## TPTP Problem File: RAL017^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : RAL017^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Algebraic curves)
% Problem  : Chart System Math III+C Blue Book, Problem 09CBCE013
% Version  : [Mat16] axioms : Especial.
% English  :

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : Chart-3C-Blue-09CBCE013.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45385 (2214 equality;22743 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39671 ( 105   ~; 234   |;1185   &;36021   @)
%                                         (1095 <=>;1031  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1246 (1199   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8069 (  66 sgn;7085   !; 439   ?; 409   ^)
%                                         (8069   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1982 (   6 prd;   9 fun;  23 num;1944 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: RCF; Level: 4; Author: Munehiro Kobayashi;
%            Generated: 2015-01-01
%            ^ [V_max_dot_0: \$real] :
%              ( V_max_dot_0
%              = ( \$product @ ( \$quotient @ ( 'sqrt/1' @ 3.0 ) @ 9.0 ) @ 'Pi/0' ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p_qustion,conjecture,
( 'find/1' @ \$real
@ ^ [V_max: \$real] :
? [V_A: '2d.Point',V_B: '2d.Point',V_C: '2d.Point'] :
( ( ( '2d.distance/2' @ V_A @ V_B )
= ( '2d.distance/2' @ V_A @ V_C ) )
& ( 2.0
= ( '2d.distance/2' @ V_B @ V_C ) )
& ( '2d.is-right/1' @ ( '2d.angle/3' @ V_C @ V_A @ V_B ) )
& ( 'maximum/2'
@ ( 'set-by-def/1' @ \$real
@ ^ [V_v: \$real] :
? [V_F1: '2d.Point',V_F2: '2d.Point',V_x0: \$real,V_y0: \$real,V_a: \$real,V_b: \$real,V_E: '2d.Shape'] :
( ( V_E
= ( '2d.set-of-cfun/1'
@ ^ [V_x: \$real,V_y: \$real] :
( 1.0
= ( \$sum @ ( '^/2' @ ( \$quotient @ ( \$difference @ V_x @ V_x0 ) @ V_a ) @ 2.0 ) @ ( '^/2' @ ( \$quotient @ ( \$difference @ V_y @ V_y0 ) @ V_b ) @ 2.0 ) ) ) ) )
& ( \$less @ 0.0 @ V_a )
& ( \$less @ 0.0 @ V_b )
& ( '2d.is-focus-of/2' @ V_F1 @ V_E )
& ( '2d.is-focus-of/2' @ V_F2 @ V_E )
& ( V_F1 != V_F2 )
& ( ( '2d.parallel/2' @ ( '2d.line/2' @ V_F1 @ V_F2 ) @ ( '2d.line/2' @ V_B @ V_C ) )
| ( '2d.perpendicular/2' @ ( '2d.line/2' @ V_F1 @ V_F2 ) @ ( '2d.line/2' @ V_B @ V_C ) ) )
& ( '2d.tangent/2' @ V_E @ ( '2d.line/2' @ V_A @ V_B ) )
& ( '2d.tangent/2' @ V_E @ ( '2d.line/2' @ V_B @ V_C ) )
& ( '2d.tangent/2' @ V_E @ ( '2d.line/2' @ V_C @ V_A ) )
& ( V_v
= ( '2d.area-of/1' @ V_E ) ) ) )
@ V_max ) ) )).

%------------------------------------------------------------------------------
```