%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU174+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n019.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 12:02:31 EDT 2023

% Result   : Theorem 20.60s 21.02s
% Output   : Proof 20.60s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU174+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n019.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 13:22:57 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 20.60/21.02  
% 20.60/21.02  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 20.60/21.02  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.60/21.02  %-----------------------------------------------------
% 20.60/21.02  ncf(matrix, plain, [(1503 ^ _210244) ^ [] : [-(element(1501 ^ [], powerset(powerset(1500 ^ []))))], (1505 ^ _210244) ^ [] : [1501 ^ [] = empty_set], (1507 ^ _210244) ^ [] : [-(complements_of_subsets(1500 ^ [], 1501 ^ []) = empty_set)], (114 ^ _210244) ^ [_213997, _213999, _214001, _214003] : [-(cartesian_product2(_214003, _213999) = cartesian_product2(_214001, _213997)), _214003 = _214001, _213999 = _213997], (124 ^ _210244) ^ [_214356, _214358, _214360, _214362] : [-(ordered_pair(_214362, _214358) = ordered_pair(_214360, _214356)), _214362 = _214360, _214358 = _214356], (134 ^ _210244) ^ [_214715, _214717, _214719, _214721] : [-(set_intersection2(_214721, _214717) = set_intersection2(_214719, _214715)), _214721 = _214719, _214717 = _214715], (144 ^ _210244) ^ [_215074, _215076, _215078, _215080] : [-(subset_complement(_215080, _215076) = subset_complement(_215078, _215074)), _215080 = _215078, _215076 = _215074], (154 ^ _210244) ^ [_215433, _215435, _215437, _215439] : [-(set_difference(_215439, _215435) = set_difference(_215437, _215433)), _215439 = _215437, _215435 = _215433], (164 ^ _210244) ^ [_215792, _215794, _215796, _215798] : [-(set_union2(_215798, _215794) = set_union2(_215796, _215792)), _215798 = _215796, _215794 = _215792], (174 ^ _210244) ^ [_216123, _216125] : [_216125 = _216123, -(union(_216125) = union(_216123))], (180 ^ _210244) ^ [_216341, _216343] : [_216343 = _216341, -(singleton(_216343) = singleton(_216341))], (186 ^ _210244) ^ [_216587, _216589, _216591, _216593] : [-(unordered_pair(_216593, _216589) = unordered_pair(_216591, _216587)), _216593 = _216591, _216589 = _216587], (196 ^ _210244) ^ [_216918, _216920] : [_216920 = _216918, -(powerset(_216920) = powerset(_216918))], (202 ^ _210244) ^ [_217144, _217146, _217148, _217150] : [-(complements_of_subsets(_217150, _217146) = complements_of_subsets(_217148, _217144)), _217150 = _217148, _217146 = _217144], (2 ^ _210244) ^ [_210388] : [-(_210388 = _210388)], (4 ^ _210244) ^ [_210495, _210497] : [_210497 = _210495, -(_210495 = _210497)], (10 ^ _210244) ^ [_210699, _210701, _210703] : [-(_210703 = _210699), _210703 = _210701, _210701 = _210699], (20 ^ _210244) ^ [_211040, _211042, _211044, _211046] : [-(proper_subset(_211044, _211040)), proper_subset(_211046, _211042), _211046 = _211044, _211042 = _211040], (34 ^ _210244) ^ [_211484, _211486, _211488, _211490] : [-(disjoint(_211488, _211484)), disjoint(_211490, _211486), _211490 = _211488, _211486 = _211484], (48 ^ _210244) ^ [_211900, _211902] : [-(empty(_211900)), _211902 = _211900, empty(_211902)], (58 ^ _210244) ^ [_212223, _212225, _212227, _212229] : [-(subset(_212227, _212223)), subset(_212229, _212225), _212229 = _212227, _212225 = _212223], (72 ^ _210244) ^ [_212667, _212669, _212671, _212673] : [-(are_equipotent(_212671, _212667)), are_equipotent(_212673, _212669), _212673 = _212671, _212669 = _212667], (86 ^ _210244) ^ [_213111, _213113, _213115, _213117] : [-(in(_213115, _213111)), in(_213117, _213113), _213117 = _213115, _213113 = _213111], (100 ^ _210244) ^ [_213535, _213537, _213539, _213541] : [-(element(_213539, _213535)), element(_213541, _213537), _213541 = _213539, _213537 = _213535], (212 ^ _210244) ^ [_217549, _217551] : [in(_217551, _217549), in(_217549, _217551)], (218 ^ _210244) ^ [_217760, _217762] : [proper_subset(_217762, _217760), proper_subset(_217760, _217762)], (224 ^ _210244) ^ [_217956, _217958] : [-(unordered_pair(_217958, _217956) = unordered_pair(_217956, _217958))], (226 ^ _210244) ^ [_218056, _218058] : [-(set_union2(_218058, _218056) = set_union2(_218056, _218058))], (228 ^ _210244) ^ [_218156, _218158] : [-(set_intersection2(_218158, _218156) = set_intersection2(_218156, _218158))], (230 ^ _210244) ^ [_218300, _218302] : [_218302 = _218300, 233 ^ _210244 : [(234 ^ _210244) ^ [] : [-(subset(_218302, _218300))], (236 ^ _210244) ^ [] : [-(subset(_218300, _218302))]]], (238 ^ _210244) ^ [_218537, _218539] : [-(_218539 = _218537), subset(_218539, _218537), subset(_218537, _218539)], (264 ^ _210244) ^ [_219388, _219390] : [-(_219388 = singleton(_219390)), 268 ^ _210244 : [(269 ^ _210244) ^ [] : [-(in(265 ^ [_219388, _219390], _219388))], (271 ^ _210244) ^ [] : [265 ^ [_219388, _219390] = _219390]], 272 ^ _210244 : [(273 ^ _210244) ^ [] : [-(265 ^ [_219388, _219390] = _219390)], (275 ^ _210244) ^ [] : [in(265 ^ [_219388, _219390], _219388)]]], (248 ^ _210244) ^ [_218867, _218869] : [_218867 = singleton(_218869), 251 ^ _210244 : [(252 ^ _210244) ^ [_219037] : [in(_219037, _218867), -(_219037 = _218869)], (258 ^ _210244) ^ [_219209] : [_219209 = _218869, -(in(_219209, _218867))]]], (279 ^ _210244) ^ [_219939] : [_219939 = empty_set, 282 ^ _210244 : [(283 ^ _210244) ^ [_220052] : [in(_220052, _219939)]]], (285 ^ _210244) ^ [_220118] : [-(in(286 ^ [_220118], _220118)), -(_220118 = empty_set)], (308 ^ _210244) ^ [_220930, _220932] : [-(_220930 = powerset(_220932)), 312 ^ _210244 : [(313 ^ _210244) ^ [] : [-(in(309 ^ [_220930, _220932], _220930))], (315 ^ _210244) ^ [] : [subset(309 ^ [_220930, _220932], _220932)]], 316 ^ _210244 : [(317 ^ _210244) ^ [] : [-(subset(309 ^ [_220930, _220932], _220932))], (319 ^ _210244) ^ [] : [in(309 ^ [_220930, _220932], _220930)]]], (292 ^ _210244) ^ [_220409, _220411] : [_220409 = powerset(_220411), 295 ^ _210244 : [(296 ^ _210244) ^ [_220579] : [in(_220579, _220409), -(subset(_220579, _220411))], (302 ^ _210244) ^ [_220751] : [subset(_220751, _220411), -(in(_220751, _220409))]]], (323 ^ _210244) ^ [_221486, _221488] : [-(empty(_221488)), 326 ^ _210244 : [(327 ^ _210244) ^ [] : [element(_221486, _221488), -(in(_221486, _221488))], (333 ^ _210244) ^ [] : [in(_221486, _221488), -(element(_221486, _221488))]]], (339 ^ _210244) ^ [_221899, _221901] : [empty(_221901), 342 ^ _210244 : [(343 ^ _210244) ^ [] : [element(_221899, _221901), -(empty(_221899))], (349 ^ _210244) ^ [] : [empty(_221899), -(element(_221899, _221901))]]], (377 ^ _210244) ^ [_223124, _223126, _223128] : [-(_223124 = unordered_pair(_223128, _223126)), 381 ^ _210244 : [(382 ^ _210244) ^ [] : [-(in(378 ^ [_223124, _223126, _223128], _223124))], (384 ^ _210244) ^ [] : [378 ^ [_223124, _223126, _223128] = _223128], (386 ^ _210244) ^ [] : [378 ^ [_223124, _223126, _223128] = _223126]], 387 ^ _210244 : [(394 ^ _210244) ^ [] : [in(378 ^ [_223124, _223126, _223128], _223124)], (388 ^ _210244) ^ [] : [-(378 ^ [_223124, _223126, _223128] = _223128), -(378 ^ [_223124, _223126, _223128] = _223126)]]], (355 ^ _210244) ^ [_222399, _222401, _222403] : [_222399 = unordered_pair(_222403, _222401), 358 ^ _210244 : [(369 ^ _210244) ^ [_222859] : [370 ^ _210244 : [(371 ^ _210244) ^ [] : [_222859 = _222403], (373 ^ _210244) ^ [] : [_222859 = _222401]], -(in(_222859, _222399))], (359 ^ _210244) ^ [_222581] : [in(_222581, _222399), -(_222581 = _222403), -(_222581 = _222401)]]], (420 ^ _210244) ^ [_224643, _224645, _224647] : [-(_224643 = set_union2(_224647, _224645)), 424 ^ _210244 : [(425 ^ _210244) ^ [] : [-(in(421 ^ [_224643, _224645, _224647], _224643))], (427 ^ _210244) ^ [] : [in(421 ^ [_224643, _224645, _224647], _224647)], (429 ^ _210244) ^ [] : [in(421 ^ [_224643, _224645, _224647], _224645)]], 430 ^ _210244 : [(437 ^ _210244) ^ [] : [in(421 ^ [_224643, _224645, _224647], _224643)], (431 ^ _210244) ^ [] : [-(in(421 ^ [_224643, _224645, _224647], _224647)), -(in(421 ^ [_224643, _224645, _224647], _224645))]]], (398 ^ _210244) ^ [_223918, _223920, _223922] : [_223918 = set_union2(_223922, _223920), 401 ^ _210244 : [(412 ^ _210244) ^ [_224378] : [413 ^ _210244 : [(414 ^ _210244) ^ [] : [in(_224378, _223922)], (416 ^ _210244) ^ [] : [in(_224378, _223920)]], -(in(_224378, _223918))], (402 ^ _210244) ^ [_224100] : [in(_224100, _223918), -(in(_224100, _223922)), -(in(_224100, _223920))]]], (471 ^ _210244) ^ [_226694, _226696, _226698] : [-(_226694 = cartesian_product2(_226698, _226696)), 489 ^ _210244 : [(490 ^ _210244) ^ [] : [-(in(487 ^ [_226694, _226696, _226698], _226698))], (492 ^ _210244) ^ [] : [-(in(488 ^ [_226694, _226696, _226698], _226696))], (494 ^ _210244) ^ [] : [-(472 ^ [_226694, _226696, _226698] = ordered_pair(487 ^ [_226694, _226696, _226698], 488 ^ [_226694, _226696, _226698]))], (496 ^ _210244) ^ [] : [in(472 ^ [_226694, _226696, _226698], _226694)]], 475 ^ _210244 : [(476 ^ _210244) ^ [] : [-(in(472 ^ [_226694, _226696, _226698], _226694))], (478 ^ _210244) ^ [_227032, _227034] : [in(_227034, _226698), in(_227032, _226696), 472 ^ [_226694, _226696, _226698] = ordered_pair(_227034, _227032)]]], (441 ^ _210244) ^ [_225437, _225439, _225441] : [_225437 = cartesian_product2(_225441, _225439), 444 ^ _210244 : [(445 ^ _210244) ^ [_225638] : [in(_225638, _225437), 450 ^ _210244 : [(451 ^ _210244) ^ [] : [-(in(448 ^ [_225437, _225439, _225441, _225638], _225441))], (453 ^ _210244) ^ [] : [-(in(449 ^ [_225437, _225439, _225441, _225638], _225439))], (455 ^ _210244) ^ [] : [-(_225638 = ordered_pair(448 ^ [_225437, _225439, _225441, _225638], 449 ^ [_225437, _225439, _225441, _225638]))]]], (457 ^ _210244) ^ [_226198] : [-(in(_226198, _225437)), 458 ^ _210244 : [(459 ^ _210244) ^ [_226328, _226330] : [in(_226330, _225441), in(_226328, _225439), _226198 = ordered_pair(_226330, _226328)]]]]], (510 ^ _210244) ^ [_228285, _228287] : [512 ^ _210244 : [(513 ^ _210244) ^ [] : [-(in(511 ^ [_228285, _228287], _228287))], (515 ^ _210244) ^ [] : [in(511 ^ [_228285, _228287], _228285)]], -(subset(_228287, _228285))], (500 ^ _210244) ^ [_227971, _227973] : [subset(_227973, _227971), 503 ^ _210244 : [(504 ^ _210244) ^ [_228108] : [in(_228108, _227973), -(in(_228108, _227971))]]], (541 ^ _210244) ^ [_229410, _229412, _229414] : [-(_229410 = set_intersection2(_229414, _229412)), 553 ^ _210244 : [(554 ^ _210244) ^ [] : [-(in(542 ^ [_229410, _229412, _229414], _229414))], (556 ^ _210244) ^ [] : [-(in(542 ^ [_229410, _229412, _229414], _229412))], (558 ^ _210244) ^ [] : [in(542 ^ [_229410, _229412, _229414], _229410)]], 545 ^ _210244 : [(546 ^ _210244) ^ [] : [-(in(542 ^ [_229410, _229412, _229414], _229410))], (548 ^ _210244) ^ [] : [in(542 ^ [_229410, _229412, _229414], _229414), in(542 ^ [_229410, _229412, _229414], _229412)]]], (519 ^ _210244) ^ [_228685, _228687, _228689] : [_228685 = set_intersection2(_228689, _228687), 522 ^ _210244 : [(523 ^ _210244) ^ [_228867] : [in(_228867, _228685), 526 ^ _210244 : [(527 ^ _210244) ^ [] : [-(in(_228867, _228689))], (529 ^ _210244) ^ [] : [-(in(_228867, _228687))]]], (531 ^ _210244) ^ [_229126] : [-(in(_229126, _228685)), in(_229126, _228689), in(_229126, _228687)]]], (585 ^ _210244) ^ [_231037, _231039] : [-(_231037 = union(_231039)), 598 ^ _210244 : [(599 ^ _210244) ^ [] : [-(in(586 ^ [_231037, _231039], 597 ^ [_231037, _231039]))], (601 ^ _210244) ^ [] : [-(in(597 ^ [_231037, _231039], _231039))], (603 ^ _210244) ^ [] : [in(586 ^ [_231037, _231039], _231037)]], 589 ^ _210244 : [(590 ^ _210244) ^ [] : [-(in(586 ^ [_231037, _231039], _231037))], (592 ^ _210244) ^ [_231320] : [in(586 ^ [_231037, _231039], _231320), in(_231320, _231039)]]], (562 ^ _210244) ^ [_230192, _230194] : [_230192 = union(_230194), 565 ^ _210244 : [(566 ^ _210244) ^ [_230373] : [in(_230373, _230192), 570 ^ _210244 : [(571 ^ _210244) ^ [] : [-(in(_230373, 569 ^ [_230192, _230194, _230373]))], (573 ^ _210244) ^ [] : [-(in(569 ^ [_230192, _230194, _230373], _230194))]]], (575 ^ _210244) ^ [_230700] : [-(in(_230700, _230192)), 576 ^ _210244 : [(577 ^ _210244) ^ [_230798] : [in(_230700, _230798), in(_230798, _230194)]]]]], (629 ^ _210244) ^ [_232658, _232660, _232662] : [-(_232658 = set_difference(_232662, _232660)), 641 ^ _210244 : [(642 ^ _210244) ^ [] : [-(in(630 ^ [_232658, _232660, _232662], _232662))], (644 ^ _210244) ^ [] : [in(630 ^ [_232658, _232660, _232662], _232660)], (646 ^ _210244) ^ [] : [in(630 ^ [_232658, _232660, _232662], _232658)]], 633 ^ _210244 : [(634 ^ _210244) ^ [] : [-(in(630 ^ [_232658, _232660, _232662], _232658))], (636 ^ _210244) ^ [] : [in(630 ^ [_232658, _232660, _232662], _232662), -(in(630 ^ [_232658, _232660, _232662], _232660))]]], (607 ^ _210244) ^ [_231927, _231929, _231931] : [_231927 = set_difference(_231931, _231929), 610 ^ _210244 : [(611 ^ _210244) ^ [_232111] : [in(_232111, _231927), 614 ^ _210244 : [(615 ^ _210244) ^ [] : [-(in(_232111, _231931))], (617 ^ _210244) ^ [] : [in(_232111, _231929)]]], (619 ^ _210244) ^ [_232371] : [-(in(_232371, _231927)), in(_232371, _231931), -(in(_232371, _231929))]]], (650 ^ _210244) ^ [_233415, _233417] : [element(_233415, powerset(_233417)), -(subset_complement(_233417, _233415) = set_difference(_233417, _233415))], (656 ^ _210244) ^ [_233626, _233628] : [-(ordered_pair(_233628, _233626) = unordered_pair(unordered_pair(_233628, _233626), singleton(_233628)))], (658 ^ _210244) ^ [_233775, _233777] : [disjoint(_233777, _233775), -(set_intersection2(_233777, _233775) = empty_set)], (664 ^ _210244) ^ [_233943, _233945] : [set_intersection2(_233945, _233943) = empty_set, -(disjoint(_233945, _233943))], (670 ^ _210244) ^ [_234161, _234163] : [element(_234161, powerset(powerset(_234163))), 673 ^ _210244 : [(674 ^ _210244) ^ [_234341] : [element(_234341, powerset(powerset(_234163))), 677 ^ _210244 : [(698 ^ _210244) ^ [] : [-(_234341 = complements_of_subsets(_234163, _234161)), 700 ^ _210244 : [(701 ^ _210244) ^ [] : [-(element(699 ^ [_234161, _234163, _234341], powerset(_234163)))], (703 ^ _210244) ^ [] : [704 ^ _210244 : [(705 ^ _210244) ^ [] : [-(in(699 ^ [_234161, _234163, _234341], _234341))], (707 ^ _210244) ^ [] : [in(subset_complement(_234163, 699 ^ [_234161, _234163, _234341]), _234161)]], 708 ^ _210244 : [(709 ^ _210244) ^ [] : [-(in(subset_complement(_234163, 699 ^ [_234161, _234163, _234341]), _234161))], (711 ^ _210244) ^ [] : [in(699 ^ [_234161, _234163, _234341], _234341)]]]]], (678 ^ _210244) ^ [] : [_234341 = complements_of_subsets(_234163, _234161), 681 ^ _210244 : [(682 ^ _210244) ^ [_234629] : [element(_234629, powerset(_234163)), 685 ^ _210244 : [(686 ^ _210244) ^ [] : [in(_234629, _234341), -(in(subset_complement(_234163, _234629), _234161))], (692 ^ _210244) ^ [] : [in(subset_complement(_234163, _234629), _234161), -(in(_234629, _234341))]]]]]]]]], (715 ^ _210244) ^ [_235752, _235754] : [proper_subset(_235754, _235752), 718 ^ _210244 : [(719 ^ _210244) ^ [] : [-(subset(_235754, _235752))], (721 ^ _210244) ^ [] : [_235754 = _235752]]], (723 ^ _210244) ^ [_235990, _235992] : [-(proper_subset(_235992, _235990)), subset(_235992, _235990), -(_235992 = _235990)], (733 ^ _210244) ^ [] : [true___, -(true___)], (739 ^ _210244) ^ [] : [true___, -(true___)], (745 ^ _210244) ^ [] : [true___, -(true___)], (751 ^ _210244) ^ [] : [true___, -(true___)], (757 ^ _210244) ^ [] : [true___, -(true___)], (763 ^ _210244) ^ [] : [true___, -(true___)], (769 ^ _210244) ^ [_237008, _237010] : [element(_237008, powerset(_237010)), -(element(subset_complement(_237010, _237008), powerset(_237010)))], (775 ^ _210244) ^ [] : [true___, -(true___)], (781 ^ _210244) ^ [] : [true___, -(true___)], (787 ^ _210244) ^ [] : [true___, -(true___)], (793 ^ _210244) ^ [] : [true___, -(true___)], (799 ^ _210244) ^ [_237708, _237710] : [element(_237708, powerset(powerset(_237710))), -(element(complements_of_subsets(_237710, _237708), powerset(powerset(_237710))))], (805 ^ _210244) ^ [] : [true___, -(true___)], (812 ^ _210244) ^ [_238069] : [-(element(810 ^ [_238069], _238069))], (814 ^ _210244) ^ [_238151] : [empty(powerset(_238151))], (816 ^ _210244) ^ [] : [-(empty(empty_set))], (818 ^ _210244) ^ [_238296, _238298] : [empty(ordered_pair(_238298, _238296))], (820 ^ _210244) ^ [_238407, _238409] : [-(empty(_238409)), empty(set_union2(_238409, _238407))], (826 ^ _210244) ^ [_238623, _238625] : [-(empty(_238625)), empty(set_union2(_238623, _238625))], (832 ^ _210244) ^ [_238824, _238826] : [-(set_union2(_238826, _238826) = _238826)], (834 ^ _210244) ^ [_238921, _238923] : [-(set_intersection2(_238923, _238923) = _238923)], (836 ^ _210244) ^ [_239033, _239035] : [element(_239033, powerset(_239035)), -(subset_complement(_239035, subset_complement(_239035, _239033)) = _239033)], (842 ^ _210244) ^ [_239259, _239261] : [element(_239259, powerset(powerset(_239261))), -(complements_of_subsets(_239261, complements_of_subsets(_239261, _239259)) = _239259)], (848 ^ _210244) ^ [_239473, _239475] : [proper_subset(_239475, _239475)], (850 ^ _210244) ^ [_239552] : [singleton(_239552) = empty_set], (852 ^ _210244) ^ [_239661, _239663] : [in(_239663, _239661), -(set_union2(singleton(_239663), _239661) = _239661)], (858 ^ _210244) ^ [_239881, _239883] : [disjoint(singleton(_239883), _239881), in(_239883, _239881)], (864 ^ _210244) ^ [_240094, _240096] : [-(in(_240096, _240094)), -(disjoint(singleton(_240096), _240094))], (870 ^ _210244) ^ [_240340, _240342] : [subset(singleton(_240342), _240340), -(in(_240342, _240340))], (876 ^ _210244) ^ [_240506, _240508] : [in(_240508, _240506), -(subset(singleton(_240508), _240506))], (882 ^ _210244) ^ [_240751, _240753] : [set_difference(_240753, _240751) = empty_set, -(subset(_240753, _240751))], (888 ^ _210244) ^ [_240919, _240921] : [subset(_240921, _240919), -(set_difference(_240921, _240919) = empty_set)], (894 ^ _210244) ^ [_241137, _241139] : [element(_241137, powerset(_241139)), 897 ^ _210244 : [(898 ^ _210244) ^ [_241278] : [in(_241278, _241137), -(in(_241278, _241139))]]], (904 ^ _210244) ^ [_241517, _241519, _241521] : [subset(_241521, _241519), -(in(_241517, _241521)), -(subset(_241521, set_difference(_241519, singleton(_241517))))], (924 ^ _210244) ^ [_242126, _242128] : [925 ^ _210244 : [(926 ^ _210244) ^ [] : [_242128 = empty_set], (928 ^ _210244) ^ [] : [_242128 = singleton(_242126)]], -(subset(_242128, singleton(_242126)))], (914 ^ _210244) ^ [_241866, _241868] : [subset(_241868, singleton(_241866)), -(_241868 = empty_set), -(_241868 = singleton(_241866))], (932 ^ _210244) ^ [_242420, _242422] : [in(_242422, _242420), -(subset(_242422, union(_242420)))], (938 ^ _210244) ^ [_242691, _242693, _242695, _242697] : [in(ordered_pair(_242697, _242695), cartesian_product2(_242693, _242691)), 941 ^ _210244 : [(942 ^ _210244) ^ [] : [-(in(_242697, _242693))], (944 ^ _210244) ^ [] : [-(in(_242695, _242691))]]], (946 ^ _210244) ^ [_242956, _242958, _242960, _242962] : [-(in(ordered_pair(_242962, _242960), cartesian_product2(_242958, _242956))), in(_242962, _242958), in(_242960, _242956)], (956 ^ _210244) ^ [_243289, _243291] : [958 ^ _210244 : [(959 ^ _210244) ^ [] : [-(in(957 ^ [_243289, _243291], _243291))], (961 ^ _210244) ^ [] : [in(957 ^ [_243289, _243291], _243289)]], -(element(_243291, powerset(_243289)))], (965 ^ _210244) ^ [_243634] : [-(empty(_243634)), 969 ^ _210244 : [(970 ^ _210244) ^ [] : [-(element(968 ^ [_243634], powerset(_243634)))], (972 ^ _210244) ^ [] : [empty(968 ^ [_243634])]]], (975 ^ _210244) ^ [] : [-(empty(973 ^ []))], (978 ^ _210244) ^ [_244106] : [-(element(976 ^ [_244106], powerset(_244106)))], (980 ^ _210244) ^ [_244157] : [-(empty(976 ^ [_244157]))], (983 ^ _210244) ^ [] : [empty(981 ^ [])], (985 ^ _210244) ^ [_244345, _244347] : [-(subset(_244347, _244347))], (987 ^ _210244) ^ [_244454, _244456] : [disjoint(_244456, _244454), -(disjoint(_244454, _244456))], (993 ^ _210244) ^ [_244721, _244723, _244725, _244727] : [in(ordered_pair(_244727, _244725), cartesian_product2(_244723, _244721)), 996 ^ _210244 : [(997 ^ _210244) ^ [] : [-(in(_244727, _244723))], (999 ^ _210244) ^ [] : [-(in(_244725, _244721))]]], (1001 ^ _210244) ^ [_244986, _244988, _244990, _244992] : [-(in(ordered_pair(_244992, _244990), cartesian_product2(_244988, _244986))), in(_244992, _244988), in(_244990, _244986)], (1011 ^ _210244) ^ [_245347, _245349, _245351, _245353] : [unordered_pair(_245353, _245351) = unordered_pair(_245349, _245347), -(_245353 = _245349), -(_245353 = _245347)], (1021 ^ _210244) ^ [_245697, _245699, _245701] : [subset(_245701, _245699), 1024 ^ _210244 : [(1025 ^ _210244) ^ [] : [-(subset(cartesian_product2(_245701, _245697), cartesian_product2(_245699, _245697)))], (1027 ^ _210244) ^ [] : [-(subset(cartesian_product2(_245697, _245701), cartesian_product2(_245697, _245699)))]]], (1029 ^ _210244) ^ [_246042, _246044, _246046, _246048] : [-(subset(cartesian_product2(_246048, _246044), cartesian_product2(_246046, _246042))), subset(_246048, _246046), subset(_246044, _246042)], (1039 ^ _210244) ^ [_246373, _246375] : [subset(_246375, _246373), -(set_union2(_246375, _246373) = _246373)], (1046 ^ _210244) ^ [_246695] : [-(in(_246695, 1044 ^ [_246695]))], (1048 ^ _210244) ^ [_246807, _246809, _246811] : [-(in(_246807, 1044 ^ [_246811])), in(_246809, 1044 ^ [_246811]), subset(_246807, _246809)], (1058 ^ _210244) ^ [_247122, _247124] : [in(_247122, 1044 ^ [_247124]), -(in(powerset(_247122), 1044 ^ [_247124]))], (1064 ^ _210244) ^ [_247322, _247324] : [subset(_247322, 1044 ^ [_247324]), -(are_equipotent(_247322, 1044 ^ [_247324])), -(in(_247322, 1044 ^ [_247324]))], (1074 ^ _210244) ^ [_247647, _247649] : [-(subset(set_intersection2(_247649, _247647), _247649))], (1076 ^ _210244) ^ [_247773, _247775, _247777] : [-(subset(_247777, set_intersection2(_247775, _247773))), subset(_247777, _247775), subset(_247777, _247773)], (1086 ^ _210244) ^ [_248059] : [-(set_union2(_248059, empty_set) = _248059)], (1088 ^ _210244) ^ [_248169, _248171] : [in(_248171, _248169), -(element(_248171, _248169))], (1094 ^ _210244) ^ [_248393, _248395, _248397] : [-(subset(_248397, _248393)), subset(_248397, _248395), subset(_248395, _248393)], (1104 ^ _210244) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (1106 ^ _210244) ^ [_248769, _248771, _248773] : [subset(_248773, _248771), -(subset(set_intersection2(_248773, _248769), set_intersection2(_248771, _248769)))], (1112 ^ _210244) ^ [_248997, _248999] : [subset(_248999, _248997), -(set_intersection2(_248999, _248997) = _248999)], (1118 ^ _210244) ^ [_249184] : [-(set_intersection2(_249184, empty_set) = empty_set)], (1120 ^ _210244) ^ [_249294, _249296] : [element(_249296, _249294), -(empty(_249294)), -(in(_249296, _249294))], (1130 ^ _210244) ^ [_249592, _249594] : [-(_249594 = _249592), 1134 ^ _210244 : [(1135 ^ _210244) ^ [] : [-(in(1131 ^ [_249592, _249594], _249594))], (1137 ^ _210244) ^ [] : [in(1131 ^ [_249592, _249594], _249592)]], 1138 ^ _210244 : [(1139 ^ _210244) ^ [] : [-(in(1131 ^ [_249592, _249594], _249592))], (1141 ^ _210244) ^ [] : [in(1131 ^ [_249592, _249594], _249594)]]], (1145 ^ _210244) ^ [_250093] : [-(subset(empty_set, _250093))], (1147 ^ _210244) ^ [_250214, _250216, _250218] : [subset(_250218, _250216), -(subset(set_difference(_250218, _250214), set_difference(_250216, _250214)))], (1153 ^ _210244) ^ [_250470, _250472, _250474, _250476] : [ordered_pair(_250476, _250474) = ordered_pair(_250472, _250470), 1156 ^ _210244 : [(1157 ^ _210244) ^ [] : [-(_250476 = _250472)], (1159 ^ _210244) ^ [] : [-(_250474 = _250470)]]], (1161 ^ _210244) ^ [_250768, _250770] : [-(subset(set_difference(_250770, _250768), _250770))], (1163 ^ _210244) ^ [_250909, _250911] : [set_difference(_250911, _250909) = empty_set, -(subset(_250911, _250909))], (1169 ^ _210244) ^ [_251077, _251079] : [subset(_251079, _251077), -(set_difference(_251079, _251077) = empty_set)], (1175 ^ _210244) ^ [_251324, _251326] : [subset(singleton(_251326), _251324), -(in(_251326, _251324))], (1181 ^ _210244) ^ [_251490, _251492] : [in(_251492, _251490), -(subset(singleton(_251492), _251490))], (1187 ^ _210244) ^ [_251749, _251751, _251753] : [subset(unordered_pair(_251753, _251751), _251749), 1190 ^ _210244 : [(1191 ^ _210244) ^ [] : [-(in(_251753, _251749))], (1193 ^ _210244) ^ [] : [-(in(_251751, _251749))]]], (1195 ^ _210244) ^ [_252000, _252002, _252004] : [-(subset(unordered_pair(_252004, _252002), _252000)), in(_252004, _252000), in(_252002, _252000)], (1205 ^ _210244) ^ [_252302, _252304] : [-(set_union2(_252304, set_difference(_252302, _252304)) = set_union2(_252304, _252302))], (1217 ^ _210244) ^ [_252709, _252711] : [1218 ^ _210244 : [(1219 ^ _210244) ^ [] : [_252711 = empty_set], (1221 ^ _210244) ^ [] : [_252711 = singleton(_252709)]], -(subset(_252711, singleton(_252709)))], (1207 ^ _210244) ^ [_252449, _252451] : [subset(_252451, singleton(_252449)), -(_252451 = empty_set), -(_252451 = singleton(_252449))], (1225 ^ _210244) ^ [_252974] : [-(set_difference(_252974, empty_set) = _252974)], (1227 ^ _210244) ^ [_253113, _253115] : [element(_253115, powerset(_253113)), -(subset(_253115, _253113))], (1233 ^ _210244) ^ [_253279, _253281] : [subset(_253281, _253279), -(element(_253281, powerset(_253279)))], (1239 ^ _210244) ^ [_253515, _253517] : [-(disjoint(_253517, _253515)), 1243 ^ _210244 : [(1244 ^ _210244) ^ [] : [-(in(1242 ^ [_253515, _253517], _253517))], (1246 ^ _210244) ^ [] : [-(in(1242 ^ [_253515, _253517], _253515))]]], (1248 ^ _210244) ^ [_253829, _253831] : [disjoint(_253831, _253829), 1249 ^ _210244 : [(1250 ^ _210244) ^ [_253921] : [in(_253921, _253831), in(_253921, _253829)]]], (1258 ^ _210244) ^ [_254178] : [subset(_254178, empty_set), -(_254178 = empty_set)], (1264 ^ _210244) ^ [_254367, _254369] : [-(set_difference(set_union2(_254369, _254367), _254367) = set_difference(_254369, _254367))], (1266 ^ _210244) ^ [_254485, _254487] : [element(_254485, powerset(_254487)), 1269 ^ _210244 : [(1270 ^ _210244) ^ [_254637] : [element(_254637, powerset(_254487)), 1273 ^ _210244 : [(1274 ^ _210244) ^ [] : [disjoint(_254485, _254637), -(subset(_254485, subset_complement(_254487, _254637)))], (1280 ^ _210244) ^ [] : [subset(_254485, subset_complement(_254487, _254637)), -(disjoint(_254485, _254637))]]]]], (1286 ^ _210244) ^ [_255135, _255137] : [subset(_255137, _255135), -(_255135 = set_union2(_255137, set_difference(_255135, _255137)))], (1292 ^ _210244) ^ [_255357, _255359] : [in(_255359, _255357), -(set_union2(singleton(_255359), _255357) = _255357)], (1298 ^ _210244) ^ [_255562, _255564] : [-(set_difference(_255564, set_difference(_255564, _255562)) = set_intersection2(_255564, _255562))], (1300 ^ _210244) ^ [_255651] : [-(set_difference(empty_set, _255651) = empty_set)], (1302 ^ _210244) ^ [_255775, _255777, _255779] : [-(element(_255779, _255775)), in(_255779, _255777), element(_255777, powerset(_255775))], (1312 ^ _210244) ^ [_256108, _256110] : [-(disjoint(_256110, _256108)), -(in(1315 ^ [_256108, _256110], set_intersection2(_256110, _256108)))], (1319 ^ _210244) ^ [_256343, _256345] : [1320 ^ _210244 : [(1321 ^ _210244) ^ [_256416] : [in(_256416, set_intersection2(_256345, _256343))]], disjoint(_256345, _256343)], (1325 ^ _210244) ^ [_256568] : [-(_256568 = empty_set), 1328 ^ _210244 : [(1329 ^ _210244) ^ [_256728] : [element(_256728, powerset(_256568)), 1332 ^ _210244 : [(1333 ^ _210244) ^ [_256882] : [element(_256882, _256568), -(in(_256882, _256728)), -(in(_256882, subset_complement(_256568, _256728)))]]]]], (1343 ^ _210244) ^ [_257228, _257230, _257232] : [element(_257228, powerset(_257232)), in(_257230, subset_complement(_257232, _257228)), in(_257230, _257228)], (1353 ^ _210244) ^ [_257562, _257564, _257566] : [in(_257566, _257564), element(_257564, powerset(_257562)), empty(_257562)], (1363 ^ _210244) ^ [_257872, _257874] : [subset(_257874, _257872), proper_subset(_257872, _257874)], (1369 ^ _210244) ^ [_258095, _258097, _258099] : [-(disjoint(_258099, _258095)), subset(_258099, _258097), disjoint(_258097, _258095)], (1379 ^ _210244) ^ [_258433, _258435] : [set_difference(_258435, singleton(_258433)) = _258435, in(_258433, _258435)], (1385 ^ _210244) ^ [_258606, _258608] : [-(in(_258606, _258608)), -(set_difference(_258608, singleton(_258606)) = _258608)], (1391 ^ _210244) ^ [_258802] : [-(unordered_pair(_258802, _258802) = singleton(_258802))], (1393 ^ _210244) ^ [_258900] : [empty(_258900), -(_258900 = empty_set)], (1399 ^ _210244) ^ [_259102, _259104] : [subset(singleton(_259104), singleton(_259102)), -(_259104 = _259102)], (1405 ^ _210244) ^ [_259320, _259322] : [in(_259322, _259320), empty(_259320)], (1411 ^ _210244) ^ [_259512, _259514] : [-(subset(_259514, set_union2(_259514, _259512)))], (1413 ^ _210244) ^ [_259653, _259655] : [disjoint(_259655, _259653), -(set_difference(_259655, _259653) = _259655)], (1419 ^ _210244) ^ [_259821, _259823] : [set_difference(_259823, _259821) = _259823, -(disjoint(_259823, _259821))], (1425 ^ _210244) ^ [_260039, _260041] : [empty(_260041), -(_260041 = _260039), empty(_260039)], (1435 ^ _210244) ^ [_260350, _260352, _260354] : [-(subset(set_union2(_260354, _260350), _260352)), subset(_260354, _260352), subset(_260350, _260352)], (1445 ^ _210244) ^ [_260679, _260681, _260683] : [singleton(_260683) = unordered_pair(_260681, _260679), -(_260683 = _260681)], (1451 ^ _210244) ^ [_260905, _260907] : [in(_260907, _260905), -(subset(_260907, union(_260905)))], (1457 ^ _210244) ^ [_261090] : [-(union(powerset(_261090)) = _261090)], (1495 ^ _210244) ^ [_262611, _262613, _262615] : [singleton(_262615) = unordered_pair(_262613, _262611), -(_262613 = _262611)], (1460 ^ _210244) ^ [_261331] : [-(in(_261331, 1458 ^ [_261331]))], (1462 ^ _210244) ^ [_261443, _261445, _261447] : [-(in(_261443, 1458 ^ [_261447])), in(_261445, 1458 ^ [_261447]), subset(_261443, _261445)], (1472 ^ _210244) ^ [_261758, _261760] : [in(_261758, 1458 ^ [_261760]), 1476 ^ _210244 : [(1477 ^ _210244) ^ [] : [-(in(1475 ^ [_261758, _261760], 1458 ^ [_261760]))], (1479 ^ _210244) ^ [_262070] : [subset(_262070, _261758), -(in(_262070, 1475 ^ [_261758, _261760]))]]], (1485 ^ _210244) ^ [_262277, _262279] : [subset(_262277, 1458 ^ [_262279]), -(are_equipotent(_262277, 1458 ^ [_262279])), -(in(_262277, 1458 ^ [_262279]))]], input).
