TPTP Problem File: GEO377^1.p
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% File : GEO377^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Geometry (Triangles)
% Problem : International Mathematical Olympiad, 1959, Problem 4
% Version : [Mat16] axioms : Especial.
% English : Construct a right triangle with given hypotenuse c such that the
% median drawn to the hypotenuse is the geometric mean of the two
% legs of the triangle.
% Refs : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
% : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source : [Mat16]
% Names : IMO-1959-4.p [Mat16]
% Status : Theorem
% Rating : ? v7.0.0
% Syntax : Number of formulae : 3486 ( 728 unt;1200 typ; 0 def)
% Number of atoms : 6796 (2211 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 39623 ( 104 ~; 233 |;1177 &;35983 @)
% (1095 <=>;1031 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Number arithmetic : 4464 ( 372 atm;1204 fun; 952 num;1936 var)
% Number of types : 40 ( 36 usr; 3 ari)
% Number of type conns : 2408 (2408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1215 (1172 usr; 69 con; 0-9 aty)
% Number of variables : 8059 ( 406 ^;7085 !; 432 ?;8059 :)
% ( 136 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_ARI
% Comments : Theory: RCF; Score: 5; Author: Yiyang Zhan;
% Generated: 2015-01-29
% : Answer
% ^ [V_X_dot_0: '2d.Shape'] :
% ? [V_alpha: $real,V_beta: $real,V_c0: $real,V_c1: $real] :
% ( ( ( $sum @ ( '^/2' @ V_alpha @ 2.0 ) @ ( '^/2' @ V_beta @ 2.0 ) )
% = 1.0 )
% & ( $greater @ 'c/0' @ 0.0 )
% & ( ( V_X_dot_0
% = ( '2d.triangle/3' @ ( '2d.vec-translate/2' @ ( '2d.point/2' @ V_c0 @ V_c1 ) @ ( '2d.mv*/2' @ ( '2d.matrix/4' @ V_alpha @ ( $uminus @ V_beta ) @ V_beta @ V_alpha ) @ ( '2d.vec2d/2' @ ( $uminus @ ( $quotient @ 'c/0' @ 2.0 ) ) @ 0.0 ) ) ) @ ( '2d.vec-translate/2' @ ( '2d.point/2' @ V_c0 @ V_c1 ) @ ( '2d.mv*/2' @ ( '2d.matrix/4' @ V_alpha @ ( $uminus @ V_beta ) @ V_beta @ V_alpha ) @ ( '2d.vec2d/2' @ ( $quotient @ 'c/0' @ 2.0 ) @ 0.0 ) ) ) @ ( '2d.vec-translate/2' @ ( '2d.point/2' @ V_c0 @ V_c1 ) @ ( '2d.mv*/2' @ ( '2d.matrix/4' @ V_alpha @ ( $uminus @ V_beta ) @ V_beta @ V_alpha ) @ ( '2d.vec2d/2' @ ( $product @ ( $quotient @ ( 'sqrt/1' @ 3.0 ) @ 4.0 ) @ 'c/0' ) @ ( $quotient @ 'c/0' @ 4.0 ) ) ) ) ) )
% | ( V_X_dot_0
% = ( '2d.triangle/3' @ ( '2d.vec-translate/2' @ ( '2d.point/2' @ V_c0 @ V_c1 ) @ ( '2d.mv*/2' @ ( '2d.matrix/4' @ V_alpha @ ( $uminus @ V_beta ) @ V_beta @ V_alpha ) @ ( '2d.vec2d/2' @ ( $uminus @ ( $quotient @ 'c/0' @ 2.0 ) ) @ 0.0 ) ) ) @ ( '2d.vec-translate/2' @ ( '2d.point/2' @ V_c0 @ V_c1 ) @ ( '2d.mv*/2' @ ( '2d.matrix/4' @ V_alpha @ ( $uminus @ V_beta ) @ V_beta @ V_alpha ) @ ( '2d.vec2d/2' @ ( $quotient @ 'c/0' @ 2.0 ) @ 0.0 ) ) ) @ ( '2d.vec-translate/2' @ ( '2d.point/2' @ V_c0 @ V_c1 ) @ ( '2d.mv*/2' @ ( '2d.matrix/4' @ V_alpha @ ( $uminus @ V_beta ) @ V_beta @ V_alpha ) @ ( '2d.vec2d/2' @ ( $uminus @ ( $product @ ( $quotient @ ( 'sqrt/1' @ 3.0 ) @ 4.0 ) @ 'c/0' ) ) @ ( $quotient @ 'c/0' @ 4.0 ) ) ) ) ) ) ) ) )
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include('Axioms/MAT001^0.ax').
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thf('c/0_type',type,
'c/0': $real ).
thf(p_qustion,conjecture,
( 'find/1' @ '2d.Shape'
@ ^ [V_X: '2d.Shape'] :
? [V_A: '2d.Point',V_B: '2d.Point',V_C: '2d.Point'] :
( ( '2d.is-triangle/3' @ V_A @ V_B @ V_C )
& ( V_X
= ( '2d.triangle/3' @ V_A @ V_B @ V_C ) )
& ( '2d.is-right/1' @ ( '2d.angle/3' @ V_A @ V_B @ V_C ) )
& ( $greater @ 'c/0' @ 0.0 )
& ( ( '2d.distance/2' @ V_A @ V_C )
= 'c/0' )
& ( ( '2d.distance^2/2' @ V_B @ ( '2d.midpoint-of/2' @ V_A @ V_C ) )
= ( $product @ ( '2d.distance/2' @ V_A @ V_B ) @ ( '2d.distance/2' @ V_B @ V_C ) ) ) ) ) ).
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