%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU187+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 12:02:34 EDT 2023

% Result   : Theorem 5.29s 5.54s
% Output   : Proof 5.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU187+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % 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 13:09:49 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 5.29/5.54  
% 5.29/5.54  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 5.29/5.54  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.29/5.54  %-----------------------------------------------------
% 5.29/5.54  ncf(matrix, plain, [(2157 ^ _302476) ^ [] : [relation_dom(empty_set) = empty_set, relation_rng(empty_set) = empty_set], (2 ^ _302476) ^ [_302620] : [-(_302620 = _302620)], (4 ^ _302476) ^ [_302727, _302729] : [_302729 = _302727, -(_302727 = _302729)], (10 ^ _302476) ^ [_302931, _302933, _302935] : [-(_302935 = _302931), _302935 = _302933, _302933 = _302931], (20 ^ _302476) ^ [_303244, _303246] : [-(relation(_303244)), _303246 = _303244, relation(_303246)], (30 ^ _302476) ^ [_303567, _303569, _303571, _303573] : [-(element(_303571, _303567)), element(_303573, _303569), _303573 = _303571, _303569 = _303567], (44 ^ _302476) ^ [_304011, _304013, _304015, _304017] : [-(proper_subset(_304015, _304011)), proper_subset(_304017, _304013), _304017 = _304015, _304013 = _304011], (58 ^ _302476) ^ [_304455, _304457, _304459, _304461] : [-(disjoint(_304459, _304455)), disjoint(_304461, _304457), _304461 = _304459, _304457 = _304455], (72 ^ _302476) ^ [_304871, _304873] : [-(empty(_304871)), _304873 = _304871, empty(_304873)], (82 ^ _302476) ^ [_305194, _305196, _305198, _305200] : [-(subset(_305198, _305194)), subset(_305200, _305196), _305200 = _305198, _305196 = _305194], (96 ^ _302476) ^ [_305638, _305640, _305642, _305644] : [-(are_equipotent(_305642, _305638)), are_equipotent(_305644, _305640), _305644 = _305642, _305640 = _305638], (110 ^ _302476) ^ [_306062, _306064, _306066, _306068] : [-(in(_306066, _306062)), in(_306068, _306064), _306068 = _306066, _306064 = _306062], (124 ^ _302476) ^ [_306498, _306500] : [_306500 = _306498, -(set_meet(_306500) = set_meet(_306498))], (130 ^ _302476) ^ [_306744, _306746, _306748, _306750] : [-(cartesian_product2(_306750, _306746) = cartesian_product2(_306748, _306744)), _306750 = _306748, _306746 = _306744], (140 ^ _302476) ^ [_307075, _307077] : [_307077 = _307075, -(relation_field(_307077) = relation_field(_307075))], (146 ^ _302476) ^ [_307293, _307295] : [_307295 = _307293, -(relation_inverse(_307295) = relation_inverse(_307293))], (152 ^ _302476) ^ [_307539, _307541, _307543, _307545] : [-(relation_composition(_307545, _307541) = relation_composition(_307543, _307539)), _307545 = _307543, _307541 = _307539], (162 ^ _302476) ^ [_307898, _307900, _307902, _307904] : [-(union_of_subsets(_307904, _307900) = union_of_subsets(_307902, _307898)), _307904 = _307902, _307900 = _307898], (172 ^ _302476) ^ [_308257, _308259, _308261, _308263] : [-(complements_of_subsets(_308263, _308259) = complements_of_subsets(_308261, _308257)), _308263 = _308261, _308259 = _308257], (182 ^ _302476) ^ [_308644, _308646, _308648, _308650, _308652, _308654] : [-(subset_difference(_308654, _308650, _308646) = subset_difference(_308652, _308648, _308644)), _308654 = _308652, _308650 = _308648, _308646 = _308644], (196 ^ _302476) ^ [_309104, _309106] : [_309106 = _309104, -(cast_to_subset(_309106) = cast_to_subset(_309104))], (202 ^ _302476) ^ [_309350, _309352, _309354, _309356] : [-(meet_of_subsets(_309356, _309352) = meet_of_subsets(_309354, _309350)), _309356 = _309354, _309352 = _309350], (212 ^ _302476) ^ [_309709, _309711, _309713, _309715] : [-(set_intersection2(_309715, _309711) = set_intersection2(_309713, _309709)), _309715 = _309713, _309711 = _309709], (222 ^ _302476) ^ [_310068, _310070, _310072, _310074] : [-(subset_complement(_310074, _310070) = subset_complement(_310072, _310068)), _310074 = _310072, _310070 = _310068], (232 ^ _302476) ^ [_310427, _310429, _310431, _310433] : [-(ordered_pair(_310433, _310429) = ordered_pair(_310431, _310427)), _310433 = _310431, _310429 = _310427], (242 ^ _302476) ^ [_310786, _310788, _310790, _310792] : [-(set_difference(_310792, _310788) = set_difference(_310790, _310786)), _310792 = _310790, _310788 = _310786], (252 ^ _302476) ^ [_311145, _311147, _311149, _311151] : [-(set_union2(_311151, _311147) = set_union2(_311149, _311145)), _311151 = _311149, _311147 = _311145], (262 ^ _302476) ^ [_311476, _311478] : [_311478 = _311476, -(union(_311478) = union(_311476))], (268 ^ _302476) ^ [_311694, _311696] : [_311696 = _311694, -(powerset(_311696) = powerset(_311694))], (274 ^ _302476) ^ [_311912, _311914] : [_311914 = _311912, -(singleton(_311914) = singleton(_311912))], (280 ^ _302476) ^ [_312158, _312160, _312162, _312164] : [-(unordered_pair(_312164, _312160) = unordered_pair(_312162, _312158)), _312164 = _312162, _312160 = _312158], (290 ^ _302476) ^ [_312489, _312491] : [_312491 = _312489, -(relation_dom(_312491) = relation_dom(_312489))], (296 ^ _302476) ^ [_312687, _312689] : [_312689 = _312687, -(relation_rng(_312689) = relation_rng(_312687))], (302 ^ _302476) ^ [_312999, _313001] : [in(_313001, _312999), in(_312999, _313001)], (308 ^ _302476) ^ [_313210, _313212] : [proper_subset(_313212, _313210), proper_subset(_313210, _313212)], (314 ^ _302476) ^ [_313407] : [empty(_313407), -(relation(_313407))], (320 ^ _302476) ^ [_313592, _313594] : [-(unordered_pair(_313594, _313592) = unordered_pair(_313592, _313594))], (322 ^ _302476) ^ [_313692, _313694] : [-(set_union2(_313694, _313692) = set_union2(_313692, _313694))], (324 ^ _302476) ^ [_313792, _313794] : [-(set_intersection2(_313794, _313792) = set_intersection2(_313792, _313794))], (326 ^ _302476) ^ [_313936, _313938] : [_313938 = _313936, 329 ^ _302476 : [(330 ^ _302476) ^ [] : [-(subset(_313938, _313936))], (332 ^ _302476) ^ [] : [-(subset(_313936, _313938))]]], (334 ^ _302476) ^ [_314173, _314175] : [-(_314175 = _314173), subset(_314175, _314173), subset(_314173, _314175)], (356 ^ _302476) ^ [_314950] : [358 ^ _302476 : [(359 ^ _302476) ^ [] : [-(in(357 ^ [_314950], _314950))], (361 ^ _302476) ^ [_315187, _315189] : [357 ^ [_314950] = ordered_pair(_315189, _315187)]], -(relation(_314950))], (344 ^ _302476) ^ [_314489] : [relation(_314489), 347 ^ _302476 : [(348 ^ _302476) ^ [_314637] : [in(_314637, _314489), -(_314637 = ordered_pair(351 ^ [_314489, _314637], 352 ^ [_314489, _314637]))]]], (414 ^ _302476) ^ [_317085, _317087] : [_317087 = empty_set, 417 ^ _302476 : [(418 ^ _302476) ^ [] : [_317085 = set_meet(_317087), -(_317085 = empty_set)], (424 ^ _302476) ^ [] : [_317085 = empty_set, -(_317085 = set_meet(_317087))]]], (365 ^ _302476) ^ [_315378, _315380] : [-(_315380 = empty_set), 368 ^ _302476 : [(392 ^ _302476) ^ [] : [-(_315378 = set_meet(_315380)), 396 ^ _302476 : [(397 ^ _302476) ^ [] : [-(in(393 ^ [_315378, _315380], _315378))], (400 ^ _302476) ^ [] : [-(in(398 ^ [_315378, _315380], _315380))], (402 ^ _302476) ^ [] : [in(393 ^ [_315378, _315380], 398 ^ [_315378, _315380])]], 403 ^ _302476 : [(410 ^ _302476) ^ [] : [in(393 ^ [_315378, _315380], _315378)], (404 ^ _302476) ^ [_316780] : [in(_316780, _315380), -(in(393 ^ [_315378, _315380], _316780))]]], (369 ^ _302476) ^ [] : [_315378 = set_meet(_315380), 372 ^ _302476 : [(383 ^ _302476) ^ [_316006] : [385 ^ _302476 : [(386 ^ _302476) ^ [] : [-(in(384 ^ [_315378, _315380, _316006], _315380))], (388 ^ _302476) ^ [] : [in(_316006, 384 ^ [_315378, _315380, _316006])]], -(in(_316006, _315378))], (373 ^ _302476) ^ [_315676] : [in(_315676, _315378), 376 ^ _302476 : [(377 ^ _302476) ^ [_315821] : [in(_315821, _315380), -(in(_315676, _315821))]]]]]]], (446 ^ _302476) ^ [_318103, _318105] : [-(_318103 = singleton(_318105)), 450 ^ _302476 : [(451 ^ _302476) ^ [] : [-(in(447 ^ [_318103, _318105], _318103))], (453 ^ _302476) ^ [] : [447 ^ [_318103, _318105] = _318105]], 454 ^ _302476 : [(455 ^ _302476) ^ [] : [-(447 ^ [_318103, _318105] = _318105)], (457 ^ _302476) ^ [] : [in(447 ^ [_318103, _318105], _318103)]]], (430 ^ _302476) ^ [_317582, _317584] : [_317582 = singleton(_317584), 433 ^ _302476 : [(434 ^ _302476) ^ [_317752] : [in(_317752, _317582), -(_317752 = _317584)], (440 ^ _302476) ^ [_317924] : [_317924 = _317584, -(in(_317924, _317582))]]], (461 ^ _302476) ^ [_318654] : [_318654 = empty_set, 464 ^ _302476 : [(465 ^ _302476) ^ [_318767] : [in(_318767, _318654)]]], (467 ^ _302476) ^ [_318833] : [-(in(468 ^ [_318833], _318833)), -(_318833 = empty_set)], (490 ^ _302476) ^ [_319645, _319647] : [-(_319645 = powerset(_319647)), 494 ^ _302476 : [(495 ^ _302476) ^ [] : [-(in(491 ^ [_319645, _319647], _319645))], (497 ^ _302476) ^ [] : [subset(491 ^ [_319645, _319647], _319647)]], 498 ^ _302476 : [(499 ^ _302476) ^ [] : [-(subset(491 ^ [_319645, _319647], _319647))], (501 ^ _302476) ^ [] : [in(491 ^ [_319645, _319647], _319645)]]], (474 ^ _302476) ^ [_319124, _319126] : [_319124 = powerset(_319126), 477 ^ _302476 : [(478 ^ _302476) ^ [_319294] : [in(_319294, _319124), -(subset(_319294, _319126))], (484 ^ _302476) ^ [_319466] : [subset(_319466, _319126), -(in(_319466, _319124))]]], (505 ^ _302476) ^ [_320201, _320203] : [-(empty(_320203)), 508 ^ _302476 : [(509 ^ _302476) ^ [] : [element(_320201, _320203), -(in(_320201, _320203))], (515 ^ _302476) ^ [] : [in(_320201, _320203), -(element(_320201, _320203))]]], (521 ^ _302476) ^ [_320614, _320616] : [empty(_320616), 524 ^ _302476 : [(525 ^ _302476) ^ [] : [element(_320614, _320616), -(empty(_320614))], (531 ^ _302476) ^ [] : [empty(_320614), -(element(_320614, _320616))]]], (559 ^ _302476) ^ [_321839, _321841, _321843] : [-(_321839 = unordered_pair(_321843, _321841)), 563 ^ _302476 : [(564 ^ _302476) ^ [] : [-(in(560 ^ [_321839, _321841, _321843], _321839))], (566 ^ _302476) ^ [] : [560 ^ [_321839, _321841, _321843] = _321843], (568 ^ _302476) ^ [] : [560 ^ [_321839, _321841, _321843] = _321841]], 569 ^ _302476 : [(576 ^ _302476) ^ [] : [in(560 ^ [_321839, _321841, _321843], _321839)], (570 ^ _302476) ^ [] : [-(560 ^ [_321839, _321841, _321843] = _321843), -(560 ^ [_321839, _321841, _321843] = _321841)]]], (537 ^ _302476) ^ [_321114, _321116, _321118] : [_321114 = unordered_pair(_321118, _321116), 540 ^ _302476 : [(551 ^ _302476) ^ [_321574] : [552 ^ _302476 : [(553 ^ _302476) ^ [] : [_321574 = _321118], (555 ^ _302476) ^ [] : [_321574 = _321116]], -(in(_321574, _321114))], (541 ^ _302476) ^ [_321296] : [in(_321296, _321114), -(_321296 = _321118), -(_321296 = _321116)]]], (602 ^ _302476) ^ [_323358, _323360, _323362] : [-(_323358 = set_union2(_323362, _323360)), 606 ^ _302476 : [(607 ^ _302476) ^ [] : [-(in(603 ^ [_323358, _323360, _323362], _323358))], (609 ^ _302476) ^ [] : [in(603 ^ [_323358, _323360, _323362], _323362)], (611 ^ _302476) ^ [] : [in(603 ^ [_323358, _323360, _323362], _323360)]], 612 ^ _302476 : [(619 ^ _302476) ^ [] : [in(603 ^ [_323358, _323360, _323362], _323358)], (613 ^ _302476) ^ [] : [-(in(603 ^ [_323358, _323360, _323362], _323362)), -(in(603 ^ [_323358, _323360, _323362], _323360))]]], (580 ^ _302476) ^ [_322633, _322635, _322637] : [_322633 = set_union2(_322637, _322635), 583 ^ _302476 : [(594 ^ _302476) ^ [_323093] : [595 ^ _302476 : [(596 ^ _302476) ^ [] : [in(_323093, _322637)], (598 ^ _302476) ^ [] : [in(_323093, _322635)]], -(in(_323093, _322633))], (584 ^ _302476) ^ [_322815] : [in(_322815, _322633), -(in(_322815, _322637)), -(in(_322815, _322635))]]], (653 ^ _302476) ^ [_325409, _325411, _325413] : [-(_325409 = cartesian_product2(_325413, _325411)), 671 ^ _302476 : [(672 ^ _302476) ^ [] : [-(in(669 ^ [_325409, _325411, _325413], _325413))], (674 ^ _302476) ^ [] : [-(in(670 ^ [_325409, _325411, _325413], _325411))], (676 ^ _302476) ^ [] : [-(654 ^ [_325409, _325411, _325413] = ordered_pair(669 ^ [_325409, _325411, _325413], 670 ^ [_325409, _325411, _325413]))], (678 ^ _302476) ^ [] : [in(654 ^ [_325409, _325411, _325413], _325409)]], 657 ^ _302476 : [(658 ^ _302476) ^ [] : [-(in(654 ^ [_325409, _325411, _325413], _325409))], (660 ^ _302476) ^ [_325747, _325749] : [in(_325749, _325413), in(_325747, _325411), 654 ^ [_325409, _325411, _325413] = ordered_pair(_325749, _325747)]]], (623 ^ _302476) ^ [_324152, _324154, _324156] : [_324152 = cartesian_product2(_324156, _324154), 626 ^ _302476 : [(627 ^ _302476) ^ [_324353] : [in(_324353, _324152), 632 ^ _302476 : [(633 ^ _302476) ^ [] : [-(in(630 ^ [_324152, _324154, _324156, _324353], _324156))], (635 ^ _302476) ^ [] : [-(in(631 ^ [_324152, _324154, _324156, _324353], _324154))], (637 ^ _302476) ^ [] : [-(_324353 = ordered_pair(630 ^ [_324152, _324154, _324156, _324353], 631 ^ [_324152, _324154, _324156, _324353]))]]], (639 ^ _302476) ^ [_324913] : [-(in(_324913, _324152)), 640 ^ _302476 : [(641 ^ _302476) ^ [_325043, _325045] : [in(_325045, _324156), in(_325043, _324154), _324913 = ordered_pair(_325045, _325043)]]]]], (692 ^ _302476) ^ [_327000, _327002] : [694 ^ _302476 : [(695 ^ _302476) ^ [] : [-(in(693 ^ [_327000, _327002], _327002))], (697 ^ _302476) ^ [] : [in(693 ^ [_327000, _327002], _327000)]], -(subset(_327002, _327000))], (682 ^ _302476) ^ [_326686, _326688] : [subset(_326688, _326686), 685 ^ _302476 : [(686 ^ _302476) ^ [_326823] : [in(_326823, _326688), -(in(_326823, _326686))]]], (723 ^ _302476) ^ [_328125, _328127, _328129] : [-(_328125 = set_intersection2(_328129, _328127)), 735 ^ _302476 : [(736 ^ _302476) ^ [] : [-(in(724 ^ [_328125, _328127, _328129], _328129))], (738 ^ _302476) ^ [] : [-(in(724 ^ [_328125, _328127, _328129], _328127))], (740 ^ _302476) ^ [] : [in(724 ^ [_328125, _328127, _328129], _328125)]], 727 ^ _302476 : [(728 ^ _302476) ^ [] : [-(in(724 ^ [_328125, _328127, _328129], _328125))], (730 ^ _302476) ^ [] : [in(724 ^ [_328125, _328127, _328129], _328129), in(724 ^ [_328125, _328127, _328129], _328127)]]], (701 ^ _302476) ^ [_327400, _327402, _327404] : [_327400 = set_intersection2(_327404, _327402), 704 ^ _302476 : [(705 ^ _302476) ^ [_327582] : [in(_327582, _327400), 708 ^ _302476 : [(709 ^ _302476) ^ [] : [-(in(_327582, _327404))], (711 ^ _302476) ^ [] : [-(in(_327582, _327402))]]], (713 ^ _302476) ^ [_327841] : [-(in(_327841, _327400)), in(_327841, _327404), in(_327841, _327402)]]], (744 ^ _302476) ^ [_328864] : [relation(_328864), 747 ^ _302476 : [(765 ^ _302476) ^ [_329676] : [-(_329676 = relation_dom(_328864)), 769 ^ _302476 : [(770 ^ _302476) ^ [] : [-(in(766 ^ [_328864, _329676], _329676))], (772 ^ _302476) ^ [_329939] : [in(ordered_pair(766 ^ [_328864, _329676], _329939), _328864)]], 774 ^ _302476 : [(775 ^ _302476) ^ [] : [-(in(ordered_pair(766 ^ [_328864, _329676], 773 ^ [_328864, _329676]), _328864))], (777 ^ _302476) ^ [] : [in(766 ^ [_328864, _329676], _329676)]]], (748 ^ _302476) ^ [_329045] : [_329045 = relation_dom(_328864), 751 ^ _302476 : [(752 ^ _302476) ^ [_329225] : [in(_329225, _329045), -(in(ordered_pair(_329225, 755 ^ [_328864, _329045, _329225]), _328864))], (759 ^ _302476) ^ [_329469] : [760 ^ _302476 : [(761 ^ _302476) ^ [_329548] : [in(ordered_pair(_329469, _329548), _328864)]], -(in(_329469, _329045))]]]]], (781 ^ _302476) ^ [_330290] : [-(cast_to_subset(_330290) = _330290)], (806 ^ _302476) ^ [_331273, _331275] : [-(_331273 = union(_331275)), 819 ^ _302476 : [(820 ^ _302476) ^ [] : [-(in(807 ^ [_331273, _331275], 818 ^ [_331273, _331275]))], (822 ^ _302476) ^ [] : [-(in(818 ^ [_331273, _331275], _331275))], (824 ^ _302476) ^ [] : [in(807 ^ [_331273, _331275], _331273)]], 810 ^ _302476 : [(811 ^ _302476) ^ [] : [-(in(807 ^ [_331273, _331275], _331273))], (813 ^ _302476) ^ [_331556] : [in(807 ^ [_331273, _331275], _331556), in(_331556, _331275)]]], (783 ^ _302476) ^ [_330428, _330430] : [_330428 = union(_330430), 786 ^ _302476 : [(787 ^ _302476) ^ [_330609] : [in(_330609, _330428), 791 ^ _302476 : [(792 ^ _302476) ^ [] : [-(in(_330609, 790 ^ [_330428, _330430, _330609]))], (794 ^ _302476) ^ [] : [-(in(790 ^ [_330428, _330430, _330609], _330430))]]], (796 ^ _302476) ^ [_330936] : [-(in(_330936, _330428)), 797 ^ _302476 : [(798 ^ _302476) ^ [_331034] : [in(_330936, _331034), in(_331034, _330430)]]]]], (850 ^ _302476) ^ [_332894, _332896, _332898] : [-(_332894 = set_difference(_332898, _332896)), 862 ^ _302476 : [(863 ^ _302476) ^ [] : [-(in(851 ^ [_332894, _332896, _332898], _332898))], (865 ^ _302476) ^ [] : [in(851 ^ [_332894, _332896, _332898], _332896)], (867 ^ _302476) ^ [] : [in(851 ^ [_332894, _332896, _332898], _332894)]], 854 ^ _302476 : [(855 ^ _302476) ^ [] : [-(in(851 ^ [_332894, _332896, _332898], _332894))], (857 ^ _302476) ^ [] : [in(851 ^ [_332894, _332896, _332898], _332898), -(in(851 ^ [_332894, _332896, _332898], _332896))]]], (828 ^ _302476) ^ [_332163, _332165, _332167] : [_332163 = set_difference(_332167, _332165), 831 ^ _302476 : [(832 ^ _302476) ^ [_332347] : [in(_332347, _332163), 835 ^ _302476 : [(836 ^ _302476) ^ [] : [-(in(_332347, _332167))], (838 ^ _302476) ^ [] : [in(_332347, _332165)]]], (840 ^ _302476) ^ [_332607] : [-(in(_332607, _332163)), in(_332607, _332167), -(in(_332607, _332165))]]], (871 ^ _302476) ^ [_333637] : [relation(_333637), 874 ^ _302476 : [(892 ^ _302476) ^ [_334449] : [-(_334449 = relation_rng(_333637)), 896 ^ _302476 : [(897 ^ _302476) ^ [] : [-(in(893 ^ [_333637, _334449], _334449))], (899 ^ _302476) ^ [_334712] : [in(ordered_pair(_334712, 893 ^ [_333637, _334449]), _333637)]], 901 ^ _302476 : [(902 ^ _302476) ^ [] : [-(in(ordered_pair(900 ^ [_333637, _334449], 893 ^ [_333637, _334449]), _333637))], (904 ^ _302476) ^ [] : [in(893 ^ [_333637, _334449], _334449)]]], (875 ^ _302476) ^ [_333818] : [_333818 = relation_rng(_333637), 878 ^ _302476 : [(879 ^ _302476) ^ [_333998] : [in(_333998, _333818), -(in(ordered_pair(882 ^ [_333637, _333818, _333998], _333998), _333637))], (886 ^ _302476) ^ [_334242] : [887 ^ _302476 : [(888 ^ _302476) ^ [_334321] : [in(ordered_pair(_334321, _334242), _333637)]], -(in(_334242, _333818))]]]]], (908 ^ _302476) ^ [_335092, _335094] : [element(_335092, powerset(_335094)), -(subset_complement(_335094, _335092) = set_difference(_335094, _335092))], (914 ^ _302476) ^ [_335303, _335305] : [-(ordered_pair(_335305, _335303) = unordered_pair(unordered_pair(_335305, _335303), singleton(_335305)))], (916 ^ _302476) ^ [_335409] : [relation(_335409), -(relation_field(_335409) = set_union2(relation_dom(_335409), relation_rng(_335409)))], (922 ^ _302476) ^ [_335615] : [relation(_335615), 925 ^ _302476 : [(926 ^ _302476) ^ [_335775] : [relation(_335775), 929 ^ _302476 : [(946 ^ _302476) ^ [] : [-(_335775 = relation_inverse(_335615)), 951 ^ _302476 : [(952 ^ _302476) ^ [] : [-(in(ordered_pair(947 ^ [_335615, _335775], 948 ^ [_335615, _335775]), _335775))], (954 ^ _302476) ^ [] : [in(ordered_pair(948 ^ [_335615, _335775], 947 ^ [_335615, _335775]), _335615)]], 955 ^ _302476 : [(956 ^ _302476) ^ [] : [-(in(ordered_pair(948 ^ [_335615, _335775], 947 ^ [_335615, _335775]), _335615))], (958 ^ _302476) ^ [] : [in(ordered_pair(947 ^ [_335615, _335775], 948 ^ [_335615, _335775]), _335775)]]], (930 ^ _302476) ^ [] : [_335775 = relation_inverse(_335615), 933 ^ _302476 : [(934 ^ _302476) ^ [_336084, _336086] : [in(ordered_pair(_336086, _336084), _335775), -(in(ordered_pair(_336084, _336086), _335615))], (940 ^ _302476) ^ [_336274, _336276] : [in(ordered_pair(_336274, _336276), _335615), -(in(ordered_pair(_336276, _336274), _335775))]]]]]]], (962 ^ _302476) ^ [_337122, _337124] : [disjoint(_337124, _337122), -(set_intersection2(_337124, _337122) = empty_set)], (968 ^ _302476) ^ [_337290, _337292] : [set_intersection2(_337292, _337290) = empty_set, -(disjoint(_337292, _337290))], (974 ^ _302476) ^ [_337494] : [relation(_337494), 977 ^ _302476 : [(978 ^ _302476) ^ [_337679] : [relation(_337679), 981 ^ _302476 : [(982 ^ _302476) ^ [_337860] : [relation(_337860), 985 ^ _302476 : [(1009 ^ _302476) ^ [] : [-(_337860 = relation_composition(_337494, _337679)), 1023 ^ _302476 : [(1024 ^ _302476) ^ [] : [-(in(ordered_pair(1010 ^ [_337494, _337679, _337860], 1022 ^ [_337494, _337679, _337860]), _337494))], (1026 ^ _302476) ^ [] : [-(in(ordered_pair(1022 ^ [_337494, _337679, _337860], 1011 ^ [_337494, _337679, _337860]), _337679))], (1028 ^ _302476) ^ [] : [in(ordered_pair(1010 ^ [_337494, _337679, _337860], 1011 ^ [_337494, _337679, _337860]), _337860)]], 1014 ^ _302476 : [(1015 ^ _302476) ^ [] : [-(in(ordered_pair(1010 ^ [_337494, _337679, _337860], 1011 ^ [_337494, _337679, _337860]), _337860))], (1017 ^ _302476) ^ [_339324] : [in(ordered_pair(1010 ^ [_337494, _337679, _337860], _339324), _337494), in(ordered_pair(_339324, 1011 ^ [_337494, _337679, _337860]), _337679)]]], (986 ^ _302476) ^ [] : [_337860 = relation_composition(_337494, _337679), 989 ^ _302476 : [(990 ^ _302476) ^ [_338195, _338197] : [in(ordered_pair(_338197, _338195), _337860), 994 ^ _302476 : [(995 ^ _302476) ^ [] : [-(in(ordered_pair(_338197, 993 ^ [_337494, _337679, _337860, _338195, _338197]), _337494))], (997 ^ _302476) ^ [] : [-(in(ordered_pair(993 ^ [_337494, _337679, _337860, _338195, _338197], _338195), _337679))]]], (999 ^ _302476) ^ [_338580, _338582] : [-(in(ordered_pair(_338582, _338580), _337860)), 1000 ^ _302476 : [(1001 ^ _302476) ^ [_338693] : [in(ordered_pair(_338582, _338693), _337494), in(ordered_pair(_338693, _338580), _337679)]]]]]]]]]]], (1032 ^ _302476) ^ [_340010, _340012] : [element(_340010, powerset(powerset(_340012))), 1035 ^ _302476 : [(1036 ^ _302476) ^ [_340190] : [element(_340190, powerset(powerset(_340012))), 1039 ^ _302476 : [(1060 ^ _302476) ^ [] : [-(_340190 = complements_of_subsets(_340012, _340010)), 1062 ^ _302476 : [(1063 ^ _302476) ^ [] : [-(element(1061 ^ [_340010, _340012, _340190], powerset(_340012)))], (1065 ^ _302476) ^ [] : [1066 ^ _302476 : [(1067 ^ _302476) ^ [] : [-(in(1061 ^ [_340010, _340012, _340190], _340190))], (1069 ^ _302476) ^ [] : [in(subset_complement(_340012, 1061 ^ [_340010, _340012, _340190]), _340010)]], 1070 ^ _302476 : [(1071 ^ _302476) ^ [] : [-(in(subset_complement(_340012, 1061 ^ [_340010, _340012, _340190]), _340010))], (1073 ^ _302476) ^ [] : [in(1061 ^ [_340010, _340012, _340190], _340190)]]]]], (1040 ^ _302476) ^ [] : [_340190 = complements_of_subsets(_340012, _340010), 1043 ^ _302476 : [(1044 ^ _302476) ^ [_340478] : [element(_340478, powerset(_340012)), 1047 ^ _302476 : [(1048 ^ _302476) ^ [] : [in(_340478, _340190), -(in(subset_complement(_340012, _340478), _340010))], (1054 ^ _302476) ^ [] : [in(subset_complement(_340012, _340478), _340010), -(in(_340478, _340190))]]]]]]]]], (1077 ^ _302476) ^ [_341601, _341603] : [proper_subset(_341603, _341601), 1080 ^ _302476 : [(1081 ^ _302476) ^ [] : [-(subset(_341603, _341601))], (1083 ^ _302476) ^ [] : [_341603 = _341601]]], (1085 ^ _302476) ^ [_341839, _341841] : [-(proper_subset(_341841, _341839)), subset(_341841, _341839), -(_341841 = _341839)], (1095 ^ _302476) ^ [] : [true___, -(true___)], (1101 ^ _302476) ^ [] : [true___, -(true___)], (1107 ^ _302476) ^ [] : [true___, -(true___)], (1113 ^ _302476) ^ [] : [true___, -(true___)], (1119 ^ _302476) ^ [] : [true___, -(true___)], (1125 ^ _302476) ^ [] : [true___, -(true___)], (1131 ^ _302476) ^ [_342828] : [-(element(cast_to_subset(_342828), powerset(_342828)))], (1133 ^ _302476) ^ [] : [true___, -(true___)], (1139 ^ _302476) ^ [] : [true___, -(true___)], (1145 ^ _302476) ^ [] : [true___, -(true___)], (1151 ^ _302476) ^ [] : [true___, -(true___)], (1157 ^ _302476) ^ [_343415, _343417] : [element(_343415, powerset(_343417)), -(element(subset_complement(_343417, _343415), powerset(_343417)))], (1163 ^ _302476) ^ [] : [true___, -(true___)], (1169 ^ _302476) ^ [] : [true___, -(true___)], (1175 ^ _302476) ^ [_343863] : [relation(_343863), -(relation(relation_inverse(_343863)))], (1181 ^ _302476) ^ [] : [true___, -(true___)], (1187 ^ _302476) ^ [] : [true___, -(true___)], (1193 ^ _302476) ^ [_344305, _344307] : [-(relation(relation_composition(_344307, _344305))), relation(_344307), relation(_344305)], (1203 ^ _302476) ^ [_344604, _344606] : [element(_344604, powerset(powerset(_344606))), -(element(union_of_subsets(_344606, _344604), powerset(_344606)))], (1209 ^ _302476) ^ [_344832, _344834] : [element(_344832, powerset(powerset(_344834))), -(element(meet_of_subsets(_344834, _344832), powerset(_344834)))], (1215 ^ _302476) ^ [_345074, _345076, _345078] : [-(element(subset_difference(_345078, _345076, _345074), powerset(_345078))), element(_345076, powerset(_345078)), element(_345074, powerset(_345078))], (1225 ^ _302476) ^ [_345403, _345405] : [element(_345403, powerset(powerset(_345405))), -(element(complements_of_subsets(_345405, _345403), powerset(powerset(_345405))))], (1231 ^ _302476) ^ [] : [true___, -(true___)], (1238 ^ _302476) ^ [_345764] : [-(element(1236 ^ [_345764], _345764))], (1240 ^ _302476) ^ [_345846] : [empty(powerset(_345846))], (1242 ^ _302476) ^ [] : [-(empty(empty_set))], (1244 ^ _302476) ^ [_345991, _345993] : [empty(ordered_pair(_345993, _345991))], (1246 ^ _302476) ^ [_346102, _346104] : [-(relation(set_union2(_346104, _346102))), relation(_346104), relation(_346102)], (1256 ^ _302476) ^ [_346371] : [empty(singleton(_346371))], (1258 ^ _302476) ^ [_346479, _346481] : [-(empty(_346481)), empty(set_union2(_346481, _346479))], (1264 ^ _302476) ^ [_346679, _346681] : [empty(unordered_pair(_346681, _346679))], (1266 ^ _302476) ^ [_346790, _346792] : [-(empty(_346792)), empty(set_union2(_346790, _346792))], (1272 ^ _302476) ^ [] : [-(empty(empty_set))], (1274 ^ _302476) ^ [] : [-(relation(empty_set))], (1276 ^ _302476) ^ [_347114, _347116] : [empty(cartesian_product2(_347116, _347114)), -(empty(_347116)), -(empty(_347114))], (1286 ^ _302476) ^ [_347406] : [empty(relation_dom(_347406)), -(empty(_347406)), relation(_347406)], (1296 ^ _302476) ^ [_347683] : [empty(relation_rng(_347683)), -(empty(_347683)), relation(_347683)], (1306 ^ _302476) ^ [_347959, _347961] : [-(set_union2(_347961, _347961) = _347961)], (1308 ^ _302476) ^ [_348056, _348058] : [-(set_intersection2(_348058, _348058) = _348058)], (1310 ^ _302476) ^ [_348168, _348170] : [element(_348168, powerset(_348170)), -(subset_complement(_348170, subset_complement(_348170, _348168)) = _348168)], (1316 ^ _302476) ^ [_348380] : [relation(_348380), -(relation_inverse(relation_inverse(_348380)) = _348380)], (1322 ^ _302476) ^ [_348590, _348592] : [element(_348590, powerset(powerset(_348592))), -(complements_of_subsets(_348592, complements_of_subsets(_348592, _348590)) = _348590)], (1328 ^ _302476) ^ [_348804, _348806] : [proper_subset(_348806, _348806)], (1330 ^ _302476) ^ [_348883] : [singleton(_348883) = empty_set], (1332 ^ _302476) ^ [_348992, _348994] : [in(_348994, _348992), -(set_union2(singleton(_348994), _348992) = _348992)], (1338 ^ _302476) ^ [_349212, _349214] : [disjoint(singleton(_349214), _349212), in(_349214, _349212)], (1344 ^ _302476) ^ [_349425, _349427] : [-(in(_349427, _349425)), -(disjoint(singleton(_349427), _349425))], (1350 ^ _302476) ^ [_349671, _349673] : [subset(singleton(_349673), _349671), -(in(_349673, _349671))], (1356 ^ _302476) ^ [_349837, _349839] : [in(_349839, _349837), -(subset(singleton(_349839), _349837))], (1362 ^ _302476) ^ [_350082, _350084] : [set_difference(_350084, _350082) = empty_set, -(subset(_350084, _350082))], (1368 ^ _302476) ^ [_350250, _350252] : [subset(_350252, _350250), -(set_difference(_350252, _350250) = empty_set)], (1374 ^ _302476) ^ [_350468, _350470] : [element(_350468, powerset(_350470)), 1377 ^ _302476 : [(1378 ^ _302476) ^ [_350609] : [in(_350609, _350468), -(in(_350609, _350470))]]], (1384 ^ _302476) ^ [_350848, _350850, _350852] : [subset(_350852, _350850), -(in(_350848, _350852)), -(subset(_350852, set_difference(_350850, singleton(_350848))))], (1404 ^ _302476) ^ [_351457, _351459] : [1405 ^ _302476 : [(1406 ^ _302476) ^ [] : [_351459 = empty_set], (1408 ^ _302476) ^ [] : [_351459 = singleton(_351457)]], -(subset(_351459, singleton(_351457)))], (1394 ^ _302476) ^ [_351197, _351199] : [subset(_351199, singleton(_351197)), -(_351199 = empty_set), -(_351199 = singleton(_351197))], (1412 ^ _302476) ^ [_351751, _351753] : [in(_351753, _351751), -(subset(_351753, union(_351751)))], (1418 ^ _302476) ^ [_352022, _352024, _352026, _352028] : [in(ordered_pair(_352028, _352026), cartesian_product2(_352024, _352022)), 1421 ^ _302476 : [(1422 ^ _302476) ^ [] : [-(in(_352028, _352024))], (1424 ^ _302476) ^ [] : [-(in(_352026, _352022))]]], (1426 ^ _302476) ^ [_352287, _352289, _352291, _352293] : [-(in(ordered_pair(_352293, _352291), cartesian_product2(_352289, _352287))), in(_352293, _352289), in(_352291, _352287)], (1436 ^ _302476) ^ [_352620, _352622] : [1438 ^ _302476 : [(1439 ^ _302476) ^ [] : [-(in(1437 ^ [_352620, _352622], _352622))], (1441 ^ _302476) ^ [] : [in(1437 ^ [_352620, _352622], _352620)]], -(element(_352622, powerset(_352620)))], (1446 ^ _302476) ^ [] : [-(empty(1444 ^ []))], (1448 ^ _302476) ^ [] : [-(relation(1444 ^ []))], (1450 ^ _302476) ^ [_353114] : [-(empty(_353114)), 1454 ^ _302476 : [(1455 ^ _302476) ^ [] : [-(element(1453 ^ [_353114], powerset(_353114)))], (1457 ^ _302476) ^ [] : [empty(1453 ^ [_353114])]]], (1460 ^ _302476) ^ [] : [-(empty(1458 ^ []))], (1463 ^ _302476) ^ [] : [empty(1461 ^ [])], (1465 ^ _302476) ^ [] : [-(relation(1461 ^ []))], (1468 ^ _302476) ^ [_353736] : [-(element(1466 ^ [_353736], powerset(_353736)))], (1470 ^ _302476) ^ [_353787] : [-(empty(1466 ^ [_353787]))], (1473 ^ _302476) ^ [] : [empty(1471 ^ [])], (1475 ^ _302476) ^ [_353990, _353992] : [element(_353990, powerset(powerset(_353992))), -(union_of_subsets(_353992, _353990) = union(_353990))], (1481 ^ _302476) ^ [_354218, _354220] : [element(_354218, powerset(powerset(_354220))), -(meet_of_subsets(_354220, _354218) = set_meet(_354218))], (1487 ^ _302476) ^ [_354460, _354462, _354464] : [-(subset_difference(_354464, _354462, _354460) = set_difference(_354462, _354460)), element(_354462, powerset(_354464)), element(_354460, powerset(_354464))], (1497 ^ _302476) ^ [_354776, _354778] : [-(subset(_354778, _354778))], (1499 ^ _302476) ^ [_354885, _354887] : [disjoint(_354887, _354885), -(disjoint(_354885, _354887))], (1505 ^ _302476) ^ [_355152, _355154, _355156, _355158] : [in(ordered_pair(_355158, _355156), cartesian_product2(_355154, _355152)), 1508 ^ _302476 : [(1509 ^ _302476) ^ [] : [-(in(_355158, _355154))], (1511 ^ _302476) ^ [] : [-(in(_355156, _355152))]]], (1513 ^ _302476) ^ [_355417, _355419, _355421, _355423] : [-(in(ordered_pair(_355423, _355421), cartesian_product2(_355419, _355417))), in(_355423, _355419), in(_355421, _355417)], (1523 ^ _302476) ^ [_355778, _355780, _355782, _355784] : [unordered_pair(_355784, _355782) = unordered_pair(_355780, _355778), -(_355784 = _355780), -(_355784 = _355778)], (1533 ^ _302476) ^ [_356128, _356130, _356132] : [subset(_356132, _356130), 1536 ^ _302476 : [(1537 ^ _302476) ^ [] : [-(subset(cartesian_product2(_356132, _356128), cartesian_product2(_356130, _356128)))], (1539 ^ _302476) ^ [] : [-(subset(cartesian_product2(_356128, _356132), cartesian_product2(_356128, _356130)))]]], (1541 ^ _302476) ^ [_356473, _356475, _356477, _356479] : [-(subset(cartesian_product2(_356479, _356475), cartesian_product2(_356477, _356473))), subset(_356479, _356477), subset(_356475, _356473)], (1551 ^ _302476) ^ [_356804, _356806] : [subset(_356806, _356804), -(set_union2(_356806, _356804) = _356804)], (1558 ^ _302476) ^ [_357126] : [-(in(_357126, 1556 ^ [_357126]))], (1560 ^ _302476) ^ [_357238, _357240, _357242] : [-(in(_357238, 1556 ^ [_357242])), in(_357240, 1556 ^ [_357242]), subset(_357238, _357240)], (1570 ^ _302476) ^ [_357553, _357555] : [in(_357553, 1556 ^ [_357555]), -(in(powerset(_357553), 1556 ^ [_357555]))], (1576 ^ _302476) ^ [_357753, _357755] : [subset(_357753, 1556 ^ [_357755]), -(are_equipotent(_357753, 1556 ^ [_357755])), -(in(_357753, 1556 ^ [_357755]))], (1586 ^ _302476) ^ [_358078, _358080] : [-(subset(set_intersection2(_358080, _358078), _358080))], (1588 ^ _302476) ^ [_358204, _358206, _358208] : [-(subset(_358208, set_intersection2(_358206, _358204))), subset(_358208, _358206), subset(_358208, _358204)], (1598 ^ _302476) ^ [_358490] : [-(set_union2(_358490, empty_set) = _358490)], (1600 ^ _302476) ^ [_358600, _358602] : [in(_358602, _358600), -(element(_358602, _358600))], (1606 ^ _302476) ^ [_358824, _358826, _358828] : [-(subset(_358828, _358824)), subset(_358828, _358826), subset(_358826, _358824)], (1616 ^ _302476) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (1618 ^ _302476) ^ [_359200, _359202, _359204] : [relation(_359200), in(ordered_pair(_359204, _359202), _359200), 1625 ^ _302476 : [(1626 ^ _302476) ^ [] : [-(in(_359204, relation_dom(_359200)))], (1628 ^ _302476) ^ [] : [-(in(_359202, relation_rng(_359200)))]]], (1630 ^ _302476) ^ [_359584] : [relation(_359584), -(subset(_359584, cartesian_product2(relation_dom(_359584), relation_rng(_359584))))], (1636 ^ _302476) ^ [_359786] : [relation(_359786), 1639 ^ _302476 : [(1640 ^ _302476) ^ [_359936] : [relation(_359936), subset(_359786, _359936), 1647 ^ _302476 : [(1648 ^ _302476) ^ [] : [-(subset(relation_dom(_359786), relation_dom(_359936)))], (1650 ^ _302476) ^ [] : [-(subset(relation_rng(_359786), relation_rng(_359936)))]]]]], (1652 ^ _302476) ^ [_360345, _360347, _360349] : [subset(_360349, _360347), -(subset(set_intersection2(_360349, _360345), set_intersection2(_360347, _360345)))], (1658 ^ _302476) ^ [_360573, _360575] : [subset(_360575, _360573), -(set_intersection2(_360575, _360573) = _360575)], (1664 ^ _302476) ^ [_360760] : [-(set_intersection2(_360760, empty_set) = empty_set)], (1666 ^ _302476) ^ [_360870, _360872] : [element(_360872, _360870), -(empty(_360870)), -(in(_360872, _360870))], (1676 ^ _302476) ^ [_361168, _361170] : [-(_361170 = _361168), 1680 ^ _302476 : [(1681 ^ _302476) ^ [] : [-(in(1677 ^ [_361168, _361170], _361170))], (1683 ^ _302476) ^ [] : [in(1677 ^ [_361168, _361170], _361168)]], 1684 ^ _302476 : [(1685 ^ _302476) ^ [] : [-(in(1677 ^ [_361168, _361170], _361168))], (1687 ^ _302476) ^ [] : [in(1677 ^ [_361168, _361170], _361170)]]], (1691 ^ _302476) ^ [_361669] : [-(subset(empty_set, _361669))], (1693 ^ _302476) ^ [_361790, _361792, _361794] : [relation(_361790), in(ordered_pair(_361794, _361792), _361790), 1700 ^ _302476 : [(1701 ^ _302476) ^ [] : [-(in(_361794, relation_field(_361790)))], (1703 ^ _302476) ^ [] : [-(in(_361792, relation_field(_361790)))]]], (1705 ^ _302476) ^ [_362202, _362204, _362206] : [subset(_362206, _362204), -(subset(set_difference(_362206, _362202), set_difference(_362204, _362202)))], (1711 ^ _302476) ^ [_362458, _362460, _362462, _362464] : [ordered_pair(_362464, _362462) = ordered_pair(_362460, _362458), 1714 ^ _302476 : [(1715 ^ _302476) ^ [] : [-(_362464 = _362460)], (1717 ^ _302476) ^ [] : [-(_362462 = _362458)]]], (1719 ^ _302476) ^ [_362756, _362758] : [-(subset(set_difference(_362758, _362756), _362758))], (1721 ^ _302476) ^ [_362854] : [relation(_362854), 1724 ^ _302476 : [(1725 ^ _302476) ^ [] : [-(relation_rng(_362854) = relation_dom(relation_inverse(_362854)))], (1727 ^ _302476) ^ [] : [-(relation_dom(_362854) = relation_rng(relation_inverse(_362854)))]]], (1729 ^ _302476) ^ [_363182, _363184] : [set_difference(_363184, _363182) = empty_set, -(subset(_363184, _363182))], (1735 ^ _302476) ^ [_363350, _363352] : [subset(_363352, _363350), -(set_difference(_363352, _363350) = empty_set)], (1741 ^ _302476) ^ [_363597, _363599] : [subset(singleton(_363599), _363597), -(in(_363599, _363597))], (1747 ^ _302476) ^ [_363763, _363765] : [in(_363765, _363763), -(subset(singleton(_363765), _363763))], (1753 ^ _302476) ^ [_364022, _364024, _364026] : [subset(unordered_pair(_364026, _364024), _364022), 1756 ^ _302476 : [(1757 ^ _302476) ^ [] : [-(in(_364026, _364022))], (1759 ^ _302476) ^ [] : [-(in(_364024, _364022))]]], (1761 ^ _302476) ^ [_364273, _364275, _364277] : [-(subset(unordered_pair(_364277, _364275), _364273)), in(_364277, _364273), in(_364275, _364273)], (1771 ^ _302476) ^ [_364575, _364577] : [-(set_union2(_364577, set_difference(_364575, _364577)) = set_union2(_364577, _364575))], (1783 ^ _302476) ^ [_364982, _364984] : [1784 ^ _302476 : [(1785 ^ _302476) ^ [] : [_364984 = empty_set], (1787 ^ _302476) ^ [] : [_364984 = singleton(_364982)]], -(subset(_364984, singleton(_364982)))], (1773 ^ _302476) ^ [_364722, _364724] : [subset(_364724, singleton(_364722)), -(_364724 = empty_set), -(_364724 = singleton(_364722))], (1791 ^ _302476) ^ [_365247] : [-(set_difference(_365247, empty_set) = _365247)], (1793 ^ _302476) ^ [_365386, _365388] : [element(_365388, powerset(_365386)), -(subset(_365388, _365386))], (1799 ^ _302476) ^ [_365552, _365554] : [subset(_365554, _365552), -(element(_365554, powerset(_365552)))], (1805 ^ _302476) ^ [_365788, _365790] : [-(disjoint(_365790, _365788)), 1809 ^ _302476 : [(1810 ^ _302476) ^ [] : [-(in(1808 ^ [_365788, _365790], _365790))], (1812 ^ _302476) ^ [] : [-(in(1808 ^ [_365788, _365790], _365788))]]], (1814 ^ _302476) ^ [_366102, _366104] : [disjoint(_366104, _366102), 1815 ^ _302476 : [(1816 ^ _302476) ^ [_366194] : [in(_366194, _366104), in(_366194, _366102)]]], (1824 ^ _302476) ^ [_366451] : [subset(_366451, empty_set), -(_366451 = empty_set)], (1830 ^ _302476) ^ [_366640, _366642] : [-(set_difference(set_union2(_366642, _366640), _366640) = set_difference(_366642, _366640))], (1832 ^ _302476) ^ [_366758, _366760] : [element(_366758, powerset(_366760)), 1835 ^ _302476 : [(1836 ^ _302476) ^ [_366910] : [element(_366910, powerset(_366760)), 1839 ^ _302476 : [(1840 ^ _302476) ^ [] : [disjoint(_366758, _366910), -(subset(_366758, subset_complement(_366760, _366910)))], (1846 ^ _302476) ^ [] : [subset(_366758, subset_complement(_366760, _366910)), -(disjoint(_366758, _366910))]]]]], (1852 ^ _302476) ^ [_367394] : [relation(_367394), 1855 ^ _302476 : [(1856 ^ _302476) ^ [_367531] : [relation(_367531), -(subset(relation_dom(relation_composition(_367394, _367531)), relation_dom(_367394)))]]], (1862 ^ _302476) ^ [_367746] : [relation(_367746), 1865 ^ _302476 : [(1866 ^ _302476) ^ [_367883] : [relation(_367883), -(subset(relation_rng(relation_composition(_367746, _367883)), relation_rng(_367883)))]]], (1872 ^ _302476) ^ [_368112, _368114] : [subset(_368114, _368112), -(_368112 = set_union2(_368114, set_difference(_368112, _368114)))], (1878 ^ _302476) ^ [_368320] : [relation(_368320), 1881 ^ _302476 : [(1882 ^ _302476) ^ [_368467] : [relation(_368467), subset(relation_rng(_368320), relation_dom(_368467)), -(relation_dom(relation_composition(_368320, _368467)) = relation_dom(_368320))]]], (1892 ^ _302476) ^ [_368793, _368795] : [element(_368793, powerset(powerset(_368795))), -(_368793 = empty_set), complements_of_subsets(_368795, _368793) = empty_set], (1902 ^ _302476) ^ [_369110, _369112] : [in(_369112, _369110), -(set_union2(singleton(_369112), _369110) = _369110)], (1908 ^ _302476) ^ [_369316] : [relation(_369316), 1911 ^ _302476 : [(1912 ^ _302476) ^ [_369463] : [relation(_369463), subset(relation_dom(_369316), relation_rng(_369463)), -(relation_rng(relation_composition(_369463, _369316)) = relation_rng(_369316))]]], (1922 ^ _302476) ^ [_369789, _369791] : [element(_369789, powerset(powerset(_369791))), -(_369789 = empty_set), -(subset_difference(_369791, cast_to_subset(_369791), union_of_subsets(_369791, _369789)) = meet_of_subsets(_369791, complements_of_subsets(_369791, _369789)))], (1932 ^ _302476) ^ [_370129, _370131] : [element(_370129, powerset(powerset(_370131))), -(_370129 = empty_set), -(union_of_subsets(_370131, complements_of_subsets(_370131, _370129)) = subset_difference(_370131, cast_to_subset(_370131), meet_of_subsets(_370131, _370129)))], (1942 ^ _302476) ^ [_370454, _370456] : [-(set_difference(_370456, set_difference(_370456, _370454)) = set_intersection2(_370456, _370454))], (1944 ^ _302476) ^ [_370543] : [-(set_difference(empty_set, _370543) = empty_set)], (1946 ^ _302476) ^ [_370667, _370669, _370671] : [-(element(_370671, _370667)), in(_370671, _370669), element(_370669, powerset(_370667))], (1956 ^ _302476) ^ [_371000, _371002] : [-(disjoint(_371002, _371000)), -(in(1959 ^ [_371000, _371002], set_intersection2(_371002, _371000)))], (1963 ^ _302476) ^ [_371235, _371237] : [1964 ^ _302476 : [(1965 ^ _302476) ^ [_371308] : [in(_371308, set_intersection2(_371237, _371235))]], disjoint(_371237, _371235)], (1969 ^ _302476) ^ [_371460] : [-(_371460 = empty_set), 1972 ^ _302476 : [(1973 ^ _302476) ^ [_371620] : [element(_371620, powerset(_371460)), 1976 ^ _302476 : [(1977 ^ _302476) ^ [_371774] : [element(_371774, _371460), -(in(_371774, _371620)), -(in(_371774, subset_complement(_371460, _371620)))]]]]], (1987 ^ _302476) ^ [_372120, _372122, _372124] : [element(_372120, powerset(_372124)), in(_372122, subset_complement(_372124, _372120)), in(_372122, _372120)], (1997 ^ _302476) ^ [_372426] : [relation(_372426), -(in(ordered_pair(2002 ^ [_372426], 2003 ^ [_372426]), _372426)), -(_372426 = empty_set)], (2009 ^ _302476) ^ [_372858, _372860, _372862] : [in(_372862, _372860), element(_372860, powerset(_372858)), empty(_372858)], (2019 ^ _302476) ^ [_373168, _373170] : [subset(_373170, _373168), proper_subset(_373168, _373170)], (2025 ^ _302476) ^ [_373391, _373393, _373395] : [-(disjoint(_373395, _373391)), subset(_373395, _373393), disjoint(_373393, _373391)], (2035 ^ _302476) ^ [_373729, _373731] : [set_difference(_373731, singleton(_373729)) = _373731, in(_373729, _373731)], (2041 ^ _302476) ^ [_373902, _373904] : [-(in(_373902, _373904)), -(set_difference(_373904, singleton(_373902)) = _373904)], (2047 ^ _302476) ^ [_374098] : [-(unordered_pair(_374098, _374098) = singleton(_374098))], (2049 ^ _302476) ^ [_374196] : [empty(_374196), -(_374196 = empty_set)], (2055 ^ _302476) ^ [_374398, _374400] : [subset(singleton(_374400), singleton(_374398)), -(_374400 = _374398)], (2061 ^ _302476) ^ [_374616, _374618] : [in(_374618, _374616), empty(_374616)], (2067 ^ _302476) ^ [_374808, _374810] : [-(subset(_374810, set_union2(_374810, _374808)))], (2069 ^ _302476) ^ [_374949, _374951] : [disjoint(_374951, _374949), -(set_difference(_374951, _374949) = _374951)], (2075 ^ _302476) ^ [_375117, _375119] : [set_difference(_375119, _375117) = _375119, -(disjoint(_375119, _375117))], (2081 ^ _302476) ^ [_375335, _375337] : [empty(_375337), -(_375337 = _375335), empty(_375335)], (2091 ^ _302476) ^ [_375646, _375648, _375650] : [-(subset(set_union2(_375650, _375646), _375648)), subset(_375650, _375648), subset(_375646, _375648)], (2101 ^ _302476) ^ [_375975, _375977, _375979] : [singleton(_375979) = unordered_pair(_375977, _375975), -(_375979 = _375977)], (2107 ^ _302476) ^ [_376201, _376203] : [in(_376203, _376201), -(subset(_376203, union(_376201)))], (2113 ^ _302476) ^ [_376386] : [-(union(powerset(_376386)) = _376386)], (2151 ^ _302476) ^ [_377907, _377909, _377911] : [singleton(_377911) = unordered_pair(_377909, _377907), -(_377909 = _377907)], (2116 ^ _302476) ^ [_376627] : [-(in(_376627, 2114 ^ [_376627]))], (2118 ^ _302476) ^ [_376739, _376741, _376743] : [-(in(_376739, 2114 ^ [_376743])), in(_376741, 2114 ^ [_376743]), subset(_376739, _376741)], (2128 ^ _302476) ^ [_377054, _377056] : [in(_377054, 2114 ^ [_377056]), 2132 ^ _302476 : [(2133 ^ _302476) ^ [] : [-(in(2131 ^ [_377054, _377056], 2114 ^ [_377056]))], (2135 ^ _302476) ^ [_377366] : [subset(_377366, _377054), -(in(_377366, 2131 ^ [_377054, _377056]))]]], (2141 ^ _302476) ^ [_377573, _377575] : [subset(_377573, 2114 ^ [_377575]), -(are_equipotent(_377573, 2114 ^ [_377575])), -(in(_377573, 2114 ^ [_377575]))]], input).
% 5.29/5.54  ncf('1',plain,[relation_dom(empty_set) = empty_set, relation_rng(empty_set) = empty_set],start(2157 ^ 0)).
% 5.29/5.54  ncf('1.1',plain,[-(relation_dom(empty_set) = empty_set), empty_set = relation_dom(empty_set)],extension(4 ^ 1,bind([[_302727, _302729], [relation_dom(empty_set), empty_set]]))).
% 5.29/5.54  ncf('1.1.1',plain,[-(empty_set = relation_dom(empty_set)), 770 : -(in(766 ^ [empty_set, empty_set], empty_set)), 775 : -(in(ordered_pair(766 ^ [empty_set, empty_set], 773 ^ [empty_set, empty_set]), empty_set)), 765 : relation(empty_set)],extension(744 ^ 2,bind([[_328864, _329676], [empty_set, empty_set]]))).
% 5.29/5.54  ncf('1.1.1.1',plain,[in(766 ^ [empty_set, empty_set], empty_set), empty(empty_set)],extension(2061 ^ 7,bind([[_374616, _374618], [empty_set, 766 ^ [empty_set, empty_set]]]))).
% 5.29/5.54  ncf('1.1.1.1.1',plain,[-(empty(empty_set))],extension(1242 ^ 8)).
% 5.29/5.54  ncf('1.1.1.2',plain,[in(ordered_pair(766 ^ [empty_set, empty_set], 773 ^ [empty_set, empty_set]), empty_set), empty(empty_set)],extension(2061 ^ 7,bind([[_374616, _374618], [empty_set, ordered_pair(766 ^ [empty_set, empty_set], 773 ^ [empty_set, empty_set])]]))).
% 5.29/5.54  ncf('1.1.1.2.1',plain,[-(empty(empty_set))],extension(1242 ^ 8)).
% 5.29/5.54  ncf('1.1.1.3',plain,[-(relation(empty_set)), empty(empty_set)],extension(314 ^ 3,bind([[_313407], [empty_set]]))).
% 5.29/5.54  ncf('1.1.1.3.1',plain,[-(empty(empty_set))],extension(1242 ^ 4)).
% 5.29/5.54  ncf('1.2',plain,[-(relation_rng(empty_set) = empty_set), empty_set = relation_rng(empty_set)],extension(4 ^ 1,bind([[_302727, _302729], [relation_rng(empty_set), empty_set]]))).
% 5.29/5.54  ncf('1.2.1',plain,[-(empty_set = relation_rng(empty_set)), 897 : -(in(893 ^ [empty_set, empty_set], empty_set)), 902 : -(in(ordered_pair(900 ^ [empty_set, empty_set], 893 ^ [empty_set, empty_set]), empty_set)), 892 : relation(empty_set)],extension(871 ^ 2,bind([[_333637, _334449], [empty_set, empty_set]]))).
% 5.29/5.54  ncf('1.2.1.1',plain,[in(893 ^ [empty_set, empty_set], empty_set), empty(empty_set)],extension(2061 ^ 7,bind([[_374616, _374618], [empty_set, 893 ^ [empty_set, empty_set]]]))).
% 5.29/5.54  ncf('1.2.1.1.1',plain,[-(empty(empty_set))],extension(1242 ^ 8)).
% 5.29/5.54  ncf('1.2.1.2',plain,[in(ordered_pair(900 ^ [empty_set, empty_set], 893 ^ [empty_set, empty_set]), empty_set), empty(empty_set)],extension(2061 ^ 7,bind([[_374616, _374618], [empty_set, ordered_pair(900 ^ [empty_set, empty_set], 893 ^ [empty_set, empty_set])]]))).
% 5.29/5.54  ncf('1.2.1.2.1',plain,[-(empty(empty_set))],extension(1242 ^ 8)).
% 5.29/5.54  ncf('1.2.1.3',plain,[-(relation(empty_set)), empty(empty_set)],extension(314 ^ 3,bind([[_313407], [empty_set]]))).
% 5.29/5.54  ncf('1.2.1.3.1',plain,[-(empty(empty_set))],extension(1242 ^ 4)).
% 5.29/5.54  %-----------------------------------------------------
% 5.29/5.54  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------