TSTP Solution File: SEU215+2 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SEU215+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:02:42 EDT 2023
% Result : Theorem 13.32s 13.78s
% Output : Proof 13.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU215+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 18 13:04:35 EDT 2023
% 0.12/0.33 % CPUTime :
% 13.32/13.78
% 13.32/13.78 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 13.32/13.78 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.32/13.78 %-----------------------------------------------------
% 13.32/13.78 ncf(matrix, plain, [(3071 ^ _19026) ^ [] : [-(relation(3069 ^ []))], (3073 ^ _19026) ^ [] : [-(function(3069 ^ []))], (3076 ^ _19026) ^ [] : [-(relation(3074 ^ []))], (3078 ^ _19026) ^ [] : [-(function(3074 ^ []))], (3080 ^ _19026) ^ [] : [-(in(3068 ^ [], relation_dom(3069 ^ [])))], (3082 ^ _19026) ^ [] : [apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = apply(3074 ^ [], apply(3069 ^ [], 3068 ^ []))], (2 ^ _19026) ^ [_19056] : [-(_19056 = _19056)], (4 ^ _19026) ^ [_19079, _19081] : [_19081 = _19079, -(_19079 = _19081)], (10 ^ _19026) ^ [_19152, _19154, _19156] : [-(_19156 = _19152), _19156 = _19154, _19154 = _19152], (20 ^ _19026) ^ [_19289, _19291] : [-(relation_empty_yielding(_19289)), _19291 = _19289, relation_empty_yielding(_19291)], (30 ^ _19026) ^ [_19414, _19416, _19418, _19420] : [-(element(_19418, _19414)), element(_19420, _19416), _19420 = _19418, _19416 = _19414], (44 ^ _19026) ^ [_19607, _19609, _19611, _19613] : [-(proper_subset(_19611, _19607)), proper_subset(_19613, _19609), _19613 = _19611, _19609 = _19607], (58 ^ _19026) ^ [_19800, _19802, _19804, _19806] : [-(disjoint(_19804, _19800)), disjoint(_19806, _19802), _19806 = _19804, _19802 = _19800], (72 ^ _19026) ^ [_19993, _19995] : [-(empty(_19993)), _19995 = _19993, empty(_19995)], (82 ^ _19026) ^ [_20118, _20120, _20122, _20124] : [-(subset(_20122, _20118)), subset(_20124, _20120), _20124 = _20122, _20120 = _20118], (96 ^ _19026) ^ [_20311, _20313, _20315, _20317] : [-(are_equipotent(_20315, _20311)), are_equipotent(_20317, _20313), _20317 = _20315, _20313 = _20311], (110 ^ _19026) ^ [_20504, _20506] : [-(relation(_20504)), _20506 = _20504, relation(_20506)], (120 ^ _19026) ^ [_20629, _20631] : [-(function(_20629)), _20631 = _20629, function(_20631)], (130 ^ _19026) ^ [_20750, _20752, _20754, _20756] : [-(in(_20754, _20750)), in(_20756, _20752), _20756 = _20754, _20752 = _20750], (144 ^ _19026) ^ [_20967, _20969] : [_20969 = _20967, -(set_meet(_20969) = set_meet(_20967))], (150 ^ _19026) ^ [_21052, _21054, _21056, _21058] : [-(relation_rng_restriction(_21058, _21054) = relation_rng_restriction(_21056, _21052)), _21058 = _21056, _21054 = _21052], (160 ^ _19026) ^ [_21201, _21203, _21205, _21207] : [-(relation_image(_21207, _21203) = relation_image(_21205, _21201)), _21207 = _21205, _21203 = _21201], (170 ^ _19026) ^ [_21350, _21352, _21354, _21356] : [-(relation_inverse_image(_21356, _21352) = relation_inverse_image(_21354, _21350)), _21356 = _21354, _21352 = _21350], (180 ^ _19026) ^ [_21499, _21501, _21503, _21505] : [-(cartesian_product2(_21505, _21501) = cartesian_product2(_21503, _21499)), _21505 = _21503, _21501 = _21499], (190 ^ _19026) ^ [_21648, _21650] : [_21650 = _21648, -(relation_field(_21650) = relation_field(_21648))], (196 ^ _19026) ^ [_21733, _21735] : [_21735 = _21733, -(relation_inverse(_21735) = relation_inverse(_21733))], (202 ^ _19026) ^ [_21818, _21820, _21822, _21824] : [-(union_of_subsets(_21824, _21820) = union_of_subsets(_21822, _21818)), _21824 = _21822, _21820 = _21818], (212 ^ _19026) ^ [_21967, _21969, _21971, _21973] : [-(complements_of_subsets(_21973, _21969) = complements_of_subsets(_21971, _21967)), _21973 = _21971, _21969 = _21967], (222 ^ _19026) ^ [_22116, _22118, _22120, _22122, _22124, _22126] : [-(subset_difference(_22126, _22122, _22118) = subset_difference(_22124, _22120, _22116)), _22126 = _22124, _22122 = _22120, _22118 = _22116], (236 ^ _19026) ^ [_22337, _22339] : [_22339 = _22337, -(cast_to_subset(_22339) = cast_to_subset(_22337))], (242 ^ _19026) ^ [_22422, _22424, _22426, _22428] : [-(meet_of_subsets(_22428, _22424) = meet_of_subsets(_22426, _22422)), _22428 = _22426, _22424 = _22422], (252 ^ _19026) ^ [_22571, _22573, _22575, _22577] : [-(subset_complement(_22577, _22573) = subset_complement(_22575, _22571)), _22577 = _22575, _22573 = _22571], (262 ^ _19026) ^ [_22720, _22722, _22724, _22726] : [-(set_difference(_22726, _22722) = set_difference(_22724, _22720)), _22726 = _22724, _22722 = _22720], (272 ^ _19026) ^ [_22869, _22871, _22873, _22875] : [-(ordered_pair(_22875, _22871) = ordered_pair(_22873, _22869)), _22875 = _22873, _22871 = _22869], (282 ^ _19026) ^ [_23018, _23020, _23022, _23024] : [-(set_union2(_23024, _23020) = set_union2(_23022, _23018)), _23024 = _23022, _23020 = _23018], (292 ^ _19026) ^ [_23167, _23169, _23171, _23173] : [-(set_intersection2(_23173, _23169) = set_intersection2(_23171, _23167)), _23173 = _23171, _23169 = _23167], (302 ^ _19026) ^ [_23316, _23318] : [_23318 = _23316, -(identity_relation(_23318) = identity_relation(_23316))], (308 ^ _19026) ^ [_23401, _23403, _23405, _23407] : [-(relation_dom_restriction(_23407, _23403) = relation_dom_restriction(_23405, _23401)), _23407 = _23405, _23403 = _23401], (318 ^ _19026) ^ [_23550, _23552] : [_23552 = _23550, -(relation_rng(_23552) = relation_rng(_23550))], (324 ^ _19026) ^ [_23635, _23637] : [_23637 = _23635, -(union(_23637) = union(_23635))], (330 ^ _19026) ^ [_23720, _23722] : [_23722 = _23720, -(powerset(_23722) = powerset(_23720))], (336 ^ _19026) ^ [_23805, _23807] : [_23807 = _23805, -(singleton(_23807) = singleton(_23805))], (342 ^ _19026) ^ [_23890, _23892, _23894, _23896] : [-(unordered_pair(_23896, _23892) = unordered_pair(_23894, _23890)), _23896 = _23894, _23892 = _23890], (352 ^ _19026) ^ [_24039, _24041] : [_24041 = _24039, -(relation_dom(_24041) = relation_dom(_24039))], (358 ^ _19026) ^ [_24124, _24126, _24128, _24130] : [-(relation_composition(_24130, _24126) = relation_composition(_24128, _24124)), _24130 = _24128, _24126 = _24124], (368 ^ _19026) ^ [_24269, _24271, _24273, _24275] : [-(apply(_24275, _24271) = apply(_24273, _24269)), _24275 = _24273, _24271 = _24269], (378 ^ _19026) ^ [_24510, _24512] : [in(_24512, _24510), in(_24510, _24512)], (384 ^ _19026) ^ [_24588, _24590] : [proper_subset(_24590, _24588), proper_subset(_24588, _24590)], (390 ^ _19026) ^ [_24666] : [empty(_24666), -(function(_24666))], (396 ^ _19026) ^ [_24737] : [empty(_24737), -(relation(_24737))], (402 ^ _19026) ^ [_24808, _24810] : [-(unordered_pair(_24810, _24808) = unordered_pair(_24808, _24810))], (404 ^ _19026) ^ [_24839, _24841] : [-(set_union2(_24841, _24839) = set_union2(_24839, _24841))], (406 ^ _19026) ^ [_24870, _24872] : [-(set_intersection2(_24872, _24870) = set_intersection2(_24870, _24872))], (408 ^ _19026) ^ [_24901, _24903] : [relation(_24901), 411 ^ _19026 : [(434 ^ _19026) ^ [] : [-(_24901 = identity_relation(_24903)), 447 ^ _19026 : [(448 ^ _19026) ^ [] : [-(in(435 ^ [_24901, _24903], _24903))], (450 ^ _19026) ^ [] : [-(435 ^ [_24901, _24903] = 436 ^ [_24901, _24903])], (452 ^ _19026) ^ [] : [in(ordered_pair(435 ^ [_24901, _24903], 436 ^ [_24901, _24903]), _24901)]], 439 ^ _19026 : [(440 ^ _19026) ^ [] : [-(in(ordered_pair(435 ^ [_24901, _24903], 436 ^ [_24901, _24903]), _24901))], (442 ^ _19026) ^ [] : [in(435 ^ [_24901, _24903], _24903), 435 ^ [_24901, _24903] = 436 ^ [_24901, _24903]]]], (412 ^ _19026) ^ [] : [_24901 = identity_relation(_24903), 415 ^ _19026 : [(416 ^ _19026) ^ [_25054, _25056] : [in(ordered_pair(_25056, _25054), _24901), 419 ^ _19026 : [(420 ^ _19026) ^ [] : [-(in(_25056, _24903))], (422 ^ _19026) ^ [] : [-(_25056 = _25054)]]], (424 ^ _19026) ^ [_25163, _25165] : [-(in(ordered_pair(_25165, _25163), _24901)), in(_25165, _24903), _25165 = _25163]]]]], (456 ^ _19026) ^ [_25690, _25692] : [_25692 = _25690, 459 ^ _19026 : [(460 ^ _19026) ^ [] : [-(subset(_25692, _25690))], (462 ^ _19026) ^ [] : [-(subset(_25690, _25692))]]], (464 ^ _19026) ^ [_25789, _25791] : [-(_25791 = _25789), subset(_25791, _25789), subset(_25789, _25791)], (474 ^ _19026) ^ [_25920] : [relation(_25920), 477 ^ _19026 : [(478 ^ _19026) ^ [_26020, _26022] : [relation(_26020), 481 ^ _19026 : [(504 ^ _19026) ^ [] : [-(_26020 = relation_dom_restriction(_25920, _26022)), 517 ^ _19026 : [(518 ^ _19026) ^ [] : [-(in(505 ^ [_25920, _26020, _26022], _26022))], (520 ^ _19026) ^ [] : [-(in(ordered_pair(505 ^ [_25920, _26020, _26022], 506 ^ [_25920, _26020, _26022]), _25920))], (522 ^ _19026) ^ [] : [in(ordered_pair(505 ^ [_25920, _26020, _26022], 506 ^ [_25920, _26020, _26022]), _26020)]], 509 ^ _19026 : [(510 ^ _19026) ^ [] : [-(in(ordered_pair(505 ^ [_25920, _26020, _26022], 506 ^ [_25920, _26020, _26022]), _26020))], (512 ^ _19026) ^ [] : [in(505 ^ [_25920, _26020, _26022], _26022), in(ordered_pair(505 ^ [_25920, _26020, _26022], 506 ^ [_25920, _26020, _26022]), _25920)]]], (482 ^ _19026) ^ [] : [_26020 = relation_dom_restriction(_25920, _26022), 485 ^ _19026 : [(486 ^ _19026) ^ [_26182, _26184] : [in(ordered_pair(_26184, _26182), _26020), 489 ^ _19026 : [(490 ^ _19026) ^ [] : [-(in(_26184, _26022))], (492 ^ _19026) ^ [] : [-(in(ordered_pair(_26184, _26182), _25920))]]], (494 ^ _19026) ^ [_26299, _26301] : [-(in(ordered_pair(_26301, _26299), _26020)), in(_26301, _26022), in(ordered_pair(_26301, _26299), _25920)]]]]]]], (526 ^ _19026) ^ [_26869, _26871] : [relation(_26869), 529 ^ _19026 : [(530 ^ _19026) ^ [_26966] : [relation(_26966), 533 ^ _19026 : [(556 ^ _19026) ^ [] : [-(_26966 = relation_rng_restriction(_26871, _26869)), 569 ^ _19026 : [(570 ^ _19026) ^ [] : [-(in(558 ^ [_26869, _26871, _26966], _26871))], (572 ^ _19026) ^ [] : [-(in(ordered_pair(557 ^ [_26869, _26871, _26966], 558 ^ [_26869, _26871, _26966]), _26869))], (574 ^ _19026) ^ [] : [in(ordered_pair(557 ^ [_26869, _26871, _26966], 558 ^ [_26869, _26871, _26966]), _26966)]], 561 ^ _19026 : [(562 ^ _19026) ^ [] : [-(in(ordered_pair(557 ^ [_26869, _26871, _26966], 558 ^ [_26869, _26871, _26966]), _26966))], (564 ^ _19026) ^ [] : [in(558 ^ [_26869, _26871, _26966], _26871), in(ordered_pair(557 ^ [_26869, _26871, _26966], 558 ^ [_26869, _26871, _26966]), _26869)]]], (534 ^ _19026) ^ [] : [_26966 = relation_rng_restriction(_26871, _26869), 537 ^ _19026 : [(538 ^ _19026) ^ [_27128, _27130] : [in(ordered_pair(_27130, _27128), _26966), 541 ^ _19026 : [(542 ^ _19026) ^ [] : [-(in(_27128, _26871))], (544 ^ _19026) ^ [] : [-(in(ordered_pair(_27130, _27128), _26869))]]], (546 ^ _19026) ^ [_27245, _27247] : [-(in(ordered_pair(_27247, _27245), _26966)), in(_27245, _26871), in(ordered_pair(_27247, _27245), _26869)]]]]]]], (578 ^ _19026) ^ [_27806] : [relation(_27806), 581 ^ _19026 : [(605 ^ _19026) ^ [_28311, _28313] : [-(_28311 = relation_image(_27806, _28313)), 618 ^ _19026 : [(619 ^ _19026) ^ [] : [-(in(ordered_pair(617 ^ [_27806, _28311, _28313], 606 ^ [_27806, _28311, _28313]), _27806))], (621 ^ _19026) ^ [] : [-(in(617 ^ [_27806, _28311, _28313], _28313))], (623 ^ _19026) ^ [] : [in(606 ^ [_27806, _28311, _28313], _28311)]], 609 ^ _19026 : [(610 ^ _19026) ^ [] : [-(in(606 ^ [_27806, _28311, _28313], _28311))], (612 ^ _19026) ^ [_28459] : [in(ordered_pair(_28459, 606 ^ [_27806, _28311, _28313]), _27806), in(_28459, _28313)]]], (582 ^ _19026) ^ [_27913, _27915] : [_27913 = relation_image(_27806, _27915), 585 ^ _19026 : [(586 ^ _19026) ^ [_28010] : [in(_28010, _27913), 590 ^ _19026 : [(591 ^ _19026) ^ [] : [-(in(ordered_pair(589 ^ [_27806, _27913, _27915, _28010], _28010), _27806))], (593 ^ _19026) ^ [] : [-(in(589 ^ [_27806, _27913, _27915, _28010], _27915))]]], (595 ^ _19026) ^ [_28146] : [-(in(_28146, _27913)), 596 ^ _19026 : [(597 ^ _19026) ^ [_28193] : [in(ordered_pair(_28193, _28146), _27806), in(_28193, _27915)]]]]]]], (627 ^ _19026) ^ [_28713] : [relation(_28713), 630 ^ _19026 : [(654 ^ _19026) ^ [_29218, _29220] : [-(_29218 = relation_inverse_image(_28713, _29220)), 667 ^ _19026 : [(668 ^ _19026) ^ [] : [-(in(ordered_pair(655 ^ [_28713, _29218, _29220], 666 ^ [_28713, _29218, _29220]), _28713))], (670 ^ _19026) ^ [] : [-(in(666 ^ [_28713, _29218, _29220], _29220))], (672 ^ _19026) ^ [] : [in(655 ^ [_28713, _29218, _29220], _29218)]], 658 ^ _19026 : [(659 ^ _19026) ^ [] : [-(in(655 ^ [_28713, _29218, _29220], _29218))], (661 ^ _19026) ^ [_29366] : [in(ordered_pair(655 ^ [_28713, _29218, _29220], _29366), _28713), in(_29366, _29220)]]], (631 ^ _19026) ^ [_28820, _28822] : [_28820 = relation_inverse_image(_28713, _28822), 634 ^ _19026 : [(635 ^ _19026) ^ [_28917] : [in(_28917, _28820), 639 ^ _19026 : [(640 ^ _19026) ^ [] : [-(in(ordered_pair(_28917, 638 ^ [_28713, _28820, _28822, _28917]), _28713))], (642 ^ _19026) ^ [] : [-(in(638 ^ [_28713, _28820, _28822, _28917], _28822))]]], (644 ^ _19026) ^ [_29053] : [-(in(_29053, _28820)), 645 ^ _19026 : [(646 ^ _19026) ^ [_29100] : [in(ordered_pair(_29053, _29100), _28713), in(_29100, _28822)]]]]]]], (688 ^ _19026) ^ [_29817] : [690 ^ _19026 : [(691 ^ _19026) ^ [] : [-(in(689 ^ [_29817], _29817))], (693 ^ _19026) ^ [_29930, _29932] : [689 ^ [_29817] = ordered_pair(_29932, _29930)]], -(relation(_29817))], (676 ^ _19026) ^ [_29632] : [relation(_29632), 679 ^ _19026 : [(680 ^ _19026) ^ [_29708] : [in(_29708, _29632), -(_29708 = ordered_pair(683 ^ [_29632, _29708], 684 ^ [_29632, _29708]))]]], (746 ^ _19026) ^ [_30795, _30797] : [_30797 = empty_set, 749 ^ _19026 : [(750 ^ _19026) ^ [] : [_30795 = set_meet(_30797), -(_30795 = empty_set)], (756 ^ _19026) ^ [] : [_30795 = empty_set, -(_30795 = set_meet(_30797))]]], (697 ^ _19026) ^ [_30002, _30004] : [-(_30004 = empty_set), 700 ^ _19026 : [(724 ^ _19026) ^ [] : [-(_30002 = set_meet(_30004)), 728 ^ _19026 : [(729 ^ _19026) ^ [] : [-(in(725 ^ [_30002, _30004], _30002))], (732 ^ _19026) ^ [] : [-(in(730 ^ [_30002, _30004], _30004))], (734 ^ _19026) ^ [] : [in(725 ^ [_30002, _30004], 730 ^ [_30002, _30004])]], 735 ^ _19026 : [(742 ^ _19026) ^ [] : [in(725 ^ [_30002, _30004], _30002)], (736 ^ _19026) ^ [_30639] : [in(_30639, _30004), -(in(725 ^ [_30002, _30004], _30639))]]], (701 ^ _19026) ^ [] : [_30002 = set_meet(_30004), 704 ^ _19026 : [(715 ^ _19026) ^ [_30295] : [717 ^ _19026 : [(718 ^ _19026) ^ [] : [-(in(716 ^ [_30002, _30004, _30295], _30004))], (720 ^ _19026) ^ [] : [in(_30295, 716 ^ [_30002, _30004, _30295])]], -(in(_30295, _30002))], (705 ^ _19026) ^ [_30149] : [in(_30149, _30002), 708 ^ _19026 : [(709 ^ _19026) ^ [_30214] : [in(_30214, _30004), -(in(_30149, _30214))]]]]]]], (778 ^ _19026) ^ [_31260, _31262] : [-(_31260 = singleton(_31262)), 782 ^ _19026 : [(783 ^ _19026) ^ [] : [-(in(779 ^ [_31260, _31262], _31260))], (785 ^ _19026) ^ [] : [779 ^ [_31260, _31262] = _31262]], 786 ^ _19026 : [(787 ^ _19026) ^ [] : [-(779 ^ [_31260, _31262] = _31262)], (789 ^ _19026) ^ [] : [in(779 ^ [_31260, _31262], _31260)]]], (762 ^ _19026) ^ [_31025, _31027] : [_31025 = singleton(_31027), 765 ^ _19026 : [(766 ^ _19026) ^ [_31104] : [in(_31104, _31025), -(_31104 = _31027)], (772 ^ _19026) ^ [_31179] : [_31179 = _31027, -(in(_31179, _31025))]]], (793 ^ _19026) ^ [_31514] : [_31514 = empty_set, 796 ^ _19026 : [(797 ^ _19026) ^ [_31575] : [in(_31575, _31514)]]], (799 ^ _19026) ^ [_31596] : [-(in(800 ^ [_31596], _31596)), -(_31596 = empty_set)], (822 ^ _19026) ^ [_31887, _31889] : [-(_31887 = powerset(_31889)), 826 ^ _19026 : [(827 ^ _19026) ^ [] : [-(in(823 ^ [_31887, _31889], _31887))], (829 ^ _19026) ^ [] : [subset(823 ^ [_31887, _31889], _31889)]], 830 ^ _19026 : [(831 ^ _19026) ^ [] : [-(subset(823 ^ [_31887, _31889], _31889))], (833 ^ _19026) ^ [] : [in(823 ^ [_31887, _31889], _31887)]]], (806 ^ _19026) ^ [_31652, _31654] : [_31652 = powerset(_31654), 809 ^ _19026 : [(810 ^ _19026) ^ [_31731] : [in(_31731, _31652), -(subset(_31731, _31654))], (816 ^ _19026) ^ [_31806] : [subset(_31806, _31654), -(in(_31806, _31652))]]], (837 ^ _19026) ^ [_32129] : [relation(_32129), 840 ^ _19026 : [(841 ^ _19026) ^ [_32215] : [relation(_32215), 844 ^ _19026 : [(861 ^ _19026) ^ [] : [-(_32129 = _32215), 866 ^ _19026 : [(867 ^ _19026) ^ [] : [-(in(ordered_pair(862 ^ [_32129, _32215], 863 ^ [_32129, _32215]), _32129))], (869 ^ _19026) ^ [] : [in(ordered_pair(862 ^ [_32129, _32215], 863 ^ [_32129, _32215]), _32215)]], 870 ^ _19026 : [(871 ^ _19026) ^ [] : [-(in(ordered_pair(862 ^ [_32129, _32215], 863 ^ [_32129, _32215]), _32215))], (873 ^ _19026) ^ [] : [in(ordered_pair(862 ^ [_32129, _32215], 863 ^ [_32129, _32215]), _32129)]]], (845 ^ _19026) ^ [] : [_32129 = _32215, 848 ^ _19026 : [(849 ^ _19026) ^ [_32361, _32363] : [in(ordered_pair(_32363, _32361), _32129), -(in(ordered_pair(_32363, _32361), _32215))], (855 ^ _19026) ^ [_32450, _32452] : [in(ordered_pair(_32452, _32450), _32215), -(in(ordered_pair(_32452, _32450), _32129))]]]]]]], (877 ^ _19026) ^ [_32840, _32842] : [-(empty(_32842)), 880 ^ _19026 : [(881 ^ _19026) ^ [] : [element(_32840, _32842), -(in(_32840, _32842))], (887 ^ _19026) ^ [] : [in(_32840, _32842), -(element(_32840, _32842))]]], (893 ^ _19026) ^ [_33040, _33042] : [empty(_33042), 896 ^ _19026 : [(897 ^ _19026) ^ [] : [element(_33040, _33042), -(empty(_33040))], (903 ^ _19026) ^ [] : [empty(_33040), -(element(_33040, _33042))]]], (931 ^ _19026) ^ [_33562, _33564, _33566] : [-(_33562 = unordered_pair(_33566, _33564)), 935 ^ _19026 : [(936 ^ _19026) ^ [] : [-(in(932 ^ [_33562, _33564, _33566], _33562))], (938 ^ _19026) ^ [] : [932 ^ [_33562, _33564, _33566] = _33566], (940 ^ _19026) ^ [] : [932 ^ [_33562, _33564, _33566] = _33564]], 941 ^ _19026 : [(948 ^ _19026) ^ [] : [in(932 ^ [_33562, _33564, _33566], _33562)], (942 ^ _19026) ^ [] : [-(932 ^ [_33562, _33564, _33566] = _33566), -(932 ^ [_33562, _33564, _33566] = _33564)]]], (909 ^ _19026) ^ [_33262, _33264, _33266] : [_33262 = unordered_pair(_33266, _33264), 912 ^ _19026 : [(923 ^ _19026) ^ [_33441] : [924 ^ _19026 : [(925 ^ _19026) ^ [] : [_33441 = _33266], (927 ^ _19026) ^ [] : [_33441 = _33264]], -(in(_33441, _33262))], (913 ^ _19026) ^ [_33351] : [in(_33351, _33262), -(_33351 = _33266), -(_33351 = _33264)]]], (974 ^ _19026) ^ [_34202, _34204, _34206] : [-(_34202 = set_union2(_34206, _34204)), 978 ^ _19026 : [(979 ^ _19026) ^ [] : [-(in(975 ^ [_34202, _34204, _34206], _34202))], (981 ^ _19026) ^ [] : [in(975 ^ [_34202, _34204, _34206], _34206)], (983 ^ _19026) ^ [] : [in(975 ^ [_34202, _34204, _34206], _34204)]], 984 ^ _19026 : [(991 ^ _19026) ^ [] : [in(975 ^ [_34202, _34204, _34206], _34202)], (985 ^ _19026) ^ [] : [-(in(975 ^ [_34202, _34204, _34206], _34206)), -(in(975 ^ [_34202, _34204, _34206], _34204))]]], (952 ^ _19026) ^ [_33902, _33904, _33906] : [_33902 = set_union2(_33906, _33904), 955 ^ _19026 : [(966 ^ _19026) ^ [_34081] : [967 ^ _19026 : [(968 ^ _19026) ^ [] : [in(_34081, _33906)], (970 ^ _19026) ^ [] : [in(_34081, _33904)]], -(in(_34081, _33902))], (956 ^ _19026) ^ [_33991] : [in(_33991, _33902), -(in(_33991, _33906)), -(in(_33991, _33904))]]], (1025 ^ _19026) ^ [_35075, _35077, _35079] : [-(_35075 = cartesian_product2(_35079, _35077)), 1043 ^ _19026 : [(1044 ^ _19026) ^ [] : [-(in(1041 ^ [_35075, _35077, _35079], _35079))], (1046 ^ _19026) ^ [] : [-(in(1042 ^ [_35075, _35077, _35079], _35077))], (1048 ^ _19026) ^ [] : [-(1026 ^ [_35075, _35077, _35079] = ordered_pair(1041 ^ [_35075, _35077, _35079], 1042 ^ [_35075, _35077, _35079]))], (1050 ^ _19026) ^ [] : [in(1026 ^ [_35075, _35077, _35079], _35075)]], 1029 ^ _19026 : [(1030 ^ _19026) ^ [] : [-(in(1026 ^ [_35075, _35077, _35079], _35075))], (1032 ^ _19026) ^ [_35245, _35247] : [in(_35247, _35079), in(_35245, _35077), 1026 ^ [_35075, _35077, _35079] = ordered_pair(_35247, _35245)]]], (995 ^ _19026) ^ [_34542, _34544, _34546] : [_34542 = cartesian_product2(_34546, _34544), 998 ^ _19026 : [(999 ^ _19026) ^ [_34650] : [in(_34650, _34542), 1004 ^ _19026 : [(1005 ^ _19026) ^ [] : [-(in(1002 ^ [_34542, _34544, _34546, _34650], _34546))], (1007 ^ _19026) ^ [] : [-(in(1003 ^ [_34542, _34544, _34546, _34650], _34544))], (1009 ^ _19026) ^ [] : [-(_34650 = ordered_pair(1002 ^ [_34542, _34544, _34546, _34650], 1003 ^ [_34542, _34544, _34546, _34650]))]]], (1011 ^ _19026) ^ [_34837] : [-(in(_34837, _34542)), 1012 ^ _19026 : [(1013 ^ _19026) ^ [_34895, _34897] : [in(_34897, _34546), in(_34895, _34544), _34837 = ordered_pair(_34897, _34895)]]]]], (1054 ^ _19026) ^ [_35593] : [relation(_35593), 1057 ^ _19026 : [(1058 ^ _19026) ^ [_35679] : [relation(_35679), 1061 ^ _19026 : [(1072 ^ _19026) ^ [] : [1075 ^ _19026 : [(1076 ^ _19026) ^ [] : [-(in(ordered_pair(1073 ^ [_35593, _35679], 1074 ^ [_35593, _35679]), _35593))], (1078 ^ _19026) ^ [] : [in(ordered_pair(1073 ^ [_35593, _35679], 1074 ^ [_35593, _35679]), _35679)]], -(subset(_35593, _35679))], (1062 ^ _19026) ^ [] : [subset(_35593, _35679), 1065 ^ _19026 : [(1066 ^ _19026) ^ [_35810, _35812] : [in(ordered_pair(_35812, _35810), _35593), -(in(ordered_pair(_35812, _35810), _35679))]]]]]]], (1092 ^ _19026) ^ [_36223, _36225] : [1094 ^ _19026 : [(1095 ^ _19026) ^ [] : [-(in(1093 ^ [_36223, _36225], _36225))], (1097 ^ _19026) ^ [] : [in(1093 ^ [_36223, _36225], _36223)]], -(subset(_36225, _36223))], (1082 ^ _19026) ^ [_36081, _36083] : [subset(_36083, _36081), 1085 ^ _19026 : [(1086 ^ _19026) ^ [_36144] : [in(_36144, _36083), -(in(_36144, _36081))]]], (1123 ^ _19026) ^ [_36714, _36716, _36718] : [-(_36714 = set_intersection2(_36718, _36716)), 1135 ^ _19026 : [(1136 ^ _19026) ^ [] : [-(in(1124 ^ [_36714, _36716, _36718], _36718))], (1138 ^ _19026) ^ [] : [-(in(1124 ^ [_36714, _36716, _36718], _36716))], (1140 ^ _19026) ^ [] : [in(1124 ^ [_36714, _36716, _36718], _36714)]], 1127 ^ _19026 : [(1128 ^ _19026) ^ [] : [-(in(1124 ^ [_36714, _36716, _36718], _36714))], (1130 ^ _19026) ^ [] : [in(1124 ^ [_36714, _36716, _36718], _36718), in(1124 ^ [_36714, _36716, _36718], _36716)]]], (1101 ^ _19026) ^ [_36383, _36385, _36387] : [_36383 = set_intersection2(_36387, _36385), 1104 ^ _19026 : [(1105 ^ _19026) ^ [_36472] : [in(_36472, _36383), 1108 ^ _19026 : [(1109 ^ _19026) ^ [] : [-(in(_36472, _36387))], (1111 ^ _19026) ^ [] : [-(in(_36472, _36385))]]], (1113 ^ _19026) ^ [_36575] : [-(in(_36575, _36383)), in(_36575, _36387), in(_36575, _36385)]]], (1144 ^ _19026) ^ [_37068] : [relation(_37068), function(_37068), 1151 ^ _19026 : [(1152 ^ _19026) ^ [_37228, _37230] : [in(_37230, relation_dom(_37068)), 1155 ^ _19026 : [(1156 ^ _19026) ^ [] : [_37228 = apply(_37068, _37230), -(in(ordered_pair(_37230, _37228), _37068))], (1162 ^ _19026) ^ [] : [in(ordered_pair(_37230, _37228), _37068), -(_37228 = apply(_37068, _37230))]]], (1168 ^ _19026) ^ [_37458, _37460] : [-(in(_37460, relation_dom(_37068))), 1171 ^ _19026 : [(1172 ^ _19026) ^ [] : [_37458 = apply(_37068, _37460), -(_37458 = empty_set)], (1178 ^ _19026) ^ [] : [_37458 = empty_set, -(_37458 = apply(_37068, _37460))]]]]], (1184 ^ _19026) ^ [_37689] : [relation(_37689), 1187 ^ _19026 : [(1205 ^ _19026) ^ [_38063] : [-(_38063 = relation_dom(_37689)), 1209 ^ _19026 : [(1210 ^ _19026) ^ [] : [-(in(1206 ^ [_37689, _38063], _38063))], (1212 ^ _19026) ^ [_38197] : [in(ordered_pair(1206 ^ [_37689, _38063], _38197), _37689)]], 1214 ^ _19026 : [(1215 ^ _19026) ^ [] : [-(in(ordered_pair(1206 ^ [_37689, _38063], 1213 ^ [_37689, _38063]), _37689))], (1217 ^ _19026) ^ [] : [in(1206 ^ [_37689, _38063], _38063)]]], (1188 ^ _19026) ^ [_37781] : [_37781 = relation_dom(_37689), 1191 ^ _19026 : [(1192 ^ _19026) ^ [_37868] : [in(_37868, _37781), -(in(ordered_pair(_37868, 1195 ^ [_37689, _37781, _37868]), _37689))], (1199 ^ _19026) ^ [_37963] : [1200 ^ _19026 : [(1201 ^ _19026) ^ [_38007] : [in(ordered_pair(_37963, _38007), _37689)]], -(in(_37963, _37781))]]]]], (1221 ^ _19026) ^ [_38344] : [-(cast_to_subset(_38344) = _38344)], (1246 ^ _19026) ^ [_38750, _38752] : [-(_38750 = union(_38752)), 1259 ^ _19026 : [(1260 ^ _19026) ^ [] : [-(in(1247 ^ [_38750, _38752], 1258 ^ [_38750, _38752]))], (1262 ^ _19026) ^ [] : [-(in(1258 ^ [_38750, _38752], _38752))], (1264 ^ _19026) ^ [] : [in(1247 ^ [_38750, _38752], _38750)]], 1250 ^ _19026 : [(1251 ^ _19026) ^ [] : [-(in(1247 ^ [_38750, _38752], _38750))], (1253 ^ _19026) ^ [_38883] : [in(1247 ^ [_38750, _38752], _38883), in(_38883, _38752)]]], (1223 ^ _19026) ^ [_38384, _38386] : [_38384 = union(_38386), 1226 ^ _19026 : [(1227 ^ _19026) ^ [_38474] : [in(_38474, _38384), 1231 ^ _19026 : [(1232 ^ _19026) ^ [] : [-(in(_38474, 1230 ^ [_38384, _38386, _38474]))], (1234 ^ _19026) ^ [] : [-(in(1230 ^ [_38384, _38386, _38474], _38386))]]], (1236 ^ _19026) ^ [_38598] : [-(in(_38598, _38384)), 1237 ^ _19026 : [(1238 ^ _19026) ^ [_38640] : [in(_38598, _38640), in(_38640, _38386)]]]]], (1290 ^ _19026) ^ [_39471, _39473, _39475] : [-(_39471 = set_difference(_39475, _39473)), 1302 ^ _19026 : [(1303 ^ _19026) ^ [] : [-(in(1291 ^ [_39471, _39473, _39475], _39475))], (1305 ^ _19026) ^ [] : [in(1291 ^ [_39471, _39473, _39475], _39473)], (1307 ^ _19026) ^ [] : [in(1291 ^ [_39471, _39473, _39475], _39471)]], 1294 ^ _19026 : [(1295 ^ _19026) ^ [] : [-(in(1291 ^ [_39471, _39473, _39475], _39471))], (1297 ^ _19026) ^ [] : [in(1291 ^ [_39471, _39473, _39475], _39475), -(in(1291 ^ [_39471, _39473, _39475], _39473))]]], (1268 ^ _19026) ^ [_39127, _39129, _39131] : [_39127 = set_difference(_39131, _39129), 1271 ^ _19026 : [(1272 ^ _19026) ^ [_39218] : [in(_39218, _39127), 1275 ^ _19026 : [(1276 ^ _19026) ^ [] : [-(in(_39218, _39131))], (1278 ^ _19026) ^ [] : [in(_39218, _39129)]]], (1280 ^ _19026) ^ [_39329] : [-(in(_39329, _39127)), in(_39329, _39131), -(in(_39329, _39129))]]], (1311 ^ _19026) ^ [_39837] : [relation(_39837), 1314 ^ _19026 : [(1332 ^ _19026) ^ [_40211] : [-(_40211 = relation_rng(_39837)), 1336 ^ _19026 : [(1337 ^ _19026) ^ [] : [-(in(1333 ^ [_39837, _40211], _40211))], (1339 ^ _19026) ^ [_40345] : [in(ordered_pair(_40345, 1333 ^ [_39837, _40211]), _39837)]], 1341 ^ _19026 : [(1342 ^ _19026) ^ [] : [-(in(ordered_pair(1340 ^ [_39837, _40211], 1333 ^ [_39837, _40211]), _39837))], (1344 ^ _19026) ^ [] : [in(1333 ^ [_39837, _40211], _40211)]]], (1315 ^ _19026) ^ [_39929] : [_39929 = relation_rng(_39837), 1318 ^ _19026 : [(1319 ^ _19026) ^ [_40016] : [in(_40016, _39929), -(in(ordered_pair(1322 ^ [_39837, _39929, _40016], _40016), _39837))], (1326 ^ _19026) ^ [_40111] : [1327 ^ _19026 : [(1328 ^ _19026) ^ [_40155] : [in(ordered_pair(_40155, _40111), _39837)]], -(in(_40111, _39929))]]]]], (1348 ^ _19026) ^ [_40492, _40494] : [element(_40492, powerset(_40494)), -(subset_complement(_40494, _40492) = set_difference(_40494, _40492))], (1354 ^ _19026) ^ [_40585, _40587] : [-(ordered_pair(_40587, _40585) = unordered_pair(unordered_pair(_40587, _40585), singleton(_40587)))], (1356 ^ _19026) ^ [_40621] : [relation(_40621), -(relation_field(_40621) = set_union2(relation_dom(_40621), relation_rng(_40621)))], (1362 ^ _19026) ^ [_40712] : [relation(_40712), 1365 ^ _19026 : [(1366 ^ _19026) ^ [_40800] : [relation(_40800), 1369 ^ _19026 : [(1386 ^ _19026) ^ [] : [-(_40800 = relation_inverse(_40712)), 1391 ^ _19026 : [(1392 ^ _19026) ^ [] : [-(in(ordered_pair(1387 ^ [_40712, _40800], 1388 ^ [_40712, _40800]), _40800))], (1394 ^ _19026) ^ [] : [in(ordered_pair(1388 ^ [_40712, _40800], 1387 ^ [_40712, _40800]), _40712)]], 1395 ^ _19026 : [(1396 ^ _19026) ^ [] : [-(in(ordered_pair(1388 ^ [_40712, _40800], 1387 ^ [_40712, _40800]), _40712))], (1398 ^ _19026) ^ [] : [in(ordered_pair(1387 ^ [_40712, _40800], 1388 ^ [_40712, _40800]), _40800)]]], (1370 ^ _19026) ^ [] : [_40800 = relation_inverse(_40712), 1373 ^ _19026 : [(1374 ^ _19026) ^ [_40950, _40952] : [in(ordered_pair(_40952, _40950), _40800), -(in(ordered_pair(_40950, _40952), _40712))], (1380 ^ _19026) ^ [_41039, _41041] : [in(ordered_pair(_41039, _41041), _40712), -(in(ordered_pair(_41041, _41039), _40800))]]]]]]], (1402 ^ _19026) ^ [_41438, _41440] : [disjoint(_41440, _41438), -(set_intersection2(_41440, _41438) = empty_set)], (1408 ^ _19026) ^ [_41517, _41519] : [set_intersection2(_41519, _41517) = empty_set, -(disjoint(_41519, _41517))], (1414 ^ _19026) ^ [_41602] : [relation(_41602), 1417 ^ _19026 : [(1418 ^ _19026) ^ [_41715] : [relation(_41715), 1421 ^ _19026 : [(1422 ^ _19026) ^ [_41820] : [relation(_41820), 1425 ^ _19026 : [(1449 ^ _19026) ^ [] : [-(_41820 = relation_composition(_41602, _41715)), 1463 ^ _19026 : [(1464 ^ _19026) ^ [] : [-(in(ordered_pair(1450 ^ [_41602, _41715, _41820], 1462 ^ [_41602, _41715, _41820]), _41602))], (1466 ^ _19026) ^ [] : [-(in(ordered_pair(1462 ^ [_41602, _41715, _41820], 1451 ^ [_41602, _41715, _41820]), _41715))], (1468 ^ _19026) ^ [] : [in(ordered_pair(1450 ^ [_41602, _41715, _41820], 1451 ^ [_41602, _41715, _41820]), _41820)]], 1454 ^ _19026 : [(1455 ^ _19026) ^ [] : [-(in(ordered_pair(1450 ^ [_41602, _41715, _41820], 1451 ^ [_41602, _41715, _41820]), _41820))], (1457 ^ _19026) ^ [_42476] : [in(ordered_pair(1450 ^ [_41602, _41715, _41820], _42476), _41602), in(ordered_pair(_42476, 1451 ^ [_41602, _41715, _41820]), _41715)]]], (1426 ^ _19026) ^ [] : [_41820 = relation_composition(_41602, _41715), 1429 ^ _19026 : [(1430 ^ _19026) ^ [_41990, _41992] : [in(ordered_pair(_41992, _41990), _41820), 1434 ^ _19026 : [(1435 ^ _19026) ^ [] : [-(in(ordered_pair(_41992, 1433 ^ [_41602, _41715, _41820, _41990, _41992]), _41602))], (1437 ^ _19026) ^ [] : [-(in(ordered_pair(1433 ^ [_41602, _41715, _41820, _41990, _41992], _41990), _41715))]]], (1439 ^ _19026) ^ [_42144, _42146] : [-(in(ordered_pair(_42146, _42144), _41820)), 1440 ^ _19026 : [(1441 ^ _19026) ^ [_42199] : [in(ordered_pair(_42146, _42199), _41602), in(ordered_pair(_42199, _42144), _41715)]]]]]]]]]]], (1472 ^ _19026) ^ [_42786, _42788] : [element(_42786, powerset(powerset(_42788))), 1475 ^ _19026 : [(1476 ^ _19026) ^ [_42892] : [element(_42892, powerset(powerset(_42788))), 1479 ^ _19026 : [(1500 ^ _19026) ^ [] : [-(_42892 = complements_of_subsets(_42788, _42786)), 1502 ^ _19026 : [(1503 ^ _19026) ^ [] : [-(element(1501 ^ [_42786, _42788, _42892], powerset(_42788)))], (1505 ^ _19026) ^ [] : [1506 ^ _19026 : [(1507 ^ _19026) ^ [] : [-(in(1501 ^ [_42786, _42788, _42892], _42892))], (1509 ^ _19026) ^ [] : [in(subset_complement(_42788, 1501 ^ [_42786, _42788, _42892]), _42786)]], 1510 ^ _19026 : [(1511 ^ _19026) ^ [] : [-(in(subset_complement(_42788, 1501 ^ [_42786, _42788, _42892]), _42786))], (1513 ^ _19026) ^ [] : [in(1501 ^ [_42786, _42788, _42892], _42892)]]]]], (1480 ^ _19026) ^ [] : [_42892 = complements_of_subsets(_42788, _42786), 1483 ^ _19026 : [(1484 ^ _19026) ^ [_43043] : [element(_43043, powerset(_42788)), 1487 ^ _19026 : [(1488 ^ _19026) ^ [] : [in(_43043, _42892), -(in(subset_complement(_42788, _43043), _42786))], (1494 ^ _19026) ^ [] : [in(subset_complement(_42788, _43043), _42786), -(in(_43043, _42892))]]]]]]]]], (1517 ^ _19026) ^ [_43583, _43585] : [proper_subset(_43585, _43583), 1520 ^ _19026 : [(1521 ^ _19026) ^ [] : [-(subset(_43585, _43583))], (1523 ^ _19026) ^ [] : [_43585 = _43583]]], (1525 ^ _19026) ^ [_43690, _43692] : [-(proper_subset(_43692, _43690)), subset(_43692, _43690), -(_43692 = _43690)], (1535 ^ _19026) ^ [] : [true___, -(true___)], (1541 ^ _19026) ^ [] : [true___, -(true___)], (1547 ^ _19026) ^ [] : [true___, -(true___)], (1553 ^ _19026) ^ [] : [true___, -(true___)], (1559 ^ _19026) ^ [] : [true___, -(true___)], (1565 ^ _19026) ^ [] : [true___, -(true___)], (1571 ^ _19026) ^ [] : [true___, -(true___)], (1577 ^ _19026) ^ [] : [true___, -(true___)], (1583 ^ _19026) ^ [_44296] : [-(element(cast_to_subset(_44296), powerset(_44296)))], (1585 ^ _19026) ^ [] : [true___, -(true___)], (1591 ^ _19026) ^ [] : [true___, -(true___)], (1597 ^ _19026) ^ [] : [true___, -(true___)], (1603 ^ _19026) ^ [] : [true___, -(true___)], (1609 ^ _19026) ^ [_44559, _44561] : [element(_44559, powerset(_44561)), -(element(subset_complement(_44561, _44559), powerset(_44561)))], (1615 ^ _19026) ^ [] : [true___, -(true___)], (1621 ^ _19026) ^ [] : [true___, -(true___)], (1627 ^ _19026) ^ [_44768] : [relation(_44768), -(relation(relation_inverse(_44768)))], (1633 ^ _19026) ^ [] : [true___, -(true___)], (1639 ^ _19026) ^ [] : [true___, -(true___)], (1645 ^ _19026) ^ [_44961, _44963] : [-(relation(relation_composition(_44963, _44961))), relation(_44963), relation(_44961)], (1655 ^ _19026) ^ [_45090, _45092] : [element(_45090, powerset(powerset(_45092))), -(element(union_of_subsets(_45092, _45090), powerset(_45092)))], (1661 ^ _19026) ^ [_45185] : [-(relation(identity_relation(_45185)))], (1663 ^ _19026) ^ [_45209, _45211] : [element(_45209, powerset(powerset(_45211))), -(element(meet_of_subsets(_45211, _45209), powerset(_45211)))], (1669 ^ _19026) ^ [_45304, _45306, _45308] : [-(element(subset_difference(_45308, _45306, _45304), powerset(_45308))), element(_45306, powerset(_45308)), element(_45304, powerset(_45308))], (1679 ^ _19026) ^ [_45457, _45459] : [relation(_45459), -(relation(relation_dom_restriction(_45459, _45457)))], (1685 ^ _19026) ^ [_45536, _45538] : [element(_45536, powerset(powerset(_45538))), -(element(complements_of_subsets(_45538, _45536), powerset(powerset(_45538))))], (1691 ^ _19026) ^ [_45635, _45637] : [relation(_45635), -(relation(relation_rng_restriction(_45637, _45635)))], (1697 ^ _19026) ^ [] : [true___, -(true___)], (1703 ^ _19026) ^ [] : [true___, -(true___)], (1710 ^ _19026) ^ [_45832] : [-(element(1708 ^ [_45832], _45832))], (1712 ^ _19026) ^ [_45860, _45862] : [1719 ^ _19026 : [(1720 ^ _19026) ^ [] : [-(empty(relation_composition(_45860, _45862)))], (1722 ^ _19026) ^ [] : [-(relation(relation_composition(_45860, _45862)))]], empty(_45862), relation(_45860)], (1724 ^ _19026) ^ [] : [-(empty(empty_set))], (1726 ^ _19026) ^ [] : [-(relation(empty_set))], (1728 ^ _19026) ^ [] : [-(relation_empty_yielding(empty_set))], (1730 ^ _19026) ^ [_46067, _46069] : [1745 ^ _19026 : [(1746 ^ _19026) ^ [] : [-(relation(relation_composition(_46069, _46067)))], (1748 ^ _19026) ^ [] : [-(function(relation_composition(_46069, _46067)))]], relation(_46069), function(_46069), relation(_46067), function(_46067)], (1750 ^ _19026) ^ [_46326, _46328] : [-(relation(set_intersection2(_46328, _46326))), relation(_46328), relation(_46326)], (1760 ^ _19026) ^ [_46464] : [empty(powerset(_46464))], (1762 ^ _19026) ^ [] : [-(empty(empty_set))], (1764 ^ _19026) ^ [_46518, _46520] : [empty(ordered_pair(_46520, _46518))], (1766 ^ _19026) ^ [_46545, _46547] : [-(relation(set_union2(_46547, _46545))), relation(_46547), relation(_46545)], (1776 ^ _19026) ^ [_46683] : [empty(singleton(_46683))], (1778 ^ _19026) ^ [_46706, _46708] : [-(empty(_46708)), empty(set_union2(_46708, _46706))], (1784 ^ _19026) ^ [_46797, _46799] : [empty(unordered_pair(_46799, _46797))], (1786 ^ _19026) ^ [_46823, _46825] : [-(empty(_46825)), empty(set_union2(_46823, _46825))], (1792 ^ _19026) ^ [] : [-(empty(empty_set))], (1794 ^ _19026) ^ [] : [-(relation(empty_set))], (1796 ^ _19026) ^ [_46934, _46936] : [empty(cartesian_product2(_46936, _46934)), -(empty(_46936)), -(empty(_46934))], (1806 ^ _19026) ^ [_47019] : [empty(relation_dom(_47019)), -(empty(_47019)), relation(_47019)], (1816 ^ _19026) ^ [_47146] : [empty(relation_rng(_47146)), -(empty(_47146)), relation(_47146)], (1826 ^ _19026) ^ [_47273] : [empty(_47273), 1829 ^ _19026 : [(1830 ^ _19026) ^ [] : [-(empty(relation_dom(_47273)))], (1832 ^ _19026) ^ [] : [-(relation(relation_dom(_47273)))]]], (1834 ^ _19026) ^ [_47376] : [empty(_47376), 1837 ^ _19026 : [(1838 ^ _19026) ^ [] : [-(empty(relation_rng(_47376)))], (1840 ^ _19026) ^ [] : [-(relation(relation_rng(_47376)))]]], (1842 ^ _19026) ^ [_47479, _47481] : [1849 ^ _19026 : [(1850 ^ _19026) ^ [] : [-(empty(relation_composition(_47481, _47479)))], (1852 ^ _19026) ^ [] : [-(relation(relation_composition(_47481, _47479)))]], empty(_47481), relation(_47479)], (1854 ^ _19026) ^ [_47638, _47640] : [-(set_union2(_47640, _47640) = _47640)], (1856 ^ _19026) ^ [_47666, _47668] : [-(set_intersection2(_47668, _47668) = _47668)], (1858 ^ _19026) ^ [_47694, _47696] : [element(_47694, powerset(_47696)), -(subset_complement(_47696, subset_complement(_47696, _47694)) = _47694)], (1864 ^ _19026) ^ [_47787] : [relation(_47787), -(relation_inverse(relation_inverse(_47787)) = _47787)], (1870 ^ _19026) ^ [_47868, _47870] : [element(_47868, powerset(powerset(_47870))), -(complements_of_subsets(_47870, complements_of_subsets(_47870, _47868)) = _47868)], (1876 ^ _19026) ^ [_47977, _47979] : [proper_subset(_47979, _47979)], (1878 ^ _19026) ^ [_48011] : [singleton(_48011) = empty_set], (1880 ^ _19026) ^ [_48036, _48038] : [in(_48038, _48036), -(set_union2(singleton(_48038), _48036) = _48036)], (1886 ^ _19026) ^ [_48123, _48125] : [disjoint(singleton(_48125), _48123), in(_48125, _48123)], (1892 ^ _19026) ^ [_48199, _48201] : [-(in(_48201, _48199)), -(disjoint(singleton(_48201), _48199))], (1898 ^ _19026) ^ [_48252, _48254] : [subset(singleton(_48254), _48252), -(in(_48254, _48252))], (1904 ^ _19026) ^ [_48329, _48331] : [in(_48331, _48329), -(subset(singleton(_48331), _48329))], (1910 ^ _19026) ^ [_48427, _48429] : [set_difference(_48429, _48427) = empty_set, -(subset(_48429, _48427))], (1916 ^ _19026) ^ [_48506, _48508] : [subset(_48508, _48506), -(set_difference(_48508, _48506) = empty_set)], (1922 ^ _19026) ^ [_48591, _48593] : [element(_48591, powerset(_48593)), 1925 ^ _19026 : [(1926 ^ _19026) ^ [_48658] : [in(_48658, _48591), -(in(_48658, _48593))]]], (1932 ^ _19026) ^ [_48741, _48743, _48745] : [subset(_48745, _48743), -(in(_48741, _48745)), -(subset(_48745, set_difference(_48743, singleton(_48741))))], (1952 ^ _19026) ^ [_48952, _48954] : [1953 ^ _19026 : [(1954 ^ _19026) ^ [] : [_48954 = empty_set], (1956 ^ _19026) ^ [] : [_48954 = singleton(_48952)]], -(subset(_48954, singleton(_48952)))], (1942 ^ _19026) ^ [_48858, _48860] : [subset(_48860, singleton(_48858)), -(_48860 = empty_set), -(_48860 = singleton(_48858))], (1960 ^ _19026) ^ [_49077, _49079] : [in(_49079, _49077), -(subset(_49079, union(_49077)))], (1966 ^ _19026) ^ [_49179, _49181, _49183, _49185] : [in(ordered_pair(_49185, _49183), cartesian_product2(_49181, _49179)), 1969 ^ _19026 : [(1970 ^ _19026) ^ [] : [-(in(_49185, _49181))], (1972 ^ _19026) ^ [] : [-(in(_49183, _49179))]]], (1974 ^ _19026) ^ [_49294, _49296, _49298, _49300] : [-(in(ordered_pair(_49300, _49298), cartesian_product2(_49296, _49294))), in(_49300, _49296), in(_49298, _49294)], (1984 ^ _19026) ^ [_49445, _49447] : [1986 ^ _19026 : [(1987 ^ _19026) ^ [] : [-(in(1985 ^ [_49445, _49447], _49447))], (1989 ^ _19026) ^ [] : [in(1985 ^ [_49445, _49447], _49445)]], -(element(_49447, powerset(_49445)))], (1994 ^ _19026) ^ [] : [-(relation(1992 ^ []))], (1996 ^ _19026) ^ [] : [-(function(1992 ^ []))], (1999 ^ _19026) ^ [] : [-(empty(1997 ^ []))], (2001 ^ _19026) ^ [] : [-(relation(1997 ^ []))], (2003 ^ _19026) ^ [_49670] : [-(empty(_49670)), 2007 ^ _19026 : [(2008 ^ _19026) ^ [] : [-(element(2006 ^ [_49670], powerset(_49670)))], (2010 ^ _19026) ^ [] : [empty(2006 ^ [_49670])]]], (2013 ^ _19026) ^ [] : [-(empty(2011 ^ []))], (2016 ^ _19026) ^ [] : [empty(2014 ^ [])], (2018 ^ _19026) ^ [] : [-(relation(2014 ^ []))], (2021 ^ _19026) ^ [_49878] : [-(element(2019 ^ [_49878], powerset(_49878)))], (2023 ^ _19026) ^ [_49905] : [-(empty(2019 ^ [_49905]))], (2026 ^ _19026) ^ [] : [empty(2024 ^ [])], (2029 ^ _19026) ^ [] : [-(relation(2027 ^ []))], (2031 ^ _19026) ^ [] : [-(relation_empty_yielding(2027 ^ []))], (2033 ^ _19026) ^ [_50005, _50007] : [element(_50005, powerset(powerset(_50007))), -(union_of_subsets(_50007, _50005) = union(_50005))], (2039 ^ _19026) ^ [_50100, _50102] : [element(_50100, powerset(powerset(_50102))), -(meet_of_subsets(_50102, _50100) = set_meet(_50100))], (2045 ^ _19026) ^ [_50195, _50197, _50199] : [-(subset_difference(_50199, _50197, _50195) = set_difference(_50197, _50195)), element(_50197, powerset(_50199)), element(_50195, powerset(_50199))], (2055 ^ _19026) ^ [_50350, _50352] : [-(subset(_50352, _50352))], (2057 ^ _19026) ^ [_50375, _50377] : [disjoint(_50377, _50375), -(disjoint(_50375, _50377))], (2063 ^ _19026) ^ [_50473, _50475, _50477, _50479] : [in(ordered_pair(_50479, _50477), cartesian_product2(_50475, _50473)), 2066 ^ _19026 : [(2067 ^ _19026) ^ [] : [-(in(_50479, _50475))], (2069 ^ _19026) ^ [] : [-(in(_50477, _50473))]]], (2071 ^ _19026) ^ [_50588, _50590, _50592, _50594] : [-(in(ordered_pair(_50594, _50592), cartesian_product2(_50590, _50588))), in(_50594, _50590), in(_50592, _50588)], (2081 ^ _19026) ^ [_50739, _50741, _50743, _50745] : [unordered_pair(_50745, _50743) = unordered_pair(_50741, _50739), -(_50745 = _50741), -(_50745 = _50739)], (2091 ^ _19026) ^ [_50849, _50851, _50853] : [relation(_50849), 2094 ^ _19026 : [(2095 ^ _19026) ^ [] : [in(_50853, relation_rng(relation_rng_restriction(_50851, _50849))), 2098 ^ _19026 : [(2099 ^ _19026) ^ [] : [-(in(_50853, _50851))], (2101 ^ _19026) ^ [] : [-(in(_50853, relation_rng(_50849)))]]], (2103 ^ _19026) ^ [] : [-(in(_50853, relation_rng(relation_rng_restriction(_50851, _50849)))), in(_50853, _50851), in(_50853, relation_rng(_50849))]]], (2113 ^ _19026) ^ [_51155, _51157] : [relation(_51155), -(subset(relation_rng(relation_rng_restriction(_51157, _51155)), _51157))], (2119 ^ _19026) ^ [_51240, _51242] : [relation(_51240), -(subset(relation_rng_restriction(_51242, _51240), _51240))], (2125 ^ _19026) ^ [_51321, _51323] : [relation(_51321), -(subset(relation_rng(relation_rng_restriction(_51323, _51321)), relation_rng(_51321)))], (2131 ^ _19026) ^ [_51410, _51412, _51414] : [subset(_51414, _51412), 2134 ^ _19026 : [(2135 ^ _19026) ^ [] : [-(subset(cartesian_product2(_51414, _51410), cartesian_product2(_51412, _51410)))], (2137 ^ _19026) ^ [] : [-(subset(cartesian_product2(_51410, _51414), cartesian_product2(_51410, _51412)))]]], (2139 ^ _19026) ^ [_51539, _51541] : [relation(_51539), -(relation_rng(relation_rng_restriction(_51541, _51539)) = set_intersection2(relation_rng(_51539), _51541))], (2145 ^ _19026) ^ [_51634, _51636, _51638, _51640] : [-(subset(cartesian_product2(_51640, _51636), cartesian_product2(_51638, _51634))), subset(_51640, _51638), subset(_51636, _51634)], (2155 ^ _19026) ^ [_51783, _51785] : [subset(_51785, _51783), -(set_union2(_51785, _51783) = _51783)], (2162 ^ _19026) ^ [_51950] : [-(in(_51950, 2160 ^ [_51950]))], (2164 ^ _19026) ^ [_51978, _51980, _51982] : [-(in(_51978, 2160 ^ [_51982])), in(_51980, 2160 ^ [_51982]), subset(_51978, _51980)], (2174 ^ _19026) ^ [_52131, _52133] : [in(_52131, 2160 ^ [_52133]), -(in(powerset(_52131), 2160 ^ [_52133]))], (2180 ^ _19026) ^ [_52228, _52230] : [subset(_52228, 2160 ^ [_52230]), -(are_equipotent(_52228, 2160 ^ [_52230])), -(in(_52228, 2160 ^ [_52230]))], (2190 ^ _19026) ^ [_52358, _52360, _52362] : [relation(_52358), -(relation_dom_restriction(relation_rng_restriction(_52362, _52358), _52360) = relation_rng_restriction(_52362, relation_dom_restriction(_52358, _52360)))], (2196 ^ _19026) ^ [_52459, _52461, _52463] : [relation(_52459), 2199 ^ _19026 : [(2200 ^ _19026) ^ [] : [in(_52463, relation_image(_52459, _52461)), 2204 ^ _19026 : [(2205 ^ _19026) ^ [] : [-(in(2203 ^ [_52459, _52461, _52463], relation_dom(_52459)))], (2207 ^ _19026) ^ [] : [-(in(ordered_pair(2203 ^ [_52459, _52461, _52463], _52463), _52459))], (2209 ^ _19026) ^ [] : [-(in(2203 ^ [_52459, _52461, _52463], _52461))]]], (2211 ^ _19026) ^ [] : [-(in(_52463, relation_image(_52459, _52461))), 2212 ^ _19026 : [(2213 ^ _19026) ^ [_52714] : [in(_52714, relation_dom(_52459)), in(ordered_pair(_52714, _52463), _52459), in(_52714, _52461)]]]]], (2225 ^ _19026) ^ [_52897, _52899] : [relation(_52897), -(subset(relation_image(_52897, _52899), relation_rng(_52897)))], (2231 ^ _19026) ^ [_52982, _52984] : [relation(_52982), -(relation_image(_52982, _52984) = relation_image(_52982, set_intersection2(relation_dom(_52982), _52984)))], (2237 ^ _19026) ^ [_53079] : [relation(_53079), -(relation_image(_53079, relation_dom(_53079)) = relation_rng(_53079))], (2243 ^ _19026) ^ [_53166] : [relation(_53166), 2246 ^ _19026 : [(2247 ^ _19026) ^ [_53234] : [relation(_53234), -(relation_rng(relation_composition(_53166, _53234)) = relation_image(_53234, relation_rng(_53166)))]]], (2253 ^ _19026) ^ [_53333, _53335, _53337] : [relation(_53333), 2256 ^ _19026 : [(2257 ^ _19026) ^ [] : [in(_53337, relation_inverse_image(_53333, _53335)), 2261 ^ _19026 : [(2262 ^ _19026) ^ [] : [-(in(2260 ^ [_53333, _53335, _53337], relation_rng(_53333)))], (2264 ^ _19026) ^ [] : [-(in(ordered_pair(_53337, 2260 ^ [_53333, _53335, _53337]), _53333))], (2266 ^ _19026) ^ [] : [-(in(2260 ^ [_53333, _53335, _53337], _53335))]]], (2268 ^ _19026) ^ [] : [-(in(_53337, relation_inverse_image(_53333, _53335))), 2269 ^ _19026 : [(2270 ^ _19026) ^ [_53588] : [in(_53588, relation_rng(_53333)), in(ordered_pair(_53337, _53588), _53333), in(_53588, _53335)]]]]], (2282 ^ _19026) ^ [_53771, _53773] : [relation(_53771), -(subset(relation_inverse_image(_53771, _53773), relation_dom(_53771)))], (2288 ^ _19026) ^ [_53856, _53858] : [relation(_53856), -(_53858 = empty_set), subset(_53858, relation_rng(_53856)), relation_inverse_image(_53856, _53858) = empty_set], (2302 ^ _19026) ^ [_54049, _54051, _54053] : [relation(_54049), subset(_54053, _54051), -(subset(relation_inverse_image(_54049, _54053), relation_inverse_image(_54049, _54051)))], (2312 ^ _19026) ^ [_54192, _54194] : [-(subset(set_intersection2(_54194, _54192), _54194))], (2314 ^ _19026) ^ [_54220, _54222, _54224] : [-(subset(_54224, set_intersection2(_54222, _54220))), subset(_54224, _54222), subset(_54224, _54220)], (2324 ^ _19026) ^ [_54359] : [-(set_union2(_54359, empty_set) = _54359)], (2326 ^ _19026) ^ [_54385, _54387] : [in(_54387, _54385), -(element(_54387, _54385))], (2332 ^ _19026) ^ [_54462, _54464, _54466] : [-(subset(_54466, _54462)), subset(_54466, _54464), subset(_54464, _54462)], (2342 ^ _19026) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (2344 ^ _19026) ^ [_54613, _54615, _54617] : [relation(_54613), in(ordered_pair(_54617, _54615), _54613), 2351 ^ _19026 : [(2352 ^ _19026) ^ [] : [-(in(_54617, relation_dom(_54613)))], (2354 ^ _19026) ^ [] : [-(in(_54615, relation_rng(_54613)))]]], (2356 ^ _19026) ^ [_54784, _54786] : [relation(_54784), function(_54784), 2363 ^ _19026 : [(2364 ^ _19026) ^ [_54923] : [relation(_54923), function(_54923), 2371 ^ _19026 : [(2372 ^ _19026) ^ [] : [in(_54786, relation_dom(relation_composition(_54923, _54784))), 2375 ^ _19026 : [(2376 ^ _19026) ^ [] : [-(in(_54786, relation_dom(_54923)))], (2378 ^ _19026) ^ [] : [-(in(apply(_54923, _54786), relation_dom(_54784)))]]], (2380 ^ _19026) ^ [] : [-(in(_54786, relation_dom(relation_composition(_54923, _54784)))), in(_54786, relation_dom(_54923)), in(apply(_54923, _54786), relation_dom(_54784))]]]]], (2390 ^ _19026) ^ [_55304] : [relation(_55304), -(subset(_55304, cartesian_product2(relation_dom(_55304), relation_rng(_55304))))], (2396 ^ _19026) ^ [_55391, _55393] : [relation(_55391), function(_55391), 2403 ^ _19026 : [(2404 ^ _19026) ^ [_55529] : [relation(_55529), function(_55529), in(_55393, relation_dom(relation_composition(_55529, _55391))), -(apply(relation_composition(_55529, _55391), _55393) = apply(_55391, apply(_55529, _55393)))]]], (2418 ^ _19026) ^ [_55754] : [relation(_55754), 2421 ^ _19026 : [(2422 ^ _19026) ^ [_55832] : [relation(_55832), subset(_55754, _55832), 2429 ^ _19026 : [(2430 ^ _19026) ^ [] : [-(subset(relation_dom(_55754), relation_dom(_55832)))], (2432 ^ _19026) ^ [] : [-(subset(relation_rng(_55754), relation_rng(_55832)))]]]]], (2434 ^ _19026) ^ [_56005, _56007, _56009] : [subset(_56009, _56007), -(subset(set_intersection2(_56009, _56005), set_intersection2(_56007, _56005)))], (2440 ^ _19026) ^ [_56096, _56098] : [subset(_56098, _56096), -(set_intersection2(_56098, _56096) = _56098)], (2446 ^ _19026) ^ [_56179] : [-(set_intersection2(_56179, empty_set) = empty_set)], (2448 ^ _19026) ^ [_56205, _56207] : [element(_56207, _56205), -(empty(_56205)), -(in(_56207, _56205))], (2458 ^ _19026) ^ [_56293, _56295] : [-(_56295 = _56293), 2462 ^ _19026 : [(2463 ^ _19026) ^ [] : [-(in(2459 ^ [_56293, _56295], _56295))], (2465 ^ _19026) ^ [] : [in(2459 ^ [_56293, _56295], _56293)]], 2466 ^ _19026 : [(2467 ^ _19026) ^ [] : [-(in(2459 ^ [_56293, _56295], _56293))], (2469 ^ _19026) ^ [] : [in(2459 ^ [_56293, _56295], _56295)]]], (2473 ^ _19026) ^ [_56529] : [-(subset(empty_set, _56529))], (2475 ^ _19026) ^ [_56552, _56554, _56556] : [relation(_56552), in(ordered_pair(_56556, _56554), _56552), 2482 ^ _19026 : [(2483 ^ _19026) ^ [] : [-(in(_56556, relation_field(_56552)))], (2485 ^ _19026) ^ [] : [-(in(_56554, relation_field(_56552)))]]], (2487 ^ _19026) ^ [_56723, _56725, _56727] : [subset(_56727, _56725), -(subset(set_difference(_56727, _56723), set_difference(_56725, _56723)))], (2493 ^ _19026) ^ [_56814, _56816, _56818, _56820] : [ordered_pair(_56820, _56818) = ordered_pair(_56816, _56814), 2496 ^ _19026 : [(2497 ^ _19026) ^ [] : [-(_56820 = _56816)], (2499 ^ _19026) ^ [] : [-(_56818 = _56814)]]], (2501 ^ _19026) ^ [_56933, _56935] : [-(subset(set_difference(_56935, _56933), _56935))], (2503 ^ _19026) ^ [_56961] : [relation(_56961), 2506 ^ _19026 : [(2507 ^ _19026) ^ [] : [-(relation_rng(_56961) = relation_dom(relation_inverse(_56961)))], (2509 ^ _19026) ^ [] : [-(relation_dom(_56961) = relation_rng(relation_inverse(_56961)))]]], (2511 ^ _19026) ^ [_57099, _57101] : [set_difference(_57101, _57099) = empty_set, -(subset(_57101, _57099))], (2517 ^ _19026) ^ [_57178, _57180] : [subset(_57180, _57178), -(set_difference(_57180, _57178) = empty_set)], (2523 ^ _19026) ^ [_57278, _57280] : [subset(singleton(_57280), _57278), -(in(_57280, _57278))], (2529 ^ _19026) ^ [_57355, _57357] : [in(_57357, _57355), -(subset(singleton(_57357), _57355))], (2535 ^ _19026) ^ [_57456, _57458, _57460] : [subset(unordered_pair(_57460, _57458), _57456), 2538 ^ _19026 : [(2539 ^ _19026) ^ [] : [-(in(_57460, _57456))], (2541 ^ _19026) ^ [] : [-(in(_57458, _57456))]]], (2543 ^ _19026) ^ [_57563, _57565, _57567] : [-(subset(unordered_pair(_57567, _57565), _57563)), in(_57567, _57563), in(_57565, _57563)], (2553 ^ _19026) ^ [_57704, _57706] : [-(set_union2(_57706, set_difference(_57704, _57706)) = set_union2(_57706, _57704))], (2565 ^ _19026) ^ [_57847, _57849] : [2566 ^ _19026 : [(2567 ^ _19026) ^ [] : [_57849 = empty_set], (2569 ^ _19026) ^ [] : [_57849 = singleton(_57847)]], -(subset(_57849, singleton(_57847)))], (2555 ^ _19026) ^ [_57753, _57755] : [subset(_57755, singleton(_57753)), -(_57755 = empty_set), -(_57755 = singleton(_57753))], (2573 ^ _19026) ^ [_57972] : [-(set_difference(_57972, empty_set) = _57972)], (2575 ^ _19026) ^ [_58013, _58015] : [element(_58015, powerset(_58013)), -(subset(_58015, _58013))], (2581 ^ _19026) ^ [_58090, _58092] : [subset(_58092, _58090), -(element(_58092, powerset(_58090)))], (2587 ^ _19026) ^ [_58179, _58181] : [-(disjoint(_58181, _58179)), 2591 ^ _19026 : [(2592 ^ _19026) ^ [] : [-(in(2590 ^ [_58179, _58181], _58181))], (2594 ^ _19026) ^ [] : [-(in(2590 ^ [_58179, _58181], _58179))]]], (2596 ^ _19026) ^ [_58262, _58264] : [disjoint(_58264, _58262), 2597 ^ _19026 : [(2598 ^ _19026) ^ [_58302] : [in(_58302, _58264), in(_58302, _58262)]]], (2606 ^ _19026) ^ [_58409] : [subset(_58409, empty_set), -(_58409 = empty_set)], (2612 ^ _19026) ^ [_58484, _58486] : [-(set_difference(set_union2(_58486, _58484), _58484) = set_difference(_58486, _58484))], (2614 ^ _19026) ^ [_58518, _58520] : [element(_58518, powerset(_58520)), 2617 ^ _19026 : [(2618 ^ _19026) ^ [_58596] : [element(_58596, powerset(_58520)), 2621 ^ _19026 : [(2622 ^ _19026) ^ [] : [disjoint(_58518, _58596), -(subset(_58518, subset_complement(_58520, _58596)))], (2628 ^ _19026) ^ [] : [subset(_58518, subset_complement(_58520, _58596)), -(disjoint(_58518, _58596))]]]]], (2634 ^ _19026) ^ [_58826] : [relation(_58826), 2637 ^ _19026 : [(2638 ^ _19026) ^ [_58891] : [relation(_58891), -(subset(relation_dom(relation_composition(_58826, _58891)), relation_dom(_58826)))]]], (2644 ^ _19026) ^ [_58984] : [relation(_58984), 2647 ^ _19026 : [(2648 ^ _19026) ^ [_59049] : [relation(_59049), -(subset(relation_rng(relation_composition(_58984, _59049)), relation_rng(_59049)))]]], (2654 ^ _19026) ^ [_59142, _59144] : [subset(_59144, _59142), -(_59142 = set_union2(_59144, set_difference(_59142, _59144)))], (2660 ^ _19026) ^ [_59231] : [relation(_59231), 2663 ^ _19026 : [(2664 ^ _19026) ^ [_59306] : [relation(_59306), subset(relation_rng(_59231), relation_dom(_59306)), -(relation_dom(relation_composition(_59231, _59306)) = relation_dom(_59231))]]], (2674 ^ _19026) ^ [_59459, _59461] : [element(_59459, powerset(powerset(_59461))), -(_59459 = empty_set), complements_of_subsets(_59461, _59459) = empty_set], (2684 ^ _19026) ^ [_59606, _59608] : [in(_59608, _59606), -(set_union2(singleton(_59608), _59606) = _59606)], (2690 ^ _19026) ^ [_59693] : [relation(_59693), 2693 ^ _19026 : [(2694 ^ _19026) ^ [_59768] : [relation(_59768), subset(relation_dom(_59693), relation_rng(_59768)), -(relation_rng(relation_composition(_59768, _59693)) = relation_rng(_59693))]]], (2704 ^ _19026) ^ [_59921, _59923] : [element(_59921, powerset(powerset(_59923))), -(_59921 = empty_set), -(subset_difference(_59923, cast_to_subset(_59923), union_of_subsets(_59923, _59921)) = meet_of_subsets(_59923, complements_of_subsets(_59923, _59921)))], (2714 ^ _19026) ^ [_60051, _60053] : [element(_60051, powerset(powerset(_60053))), -(_60051 = empty_set), -(union_of_subsets(_60053, complements_of_subsets(_60053, _60051)) = subset_difference(_60053, cast_to_subset(_60053), meet_of_subsets(_60053, _60051)))], (2724 ^ _19026) ^ [_60181, _60183] : [-(set_difference(_60183, set_difference(_60183, _60181)) = set_intersection2(_60183, _60181))], (2726 ^ _19026) ^ [_60215] : [-(set_difference(empty_set, _60215) = empty_set)], (2728 ^ _19026) ^ [_60241, _60243, _60245] : [-(element(_60245, _60241)), in(_60245, _60243), element(_60243, powerset(_60241))], (2738 ^ _19026) ^ [_60384, _60386] : [-(disjoint(_60386, _60384)), -(in(2741 ^ [_60384, _60386], set_intersection2(_60386, _60384)))], (2745 ^ _19026) ^ [_60426, _60428] : [2746 ^ _19026 : [(2747 ^ _19026) ^ [_60468] : [in(_60468, set_intersection2(_60428, _60426))]], disjoint(_60428, _60426)], (2751 ^ _19026) ^ [_60522] : [-(_60522 = empty_set), 2754 ^ _19026 : [(2755 ^ _19026) ^ [_60605] : [element(_60605, powerset(_60522)), 2758 ^ _19026 : [(2759 ^ _19026) ^ [_60683] : [element(_60683, _60522), -(in(_60683, _60605)), -(in(_60683, subset_complement(_60522, _60605)))]]]]], (2769 ^ _19026) ^ [_60791, _60793, _60795] : [element(_60791, powerset(_60795)), in(_60793, subset_complement(_60795, _60791)), in(_60793, _60791)], (2779 ^ _19026) ^ [_60935] : [relation(_60935), -(in(ordered_pair(2784 ^ [_60935], 2785 ^ [_60935]), _60935)), -(_60935 = empty_set)], (2791 ^ _19026) ^ [_61049, _61051, _61053] : [in(_61053, _61051), element(_61051, powerset(_61049)), empty(_61049)], (2801 ^ _19026) ^ [] : [-(relation_dom(empty_set) = empty_set)], (2803 ^ _19026) ^ [] : [-(relation_rng(empty_set) = empty_set)], (2805 ^ _19026) ^ [_61216, _61218] : [subset(_61218, _61216), proper_subset(_61216, _61218)], (2811 ^ _19026) ^ [_61292, _61294, _61296] : [-(disjoint(_61296, _61292)), subset(_61296, _61294), disjoint(_61294, _61292)], (2821 ^ _19026) ^ [_61425] : [relation(_61425), 2826 ^ _19026 : [(2827 ^ _19026) ^ [] : [relation_dom(_61425) = empty_set], (2829 ^ _19026) ^ [] : [relation_rng(_61425) = empty_set]], -(_61425 = empty_set)], (2833 ^ _19026) ^ [_61594] : [relation(_61594), 2836 ^ _19026 : [(2837 ^ _19026) ^ [] : [relation_dom(_61594) = empty_set, -(relation_rng(_61594) = empty_set)], (2843 ^ _19026) ^ [] : [relation_rng(_61594) = empty_set, -(relation_dom(_61594) = empty_set)]]], (2849 ^ _19026) ^ [_61820, _61822] : [set_difference(_61822, singleton(_61820)) = _61822, in(_61820, _61822)], (2855 ^ _19026) ^ [_61902, _61904] : [-(in(_61902, _61904)), -(set_difference(_61904, singleton(_61902)) = _61904)], (2861 ^ _19026) ^ [_61945] : [-(unordered_pair(_61945, _61945) = singleton(_61945))], (2863 ^ _19026) ^ [_61973] : [empty(_61973), -(_61973 = empty_set)], (2869 ^ _19026) ^ [_62046, _62048] : [subset(singleton(_62048), singleton(_62046)), -(_62048 = _62046)], (2875 ^ _19026) ^ [_62129] : [-(relation_dom(identity_relation(_62129)) = _62129)], (2877 ^ _19026) ^ [_62153] : [-(relation_rng(identity_relation(_62153)) = _62153)], (2879 ^ _19026) ^ [_62182, _62184, _62186, _62188] : [relation(_62182), 2882 ^ _19026 : [(2883 ^ _19026) ^ [] : [in(ordered_pair(_62188, _62186), relation_composition(identity_relation(_62184), _62182)), 2886 ^ _19026 : [(2887 ^ _19026) ^ [] : [-(in(_62188, _62184))], (2889 ^ _19026) ^ [] : [-(in(ordered_pair(_62188, _62186), _62182))]]], (2891 ^ _19026) ^ [] : [-(in(ordered_pair(_62188, _62186), relation_composition(identity_relation(_62184), _62182))), in(_62188, _62184), in(ordered_pair(_62188, _62186), _62182)]]], (2901 ^ _19026) ^ [_62508, _62510] : [in(_62510, _62508), empty(_62508)], (2907 ^ _19026) ^ [_62582, _62584] : [-(subset(_62584, set_union2(_62584, _62582)))], (2909 ^ _19026) ^ [_62625, _62627] : [disjoint(_62627, _62625), -(set_difference(_62627, _62625) = _62627)], (2915 ^ _19026) ^ [_62704, _62706] : [set_difference(_62706, _62704) = _62706, -(disjoint(_62706, _62704))], (2921 ^ _19026) ^ [_62789, _62791, _62793] : [relation(_62789), 2924 ^ _19026 : [(2925 ^ _19026) ^ [] : [in(_62793, relation_dom(relation_dom_restriction(_62789, _62791))), 2928 ^ _19026 : [(2929 ^ _19026) ^ [] : [-(in(_62793, _62791))], (2931 ^ _19026) ^ [] : [-(in(_62793, relation_dom(_62789)))]]], (2933 ^ _19026) ^ [] : [-(in(_62793, relation_dom(relation_dom_restriction(_62789, _62791)))), in(_62793, _62791), in(_62793, relation_dom(_62789))]]], (2943 ^ _19026) ^ [_63095, _63097] : [relation(_63095), -(subset(relation_dom_restriction(_63095, _63097), _63095))], (2949 ^ _19026) ^ [_63176, _63178] : [empty(_63178), -(_63178 = _63176), empty(_63176)], (2959 ^ _19026) ^ [_63303, _63305, _63307] : [relation(_63303), function(_63303), 2966 ^ _19026 : [(2967 ^ _19026) ^ [] : [in(ordered_pair(_63307, _63305), _63303), 2970 ^ _19026 : [(2971 ^ _19026) ^ [] : [-(in(_63307, relation_dom(_63303)))], (2973 ^ _19026) ^ [] : [-(_63305 = apply(_63303, _63307))]]], (2975 ^ _19026) ^ [] : [-(in(ordered_pair(_63307, _63305), _63303)), in(_63307, relation_dom(_63303)), _63305 = apply(_63303, _63307)]]], (2985 ^ _19026) ^ [_63666, _63668, _63670] : [-(subset(set_union2(_63670, _63666), _63668)), subset(_63670, _63668), subset(_63666, _63668)], (2995 ^ _19026) ^ [_63805, _63807, _63809] : [singleton(_63809) = unordered_pair(_63807, _63805), -(_63809 = _63807)], (3001 ^ _19026) ^ [_63894, _63896] : [relation(_63894), -(relation_dom(relation_dom_restriction(_63894, _63896)) = set_intersection2(relation_dom(_63894), _63896))], (3007 ^ _19026) ^ [_63989, _63991] : [in(_63991, _63989), -(subset(_63991, union(_63989)))], (3013 ^ _19026) ^ [_64070, _64072] : [relation(_64070), -(relation_dom_restriction(_64070, _64072) = relation_composition(identity_relation(_64072), _64070))], (3019 ^ _19026) ^ [_64161, _64163] : [relation(_64161), -(subset(relation_rng(relation_dom_restriction(_64161, _64163)), relation_rng(_64161)))], (3025 ^ _19026) ^ [_64250] : [-(union(powerset(_64250)) = _64250)], (3063 ^ _19026) ^ [_64933, _64935, _64937] : [singleton(_64937) = unordered_pair(_64935, _64933), -(_64935 = _64933)], (3028 ^ _19026) ^ [_64385] : [-(in(_64385, 3026 ^ [_64385]))], (3030 ^ _19026) ^ [_64413, _64415, _64417] : [-(in(_64413, 3026 ^ [_64417])), in(_64415, 3026 ^ [_64417]), subset(_64413, _64415)], (3040 ^ _19026) ^ [_64566, _64568] : [in(_64566, 3026 ^ [_64568]), 3044 ^ _19026 : [(3045 ^ _19026) ^ [] : [-(in(3043 ^ [_64566, _64568], 3026 ^ [_64568]))], (3047 ^ _19026) ^ [_64712] : [subset(_64712, _64566), -(in(_64712, 3043 ^ [_64566, _64568]))]]], (3053 ^ _19026) ^ [_64807, _64809] : [subset(_64807, 3026 ^ [_64809]), -(are_equipotent(_64807, 3026 ^ [_64809])), -(in(_64807, 3026 ^ [_64809]))]], input).
% 13.32/13.78 ncf('1',plain,[apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = apply(3074 ^ [], apply(3069 ^ [], 3068 ^ []))],start(3082 ^ 0)).
% 13.32/13.78 ncf('1.1',plain,[-(apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = apply(3074 ^ [], apply(3069 ^ [], 3068 ^ []))), 1178 : apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = empty_set, 1178 : -(in(apply(3069 ^ [], 3068 ^ []), relation_dom(3074 ^ []))), 1168 : relation(3074 ^ []), 1168 : function(3074 ^ [])],extension(1144 ^ 1,bind([[_37068, _37458, _37460], [3074 ^ [], apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []), apply(3069 ^ [], 3068 ^ [])]]))).
% 13.32/13.78 ncf('1.1.1',plain,[-(apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = empty_set), 1172 : apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []), 1172 : -(in(3068 ^ [], relation_dom(relation_composition(3069 ^ [], 3074 ^ [])))), 1168 : relation(relation_composition(3069 ^ [], 3074 ^ [])), 1168 : function(relation_composition(3069 ^ [], 3074 ^ []))],extension(1144 ^ 6,bind([[_37068, _37458, _37460], [relation_composition(3069 ^ [], 3074 ^ []), apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []), 3068 ^ []]]))).
% 13.32/13.78 ncf('1.1.1.1',plain,[-(apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []))],extension(2 ^ 11,bind([[_19056], [apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ [])]]))).
% 13.32/13.78 ncf('1.1.1.2',plain,[in(3068 ^ [], relation_dom(relation_composition(3069 ^ [], 3074 ^ []))), 2404 : relation(3069 ^ []), 2404 : function(3069 ^ []), 2404 : -(apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = apply(3074 ^ [], apply(3069 ^ [], 3068 ^ []))), 2404 : relation(3074 ^ []), 2404 : function(3074 ^ [])],extension(2396 ^ 9,bind([[_55391, _55393, _55529], [3074 ^ [], 3068 ^ [], 3069 ^ []]]))).
% 13.32/13.78 ncf('1.1.1.2.1',plain,[-(relation(3069 ^ []))],extension(3071 ^ 12)).
% 13.32/13.78 ncf('1.1.1.2.2',plain,[-(function(3069 ^ []))],extension(3073 ^ 12)).
% 13.32/13.78 ncf('1.1.1.2.3',plain,[apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = apply(3074 ^ [], apply(3069 ^ [], 3068 ^ []))],reduction('1')).
% 13.32/13.78 ncf('1.1.1.2.4',plain,[-(relation(3074 ^ []))],extension(3076 ^ 10)).
% 13.32/13.78 ncf('1.1.1.2.5',plain,[-(function(3074 ^ []))],extension(3078 ^ 10)).
% 13.32/13.78 ncf('1.1.1.3',plain,[-(relation(relation_composition(3069 ^ [], 3074 ^ []))), relation(3069 ^ []), relation(3074 ^ [])],extension(1645 ^ 7,bind([[_44961, _44963], [3074 ^ [], 3069 ^ []]]))).
% 13.32/13.78 ncf('1.1.1.3.1',plain,[-(relation(3069 ^ []))],extension(3071 ^ 8)).
% 13.32/13.78 ncf('1.1.1.3.2',plain,[-(relation(3074 ^ []))],extension(3076 ^ 8)).
% 13.32/13.78 ncf('1.1.1.4',plain,[-(function(relation_composition(3069 ^ [], 3074 ^ []))), relation(3069 ^ []), function(3069 ^ []), relation(3074 ^ []), function(3074 ^ [])],extension(1730 ^ 7,bind([[_46067, _46069], [3074 ^ [], 3069 ^ []]]))).
% 13.32/13.78 ncf('1.1.1.4.1',plain,[-(relation(3069 ^ []))],extension(3071 ^ 8)).
% 13.32/13.78 ncf('1.1.1.4.2',plain,[-(function(3069 ^ []))],extension(3073 ^ 8)).
% 13.32/13.78 ncf('1.1.1.4.3',plain,[-(relation(3074 ^ []))],extension(3076 ^ 8)).
% 13.32/13.78 ncf('1.1.1.4.4',plain,[-(function(3074 ^ []))],extension(3078 ^ 8)).
% 13.32/13.78 ncf('1.1.2',plain,[in(apply(3069 ^ [], 3068 ^ []), relation_dom(3074 ^ [])), 2380 : -(in(3068 ^ [], relation_dom(relation_composition(3069 ^ [], 3074 ^ [])))), 2380 : in(3068 ^ [], relation_dom(3069 ^ [])), 2380 : relation(3069 ^ []), 2380 : function(3069 ^ []), 2364 : relation(3074 ^ []), 2364 : function(3074 ^ [])],extension(2356 ^ 4,bind([[_54784, _54786, _54923], [3074 ^ [], 3068 ^ [], 3069 ^ []]]))).
% 13.32/13.78 ncf('1.1.2.1',plain,[in(3068 ^ [], relation_dom(relation_composition(3069 ^ [], 3074 ^ []))), 2404 : relation(3069 ^ []), 2404 : function(3069 ^ []), 2404 : -(apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = apply(3074 ^ [], apply(3069 ^ [], 3068 ^ []))), 2404 : relation(3074 ^ []), 2404 : function(3074 ^ [])],extension(2396 ^ 9,bind([[_55391, _55393, _55529], [3074 ^ [], 3068 ^ [], 3069 ^ []]]))).
% 13.32/13.78 ncf('1.1.2.1.1',plain,[-(relation(3069 ^ []))],extension(3071 ^ 12)).
% 13.32/13.78 ncf('1.1.2.1.2',plain,[-(function(3069 ^ []))],extension(3073 ^ 12)).
% 13.32/13.78 ncf('1.1.2.1.3',plain,[apply(relation_composition(3069 ^ [], 3074 ^ []), 3068 ^ []) = apply(3074 ^ [], apply(3069 ^ [], 3068 ^ []))],reduction('1')).
% 13.32/13.78 ncf('1.1.2.1.4',plain,[-(relation(3074 ^ []))],extension(3076 ^ 10)).
% 13.32/13.78 ncf('1.1.2.1.5',plain,[-(function(3074 ^ []))],extension(3078 ^ 10)).
% 13.32/13.78 ncf('1.1.2.2',plain,[-(in(3068 ^ [], relation_dom(3069 ^ [])))],extension(3080 ^ 9)).
% 13.32/13.78 ncf('1.1.2.3',plain,[-(relation(3069 ^ []))],extension(3071 ^ 7)).
% 13.32/13.78 ncf('1.1.2.4',plain,[-(function(3069 ^ []))],extension(3073 ^ 7)).
% 13.32/13.78 ncf('1.1.2.5',plain,[-(relation(3074 ^ []))],extension(3076 ^ 5)).
% 13.32/13.78 ncf('1.1.2.6',plain,[-(function(3074 ^ []))],extension(3078 ^ 5)).
% 13.32/13.78 ncf('1.1.3',plain,[-(relation(3074 ^ []))],extension(3076 ^ 2)).
% 13.32/13.78 ncf('1.1.4',plain,[-(function(3074 ^ []))],extension(3078 ^ 2)).
% 13.32/13.78 %-----------------------------------------------------
% 13.32/13.78 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------