## TPTP Problem File: RAL016^1.p

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```%------------------------------------------------------------------------------
% File     : RAL016^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Algebraic curves)
% Problem  : Chart System Math III+C Blue Book, Problem 09CBCE009
% 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-09CBCE009.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45346 (2212 equality;22714 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39637 ( 105   ~; 233   |;1177   &;35996   @)
%                                         (1095 <=>;1031  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1248 (1199   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8061 (  66 sgn;7085   !; 432   ?; 408   ^)
%                                         (8061   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1978 (   6 prd;   9 fun;  25 num;1938 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: RCF; Level: 4; Author: Munehiro Kobayashi;
%            Generated: 2015-01-01
%            ^ [V_answer_dot_0: ( ''ListOf'' @ \$real )] :
%              = ( 'cons/2' @ \$real @ 3.0 @ ( 'cons/2' @ \$real @ 0.0 @ ( 'cons/2' @ \$real @ -3.0 @ ( 'cons/2' @ \$real @ 0.0 @ ( 'nil/0' @ \$real ) ) ) ) ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p1_qustion,conjecture,
( 'find/1' @ ( 'ListOf' @ \$real )
@ ( ^ [V_answer: ( 'ListOf' @ \$real )] :
? [V_E: '2d.Shape',V_F1: '2d.Point',V_F2: '2d.Point'] :
( ( V_E
= ( '2d.set-of-cfun/1'
@ ( ^ [V_x: \$real,V_y: \$real] :
( 1.0
= ( \$sum @ ( \$quotient @ ( '^/2' @ V_x @ 2.0 ) @ 25.0 ) @ ( \$quotient @ ( '^/2' @ V_y @ 2.0 ) @ 16.0 ) ) ) ) ) )
& ( \$less @ 0.0 @ ( '2d.x-coord/1' @ V_F1 ) )
& ( V_F1 != V_F2 )
& ( '2d.is-focus-of/2' @ V_F1 @ V_E )
& ( '2d.is-focus-of/2' @ V_F2 @ V_E )