%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : GEO222+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n004.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 11:12:17 EDT 2023
% Result : Theorem 0.92s 1.38s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO222+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : nanocop.sh %s %d
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Fri May 19 04:17:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.92/1.38
% 0.92/1.38 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.92/1.38 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.38 %-----------------------------------------------------
% 0.92/1.38 ncf(matrix, plain, [(176 ^ _35402) ^ [] : [-(convergent_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))], (110 ^ _35402) ^ [_39056, _39058] : [convergent_lines(parallel_through_point(_39056, _39058), _39056)], (112 ^ _35402) ^ [_39152, _39154] : [apart_point_and_line(_39154, parallel_through_point(_39152, _39154))], (114 ^ _35402) ^ [_39258, _39260, _39262] : [distinct_lines(_39260, _39258), -(apart_point_and_line(_39262, _39260)), -(apart_point_and_line(_39262, _39258)), -(convergent_lines(_39260, _39258))], (128 ^ _35402) ^ [_39666, _39668] : [-(convergent_lines(_39668, _39666)), -(unorthogonal_lines(_39668, _39666))], (134 ^ _35402) ^ [_39891, _39893, _39895] : [convergent_lines(_39895, _39893), unorthogonal_lines(_39895, _39893), 143 ^ _35402 : [(144 ^ _35402) ^ [] : [-(convergent_lines(_39895, _39891))], (146 ^ _35402) ^ [] : [-(unorthogonal_lines(_39895, _39891))]], 147 ^ _35402 : [(148 ^ _35402) ^ [] : [-(convergent_lines(_39893, _39891))], (150 ^ _35402) ^ [] : [-(unorthogonal_lines(_39893, _39891))]]], (152 ^ _35402) ^ [_40434, _40436] : [unorthogonal_lines(orthogonal_through_point(_40434, _40436), _40434)], (154 ^ _35402) ^ [_40530, _40532] : [apart_point_and_line(_40532, orthogonal_through_point(_40530, _40532))], (156 ^ _35402) ^ [_40650, _40652, _40654, _40656] : [distinct_lines(_40654, _40652), -(apart_point_and_line(_40656, _40654)), -(apart_point_and_line(_40656, _40652)), -(unorthogonal_lines(_40654, _40650)), -(unorthogonal_lines(_40652, _40650))], (2 ^ _35402) ^ [_35505] : [distinct_points(_35505, _35505)], (4 ^ _35402) ^ [_35582] : [distinct_lines(_35582, _35582)], (6 ^ _35402) ^ [_35659] : [convergent_lines(_35659, _35659)], (8 ^ _35402) ^ [_35780, _35782, _35784] : [distinct_points(_35784, _35782), -(distinct_points(_35784, _35780)), -(distinct_points(_35782, _35780))], (18 ^ _35402) ^ [_36104, _36106, _36108] : [distinct_lines(_36108, _36106), -(distinct_lines(_36108, _36104)), -(distinct_lines(_36106, _36104))], (28 ^ _35402) ^ [_36428, _36430, _36432] : [convergent_lines(_36432, _36430), -(convergent_lines(_36432, _36428)), -(convergent_lines(_36430, _36428))], (38 ^ _35402) ^ [_36752, _36754, _36756] : [distinct_points(_36756, _36754), apart_point_and_line(_36752, line_connecting(_36756, _36754)), 45 ^ _35402 : [(46 ^ _35402) ^ [] : [-(distinct_points(_36752, _36756))], (48 ^ _35402) ^ [] : [-(distinct_points(_36752, _36754))]]], (50 ^ _35402) ^ [_37158, _37160, _37162] : [convergent_lines(_37162, _37160), 55 ^ _35402 : [(56 ^ _35402) ^ [] : [apart_point_and_line(_37158, _37162)], (58 ^ _35402) ^ [] : [apart_point_and_line(_37158, _37160)]], -(distinct_points(_37158, intersection_point(_37162, _37160)))], (62 ^ _35402) ^ [_37577, _37579, _37581, _37583] : [distinct_points(_37583, _37581), distinct_lines(_37579, _37577), -(apart_point_and_line(_37583, _37579)), -(apart_point_and_line(_37583, _37577)), -(apart_point_and_line(_37581, _37579)), -(apart_point_and_line(_37581, _37577))], (84 ^ _35402) ^ [_38206, _38208, _38210] : [apart_point_and_line(_38210, _38208), -(distinct_points(_38210, _38206)), -(apart_point_and_line(_38206, _38208))], (104 ^ _35402) ^ [_38820, _38822] : [convergent_lines(_38822, _38820), -(distinct_lines(_38822, _38820))], (94 ^ _35402) ^ [_38530, _38532, _38534] : [apart_point_and_line(_38534, _38532), -(distinct_lines(_38532, _38530)), -(apart_point_and_line(_38534, _38530))]], input).
