%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : GEO268+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n018.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 11:12:24 EDT 2023

% Result   : Theorem 0.44s 1.40s
% Output   : Proof 0.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GEO268+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri May 19 04:36:43 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.44/1.40  
% 0.44/1.40  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.44/1.40  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.44/1.40  %-----------------------------------------------------
% 0.44/1.40  ncf(matrix, plain, [(438 ^ _60428) ^ [] : [439 ^ _60428 : [(440 ^ _60428) ^ [] : [-(unequally_directed_lines(435 ^ [], 436 ^ []))], (442 ^ _60428) ^ [] : [unequally_directed_opposite_lines(435 ^ [], reverse_line(436 ^ []))]], 443 ^ _60428 : [(444 ^ _60428) ^ [] : [-(unequally_directed_opposite_lines(435 ^ [], reverse_line(436 ^ [])))], (446 ^ _60428) ^ [] : [unequally_directed_lines(435 ^ [], 436 ^ [])]]], (2 ^ _60428) ^ [_60570, _60572] : [unequally_directed_opposite_lines(_60572, _60570), -(unequally_directed_lines(_60572, reverse_line(_60570)))], (8 ^ _60428) ^ [_60736, _60738] : [unequally_directed_lines(_60738, reverse_line(_60736)), -(unequally_directed_opposite_lines(_60738, _60736))], (14 ^ _60428) ^ [_60981, _60983] : [right_apart_point(_60983, _60981), -(left_apart_point(_60983, reverse_line(_60981)))], (20 ^ _60428) ^ [_61147, _61149] : [left_apart_point(_61149, reverse_line(_61147)), -(right_apart_point(_61149, _61147))], (26 ^ _60428) ^ [_61392, _61394] : [right_convergent_lines(_61394, _61392), -(left_convergent_lines(_61394, reverse_line(_61392)))], (32 ^ _60428) ^ [_61558, _61560] : [left_convergent_lines(_61560, reverse_line(_61558)), -(right_convergent_lines(_61560, _61558))], (38 ^ _60428) ^ [_61803, _61805] : [equally_directed_lines(_61805, _61803), unequally_directed_lines(_61805, _61803)], (44 ^ _60428) ^ [_61966, _61968] : [-(unequally_directed_lines(_61968, _61966)), -(equally_directed_lines(_61968, _61966))], (50 ^ _60428) ^ [_62210, _62212] : [equally_directed_opposite_lines(_62212, _62210), unequally_directed_opposite_lines(_62212, _62210)], (56 ^ _60428) ^ [_62373, _62375] : [-(unequally_directed_opposite_lines(_62375, _62373)), -(equally_directed_opposite_lines(_62375, _62373))], (72 ^ _60428) ^ [_62869, _62871] : [73 ^ _60428 : [(74 ^ _60428) ^ [] : [left_apart_point(_62871, _62869)], (76 ^ _60428) ^ [] : [right_apart_point(_62871, _62869)]], -(apart_point_and_line(_62871, _62869))], (62 ^ _60428) ^ [_62617, _62619] : [apart_point_and_line(_62619, _62617), -(left_apart_point(_62619, _62617)), -(right_apart_point(_62619, _62617))], (80 ^ _60428) ^ [_63184, _63186] : [convergent_lines(_63186, _63184), 83 ^ _60428 : [(84 ^ _60428) ^ [] : [-(unequally_directed_lines(_63186, _63184))], (86 ^ _60428) ^ [] : [-(unequally_directed_opposite_lines(_63186, _63184))]]], (88 ^ _60428) ^ [_63421, _63423] : [-(convergent_lines(_63423, _63421)), unequally_directed_lines(_63423, _63421), unequally_directed_opposite_lines(_63423, _63421)], (98 ^ _60428) ^ [_63765, _63767, _63769] : [divides_points(_63765, _63769, _63767), 103 ^ _60428 : [(104 ^ _60428) ^ [] : [-(left_apart_point(_63769, _63765))], (106 ^ _60428) ^ [] : [-(right_apart_point(_63767, _63765))]], 107 ^ _60428 : [(108 ^ _60428) ^ [] : [-(right_apart_point(_63769, _63765))], (110 ^ _60428) ^ [] : [-(left_apart_point(_63767, _63765))]]], (112 ^ _60428) ^ [_64183, _64185, _64187] : [-(divides_points(_64183, _64187, _64185)), 113 ^ _60428 : [(114 ^ _60428) ^ [] : [left_apart_point(_64187, _64183), right_apart_point(_64185, _64183)], (120 ^ _60428) ^ [] : [right_apart_point(_64187, _64183), left_apart_point(_64185, _64183)]]], (128 ^ _60428) ^ [_64708, _64710, _64712] : [before_on_line(_64712, _64710, _64708), 131 ^ _60428 : [(132 ^ _60428) ^ [] : [-(distinct_points(_64710, _64708))], (134 ^ _60428) ^ [] : [-(incident_point_and_line(_64710, _64712))], (136 ^ _60428) ^ [] : [-(incident_point_and_line(_64708, _64712))], (138 ^ _60428) ^ [] : [-(equally_directed_lines(_64712, line_connecting(_64710, _64708)))]]], (140 ^ _60428) ^ [_65113, _65115, _65117] : [-(before_on_line(_65117, _65115, _65113)), distinct_points(_65115, _65113), incident_point_and_line(_65115, _65117), incident_point_and_line(_65113, _65117), equally_directed_lines(_65117, line_connecting(_65115, _65113))], (158 ^ _60428) ^ [_65675, _65677, _65679, _65681] : [between_on_line(_65681, _65679, _65677, _65675), 163 ^ _60428 : [(164 ^ _60428) ^ [] : [-(before_on_line(_65681, _65679, _65677))], (166 ^ _60428) ^ [] : [-(before_on_line(_65681, _65677, _65675))]], 167 ^ _60428 : [(168 ^ _60428) ^ [] : [-(before_on_line(_65681, _65675, _65677))], (170 ^ _60428) ^ [] : [-(before_on_line(_65681, _65677, _65679))]]], (172 ^ _60428) ^ [_66117, _66119, _66121, _66123] : [-(between_on_line(_66123, _66121, _66119, _66117)), 173 ^ _60428 : [(174 ^ _60428) ^ [] : [before_on_line(_66123, _66121, _66119), before_on_line(_66123, _66119, _66117)], (180 ^ _60428) ^ [] : [before_on_line(_66123, _66117, _66119), before_on_line(_66123, _66119, _66121)]]], (188 ^ _60428) ^ [_66595] : [distinct_points(_66595, _66595)], (190 ^ _60428) ^ [_66716, _66718, _66720] : [distinct_points(_66720, _66718), -(distinct_points(_66720, _66716)), -(distinct_points(_66718, _66716))], (200 ^ _60428) ^ [_66996] : [distinct_lines(_66996, _66996)], (202 ^ _60428) ^ [_67117, _67119, _67121] : [distinct_lines(_67121, _67119), -(distinct_lines(_67121, _67117)), -(distinct_lines(_67119, _67117))], (212 ^ _60428) ^ [_67398] : [-(equally_directed_lines(_67398, _67398))], (214 ^ _60428) ^ [_67519, _67521, _67523] : [unequally_directed_lines(_67523, _67521), -(unequally_directed_lines(_67523, _67519)), -(unequally_directed_lines(_67521, _67519))], (224 ^ _60428) ^ [_67843, _67845, _67847] : [unequally_directed_lines(_67847, _67845), unequally_directed_lines(_67847, reverse_line(_67845)), 233 ^ _60428 : [(234 ^ _60428) ^ [] : [-(unequally_directed_lines(_67847, _67843))], (236 ^ _60428) ^ [] : [-(unequally_directed_lines(_67847, reverse_line(_67843)))]], 237 ^ _60428 : [(238 ^ _60428) ^ [] : [-(unequally_directed_lines(_67845, _67843))], (240 ^ _60428) ^ [] : [-(unequally_directed_lines(_67845, reverse_line(_67843)))]]], (242 ^ _60428) ^ [_68414, _68416] : [-(unequally_directed_lines(_68416, _68414)), -(unequally_directed_lines(_68416, reverse_line(_68414)))], (248 ^ _60428) ^ [_68629, _68631] : [unequally_directed_lines(_68631, _68629), unequally_directed_lines(_68631, reverse_line(_68629)), -(left_convergent_lines(_68631, _68629)), -(left_convergent_lines(_68631, reverse_line(_68629)))], (262 ^ _60428) ^ [_69032, _69034] : [left_apart_point(_69034, _69032)], (264 ^ _60428) ^ [_69077, _69079] : [left_apart_point(_69079, reverse_line(_69077))], (266 ^ _60428) ^ [_69194, _69196] : [left_convergent_lines(_69196, _69194)], (268 ^ _60428) ^ [_69239, _69241] : [left_convergent_lines(_69241, reverse_line(_69239))], (270 ^ _60428) ^ [_69352, _69354] : [-(line(line_connecting(_69354, _69352))), point(_69354), point(_69352), distinct_points(_69354, _69352)], (284 ^ _60428) ^ [_69740, _69742] : [-(point(intersection_point(_69742, _69740))), line(_69742), line(_69740), unequally_directed_lines(_69742, _69740), unequally_directed_lines(_69742, reverse_line(_69740))], (302 ^ _60428) ^ [_70221, _70223] : [-(line(parallel_through_point(_70223, _70221))), point(_70221), line(_70223)], (312 ^ _60428) ^ [_70506] : [line(_70506), -(line(reverse_line(_70506)))], (318 ^ _60428) ^ [_70710, _70712] : [distinct_points(_70712, _70710), 321 ^ _60428 : [(322 ^ _60428) ^ [] : [apart_point_and_line(_70712, line_connecting(_70712, _70710))], (324 ^ _60428) ^ [] : [apart_point_and_line(_70710, line_connecting(_70712, _70710))]]], (326 ^ _60428) ^ [_71009, _71011] : [333 ^ _60428 : [(334 ^ _60428) ^ [] : [apart_point_and_line(intersection_point(_71011, _71009), _71011)], (336 ^ _60428) ^ [] : [apart_point_and_line(intersection_point(_71011, _71009), _71009)]], unequally_directed_lines(_71011, _71009), unequally_directed_lines(_71011, reverse_line(_71009))], (338 ^ _60428) ^ [_71385, _71387] : [apart_point_and_line(_71387, parallel_through_point(_71385, _71387))], (340 ^ _60428) ^ [_71467] : [distinct_lines(_71467, reverse_line(_71467))], (342 ^ _60428) ^ [_71576, _71578] : [distinct_points(_71578, _71576), -(equally_directed_lines(line_connecting(_71578, _71576), reverse_line(line_connecting(_71576, _71578))))], (348 ^ _60428) ^ [_71787, _71789] : [-(equally_directed_lines(parallel_through_point(_71787, _71789), _71787))], (350 ^ _60428) ^ [_71927, _71929, _71931, _71933] : [distinct_points(_71933, _71931), distinct_lines(_71929, _71927), -(left_apart_point(_71933, _71929)), -(left_apart_point(_71931, _71929)), -(left_apart_point(_71933, _71927)), -(left_apart_point(_71931, _71927)), -(left_apart_point(_71933, reverse_line(_71929))), -(left_apart_point(_71931, reverse_line(_71929))), -(left_apart_point(_71933, reverse_line(_71927))), -(left_apart_point(_71931, reverse_line(_71927)))], (388 ^ _60428) ^ [_72964, _72966, _72968] : [distinct_points(_72968, _72966), left_apart_point(_72968, _72964), -(left_apart_point(_72966, _72964)), -(left_convergent_lines(line_connecting(_72968, _72966), _72964))], (402 ^ _60428) ^ [_73389, _73391, _73393] : [left_apart_point(_73393, _73389), -(distinct_points(_73393, _73391)), -(left_apart_point(_73391, _73389))], (426 ^ _60428) ^ [_74116, _74118, _74120] : [left_convergent_lines(_74120, _74118), -(unequally_directed_lines(_74118, _74116)), -(left_convergent_lines(_74120, _74116))], (412 ^ _60428) ^ [_73713, _73715, _73717] : [left_apart_point(_73717, _73715), unequally_directed_lines(_73715, _73713), -(distinct_lines(_73715, _73713)), -(left_apart_point(_73717, reverse_line(_73713)))]], input).
