TSTP Solution File: GEO181+2 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : GEO181+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n011.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 11:12:05 EDT 2023

% Result   : Theorem 43.33s 42.72s
% Output   : Proof 43.33s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO181+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n011.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
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Fri May 19 04:27:03 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 43.33/42.72  
% 43.33/42.72  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 43.33/42.72  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.33/42.72  %-----------------------------------------------------
% 43.33/42.72  ncf(matrix, plain, [(117 ^ _32023) ^ [] : [apart_point_and_line(110 ^ [], line_connecting(109 ^ [], 111 ^ []))], (115 ^ _32023) ^ [] : [-(apart_point_and_line(111 ^ [], line_connecting(109 ^ [], 110 ^ [])))], (113 ^ _32023) ^ [] : [-(distinct_points(109 ^ [], 110 ^ []))], !, (62 ^ _28332) ^ [_30467, _30469, _30471, _30473] : [distinct_points(_30473, _30471), distinct_lines(_30469, _30467), -(apart_point_and_line(_30473, _30469)), -(apart_point_and_line(_30473, _30467)), -(apart_point_and_line(_30471, _30469)), -(apart_point_and_line(_30471, _30467))], (8 ^ _28332) ^ [_28670, _28672, _28674] : [distinct_points(_28674, _28672), -(distinct_points(_28674, _28670)), -(distinct_points(_28672, _28670))], (94 ^ _28332) ^ [_31420, _31422, _31424] : [apart_point_and_line(_31424, _31422), -(distinct_lines(_31422, _31420)), -(apart_point_and_line(_31424, _31420))], (4 ^ _28332) ^ [_28472] : [distinct_lines(_28472, _28472)], (18 ^ _28332) ^ [_28994, _28996, _28998] : [distinct_lines(_28998, _28996), -(distinct_lines(_28998, _28994)), -(distinct_lines(_28996, _28994))], (28 ^ _28332) ^ [_29318, _29320, _29322] : [convergent_lines(_29322, _29320), -(convergent_lines(_29322, _29318)), -(convergent_lines(_29320, _29318))], (104 ^ _28332) ^ [_31710, _31712] : [convergent_lines(_31712, _31710), -(distinct_lines(_31712, _31710))], (6 ^ _28332) ^ [_28549] : [convergent_lines(_28549, _28549)], (2 ^ _28332) ^ [_28395] : [distinct_points(_28395, _28395)], (38 ^ _28332) ^ [_29642, _29644, _29646] : [distinct_points(_29646, _29644), apart_point_and_line(_29642, line_connecting(_29646, _29644)), 45 ^ _28332 : [(48 ^ _28332) ^ [] : [-(distinct_points(_29642, _29644))], (46 ^ _28332) ^ [] : [-(distinct_points(_29642, _29646))]]], (84 ^ _28332) ^ [_31096, _31098, _31100] : [apart_point_and_line(_31100, _31098), -(distinct_points(_31100, _31096)), -(apart_point_and_line(_31096, _31098))], (50 ^ _28332) ^ [_30048, _30050, _30052] : [convergent_lines(_30052, _30050), 55 ^ _28332 : [(58 ^ _28332) ^ [] : [apart_point_and_line(_30048, _30050)], (56 ^ _28332) ^ [] : [apart_point_and_line(_30048, _30052)]], -(distinct_points(_30048, intersection_point(_30052, _30050)))]], input).
% 43.33/42.72  ncf('1',plain,[apart_point_and_line(110 ^ [], line_connecting(109 ^ [], 111 ^ []))],start(117 ^ 0)).
% 43.33/42.72  ncf('1.1',plain,[-(apart_point_and_line(110 ^ [], line_connecting(109 ^ [], 111 ^ []))), distinct_points(109 ^ [], 110 ^ []), distinct_lines(line_connecting(109 ^ [], 111 ^ []), line_connecting(109 ^ [], 110 ^ [])), -(apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 111 ^ []))), -(apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ []))), -(apart_point_and_line(110 ^ [], line_connecting(109 ^ [], 110 ^ [])))],extension(62 ^ 1,bind([[_30467, _30469, _30471, _30473], [line_connecting(109 ^ [], 110 ^ []), line_connecting(109 ^ [], 111 ^ []), 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.1',plain,[-(distinct_points(109 ^ [], 110 ^ []))],extension(113 ^ 2)).
