%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU194+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n028.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 9.06s 9.69s
% Output   : Proof 9.06s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU194+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n028.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 13:53:18 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 9.06/9.69  
% 9.06/9.69  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 9.06/9.69  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.06/9.69  %-----------------------------------------------------
% 9.06/9.69  ncf(matrix, plain, [(2447 ^ _335709) ^ [] : [-(relation(2445 ^ []))], (2449 ^ _335709) ^ [] : [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])) = set_intersection2(relation_dom(2445 ^ []), 2444 ^ [])], (2 ^ _335709) ^ [_335853] : [-(_335853 = _335853)], (4 ^ _335709) ^ [_335960, _335962] : [_335962 = _335960, -(_335960 = _335962)], (10 ^ _335709) ^ [_336164, _336166, _336168] : [-(_336168 = _336164), _336168 = _336166, _336166 = _336164], (20 ^ _335709) ^ [_336505, _336507, _336509, _336511] : [-(element(_336509, _336505)), element(_336511, _336507), _336511 = _336509, _336507 = _336505], (34 ^ _335709) ^ [_336949, _336951, _336953, _336955] : [-(proper_subset(_336953, _336949)), proper_subset(_336955, _336951), _336955 = _336953, _336951 = _336949], (48 ^ _335709) ^ [_337393, _337395, _337397, _337399] : [-(disjoint(_337397, _337393)), disjoint(_337399, _337395), _337399 = _337397, _337395 = _337393], (62 ^ _335709) ^ [_337809, _337811] : [-(empty(_337809)), _337811 = _337809, empty(_337811)], (72 ^ _335709) ^ [_338132, _338134, _338136, _338138] : [-(subset(_338136, _338132)), subset(_338138, _338134), _338138 = _338136, _338134 = _338132], (86 ^ _335709) ^ [_338576, _338578, _338580, _338582] : [-(are_equipotent(_338580, _338576)), are_equipotent(_338582, _338578), _338582 = _338580, _338578 = _338576], (114 ^ _335709) ^ [_339416, _339418] : [-(relation(_339416)), _339418 = _339416, relation(_339418)], (100 ^ _335709) ^ [_339020, _339022, _339024, _339026] : [-(in(_339024, _339020)), in(_339026, _339022), _339026 = _339024, _339022 = _339020], (124 ^ _335709) ^ [_339731, _339733] : [_339733 = _339731, -(set_meet(_339733) = set_meet(_339731))], (130 ^ _335709) ^ [_339977, _339979, _339981, _339983] : [-(cartesian_product2(_339983, _339979) = cartesian_product2(_339981, _339977)), _339983 = _339981, _339979 = _339977], (140 ^ _335709) ^ [_340308, _340310] : [_340310 = _340308, -(relation_field(_340310) = relation_field(_340308))], (146 ^ _335709) ^ [_340526, _340528] : [_340528 = _340526, -(relation_inverse(_340528) = relation_inverse(_340526))], (152 ^ _335709) ^ [_340772, _340774, _340776, _340778] : [-(union_of_subsets(_340778, _340774) = union_of_subsets(_340776, _340772)), _340778 = _340776, _340774 = _340772], (162 ^ _335709) ^ [_341131, _341133, _341135, _341137] : [-(complements_of_subsets(_341137, _341133) = complements_of_subsets(_341135, _341131)), _341137 = _341135, _341133 = _341131], (172 ^ _335709) ^ [_341518, _341520, _341522, _341524, _341526, _341528] : [-(subset_difference(_341528, _341524, _341520) = subset_difference(_341526, _341522, _341518)), _341528 = _341526, _341524 = _341522, _341520 = _341518], (186 ^ _335709) ^ [_341978, _341980] : [_341980 = _341978, -(cast_to_subset(_341980) = cast_to_subset(_341978))], (192 ^ _335709) ^ [_342224, _342226, _342228, _342230] : [-(meet_of_subsets(_342230, _342226) = meet_of_subsets(_342228, _342224)), _342230 = _342228, _342226 = _342224], (202 ^ _335709) ^ [_342583, _342585, _342587, _342589] : [-(subset_complement(_342589, _342585) = subset_complement(_342587, _342583)), _342589 = _342587, _342585 = _342583], (212 ^ _335709) ^ [_342914, _342916] : [_342916 = _342914, -(relation_rng(_342916) = relation_rng(_342914))], (218 ^ _335709) ^ [_343160, _343162, _343164, _343166] : [-(relation_composition(_343166, _343162) = relation_composition(_343164, _343160)), _343166 = _343164, _343162 = _343160], (228 ^ _335709) ^ [_343491, _343493] : [_343493 = _343491, -(identity_relation(_343493) = identity_relation(_343491))], (234 ^ _335709) ^ [_343737, _343739, _343741, _343743] : [-(ordered_pair(_343743, _343739) = ordered_pair(_343741, _343737)), _343743 = _343741, _343739 = _343737], (244 ^ _335709) ^ [_344096, _344098, _344100, _344102] : [-(set_difference(_344102, _344098) = set_difference(_344100, _344096)), _344102 = _344100, _344098 = _344096], (254 ^ _335709) ^ [_344455, _344457, _344459, _344461] : [-(set_union2(_344461, _344457) = set_union2(_344459, _344455)), _344461 = _344459, _344457 = _344455], (264 ^ _335709) ^ [_344786, _344788] : [_344788 = _344786, -(union(_344788) = union(_344786))], (270 ^ _335709) ^ [_345004, _345006] : [_345006 = _345004, -(powerset(_345006) = powerset(_345004))], (276 ^ _335709) ^ [_345222, _345224] : [_345224 = _345222, -(singleton(_345224) = singleton(_345222))], (282 ^ _335709) ^ [_345468, _345470, _345472, _345474] : [-(unordered_pair(_345474, _345470) = unordered_pair(_345472, _345468)), _345474 = _345472, _345470 = _345468], (292 ^ _335709) ^ [_345827, _345829, _345831, _345833] : [-(relation_dom_restriction(_345833, _345829) = relation_dom_restriction(_345831, _345827)), _345833 = _345831, _345829 = _345827], (312 ^ _335709) ^ [_346497, _346499] : [_346499 = _346497, -(relation_dom(_346499) = relation_dom(_346497))], (302 ^ _335709) ^ [_346186, _346188, _346190, _346192] : [-(set_intersection2(_346192, _346188) = set_intersection2(_346190, _346186)), _346192 = _346190, _346188 = _346186], (318 ^ _335709) ^ [_346817, _346819] : [in(_346819, _346817), in(_346817, _346819)], (324 ^ _335709) ^ [_347028, _347030] : [proper_subset(_347030, _347028), proper_subset(_347028, _347030)], (330 ^ _335709) ^ [_347225] : [empty(_347225), -(relation(_347225))], (336 ^ _335709) ^ [_347410, _347412] : [-(unordered_pair(_347412, _347410) = unordered_pair(_347410, _347412))], (338 ^ _335709) ^ [_347510, _347512] : [-(set_union2(_347512, _347510) = set_union2(_347510, _347512))], (340 ^ _335709) ^ [_347610, _347612] : [-(set_intersection2(_347612, _347610) = set_intersection2(_347610, _347612))], (342 ^ _335709) ^ [_347725, _347727] : [relation(_347725), 345 ^ _335709 : [(368 ^ _335709) ^ [] : [-(_347725 = identity_relation(_347727)), 381 ^ _335709 : [(382 ^ _335709) ^ [] : [-(in(369 ^ [_347725, _347727], _347727))], (384 ^ _335709) ^ [] : [-(369 ^ [_347725, _347727] = 370 ^ [_347725, _347727])], (386 ^ _335709) ^ [] : [in(ordered_pair(369 ^ [_347725, _347727], 370 ^ [_347725, _347727]), _347725)]], 373 ^ _335709 : [(374 ^ _335709) ^ [] : [-(in(ordered_pair(369 ^ [_347725, _347727], 370 ^ [_347725, _347727]), _347725))], (376 ^ _335709) ^ [] : [in(369 ^ [_347725, _347727], _347727), 369 ^ [_347725, _347727] = 370 ^ [_347725, _347727]]]], (346 ^ _335709) ^ [] : [_347725 = identity_relation(_347727), 349 ^ _335709 : [(350 ^ _335709) ^ [_348035, _348037] : [in(ordered_pair(_348037, _348035), _347725), 353 ^ _335709 : [(354 ^ _335709) ^ [] : [-(in(_348037, _347727))], (356 ^ _335709) ^ [] : [-(_348037 = _348035)]]], (358 ^ _335709) ^ [_348298, _348300] : [-(in(ordered_pair(_348300, _348298), _347725)), in(_348300, _347727), _348300 = _348298]]]]], (390 ^ _335709) ^ [_349406, _349408] : [_349408 = _349406, 393 ^ _335709 : [(394 ^ _335709) ^ [] : [-(subset(_349408, _349406))], (396 ^ _335709) ^ [] : [-(subset(_349406, _349408))]]], (398 ^ _335709) ^ [_349643, _349645] : [-(_349645 = _349643), subset(_349645, _349643), subset(_349643, _349645)], (408 ^ _335709) ^ [_349930] : [relation(_349930), 411 ^ _335709 : [(412 ^ _335709) ^ [_350116, _350118] : [relation(_350116), 415 ^ _335709 : [(438 ^ _335709) ^ [] : [-(_350116 = relation_dom_restriction(_349930, _350118)), 451 ^ _335709 : [(452 ^ _335709) ^ [] : [-(in(439 ^ [_349930, _350116, _350118], _350118))], (454 ^ _335709) ^ [] : [-(in(ordered_pair(439 ^ [_349930, _350116, _350118], 440 ^ [_349930, _350116, _350118]), _349930))], (456 ^ _335709) ^ [] : [in(ordered_pair(439 ^ [_349930, _350116, _350118], 440 ^ [_349930, _350116, _350118]), _350116)]], 443 ^ _335709 : [(444 ^ _335709) ^ [] : [-(in(ordered_pair(439 ^ [_349930, _350116, _350118], 440 ^ [_349930, _350116, _350118]), _350116))], (446 ^ _335709) ^ [] : [in(439 ^ [_349930, _350116, _350118], _350118), in(ordered_pair(439 ^ [_349930, _350116, _350118], 440 ^ [_349930, _350116, _350118]), _349930)]]], (416 ^ _335709) ^ [] : [_350116 = relation_dom_restriction(_349930, _350118), 419 ^ _335709 : [(420 ^ _335709) ^ [_350441, _350443] : [in(ordered_pair(_350443, _350441), _350116), 423 ^ _335709 : [(424 ^ _335709) ^ [] : [-(in(_350443, _350118))], (426 ^ _335709) ^ [] : [-(in(ordered_pair(_350443, _350441), _349930))]]], (428 ^ _335709) ^ [_350720, _350722] : [-(in(ordered_pair(_350722, _350720), _350116)), in(_350722, _350118), in(ordered_pair(_350722, _350720), _349930)]]]]]]], (472 ^ _335709) ^ [_352365] : [474 ^ _335709 : [(475 ^ _335709) ^ [] : [-(in(473 ^ [_352365], _352365))], (477 ^ _335709) ^ [_352602, _352604] : [473 ^ [_352365] = ordered_pair(_352604, _352602)]], -(relation(_352365))], (460 ^ _335709) ^ [_351904] : [relation(_351904), 463 ^ _335709 : [(464 ^ _335709) ^ [_352052] : [in(_352052, _351904), -(_352052 = ordered_pair(467 ^ [_351904, _352052], 468 ^ [_351904, _352052]))]]], (530 ^ _335709) ^ [_354500, _354502] : [_354502 = empty_set, 533 ^ _335709 : [(534 ^ _335709) ^ [] : [_354500 = set_meet(_354502), -(_354500 = empty_set)], (540 ^ _335709) ^ [] : [_354500 = empty_set, -(_354500 = set_meet(_354502))]]], (481 ^ _335709) ^ [_352793, _352795] : [-(_352795 = empty_set), 484 ^ _335709 : [(508 ^ _335709) ^ [] : [-(_352793 = set_meet(_352795)), 512 ^ _335709 : [(513 ^ _335709) ^ [] : [-(in(509 ^ [_352793, _352795], _352793))], (516 ^ _335709) ^ [] : [-(in(514 ^ [_352793, _352795], _352795))], (518 ^ _335709) ^ [] : [in(509 ^ [_352793, _352795], 514 ^ [_352793, _352795])]], 519 ^ _335709 : [(526 ^ _335709) ^ [] : [in(509 ^ [_352793, _352795], _352793)], (520 ^ _335709) ^ [_354195] : [in(_354195, _352795), -(in(509 ^ [_352793, _352795], _354195))]]], (485 ^ _335709) ^ [] : [_352793 = set_meet(_352795), 488 ^ _335709 : [(499 ^ _335709) ^ [_353421] : [501 ^ _335709 : [(502 ^ _335709) ^ [] : [-(in(500 ^ [_352793, _352795, _353421], _352795))], (504 ^ _335709) ^ [] : [in(_353421, 500 ^ [_352793, _352795, _353421])]], -(in(_353421, _352793))], (489 ^ _335709) ^ [_353091] : [in(_353091, _352793), 492 ^ _335709 : [(493 ^ _335709) ^ [_353236] : [in(_353236, _352795), -(in(_353091, _353236))]]]]]]], (562 ^ _335709) ^ [_355518, _355520] : [-(_355518 = singleton(_355520)), 566 ^ _335709 : [(567 ^ _335709) ^ [] : [-(in(563 ^ [_355518, _355520], _355518))], (569 ^ _335709) ^ [] : [563 ^ [_355518, _355520] = _355520]], 570 ^ _335709 : [(571 ^ _335709) ^ [] : [-(563 ^ [_355518, _355520] = _355520)], (573 ^ _335709) ^ [] : [in(563 ^ [_355518, _355520], _355518)]]], (546 ^ _335709) ^ [_354997, _354999] : [_354997 = singleton(_354999), 549 ^ _335709 : [(550 ^ _335709) ^ [_355167] : [in(_355167, _354997), -(_355167 = _354999)], (556 ^ _335709) ^ [_355339] : [_355339 = _354999, -(in(_355339, _354997))]]], (577 ^ _335709) ^ [_356069] : [_356069 = empty_set, 580 ^ _335709 : [(581 ^ _335709) ^ [_356182] : [in(_356182, _356069)]]], (583 ^ _335709) ^ [_356248] : [-(in(584 ^ [_356248], _356248)), -(_356248 = empty_set)], (606 ^ _335709) ^ [_357060, _357062] : [-(_357060 = powerset(_357062)), 610 ^ _335709 : [(611 ^ _335709) ^ [] : [-(in(607 ^ [_357060, _357062], _357060))], (613 ^ _335709) ^ [] : [subset(607 ^ [_357060, _357062], _357062)]], 614 ^ _335709 : [(615 ^ _335709) ^ [] : [-(subset(607 ^ [_357060, _357062], _357062))], (617 ^ _335709) ^ [] : [in(607 ^ [_357060, _357062], _357060)]]], (590 ^ _335709) ^ [_356539, _356541] : [_356539 = powerset(_356541), 593 ^ _335709 : [(594 ^ _335709) ^ [_356709] : [in(_356709, _356539), -(subset(_356709, _356541))], (600 ^ _335709) ^ [_356881] : [subset(_356881, _356541), -(in(_356881, _356539))]]], (621 ^ _335709) ^ [_357616, _357618] : [-(empty(_357618)), 624 ^ _335709 : [(625 ^ _335709) ^ [] : [element(_357616, _357618), -(in(_357616, _357618))], (631 ^ _335709) ^ [] : [in(_357616, _357618), -(element(_357616, _357618))]]], (637 ^ _335709) ^ [_358029, _358031] : [empty(_358031), 640 ^ _335709 : [(641 ^ _335709) ^ [] : [element(_358029, _358031), -(empty(_358029))], (647 ^ _335709) ^ [] : [empty(_358029), -(element(_358029, _358031))]]], (675 ^ _335709) ^ [_359254, _359256, _359258] : [-(_359254 = unordered_pair(_359258, _359256)), 679 ^ _335709 : [(680 ^ _335709) ^ [] : [-(in(676 ^ [_359254, _359256, _359258], _359254))], (682 ^ _335709) ^ [] : [676 ^ [_359254, _359256, _359258] = _359258], (684 ^ _335709) ^ [] : [676 ^ [_359254, _359256, _359258] = _359256]], 685 ^ _335709 : [(692 ^ _335709) ^ [] : [in(676 ^ [_359254, _359256, _359258], _359254)], (686 ^ _335709) ^ [] : [-(676 ^ [_359254, _359256, _359258] = _359258), -(676 ^ [_359254, _359256, _359258] = _359256)]]], (653 ^ _335709) ^ [_358529, _358531, _358533] : [_358529 = unordered_pair(_358533, _358531), 656 ^ _335709 : [(667 ^ _335709) ^ [_358989] : [668 ^ _335709 : [(669 ^ _335709) ^ [] : [_358989 = _358533], (671 ^ _335709) ^ [] : [_358989 = _358531]], -(in(_358989, _358529))], (657 ^ _335709) ^ [_358711] : [in(_358711, _358529), -(_358711 = _358533), -(_358711 = _358531)]]], (718 ^ _335709) ^ [_360773, _360775, _360777] : [-(_360773 = set_union2(_360777, _360775)), 722 ^ _335709 : [(723 ^ _335709) ^ [] : [-(in(719 ^ [_360773, _360775, _360777], _360773))], (725 ^ _335709) ^ [] : [in(719 ^ [_360773, _360775, _360777], _360777)], (727 ^ _335709) ^ [] : [in(719 ^ [_360773, _360775, _360777], _360775)]], 728 ^ _335709 : [(735 ^ _335709) ^ [] : [in(719 ^ [_360773, _360775, _360777], _360773)], (729 ^ _335709) ^ [] : [-(in(719 ^ [_360773, _360775, _360777], _360777)), -(in(719 ^ [_360773, _360775, _360777], _360775))]]], (696 ^ _335709) ^ [_360048, _360050, _360052] : [_360048 = set_union2(_360052, _360050), 699 ^ _335709 : [(710 ^ _335709) ^ [_360508] : [711 ^ _335709 : [(712 ^ _335709) ^ [] : [in(_360508, _360052)], (714 ^ _335709) ^ [] : [in(_360508, _360050)]], -(in(_360508, _360048))], (700 ^ _335709) ^ [_360230] : [in(_360230, _360048), -(in(_360230, _360052)), -(in(_360230, _360050))]]], (769 ^ _335709) ^ [_362824, _362826, _362828] : [-(_362824 = cartesian_product2(_362828, _362826)), 787 ^ _335709 : [(788 ^ _335709) ^ [] : [-(in(785 ^ [_362824, _362826, _362828], _362828))], (790 ^ _335709) ^ [] : [-(in(786 ^ [_362824, _362826, _362828], _362826))], (792 ^ _335709) ^ [] : [-(770 ^ [_362824, _362826, _362828] = ordered_pair(785 ^ [_362824, _362826, _362828], 786 ^ [_362824, _362826, _362828]))], (794 ^ _335709) ^ [] : [in(770 ^ [_362824, _362826, _362828], _362824)]], 773 ^ _335709 : [(774 ^ _335709) ^ [] : [-(in(770 ^ [_362824, _362826, _362828], _362824))], (776 ^ _335709) ^ [_363162, _363164] : [in(_363164, _362828), in(_363162, _362826), 770 ^ [_362824, _362826, _362828] = ordered_pair(_363164, _363162)]]], (739 ^ _335709) ^ [_361567, _361569, _361571] : [_361567 = cartesian_product2(_361571, _361569), 742 ^ _335709 : [(743 ^ _335709) ^ [_361768] : [in(_361768, _361567), 748 ^ _335709 : [(749 ^ _335709) ^ [] : [-(in(746 ^ [_361567, _361569, _361571, _361768], _361571))], (751 ^ _335709) ^ [] : [-(in(747 ^ [_361567, _361569, _361571, _361768], _361569))], (753 ^ _335709) ^ [] : [-(_361768 = ordered_pair(746 ^ [_361567, _361569, _361571, _361768], 747 ^ [_361567, _361569, _361571, _361768]))]]], (755 ^ _335709) ^ [_362328] : [-(in(_362328, _361567)), 756 ^ _335709 : [(757 ^ _335709) ^ [_362458, _362460] : [in(_362460, _361571), in(_362458, _361569), _362328 = ordered_pair(_362460, _362458)]]]]], (798 ^ _335709) ^ [_364058] : [relation(_364058), 801 ^ _335709 : [(802 ^ _335709) ^ [_364216] : [relation(_364216), 805 ^ _335709 : [(816 ^ _335709) ^ [] : [819 ^ _335709 : [(820 ^ _335709) ^ [] : [-(in(ordered_pair(817 ^ [_364058, _364216], 818 ^ [_364058, _364216]), _364058))], (822 ^ _335709) ^ [] : [in(ordered_pair(817 ^ [_364058, _364216], 818 ^ [_364058, _364216]), _364216)]], -(subset(_364058, _364216))], (806 ^ _335709) ^ [] : [subset(_364058, _364216), 809 ^ _335709 : [(810 ^ _335709) ^ [_364492, _364494] : [in(ordered_pair(_364494, _364492), _364058), -(in(ordered_pair(_364494, _364492), _364216))]]]]]]], (836 ^ _335709) ^ [_365455, _365457] : [838 ^ _335709 : [(839 ^ _335709) ^ [] : [-(in(837 ^ [_365455, _365457], _365457))], (841 ^ _335709) ^ [] : [in(837 ^ [_365455, _365457], _365455)]], -(subset(_365457, _365455))], (826 ^ _335709) ^ [_365141, _365143] : [subset(_365143, _365141), 829 ^ _335709 : [(830 ^ _335709) ^ [_365278] : [in(_365278, _365143), -(in(_365278, _365141))]]], (867 ^ _335709) ^ [_366580, _366582, _366584] : [-(_366580 = set_intersection2(_366584, _366582)), 879 ^ _335709 : [(880 ^ _335709) ^ [] : [-(in(868 ^ [_366580, _366582, _366584], _366584))], (882 ^ _335709) ^ [] : [-(in(868 ^ [_366580, _366582, _366584], _366582))], (884 ^ _335709) ^ [] : [in(868 ^ [_366580, _366582, _366584], _366580)]], 871 ^ _335709 : [(872 ^ _335709) ^ [] : [-(in(868 ^ [_366580, _366582, _366584], _366580))], (874 ^ _335709) ^ [] : [in(868 ^ [_366580, _366582, _366584], _366584), in(868 ^ [_366580, _366582, _366584], _366582)]]], (845 ^ _335709) ^ [_365855, _365857, _365859] : [_365855 = set_intersection2(_365859, _365857), 848 ^ _335709 : [(849 ^ _335709) ^ [_366037] : [in(_366037, _365855), 852 ^ _335709 : [(853 ^ _335709) ^ [] : [-(in(_366037, _365859))], (855 ^ _335709) ^ [] : [-(in(_366037, _365857))]]], (857 ^ _335709) ^ [_366296] : [-(in(_366296, _365855)), in(_366296, _365859), in(_366296, _365857)]]], (888 ^ _335709) ^ [_367319] : [relation(_367319), 891 ^ _335709 : [(909 ^ _335709) ^ [_368131] : [-(_368131 = relation_dom(_367319)), 913 ^ _335709 : [(914 ^ _335709) ^ [] : [-(in(910 ^ [_367319, _368131], _368131))], (916 ^ _335709) ^ [_368394] : [in(ordered_pair(910 ^ [_367319, _368131], _368394), _367319)]], 918 ^ _335709 : [(919 ^ _335709) ^ [] : [-(in(ordered_pair(910 ^ [_367319, _368131], 917 ^ [_367319, _368131]), _367319))], (921 ^ _335709) ^ [] : [in(910 ^ [_367319, _368131], _368131)]]], (892 ^ _335709) ^ [_367500] : [_367500 = relation_dom(_367319), 895 ^ _335709 : [(896 ^ _335709) ^ [_367680] : [in(_367680, _367500), -(in(ordered_pair(_367680, 899 ^ [_367319, _367500, _367680]), _367319))], (903 ^ _335709) ^ [_367924] : [904 ^ _335709 : [(905 ^ _335709) ^ [_368003] : [in(ordered_pair(_367924, _368003), _367319)]], -(in(_367924, _367500))]]]]], (925 ^ _335709) ^ [_368745] : [-(cast_to_subset(_368745) = _368745)], (950 ^ _335709) ^ [_369728, _369730] : [-(_369728 = union(_369730)), 963 ^ _335709 : [(964 ^ _335709) ^ [] : [-(in(951 ^ [_369728, _369730], 962 ^ [_369728, _369730]))], (966 ^ _335709) ^ [] : [-(in(962 ^ [_369728, _369730], _369730))], (968 ^ _335709) ^ [] : [in(951 ^ [_369728, _369730], _369728)]], 954 ^ _335709 : [(955 ^ _335709) ^ [] : [-(in(951 ^ [_369728, _369730], _369728))], (957 ^ _335709) ^ [_370011] : [in(951 ^ [_369728, _369730], _370011), in(_370011, _369730)]]], (927 ^ _335709) ^ [_368883, _368885] : [_368883 = union(_368885), 930 ^ _335709 : [(931 ^ _335709) ^ [_369064] : [in(_369064, _368883), 935 ^ _335709 : [(936 ^ _335709) ^ [] : [-(in(_369064, 934 ^ [_368883, _368885, _369064]))], (938 ^ _335709) ^ [] : [-(in(934 ^ [_368883, _368885, _369064], _368885))]]], (940 ^ _335709) ^ [_369391] : [-(in(_369391, _368883)), 941 ^ _335709 : [(942 ^ _335709) ^ [_369489] : [in(_369391, _369489), in(_369489, _368885)]]]]], (994 ^ _335709) ^ [_371349, _371351, _371353] : [-(_371349 = set_difference(_371353, _371351)), 1006 ^ _335709 : [(1007 ^ _335709) ^ [] : [-(in(995 ^ [_371349, _371351, _371353], _371353))], (1009 ^ _335709) ^ [] : [in(995 ^ [_371349, _371351, _371353], _371351)], (1011 ^ _335709) ^ [] : [in(995 ^ [_371349, _371351, _371353], _371349)]], 998 ^ _335709 : [(999 ^ _335709) ^ [] : [-(in(995 ^ [_371349, _371351, _371353], _371349))], (1001 ^ _335709) ^ [] : [in(995 ^ [_371349, _371351, _371353], _371353), -(in(995 ^ [_371349, _371351, _371353], _371351))]]], (972 ^ _335709) ^ [_370618, _370620, _370622] : [_370618 = set_difference(_370622, _370620), 975 ^ _335709 : [(976 ^ _335709) ^ [_370802] : [in(_370802, _370618), 979 ^ _335709 : [(980 ^ _335709) ^ [] : [-(in(_370802, _370622))], (982 ^ _335709) ^ [] : [in(_370802, _370620)]]], (984 ^ _335709) ^ [_371062] : [-(in(_371062, _370618)), in(_371062, _370622), -(in(_371062, _370620))]]], (1015 ^ _335709) ^ [_372092] : [relation(_372092), 1018 ^ _335709 : [(1036 ^ _335709) ^ [_372904] : [-(_372904 = relation_rng(_372092)), 1040 ^ _335709 : [(1041 ^ _335709) ^ [] : [-(in(1037 ^ [_372092, _372904], _372904))], (1043 ^ _335709) ^ [_373167] : [in(ordered_pair(_373167, 1037 ^ [_372092, _372904]), _372092)]], 1045 ^ _335709 : [(1046 ^ _335709) ^ [] : [-(in(ordered_pair(1044 ^ [_372092, _372904], 1037 ^ [_372092, _372904]), _372092))], (1048 ^ _335709) ^ [] : [in(1037 ^ [_372092, _372904], _372904)]]], (1019 ^ _335709) ^ [_372273] : [_372273 = relation_rng(_372092), 1022 ^ _335709 : [(1023 ^ _335709) ^ [_372453] : [in(_372453, _372273), -(in(ordered_pair(1026 ^ [_372092, _372273, _372453], _372453), _372092))], (1030 ^ _335709) ^ [_372697] : [1031 ^ _335709 : [(1032 ^ _335709) ^ [_372776] : [in(ordered_pair(_372776, _372697), _372092)]], -(in(_372697, _372273))]]]]], (1052 ^ _335709) ^ [_373547, _373549] : [element(_373547, powerset(_373549)), -(subset_complement(_373549, _373547) = set_difference(_373549, _373547))], (1058 ^ _335709) ^ [_373758, _373760] : [-(ordered_pair(_373760, _373758) = unordered_pair(unordered_pair(_373760, _373758), singleton(_373760)))], (1060 ^ _335709) ^ [_373864] : [relation(_373864), -(relation_field(_373864) = set_union2(relation_dom(_373864), relation_rng(_373864)))], (1066 ^ _335709) ^ [_374070] : [relation(_374070), 1069 ^ _335709 : [(1070 ^ _335709) ^ [_374230] : [relation(_374230), 1073 ^ _335709 : [(1090 ^ _335709) ^ [] : [-(_374230 = relation_inverse(_374070)), 1095 ^ _335709 : [(1096 ^ _335709) ^ [] : [-(in(ordered_pair(1091 ^ [_374070, _374230], 1092 ^ [_374070, _374230]), _374230))], (1098 ^ _335709) ^ [] : [in(ordered_pair(1092 ^ [_374070, _374230], 1091 ^ [_374070, _374230]), _374070)]], 1099 ^ _335709 : [(1100 ^ _335709) ^ [] : [-(in(ordered_pair(1092 ^ [_374070, _374230], 1091 ^ [_374070, _374230]), _374070))], (1102 ^ _335709) ^ [] : [in(ordered_pair(1091 ^ [_374070, _374230], 1092 ^ [_374070, _374230]), _374230)]]], (1074 ^ _335709) ^ [] : [_374230 = relation_inverse(_374070), 1077 ^ _335709 : [(1078 ^ _335709) ^ [_374539, _374541] : [in(ordered_pair(_374541, _374539), _374230), -(in(ordered_pair(_374539, _374541), _374070))], (1084 ^ _335709) ^ [_374729, _374731] : [in(ordered_pair(_374729, _374731), _374070), -(in(ordered_pair(_374731, _374729), _374230))]]]]]]], (1106 ^ _335709) ^ [_375577, _375579] : [disjoint(_375579, _375577), -(set_intersection2(_375579, _375577) = empty_set)], (1112 ^ _335709) ^ [_375745, _375747] : [set_intersection2(_375747, _375745) = empty_set, -(disjoint(_375747, _375745))], (1118 ^ _335709) ^ [_375949] : [relation(_375949), 1121 ^ _335709 : [(1122 ^ _335709) ^ [_376134] : [relation(_376134), 1125 ^ _335709 : [(1126 ^ _335709) ^ [_376315] : [relation(_376315), 1129 ^ _335709 : [(1153 ^ _335709) ^ [] : [-(_376315 = relation_composition(_375949, _376134)), 1167 ^ _335709 : [(1168 ^ _335709) ^ [] : [-(in(ordered_pair(1154 ^ [_375949, _376134, _376315], 1166 ^ [_375949, _376134, _376315]), _375949))], (1170 ^ _335709) ^ [] : [-(in(ordered_pair(1166 ^ [_375949, _376134, _376315], 1155 ^ [_375949, _376134, _376315]), _376134))], (1172 ^ _335709) ^ [] : [in(ordered_pair(1154 ^ [_375949, _376134, _376315], 1155 ^ [_375949, _376134, _376315]), _376315)]], 1158 ^ _335709 : [(1159 ^ _335709) ^ [] : [-(in(ordered_pair(1154 ^ [_375949, _376134, _376315], 1155 ^ [_375949, _376134, _376315]), _376315))], (1161 ^ _335709) ^ [_377779] : [in(ordered_pair(1154 ^ [_375949, _376134, _376315], _377779), _375949), in(ordered_pair(_377779, 1155 ^ [_375949, _376134, _376315]), _376134)]]], (1130 ^ _335709) ^ [] : [_376315 = relation_composition(_375949, _376134), 1133 ^ _335709 : [(1134 ^ _335709) ^ [_376650, _376652] : [in(ordered_pair(_376652, _376650), _376315), 1138 ^ _335709 : [(1139 ^ _335709) ^ [] : [-(in(ordered_pair(_376652, 1137 ^ [_375949, _376134, _376315, _376650, _376652]), _375949))], (1141 ^ _335709) ^ [] : [-(in(ordered_pair(1137 ^ [_375949, _376134, _376315, _376650, _376652], _376650), _376134))]]], (1143 ^ _335709) ^ [_377035, _377037] : [-(in(ordered_pair(_377037, _377035), _376315)), 1144 ^ _335709 : [(1145 ^ _335709) ^ [_377148] : [in(ordered_pair(_377037, _377148), _375949), in(ordered_pair(_377148, _377035), _376134)]]]]]]]]]]], (1176 ^ _335709) ^ [_378465, _378467] : [element(_378465, powerset(powerset(_378467))), 1179 ^ _335709 : [(1180 ^ _335709) ^ [_378645] : [element(_378645, powerset(powerset(_378467))), 1183 ^ _335709 : [(1204 ^ _335709) ^ [] : [-(_378645 = complements_of_subsets(_378467, _378465)), 1206 ^ _335709 : [(1207 ^ _335709) ^ [] : [-(element(1205 ^ [_378465, _378467, _378645], powerset(_378467)))], (1209 ^ _335709) ^ [] : [1210 ^ _335709 : [(1211 ^ _335709) ^ [] : [-(in(1205 ^ [_378465, _378467, _378645], _378645))], (1213 ^ _335709) ^ [] : [in(subset_complement(_378467, 1205 ^ [_378465, _378467, _378645]), _378465)]], 1214 ^ _335709 : [(1215 ^ _335709) ^ [] : [-(in(subset_complement(_378467, 1205 ^ [_378465, _378467, _378645]), _378465))], (1217 ^ _335709) ^ [] : [in(1205 ^ [_378465, _378467, _378645], _378645)]]]]], (1184 ^ _335709) ^ [] : [_378645 = complements_of_subsets(_378467, _378465), 1187 ^ _335709 : [(1188 ^ _335709) ^ [_378933] : [element(_378933, powerset(_378467)), 1191 ^ _335709 : [(1192 ^ _335709) ^ [] : [in(_378933, _378645), -(in(subset_complement(_378467, _378933), _378465))], (1198 ^ _335709) ^ [] : [in(subset_complement(_378467, _378933), _378465), -(in(_378933, _378645))]]]]]]]]], (1221 ^ _335709) ^ [_380056, _380058] : [proper_subset(_380058, _380056), 1224 ^ _335709 : [(1225 ^ _335709) ^ [] : [-(subset(_380058, _380056))], (1227 ^ _335709) ^ [] : [_380058 = _380056]]], (1229 ^ _335709) ^ [_380294, _380296] : [-(proper_subset(_380296, _380294)), subset(_380296, _380294), -(_380296 = _380294)], (1239 ^ _335709) ^ [] : [true___, -(true___)], (1245 ^ _335709) ^ [] : [true___, -(true___)], (1251 ^ _335709) ^ [] : [true___, -(true___)], (1257 ^ _335709) ^ [] : [true___, -(true___)], (1263 ^ _335709) ^ [] : [true___, -(true___)], (1269 ^ _335709) ^ [] : [true___, -(true___)], (1275 ^ _335709) ^ [_381283] : [-(element(cast_to_subset(_381283), powerset(_381283)))], (1277 ^ _335709) ^ [] : [true___, -(true___)], (1283 ^ _335709) ^ [] : [true___, -(true___)], (1289 ^ _335709) ^ [] : [true___, -(true___)], (1295 ^ _335709) ^ [] : [true___, -(true___)], (1301 ^ _335709) ^ [_381870, _381872] : [element(_381870, powerset(_381872)), -(element(subset_complement(_381872, _381870), powerset(_381872)))], (1307 ^ _335709) ^ [] : [true___, -(true___)], (1313 ^ _335709) ^ [] : [true___, -(true___)], (1319 ^ _335709) ^ [_382318] : [relation(_382318), -(relation(relation_inverse(_382318)))], (1325 ^ _335709) ^ [] : [true___, -(true___)], (1331 ^ _335709) ^ [] : [true___, -(true___)], (1337 ^ _335709) ^ [_382760, _382762] : [-(relation(relation_composition(_382762, _382760))), relation(_382762), relation(_382760)], (1347 ^ _335709) ^ [_383059, _383061] : [element(_383059, powerset(powerset(_383061))), -(element(union_of_subsets(_383061, _383059), powerset(_383061)))], (1353 ^ _335709) ^ [_383258] : [-(relation(identity_relation(_383258)))], (1355 ^ _335709) ^ [_383366, _383368] : [element(_383366, powerset(powerset(_383368))), -(element(meet_of_subsets(_383368, _383366), powerset(_383368)))], (1361 ^ _335709) ^ [_383608, _383610, _383612] : [-(element(subset_difference(_383612, _383610, _383608), powerset(_383612))), element(_383610, powerset(_383612)), element(_383608, powerset(_383612))], (1371 ^ _335709) ^ [_383937, _383939] : [relation(_383939), -(relation(relation_dom_restriction(_383939, _383937)))], (1377 ^ _335709) ^ [_384149, _384151] : [element(_384149, powerset(powerset(_384151))), -(element(complements_of_subsets(_384151, _384149), powerset(powerset(_384151))))], (1383 ^ _335709) ^ [] : [true___, -(true___)], (1390 ^ _335709) ^ [_384510] : [-(element(1388 ^ [_384510], _384510))], (1392 ^ _335709) ^ [_384622, _384624] : [1399 ^ _335709 : [(1400 ^ _335709) ^ [] : [-(empty(relation_composition(_384622, _384624)))], (1402 ^ _335709) ^ [] : [-(relation(relation_composition(_384622, _384624)))]], empty(_384624), relation(_384622)], (1404 ^ _335709) ^ [_385000, _385002] : [-(relation(set_intersection2(_385002, _385000))), relation(_385002), relation(_385000)], (1414 ^ _335709) ^ [_385269] : [empty(powerset(_385269))], (1416 ^ _335709) ^ [] : [-(empty(empty_set))], (1418 ^ _335709) ^ [_385414, _385416] : [empty(ordered_pair(_385416, _385414))], (1420 ^ _335709) ^ [_385525, _385527] : [-(relation(set_union2(_385527, _385525))), relation(_385527), relation(_385525)], (1430 ^ _335709) ^ [_385794] : [empty(singleton(_385794))], (1432 ^ _335709) ^ [_385902, _385904] : [-(empty(_385904)), empty(set_union2(_385904, _385902))], (1438 ^ _335709) ^ [_386102, _386104] : [empty(unordered_pair(_386104, _386102))], (1440 ^ _335709) ^ [_386213, _386215] : [-(empty(_386215)), empty(set_union2(_386213, _386215))], (1446 ^ _335709) ^ [] : [-(empty(empty_set))], (1448 ^ _335709) ^ [] : [-(relation(empty_set))], (1450 ^ _335709) ^ [_386537, _386539] : [empty(cartesian_product2(_386539, _386537)), -(empty(_386539)), -(empty(_386537))], (1460 ^ _335709) ^ [_386829] : [empty(relation_dom(_386829)), -(empty(_386829)), relation(_386829)], (1470 ^ _335709) ^ [_387106] : [empty(relation_rng(_387106)), -(empty(_387106)), relation(_387106)], (1480 ^ _335709) ^ [_387383] : [empty(_387383), 1483 ^ _335709 : [(1484 ^ _335709) ^ [] : [-(empty(relation_dom(_387383)))], (1486 ^ _335709) ^ [] : [-(relation(relation_dom(_387383)))]]], (1488 ^ _335709) ^ [_387648] : [empty(_387648), 1491 ^ _335709 : [(1492 ^ _335709) ^ [] : [-(empty(relation_rng(_387648)))], (1494 ^ _335709) ^ [] : [-(relation(relation_rng(_387648)))]]], (1496 ^ _335709) ^ [_387927, _387929] : [1503 ^ _335709 : [(1504 ^ _335709) ^ [] : [-(empty(relation_composition(_387929, _387927)))], (1506 ^ _335709) ^ [] : [-(relation(relation_composition(_387929, _387927)))]], empty(_387929), relation(_387927)], (1508 ^ _335709) ^ [_388290, _388292] : [-(set_union2(_388292, _388292) = _388292)], (1510 ^ _335709) ^ [_388387, _388389] : [-(set_intersection2(_388389, _388389) = _388389)], (1512 ^ _335709) ^ [_388499, _388501] : [element(_388499, powerset(_388501)), -(subset_complement(_388501, subset_complement(_388501, _388499)) = _388499)], (1518 ^ _335709) ^ [_388711] : [relation(_388711), -(relation_inverse(relation_inverse(_388711)) = _388711)], (1524 ^ _335709) ^ [_388921, _388923] : [element(_388921, powerset(powerset(_388923))), -(complements_of_subsets(_388923, complements_of_subsets(_388923, _388921)) = _388921)], (1530 ^ _335709) ^ [_389135, _389137] : [proper_subset(_389137, _389137)], (1532 ^ _335709) ^ [_389214] : [singleton(_389214) = empty_set], (1534 ^ _335709) ^ [_389323, _389325] : [in(_389325, _389323), -(set_union2(singleton(_389325), _389323) = _389323)], (1540 ^ _335709) ^ [_389543, _389545] : [disjoint(singleton(_389545), _389543), in(_389545, _389543)], (1546 ^ _335709) ^ [_389756, _389758] : [-(in(_389758, _389756)), -(disjoint(singleton(_389758), _389756))], (1552 ^ _335709) ^ [_390002, _390004] : [subset(singleton(_390004), _390002), -(in(_390004, _390002))], (1558 ^ _335709) ^ [_390168, _390170] : [in(_390170, _390168), -(subset(singleton(_390170), _390168))], (1564 ^ _335709) ^ [_390413, _390415] : [set_difference(_390415, _390413) = empty_set, -(subset(_390415, _390413))], (1570 ^ _335709) ^ [_390581, _390583] : [subset(_390583, _390581), -(set_difference(_390583, _390581) = empty_set)], (1576 ^ _335709) ^ [_390799, _390801] : [element(_390799, powerset(_390801)), 1579 ^ _335709 : [(1580 ^ _335709) ^ [_390940] : [in(_390940, _390799), -(in(_390940, _390801))]]], (1586 ^ _335709) ^ [_391179, _391181, _391183] : [subset(_391183, _391181), -(in(_391179, _391183)), -(subset(_391183, set_difference(_391181, singleton(_391179))))], (1606 ^ _335709) ^ [_391788, _391790] : [1607 ^ _335709 : [(1608 ^ _335709) ^ [] : [_391790 = empty_set], (1610 ^ _335709) ^ [] : [_391790 = singleton(_391788)]], -(subset(_391790, singleton(_391788)))], (1596 ^ _335709) ^ [_391528, _391530] : [subset(_391530, singleton(_391528)), -(_391530 = empty_set), -(_391530 = singleton(_391528))], (1614 ^ _335709) ^ [_392082, _392084] : [in(_392084, _392082), -(subset(_392084, union(_392082)))], (1620 ^ _335709) ^ [_392353, _392355, _392357, _392359] : [in(ordered_pair(_392359, _392357), cartesian_product2(_392355, _392353)), 1623 ^ _335709 : [(1624 ^ _335709) ^ [] : [-(in(_392359, _392355))], (1626 ^ _335709) ^ [] : [-(in(_392357, _392353))]]], (1628 ^ _335709) ^ [_392618, _392620, _392622, _392624] : [-(in(ordered_pair(_392624, _392622), cartesian_product2(_392620, _392618))), in(_392624, _392620), in(_392622, _392618)], (1638 ^ _335709) ^ [_392951, _392953] : [1640 ^ _335709 : [(1641 ^ _335709) ^ [] : [-(in(1639 ^ [_392951, _392953], _392953))], (1643 ^ _335709) ^ [] : [in(1639 ^ [_392951, _392953], _392951)]], -(element(_392953, powerset(_392951)))], (1648 ^ _335709) ^ [] : [-(empty(1646 ^ []))], (1650 ^ _335709) ^ [] : [-(relation(1646 ^ []))], (1652 ^ _335709) ^ [_393445] : [-(empty(_393445)), 1656 ^ _335709 : [(1657 ^ _335709) ^ [] : [-(element(1655 ^ [_393445], powerset(_393445)))], (1659 ^ _335709) ^ [] : [empty(1655 ^ [_393445])]]], (1662 ^ _335709) ^ [] : [-(empty(1660 ^ []))], (1665 ^ _335709) ^ [] : [empty(1663 ^ [])], (1667 ^ _335709) ^ [] : [-(relation(1663 ^ []))], (1670 ^ _335709) ^ [_394067] : [-(element(1668 ^ [_394067], powerset(_394067)))], (1672 ^ _335709) ^ [_394118] : [-(empty(1668 ^ [_394118]))], (1675 ^ _335709) ^ [] : [empty(1673 ^ [])], (1677 ^ _335709) ^ [_394321, _394323] : [element(_394321, powerset(powerset(_394323))), -(union_of_subsets(_394323, _394321) = union(_394321))], (1683 ^ _335709) ^ [_394549, _394551] : [element(_394549, powerset(powerset(_394551))), -(meet_of_subsets(_394551, _394549) = set_meet(_394549))], (1689 ^ _335709) ^ [_394791, _394793, _394795] : [-(subset_difference(_394795, _394793, _394791) = set_difference(_394793, _394791)), element(_394793, powerset(_394795)), element(_394791, powerset(_394795))], (1699 ^ _335709) ^ [_395107, _395109] : [-(subset(_395109, _395109))], (1701 ^ _335709) ^ [_395216, _395218] : [disjoint(_395218, _395216), -(disjoint(_395216, _395218))], (1707 ^ _335709) ^ [_395483, _395485, _395487, _395489] : [in(ordered_pair(_395489, _395487), cartesian_product2(_395485, _395483)), 1710 ^ _335709 : [(1711 ^ _335709) ^ [] : [-(in(_395489, _395485))], (1713 ^ _335709) ^ [] : [-(in(_395487, _395483))]]], (1715 ^ _335709) ^ [_395748, _395750, _395752, _395754] : [-(in(ordered_pair(_395754, _395752), cartesian_product2(_395750, _395748))), in(_395754, _395750), in(_395752, _395748)], (1725 ^ _335709) ^ [_396109, _396111, _396113, _396115] : [unordered_pair(_396115, _396113) = unordered_pair(_396111, _396109), -(_396115 = _396111), -(_396115 = _396109)], (1735 ^ _335709) ^ [_396459, _396461, _396463] : [subset(_396463, _396461), 1738 ^ _335709 : [(1739 ^ _335709) ^ [] : [-(subset(cartesian_product2(_396463, _396459), cartesian_product2(_396461, _396459)))], (1741 ^ _335709) ^ [] : [-(subset(cartesian_product2(_396459, _396463), cartesian_product2(_396459, _396461)))]]], (1743 ^ _335709) ^ [_396804, _396806, _396808, _396810] : [-(subset(cartesian_product2(_396810, _396806), cartesian_product2(_396808, _396804))), subset(_396810, _396808), subset(_396806, _396804)], (1753 ^ _335709) ^ [_397135, _397137] : [subset(_397137, _397135), -(set_union2(_397137, _397135) = _397135)], (1760 ^ _335709) ^ [_397457] : [-(in(_397457, 1758 ^ [_397457]))], (1762 ^ _335709) ^ [_397569, _397571, _397573] : [-(in(_397569, 1758 ^ [_397573])), in(_397571, 1758 ^ [_397573]), subset(_397569, _397571)], (1772 ^ _335709) ^ [_397884, _397886] : [in(_397884, 1758 ^ [_397886]), -(in(powerset(_397884), 1758 ^ [_397886]))], (1778 ^ _335709) ^ [_398084, _398086] : [subset(_398084, 1758 ^ [_398086]), -(are_equipotent(_398084, 1758 ^ [_398086])), -(in(_398084, 1758 ^ [_398086]))], (1788 ^ _335709) ^ [_398409, _398411] : [-(subset(set_intersection2(_398411, _398409), _398411))], (1790 ^ _335709) ^ [_398535, _398537, _398539] : [-(subset(_398539, set_intersection2(_398537, _398535))), subset(_398539, _398537), subset(_398539, _398535)], (1800 ^ _335709) ^ [_398821] : [-(set_union2(_398821, empty_set) = _398821)], (1802 ^ _335709) ^ [_398931, _398933] : [in(_398933, _398931), -(element(_398933, _398931))], (1808 ^ _335709) ^ [_399155, _399157, _399159] : [-(subset(_399159, _399155)), subset(_399159, _399157), subset(_399157, _399155)], (1818 ^ _335709) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (1820 ^ _335709) ^ [_399531, _399533, _399535] : [relation(_399531), in(ordered_pair(_399535, _399533), _399531), 1827 ^ _335709 : [(1828 ^ _335709) ^ [] : [-(in(_399535, relation_dom(_399531)))], (1830 ^ _335709) ^ [] : [-(in(_399533, relation_rng(_399531)))]]], (1832 ^ _335709) ^ [_399915] : [relation(_399915), -(subset(_399915, cartesian_product2(relation_dom(_399915), relation_rng(_399915))))], (1838 ^ _335709) ^ [_400117] : [relation(_400117), 1841 ^ _335709 : [(1842 ^ _335709) ^ [_400267] : [relation(_400267), subset(_400117, _400267), 1849 ^ _335709 : [(1850 ^ _335709) ^ [] : [-(subset(relation_dom(_400117), relation_dom(_400267)))], (1852 ^ _335709) ^ [] : [-(subset(relation_rng(_400117), relation_rng(_400267)))]]]]], (1854 ^ _335709) ^ [_400676, _400678, _400680] : [subset(_400680, _400678), -(subset(set_intersection2(_400680, _400676), set_intersection2(_400678, _400676)))], (1860 ^ _335709) ^ [_400904, _400906] : [subset(_400906, _400904), -(set_intersection2(_400906, _400904) = _400906)], (1866 ^ _335709) ^ [_401091] : [-(set_intersection2(_401091, empty_set) = empty_set)], (1868 ^ _335709) ^ [_401201, _401203] : [element(_401203, _401201), -(empty(_401201)), -(in(_401203, _401201))], (1878 ^ _335709) ^ [_401499, _401501] : [-(_401501 = _401499), 1882 ^ _335709 : [(1883 ^ _335709) ^ [] : [-(in(1879 ^ [_401499, _401501], _401501))], (1885 ^ _335709) ^ [] : [in(1879 ^ [_401499, _401501], _401499)]], 1886 ^ _335709 : [(1887 ^ _335709) ^ [] : [-(in(1879 ^ [_401499, _401501], _401499))], (1889 ^ _335709) ^ [] : [in(1879 ^ [_401499, _401501], _401501)]]], (1893 ^ _335709) ^ [_402000] : [-(subset(empty_set, _402000))], (1895 ^ _335709) ^ [_402121, _402123, _402125] : [relation(_402121), in(ordered_pair(_402125, _402123), _402121), 1902 ^ _335709 : [(1903 ^ _335709) ^ [] : [-(in(_402125, relation_field(_402121)))], (1905 ^ _335709) ^ [] : [-(in(_402123, relation_field(_402121)))]]], (1907 ^ _335709) ^ [_402533, _402535, _402537] : [subset(_402537, _402535), -(subset(set_difference(_402537, _402533), set_difference(_402535, _402533)))], (1913 ^ _335709) ^ [_402789, _402791, _402793, _402795] : [ordered_pair(_402795, _402793) = ordered_pair(_402791, _402789), 1916 ^ _335709 : [(1917 ^ _335709) ^ [] : [-(_402795 = _402791)], (1919 ^ _335709) ^ [] : [-(_402793 = _402789)]]], (1921 ^ _335709) ^ [_403087, _403089] : [-(subset(set_difference(_403089, _403087), _403089))], (1923 ^ _335709) ^ [_403185] : [relation(_403185), 1926 ^ _335709 : [(1927 ^ _335709) ^ [] : [-(relation_rng(_403185) = relation_dom(relation_inverse(_403185)))], (1929 ^ _335709) ^ [] : [-(relation_dom(_403185) = relation_rng(relation_inverse(_403185)))]]], (1931 ^ _335709) ^ [_403513, _403515] : [set_difference(_403515, _403513) = empty_set, -(subset(_403515, _403513))], (1937 ^ _335709) ^ [_403681, _403683] : [subset(_403683, _403681), -(set_difference(_403683, _403681) = empty_set)], (1943 ^ _335709) ^ [_403928, _403930] : [subset(singleton(_403930), _403928), -(in(_403930, _403928))], (1949 ^ _335709) ^ [_404094, _404096] : [in(_404096, _404094), -(subset(singleton(_404096), _404094))], (1955 ^ _335709) ^ [_404353, _404355, _404357] : [subset(unordered_pair(_404357, _404355), _404353), 1958 ^ _335709 : [(1959 ^ _335709) ^ [] : [-(in(_404357, _404353))], (1961 ^ _335709) ^ [] : [-(in(_404355, _404353))]]], (1963 ^ _335709) ^ [_404604, _404606, _404608] : [-(subset(unordered_pair(_404608, _404606), _404604)), in(_404608, _404604), in(_404606, _404604)], (1973 ^ _335709) ^ [_404906, _404908] : [-(set_union2(_404908, set_difference(_404906, _404908)) = set_union2(_404908, _404906))], (1985 ^ _335709) ^ [_405313, _405315] : [1986 ^ _335709 : [(1987 ^ _335709) ^ [] : [_405315 = empty_set], (1989 ^ _335709) ^ [] : [_405315 = singleton(_405313)]], -(subset(_405315, singleton(_405313)))], (1975 ^ _335709) ^ [_405053, _405055] : [subset(_405055, singleton(_405053)), -(_405055 = empty_set), -(_405055 = singleton(_405053))], (1993 ^ _335709) ^ [_405578] : [-(set_difference(_405578, empty_set) = _405578)], (1995 ^ _335709) ^ [_405717, _405719] : [element(_405719, powerset(_405717)), -(subset(_405719, _405717))], (2001 ^ _335709) ^ [_405883, _405885] : [subset(_405885, _405883), -(element(_405885, powerset(_405883)))], (2007 ^ _335709) ^ [_406119, _406121] : [-(disjoint(_406121, _406119)), 2011 ^ _335709 : [(2012 ^ _335709) ^ [] : [-(in(2010 ^ [_406119, _406121], _406121))], (2014 ^ _335709) ^ [] : [-(in(2010 ^ [_406119, _406121], _406119))]]], (2016 ^ _335709) ^ [_406433, _406435] : [disjoint(_406435, _406433), 2017 ^ _335709 : [(2018 ^ _335709) ^ [_406525] : [in(_406525, _406435), in(_406525, _406433)]]], (2026 ^ _335709) ^ [_406782] : [subset(_406782, empty_set), -(_406782 = empty_set)], (2032 ^ _335709) ^ [_406971, _406973] : [-(set_difference(set_union2(_406973, _406971), _406971) = set_difference(_406973, _406971))], (2034 ^ _335709) ^ [_407089, _407091] : [element(_407089, powerset(_407091)), 2037 ^ _335709 : [(2038 ^ _335709) ^ [_407241] : [element(_407241, powerset(_407091)), 2041 ^ _335709 : [(2042 ^ _335709) ^ [] : [disjoint(_407089, _407241), -(subset(_407089, subset_complement(_407091, _407241)))], (2048 ^ _335709) ^ [] : [subset(_407089, subset_complement(_407091, _407241)), -(disjoint(_407089, _407241))]]]]], (2054 ^ _335709) ^ [_407725] : [relation(_407725), 2057 ^ _335709 : [(2058 ^ _335709) ^ [_407862] : [relation(_407862), -(subset(relation_dom(relation_composition(_407725, _407862)), relation_dom(_407725)))]]], (2064 ^ _335709) ^ [_408077] : [relation(_408077), 2067 ^ _335709 : [(2068 ^ _335709) ^ [_408214] : [relation(_408214), -(subset(relation_rng(relation_composition(_408077, _408214)), relation_rng(_408214)))]]], (2074 ^ _335709) ^ [_408443, _408445] : [subset(_408445, _408443), -(_408443 = set_union2(_408445, set_difference(_408443, _408445)))], (2080 ^ _335709) ^ [_408651] : [relation(_408651), 2083 ^ _335709 : [(2084 ^ _335709) ^ [_408798] : [relation(_408798), subset(relation_rng(_408651), relation_dom(_408798)), -(relation_dom(relation_composition(_408651, _408798)) = relation_dom(_408651))]]], (2094 ^ _335709) ^ [_409124, _409126] : [element(_409124, powerset(powerset(_409126))), -(_409124 = empty_set), complements_of_subsets(_409126, _409124) = empty_set], (2104 ^ _335709) ^ [_409441, _409443] : [in(_409443, _409441), -(set_union2(singleton(_409443), _409441) = _409441)], (2110 ^ _335709) ^ [_409647] : [relation(_409647), 2113 ^ _335709 : [(2114 ^ _335709) ^ [_409794] : [relation(_409794), subset(relation_dom(_409647), relation_rng(_409794)), -(relation_rng(relation_composition(_409794, _409647)) = relation_rng(_409647))]]], (2124 ^ _335709) ^ [_410120, _410122] : [element(_410120, powerset(powerset(_410122))), -(_410120 = empty_set), -(subset_difference(_410122, cast_to_subset(_410122), union_of_subsets(_410122, _410120)) = meet_of_subsets(_410122, complements_of_subsets(_410122, _410120)))], (2134 ^ _335709) ^ [_410460, _410462] : [element(_410460, powerset(powerset(_410462))), -(_410460 = empty_set), -(union_of_subsets(_410462, complements_of_subsets(_410462, _410460)) = subset_difference(_410462, cast_to_subset(_410462), meet_of_subsets(_410462, _410460)))], (2144 ^ _335709) ^ [_410785, _410787] : [-(set_difference(_410787, set_difference(_410787, _410785)) = set_intersection2(_410787, _410785))], (2146 ^ _335709) ^ [_410874] : [-(set_difference(empty_set, _410874) = empty_set)], (2148 ^ _335709) ^ [_410998, _411000, _411002] : [-(element(_411002, _410998)), in(_411002, _411000), element(_411000, powerset(_410998))], (2158 ^ _335709) ^ [_411331, _411333] : [-(disjoint(_411333, _411331)), -(in(2161 ^ [_411331, _411333], set_intersection2(_411333, _411331)))], (2165 ^ _335709) ^ [_411566, _411568] : [2166 ^ _335709 : [(2167 ^ _335709) ^ [_411639] : [in(_411639, set_intersection2(_411568, _411566))]], disjoint(_411568, _411566)], (2171 ^ _335709) ^ [_411791] : [-(_411791 = empty_set), 2174 ^ _335709 : [(2175 ^ _335709) ^ [_411951] : [element(_411951, powerset(_411791)), 2178 ^ _335709 : [(2179 ^ _335709) ^ [_412105] : [element(_412105, _411791), -(in(_412105, _411951)), -(in(_412105, subset_complement(_411791, _411951)))]]]]], (2189 ^ _335709) ^ [_412451, _412453, _412455] : [element(_412451, powerset(_412455)), in(_412453, subset_complement(_412455, _412451)), in(_412453, _412451)], (2199 ^ _335709) ^ [_412757] : [relation(_412757), -(in(ordered_pair(2204 ^ [_412757], 2205 ^ [_412757]), _412757)), -(_412757 = empty_set)], (2211 ^ _335709) ^ [_413189, _413191, _413193] : [in(_413193, _413191), element(_413191, powerset(_413189)), empty(_413189)], (2221 ^ _335709) ^ [] : [-(relation_dom(empty_set) = empty_set)], (2223 ^ _335709) ^ [] : [-(relation_rng(empty_set) = empty_set)], (2225 ^ _335709) ^ [_413607, _413609] : [subset(_413609, _413607), proper_subset(_413607, _413609)], (2231 ^ _335709) ^ [_413830, _413832, _413834] : [-(disjoint(_413834, _413830)), subset(_413834, _413832), disjoint(_413832, _413830)], (2241 ^ _335709) ^ [_414125] : [relation(_414125), 2246 ^ _335709 : [(2247 ^ _335709) ^ [] : [relation_dom(_414125) = empty_set], (2249 ^ _335709) ^ [] : [relation_rng(_414125) = empty_set]], -(_414125 = empty_set)], (2253 ^ _335709) ^ [_414478] : [relation(_414478), 2256 ^ _335709 : [(2257 ^ _335709) ^ [] : [relation_dom(_414478) = empty_set, -(relation_rng(_414478) = empty_set)], (2263 ^ _335709) ^ [] : [relation_rng(_414478) = empty_set, -(relation_dom(_414478) = empty_set)]]], (2269 ^ _335709) ^ [_414961, _414963] : [set_difference(_414963, singleton(_414961)) = _414963, in(_414961, _414963)], (2275 ^ _335709) ^ [_415134, _415136] : [-(in(_415134, _415136)), -(set_difference(_415136, singleton(_415134)) = _415136)], (2281 ^ _335709) ^ [_415330] : [-(unordered_pair(_415330, _415330) = singleton(_415330))], (2283 ^ _335709) ^ [_415428] : [empty(_415428), -(_415428 = empty_set)], (2289 ^ _335709) ^ [_415630, _415632] : [subset(singleton(_415632), singleton(_415630)), -(_415632 = _415630)], (2295 ^ _335709) ^ [_415839] : [-(relation_dom(identity_relation(_415839)) = _415839)], (2297 ^ _335709) ^ [_415887] : [-(relation_rng(identity_relation(_415887)) = _415887)], (2299 ^ _335709) ^ [_416028, _416030, _416032, _416034] : [relation(_416028), 2302 ^ _335709 : [(2303 ^ _335709) ^ [] : [in(ordered_pair(_416034, _416032), relation_composition(identity_relation(_416030), _416028)), 2306 ^ _335709 : [(2307 ^ _335709) ^ [] : [-(in(_416034, _416030))], (2309 ^ _335709) ^ [] : [-(in(ordered_pair(_416034, _416032), _416028))]]], (2311 ^ _335709) ^ [] : [-(in(ordered_pair(_416034, _416032), relation_composition(identity_relation(_416030), _416028))), in(_416034, _416030), in(ordered_pair(_416034, _416032), _416028)]]], (2321 ^ _335709) ^ [_416721, _416723] : [in(_416723, _416721), empty(_416721)], (2327 ^ _335709) ^ [_416913, _416915] : [-(subset(_416915, set_union2(_416915, _416913)))], (2329 ^ _335709) ^ [_417054, _417056] : [disjoint(_417056, _417054), -(set_difference(_417056, _417054) = _417056)], (2335 ^ _335709) ^ [_417222, _417224] : [set_difference(_417224, _417222) = _417224, -(disjoint(_417224, _417222))], (2341 ^ _335709) ^ [_417454, _417456, _417458] : [relation(_417454), 2344 ^ _335709 : [(2345 ^ _335709) ^ [] : [in(_417458, relation_dom(relation_dom_restriction(_417454, _417456))), 2348 ^ _335709 : [(2349 ^ _335709) ^ [] : [-(in(_417458, _417456))], (2351 ^ _335709) ^ [] : [-(in(_417458, relation_dom(_417454)))]]], (2353 ^ _335709) ^ [] : [-(in(_417458, relation_dom(relation_dom_restriction(_417454, _417456)))), in(_417458, _417456), in(_417458, relation_dom(_417454))]]], (2363 ^ _335709) ^ [_418113, _418115] : [relation(_418113), -(subset(relation_dom_restriction(_418113, _418115), _418113))], (2369 ^ _335709) ^ [_418327, _418329] : [empty(_418329), -(_418329 = _418327), empty(_418327)], (2379 ^ _335709) ^ [_418638, _418640, _418642] : [-(subset(set_union2(_418642, _418638), _418640)), subset(_418642, _418640), subset(_418638, _418640)], (2389 ^ _335709) ^ [_418967, _418969, _418971] : [singleton(_418971) = unordered_pair(_418969, _418967), -(_418971 = _418969)], (2395 ^ _335709) ^ [_419193, _419195] : [in(_419195, _419193), -(subset(_419195, union(_419193)))], (2401 ^ _335709) ^ [_419378] : [-(union(powerset(_419378)) = _419378)], (2439 ^ _335709) ^ [_420899, _420901, _420903] : [singleton(_420903) = unordered_pair(_420901, _420899), -(_420901 = _420899)], (2404 ^ _335709) ^ [_419619] : [-(in(_419619, 2402 ^ [_419619]))], (2406 ^ _335709) ^ [_419731, _419733, _419735] : [-(in(_419731, 2402 ^ [_419735])), in(_419733, 2402 ^ [_419735]), subset(_419731, _419733)], (2416 ^ _335709) ^ [_420046, _420048] : [in(_420046, 2402 ^ [_420048]), 2420 ^ _335709 : [(2421 ^ _335709) ^ [] : [-(in(2419 ^ [_420046, _420048], 2402 ^ [_420048]))], (2423 ^ _335709) ^ [_420358] : [subset(_420358, _420046), -(in(_420358, 2419 ^ [_420046, _420048]))]]], (2429 ^ _335709) ^ [_420565, _420567] : [subset(_420565, 2402 ^ [_420567]), -(are_equipotent(_420565, 2402 ^ [_420567])), -(in(_420565, 2402 ^ [_420567]))]], input).
% 9.06/9.69  ncf('1',plain,[relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])) = set_intersection2(relation_dom(2445 ^ []), 2444 ^ [])],start(2449 ^ 0)).
% 9.06/9.69  ncf('1.1',plain,[-(relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])) = set_intersection2(relation_dom(2445 ^ []), 2444 ^ [])), 880 : -(in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(2445 ^ []))), 874 : in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(2445 ^ [])), 874 : in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], 2444 ^ [])],extension(867 ^ 1,bind([[_366580, _366582, _366584], [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])]]))).
% 9.06/9.69  ncf('1.1.1',plain,[in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(2445 ^ [])), 2353 : -(in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])))), 2353 : in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], 2444 ^ []), 2353 : relation(2445 ^ [])],extension(2341 ^ 4,bind([[_417454, _417456, _417458], [2445 ^ [], 2444 ^ [], 868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])]]]))).
% 9.06/9.69  ncf('1.1.1.1',plain,[in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])))],extension(884 ^ 7)).
% 9.06/9.69  ncf('1.1.1.2',plain,[-(in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], 2444 ^ []))],extension(882 ^ 7)).
% 9.06/9.69  ncf('1.1.1.3',plain,[-(relation(2445 ^ []))],extension(2447 ^ 5)).
% 9.06/9.69  ncf('1.1.2',plain,[-(in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(2445 ^ []))), 2345 : in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ []))), 2345 : relation(2445 ^ [])],extension(2341 ^ 4,bind([[_417454, _417456, _417458], [2445 ^ [], 2444 ^ [], 868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])]]]))).
% 9.06/9.69  ncf('1.1.2.1',plain,[-(in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ []))))],extension(872 ^ 7)).
% 9.06/9.69  ncf('1.1.2.2',plain,[-(relation(2445 ^ []))],extension(2447 ^ 5)).
% 9.06/9.69  ncf('1.1.3',plain,[-(in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], 2444 ^ [])), 2345 : in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ []))), 2345 : relation(2445 ^ [])],extension(2341 ^ 4,bind([[_417454, _417456, _417458], [2445 ^ [], 2444 ^ [], 868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])]]]))).
% 9.06/9.69  ncf('1.1.3.1',plain,[-(in(868 ^ [relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ [])), 2444 ^ [], relation_dom(2445 ^ [])], relation_dom(relation_dom_restriction(2445 ^ [], 2444 ^ []))))],extension(872 ^ 7)).
% 9.06/9.69  ncf('1.1.3.2',plain,[-(relation(2445 ^ []))],extension(2447 ^ 5)).
% 9.06/9.69  %-----------------------------------------------------
% 9.06/9.69  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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