, _128101] : [unordered_pair(_128101, _128099) = unordered_pair(_128097, _128095), -(_128101 = _128097), -(_128101 = _128095)], (3049 ^ _24642) ^ [_128445, _128447, _128449] : [relation(_128445), 3052 ^ _24642 : [(3053 ^ _24642) ^ [] : [in(_128449, relation_rng(relation_rng_restriction(_128447, _128445))), 3056 ^ _24642 : [(3057 ^ _24642) ^ [] : [-(in(_128449, _128447))], (3059 ^ _24642) ^ [] : [-(in(_128449, relation_rng(_128445)))]]], (3061 ^ _24642) ^ [] : [-(in(_128449, relation_rng(relation_rng_restriction(_128447, _128445)))), in(_128449, _128447), in(_128449, relation_rng(_128445))]]], (3071 ^ _24642) ^ [_129104, _129106] : [relation(_129104), -(subset(relation_rng(relation_rng_restriction(_129106, _129104)), _129106))], (3077 ^ _24642) ^ [_129322, _129324] : [relation(_129322), -(subset(relation_rng_restriction(_129324, _129322), _129322))], (3083 ^ _24642) ^ [_129536, _129538] : [relation(_129536), -(subset(relation_rng(relation_rng_restriction(_129538, _129536)), relation_rng(_129536)))], (3089 ^ _24642) ^ [_129772, _129774, _129776] : [subset(_129776, _129774), 3092 ^ _24642 : [(3093 ^ _24642) ^ [] : [-(subset(cartesian_product2(_129776, _129772), cartesian_product2(_129774, _129772)))], (3095 ^ _24642) ^ [] : [-(subset(cartesian_product2(_129772, _129776), cartesian_product2(_129772, _129774)))]]], (3097 ^ _24642) ^ [_130089, _130091] : [relation(_130089), -(relation_rng(relation_rng_restriction(_130091, _130089)) = set_intersection2(relation_rng(_130089), _130091))], (3103 ^ _24642) ^ [_130345, _130347, _130349, _130351] : [-(subset(cartesian_product2(_130351, _130347), cartesian_product2(_130349, _130345))), subset(_130351, _130349), subset(_130347, _130345)], (3113 ^ _24642) ^ [_130676, _130678] : [subset(_130678, _130676), -(set_union2(_130678, _130676) = _130676)], (3120 ^ _24642) ^ [_130998] : [-(in(_130998, 3118 ^ [_130998]))], (3122 ^ _24642) ^ [_131110, _131112, _131114] : [-(in(_131110, 3118 ^ [_131114])), in(_131112, 3118 ^ [_131114]), subset(_131110, _131112)], (3132 ^ _24642) ^ [_131425, _131427] : [in(_131425, 3118 ^ [_131427]), -(in(powerset(_131425), 3118 ^ [_131427]))], (3138 ^ _24642) ^ [_131625, _131627] : [subset(_131625, 3118 ^ [_131627]), -(are_equipotent(_131625, 3118 ^ [_131627])), -(in(_131625, 3118 ^ [_131627]))], (3148 ^ _24642) ^ [_131979, _131981, _131983] : [relation(_131979), -(relation_dom_restriction(relation_rng_restriction(_131983, _131979), _131981) = relation_rng_restriction(_131983, relation_dom_restriction(_131979, _131981)))], (3154 ^ _24642) ^ [_132231, _132233, _132235] : [relation(_132231), 3157 ^ _24642 : [(3158 ^ _24642) ^ [] : [in(_132235, relation_image(_132231, _132233)), 3162 ^ _24642 : [(3163 ^ _24642) ^ [] : [-(in(3161 ^ [_132231, _132233, _132235], relation_dom(_132231)))], (3165 ^ _24642) ^ [] : [-(in(ordered_pair(3161 ^ [_132231, _132233, _132235], _132235), _132231))], (3167 ^ _24642) ^ [] : [-(in(3161 ^ [_132231, _132233, _132235], _132233))]]], (3169 ^ _24642) ^ [] : [-(in(_132235, relation_image(_132231, _132233))), 3170 ^ _24642 : [(3171 ^ _24642) ^ [_132832] : [in(_132832, relation_dom(_132231)), in(ordered_pair(_132832, _132235), _132231), in(_132832, _132233)]]]]], (3183 ^ _24642) ^ [_133229, _133231] : [relation(_133229), -(subset(relation_image(_133229, _133231), relation_rng(_133229)))], (3189 ^ _24642) ^ [_133447, _133449] : [-(subset(relation_image(_133447, relation_inverse_image(_133447, _133449)), _133449)), relation(_133447), function(_133447)], (3199 ^ _24642) ^ [_133754, _133756] : [relation(_133754), -(relation_image(_133754, _133756) = relation_image(_133754, set_intersection2(relation_dom(_133754), _133756)))], (3205 ^ _24642) ^ [_133984, _133986] : [relation(_133984), subset(_133986, relation_dom(_133984)), -(subset(_133986, relation_inverse_image(_133984, relation_image(_133984, _133986))))], (3215 ^ _24642) ^ [_134283] : [relation(_134283), -(relation_image(_134283, relation_dom(_134283)) = relation_rng(_134283))], (3221 ^ _24642) ^ [_134499, _134501] : [relation(_134499), function(_134499), subset(_134501, relation_rng(_134499)), -(relation_image(_134499, relation_inverse_image(_134499, _134501)) = _134501)], (3235 ^ _24642) ^ [_134887] : [relation(_134887), 3238 ^ _24642 : [(3239 ^ _24642) ^ [_135027] : [relation(_135027), -(relation_rng(relation_composition(_134887, _135027)) = relation_image(_135027, relation_rng(_134887)))]]], (3245 ^ _24642) ^ [_135276, _135278, _135280] : [relation(_135276), 3248 ^ _24642 : [(3249 ^ _24642) ^ [] : [in(_135280, relation_inverse_image(_135276, _135278)), 3253 ^ _24642 : [(3254 ^ _24642) ^ [] : [-(in(3252 ^ [_135276, _135278, _135280], relation_rng(_135276)))], (3256 ^ _24642) ^ [] : [-(in(ordered_pair(_135280, 3252 ^ [_135276, _135278, _135280]), _135276))], (3258 ^ _24642) ^ [] : [-(in(3252 ^ [_135276, _135278, _135280], _135278))]]], (3260 ^ _24642) ^ [] : [-(in(_135280, relation_inverse_image(_135276, _135278))), 3261 ^ _24642 : [(3262 ^ _24642) ^ [_135877] : [in(_135877, relation_rng(_135276)), in(ordered_pair(_135280, _135877), _135276), in(_135877, _135278)]]]]], (3274 ^ _24642) ^ [_136274, _136276] : [relation(_136274), -(subset(relation_inverse_image(_136274, _136276), relation_dom(_136274)))], (3280 ^ _24642) ^ [_136506, _136508, _136510] : [relation(_136506), 3283 ^ _24642 : [(3284 ^ _24642) ^ [] : [in(_136510, relation_restriction(_136506, _136508)), 3287 ^ _24642 : [(3288 ^ _24642) ^ [] : [-(in(_136510, _136506))], (3290 ^ _24642) ^ [] : [-(in(_136510, cartesian_product2(_136508, _136508)))]]], (3292 ^ _24642) ^ [] : [-(in(_136510, relation_restriction(_136506, _136508))), in(_136510, _136506), in(_136510, cartesian_product2(_136508, _136508))]]], (3302 ^ _24642) ^ [_137162, _137164] : [relation(_137162), -(_137164 = empty_set), subset(_137164, relation_rng(_137162)), relation_inverse_image(_137162, _137164) = empty_set], (3316 ^ _24642) ^ [_137576, _137578, _137580] : [relation(_137576), subset(_137580, _137578), -(subset(relation_inverse_image(_137576, _137580), relation_inverse_image(_137576, _137578)))], (3326 ^ _24642) ^ [_137895, _137897] : [relation(_137895), -(relation_restriction(_137895, _137897) = relation_dom_restriction(relation_rng_restriction(_137897, _137895), _137897))], (3332 ^ _24642) ^ [_138106, _138108] : [-(subset(set_intersection2(_138108, _138106), _138108))], (3334 ^ _24642) ^ [_138218, _138220] : [relation(_138218), -(relation_restriction(_138218, _138220) = relation_rng_restriction(_138220, relation_dom_restriction(_138218, _138220)))], (3340 ^ _24642) ^ [_138458, _138460, _138462] : [relation(_138458), in(_138462, relation_field(relation_restriction(_138458, _138460))), 3347 ^ _24642 : [(3348 ^ _24642) ^ [] : [-(in(_138462, relation_field(_138458)))], (3350 ^ _24642) ^ [] : [-(in(_138462, _138460))]]], (3352 ^ _24642) ^ [_138870, _138872, _138874] : [-(subset(_138874, set_intersection2(_138872, _138870))), subset(_138874, _138872), subset(_138874, _138870)], (3362 ^ _24642) ^ [_139156] : [-(set_union2(_139156, empty_set) = _139156)], (3364 ^ _24642) ^ [_139266, _139268] : [in(_139268, _139266), -(element(_139268, _139266))], (3370 ^ _24642) ^ [_139490, _139492, _139494] : [-(subset(_139494, _139490)), subset(_139494, _139492), subset(_139492, _139490)], (3380 ^ _24642) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (3382 ^ _24642) ^ [_139866, _139868, _139870] : [relation(_139866), in(ordered_pair(_139870, _139868), _139866), 3389 ^ _24642 : [(3390 ^ _24642) ^ [] : [-(in(_139870, relation_dom(_139866)))], (3392 ^ _24642) ^ [] : [-(in(_139868, relation_rng(_139866)))]]], (3394 ^ _24642) ^ [_140264, _140266] : [relation(_140264), 3397 ^ _24642 : [(3398 ^ _24642) ^ [] : [-(subset(relation_field(relation_restriction(_140264, _140266)), relation_field(_140264)))], (3400 ^ _24642) ^ [] : [-(subset(relation_field(relation_restriction(_140264, _140266)), _140266))]]], (3402 ^ _24642) ^ [_140571, _140573] : [relation(_140571), function(_140571), 3409 ^ _24642 : [(3410 ^ _24642) ^ [_140821] : [relation(_140821), function(_140821), 3417 ^ _24642 : [(3418 ^ _24642) ^ [] : [in(_140573, relation_dom(relation_composition(_140821, _140571))), 3421 ^ _24642 : [(3422 ^ _24642) ^ [] : [-(in(_140573, relation_dom(_140821)))], (3424 ^ _24642) ^ [] : [-(in(apply(_140821, _140573), relation_dom(_140571)))]]], (3426 ^ _24642) ^ [] : [-(in(_140573, relation_dom(relation_composition(_140821, _140571)))), in(_140573, relation_dom(_140821)), in(apply(_140821, _140573), relation_dom(_140571))]]]]], (3436 ^ _24642) ^ [_141585] : [epsilon_transitive(_141585), 3439 ^ _24642 : [(3440 ^ _24642) ^ [_141721] : [ordinal(_141721), proper_subset(_141585, _141721), -(in(_141585, _141721))]]], (3450 ^ _24642) ^ [_142011] : [relation(_142011), -(subset(_142011, cartesian_product2(relation_dom(_142011), relation_rng(_142011))))], (3456 ^ _24642) ^ [_142241, _142243, _142245] : [relation(_142241), -(subset(fiber(relation_restriction(_142241, _142245), _142243), fiber(_142241, _142243)))], (3462 ^ _24642) ^ [_142473, _142475] : [relation(_142473), function(_142473), 3469 ^ _24642 : [(3470 ^ _24642) ^ [_142722] : [relation(_142722), function(_142722), in(_142475, relation_dom(relation_composition(_142722, _142473))), -(apply(relation_composition(_142722, _142473), _142475) = apply(_142473, apply(_142722, _142475)))]]], (3484 ^ _24642) ^ [_143167, _143169] : [relation(_143167), reflexive(_143167), -(reflexive(relation_restriction(_143167, _143169)))], (3494 ^ _24642) ^ [_143466, _143468] : [relation(_143466), function(_143466), 3501 ^ _24642 : [(3502 ^ _24642) ^ [_143712] : [relation(_143712), function(_143712), in(_143468, relation_dom(_143466)), -(apply(relation_composition(_143466, _143712), _143468) = apply(_143712, apply(_143466, _143468)))]]], (3516 ^ _24642) ^ [_144151, _144153] : [ordinal(_144151), in(_144153, _144151), -(ordinal(_144153))], (3526 ^ _24642) ^ [_144446, _144448] : [relation(_144446), connected(_144446), -(connected(relation_restriction(_144446, _144448)))], (3536 ^ _24642) ^ [_144731] : [ordinal(_144731), 3539 ^ _24642 : [(3540 ^ _24642) ^ [_144881] : [ordinal(_144881), -(in(_144731, _144881)), -(_144731 = _144881), -(in(_144881, _144731))]]], (3554 ^ _24642) ^ [_145284, _145286] : [relation(_145284), transitive(_145284), -(transitive(relation_restriction(_145284, _145286)))], (3564 ^ _24642) ^ [_145569] : [relation(_145569), 3567 ^ _24642 : [(3568 ^ _24642) ^ [_145719] : [relation(_145719), subset(_145569, _145719), 3575 ^ _24642 : [(3576 ^ _24642) ^ [] : [-(subset(relation_dom(_145569), relation_dom(_145719)))], (3578 ^ _24642) ^ [] : [-(subset(relation_rng(_145569), relation_rng(_145719)))]]]]], (3580 ^ _24642) ^ [_146114, _146116] : [relation(_146114), antisymmetric(_146114), -(antisymmetric(relation_restriction(_146114, _146116)))], (3590 ^ _24642) ^ [_146427, _146429, _146431] : [subset(_146431, _146429), -(subset(set_intersection2(_146431, _146427), set_intersection2(_146429, _146427)))], (3596 ^ _24642) ^ [_146655, _146657] : [subset(_146657, _146655), -(set_intersection2(_146657, _146655) = _146657)], (3602 ^ _24642) ^ [_146842] : [-(set_intersection2(_146842, empty_set) = empty_set)], (3604 ^ _24642) ^ [_146952, _146954] : [element(_146954, _146952), -(empty(_146952)), -(in(_146954, _146952))], (3614 ^ _24642) ^ [_147250, _147252] : [-(_147252 = _147250), 3618 ^ _24642 : [(3619 ^ _24642) ^ [] : [-(in(3615 ^ [_147250, _147252], _147252))], (3621 ^ _24642) ^ [] : [in(3615 ^ [_147250, _147252], _147250)]], 3622 ^ _24642 : [(3623 ^ _24642) ^ [] : [-(in(3615 ^ [_147250, _147252], _147250))], (3625 ^ _24642) ^ [] : [in(3615 ^ [_147250, _147252], _147252)]]], (3629 ^ _24642) ^ [_147751] : [-(subset(empty_set, _147751))], (3631 ^ _24642) ^ [_147872, _147874, _147876] : [relation(_147872), in(ordered_pair(_147876, _147874), _147872), 3638 ^ _24642 : [(3639 ^ _24642) ^ [] : [-(in(_147876, relation_field(_147872)))], (3641 ^ _24642) ^ [] : [-(in(_147874, relation_field(_147872)))]]], (3643 ^ _24642) ^ [_148256] : [-(ordinal(_148256)), 3645 ^ _24642 : [(3646 ^ _24642) ^ [] : [-(in(3644 ^ [_148256], _148256))], (3648 ^ _24642) ^ [] : [ordinal(3644 ^ [_148256]), subset(3644 ^ [_148256], _148256)]]], (3656 ^ _24642) ^ [_148686, _148688] : [relation(_148686), well_founded_relation(_148686), -(well_founded_relation(relation_restriction(_148686, _148688)))], (3666 ^ _24642) ^ [_148985, _148987] : [ordinal(_148985), subset(_148987, _148985), -(_148987 = empty_set), 3678 ^ _24642 : [(3679 ^ _24642) ^ [] : [-(ordinal(3677 ^ [_148985, _148987]))], (3681 ^ _24642) ^ [] : [-(in(3677 ^ [_148985, _148987], _148987))], (3683 ^ _24642) ^ [_149537] : [ordinal(_149537), in(_149537, _148987), -(ordinal_subset(3677 ^ [_148985, _148987], _149537))]]], (3693 ^ _24642) ^ [_149879, _149881] : [relation(_149879), well_ordering(_149879), -(well_ordering(relation_restriction(_149879, _149881)))], (3703 ^ _24642) ^ [_150164] : [ordinal(_150164), 3706 ^ _24642 : [(3707 ^ _24642) ^ [_150302] : [ordinal(_150302), 3710 ^ _24642 : [(3711 ^ _24642) ^ [] : [in(_150164, _150302), -(ordinal_subset(succ(_150164), _150302))], (3717 ^ _24642) ^ [] : [ordinal_subset(succ(_150164), _150302), -(in(_150164, _150302))]]]]], (3723 ^ _24642) ^ [_150787, _150789, _150791] : [subset(_150791, _150789), -(subset(set_difference(_150791, _150787), set_difference(_150789, _150787)))], (3729 ^ _24642) ^ [_151043, _151045, _151047, _151049] : [ordered_pair(_151049, _151047) = ordered_pair(_151045, _151043), 3732 ^ _24642 : [(3733 ^ _24642) ^ [] : [-(_151049 = _151045)], (3735 ^ _24642) ^ [] : [-(_151047 = _151043)]]], (3737 ^ _24642) ^ [_151356, _151358] : [relation(_151356), function(_151356), 3744 ^ _24642 : [(3745 ^ _24642) ^ [] : [_151356 = identity_relation(_151358), 3748 ^ _24642 : [(3749 ^ _24642) ^ [] : [-(relation_dom(_151356) = _151358)], (3751 ^ _24642) ^ [_151775] : [in(_151775, _151358), -(apply(_151356, _151775) = _151775)]]], (3757 ^ _24642) ^ [] : [-(_151356 = identity_relation(_151358)), relation_dom(_151356) = _151358, 3763 ^ _24642 : [(3764 ^ _24642) ^ [] : [-(in(3762 ^ [_151356, _151358], _151358))], (3766 ^ _24642) ^ [] : [apply(_151356, 3762 ^ [_151356, _151358]) = 3762 ^ [_151356, _151358]]]]]], (3770 ^ _24642) ^ [_152380, _152382] : [in(_152380, _152382), -(apply(identity_relation(_152382), _152380) = _152380)], (3776 ^ _24642) ^ [_152585, _152587] : [-(subset(set_difference(_152587, _152585), _152587))], (3778 ^ _24642) ^ [_152683] : [relation(_152683), 3781 ^ _24642 : [(3782 ^ _24642) ^ [] : [-(relation_rng(_152683) = relation_dom(relation_inverse(_152683)))], (3784 ^ _24642) ^ [] : [-(relation_dom(_152683) = relation_rng(relation_inverse(_152683)))]]], (3786 ^ _24642) ^ [_153011, _153013] : [set_difference(_153013, _153011) = empty_set, -(subset(_153013, _153011))], (3792 ^ _24642) ^ [_153179, _153181] : [subset(_153181, _153179), -(set_difference(_153181, _153179) = empty_set)], (3798 ^ _24642) ^ [_153426, _153428] : [subset(singleton(_153428), _153426), -(in(_153428, _153426))], (3804 ^ _24642) ^ [_153592, _153594] : [in(_153594, _153592), -(subset(singleton(_153594), _153592))], (3810 ^ _24642) ^ [_153851, _153853, _153855] : [subset(unordered_pair(_153855, _153853), _153851), 3813 ^ _24642 : [(3814 ^ _24642) ^ [] : [-(in(_153855, _153851))], (3816 ^ _24642) ^ [] : [-(in(_153853, _153851))]]], (3818 ^ _24642) ^ [_154102, _154104, _154106] : [-(subset(unordered_pair(_154106, _154104), _154102)), in(_154106, _154102), in(_154104, _154102)], (3828 ^ _24642) ^ [_154419, _154421] : [relation(_154419), -(relation_field(relation_restriction(_154419, _154421)) = _154421), well_ordering(_154419), subset(_154421, relation_field(_154419))], (3842 ^ _24642) ^ [_154802, _154804] : [-(set_union2(_154804, set_difference(_154802, _154804)) = set_union2(_154804, _154802))], (3854 ^ _24642) ^ [_155209, _155211] : [3855 ^ _24642 : [(3856 ^ _24642) ^ [] : [_155211 = empty_set], (3858 ^ _24642) ^ [] : [_155211 = singleton(_155209)]], -(subset(_155211, singleton(_155209)))], (3844 ^ _24642) ^ [_154949, _154951] : [subset(_154951, singleton(_154949)), -(_154951 = empty_set), -(_154951 = singleton(_154949))], (3862 ^ _24642) ^ [_155474] : [-(set_difference(_155474, empty_set) = _155474)], (3864 ^ _24642) ^ [_155598, _155600, _155602] : [in(_155602, _155600), in(_155600, _155598), in(_155598, _155602)], (3874 ^ _24642) ^ [_155935, _155937] : [element(_155937, powerset(_155935)), -(subset(_155937, _155935))], (3880 ^ _24642) ^ [_156101, _156103] : [subset(_156103, _156101), -(element(_156103, powerset(_156101)))], (3886 ^ _24642) ^ [_156337, _156339] : [-(disjoint(_156339, _156337)), 3890 ^ _24642 : [(3891 ^ _24642) ^ [] : [-(in(3889 ^ [_156337, _156339], _156339))], (3893 ^ _24642) ^ [] : [-(in(3889 ^ [_156337, _156339], _156337))]]], (3895 ^ _24642) ^ [_156651, _156653] : [disjoint(_156653, _156651), 3896 ^ _24642 : [(3897 ^ _24642) ^ [_156743] : [in(_156743, _156653), in(_156743, _156651)]]], (3905 ^ _24642) ^ [_157000] : [subset(_157000, empty_set), -(_157000 = empty_set)], (3911 ^ _24642) ^ [_157189, _157191] : [-(set_difference(set_union2(_157191, _157189), _157189) = set_difference(_157191, _157189))], (3913 ^ _24642) ^ [_157293] : [ordinal(_157293), 3916 ^ _24642 : [(3931 ^ _24642) ^ [] : [3933 ^ _24642 : [(3934 ^ _24642) ^ [] : [-(ordinal(3932 ^ [_157293]))], (3936 ^ _24642) ^ [] : [-(in(3932 ^ [_157293], _157293))], (3938 ^ _24642) ^ [] : [in(succ(3932 ^ [_157293]), _157293)]], -(being_limit_ordinal(_157293))], (3917 ^ _24642) ^ [] : [being_limit_ordinal(_157293), 3920 ^ _24642 : [(3921 ^ _24642) ^ [_157539] : [ordinal(_157539), in(_157539, _157293), -(in(succ(_157539), _157293))]]]]], (3942 ^ _24642) ^ [_158165] : [ordinal(_158165), 3945 ^ _24642 : [(3946 ^ _24642) ^ [] : [-(being_limit_ordinal(_158165)), 3950 ^ _24642 : [(3951 ^ _24642) ^ [] : [-(ordinal(3949 ^ [_158165]))], (3953 ^ _24642) ^ [] : [-(_158165 = succ(3949 ^ [_158165]))]]], (3955 ^ _24642) ^ [] : [being_limit_ordinal(_158165), 3956 ^ _24642 : [(3957 ^ _24642) ^ [_158636] : [ordinal(_158636), _158165 = succ(_158636)]]]]], (3965 ^ _24642) ^ [_158903, _158905] : [element(_158903, powerset(_158905)), 3968 ^ _24642 : [(3969 ^ _24642) ^ [_159055] : [element(_159055, powerset(_158905)), 3972 ^ _24642 : [(3973 ^ _24642) ^ [] : [disjoint(_158903, _159055), -(subset(_158903, subset_complement(_158905, _159055)))], (3979 ^ _24642) ^ [] : [subset(_158903, subset_complement(_158905, _159055)), -(disjoint(_158903, _159055))]]]]], (3985 ^ _24642) ^ [_159539] : [relation(_159539), 3988 ^ _24642 : [(3989 ^ _24642) ^ [_159676] : [relation(_159676), -(subset(relation_dom(relation_composition(_159539, _159676)), relation_dom(_159539)))]]], (3995 ^ _24642) ^ [_159891] : [relation(_159891), 3998 ^ _24642 : [(3999 ^ _24642) ^ [_160028] : [relation(_160028), -(subset(relation_rng(relation_composition(_159891, _160028)), relation_rng(_160028)))]]], (4005 ^ _24642) ^ [_160257, _160259] : [subset(_160259, _160257), -(_160257 = set_union2(_160259, set_difference(_160257, _160259)))], (4011 ^ _24642) ^ [_160465] : [relation(_160465), 4014 ^ _24642 : [(4015 ^ _24642) ^ [_160612] : [relation(_160612), subset(relation_rng(_160465), relation_dom(_160612)), -(relation_dom(relation_composition(_160465, _160612)) = relation_dom(_160465))]]], (4025 ^ _24642) ^ [_160938, _160940] : [element(_160938, powerset(powerset(_160940))), -(_160938 = empty_set), complements_of_subsets(_160940, _160938) = empty_set], (4035 ^ _24642) ^ [_161255, _161257] : [in(_161257, _161255), -(set_union2(singleton(_161257), _161255) = _161255)], (4041 ^ _24642) ^ [_161461] : [relation(_161461), 4044 ^ _24642 : [(4045 ^ _24642) ^ [_161608] : [relation(_161608), subset(relation_dom(_161461), relation_rng(_161608)), -(relation_rng(relation_composition(_161608, _161461)) = relation_rng(_161461))]]], (4055 ^ _24642) ^ [_161934, _161936] : [element(_161934, powerset(powerset(_161936))), -(_161934 = empty_set), -(subset_difference(_161936, cast_to_subset(_161936), union_of_subsets(_161936, _161934)) = meet_of_subsets(_161936, complements_of_subsets(_161936, _161934)))], (4065 ^ _24642) ^ [_162274, _162276] : [element(_162274, powerset(powerset(_162276))), -(_162274 = empty_set), -(union_of_subsets(_162276, complements_of_subsets(_162276, _162274)) = subset_difference(_162276, cast_to_subset(_162276), meet_of_subsets(_162276, _162274)))], (4075 ^ _24642) ^ [_162599, _162601] : [-(set_difference(_162601, set_difference(_162601, _162599)) = set_intersection2(_162601, _162599))], (4077 ^ _24642) ^ [_162703] : [relation(_162703), 4080 ^ _24642 : [(4081 ^ _24642) ^ [_162858] : [relation(_162858), 4084 ^ _24642 : [(4085 ^ _24642) ^ [_163009] : [relation(_163009), function(_163009), relation_isomorphism(_162703, _162858, _163009), -(relation_isomorphism(_162858, _162703, function_inverse(_163009)))]]]]], (4099 ^ _24642) ^ [_163402] : [-(set_difference(empty_set, _163402) = empty_set)], (4101 ^ _24642) ^ [_163526, _163528, _163530] : [-(element(_163530, _163526)), in(_163530, _163528), element(_163528, powerset(_163526))], (4111 ^ _24642) ^ [_163859, _163861] : [-(disjoint(_163861, _163859)), -(in(4114 ^ [_163859, _163861], set_intersection2(_163861, _163859)))], (4118 ^ _24642) ^ [_164094, _164096] : [4119 ^ _24642 : [(4120 ^ _24642) ^ [_164167] : [in(_164167, set_intersection2(_164096, _164094))]], disjoint(_164096, _164094)], (4124 ^ _24642) ^ [_164319] : [-(_164319 = empty_set), 4127 ^ _24642 : [(4128 ^ _24642) ^ [_164479] : [element(_164479, powerset(_164319)), 4131 ^ _24642 : [(4132 ^ _24642) ^ [_164633] : [element(_164633, _164319), -(in(_164633, _164479)), -(in(_164633, subset_complement(_164319, _164479)))]]]]], (4142 ^ _24642) ^ [_164951] : [relation(_164951), 4145 ^ _24642 : [(4146 ^ _24642) ^ [_165147] : [relation(_165147), 4149 ^ _24642 : [(4150 ^ _24642) ^ [_165339] : [relation(_165339), function(_165339), relation_isomorphism(_164951, _165147, _165339), 4161 ^ _24642 : [(4162 ^ _24642) ^ [] : [reflexive(_164951), -(reflexive(_165147))], (4168 ^ _24642) ^ [] : [transitive(_164951), -(transitive(_165147))], (4174 ^ _24642) ^ [] : [connected(_164951), -(connected(_165147))], (4180 ^ _24642) ^ [] : [antisymmetric(_164951), -(antisymmetric(_165147))], (4186 ^ _24642) ^ [] : [well_founded_relation(_164951), -(well_founded_relation(_165147))]]]]]]], (4192 ^ _24642) ^ [_166491] : [relation(_166491), function(_166491), one_to_one(_166491), 4203 ^ _24642 : [(4204 ^ _24642) ^ [_166878] : [relation(_166878), function(_166878), 4211 ^ _24642 : [(4242 ^ _24642) ^ [] : [-(_166878 = function_inverse(_166491)), relation_dom(_166878) = relation_rng(_166491), 4251 ^ _24642 : [(4252 ^ _24642) ^ [] : [-(in(4247 ^ [_166491, _166878], relation_rng(_166491)))], (4254 ^ _24642) ^ [] : [-(4248 ^ [_166491, _166878] = apply(_166878, 4247 ^ [_166491, _166878]))], (4256 ^ _24642) ^ [] : [in(4248 ^ [_166491, _166878], relation_dom(_166491)), 4247 ^ [_166491, _166878] = apply(_166491, 4248 ^ [_166491, _166878])]], 4261 ^ _24642 : [(4262 ^ _24642) ^ [] : [-(in(4248 ^ [_166491, _166878], relation_dom(_166491)))], (4264 ^ _24642) ^ [] : [-(4247 ^ [_166491, _166878] = apply(_166491, 4248 ^ [_166491, _166878]))], (4266 ^ _24642) ^ [] : [in(4247 ^ [_166491, _166878], relation_rng(_166491)), 4248 ^ [_166491, _166878] = apply(_166878, 4247 ^ [_166491, _166878])]]], (4212 ^ _24642) ^ [] : [_166878 = function_inverse(_166491), 4215 ^ _24642 : [(4216 ^ _24642) ^ [] : [-(relation_dom(_166878) = relation_rng(_166491))], (4218 ^ _24642) ^ [_167395, _167397] : [4225 ^ _24642 : [(4226 ^ _24642) ^ [] : [-(in(_167395, relation_dom(_166491)))], (4228 ^ _24642) ^ [] : [-(_167397 = apply(_166491, _167395))]], in(_167397, relation_rng(_166491)), _167395 = apply(_166878, _167397)], (4230 ^ _24642) ^ [_167769, _167771] : [4237 ^ _24642 : [(4238 ^ _24642) ^ [] : [-(in(_167771, relation_rng(_166491)))], (4240 ^ _24642) ^ [] : [-(_167769 = apply(_166878, _167771))]], in(_167769, relation_dom(_166491)), _167771 = apply(_166491, _167769)]]]]]]], (4274 ^ _24642) ^ [_169344, _169346, _169348] : [element(_169344, powerset(_169348)), in(_169346, subset_complement(_169348, _169344)), in(_169346, _169344)], (4284 ^ _24642) ^ [_169650] : [relation(_169650), function(_169650), one_to_one(_169650), 4295 ^ _24642 : [(4296 ^ _24642) ^ [] : [-(relation_rng(_169650) = relation_dom(function_inverse(_169650)))], (4298 ^ _24642) ^ [] : [-(relation_dom(_169650) = relation_rng(function_inverse(_169650)))]]], (4300 ^ _24642) ^ [_170103] : [relation(_170103), -(in(ordered_pair(4305 ^ [_170103], 4306 ^ [_170103]), _170103)), -(_170103 = empty_set)], (4312 ^ _24642) ^ [_170521, _170523] : [relation(_170521), function(_170521), 4327 ^ _24642 : [(4328 ^ _24642) ^ [] : [-(_170523 = apply(_170521, apply(function_inverse(_170521), _170523)))], (4330 ^ _24642) ^ [] : [-(_170523 = apply(relation_composition(function_inverse(_170521), _170521), _170523))]], one_to_one(_170521), in(_170523, relation_rng(_170521))], (4332 ^ _24642) ^ [_171119, _171121, _171123] : [in(_171123, _171121), element(_171121, powerset(_171119)), empty(_171119)], (4342 ^ _24642) ^ [_171415] : [relation(_171415), 4345 ^ _24642 : [(4346 ^ _24642) ^ [] : [well_founded_relation(_171415), -(is_well_founded_in(_171415, relation_field(_171415)))], (4352 ^ _24642) ^ [] : [is_well_founded_in(_171415, relation_field(_171415)), -(well_founded_relation(_171415))]]], (4358 ^ _24642) ^ [] : [-(relation_dom(empty_set) = empty_set)], (4360 ^ _24642) ^ [] : [-(relation_rng(empty_set) = empty_set)], (4362 ^ _24642) ^ [_171968, _171970] : [subset(_171970, _171968), proper_subset(_171968, _171970)], (4368 ^ _24642) ^ [_172163] : [relation(_172163), function(_172163), one_to_one(_172163), -(one_to_one(function_inverse(_172163)))], (4382 ^ _24642) ^ [_172549, _172551, _172553] : [-(disjoint(_172553, _172549)), subset(_172553, _172551), disjoint(_172551, _172549)], (4392 ^ _24642) ^ [_172844] : [relation(_172844), 4397 ^ _24642 : [(4398 ^ _24642) ^ [] : [relation_dom(_172844) = empty_set], (4400 ^ _24642) ^ [] : [relation_rng(_172844) = empty_set]], -(_172844 = empty_set)], (4404 ^ _24642) ^ [_173197] : [relation(_173197), 4407 ^ _24642 : [(4408 ^ _24642) ^ [] : [relation_dom(_173197) = empty_set, -(relation_rng(_173197) = empty_set)], (4414 ^ _24642) ^ [] : [relation_rng(_173197) = empty_set, -(relation_dom(_173197) = empty_set)]]], (4420 ^ _24642) ^ [_173680, _173682] : [set_difference(_173682, singleton(_173680)) = _173682, in(_173680, _173682)], (4426 ^ _24642) ^ [_173853, _173855] : [-(in(_173853, _173855)), -(set_difference(_173855, singleton(_173853)) = _173855)], (4432 ^ _24642) ^ [_174078, _174080] : [relation(_174078), function(_174078), 4439 ^ _24642 : [(4440 ^ _24642) ^ [_174345] : [relation(_174345), function(_174345), 4447 ^ _24642 : [(4448 ^ _24642) ^ [] : [_174078 = relation_dom_restriction(_174345, _174080), 4451 ^ _24642 : [(4452 ^ _24642) ^ [] : [-(relation_dom(_174078) = set_intersection2(relation_dom(_174345), _174080))], (4454 ^ _24642) ^ [_174799] : [in(_174799, relation_dom(_174078)), -(apply(_174078, _174799) = apply(_174345, _174799))]]], (4460 ^ _24642) ^ [] : [-(_174078 = relation_dom_restriction(_174345, _174080)), relation_dom(_174078) = set_intersection2(relation_dom(_174345), _174080), 4466 ^ _24642 : [(4467 ^ _24642) ^ [] : [-(in(4465 ^ [_174078, _174080, _174345], relation_dom(_174078)))], (4469 ^ _24642) ^ [] : [apply(_174078, 4465 ^ [_174078, _174080, _174345]) = apply(_174345, 4465 ^ [_174078, _174080, _174345])]]]]]]], (4473 ^ _24642) ^ [_175438] : [-(unordered_pair(_175438, _175438) = singleton(_175438))], (4475 ^ _24642) ^ [_175536] : [empty(_175536), -(_175536 = empty_set)], (4481 ^ _24642) ^ [_175738, _175740] : [subset(singleton(_175740), singleton(_175738)), -(_175740 = _175738)], (4487 ^ _24642) ^ [_175970, _175972, _175974] : [relation(_175970), function(_175970), in(_175972, relation_dom(relation_dom_restriction(_175970, _175974))), -(apply(relation_dom_restriction(_175970, _175974), _175972) = apply(_175970, _175972))], (4501 ^ _24642) ^ [_176389] : [-(relation_dom(identity_relation(_176389)) = _176389)], (4503 ^ _24642) ^ [_176437] : [-(relation_rng(identity_relation(_176437)) = _176437)], (4505 ^ _24642) ^ [_176564, _176566, _176568] : [relation(_176564), function(_176564), in(_176566, _176568), -(apply(relation_dom_restriction(_176564, _176568), _176566) = apply(_176564, _176566))], (4519 ^ _24642) ^ [_177010, _177012, _177014, _177016] : [relation(_177010), 4522 ^ _24642 : [(4523 ^ _24642) ^ [] : [in(ordered_pair(_177016, _177014), relation_composition(identity_relation(_177012), _177010)), 4526 ^ _24642 : [(4527 ^ _24642) ^ [] : [-(in(_177016, _177012))], (4529 ^ _24642) ^ [] : [-(in(ordered_pair(_177016, _177014), _177010))]]], (4531 ^ _24642) ^ [] : [-(in(ordered_pair(_177016, _177014), relation_composition(identity_relation(_177012), _177010))), in(_177016, _177012), in(ordered_pair(_177016, _177014), _177010)]]], (4541 ^ _24642) ^ [_177703, _177705] : [in(_177705, _177703), empty(_177703)], (4547 ^ _24642) ^ [_177910, _177912] : [in(_177912, _177910), 4551 ^ _24642 : [(4552 ^ _24642) ^ [] : [-(in(4550 ^ [_177910, _177912], _177910))], (4554 ^ _24642) ^ [_178201] : [in(_178201, _177910), in(_178201, 4550 ^ [_177910, _177912])]]], (4560 ^ _24642) ^ [_178426, _178428] : [-(subset(_178428, set_union2(_178428, _178426)))], (4562 ^ _24642) ^ [_178567, _178569] : [disjoint(_178569, _178567), -(set_difference(_178569, _178567) = _178569)], (4568 ^ _24642) ^ [_178735, _178737] : [set_difference(_178737, _178735) = _178737, -(disjoint(_178737, _178735))], (4574 ^ _24642) ^ [_178967, _178969, _178971] : [relation(_178967), 4577 ^ _24642 : [(4578 ^ _24642) ^ [] : [in(_178971, relation_dom(relation_dom_restriction(_178967, _178969))), 4581 ^ _24642 : [(4582 ^ _24642) ^ [] : [-(in(_178971, _178969))], (4584 ^ _24642) ^ [] : [-(in(_178971, relation_dom(_178967)))]]], (4586 ^ _24642) ^ [] : [-(in(_178971, relation_dom(relation_dom_restriction(_178967, _178969)))), in(_178971, _178969), in(_178971, relation_dom(_178967))]]], (4596 ^ _24642) ^ [_179626, _179628] : [relation(_179626), -(subset(relation_dom_restriction(_179626, _179628), _179626))], (4602 ^ _24642) ^ [_179840, _179842] : [empty(_179842), -(_179842 = _179840), empty(_179840)], (4612 ^ _24642) ^ [_180151, _180153, _180155] : [relation(_180151), function(_180151), 4619 ^ _24642 : [(4620 ^ _24642) ^ [] : [in(ordered_pair(_180155, _180153), _180151), 4623 ^ _24642 : [(4624 ^ _24642) ^ [] : [-(in(_180155, relation_dom(_180151)))], (4626 ^ _24642) ^ [] : [-(_180153 = apply(_180151, _180155))]]], (4628 ^ _24642) ^ [] : [-(in(ordered_pair(_180155, _180153), _180151)), in(_180155, relation_dom(_180151)), _180153 = apply(_180151, _180155)]]], (4638 ^ _24642) ^ [_180892] : [relation(_180892), 4641 ^ _24642 : [(4642 ^ _24642) ^ [] : [well_orders(_180892, relation_field(_180892)), -(well_ordering(_180892))], (4648 ^ _24642) ^ [] : [well_ordering(_180892), -(well_orders(_180892, relation_field(_180892)))]]], (4654 ^ _24642) ^ [_181351, _181353, _181355] : [-(subset(set_union2(_181355, _181351), _181353)), subset(_181355, _181353), subset(_181351, _181353)], (4664 ^ _24642) ^ [_181680, _181682, _181684] : [singleton(_181684) = unordered_pair(_181682, _181680), -(_181684 = _181682)], (4670 ^ _24642) ^ [_181906, _181908] : [relation(_181906), -(relation_dom(relation_dom_restriction(_181906, _181908)) = set_intersection2(relation_dom(_181906), _181908))], (4676 ^ _24642) ^ [_182134, _182136] : [in(_182136, _182134), -(subset(_182136, union(_182134)))], (4682 ^ _24642) ^ [_182348, _182350] : [relation(_182348), -(relation_dom_restriction(_182348, _182350) = relation_composition(identity_relation(_182350), _182348))], (4688 ^ _24642) ^ [_182572, _182574] : [relation(_182572), -(subset(relation_rng(relation_dom_restriction(_182572, _182574)), relation_rng(_182572)))], (4694 ^ _24642) ^ [_182765] : [-(union(powerset(_182765)) = _182765)], (4732 ^ _24642) ^ [_184286, _184288, _184290] : [singleton(_184290) = unordered_pair(_184288, _184286), -(_184288 = _184286)], (4697 ^ _24642) ^ [_183006] : [-(in(_183006, 4695 ^ [_183006]))], (4699 ^ _24642) ^ [_183118, _183120, _183122] : [-(in(_183118, 4695 ^ [_183122])), in(_183120, 4695 ^ [_183122]), subset(_183118, _183120)], (4709 ^ _24642) ^ [_183433, _183435] : [in(_183433, 4695 ^ [_183435]), 4713 ^ _24642 : [(4714 ^ _24642) ^ [] : [-(in(4712 ^ [_183433, _183435], 4695 ^ [_183435]))], (4716 ^ _24642) ^ [_183745] : [subset(_183745, _183433), -(in(_183745, 4712 ^ [_183433, _183435]))]]], (4722 ^ _24642) ^ [_183952, _183954] : [subset(_183952, 4695 ^ [_183954]), -(are_equipotent(_183952, 4695 ^ [_183954])), -(in(_183952, 4695 ^ [_183954]))]], input).
% 145.72/141.51  ncf('1',plain,[well_ordering(4740 ^ [])],start(4753 ^ 0)).
% 145.72/141.51  ncf('1.1',plain,[-(well_ordering(4740 ^ [])), 1450 : reflexive(4740 ^ []), 1450 : transitive(4740 ^ []), 1450 : antisymmetric(4740 ^ []), 1450 : connected(4740 ^ []), 1450 : well_founded_relation(4740 ^ []), 1450 : relation(4740 ^ [])],extension(1432 ^ 1,bind([[_74743], [4740 ^ []]]))).
% 145.72/141.51  ncf('1.1.1',plain,[-(reflexive(4740 ^ [])), 4162 : reflexive(4737 ^ []), 4162 : relation(4743 ^ []), 4162 : function(4743 ^ []), 4162 : relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []), 4150 : relation(4740 ^ []), 4146 : relation(4737 ^ [])],extension(4142 ^ 4,bind([[_164951, _165147, _165339], [4737 ^ [], 4740 ^ [], 4743 ^ []]]))).
% 145.72/141.51  ncf('1.1.1.1',plain,[-(reflexive(4737 ^ [])), 1436 : well_ordering(4737 ^ []), 1436 : relation(4737 ^ [])],extension(1432 ^ 11,bind([[_74743], [4737 ^ []]]))).
% 145.72/141.51  ncf('1.1.1.1.1',plain,[-(well_ordering(4737 ^ []))],extension(4749 ^ 14)).
% 145.72/141.51  ncf('1.1.1.1.2',plain,[-(relation(4737 ^ []))],extension(4739 ^ 12)).
% 145.72/141.51  ncf('1.1.1.2',plain,[-(relation(4743 ^ []))],extension(4745 ^ 9)).
% 145.72/141.51  ncf('1.1.1.3',plain,[-(function(4743 ^ []))],extension(4747 ^ 9)).
% 145.72/141.51  ncf('1.1.1.4',plain,[-(relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []))],extension(4751 ^ 9)).
% 145.72/141.51  ncf('1.1.1.5',plain,[-(relation(4740 ^ []))],extension(4742 ^ 7)).
% 145.72/141.51  ncf('1.1.1.6',plain,[-(relation(4737 ^ []))],extension(4739 ^ 5)).
% 145.72/141.51  ncf('1.1.2',plain,[-(transitive(4740 ^ [])), 4168 : transitive(4737 ^ []), 4168 : relation(4743 ^ []), 4168 : function(4743 ^ []), 4168 : relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []), 4150 : relation(4740 ^ []), 4146 : relation(4737 ^ [])],extension(4142 ^ 4,bind([[_164951, _165147, _165339], [4737 ^ [], 4740 ^ [], 4743 ^ []]]))).
