%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : GEO117+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.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
% 0.11/0.11  % Problem  : GEO117+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n023.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 04:51:13 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.34/1.37  
% 0.34/1.37  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.34/1.37  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.34/1.37  %-----------------------------------------------------
% 0.34/1.37  ncf(matrix, plain, [(846 ^ _103935) ^ [] : [-(ordered_by(843 ^ [], 844 ^ [], 844 ^ []))], (228 ^ _103935) ^ [_111548, _111550] : [_111550 = _111548, -(underlying_curve(_111550) = underlying_curve(_111548))], (218 ^ _103935) ^ [_111237, _111239, _111241, _111243] : [-(sum(_111243, _111239) = sum(_111241, _111237)), _111243 = _111241, _111239 = _111237], (2 ^ _103935) ^ [_104079] : [-(_104079 = _104079)], (4 ^ _103935) ^ [_104186, _104188] : [_104188 = _104186, -(_104186 = _104188)], (10 ^ _103935) ^ [_104390, _104392, _104394] : [-(_104394 = _104390), _104394 = _104392, _104392 = _104390], (20 ^ _103935) ^ [_104703, _104705] : [-(closed(_104703)), _104705 = _104703, closed(_104705)], (30 ^ _103935) ^ [_105054, _105056, _105058, _105060, _105062, _105064] : [-(meet(_105062, _105058, _105054)), meet(_105064, _105060, _105056), _105064 = _105062, _105060 = _105058, _105056 = _105054], (48 ^ _103935) ^ [_105635, _105637, _105639, _105641] : [-(part_of(_105639, _105635)), part_of(_105641, _105637), _105641 = _105639, _105637 = _105635], (62 ^ _103935) ^ [_106079, _106081, _106083, _106085] : [-(end_point(_106083, _106079)), end_point(_106085, _106081), _106085 = _106083, _106081 = _106079], (76 ^ _103935) ^ [_106523, _106525, _106527, _106529] : [-(inner_point(_106527, _106523)), inner_point(_106529, _106525), _106529 = _106527, _106525 = _106523], (90 ^ _103935) ^ [_106967, _106969, _106971, _106973] : [-(finish_point(_106971, _106967)), finish_point(_106973, _106969), _106973 = _106971, _106969 = _106967], (104 ^ _103935) ^ [_107467, _107469, _107471, _107473, _107475, _107477, _107479, _107481] : [-(between_o(_107479, _107475, _107471, _107467)), between_o(_107481, _107477, _107473, _107469), _107481 = _107479, _107477 = _107475, _107473 = _107471, _107469 = _107467], (126 ^ _103935) ^ [_108257, _108259, _108261, _108263, _108265, _108267, _108269, _108271] : [-(between_c(_108269, _108265, _108261, _108257)), between_c(_108271, _108267, _108263, _108259), _108271 = _108269, _108267 = _108265, _108263 = _108261, _108259 = _108257], (148 ^ _103935) ^ [_108991, _108993, _108995, _108997] : [-(start_point(_108995, _108991)), start_point(_108997, _108993), _108997 = _108995, _108993 = _108991], (162 ^ _103935) ^ [_109407, _109409] : [-(open(_109407)), _109409 = _109407, open(_109409)], (172 ^ _103935) ^ [_109730, _109732, _109734, _109736] : [-(incident_o(_109734, _109730)), incident_o(_109736, _109732), _109736 = _109734, _109732 = _109730], (186 ^ _103935) ^ [_110174, _110176, _110178, _110180] : [-(incident_c(_110178, _110174)), incident_c(_110180, _110176), _110180 = _110178, _110176 = _110174], (200 ^ _103935) ^ [_110626, _110628, _110630, _110632, _110634, _110636] : [-(ordered_by(_110634, _110630, _110626)), ordered_by(_110636, _110632, _110628), _110636 = _110634, _110632 = _110630, _110628 = _110626], (573 ^ _103935) ^ [_123522, _123524, _123526, _123528] : [between_c(_123528, _123526, _123524, _123522), 576 ^ _103935 : [(577 ^ _103935) ^ [] : [_123526 = _123522], (580 ^ _103935) ^ [] : [-(part_of(578 ^ [_123522, _123524, _123526, _123528], _123528))], (582 ^ _103935) ^ [] : [-(end_point(_123526, 578 ^ [_123522, _123524, _123526, _123528]))], (584 ^ _103935) ^ [] : [-(end_point(_123522, 578 ^ [_123522, _123524, _123526, _123528]))], (586 ^ _103935) ^ [] : [-(inner_point(_123524, 578 ^ [_123522, _123524, _123526, _123528]))]]], (588 ^ _103935) ^ [_124134, _124136, _124138, _124140] : [-(between_c(_124140, _124138, _124136, _124134)), -(_124138 = _124134), 593 ^ _103935 : [(594 ^ _103935) ^ [_124340] : [part_of(_124340, _124140), end_point(_124138, _124340), end_point(_124134, _124340), inner_point(_124136, _124340)]]], (610 ^ _103935) ^ [_124897, _124899, _124901, _124903] : [between_o(_124903, _124901, _124899, _124897), 615 ^ _103935 : [(616 ^ _103935) ^ [] : [-(ordered_by(_124903, _124901, _124899))], (618 ^ _103935) ^ [] : [-(ordered_by(_124903, _124899, _124897))]], 619 ^ _103935 : [(620 ^ _103935) ^ [] : [-(ordered_by(_124903, _124897, _124899))], (622 ^ _103935) ^ [] : [-(ordered_by(_124903, _124899, _124901))]]], (624 ^ _103935) ^ [_125339, _125341, _125343, _125345] : [-(between_o(_125345, _125343, _125341, _125339)), 625 ^ _103935 : [(626 ^ _103935) ^ [] : [ordered_by(_125345, _125343, _125341), ordered_by(_125345, _125341, _125339)], (632 ^ _103935) ^ [] : [ordered_by(_125345, _125339, _125341), ordered_by(_125345, _125341, _125343)]]], (656 ^ _103935) ^ [_126371, _126373] : [-(start_point(_126373, _126371)), incident_o(_126373, _126371), 662 ^ _103935 : [(663 ^ _103935) ^ [] : [_126373 = 661 ^ [_126371, _126373]], (665 ^ _103935) ^ [] : [-(incident_o(661 ^ [_126371, _126373], _126371))], (667 ^ _103935) ^ [] : [ordered_by(_126371, _126373, 661 ^ [_126371, _126373])]]], (640 ^ _103935) ^ [_125876, _125878] : [start_point(_125878, _125876), 643 ^ _103935 : [(644 ^ _103935) ^ [] : [-(incident_o(_125878, _125876))], (646 ^ _103935) ^ [_126094] : [-(ordered_by(_125876, _125878, _126094)), -(_125878 = _126094), incident_o(_126094, _125876)]]], (687 ^ _103935) ^ [_127436, _127438] : [-(finish_point(_127438, _127436)), incident_o(_127438, _127436), 