%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU217+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n031.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 12:02:42 EDT 2023

% Result   : Theorem 0.55s 1.38s
% Output   : Proof 0.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU217+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n031.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 13:09:55 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.55/1.38  
% 0.55/1.38  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.55/1.38  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/1.38  %-----------------------------------------------------
% 0.55/1.38  ncf(matrix, plain, [(3130 ^ _18524) ^ [] : [-(in(3128 ^ [], 3127 ^ []))], (3132 ^ _18524) ^ [] : [apply(identity_relation(3127 ^ []), 3128 ^ []) = 3128 ^ []], (2 ^ _18524) ^ [_18554] : [-(_18554 = _18554)], (4 ^ _18524) ^ [_18577, _18579] : [_18579 = _18577, -(_18577 = _18579)], (10 ^ _18524) ^ [_18650, _18652, _18654] : [-(_18654 = _18650), _18654 = _18652, _18652 = _18650], (20 ^ _18524) ^ [_18787, _18789] : [-(relation_empty_yielding(_18787)), _18789 = _18787, relation_empty_yielding(_18789)], (30 ^ _18524) ^ [_18912, _18914, _18916, _18918] : [-(element(_18916, _18912)), element(_18918, _18914), _18918 = _18916, _18914 = _18912], (44 ^ _18524) ^ [_19105, _19107, _19109, _19111] : [-(proper_subset(_19109, _19105)), proper_subset(_19111, _19107), _19111 = _19109, _19107 = _19105], (58 ^ _18524) ^ [_19298, _19300, _19302, _19304] : [-(disjoint(_19302, _19298)), disjoint(_19304, _19300), _19304 = _19302, _19300 = _19298], (72 ^ _18524) ^ [_19491, _19493] : [-(empty(_19491)), _19493 = _19491, empty(_19493)], (82 ^ _18524) ^ [_19616, _19618] : [-(function(_19616)), _19618 = _19616, function(_19618)], (92 ^ _18524) ^ [_19741, _19743] : [-(relation(_19741)), _19743 = _19741, relation(_19743)], (102 ^ _18524) ^ [_19866, _19868, _19870, _19872] : [-(subset(_19870, _19866)), subset(_19872, _19868), _19872 = _19870, _19868 = _19866], (116 ^ _18524) ^ [_20059, _20061, _20063, _20065] : [-(are_equipotent(_20063, _20059)), are_equipotent(_20065, _20061), _20065 = _20063, _20061 = _20059], (130 ^ _18524) ^ [_20248, _20250, _20252, _20254] : [-(in(_20252, _20248)), in(_20254, _20250), _20254 = _20252, _20250 = _20248], (144 ^ _18524) ^ [_20465, _20467] : [_20467 = _20465, -(set_meet(_20467) = set_meet(_20465))], (150 ^ _18524) ^ [_20550, _20552, _20554, _20556] : [-(relation_rng_restriction(_20556, _20552) = relation_rng_restriction(_20554, _20550)), _20556 = _20554, _20552 = _20550], (160 ^ _18524) ^ [_20699, _20701, _20703, _20705] : [-(relation_image(_20705, _20701) = relation_image(_20703, _20699)), _20705 = _20703, _20701 = _20699], (170 ^ _18524) ^ [_20848, _20850, _20852, _20854] : [-(relation_inverse_image(_20854, _20850) = relation_inverse_image(_20852, _20848)), _20854 = _20852, _20850 = _20848], (180 ^ _18524) ^ [_20997, _20999, _21001, _21003] : [-(cartesian_product2(_21003, _20999) = cartesian_product2(_21001, _20997)), _21003 = _21001, _20999 = _20997], (190 ^ _18524) ^ [_21146, _21148] : [_21148 = _21146, -(relation_field(_21148) = relation_field(_21146))], (196 ^ _18524) ^ [_21231, _21233] : [_21233 = _21231, -(relation_inverse(_21233) = relation_inverse(_21231))], (202 ^ _18524) ^ [_21316, _21318, _21320, _21322] : [-(union_of_subsets(_21322, _21318) = union_of_subsets(_21320, _21316)), _21322 = _21320, _21318 = _21316], (212 ^ _18524) ^ [_21465, _21467, _21469, _21471] : [-(complements_of_subsets(_21471, _21467) = complements_of_subsets(_21469, _21465)), _21471 = _21469, _21467 = _21465], (222 ^ _18524) ^ [_21614, _21616, _21618, _21620, _21622, _21624] : [-(subset_difference(_21624, _21620, _21616) = subset_difference(_21622, _21618, _21614)), _21624 = _21622, _21620 = _21618, _21616 = _21614], (236 ^ _18524) ^ [_21835, _21837] : [_21837 = _21835, -(cast_to_subset(_21837) = cast_to_subset(_21835))], (242 ^ _18524) ^ [_21920, _21922, _21924, _21926] : [-(meet_of_subsets(_21926, _21922) = meet_of_subsets(_21924, _21920)), _21926 = _21924, _21922 = _21920], (252 ^ _18524) ^ [_22069, _22071, _22073, _22075] : [-(subset_complement(_22075, _22071) = subset_complement(_22073, _22069)), _22075 = _22073, _22071 = _22069], (262 ^ _18524) ^ [_22218, _22220, _22222, _22224] : [-(set_difference(_22224, _22220) = set_difference(_22222, _22218)), _22224 = _22222, _22220 = _22218], (272 ^ _18524) ^ [_22367, _22369, _22371, _22373] : [-(ordered_pair(_22373, _22369) = ordered_pair(_22371, _22367)), _22373 = _22371, _22369 = _22367], (282 ^ _18524) ^ [_22516, _22518, _22520, _22522] : [-(set_union2(_22522, _22518) = set_union2(_22520, _22516)), _22522 = _22520, _22518 = _22516], (292 ^ _18524) ^ [_22665, _22667, _22669, _22671] : [-(set_intersection2(_22671, _22667) = set_intersection2(_22669, _22665)), _22671 = _22669, _22667 = _22665], (302 ^ _18524) ^ [_22814, _22816] : [_22816 = _22814, -(relation_dom(_22816) = relation_dom(_22814))], (308 ^ _18524) ^ [_22899, _22901, _22903, _22905] : [-(relation_composition(_22905, _22901) = relation_composition(_22903, _22899)), _22905 = _22903, _22901 = _22899], (318 ^ _18524) ^ [_23048, _23050, _23052, _23054] : [-(relation_dom_restriction(_23054, _23050) = relation_dom_restriction(_23052, _23048)), _23054 = _23052, _23050 = _23048], (328 ^ _18524) ^ [_23197, _23199] : [_23199 = _23197, -(relation_rng(_23199) = relation_rng(_23197))], (334 ^ _18524) ^ [_23282, _23284] : [_23284 = _23282, -(union(_23284) = union(_23282))], (340 ^ _18524) ^ [_23367, _23369] : [_23369 = _23367, -(powerset(_23369) = powerset(_23367))], (346 ^ _18524) ^ [_23452, _23454] : [_23454 = _23452, -(singleton(_23454) = singleton(_23452))], (352 ^ _18524) ^ [_23537, _23539, _23541, _23543] : [-(unordered_pair(_23543, _23539) = unordered_pair(_23541, _23537)), _23543 = _23541, _23539 = _23537], (372 ^ _18524) ^ [_23831, _23833] : [_23833 = _23831, -(identity_relation(_23833) = identity_relation(_23831))], (362 ^ _18524) ^ [_23686, _23688, _23690, _23692] : [-(apply(_23692, _23688) = apply(_23690, _23686)), _23692 = _23690, _23688 = _23686], (378 ^ _18524) ^ [_24008, _24010] : [in(_24010, _24008), in(_24008, _24010)], (384 ^ _18524) ^ [_24086, _24088] : [proper_subset(_24088, _24086), proper_subset(_24086, _24088)], (390 ^ _18524) ^ [_24164] : [empty(_24164), -(function(_24164))], (396 ^ _18524) ^ [_24235] : [empty(_24235), -(relation(_24235))], (402 ^ _18524) ^ [_24306, _24308] : [-(unordered_pair(_24308, _24306) = unordered_pair(_24306, _24308))], (404 ^ _18524) ^ [_24337, _24339] : [-(set_union2(_24339, _24337) = set_union2(_24337, _24339))], (406 ^ _18524) ^ [_24368, _24370] : [-(set_intersection2(_24370, _24368) = set_intersection2(_24368, _24370))], (408 ^ _18524) ^ [_24399, _24401] : [relation(_24399), 411 ^ _18524 : [(434 ^ _18524) ^ [] : [-(_24399 = identity_relation(_24401)), 447 ^ _18524 : [(448 ^ _18524) ^ [] : [-(in(435 ^ [_24399, _24401], _24401))], (450 ^ _18524) ^ [] : [-(435 ^ [_24399, _24401] = 436 ^ [_24399, _24401])], (452 ^ _18524) ^ [] : [in(ordered_pair(435 ^ [_24399, _24401], 436 ^ [_24399, _24401]), _24399)]], 439 ^ _18524 : [(440 ^ _18524) ^ [] : [-(in(ordered_pair(435 ^ [_24399, _24401], 436 ^ [_24399, _24401]), _24399))], (442 ^ _18524) ^ [] : [in(435 ^ [_24399, _24401], _24401), 435 ^ [_24399, _24401] = 436 ^ [_24399, _24401]]]], (412 ^ _18524) ^ [] : [_24399 = identity_relation(_24401), 415 ^ _18524 : [(416 ^ _18524) ^ [_24552, _24554] : [in(ordered_pair(_24554, _24552), _24399), 419 ^ _18524 : [(420 ^ _18524) ^ [] : [-(in(_24554, _24401))], (422 ^ _18524) ^ [] : [-(_24554 = _24552)]]], (424 ^ _18524) ^ [_24661, _24663] : [-(in(ordered_pair(_24663, _24661), _24399)), in(_24663, _24401), _24663 = _24661]]]]], (456 ^ _18524) ^ [_25188, _25190] : [_25190 = _25188, 459 ^ _18524 : [(460 ^ _18524) ^ [] : [-(subset(_25190, _25188))], (462 ^ _18524) ^ [] : [-(subset(_25188, _25190))]]], (464 ^ _18524) ^ [_25287, _25289] : [-(_25289 = _25287), subset(_25289, _25287), subset(_25287, _25289)], (474 ^ _18524) ^ [_25418] : [relation(_25418), 477 ^ _18524 : [(478 ^ _18524) ^ [_25518, _25520] : [relation(_25518), 481 ^ _18524 : [(504 ^ _18524) ^ [] : [-(_25518 = relation_dom_restriction(_25418, _25520)), 517 ^ _18524 : [(518 ^ _18524) ^ [] : [-(in(505 ^ [_25418, _25518, _25520], _25520))], (520 ^ _18524) ^ [] : [-(in(ordered_pair(505 ^ [_25418, _25518, _25520], 506 ^ [_25418, _25518, _25520]), _25418))], (522 ^ _18524) ^ [] : [in(ordered_pair(505 ^ [_25418, _25518, _25520], 506 ^ [_25418, _25518, _25520]), _25518)]], 509 ^ _18524 : [(510 ^ _18524) ^ [] : [-(in(ordered_pair(505 ^ [_25418, _25518, _25520], 506 ^ [_25418, _25518, _25520]), _25518))], (512 ^ _18524) ^ [] : [in(505 ^ [_25418, _25518, _25520], _25520), in(ordered_pair(505 ^ [_25418, _25518, _25520], 506 ^ [_25418, _25518, _25520]), _25418)]]], (482 ^ _18524) ^ [] : [_25518 = relation_dom_restriction(_25418, _25520), 485 ^ _18524 : [(486 ^ _18524) ^ [_25680, _25682] : [in(ordered_pair(_25682, _25680), _25518), 489 ^ _18524 : [(490 ^ _18524) ^ [] : [-(in(_25682, _25520))], (492 ^ _18524) ^ [] : [-(in(ordered_pair(_25682, _25680), _25418))]]], (494 ^ _18524) ^ [_25797, _25799] : [-(in(ordered_pair(_25799, _25797), _25518)), in(_25799, _25520), in(ordered_pair(_25799, _25797), _25418)]]]]]]], (526 ^ _18524) ^ [_26367, _26369] : [relation(_26367), 529 ^ _18524 : [(530 ^ _18524) ^ [_26464] : [relation(_26464), 533 ^ _18524 : [(556 ^ _18524) ^ [] : [-(_26464 = relation_rng_restriction(_26369, _26367)), 569 ^ _18524 : [(570 ^ _18524) ^ [] : [-(in(558 ^ [_26367, _26369, _26464], _26369))], (572 ^ _18524) ^ [] : [-(in(ordered_pair(557 ^ [_26367, _26369, _26464], 558 ^ [_26367, _26369, _26464]), _26367))], (574 ^ _18524) ^ [] : [in(ordered_pair(557 ^ [_26367, _26369, _26464], 558 ^ [_26367, _26369, _26464]), _26464)]], 561 ^ _18524 : [(562 ^ _18524) ^ [] : [-(in(ordered_pair(557 ^ [_26367, _26369, _26464], 558 ^ [_26367, _26369, _26464]), _26464))], (564 ^ _18524) ^ [] : [in(558 ^ [_26367, _26369, _26464], _26369), in(ordered_pair(557 ^ [_26367, _26369, _26464], 558 ^ [_26367, _26369, _26464]), _26367)]]], (534 ^ _18524) ^ [] : [_26464 = relation_rng_restriction(_26369, _26367), 537 ^ _18524 : [(538 ^ _18524) ^ [_26626, _26628] : [in(ordered_pair(_26628, _26626), _26464), 541 ^ _18524 : [(542 ^ _18524) ^ [] : [-(in(_26626, _26369))], (544 ^ _18524) ^ [] : [-(in(ordered_pair(_26628, _26626), _26367))]]], (546 ^ _18524) ^ [_26743, _26745] : [-(in(ordered_pair(_26745, _26743), _26464)), in(_26743, _26369), in(ordered_pair(_26745, _26743), _26367)]]]]]]], (578 ^ _18524) ^ [_27304] : [relation(_27304), 581 ^ _18524 : [(605 ^ _18524) ^ [_27809, _27811] : [-(_27809 = relation_image(_27304, _27811)), 618 ^ _18524 : [(619 ^ _18524) ^ [] : [-(in(ordered_pair(617 ^ [_27304, _27809, _27811], 606 ^ [_27304, _27809, _27811]), _27304))], (621 ^ _18524) ^ [] : [-(in(617 ^ [_27304, _27809, _27811], _27811))], (623 ^ _18524) ^ [] : [in(606 ^ [_27304, _27809, _27811], _27809)]], 609 ^ _18524 : [(610 ^ _18524) ^ [] : [-(in(606 ^ [_27304, _27809, _27811], _27809))], (612 ^ _18524) ^ [_27957] : [in(ordered_pair(_27957, 606 ^ [_27304, _27809, _27811]), _27304), in(_27957, _27811)]]], (582 ^ _18524) ^ [_27411, _27413] : [_27411 = relation_image(_27304, _27413), 585 ^ _18524 : [(586 ^ _18524) ^ [_27508] : [in(_27508, _27411), 590 ^ _18524 : [(591 ^ _18524) ^ [] : [-(in(ordered_pair(589 ^ [_27304, _27411, _27413, _27508], _27508), _27304))], (593 ^ _18524) ^ [] : [-(in(589 ^ [_27304, _27411, _27413, _27508], _27413))]]], (595 ^ _18524) ^ [_27644] : [-(in(_27644, _27411)), 596 ^ _18524 : [(597 ^ _18524) ^ [_27691] : [in(ordered_pair(_27691, _27644), _27304), in(_27691, _27413)]]]]]]], (627 ^ _18524) ^ [_28211] : [relation(_28211), 630 ^ _18524 : [(654 ^ _18524) ^ [_28716, _28718] : [-(_28716 = relation_inverse_image(_28211, _28718)), 667 ^ _18524 : [(668 ^ _18524) ^ [] : [-(in(ordered_pair(655 ^ [_28211, _28716, _28718], 666 ^ [_28211, _28716, _28718]), _28211))], (670 ^ _18524) ^ [] : [-(in(666 ^ [_28211, _28716, _28718], _28718))], (672 ^ _18524) ^ [] : [in(655 ^ [_28211, _28716, _28718], _28716)]], 658 ^ _18524 : [(659 ^ _18524) ^ [] : [-(in(655 ^ [_28211, _28716, _28718], _28716))], (661 ^ _18524) ^ [_28864] : [in(ordered_pair(655 ^ [_28211, _28716, _28718], _28864), _28211), in(_28864, _28718)]]], (631 ^ _18524) ^ [_28318, _28320] : [_28318 = relation_inverse_image(_28211, _28320), 634 ^ _18524 : [(635 ^ _18524) ^ [_28415] : [in(_28415, _28318), 639 ^ _18524 : [(640 ^ _18524) ^ [] : [-(in(ordered_pair(_28415, 638 ^ [_28211, _28318, _28320, _28415]), _28211))], (642 ^ _18524) ^ [] : [-(in(638 ^ [_28211, _28318, _28320, _28415], _28320))]]], (644 ^ _18524) ^ [_28551] : [-(in(_28551, _28318)), 645 ^ _18524 : [(646 ^ _18524) ^ [_28598] : [in(ordered_pair(_28551, _28598), _28211), in(_28598, _28320)]]]]]]], (688 ^ _18524) ^ [_29315] : [690 ^ _18524 : [(691 ^ _18524) ^ [] : [-(in(689 ^ [_29315], _29315))], (693 ^ _18524) ^ [_29428, _29430] : [689 ^ [_29315] = ordered_pair(_29430, _29428)]], -(relation(_29315))], (676 ^ _18524) ^ [_29130] : [relation(_29130), 679 ^ _18524 : [(680 ^ _18524) ^ [_29206] : [in(_29206, _29130), -(_29206 = ordered_pair(683 ^ [_29130, _29206], 684 ^ [_29130, _29206]))]]], (746 ^ _18524) ^ [_30293, _30295] : [_30295 = empty_set, 749 ^ _18524 : [(750 ^ _18524) ^ [] : [_30293 = set_meet(_30295), -(_30293 = empty_set)], (756 ^ _18524) ^ [] : [_30293 = empty_set, -(_30293 = set_meet(_30295))]]], (697 ^ _18524) ^ [_29500, _29502] : [-(_29502 = empty_set), 700 ^ _18524 : [(724 ^ _18524) ^ [] : [-(_29500 = set_meet(_29502)), 728 ^ _18524 : [(729 ^ _18524) ^ [] : [-(in(725 ^ [_29500, _29502], _29500))], (732 ^ _18524) ^ [] : [-(in(730 ^ [_29500, _29502], _29502))], (734 ^ _18524) ^ [] : [in(725 ^ [_29500, _29502], 730 ^ [_29500, _29502])]], 735 ^ _18524 : [(742 ^ _18524) ^ [] : [in(725 ^ [_29500, _29502], _29500)], (736 ^ _18524) ^ [_30137] : [in(_30137, _29502), -(in(725 ^ [_29500, _29502], _30137))]]], (701 ^ _18524) ^ [] : [_29500 = set_meet(_29502), 704 ^ _18524 : [(715 ^ _18524) ^ [_29793] : [717 ^ _18524 : [(718 ^ _18524) ^ [] : [-(in(716 ^ [_29500, _29502, _29793], _29502))], (720 ^ _18524) ^ [] : [in(_29793, 716 ^ [_29500, _29502, _29793])]], -(in(_29793, _29500))], (705 ^ _18524) ^ [_29647] : [in(_29647, _29500), 708 ^ _18524 : [(709 ^ _18524) ^ [_29712] : [in(_29712, _29502), -(in(_29647, _29712))]]]]]]], (778 ^ _18524) ^ [_30758, _30760] : [-(_30758 = singleton(_30760)), 782 ^ _18524 : [(783 ^ _18524) ^ [] : [-(in(779 ^ [_30758, _30760], _30758))], (785 ^ _18524) ^ [] : [779 ^ [_30758, _30760] = _30760]], 786 ^ _18524 : [(787 ^ _18524) ^ [] : [-(779 ^ [_30758, _30760] = _30760)], (789 ^ _18524) ^ [] : [in(779 ^ [_30758, _30760], _30758)]]], (762 ^ _18524) ^ [_30523, _30525] : [_30523 = singleton(_30525), 765 ^ _18524 : [(766 ^ _18524) ^ [_30602] : [in(_30602, _30523), -(_30602 = _30525)], (772 ^ _18524) ^ [_30677] : [_30677 = _30525, -(in(_30677, _30523))]]], (793 ^ _18524) ^ [_31012] : [_31012 = empty_set, 796 ^ _18524 : [(797 ^ _18524) ^ [_31073] : [in(_31073, _31012)]]], (799 ^ _18524) ^ [_31094] : [-(in(800 ^ [_31094], _31094)), -(_31094 = empty_set)], (822 ^ _18524) ^ [_31385, _31387] : [-(_31385 = powerset(_31387)), 826 ^ _18524 : [(827 ^ _18524) ^ [] : [-(in(823 ^ [_31385, _31387], _31385))], (829 ^ _18524) ^ [] : [subset(823 ^ [_31385, _31387], _31387)]], 830 ^ _18524 : [(831 ^ _18524) ^ [] : [-(subset(823 ^ [_31385, _31387], _31387))], (833 ^ _18524) ^ [] : [in(823 ^ [_31385, _31387], _31385)]]], (806 ^ _18524) ^ [_31150, _31152] : [_31150 = powerset(_31152), 809 ^ _18524 : [(810 ^ _18524) ^ [_31229] : [in(_31229, _31150), -(subset(_31229, _31152))], (816 ^ _18524) ^ [_31304] : [subset(_31304, _31152), -(in(_31304, _31150))]]], (837 ^ _18524) ^ [_31627] : [relation(_31627), 840 ^ _18524 : [(841 ^ _18524) ^ [_31713] : [relation(_31713), 844 ^ _18524 : [(861 ^ _18524) ^ [] : [-(_31627 = _31713), 866 ^ _18524 : [(867 ^ _18524) ^ [] : [-(in(ordered_pair(862 ^ [_31627, _31713], 863 ^ [_31627, _31713]), _31627))], (869 ^ _18524) ^ [] : [in(ordered_pair(862 ^ [_31627, _31713], 863 ^ [_31627, _31713]), _31713)]], 870 ^ _18524 : [(871 ^ _18524) ^ [] : [-(in(ordered_pair(862 ^ [_31627, _31713], 863 ^ [_31627, _31713]), _31713))], (873 ^ _18524) ^ [] : [in(ordered_pair(862 ^ [_31627, _31713], 863 ^ [_31627, _31713]), _31627)]]], (845 ^ _18524) ^ [] : [_31627 = _31713, 848 ^ _18524 : [(849 ^ _18524) ^ [_31859, _31861] : [in(ordered_pair(_31861, _31859), _31627), -(in(ordered_pair(_31861, _31859), _31713))], (855 ^ _18524) ^ [_31948, _31950] : [in(ordered_pair(_31950, _31948), _31713), -(in(ordered_pair(_31950, _31948), _31627))]]]]]]], (877 ^ _18524) ^ [_32338, _32340] : [-(empty(_32340)), 880 ^ _18524 : [(881 ^ _18524) ^ [] : [element(_32338, _32340), -(in(_32338, _32340))], (887 ^ _18524) ^ [] : [in(_32338, _32340), -(element(_32338, _32340))]]], (893 ^ _18524) ^ [_32538, _32540] : [empty(_32540), 896 ^ _18524 : [(897 ^ _18524) ^ [] : [element(_32538, _32540), -(empty(_32538))], (903 ^ _18524) ^ [] : [empty(_32538), -(element(_32538, _32540))]]], (931 ^ _18524) ^ [_33060, _33062, _33064] : [-(_33060 = unordered_pair(_33064, _33062)), 935 ^ _18524 : [(936 ^ _18524) ^ [] : [-(in(932 ^ [_33060, _33062, _33064], _33060))], (938 ^ _18524) ^ [] : [932 ^ [_33060, _33062, _33064] = _33064], (940 ^ _18524) ^ [] : [932 ^ [_33060, _33062, _33064] = _33062]], 941 ^ _18524 : [(948 ^ _18524) ^ [] : [in(932 ^ [_33060, _33062, _33064], _33060)], (942 ^ _18524) ^ [] : [-(932 ^ [_33060, _33062, _33064] = _33064), -(932 ^ [_33060, _33062, _33064] = _33062)]]], (909 ^ _18524) ^ [_32760, _32762, _32764] : [_32760 = unordered_pair(_32764, _32762), 912 ^ _18524 : [(923 ^ _18524) ^ [_32939] : [924 ^ _18524 : [(925 ^ _18524) ^ [] : [_32939 = _32764], (927 ^ _18524) ^ [] : [_32939 = _32762]], -(in(_32939, _32760))], (913 ^ _18524) ^ [_32849] : [in(_32849, _32760), -(_32849 = _32764), -(_32849 = _32762)]]], (974 ^ _18524) ^ [_33700, _33702, _33704] : [-(_33700 = set_union2(_33704, _33702)), 978 ^ _18524 : [(979 ^ _18524) ^ [] : [-(in(975 ^ [_33700, _33702, _33704], _33700))], (981 ^ _18524) ^ [] : [in(975 ^ [_33700, _33702, _33704], _33704)], (983 ^ _18524) ^ [] : [in(975 ^ [_33700, _33702, _33704], _33702)]], 984 ^ _18524 : [(991 ^ _18524) ^ [] : [in(975 ^ [_33700, _33702, _33704], _33700)], (985 ^ _18524) ^ [] : [-(in(975 ^ [_33700, _33702, _33704], _33704)), -(in(975 ^ [_33700, _33702, _33704], _33702))]]], (952 ^ _18524) ^ [_33400, _33402, _33404] : [_33400 = set_union2(_33404, _33402), 955 ^ _18524 : [(966 ^ _18524) ^ [_33579] : [967 ^ _18524 : [(968 ^ _18524) ^ [] : [in(_33579, _33404)], (970 ^ _18524) ^ [] : [in(_33579, _33402)]], -(in(_33579, _33400))], (956 ^ _18524) ^ [_33489] : [in(_33489, _33400), -(in(_33489, _33404)), -(in(_33489, _33402))]]], (1025 ^ _18524) ^ [_34573, _34575, _34577] : [-(_34573 = cartesian_product2(_34577, _34575)), 1043 ^ _18524 : [(1044 ^ _18524) ^ [] : [-(in(1041 ^ [_34573, _34575, _34577], _34577))], (1046 ^ _18524) ^ [] : [-(in(1042 ^ [_34573, _34575, _34577], _34575))], (1048 ^ _18524) ^ [] : [-(1026 ^ [_34573, _34575, _34577] = ordered_pair(1041 ^ [_34573, _34575, _34577], 1042 ^ [_34573, _34575, _34577]))], (1050 ^ _18524) ^ [] : [in(1026 ^ [_34573, _34575, _34577], _34573)]], 1029 ^ _18524 : [(1030 ^ _18524) ^ [] : [-(in(1026 ^ [_34573, _34575, _34577], _34573))], (1032 ^ _18524) ^ [_34743, _34745] : [in(_34745, _34577), in(_34743, _34575), 1026 ^ [_34573, _34575, _34577] = ordered_pair(_34745, _34743)]]], (995 ^ _18524) ^ [_34040, _34042, _34044] : [_34040 = cartesian_product2(_34044, _34042), 998 ^ _18524 : [(999 ^ _18524) ^ [_34148] : [in(_34148, _34040), 1004 ^ _18524 : [(1005 ^ _18524) ^ [] : [-(in(1002 ^ [_34040, _34042, _34044, _34148], _34044))], (1007 ^ _18524) ^ [] : [-(in(1003 ^ [_34040, _34042, _34044, _34148], _34042))], (1009 ^ _18524) ^ [] : [-(_34148 = ordered_pair(1002 ^ [_34040, _34042, _34044, _34148], 1003 ^ [_34040, _34042, _34044, _34148]))]]], (1011 ^ _18524) ^ [_34335] : [-(in(_34335, _34040)), 1012 ^ _18524 : [(1013 ^ _18524) ^ [_34393, _34395] : [in(_34395, _34044), in(_34393, _34042), _34335 = ordered_pair(_34395, _34393)]]]]], (1054 ^ _18524) ^ [_35091] : [relation(_35091), 1057 ^ _18524 : [(1058 ^ _18524) ^ [_35177] : [relation(_35177), 1061 ^ _18524 : [(1072 ^ _18524) ^ [] : [1075 ^ _18524 : [(1076 ^ _18524) ^ [] : [-(in(ordered_pair(1073 ^ [_35091, _35177], 1074 ^ [_35091, _35177]), _35091))], (1078 ^ _18524) ^ [] : [in(ordered_pair(1073 ^ [_35091, _35177], 1074 ^ [_35091, _35177]), _35177)]], -(subset(_35091, _35177))], (1062 ^ _18524) ^ [] : [subset(_35091, _35177), 1065 ^ _18524 : [(1066 ^ _18524) ^ [_35308, _35310] : [in(ordered_pair(_35310, _35308), _35091), -(in(ordered_pair(_35310, _35308), _35177))]]]]]]], (1092 ^ _18524) ^ [_35721, _35723] : [1094 ^ _18524 : [(1095 ^ _18524) ^ [] : [-(in(1093 ^ [_35721, _35723], _35723))], (1097 ^ _18524) ^ [] : [in(1093 ^ [_35721, _35723], _35721)]], -(subset(_35723, _35721))], (1082 ^ _18524) ^ [_35579, _35581] : [subset(_35581, _35579), 1085 ^ _18524 : [(1086 ^ _18524) ^ [_35642] : [in(_35642, _35581), -(in(_35642, _35579))]]], (1123 ^ _18524) ^ [_36212, _36214, _36216] : [-(_36212 = set_intersection2(_36216, _36214)), 1135 ^ _18524 : [(1136 ^ _18524) ^ [] : [-(in(1124 ^ [_36212, _36214, _36216], _36216))], (1138 ^ _18524) ^ [] : [-(in(1124 ^ [_36212, _36214, _36216], _36214))], (1140 ^ _18524) ^ [] : [in(1124 ^ [_36212, _36214, _36216], _36212)]], 1127 ^ _18524 : [(1128 ^ _18524) ^ [] : [-(in(1124 ^ [_36212, _36214, _36216], _36212))], (1130 ^ _18524) ^ [] : [in(1124 ^ [_36212, _36214, _36216], _36216), in(1124 ^ [_36212, _36214, _36216], _36214)]]], (1101 ^ _18524) ^ [_35881, _35883, _35885] : [_35881 = set_intersection2(_35885, _35883), 1104 ^ _18524 : [(1105 ^ _18524) ^ [_35970] : [in(_35970, _35881), 1108 ^ _18524 : [(1109 ^ _18524) ^ [] : [-(in(_35970, _35885))], (1111 ^ _18524) ^ [] : [-(in(_35970, _35883))]]], (1113 ^ _18524) ^ [_36073] : [-(in(_36073, _35881)), in(_36073, _35885), in(_36073, _35883)]]], (1144 ^ _18524) ^ [_36566] : [relation(_36566), function(_36566), 1151 ^ _18524 : [(1152 ^ _18524) ^ [_36726, _36728] : [in(_36728, relation_dom(_36566)), 1155 ^ _18524 : [(1156 ^ _18524) ^ [] : [_36726 = apply(_36566, _36728), -(in(ordered_pair(_36728, _36726), _36566))], (1162 ^ _18524) ^ [] : [in(ordered_pair(_36728, _36726), _36566), -(_36726 = apply(_36566, _36728))]]], (1168 ^ _18524) ^ [_36956, _36958] : [-(in(_36958, relation_dom(_36566))), 1171 ^ _18524 : [(1172 ^ _18524) ^ [] : [_36956 = apply(_36566, _36958), -(_36956 = empty_set)], (1178 ^ _18524) ^ [] : [_36956 = empty_set, -(_36956 = apply(_36566, _36958))]]]]], (1184 ^ _18524) ^ [_37187] : [relation(_37187), 1187 ^ _18524 : [(1205 ^ _18524) ^ [_37561] : [-(_37561 = relation_dom(_37187)), 1209 ^ _18524 : [(1210 ^ _18524) ^ [] : [-(in(1206 ^ [_37187, _37561], _37561))], (1212 ^ _18524) ^ [_37695] : [in(ordered_pair(1206 ^ [_37187, _37561], _37695), _37187)]], 1214 ^ _18524 : [(1215 ^ _18524) ^ [] : [-(in(ordered_pair(1206 ^ [_37187, _37561], 1213 ^ [_37187, _37561]), _37187))], (1217 ^ _18524) ^ [] : [in(1206 ^ [_37187, _37561], _37561)]]], (1188 ^ _18524) ^ [_37279] : [_37279 = relation_dom(_37187), 1191 ^ _18524 : [(1192 ^ _18524) ^ [_37366] : [in(_37366, _37279), -(in(ordered_pair(_37366, 1195 ^ [_37187, _37279, _37366]), _37187))], (1199 ^ _18524) ^ [_37461] : [1200 ^ _18524 : [(1201 ^ _18524) ^ [_37505] : [in(ordered_pair(_37461, _37505), _37187)]], -(in(_37461, _37279))]]]]], (1221 ^ _18524) ^ [_37842] : [-(cast_to_subset(_37842) = _37842)], (1246 ^ _18524) ^ [_38248, _38250] : [-(_38248 = union(_38250)), 1259 ^ _18524 : [(1260 ^ _18524) ^ [] : [-(in(1247 ^ [_38248, _38250], 1258 ^ [_38248, _38250]))], (1262 ^ _18524) ^ [] : [-(in(1258 ^ [_38248, _38250], _38250))], (1264 ^ _18524) ^ [] : [in(1247 ^ [_38248, _38250], _38248)]], 1250 ^ _18524 : [(1251 ^ _18524) ^ [] : [-(in(1247 ^ [_38248, _38250], _38248))], (1253 ^ _18524) ^ [_38381] : [in(1247 ^ [_38248, _38250], _38381), in(_38381, _38250)]]], (1223 ^ _18524) ^ [_37882, _37884] : [_37882 = union(_37884), 1226 ^ _18524 : [(1227 ^ _18524) ^ [_37972] : [in(_37972, _37882), 1231 ^ _18524 : [(1232 ^ _18524) ^ [] : [-(in(_37972, 1230 ^ [_37882, _37884, _37972]))], (1234 ^ _18524) ^ [] : [-(in(1230 ^ [_37882, _37884, _37972], _37884))]]], (1236 ^ _18524) ^ [_38096] : [-(in(_38096, _37882)), 1237 ^ _18524 : [(1238 ^ _18524) ^ [_38138] : [in(_38096, _38138), in(_38138, _37884)]]]]], (1290 ^ _18524) ^ [_38969, _38971, _38973] : [-(_38969 = set_difference(_38973, _38971)), 1302 ^ _18524 : [(1303 ^ _18524) ^ [] : [-(in(1291 ^ [_38969, _38971, _38973], _38973))], (1305 ^ _18524) ^ [] : [in(1291 ^ [_38969, _38971, _38973], _38971)], (1307 ^ _18524) ^ [] : [in(1291 ^ [_38969, _38971, _38973], _38969)]], 1294 ^ _18524 : [(1295 ^ _18524) ^ [] : [-(in(1291 ^ [_38969, _38971, _38973], _38969))], (1297 ^ _18524) ^ [] : [in(1291 ^ [_38969, _38971, _38973], _38973), -(in(1291 ^ [_38969, _38971, _38973], _38971))]]], (1268 ^ _18524) ^ [_38625, _38627, _38629] : [_38625 = set_difference(_38629, _38627), 1271 ^ _18524 : [(1272 ^ _18524) ^ [_38716] : [in(_38716, _38625), 1275 ^ _18524 : [(1276 ^ _18524) ^ [] : [-(in(_38716, _38629))], (1278 ^ _18524) ^ [] : [in(_38716, _38627)]]], (1280 ^ _18524) ^ [_38827] : [-(in(_38827, _38625)), in(_38827, _38629), -(in(_38827, _38627))]]], (1311 ^ _18524) ^ [_39335] : [relation(_39335), 1314 ^ _18524 : [(1332 ^ _18524) ^ [_39709] : [-(_39709 = relation_rng(_39335)), 1336 ^ _18524 : [(1337 ^ _18524) ^ [] : [-(in(1333 ^ [_39335, _39709], _39709))], (1339 ^ _18524) ^ [_39843] : [in(ordered_pair(_39843, 1333 ^ [_39335, _39709]), _39335)]], 1341 ^ _18524 : [(1342 ^ _18524) ^ [] : [-(in(ordered_pair(1340 ^ [_39335, _39709], 1333 ^ [_39335, _39709]), _39335))], (1344 ^ _18524) ^ [] : [in(1333 ^ [_39335, _39709], _39709)]]], (1315 ^ _18524) ^ [_39427] : [_39427 = relation_rng(_39335), 1318 ^ _18524 : [(1319 ^ _18524) ^ [_39514] : [in(_39514, _39427), -(in(ordered_pair(1322 ^ [_39335, _39427, _39514], _39514), _39335))], (1326 ^ _18524) ^ [_39609] : [1327 ^ _18524 : [(1328 ^ _18524) ^ [_39653] : [in(ordered_pair(_39653, _39609), _39335)]], -(in(_39609, _39427))]]]]], (1348 ^ _18524) ^ [_39990, _39992] : [element(_39990, powerset(_39992)), -(subset_complement(_39992, _39990) = set_difference(_39992, _39990))], (1354 ^ _18524) ^ [_40083, _40085] : [-(ordered_pair(_40085, _40083) = unordered_pair(unordered_pair(_40085, _40083), singleton(_40085)))], (1356 ^ _18524) ^ [_40119] : [relation(_40119), -(relation_field(_40119) = set_union2(relation_dom(_40119), relation_rng(_40119)))], (1362 ^ _18524) ^ [_40210] : [relation(_40210), 1365 ^ _18524 : [(1366 ^ _18524) ^ [_40298] : [relation(_40298), 1369 ^ _18524 : [(1386 ^ _18524) ^ [] : [-(_40298 = relation_inverse(_40210)), 1391 ^ _18524 : [(1392 ^ _18524) ^ [] : [-(in(ordered_pair(1387 ^ [_40210, _40298], 1388 ^ [_40210, _40298]), _40298))], (1394 ^ _18524) ^ [] : [in(ordered_pair(1388 ^ [_40210, _40298], 1387 ^ [_40210, _40298]), _40210)]], 1395 ^ _18524 : [(1396 ^ _18524) ^ [] : [-(in(ordered_pair(1388 ^ [_40210, _40298], 1387 ^ [_40210, _40298]), _40210))], (1398 ^ _18524) ^ [] : [in(ordered_pair(1387 ^ [_40210, _40298], 1388 ^ [_40210, _40298]), _40298)]]], (1370 ^ _18524) ^ [] : [_40298 = relation_inverse(_40210), 1373 ^ _18524 : [(1374 ^ _18524) ^ [_40448, _40450] : [in(ordered_pair(_40450, _40448), _40298), -(in(ordered_pair(_40448, _40450), _40210))], (1380 ^ _18524) ^ [_40537, _40539] : [in(ordered_pair(_40537, _40539), _40210), -(in(ordered_pair(_40539, _40537), _40298))]]]]]]], (1402 ^ _18524) ^ [_40936, _40938] : [disjoint(_40938, _40936), -(set_intersection2(_40938, _40936) = empty_set)], (1408 ^ _18524) ^ [_41015, _41017] : [set_intersection2(_41017, _41015) = empty_set, -(disjoint(_41017, _41015))], (1414 ^ _18524) ^ [_41100] : [relation(_41100), 1417 ^ _18524 : [(1418 ^ _18524) ^ [_41213] : [relation(_41213), 1421 ^ _18524 : [(1422 ^ _18524) ^ [_41318] : [relation(_41318), 1425 ^ _18524 : [(1449 ^ _18524) ^ [] : [-(_41318 = relation_composition(_41100, _41213)), 1463 ^ _18524 : [(1464 ^ _18524) ^ [] : [-(in(ordered_pair(1450 ^ [_41100, _41213, _41318], 1462 ^ [_41100, _41213, _41318]), _41100))], (1466 ^ _18524) ^ [] : [-(in(ordered_pair(1462 ^ [_41100, _41213, _41318], 1451 ^ [_41100, _41213, _41318]), _41213))], (1468 ^ _18524) ^ [] : [in(ordered_pair(1450 ^ [_41100, _41213, _41318], 1451 ^ [_41100, _41213, _41318]), _41318)]], 1454 ^ _18524 : [(1455 ^ _18524) ^ [] : [-(in(ordered_pair(1450 ^ [_41100, _41213, _41318], 1451 ^ [_41100, _41213, _41318]), _41318))], (1457 ^ _18524) ^ [_41974] : [in(ordered_pair(1450 ^ [_41100, _41213, _41318], _41974), _41100), in(ordered_pair(_41974, 1451 ^ [_41100, _41213, _41318]), _41213)]]], (1426 ^ _18524) ^ [] : [_41318 = relation_composition(_41100, _41213), 1429 ^ _18524 : [(1430 ^ _18524) ^ [_41488, _41490] : [in(ordered_pair(_41490, _41488), _41318), 1434 ^ _18524 : [(1435 ^ _18524) ^ [] : [-(in(ordered_pair(_41490, 1433 ^ [_41100, _41213, _41318, _41488, _41490]), _41100))], (1437 ^ _18524) ^ [] : [-(in(ordered_pair(1433 ^ [_41100, _41213, _41318, _41488, _41490], _41488), _41213))]]], (1439 ^ _18524) ^ [_41642, _41644] : [-(in(ordered_pair(_41644, _41642), _41318)), 1440 ^ _18524 : [(1441 ^ _18524) ^ [_41697] : [in(ordered_pair(_41644, _41697), _41100), in(ordered_pair(_41697, _41642), _41213)]]]]]]]]]]], (1472 ^ _18524) ^ [_42284, _42286] : [element(_42284, powerset(powerset(_42286))), 1475 ^ _18524 : [(1476 ^ _18524) ^ [_42390] : [element(_42390, powerset(powerset(_42286))), 1479 ^ _18524 : [(1500 ^ _18524) ^ [] : [-(_42390 = complements_of_subsets(_42286, _42284)), 1502 ^ _18524 : [(1503 ^ _18524) ^ [] : [-(element(1501 ^ [_42284, _42286, _42390], powerset(_42286)))], (1505 ^ _18524) ^ [] : [1506 ^ _18524 : [(1507 ^ _18524) ^ [] : [-(in(1501 ^ [_42284, _42286, _42390], _42390))], (1509 ^ _18524) ^ [] : [in(subset_complement(_42286, 1501 ^ [_42284, _42286, _42390]), _42284)]], 1510 ^ _18524 : [(1511 ^ _18524) ^ [] : [-(in(subset_complement(_42286, 1501 ^ [_42284, _42286, _42390]), _42284))], (1513 ^ _18524) ^ [] : [in(1501 ^ [_42284, _42286, _42390], _42390)]]]]], (1480 ^ _18524) ^ [] : [_42390 = complements_of_subsets(_42286, _42284), 1483 ^ _18524 : [(1484 ^ _18524) ^ [_42541] : [element(_42541, powerset(_42286)), 1487 ^ _18524 : [(1488 ^ _18524) ^ [] : [in(_42541, _42390), -(in(subset_complement(_42286, _42541), _42284))], (1494 ^ _18524) ^ [] : [in(subset_complement(_42286, _42541), _42284), -(in(_42541, _42390))]]]]]]]]], (1517 ^ _18524) ^ [_43081, _43083] : [proper_subset(_43083, _43081), 1520 ^ _18524 : [(1521 ^ _18524) ^ [] : [-(subset(_43083, _43081))], (1523 ^ _18524) ^ [] : [_43083 = _43081]]], (1525 ^ _18524) ^ [_43188, _43190] : [-(proper_subset(_43190, _43188)), subset(_43190, _43188), -(_43190 = _43188)], (1535 ^ _18524) ^ [] : [true___, -(true___)], (1541 ^ _18524) ^ [] : [true___, -(true___)], (1547 ^ _18524) ^ [] : [true___, -(true___)], (1553 ^ _18524) ^ [] : [true___, -(true___)], (1559 ^ _18524) ^ [] : [true___, -(true___)], (1565 ^ _18524) ^ [] : [true___, -(true___)], (1571 ^ _18524) ^ [] : [true___, -(true___)], (1577 ^ _18524) ^ [] : [true___, -(true___)], (1583 ^ _18524) ^ [_43794] : [-(element(cast_to_subset(_43794), powerset(_43794)))], (1585 ^ _18524) ^ [] : [true___, -(true___)], (1591 ^ _18524) ^ [] : [true___, -(true___)], (1597 ^ _18524) ^ [] : [true___, -(true___)], (1603 ^ _18524) ^ [] : [true___, -(true___)], (1609 ^ _18524) ^ [_44057, _44059] : [element(_44057, powerset(_44059)), -(element(subset_complement(_44059, _44057), powerset(_44059)))], (1615 ^ _18524) ^ [] : [true___, -(true___)], (1621 ^ _18524) ^ [] : [true___, -(true___)], (1627 ^ _18524) ^ [_44266] : [relation(_44266), -(relation(relation_inverse(_44266)))], (1633 ^ _18524) ^ [] : [true___, -(true___)], (1639 ^ _18524) ^ [] : [true___, -(true___)], (1645 ^ _18524) ^ [_44459, _44461] : [-(relation(relation_composition(_44461, _44459))), relation(_44461), relation(_44459)], (1655 ^ _18524) ^ [_44588, _44590] : [element(_44588, powerset(powerset(_44590))), -(element(union_of_subsets(_44590, _44588), powerset(_44590)))], (1661 ^ _18524) ^ [_44683] : [-(relation(identity_relation(_44683)))], (1663 ^ _18524) ^ [_44707, _44709] : [element(_44707, powerset(powerset(_44709))), -(element(meet_of_subsets(_44709, _44707), powerset(_44709)))], (1669 ^ _18524) ^ [_44802, _44804, _44806] : [-(element(subset_difference(_44806, _44804, _44802), powerset(_44806))), element(_44804, powerset(_44806)), element(_44802, powerset(_44806))], (1679 ^ _18524) ^ [_44955, _44957] : [relation(_44957), -(relation(relation_dom_restriction(_44957, _44955)))], (1685 ^ _18524) ^ [_45034, _45036] : [element(_45034, powerset(powerset(_45036))), -(element(complements_of_subsets(_45036, _45034), powerset(powerset(_45036))))], (1691 ^ _18524) ^ [_45133, _45135] : [relation(_45133), -(relation(relation_rng_restriction(_45135, _45133)))], (1697 ^ _18524) ^ [] : [true___, -(true___)], (1703 ^ _18524) ^ [] : [true___, -(true___)], (1710 ^ _18524) ^ [_45330] : [-(element(1708 ^ [_45330], _45330))], (1712 ^ _18524) ^ [_45358, _45360] : [1719 ^ _18524 : [(1720 ^ _18524) ^ [] : [-(empty(relation_composition(_45358, _45360)))], (1722 ^ _18524) ^ [] : [-(relation(relation_composition(_45358, _45360)))]], empty(_45360), relation(_45358)], (1724 ^ _18524) ^ [] : [-(empty(empty_set))], (1726 ^ _18524) ^ [] : [-(relation(empty_set))], (1728 ^ _18524) ^ [] : [-(relation_empty_yielding(empty_set))], (1730 ^ _18524) ^ [_45565, _45567] : [1745 ^ _18524 : [(1746 ^ _18524) ^ [] : [-(relation(relation_composition(_45567, _45565)))], (1748 ^ _18524) ^ [] : [-(function(relation_composition(_45567, _45565)))]], relation(_45567), function(_45567), relation(_45565), function(_45565)], (1750 ^ _18524) ^ [_45824, _45826] : [-(relation(set_intersection2(_45826, _45824))), relation(_45826), relation(_45824)], (1760 ^ _18524) ^ [_45962] : [empty(powerset(_45962))], (1762 ^ _18524) ^ [] : [-(empty(empty_set))], (1764 ^ _18524) ^ [_46016, _46018] : [empty(ordered_pair(_46018, _46016))], (1766 ^ _18524) ^ [_46041] : [-(relation(identity_relation(_46041)))], (1768 ^ _18524) ^ [_46062] : [-(function(identity_relation(_46062)))], (1770 ^ _18524) ^ [_46088, _46090] : [-(relation(set_union2(_46090, _46088))), relation(_46090), relation(_46088)], (1780 ^ _18524) ^ [_46226] : [empty(singleton(_46226))], (1782 ^ _18524) ^ [_46249, _46251] : [-(empty(_46251)), empty(set_union2(_46251, _46249))], (1788 ^ _18524) ^ [_46340, _46342] : [empty(unordered_pair(_46342, _46340))], (1790 ^ _18524) ^ [_46366, _46368] : [-(empty(_46368)), empty(set_union2(_46366, _46368))], (1796 ^ _18524) ^ [] : [-(empty(empty_set))], (1798 ^ _18524) ^ [] : [-(relation(empty_set))], (1800 ^ _18524) ^ [_46477, _46479] : [empty(cartesian_product2(_46479, _46477)), -(empty(_46479)), -(empty(_46477))], (1810 ^ _18524) ^ [_46562] : [empty(relation_dom(_46562)), -(empty(_46562)), relation(_46562)], (1820 ^ _18524) ^ [_46689] : [empty(relation_rng(_46689)), -(empty(_46689)), relation(_46689)], (1830 ^ _18524) ^ [_46816] : [empty(_46816), 1833 ^ _18524 : [(1834 ^ _18524) ^ [] : [-(empty(relation_dom(_46816)))], (1836 ^ _18524) ^ [] : [-(relation(relation_dom(_46816)))]]], (1838 ^ _18524) ^ [_46919] : [empty(_46919), 1841 ^ _18524 : [(1842 ^ _18524) ^ [] : [-(empty(relation_rng(_46919)))], (1844 ^ _18524) ^ [] : [-(relation(relation_rng(_46919)))]]], (1846 ^ _18524) ^ [_47022, _47024] : [1853 ^ _18524 : [(1854 ^ _18524) ^ [] : [-(empty(relation_composition(_47024, _47022)))], (1856 ^ _18524) ^ [] : [-(relation(relation_composition(_47024, _47022)))]], empty(_47024), relation(_47022)], (1858 ^ _18524) ^ [_47181, _47183] : [-(set_union2(_47183, _47183) = _47183)], (1860 ^ _18524) ^ [_47209, _47211] : [-(set_intersection2(_47211, _47211) = _47211)], (1862 ^ _18524) ^ [_47237, _47239] : [element(_47237, powerset(_47239)), -(subset_complement(_47239, subset_complement(_47239, _47237)) = _47237)], (1868 ^ _18524) ^ [_47330] : [relation(_47330), -(relation_inverse(relation_inverse(_47330)) = _47330)], (1874 ^ _18524) ^ [_47411, _47413] : [element(_47411, powerset(powerset(_47413))), -(complements_of_subsets(_47413, complements_of_subsets(_47413, _47411)) = _47411)], (1880 ^ _18524) ^ [_47520, _47522] : [proper_subset(_47522, _47522)], (1882 ^ _18524) ^ [_47554] : [singleton(_47554) = empty_set], (1884 ^ _18524) ^ [_47579, _47581] : [in(_47581, _47579), -(set_union2(singleton(_47581), _47579) = _47579)], (1890 ^ _18524) ^ [_47666, _47668] : [disjoint(singleton(_47668), _47666), in(_47668, _47666)], (1896 ^ _18524) ^ [_47742, _47744] : [-(in(_47744, _47742)), -(disjoint(singleton(_47744), _47742))], (1902 ^ _18524) ^ [_47795, _47797] : [subset(singleton(_47797), _47795), -(in(_47797, _47795))], (1908 ^ _18524) ^ [_47872, _47874] : [in(_47874, _47872), -(subset(singleton(_47874), _47872))], (1914 ^ _18524) ^ [_47970, _47972] : [set_difference(_47972, _47970) = empty_set, -(subset(_47972, _47970))], (1920 ^ _18524) ^ [_48049, _48051] : [subset(_48051, _48049), -(set_difference(_48051, _48049) = empty_set)], (1926 ^ _18524) ^ [_48134, _48136] : [element(_48134, powerset(_48136)), 1929 ^ _18524 : [(1930 ^ _18524) ^ [_48201] : [in(_48201, _48134), -(in(_48201, _48136))]]], (1936 ^ _18524) ^ [_48284, _48286, _48288] : [subset(_48288, _48286), -(in(_48284, _48288)), -(subset(_48288, set_difference(_48286, singleton(_48284))))], (1956 ^ _18524) ^ [_48495, _48497] : [1957 ^ _18524 : [(1958 ^ _18524) ^ [] : [_48497 = empty_set], (1960 ^ _18524) ^ [] : [_48497 = singleton(_48495)]], -(subset(_48497, singleton(_48495)))], (1946 ^ _18524) ^ [_48401, _48403] : [subset(_48403, singleton(_48401)), -(_48403 = empty_set), -(_48403 = singleton(_48401))], (1964 ^ _18524) ^ [_48620, _48622] : [in(_48622, _48620), -(subset(_48622, union(_48620)))], (1970 ^ _18524) ^ [_48722, _48724, _48726, _48728] : [in(ordered_pair(_48728, _48726), cartesian_product2(_48724, _48722)), 1973 ^ _18524 : [(1974 ^ _18524) ^ [] : [-(in(_48728, _48724))], (1976 ^ _18524) ^ [] : [-(in(_48726, _48722))]]], (1978 ^ _18524) ^ [_48837, _48839, _48841, _48843] : [-(in(ordered_pair(_48843, _48841), cartesian_product2(_48839, _48837))), in(_48843, _48839), in(_48841, _48837)], (1988 ^ _18524) ^ [_48988, _48990] : [1990 ^ _18524 : [(1991 ^ _18524) ^ [] : [-(in(1989 ^ [_48988, _48990], _48990))], (1993 ^ _18524) ^ [] : [in(1989 ^ [_48988, _48990], _48988)]], -(element(_48990, powerset(_48988)))], (1998 ^ _18524) ^ [] : [-(relation(1996 ^ []))], (2000 ^ _18524) ^ [] : [-(function(1996 ^ []))], (2003 ^ _18524) ^ [] : [-(empty(2001 ^ []))], (2005 ^ _18524) ^ [] : [-(relation(2001 ^ []))], (2007 ^ _18524) ^ [_49213] : [-(empty(_49213)), 2011 ^ _18524 : [(2012 ^ _18524) ^ [] : [-(element(2010 ^ [_49213], powerset(_49213)))], (2014 ^ _18524) ^ [] : [empty(2010 ^ [_49213])]]], (2017 ^ _18524) ^ [] : [-(empty(2015 ^ []))], (2020 ^ _18524) ^ [] : [empty(2018 ^ [])], (2022 ^ _18524) ^ [] : [-(relation(2018 ^ []))], (2025 ^ _18524) ^ [_49421] : [-(element(2023 ^ [_49421], powerset(_49421)))], (2027 ^ _18524) ^ [_49448] : [-(empty(2023 ^ [_49448]))], (2030 ^ _18524) ^ [] : [empty(2028 ^ [])], (2033 ^ _18524) ^ [] : [-(relation(2031 ^ []))], (2035 ^ _18524) ^ [] : [-(relation_empty_yielding(2031 ^ []))], (2037 ^ _18524) ^ [_49548, _49550] : [element(_49548, powerset(powerset(_49550))), -(union_of_subsets(_49550, _49548) = union(_49548))], (2043 ^ _18524) ^ [_49643, _49645] : [element(_49643, powerset(powerset(_49645))), -(meet_of_subsets(_49645, _49643) = set_meet(_49643))], (2049 ^ _18524) ^ [_49738, _49740, _49742] : [-(subset_difference(_49742, _49740, _49738) = set_difference(_49740, _49738)), element(_49740, powerset(_49742)), element(_49738, powerset(_49742))], (2059 ^ _18524) ^ [_49893, _49895] : [-(subset(_49895, _49895))], (2061 ^ _18524) ^ [_49918, _49920] : [disjoint(_49920, _49918), -(disjoint(_49918, _49920))], (2067 ^ _18524) ^ [_50016, _50018, _50020, _50022] : [in(ordered_pair(_50022, _50020), cartesian_product2(_50018, _50016)), 2070 ^ _18524 : [(2071 ^ _18524) ^ [] : [-(in(_50022, _50018))], (2073 ^ _18524) ^ [] : [-(in(_50020, _50016))]]], (2075 ^ _18524) ^ [_50131, _50133, _50135, _50137] : [-(in(ordered_pair(_50137, _50135), cartesian_product2(_50133, _50131))), in(_50137, _50133), in(_50135, _50131)], (2085 ^ _18524) ^ [_50282, _50284, _50286, _50288] : [unordered_pair(_50288, _50286) = unordered_pair(_50284, _50282), -(_50288 = _50284), -(_50288 = _50282)], (2095 ^ _18524) ^ [_50392, _50394, _50396] : [relation(_50392), 2098 ^ _18524 : [(2099 ^ _18524) ^ [] : [in(_50396, relation_rng(relation_rng_restriction(_50394, _50392))), 2102 ^ _18524 : [(2103 ^ _18524) ^ [] : [-(in(_50396, _50394))], (2105 ^ _18524) ^ [] : [-(in(_50396, relation_rng(_50392)))]]], (2107 ^ _18524) ^ [] : [-(in(_50396, relation_rng(relation_rng_restriction(_50394, _50392)))), in(_50396, _50394), in(_50396, relation_rng(_50392))]]], (2117 ^ _18524) ^ [_50698, _50700] : [relation(_50698), -(subset(relation_rng(relation_rng_restriction(_50700, _50698)), _50700))], (2123 ^ _18524) ^ [_50783, _50785] : [relation(_50783), -(subset(relation_rng_restriction(_50785, _50783), _50783))], (2129 ^ _18524) ^ [_50864, _50866] : [relation(_50864), -(subset(relation_rng(relation_rng_restriction(_50866, _50864)), relation_rng(_50864)))], (2135 ^ _18524) ^ [_50953, _50955, _50957] : [subset(_50957, _50955), 2138 ^ _18524 : [(2139 ^ _18524) ^ [] : [-(subset(cartesian_product2(_50957, _50953), cartesian_product2(_50955, _50953)))], (2141 ^ _18524) ^ [] : [-(subset(cartesian_product2(_50953, _50957), cartesian_product2(_50953, _50955)))]]], (2143 ^ _18524) ^ [_51082, _51084] : [relation(_51082), -(relation_rng(relation_rng_restriction(_51084, _51082)) = set_intersection2(relation_rng(_51082), _51084))], (2149 ^ _18524) ^ [_51177, _51179, _51181, _51183] : [-(subset(cartesian_product2(_51183, _51179), cartesian_product2(_51181, _51177))), subset(_51183, _51181), subset(_51179, _51177)], (2159 ^ _18524) ^ [_51326, _51328] : [subset(_51328, _51326), -(set_union2(_51328, _51326) = _51326)], (2166 ^ _18524) ^ [_51493] : [-(in(_51493, 2164 ^ [_51493]))], (2168 ^ _18524) ^ [_51521, _51523, _51525] : [-(in(_51521, 2164 ^ [_51525])), in(_51523, 2164 ^ [_51525]), subset(_51521, _51523)], (2178 ^ _18524) ^ [_51674, _51676] : [in(_51674, 2164 ^ [_51676]), -(in(powerset(_51674), 2164 ^ [_51676]))], (2184 ^ _18524) ^ [_51771, _51773] : [subset(_51771, 2164 ^ [_51773]), -(are_equipotent(_51771, 2164 ^ [_51773])), -(in(_51771, 2164 ^ [_51773]))], (2194 ^ _18524) ^ [_51901, _51903, _51905] : [relation(_51901), -(relation_dom_restriction(relation_rng_restriction(_51905, _51901), _51903) = relation_rng_restriction(_51905, relation_dom_restriction(_51901, _51903)))], (2200 ^ _18524) ^ [_52002, _52004, _52006] : [relation(_52002), 2203 ^ _18524 : [(2204 ^ _18524) ^ [] : [in(_52006, relation_image(_52002, _52004)), 2208 ^ _18524 : [(2209 ^ _18524) ^ [] : [-(in(2207 ^ [_52002, _52004, _52006], relation_dom(_52002)))], (2211 ^ _18524) ^ [] : [-(in(ordered_pair(2207 ^ [_52002, _52004, _52006], _52006), _52002))], (2213 ^ _18524) ^ [] : [-(in(2207 ^ [_52002, _52004, _52006], _52004))]]], (2215 ^ _18524) ^ [] : [-(in(_52006, relation_image(_52002, _52004))), 2216 ^ _18524 : [(2217 ^ _18524) ^ [_52257] : [in(_52257, relation_dom(_52002)), in(ordered_pair(_52257, _52006), _52002), in(_52257, _52004)]]]]], (2229 ^ _18524) ^ [_52440, _52442] : [relation(_52440), -(subset(relation_image(_52440, _52442), relation_rng(_52440)))], (2235 ^ _18524) ^ [_52525, _52527] : [relation(_52525), -(relation_image(_52525, _52527) = relation_image(_52525, set_intersection2(relation_dom(_52525), _52527)))], (2241 ^ _18524) ^ [_52622] : [relation(_52622), -(relation_image(_52622, relation_dom(_52622)) = relation_rng(_52622))], (2247 ^ _18524) ^ [_52709] : [relation(_52709), 2250 ^ _18524 : [(2251 ^ _18524) ^ [_52777] : [relation(_52777), -(relation_rng(relation_composition(_52709, _52777)) = relation_image(_52777, relation_rng(_52709)))]]], (2257 ^ _18524) ^ [_52876, _52878, _52880] : [relation(_52876), 2260 ^ _18524 : [(2261 ^ _18524) ^ [] : [in(_52880, relation_inverse_image(_52876, _52878)), 2265 ^ _18524 : [(2266 ^ _18524) ^ [] : [-(in(2264 ^ [_52876, _52878, _52880], relation_rng(_52876)))], (2268 ^ _18524) ^ [] : [-(in(ordered_pair(_52880, 2264 ^ [_52876, _52878, _52880]), _52876))], (2270 ^ _18524) ^ [] : [-(in(2264 ^ [_52876, _52878, _52880], _52878))]]], (2272 ^ _18524) ^ [] : [-(in(_52880, relation_inverse_image(_52876, _52878))), 2273 ^ _18524 : [(2274 ^ _18524) ^ [_53131] : [in(_53131, relation_rng(_52876)), in(ordered_pair(_52880, _53131), _52876), in(_53131, _52878)]]]]], (2286 ^ _18524) ^ [_53314, _53316] : [relation(_53314), -(subset(relation_inverse_image(_53314, _53316), relation_dom(_53314)))], (2292 ^ _18524) ^ [_53399, _53401] : [relation(_53399), -(_53401 = empty_set), subset(_53401, relation_rng(_53399)), relation_inverse_image(_53399, _53401) = empty_set], (2306 ^ _18524) ^ [_53592, _53594, _53596] : [relation(_53592), subset(_53596, _53594), -(subset(relation_inverse_image(_53592, _53596), relation_inverse_image(_53592, _53594)))], (2316 ^ _18524) ^ [_53735, _53737] : [-(subset(set_intersection2(_53737, _53735), _53737))], (2318 ^ _18524) ^ [_53763, _53765, _53767] : [-(subset(_53767, set_intersection2(_53765, _53763))), subset(_53767, _53765), subset(_53767, _53763)], (2328 ^ _18524) ^ [_53902] : [-(set_union2(_53902, empty_set) = _53902)], (2330 ^ _18524) ^ [_53928, _53930] : [in(_53930, _53928), -(element(_53930, _53928))], (2336 ^ _18524) ^ [_54005, _54007, _54009] : [-(subset(_54009, _54005)), subset(_54009, _54007), subset(_54007, _54005)], (2346 ^ _18524) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (2348 ^ _18524) ^ [_54156, _54158, _54160] : [relation(_54156), in(ordered_pair(_54160, _54158), _54156), 2355 ^ _18524 : [(2356 ^ _18524) ^ [] : [-(in(_54160, relation_dom(_54156)))], (2358 ^ _18524) ^ [] : [-(in(_54158, relation_rng(_54156)))]]], (2360 ^ _18524) ^ [_54327, _54329] : [relation(_54327), function(_54327), 2367 ^ _18524 : [(2368 ^ _18524) ^ [_54466] : [relation(_54466), function(_54466), 2375 ^ _18524 : [(2376 ^ _18524) ^ [] : [in(_54329, relation_dom(relation_composition(_54466, _54327))), 2379 ^ _18524 : [(2380 ^ _18524) ^ [] : [-(in(_54329, relation_dom(_54466)))], (2382 ^ _18524) ^ [] : [-(in(apply(_54466, _54329), relation_dom(_54327)))]]], (2384 ^ _18524) ^ [] : [-(in(_54329, relation_dom(relation_composition(_54466, _54327)))), in(_54329, relation_dom(_54466)), in(apply(_54466, _54329), relation_dom(_54327))]]]]], (2394 ^ _18524) ^ [_54847] : [relation(_54847), -(subset(_54847, cartesian_product2(relation_dom(_54847), relation_rng(_54847))))], (2400 ^ _18524) ^ [_54934, _54936] : [relation(_54934), function(_54934), 2407 ^ _18524 : [(2408 ^ _18524) ^ [_55072] : [relation(_55072), function(_55072), in(_54936, relation_dom(relation_composition(_55072, _54934))), -(apply(relation_composition(_55072, _54934), _54936) = apply(_54934, apply(_55072, _54936)))]]], (2422 ^ _18524) ^ [_55297, _55299] : [relation(_55297), function(_55297), 2429 ^ _18524 : [(2430 ^ _18524) ^ [_55432] : [relation(_55432), function(_55432), in(_55299, relation_dom(_55297)), -(apply(relation_composition(_55297, _55432), _55299) = apply(_55432, apply(_55297, _55299)))]]], (2444 ^ _18524) ^ [_55651] : [relation(_55651), 2447 ^ _18524 : [(2448 ^ _18524) ^ [_55729] : [relation(_55729), subset(_55651, _55729), 2455 ^ _18524 : [(2456 ^ _18524) ^ [] : [-(subset(relation_dom(_55651), relation_dom(_55729)))], (2458 ^ _18524) ^ [] : [-(subset(relation_rng(_55651), relation_rng(_55729)))]]]]], (2460 ^ _18524) ^ [_55902, _55904, _55906] : [subset(_55906, _55904), -(subset(set_intersection2(_55906, _55902), set_intersection2(_55904, _55902)))], (2466 ^ _18524) ^ [_55993, _55995] : [subset(_55995, _55993), -(set_intersection2(_55995, _55993) = _55995)], (2472 ^ _18524) ^ [_56076] : [-(set_intersection2(_56076, empty_set) = empty_set)], (2474 ^ _18524) ^ [_56102, _56104] : [element(_56104, _56102), -(empty(_56102)), -(in(_56104, _56102))], (2484 ^ _18524) ^ [_56190, _56192] : [-(_56192 = _56190), 2488 ^ _18524 : [(2489 ^ _18524) ^ [] : [-(in(2485 ^ [_56190, _56192], _56192))], (2491 ^ _18524) ^ [] : [in(2485 ^ [_56190, _56192], _56190)]], 2492 ^ _18524 : [(2493 ^ _18524) ^ [] : [-(in(2485 ^ [_56190, _56192], _56190))], (2495 ^ _18524) ^ [] : [in(2485 ^ [_56190, _56192], _56192)]]], (2499 ^ _18524) ^ [_56426] : [-(subset(empty_set, _56426))], (2501 ^ _18524) ^ [_56449, _56451, _56453] : [relation(_56449), in(ordered_pair(_56453, _56451), _56449), 2508 ^ _18524 : [(2509 ^ _18524) ^ [] : [-(in(_56453, relation_field(_56449)))], (2511 ^ _18524) ^ [] : [-(in(_56451, relation_field(_56449)))]]], (2513 ^ _18524) ^ [_56620, _56622, _56624] : [subset(_56624, _56622), -(subset(set_difference(_56624, _56620), set_difference(_56622, _56620)))], (2519 ^ _18524) ^ [_56711, _56713, _56715, _56717] : [ordered_pair(_56717, _56715) = ordered_pair(_56713, _56711), 2522 ^ _18524 : [(2523 ^ _18524) ^ [] : [-(_56717 = _56713)], (2525 ^ _18524) ^ [] : [-(_56715 = _56711)]]], (2527 ^ _18524) ^ [_56830, _56832] : [relation(_56830), function(_56830), 2534 ^ _18524 : [(2535 ^ _18524) ^ [] : [_56830 = identity_relation(_56832), 2538 ^ _18524 : [(2539 ^ _18524) ^ [] : [-(relation_dom(_56830) = _56832)], (2541 ^ _18524) ^ [_57038] : [in(_57038, _56832), -(apply(_56830, _57038) = _57038)]]], (2547 ^ _18524) ^ [] : [-(_56830 = identity_relation(_56832)), relation_dom(_56830) = _56832, 2553 ^ _18524 : [(2554 ^ _18524) ^ [] : [-(in(2552 ^ [_56830, _56832], _56832))], (2556 ^ _18524) ^ [] : [apply(_56830, 2552 ^ [_56830, _56832]) = 2552 ^ [_56830, _56832]]]]]], (2560 ^ _18524) ^ [_57317, _57319] : [-(subset(set_difference(_57319, _57317), _57319))], (2562 ^ _18524) ^ [_57345] : [relation(_57345), 2565 ^ _18524 : [(2566 ^ _18524) ^ [] : [-(relation_rng(_57345) = relation_dom(relation_inverse(_57345)))], (2568 ^ _18524) ^ [] : [-(relation_dom(_57345) = relation_rng(relation_inverse(_57345)))]]], (2570 ^ _18524) ^ [_57483, _57485] : [set_difference(_57485, _57483) = empty_set, -(subset(_57485, _57483))], (2576 ^ _18524) ^ [_57562, _57564] : [subset(_57564, _57562), -(set_difference(_57564, _57562) = empty_set)], (2582 ^ _18524) ^ [_57662, _57664] : [subset(singleton(_57664), _57662), -(in(_57664, _57662))], (2588 ^ _18524) ^ [_57739, _57741] : [in(_57741, _57739), -(subset(singleton(_57741), _57739))], (2594 ^ _18524) ^ [_57840, _57842, _57844] : [subset(unordered_pair(_57844, _57842), _57840), 2597 ^ _18524 : [(2598 ^ _18524) ^ [] : [-(in(_57844, _57840))], (2600 ^ _18524) ^ [] : [-(in(_57842, _57840))]]], (2602 ^ _18524) ^ [_57947, _57949, _57951] : [-(subset(unordered_pair(_57951, _57949), _57947)), in(_57951, _57947), in(_57949, _57947)], (2612 ^ _18524) ^ [_58088, _58090] : [-(set_union2(_58090, set_difference(_58088, _58090)) = set_union2(_58090, _58088))], (2624 ^ _18524) ^ [_58231, _58233] : [2625 ^ _18524 : [(2626 ^ _18524) ^ [] : [_58233 = empty_set], (2628 ^ _18524) ^ [] : [_58233 = singleton(_58231)]], -(subset(_58233, singleton(_58231)))], (2614 ^ _18524) ^ [_58137, _58139] : [subset(_58139, singleton(_58137)), -(_58139 = empty_set), -(_58139 = singleton(_58137))], (2632 ^ _18524) ^ [_58356] : [-(set_difference(_58356, empty_set) = _58356)], (2634 ^ _18524) ^ [_58397, _58399] : [element(_58399, powerset(_58397)), -(subset(_58399, _58397))], (2640 ^ _18524) ^ [_58474, _58476] : [subset(_58476, _58474), -(element(_58476, powerset(_58474)))], (2646 ^ _18524) ^ [_58563, _58565] : [-(disjoint(_58565, _58563)), 2650 ^ _18524 : [(2651 ^ _18524) ^ [] : [-(in(2649 ^ [_58563, _58565], _58565))], (2653 ^ _18524) ^ [] : [-(in(2649 ^ [_58563, _58565], _58563))]]], (2655 ^ _18524) ^ [_58646, _58648] : [disjoint(_58648, _58646), 2656 ^ _18524 : [(2657 ^ _18524) ^ [_58686] : [in(_58686, _58648), in(_58686, _58646)]]], (2665 ^ _18524) ^ [_58793] : [subset(_58793, empty_set), -(_58793 = empty_set)], (2671 ^ _18524) ^ [_58868, _58870] : [-(set_difference(set_union2(_58870, _58868), _58868) = set_difference(_58870, _58868))], (2673 ^ _18524) ^ [_58902, _58904] : [element(_58902, powerset(_58904)), 2676 ^ _18524 : [(2677 ^ _18524) ^ [_58980] : [element(_58980, powerset(_58904)), 2680 ^ _18524 : [(2681 ^ _18524) ^ [] : [disjoint(_58902, _58980), -(subset(_58902, subset_complement(_58904, _58980)))], (2687 ^ _18524) ^ [] : [subset(_58902, subset_complement(_58904, _58980)), -(disjoint(_58902, _58980))]]]]], (2693 ^ _18524) ^ [_59210] : [relation(_59210), 2696 ^ _18524 : [(2697 ^ _18524) ^ [_59275] : [relation(_59275), -(subset(relation_dom(relation_composition(_59210, _59275)), relation_dom(_59210)))]]], (2703 ^ _18524) ^ [_59368] : [relation(_59368), 2706 ^ _18524 : [(2707 ^ _18524) ^ [_59433] : [relation(_59433), -(subset(relation_rng(relation_composition(_59368, _59433)), relation_rng(_59433)))]]], (2713 ^ _18524) ^ [_59526, _59528] : [subset(_59528, _59526), -(_59526 = set_union2(_59528, set_difference(_59526, _59528)))], (2719 ^ _18524) ^ [_59615] : [relation(_59615), 2722 ^ _18524 : [(2723 ^ _18524) ^ [_59690] : [relation(_59690), subset(relation_rng(_59615), relation_dom(_59690)), -(relation_dom(relation_composition(_59615, _59690)) = relation_dom(_59615))]]], (2733 ^ _18524) ^ [_59843, _59845] : [element(_59843, powerset(powerset(_59845))), -(_59843 = empty_set), complements_of_subsets(_59845, _59843) = empty_set], (2743 ^ _18524) ^ [_59990, _59992] : [in(_59992, _59990), -(set_union2(singleton(_59992), _59990) = _59990)], (2749 ^ _18524) ^ [_60077] : [relation(_60077), 2752 ^ _18524 : [(2753 ^ _18524) ^ [_60152] : [relation(_60152), subset(relation_dom(_60077), relation_rng(_60152)), -(relation_rng(relation_composition(_60152, _60077)) = relation_rng(_60077))]]], (2763 ^ _18524) ^ [_60305, _60307] : [element(_60305, powerset(powerset(_60307))), -(_60305 = empty_set), -(subset_difference(_60307, cast_to_subset(_60307), union_of_subsets(_60307, _60305)) = meet_of_subsets(_60307, complements_of_subsets(_60307, _60305)))], (2773 ^ _18524) ^ [_60435, _60437] : [element(_60435, powerset(powerset(_60437))), -(_60435 = empty_set), -(union_of_subsets(_60437, complements_of_subsets(_60437, _60435)) = subset_difference(_60437, cast_to_subset(_60437), meet_of_subsets(_60437, _60435)))], (2783 ^ _18524) ^ [_60565, _60567] : [-(set_difference(_60567, set_difference(_60567, _60565)) = set_intersection2(_60567, _60565))], (2785 ^ _18524) ^ [_60599] : [-(set_difference(empty_set, _60599) = empty_set)], (2787 ^ _18524) ^ [_60625, _60627, _60629] : [-(element(_60629, _60625)), in(_60629, _60627), element(_60627, powerset(_60625))], (2797 ^ _18524) ^ [_60768, _60770] : [-(disjoint(_60770, _60768)), -(in(2800 ^ [_60768, _60770], set_intersection2(_60770, _60768)))], (2804 ^ _18524) ^ [_60810, _60812] : [2805 ^ _18524 : [(2806 ^ _18524) ^ [_60852] : [in(_60852, set_intersection2(_60812, _60810))]], disjoint(_60812, _60810)], (2810 ^ _18524) ^ [_60906] : [-(_60906 = empty_set), 2813 ^ _18524 : [(2814 ^ _18524) ^ [_60989] : [element(_60989, powerset(_60906)), 2817 ^ _18524 : [(2818 ^ _18524) ^ [_61067] : [element(_61067, _60906), -(in(_61067, _60989)), -(in(_61067, subset_complement(_60906, _60989)))]]]]], (2828 ^ _18524) ^ [_61175, _61177, _61179] : [element(_61175, powerset(_61179)), in(_61177, subset_complement(_61179, _61175)), in(_61177, _61175)], (2838 ^ _18524) ^ [_61319] : [relation(_61319), -(in(ordered_pair(2843 ^ [_61319], 2844 ^ [_61319]), _61319)), -(_61319 = empty_set)], (2850 ^ _18524) ^ [_61433, _61435, _61437] : [in(_61437, _61435), element(_61435, powerset(_61433)), empty(_61433)], (2860 ^ _18524) ^ [] : [-(relation_dom(empty_set) = empty_set)], (2862 ^ _18524) ^ [] : [-(relation_rng(empty_set) = empty_set)], (2864 ^ _18524) ^ [_61600, _61602] : [subset(_61602, _61600), proper_subset(_61600, _61602)], (2870 ^ _18524) ^ [_61676, _61678, _61680] : [-(disjoint(_61680, _61676)), subset(_61680, _61678), disjoint(_61678, _61676)], (2880 ^ _18524) ^ [_61809] : [relation(_61809), 2885 ^ _18524 : [(2886 ^ _18524) ^ [] : [relation_dom(_61809) = empty_set], (2888 ^ _18524) ^ [] : [relation_rng(_61809) = empty_set]], -(_61809 = empty_set)], (2892 ^ _18524) ^ [_61978] : [relation(_61978), 2895 ^ _18524 : [(2896 ^ _18524) ^ [] : [relation_dom(_61978) = empty_set, -(relation_rng(_61978) = empty_set)], (2902 ^ _18524) ^ [] : [relation_rng(_61978) = empty_set, -(relation_dom(_61978) = empty_set)]]], (2908 ^ _18524) ^ [_62204, _62206] : [set_difference(_62206, singleton(_62204)) = _62206, in(_62204, _62206)], (2914 ^ _18524) ^ [_62286, _62288] : [-(in(_62286, _62288)), -(set_difference(_62288, singleton(_62286)) = _62288)], (2920 ^ _18524) ^ [_62329] : [-(unordered_pair(_62329, _62329) = singleton(_62329))], (2922 ^ _18524) ^ [_62357] : [empty(_62357), -(_62357 = empty_set)], (2928 ^ _18524) ^ [_62430, _62432] : [subset(singleton(_62432), singleton(_62430)), -(_62432 = _62430)], (2934 ^ _18524) ^ [_62513] : [-(relation_dom(identity_relation(_62513)) = _62513)], (2936 ^ _18524) ^ [_62537] : [-(relation_rng(identity_relation(_62537)) = _62537)], (2938 ^ _18524) ^ [_62566, _62568, _62570, _62572] : [relation(_62566), 2941 ^ _18524 : [(2942 ^ _18524) ^ [] : [in(ordered_pair(_62572, _62570), relation_composition(identity_relation(_62568), _62566)), 2945 ^ _18524 : [(2946 ^ _18524) ^ [] : [-(in(_62572, _62568))], (2948 ^ _18524) ^ [] : [-(in(ordered_pair(_62572, _62570), _62566))]]], (2950 ^ _18524) ^ [] : [-(in(ordered_pair(_62572, _62570), relation_composition(identity_relation(_62568), _62566))), in(_62572, _62568), in(ordered_pair(_62572, _62570), _62566)]]], (2960 ^ _18524) ^ [_62892, _62894] : [in(_62894, _62892), empty(_62892)], (2966 ^ _18524) ^ [_62966, _62968] : [-(subset(_62968, set_union2(_62968, _62966)))], (2968 ^ _18524) ^ [_63009, _63011] : [disjoint(_63011, _63009), -(set_difference(_63011, _63009) = _63011)], (2974 ^ _18524) ^ [_63088, _63090] : [set_difference(_63090, _63088) = _63090, -(disjoint(_63090, _63088))], (2980 ^ _18524) ^ [_63173, _63175, _63177] : [relation(_63173), 2983 ^ _18524 : [(2984 ^ _18524) ^ [] : [in(_63177, relation_dom(relation_dom_restriction(_63173, _63175))), 2987 ^ _18524 : [(2988 ^ _18524) ^ [] : [-(in(_63177, _63175))], (2990 ^ _18524) ^ [] : [-(in(_63177, relation_dom(_63173)))]]], (2992 ^ _18524) ^ [] : [-(in(_63177, relation_dom(relation_dom_restriction(_63173, _63175)))), in(_63177, _63175), in(_63177, relation_dom(_63173))]]], (3002 ^ _18524) ^ [_63479, _63481] : [relation(_63479), -(subset(relation_dom_restriction(_63479, _63481), _63479))], (3008 ^ _18524) ^ [_63560, _63562] : [empty(_63562), -(_63562 = _63560), empty(_63560)], (3018 ^ _18524) ^ [_63687, _63689, _63691] : [relation(_63687), function(_63687), 3025 ^ _18524 : [(3026 ^ _18524) ^ [] : [in(ordered_pair(_63691, _63689), _63687), 3029 ^ _18524 : [(3030 ^ _18524) ^ [] : [-(in(_63691, relation_dom(_63687)))], (3032 ^ _18524) ^ [] : [-(_63689 = apply(_63687, _63691))]]], (3034 ^ _18524) ^ [] : [-(in(ordered_pair(_63691, _63689), _63687)), in(_63691, relation_dom(_63687)), _63689 = apply(_63687, _63691)]]], (3044 ^ _18524) ^ [_64050, _64052, _64054] : [-(subset(set_union2(_64054, _64050), _64052)), subset(_64054, _64052), subset(_64050, _64052)], (3054 ^ _18524) ^ [_64189, _64191, _64193] : [singleton(_64193) = unordered_pair(_64191, _64189), -(_64193 = _64191)], (3060 ^ _18524) ^ [_64278, _64280] : [relation(_64278), -(relation_dom(relation_dom_restriction(_64278, _64280)) = set_intersection2(relation_dom(_64278), _64280))], (3066 ^ _18524) ^ [_64373, _64375] : [in(_64375, _64373), -(subset(_64375, union(_64373)))], (3072 ^ _18524) ^ [_64454, _64456] : [relation(_64454), -(relation_dom_restriction(_64454, _64456) = relation_composition(identity_relation(_64456), _64454))], (3078 ^ _18524) ^ [_64545, _64547] : [relation(_64545), -(subset(relation_rng(relation_dom_restriction(_64545, _64547)), relation_rng(_64545)))], (3084 ^ _18524) ^ [_64634] : [-(union(powerset(_64634)) = _64634)], (3122 ^ _18524) ^ [_65317, _65319, _65321] : [singleton(_65321) = unordered_pair(_65319, _65317), -(_65319 = _65317)], (3087 ^ _18524) ^ [_64769] : [-(in(_64769, 3085 ^ [_64769]))], (3089 ^ _18524) ^ [_64797, _64799, _64801] : [-(in(_64797, 3085 ^ [_64801])), in(_64799, 3085 ^ [_64801]), subset(_64797, _64799)], (3099 ^ _18524) ^ [_64950, _64952] : [in(_64950, 3085 ^ [_64952]), 3103 ^ _18524 : [(3104 ^ _18524) ^ [] : [-(in(3102 ^ [_64950, _64952], 3085 ^ [_64952]))], (3106 ^ _18524) ^ [_65096] : [subset(_65096, _64950), -(in(_65096, 3102 ^ [_64950, _64952]))]]], (3112 ^ _18524) ^ [_65191, _65193] : [subset(_65191, 3085 ^ [_65193]), -(are_equipotent(_65191, 3085 ^ [_65193])), -(in(_65191, 3085 ^ [_65193]))]], input).
% 0.55/1.38  ncf('1',plain,[apply(identity_relation(3127 ^ []), 3128 ^ []) = 3128 ^ []],start(3132 ^ 0)).
% 0.55/1.38  ncf('1.1',plain,[-(apply(identity_relation(3127 ^ []), 3128 ^ []) = 3128 ^ []), 2541 : in(3128 ^ [], 3127 ^ []), 2541 : identity_relation(3127 ^ []) = identity_relation(3127 ^ []), 2535 : relation(identity_relation(3127 ^ [])), 2535 : function(identity_relation(3127 ^ []))],extension(2527 ^ 1,bind([[_56830, _56832, _57038], [identity_relation(3127 ^ []), 3127 ^ [], 3128 ^ []]]))).
% 0.55/1.38  ncf('1.1.1',plain,[-(in(3128 ^ [], 3127 ^ []))],extension(3130 ^ 6)).
% 0.55/1.38  ncf('1.1.2',plain,[-(identity_relation(3127 ^ []) = identity_relation(3127 ^ []))],extension(2 ^ 4,bind([[_18554], [identity_relation(3127 ^ [])]]))).
% 0.55/1.38  ncf('1.1.3',plain,[-(relation(identity_relation(3127 ^ [])))],extension(1661 ^ 2,bind([[_44683], [3127 ^ []]]))).
% 0.55/1.38  ncf('1.1.4',plain,[-(function(identity_relation(3127 ^ [])))],extension(1768 ^ 2,bind([[_46062], [3127 ^ []]]))).
% 0.55/1.38  %-----------------------------------------------------
% 0.55/1.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------