%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU224+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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 12:02:45 EDT 2023

% Result   : Theorem 0.41s 1.37s
% Output   : Proof 0.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SEU224+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n023.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 13:18:29 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.41/1.37  
% 0.41/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.41/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/1.37  %-----------------------------------------------------
% 0.41/1.37  ncf(matrix, plain, [(3486 ^ _20480) ^ [] : [-(relation(3484 ^ []))], (3488 ^ _20480) ^ [] : [-(function(3484 ^ []))], (3490 ^ _20480) ^ [] : [3499 ^ _20480 : [(3500 ^ _20480) ^ [] : [-(in(3483 ^ [], relation_dom(3484 ^ [])))], (3502 ^ _20480) ^ [] : [-(in(3483 ^ [], 3482 ^ []))], (3504 ^ _20480) ^ [] : [in(3483 ^ [], relation_dom(relation_dom_restriction(3484 ^ [], 3482 ^ [])))]], 3491 ^ _20480 : [(3492 ^ _20480) ^ [] : [-(in(3483 ^ [], relation_dom(relation_dom_restriction(3484 ^ [], 3482 ^ []))))], (3494 ^ _20480) ^ [] : [in(3483 ^ [], relation_dom(3484 ^ [])), in(3483 ^ [], 3482 ^ [])]]], (2 ^ _20480) ^ [_20510] : [-(_20510 = _20510)], (4 ^ _20480) ^ [_20533, _20535] : [_20535 = _20533, -(_20533 = _20535)], (10 ^ _20480) ^ [_20606, _20608, _20610] : [-(_20610 = _20606), _20610 = _20608, _20608 = _20606], (20 ^ _20480) ^ [_20743, _20745] : [-(relation_empty_yielding(_20743)), _20745 = _20743, relation_empty_yielding(_20745)], (30 ^ _20480) ^ [_20868, _20870, _20872, _20874] : [-(element(_20872, _20868)), element(_20874, _20870), _20874 = _20872, _20870 = _20868], (44 ^ _20480) ^ [_21061, _21063, _21065, _21067] : [-(proper_subset(_21065, _21061)), proper_subset(_21067, _21063), _21067 = _21065, _21063 = _21061], (58 ^ _20480) ^ [_21254, _21256] : [-(one_to_one(_21254)), _21256 = _21254, one_to_one(_21256)], (68 ^ _20480) ^ [_21379, _21381, _21383, _21385] : [-(disjoint(_21383, _21379)), disjoint(_21385, _21381), _21385 = _21383, _21381 = _21379], (82 ^ _20480) ^ [_21572, _21574] : [-(empty(_21572)), _21574 = _21572, empty(_21574)], (92 ^ _20480) ^ [_21697, _21699, _21701, _21703] : [-(subset(_21701, _21697)), subset(_21703, _21699), _21703 = _21701, _21699 = _21697], (106 ^ _20480) ^ [_21890, _21892, _21894, _21896] : [-(are_equipotent(_21894, _21890)), are_equipotent(_21896, _21892), _21896 = _21894, _21892 = _21890], (120 ^ _20480) ^ [_22083, _22085] : [-(relation(_22083)), _22085 = _22083, relation(_22085)], (130 ^ _20480) ^ [_22208, _22210] : [-(function(_22208)), _22210 = _22208, function(_22210)], (140 ^ _20480) ^ [_22329, _22331, _22333, _22335] : [-(in(_22333, _22329)), in(_22335, _22331), _22335 = _22333, _22331 = _22329], (154 ^ _20480) ^ [_22548, _22550] : [_22550 = _22548, -(set_meet(_22550) = set_meet(_22548))], (160 ^ _20480) ^ [_22633, _22635, _22637, _22639] : [-(relation_rng_restriction(_22639, _22635) = relation_rng_restriction(_22637, _22633)), _22639 = _22637, _22635 = _22633], (170 ^ _20480) ^ [_22782, _22784, _22786, _22788] : [-(relation_image(_22788, _22784) = relation_image(_22786, _22782)), _22788 = _22786, _22784 = _22782], (180 ^ _20480) ^ [_22931, _22933, _22935, _22937] : [-(relation_inverse_image(_22937, _22933) = relation_inverse_image(_22935, _22931)), _22937 = _22935, _22933 = _22931], (190 ^ _20480) ^ [_23080, _23082, _23084, _23086] : [-(cartesian_product2(_23086, _23082) = cartesian_product2(_23084, _23080)), _23086 = _23084, _23082 = _23080], (200 ^ _20480) ^ [_23229, _23231] : [_23231 = _23229, -(relation_field(_23231) = relation_field(_23229))], (206 ^ _20480) ^ [_23314, _23316] : [_23316 = _23314, -(relation_inverse(_23316) = relation_inverse(_23314))], (212 ^ _20480) ^ [_23399, _23401, _23403, _23405] : [-(union_of_subsets(_23405, _23401) = union_of_subsets(_23403, _23399)), _23405 = _23403, _23401 = _23399], (222 ^ _20480) ^ [_23548, _23550, _23552, _23554] : [-(complements_of_subsets(_23554, _23550) = complements_of_subsets(_23552, _23548)), _23554 = _23552, _23550 = _23548], (232 ^ _20480) ^ [_23697, _23699, _23701, _23703, _23705, _23707] : [-(subset_difference(_23707, _23703, _23699) = subset_difference(_23705, _23701, _23697)), _23707 = _23705, _23703 = _23701, _23699 = _23697], (246 ^ _20480) ^ [_23918, _23920] : [_23920 = _23918, -(cast_to_subset(_23920) = cast_to_subset(_23918))], (252 ^ _20480) ^ [_24003, _24005, _24007, _24009] : [-(meet_of_subsets(_24009, _24005) = meet_of_subsets(_24007, _24003)), _24009 = _24007, _24005 = _24003], (262 ^ _20480) ^ [_24152, _24154, _24156, _24158] : [-(subset_complement(_24158, _24154) = subset_complement(_24156, _24152)), _24158 = _24156, _24154 = _24152], (272 ^ _20480) ^ [_24301, _24303] : [_24303 = _24301, -(function_inverse(_24303) = function_inverse(_24301))], (278 ^ _20480) ^ [_24386, _24388, _24390, _24392] : [-(set_difference(_24392, _24388) = set_difference(_24390, _24386)), _24392 = _24390, _24388 = _24386], (288 ^ _20480) ^ [_24535, _24537, _24539, _24541] : [-(ordered_pair(_24541, _24537) = ordered_pair(_24539, _24535)), _24541 = _24539, _24537 = _24535], (298 ^ _20480) ^ [_24684, _24686, _24688, _24690] : [-(apply(_24690, _24686) = apply(_24688, _24684)), _24690 = _24688, _24686 = _24684], (308 ^ _20480) ^ [_24833, _24835, _24837, _24839] : [-(set_union2(_24839, _24835) = set_union2(_24837, _24833)), _24839 = _24837, _24835 = _24833], (318 ^ _20480) ^ [_24982, _24984, _24986, _24988] : [-(set_intersection2(_24988, _24984) = set_intersection2(_24986, _24982)), _24988 = _24986, _24984 = _24982], (328 ^ _20480) ^ [_25131, _25133, _25135, _25137] : [-(relation_composition(_25137, _25133) = relation_composition(_25135, _25131)), _25137 = _25135, _25133 = _25131], (338 ^ _20480) ^ [_25280, _25282] : [_25282 = _25280, -(identity_relation(_25282) = identity_relation(_25280))], (344 ^ _20480) ^ [_25365, _25367] : [_25367 = _25365, -(relation_rng(_25367) = relation_rng(_25365))], (350 ^ _20480) ^ [_25450, _25452] : [_25452 = _25450, -(union(_25452) = union(_25450))], (356 ^ _20480) ^ [_25535, _25537] : [_25537 = _25535, -(powerset(_25537) = powerset(_25535))], (362 ^ _20480) ^ [_25620, _25622] : [_25622 = _25620, -(singleton(_25622) = singleton(_25620))], (368 ^ _20480) ^ [_25705, _25707, _25709, _25711] : [-(unordered_pair(_25711, _25707) = unordered_pair(_25709, _25705)), _25711 = _25709, _25707 = _25705], (388 ^ _20480) ^ [_25999, _26001] : [_26001 = _25999, -(relation_dom(_26001) = relation_dom(_25999))], (378 ^ _20480) ^ [_25854, _25856, _25858, _25860] : [-(relation_dom_restriction(_25860, _25856) = relation_dom_restriction(_25858, _25854)), _25860 = _25858, _25856 = _25854], (394 ^ _20480) ^ [_26182, _26184] : [in(_26184, _26182), in(_26182, _26184)], (400 ^ _20480) ^ [_26260, _26262] : [proper_subset(_26262, _26260), proper_subset(_26260, _26262)], (406 ^ _20480) ^ [_26338] : [empty(_26338), -(function(_26338))], (412 ^ _20480) ^ [_26409] : [empty(_26409), -(relation(_26409))], (418 ^ _20480) ^ [_26480] : [429 ^ _20480 : [(430 ^ _20480) ^ [] : [-(relation(_26480))], (432 ^ _20480) ^ [] : [-(function(_26480))], (434 ^ _20480) ^ [] : [-(one_to_one(_26480))]], relation(_26480), empty(_26480), function(_26480)], (436 ^ _20480) ^ [_26693, _26695] : [-(unordered_pair(_26695, _26693) = unordered_pair(_26693, _26695))], (438 ^ _20480) ^ [_26724, _26726] : [-(set_union2(_26726, _26724) = set_union2(_26724, _26726))], (440 ^ _20480) ^ [_26755, _26757] : [-(set_intersection2(_26757, _26755) = set_intersection2(_26755, _26757))], (442 ^ _20480) ^ [_26786, _26788] : [relation(_26786), 445 ^ _20480 : [(468 ^ _20480) ^ [] : [-(_26786 = identity_relation(_26788)), 481 ^ _20480 : [(482 ^ _20480) ^ [] : [-(in(469 ^ [_26786, _26788], _26788))], (484 ^ _20480) ^ [] : [-(469 ^ [_26786, _26788] = 470 ^ [_26786, _26788])], (486 ^ _20480) ^ [] : [in(ordered_pair(469 ^ [_26786, _26788], 470 ^ [_26786, _26788]), _26786)]], 473 ^ _20480 : [(474 ^ _20480) ^ [] : [-(in(ordered_pair(469 ^ [_26786, _26788], 470 ^ [_26786, _26788]), _26786))], (476 ^ _20480) ^ [] : [in(469 ^ [_26786, _26788], _26788), 469 ^ [_26786, _26788] = 470 ^ [_26786, _26788]]]], (446 ^ _20480) ^ [] : [_26786 = identity_relation(_26788), 449 ^ _20480 : [(450 ^ _20480) ^ [_26939, _26941] : [in(ordered_pair(_26941, _26939), _26786), 453 ^ _20480 : [(454 ^ _20480) ^ [] : [-(in(_26941, _26788))], (456 ^ _20480) ^ [] : [-(_26941 = _26939)]]], (458 ^ _20480) ^ [_27048, _27050] : [-(in(ordered_pair(_27050, _27048), _26786)), in(_27050, _26788), _27050 = _27048]]]]], (490 ^ _20480) ^ [_27575, _27577] : [_27577 = _27575, 493 ^ _20480 : [(494 ^ _20480) ^ [] : [-(subset(_27577, _27575))], (496 ^ _20480) ^ [] : [-(subset(_27575, _27577))]]], (498 ^ _20480) ^ [_27674, _27676] : [-(_27676 = _27674), subset(_27676, _27674), subset(_27674, _27676)], (508 ^ _20480) ^ [_27805] : [relation(_27805), 511 ^ _20480 : [(512 ^ _20480) ^ [_27905, _27907] : [relation(_27905), 515 ^ _20480 : [(538 ^ _20480) ^ [] : [-(_27905 = relation_dom_restriction(_27805, _27907)), 551 ^ _20480 : [(552 ^ _20480) ^ [] : [-(in(539 ^ [_27805, _27905, _27907], _27907))], (554 ^ _20480) ^ [] : [-(in(ordered_pair(539 ^ [_27805, _27905, _27907], 540 ^ [_27805, _27905, _27907]), _27805))], (556 ^ _20480) ^ [] : [in(ordered_pair(539 ^ [_27805, _27905, _27907], 540 ^ [_27805, _27905, _27907]), _27905)]], 543 ^ _20480 : [(544 ^ _20480) ^ [] : [-(in(ordered_pair(539 ^ [_27805, _27905, _27907], 540 ^ [_27805, _27905, _27907]), _27905))], (546 ^ _20480) ^ [] : [in(539 ^ [_27805, _27905, _27907], _27907), in(ordered_pair(539 ^ [_27805, _27905, _27907], 540 ^ [_27805, _27905, _27907]), _27805)]]], (516 ^ _20480) ^ [] : [_27905 = relation_dom_restriction(_27805, _27907), 519 ^ _20480 : [(520 ^ _20480) ^ [_28067, _28069] : [in(ordered_pair(_28069, _28067), _27905), 523 ^ _20480 : [(524 ^ _20480) ^ [] : [-(in(_28069, _27907))], (526 ^ _20480) ^ [] : [-(in(ordered_pair(_28069, _28067), _27805))]]], (528 ^ _20480) ^ [_28184, _28186] : [-(in(ordered_pair(_28186, _28184), _27905)), in(_28186, _27907), in(ordered_pair(_28186, _28184), _27805)]]]]]]], (560 ^ _20480) ^ [_28754, _28756] : [relation(_28754), 563 ^ _20480 : [(564 ^ _20480) ^ [_28851] : [relation(_28851), 567 ^ _20480 : [(590 ^ _20480) ^ [] : [-(_28851 = relation_rng_restriction(_28756, _28754)), 603 ^ _20480 : [(604 ^ _20480) ^ [] : [-(in(592 ^ [_28754, _28756, _28851], _28756))], (606 ^ _20480) ^ [] : [-(in(ordered_pair(591 ^ [_28754, _28756, _28851], 592 ^ [_28754, _28756, _28851]), _28754))], (608 ^ _20480) ^ [] : [in(ordered_pair(591 ^ [_28754, _28756, _28851], 592 ^ [_28754, _28756, _28851]), _28851)]], 595 ^ _20480 : [(596 ^ _20480) ^ [] : [-(in(ordered_pair(591 ^ [_28754, _28756, _28851], 592 ^ [_28754, _28756, _28851]), _28851))], (598 ^ _20480) ^ [] : [in(592 ^ [_28754, _28756, _28851], _28756), in(ordered_pair(591 ^ [_28754, _28756, _28851], 592 ^ [_28754, _28756, _28851]), _28754)]]], (568 ^ _20480) ^ [] : [_28851 = relation_rng_restriction(_28756, _28754), 571 ^ _20480 : [(572 ^ _20480) ^ [_29013, _29015] : [in(ordered_pair(_29015, _29013), _28851), 575 ^ _20480 : [(576 ^ _20480) ^ [] : [-(in(_29013, _28756))], (578 ^ _20480) ^ [] : [-(in(ordered_pair(_29015, _29013), _28754))]]], (580 ^ _20480) ^ [_29130, _29132] : [-(in(ordered_pair(_29132, _29130), _28851)), in(_29130, _28756), in(ordered_pair(_29132, _29130), _28754)]]]]]]], (612 ^ _20480) ^ [_29691] : [relation(_29691), 615 ^ _20480 : [(639 ^ _20480) ^ [_30196, _30198] : [-(_30196 = relation_image(_29691, _30198)), 652 ^ _20480 : [(653 ^ _20480) ^ [] : [-(in(ordered_pair(651 ^ [_29691, _30196, _30198], 640 ^ [_29691, _30196, _30198]), _29691))], (655 ^ _20480) ^ [] : [-(in(651 ^ [_29691, _30196, _30198], _30198))], (657 ^ _20480) ^ [] : [in(640 ^ [_29691, _30196, _30198], _30196)]], 643 ^ _20480 : [(644 ^ _20480) ^ [] : [-(in(640 ^ [_29691, _30196, _30198], _30196))], (646 ^ _20480) ^ [_30344] : [in(ordered_pair(_30344, 640 ^ [_29691, _30196, _30198]), _29691), in(_30344, _30198)]]], (616 ^ _20480) ^ [_29798, _29800] : [_29798 = relation_image(_29691, _29800), 619 ^ _20480 : [(620 ^ _20480) ^ [_29895] : [in(_29895, _29798), 624 ^ _20480 : [(625 ^ _20480) ^ [] : [-(in(ordered_pair(623 ^ [_29691, _29798, _29800, _29895], _29895), _29691))], (627 ^ _20480) ^ [] : [-(in(623 ^ [_29691, _29798, _29800, _29895], _29800))]]], (629 ^ _20480) ^ [_30031] : [-(in(_30031, _29798)), 630 ^ _20480 : [(631 ^ _20480) ^ [_30078] : [in(ordered_pair(_30078, _30031), _29691), in(_30078, _29800)]]]]]]], (661 ^ _20480) ^ [_30598] : [relation(_30598), 664 ^ _20480 : [(688 ^ _20480) ^ [_31103, _31105] : [-(_31103 = relation_inverse_image(_30598, _31105)), 701 ^ _20480 : [(702 ^ _20480) ^ [] : [-(in(ordered_pair(689 ^ [_30598, _31103, _31105], 700 ^ [_30598, _31103, _31105]), _30598))], (704 ^ _20480) ^ [] : [-(in(700 ^ [_30598, _31103, _31105], _31105))], (706 ^ _20480) ^ [] : [in(689 ^ [_30598, _31103, _31105], _31103)]], 692 ^ _20480 : [(693 ^ _20480) ^ [] : [-(in(689 ^ [_30598, _31103, _31105], _31103))], (695 ^ _20480) ^ [_31251] : [in(ordered_pair(689 ^ [_30598, _31103, _31105], _31251), _30598), in(_31251, _31105)]]], (665 ^ _20480) ^ [_30705, _30707] : [_30705 = relation_inverse_image(_30598, _30707), 668 ^ _20480 : [(669 ^ _20480) ^ [_30802] : [in(_30802, _30705), 673 ^ _20480 : [(674 ^ _20480) ^ [] : [-(in(ordered_pair(_30802, 672 ^ [_30598, _30705, _30707, _30802]), _30598))], (676 ^ _20480) ^ [] : [-(in(672 ^ [_30598, _30705, _30707, _30802], _30707))]]], (678 ^ _20480) ^ [_30938] : [-(in(_30938, _30705)), 679 ^ _20480 : [(680 ^ _20480) ^ [_30985] : [in(ordered_pair(_30938, _30985), _30598), in(_30985, _30707)]]]]]]], (722 ^ _20480) ^ [_31702] : [724 ^ _20480 : [(725 ^ _20480) ^ [] : [-(in(723 ^ [_31702], _31702))], (727 ^ _20480) ^ [_31815, _31817] : [723 ^ [_31702] = ordered_pair(_31817, _31815)]], -(relation(_31702))], (710 ^ _20480) ^ [_31517] : [relation(_31517), 713 ^ _20480 : [(714 ^ _20480) ^ [_31593] : [in(_31593, _31517), -(_31593 = ordered_pair(717 ^ [_31517, _31593], 718 ^ [_31517, _31593]))]]], (780 ^ _20480) ^ [_32680, _32682] : [_32682 = empty_set, 783 ^ _20480 : [(784 ^ _20480) ^ [] : [_32680 = set_meet(_32682), -(_32680 = empty_set)], (790 ^ _20480) ^ [] : [_32680 = empty_set, -(_32680 = set_meet(_32682))]]], (731 ^ _20480) ^ [_31887, _31889] : [-(_31889 = empty_set), 734 ^ _20480 : [(758 ^ _20480) ^ [] : [-(_31887 = set_meet(_31889)), 762 ^ _20480 : [(763 ^ _20480) ^ [] : [-(in(759 ^ [_31887, _31889], _31887))], (766 ^ _20480) ^ [] : [-(in(764 ^ [_31887, _31889], _31889))], (768 ^ _20480) ^ [] : [in(759 ^ [_31887, _31889], 764 ^ [_31887, _31889])]], 769 ^ _20480 : [(776 ^ _20480) ^ [] : [in(759 ^ [_31887, _31889], _31887)], (770 ^ _20480) ^ [_32524] : [in(_32524, _31889), -(in(759 ^ [_31887, _31889], _32524))]]], (735 ^ _20480) ^ [] : [_31887 = set_meet(_31889), 738 ^ _20480 : [(749 ^ _20480) ^ [_32180] : [751 ^ _20480 : [(752 ^ _20480) ^ [] : [-(in(750 ^ [_31887, _31889, _32180], _31889))], (754 ^ _20480) ^ [] : [in(_32180, 750 ^ [_31887, _31889, _32180])]], -(in(_32180, _31887))], (739 ^ _20480) ^ [_32034] : [in(_32034, _31887), 742 ^ _20480 : [(743 ^ _20480) ^ [_32099] : [in(_32099, _31889), -(in(_32034, _32099))]]]]]]], (812 ^ _20480) ^ [_33145, _33147] : [-(_33145 = singleton(_33147)), 816 ^ _20480 : [(817 ^ _20480) ^ [] : [-(in(813 ^ [_33145, _33147], _33145))], (819 ^ _20480) ^ [] : [813 ^ [_33145, _33147] = _33147]], 820 ^ _20480 : [(821 ^ _20480) ^ [] : [-(813 ^ [_33145, _33147] = _33147)], (823 ^ _20480) ^ [] : [in(813 ^ [_33145, _33147], _33145)]]], (796 ^ _20480) ^ [_32910, _32912] : [_32910 = singleton(_32912), 799 ^ _20480 : [(800 ^ _20480) ^ [_32989] : [in(_32989, _32910), -(_32989 = _32912)], (806 ^ _20480) ^ [_33064] : [_33064 = _32912, -(in(_33064, _32910))]]], (827 ^ _20480) ^ [_33399] : [_33399 = empty_set, 830 ^ _20480 : [(831 ^ _20480) ^ [_33460] : [in(_33460, _33399)]]], (833 ^ _20480) ^ [_33481] : [-(in(834 ^ [_33481], _33481)), -(_33481 = empty_set)], (856 ^ _20480) ^ [_33772, _33774] : [-(_33772 = powerset(_33774)), 860 ^ _20480 : [(861 ^ _20480) ^ [] : [-(in(857 ^ [_33772, _33774], _33772))], (863 ^ _20480) ^ [] : [subset(857 ^ [_33772, _33774], _33774)]], 864 ^ _20480 : [(865 ^ _20480) ^ [] : [-(subset(857 ^ [_33772, _33774], _33774))], (867 ^ _20480) ^ [] : [in(857 ^ [_33772, _33774], _33772)]]], (840 ^ _20480) ^ [_33537, _33539] : [_33537 = powerset(_33539), 843 ^ _20480 : [(844 ^ _20480) ^ [_33616] : [in(_33616, _33537), -(subset(_33616, _33539))], (850 ^ _20480) ^ [_33691] : [subset(_33691, _33539), -(in(_33691, _33537))]]], (871 ^ _20480) ^ [_34014] : [relation(_34014), 874 ^ _20480 : [(875 ^ _20480) ^ [_34100] : [relation(_34100), 878 ^ _20480 : [(895 ^ _20480) ^ [] : [-(_34014 = _34100), 900 ^ _20480 : [(901 ^ _20480) ^ [] : [-(in(ordered_pair(896 ^ [_34014, _34100], 897 ^ [_34014, _34100]), _34014))], (903 ^ _20480) ^ [] : [in(ordered_pair(896 ^ [_34014, _34100], 897 ^ [_34014, _34100]), _34100)]], 904 ^ _20480 : [(905 ^ _20480) ^ [] : [-(in(ordered_pair(896 ^ [_34014, _34100], 897 ^ [_34014, _34100]), _34100))], (907 ^ _20480) ^ [] : [in(ordered_pair(896 ^ [_34014, _34100], 897 ^ [_34014, _34100]), _34014)]]], (879 ^ _20480) ^ [] : [_34014 = _34100, 882 ^ _20480 : [(883 ^ _20480) ^ [_34246, _34248] : [in(ordered_pair(_34248, _34246), _34014), -(in(ordered_pair(_34248, _34246), _34100))], (889 ^ _20480) ^ [_34335, _34337] : [in(ordered_pair(_34337, _34335), _34100), -(in(ordered_pair(_34337, _34335), _34014))]]]]]]], (911 ^ _20480) ^ [_34725, _34727] : [-(empty(_34727)), 914 ^ _20480 : [(915 ^ _20480) ^ [] : [element(_34725, _34727), -(in(_34725, _34727))], (921 ^ _20480) ^ [] : [in(_34725, _34727), -(element(_34725, _34727))]]], (927 ^ _20480) ^ [_34925, _34927] : [empty(_34927), 930 ^ _20480 : [(931 ^ _20480) ^ [] : [element(_34925, _34927), -(empty(_34925))], (937 ^ _20480) ^ [] : [empty(_34925), -(element(_34925, _34927))]]], (965 ^ _20480) ^ [_35447, _35449, _35451] : [-(_35447 = unordered_pair(_35451, _35449)), 969 ^ _20480 : [(970 ^ _20480) ^ [] : [-(in(966 ^ [_35447, _35449, _35451], _35447))], (972 ^ _20480) ^ [] : [966 ^ [_35447, _35449, _35451] = _35451], (974 ^ _20480) ^ [] : [966 ^ [_35447, _35449, _35451] = _35449]], 975 ^ _20480 : [(982 ^ _20480) ^ [] : [in(966 ^ [_35447, _35449, _35451], _35447)], (976 ^ _20480) ^ [] : [-(966 ^ [_35447, _35449, _35451] = _35451), -(966 ^ [_35447, _35449, _35451] = _35449)]]], (943 ^ _20480) ^ [_35147, _35149, _35151] : [_35147 = unordered_pair(_35151, _35149), 946 ^ _20480 : [(957 ^ _20480) ^ [_35326] : [958 ^ _20480 : [(959 ^ _20480) ^ [] : [_35326 = _35151], (961 ^ _20480) ^ [] : [_35326 = _35149]], -(in(_35326, _35147))], (947 ^ _20480) ^ [_35236] : [in(_35236, _35147), -(_35236 = _35151), -(_35236 = _35149)]]], (1008 ^ _20480) ^ [_36087, _36089, _36091] : [-(_36087 = set_union2(_36091, _36089)), 1012 ^ _20480 : [(1013 ^ _20480) ^ [] : [-(in(1009 ^ [_36087, _36089, _36091], _36087))], (1015 ^ _20480) ^ [] : [in(1009 ^ [_36087, _36089, _36091], _36091)], (1017 ^ _20480) ^ [] : [in(1009 ^ [_36087, _36089, _36091], _36089)]], 1018 ^ _20480 : [(1025 ^ _20480) ^ [] : [in(1009 ^ [_36087, _36089, _36091], _36087)], (1019 ^ _20480) ^ [] : [-(in(1009 ^ [_36087, _36089, _36091], _36091)), -(in(1009 ^ [_36087, _36089, _36091], _36089))]]], (986 ^ _20480) ^ [_35787, _35789, _35791] : [_35787 = set_union2(_35791, _35789), 989 ^ _20480 : [(1000 ^ _20480) ^ [_35966] : [1001 ^ _20480 : [(1002 ^ _20480) ^ [] : [in(_35966, _35791)], (1004 ^ _20480) ^ [] : [in(_35966, _35789)]], -(in(_35966, _35787))], (990 ^ _20480) ^ [_35876] : [in(_35876, _35787), -(in(_35876, _35791)), -(in(_35876, _35789))]]], (1059 ^ _20480) ^ [_36960, _36962, _36964] : [-(_36960 = cartesian_product2(_36964, _36962)), 1077 ^ _20480 : [(1078 ^ _20480) ^ [] : [-(in(1075 ^ [_36960, _36962, _36964], _36964))], (1080 ^ _20480) ^ [] : [-(in(1076 ^ [_36960, _36962, _36964], _36962))], (1082 ^ _20480) ^ [] : [-(1060 ^ [_36960, _36962, _36964] = ordered_pair(1075 ^ [_36960, _36962, _36964], 1076 ^ [_36960, _36962, _36964]))], (1084 ^ _20480) ^ [] : [in(1060 ^ [_36960, _36962, _36964], _36960)]], 1063 ^ _20480 : [(1064 ^ _20480) ^ [] : [-(in(1060 ^ [_36960, _36962, _36964], _36960))], (1066 ^ _20480) ^ [_37130, _37132] : [in(_37132, _36964), in(_37130, _36962), 1060 ^ [_36960, _36962, _36964] = ordered_pair(_37132, _37130)]]], (1029 ^ _20480) ^ [_36427, _36429, _36431] : [_36427 = cartesian_product2(_36431, _36429), 1032 ^ _20480 : [(1033 ^ _20480) ^ [_36535] : [in(_36535, _36427), 1038 ^ _20480 : [(1039 ^ _20480) ^ [] : [-(in(1036 ^ [_36427, _36429, _36431, _36535], _36431))], (1041 ^ _20480) ^ [] : [-(in(1037 ^ [_36427, _36429, _36431, _36535], _36429))], (1043 ^ _20480) ^ [] : [-(_36535 = ordered_pair(1036 ^ [_36427, _36429, _36431, _36535], 1037 ^ [_36427, _36429, _36431, _36535]))]]], (1045 ^ _20480) ^ [_36722] : [-(in(_36722, _36427)), 1046 ^ _20480 : [(1047 ^ _20480) ^ [_36780, _36782] : [in(_36782, _36431), in(_36780, _36429), _36722 = ordered_pair(_36782, _36780)]]]]], (1088 ^ _20480) ^ [_37478] : [relation(_37478), 1091 ^ _20480 : [(1092 ^ _20480) ^ [_37564] : [relation(_37564), 1095 ^ _20480 : [(1106 ^ _20480) ^ [] : [1109 ^ _20480 : [(1110 ^ _20480) ^ [] : [-(in(ordered_pair(1107 ^ [_37478, _37564], 1108 ^ [_37478, _37564]), _37478))], (1112 ^ _20480) ^ [] : [in(ordered_pair(1107 ^ [_37478, _37564], 1108 ^ [_37478, _37564]), _37564)]], -(subset(_37478, _37564))], (1096 ^ _20480) ^ [] : [subset(_37478, _37564), 1099 ^ _20480 : [(1100 ^ _20480) ^ [_37695, _37697] : [in(ordered_pair(_37697, _37695), _37478), -(in(ordered_pair(_37697, _37695), _37564))]]]]]]], (1126 ^ _20480) ^ [_38108, _38110] : [1128 ^ _20480 : [(1129 ^ _20480) ^ [] : [-(in(1127 ^ [_38108, _38110], _38110))], (1131 ^ _20480) ^ [] : [in(1127 ^ [_38108, _38110], _38108)]], -(subset(_38110, _38108))], (1116 ^ _20480) ^ [_37966, _37968] : [subset(_37968, _37966), 1119 ^ _20480 : [(1120 ^ _20480) ^ [_38029] : [in(_38029, _37968), -(in(_38029, _37966))]]], (1157 ^ _20480) ^ [_38599, _38601, _38603] : [-(_38599 = set_intersection2(_38603, _38601)), 1169 ^ _20480 : [(1170 ^ _20480) ^ [] : [-(in(1158 ^ [_38599, _38601, _38603], _38603))], (1172 ^ _20480) ^ [] : [-(in(1158 ^ [_38599, _38601, _38603], _38601))], (1174 ^ _20480) ^ [] : [in(1158 ^ [_38599, _38601, _38603], _38599)]], 1161 ^ _20480 : [(1162 ^ _20480) ^ [] : [-(in(1158 ^ [_38599, _38601, _38603], _38599))], (1164 ^ _20480) ^ [] : [in(1158 ^ [_38599, _38601, _38603], _38603), in(1158 ^ [_38599, _38601, _38603], _38601)]]], (1135 ^ _20480) ^ [_38268, _38270, _38272] : [_38268 = set_intersection2(_38272, _38270), 1138 ^ _20480 : [(1139 ^ _20480) ^ [_38357] : [in(_38357, _38268), 1142 ^ _20480 : [(1143 ^ _20480) ^ [] : [-(in(_38357, _38272))], (1145 ^ _20480) ^ [] : [-(in(_38357, _38270))]]], (1147 ^ _20480) ^ [_38460] : [-(in(_38460, _38268)), in(_38460, _38272), in(_38460, _38270)]]], (1178 ^ _20480) ^ [_38953] : [relation(_38953), function(_38953), 1185 ^ _20480 : [(1186 ^ _20480) ^ [_39113, _39115] : [in(_39115, relation_dom(_38953)), 1189 ^ _20480 : [(1190 ^ _20480) ^ [] : [_39113 = apply(_38953, _39115), -(in(ordered_pair(_39115, _39113), _38953))], (1196 ^ _20480) ^ [] : [in(ordered_pair(_39115, _39113), _38953), -(_39113 = apply(_38953, _39115))]]], (1202 ^ _20480) ^ [_39343, _39345] : [-(in(_39345, relation_dom(_38953))), 1205 ^ _20480 : [(1206 ^ _20480) ^ [] : [_39343 = apply(_38953, _39345), -(_39343 = empty_set)], (1212 ^ _20480) ^ [] : [_39343 = empty_set, -(_39343 = apply(_38953, _39345))]]]]], (1218 ^ _20480) ^ [_39574] : [relation(_39574), 1221 ^ _20480 : [(1239 ^ _20480) ^ [_39948] : [-(_39948 = relation_dom(_39574)), 1243 ^ _20480 : [(1244 ^ _20480) ^ [] : [-(in(1240 ^ [_39574, _39948], _39948))], (1246 ^ _20480) ^ [_40082] : [in(ordered_pair(1240 ^ [_39574, _39948], _40082), _39574)]], 1248 ^ _20480 : [(1249 ^ _20480) ^ [] : [-(in(ordered_pair(1240 ^ [_39574, _39948], 1247 ^ [_39574, _39948]), _39574))], (1251 ^ _20480) ^ [] : [in(1240 ^ [_39574, _39948], _39948)]]], (1222 ^ _20480) ^ [_39666] : [_39666 = relation_dom(_39574), 1225 ^ _20480 : [(1226 ^ _20480) ^ [_39753] : [in(_39753, _39666), -(in(ordered_pair(_39753, 1229 ^ [_39574, _39666, _39753]), _39574))], (1233 ^ _20480) ^ [_39848] : [1234 ^ _20480 : [(1235 ^ _20480) ^ [_39892] : [in(ordered_pair(_39848, _39892), _39574)]], -(in(_39848, _39666))]]]]], (1255 ^ _20480) ^ [_40229] : [-(cast_to_subset(_40229) = _40229)], (1280 ^ _20480) ^ [_40635, _40637] : [-(_40635 = union(_40637)), 1293 ^ _20480 : [(1294 ^ _20480) ^ [] : [-(in(1281 ^ [_40635, _40637], 1292 ^ [_40635, _40637]))], (1296 ^ _20480) ^ [] : [-(in(1292 ^ [_40635, _40637], _40637))], (1298 ^ _20480) ^ [] : [in(1281 ^ [_40635, _40637], _40635)]], 1284 ^ _20480 : [(1285 ^ _20480) ^ [] : [-(in(1281 ^ [_40635, _40637], _40635))], (1287 ^ _20480) ^ [_40768] : [in(1281 ^ [_40635, _40637], _40768), in(_40768, _40637)]]], (1257 ^ _20480) ^ [_40269, _40271] : [_40269 = union(_40271), 1260 ^ _20480 : [(1261 ^ _20480) ^ [_40359] : [in(_40359, _40269), 1265 ^ _20480 : [(1266 ^ _20480) ^ [] : [-(in(_40359, 1264 ^ [_40269, _40271, _40359]))], (1268 ^ _20480) ^ [] : [-(in(1264 ^ [_40269, _40271, _40359], _40271))]]], (1270 ^ _20480) ^ [_40483] : [-(in(_40483, _40269)), 1271 ^ _20480 : [(1272 ^ _20480) ^ [_40525] : [in(_40483, _40525), in(_40525, _40271)]]]]], (1324 ^ _20480) ^ [_41356, _41358, _41360] : [-(_41356 = set_difference(_41360, _41358)), 1336 ^ _20480 : [(1337 ^ _20480) ^ [] : [-(in(1325 ^ [_41356, _41358, _41360], _41360))], (1339 ^ _20480) ^ [] : [in(1325 ^ [_41356, _41358, _41360], _41358)], (1341 ^ _20480) ^ [] : [in(1325 ^ [_41356, _41358, _41360], _41356)]], 1328 ^ _20480 : [(1329 ^ _20480) ^ [] : [-(in(1325 ^ [_41356, _41358, _41360], _41356))], (1331 ^ _20480) ^ [] : [in(1325 ^ [_41356, _41358, _41360], _41360), -(in(1325 ^ [_41356, _41358, _41360], _41358))]]], (1302 ^ _20480) ^ [_41012, _41014, _41016] : [_41012 = set_difference(_41016, _41014), 1305 ^ _20480 : [(1306 ^ _20480) ^ [_41103] : [in(_41103, _41012), 1309 ^ _20480 : [(1310 ^ _20480) ^ [] : [-(in(_41103, _41016))], (1312 ^ _20480) ^ [] : [in(_41103, _41014)]]], (1314 ^ _20480) ^ [_41214] : [-(in(_41214, _41012)), in(_41214, _41016), -(in(_41214, _41014))]]], (1345 ^ _20480) ^ [_41722] : [relation(_41722), 1348 ^ _20480 : [(1366 ^ _20480) ^ [_42096] : [-(_42096 = relation_rng(_41722)), 1370 ^ _20480 : [(1371 ^ _20480) ^ [] : [-(in(1367 ^ [_41722, _42096], _42096))], (1373 ^ _20480) ^ [_42230] : [in(ordered_pair(_42230, 1367 ^ [_41722, _42096]), _41722)]], 1375 ^ _20480 : [(1376 ^ _20480) ^ [] : [-(in(ordered_pair(1374 ^ [_41722, _42096], 1367 ^ [_41722, _42096]), _41722))], (1378 ^ _20480) ^ [] : [in(1367 ^ [_41722, _42096], _42096)]]], (1349 ^ _20480) ^ [_41814] : [_41814 = relation_rng(_41722), 1352 ^ _20480 : [(1353 ^ _20480) ^ [_41901] : [in(_41901, _41814), -(in(ordered_pair(1356 ^ [_41722, _41814, _41901], _41901), _41722))], (1360 ^ _20480) ^ [_41996] : [1361 ^ _20480 : [(1362 ^ _20480) ^ [_42040] : [in(ordered_pair(_42040, _41996), _41722)]], -(in(_41996, _41814))]]]]], (1382 ^ _20480) ^ [_42377, _42379] : [element(_42377, powerset(_42379)), -(subset_complement(_42379, _42377) = set_difference(_42379, _42377))], (1388 ^ _20480) ^ [_42470, _42472] : [-(ordered_pair(_42472, _42470) = unordered_pair(unordered_pair(_42472, _42470), singleton(_42472)))], (1390 ^ _20480) ^ [_42506] : [relation(_42506), -(relation_field(_42506) = set_union2(relation_dom(_42506), relation_rng(_42506)))], (1396 ^ _20480) ^ [_42597] : [relation(_42597), 1399 ^ _20480 : [(1400 ^ _20480) ^ [_42685] : [relation(_42685), 1403 ^ _20480 : [(1420 ^ _20480) ^ [] : [-(_42685 = relation_inverse(_42597)), 1425 ^ _20480 : [(1426 ^ _20480) ^ [] : [-(in(ordered_pair(1421 ^ [_42597, _42685], 1422 ^ [_42597, _42685]), _42685))], (1428 ^ _20480) ^ [] : [in(ordered_pair(1422 ^ [_42597, _42685], 1421 ^ [_42597, _42685]), _42597)]], 1429 ^ _20480 : [(1430 ^ _20480) ^ [] : [-(in(ordered_pair(1422 ^ [_42597, _42685], 1421 ^ [_42597, _42685]), _42597))], (1432 ^ _20480) ^ [] : [in(ordered_pair(1421 ^ [_42597, _42685], 1422 ^ [_42597, _42685]), _42685)]]], (1404 ^ _20480) ^ [] : [_42685 = relation_inverse(_42597), 1407 ^ _20480 : [(1408 ^ _20480) ^ [_42835, _42837] : [in(ordered_pair(_42837, _42835), _42685), -(in(ordered_pair(_42835, _42837), _42597))], (1414 ^ _20480) ^ [_42924, _42926] : [in(ordered_pair(_42924, _42926), _42597), -(in(ordered_pair(_42926, _42924), _42685))]]]]]]], (1436 ^ _20480) ^ [_43323, _43325] : [disjoint(_43325, _43323), -(set_intersection2(_43325, _43323) = empty_set)], (1442 ^ _20480) ^ [_43402, _43404] : [set_intersection2(_43404, _43402) = empty_set, -(disjoint(_43404, _43402))], (1448 ^ _20480) ^ [_43487] : [relation(_43487), function(_43487), 1455 ^ _20480 : [(1474 ^ _20480) ^ [] : [1477 ^ _20480 : [(1478 ^ _20480) ^ [] : [-(in(1475 ^ [_43487], relation_dom(_43487)))], (1480 ^ _20480) ^ [] : [-(in(1476 ^ [_43487], relation_dom(_43487)))], (1482 ^ _20480) ^ [] : [-(apply(_43487, 1475 ^ [_43487]) = apply(_43487, 1476 ^ [_43487]))], (1484 ^ _20480) ^ [] : [1475 ^ [_43487] = 1476 ^ [_43487]]], -(one_to_one(_43487))], (1456 ^ _20480) ^ [] : [one_to_one(_43487), 1459 ^ _20480 : [(1460 ^ _20480) ^ [_43676, _43678] : [-(_43678 = _43676), in(_43678, relation_dom(_43487)), in(_43676, relation_dom(_43487)), apply(_43487, _43678) = apply(_43487, _43676)]]]]], (1488 ^ _20480) ^ [_44079] : [relation(_44079), 1491 ^ _20480 : [(1492 ^ _20480) ^ [_44192] : [relation(_44192), 1495 ^ _20480 : [(1496 ^ _20480) ^ [_44297] : [relation(_44297), 1499 ^ _20480 : [(1523 ^ _20480) ^ [] : [-(_44297 = relation_composition(_44079, _44192)), 1537 ^ _20480 : [(1538 ^ _20480) ^ [] : [-(in(ordered_pair(1524 ^ [_44079, _44192, _44297], 1536 ^ [_44079, _44192, _44297]), _44079))], (1540 ^ _20480) ^ [] : [-(in(ordered_pair(1536 ^ [_44079, _44192, _44297], 1525 ^ [_44079, _44192, _44297]), _44192))], (1542 ^ _20480) ^ [] : [in(ordered_pair(1524 ^ [_44079, _44192, _44297], 1525 ^ [_44079, _44192, _44297]), _44297)]], 1528 ^ _20480 : [(1529 ^ _20480) ^ [] : [-(in(ordered_pair(1524 ^ [_44079, _44192, _44297], 1525 ^ [_44079, _44192, _44297]), _44297))], (1531 ^ _20480) ^ [_44953] : [in(ordered_pair(1524 ^ [_44079, _44192, _44297], _44953), _44079), in(ordered_pair(_44953, 1525 ^ [_44079, _44192, _44297]), _44192)]]], (1500 ^ _20480) ^ [] : [_44297 = relation_composition(_44079, _44192), 1503 ^ _20480 : [(1504 ^ _20480) ^ [_44467, _44469] : [in(ordered_pair(_44469, _44467), _44297), 1508 ^ _20480 : [(1509 ^ _20480) ^ [] : [-(in(ordered_pair(_44469, 1507 ^ [_44079, _44192, _44297, _44467, _44469]), _44079))], (1511 ^ _20480) ^ [] : [-(in(ordered_pair(1507 ^ [_44079, _44192, _44297, _44467, _44469], _44467), _44192))]]], (1513 ^ _20480) ^ [_44621, _44623] : [-(in(ordered_pair(_44623, _44621), _44297)), 1514 ^ _20480 : [(1515 ^ _20480) ^ [_44676] : [in(ordered_pair(_44623, _44676), _44079), in(ordered_pair(_44676, _44621), _44192)]]]]]]]]]]], (1546 ^ _20480) ^ [_45263, _45265] : [element(_45263, powerset(powerset(_45265))), 1549 ^ _20480 : [(1550 ^ _20480) ^ [_45369] : [element(_45369, powerset(powerset(_45265))), 1553 ^ _20480 : [(1574 ^ _20480) ^ [] : [-(_45369 = complements_of_subsets(_45265, _45263)), 1576 ^ _20480 : [(1577 ^ _20480) ^ [] : [-(element(1575 ^ [_45263, _45265, _45369], powerset(_45265)))], (1579 ^ _20480) ^ [] : [1580 ^ _20480 : [(1581 ^ _20480) ^ [] : [-(in(1575 ^ [_45263, _45265, _45369], _45369))], (1583 ^ _20480) ^ [] : [in(subset_complement(_45265, 1575 ^ [_45263, _45265, _45369]), _45263)]], 1584 ^ _20480 : [(1585 ^ _20480) ^ [] : [-(in(subset_complement(_45265, 1575 ^ [_45263, _45265, _45369]), _45263))], (1587 ^ _20480) ^ [] : [in(1575 ^ [_45263, _45265, _45369], _45369)]]]]], (1554 ^ _20480) ^ [] : [_45369 = complements_of_subsets(_45265, _45263), 1557 ^ _20480 : [(1558 ^ _20480) ^ [_45520] : [element(_45520, powerset(_45265)), 1561 ^ _20480 : [(1562 ^ _20480) ^ [] : [in(_45520, _45369), -(in(subset_complement(_45265, _45520), _45263))], (1568 ^ _20480) ^ [] : [in(subset_complement(_45265, _45520), _45263), -(in(_45520, _45369))]]]]]]]]], (1591 ^ _20480) ^ [_46060, _46062] : [proper_subset(_46062, _46060), 1594 ^ _20480 : [(1595 ^ _20480) ^ [] : [-(subset(_46062, _46060))], (1597 ^ _20480) ^ [] : [_46062 = _46060]]], (1599 ^ _20480) ^ [_46167, _46169] : [-(proper_subset(_46169, _46167)), subset(_46169, _46167), -(_46169 = _46167)], (1609 ^ _20480) ^ [_46301] : [relation(_46301), function(_46301), one_to_one(_46301), -(function_inverse(_46301) = relation_inverse(_46301))], (1623 ^ _20480) ^ [] : [true___, -(true___)], (1629 ^ _20480) ^ [] : [true___, -(true___)], (1635 ^ _20480) ^ [] : [true___, -(true___)], (1641 ^ _20480) ^ [] : [true___, -(true___)], (1647 ^ _20480) ^ [] : [true___, -(true___)], (1653 ^ _20480) ^ [] : [true___, -(true___)], (1659 ^ _20480) ^ [] : [true___, -(true___)], (1665 ^ _20480) ^ [_46893] : [1672 ^ _20480 : [(1673 ^ _20480) ^ [] : [-(relation(function_inverse(_46893)))], (1675 ^ _20480) ^ [] : [-(function(function_inverse(_46893)))]], relation(_46893), function(_46893)], (1677 ^ _20480) ^ [] : [true___, -(true___)], (1683 ^ _20480) ^ [_47103] : [-(element(cast_to_subset(_47103), powerset(_47103)))], (1685 ^ _20480) ^ [] : [true___, -(true___)], (1691 ^ _20480) ^ [] : [true___, -(true___)], (1697 ^ _20480) ^ [] : [true___, -(true___)], (1703 ^ _20480) ^ [] : [true___, -(true___)], (1709 ^ _20480) ^ [_47366, _47368] : [element(_47366, powerset(_47368)), -(element(subset_complement(_47368, _47366), powerset(_47368)))], (1715 ^ _20480) ^ [] : [true___, -(true___)], (1721 ^ _20480) ^ [] : [true___, -(true___)], (1727 ^ _20480) ^ [_47575] : [relation(_47575), -(relation(relation_inverse(_47575)))], (1733 ^ _20480) ^ [] : [true___, -(true___)], (1739 ^ _20480) ^ [] : [true___, -(true___)], (1745 ^ _20480) ^ [_47768, _47770] : [-(relation(relation_composition(_47770, _47768))), relation(_47770), relation(_47768)], (1755 ^ _20480) ^ [_47897, _47899] : [element(_47897, powerset(powerset(_47899))), -(element(union_of_subsets(_47899, _47897), powerset(_47899)))], (1761 ^ _20480) ^ [_47992] : [-(relation(identity_relation(_47992)))], (1763 ^ _20480) ^ [_48016, _48018] : [element(_48016, powerset(powerset(_48018))), -(element(meet_of_subsets(_48018, _48016), powerset(_48018)))], (1769 ^ _20480) ^ [_48111, _48113, _48115] : [-(element(subset_difference(_48115, _48113, _48111), powerset(_48115))), element(_48113, powerset(_48115)), element(_48111, powerset(_48115))], (1779 ^ _20480) ^ [_48264, _48266] : [relation(_48266), -(relation(relation_dom_restriction(_48266, _48264)))], (1785 ^ _20480) ^ [_48343, _48345] : [element(_48343, powerset(powerset(_48345))), -(element(complements_of_subsets(_48345, _48343), powerset(powerset(_48345))))], (1791 ^ _20480) ^ [_48442, _48444] : [relation(_48442), -(relation(relation_rng_restriction(_48444, _48442)))], (1797 ^ _20480) ^ [] : [true___, -(true___)], (1803 ^ _20480) ^ [] : [true___, -(true___)], (1810 ^ _20480) ^ [_48639] : [-(element(1808 ^ [_48639], _48639))], (1812 ^ _20480) ^ [_48667, _48669] : [1819 ^ _20480 : [(1820 ^ _20480) ^ [] : [-(empty(relation_composition(_48667, _48669)))], (1822 ^ _20480) ^ [] : [-(relation(relation_composition(_48667, _48669)))]], empty(_48669), relation(_48667)], (1824 ^ _20480) ^ [_48954] : [empty(_48954), 1827 ^ _20480 : [(1828 ^ _20480) ^ [] : [-(empty(relation_inverse(_48954)))], (1830 ^ _20480) ^ [] : [-(relation(relation_inverse(_48954)))]]], (1832 ^ _20480) ^ [] : [-(empty(empty_set))], (1834 ^ _20480) ^ [] : [-(relation(empty_set))], (1836 ^ _20480) ^ [] : [-(relation_empty_yielding(empty_set))], (1838 ^ _20480) ^ [_49396, _49398] : [1845 ^ _20480 : [(1846 ^ _20480) ^ [] : [-(relation(relation_dom_restriction(_49398, _49396)))], (1848 ^ _20480) ^ [] : [-(relation_empty_yielding(relation_dom_restriction(_49398, _49396)))]], relation(_49398), relation_empty_yielding(_49398)], (1850 ^ _20480) ^ [_49774, _49776] : [1865 ^ _20480 : [(1866 ^ _20480) ^ [] : [-(relation(relation_composition(_49776, _49774)))], (1868 ^ _20480) ^ [] : [-(function(relation_composition(_49776, _49774)))]], relation(_49776), function(_49776), relation(_49774), function(_49774)], (1870 ^ _20480) ^ [_50326, _50328] : [-(relation(set_intersection2(_50328, _50326))), relation(_50328), relation(_50326)], (1880 ^ _20480) ^ [_50595] : [empty(powerset(_50595))], (1882 ^ _20480) ^ [] : [-(empty(empty_set))], (1884 ^ _20480) ^ [_50740, _50742] : [empty(ordered_pair(_50742, _50740))], (1886 ^ _20480) ^ [_50842] : [-(relation(identity_relation(_50842)))], (1888 ^ _20480) ^ [_50887] : [-(function(identity_relation(_50887)))], (1890 ^ _20480) ^ [_50997, _50999] : [-(relation(set_union2(_50999, _50997))), relation(_50999), relation(_50997)], (1900 ^ _20480) ^ [_51266] : [empty(singleton(_51266))], (1902 ^ _20480) ^ [_51374, _51376] : [-(empty(_51376)), empty(set_union2(_51376, _51374))], (1908 ^ _20480) ^ [_51576] : [1919 ^ _20480 : [(1920 ^ _20480) ^ [] : [-(relation(relation_inverse(_51576)))], (1922 ^ _20480) ^ [] : [-(function(relation_inverse(_51576)))]], relation(_51576), function(_51576), one_to_one(_51576)], (1924 ^ _20480) ^ [_52005, _52007] : [empty(unordered_pair(_52007, _52005))], (1926 ^ _20480) ^ [_52116, _52118] : [-(empty(_52118)), empty(set_union2(_52116, _52118))], (1932 ^ _20480) ^ [_52332, _52334] : [1939 ^ _20480 : [(1940 ^ _20480) ^ [] : [-(relation(relation_dom_restriction(_52334, _52332)))], (1942 ^ _20480) ^ [] : [-(function(relation_dom_restriction(_52334, _52332)))]], relation(_52334), function(_52334)], (1944 ^ _20480) ^ [] : [-(empty(empty_set))], (1946 ^ _20480) ^ [] : [-(relation(empty_set))], (1948 ^ _20480) ^ [_52818, _52820] : [empty(cartesian_product2(_52820, _52818)), -(empty(_52820)), -(empty(_52818))], (1958 ^ _20480) ^ [_53110] : [empty(relation_dom(_53110)), -(empty(_53110)), relation(_53110)], (1968 ^ _20480) ^ [_53387] : [empty(relation_rng(_53387)), -(empty(_53387)), relation(_53387)], (1978 ^ _20480) ^ [_53664] : [empty(_53664), 1981 ^ _20480 : [(1982 ^ _20480) ^ [] : [-(empty(relation_dom(_53664)))], (1984 ^ _20480) ^ [] : [-(relation(relation_dom(_53664)))]]], (1986 ^ _20480) ^ [_53929] : [empty(_53929), 1989 ^ _20480 : [(1990 ^ _20480) ^ [] : [-(empty(relation_rng(_53929)))], (1992 ^ _20480) ^ [] : [-(relation(relation_rng(_53929)))]]], (1994 ^ _20480) ^ [_54208, _54210] : [2001 ^ _20480 : [(2002 ^ _20480) ^ [] : [-(empty(relation_composition(_54210, _54208)))], (2004 ^ _20480) ^ [] : [-(relation(relation_composition(_54210, _54208)))]], empty(_54210), relation(_54208)], (2006 ^ _20480) ^ [_54571, _54573] : [-(set_union2(_54573, _54573) = _54573)], (2008 ^ _20480) ^ [_54668, _54670] : [-(set_intersection2(_54670, _54670) = _54670)], (2010 ^ _20480) ^ [_54780, _54782] : [element(_54780, powerset(_54782)), -(subset_complement(_54782, subset_complement(_54782, _54780)) = _54780)], (2016 ^ _20480) ^ [_54992] : [relation(_54992), -(relation_inverse(relation_inverse(_54992)) = _54992)], (2022 ^ _20480) ^ [_55202, _55204] : [element(_55202, powerset(powerset(_55204))), -(complements_of_subsets(_55204, complements_of_subsets(_55204, _55202)) = _55202)], (2028 ^ _20480) ^ [_55416, _55418] : [proper_subset(_55418, _55418)], (2030 ^ _20480) ^ [_55495] : [singleton(_55495) = empty_set], (2032 ^ _20480) ^ [_55604, _55606] : [in(_55606, _55604), -(set_union2(singleton(_55606), _55604) = _55604)], (2038 ^ _20480) ^ [_55824, _55826] : [disjoint(singleton(_55826), _55824), in(_55826, _55824)], (2044 ^ _20480) ^ [_56037, _56039] : [-(in(_56039, _56037)), -(disjoint(singleton(_56039), _56037))], (2050 ^ _20480) ^ [_56283, _56285] : [subset(singleton(_56285), _56283), -(in(_56285, _56283))], (2056 ^ _20480) ^ [_56449, _56451] : [in(_56451, _56449), -(subset(singleton(_56451), _56449))], (2062 ^ _20480) ^ [_56694, _56696] : [set_difference(_56696, _56694) = empty_set, -(subset(_56696, _56694))], (2068 ^ _20480) ^ [_56862, _56864] : [subset(_56864, _56862), -(set_difference(_56864, _56862) = empty_set)], (2074 ^ _20480) ^ [_57080, _57082] : [element(_57080, powerset(_57082)), 2077 ^ _20480 : [(2078 ^ _20480) ^ [_57221] : [in(_57221, _57080), -(in(_57221, _57082))]]], (2084 ^ _20480) ^ [_57460, _57462, _57464] : [subset(_57464, _57462), -(in(_57460, _57464)), -(subset(_57464, set_difference(_57462, singleton(_57460))))], (2104 ^ _20480) ^ [_58069, _58071] : [2105 ^ _20480 : [(2106 ^ _20480) ^ [] : [_58071 = empty_set], (2108 ^ _20480) ^ [] : [_58071 = singleton(_58069)]], -(subset(_58071, singleton(_58069)))], (2094 ^ _20480) ^ [_57809, _57811] : [subset(_57811, singleton(_57809)), -(_57811 = empty_set), -(_57811 = singleton(_57809))], (2112 ^ _20480) ^ [_58363, _58365] : [in(_58365, _58363), -(subset(_58365, union(_58363)))], (2118 ^ _20480) ^ [_58634, _58636, _58638, _58640] : [in(ordered_pair(_58640, _58638), cartesian_product2(_58636, _58634)), 2121 ^ _20480 : [(2122 ^ _20480) ^ [] : [-(in(_58640, _58636))], (2124 ^ _20480) ^ [] : [-(in(_58638, _58634))]]], (2126 ^ _20480) ^ [_58899, _58901, _58903, _58905] : [-(in(ordered_pair(_58905, _58903), cartesian_product2(_58901, _58899))), in(_58905, _58901), in(_58903, _58899)], (2136 ^ _20480) ^ [_59232, _59234] : [2138 ^ _20480 : [(2139 ^ _20480) ^ [] : [-(in(2137 ^ [_59232, _59234], _59234))], (2141 ^ _20480) ^ [] : [in(2137 ^ [_59232, _59234], _59232)]], -(element(_59234, powerset(_59232)))], (2146 ^ _20480) ^ [] : [-(relation(2144 ^ []))], (2148 ^ _20480) ^ [] : [-(function(2144 ^ []))], (2151 ^ _20480) ^ [] : [-(empty(2149 ^ []))], (2153 ^ _20480) ^ [] : [-(relation(2149 ^ []))], (2155 ^ _20480) ^ [_59875] : [-(empty(_59875)), 2159 ^ _20480 : [(2160 ^ _20480) ^ [] : [-(element(2158 ^ [_59875], powerset(_59875)))], (2162 ^ _20480) ^ [] : [empty(2158 ^ [_59875])]]], (2165 ^ _20480) ^ [] : [-(empty(2163 ^ []))], (2168 ^ _20480) ^ [] : [-(relation(2166 ^ []))], (2170 ^ _20480) ^ [] : [-(empty(2166 ^ []))], (2172 ^ _20480) ^ [] : [-(function(2166 ^ []))], (2175 ^ _20480) ^ [] : [empty(2173 ^ [])], (2177 ^ _20480) ^ [] : [-(relation(2173 ^ []))], (2180 ^ _20480) ^ [_60706] : [-(element(2178 ^ [_60706], powerset(_60706)))], (2182 ^ _20480) ^ [_60757] : [-(empty(2178 ^ [_60757]))], (2185 ^ _20480) ^ [] : [empty(2183 ^ [])], (2188 ^ _20480) ^ [] : [-(relation(2186 ^ []))], (2190 ^ _20480) ^ [] : [-(function(2186 ^ []))], (2192 ^ _20480) ^ [] : [-(one_to_one(2186 ^ []))], (2195 ^ _20480) ^ [] : [-(relation(2193 ^ []))], (2197 ^ _20480) ^ [] : [-(relation_empty_yielding(2193 ^ []))], (2199 ^ _20480) ^ [_61318, _61320] : [element(_61318, powerset(powerset(_61320))), -(union_of_subsets(_61320, _61318) = union(_61318))], (2205 ^ _20480) ^ [_61546, _61548] : [element(_61546, powerset(powerset(_61548))), -(meet_of_subsets(_61548, _61546) = set_meet(_61546))], (2211 ^ _20480) ^ [_61788, _61790, _61792] : [-(subset_difference(_61792, _61790, _61788) = set_difference(_61790, _61788)), element(_61790, powerset(_61792)), element(_61788, powerset(_61792))], (2221 ^ _20480) ^ [_62104, _62106] : [-(subset(_62106, _62106))], (2223 ^ _20480) ^ [_62213, _62215] : [disjoint(_62215, _62213), -(disjoint(_62213, _62215))], (2229 ^ _20480) ^ [_62480, _62482, _62484, _62486] : [in(ordered_pair(_62486, _62484), cartesian_product2(_62482, _62480)), 2232 ^ _20480 : [(2233 ^ _20480) ^ [] : [-(in(_62486, _62482))], (2235 ^ _20480) ^ [] : [-(in(_62484, _62480))]]], (2237 ^ _20480) ^ [_62745, _62747, _62749, _62751] : [-(in(ordered_pair(_62751, _62749), cartesian_product2(_62747, _62745))), in(_62751, _62747), in(_62749, _62745)], (2247 ^ _20480) ^ [_63106, _63108, _63110, _63112] : [unordered_pair(_63112, _63110) = unordered_pair(_63108, _63106), -(_63112 = _63108), -(_63112 = _63106)], (2257 ^ _20480) ^ [_63456, _63458, _63460] : [relation(_63456), 2260 ^ _20480 : [(2261 ^ _20480) ^ [] : [in(_63460, relation_rng(relation_rng_restriction(_63458, _63456))), 2264 ^ _20480 : [(2265 ^ _20480) ^ [] : [-(in(_63460, _63458))], (2267 ^ _20480) ^ [] : [-(in(_63460, relation_rng(_63456)))]]], (2269 ^ _20480) ^ [] : [-(in(_63460, relation_rng(relation_rng_restriction(_63458, _63456)))), in(_63460, _63458), in(_63460, relation_rng(_63456))]]], (2279 ^ _20480) ^ [_64115, _64117] : [relation(_64115), -(subset(relation_rng(relation_rng_restriction(_64117, _64115)), _64117))], (2285 ^ _20480) ^ [_64333, _64335] : [relation(_64333), -(subset(relation_rng_restriction(_64335, _64333), _64333))], (2291 ^ _20480) ^ [_64547, _64549] : [relation(_64547), -(subset(relation_rng(relation_rng_restriction(_64549, _64547)), relation_rng(_64547)))], (2297 ^ _20480) ^ [_64783, _64785, _64787] : [subset(_64787, _64785), 2300 ^ _20480 : [(2301 ^ _20480) ^ [] : [-(subset(cartesian_product2(_64787, _64783), cartesian_product2(_64785, _64783)))], (2303 ^ _20480) ^ [] : [-(subset(cartesian_product2(_64783, _64787), cartesian_product2(_64783, _64785)))]]], (2305 ^ _20480) ^ [_65100, _65102] : [relation(_65100), -(relation_rng(relation_rng_restriction(_65102, _65100)) = set_intersection2(relation_rng(_65100), _65102))], (2311 ^ _20480) ^ [_65356, _65358, _65360, _65362] : [-(subset(cartesian_product2(_65362, _65358), cartesian_product2(_65360, _65356))), subset(_65362, _65360), subset(_65358, _65356)], (2321 ^ _20480) ^ [_65687, _65689] : [subset(_65689, _65687), -(set_union2(_65689, _65687) = _65687)], (2328 ^ _20480) ^ [_66009] : [-(in(_66009, 2326 ^ [_66009]))], (2330 ^ _20480) ^ [_66121, _66123, _66125] : [-(in(_66121, 2326 ^ [_66125])), in(_66123, 2326 ^ [_66125]), subset(_66121, _66123)], (2340 ^ _20480) ^ [_66436, _66438] : [in(_66436, 2326 ^ [_66438]), -(in(powerset(_66436), 2326 ^ [_66438]))], (2346 ^ _20480) ^ [_66636, _66638] : [subset(_66636, 2326 ^ [_66638]), -(are_equipotent(_66636, 2326 ^ [_66638])), -(in(_66636, 2326 ^ [_66638]))], (2356 ^ _20480) ^ [_66990, _66992, _66994] : [relation(_66990), -(relation_dom_restriction(relation_rng_restriction(_66994, _66990), _66992) = relation_rng_restriction(_66994, relation_dom_restriction(_66990, _66992)))], (2362 ^ _20480) ^ [_67242, _67244, _67246] : [relation(_67242), 2365 ^ _20480 : [(2366 ^ _20480) ^ [] : [in(_67246, relation_image(_67242, _67244)), 2370 ^ _20480 : [(2371 ^ _20480) ^ [] : [-(in(2369 ^ [_67242, _67244, _67246], relation_dom(_67242)))], (2373 ^ _20480) ^ [] : [-(in(ordered_pair(2369 ^ [_67242, _67244, _67246], _67246), _67242))], (2375 ^ _20480) ^ [] : [-(in(2369 ^ [_67242, _67244, _67246], _67244))]]], (2377 ^ _20480) ^ [] : [-(in(_67246, relation_image(_67242, _67244))), 2378 ^ _20480 : [(2379 ^ _20480) ^ [_67843] : [in(_67843, relation_dom(_67242)), in(ordered_pair(_67843, _67246), _67242), in(_67843, _67244)]]]]], (2391 ^ _20480) ^ [_68240, _68242] : [relation(_68240), -(subset(relation_image(_68240, _68242), relation_rng(_68240)))], (2397 ^ _20480) ^ [_68458, _68460] : [relation(_68458), -(relation_image(_68458, _68460) = relation_image(_68458, set_intersection2(relation_dom(_68458), _68460)))], (2403 ^ _20480) ^ [_68674] : [relation(_68674), -(relation_image(_68674, relation_dom(_68674)) = relation_rng(_68674))], (2409 ^ _20480) ^ [_68876] : [relation(_68876), 2412 ^ _20480 : [(2413 ^ _20480) ^ [_69016] : [relation(_69016), -(relation_rng(relation_composition(_68876, _69016)) = relation_image(_69016, relation_rng(_68876)))]]], (2419 ^ _20480) ^ [_69265, _69267, _69269] : [relation(_69265), 2422 ^ _20480 : [(2423 ^ _20480) ^ [] : [in(_69269, relation_inverse_image(_69265, _69267)), 2427 ^ _20480 : [(2428 ^ _20480) ^ [] : [-(in(2426 ^ [_69265, _69267, _69269], relation_rng(_69265)))], (2430 ^ _20480) ^ [] : [-(in(ordered_pair(_69269, 2426 ^ [_69265, _69267, _69269]), _69265))], (2432 ^ _20480) ^ [] : [-(in(2426 ^ [_69265, _69267, _69269], _69267))]]], (2434 ^ _20480) ^ [] : [-(in(_69269, relation_inverse_image(_69265, _69267))), 2435 ^ _20480 : [(2436 ^ _20480) ^ [_69866] : [in(_69866, relation_rng(_69265)), in(ordered_pair(_69269, _69866), _69265), in(_69866, _69267)]]]]], (2448 ^ _20480) ^ [_70263, _70265] : [relation(_70263), -(subset(relation_inverse_image(_70263, _70265), relation_dom(_70263)))], (2454 ^ _20480) ^ [_70481, _70483] : [relation(_70481), -(_70483 = empty_set), subset(_70483, relation_rng(_70481)), relation_inverse_image(_70481, _70483) = empty_set], (2468 ^ _20480) ^ [_70895, _70897, _70899] : [relation(_70895), subset(_70899, _70897), -(subset(relation_inverse_image(_70895, _70899), relation_inverse_image(_70895, _70897)))], (2478 ^ _20480) ^ [_71199, _71201] : [-(subset(set_intersection2(_71201, _71199), _71201))], (2480 ^ _20480) ^ [_71325, _71327, _71329] : [-(subset(_71329, set_intersection2(_71327, _71325))), subset(_71329, _71327), subset(_71329, _71325)], (2490 ^ _20480) ^ [_71611] : [-(set_union2(_71611, empty_set) = _71611)], (2492 ^ _20480) ^ [_71721, _71723] : [in(_71723, _71721), -(element(_71723, _71721))], (2498 ^ _20480) ^ [_71945, _71947, _71949] : [-(subset(_71949, _71945)), subset(_71949, _71947), subset(_71947, _71945)], (2508 ^ _20480) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (2510 ^ _20480) ^ [_72321, _72323, _72325] : [relation(_72321), in(ordered_pair(_72325, _72323), _72321), 2517 ^ _20480 : [(2518 ^ _20480) ^ [] : [-(in(_72325, relation_dom(_72321)))], (2520 ^ _20480) ^ [] : [-(in(_72323, relation_rng(_72321)))]]], (2522 ^ _20480) ^ [_72719, _72721] : [relation(_72719), function(_72719), 2529 ^ _20480 : [(2530 ^ _20480) ^ [_72969] : [relation(_72969), function(_72969), 2537 ^ _20480 : [(2538 ^ _20480) ^ [] : [in(_72721, relation_dom(relation_composition(_72969, _72719))), 2541 ^ _20480 : [(2542 ^ _20480) ^ [] : [-(in(_72721, relation_dom(_72969)))], (2544 ^ _20480) ^ [] : [-(in(apply(_72969, _72721), relation_dom(_72719)))]]], (2546 ^ _20480) ^ [] : [-(in(_72721, relation_dom(relation_composition(_72969, _72719)))), in(_72721, relation_dom(_72969)), in(apply(_72969, _72721), relation_dom(_72719))]]]]], (2556 ^ _20480) ^ [_73733] : [relation(_73733), -(subset(_73733, cartesian_product2(relation_dom(_73733), relation_rng(_73733))))], (2562 ^ _20480) ^ [_73949, _73951] : [relation(_73949), function(_73949), 2569 ^ _20480 : [(2570 ^ _20480) ^ [_74198] : [relation(_74198), function(_74198), in(_73951, relation_dom(relation_composition(_74198, _73949))), -(apply(relation_composition(_74198, _73949), _73951) = apply(_73949, apply(_74198, _73951)))]]], (2584 ^ _20480) ^ [_74643, _74645] : [relation(_74643), function(_74643), 2591 ^ _20480 : [(2592 ^ _20480) ^ [_74889] : [relation(_74889), function(_74889), in(_74645, relation_dom(_74643)), -(apply(relation_composition(_74643, _74889), _74645) = apply(_74889, apply(_74643, _74645)))]]], (2606 ^ _20480) ^ [_75314] : [relation(_75314), 2609 ^ _20480 : [(2610 ^ _20480) ^ [_75464] : [relation(_75464), subset(_75314, _75464), 2617 ^ _20480 : [(2618 ^ _20480) ^ [] : [-(subset(relation_dom(_75314), relation_dom(_75464)))], (2620 ^ _20480) ^ [] : [-(subset(relation_rng(_75314), relation_rng(_75464)))]]]]], (2622 ^ _20480) ^ [_75873, _75875, _75877] : [subset(_75877, _75875), -(subset(set_intersection2(_75877, _75873), set_intersection2(_75875, _75873)))], (2628 ^ _20480) ^ [_76101, _76103] : [subset(_76103, _76101), -(set_intersection2(_76103, _76101) = _76103)], (2634 ^ _20480) ^ [_76288] : [-(set_intersection2(_76288, empty_set) = empty_set)], (2636 ^ _20480) ^ [_76398, _76400] : [element(_76400, _76398), -(empty(_76398)), -(in(_76400, _76398))], (2646 ^ _20480) ^ [_76696, _76698] : [-(_76698 = _76696), 2650 ^ _20480 : [(2651 ^ _20480) ^ [] : [-(in(2647 ^ [_76696, _76698], _76698))], (2653 ^ _20480) ^ [] : [in(2647 ^ [_76696, _76698], _76696)]], 2654 ^ _20480 : [(2655 ^ _20480) ^ [] : [-(in(2647 ^ [_76696, _76698], _76696))], (2657 ^ _20480) ^ [] : [in(2647 ^ [_76696, _76698], _76698)]]], (2661 ^ _20480) ^ [_77197] : [-(subset(empty_set, _77197))], (2663 ^ _20480) ^ [_77318, _77320, _77322] : [relation(_77318), in(ordered_pair(_77322, _77320), _77318), 2670 ^ _20480 : [(2671 ^ _20480) ^ [] : [-(in(_77322, relation_field(_77318)))], (2673 ^ _20480) ^ [] : [-(in(_77320, relation_field(_77318)))]]], (2675 ^ _20480) ^ [_77730, _77732, _77734] : [subset(_77734, _77732), -(subset(set_difference(_77734, _77730), set_difference(_77732, _77730)))], (2681 ^ _20480) ^ [_77986, _77988, _77990, _77992] : [ordered_pair(_77992, _77990) = ordered_pair(_77988, _77986), 2684 ^ _20480 : [(2685 ^ _20480) ^ [] : [-(_77992 = _77988)], (2687 ^ _20480) ^ [] : [-(_77990 = _77986)]]], (2689 ^ _20480) ^ [_78299, _78301] : [relation(_78299), function(_78299), 2696 ^ _20480 : [(2697 ^ _20480) ^ [] : [_78299 = identity_relation(_78301), 2700 ^ _20480 : [(2701 ^ _20480) ^ [] : [-(relation_dom(_78299) = _78301)], (2703 ^ _20480) ^ [_78718] : [in(_78718, _78301), -(apply(_78299, _78718) = _78718)]]], (2709 ^ _20480) ^ [] : [-(_78299 = identity_relation(_78301)), relation_dom(_78299) = _78301, 2715 ^ _20480 : [(2716 ^ _20480) ^ [] : [-(in(2714 ^ [_78299, _78301], _78301))], (2718 ^ _20480) ^ [] : [apply(_78299, 2714 ^ [_78299, _78301]) = 2714 ^ [_78299, _78301]]]]]], (2722 ^ _20480) ^ [_79323, _79325] : [in(_79323, _79325), -(apply(identity_relation(_79325), _79323) = _79323)], (2728 ^ _20480) ^ [_79528, _79530] : [-(subset(set_difference(_79530, _79528), _79530))], (2730 ^ _20480) ^ [_79626] : [relation(_79626), 2733 ^ _20480 : [(2734 ^ _20480) ^ [] : [-(relation_rng(_79626) = relation_dom(relation_inverse(_79626)))], (2736 ^ _20480) ^ [] : [-(relation_dom(_79626) = relation_rng(relation_inverse(_79626)))]]], (2738 ^ _20480) ^ [_79954, _79956] : [set_difference(_79956, _79954) = empty_set, -(subset(_79956, _79954))], (2744 ^ _20480) ^ [_80122, _80124] : [subset(_80124, _80122), -(set_difference(_80124, _80122) = empty_set)], (2750 ^ _20480) ^ [_80369, _80371] : [subset(singleton(_80371), _80369), -(in(_80371, _80369))], (2756 ^ _20480) ^ [_80535, _80537] : [in(_80537, _80535), -(subset(singleton(_80537), _80535))], (2762 ^ _20480) ^ [_80794, _80796, _80798] : [subset(unordered_pair(_80798, _80796), _80794), 2765 ^ _20480 : [(2766 ^ _20480) ^ [] : [-(in(_80798, _80794))], (2768 ^ _20480) ^ [] : [-(in(_80796, _80794))]]], (2770 ^ _20480) ^ [_81045, _81047, _81049] : [-(subset(unordered_pair(_81049, _81047), _81045)), in(_81049, _81045), in(_81047, _81045)], (2780 ^ _20480) ^ [_81347, _81349] : [-(set_union2(_81349, set_difference(_81347, _81349)) = set_union2(_81349, _81347))], (2792 ^ _20480) ^ [_81754, _81756] : [2793 ^ _20480 : [(2794 ^ _20480) ^ [] : [_81756 = empty_set], (2796 ^ _20480) ^ [] : [_81756 = singleton(_81754)]], -(subset(_81756, singleton(_81754)))], (2782 ^ _20480) ^ [_81494, _81496] : [subset(_81496, singleton(_81494)), -(_81496 = empty_set), -(_81496 = singleton(_81494))], (2800 ^ _20480) ^ [_82019] : [-(set_difference(_82019, empty_set) = _82019)], (2802 ^ _20480) ^ [_82158, _82160] : [element(_82160, powerset(_82158)), -(subset(_82160, _82158))], (2808 ^ _20480) ^ [_82324, _82326] : [subset(_82326, _82324), -(element(_82326, powerset(_82324)))], (2814 ^ _20480) ^ [_82560, _82562] : [-(disjoint(_82562, _82560)), 2818 ^ _20480 : [(2819 ^ _20480) ^ [] : [-(in(2817 ^ [_82560, _82562], _82562))], (2821 ^ _20480) ^ [] : [-(in(2817 ^ [_82560, _82562], _82560))]]], (2823 ^ _20480) ^ [_82874, _82876] : [disjoint(_82876, _82874), 2824 ^ _20480 : [(2825 ^ _20480) ^ [_82966] : [in(_82966, _82876), in(_82966, _82874)]]], (2833 ^ _20480) ^ [_83223] : [subset(_83223, empty_set), -(_83223 = empty_set)], (2839 ^ _20480) ^ [_83412, _83414] : [-(set_difference(set_union2(_83414, _83412), _83412) = set_difference(_83414, _83412))], (2841 ^ _20480) ^ [_83530, _83532] : [element(_83530, powerset(_83532)), 2844 ^ _20480 : [(2845 ^ _20480) ^ [_83682] : [element(_83682, powerset(_83532)), 2848 ^ _20480 : [(2849 ^ _20480) ^ [] : [disjoint(_83530, _83682), -(subset(_83530, subset_complement(_83532, _83682)))], (2855 ^ _20480) ^ [] : [subset(_83530, subset_complement(_83532, _83682)), -(disjoint(_83530, _83682))]]]]], (2861 ^ _20480) ^ [_84166] : [relation(_84166), 2864 ^ _20480 : [(2865 ^ _20480) ^ [_84303] : [relation(_84303), -(subset(relation_dom(relation_composition(_84166, _84303)), relation_dom(_84166)))]]], (2871 ^ _20480) ^ [_84518] : [relation(_84518), 2874 ^ _20480 : [(2875 ^ _20480) ^ [_84655] : [relation(_84655), -(subset(relation_rng(relation_composition(_84518, _84655)), relation_rng(_84655)))]]], (2881 ^ _20480) ^ [_84884, _84886] : [subset(_84886, _84884), -(_84884 = set_union2(_84886, set_difference(_84884, _84886)))], (2887 ^ _20480) ^ [_85092] : [relation(_85092), 2890 ^ _20480 : [(2891 ^ _20480) ^ [_85239] : [relation(_85239), subset(relation_rng(_85092), relation_dom(_85239)), -(relation_dom(relation_composition(_85092, _85239)) = relation_dom(_85092))]]], (2901 ^ _20480) ^ [_85565, _85567] : [element(_85565, powerset(powerset(_85567))), -(_85565 = empty_set), complements_of_subsets(_85567, _85565) = empty_set], (2911 ^ _20480) ^ [_85882, _85884] : [in(_85884, _85882), -(set_union2(singleton(_85884), _85882) = _85882)], (2917 ^ _20480) ^ [_86088] : [relation(_86088), 2920 ^ _20480 : [(2921 ^ _20480) ^ [_86235] : [relation(_86235), subset(relation_dom(_86088), relation_rng(_86235)), -(relation_rng(relation_composition(_86235, _86088)) = relation_rng(_86088))]]], (2931 ^ _20480) ^ [_86561, _86563] : [element(_86561, powerset(powerset(_86563))), -(_86561 = empty_set), -(subset_difference(_86563, cast_to_subset(_86563), union_of_subsets(_86563, _86561)) = meet_of_subsets(_86563, complements_of_subsets(_86563, _86561)))], (2941 ^ _20480) ^ [_86901, _86903] : [element(_86901, powerset(powerset(_86903))), -(_86901 = empty_set), -(union_of_subsets(_86903, complements_of_subsets(_86903, _86901)) = subset_difference(_86903, cast_to_subset(_86903), meet_of_subsets(_86903, _86901)))], (2951 ^ _20480) ^ [_87226, _87228] : [-(set_difference(_87228, set_difference(_87228, _87226)) = set_intersection2(_87228, _87226))], (2953 ^ _20480) ^ [_87315] : [-(set_difference(empty_set, _87315) = empty_set)], (2955 ^ _20480) ^ [_87439, _87441, _87443] : [-(element(_87443, _87439)), in(_87443, _87441), element(_87441, powerset(_87439))], (2965 ^ _20480) ^ [_87772, _87774] : [-(disjoint(_87774, _87772)), -(in(2968 ^ [_87772, _87774], set_intersection2(_87774, _87772)))], (2972 ^ _20480) ^ [_88007, _88009] : [2973 ^ _20480 : [(2974 ^ _20480) ^ [_88080] : [in(_88080, set_intersection2(_88009, _88007))]], disjoint(_88009, _88007)], (2978 ^ _20480) ^ [_88232] : [-(_88232 = empty_set), 2981 ^ _20480 : [(2982 ^ _20480) ^ [_88392] : [element(_88392, powerset(_88232)), 2985 ^ _20480 : [(2986 ^ _20480) ^ [_88546] : [element(_88546, _88232), -(in(_88546, _88392)), -(in(_88546, subset_complement(_88232, _88392)))]]]]], (2996 ^ _20480) ^ [_88864] : [relation(_88864), function(_88864), one_to_one(_88864), 3007 ^ _20480 : [(3008 ^ _20480) ^ [_89251] : [relation(_89251), function(_89251), 3015 ^ _20480 : [(3046 ^ _20480) ^ [] : [-(_89251 = function_inverse(_88864)), relation_dom(_89251) = relation_rng(_88864), 3055 ^ _20480 : [(3056 ^ _20480) ^ [] : [-(in(3051 ^ [_88864, _89251], relation_rng(_88864)))], (3058 ^ _20480) ^ [] : [-(3052 ^ [_88864, _89251] = apply(_89251, 3051 ^ [_88864, _89251]))], (3060 ^ _20480) ^ [] : [in(3052 ^ [_88864, _89251], relation_dom(_88864)), 3051 ^ [_88864, _89251] = apply(_88864, 3052 ^ [_88864, _89251])]], 3065 ^ _20480 : [(3066 ^ _20480) ^ [] : [-(in(3052 ^ [_88864, _89251], relation_dom(_88864)))], (3068 ^ _20480) ^ [] : [-(3051 ^ [_88864, _89251] = apply(_88864, 3052 ^ [_88864, _89251]))], (3070 ^ _20480) ^ [] : [in(3051 ^ [_88864, _89251], relation_rng(_88864)), 3052 ^ [_88864, _89251] = apply(_89251, 3051 ^ [_88864, _89251])]]], (3016 ^ _20480) ^ [] : [_89251 = function_inverse(_88864), 3019 ^ _20480 : [(3020 ^ _20480) ^ [] : [-(relation_dom(_89251) = relation_rng(_88864))], (3022 ^ _20480) ^ [_89768, _89770] : [3029 ^ _20480 : [(3030 ^ _20480) ^ [] : [-(in(_89768, relation_dom(_88864)))], (3032 ^ _20480) ^ [] : [-(_89770 = apply(_88864, _89768))]], in(_89770, relation_rng(_88864)), _89768 = apply(_89251, _89770)], (3034 ^ _20480) ^ [_90142, _90144] : [3041 ^ _20480 : [(3042 ^ _20480) ^ [] : [-(in(_90144, relation_rng(_88864)))], (3044 ^ _20480) ^ [] : [-(_90142 = apply(_89251, _90144))]], in(_90142, relation_dom(_88864)), _90144 = apply(_88864, _90142)]]]]]]], (3078 ^ _20480) ^ [_91717, _91719, _91721] : [element(_91717, powerset(_91721)), in(_91719, subset_complement(_91721, _91717)), in(_91719, _91717)], (3088 ^ _20480) ^ [_92023] : [relation(_92023), function(_92023), one_to_one(_92023), 3099 ^ _20480 : [(3100 ^ _20480) ^ [] : [-(relation_rng(_92023) = relation_dom(function_inverse(_92023)))], (3102 ^ _20480) ^ [] : [-(relation_dom(_92023) = relation_rng(function_inverse(_92023)))]]], (3104 ^ _20480) ^ [_92476] : [relation(_92476), -(in(ordered_pair(3109 ^ [_92476], 3110 ^ [_92476]), _92476)), -(_92476 = empty_set)], (3116 ^ _20480) ^ [_92894, _92896] : [relation(_92894), function(_92894), 3131 ^ _20480 : [(3132 ^ _20480) ^ [] : [-(_92896 = apply(_92894, apply(function_inverse(_92894), _92896)))], (3134 ^ _20480) ^ [] : [-(_92896 = apply(relation_composition(function_inverse(_92894), _92894), _92896))]], one_to_one(_92894), in(_92896, relation_rng(_92894))], (3136 ^ _20480) ^ [_93492, _93494, _93496] : [in(_93496, _93494), element(_93494, powerset(_93492)), empty(_93492)], (3146 ^ _20480) ^ [] : [-(relation_dom(empty_set) = empty_set)], (3148 ^ _20480) ^ [] : [-(relation_rng(empty_set) = empty_set)], (3150 ^ _20480) ^ [_93910, _93912] : [subset(_93912, _93910), proper_subset(_93910, _93912)], (3156 ^ _20480) ^ [_94105] : [relation(_94105), function(_94105), one_to_one(_94105), -(one_to_one(function_inverse(_94105)))], (3170 ^ _20480) ^ [_94491, _94493, _94495] : [-(disjoint(_94495, _94491)), subset(_94495, _94493), disjoint(_94493, _94491)], (3180 ^ _20480) ^ [_94786] : [relation(_94786), 3185 ^ _20480 : [(3186 ^ _20480) ^ [] : [relation_dom(_94786) = empty_set], (3188 ^ _20480) ^ [] : [relation_rng(_94786) = empty_set]], -(_94786 = empty_set)], (3192 ^ _20480) ^ [_95139] : [relation(_95139), 3195 ^ _20480 : [(3196 ^ _20480) ^ [] : [relation_dom(_95139) = empty_set, -(relation_rng(_95139) = empty_set)], (3202 ^ _20480) ^ [] : [relation_rng(_95139) = empty_set, -(relation_dom(_95139) = empty_set)]]], (3208 ^ _20480) ^ [_95622, _95624] : [set_difference(_95624, singleton(_95622)) = _95624, in(_95622, _95624)], (3214 ^ _20480) ^ [_95795, _95797] : [-(in(_95795, _95797)), -(set_difference(_95797, singleton(_95795)) = _95797)], (3220 ^ _20480) ^ [_96020, _96022] : [relation(_96020), function(_96020), 3227 ^ _20480 : [(3228 ^ _20480) ^ [_96287] : [relation(_96287), function(_96287), 3235 ^ _20480 : [(3236 ^ _20480) ^ [] : [_96020 = relation_dom_restriction(_96287, _96022), 3239 ^ _20480 : [(3240 ^ _20480) ^ [] : [-(relation_dom(_96020) = set_intersection2(relation_dom(_96287), _96022))], (3242 ^ _20480) ^ [_96741] : [in(_96741, relation_dom(_96020)), -(apply(_96020, _96741) = apply(_96287, _96741))]]], (3248 ^ _20480) ^ [] : [-(_96020 = relation_dom_restriction(_96287, _96022)), relation_dom(_96020) = set_intersection2(relation_dom(_96287), _96022), 3254 ^ _20480 : [(3255 ^ _20480) ^ [] : [-(in(3253 ^ [_96020, _96022, _96287], relation_dom(_96020)))], (3257 ^ _20480) ^ [] : [apply(_96020, 3253 ^ [_96020, _96022, _96287]) = apply(_96287, 3253 ^ [_96020, _96022, _96287])]]]]]]], (3261 ^ _20480) ^ [_97380] : [-(unordered_pair(_97380, _97380) = singleton(_97380))], (3263 ^ _20480) ^ [_97478] : [empty(_97478), -(_97478 = empty_set)], (3269 ^ _20480) ^ [_97680, _97682] : [subset(singleton(_97682), singleton(_97680)), -(_97682 = _97680)], (3275 ^ _20480) ^ [_97912, _97914, _97916] : [relation(_97912), function(_97912), in(_97914, relation_dom(relation_dom_restriction(_97912, _97916))), -(apply(relation_dom_restriction(_97912, _97916), _97914) = apply(_97912, _97914))], (3289 ^ _20480) ^ [_98331] : [-(relation_dom(identity_relation(_98331)) = _98331)], (3291 ^ _20480) ^ [_98379] : [-(relation_rng(identity_relation(_98379)) = _98379)], (3293 ^ _20480) ^ [_98520, _98522, _98524, _98526] : [relation(_98520), 3296 ^ _20480 : [(3297 ^ _20480) ^ [] : [in(ordered_pair(_98526, _98524), relation_composition(identity_relation(_98522), _98520)), 3300 ^ _20480 : [(3301 ^ _20480) ^ [] : [-(in(_98526, _98522))], (3303 ^ _20480) ^ [] : [-(in(ordered_pair(_98526, _98524), _98520))]]], (3305 ^ _20480) ^ [] : [-(in(ordered_pair(_98526, _98524), relation_composition(identity_relation(_98522), _98520))), in(_98526, _98522), in(ordered_pair(_98526, _98524), _98520)]]], (3315 ^ _20480) ^ [_99213, _99215] : [in(_99215, _99213), empty(_99213)], (3321 ^ _20480) ^ [_99405, _99407] : [-(subset(_99407, set_union2(_99407, _99405)))], (3323 ^ _20480) ^ [_99546, _99548] : [disjoint(_99548, _99546), -(set_difference(_99548, _99546) = _99548)], (3329 ^ _20480) ^ [_99714, _99716] : [set_difference(_99716, _99714) = _99716, -(disjoint(_99716, _99714))], (3335 ^ _20480) ^ [_99946, _99948, _99950] : [relation(_99946), 3338 ^ _20480 : [(3339 ^ _20480) ^ [] : [in(_99950, relation_dom(relation_dom_restriction(_99946, _99948))), 3342 ^ _20480 : [(3343 ^ _20480) ^ [] : [-(in(_99950, _99948))], (3345 ^ _20480) ^ [] : [-(in(_99950, relation_dom(_99946)))]]], (3347 ^ _20480) ^ [] : [-(in(_99950, relation_dom(relation_dom_restriction(_99946, _99948)))), in(_99950, _99948), in(_99950, relation_dom(_99946))]]], (3357 ^ _20480) ^ [_100605, _100607] : [relation(_100605), -(subset(relation_dom_restriction(_100605, _100607), _100605))], (3363 ^ _20480) ^ [_100819, _100821] : [empty(_100821), -(_100821 = _100819), empty(_100819)], (3373 ^ _20480) ^ [_101130, _101132, _101134] : [relation(_101130), function(_101130), 3380 ^ _20480 : [(3381 ^ _20480) ^ [] : [in(ordered_pair(_101134, _101132), _101130), 3384 ^ _20480 : [(3385 ^ _20480) ^ [] : [-(in(_101134, relation_dom(_101130)))], (3387 ^ _20480) ^ [] : [-(_101132 = apply(_101130, _101134))]]], (3389 ^ _20480) ^ [] : [-(in(ordered_pair(_101134, _101132), _101130)), in(_101134, relation_dom(_101130)), _101132 = apply(_101130, _101134)]]], (3399 ^ _20480) ^ [_101899, _101901, _101903] : [-(subset(set_union2(_101903, _101899), _101901)), subset(_101903, _101901), subset(_101899, _101901)], (3409 ^ _20480) ^ [_102228, _102230, _102232] : [singleton(_102232) = unordered_pair(_102230, _102228), -(_102232 = _102230)], (3415 ^ _20480) ^ [_102454, _102456] : [relation(_102454), -(relation_dom(relation_dom_restriction(_102454, _102456)) = set_intersection2(relation_dom(_102454), _102456))], (3421 ^ _20480) ^ [_102682, _102684] : [in(_102684, _102682), -(subset(_102684, union(_102682)))], (3427 ^ _20480) ^ [_102896, _102898] : [relation(_102896), -(relation_dom_restriction(_102896, _102898) = relation_composition(identity_relation(_102898), _102896))], (3433 ^ _20480) ^ [_103120, _103122] : [relation(_103120), -(subset(relation_rng(relation_dom_restriction(_103120, _103122)), relation_rng(_103120)))], (3439 ^ _20480) ^ [_103313] : [-(union(powerset(_103313)) = _103313)], (3477 ^ _20480) ^ [_104834, _104836, _104838] : [singleton(_104838) = unordered_pair(_104836, _104834), -(_104836 = _104834)], (3442 ^ _20480) ^ [_103554] : [-(in(_103554, 3440 ^ [_103554]))], (3444 ^ _20480) ^ [_103666, _103668, _103670] : [-(in(_103666, 3440 ^ [_103670])), in(_103668, 3440 ^ [_103670]), subset(_103666, _103668)], (3454 ^ _20480) ^ [_103981, _103983] : [in(_103981, 3440 ^ [_103983]), 3458 ^ _20480 : [(3459 ^ _20480) ^ [] : [-(in(3457 ^ [_103981, _103983], 3440 ^ [_103983]))], (3461 ^ _20480) ^ [_104293] : [subset(_104293, _103981), -(in(_104293, 3457 ^ [_103981, _103983]))]]], (3467 ^ _20480) ^ [_104500, _104502] : [subset(_104500, 3440 ^ [_104502]), -(are_equipotent(_104500, 3440 ^ [_104502])), -(in(_104500, 3440 ^ [_104502]))]], input).
% 0.41/1.37  ncf('1',plain,[3504 : in(3483 ^ [], relation_dom(relation_dom_restriction(3484 ^ [], 3482 ^ []))), 3494 : in(3483 ^ [], relation_dom(3484 ^ [])), 3494 : in(3483 ^ [], 3482 ^ [])],start(3490 ^ 0)).
% 0.41/1.37  ncf('1.1',plain,[-(in(3483 ^ [], relation_dom(relation_dom_restriction(3484 ^ [], 3482 ^ [])))), 3347 : in(3483 ^ [], 3482 ^ []), 3347 : in(3483 ^ [], relation_dom(3484 ^ [])), 3347 : relation(3484 ^ [])],extension(3335 ^ 3,bind([[_99946, _99948, _99950], [3484 ^ [], 3482 ^ [], 3483 ^ []]]))).
% 0.41/1.37  ncf('1.1.1',plain,[-(in(3483 ^ [], 3482 ^ []))],extension(3502 ^ 6)).
% 0.41/1.37  ncf('1.1.2',plain,[-(in(3483 ^ [], relation_dom(3484 ^ [])))],extension(3500 ^ 6)).
% 0.41/1.37  ncf('1.1.3',plain,[-(relation(3484 ^ []))],extension(3486 ^ 4)).
% 0.41/1.37  ncf('1.2',plain,[-(in(3483 ^ [], relation_dom(3484 ^ []))), 3339 : in(3483 ^ [], relation_dom(relation_dom_restriction(3484 ^ [], 3482 ^ []))), 3339 : relation(3484 ^ [])],extension(3335 ^ 3,bind([[_99946, _99948, _99950], [3484 ^ [], 3482 ^ [], 3483 ^ []]]))).
% 0.41/1.37  ncf('1.2.1',plain,[-(in(3483 ^ [], relation_dom(relation_dom_restriction(3484 ^ [], 3482 ^ []))))],extension(3492 ^ 6)).
% 0.41/1.37  ncf('1.2.2',plain,[-(relation(3484 ^ []))],extension(3486 ^ 4)).
% 0.41/1.37  ncf('1.3',plain,[-(in(3483 ^ [], 3482 ^ [])), 3339 : in(3483 ^ [], relation_dom(relation_dom_restriction(3484 ^ [], 3482 ^ []))), 3339 : relation(3484 ^ [])],extension(3335 ^ 3,bind([[_99946, _99948, _99950], [3484 ^ [], 3482 ^ [], 3483 ^ []]]))).
% 0.41/1.37  ncf('1.3.1',plain,[-(in(3483 ^ [], relation_dom(relation_dom_restriction(3484 ^ [], 3482 ^ []))))],extension(3492 ^ 6)).
% 0.41/1.37  ncf('1.3.2',plain,[-(relation(3484 ^ []))],extension(3486 ^ 4)).
% 0.41/1.37  %-----------------------------------------------------
% 0.41/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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