693 ^ _103935 : [(694 ^ _103935) ^ [] : [_127438 = 692 ^ [_127436, _127438]], (696 ^ _103935) ^ [] : [-(incident_o(692 ^ [_127436, _127438], _127436))], (698 ^ _103935) ^ [] : [ordered_by(_127436, 692 ^ [_127436, _127438], _127438)]]], (671 ^ _103935) ^ [_126941, _126943] : [finish_point(_126943, _126941), 674 ^ _103935 : [(675 ^ _103935) ^ [] : [-(incident_o(_126943, _126941))], (677 ^ _103935) ^ [_127159] : [-(ordered_by(_126941, _127159, _126943)), -(_126943 = _127159), incident_o(_127159, _126941)]]], (702 ^ _103935) ^ [_127991, _127993, _127995] : [ordered_by(_127995, _127993, _127991), 705 ^ _103935 : [(706 ^ _103935) ^ [] : [-(incident_o(_127993, _127995))], (708 ^ _103935) ^ [] : [-(incident_o(_127991, _127995))]]], (711 ^ _103935) ^ [_128332] : [-(open(709 ^ [_128332]))], (713 ^ _103935) ^ [_128438, _128440] : [incident_o(_128438, _128440), -(incident_c(_128438, 709 ^ [_128440]))], (719 ^ _103935) ^ [_128610, _128612] : [incident_c(_128610, 709 ^ [_128612]), -(incident_o(_128610, _128612))], (744 ^ _103935) ^ [_129666, _129668, _129670, _129672] : [-(between_o(_129666, _129672, _129670, _129668)), 745 ^ _103935 : [(746 ^ _103935) ^ [_129777] : [between_c(_129777, _129672, _129670, _129668), 750 ^ _103935 : [(751 ^ _103935) ^ [] : [-(incident_o(747 ^ [_129666, _129668, _129670, _129672, _129777], _129666))], (753 ^ _103935) ^ [] : [incident_c(747 ^ [_129666, _129668, _129670, _129672, _129777], _129777)]], 754 ^ _103935 : [(755 ^ _103935) ^ [] : [-(incident_c(747 ^ [_129666, _129668, _129670, _129672, _129777], _129777))], (757 ^ _103935) ^ [] : [incident_o(747 ^ [_129666, _129668, _129670, _129672, _129777], _129666)]]]]], (725 ^ _103935) ^ [_128891, _128893, _128895, _128897] : [between_o(_128891, _128897, _128895, _128893), 729 ^ _103935 : [(742 ^ _103935) ^ [] : [-(between_c(728 ^ [_128891, _128893, _128895, _128897], _128897, _128895, _128893))], (730 ^ _103935) ^ [_129174] : [incident_o(_129174, _128891), -(incident_c(_129174, 728 ^ [_128891, _128893, _128895, _128897]))], (736 ^ _103935) ^ [_129384] : [incident_c(_129384, 728 ^ [_128891, _128893, _128895, _128897]), -(incident_o(_129384, _128891))]]], (764 ^ _103935) ^ [_130465] : [-(start_point(762 ^ [_130465], _130465))], (766 ^ _103935) ^ [_130591, _130593, _130595] : [open(_130591), -(_130595 = _130593), incident_c(_130595, _130591), incident_c(_130593, _130591), 782 ^ _103935 : [(795 ^ _103935) ^ [] : [-(ordered_by(781 ^ [_130591, _130593, _130595], _130595, _130593))], (783 ^ _103935) ^ [_131140] : [incident_o(_131140, 781 ^ [_130591, _130593, _130595]), -(incident_c(_131140, _130591))], (789 ^ _103935) ^ [_131338] : [incident_c(_131338, _130591), -(incident_o(_131338, 781 ^ [_130591, _130593, _130595]))]]], (797 ^ _103935) ^ [_131657, _131659] : [-(_131659 = _131657), 802 ^ _103935 : [(803 ^ _103935) ^ [] : [-(ordered_by(_131659, 798 ^ [_131657, _131659], 799 ^ [_131657, _131659]))], (805 ^ _103935) ^ [] : [ordered_by(_131657, 798 ^ [_131657, _131659], 799 ^ [_131657, _131659])]], 806 ^ _103935 : [(807 ^ _103935) ^ [] : [-(ordered_by(_131657, 798 ^ [_131657, _131659], 799 ^ [_131657, _131659]))], (809 ^ _103935) ^ [] : [ordered_by(_131659, 798 ^ [_131657, _131659], 799 ^ [_131657, _131659])]]], (829 ^ _103935) ^ [_132830, _132832] : [-(_132832 = underlying_curve(_132830)), 833 ^ _103935 : [(834 ^ _103935) ^ [] : [-(incident_o(830 ^ [_132830, _132832], _132830))], (836 ^ _103935) ^ [] : [incident_c(830 ^ [_132830, _132832], _132832)]], 837 ^ _103935 : [(838 ^ _103935) ^ [] : [-(incident_c(830 ^ [_132830, _132832], _132832))], (840 ^ _103935) ^ [] : [incident_o(830 ^ [_132830, _132832], _132830)]]], (813 ^ _103935) ^ [_132309, _132311] : [_132311 = underlying_curve(_132309), 816 ^ _103935 : [(817 ^ _103935) ^ [_132479] : [incident_o(_132479, _132309), -(incident_c(_132479, _132311))], (823 ^ _103935) ^ [_132651] : [incident_c(_132651, _132311), -(incident_o(_132651, _132309))]]], (244 ^ _103935) ^ [_112167, _112169] : [246 ^ _103935 : [(247 ^ _103935) ^ [] : [-(incident_c(245 ^ [_112167, _112169], _112167))], (249 ^ _103935) ^ [] : [incident_c(245 ^ [_112167, _112169], _112169)]], -(part_of(_112167, _112169))], (234 ^ _103935) ^ [_111853, _111855] : [part_of(_111853, _111855), 237 ^ _103935 : [(238 ^ _103935) ^ [_111990] : [incident_c(_111990, _111853), -(incident_c(_111990, _111855))]]], (275 ^ _103935) ^ [_113292, _113294, _113296] : [-(_113296 = sum(_113294, _113292)), 279 ^ _103935 : [(280 ^ _103935) ^ [] : [-(incident_c(276 ^ [_113292, _113294, _113296], _113296))], (282 ^ _103935) ^ [] : [incident_c(276 ^ [_113292, _113294, _113296], _113294)], (284 ^ _103935) ^ [] : [incident_c(276 ^ [_113292, _113294, _113296], _113292)]], 285 ^ _103935 : [(292 ^ _103935) ^ [] : [incident_c(276 ^ [_113292, _113294, _113296], _113296)], (286 ^ _103935) ^ [] : [-(incident_c(276 ^ [_113292, _113294, _113296], _113294)), -(incident_c(276 ^ [_113292, _113294, _113296], _113292))]]], (253 ^ _103935) ^ [_112567, _112569, _112571] : [_112571 = sum(_112569, _112567), 256 ^ _103935 : [(267 ^ _103935) ^ [_113027] : [268 ^ _103935 : [(269 ^ _103935) ^ [] : [incident_c(_113027, _112569)], (271 ^ _103935) ^ [] : [incident_c(_113027, _112567)]], -(incident_c(_113027, _112571))], (257 ^ _103935) ^ [_112749] : [incident_c(_112749, _112571), -(incident_c(_112749, _112569)), -(incident_c(_112749, _112567))]]], (324 ^ _103935) ^ [_114900, _114902] : [-(end_point(_114902, _114900)), incident_c(_114902, _114900), 331 ^ _103935 : [(332 ^ _103935) ^ [] : [-(part_of(329 ^ [_114900, _114902], _114900))], (334 ^ _103935) ^ [] : [-(part_of(330 ^ [_114900, _114902], _114900))], (336 ^ _103935) ^ [] : [-(incident_c(_114902, 329 ^ [_114900, _114902]))], (338 ^ _103935) ^ [] : [-(incident_c(_114902, 