%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n002.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 12:02:44 EDT 2023

% Result   : Theorem 0.72s 1.39s
% Output   : Proof 0.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 13:08:19 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.72/1.39  
% 0.72/1.39  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.72/1.39  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.72/1.39  %-----------------------------------------------------
% 0.72/1.39  ncf(matrix, plain, [(3472 ^ _20308) ^ [] : [-(relation(3470 ^ []))], (3474 ^ _20308) ^ [] : [-(function(3470 ^ []))], (3476 ^ _20308) ^ [] : [-(in(3469 ^ [], relation_dom(relation_dom_restriction(3470 ^ [], 3468 ^ []))))], (3478 ^ _20308) ^ [] : [apply(relation_dom_restriction(3470 ^ [], 3468 ^ []), 3469 ^ []) = apply(3470 ^ [], 3469 ^ [])], (2 ^ _20308) ^ [_20338] : [-(_20338 = _20338)], (4 ^ _20308) ^ [_20361, _20363] : [_20363 = _20361, -(_20361 = _20363)], (10 ^ _20308) ^ [_20434, _20436, _20438] : [-(_20438 = _20434), _20438 = _20436, _20436 = _20434], (20 ^ _20308) ^ [_20571, _20573] : [-(relation_empty_yielding(_20571)), _20573 = _20571, relation_empty_yielding(_20573)], (30 ^ _20308) ^ [_20696, _20698, _20700, _20702] : [-(element(_20700, _20696)), element(_20702, _20698), _20702 = _20700, _20698 = _20696], (44 ^ _20308) ^ [_20889, _20891, _20893, _20895] : [-(proper_subset(_20893, _20889)), proper_subset(_20895, _20891), _20895 = _20893, _20891 = _20889], (58 ^ _20308) ^ [_21082, _21084] : [-(one_to_one(_21082)), _21084 = _21082, one_to_one(_21084)], (68 ^ _20308) ^ [_21207, _21209, _21211, _21213] : [-(disjoint(_21211, _21207)), disjoint(_21213, _21209), _21213 = _21211, _21209 = _21207], (82 ^ _20308) ^ [_21400, _21402] : [-(empty(_21400)), _21402 = _21400, empty(_21402)], (92 ^ _20308) ^ [_21525, _21527, _21529, _21531] : [-(subset(_21529, _21525)), subset(_21531, _21527), _21531 = _21529, _21527 = _21525], (106 ^ _20308) ^ [_21718, _21720, _21722, _21724] : [-(are_equipotent(_21722, _21718)), are_equipotent(_21724, _21720), _21724 = _21722, _21720 = _21718], (120 ^ _20308) ^ [_21911, _21913] : [-(relation(_21911)), _21913 = _21911, relation(_21913)], (130 ^ _20308) ^ [_22036, _22038] : [-(function(_22036)), _22038 = _22036, function(_22038)], (140 ^ _20308) ^ [_22157, _22159, _22161, _22163] : [-(in(_22161, _22157)), in(_22163, _22159), _22163 = _22161, _22159 = _22157], (154 ^ _20308) ^ [_22376, _22378] : [_22378 = _22376, -(set_meet(_22378) = set_meet(_22376))], (160 ^ _20308) ^ [_22461, _22463, _22465, _22467] : [-(relation_rng_restriction(_22467, _22463) = relation_rng_restriction(_22465, _22461)), _22467 = _22465, _22463 = _22461], (170 ^ _20308) ^ [_22610, _22612, _22614, _22616] : [-(relation_image(_22616, _22612) = relation_image(_22614, _22610)), _22616 = _22614, _22612 = _22610], (180 ^ _20308) ^ [_22759, _22761, _22763, _22765] : [-(relation_inverse_image(_22765, _22761) = relation_inverse_image(_22763, _22759)), _22765 = _22763, _22761 = _22759], (190 ^ _20308) ^ [_22908, _22910, _22912, _22914] : [-(cartesian_product2(_22914, _22910) = cartesian_product2(_22912, _22908)), _22914 = _22912, _22910 = _22908], (200 ^ _20308) ^ [_23057, _23059] : [_23059 = _23057, -(relation_field(_23059) = relation_field(_23057))], (206 ^ _20308) ^ [_23142, _23144] : [_23144 = _23142, -(relation_inverse(_23144) = relation_inverse(_23142))], (212 ^ _20308) ^ [_23227, _23229, _23231, _23233] : [-(union_of_subsets(_23233, _23229) = union_of_subsets(_23231, _23227)), _23233 = _23231, _23229 = _23227], (222 ^ _20308) ^ [_23376, _23378, _23380, _23382] : [-(complements_of_subsets(_23382, _23378) = complements_of_subsets(_23380, _23376)), _23382 = _23380, _23378 = _23376], (232 ^ _20308) ^ [_23525, _23527, _23529, _23531, _23533, _23535] : [-(subset_difference(_23535, _23531, _23527) = subset_difference(_23533, _23529, _23525)), _23535 = _23533, _23531 = _23529, _23527 = _23525], (246 ^ _20308) ^ [_23746, _23748] : [_23748 = _23746, -(cast_to_subset(_23748) = cast_to_subset(_23746))], (252 ^ _20308) ^ [_23831, _23833, _23835, _23837] : [-(meet_of_subsets(_23837, _23833) = meet_of_subsets(_23835, _23831)), _23837 = _23835, _23833 = _23831], (262 ^ _20308) ^ [_23980, _23982, _23984, _23986] : [-(subset_complement(_23986, _23982) = subset_complement(_23984, _23980)), _23986 = _23984, _23982 = _23980], (272 ^ _20308) ^ [_24129, _24131] : [_24131 = _24129, -(function_inverse(_24131) = function_inverse(_24129))], (278 ^ _20308) ^ [_24214, _24216, _24218, _24220] : [-(set_difference(_24220, _24216) = set_difference(_24218, _24214)), _24220 = _24218, _24216 = _24214], (288 ^ _20308) ^ [_24363, _24365, _24367, _24369] : [-(ordered_pair(_24369, _24365) = ordered_pair(_24367, _24363)), _24369 = _24367, _24365 = _24363], (298 ^ _20308) ^ [_24512, _24514, _24516, _24518] : [-(set_union2(_24518, _24514) = set_union2(_24516, _24512)), _24518 = _24516, _24514 = _24512], (308 ^ _20308) ^ [_24661, _24663, _24665, _24667] : [-(set_intersection2(_24667, _24663) = set_intersection2(_24665, _24661)), _24667 = _24665, _24663 = _24661], (318 ^ _20308) ^ [_24810, _24812, _24814, _24816] : [-(relation_composition(_24816, _24812) = relation_composition(_24814, _24810)), _24816 = _24814, _24812 = _24810], (328 ^ _20308) ^ [_24959, _24961] : [_24961 = _24959, -(identity_relation(_24961) = identity_relation(_24959))], (334 ^ _20308) ^ [_25044, _25046] : [_25046 = _25044, -(relation_rng(_25046) = relation_rng(_25044))], (340 ^ _20308) ^ [_25129, _25131] : [_25131 = _25129, -(union(_25131) = union(_25129))], (346 ^ _20308) ^ [_25214, _25216] : [_25216 = _25214, -(powerset(_25216) = powerset(_25214))], (352 ^ _20308) ^ [_25299, _25301] : [_25301 = _25299, -(singleton(_25301) = singleton(_25299))], (358 ^ _20308) ^ [_25384, _25386, _25388, _25390] : [-(unordered_pair(_25390, _25386) = unordered_pair(_25388, _25384)), _25390 = _25388, _25386 = _25384], (368 ^ _20308) ^ [_25533, _25535] : [_25535 = _25533, -(relation_dom(_25535) = relation_dom(_25533))], (374 ^ _20308) ^ [_25618, _25620, _25622, _25624] : [-(relation_dom_restriction(_25624, _25620) = relation_dom_restriction(_25622, _25618)), _25624 = _25622, _25620 = _25618], (384 ^ _20308) ^ [_25763, _25765, _25767, _25769] : [-(apply(_25769, _25765) = apply(_25767, _25763)), _25769 = _25767, _25765 = _25763], (394 ^ _20308) ^ [_26010, _26012] : [in(_26012, _26010), in(_26010, _26012)], (400 ^ _20308) ^ [_26088, _26090] : [proper_subset(_26090, _26088), proper_subset(_26088, _26090)], (406 ^ _20308) ^ [_26166] : [empty(_26166), -(function(_26166))], (412 ^ _20308) ^ [_26237] : [empty(_26237), -(relation(_26237))], (418 ^ _20308) ^ [_26308] : [429 ^ _20308 : [(430 ^ _20308) ^ [] : [-(relation(_26308))], (432 ^ _20308) ^ [] : [-(function(_26308))], (434 ^ _20308) ^ [] : [-(one_to_one(_26308))]], relation(_26308), empty(_26308), function(_26308)], (436 ^ _20308) ^ [_26521, _26523] : [-(unordered_pair(_26523, _26521) = unordered_pair(_26521, _26523))], (438 ^ _20308) ^ [_26552, _26554] : [-(set_union2(_26554, _26552) = set_union2(_26552, _26554))], (440 ^ _20308) ^ [_26583, _26585] : [-(set_intersection2(_26585, _26583) = set_intersection2(_26583, _26585))], (442 ^ _20308) ^ [_26614, _26616] : [relation(_26614), 445 ^ _20308 : [(468 ^ _20308) ^ [] : [-(_26614 = identity_relation(_26616)), 481 ^ _20308 : [(482 ^ _20308) ^ [] : [-(in(469 ^ [_26614, _26616], _26616))], (484 ^ _20308) ^ [] : [-(469 ^ [_26614, _26616] = 470 ^ [_26614, _26616])], (486 ^ _20308) ^ [] : [in(ordered_pair(469 ^ [_26614, _26616], 470 ^ [_26614, _26616]), _26614)]], 473 ^ _20308 : [(474 ^ _20308) ^ [] : [-(in(ordered_pair(469 ^ [_26614, _26616], 470 ^ [_26614, _26616]), _26614))], (476 ^ _20308) ^ [] : [in(469 ^ [_26614, _26616], _26616), 469 ^ [_26614, _26616] = 470 ^ [_26614, _26616]]]], (446 ^ _20308) ^ [] : [_26614 = identity_relation(_26616), 449 ^ _20308 : [(450 ^ _20308) ^ [_26767, _26769] : [in(ordered_pair(_26769, _26767), _26614), 453 ^ _20308 : [(454 ^ _20308) ^ [] : [-(in(_26769, _26616))], (456 ^ _20308) ^ [] : [-(_26769 = _26767)]]], (458 ^ _20308) ^ [_26876, _26878] : [-(in(ordered_pair(_26878, _26876), _26614)), in(_26878, _26616), _26878 = _26876]]]]], (490 ^ _20308) ^ [_27403, _27405] : [_27405 = _27403, 493 ^ _20308 : [(494 ^ _20308) ^ [] : [-(subset(_27405, _27403))], (496 ^ _20308) ^ [] : [-(subset(_27403, _27405))]]], (498 ^ _20308) ^ [_27502, _27504] : [-(_27504 = _27502), subset(_27504, _27502), subset(_27502, _27504)], (508 ^ _20308) ^ [_27633] : [relation(_27633), 511 ^ _20308 : [(512 ^ _20308) ^ [_27733, _27735] : [relation(_27733), 515 ^ _20308 : [(538 ^ _20308) ^ [] : [-(_27733 = relation_dom_restriction(_27633, _27735)), 551 ^ _20308 : [(552 ^ _20308) ^ [] : [-(in(539 ^ [_27633, _27733, _27735], _27735))], (554 ^ _20308) ^ [] : [-(in(ordered_pair(539 ^ [_27633, _27733, _27735], 540 ^ [_27633, _27733, _27735]), _27633))], (556 ^ _20308) ^ [] : [in(ordered_pair(539 ^ [_27633, _27733, _27735], 540 ^ [_27633, _27733, _27735]), _27733)]], 543 ^ _20308 : [(544 ^ _20308) ^ [] : [-(in(ordered_pair(539 ^ [_27633, _27733, _27735], 540 ^ [_27633, _27733, _27735]), _27733))], (546 ^ _20308) ^ [] : [in(539 ^ [_27633, _27733, _27735], _27735), in(ordered_pair(539 ^ [_27633, _27733, _27735], 540 ^ [_27633, _27733, _27735]), _27633)]]], (516 ^ _20308) ^ [] : [_27733 = relation_dom_restriction(_27633, _27735), 519 ^ _20308 : [(520 ^ _20308) ^ [_27895, _27897] : [in(ordered_pair(_27897, _27895), _27733), 523 ^ _20308 : [(524 ^ _20308) ^ [] : [-(in(_27897, _27735))], (526 ^ _20308) ^ [] : [-(in(ordered_pair(_27897, _27895), _27633))]]], (528 ^ _20308) ^ [_28012, _28014] : [-(in(ordered_pair(_28014, _28012), _27733)), in(_28014, _27735), in(ordered_pair(_28014, _28012), _27633)]]]]]]], (560 ^ _20308) ^ [_28582, _28584] : [relation(_28582), 563 ^ _20308 : [(564 ^ _20308) ^ [_28679] : [relation(_28679), 567 ^ _20308 : [(590 ^ _20308) ^ [] : [-(_28679 = relation_rng_restriction(_28584, _28582)), 603 ^ _20308 : [(604 ^ _20308) ^ [] : [-(in(592 ^ [_28582, _28584, _28679], _28584))], (606 ^ _20308) ^ [] : [-(in(ordered_pair(591 ^ [_28582, _28584, _28679], 592 ^ [_28582, _28584, _28679]), _28582))], (608 ^ _20308) ^ [] : [in(ordered_pair(591 ^ [_28582, _28584, _28679], 592 ^ [_28582, _28584, _28679]), _28679)]], 595 ^ _20308 : [(596 ^ _20308) ^ [] : [-(in(ordered_pair(591 ^ [_28582, _28584, _28679], 592 ^ [_28582, _28584, _28679]), _28679))], (598 ^ _20308) ^ [] : [in(592 ^ [_28582, _28584, _28679], _28584), in(ordered_pair(591 ^ [_28582, _28584, _28679], 592 ^ [_28582, _28584, _28679]), _28582)]]], (568 ^ _20308) ^ [] : [_28679 = relation_rng_restriction(_28584, _28582), 571 ^ _20308 : [(572 ^ _20308) ^ [_28841, _28843] : [in(ordered_pair(_28843, _28841), _28679), 575 ^ _20308 : [(576 ^ _20308) ^ [] : [-(in(_28841, _28584))], (578 ^ _20308) ^ [] : [-(in(ordered_pair(_28843, _28841), _28582))]]], (580 ^ _20308) ^ [_28958, _28960] : [-(in(ordered_pair(_28960, _28958), _28679)), in(_28958, _28584), in(ordered_pair(_28960, _28958), _28582)]]]]]]], (612 ^ _20308) ^ [_29519] : [relation(_29519), 615 ^ _20308 : [(639 ^ _20308) ^ [_30024, _30026] : [-(_30024 = relation_image(_29519, _30026)), 652 ^ _20308 : [(653 ^ _20308) ^ [] : [-(in(ordered_pair(651 ^ [_29519, _30024, _30026], 640 ^ [_29519, _30024, _30026]), _29519))], (655 ^ _20308) ^ [] : [-(in(651 ^ [_29519, _30024, _30026], _30026))], (657 ^ _20308) ^ [] : [in(640 ^ [_29519, _30024, _30026], _30024)]], 643 ^ _20308 : [(644 ^ _20308) ^ [] : [-(in(640 ^ [_29519, _30024, _30026], _30024))], (646 ^ _20308) ^ [_30172] : [in(ordered_pair(_30172, 640 ^ [_29519, _30024, _30026]), _29519), in(_30172, _30026)]]], (616 ^ _20308) ^ [_29626, _29628] : [_29626 = relation_image(_29519, _29628), 619 ^ _20308 : [(620 ^ _20308) ^ [_29723] : [in(_29723, _29626), 624 ^ _20308 : [(625 ^ _20308) ^ [] : [-(in(ordered_pair(623 ^ [_29519, _29626, _29628, _29723], _29723), _29519))], (627 ^ _20308) ^ [] : [-(in(623 ^ [_29519, _29626, _29628, _29723], _29628))]]], (629 ^ _20308) ^ [_29859] : [-(in(_29859, _29626)), 630 ^ _20308 : [(631 ^ _20308) ^ [_29906] : [in(ordered_pair(_29906, _29859), _29519), in(_29906, _29628)]]]]]]], (661 ^ _20308) ^ [_30426] : [relation(_30426), 664 ^ _20308 : [(688 ^ _20308) ^ [_30931, _30933] : [-(_30931 = relation_inverse_image(_30426, _30933)), 701 ^ _20308 : [(702 ^ _20308) ^ [] : [-(in(ordered_pair(689 ^ [_30426, _30931, _30933], 700 ^ [_30426, _30931, _30933]), _30426))], (704 ^ _20308) ^ [] : [-(in(700 ^ [_30426, _30931, _30933], _30933))], (706 ^ _20308) ^ [] : [in(689 ^ [_30426, _30931, _30933], _30931)]], 692 ^ _20308 : [(693 ^ _20308) ^ [] : [-(in(689 ^ [_30426, _30931, _30933], _30931))], (695 ^ _20308) ^ [_31079] : [in(ordered_pair(689 ^ [_30426, _30931, _30933], _31079), _30426), in(_31079, _30933)]]], (665 ^ _20308) ^ [_30533, _30535] : [_30533 = relation_inverse_image(_30426, _30535), 668 ^ _20308 : [(669 ^ _20308) ^ [_30630] : [in(_30630, _30533), 673 ^ _20308 : [(674 ^ _20308) ^ [] : [-(in(ordered_pair(_30630, 672 ^ [_30426, _30533, _30535, _30630]), _30426))], (676 ^ _20308) ^ [] : [-(in(672 ^ [_30426, _30533, _30535, _30630], _30535))]]], (678 ^ _20308) ^ [_30766] : [-(in(_30766, _30533)), 679 ^ _20308 : [(680 ^ _20308) ^ [_30813] : [in(ordered_pair(_30766, _30813), _30426), in(_30813, _30535)]]]]]]], (722 ^ _20308) ^ [_31530] : [724 ^ _20308 : [(725 ^ _20308) ^ [] : [-(in(723 ^ [_31530], _31530))], (727 ^ _20308) ^ [_31643, _31645] : [723 ^ [_31530] = ordered_pair(_31645, _31643)]], -(relation(_31530))], (710 ^ _20308) ^ [_31345] : [relation(_31345), 713 ^ _20308 : [(714 ^ _20308) ^ [_31421] : [in(_31421, _31345), -(_31421 = ordered_pair(717 ^ [_31345, _31421], 718 ^ [_31345, _31421]))]]], (780 ^ _20308) ^ [_32508, _32510] : [_32510 = empty_set, 783 ^ _20308 : [(784 ^ _20308) ^ [] : [_32508 = set_meet(_32510), -(_32508 = empty_set)], (790 ^ _20308) ^ [] : [_32508 = empty_set, -(_32508 = set_meet(_32510))]]], (731 ^ _20308) ^ [_31715, _31717] : [-(_31717 = empty_set), 734 ^ _20308 : [(758 ^ _20308) ^ [] : [-(_31715 = set_meet(_31717)), 762 ^ _20308 : [(763 ^ _20308) ^ [] : [-(in(759 ^ [_31715, _31717], _31715))], (766 ^ _20308) ^ [] : [-(in(764 ^ [_31715, _31717], _31717))], (768 ^ _20308) ^ [] : [in(759 ^ [_31715, _31717], 764 ^ [_31715, _31717])]], 769 ^ _20308 : [(776 ^ _20308) ^ [] : [in(759 ^ [_31715, _31717], _31715)], (770 ^ _20308) ^ [_32352] : [in(_32352, _31717), -(in(759 ^ [_31715, _31717], _32352))]]], (735 ^ _20308) ^ [] : [_31715 = set_meet(_31717), 738 ^ _20308 : [(749 ^ _20308) ^ [_32008] : [751 ^ _20308 : [(752 ^ _20308) ^ [] : [-(in(750 ^ [_31715, _31717, _32008], _31717))], (754 ^ _20308) ^ [] : [in(_32008, 750 ^ [_31715, _31717, _32008])]], -(in(_32008, _31715))], (739 ^ _20308) ^ [_31862] : [in(_31862, _31715), 742 ^ _20308 : [(743 ^ _20308) ^ [_31927] : [in(_31927, _31717), -(in(_31862, _31927))]]]]]]], (812 ^ _20308) ^ [_32973, _32975] : [-(_32973 = singleton(_32975)), 816 ^ _20308 : [(817 ^ _20308) ^ [] : [-(in(813 ^ [_32973, _32975], _32973))], (819 ^ _20308) ^ [] : [813 ^ [_32973, _32975] = _32975]], 820 ^ _20308 : [(821 ^ _20308) ^ [] : [-(813 ^ [_32973, _32975] = _32975)], (823 ^ _20308) ^ [] : [in(813 ^ [_32973, _32975], _32973)]]], (796 ^ _20308) ^ [_32738, _32740] : [_32738 = singleton(_32740), 799 ^ _20308 : [(800 ^ _20308) ^ [_32817] : [in(_32817, _32738), -(_32817 = _32740)], (806 ^ _20308) ^ [_32892] : [_32892 = _32740, -(in(_32892, _32738))]]], (827 ^ _20308) ^ [_33227] : [_33227 = empty_set, 830 ^ _20308 : [(831 ^ _20308) ^ [_33288] : [in(_33288, _33227)]]], (833 ^ _20308) ^ [_33309] : [-(in(834 ^ [_33309], _33309)), -(_33309 = empty_set)], (856 ^ _20308) ^ [_33600, _33602] : [-(_33600 = powerset(_33602)), 860 ^ _20308 : [(861 ^ _20308) ^ [] : [-(in(857 ^ [_33600, _33602], _33600))], (863 ^ _20308) ^ [] : [subset(857 ^ [_33600, _33602], _33602)]], 864 ^ _20308 : [(865 ^ _20308) ^ [] : [-(subset(857 ^ [_33600, _33602], _33602))], (867 ^ _20308) ^ [] : [in(857 ^ [_33600, _33602], _33600)]]], (840 ^ _20308) ^ [_33365, _33367] : [_33365 = powerset(_33367), 843 ^ _20308 : [(844 ^ _20308) ^ [_33444] : [in(_33444, _33365), -(subset(_33444, _33367))], (850 ^ _20308) ^ [_33519] : [subset(_33519, _33367), -(in(_33519, _33365))]]], (871 ^ _20308) ^ [_33842] : [relation(_33842), 874 ^ _20308 : [(875 ^ _20308) ^ [_33928] : [relation(_33928), 878 ^ _20308 : [(895 ^ _20308) ^ [] : [-(_33842 = _33928), 900 ^ _20308 : [(901 ^ _20308) ^ [] : [-(in(ordered_pair(896 ^ [_33842, _33928], 897 ^ [_33842, _33928]), _33842))], (903 ^ _20308) ^ [] : [in(ordered_pair(896 ^ [_33842, _33928], 897 ^ [_33842, _33928]), _33928)]], 904 ^ _20308 : [(905 ^ _20308) ^ [] : [-(in(ordered_pair(896 ^ [_33842, _33928], 897 ^ [_33842, _33928]), _33928))], (907 ^ _20308) ^ [] : [in(ordered_pair(896 ^ [_33842, _33928], 897 ^ [_33842, _33928]), _33842)]]], (879 ^ _20308) ^ [] : [_33842 = _33928, 882 ^ _20308 : [(883 ^ _20308) ^ [_34074, _34076] : [in(ordered_pair(_34076, _34074), _33842), -(in(ordered_pair(_34076, _34074), _33928))], (889 ^ _20308) ^ [_34163, _34165] : [in(ordered_pair(_34165, _34163), _33928), -(in(ordered_pair(_34165, _34163), _33842))]]]]]]], (911 ^ _20308) ^ [_34553, _34555] : [-(empty(_34555)), 914 ^ _20308 : [(915 ^ _20308) ^ [] : [element(_34553, _34555), -(in(_34553, _34555))], (921 ^ _20308) ^ [] : [in(_34553, _34555), -(element(_34553, _34555))]]], (927 ^ _20308) ^ [_34753, _34755] : [empty(_34755), 930 ^ _20308 : [(931 ^ _20308) ^ [] : [element(_34753, _34755), -(empty(_34753))], (937 ^ _20308) ^ [] : [empty(_34753), -(element(_34753, _34755))]]], (965 ^ _20308) ^ [_35275, _35277, _35279] : [-(_35275 = unordered_pair(_35279, _35277)), 969 ^ _20308 : [(970 ^ _20308) ^ [] : [-(in(966 ^ [_35275, _35277, _35279], _35275))], (972 ^ _20308) ^ [] : [966 ^ [_35275, _35277, _35279] = _35279], (974 ^ _20308) ^ [] : [966 ^ [_35275, _35277, _35279] = _35277]], 975 ^ _20308 : [(982 ^ _20308) ^ [] : [in(966 ^ [_35275, _35277, _35279], _35275)], (976 ^ _20308) ^ [] : [-(966 ^ [_35275, _35277, _35279] = _35279), -(966 ^ [_35275, _35277, _35279] = _35277)]]], (943 ^ _20308) ^ [_34975, _34977, _34979] : [_34975 = unordered_pair(_34979, _34977), 946 ^ _20308 : [(957 ^ _20308) ^ [_35154] : [958 ^ _20308 : [(959 ^ _20308) ^ [] : [_35154 = _34979], (961 ^ _20308) ^ [] : [_35154 = _34977]], -(in(_35154, _34975))], (947 ^ _20308) ^ [_35064] : [in(_35064, _34975), -(_35064 = _34979), -(_35064 = _34977)]]], (1008 ^ _20308) ^ [_35915, _35917, _35919] : [-(_35915 = set_union2(_35919, _35917)), 1012 ^ _20308 : [(1013 ^ _20308) ^ [] : [-(in(1009 ^ [_35915, _35917, _35919], _35915))], (1015 ^ _20308) ^ [] : [in(1009 ^ [_35915, _35917, _35919], _35919)], (1017 ^ _20308) ^ [] : [in(1009 ^ [_35915, _35917, _35919], _35917)]], 1018 ^ _20308 : [(1025 ^ _20308) ^ [] : [in(1009 ^ [_35915, _35917, _35919], _35915)], (1019 ^ _20308) ^ [] : [-(in(1009 ^ [_35915, _35917, _35919], _35919)), -(in(1009 ^ [_35915, _35917, _35919], _35917))]]], (986 ^ _20308) ^ [_35615, _35617, _35619] : [_35615 = set_union2(_35619, _35617), 989 ^ _20308 : [(1000 ^ _20308) ^ [_35794] : [1001 ^ _20308 : [(1002 ^ _20308) ^ [] : [in(_35794, _35619)], (1004 ^ _20308) ^ [] : [in(_35794, _35617)]], -(in(_35794, _35615))], (990 ^ _20308) ^ [_35704] : [in(_35704, _35615), -(in(_35704, _35619)), -(in(_35704, _35617))]]], (1059 ^ _20308) ^ [_36788, _36790, _36792] : [-(_36788 = cartesian_product2(_36792, _36790)), 1077 ^ _20308 : [(1078 ^ _20308) ^ [] : [-(in(1075 ^ [_36788, _36790, _36792], _36792))], (1080 ^ _20308) ^ [] : [-(in(1076 ^ [_36788, _36790, _36792], _36790))], (1082 ^ _20308) ^ [] : [-(1060 ^ [_36788, _36790, _36792] = ordered_pair(1075 ^ [_36788, _36790, _36792], 1076 ^ [_36788, _36790, _36792]))], (1084 ^ _20308) ^ [] : [in(1060 ^ [_36788, _36790, _36792], _36788)]], 1063 ^ _20308 : [(1064 ^ _20308) ^ [] : [-(in(1060 ^ [_36788, _36790, _36792], _36788))], (1066 ^ _20308) ^ [_36958, _36960] : [in(_36960, _36792), in(_36958, _36790), 1060 ^ [_36788, _36790, _36792] = ordered_pair(_36960, _36958)]]], (1029 ^ _20308) ^ [_36255, _36257, _36259] : [_36255 = cartesian_product2(_36259, _36257), 1032 ^ _20308 : [(1033 ^ _20308) ^ [_36363] : [in(_36363, _36255), 1038 ^ _20308 : [(1039 ^ _20308) ^ [] : [-(in(1036 ^ [_36255, _36257, _36259, _36363], _36259))], (1041 ^ _20308) ^ [] : [-(in(1037 ^ [_36255, _36257, _36259, _36363], _36257))], (1043 ^ _20308) ^ [] : [-(_36363 = ordered_pair(1036 ^ [_36255, _36257, _36259, _36363], 1037 ^ [_36255, _36257, _36259, _36363]))]]], (1045 ^ _20308) ^ [_36550] : [-(in(_36550, _36255)), 1046 ^ _20308 : [(1047 ^ _20308) ^ [_36608, _36610] : [in(_36610, _36259), in(_36608, _36257), _36550 = ordered_pair(_36610, _36608)]]]]], (1088 ^ _20308) ^ [_37306] : [relation(_37306), 1091 ^ _20308 : [(1092 ^ _20308) ^ [_37392] : [relation(_37392), 1095 ^ _20308 : [(1106 ^ _20308) ^ [] : [1109 ^ _20308 : [(1110 ^ _20308) ^ [] : [-(in(ordered_pair(1107 ^ [_37306, _37392], 1108 ^ [_37306, _37392]), _37306))], (1112 ^ _20308) ^ [] : [in(ordered_pair(1107 ^ [_37306, _37392], 1108 ^ [_37306, _37392]), _37392)]], -(subset(_37306, _37392))], (1096 ^ _20308) ^ [] : [subset(_37306, _37392), 1099 ^ _20308 : [(1100 ^ _20308) ^ [_37523, _37525] : [in(ordered_pair(_37525, _37523), _37306), -(in(ordered_pair(_37525, _37523), _37392))]]]]]]], (1126 ^ _20308) ^ [_37936, _37938] : [1128 ^ _20308 : [(1129 ^ _20308) ^ [] : [-(in(1127 ^ [_37936, _37938], _37938))], (1131 ^ _20308) ^ [] : [in(1127 ^ [_37936, _37938], _37936)]], -(subset(_37938, _37936))], (1116 ^ _20308) ^ [_37794, _37796] : [subset(_37796, _37794), 1119 ^ _20308 : [(1120 ^ _20308) ^ [_37857] : [in(_37857, _37796), -(in(_37857, _37794))]]], (1157 ^ _20308) ^ [_38427, _38429, _38431] : [-(_38427 = set_intersection2(_38431, _38429)), 1169 ^ _20308 : [(1170 ^ _20308) ^ [] : [-(in(1158 ^ [_38427, _38429, _38431], _38431))], (1172 ^ _20308) ^ [] : [-(in(1158 ^ [_38427, _38429, _38431], _38429))], (1174 ^ _20308) ^ [] : [in(1158 ^ [_38427, _38429, _38431], _38427)]], 1161 ^ _20308 : [(1162 ^ _20308) ^ [] : [-(in(1158 ^ [_38427, _38429, _38431], _38427))], (1164 ^ _20308) ^ [] : [in(1158 ^ [_38427, _38429, _38431], _38431), in(1158 ^ [_38427, _38429, _38431], _38429)]]], (1135 ^ _20308) ^ [_38096, _38098, _38100] : [_38096 = set_intersection2(_38100, _38098), 1138 ^ _20308 : [(1139 ^ _20308) ^ [_38185] : [in(_38185, _38096), 1142 ^ _20308 : [(1143 ^ _20308) ^ [] : [-(in(_38185, _38100))], (1145 ^ _20308) ^ [] : [-(in(_38185, _38098))]]], (1147 ^ _20308) ^ [_38288] : [-(in(_38288, _38096)), in(_38288, _38100), in(_38288, _38098)]]], (1178 ^ _20308) ^ [_38781] : [relation(_38781), function(_38781), 1185 ^ _20308 : [(1186 ^ _20308) ^ [_38941, _38943] : [in(_38943, relation_dom(_38781)), 1189 ^ _20308 : [(1190 ^ _20308) ^ [] : [_38941 = apply(_38781, _38943), -(in(ordered_pair(_38943, _38941), _38781))], (1196 ^ _20308) ^ [] : [in(ordered_pair(_38943, _38941), _38781), -(_38941 = apply(_38781, _38943))]]], (1202 ^ _20308) ^ [_39171, _39173] : [-(in(_39173, relation_dom(_38781))), 1205 ^ _20308 : [(1206 ^ _20308) ^ [] : [_39171 = apply(_38781, _39173), -(_39171 = empty_set)], (1212 ^ _20308) ^ [] : [_39171 = empty_set, -(_39171 = apply(_38781, _39173))]]]]], (1218 ^ _20308) ^ [_39402] : [relation(_39402), 1221 ^ _20308 : [(1239 ^ _20308) ^ [_39776] : [-(_39776 = relation_dom(_39402)), 1243 ^ _20308 : [(1244 ^ _20308) ^ [] : [-(in(1240 ^ [_39402, _39776], _39776))], (1246 ^ _20308) ^ [_39910] : [in(ordered_pair(1240 ^ [_39402, _39776], _39910), _39402)]], 1248 ^ _20308 : [(1249 ^ _20308) ^ [] : [-(in(ordered_pair(1240 ^ [_39402, _39776], 1247 ^ [_39402, _39776]), _39402))], (1251 ^ _20308) ^ [] : [in(1240 ^ [_39402, _39776], _39776)]]], (1222 ^ _20308) ^ [_39494] : [_39494 = relation_dom(_39402), 1225 ^ _20308 : [(1226 ^ _20308) ^ [_39581] : [in(_39581, _39494), -(in(ordered_pair(_39581, 1229 ^ [_39402, _39494, _39581]), _39402))], (1233 ^ _20308) ^ [_39676] : [1234 ^ _20308 : [(1235 ^ _20308) ^ [_39720] : [in(ordered_pair(_39676, _39720), _39402)]], -(in(_39676, _39494))]]]]], (1255 ^ _20308) ^ [_40057] : [-(cast_to_subset(_40057) = _40057)], (1280 ^ _20308) ^ [_40463, _40465] : [-(_40463 = union(_40465)), 1293 ^ _20308 : [(1294 ^ _20308) ^ [] : [-(in(1281 ^ [_40463, _40465], 1292 ^ [_40463, _40465]))], (1296 ^ _20308) ^ [] : [-(in(1292 ^ [_40463, _40465], _40465))], (1298 ^ _20308) ^ [] : [in(1281 ^ [_40463, _40465], _40463)]], 1284 ^ _20308 : [(1285 ^ _20308) ^ [] : [-(in(1281 ^ [_40463, _40465], _40463))], (1287 ^ _20308) ^ [_40596] : [in(1281 ^ [_40463, _40465], _40596), in(_40596, _40465)]]], (1257 ^ _20308) ^ [_40097, _40099] : [_40097 = union(_40099), 1260 ^ _20308 : [(1261 ^ _20308) ^ [_40187] : [in(_40187, _40097), 1265 ^ _20308 : [(1266 ^ _20308) ^ [] : [-(in(_40187, 1264 ^ [_40097, _40099, _40187]))], (1268 ^ _20308) ^ [] : [-(in(1264 ^ [_40097, _40099, _40187], _40099))]]], (1270 ^ _20308) ^ [_40311] : [-(in(_40311, _40097)), 1271 ^ _20308 : [(1272 ^ _20308) ^ [_40353] : [in(_40311, _40353), in(_40353, _40099)]]]]], (1324 ^ _20308) ^ [_41184, _41186, _41188] : [-(_41184 = set_difference(_41188, _41186)), 1336 ^ _20308 : [(1337 ^ _20308) ^ [] : [-(in(1325 ^ [_41184, _41186, _41188], _41188))], (1339 ^ _20308) ^ [] : [in(1325 ^ [_41184, _41186, _41188], _41186)], (1341 ^ _20308) ^ [] : [in(1325 ^ [_41184, _41186, _41188], _41184)]], 1328 ^ _20308 : [(1329 ^ _20308) ^ [] : [-(in(1325 ^ [_41184, _41186, _41188], _41184))], (1331 ^ _20308) ^ [] : [in(1325 ^ [_41184, _41186, _41188], _41188), -(in(1325 ^ [_41184, _41186, _41188], _41186))]]], (1302 ^ _20308) ^ [_40840, _40842, _40844] : [_40840 = set_difference(_40844, _40842), 1305 ^ _20308 : [(1306 ^ _20308) ^ [_40931] : [in(_40931, _40840), 1309 ^ _20308 : [(1310 ^ _20308) ^ [] : [-(in(_40931, _40844))], (1312 ^ _20308) ^ [] : [in(_40931, _40842)]]], (1314 ^ _20308) ^ [_41042] : [-(in(_41042, _40840)), in(_41042, _40844), -(in(_41042, _40842))]]], (1345 ^ _20308) ^ [_41550] : [relation(_41550), 1348 ^ _20308 : [(1366 ^ _20308) ^ [_41924] : [-(_41924 = relation_rng(_41550)), 1370 ^ _20308 : [(1371 ^ _20308) ^ [] : [-(in(1367 ^ [_41550, _41924], _41924))], (1373 ^ _20308) ^ [_42058] : [in(ordered_pair(_42058, 1367 ^ [_41550, _41924]), _41550)]], 1375 ^ _20308 : [(1376 ^ _20308) ^ [] : [-(in(ordered_pair(1374 ^ [_41550, _41924], 1367 ^ [_41550, _41924]), _41550))], (1378 ^ _20308) ^ [] : [in(1367 ^ [_41550, _41924], _41924)]]], (1349 ^ _20308) ^ [_41642] : [_41642 = relation_rng(_41550), 1352 ^ _20308 : [(1353 ^ _20308) ^ [_41729] : [in(_41729, _41642), -(in(ordered_pair(1356 ^ [_41550, _41642, _41729], _41729), _41550))], (1360 ^ _20308) ^ [_41824] : [1361 ^ _20308 : [(1362 ^ _20308) ^ [_41868] : [in(ordered_pair(_41868, _41824), _41550)]], -(in(_41824, _41642))]]]]], (1382 ^ _20308) ^ [_42205, _42207] : [element(_42205, powerset(_42207)), -(subset_complement(_42207, _42205) = set_difference(_42207, _42205))], (1388 ^ _20308) ^ [_42298, _42300] : [-(ordered_pair(_42300, _42298) = unordered_pair(unordered_pair(_42300, _42298), singleton(_42300)))], (1390 ^ _20308) ^ [_42334] : [relation(_42334), -(relation_field(_42334) = set_union2(relation_dom(_42334), relation_rng(_42334)))], (1396 ^ _20308) ^ [_42425] : [relation(_42425), 1399 ^ _20308 : [(1400 ^ _20308) ^ [_42513] : [relation(_42513), 1403 ^ _20308 : [(1420 ^ _20308) ^ [] : [-(_42513 = relation_inverse(_42425)), 1425 ^ _20308 : [(1426 ^ _20308) ^ [] : [-(in(ordered_pair(1421 ^ [_42425, _42513], 1422 ^ [_42425, _42513]), _42513))], (1428 ^ _20308) ^ [] : [in(ordered_pair(1422 ^ [_42425, _42513], 1421 ^ [_42425, _42513]), _42425)]], 1429 ^ _20308 : [(1430 ^ _20308) ^ [] : [-(in(ordered_pair(1422 ^ [_42425, _42513], 1421 ^ [_42425, _42513]), _42425))], (1432 ^ _20308) ^ [] : [in(ordered_pair(1421 ^ [_42425, _42513], 1422 ^ [_42425, _42513]), _42513)]]], (1404 ^ _20308) ^ [] : [_42513 = relation_inverse(_42425), 1407 ^ _20308 : [(1408 ^ _20308) ^ [_42663, _42665] : [in(ordered_pair(_42665, _42663), _42513), -(in(ordered_pair(_42663, _42665), _42425))], (1414 ^ _20308) ^ [_42752, _42754] : [in(ordered_pair(_42752, _42754), _42425), -(in(ordered_pair(_42754, _42752), _42513))]]]]]]], (1436 ^ _20308) ^ [_43151, _43153] : [disjoint(_43153, _43151), -(set_intersection2(_43153, _43151) = empty_set)], (1442 ^ _20308) ^ [_43230, _43232] : [set_intersection2(_43232, _43230) = empty_set, -(disjoint(_43232, _43230))], (1448 ^ _20308) ^ [_43315] : [relation(_43315), function(_43315), 1455 ^ _20308 : [(1474 ^ _20308) ^ [] : [1477 ^ _20308 : [(1478 ^ _20308) ^ [] : [-(in(1475 ^ [_43315], relation_dom(_43315)))], (1480 ^ _20308) ^ [] : [-(in(1476 ^ [_43315], relation_dom(_43315)))], (1482 ^ _20308) ^ [] : [-(apply(_43315, 1475 ^ [_43315]) = apply(_43315, 1476 ^ [_43315]))], (1484 ^ _20308) ^ [] : [1475 ^ [_43315] = 1476 ^ [_43315]]], -(one_to_one(_43315))], (1456 ^ _20308) ^ [] : [one_to_one(_43315), 1459 ^ _20308 : [(1460 ^ _20308) ^ [_43504, _43506] : [-(_43506 = _43504), in(_43506, relation_dom(_43315)), in(_43504, relation_dom(_43315)), apply(_43315, _43506) = apply(_43315, _43504)]]]]], (1488 ^ _20308) ^ [_43907] : [relation(_43907), 1491 ^ _20308 : [(1492 ^ _20308) ^ [_44020] : [relation(_44020), 1495 ^ _20308 : [(1496 ^ _20308) ^ [_44125] : [relation(_44125), 1499 ^ _20308 : [(1523 ^ _20308) ^ [] : [-(_44125 = relation_composition(_43907, _44020)), 1537 ^ _20308 : [(1538 ^ _20308) ^ [] : [-(in(ordered_pair(1524 ^ [_43907, _44020, _44125], 1536 ^ [_43907, _44020, _44125]), _43907))], (1540 ^ _20308) ^ [] : [-(in(ordered_pair(1536 ^ [_43907, _44020, _44125], 1525 ^ [_43907, _44020, _44125]), _44020))], (1542 ^ _20308) ^ [] : [in(ordered_pair(1524 ^ [_43907, _44020, _44125], 1525 ^ [_43907, _44020, _44125]), _44125)]], 1528 ^ _20308 : [(1529 ^ _20308) ^ [] : [-(in(ordered_pair(1524 ^ [_43907, _44020, _44125], 1525 ^ [_43907, _44020, _44125]), _44125))], (1531 ^ _20308) ^ [_44781] : [in(ordered_pair(1524 ^ [_43907, _44020, _44125], _44781), _43907), in(ordered_pair(_44781, 1525 ^ [_43907, _44020, _44125]), _44020)]]], (1500 ^ _20308) ^ [] : [_44125 = relation_composition(_43907, _44020), 1503 ^ _20308 : [(1504 ^ _20308) ^ [_44295, _44297] : [in(ordered_pair(_44297, _44295), _44125), 1508 ^ _20308 : [(1509 ^ _20308) ^ [] : [-(in(ordered_pair(_44297, 1507 ^ [_43907, _44020, _44125, _44295, _44297]), _43907))], (1511 ^ _20308) ^ [] : [-(in(ordered_pair(1507 ^ [_43907, _44020, _44125, _44295, _44297], _44295), _44020))]]], (1513 ^ _20308) ^ [_44449, _44451] : [-(in(ordered_pair(_44451, _44449), _44125)), 1514 ^ _20308 : [(1515 ^ _20308) ^ [_44504] : [in(ordered_pair(_44451, _44504), _43907), in(ordered_pair(_44504, _44449), _44020)]]]]]]]]]]], (1546 ^ _20308) ^ [_45091, _45093] : [element(_45091, powerset(powerset(_45093))), 1549 ^ _20308 : [(1550 ^ _20308) ^ [_45197] : [element(_45197, powerset(powerset(_45093))), 1553 ^ _20308 : [(1574 ^ _20308) ^ [] : [-(_45197 = complements_of_subsets(_45093, _45091)), 1576 ^ _20308 : [(1577 ^ _20308) ^ [] : [-(element(1575 ^ [_45091, _45093, _45197], powerset(_45093)))], (1579 ^ _20308) ^ [] : [1580 ^ _20308 : [(1581 ^ _20308) ^ [] : [-(in(1575 ^ [_45091, _45093, _45197], _45197))], (1583 ^ _20308) ^ [] : [in(subset_complement(_45093, 1575 ^ [_45091, _45093, _45197]), _45091)]], 1584 ^ _20308 : [(1585 ^ _20308) ^ [] : [-(in(subset_complement(_45093, 1575 ^ [_45091, _45093, _45197]), _45091))], (1587 ^ _20308) ^ [] : [in(1575 ^ [_45091, _45093, _45197], _45197)]]]]], (1554 ^ _20308) ^ [] : [_45197 = complements_of_subsets(_45093, _45091), 1557 ^ _20308 : [(1558 ^ _20308) ^ [_45348] : [element(_45348, powerset(_45093)), 1561 ^ _20308 : [(1562 ^ _20308) ^ [] : [in(_45348, _45197), -(in(subset_complement(_45093, _45348), _45091))], (1568 ^ _20308) ^ [] : [in(subset_complement(_45093, _45348), _45091), -(in(_45348, _45197))]]]]]]]]], (1591 ^ _20308) ^ [_45888, _45890] : [proper_subset(_45890, _45888), 1594 ^ _20308 : [(1595 ^ _20308) ^ [] : [-(subset(_45890, _45888))], (1597 ^ _20308) ^ [] : [_45890 = _45888]]], (1599 ^ _20308) ^ [_45995, _45997] : [-(proper_subset(_45997, _45995)), subset(_45997, _45995), -(_45997 = _45995)], (1609 ^ _20308) ^ [_46129] : [relation(_46129), function(_46129), one_to_one(_46129), -(function_inverse(_46129) = relation_inverse(_46129))], (1623 ^ _20308) ^ [] : [true___, -(true___)], (1629 ^ _20308) ^ [] : [true___, -(true___)], (1635 ^ _20308) ^ [] : [true___, -(true___)], (1641 ^ _20308) ^ [] : [true___, -(true___)], (1647 ^ _20308) ^ [] : [true___, -(true___)], (1653 ^ _20308) ^ [] : [true___, -(true___)], (1659 ^ _20308) ^ [] : [true___, -(true___)], (1665 ^ _20308) ^ [_46721] : [1672 ^ _20308 : [(1673 ^ _20308) ^ [] : [-(relation(function_inverse(_46721)))], (1675 ^ _20308) ^ [] : [-(function(function_inverse(_46721)))]], relation(_46721), function(_46721)], (1677 ^ _20308) ^ [] : [true___, -(true___)], (1683 ^ _20308) ^ [_46931] : [-(element(cast_to_subset(_46931), powerset(_46931)))], (1685 ^ _20308) ^ [] : [true___, -(true___)], (1691 ^ _20308) ^ [] : [true___, -(true___)], (1697 ^ _20308) ^ [] : [true___, -(true___)], (1703 ^ _20308) ^ [] : [true___, -(true___)], (1709 ^ _20308) ^ [_47194, _47196] : [element(_47194, powerset(_47196)), -(element(subset_complement(_47196, _47194), powerset(_47196)))], (1715 ^ _20308) ^ [] : [true___, -(true___)], (1721 ^ _20308) ^ [] : [true___, -(true___)], (1727 ^ _20308) ^ [_47403] : [relation(_47403), -(relation(relation_inverse(_47403)))], (1733 ^ _20308) ^ [] : [true___, -(true___)], (1739 ^ _20308) ^ [] : [true___, -(true___)], (1745 ^ _20308) ^ [_47596, _47598] : [-(relation(relation_composition(_47598, _47596))), relation(_47598), relation(_47596)], (1755 ^ _20308) ^ [_47725, _47727] : [element(_47725, powerset(powerset(_47727))), -(element(union_of_subsets(_47727, _47725), powerset(_47727)))], (1761 ^ _20308) ^ [_47820] : [-(relation(identity_relation(_47820)))], (1763 ^ _20308) ^ [_47844, _47846] : [element(_47844, powerset(powerset(_47846))), -(element(meet_of_subsets(_47846, _47844), powerset(_47846)))], (1769 ^ _20308) ^ [_47939, _47941, _47943] : [-(element(subset_difference(_47943, _47941, _47939), powerset(_47943))), element(_47941, powerset(_47943)), element(_47939, powerset(_47943))], (1779 ^ _20308) ^ [_48092, _48094] : [relation(_48094), -(relation(relation_dom_restriction(_48094, _48092)))], (1785 ^ _20308) ^ [_48171, _48173] : [element(_48171, powerset(powerset(_48173))), -(element(complements_of_subsets(_48173, _48171), powerset(powerset(_48173))))], (1791 ^ _20308) ^ [_48270, _48272] : [relation(_48270), -(relation(relation_rng_restriction(_48272, _48270)))], (1797 ^ _20308) ^ [] : [true___, -(true___)], (1803 ^ _20308) ^ [] : [true___, -(true___)], (1810 ^ _20308) ^ [_48467] : [-(element(1808 ^ [_48467], _48467))], (1812 ^ _20308) ^ [_48495, _48497] : [1819 ^ _20308 : [(1820 ^ _20308) ^ [] : [-(empty(relation_composition(_48495, _48497)))], (1822 ^ _20308) ^ [] : [-(relation(relation_composition(_48495, _48497)))]], empty(_48497), relation(_48495)], (1824 ^ _20308) ^ [_48654] : [empty(_48654), 1827 ^ _20308 : [(1828 ^ _20308) ^ [] : [-(empty(relation_inverse(_48654)))], (1830 ^ _20308) ^ [] : [-(relation(relation_inverse(_48654)))]]], (1832 ^ _20308) ^ [] : [-(empty(empty_set))], (1834 ^ _20308) ^ [] : [-(relation(empty_set))], (1836 ^ _20308) ^ [] : [-(relation_empty_yielding(empty_set))], (1838 ^ _20308) ^ [_48805, _48807] : [1845 ^ _20308 : [(1846 ^ _20308) ^ [] : [-(relation(relation_dom_restriction(_48807, _48805)))], (1848 ^ _20308) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_48807, _48805)))]], relation(_48807), relation_empty_yielding(_48807)], (1850 ^ _20308) ^ [_48964, _48966] : [1865 ^ _20308 : [(1866 ^ _20308) ^ [] : [-(relation(relation_composition(_48966, _48964)))], (1868 ^ _20308) ^ [] : [-(function(relation_composition(_48966, _48964)))]], relation(_48966), function(_48966), relation(_48964), function(_48964)], (1870 ^ _20308) ^ [_49223, _49225] : [-(relation(set_intersection2(_49225, _49223))), relation(_49225), relation(_49223)], (1880 ^ _20308) ^ [_49361] : [empty(powerset(_49361))], (1882 ^ _20308) ^ [] : [-(empty(empty_set))], (1884 ^ _20308) ^ [_49415, _49417] : [empty(ordered_pair(_49417, _49415))], (1886 ^ _20308) ^ [_49440] : [-(relation(identity_relation(_49440)))], (1888 ^ _20308) ^ [_49461] : [-(function(identity_relation(_49461)))], (1890 ^ _20308) ^ [_49487, _49489] : [-(relation(set_union2(_49489, _49487))), relation(_49489), relation(_49487)], (1900 ^ _20308) ^ [_49625] : [empty(singleton(_49625))], (1902 ^ _20308) ^ [_49648, _49650] : [-(empty(_49650)), empty(set_union2(_49650, _49648))], (1908 ^ _20308) ^ [_49727] : [1919 ^ _20308 : [(1920 ^ _20308) ^ [] : [-(relation(relation_inverse(_49727)))], (1922 ^ _20308) ^ [] : [-(function(relation_inverse(_49727)))]], relation(_49727), function(_49727), one_to_one(_49727)], (1924 ^ _20308) ^ [_49938, _49940] : [empty(unordered_pair(_49940, _49938))], (1926 ^ _20308) ^ [_49964, _49966] : [-(empty(_49966)), empty(set_union2(_49964, _49966))], (1932 ^ _20308) ^ [_50043, _50045] : [1939 ^ _20308 : [(1940 ^ _20308) ^ [] : [-(relation(relation_dom_restriction(_50045, _50043)))], (1942 ^ _20308) ^ [] : [-(function(relation_dom_restriction(_50045, _50043)))]], relation(_50045), function(_50045)], (1944 ^ _20308) ^ [] : [-(empty(empty_set))], (1946 ^ _20308) ^ [] : [-(relation(empty_set))], (1948 ^ _20308) ^ [_50234, _50236] : [empty(cartesian_product2(_50236, _50234)), -(empty(_50236)), -(empty(_50234))], (1958 ^ _20308) ^ [_50319] : [empty(relation_dom(_50319)), -(empty(_50319)), relation(_50319)], (1968 ^ _20308) ^ [_50446] : [empty(relation_rng(_50446)), -(empty(_50446)), relation(_50446)], (1978 ^ _20308) ^ [_50573] : [empty(_50573), 1981 ^ _20308 : [(1982 ^ _20308) ^ [] : [-(empty(relation_dom(_50573)))], (1984 ^ _20308) ^ [] : [-(relation(relation_dom(_50573)))]]], (1986 ^ _20308) ^ [_50676] : [empty(_50676), 1989 ^ _20308 : [(1990 ^ _20308) ^ [] : [-(empty(relation_rng(_50676)))], (1992 ^ _20308) ^ [] : [-(relation(relation_rng(_50676)))]]], (1994 ^ _20308) ^ [_50823, _50825] : [2001 ^ _20308 : [(2002 ^ _20308) ^ [] : [-(empty(relation_composition(_50825, _50823)))], (2004 ^ _20308) ^ [] : [-(relation(relation_composition(_50825, _50823)))]], empty(_50825), relation(_50823)], (2006 ^ _20308) ^ [_51186, _51188] : [-(set_union2(_51188, _51188) = _51188)], (2008 ^ _20308) ^ [_51283, _51285] : [-(set_intersection2(_51285, _51285) = _51285)], (2010 ^ _20308) ^ [_51395, _51397] : [element(_51395, powerset(_51397)), -(subset_complement(_51397, subset_complement(_51397, _51395)) = _51395)], (2016 ^ _20308) ^ [_51607] : [relation(_51607), -(relation_inverse(relation_inverse(_51607)) = _51607)], (2022 ^ _20308) ^ [_51817, _51819] : [element(_51817, powerset(powerset(_51819))), -(complements_of_subsets(_51819, complements_of_subsets(_51819, _51817)) = _51817)], (2028 ^ _20308) ^ [_52031, _52033] : [proper_subset(_52033, _52033)], (2030 ^ _20308) ^ [_52110] : [singleton(_52110) = empty_set], (2032 ^ _20308) ^ [_52219, _52221] : [in(_52221, _52219), -(set_union2(singleton(_52221), _52219) = _52219)], (2038 ^ _20308) ^ [_52439, _52441] : [disjoint(singleton(_52441), _52439), in(_52441, _52439)], (2044 ^ _20308) ^ [_52652, _52654] : [-(in(_52654, _52652)), -(disjoint(singleton(_52654), _52652))], (2050 ^ _20308) ^ [_52898, _52900] : [subset(singleton(_52900), _52898), -(in(_52900, _52898))], (2056 ^ _20308) ^ [_53064, _53066] : [in(_53066, _53064), -(subset(singleton(_53066), _53064))], (2062 ^ _20308) ^ [_53309, _53311] : [set_difference(_53311, _53309) = empty_set, -(subset(_53311, _53309))], (2068 ^ _20308) ^ [_53477, _53479] : [subset(_53479, _53477), -(set_difference(_53479, _53477) = empty_set)], (2074 ^ _20308) ^ [_53695, _53697] : [element(_53695, powerset(_53697)), 2077 ^ _20308 : [(2078 ^ _20308) ^ [_53836] : [in(_53836, _53695), -(in(_53836, _53697))]]], (2084 ^ _20308) ^ [_54075, _54077, _54079] : [subset(_54079, _54077), -(in(_54075, _54079)), -(subset(_54079, set_difference(_54077, singleton(_54075))))], (2104 ^ _20308) ^ [_54684, _54686] : [2105 ^ _20308 : [(2106 ^ _20308) ^ [] : [_54686 = empty_set], (2108 ^ _20308) ^ [] : [_54686 = singleton(_54684)]], -(subset(_54686, singleton(_54684)))], (2094 ^ _20308) ^ [_54424, _54426] : [subset(_54426, singleton(_54424)), -(_54426 = empty_set), -(_54426 = singleton(_54424))], (2112 ^ _20308) ^ [_54978, _54980] : [in(_54980, _54978), -(subset(_54980, union(_54978)))], (2118 ^ _20308) ^ [_55249, _55251, _55253, _55255] : [in(ordered_pair(_55255, _55253), cartesian_product2(_55251, _55249)), 2121 ^ _20308 : [(2122 ^ _20308) ^ [] : [-(in(_55255, _55251))], (2124 ^ _20308) ^ [] : [-(in(_55253, _55249))]]], (2126 ^ _20308) ^ [_55514, _55516, _55518, _55520] : [-(in(ordered_pair(_55520, _55518), cartesian_product2(_55516, _55514))), in(_55520, _55516), in(_55518, _55514)], (2136 ^ _20308) ^ [_55847, _55849] : [2138 ^ _20308 : [(2139 ^ _20308) ^ [] : [-(in(2137 ^ [_55847, _55849], _55849))], (2141 ^ _20308) ^ [] : [in(2137 ^ [_55847, _55849], _55847)]], -(element(_55849, powerset(_55847)))], (2146 ^ _20308) ^ [] : [-(relation(2144 ^ []))], (2148 ^ _20308) ^ [] : [-(function(2144 ^ []))], (2151 ^ _20308) ^ [] : [-(empty(2149 ^ []))], (2153 ^ _20308) ^ [] : [-(relation(2149 ^ []))], (2155 ^ _20308) ^ [_56490] : [-(empty(_56490)), 2159 ^ _20308 : [(2160 ^ _20308) ^ [] : [-(element(2158 ^ [_56490], powerset(_56490)))], (2162 ^ _20308) ^ [] : [empty(2158 ^ [_56490])]]], (2165 ^ _20308) ^ [] : [-(empty(2163 ^ []))], (2168 ^ _20308) ^ [] : [-(relation(2166 ^ []))], (2170 ^ _20308) ^ [] : [-(empty(2166 ^ []))], (2172 ^ _20308) ^ [] : [-(function(2166 ^ []))], (2175 ^ _20308) ^ [] : [empty(2173 ^ [])], (2177 ^ _20308) ^ [] : [-(relation(2173 ^ []))], (2180 ^ _20308) ^ [_57321] : [-(element(2178 ^ [_57321], powerset(_57321)))], (2182 ^ _20308) ^ [_57372] : [-(empty(2178 ^ [_57372]))], (2185 ^ _20308) ^ [] : [empty(2183 ^ [])], (2188 ^ _20308) ^ [] : [-(relation(2186 ^ []))], (2190 ^ _20308) ^ [] : [-(function(2186 ^ []))], (2192 ^ _20308) ^ [] : [-(one_to_one(2186 ^ []))], (2195 ^ _20308) ^ [] : [-(relation(2193 ^ []))], (2197 ^ _20308) ^ [] : [-(relation_empty_yielding(2193 ^ []))], (2199 ^ _20308) ^ [_57933, _57935] : [element(_57933, powerset(powerset(_57935))), -(union_of_subsets(_57935, _57933) = union(_57933))], (2205 ^ _20308) ^ [_58161, _58163] : [element(_58161, powerset(powerset(_58163))), -(meet_of_subsets(_58163, _58161) = set_meet(_58161))], (2211 ^ _20308) ^ [_58403, _58405, _58407] : [-(subset_difference(_58407, _58405, _58403) = set_difference(_58405, _58403)), element(_58405, powerset(_58407)), element(_58403, powerset(_58407))], (2221 ^ _20308) ^ [_58719, _58721] : [-(subset(_58721, _58721))], (2223 ^ _20308) ^ [_58828, _58830] : [disjoint(_58830, _58828), -(disjoint(_58828, _58830))], (2229 ^ _20308) ^ [_59095, _59097, _59099, _59101] : [in(ordered_pair(_59101, _59099), cartesian_product2(_59097, _59095)), 2232 ^ _20308 : [(2233 ^ _20308) ^ [] : [-(in(_59101, _59097))], (2235 ^ _20308) ^ [] : [-(in(_59099, _59095))]]], (2237 ^ _20308) ^ [_59360, _59362, _59364, _59366] : [-(in(ordered_pair(_59366, _59364), cartesian_product2(_59362, _59360))), in(_59366, _59362), in(_59364, _59360)], (2247 ^ _20308) ^ [_59721, _59723, _59725, _59727] : [unordered_pair(_59727, _59725) = unordered_pair(_59723, _59721), -(_59727 = _59723), -(_59727 = _59721)], (2257 ^ _20308) ^ [_60071, _60073, _60075] : [relation(_60071), 2260 ^ _20308 : [(2261 ^ _20308) ^ [] : [in(_60075, relation_rng(relation_rng_restriction(_60073, _60071))), 2264 ^ _20308 : [(2265 ^ _20308) ^ [] : [-(in(_60075, _60073))], (2267 ^ _20308) ^ [] : [-(in(_60075, relation_rng(_60071)))]]], (2269 ^ _20308) ^ [] : [-(in(_60075, relation_rng(relation_rng_restriction(_60073, _60071)))), in(_60075, _60073), in(_60075, relation_rng(_60071))]]], (2279 ^ _20308) ^ [_60730, _60732] : [relation(_60730), -(subset(relation_rng(relation_rng_restriction(_60732, _60730)), _60732))], (2285 ^ _20308) ^ [_60948, _60950] : [relation(_60948), -(subset(relation_rng_restriction(_60950, _60948), _60948))], (2291 ^ _20308) ^ [_61162, _61164] : [relation(_61162), -(subset(relation_rng(relation_rng_restriction(_61164, _61162)), relation_rng(_61162)))], (2297 ^ _20308) ^ [_61398, _61400, _61402] : [subset(_61402, _61400), 2300 ^ _20308 : [(2301 ^ _20308) ^ [] : [-(subset(cartesian_product2(_61402, _61398), cartesian_product2(_61400, _61398)))], (2303 ^ _20308) ^ [] : [-(subset(cartesian_product2(_61398, _61402), cartesian_product2(_61398, _61400)))]]], (2305 ^ _20308) ^ [_61715, _61717] : [relation(_61715), -(relation_rng(relation_rng_restriction(_61717, _61715)) = set_intersection2(relation_rng(_61715), _61717))], (2311 ^ _20308) ^ [_61971, _61973, _61975, _61977] : [-(subset(cartesian_product2(_61977, _61973), cartesian_product2(_61975, _61971))), subset(_61977, _61975), subset(_61973, _61971)], (2321 ^ _20308) ^ [_62302, _62304] : [subset(_62304, _62302), -(set_union2(_62304, _62302) = _62302)], (2328 ^ _20308) ^ [_62624] : [-(in(_62624, 2326 ^ [_62624]))], (2330 ^ _20308) ^ [_62736, _62738, _62740] : [-(in(_62736, 2326 ^ [_62740])), in(_62738, 2326 ^ [_62740]), subset(_62736, _62738)], (2340 ^ _20308) ^ [_63051, _63053] : [in(_63051, 2326 ^ [_63053]), -(in(powerset(_63051), 2326 ^ [_63053]))], (2346 ^ _20308) ^ [_63251, _63253] : [subset(_63251, 2326 ^ [_63253]), -(are_equipotent(_63251, 2326 ^ [_63253])), -(in(_63251, 2326 ^ [_63253]))], (2356 ^ _20308) ^ [_63605, _63607, _63609] : [relation(_63605), -(relation_dom_restriction(relation_rng_restriction(_63609, _63605), _63607) = relation_rng_restriction(_63609, relation_dom_restriction(_63605, _63607)))], (2362 ^ _20308) ^ [_63857, _63859, _63861] : [relation(_63857), 2365 ^ _20308 : [(2366 ^ _20308) ^ [] : [in(_63861, relation_image(_63857, _63859)), 2370 ^ _20308 : [(2371 ^ _20308) ^ [] : [-(in(2369 ^ [_63857, _63859, _63861], relation_dom(_63857)))], (2373 ^ _20308) ^ [] : [-(in(ordered_pair(2369 ^ [_63857, _63859, _63861], _63861), _63857))], (2375 ^ _20308) ^ [] : [-(in(2369 ^ [_63857, _63859, _63861], _63859))]]], (2377 ^ _20308) ^ [] : [-(in(_63861, relation_image(_63857, _63859))), 2378 ^ _20308 : [(2379 ^ _20308) ^ [_64458] : [in(_64458, relation_dom(_63857)), in(ordered_pair(_64458, _63861), _63857), in(_64458, _63859)]]]]], (2391 ^ _20308) ^ [_64855, _64857] : [relation(_64855), -(subset(relation_image(_64855, _64857), relation_rng(_64855)))], (2397 ^ _20308) ^ [_65073, _65075] : [relation(_65073), -(relation_image(_65073, _65075) = relation_image(_65073, set_intersection2(relation_dom(_65073), _65075)))], (2403 ^ _20308) ^ [_65289] : [relation(_65289), -(relation_image(_65289, relation_dom(_65289)) = relation_rng(_65289))], (2409 ^ _20308) ^ [_65491] : [relation(_65491), 2412 ^ _20308 : [(2413 ^ _20308) ^ [_65631] : [relation(_65631), -(relation_rng(relation_composition(_65491, _65631)) = relation_image(_65631, relation_rng(_65491)))]]], (2419 ^ _20308) ^ [_65880, _65882, _65884] : [relation(_65880), 2422 ^ _20308 : [(2423 ^ _20308) ^ [] : [in(_65884, relation_inverse_image(_65880, _65882)), 2427 ^ _20308 : [(2428 ^ _20308) ^ [] : [-(in(2426 ^ [_65880, _65882, _65884], relation_rng(_65880)))], (2430 ^ _20308) ^ [] : [-(in(ordered_pair(_65884, 2426 ^ [_65880, _65882, _65884]), _65880))], (2432 ^ _20308) ^ [] : [-(in(2426 ^ [_65880, _65882, _65884], _65882))]]], (2434 ^ _20308) ^ [] : [-(in(_65884, relation_inverse_image(_65880, _65882))), 2435 ^ _20308 : [(2436 ^ _20308) ^ [_66481] : [in(_66481, relation_rng(_65880)), in(ordered_pair(_65884, _66481), _65880), in(_66481, _65882)]]]]], (2448 ^ _20308) ^ [_66878, _66880] : [relation(_66878), -(subset(relation_inverse_image(_66878, _66880), relation_dom(_66878)))], (2454 ^ _20308) ^ [_67096, _67098] : [relation(_67096), -(_67098 = empty_set), subset(_67098, relation_rng(_67096)), relation_inverse_image(_67096, _67098) = empty_set], (2468 ^ _20308) ^ [_67510, _67512, _67514] : [relation(_67510), subset(_67514, _67512), -(subset(relation_inverse_image(_67510, _67514), relation_inverse_image(_67510, _67512)))], (2478 ^ _20308) ^ [_67814, _67816] : [-(subset(set_intersection2(_67816, _67814), _67816))], (2480 ^ _20308) ^ [_67940, _67942, _67944] : [-(subset(_67944, set_intersection2(_67942, _67940))), subset(_67944, _67942), subset(_67944, _67940)], (2490 ^ _20308) ^ [_68226] : [-(set_union2(_68226, empty_set) = _68226)], (2492 ^ _20308) ^ [_68336, _68338] : [in(_68338, _68336), -(element(_68338, _68336))], (2498 ^ _20308) ^ [_68560, _68562, _68564] : [-(subset(_68564, _68560)), subset(_68564, _68562), subset(_68562, _68560)], (2508 ^ _20308) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (2510 ^ _20308) ^ [_68936, _68938, _68940] : [relation(_68936), in(ordered_pair(_68940, _68938), _68936), 2517 ^ _20308 : [(2518 ^ _20308) ^ [] : [-(in(_68940, relation_dom(_68936)))], (2520 ^ _20308) ^ [] : [-(in(_68938, relation_rng(_68936)))]]], (2522 ^ _20308) ^ [_69334, _69336] : [relation(_69334), function(_69334), 2529 ^ _20308 : [(2530 ^ _20308) ^ [_69584] : [relation(_69584), function(_69584), 2537 ^ _20308 : [(2538 ^ _20308) ^ [] : [in(_69336, relation_dom(relation_composition(_69584, _69334))), 2541 ^ _20308 : [(2542 ^ _20308) ^ [] : [-(in(_69336, relation_dom(_69584)))], (2544 ^ _20308) ^ [] : [-(in(apply(_69584, _69336), relation_dom(_69334)))]]], (2546 ^ _20308) ^ [] : [-(in(_69336, relation_dom(relation_composition(_69584, _69334)))), in(_69336, relation_dom(_69584)), in(apply(_69584, _69336), relation_dom(_69334))]]]]], (2556 ^ _20308) ^ [_70348] : [relation(_70348), -(subset(_70348, cartesian_product2(relation_dom(_70348), relation_rng(_70348))))], (2562 ^ _20308) ^ [_70564, _70566] : [relation(_70564), function(_70564), 2569 ^ _20308 : [(2570 ^ _20308) ^ [_70813] : [relation(_70813), function(_70813), in(_70566, relation_dom(relation_composition(_70813, _70564))), -(apply(relation_composition(_70813, _70564), _70566) = apply(_70564, apply(_70813, _70566)))]]], (2584 ^ _20308) ^ [_71258, _71260] : [relation(_71258), function(_71258), 2591 ^ _20308 : [(2592 ^ _20308) ^ [_71504] : [relation(_71504), function(_71504), in(_71260, relation_dom(_71258)), -(apply(relation_composition(_71258, _71504), _71260) = apply(_71504, apply(_71258, _71260)))]]], (2606 ^ _20308) ^ [_71929] : [relation(_71929), 2609 ^ _20308 : [(2610 ^ _20308) ^ [_72079] : [relation(_72079), subset(_71929, _72079), 2617 ^ _20308 : [(2618 ^ _20308) ^ [] : [-(subset(relation_dom(_71929), relation_dom(_72079)))], (2620 ^ _20308) ^ [] : [-(subset(relation_rng(_71929), relation_rng(_72079)))]]]]], (2622 ^ _20308) ^ [_72488, _72490, _72492] : [subset(_72492, _72490), -(subset(set_intersection2(_72492, _72488), set_intersection2(_72490, _72488)))], (2628 ^ _20308) ^ [_72716, _72718] : [subset(_72718, _72716), -(set_intersection2(_72718, _72716) = _72718)], (2634 ^ _20308) ^ [_72903] : [-(set_intersection2(_72903, empty_set) = empty_set)], (2636 ^ _20308) ^ [_73013, _73015] : [element(_73015, _73013), -(empty(_73013)), -(in(_73015, _73013))], (2646 ^ _20308) ^ [_73311, _73313] : [-(_73313 = _73311), 2650 ^ _20308 : [(2651 ^ _20308) ^ [] : [-(in(2647 ^ [_73311, _73313], _73313))], (2653 ^ _20308) ^ [] : [in(2647 ^ [_73311, _73313], _73311)]], 2654 ^ _20308 : [(2655 ^ _20308) ^ [] : [-(in(2647 ^ [_73311, _73313], _73311))], (2657 ^ _20308) ^ [] : [in(2647 ^ [_73311, _73313], _73313)]]], (2661 ^ _20308) ^ [_73812] : [-(subset(empty_set, _73812))], (2663 ^ _20308) ^ [_73933, _73935, _73937] : [relation(_73933), in(ordered_pair(_73937, _73935), _73933), 2670 ^ _20308 : [(2671 ^ _20308) ^ [] : [-(in(_73937, relation_field(_73933)))], (2673 ^ _20308) ^ [] : [-(in(_73935, relation_field(_73933)))]]], (2675 ^ _20308) ^ [_74345, _74347, _74349] : [subset(_74349, _74347), -(subset(set_difference(_74349, _74345), set_difference(_74347, _74345)))], (2681 ^ _20308) ^ [_74601, _74603, _74605, _74607] : [ordered_pair(_74607, _74605) = ordered_pair(_74603, _74601), 2684 ^ _20308 : [(2685 ^ _20308) ^ [] : [-(_74607 = _74603)], (2687 ^ _20308) ^ [] : [-(_74605 = _74601)]]], (2689 ^ _20308) ^ [_74914, _74916] : [relation(_74914), function(_74914), 2696 ^ _20308 : [(2697 ^ _20308) ^ [] : [_74914 = identity_relation(_74916), 2700 ^ _20308 : [(2701 ^ _20308) ^ [] : [-(relation_dom(_74914) = _74916)], (2703 ^ _20308) ^ [_75333] : [in(_75333, _74916), -(apply(_74914, _75333) = _75333)]]], (2709 ^ _20308) ^ [] : [-(_74914 = identity_relation(_74916)), relation_dom(_74914) = _74916, 2715 ^ _20308 : [(2716 ^ _20308) ^ [] : [-(in(2714 ^ [_74914, _74916], _74916))], (2718 ^ _20308) ^ [] : [apply(_74914, 2714 ^ [_74914, _74916]) = 2714 ^ [_74914, _74916]]]]]], (2722 ^ _20308) ^ [_75938, _75940] : [in(_75938, _75940), -(apply(identity_relation(_75940), _75938) = _75938)], (2728 ^ _20308) ^ [_76143, _76145] : [-(subset(set_difference(_76145, _76143), _76145))], (2730 ^ _20308) ^ [_76241] : [relation(_76241), 2733 ^ _20308 : [(2734 ^ _20308) ^ [] : [-(relation_rng(_76241) = relation_dom(relation_inverse(_76241)))], (2736 ^ _20308) ^ [] : [-(relation_dom(_76241) = relation_rng(relation_inverse(_76241)))]]], (2738 ^ _20308) ^ [_76569, _76571] : [set_difference(_76571, _76569) = empty_set, -(subset(_76571, _76569))], (2744 ^ _20308) ^ [_76737, _76739] : [subset(_76739, _76737), -(set_difference(_76739, _76737) = empty_set)], (2750 ^ _20308) ^ [_76984, _76986] : [subset(singleton(_76986), _76984), -(in(_76986, _76984))], (2756 ^ _20308) ^ [_77150, _77152] : [in(_77152, _77150), -(subset(singleton(_77152), _77150))], (2762 ^ _20308) ^ [_77409, _77411, _77413] : [subset(unordered_pair(_77413, _77411), _77409), 2765 ^ _20308 : [(2766 ^ _20308) ^ [] : [-(in(_77413, _77409))], (2768 ^ _20308) ^ [] : [-(in(_77411, _77409))]]], (2770 ^ _20308) ^ [_77660, _77662, _77664] : [-(subset(unordered_pair(_77664, _77662), _77660)), in(_77664, _77660), in(_77662, _77660)], (2780 ^ _20308) ^ [_77962, _77964] : [-(set_union2(_77964, set_difference(_77962, _77964)) = set_union2(_77964, _77962))], (2792 ^ _20308) ^ [_78369, _78371] : [2793 ^ _20308 : [(2794 ^ _20308) ^ [] : [_78371 = empty_set], (2796 ^ _20308) ^ [] : [_78371 = singleton(_78369)]], -(subset(_78371, singleton(_78369)))], (2782 ^ _20308) ^ [_78109, _78111] : [subset(_78111, singleton(_78109)), -(_78111 = empty_set), -(_78111 = singleton(_78109))], (2800 ^ _20308) ^ [_78634] : [-(set_difference(_78634, empty_set) = _78634)], (2802 ^ _20308) ^ [_78773, _78775] : [element(_78775, powerset(_78773)), -(subset(_78775, _78773))], (2808 ^ _20308) ^ [_78939, _78941] : [subset(_78941, _78939), -(element(_78941, powerset(_78939)))], (2814 ^ _20308) ^ [_79175, _79177] : [-(disjoint(_79177, _79175)), 2818 ^ _20308 : [(2819 ^ _20308) ^ [] : [-(in(2817 ^ [_79175, _79177], _79177))], (2821 ^ _20308) ^ [] : [-(in(2817 ^ [_79175, _79177], _79175))]]], (2823 ^ _20308) ^ [_79489, _79491] : [disjoint(_79491, _79489), 2824 ^ _20308 : [(2825 ^ _20308) ^ [_79581] : [in(_79581, _79491), in(_79581, _79489)]]], (2833 ^ _20308) ^ [_79838] : [subset(_79838, empty_set), -(_79838 = empty_set)], (2839 ^ _20308) ^ [_80027, _80029] : [-(set_difference(set_union2(_80029, _80027), _80027) = set_difference(_80029, _80027))], (2841 ^ _20308) ^ [_80145, _80147] : [element(_80145, powerset(_80147)), 2844 ^ _20308 : [(2845 ^ _20308) ^ [_80297] : [element(_80297, powerset(_80147)), 2848 ^ _20308 : [(2849 ^ _20308) ^ [] : [disjoint(_80145, _80297), -(subset(_80145, subset_complement(_80147, _80297)))], (2855 ^ _20308) ^ [] : [subset(_80145, subset_complement(_80147, _80297)), -(disjoint(_80145, _80297))]]]]], (2861 ^ _20308) ^ [_80781] : [relation(_80781), 2864 ^ _20308 : [(2865 ^ _20308) ^ [_80918] : [relation(_80918), -(subset(relation_dom(relation_composition(_80781, _80918)), relation_dom(_80781)))]]], (2871 ^ _20308) ^ [_81133] : [relation(_81133), 2874 ^ _20308 : [(2875 ^ _20308) ^ [_81270] : [relation(_81270), -(subset(relation_rng(relation_composition(_81133, _81270)), relation_rng(_81270)))]]], (2881 ^ _20308) ^ [_81499, _81501] : [subset(_81501, _81499), -(_81499 = set_union2(_81501, set_difference(_81499, _81501)))], (2887 ^ _20308) ^ [_81707] : [relation(_81707), 2890 ^ _20308 : [(2891 ^ _20308) ^ [_81854] : [relation(_81854), subset(relation_rng(_81707), relation_dom(_81854)), -(relation_dom(relation_composition(_81707, _81854)) = relation_dom(_81707))]]], (2901 ^ _20308) ^ [_82180, _82182] : [element(_82180, powerset(powerset(_82182))), -(_82180 = empty_set), complements_of_subsets(_82182, _82180) = empty_set], (2911 ^ _20308) ^ [_82497, _82499] : [in(_82499, _82497), -(set_union2(singleton(_82499), _82497) = _82497)], (2917 ^ _20308) ^ [_82703] : [relation(_82703), 2920 ^ _20308 : [(2921 ^ _20308) ^ [_82850] : [relation(_82850), subset(relation_dom(_82703), relation_rng(_82850)), -(relation_rng(relation_composition(_82850, _82703)) = relation_rng(_82703))]]], (2931 ^ _20308) ^ [_83176, _83178] : [element(_83176, powerset(powerset(_83178))), -(_83176 = empty_set), -(subset_difference(_83178, cast_to_subset(_83178), union_of_subsets(_83178, _83176)) = meet_of_subsets(_83178, complements_of_subsets(_83178, _83176)))], (2941 ^ _20308) ^ [_83516, _83518] : [element(_83516, powerset(powerset(_83518))), -(_83516 = empty_set), -(union_of_subsets(_83518, complements_of_subsets(_83518, _83516)) = subset_difference(_83518, cast_to_subset(_83518), meet_of_subsets(_83518, _83516)))], (2951 ^ _20308) ^ [_83841, _83843] : [-(set_difference(_83843, set_difference(_83843, _83841)) = set_intersection2(_83843, _83841))], (2953 ^ _20308) ^ [_83930] : [-(set_difference(empty_set, _83930) = empty_set)], (2955 ^ _20308) ^ [_84054, _84056, _84058] : [-(element(_84058, _84054)), in(_84058, _84056), element(_84056, powerset(_84054))], (2965 ^ _20308) ^ [_84387, _84389] : [-(disjoint(_84389, _84387)), -(in(2968 ^ [_84387, _84389], set_intersection2(_84389, _84387)))], (2972 ^ _20308) ^ [_84622, _84624] : [2973 ^ _20308 : [(2974 ^ _20308) ^ [_84695] : [in(_84695, set_intersection2(_84624, _84622))]], disjoint(_84624, _84622)], (2978 ^ _20308) ^ [_84847] : [-(_84847 = empty_set), 2981 ^ _20308 : [(2982 ^ _20308) ^ [_85007] : [element(_85007, powerset(_84847)), 2985 ^ _20308 : [(2986 ^ _20308) ^ [_85161] : [element(_85161, _84847), -(in(_85161, _85007)), -(in(_85161, subset_complement(_84847, _85007)))]]]]], (2996 ^ _20308) ^ [_85479] : [relation(_85479), function(_85479), one_to_one(_85479), 3007 ^ _20308 : [(3008 ^ _20308) ^ [_85866] : [relation(_85866), function(_85866), 3015 ^ _20308 : [(3046 ^ _20308) ^ [] : [-(_85866 = function_inverse(_85479)), relation_dom(_85866) = relation_rng(_85479), 3055 ^ _20308 : [(3056 ^ _20308) ^ [] : [-(in(3051 ^ [_85479, _85866], relation_rng(_85479)))], (3058 ^ _20308) ^ [] : [-(3052 ^ [_85479, _85866] = apply(_85866, 3051 ^ [_85479, _85866]))], (3060 ^ _20308) ^ [] : [in(3052 ^ [_85479, _85866], relation_dom(_85479)), 3051 ^ [_85479, _85866] = apply(_85479, 3052 ^ [_85479, _85866])]], 3065 ^ _20308 : [(3066 ^ _20308) ^ [] : [-(in(3052 ^ [_85479, _85866], relation_dom(_85479)))], (3068 ^ _20308) ^ [] : [-(3051 ^ [_85479, _85866] = apply(_85479, 3052 ^ [_85479, _85866]))], (3070 ^ _20308) ^ [] : [in(3051 ^ [_85479, _85866], relation_rng(_85479)), 3052 ^ [_85479, _85866] = apply(_85866, 3051 ^ [_85479, _85866])]]], (3016 ^ _20308) ^ [] : [_85866 = function_inverse(_85479), 3019 ^ _20308 : [(3020 ^ _20308) ^ [] : [-(relation_dom(_85866) = relation_rng(_85479))], (3022 ^ _20308) ^ [_86383, _86385] : [3029 ^ _20308 : [(3030 ^ _20308) ^ [] : [-(in(_86383, relation_dom(_85479)))], (3032 ^ _20308) ^ [] : [-(_86385 = apply(_85479, _86383))]], in(_86385, relation_rng(_85479)), _86383 = apply(_85866, _86385)], (3034 ^ _20308) ^ [_86757, _86759] : [3041 ^ _20308 : [(3042 ^ _20308) ^ [] : [-(in(_86759, relation_rng(_85479)))], (3044 ^ _20308) ^ [] : [-(_86757 = apply(_85866, _86759))]], in(_86757, relation_dom(_85479)), _86759 = apply(_85479, _86757)]]]]]]], (3078 ^ _20308) ^ [_88332, _88334, _88336] : [element(_88332, powerset(_88336)), in(_88334, subset_complement(_88336, _88332)), in(_88334, _88332)], (3088 ^ _20308) ^ [_88638] : [relation(_88638), function(_88638), one_to_one(_88638), 3099 ^ _20308 : [(3100 ^ _20308) ^ [] : [-(relation_rng(_88638) = relation_dom(function_inverse(_88638)))], (3102 ^ _20308) ^ [] : [-(relation_dom(_88638) = relation_rng(function_inverse(_88638)))]]], (3104 ^ _20308) ^ [_89091] : [relation(_89091), -(in(ordered_pair(3109 ^ [_89091], 3110 ^ [_89091]), _89091)), -(_89091 = empty_set)], (3116 ^ _20308) ^ [_89509, _89511] : [relation(_89509), function(_89509), 3131 ^ _20308 : [(3132 ^ _20308) ^ [] : [-(_89511 = apply(_89509, apply(function_inverse(_89509), _89511)))], (3134 ^ _20308) ^ [] : [-(_89511 = apply(relation_composition(function_inverse(_89509), _89509), _89511))]], one_to_one(_89509), in(_89511, relation_rng(_89509))], (3136 ^ _20308) ^ [_90107, _90109, _90111] : [in(_90111, _90109), element(_90109, powerset(_90107)), empty(_90107)], (3146 ^ _20308) ^ [] : [-(relation_dom(empty_set) = empty_set)], (3148 ^ _20308) ^ [] : [-(relation_rng(empty_set) = empty_set)], (3150 ^ _20308) ^ [_90525, _90527] : [subset(_90527, _90525), proper_subset(_90525, _90527)], (3156 ^ _20308) ^ [_90720] : [relation(_90720), function(_90720), one_to_one(_90720), -(one_to_one(function_inverse(_90720)))], (3170 ^ _20308) ^ [_91106, _91108, _91110] : [-(disjoint(_91110, _91106)), subset(_91110, _91108), disjoint(_91108, _91106)], (3180 ^ _20308) ^ [_91401] : [relation(_91401), 3185 ^ _20308 : [(3186 ^ _20308) ^ [] : [relation_dom(_91401) = empty_set], (3188 ^ _20308) ^ [] : [relation_rng(_91401) = empty_set]], -(_91401 = empty_set)], (3192 ^ _20308) ^ [_91754] : [relation(_91754), 3195 ^ _20308 : [(3196 ^ _20308) ^ [] : [relation_dom(_91754) = empty_set, -(relation_rng(_91754) = empty_set)], (3202 ^ _20308) ^ [] : [relation_rng(_91754) = empty_set, -(relation_dom(_91754) = empty_set)]]], (3208 ^ _20308) ^ [_92237, _92239] : [set_difference(_92239, singleton(_92237)) = _92239, in(_92237, _92239)], (3214 ^ _20308) ^ [_92410, _92412] : [-(in(_92410, _92412)), -(set_difference(_92412, singleton(_92410)) = _92412)], (3220 ^ _20308) ^ [_92635, _92637] : [relation(_92635), function(_92635), 3227 ^ _20308 : [(3228 ^ _20308) ^ [_92902] : [relation(_92902), function(_92902), 3235 ^ _20308 : [(3236 ^ _20308) ^ [] : [_92635 = relation_dom_restriction(_92902, _92637), 3239 ^ _20308 : [(3240 ^ _20308) ^ [] : [-(relation_dom(_92635) = set_intersection2(relation_dom(_92902), _92637))], (3242 ^ _20308) ^ [_93356] : [in(_93356, relation_dom(_92635)), -(apply(_92635, _93356) = apply(_92902, _93356))]]], (3248 ^ _20308) ^ [] : [-(_92635 = relation_dom_restriction(_92902, _92637)), relation_dom(_92635) = set_intersection2(relation_dom(_92902), _92637), 3254 ^ _20308 : [(3255 ^ _20308) ^ [] : [-(in(3253 ^ [_92635, _92637, _92902], relation_dom(_92635)))], (3257 ^ _20308) ^ [] : [apply(_92635, 3253 ^ [_92635, _92637, _92902]) = apply(_92902, 3253 ^ [_92635, _92637, _92902])]]]]]]], (3261 ^ _20308) ^ [_93995] : [-(unordered_pair(_93995, _93995) = singleton(_93995))], (3263 ^ _20308) ^ [_94093] : [empty(_94093), -(_94093 = empty_set)], (3269 ^ _20308) ^ [_94295, _94297] : [subset(singleton(_94297), singleton(_94295)), -(_94297 = _94295)], (3275 ^ _20308) ^ [_94504] : [-(relation_dom(identity_relation(_94504)) = _94504)], (3277 ^ _20308) ^ [_94552] : [-(relation_rng(identity_relation(_94552)) = _94552)], (3279 ^ _20308) ^ [_94693, _94695, _94697, _94699] : [relation(_94693), 3282 ^ _20308 : [(3283 ^ _20308) ^ [] : [in(ordered_pair(_94699, _94697), relation_composition(identity_relation(_94695), _94693)), 3286 ^ _20308 : [(3287 ^ _20308) ^ [] : [-(in(_94699, _94695))], (3289 ^ _20308) ^ [] : [-(in(ordered_pair(_94699, _94697), _94693))]]], (3291 ^ _20308) ^ [] : [-(in(ordered_pair(_94699, _94697), relation_composition(identity_relation(_94695), _94693))), in(_94699, _94695), in(ordered_pair(_94699, _94697), _94693)]]], (3301 ^ _20308) ^ [_95386, _95388] : [in(_95388, _95386), empty(_95386)], (3307 ^ _20308) ^ [_95578, _95580] : [-(subset(_95580, set_union2(_95580, _95578)))], (3309 ^ _20308) ^ [_95719, _95721] : [disjoint(_95721, _95719), -(set_difference(_95721, _95719) = _95721)], (3315 ^ _20308) ^ [_95887, _95889] : [set_difference(_95889, _95887) = _95889, -(disjoint(_95889, _95887))], (3321 ^ _20308) ^ [_96119, _96121, _96123] : [relation(_96119), 3324 ^ _20308 : [(3325 ^ _20308) ^ [] : [in(_96123, relation_dom(relation_dom_restriction(_96119, _96121))), 3328 ^ _20308 : [(3329 ^ _20308) ^ [] : [-(in(_96123, _96121))], (3331 ^ _20308) ^ [] : [-(in(_96123, relation_dom(_96119)))]]], (3333 ^ _20308) ^ [] : [-(in(_96123, relation_dom(relation_dom_restriction(_96119, _96121)))), in(_96123, _96121), in(_96123, relation_dom(_96119))]]], (3343 ^ _20308) ^ [_96778, _96780] : [relation(_96778), -(subset(relation_dom_restriction(_96778, _96780), _96778))], (3349 ^ _20308) ^ [_96992, _96994] : [empty(_96994), -(_96994 = _96992), empty(_96992)], (3359 ^ _20308) ^ [_97303, _97305, _97307] : [relation(_97303), function(_97303), 3366 ^ _20308 : [(3367 ^ _20308) ^ [] : [in(ordered_pair(_97307, _97305), _97303), 3370 ^ _20308 : [(3371 ^ _20308) ^ [] : [-(in(_97307, relation_dom(_97303)))], (3373 ^ _20308) ^ [] : [-(_97305 = apply(_97303, _97307))]]], (3375 ^ _20308) ^ [] : [-(in(ordered_pair(_97307, _97305), _97303)), in(_97307, relation_dom(_97303)), _97305 = apply(_97303, _97307)]]], (3385 ^ _20308) ^ [_98072, _98074, _98076] : [-(subset(set_union2(_98076, _98072), _98074)), subset(_98076, _98074), subset(_98072, _98074)], (3395 ^ _20308) ^ [_98401, _98403, _98405] : [singleton(_98405) = unordered_pair(_98403, _98401), -(_98405 = _98403)], (3401 ^ _20308) ^ [_98627, _98629] : [relation(_98627), -(relation_dom(relation_dom_restriction(_98627, _98629)) = set_intersection2(relation_dom(_98627), _98629))], (3407 ^ _20308) ^ [_98855, _98857] : [in(_98857, _98855), -(subset(_98857, union(_98855)))], (3413 ^ _20308) ^ [_99069, _99071] : [relation(_99069), -(relation_dom_restriction(_99069, _99071) = relation_composition(identity_relation(_99071), _99069))], (3419 ^ _20308) ^ [_99293, _99295] : [relation(_99293), -(subset(relation_rng(relation_dom_restriction(_99293, _99295)), relation_rng(_99293)))], (3425 ^ _20308) ^ [_99486] : [-(union(powerset(_99486)) = _99486)], (3463 ^ _20308) ^ [_101007, _101009, _101011] : [singleton(_101011) = unordered_pair(_101009, _101007), -(_101009 = _101007)], (3428 ^ _20308) ^ [_99727] : [-(in(_99727, 3426 ^ [_99727]))], (3430 ^ _20308) ^ [_99839, _99841, _99843] : [-(in(_99839, 3426 ^ [_99843])), in(_99841, 3426 ^ [_99843]), subset(_99839, _99841)], (3440 ^ _20308) ^ [_100154, _100156] : [in(_100154, 3426 ^ [_100156]), 3444 ^ _20308 : [(3445 ^ _20308) ^ [] : [-(in(3443 ^ [_100154, _100156], 3426 ^ [_100156]))], (3447 ^ _20308) ^ [_100466] : [subset(_100466, _100154), -(in(_100466, 3443 ^ [_100154, _100156]))]]], (3453 ^ _20308) ^ [_100673, _100675] : [subset(_100673, 3426 ^ [_100675]), -(are_equipotent(_100673, 3426 ^ [_100675])), -(in(_100673, 3426 ^ [_100675]))]], input).
% 0.72/1.39  ncf('1',plain,[apply(relation_dom_restriction(3470 ^ [], 3468 ^ []), 3469 ^ []) = apply(3470 ^ [], 3469 ^ [])],start(3478 ^ 0)).
% 0.72/1.39  ncf('1.1',plain,[-(apply(relation_dom_restriction(3470 ^ [], 3468 ^ []), 3469 ^ []) = apply(3470 ^ [], 3469 ^ [])), 3242 : in(3469 ^ [], relation_dom(relation_dom_restriction(3470 ^ [], 3468 ^ []))), 3242 : relation_dom_restriction(3470 ^ [], 3468 ^ []) = relation_dom_restriction(3470 ^ [], 3468 ^ []), 3236 : relation(3470 ^ []), 3236 : function(3470 ^ []), 3228 : relation(relation_dom_restriction(3470 ^ [], 3468 ^ [])), 3228 : function(relation_dom_restriction(3470 ^ [], 3468 ^ []))],extension(3220 ^ 1,bind([[_92635, _92637, _92902, _93356], [relation_dom_restriction(3470 ^ [], 3468 ^ []), 3468 ^ [], 3470 ^ [], 3469 ^ []]]))).
% 0.72/1.39  ncf('1.1.1',plain,[-(in(3469 ^ [], relation_dom(relation_dom_restriction(3470 ^ [], 3468 ^ []))))],extension(3476 ^ 8)).
% 0.72/1.39  ncf('1.1.2',plain,[-(relation_dom_restriction(3470 ^ [], 3468 ^ []) = relation_dom_restriction(3470 ^ [], 3468 ^ []))],extension(2 ^ 6,bind([[_20338], [relation_dom_restriction(3470 ^ [], 3468 ^ [])]]))).
% 0.72/1.39  ncf('1.1.3',plain,[-(relation(3470 ^ []))],extension(3472 ^ 4)).
% 0.72/1.39  ncf('1.1.4',plain,[-(function(3470 ^ []))],extension(3474 ^ 4)).
% 0.72/1.39  ncf('1.1.5',plain,[-(relation(relation_dom_restriction(3470 ^ [], 3468 ^ []))), relation(3470 ^ [])],extension(1779 ^ 2,bind([[_48092, _48094], [3468 ^ [], 3470 ^ []]]))).
% 0.72/1.39  ncf('1.1.5.1',plain,[-(relation(3470 ^ []))],extension(3472 ^ 3)).
% 0.72/1.39  ncf('1.1.6',plain,[-(function(relation_dom_restriction(3470 ^ [], 3468 ^ []))), relation(3470 ^ []), function(3470 ^ [])],extension(1932 ^ 2,bind([[_50043, _50045], [3468 ^ [], 3470 ^ []]]))).
% 0.72/1.39  ncf('1.1.6.1',plain,[-(relation(3470 ^ []))],extension(3472 ^ 3)).
% 0.72/1.39  ncf('1.1.6.2',plain,[-(function(3470 ^ []))],extension(3474 ^ 3)).
% 0.72/1.39  %-----------------------------------------------------
% 0.72/1.39  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------