% 0.44/1.40  ncf('1',plain,[442 : unequally_directed_opposite_lines(435 ^ [], reverse_line(436 ^ [])), 446 : unequally_directed_lines(435 ^ [], 436 ^ [])],start(438 ^ 0)).
% 0.44/1.40  ncf('1.1',plain,[-(unequally_directed_opposite_lines(435 ^ [], reverse_line(436 ^ []))), unequally_directed_lines(435 ^ [], reverse_line(reverse_line(436 ^ [])))],extension(8 ^ 3,bind([[_60736, _60738], [reverse_line(436 ^ []), 435 ^ []]]))).
% 0.44/1.40  ncf('1.1.1',plain,[-(unequally_directed_lines(435 ^ [], reverse_line(reverse_line(436 ^ [])))), unequally_directed_lines(435 ^ [], 436 ^ []), unequally_directed_lines(435 ^ [], reverse_line(436 ^ [])), 238 : -(unequally_directed_lines(436 ^ [], reverse_line(reverse_line(436 ^ []))))],extension(224 ^ 4,bind([[_67843, _67845, _67847], [reverse_line(reverse_line(436 ^ [])), 436 ^ [], 435 ^ []]]))).
% 0.44/1.40  ncf('1.1.1.1',plain,[-(unequally_directed_lines(435 ^ [], 436 ^ []))],extension(440 ^ 5)).
% 0.44/1.40  ncf('1.1.1.2',plain,[-(unequally_directed_lines(435 ^ [], reverse_line(436 ^ []))), -(unequally_directed_lines(435 ^ [], reverse_line(reverse_line(436 ^ []))))],extension(242 ^ 5,bind([[_68414, _68416], [reverse_line(436 ^ []), 435 ^ []]]))).
% 0.44/1.40  ncf('1.1.1.2.1',plain,[unequally_directed_lines(435 ^ [], reverse_line(reverse_line(436 ^ [])))],reduction('1.1')).
% 0.44/1.40  ncf('1.1.1.3',plain,[unequally_directed_lines(436 ^ [], reverse_line(reverse_line(436 ^ []))), unequally_directed_lines(436 ^ [], reverse_line(reverse_line(reverse_line(436 ^ [])))), -(left_convergent_lines(436 ^ [], reverse_line(reverse_line(436 ^ [])))), -(left_convergent_lines(436 ^ [], reverse_line(reverse_line(reverse_line(436 ^ [])))))],extension(248 ^ 7,bind([[_68629, _68631], [reverse_line(reverse_line(436 ^ [])), 436 ^ []]]))).
% 0.44/1.40  ncf('1.1.1.3.1',plain,[-(unequally_directed_lines(436 ^ [], reverse_line(reverse_line(reverse_line(436 ^ [])))))],extension(240 ^ 8)).
% 0.44/1.40  ncf('1.1.1.3.2',plain,[left_convergent_lines(436 ^ [], reverse_line(reverse_line(436 ^ [])))],extension(266 ^ 8,bind([[_69194, _69196], [reverse_line(reverse_line(436 ^ [])), 436 ^ []]]))).
% 0.44/1.40  ncf('1.1.1.3.3',plain,[left_convergent_lines(436 ^ [], reverse_line(reverse_line(reverse_line(436 ^ []))))],extension(266 ^ 8,bind([[_69194, _69196], [reverse_line(reverse_line(reverse_line(436 ^ []))), 436 ^ []]]))).
% 0.44/1.40  ncf('1.2',plain,[-(unequally_directed_lines(435 ^ [], 436 ^ [])), unequally_directed_lines(435 ^ [], reverse_line(reverse_line(436 ^ []))), -(unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), 436 ^ []))],extension(214 ^ 3,bind([[_67519, _67521, _67523], [436 ^ [], reverse_line(reverse_line(436 ^ [])), 435 ^ []]]))).