330 ^ [_114900, _114902]))], (340 ^ _103935) ^ [] : [part_of(329 ^ [_114900, _114902], 330 ^ [_114900, _114902])], (342 ^ _103935) ^ [] : [part_of(330 ^ [_114900, _114902], 329 ^ [_114900, _114902])]]], (296 ^ _103935) ^ [_114072, _114074] : [end_point(_114074, _114072), 299 ^ _103935 : [(300 ^ _103935) ^ [] : [-(incident_c(_114074, _114072))], (302 ^ _103935) ^ [_114324, _114326] : [-(part_of(_114326, _114324)), -(part_of(_114324, _114326)), part_of(_114326, _114072), part_of(_114324, _114072), incident_c(_114074, _114326), incident_c(_114074, _114324)]]], (346 ^ _103935) ^ [_115855, _115857] : [inner_point(_115857, _115855), 349 ^ _103935 : [(350 ^ _103935) ^ [] : [-(incident_c(_115857, _115855))], (352 ^ _103935) ^ [] : [end_point(_115857, _115855)]]], (354 ^ _103935) ^ [_116093, _116095] : [-(inner_point(_116095, _116093)), incident_c(_116095, _116093), -(end_point(_116095, _116093))], (364 ^ _103935) ^ [_116440, _116442, _116444] : [meet(_116444, _116442, _116440), 367 ^ _103935 : [(368 ^ _103935) ^ [] : [-(incident_c(_116444, _116442))], (370 ^ _103935) ^ [] : [-(incident_c(_116444, _116440))], (372 ^ _103935) ^ [_116743] : [379 ^ _103935 : [(380 ^ _103935) ^ [] : [-(end_point(_116743, _116442))], (382 ^ _103935) ^ [] : [-(end_point(_116743, _116440))]], incident_c(_116743, _116442), incident_c(_116743, _116440)]]], (384 ^ _103935) ^ [_117108, _117110, _117112] : [-(meet(_117112, _117110, _117108)), incident_c(_117112, _117110), incident_c(_117112, _117108), 394 ^ _103935 : [(395 ^ _103935) ^ [] : [-(incident_c(393 ^ [_117108, _117110, _117112], _117110))], (397 ^ _103935) ^ [] : [-(incident_c(393 ^ [_117108, _117110, _117112], _117108))], (399 ^ _103935) ^ [] : [end_point(393 ^ [_117108, _117110, _117112], _117110), end_point(393 ^ [_117108, _117110, _117112], _117108)]]], (407 ^ _103935) ^ [_117885] : [closed(_117885), 410 ^ _103935 : [(411 ^ _103935) ^ [_117996] : [end_point(_117996, _117885)]]], (413 ^ _103935) ^ [_118062] : [-(end_point(414 ^ [_118062], _118062)), -(closed(_118062))], (420 ^ _103935) ^ [_118335] : [open(_118335), -(end_point(423 ^ [_118335], _118335))], (427 ^ _103935) ^ [_118540] : [428 ^ _103935 : [(429 ^ _103935) ^ [_118607] : [end_point(_118607, _118540)]], -(open(_118540))], (433 ^ _103935) ^ [_118766, _118768] : [-(open(_118766)), part_of(_118766, _118768), -(_118766 = _118768)], (443 ^ _103935) ^ [_119094, _119096, _119098, _119100] : [part_of(_119098, _119100), part_of(_119096, _119100), part_of(_119094, _119100), 456 ^ _103935 : [(457 ^ _103935) ^ [_119505] : [end_point(_119505, _119098), end_point(_119505, _119096), end_point(_119505, _119094)]], -(part_of(_119096, _119094)), -(part_of(_119094, _119096)), -(part_of(_119098, _119096)), -(part_of(_119096, _119098)), -(part_of(_119098, _119094)), -(part_of(_119094, _119098))], (490 ^ _103935) ^ [_120384] : [-(inner_point(488 ^ [_120384], _120384))], (492 ^ _103935) ^ [_120496, _120498] : [inner_point(_120496, _120498), 497 ^ _103935 : [(498 ^ _103935) ^ [] : [-(meet(_120496, 495 ^ [_120496, _120498], 496 ^ [_120496, _120498]))], (500 ^ _103935) ^ [] : [-(_120498 = sum(495 ^ [_120496, _120498], 496 ^ [_120496, _120498]))]]], (502 ^ _103935) ^ [_120984, _120986, _120988, _120990] : [end_point(_120988, _120990), end_point(_120986, _120990), end_point(_120984, _120990), -(_120988 = _120986), -(_120988 = _120984), -(_120986 = _120984)], (524 ^ _103935) ^ [_121600, _121602] : [end_point(_121600, _121602), 528 ^ _103935 : [(529 ^ _103935) ^ [] : [-(end_point(527 ^ [_121600, _121602], _121602))], (531 ^ _103935) ^ [] : [_121600 = 527 ^ [_121600, _121602]]]], (533 ^ _103935) ^ [_121986, _121988, _121990, _121992] : [544 ^ _103935 : [(545 ^ _103935) ^ [_122332] : [end_point(_122332, _121990), -(meet(_122332, _121990, _121988))]], closed(_121992), meet(_121986, _121990, _121988), _121992 = sum(_121990, _121988)], (551 ^ _103935) ^ [_122575, _122577] : [552 ^ _103935 : [(553 ^ _103935) ^ [_122654] : [meet(_122654, _122577, _122575)]], -(554 ^ [_122575, _122577] = sum(_122577, _122575))], (558 ^ _103935) ^ [_122855, _122857] : [-(_122857 = _122855), 562 ^ _103935 : [(563 ^ _103935) ^ [] : [-(incident_c(559 ^ [_122855, _122857], _122857))], (565 ^ _103935) ^ [] : [incident_c(559 ^ [_122855, _122857], _122855)]], 566 ^ _103935 : [(567 ^ _103935) ^ [] : [-(incident_c(559 ^ [_122855, _122857], _122855))], (569 ^ _103935) ^ [] : [incident_c(559 ^ [_122855, _122857], _122857)]]]], input).
% 0.34/1.37  ncf('1',plain,[between_c(728 ^ [843 ^ [], 844 ^ [], 844 ^ [], 844 ^ []], 844 ^ [], 844 ^ [], 844 ^ []), 577 : 844 ^ [] = 844 ^ []],start(573 ^ 0,bind([[_123522, _123524, _123526, _123528], [844 ^ [], 844 ^ [], 844 ^ [], 728 ^ [843 ^ [], 844 ^ [], 844 ^ [], 844 ^ []]]]))).
% 0.34/1.37  ncf('1.1',plain,[-(between_c(728 ^ [843 ^ [], 844 ^ [], 844 ^ [], 844 ^ []], 844 ^ [], 844 ^ [], 844 ^ [])), between_o(843 ^ [], 844 ^ [], 844 ^ [], 844 ^ [])],extension(725 ^ 1,bind([[_128891, _128893, _128895, _128897], [843 ^ [], 844 ^ [], 844 ^ [], 844 ^ []]]))).
% 0.34/1.37  ncf('1.1.1',plain,[-(between_o(843 ^ [], 844 ^ [], 844 ^ [], 844 ^ [])), 626 : ordered_by(843 ^ [], 844 ^ [], 844 ^ []), 626 : ordered_by(843 ^ [], 844 ^ [], 844 ^ [])],extension(624 ^ 2,bind([[_125339, _125341, _125343, _125345], [844 ^ [], 844 ^ [], 844 ^ [], 843 ^ []]]))).
% 0.34/1.37  ncf('1.1.1.1',plain,[-(ordered_by(843 ^ [], 844 ^ [], 844 ^ []))],extension(846 ^ 5)).
% 0.34/1.37  ncf('1.1.1.2',plain,[-(ordered_by(843 ^ [], 844 ^ [], 844 ^ []))],extension(846 ^ 5)).
% 0.34/1.37  ncf('1.2',plain,[-(844 ^ [] = 844 ^ [])],extension(2 ^ 3,bind([[_104079], [844 ^ []]]))).
% 0.34/1.37  %-----------------------------------------------------
% 0.34/1.37  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------