% 43.33/42.72  ncf('1.1.2',plain,[-(distinct_lines(line_connecting(109 ^ [], 111 ^ []), line_connecting(109 ^ [], 110 ^ []))), apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 111 ^ [])), -(apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])))],extension(94 ^ 2,bind([[_31420, _31422, _31424], [line_connecting(109 ^ [], 110 ^ []), line_connecting(109 ^ [], 111 ^ []), 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1',plain,[-(apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 111 ^ []))), distinct_points(109 ^ [], 110 ^ []), distinct_lines(line_connecting(109 ^ [], 110 ^ []), line_connecting(109 ^ [], 111 ^ [])), -(apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ []))), -(apart_point_and_line(110 ^ [], line_connecting(109 ^ [], 110 ^ []))), -(apart_point_and_line(110 ^ [], line_connecting(109 ^ [], 111 ^ [])))],extension(62 ^ 3,bind([[_30467, _30469, _30471, _30473], [line_connecting(109 ^ [], 111 ^ []), line_connecting(109 ^ [], 110 ^ []), 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.1',plain,[-(distinct_points(109 ^ [], 110 ^ []))],extension(113 ^ 4)).
% 43.33/42.72  ncf('1.1.2.1.2',plain,[-(distinct_lines(line_connecting(109 ^ [], 110 ^ []), line_connecting(109 ^ [], 111 ^ []))), apart_point_and_line(111 ^ [], line_connecting(109 ^ [], 110 ^ [])), -(apart_point_and_line(111 ^ [], line_connecting(109 ^ [], 111 ^ [])))],extension(94 ^ 4,bind([[_31420, _31422, _31424], [line_connecting(109 ^ [], 111 ^ []), line_connecting(109 ^ [], 110 ^ []), 111 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.2.1',plain,[-(apart_point_and_line(111 ^ [], line_connecting(109 ^ [], 110 ^ [])))],extension(115 ^ 5)).
% 43.33/42.72  ncf('1.1.2.1.2.2',plain,[apart_point_and_line(111 ^ [], line_connecting(109 ^ [], 111 ^ [])), distinct_points(109 ^ [], 111 ^ []), 48 : -(distinct_points(111 ^ [], 111 ^ []))],extension(38 ^ 5,bind([[_29642, _29644, _29646], [111 ^ [], 111 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.2.2.1',plain,[-(distinct_points(109 ^ [], 111 ^ [])), distinct_points(111 ^ [], 109 ^ []), -(distinct_points(111 ^ [], 111 ^ []))],extension(8 ^ 6,bind([[_28670, _28672, _28674], [111 ^ [], 109 ^ [], 111 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.2.2.1.1',plain,[-(distinct_points(111 ^ [], 109 ^ [])), distinct_points(109 ^ [], 110 ^ []), apart_point_and_line(111 ^ [], line_connecting(109 ^ [], 110 ^ []))],extension(38 ^ 7,bind([[_29642, _29644, _29646], [111 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.2.2.1.1.1',plain,[-(distinct_points(109 ^ [], 110 ^ []))],extension(113 ^ 8)).
% 43.33/42.72  ncf('1.1.2.1.2.2.1.1.2',plain,[-(apart_point_and_line(111 ^ [], line_connecting(109 ^ [], 110 ^ [])))],extension(115 ^ 8)).
% 43.33/42.72  ncf('1.1.2.1.2.2.1.2',plain,[distinct_points(111 ^ [], 111 ^ [])],extension(2 ^ 7,bind([[_28395], [111 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.2.2.2',plain,[distinct_points(111 ^ [], 111 ^ [])],extension(2 ^ 8,bind([[_28395], [111 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.3',plain,[apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])), distinct_points(109 ^ [], 110 ^ []), 48 : -(distinct_points(109 ^ [], 110 ^ []))],extension(38 ^ 4,bind([[_29642, _29644, _29646], [109 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.3.1',plain,[-(distinct_points(109 ^ [], 110 ^ []))],lemmata('[2, 1, 1].x')).
% 43.33/42.72  ncf('1.1.2.1.3.2',plain,[distinct_points(109 ^ [], 110 ^ []), apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])), 46 : -(distinct_points(109 ^ [], 109 ^ []))],extension(38 ^ 7,bind([[_29642, _29644, _29646], [109 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.3.2.1',plain,[-(apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])))],reduction('1.1.2.1')).