% 0.92/1.38 ncf('1',plain,[unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))],start(152 ^ 0,bind([[_40434, _40436], [orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []]]))).
% 0.92/1.38 ncf('1.1',plain,[-(unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))), distinct_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), -(apart_point_and_line(intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), 174 ^ [])), -(apart_point_and_line(intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))), -(unorthogonal_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])))],extension(156 ^ 1,bind([[_40650, _40652, _40654, _40656], [orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), 174 ^ [], intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))]]))).
% 0.92/1.38 ncf('1.1.1',plain,[-(distinct_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))), distinct_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), -(distinct_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))],extension(18 ^ 2,bind([[_36104, _36106, _36108], [orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), 174 ^ []]]))).
% 0.92/1.38 ncf('1.1.1.1',plain,[-(distinct_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))), distinct_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), -(distinct_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))],extension(18 ^ 3,bind([[_36104, _36106, _36108], [orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), 174 ^ []]]))).
% 0.92/1.38 ncf('1.1.1.1.1',plain,[-(distinct_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))), distinct_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), -(distinct_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))],extension(18 ^ 4,bind([[_36104, _36106, _36108], [orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), 174 ^ []]]))).
% 0.92/1.38 ncf('1.1.1.1.1.1',plain,[-(distinct_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))), convergent_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))],extension(104 ^ 5,bind([[_38820, _38822], [orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), 174 ^ []]]))).
% 0.92/1.38 ncf('1.1.1.1.1.1.1',plain,[-(convergent_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))],extension(176 ^ 6)).
% 0.92/1.38 ncf('1.1.1.1.1.2',plain,[distinct_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))],extension(4 ^ 5,bind([[_35582], [orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.1.1.2',plain,[distinct_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))],extension(4 ^ 4,bind([[_35582], [orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.1.2',plain,[distinct_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), -(apart_point_and_line(173 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))), -(apart_point_and_line(173 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))), -(convergent_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))],extension(114 ^ 3,bind([[_39258, _39260, _39262], [orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), 173 ^ []]]))).
% 0.92/1.38 ncf('1.1.1.2.1',plain,[apart_point_and_line(173 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))],extension(154 ^ 4,bind([[_40530, _40532], [orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []]]))).
% 0.92/1.38 ncf('1.1.1.2.2',plain,[apart_point_and_line(173 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))],extension(154 ^ 4,bind([[_40530, _40532], [orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []]]))).
% 0.92/1.38 ncf('1.1.1.2.3',plain,[convergent_lines(orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))],extension(6 ^ 4,bind([[_35659], [orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.2',plain,[apart_point_and_line(intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), 174 ^ []), convergent_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), -(distinct_points(intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))))],extension(50 ^ 2,bind([[_37158, _37160, _37162], [intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), 174 ^ []]]))).
% 0.92/1.38 ncf('1.1.2.1',plain,[-(convergent_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))],extension(176 ^ 3)).
% 0.92/1.38 ncf('1.1.2.2',plain,[distinct_points(intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))],extension(2 ^ 3,bind([[_35505], [intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))]]))).
% 0.92/1.38 ncf('1.1.3',plain,[apart_point_and_line(intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), convergent_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), -(distinct_points(intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))))],extension(50 ^ 2,bind([[_37158, _37160, _37162], [intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []), 174 ^ []]]))).
% 0.92/1.38 ncf('1.1.3.1',plain,[-(convergent_lines(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))],extension(176 ^ 3)).
% 0.92/1.38 ncf('1.1.3.2',plain,[distinct_points(intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])), intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ [])))],extension(2 ^ 3,bind([[_35505], [intersection_point(174 ^ [], orthogonal_through_point(orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []))]]))).
% 0.92/1.38 ncf('1.1.4',plain,[unorthogonal_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])), convergent_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])), 144 : -(convergent_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ []))), 148 : -(convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])))],extension(134 ^ 2,bind([[_39891, _39893, _39895], [orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ []]]))).
% 0.92/1.38 ncf('1.1.4.1',plain,[-(convergent_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ []))), convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ []), -(convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])))],extension(28 ^ 3,bind([[_36428, _36430, _36432], [orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.4.1.1',plain,[-(convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ [])), -(unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ []))],extension(128 ^ 4,bind([[_39666, _39668], [174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.4.1.1.1',plain,[unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ [])],extension(152 ^ 5,bind([[_40434, _40436], [174 ^ [], 173 ^ []]]))).
