%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : GEO118+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n010.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 11:11:58 EDT 2023

% Result   : Theorem 0.34s 1.37s
% Output   : Proof 0.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GEO118+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n010.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 : Fri May 19 04:05:42 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.34/1.37  
% 0.34/1.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.34/1.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.34/1.37  %-----------------------------------------------------
% 0.34/1.37  ncf(matrix, plain, [(847 ^ _104541) ^ [] : [-(ordered_by(843 ^ [], 844 ^ [], 845 ^ []))], (849 ^ _104541) ^ [] : [-(ordered_by(843 ^ [], 845 ^ [], 844 ^ []))], (228 ^ _104541) ^ [_112154, _112156] : [_112156 = _112154, -(underlying_curve(_112156) = underlying_curve(_112154))], (218 ^ _104541) ^ [_111843, _111845, _111847, _111849] : [-(sum(_111849, _111845) = sum(_111847, _111843)), _111849 = _111847, _111845 = _111843], (2 ^ _104541) ^ [_104685] : [-(_104685 = _104685)], (4 ^ _104541) ^ [_104792, _104794] : [_104794 = _104792, -(_104792 = _104794)], (10 ^ _104541) ^ [_104996, _104998, _105000] : [-(_105000 = _104996), _105000 = _104998, _104998 = _104996], (20 ^ _104541) ^ [_105309, _105311] : [-(closed(_105309)), _105311 = _105309, closed(_105311)], (30 ^ _104541) ^ [_105660, _105662, _105664, _105666, _105668, _105670] : [-(meet(_105668, _105664, _105660)), meet(_105670, _105666, _105662), _105670 = _105668, _105666 = _105664, _105662 = _105660], (48 ^ _104541) ^ [_106241, _106243, _106245, _106247] : [-(part_of(_106245, _106241)), part_of(_106247, _106243), _106247 = _106245, _106243 = _106241], (62 ^ _104541) ^ [_106685, _106687, _106689, _106691] : [-(end_point(_106689, _106685)), end_point(_106691, _106687), _106691 = _106689, _106687 = _106685], (76 ^ _104541) ^ [_107129, _107131, _107133, _107135] : [-(inner_point(_107133, _107129)), inner_point(_107135, _107131), _107135 = _107133, _107131 = _107129], (90 ^ _104541) ^ [_107573, _107575, _107577, _107579] : [-(finish_point(_107577, _107573)), finish_point(_107579, _107575), _107579 = _107577, _107575 = _107573], (104 ^ _104541) ^ [_108073, _108075, _108077, _108079, _108081, _108083, _108085, _108087] : [-(between_o(_108085, _108081, _108077, _108073)), between_o(_108087, _108083, _108079, _108075), _108087 = _108085, _108083 = _108081, _108079 = _108077, _108075 = _108073], (126 ^ _104541) ^ [_108863, _108865, _108867, _108869, _108871, _108873, _108875, _108877] : [-(between_c(_108875, _108871, _108867, _108863)), between_c(_108877, _108873, _108869, _108865), _108877 = _108875, _108873 = _108871, _108869 = _108867, _108865 = _108863], (148 ^ _104541) ^ [_109597, _109599, _109601, _109603] : [-(start_point(_109601, _109597)), start_point(_109603, _109599), _109603 = _109601, _109599 = _109597], (162 ^ _104541) ^ [_110013, _110015] : [-(open(_110013)), _110015 = _110013, open(_110015)], (172 ^ _104541) ^ [_110336, _110338, _110340, _110342] : [-(incident_o(_110340, _110336)), incident_o(_110342, _110338), _110342 = _110340, _110338 = _110336], (186 ^ _104541) ^ [_110780, _110782, _110784, _110786] : [-(incident_c(_110784, _110780)), incident_c(_110786, _110782), _110786 = _110784, _110782 = _110780], (200 ^ _104541) ^ [_111232, _111234, _111236, _111238, _111240, _111242] : [-(ordered_by(_111240, _111236, _111232)), ordered_by(_111242, _111238, _111234), _111242 = _111240, _111238 = _111236, _111234 = _111232], (573 ^ _104541) ^ [_124128, _124130, _124132, _124134] : [between_c(_124134, _124132, _124130, _124128), 576 ^ _104541 : [(577 ^ _104541) ^ [] : [_124132 = _124128], (580 ^ _104541) ^ [] : [-(part_of(578 ^ [_124128, _124130, _124132, _124134], _124134))], (582 ^ _104541) ^ [] : [-(end_point(_124132, 578 ^ [_124128, _124130, _124132, _124134]))], (584 ^ _104541) ^ [] : [-(end_point(_124128, 578 ^ [_124128, _124130, _124132, _124134]))], (586 ^ _104541) ^ [] : [-(inner_point(_124130, 578 ^ [_124128, _124130, _124132, _124134]))]]], (588 ^ _104541) ^ [_124740, _124742, _124744, _124746] : [-(between_c(_124746, _124744, _124742, _124740)), -(_124744 = _124740), 593 ^ _104541 : [(594 ^ _104541) ^ [_124946] : [part_of(_124946, _124746), end_point(_124744, _124946), end_point(_124740, _124946), inner_point(_124742, _124946)]]], (610 ^ _104541) ^ [_125503, _125505, _125507, _125509] : [between_o(_125509, _125507, _125505, _125503), 615 ^ _104541 : [(616 ^ _104541) ^ [] : [-(ordered_by(_125509, _125507, _125505))], (618 ^ _104541) ^ [] : [-(ordered_by(_125509, _125505, _125503))]], 619 ^ _104541 : [(620 ^ _104541) ^ [] : [-(ordered_by(_125509, _125503, _125505))], (622 ^ _104541) ^ [] : [-(ordered_by(_125509, _125505, _125507))]]], (624 ^ _104541) ^ [_125945, _125947, _125949, _125951] : [-(between_o(_125951, _125949, _125947, _125945)), 625 ^ _104541 : [(626 ^ _104541) ^ [] : [ordered_by(_125951, _125949, _125947), ordered_by(_125951, _125947, _125945)], (632 ^ _104541) ^ [] : [ordered_by(_125951, _125945, _125947), ordered_by(_125951, _125947, _125949)]]], (656 ^ _104541) ^ [_126977, _126979] : [-(start_point(_126979, _126977)), incident_o(_126979, _126977), 662 ^ _104541 : [(663 ^ _104541) ^ [] : [_126979 = 661 ^ [_126977, _126979]], (665 ^ _104541) ^ [] : [-(incident_o(661 ^ [_126977, _126979], _126977))], (667 ^ _104541) ^ [] : [ordered_by(_126977, _126979, 661 ^ [_126977, _126979])]]], (640 ^ _104541) ^ [_126482, _126484] : [start_point(_126484, _126482), 643 ^ _104541 : [(644 ^ _104541) ^ [] : [-(incident_o(_126484, _126482))], (646 ^ _104541) ^ [_126700] : [-(ordered_by(_126482, _126484, _126700)), -(_126484 = _126700), incident_o(_126700, _126482)]]], (687 ^ _104541) ^ [_128042, _128044] : [-(finish_point(_128044, _128042)), incident_o(_128044, _128042), 693 ^ _104541 : [(694 ^ _104541) ^ [] : [_128044 = 692 ^ [_128042, _128044]], (696 ^ _104541) ^ [] : [-(incident_o(692 ^ [_128042, _128044], _128042))], (698 ^ _104541) ^ [] : [ordered_by(_128042, 692 ^ [_128042, _128044], _128044)]]], (671 ^ _104541) ^ [_127547, _127549] : [finish_point(_127549, _127547), 674 ^ _104541 : [(675 ^ _104541) ^ [] : [-(incident_o(_127549, _127547))], (677 ^ _104541) ^ [_127765] : [-(ordered_by(_127547, _127765, _127549)), -(_127549 = _127765), incident_o(_127765, _127547)]]], (702 ^ _104541) ^ [_128597, _128599, _128601] : [ordered_by(_128601, _128599, _128597), 705 ^ _104541 : [(706 ^ _104541) ^ [] : [-(incident_o(_128599, _128601))], (708 ^ _104541) ^ [] : [-(incident_o(_128597, _128601))]]], (711 ^ _104541) ^ [_128938] : [-(open(709 ^ [_128938]))], (713 ^ _104541) ^ [_129044, _129046] : [incident_o(_129044, _129046), -(incident_c(_129044, 709 ^ [_129046]))], (719 ^ _104541) ^ [_129216, _129218] : [incident_c(_129216, 709 ^ [_129218]), -(incident_o(_129216, _129218))], (744 ^ _104541) ^ [_130272, _130274, _130276, _130278] : [-(between_o(_130272, _130278, _130276, _130274)), 745 ^ _104541 : [(746 ^ _104541) ^ [_130383] : [between_c(_130383, _130278, _130276, _130274), 750 ^ _104541 : [(751 ^ _104541) ^ [] : [-(incident_o(747 ^ [_130272, _130274, _130276, _130278, _130383], _130272))], (753 ^ _104541) ^ [] : [incident_c(747 ^ [_130272, _130274, _130276, _130278, _130383], _130383)]], 754 ^ _104541 : [(755 ^ _104541) ^ [] : [-(incident_c(747 ^ [_130272, _130274, _130276, _130278, _130383], _130383))], (757 ^ _104541) ^ [] : [incident_o(747 ^ [_130272, _130274, _130276, _130278, _130383], _130272)]]]]], (725 ^ _104541) ^ [_129497, _129499, _129501, _129503] : [between_o(_129497, _129503, _129501, _129499), 729 ^ _104541 : [(742 ^ _104541) ^ [] : [-(between_c(728 ^ [_129497, _129499, _129501, _129503], _129503, _129501, _129499))], (730 ^ _104541) ^ [_129780] : [incident_o(_129780, _129497), -(incident_c(_129780, 728 ^ [_129497, _129499, _129501, _129503]))], (736 ^ _104541) ^ [_129990] : [incident_c(_129990, 728 ^ [_129497, _129499, _129501, _129503]), -(incident_o(_129990, _129497))]]], (764 ^ _104541) ^ [_131071] : [-(start_point(762 ^ [_131071], _131071))], (766 ^ _104541) ^ [_131197, _131199, _131201] : [open(_131197), -(_131201 = _131199), incident_c(_131201, _131197), incident_c(_131199, _131197), 782 ^ _104541 : [(795 ^ _104541) ^ [] : [-(ordered_by(781 ^ [_131197, _131199, _131201], _131201, _131199))], (783 ^ _104541) ^ [_131746] : [incident_o(_131746, 781 ^ [_131197, _131199, _131201]), -(incident_c(_131746, _131197))], (789 ^ _104541) ^ [_131944] : [incident_c(_131944, _131197), -(incident_o(_131944, 781 ^ [_131197, _131199, _131201]))]]], (797 ^ _104541) ^ [_132263, _132265] : [-(_132265 = _132263), 802 ^ _104541 : [(803 ^ _104541) ^ [] : [-(ordered_by(_132265, 798 ^ [_132263, _132265], 799 ^ [_132263, _132265]))], (805 ^ _104541) ^ [] : [ordered_by(_132263, 798 ^ [_132263, _132265], 799 ^ [_132263, _132265])]], 806 ^ _104541 : [(807 ^ _104541) ^ [] : [-(ordered_by(_132263, 798 ^ [_132263, _132265], 799 ^ [_132263, _132265]))], (809 ^ _104541) ^ [] : [ordered_by(_132265, 798 ^ [_132263, _132265], 799 ^ [_132263, _132265])]]], (829 ^ _104541) ^ [_133436, _133438] : [-(_133438 = underlying_curve(_133436)), 833 ^ _104541 : [(834 ^ _104541) ^ [] : [-(incident_o(830 ^ [_133436, _133438], _133436))], (836 ^ _104541) ^ [] : [incident_c(830 ^ [_133436, _133438], _133438)]], 837 ^ _104541 : [(838 ^ _104541) ^ [] : [-(incident_c(830 ^ [_133436, _133438], _133438))], (840 ^ _104541) ^ [] : [incident_o(830 ^ [_133436, _133438], _133436)]]], (813 ^ _104541) ^ [_132915, _132917] : [_132917 = underlying_curve(_132915), 816 ^ _104541 : [(817 ^ _104541) ^ [_133085] : [incident_o(_133085, _132915), -(incident_c(_133085, _132917))], (823 ^ _104541) ^ [_133257] : [incident_c(_133257, _132917), -(incident_o(_133257, _132915))]]], (244 ^ _104541) ^ [_112773, _112775] : [246 ^ _104541 : [(247 ^ _104541) ^ [] : [-(incident_c(245 ^ [_112773, _112775], _112773))], (249 ^ _104541) ^ [] : [incident_c(245 ^ [_112773, _112775], _112775)]], -(part_of(_112773, _112775))], (234 ^ _104541) ^ [_112459, _112461] : [part_of(_112459, _112461), 237 ^ _104541 : [(238 ^ _104541) ^ [_112596] : [incident_c(_112596, _112459), -(incident_c(_112596, _112461))]]], (275 ^ _104541) ^ [_113898, _113900, _113902] : [-(_113902 = sum(_113900, _113898)), 279 ^ _104541 : [(280 ^ _104541) ^ [] : [-(incident_c(276 ^ [_113898, _113900, _113902], _113902))], (282 ^ _104541) ^ [] : [incident_c(276 ^ [_113898, _113900, _113902], _113900)], (284 ^ _104541) ^ [] : [incident_c(276 ^ [_113898, _113900, _113902], _113898)]], 285 ^ _104541 : [(292 ^ _104541) ^ [] : [incident_c(276 ^ [_113898, _113900, _113902], _113902)], (286 ^ _104541) ^ [] : [-(incident_c(276 ^ [_113898, _113900, _113902], _113900)), -(incident_c(276 ^ [_113898, _113900, _113902], _113898))]]], (253 ^ _104541) ^ [_113173, _113175, _113177] : [_113177 = sum(_113175, _113173), 256 ^ _104541 : [(267 ^ _104541) ^ [_113633] : [268 ^ _104541 : [(269 ^ _104541) ^ [] : [incident_c(_113633, _113175)], (271 ^ _104541) ^ [] : [incident_c(_113633, _113173)]], -(incident_c(_113633, _113177))], (257 ^ _104541) ^ [_113355] : [incident_c(_113355, _113177), -(incident_c(_113355, _113175)), -(incident_c(_113355, _113173))]]], (324 ^ _104541) ^ [_115506, _115508] : [-(end_point(_115508, _115506)), incident_c(_115508, _115506), 331 ^ _104541 : [(332 ^ _104541) ^ [] : [-(part_of(329 ^ [_115506, _115508], _115506))], (334 ^ _104541) ^ [] : [-(part_of(330 ^ [_115506, _115508], _115506))], (336 ^ _104541) ^ [] : [-(incident_c(_115508, 329 ^ [_115506, _115508]))], (338 ^ _104541) ^ [] : [-(incident_c(_115508, 330 ^ [_115506, _115508]))], (340 ^ _104541) ^ [] : [part_of(329 ^ [_115506, _115508], 330 ^ [_115506, _115508])], (342 ^ _104541) ^ [] : [part_of(330 ^ [_115506, _115508], 329 ^ [_115506, _115508])]]], (296 ^ _104541) ^ [_114678, _114680] : [end_point(_114680, _114678), 299 ^ _104541 : [(300 ^ _104541) ^ [] : [-(incident_c(_114680, _114678))], (302 ^ _104541) ^ [_114930, _114932] : [-(part_of(_114932, _114930)), -(part_of(_114930, _114932)), part_of(_114932, _114678), part_of(_114930, _114678), incident_c(_114680, _114932), incident_c(_114680, _114930)]]], (346 ^ _104541) ^ [_116461, _116463] : [inner_point(_116463, _116461), 349 ^ _104541 : [(350 ^ _104541) ^ [] : [-(incident_c(_116463, _116461))], (352 ^ _104541) ^ [] : [end_point(_116463, _116461)]]], (354 ^ _104541) ^ [_116699, _116701] : [-(inner_point(_116701, _116699)), incident_c(_116701, _116699), -(end_point(_116701, _116699))], (364 ^ _104541) ^ [_117046, _117048, _117050] : [meet(_117050, _117048, _117046), 367 ^ _104541 : [(368 ^ _104541) ^ [] : [-(incident_c(_117050, _117048))], (370 ^ _104541) ^ [] : [-(incident_c(_117050, _117046))], (372 ^ _104541) ^ [_117349] : [379 ^ _104541 : [(380 ^ _104541) ^ [] : [-(end_point(_117349, _117048))], (382 ^ _104541) ^ [] : [-(end_point(_117349, _117046))]], incident_c(_117349, _117048), incident_c(_117349, _117046)]]], (384 ^ _104541) ^ [_117714, _117716, _117718] : [-(meet(_117718, _117716, _117714)), incident_c(_117718, _117716), incident_c(_117718, _117714), 394 ^ _104541 : [(395 ^ _104541) ^ [] : [-(incident_c(393 ^ [_117714, _117716, _117718], _117716))], (397 ^ _104541) ^ [] : [-(incident_c(393 ^ [_117714, _117716, _117718], _117714))], (399 ^ _104541) ^ [] : [end_point(393 ^ [_117714, _117716, _117718], _117716), end_point(393 ^ [_117714, _117716, _117718], _117714)]]], (407 ^ _104541) ^ [_118491] : [closed(_118491), 410 ^ _104541 : [(411 ^ _104541) ^ [_118602] : [end_point(_118602, _118491)]]], (413 ^ _104541) ^ [_118668] : [-(end_point(414 ^ [_118668], _118668)), -(closed(_118668))], (420 ^ _104541) ^ [_118941] : [open(_118941), -(end_point(423 ^ [_118941], _118941))], (427 ^ _104541) ^ [_119146] : [428 ^ _104541 : [(429 ^ _104541) ^ [_119213] : [end_point(_119213, _119146)]], -(open(_119146))], (433 ^ _104541) ^ [_119372, _119374] : [-(open(_119372)), part_of(_119372, _119374), -(_119372 = _119374)], (443 ^ _104541) ^ [_119700, _119702, _119704, _119706] : [part_of(_119704, _119706), part_of(_119702, _119706), part_of(_119700, _119706), 456 ^ _104541 : [(457 ^ _104541) ^ [_120111] : [end_point(_120111, _119704), end_point(_120111, _119702), end_point(_120111, _119700)]], -(part_of(_119702, _119700)), -(part_of(_119700, _119702)), -(part_of(_119704, _119702)), -(part_of(_119702, _119704)), -(part_of(_119704, _119700)), -(part_of(_119700, _119704))], (490 ^ _104541) ^ [_120990] : [-(inner_point(488 ^ [_120990], _120990))], (492 ^ _104541) ^ [_121102, _121104] : [inner_point(_121102, _121104), 497 ^ _104541 : [(498 ^ _104541) ^ [] : [-(meet(_121102, 495 ^ [_121102, _121104], 496 ^ [_121102, _121104]))], (500 ^ _104541) ^ [] : [-(_121104 = sum(495 ^ [_121102, _121104], 496 ^ [_121102, _121104]))]]], (502 ^ _104541) ^ [_121590, _121592, _121594, _121596] : [end_point(_121594, _121596), end_point(_121592, _121596), end_point(_121590, _121596), -(_121594 = _121592), -(_121594 = _121590), -(_121592 = _121590)], (524 ^ _104541) ^ [_122206, _122208] : [end_point(_122206, _122208), 528 ^ _104541 : [(529 ^ _104541) ^ [] : [-(end_point(527 ^ [_122206, _122208], _122208))], (531 ^ _104541) ^ [] : [_122206 = 527 ^ [_122206, _122208]]]], (533 ^ _104541) ^ [_122592, _122594, _122596, _122598] : [544 ^ _104541 : [(545 ^ _104541) ^ [_122938] : [end_point(_122938, _122596), -(meet(_122938, _122596, _122594))]], closed(_122598), meet(_122592, _122596, _122594), _122598 = sum(_122596, _122594)], (551 ^ _104541) ^ [_123181, _123183] : [552 ^ _104541 : [(553 ^ _104541) ^ [_123260] : [meet(_123260, _123183, _123181)]], -(554 ^ [_123181, _123183] = sum(_123183, _123181))], (558 ^ _104541) ^ [_123461, _123463] : [-(_123463 = _123461), 562 ^ _104541 : [(563 ^ _104541) ^ [] : [-(incident_c(559 ^ [_123461, _123463], _123463))], (565 ^ _104541) ^ [] : [incident_c(559 ^ [_123461, _123463], _123461)]], 566 ^ _104541 : [(567 ^ _104541) ^ [] : [-(incident_c(559 ^ [_123461, _123463], _123461))], (569 ^ _104541) ^ [] : [incident_c(559 ^ [_123461, _123463], _123463)]]]], input).
% 0.34/1.37  ncf('1',plain,[between_c(728 ^ [843 ^ [], 844 ^ [], 845 ^ [], 844 ^ []], 844 ^ [], 845 ^ [], 844 ^ []), 577 : 844 ^ [] = 844 ^ []],start(573 ^ 0,bind([[_124128, _124130, _124132, _124134], [844 ^ [], 845 ^ [], 844 ^ [], 728 ^ [843 ^ [], 844 ^ [], 845 ^ [], 844 ^ []]]]))).
% 0.34/1.37  ncf('1.1',plain,[-(between_c(728 ^ [843 ^ [], 844 ^ [], 845 ^ [], 844 ^ []], 844 ^ [], 845 ^ [], 844 ^ [])), between_o(843 ^ [], 844 ^ [], 845 ^ [], 844 ^ [])],extension(725 ^ 1,bind([[_129497, _129499, _129501, _129503], [843 ^ [], 844 ^ [], 845 ^ [], 844 ^ []]]))).
% 0.34/1.37  ncf('1.1.1',plain,[-(between_o(843 ^ [], 844 ^ [], 845 ^ [], 844 ^ [])), 626 : ordered_by(843 ^ [], 844 ^ [], 845 ^ []), 626 : ordered_by(843 ^ [], 845 ^ [], 844 ^ [])],extension(624 ^ 2,bind([[_125945, _125947, _125949, _125951], [844 ^ [], 845 ^ [], 844 ^ [], 843 ^ []]]))).
% 0.34/1.37  ncf('1.1.1.1',plain,[-(ordered_by(843 ^ [], 844 ^ [], 845 ^ []))],extension(847 ^ 5)).
% 0.34/1.37  ncf('1.1.1.2',plain,[-(ordered_by(843 ^ [], 845 ^ [], 844 ^ []))],extension(849 ^ 5)).
% 0.34/1.37  ncf('1.2',plain,[-(844 ^ [] = 844 ^ [])],extension(2 ^ 3,bind([[_104685], [844 ^ []]]))).
% 0.34/1.37  %-----------------------------------------------------
% 0.34/1.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------