% 0.44/1.40  ncf('1.2.1',plain,[-(unequally_directed_lines(435 ^ [], reverse_line(reverse_line(436 ^ [])))), unequally_directed_opposite_lines(435 ^ [], reverse_line(436 ^ []))],extension(2 ^ 4,bind([[_60570, _60572], [reverse_line(436 ^ []), 435 ^ []]]))).
% 0.44/1.40  ncf('1.2.1.1',plain,[-(unequally_directed_opposite_lines(435 ^ [], reverse_line(436 ^ [])))],extension(444 ^ 5)).
% 0.44/1.40  ncf('1.2.2',plain,[unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), 436 ^ []), unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(436 ^ [])), 234 : -(unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(reverse_line(436 ^ [])))), 238 : -(unequally_directed_lines(436 ^ [], reverse_line(reverse_line(436 ^ []))))],extension(224 ^ 4,bind([[_67843, _67845, _67847], [reverse_line(reverse_line(436 ^ [])), 436 ^ [], reverse_line(reverse_line(436 ^ []))]]))).
% 0.44/1.40  ncf('1.2.2.1',plain,[-(unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(436 ^ []))), -(unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(reverse_line(436 ^ []))))],extension(242 ^ 5,bind([[_68414, _68416], [reverse_line(436 ^ []), reverse_line(reverse_line(436 ^ []))]]))).
% 0.44/1.40  ncf('1.2.2.1.1',plain,[unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(reverse_line(436 ^ []))), -(unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(436 ^ []))), -(unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(436 ^ [])))],extension(214 ^ 6,bind([[_67519, _67521, _67523], [reverse_line(436 ^ []), reverse_line(reverse_line(436 ^ [])), reverse_line(reverse_line(436 ^ []))]]))).
% 0.44/1.40  ncf('1.2.2.1.1.1',plain,[unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(436 ^ []))],reduction('1.2.2')).
% 0.44/1.40  ncf('1.2.2.1.1.2',plain,[unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(436 ^ []))],lemmata('[1, 2, 2, 1].x')).
% 0.44/1.40  ncf('1.2.2.2',plain,[unequally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(reverse_line(436 ^ []))), equally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(reverse_line(436 ^ [])))],extension(38 ^ 7,bind([[_61803, _61805], [reverse_line(reverse_line(436 ^ [])), reverse_line(reverse_line(436 ^ []))]]))).
% 0.44/1.40  ncf('1.2.2.2.1',plain,[-(equally_directed_lines(reverse_line(reverse_line(436 ^ [])), reverse_line(reverse_line(436 ^ []))))],extension(212 ^ 8,bind([[_67398], [reverse_line(reverse_line(436 ^ []))]]))).
% 0.44/1.40  ncf('1.2.2.3',plain,[unequally_directed_lines(436 ^ [], reverse_line(reverse_line(436 ^ []))), unequally_directed_lines(436 ^ [], reverse_line(reverse_line(reverse_line(436 ^ [])))), -(left_convergent_lines(436 ^ [], reverse_line(reverse_line(436 ^ [])))), -(left_convergent_lines(436 ^ [], reverse_line(reverse_line(reverse_line(436 ^ [])))))],extension(248 ^ 7,bind([[_68629, _68631], [reverse_line(reverse_line(436 ^ [])), 436 ^ []]]))).
% 0.44/1.40  ncf('1.2.2.3.1',plain,[-(unequally_directed_lines(436 ^ [], reverse_line(reverse_line(reverse_line(436 ^ [])))))],extension(240 ^ 8)).
% 0.44/1.40  ncf('1.2.2.3.2',plain,[left_convergent_lines(436 ^ [], reverse_line(reverse_line(436 ^ [])))],extension(266 ^ 8,bind([[_69194, _69196], [reverse_line(reverse_line(436 ^ [])), 436 ^ []]]))).
% 0.44/1.40  ncf('1.2.2.3.3',plain,[left_convergent_lines(436 ^ [], reverse_line(reverse_line(reverse_line(436 ^ []))))],extension(266 ^ 8,bind([[_69194, _69196], [reverse_line(reverse_line(reverse_line(436 ^ []))), 436 ^ []]]))).
% 0.44/1.40  %-----------------------------------------------------
% 0.44/1.40  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------