%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU196+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n001.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 12:02:36 EDT 2023

% Result   : Theorem 0.63s 1.40s
% Output   : Proof 0.63s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU196+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n001.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 13:26:49 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.63/1.40  
% 0.63/1.40  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.63/1.40  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/1.40  %-----------------------------------------------------
% 0.63/1.40  ncf(matrix, plain, [(2499 ^ _337146) ^ [] : [-(relation(2497 ^ []))], (2501 ^ _337146) ^ [] : [subset(relation_rng(relation_dom_restriction(2497 ^ [], 2496 ^ [])), relation_rng(2497 ^ []))], (2 ^ _337146) ^ [_337290] : [-(_337290 = _337290)], (4 ^ _337146) ^ [_337397, _337399] : [_337399 = _337397, -(_337397 = _337399)], (10 ^ _337146) ^ [_337601, _337603, _337605] : [-(_337605 = _337601), _337605 = _337603, _337603 = _337601], (20 ^ _337146) ^ [_337942, _337944, _337946, _337948] : [-(element(_337946, _337942)), element(_337948, _337944), _337948 = _337946, _337944 = _337942], (34 ^ _337146) ^ [_338386, _338388, _338390, _338392] : [-(proper_subset(_338390, _338386)), proper_subset(_338392, _338388), _338392 = _338390, _338388 = _338386], (48 ^ _337146) ^ [_338830, _338832, _338834, _338836] : [-(disjoint(_338834, _338830)), disjoint(_338836, _338832), _338836 = _338834, _338832 = _338830], (62 ^ _337146) ^ [_339246, _339248] : [-(empty(_339246)), _339248 = _339246, empty(_339248)], (72 ^ _337146) ^ [_339569, _339571, _339573, _339575] : [-(are_equipotent(_339573, _339569)), are_equipotent(_339575, _339571), _339575 = _339573, _339571 = _339569], (86 ^ _337146) ^ [_340013, _340015, _340017, _340019] : [-(in(_340017, _340013)), in(_340019, _340015), _340019 = _340017, _340015 = _340013], (100 ^ _337146) ^ [_340429, _340431] : [-(relation(_340429)), _340431 = _340429, relation(_340431)], (110 ^ _337146) ^ [_340732, _340734, _340736, _340738] : [-(subset(_340736, _340732)), subset(_340738, _340734), _340738 = _340736, _340734 = _340732], (124 ^ _337146) ^ [_341168, _341170] : [_341170 = _341168, -(set_meet(_341170) = set_meet(_341168))], (130 ^ _337146) ^ [_341414, _341416, _341418, _341420] : [-(cartesian_product2(_341420, _341416) = cartesian_product2(_341418, _341414)), _341420 = _341418, _341416 = _341414], (140 ^ _337146) ^ [_341745, _341747] : [_341747 = _341745, -(relation_field(_341747) = relation_field(_341745))], (146 ^ _337146) ^ [_341963, _341965] : [_341965 = _341963, -(relation_inverse(_341965) = relation_inverse(_341963))], (152 ^ _337146) ^ [_342209, _342211, _342213, _342215] : [-(union_of_subsets(_342215, _342211) = union_of_subsets(_342213, _342209)), _342215 = _342213, _342211 = _342209], (162 ^ _337146) ^ [_342568, _342570, _342572, _342574] : [-(complements_of_subsets(_342574, _342570) = complements_of_subsets(_342572, _342568)), _342574 = _342572, _342570 = _342568], (172 ^ _337146) ^ [_342955, _342957, _342959, _342961, _342963, _342965] : [-(subset_difference(_342965, _342961, _342957) = subset_difference(_342963, _342959, _342955)), _342965 = _342963, _342961 = _342959, _342957 = _342955], (186 ^ _337146) ^ [_343415, _343417] : [_343417 = _343415, -(cast_to_subset(_343417) = cast_to_subset(_343415))], (192 ^ _337146) ^ [_343661, _343663, _343665, _343667] : [-(meet_of_subsets(_343667, _343663) = meet_of_subsets(_343665, _343661)), _343667 = _343665, _343663 = _343661], (202 ^ _337146) ^ [_344020, _344022, _344024, _344026] : [-(subset_complement(_344026, _344022) = subset_complement(_344024, _344020)), _344026 = _344024, _344022 = _344020], (212 ^ _337146) ^ [_344379, _344381, _344383, _344385] : [-(ordered_pair(_344385, _344381) = ordered_pair(_344383, _344379)), _344385 = _344383, _344381 = _344379], (222 ^ _337146) ^ [_344738, _344740, _344742, _344744] : [-(set_difference(_344744, _344740) = set_difference(_344742, _344738)), _344744 = _344742, _344740 = _344738], (232 ^ _337146) ^ [_345097, _345099, _345101, _345103] : [-(set_union2(_345103, _345099) = set_union2(_345101, _345097)), _345103 = _345101, _345099 = _345097], (242 ^ _337146) ^ [_345456, _345458, _345460, _345462] : [-(set_intersection2(_345462, _345458) = set_intersection2(_345460, _345456)), _345462 = _345460, _345458 = _345456], (252 ^ _337146) ^ [_345787, _345789] : [_345789 = _345787, -(relation_dom(_345789) = relation_dom(_345787))], (258 ^ _337146) ^ [_346033, _346035, _346037, _346039] : [-(relation_composition(_346039, _346035) = relation_composition(_346037, _346033)), _346039 = _346037, _346035 = _346033], (268 ^ _337146) ^ [_346364, _346366] : [_346366 = _346364, -(identity_relation(_346366) = identity_relation(_346364))], (274 ^ _337146) ^ [_346582, _346584] : [_346584 = _346582, -(union(_346584) = union(_346582))], (280 ^ _337146) ^ [_346800, _346802] : [_346802 = _346800, -(powerset(_346802) = powerset(_346800))], (286 ^ _337146) ^ [_347018, _347020] : [_347020 = _347018, -(singleton(_347020) = singleton(_347018))], (292 ^ _337146) ^ [_347264, _347266, _347268, _347270] : [-(unordered_pair(_347270, _347266) = unordered_pair(_347268, _347264)), _347270 = _347268, _347266 = _347264], (312 ^ _337146) ^ [_347934, _347936] : [_347936 = _347934, -(relation_rng(_347936) = relation_rng(_347934))], (302 ^ _337146) ^ [_347623, _347625, _347627, _347629] : [-(relation_dom_restriction(_347629, _347625) = relation_dom_restriction(_347627, _347623)), _347629 = _347627, _347625 = _347623], (318 ^ _337146) ^ [_348254, _348256] : [in(_348256, _348254), in(_348254, _348256)], (324 ^ _337146) ^ [_348465, _348467] : [proper_subset(_348467, _348465), proper_subset(_348465, _348467)], (330 ^ _337146) ^ [_348662] : [empty(_348662), -(relation(_348662))], (336 ^ _337146) ^ [_348847, _348849] : [-(unordered_pair(_348849, _348847) = unordered_pair(_348847, _348849))], (338 ^ _337146) ^ [_348947, _348949] : [-(set_union2(_348949, _348947) = set_union2(_348947, _348949))], (340 ^ _337146) ^ [_349047, _349049] : [-(set_intersection2(_349049, _349047) = set_intersection2(_349047, _349049))], (342 ^ _337146) ^ [_349162, _349164] : [relation(_349162), 345 ^ _337146 : [(368 ^ _337146) ^ [] : [-(_349162 = identity_relation(_349164)), 381 ^ _337146 : [(382 ^ _337146) ^ [] : [-(in(369 ^ [_349162, _349164], _349164))], (384 ^ _337146) ^ [] : [-(369 ^ [_349162, _349164] = 370 ^ [_349162, _349164])], (386 ^ _337146) ^ [] : [in(ordered_pair(369 ^ [_349162, _349164], 370 ^ [_349162, _349164]), _349162)]], 373 ^ _337146 : [(374 ^ _337146) ^ [] : [-(in(ordered_pair(369 ^ [_349162, _349164], 370 ^ [_349162, _349164]), _349162))], (376 ^ _337146) ^ [] : [in(369 ^ [_349162, _349164], _349164), 369 ^ [_349162, _349164] = 370 ^ [_349162, _349164]]]], (346 ^ _337146) ^ [] : [_349162 = identity_relation(_349164), 349 ^ _337146 : [(350 ^ _337146) ^ [_349472, _349474] : [in(ordered_pair(_349474, _349472), _349162), 353 ^ _337146 : [(354 ^ _337146) ^ [] : [-(in(_349474, _349164))], (356 ^ _337146) ^ [] : [-(_349474 = _349472)]]], (358 ^ _337146) ^ [_349735, _349737] : [-(in(ordered_pair(_349737, _349735), _349162)), in(_349737, _349164), _349737 = _349735]]]]], (390 ^ _337146) ^ [_350843, _350845] : [_350845 = _350843, 393 ^ _337146 : [(394 ^ _337146) ^ [] : [-(subset(_350845, _350843))], (396 ^ _337146) ^ [] : [-(subset(_350843, _350845))]]], (398 ^ _337146) ^ [_351080, _351082] : [-(_351082 = _351080), subset(_351082, _351080), subset(_351080, _351082)], (408 ^ _337146) ^ [_351367] : [relation(_351367), 411 ^ _337146 : [(412 ^ _337146) ^ [_351553, _351555] : [relation(_351553), 415 ^ _337146 : [(438 ^ _337146) ^ [] : [-(_351553 = relation_dom_restriction(_351367, _351555)), 451 ^ _337146 : [(452 ^ _337146) ^ [] : [-(in(439 ^ [_351367, _351553, _351555], _351555))], (454 ^ _337146) ^ [] : [-(in(ordered_pair(439 ^ [_351367, _351553, _351555], 440 ^ [_351367, _351553, _351555]), _351367))], (456 ^ _337146) ^ [] : [in(ordered_pair(439 ^ [_351367, _351553, _351555], 440 ^ [_351367, _351553, _351555]), _351553)]], 443 ^ _337146 : [(444 ^ _337146) ^ [] : [-(in(ordered_pair(439 ^ [_351367, _351553, _351555], 440 ^ [_351367, _351553, _351555]), _351553))], (446 ^ _337146) ^ [] : [in(439 ^ [_351367, _351553, _351555], _351555), in(ordered_pair(439 ^ [_351367, _351553, _351555], 440 ^ [_351367, _351553, _351555]), _351367)]]], (416 ^ _337146) ^ [] : [_351553 = relation_dom_restriction(_351367, _351555), 419 ^ _337146 : [(420 ^ _337146) ^ [_351878, _351880] : [in(ordered_pair(_351880, _351878), _351553), 423 ^ _337146 : [(424 ^ _337146) ^ [] : [-(in(_351880, _351555))], (426 ^ _337146) ^ [] : [-(in(ordered_pair(_351880, _351878), _351367))]]], (428 ^ _337146) ^ [_352157, _352159] : [-(in(ordered_pair(_352159, _352157), _351553)), in(_352159, _351555), in(ordered_pair(_352159, _352157), _351367)]]]]]]], (472 ^ _337146) ^ [_353802] : [474 ^ _337146 : [(475 ^ _337146) ^ [] : [-(in(473 ^ [_353802], _353802))], (477 ^ _337146) ^ [_354039, _354041] : [473 ^ [_353802] = ordered_pair(_354041, _354039)]], -(relation(_353802))], (460 ^ _337146) ^ [_353341] : [relation(_353341), 463 ^ _337146 : [(464 ^ _337146) ^ [_353489] : [in(_353489, _353341), -(_353489 = ordered_pair(467 ^ [_353341, _353489], 468 ^ [_353341, _353489]))]]], (530 ^ _337146) ^ [_355937, _355939] : [_355939 = empty_set, 533 ^ _337146 : [(534 ^ _337146) ^ [] : [_355937 = set_meet(_355939), -(_355937 = empty_set)], (540 ^ _337146) ^ [] : [_355937 = empty_set, -(_355937 = set_meet(_355939))]]], (481 ^ _337146) ^ [_354230, _354232] : [-(_354232 = empty_set), 484 ^ _337146 : [(508 ^ _337146) ^ [] : [-(_354230 = set_meet(_354232)), 512 ^ _337146 : [(513 ^ _337146) ^ [] : [-(in(509 ^ [_354230, _354232], _354230))], (516 ^ _337146) ^ [] : [-(in(514 ^ [_354230, _354232], _354232))], (518 ^ _337146) ^ [] : [in(509 ^ [_354230, _354232], 514 ^ [_354230, _354232])]], 519 ^ _337146 : [(526 ^ _337146) ^ [] : [in(509 ^ [_354230, _354232], _354230)], (520 ^ _337146) ^ [_355632] : [in(_355632, _354232), -(in(509 ^ [_354230, _354232], _355632))]]], (485 ^ _337146) ^ [] : [_354230 = set_meet(_354232), 488 ^ _337146 : [(499 ^ _337146) ^ [_354858] : [501 ^ _337146 : [(502 ^ _337146) ^ [] : [-(in(500 ^ [_354230, _354232, _354858], _354232))], (504 ^ _337146) ^ [] : [in(_354858, 500 ^ [_354230, _354232, _354858])]], -(in(_354858, _354230))], (489 ^ _337146) ^ [_354528] : [in(_354528, _354230), 492 ^ _337146 : [(493 ^ _337146) ^ [_354673] : [in(_354673, _354232), -(in(_354528, _354673))]]]]]]], (562 ^ _337146) ^ [_356955, _356957] : [-(_356955 = singleton(_356957)), 566 ^ _337146 : [(567 ^ _337146) ^ [] : [-(in(563 ^ [_356955, _356957], _356955))], (569 ^ _337146) ^ [] : [563 ^ [_356955, _356957] = _356957]], 570 ^ _337146 : [(571 ^ _337146) ^ [] : [-(563 ^ [_356955, _356957] = _356957)], (573 ^ _337146) ^ [] : [in(563 ^ [_356955, _356957], _356955)]]], (546 ^ _337146) ^ [_356434, _356436] : [_356434 = singleton(_356436), 549 ^ _337146 : [(550 ^ _337146) ^ [_356604] : [in(_356604, _356434), -(_356604 = _356436)], (556 ^ _337146) ^ [_356776] : [_356776 = _356436, -(in(_356776, _356434))]]], (577 ^ _337146) ^ [_357506] : [_357506 = empty_set, 580 ^ _337146 : [(581 ^ _337146) ^ [_357619] : [in(_357619, _357506)]]], (583 ^ _337146) ^ [_357685] : [-(in(584 ^ [_357685], _357685)), -(_357685 = empty_set)], (606 ^ _337146) ^ [_358497, _358499] : [-(_358497 = powerset(_358499)), 610 ^ _337146 : [(611 ^ _337146) ^ [] : [-(in(607 ^ [_358497, _358499], _358497))], (613 ^ _337146) ^ [] : [subset(607 ^ [_358497, _358499], _358499)]], 614 ^ _337146 : [(615 ^ _337146) ^ [] : [-(subset(607 ^ [_358497, _358499], _358499))], (617 ^ _337146) ^ [] : [in(607 ^ [_358497, _358499], _358497)]]], (590 ^ _337146) ^ [_357976, _357978] : [_357976 = powerset(_357978), 593 ^ _337146 : [(594 ^ _337146) ^ [_358146] : [in(_358146, _357976), -(subset(_358146, _357978))], (600 ^ _337146) ^ [_358318] : [subset(_358318, _357978), -(in(_358318, _357976))]]], (621 ^ _337146) ^ [_359019] : [relation(_359019), 624 ^ _337146 : [(625 ^ _337146) ^ [_359177] : [relation(_359177), 628 ^ _337146 : [(645 ^ _337146) ^ [] : [-(_359019 = _359177), 650 ^ _337146 : [(651 ^ _337146) ^ [] : [-(in(ordered_pair(646 ^ [_359019, _359177], 647 ^ [_359019, _359177]), _359019))], (653 ^ _337146) ^ [] : [in(ordered_pair(646 ^ [_359019, _359177], 647 ^ [_359019, _359177]), _359177)]], 654 ^ _337146 : [(655 ^ _337146) ^ [] : [-(in(ordered_pair(646 ^ [_359019, _359177], 647 ^ [_359019, _359177]), _359177))], (657 ^ _337146) ^ [] : [in(ordered_pair(646 ^ [_359019, _359177], 647 ^ [_359019, _359177]), _359019)]]], (629 ^ _337146) ^ [] : [_359019 = _359177, 632 ^ _337146 : [(633 ^ _337146) ^ [_359482, _359484] : [in(ordered_pair(_359484, _359482), _359019), -(in(ordered_pair(_359484, _359482), _359177))], (639 ^ _337146) ^ [_359672, _359674] : [in(ordered_pair(_359674, _359672), _359177), -(in(ordered_pair(_359674, _359672), _359019))]]]]]]], (661 ^ _337146) ^ [_360509, _360511] : [-(empty(_360511)), 664 ^ _337146 : [(665 ^ _337146) ^ [] : [element(_360509, _360511), -(in(_360509, _360511))], (671 ^ _337146) ^ [] : [in(_360509, _360511), -(element(_360509, _360511))]]], (677 ^ _337146) ^ [_360922, _360924] : [empty(_360924), 680 ^ _337146 : [(681 ^ _337146) ^ [] : [element(_360922, _360924), -(empty(_360922))], (687 ^ _337146) ^ [] : [empty(_360922), -(element(_360922, _360924))]]], (715 ^ _337146) ^ [_362147, _362149, _362151] : [-(_362147 = unordered_pair(_362151, _362149)), 719 ^ _337146 : [(720 ^ _337146) ^ [] : [-(in(716 ^ [_362147, _362149, _362151], _362147))], (722 ^ _337146) ^ [] : [716 ^ [_362147, _362149, _362151] = _362151], (724 ^ _337146) ^ [] : [716 ^ [_362147, _362149, _362151] = _362149]], 725 ^ _337146 : [(732 ^ _337146) ^ [] : [in(716 ^ [_362147, _362149, _362151], _362147)], (726 ^ _337146) ^ [] : [-(716 ^ [_362147, _362149, _362151] = _362151), -(716 ^ [_362147, _362149, _362151] = _362149)]]], (693 ^ _337146) ^ [_361422, _361424, _361426] : [_361422 = unordered_pair(_361426, _361424), 696 ^ _337146 : [(707 ^ _337146) ^ [_361882] : [708 ^ _337146 : [(709 ^ _337146) ^ [] : [_361882 = _361426], (711 ^ _337146) ^ [] : [_361882 = _361424]], -(in(_361882, _361422))], (697 ^ _337146) ^ [_361604] : [in(_361604, _361422), -(_361604 = _361426), -(_361604 = _361424)]]], (758 ^ _337146) ^ [_363666, _363668, _363670] : [-(_363666 = set_union2(_363670, _363668)), 762 ^ _337146 : [(763 ^ _337146) ^ [] : [-(in(759 ^ [_363666, _363668, _363670], _363666))], (765 ^ _337146) ^ [] : [in(759 ^ [_363666, _363668, _363670], _363670)], (767 ^ _337146) ^ [] : [in(759 ^ [_363666, _363668, _363670], _363668)]], 768 ^ _337146 : [(775 ^ _337146) ^ [] : [in(759 ^ [_363666, _363668, _363670], _363666)], (769 ^ _337146) ^ [] : [-(in(759 ^ [_363666, _363668, _363670], _363670)), -(in(759 ^ [_363666, _363668, _363670], _363668))]]], (736 ^ _337146) ^ [_362941, _362943, _362945] : [_362941 = set_union2(_362945, _362943), 739 ^ _337146 : [(750 ^ _337146) ^ [_363401] : [751 ^ _337146 : [(752 ^ _337146) ^ [] : [in(_363401, _362945)], (754 ^ _337146) ^ [] : [in(_363401, _362943)]], -(in(_363401, _362941))], (740 ^ _337146) ^ [_363123] : [in(_363123, _362941), -(in(_363123, _362945)), -(in(_363123, _362943))]]], (809 ^ _337146) ^ [_365717, _365719, _365721] : [-(_365717 = cartesian_product2(_365721, _365719)), 827 ^ _337146 : [(828 ^ _337146) ^ [] : [-(in(825 ^ [_365717, _365719, _365721], _365721))], (830 ^ _337146) ^ [] : [-(in(826 ^ [_365717, _365719, _365721], _365719))], (832 ^ _337146) ^ [] : [-(810 ^ [_365717, _365719, _365721] = ordered_pair(825 ^ [_365717, _365719, _365721], 826 ^ [_365717, _365719, _365721]))], (834 ^ _337146) ^ [] : [in(810 ^ [_365717, _365719, _365721], _365717)]], 813 ^ _337146 : [(814 ^ _337146) ^ [] : [-(in(810 ^ [_365717, _365719, _365721], _365717))], (816 ^ _337146) ^ [_366055, _366057] : [in(_366057, _365721), in(_366055, _365719), 810 ^ [_365717, _365719, _365721] = ordered_pair(_366057, _366055)]]], (779 ^ _337146) ^ [_364460, _364462, _364464] : [_364460 = cartesian_product2(_364464, _364462), 782 ^ _337146 : [(783 ^ _337146) ^ [_364661] : [in(_364661, _364460), 788 ^ _337146 : [(789 ^ _337146) ^ [] : [-(in(786 ^ [_364460, _364462, _364464, _364661], _364464))], (791 ^ _337146) ^ [] : [-(in(787 ^ [_364460, _364462, _364464, _364661], _364462))], (793 ^ _337146) ^ [] : [-(_364661 = ordered_pair(786 ^ [_364460, _364462, _364464, _364661], 787 ^ [_364460, _364462, _364464, _364661]))]]], (795 ^ _337146) ^ [_365221] : [-(in(_365221, _364460)), 796 ^ _337146 : [(797 ^ _337146) ^ [_365351, _365353] : [in(_365353, _364464), in(_365351, _364462), _365221 = ordered_pair(_365353, _365351)]]]]], (838 ^ _337146) ^ [_366951] : [relation(_366951), 841 ^ _337146 : [(842 ^ _337146) ^ [_367109] : [relation(_367109), 845 ^ _337146 : [(856 ^ _337146) ^ [] : [859 ^ _337146 : [(860 ^ _337146) ^ [] : [-(in(ordered_pair(857 ^ [_366951, _367109], 858 ^ [_366951, _367109]), _366951))], (862 ^ _337146) ^ [] : [in(ordered_pair(857 ^ [_366951, _367109], 858 ^ [_366951, _367109]), _367109)]], -(subset(_366951, _367109))], (846 ^ _337146) ^ [] : [subset(_366951, _367109), 849 ^ _337146 : [(850 ^ _337146) ^ [_367385, _367387] : [in(ordered_pair(_367387, _367385), _366951), -(in(ordered_pair(_367387, _367385), _367109))]]]]]]], (876 ^ _337146) ^ [_368348, _368350] : [878 ^ _337146 : [(879 ^ _337146) ^ [] : [-(in(877 ^ [_368348, _368350], _368350))], (881 ^ _337146) ^ [] : [in(877 ^ [_368348, _368350], _368348)]], -(subset(_368350, _368348))], (866 ^ _337146) ^ [_368034, _368036] : [subset(_368036, _368034), 869 ^ _337146 : [(870 ^ _337146) ^ [_368171] : [in(_368171, _368036), -(in(_368171, _368034))]]], (907 ^ _337146) ^ [_369473, _369475, _369477] : [-(_369473 = set_intersection2(_369477, _369475)), 919 ^ _337146 : [(920 ^ _337146) ^ [] : [-(in(908 ^ [_369473, _369475, _369477], _369477))], (922 ^ _337146) ^ [] : [-(in(908 ^ [_369473, _369475, _369477], _369475))], (924 ^ _337146) ^ [] : [in(908 ^ [_369473, _369475, _369477], _369473)]], 911 ^ _337146 : [(912 ^ _337146) ^ [] : [-(in(908 ^ [_369473, _369475, _369477], _369473))], (914 ^ _337146) ^ [] : [in(908 ^ [_369473, _369475, _369477], _369477), in(908 ^ [_369473, _369475, _369477], _369475)]]], (885 ^ _337146) ^ [_368748, _368750, _368752] : [_368748 = set_intersection2(_368752, _368750), 888 ^ _337146 : [(889 ^ _337146) ^ [_368930] : [in(_368930, _368748), 892 ^ _337146 : [(893 ^ _337146) ^ [] : [-(in(_368930, _368752))], (895 ^ _337146) ^ [] : [-(in(_368930, _368750))]]], (897 ^ _337146) ^ [_369189] : [-(in(_369189, _368748)), in(_369189, _368752), in(_369189, _368750)]]], (928 ^ _337146) ^ [_370212] : [relation(_370212), 931 ^ _337146 : [(949 ^ _337146) ^ [_371024] : [-(_371024 = relation_dom(_370212)), 953 ^ _337146 : [(954 ^ _337146) ^ [] : [-(in(950 ^ [_370212, _371024], _371024))], (956 ^ _337146) ^ [_371287] : [in(ordered_pair(950 ^ [_370212, _371024], _371287), _370212)]], 958 ^ _337146 : [(959 ^ _337146) ^ [] : [-(in(ordered_pair(950 ^ [_370212, _371024], 957 ^ [_370212, _371024]), _370212))], (961 ^ _337146) ^ [] : [in(950 ^ [_370212, _371024], _371024)]]], (932 ^ _337146) ^ [_370393] : [_370393 = relation_dom(_370212), 935 ^ _337146 : [(936 ^ _337146) ^ [_370573] : [in(_370573, _370393), -(in(ordered_pair(_370573, 939 ^ [_370212, _370393, _370573]), _370212))], (943 ^ _337146) ^ [_370817] : [944 ^ _337146 : [(945 ^ _337146) ^ [_370896] : [in(ordered_pair(_370817, _370896), _370212)]], -(in(_370817, _370393))]]]]], (965 ^ _337146) ^ [_371638] : [-(cast_to_subset(_371638) = _371638)], (990 ^ _337146) ^ [_372621, _372623] : [-(_372621 = union(_372623)), 1003 ^ _337146 : [(1004 ^ _337146) ^ [] : [-(in(991 ^ [_372621, _372623], 1002 ^ [_372621, _372623]))], (1006 ^ _337146) ^ [] : [-(in(1002 ^ [_372621, _372623], _372623))], (1008 ^ _337146) ^ [] : [in(991 ^ [_372621, _372623], _372621)]], 994 ^ _337146 : [(995 ^ _337146) ^ [] : [-(in(991 ^ [_372621, _372623], _372621))], (997 ^ _337146) ^ [_372904] : [in(991 ^ [_372621, _372623], _372904), in(_372904, _372623)]]], (967 ^ _337146) ^ [_371776, _371778] : [_371776 = union(_371778), 970 ^ _337146 : [(971 ^ _337146) ^ [_371957] : [in(_371957, _371776), 975 ^ _337146 : [(976 ^ _337146) ^ [] : [-(in(_371957, 974 ^ [_371776, _371778, _371957]))], (978 ^ _337146) ^ [] : [-(in(974 ^ [_371776, _371778, _371957], _371778))]]], (980 ^ _337146) ^ [_372284] : [-(in(_372284, _371776)), 981 ^ _337146 : [(982 ^ _337146) ^ [_372382] : [in(_372284, _372382), in(_372382, _371778)]]]]], (1034 ^ _337146) ^ [_374242, _374244, _374246] : [-(_374242 = set_difference(_374246, _374244)), 1046 ^ _337146 : [(1047 ^ _337146) ^ [] : [-(in(1035 ^ [_374242, _374244, _374246], _374246))], (1049 ^ _337146) ^ [] : [in(1035 ^ [_374242, _374244, _374246], _374244)], (1051 ^ _337146) ^ [] : [in(1035 ^ [_374242, _374244, _374246], _374242)]], 1038 ^ _337146 : [(1039 ^ _337146) ^ [] : [-(in(1035 ^ [_374242, _374244, _374246], _374242))], (1041 ^ _337146) ^ [] : [in(1035 ^ [_374242, _374244, _374246], _374246), -(in(1035 ^ [_374242, _374244, _374246], _374244))]]], (1012 ^ _337146) ^ [_373511, _373513, _373515] : [_373511 = set_difference(_373515, _373513), 1015 ^ _337146 : [(1016 ^ _337146) ^ [_373695] : [in(_373695, _373511), 1019 ^ _337146 : [(1020 ^ _337146) ^ [] : [-(in(_373695, _373515))], (1022 ^ _337146) ^ [] : [in(_373695, _373513)]]], (1024 ^ _337146) ^ [_373955] : [-(in(_373955, _373511)), in(_373955, _373515), -(in(_373955, _373513))]]], (1055 ^ _337146) ^ [_374985] : [relation(_374985), 1058 ^ _337146 : [(1076 ^ _337146) ^ [_375797] : [-(_375797 = relation_rng(_374985)), 1080 ^ _337146 : [(1081 ^ _337146) ^ [] : [-(in(1077 ^ [_374985, _375797], _375797))], (1083 ^ _337146) ^ [_376060] : [in(ordered_pair(_376060, 1077 ^ [_374985, _375797]), _374985)]], 1085 ^ _337146 : [(1086 ^ _337146) ^ [] : [-(in(ordered_pair(1084 ^ [_374985, _375797], 1077 ^ [_374985, _375797]), _374985))], (1088 ^ _337146) ^ [] : [in(1077 ^ [_374985, _375797], _375797)]]], (1059 ^ _337146) ^ [_375166] : [_375166 = relation_rng(_374985), 1062 ^ _337146 : [(1063 ^ _337146) ^ [_375346] : [in(_375346, _375166), -(in(ordered_pair(1066 ^ [_374985, _375166, _375346], _375346), _374985))], (1070 ^ _337146) ^ [_375590] : [1071 ^ _337146 : [(1072 ^ _337146) ^ [_375669] : [in(ordered_pair(_375669, _375590), _374985)]], -(in(_375590, _375166))]]]]], (1092 ^ _337146) ^ [_376440, _376442] : [element(_376440, powerset(_376442)), -(subset_complement(_376442, _376440) = set_difference(_376442, _376440))], (1098 ^ _337146) ^ [_376651, _376653] : [-(ordered_pair(_376653, _376651) = unordered_pair(unordered_pair(_376653, _376651), singleton(_376653)))], (1100 ^ _337146) ^ [_376757] : [relation(_376757), -(relation_field(_376757) = set_union2(relation_dom(_376757), relation_rng(_376757)))], (1106 ^ _337146) ^ [_376963] : [relation(_376963), 1109 ^ _337146 : [(1110 ^ _337146) ^ [_377123] : [relation(_377123), 1113 ^ _337146 : [(1130 ^ _337146) ^ [] : [-(_377123 = relation_inverse(_376963)), 1135 ^ _337146 : [(1136 ^ _337146) ^ [] : [-(in(ordered_pair(1131 ^ [_376963, _377123], 1132 ^ [_376963, _377123]), _377123))], (1138 ^ _337146) ^ [] : [in(ordered_pair(1132 ^ [_376963, _377123], 1131 ^ [_376963, _377123]), _376963)]], 1139 ^ _337146 : [(1140 ^ _337146) ^ [] : [-(in(ordered_pair(1132 ^ [_376963, _377123], 1131 ^ [_376963, _377123]), _376963))], (1142 ^ _337146) ^ [] : [in(ordered_pair(1131 ^ [_376963, _377123], 1132 ^ [_376963, _377123]), _377123)]]], (1114 ^ _337146) ^ [] : [_377123 = relation_inverse(_376963), 1117 ^ _337146 : [(1118 ^ _337146) ^ [_377432, _377434] : [in(ordered_pair(_377434, _377432), _377123), -(in(ordered_pair(_377432, _377434), _376963))], (1124 ^ _337146) ^ [_377622, _377624] : [in(ordered_pair(_377622, _377624), _376963), -(in(ordered_pair(_377624, _377622), _377123))]]]]]]], (1146 ^ _337146) ^ [_378470, _378472] : [disjoint(_378472, _378470), -(set_intersection2(_378472, _378470) = empty_set)], (1152 ^ _337146) ^ [_378638, _378640] : [set_intersection2(_378640, _378638) = empty_set, -(disjoint(_378640, _378638))], (1158 ^ _337146) ^ [_378842] : [relation(_378842), 1161 ^ _337146 : [(1162 ^ _337146) ^ [_379027] : [relation(_379027), 1165 ^ _337146 : [(1166 ^ _337146) ^ [_379208] : [relation(_379208), 1169 ^ _337146 : [(1193 ^ _337146) ^ [] : [-(_379208 = relation_composition(_378842, _379027)), 1207 ^ _337146 : [(1208 ^ _337146) ^ [] : [-(in(ordered_pair(1194 ^ [_378842, _379027, _379208], 1206 ^ [_378842, _379027, _379208]), _378842))], (1210 ^ _337146) ^ [] : [-(in(ordered_pair(1206 ^ [_378842, _379027, _379208], 1195 ^ [_378842, _379027, _379208]), _379027))], (1212 ^ _337146) ^ [] : [in(ordered_pair(1194 ^ [_378842, _379027, _379208], 1195 ^ [_378842, _379027, _379208]), _379208)]], 1198 ^ _337146 : [(1199 ^ _337146) ^ [] : [-(in(ordered_pair(1194 ^ [_378842, _379027, _379208], 1195 ^ [_378842, _379027, _379208]), _379208))], (1201 ^ _337146) ^ [_380672] : [in(ordered_pair(1194 ^ [_378842, _379027, _379208], _380672), _378842), in(ordered_pair(_380672, 1195 ^ [_378842, _379027, _379208]), _379027)]]], (1170 ^ _337146) ^ [] : [_379208 = relation_composition(_378842, _379027), 1173 ^ _337146 : [(1174 ^ _337146) ^ [_379543, _379545] : [in(ordered_pair(_379545, _379543), _379208), 1178 ^ _337146 : [(1179 ^ _337146) ^ [] : [-(in(ordered_pair(_379545, 1177 ^ [_378842, _379027, _379208, _379543, _379545]), _378842))], (1181 ^ _337146) ^ [] : [-(in(ordered_pair(1177 ^ [_378842, _379027, _379208, _379543, _379545], _379543), _379027))]]], (1183 ^ _337146) ^ [_379928, _379930] : [-(in(ordered_pair(_379930, _379928), _379208)), 1184 ^ _337146 : [(1185 ^ _337146) ^ [_380041] : [in(ordered_pair(_379930, _380041), _378842), in(ordered_pair(_380041, _379928), _379027)]]]]]]]]]]], (1216 ^ _337146) ^ [_381358, _381360] : [element(_381358, powerset(powerset(_381360))), 1219 ^ _337146 : [(1220 ^ _337146) ^ [_381538] : [element(_381538, powerset(powerset(_381360))), 1223 ^ _337146 : [(1244 ^ _337146) ^ [] : [-(_381538 = complements_of_subsets(_381360, _381358)), 1246 ^ _337146 : [(1247 ^ _337146) ^ [] : [-(element(1245 ^ [_381358, _381360, _381538], powerset(_381360)))], (1249 ^ _337146) ^ [] : [1250 ^ _337146 : [(1251 ^ _337146) ^ [] : [-(in(1245 ^ [_381358, _381360, _381538], _381538))], (1253 ^ _337146) ^ [] : [in(subset_complement(_381360, 1245 ^ [_381358, _381360, _381538]), _381358)]], 1254 ^ _337146 : [(1255 ^ _337146) ^ [] : [-(in(subset_complement(_381360, 1245 ^ [_381358, _381360, _381538]), _381358))], (1257 ^ _337146) ^ [] : [in(1245 ^ [_381358, _381360, _381538], _381538)]]]]], (1224 ^ _337146) ^ [] : [_381538 = complements_of_subsets(_381360, _381358), 1227 ^ _337146 : [(1228 ^ _337146) ^ [_381826] : [element(_381826, powerset(_381360)), 1231 ^ _337146 : [(1232 ^ _337146) ^ [] : [in(_381826, _381538), -(in(subset_complement(_381360, _381826), _381358))], (1238 ^ _337146) ^ [] : [in(subset_complement(_381360, _381826), _381358), -(in(_381826, _381538))]]]]]]]]], (1261 ^ _337146) ^ [_382949, _382951] : [proper_subset(_382951, _382949), 1264 ^ _337146 : [(1265 ^ _337146) ^ [] : [-(subset(_382951, _382949))], (1267 ^ _337146) ^ [] : [_382951 = _382949]]], (1269 ^ _337146) ^ [_383187, _383189] : [-(proper_subset(_383189, _383187)), subset(_383189, _383187), -(_383189 = _383187)], (1279 ^ _337146) ^ [] : [true___, -(true___)], (1285 ^ _337146) ^ [] : [true___, -(true___)], (1291 ^ _337146) ^ [] : [true___, -(true___)], (1297 ^ _337146) ^ [] : [true___, -(true___)], (1303 ^ _337146) ^ [] : [true___, -(true___)], (1309 ^ _337146) ^ [] : [true___, -(true___)], (1315 ^ _337146) ^ [_384176] : [-(element(cast_to_subset(_384176), powerset(_384176)))], (1317 ^ _337146) ^ [] : [true___, -(true___)], (1323 ^ _337146) ^ [] : [true___, -(true___)], (1329 ^ _337146) ^ [] : [true___, -(true___)], (1335 ^ _337146) ^ [] : [true___, -(true___)], (1341 ^ _337146) ^ [_384763, _384765] : [element(_384763, powerset(_384765)), -(element(subset_complement(_384765, _384763), powerset(_384765)))], (1347 ^ _337146) ^ [] : [true___, -(true___)], (1353 ^ _337146) ^ [] : [true___, -(true___)], (1359 ^ _337146) ^ [_385211] : [relation(_385211), -(relation(relation_inverse(_385211)))], (1365 ^ _337146) ^ [] : [true___, -(true___)], (1371 ^ _337146) ^ [] : [true___, -(true___)], (1377 ^ _337146) ^ [_385653, _385655] : [-(relation(relation_composition(_385655, _385653))), relation(_385655), relation(_385653)], (1387 ^ _337146) ^ [_385952, _385954] : [element(_385952, powerset(powerset(_385954))), -(element(union_of_subsets(_385954, _385952), powerset(_385954)))], (1393 ^ _337146) ^ [_386151] : [-(relation(identity_relation(_386151)))], (1395 ^ _337146) ^ [_386259, _386261] : [element(_386259, powerset(powerset(_386261))), -(element(meet_of_subsets(_386261, _386259), powerset(_386261)))], (1401 ^ _337146) ^ [_386501, _386503, _386505] : [-(element(subset_difference(_386505, _386503, _386501), powerset(_386505))), element(_386503, powerset(_386505)), element(_386501, powerset(_386505))], (1411 ^ _337146) ^ [_386830, _386832] : [relation(_386832), -(relation(relation_dom_restriction(_386832, _386830)))], (1417 ^ _337146) ^ [_387042, _387044] : [element(_387042, powerset(powerset(_387044))), -(element(complements_of_subsets(_387044, _387042), powerset(powerset(_387044))))], (1423 ^ _337146) ^ [] : [true___, -(true___)], (1430 ^ _337146) ^ [_387403] : [-(element(1428 ^ [_387403], _387403))], (1432 ^ _337146) ^ [_387515, _387517] : [1439 ^ _337146 : [(1440 ^ _337146) ^ [] : [-(empty(relation_composition(_387515, _387517)))], (1442 ^ _337146) ^ [] : [-(relation(relation_composition(_387515, _387517)))]], empty(_387517), relation(_387515)], (1444 ^ _337146) ^ [_387893, _387895] : [-(relation(set_intersection2(_387895, _387893))), relation(_387895), relation(_387893)], (1454 ^ _337146) ^ [_388162] : [empty(powerset(_388162))], (1456 ^ _337146) ^ [] : [-(empty(empty_set))], (1458 ^ _337146) ^ [_388307, _388309] : [empty(ordered_pair(_388309, _388307))], (1460 ^ _337146) ^ [_388418, _388420] : [-(relation(set_union2(_388420, _388418))), relation(_388420), relation(_388418)], (1470 ^ _337146) ^ [_388687] : [empty(singleton(_388687))], (1472 ^ _337146) ^ [_388795, _388797] : [-(empty(_388797)), empty(set_union2(_388797, _388795))], (1478 ^ _337146) ^ [_388995, _388997] : [empty(unordered_pair(_388997, _388995))], (1480 ^ _337146) ^ [_389106, _389108] : [-(empty(_389108)), empty(set_union2(_389106, _389108))], (1486 ^ _337146) ^ [] : [-(empty(empty_set))], (1488 ^ _337146) ^ [] : [-(relation(empty_set))], (1490 ^ _337146) ^ [_389430, _389432] : [empty(cartesian_product2(_389432, _389430)), -(empty(_389432)), -(empty(_389430))], (1500 ^ _337146) ^ [_389722] : [empty(relation_dom(_389722)), -(empty(_389722)), relation(_389722)], (1510 ^ _337146) ^ [_389999] : [empty(relation_rng(_389999)), -(empty(_389999)), relation(_389999)], (1520 ^ _337146) ^ [_390276] : [empty(_390276), 1523 ^ _337146 : [(1524 ^ _337146) ^ [] : [-(empty(relation_dom(_390276)))], (1526 ^ _337146) ^ [] : [-(relation(relation_dom(_390276)))]]], (1528 ^ _337146) ^ [_390541] : [empty(_390541), 1531 ^ _337146 : [(1532 ^ _337146) ^ [] : [-(empty(relation_rng(_390541)))], (1534 ^ _337146) ^ [] : [-(relation(relation_rng(_390541)))]]], (1536 ^ _337146) ^ [_390820, _390822] : [1543 ^ _337146 : [(1544 ^ _337146) ^ [] : [-(empty(relation_composition(_390822, _390820)))], (1546 ^ _337146) ^ [] : [-(relation(relation_composition(_390822, _390820)))]], empty(_390822), relation(_390820)], (1548 ^ _337146) ^ [_391183, _391185] : [-(set_union2(_391185, _391185) = _391185)], (1550 ^ _337146) ^ [_391280, _391282] : [-(set_intersection2(_391282, _391282) = _391282)], (1552 ^ _337146) ^ [_391392, _391394] : [element(_391392, powerset(_391394)), -(subset_complement(_391394, subset_complement(_391394, _391392)) = _391392)], (1558 ^ _337146) ^ [_391604] : [relation(_391604), -(relation_inverse(relation_inverse(_391604)) = _391604)], (1564 ^ _337146) ^ [_391814, _391816] : [element(_391814, powerset(powerset(_391816))), -(complements_of_subsets(_391816, complements_of_subsets(_391816, _391814)) = _391814)], (1570 ^ _337146) ^ [_392028, _392030] : [proper_subset(_392030, _392030)], (1572 ^ _337146) ^ [_392107] : [singleton(_392107) = empty_set], (1574 ^ _337146) ^ [_392216, _392218] : [in(_392218, _392216), -(set_union2(singleton(_392218), _392216) = _392216)], (1580 ^ _337146) ^ [_392436, _392438] : [disjoint(singleton(_392438), _392436), in(_392438, _392436)], (1586 ^ _337146) ^ [_392649, _392651] : [-(in(_392651, _392649)), -(disjoint(singleton(_392651), _392649))], (1592 ^ _337146) ^ [_392895, _392897] : [subset(singleton(_392897), _392895), -(in(_392897, _392895))], (1598 ^ _337146) ^ [_393061, _393063] : [in(_393063, _393061), -(subset(singleton(_393063), _393061))], (1604 ^ _337146) ^ [_393306, _393308] : [set_difference(_393308, _393306) = empty_set, -(subset(_393308, _393306))], (1610 ^ _337146) ^ [_393474, _393476] : [subset(_393476, _393474), -(set_difference(_393476, _393474) = empty_set)], (1616 ^ _337146) ^ [_393692, _393694] : [element(_393692, powerset(_393694)), 1619 ^ _337146 : [(1620 ^ _337146) ^ [_393833] : [in(_393833, _393692), -(in(_393833, _393694))]]], (1626 ^ _337146) ^ [_394072, _394074, _394076] : [subset(_394076, _394074), -(in(_394072, _394076)), -(subset(_394076, set_difference(_394074, singleton(_394072))))], (1646 ^ _337146) ^ [_394681, _394683] : [1647 ^ _337146 : [(1648 ^ _337146) ^ [] : [_394683 = empty_set], (1650 ^ _337146) ^ [] : [_394683 = singleton(_394681)]], -(subset(_394683, singleton(_394681)))], (1636 ^ _337146) ^ [_394421, _394423] : [subset(_394423, singleton(_394421)), -(_394423 = empty_set), -(_394423 = singleton(_394421))], (1654 ^ _337146) ^ [_394975, _394977] : [in(_394977, _394975), -(subset(_394977, union(_394975)))], (1660 ^ _337146) ^ [_395246, _395248, _395250, _395252] : [in(ordered_pair(_395252, _395250), cartesian_product2(_395248, _395246)), 1663 ^ _337146 : [(1664 ^ _337146) ^ [] : [-(in(_395252, _395248))], (1666 ^ _337146) ^ [] : [-(in(_395250, _395246))]]], (1668 ^ _337146) ^ [_395511, _395513, _395515, _395517] : [-(in(ordered_pair(_395517, _395515), cartesian_product2(_395513, _395511))), in(_395517, _395513), in(_395515, _395511)], (1678 ^ _337146) ^ [_395844, _395846] : [1680 ^ _337146 : [(1681 ^ _337146) ^ [] : [-(in(1679 ^ [_395844, _395846], _395846))], (1683 ^ _337146) ^ [] : [in(1679 ^ [_395844, _395846], _395844)]], -(element(_395846, powerset(_395844)))], (1688 ^ _337146) ^ [] : [-(empty(1686 ^ []))], (1690 ^ _337146) ^ [] : [-(relation(1686 ^ []))], (1692 ^ _337146) ^ [_396338] : [-(empty(_396338)), 1696 ^ _337146 : [(1697 ^ _337146) ^ [] : [-(element(1695 ^ [_396338], powerset(_396338)))], (1699 ^ _337146) ^ [] : [empty(1695 ^ [_396338])]]], (1702 ^ _337146) ^ [] : [-(empty(1700 ^ []))], (1705 ^ _337146) ^ [] : [empty(1703 ^ [])], (1707 ^ _337146) ^ [] : [-(relation(1703 ^ []))], (1710 ^ _337146) ^ [_396960] : [-(element(1708 ^ [_396960], powerset(_396960)))], (1712 ^ _337146) ^ [_397011] : [-(empty(1708 ^ [_397011]))], (1715 ^ _337146) ^ [] : [empty(1713 ^ [])], (1717 ^ _337146) ^ [_397214, _397216] : [element(_397214, powerset(powerset(_397216))), -(union_of_subsets(_397216, _397214) = union(_397214))], (1723 ^ _337146) ^ [_397442, _397444] : [element(_397442, powerset(powerset(_397444))), -(meet_of_subsets(_397444, _397442) = set_meet(_397442))], (1729 ^ _337146) ^ [_397684, _397686, _397688] : [-(subset_difference(_397688, _397686, _397684) = set_difference(_397686, _397684)), element(_397686, powerset(_397688)), element(_397684, powerset(_397688))], (1739 ^ _337146) ^ [_398000, _398002] : [-(subset(_398002, _398002))], (1741 ^ _337146) ^ [_398109, _398111] : [disjoint(_398111, _398109), -(disjoint(_398109, _398111))], (1747 ^ _337146) ^ [_398376, _398378, _398380, _398382] : [in(ordered_pair(_398382, _398380), cartesian_product2(_398378, _398376)), 1750 ^ _337146 : [(1751 ^ _337146) ^ [] : [-(in(_398382, _398378))], (1753 ^ _337146) ^ [] : [-(in(_398380, _398376))]]], (1755 ^ _337146) ^ [_398641, _398643, _398645, _398647] : [-(in(ordered_pair(_398647, _398645), cartesian_product2(_398643, _398641))), in(_398647, _398643), in(_398645, _398641)], (1765 ^ _337146) ^ [_399002, _399004, _399006, _399008] : [unordered_pair(_399008, _399006) = unordered_pair(_399004, _399002), -(_399008 = _399004), -(_399008 = _399002)], (1775 ^ _337146) ^ [_399352, _399354, _399356] : [subset(_399356, _399354), 1778 ^ _337146 : [(1779 ^ _337146) ^ [] : [-(subset(cartesian_product2(_399356, _399352), cartesian_product2(_399354, _399352)))], (1781 ^ _337146) ^ [] : [-(subset(cartesian_product2(_399352, _399356), cartesian_product2(_399352, _399354)))]]], (1783 ^ _337146) ^ [_399697, _399699, _399701, _399703] : [-(subset(cartesian_product2(_399703, _399699), cartesian_product2(_399701, _399697))), subset(_399703, _399701), subset(_399699, _399697)], (1793 ^ _337146) ^ [_400028, _400030] : [subset(_400030, _400028), -(set_union2(_400030, _400028) = _400028)], (1800 ^ _337146) ^ [_400350] : [-(in(_400350, 1798 ^ [_400350]))], (1802 ^ _337146) ^ [_400462, _400464, _400466] : [-(in(_400462, 1798 ^ [_400466])), in(_400464, 1798 ^ [_400466]), subset(_400462, _400464)], (1812 ^ _337146) ^ [_400777, _400779] : [in(_400777, 1798 ^ [_400779]), -(in(powerset(_400777), 1798 ^ [_400779]))], (1818 ^ _337146) ^ [_400977, _400979] : [subset(_400977, 1798 ^ [_400979]), -(are_equipotent(_400977, 1798 ^ [_400979])), -(in(_400977, 1798 ^ [_400979]))], (1828 ^ _337146) ^ [_401302, _401304] : [-(subset(set_intersection2(_401304, _401302), _401304))], (1830 ^ _337146) ^ [_401428, _401430, _401432] : [-(subset(_401432, set_intersection2(_401430, _401428))), subset(_401432, _401430), subset(_401432, _401428)], (1840 ^ _337146) ^ [_401714] : [-(set_union2(_401714, empty_set) = _401714)], (1842 ^ _337146) ^ [_401824, _401826] : [in(_401826, _401824), -(element(_401826, _401824))], (1848 ^ _337146) ^ [_402048, _402050, _402052] : [-(subset(_402052, _402048)), subset(_402052, _402050), subset(_402050, _402048)], (1858 ^ _337146) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (1860 ^ _337146) ^ [_402424, _402426, _402428] : [relation(_402424), in(ordered_pair(_402428, _402426), _402424), 1867 ^ _337146 : [(1868 ^ _337146) ^ [] : [-(in(_402428, relation_dom(_402424)))], (1870 ^ _337146) ^ [] : [-(in(_402426, relation_rng(_402424)))]]], (1872 ^ _337146) ^ [_402808] : [relation(_402808), -(subset(_402808, cartesian_product2(relation_dom(_402808), relation_rng(_402808))))], (1878 ^ _337146) ^ [_403010] : [relation(_403010), 1881 ^ _337146 : [(1882 ^ _337146) ^ [_403160] : [relation(_403160), subset(_403010, _403160), 1889 ^ _337146 : [(1890 ^ _337146) ^ [] : [-(subset(relation_dom(_403010), relation_dom(_403160)))], (1892 ^ _337146) ^ [] : [-(subset(relation_rng(_403010), relation_rng(_403160)))]]]]], (1894 ^ _337146) ^ [_403569, _403571, _403573] : [subset(_403573, _403571), -(subset(set_intersection2(_403573, _403569), set_intersection2(_403571, _403569)))], (1900 ^ _337146) ^ [_403797, _403799] : [subset(_403799, _403797), -(set_intersection2(_403799, _403797) = _403799)], (1906 ^ _337146) ^ [_403984] : [-(set_intersection2(_403984, empty_set) = empty_set)], (1908 ^ _337146) ^ [_404094, _404096] : [element(_404096, _404094), -(empty(_404094)), -(in(_404096, _404094))], (1918 ^ _337146) ^ [_404392, _404394] : [-(_404394 = _404392), 1922 ^ _337146 : [(1923 ^ _337146) ^ [] : [-(in(1919 ^ [_404392, _404394], _404394))], (1925 ^ _337146) ^ [] : [in(1919 ^ [_404392, _404394], _404392)]], 1926 ^ _337146 : [(1927 ^ _337146) ^ [] : [-(in(1919 ^ [_404392, _404394], _404392))], (1929 ^ _337146) ^ [] : [in(1919 ^ [_404392, _404394], _404394)]]], (1933 ^ _337146) ^ [_404893] : [-(subset(empty_set, _404893))], (1935 ^ _337146) ^ [_405014, _405016, _405018] : [relation(_405014), in(ordered_pair(_405018, _405016), _405014), 1942 ^ _337146 : [(1943 ^ _337146) ^ [] : [-(in(_405018, relation_field(_405014)))], (1945 ^ _337146) ^ [] : [-(in(_405016, relation_field(_405014)))]]], (1947 ^ _337146) ^ [_405426, _405428, _405430] : [subset(_405430, _405428), -(subset(set_difference(_405430, _405426), set_difference(_405428, _405426)))], (1953 ^ _337146) ^ [_405682, _405684, _405686, _405688] : [ordered_pair(_405688, _405686) = ordered_pair(_405684, _405682), 1956 ^ _337146 : [(1957 ^ _337146) ^ [] : [-(_405688 = _405684)], (1959 ^ _337146) ^ [] : [-(_405686 = _405682)]]], (1961 ^ _337146) ^ [_405980, _405982] : [-(subset(set_difference(_405982, _405980), _405982))], (1963 ^ _337146) ^ [_406078] : [relation(_406078), 1966 ^ _337146 : [(1967 ^ _337146) ^ [] : [-(relation_rng(_406078) = relation_dom(relation_inverse(_406078)))], (1969 ^ _337146) ^ [] : [-(relation_dom(_406078) = relation_rng(relation_inverse(_406078)))]]], (1971 ^ _337146) ^ [_406406, _406408] : [set_difference(_406408, _406406) = empty_set, -(subset(_406408, _406406))], (1977 ^ _337146) ^ [_406574, _406576] : [subset(_406576, _406574), -(set_difference(_406576, _406574) = empty_set)], (1983 ^ _337146) ^ [_406821, _406823] : [subset(singleton(_406823), _406821), -(in(_406823, _406821))], (1989 ^ _337146) ^ [_406987, _406989] : [in(_406989, _406987), -(subset(singleton(_406989), _406987))], (1995 ^ _337146) ^ [_407246, _407248, _407250] : [subset(unordered_pair(_407250, _407248), _407246), 1998 ^ _337146 : [(1999 ^ _337146) ^ [] : [-(in(_407250, _407246))], (2001 ^ _337146) ^ [] : [-(in(_407248, _407246))]]], (2003 ^ _337146) ^ [_407497, _407499, _407501] : [-(subset(unordered_pair(_407501, _407499), _407497)), in(_407501, _407497), in(_407499, _407497)], (2013 ^ _337146) ^ [_407799, _407801] : [-(set_union2(_407801, set_difference(_407799, _407801)) = set_union2(_407801, _407799))], (2025 ^ _337146) ^ [_408206, _408208] : [2026 ^ _337146 : [(2027 ^ _337146) ^ [] : [_408208 = empty_set], (2029 ^ _337146) ^ [] : [_408208 = singleton(_408206)]], -(subset(_408208, singleton(_408206)))], (2015 ^ _337146) ^ [_407946, _407948] : [subset(_407948, singleton(_407946)), -(_407948 = empty_set), -(_407948 = singleton(_407946))], (2033 ^ _337146) ^ [_408471] : [-(set_difference(_408471, empty_set) = _408471)], (2035 ^ _337146) ^ [_408610, _408612] : [element(_408612, powerset(_408610)), -(subset(_408612, _408610))], (2041 ^ _337146) ^ [_408776, _408778] : [subset(_408778, _408776), -(element(_408778, powerset(_408776)))], (2047 ^ _337146) ^ [_409012, _409014] : [-(disjoint(_409014, _409012)), 2051 ^ _337146 : [(2052 ^ _337146) ^ [] : [-(in(2050 ^ [_409012, _409014], _409014))], (2054 ^ _337146) ^ [] : [-(in(2050 ^ [_409012, _409014], _409012))]]], (2056 ^ _337146) ^ [_409326, _409328] : [disjoint(_409328, _409326), 2057 ^ _337146 : [(2058 ^ _337146) ^ [_409418] : [in(_409418, _409328), in(_409418, _409326)]]], (2066 ^ _337146) ^ [_409675] : [subset(_409675, empty_set), -(_409675 = empty_set)], (2072 ^ _337146) ^ [_409864, _409866] : [-(set_difference(set_union2(_409866, _409864), _409864) = set_difference(_409866, _409864))], (2074 ^ _337146) ^ [_409982, _409984] : [element(_409982, powerset(_409984)), 2077 ^ _337146 : [(2078 ^ _337146) ^ [_410134] : [element(_410134, powerset(_409984)), 2081 ^ _337146 : [(2082 ^ _337146) ^ [] : [disjoint(_409982, _410134), -(subset(_409982, subset_complement(_409984, _410134)))], (2088 ^ _337146) ^ [] : [subset(_409982, subset_complement(_409984, _410134)), -(disjoint(_409982, _410134))]]]]], (2094 ^ _337146) ^ [_410618] : [relation(_410618), 2097 ^ _337146 : [(2098 ^ _337146) ^ [_410755] : [relation(_410755), -(subset(relation_dom(relation_composition(_410618, _410755)), relation_dom(_410618)))]]], (2104 ^ _337146) ^ [_410970] : [relation(_410970), 2107 ^ _337146 : [(2108 ^ _337146) ^ [_411107] : [relation(_411107), -(subset(relation_rng(relation_composition(_410970, _411107)), relation_rng(_411107)))]]], (2114 ^ _337146) ^ [_411336, _411338] : [subset(_411338, _411336), -(_411336 = set_union2(_411338, set_difference(_411336, _411338)))], (2120 ^ _337146) ^ [_411544] : [relation(_411544), 2123 ^ _337146 : [(2124 ^ _337146) ^ [_411691] : [relation(_411691), subset(relation_rng(_411544), relation_dom(_411691)), -(relation_dom(relation_composition(_411544, _411691)) = relation_dom(_411544))]]], (2134 ^ _337146) ^ [_412017, _412019] : [element(_412017, powerset(powerset(_412019))), -(_412017 = empty_set), complements_of_subsets(_412019, _412017) = empty_set], (2144 ^ _337146) ^ [_412334, _412336] : [in(_412336, _412334), -(set_union2(singleton(_412336), _412334) = _412334)], (2150 ^ _337146) ^ [_412540] : [relation(_412540), 2153 ^ _337146 : [(2154 ^ _337146) ^ [_412687] : [relation(_412687), subset(relation_dom(_412540), relation_rng(_412687)), -(relation_rng(relation_composition(_412687, _412540)) = relation_rng(_412540))]]], (2164 ^ _337146) ^ [_413013, _413015] : [element(_413013, powerset(powerset(_413015))), -(_413013 = empty_set), -(subset_difference(_413015, cast_to_subset(_413015), union_of_subsets(_413015, _413013)) = meet_of_subsets(_413015, complements_of_subsets(_413015, _413013)))], (2174 ^ _337146) ^ [_413353, _413355] : [element(_413353, powerset(powerset(_413355))), -(_413353 = empty_set), -(union_of_subsets(_413355, complements_of_subsets(_413355, _413353)) = subset_difference(_413355, cast_to_subset(_413355), meet_of_subsets(_413355, _413353)))], (2184 ^ _337146) ^ [_413678, _413680] : [-(set_difference(_413680, set_difference(_413680, _413678)) = set_intersection2(_413680, _413678))], (2186 ^ _337146) ^ [_413767] : [-(set_difference(empty_set, _413767) = empty_set)], (2188 ^ _337146) ^ [_413891, _413893, _413895] : [-(element(_413895, _413891)), in(_413895, _413893), element(_413893, powerset(_413891))], (2198 ^ _337146) ^ [_414224, _414226] : [-(disjoint(_414226, _414224)), -(in(2201 ^ [_414224, _414226], set_intersection2(_414226, _414224)))], (2205 ^ _337146) ^ [_414459, _414461] : [2206 ^ _337146 : [(2207 ^ _337146) ^ [_414532] : [in(_414532, set_intersection2(_414461, _414459))]], disjoint(_414461, _414459)], (2211 ^ _337146) ^ [_414684] : [-(_414684 = empty_set), 2214 ^ _337146 : [(2215 ^ _337146) ^ [_414844] : [element(_414844, powerset(_414684)), 2218 ^ _337146 : [(2219 ^ _337146) ^ [_414998] : [element(_414998, _414684), -(in(_414998, _414844)), -(in(_414998, subset_complement(_414684, _414844)))]]]]], (2229 ^ _337146) ^ [_415344, _415346, _415348] : [element(_415344, powerset(_415348)), in(_415346, subset_complement(_415348, _415344)), in(_415346, _415344)], (2239 ^ _337146) ^ [_415650] : [relation(_415650), -(in(ordered_pair(2244 ^ [_415650], 2245 ^ [_415650]), _415650)), -(_415650 = empty_set)], (2251 ^ _337146) ^ [_416082, _416084, _416086] : [in(_416086, _416084), element(_416084, powerset(_416082)), empty(_416082)], (2261 ^ _337146) ^ [] : [-(relation_dom(empty_set) = empty_set)], (2263 ^ _337146) ^ [] : [-(relation_rng(empty_set) = empty_set)], (2265 ^ _337146) ^ [_416500, _416502] : [subset(_416502, _416500), proper_subset(_416500, _416502)], (2271 ^ _337146) ^ [_416723, _416725, _416727] : [-(disjoint(_416727, _416723)), subset(_416727, _416725), disjoint(_416725, _416723)], (2281 ^ _337146) ^ [_417018] : [relation(_417018), 2286 ^ _337146 : [(2287 ^ _337146) ^ [] : [relation_dom(_417018) = empty_set], (2289 ^ _337146) ^ [] : [relation_rng(_417018) = empty_set]], -(_417018 = empty_set)], (2293 ^ _337146) ^ [_417371] : [relation(_417371), 2296 ^ _337146 : [(2297 ^ _337146) ^ [] : [relation_dom(_417371) = empty_set, -(relation_rng(_417371) = empty_set)], (2303 ^ _337146) ^ [] : [relation_rng(_417371) = empty_set, -(relation_dom(_417371) = empty_set)]]], (2309 ^ _337146) ^ [_417854, _417856] : [set_difference(_417856, singleton(_417854)) = _417856, in(_417854, _417856)], (2315 ^ _337146) ^ [_418027, _418029] : [-(in(_418027, _418029)), -(set_difference(_418029, singleton(_418027)) = _418029)], (2321 ^ _337146) ^ [_418223] : [-(unordered_pair(_418223, _418223) = singleton(_418223))], (2323 ^ _337146) ^ [_418321] : [empty(_418321), -(_418321 = empty_set)], (2329 ^ _337146) ^ [_418523, _418525] : [subset(singleton(_418525), singleton(_418523)), -(_418525 = _418523)], (2335 ^ _337146) ^ [_418732] : [-(relation_dom(identity_relation(_418732)) = _418732)], (2337 ^ _337146) ^ [_418780] : [-(relation_rng(identity_relation(_418780)) = _418780)], (2339 ^ _337146) ^ [_418921, _418923, _418925, _418927] : [relation(_418921), 2342 ^ _337146 : [(2343 ^ _337146) ^ [] : [in(ordered_pair(_418927, _418925), relation_composition(identity_relation(_418923), _418921)), 2346 ^ _337146 : [(2347 ^ _337146) ^ [] : [-(in(_418927, _418923))], (2349 ^ _337146) ^ [] : [-(in(ordered_pair(_418927, _418925), _418921))]]], (2351 ^ _337146) ^ [] : [-(in(ordered_pair(_418927, _418925), relation_composition(identity_relation(_418923), _418921))), in(_418927, _418923), in(ordered_pair(_418927, _418925), _418921)]]], (2361 ^ _337146) ^ [_419614, _419616] : [in(_419616, _419614), empty(_419614)], (2367 ^ _337146) ^ [_419806, _419808] : [-(subset(_419808, set_union2(_419808, _419806)))], (2369 ^ _337146) ^ [_419947, _419949] : [disjoint(_419949, _419947), -(set_difference(_419949, _419947) = _419949)], (2375 ^ _337146) ^ [_420115, _420117] : [set_difference(_420117, _420115) = _420117, -(disjoint(_420117, _420115))], (2381 ^ _337146) ^ [_420347, _420349, _420351] : [relation(_420347), 2384 ^ _337146 : [(2385 ^ _337146) ^ [] : [in(_420351, relation_dom(relation_dom_restriction(_420347, _420349))), 2388 ^ _337146 : [(2389 ^ _337146) ^ [] : [-(in(_420351, _420349))], (2391 ^ _337146) ^ [] : [-(in(_420351, relation_dom(_420347)))]]], (2393 ^ _337146) ^ [] : [-(in(_420351, relation_dom(relation_dom_restriction(_420347, _420349)))), in(_420351, _420349), in(_420351, relation_dom(_420347))]]], (2403 ^ _337146) ^ [_421006, _421008] : [relation(_421006), -(subset(relation_dom_restriction(_421006, _421008), _421006))], (2409 ^ _337146) ^ [_421220, _421222] : [empty(_421222), -(_421222 = _421220), empty(_421220)], (2419 ^ _337146) ^ [_421531, _421533, _421535] : [-(subset(set_union2(_421535, _421531), _421533)), subset(_421535, _421533), subset(_421531, _421533)], (2429 ^ _337146) ^ [_421860, _421862, _421864] : [singleton(_421864) = unordered_pair(_421862, _421860), -(_421864 = _421862)], (2435 ^ _337146) ^ [_422086, _422088] : [relation(_422086), -(relation_dom(relation_dom_restriction(_422086, _422088)) = set_intersection2(relation_dom(_422086), _422088))], (2441 ^ _337146) ^ [_422314, _422316] : [in(_422316, _422314), -(subset(_422316, union(_422314)))], (2447 ^ _337146) ^ [_422528, _422530] : [relation(_422528), -(relation_dom_restriction(_422528, _422530) = relation_composition(identity_relation(_422530), _422528))], (2453 ^ _337146) ^ [_422723] : [-(union(powerset(_422723)) = _422723)], (2491 ^ _337146) ^ [_424244, _424246, _424248] : [singleton(_424248) = unordered_pair(_424246, _424244), -(_424246 = _424244)], (2456 ^ _337146) ^ [_422964] : [-(in(_422964, 2454 ^ [_422964]))], (2458 ^ _337146) ^ [_423076, _423078, _423080] : [-(in(_423076, 2454 ^ [_423080])), in(_423078, 2454 ^ [_423080]), subset(_423076, _423078)], (2468 ^ _337146) ^ [_423391, _423393] : [in(_423391, 2454 ^ [_423393]), 2472 ^ _337146 : [(2473 ^ _337146) ^ [] : [-(in(2471 ^ [_423391, _423393], 2454 ^ [_423393]))], (2475 ^ _337146) ^ [_423703] : [subset(_423703, _423391), -(in(_423703, 2471 ^ [_423391, _423393]))]]], (2481 ^ _337146) ^ [_423910, _423912] : [subset(_423910, 2454 ^ [_423912]), -(are_equipotent(_423910, 2454 ^ [_423912])), -(in(_423910, 2454 ^ [_423912]))]], input).
% 0.63/1.40  ncf('1',plain,[subset(relation_rng(relation_dom_restriction(2497 ^ [], 2496 ^ [])), relation_rng(2497 ^ []))],start(2501 ^ 0)).
% 0.63/1.40  ncf('1.1',plain,[-(subset(relation_rng(relation_dom_restriction(2497 ^ [], 2496 ^ [])), relation_rng(2497 ^ []))), 1882 : relation(2497 ^ []), 1882 : subset(relation_dom_restriction(2497 ^ [], 2496 ^ []), 2497 ^ []), 1882 : relation(relation_dom_restriction(2497 ^ [], 2496 ^ []))],extension(1878 ^ 1,bind([[_403010, _403160], [relation_dom_restriction(2497 ^ [], 2496 ^ []), 2497 ^ []]]))).
% 0.63/1.40  ncf('1.1.1',plain,[-(relation(2497 ^ []))],extension(2499 ^ 4)).
% 0.63/1.40  ncf('1.1.2',plain,[-(subset(relation_dom_restriction(2497 ^ [], 2496 ^ []), 2497 ^ [])), relation(2497 ^ [])],extension(2403 ^ 4,bind([[_421006, _421008], [2497 ^ [], 2496 ^ []]]))).
% 0.63/1.40  ncf('1.1.2.1',plain,[-(relation(2497 ^ []))],lemmata('[1].x')).
% 0.63/1.40  ncf('1.1.3',plain,[-(relation(relation_dom_restriction(2497 ^ [], 2496 ^ []))), relation(2497 ^ [])],extension(1411 ^ 2,bind([[_386830, _386832], [2496 ^ [], 2497 ^ []]]))).
% 0.63/1.40  ncf('1.1.3.1',plain,[-(relation(2497 ^ []))],extension(2499 ^ 3)).
% 0.63/1.40  %-----------------------------------------------------
% 0.63/1.40  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------