% 20.60/21.02  ncf('1',plain,[disjoint(singleton(699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set]), empty_set), in(699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set], empty_set)],start(858 ^ 0,bind([[_239881, _239883], [empty_set, 699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set]]]))).
% 20.60/21.02  ncf('1.1',plain,[-(disjoint(singleton(699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set]), empty_set)), set_intersection2(singleton(699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set]), empty_set) = empty_set],extension(664 ^ 1,bind([[_233943, _233945], [empty_set, singleton(699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set])]]))).
% 20.60/21.02  ncf('1.1.1',plain,[-(set_intersection2(singleton(699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set]), empty_set) = empty_set)],extension(1118 ^ 2,bind([[_249184], [singleton(699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set])]]))).
% 20.60/21.02  ncf('1.2',plain,[-(in(699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set], empty_set)), 709 : -(in(subset_complement(1500 ^ [], 699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set]), complements_of_subsets(1500 ^ [], 1501 ^ []))), 703 : -(empty_set = complements_of_subsets(1500 ^ [], complements_of_subsets(1500 ^ [], 1501 ^ []))), 698 : element(empty_set, powerset(powerset(1500 ^ []))), 674 : element(complements_of_subsets(1500 ^ [], 1501 ^ []), powerset(powerset(1500 ^ [])))],extension(670 ^ 1,bind([[_234161, _234163, _234341], [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set]]))).
% 20.60/21.02  ncf('1.2.1',plain,[in(subset_complement(1500 ^ [], 699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set]), complements_of_subsets(1500 ^ [], 1501 ^ [])), complements_of_subsets(1500 ^ [], 1501 ^ []) = empty_set],extension(279 ^ 10,bind([[_219939, _220052], [complements_of_subsets(1500 ^ [], 1501 ^ []), subset_complement(1500 ^ [], 699 ^ [complements_of_subsets(1500 ^ [], 1501 ^ []), 1500 ^ [], empty_set])]]))).
% 20.60/21.02  ncf('1.2.1.1',plain,[-(complements_of_subsets(1500 ^ [], 1501 ^ []) = empty_set)],extension(1507 ^ 11)).
% 20.60/21.02  ncf('1.2.2',plain,[empty_set = complements_of_subsets(1500 ^ [], complements_of_subsets(1500 ^ [], 1501 ^ [])), -(empty_set = 1501 ^ []), complements_of_subsets(1500 ^ [], complements_of_subsets(1500 ^ [], 1501 ^ [])) = 1501 ^ []],extension(10 ^ 6,bind([[_210699, _210701, _210703], [1501 ^ [], complements_of_subsets(1500 ^ [], complements_of_subsets(1500 ^ [], 1501 ^ [])), empty_set]]))).
% 20.60/21.02  ncf('1.2.2.1',plain,[empty_set = 1501 ^ [], -(1501 ^ [] = empty_set)],extension(4 ^ 7,bind([[_210495, _210497], [1501 ^ [], empty_set]]))).
% 20.60/21.02  ncf('1.2.2.1.1',plain,[1501 ^ [] = empty_set],extension(1505 ^ 8)).
% 20.60/21.02  ncf('1.2.2.2',plain,[-(complements_of_subsets(1500 ^ [], complements_of_subsets(1500 ^ [], 1501 ^ [])) = 1501 ^ []), element(1501 ^ [], powerset(powerset(1500 ^ [])))],extension(842 ^ 7,bind([[_239259, _239261], [1501 ^ [], 1500 ^ []]]))).
% 20.60/21.02  ncf('1.2.2.2.1',plain,[-(element(1501 ^ [], powerset(powerset(1500 ^ []))))],extension(1503 ^ 8)).
% 20.60/21.02  ncf('1.2.3',plain,[-(element(empty_set, powerset(powerset(1500 ^ [])))), 959 : -(in(957 ^ [powerset(1500 ^ []), empty_set], empty_set))],extension(956 ^ 4,bind([[_243289, _243291], [powerset(1500 ^ []), empty_set]]))).
% 20.60/21.02  ncf('1.2.3.1',plain,[in(957 ^ [powerset(1500 ^ []), empty_set], empty_set), empty(empty_set)],extension(1405 ^ 7,bind([[_259320, _259322], [empty_set, 957 ^ [powerset(1500 ^ []), empty_set]]]))).
% 20.60/21.02  ncf('1.2.3.1.1',plain,[-(empty(empty_set))],extension(816 ^ 8)).
% 20.60/21.02  ncf('1.2.4',plain,[-(element(complements_of_subsets(1500 ^ [], 1501 ^ []), powerset(powerset(1500 ^ [])))), element(1501 ^ [], powerset(powerset(1500 ^ [])))],extension(799 ^ 2,bind([[_237708, _237710], [1501 ^ [], 1500 ^ []]]))).
% 20.60/21.02  ncf('1.2.4.1',plain,[-(element(1501 ^ [], powerset(powerset(1500 ^ []))))],extension(1503 ^ 3)).
% 20.60/21.02  %-----------------------------------------------------
% 20.60/21.02  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------