% 145.72/141.51  ncf('1.1.2.1',plain,[-(transitive(4737 ^ [])), 1436 : well_ordering(4737 ^ []), 1436 : relation(4737 ^ [])],extension(1432 ^ 11,bind([[_74743], [4737 ^ []]]))).
% 145.72/141.51  ncf('1.1.2.1.1',plain,[-(well_ordering(4737 ^ []))],extension(4749 ^ 14)).
% 145.72/141.51  ncf('1.1.2.1.2',plain,[-(relation(4737 ^ []))],extension(4739 ^ 12)).
% 145.72/141.51  ncf('1.1.2.2',plain,[-(relation(4743 ^ []))],extension(4745 ^ 9)).
% 145.72/141.51  ncf('1.1.2.3',plain,[-(function(4743 ^ []))],extension(4747 ^ 9)).
% 145.72/141.51  ncf('1.1.2.4',plain,[-(relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []))],extension(4751 ^ 9)).
% 145.72/141.51  ncf('1.1.2.5',plain,[-(relation(4740 ^ []))],extension(4742 ^ 7)).
% 145.72/141.51  ncf('1.1.2.6',plain,[-(relation(4737 ^ []))],extension(4739 ^ 5)).
% 145.72/141.51  ncf('1.1.3',plain,[-(antisymmetric(4740 ^ [])), 4180 : antisymmetric(4737 ^ []), 4180 : relation(4743 ^ []), 4180 : function(4743 ^ []), 4180 : relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []), 4150 : relation(4740 ^ []), 4146 : relation(4737 ^ [])],extension(4142 ^ 4,bind([[_164951, _165147, _165339], [4737 ^ [], 4740 ^ [], 4743 ^ []]]))).
% 145.72/141.51  ncf('1.1.3.1',plain,[-(antisymmetric(4737 ^ [])), 1436 : well_ordering(4737 ^ []), 1436 : relation(4737 ^ [])],extension(1432 ^ 11,bind([[_74743], [4737 ^ []]]))).
% 145.72/141.51  ncf('1.1.3.1.1',plain,[-(well_ordering(4737 ^ []))],extension(4749 ^ 14)).
% 145.72/141.51  ncf('1.1.3.1.2',plain,[-(relation(4737 ^ []))],extension(4739 ^ 12)).
% 145.72/141.51  ncf('1.1.3.2',plain,[-(relation(4743 ^ []))],extension(4745 ^ 9)).
% 145.72/141.51  ncf('1.1.3.3',plain,[-(function(4743 ^ []))],extension(4747 ^ 9)).
% 145.72/141.51  ncf('1.1.3.4',plain,[-(relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []))],extension(4751 ^ 9)).
% 145.72/141.51  ncf('1.1.3.5',plain,[-(relation(4740 ^ []))],extension(4742 ^ 7)).
% 145.72/141.51  ncf('1.1.3.6',plain,[-(relation(4737 ^ []))],extension(4739 ^ 5)).
% 145.72/141.51  ncf('1.1.4',plain,[-(connected(4740 ^ [])), 4174 : connected(4737 ^ []), 4174 : relation(4743 ^ []), 4174 : function(4743 ^ []), 4174 : relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []), 4150 : relation(4740 ^ []), 4146 : relation(4737 ^ [])],extension(4142 ^ 4,bind([[_164951, _165147, _165339], [4737 ^ [], 4740 ^ [], 4743 ^ []]]))).
% 145.72/141.51  ncf('1.1.4.1',plain,[-(connected(4737 ^ [])), 1436 : well_ordering(4737 ^ []), 1436 : relation(4737 ^ [])],extension(1432 ^ 11,bind([[_74743], [4737 ^ []]]))).
% 145.72/141.51  ncf('1.1.4.1.1',plain,[-(well_ordering(4737 ^ []))],extension(4749 ^ 14)).
% 145.72/141.51  ncf('1.1.4.1.2',plain,[-(relation(4737 ^ []))],extension(4739 ^ 12)).
% 145.72/141.51  ncf('1.1.4.2',plain,[-(relation(4743 ^ []))],extension(4745 ^ 9)).
% 145.72/141.51  ncf('1.1.4.3',plain,[-(function(4743 ^ []))],extension(4747 ^ 9)).
% 145.72/141.51  ncf('1.1.4.4',plain,[-(relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []))],extension(4751 ^ 9)).
% 145.72/141.51  ncf('1.1.4.5',plain,[-(relation(4740 ^ []))],extension(4742 ^ 7)).
% 145.72/141.51  ncf('1.1.4.6',plain,[-(relation(4737 ^ []))],extension(4739 ^ 5)).
% 145.72/141.51  ncf('1.1.5',plain,[-(well_founded_relation(4740 ^ [])), 4186 : well_founded_relation(4737 ^ []), 4186 : relation(4743 ^ []), 4186 : function(4743 ^ []), 4186 : relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []), 4150 : relation(4740 ^ []), 4146 : relation(4737 ^ [])],extension(4142 ^ 4,bind([[_164951, _165147, _165339], [4737 ^ [], 4740 ^ [], 4743 ^ []]]))).
% 145.72/141.51  ncf('1.1.5.1',plain,[-(well_founded_relation(4737 ^ [])), 1436 : well_ordering(4737 ^ []), 1436 : relation(4737 ^ [])],extension(1432 ^ 11,bind([[_74743], [4737 ^ []]]))).
% 145.72/141.51  ncf('1.1.5.1.1',plain,[-(well_ordering(4737 ^ []))],extension(4749 ^ 14)).
% 145.72/141.51  ncf('1.1.5.1.2',plain,[-(relation(4737 ^ []))],extension(4739 ^ 12)).
% 145.72/141.51  ncf('1.1.5.2',plain,[-(relation(4743 ^ []))],extension(4745 ^ 9)).
% 145.72/141.51  ncf('1.1.5.3',plain,[-(function(4743 ^ []))],extension(4747 ^ 9)).
% 145.72/141.51  ncf('1.1.5.4',plain,[-(relation_isomorphism(4737 ^ [], 4740 ^ [], 4743 ^ []))],extension(4751 ^ 9)).
% 145.72/141.51  ncf('1.1.5.5',plain,[-(relation(4740 ^ []))],extension(4742 ^ 7)).
% 145.72/141.51  ncf('1.1.5.6',plain,[-(relation(4737 ^ []))],extension(4739 ^ 5)).
% 145.72/141.51  ncf('1.1.6',plain,[-(relation(4740 ^ []))],extension(4742 ^ 2)).
% 145.72/141.51  %-----------------------------------------------------
% 145.72/141.51  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------