%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SEU148+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 12:02:22 EDT 2023

% Result   : Theorem 0.35s 1.37s
% Output   : Proof 0.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU148+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % 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 13:38:42 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.35/1.37  
% 0.35/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.35/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/1.37  %-----------------------------------------------------
% 0.35/1.37  ncf(matrix, plain, [(803 ^ _105846) ^ [] : [-(subset(singleton(800 ^ []), singleton(801 ^ [])))], (805 ^ _105846) ^ [] : [800 ^ [] = 801 ^ []], (86 ^ _105846) ^ [_108679, _108681] : [_108681 = _108679, -(powerset(_108681) = powerset(_108679))], (92 ^ _105846) ^ [_108925, _108927, _108929, _108931] : [-(set_intersection2(_108931, _108927) = set_intersection2(_108929, _108925)), _108931 = _108929, _108927 = _108925], (102 ^ _105846) ^ [_109284, _109286, _109288, _109290] : [-(unordered_pair(_109290, _109286) = unordered_pair(_109288, _109284)), _109290 = _109288, _109286 = _109284], (112 ^ _105846) ^ [_109643, _109645, _109647, _109649] : [-(set_difference(_109649, _109645) = set_difference(_109647, _109643)), _109649 = _109647, _109645 = _109643], (132 ^ _105846) ^ [_110313, _110315] : [_110315 = _110313, -(singleton(_110315) = singleton(_110313))], (122 ^ _105846) ^ [_110002, _110004, _110006, _110008] : [-(set_union2(_110008, _110004) = set_union2(_110006, _110002)), _110008 = _110006, _110004 = _110002], (2 ^ _105846) ^ [_105990] : [-(_105990 = _105990)], (4 ^ _105846) ^ [_106097, _106099] : [_106099 = _106097, -(_106097 = _106099)], (10 ^ _105846) ^ [_106301, _106303, _106305] : [-(_106305 = _106301), _106305 = _106303, _106303 = _106301], (20 ^ _105846) ^ [_106642, _106644, _106646, _106648] : [-(proper_subset(_106646, _106642)), proper_subset(_106648, _106644), _106648 = _106646, _106644 = _106642], (34 ^ _105846) ^ [_107086, _107088, _107090, _107092] : [-(in(_107090, _107086)), in(_107092, _107088), _107092 = _107090, _107088 = _107086], (48 ^ _105846) ^ [_107530, _107532, _107534, _107536] : [-(disjoint(_107534, _107530)), disjoint(_107536, _107532), _107536 = _107534, _107532 = _107530], (62 ^ _105846) ^ [_107946, _107948] : [-(empty(_107946)), _107948 = _107946, empty(_107948)], (72 ^ _105846) ^ [_108249, _108251, _108253, _108255] : [-(subset(_108253, _108249)), subset(_108255, _108251), _108255 = _108253, _108251 = _108249], (138 ^ _105846) ^ [_110553, _110555] : [in(_110555, _110553), in(_110553, _110555)], (144 ^ _105846) ^ [_110764, _110766] : [proper_subset(_110766, _110764), proper_subset(_110764, _110766)], (150 ^ _105846) ^ [_110960, _110962] : [-(unordered_pair(_110962, _110960) = unordered_pair(_110960, _110962))], (152 ^ _105846) ^ [_111060, _111062] : [-(set_union2(_111062, _111060) = set_union2(_111060, _111062))], (154 ^ _105846) ^ [_111160, _111162] : [-(set_intersection2(_111162, _111160) = set_intersection2(_111160, _111162))], (156 ^ _105846) ^ [_111304, _111306] : [_111306 = _111304, 159 ^ _105846 : [(160 ^ _105846) ^ [] : [-(subset(_111306, _111304))], (162 ^ _105846) ^ [] : [-(subset(_111304, _111306))]]], (164 ^ _105846) ^ [_111541, _111543] : [-(_111543 = _111541), subset(_111543, _111541), subset(_111541, _111543)], (190 ^ _105846) ^ [_112392, _112394] : [-(_112392 = singleton(_112394)), 194 ^ _105846 : [(195 ^ _105846) ^ [] : [-(in(191 ^ [_112392, _112394], _112392))], (197 ^ _105846) ^ [] : [191 ^ [_112392, _112394] = _112394]], 198 ^ _105846 : [(199 ^ _105846) ^ [] : [-(191 ^ [_112392, _112394] = _112394)], (201 ^ _105846) ^ [] : [in(191 ^ [_112392, _112394], _112392)]]], (174 ^ _105846) ^ [_111871, _111873] : [_111871 = singleton(_111873), 177 ^ _105846 : [(178 ^ _105846) ^ [_112041] : [in(_112041, _111871), -(_112041 = _111873)], (184 ^ _105846) ^ [_112213] : [_112213 = _111873, -(in(_112213, _111871))]]], (205 ^ _105846) ^ [_112943] : [_112943 = empty_set, 208 ^ _105846 : [(209 ^ _105846) ^ [_113056] : [in(_113056, _112943)]]], (211 ^ _105846) ^ [_113122] : [-(in(212 ^ [_113122], _113122)), -(_113122 = empty_set)], (234 ^ _105846) ^ [_113934, _113936] : [-(_113934 = powerset(_113936)), 238 ^ _105846 : [(239 ^ _105846) ^ [] : [-(in(235 ^ [_113934, _113936], _113934))], (241 ^ _105846) ^ [] : [subset(235 ^ [_113934, _113936], _113936)]], 242 ^ _105846 : [(243 ^ _105846) ^ [] : [-(subset(235 ^ [_113934, _113936], _113936))], (245 ^ _105846) ^ [] : [in(235 ^ [_113934, _113936], _113934)]]], (218 ^ _105846) ^ [_113413, _113415] : [_113413 = powerset(_113415), 221 ^ _105846 : [(222 ^ _105846) ^ [_113583] : [in(_113583, _113413), -(subset(_113583, _113415))], (228 ^ _105846) ^ [_113755] : [subset(_113755, _113415), -(in(_113755, _113413))]]], (271 ^ _105846) ^ [_115238, _115240, _115242] : [-(_115238 = unordered_pair(_115242, _115240)), 275 ^ _105846 : [(276 ^ _105846) ^ [] : [-(in(272 ^ [_115238, _115240, _115242], _115238))], (278 ^ _105846) ^ [] : [272 ^ [_115238, _115240, _115242] = _115242], (280 ^ _105846) ^ [] : [272 ^ [_115238, _115240, _115242] = _115240]], 281 ^ _105846 : [(288 ^ _105846) ^ [] : [in(272 ^ [_115238, _115240, _115242], _115238)], (282 ^ _105846) ^ [] : [-(272 ^ [_115238, _115240, _115242] = _115242), -(272 ^ [_115238, _115240, _115242] = _115240)]]], (249 ^ _105846) ^ [_114513, _114515, _114517] : [_114513 = unordered_pair(_114517, _114515), 252 ^ _105846 : [(263 ^ _105846) ^ [_114973] : [264 ^ _105846 : [(265 ^ _105846) ^ [] : [_114973 = _114517], (267 ^ _105846) ^ [] : [_114973 = _114515]], -(in(_114973, _114513))], (253 ^ _105846) ^ [_114695] : [in(_114695, _114513), -(_114695 = _114517), -(_114695 = _114515)]]], (314 ^ _105846) ^ [_116757, _116759, _116761] : [-(_116757 = set_union2(_116761, _116759)), 318 ^ _105846 : [(319 ^ _105846) ^ [] : [-(in(315 ^ [_116757, _116759, _116761], _116757))], (321 ^ _105846) ^ [] : [in(315 ^ [_116757, _116759, _116761], _116761)], (323 ^ _105846) ^ [] : [in(315 ^ [_116757, _116759, _116761], _116759)]], 324 ^ _105846 : [(331 ^ _105846) ^ [] : [in(315 ^ [_116757, _116759, _116761], _116757)], (325 ^ _105846) ^ [] : [-(in(315 ^ [_116757, _116759, _116761], _116761)), -(in(315 ^ [_116757, _116759, _116761], _116759))]]], (292 ^ _105846) ^ [_116032, _116034, _116036] : [_116032 = set_union2(_116036, _116034), 295 ^ _105846 : [(306 ^ _105846) ^ [_116492] : [307 ^ _105846 : [(308 ^ _105846) ^ [] : [in(_116492, _116036)], (310 ^ _105846) ^ [] : [in(_116492, _116034)]], -(in(_116492, _116032))], (296 ^ _105846) ^ [_116214] : [in(_116214, _116032), -(in(_116214, _116036)), -(in(_116214, _116034))]]], (345 ^ _105846) ^ [_117851, _117853] : [347 ^ _105846 : [(348 ^ _105846) ^ [] : [-(in(346 ^ [_117851, _117853], _117853))], (350 ^ _105846) ^ [] : [in(346 ^ [_117851, _117853], _117851)]], -(subset(_117853, _117851))], (335 ^ _105846) ^ [_117537, _117539] : [subset(_117539, _117537), 338 ^ _105846 : [(339 ^ _105846) ^ [_117674] : [in(_117674, _117539), -(in(_117674, _117537))]]], (376 ^ _105846) ^ [_118976, _118978, _118980] : [-(_118976 = set_intersection2(_118980, _118978)), 388 ^ _105846 : [(389 ^ _105846) ^ [] : [-(in(377 ^ [_118976, _118978, _118980], _118980))], (391 ^ _105846) ^ [] : [-(in(377 ^ [_118976, _118978, _118980], _118978))], (393 ^ _105846) ^ [] : [in(377 ^ [_118976, _118978, _118980], _118976)]], 380 ^ _105846 : [(381 ^ _105846) ^ [] : [-(in(377 ^ [_118976, _118978, _118980], _118976))], (383 ^ _105846) ^ [] : [in(377 ^ [_118976, _118978, _118980], _118980), in(377 ^ [_118976, _118978, _118980], _118978)]]], (354 ^ _105846) ^ [_118251, _118253, _118255] : [_118251 = set_intersection2(_118255, _118253), 357 ^ _105846 : [(358 ^ _105846) ^ [_118433] : [in(_118433, _118251), 361 ^ _105846 : [(362 ^ _105846) ^ [] : [-(in(_118433, _118255))], (364 ^ _105846) ^ [] : [-(in(_118433, _118253))]]], (366 ^ _105846) ^ [_118692] : [-(in(_118692, _118251)), in(_118692, _118255), in(_118692, _118253)]]], (419 ^ _105846) ^ [_120503, _120505, _120507] : [-(_120503 = set_difference(_120507, _120505)), 431 ^ _105846 : [(432 ^ _105846) ^ [] : [-(in(420 ^ [_120503, _120505, _120507], _120507))], (434 ^ _105846) ^ [] : [in(420 ^ [_120503, _120505, _120507], _120505)], (436 ^ _105846) ^ [] : [in(420 ^ [_120503, _120505, _120507], _120503)]], 423 ^ _105846 : [(424 ^ _105846) ^ [] : [-(in(420 ^ [_120503, _120505, _120507], _120503))], (426 ^ _105846) ^ [] : [in(420 ^ [_120503, _120505, _120507], _120507), -(in(420 ^ [_120503, _120505, _120507], _120505))]]], (397 ^ _105846) ^ [_119772, _119774, _119776] : [_119772 = set_difference(_119776, _119774), 400 ^ _105846 : [(401 ^ _105846) ^ [_119956] : [in(_119956, _119772), 404 ^ _105846 : [(405 ^ _105846) ^ [] : [-(in(_119956, _119776))], (407 ^ _105846) ^ [] : [in(_119956, _119774)]]], (409 ^ _105846) ^ [_120216] : [-(in(_120216, _119772)), in(_120216, _119776), -(in(_120216, _119774))]]], (440 ^ _105846) ^ [_121289, _121291] : [disjoint(_121291, _121289), -(set_intersection2(_121291, _121289) = empty_set)], (446 ^ _105846) ^ [_121457, _121459] : [set_intersection2(_121459, _121457) = empty_set, -(disjoint(_121459, _121457))], (452 ^ _105846) ^ [_121704, _121706] : [proper_subset(_121706, _121704), 455 ^ _105846 : [(456 ^ _105846) ^ [] : [-(subset(_121706, _121704))], (458 ^ _105846) ^ [] : [_121706 = _121704]]], (460 ^ _105846) ^ [_121942, _121944] : [-(proper_subset(_121944, _121942)), subset(_121944, _121942), -(_121944 = _121942)], (470 ^ _105846) ^ [] : [true___, -(true___)], (476 ^ _105846) ^ [] : [true___, -(true___)], (482 ^ _105846) ^ [] : [true___, -(true___)], (488 ^ _105846) ^ [] : [true___, -(true___)], (494 ^ _105846) ^ [] : [true___, -(true___)], (500 ^ _105846) ^ [] : [true___, -(true___)], (506 ^ _105846) ^ [] : [true___, -(true___)], (512 ^ _105846) ^ [] : [-(empty(empty_set))], (514 ^ _105846) ^ [_123132, _123134] : [-(empty(_123134)), empty(set_union2(_123134, _123132))], (520 ^ _105846) ^ [_123348, _123350] : [-(empty(_123350)), empty(set_union2(_123348, _123350))], (526 ^ _105846) ^ [_123549, _123551] : [-(set_union2(_123551, _123551) = _123551)], (528 ^ _105846) ^ [_123646, _123648] : [-(set_intersection2(_123648, _123648) = _123648)], (530 ^ _105846) ^ [_123742, _123744] : [proper_subset(_123744, _123744)], (532 ^ _105846) ^ [_123821] : [singleton(_123821) = empty_set], (534 ^ _105846) ^ [_123959, _123961] : [subset(singleton(_123961), _123959), -(in(_123961, _123959))], (540 ^ _105846) ^ [_124125, _124127] : [in(_124127, _124125), -(subset(singleton(_124127), _124125))], (546 ^ _105846) ^ [_124370, _124372] : [set_difference(_124372, _124370) = empty_set, -(subset(_124372, _124370))], (552 ^ _105846) ^ [_124538, _124540] : [subset(_124540, _124538), -(set_difference(_124540, _124538) = empty_set)], (558 ^ _105846) ^ [_124770, _124772, _124774] : [subset(_124774, _124772), -(in(_124770, _124774)), -(subset(_124774, set_difference(_124772, singleton(_124770))))], (578 ^ _105846) ^ [_125379, _125381] : [579 ^ _105846 : [(580 ^ _105846) ^ [] : [_125381 = empty_set], (582 ^ _105846) ^ [] : [_125381 = singleton(_125379)]], -(subset(_125381, singleton(_125379)))], (568 ^ _105846) ^ [_125119, _125121] : [subset(_125121, singleton(_125119)), -(_125121 = empty_set), -(_125121 = singleton(_125119))], (587 ^ _105846) ^ [] : [-(empty(585 ^ []))], (590 ^ _105846) ^ [] : [empty(588 ^ [])], (592 ^ _105846) ^ [_125837, _125839] : [-(subset(_125839, _125839))], (594 ^ _105846) ^ [_125946, _125948] : [disjoint(_125948, _125946), -(disjoint(_125946, _125948))], (600 ^ _105846) ^ [_126156, _126158] : [subset(_126158, _126156), -(set_union2(_126158, _126156) = _126156)], (606 ^ _105846) ^ [_126357, _126359] : [-(subset(set_intersection2(_126359, _126357), _126359))], (608 ^ _105846) ^ [_126483, _126485, _126487] : [-(subset(_126487, set_intersection2(_126485, _126483))), subset(_126487, _126485), subset(_126487, _126483)], (618 ^ _105846) ^ [_126769] : [-(set_union2(_126769, empty_set) = _126769)], (620 ^ _105846) ^ [_126893, _126895, _126897] : [-(subset(_126897, _126893)), subset(_126897, _126895), subset(_126895, _126893)], (630 ^ _105846) ^ [] : [-(powerset(empty_set) = singleton(empty_set))], (632 ^ _105846) ^ [_127269, _127271, _127273] : [subset(_127273, _127271), -(subset(set_intersection2(_127273, _127269), set_intersection2(_127271, _127269)))], (638 ^ _105846) ^ [_127497, _127499] : [subset(_127499, _127497), -(set_intersection2(_127499, _127497) = _127499)], (644 ^ _105846) ^ [_127684] : [-(set_intersection2(_127684, empty_set) = empty_set)], (646 ^ _105846) ^ [_127794, _127796] : [-(_127796 = _127794), 650 ^ _105846 : [(651 ^ _105846) ^ [] : [-(in(647 ^ [_127794, _127796], _127796))], (653 ^ _105846) ^ [] : [in(647 ^ [_127794, _127796], _127794)]], 654 ^ _105846 : [(655 ^ _105846) ^ [] : [-(in(647 ^ [_127794, _127796], _127794))], (657 ^ _105846) ^ [] : [in(647 ^ [_127794, _127796], _127796)]]], (661 ^ _105846) ^ [_128295] : [-(subset(empty_set, _128295))], (663 ^ _105846) ^ [_128416, _128418, _128420] : [subset(_128420, _128418), -(subset(set_difference(_128420, _128416), set_difference(_128418, _128416)))], (669 ^ _105846) ^ [_128629, _128631] : [-(subset(set_difference(_128631, _128629), _128631))], (671 ^ _105846) ^ [_128770, _128772] : [set_difference(_128772, _128770) = empty_set, -(subset(_128772, _128770))], (677 ^ _105846) ^ [_128938, _128940] : [subset(_128940, _128938), -(set_difference(_128940, _128938) = empty_set)], (683 ^ _105846) ^ [_129141, _129143] : [-(set_union2(_129143, set_difference(_129141, _129143)) = set_union2(_129143, _129141))], (685 ^ _105846) ^ [_129230] : [-(set_difference(_129230, empty_set) = _129230)], (687 ^ _105846) ^ [_129360, _129362] : [-(disjoint(_129362, _129360)), 691 ^ _105846 : [(692 ^ _105846) ^ [] : [-(in(690 ^ [_129360, _129362], _129362))], (694 ^ _105846) ^ [] : [-(in(690 ^ [_129360, _129362], _129360))]]], (696 ^ _105846) ^ [_129674, _129676] : [disjoint(_129676, _129674), 697 ^ _105846 : [(698 ^ _105846) ^ [_129766] : [in(_129766, _129676), in(_129766, _129674)]]], (706 ^ _105846) ^ [_130023] : [subset(_130023, empty_set), -(_130023 = empty_set)], (712 ^ _105846) ^ [_130212, _130214] : [-(set_difference(set_union2(_130214, _130212), _130212) = set_difference(_130214, _130212))], (714 ^ _105846) ^ [_130330, _130332] : [subset(_130332, _130330), -(_130330 = set_union2(_130332, set_difference(_130330, _130332)))], (720 ^ _105846) ^ [_130537, _130539] : [-(set_difference(_130539, set_difference(_130539, _130537)) = set_intersection2(_130539, _130537))], (722 ^ _105846) ^ [_130626] : [-(set_difference(empty_set, _130626) = empty_set)], (724 ^ _105846) ^ [_130756, _130758] : [-(disjoint(_130758, _130756)), -(in(727 ^ [_130756, _130758], set_intersection2(_130758, _130756)))], (731 ^ _105846) ^ [_130991, _130993] : [732 ^ _105846 : [(733 ^ _105846) ^ [_131064] : [in(_131064, set_intersection2(_130993, _130991))]], disjoint(_130993, _130991)], (737 ^ _105846) ^ [_131230, _131232] : [subset(_131232, _131230), proper_subset(_131230, _131232)], (743 ^ _105846) ^ [_131453, _131455, _131457] : [-(disjoint(_131457, _131453)), subset(_131457, _131455), disjoint(_131455, _131453)], (753 ^ _105846) ^ [_131733] : [-(unordered_pair(_131733, _131733) = singleton(_131733))], (755 ^ _105846) ^ [_131831] : [empty(_131831), -(_131831 = empty_set)], (761 ^ _105846) ^ [_132033, _132035] : [in(_132035, _132033), empty(_132033)], (767 ^ _105846) ^ [_132225, _132227] : [-(subset(_132227, set_union2(_132227, _132225)))], (769 ^ _105846) ^ [_132366, _132368] : [disjoint(_132368, _132366), -(set_difference(_132368, _132366) = _132368)], (775 ^ _105846) ^ [_132534, _132536] : [set_difference(_132536, _132534) = _132536, -(disjoint(_132536, _132534))], (781 ^ _105846) ^ [_132752, _132754] : [empty(_132754), -(_132754 = _132752), empty(_132752)], (791 ^ _105846) ^ [_133043, _133045, _133047] : [-(subset(set_union2(_133047, _133043), _133045)), subset(_133047, _133045), subset(_133043, _133045)]], input).
% 0.35/1.37  ncf('1',plain,[800 ^ [] = 801 ^ []],start(805 ^ 0)).
% 0.35/1.37  ncf('1.1',plain,[-(800 ^ [] = 801 ^ []), 178 : in(800 ^ [], singleton(801 ^ [])), 178 : singleton(801 ^ []) = singleton(801 ^ [])],extension(174 ^ 1,bind([[_111871, _111873, _112041], [singleton(801 ^ []), 801 ^ [], 800 ^ []]]))).
% 0.35/1.37  ncf('1.1.1',plain,[-(in(800 ^ [], singleton(801 ^ []))), subset(singleton(800 ^ []), singleton(801 ^ []))],extension(534 ^ 4,bind([[_123959, _123961], [singleton(801 ^ []), 800 ^ []]]))).
% 0.35/1.37  ncf('1.1.1.1',plain,[-(subset(singleton(800 ^ []), singleton(801 ^ [])))],extension(803 ^ 5)).
% 0.35/1.37  ncf('1.1.2',plain,[-(singleton(801 ^ []) = singleton(801 ^ []))],extension(2 ^ 2,bind([[_105990], [singleton(801 ^ [])]]))).
% 0.35/1.37  %-----------------------------------------------------
% 0.35/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------