% 43.33/42.72  ncf('1.1.2.1.3.2.2',plain,[distinct_points(109 ^ [], 109 ^ [])],extension(2 ^ 10,bind([[_28395], [109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.4',plain,[apart_point_and_line(110 ^ [], line_connecting(109 ^ [], 110 ^ [])), distinct_points(109 ^ [], 110 ^ []), 48 : -(distinct_points(110 ^ [], 110 ^ []))],extension(38 ^ 4,bind([[_29642, _29644, _29646], [110 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.4.1',plain,[-(distinct_points(109 ^ [], 110 ^ []))],lemmata('[2, 1, 1].x')).
% 43.33/42.72  ncf('1.1.2.1.4.2',plain,[distinct_points(110 ^ [], 110 ^ [])],extension(2 ^ 7,bind([[_28395], [110 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.1.5',plain,[apart_point_and_line(110 ^ [], line_connecting(109 ^ [], 111 ^ []))],reduction('1')).
% 43.33/42.72  ncf('1.1.2.2',plain,[apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])), distinct_points(109 ^ [], 110 ^ []), 48 : -(distinct_points(109 ^ [], 110 ^ []))],extension(38 ^ 3,bind([[_29642, _29644, _29646], [109 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.2.1',plain,[-(distinct_points(109 ^ [], 110 ^ []))],extension(113 ^ 4)).
% 43.33/42.72  ncf('1.1.2.2.2',plain,[distinct_points(109 ^ [], 110 ^ []), apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])), 46 : -(distinct_points(109 ^ [], 109 ^ []))],extension(38 ^ 6,bind([[_29642, _29644, _29646], [109 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.2.2.2.1',plain,[-(apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])))],reduction('1.1.2')).
% 43.33/42.72  ncf('1.1.2.2.2.2',plain,[distinct_points(109 ^ [], 109 ^ [])],extension(2 ^ 9,bind([[_28395], [109 ^ []]]))).
% 43.33/42.72  ncf('1.1.3',plain,[apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 111 ^ [])), distinct_points(109 ^ [], 111 ^ []), 48 : -(distinct_points(109 ^ [], 111 ^ []))],extension(38 ^ 2,bind([[_29642, _29644, _29646], [109 ^ [], 111 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1',plain,[-(distinct_points(109 ^ [], 111 ^ [])), distinct_points(109 ^ [], 110 ^ []), -(distinct_points(110 ^ [], 111 ^ []))],extension(8 ^ 3,bind([[_28670, _28672, _28674], [111 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.1',plain,[-(distinct_points(109 ^ [], 110 ^ []))],extension(113 ^ 4)).
% 43.33/42.72  ncf('1.1.3.1.2',plain,[distinct_points(110 ^ [], 111 ^ []), -(distinct_points(110 ^ [], 110 ^ [])), -(distinct_points(111 ^ [], 110 ^ []))],extension(8 ^ 4,bind([[_28670, _28672, _28674], [110 ^ [], 111 ^ [], 110 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.1',plain,[distinct_points(110 ^ [], 110 ^ []), -(distinct_points(110 ^ [], 110 ^ [])), -(distinct_points(110 ^ [], 110 ^ []))],extension(8 ^ 5,bind([[_28670, _28672, _28674], [110 ^ [], 110 ^ [], 110 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.1.1',plain,[distinct_points(110 ^ [], 110 ^ []), -(distinct_points(110 ^ [], 110 ^ [])), -(distinct_points(110 ^ [], 110 ^ []))],extension(8 ^ 6,bind([[_28670, _28672, _28674], [110 ^ [], 110 ^ [], 110 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.1.1.1',plain,[distinct_points(110 ^ [], 110 ^ [])],extension(2 ^ 7,bind([[_28395], [110 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.1.1.2',plain,[distinct_points(110 ^ [], 110 ^ [])],extension(2 ^ 7,bind([[_28395], [110 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.1.2',plain,[distinct_points(110 ^ [], 110 ^ [])],extension(2 ^ 6,bind([[_28395], [110 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.2',plain,[distinct_points(111 ^ [], 110 ^ []), -(distinct_points(111 ^ [], 109 ^ [])), -(distinct_points(110 ^ [], 109 ^ []))],extension(8 ^ 5,bind([[_28670, _28672, _28674], [109 ^ [], 110 ^ [], 111 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.2.1',plain,[distinct_points(111 ^ [], 109 ^ []), -(distinct_points(111 ^ [], 111 ^ [])), -(distinct_points(109 ^ [], 111 ^ []))],extension(8 ^ 6,bind([[_28670, _28672, _28674], [111 ^ [], 109 ^ [], 111 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.2.1.1',plain,[distinct_points(111 ^ [], 111 ^ [])],extension(2 ^ 7,bind([[_28395], [111 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.2.1.2',plain,[distinct_points(109 ^ [], 111 ^ [])],reduction('1.1.3')).