% 0.92/1.38 ncf('1.1.4.1.2',plain,[convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))],extension(6 ^ 4,bind([[_35659], [orthogonal_through_point(174 ^ [], 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.4.2',plain,[convergent_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])), unorthogonal_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])), 144 : -(convergent_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ []))), 148 : -(convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])))],extension(134 ^ 5,bind([[_39891, _39893, _39895], [orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ []]]))).
% 0.92/1.38 ncf('1.1.4.2.1',plain,[-(unorthogonal_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])))],reduction('1.1')).
% 0.92/1.38 ncf('1.1.4.2.2',plain,[convergent_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])), unorthogonal_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])), 144 : -(convergent_lines(174 ^ [], 174 ^ [])), 150 : -(unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ []))],extension(134 ^ 8,bind([[_39891, _39893, _39895], [174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ []]]))).
% 0.92/1.38 ncf('1.1.4.2.2.1',plain,[-(unorthogonal_lines(174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ [])))],reduction('1.1')).
% 0.92/1.38 ncf('1.1.4.2.2.2',plain,[convergent_lines(174 ^ [], 174 ^ [])],extension(6 ^ 11,bind([[_35659], [174 ^ []]]))).
% 0.92/1.38 ncf('1.1.4.2.2.3',plain,[unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ [])],extension(152 ^ 11,bind([[_40434, _40436], [174 ^ [], 173 ^ []]]))).
% 0.92/1.38 ncf('1.1.4.2.3',plain,[convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))],extension(6 ^ 8,bind([[_35659], [orthogonal_through_point(174 ^ [], 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.4.3',plain,[convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])), unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])), 144 : -(convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))), 150 : -(unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])))],extension(134 ^ 5,bind([[_39891, _39893, _39895], [orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.4.3.1',plain,[-(unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))), distinct_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])), -(apart_point_and_line(173 ^ [], orthogonal_through_point(174 ^ [], 173 ^ []))), -(apart_point_and_line(173 ^ [], orthogonal_through_point(174 ^ [], 173 ^ []))), -(unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])))],extension(156 ^ 6,bind([[_40650, _40652, _40654, _40656], [orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []), 173 ^ []]]))).
% 0.92/1.38 ncf('1.1.4.3.1.1',plain,[-(distinct_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))), convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))],extension(104 ^ 7,bind([[_38820, _38822], [orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.4.3.1.1.1',plain,[-(convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])))],reduction('1.1.4')).
% 0.92/1.38 ncf('1.1.4.3.1.2',plain,[apart_point_and_line(173 ^ [], orthogonal_through_point(174 ^ [], 173 ^ []))],extension(154 ^ 7,bind([[_40530, _40532], [174 ^ [], 173 ^ []]]))).
% 0.92/1.38 ncf('1.1.4.3.1.3',plain,[apart_point_and_line(173 ^ [], orthogonal_through_point(174 ^ [], 173 ^ []))],lemmata('[3, 4, 1, 1].x')).
% 0.92/1.38 ncf('1.1.4.3.1.4',plain,[unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))],reduction('1.1.4.3')).
% 0.92/1.38 ncf('1.1.4.3.2',plain,[convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ []))],extension(6 ^ 8,bind([[_35659], [orthogonal_through_point(174 ^ [], 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.4.3.3',plain,[unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])), convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])), 146 : -(unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ [])), 150 : -(unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ []))],extension(134 ^ 8,bind([[_39891, _39893, _39895], [174 ^ [], orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])]]))).
% 0.92/1.38 ncf('1.1.4.3.3.1',plain,[-(convergent_lines(orthogonal_through_point(174 ^ [], 173 ^ []), orthogonal_through_point(174 ^ [], 173 ^ [])))],reduction('1.1.4')).
% 0.92/1.38 ncf('1.1.4.3.3.2',plain,[unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ [])],extension(152 ^ 11,bind([[_40434, _40436], [174 ^ [], 173 ^ []]]))).
% 0.92/1.38 ncf('1.1.4.3.3.3',plain,[unorthogonal_lines(orthogonal_through_point(174 ^ [], 173 ^ []), 174 ^ [])],extension(152 ^ 11,bind([[_40434, _40436], [174 ^ [], 173 ^ []]]))).
% 0.92/1.38 %-----------------------------------------------------
% 0.92/1.38 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------