TPTP Problem File: GEO414^1.p
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% File : GEO414^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Geometry (Transformational geometry)
% Problem : International Mathematical Olympiad, 1992, Problem 4
% Version : [Mat16] axioms : Especial.
% English : In the plane let C be a circle, L a line tangent to the circle C,
% and M a point on L. Find the locus of all points P with the
% following property: there exists two points Q, R on L such that
% M is the midpoint of QR and C is the inscribed circle of triangle
% PQR.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1992-4.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3487 ( 726 unt;1201 typ; 0 def)
% Number of atoms : 6834 (2213 equ; 0 cnn)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 39628 ( 104 ~; 233 |;1181 &;35984 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4467 ( 373 atm;1203 fun; 955 num;1936 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1218 (1175 usr; 72 con; 0-9 aty)
% Number of variables : 8062 ( 407 ^;7085 !; 434 ?;8062 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF; Score: 7; Author: Munehiro Kobayashi;
% Generated: 2014-11-13
% : Answer
% ^ [V_answer_dot_0: '2d.Shape'] :
% ( ( $less @ 0.0 @ 'r/0' )
% & ? [V_C_dot_0: '2d.Shape',V_L_dot_0: '2d.Shape',V_lp: '2d.Shape',V_M_dot_0: '2d.Point',V_X: '2d.Point',V_Y: '2d.Point',V_Z: '2d.Point',V_U: '2d.Point'] :
% ( ( V_C_dot_0
% = ( '2d.circle/2' @ ( '2d.point/2' @ 0.0 @ 'r/0' ) @ 'r/0' ) )
% & ( V_answer_dot_0
% = ( '2d.shape-of-cpfun/1'
% @ ^ [V_p: '2d.Point'] :
% ( '2d.on/2' @ V_p @ ( '2d.inner-part-of/1' @ ( '2d.half-line/2' @ V_Z @ V_U ) ) ) ) )
% & ( V_L_dot_0 = '2d.x-axis/0' )
% & ( '2d.tangent/3' @ V_L_dot_0 @ V_C_dot_0 @ V_X )
% & ( '2d.is-diameter-of/2' @ ( '2d.seg/2' @ V_X @ V_Z ) @ V_C_dot_0 )
% & ( V_M_dot_0
% = ( '2d.point/2' @ 'Mx/0' @ 0.0 ) )
% & ( '2d.on/2' @ V_Y @ V_L_dot_0 )
% & ( '2d.point-symmetry/3' @ V_X @ V_Y @ V_M_dot_0 )
% & ( V_lp
% = ( '2d.line/2' @ V_Y @ V_Z ) )
% & ( '2d.point-symmetry/3' @ V_Y @ V_U @ V_Z ) ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
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thf('Mx/0_type',type,
'Mx/0': $real ).
thf('r/0_type',type,
'r/0': $real ).
thf(p_qustion,conjecture,
( 'find/1' @ '2d.Shape'
@ ^ [V_answer: '2d.Shape'] :
( ( $less @ 0.0 @ 'r/0' )
& ? [V_L: '2d.Shape',V_C: '2d.Shape',V_M: '2d.Point'] :
( ( V_L = '2d.x-axis/0' )
& ( V_C
= ( '2d.circle/2' @ ( '2d.point/2' @ 0.0 @ 'r/0' ) @ 'r/0' ) )
& ( $less @ 0.0 @ 'r/0' )
& ( V_M
= ( '2d.point/2' @ 'Mx/0' @ 0.0 ) )
& ( V_answer
= ( '2d.shape-of-cpfun/1'
@ ^ [V_P: '2d.Point'] :
? [V_Q: '2d.Point',V_R: '2d.Point'] :
( ( '2d.on/2' @ V_Q @ V_L )
& ( '2d.on/2' @ V_R @ V_L )
& ( V_M
= ( '2d.midpoint-of/2' @ V_Q @ V_R ) )
& ( '2d.is-triangle/3' @ V_P @ V_Q @ V_R )
& ( '2d.is-inscribed-in/2' @ V_C @ ( '2d.triangle/3' @ V_P @ V_Q @ V_R ) ) ) ) ) ) ) ) ).
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