% 43.33/42.72  ncf('1.1.3.1.2.2.2',plain,[distinct_points(110 ^ [], 109 ^ []), -(distinct_points(110 ^ [], 110 ^ [])), -(distinct_points(109 ^ [], 110 ^ []))],extension(8 ^ 6,bind([[_28670, _28672, _28674], [110 ^ [], 109 ^ [], 110 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.2.2.1',plain,[distinct_points(110 ^ [], 110 ^ [])],extension(2 ^ 7,bind([[_28395], [110 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.2.2.2',plain,[distinct_points(109 ^ [], 110 ^ []), apart_point_and_line(111 ^ [], line_connecting(109 ^ [], 110 ^ [])), 46 : -(distinct_points(111 ^ [], 109 ^ []))],extension(38 ^ 7,bind([[_29642, _29644, _29646], [111 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.1.2.2.2.2.1',plain,[-(apart_point_and_line(111 ^ [], line_connecting(109 ^ [], 110 ^ [])))],extension(115 ^ 8)).
% 43.33/42.72  ncf('1.1.3.1.2.2.2.2.2',plain,[distinct_points(111 ^ [], 109 ^ [])],lemmata('[2, 1, 3, 1, 1].x')).
% 43.33/42.72  ncf('1.1.3.2',plain,[distinct_points(109 ^ [], 111 ^ []), apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 111 ^ [])), 46 : -(distinct_points(109 ^ [], 109 ^ []))],extension(38 ^ 5,bind([[_29642, _29644, _29646], [109 ^ [], 111 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.3.2.1',plain,[-(apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 111 ^ [])))],reduction('1.1')).
% 43.33/42.72  ncf('1.1.3.2.2',plain,[distinct_points(109 ^ [], 109 ^ [])],extension(2 ^ 8,bind([[_28395], [109 ^ []]]))).
% 43.33/42.72  ncf('1.1.4',plain,[apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])), distinct_points(109 ^ [], 110 ^ []), 48 : -(distinct_points(109 ^ [], 110 ^ []))],extension(38 ^ 2,bind([[_29642, _29644, _29646], [109 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.4.1',plain,[-(distinct_points(109 ^ [], 110 ^ []))],lemmata('[1].x')).
% 43.33/42.72  ncf('1.1.4.2',plain,[distinct_points(109 ^ [], 110 ^ []), apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])), 46 : -(distinct_points(109 ^ [], 109 ^ []))],extension(38 ^ 5,bind([[_29642, _29644, _29646], [109 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.4.2.1',plain,[-(apart_point_and_line(109 ^ [], line_connecting(109 ^ [], 110 ^ [])))],reduction('1.1')).
% 43.33/42.72  ncf('1.1.4.2.2',plain,[distinct_points(109 ^ [], 109 ^ [])],extension(2 ^ 8,bind([[_28395], [109 ^ []]]))).
% 43.33/42.72  ncf('1.1.5',plain,[apart_point_and_line(110 ^ [], line_connecting(109 ^ [], 110 ^ [])), distinct_points(109 ^ [], 110 ^ []), 48 : -(distinct_points(110 ^ [], 110 ^ []))],extension(38 ^ 2,bind([[_29642, _29644, _29646], [110 ^ [], 110 ^ [], 109 ^ []]]))).
% 43.33/42.72  ncf('1.1.5.1',plain,[-(distinct_points(109 ^ [], 110 ^ []))],lemmata('[1].x')).
% 43.33/42.72  ncf('1.1.5.2',plain,[distinct_points(110 ^ [], 110 ^ [])],extension(2 ^ 5,bind([[_28395], [110 ^ []]]))).
% 43.33/42.72  %-----------------------------------------------------
% 43.33/42.72  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------