## TPTP Problem File: RAL001^1.p

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```%------------------------------------------------------------------------------
% File     : RAL001^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Quadratic functions)
% Problem  : Chart System Math I+A Blue Book, Problem 07CB1E014
% 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-1A-Blue-07CB1E014.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45321 (2209 equality;22705 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39616 ( 104   ~; 233   |;1173   &;35980   @)
%                                         (1095 <=>;1031  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1247 (1199   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8058 (  66 sgn;7085   !; 431   ?; 406   ^)
%                                         (8058   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1976 (   6 prd;   9 fun;  23 num;1938 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: PA; Level: 4; Author: Munehiro Kobayashi;
%            Generated: 2015-01-07
%            ^ [V_x_dot_0: \$real] :
%              ( ( \$lesseq @ -3.0 @ V_x_dot_0 )
%              & ( \$lesseq @ V_x_dot_0 @ 5.0 ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p1_qustion,conjecture,
( 'find/1' @ \$real
@ ( ^ [V_x: \$real] :
? [V_f: 'Equation',V_k: \$real] :
( ( V_f
= ( 'poly-equation/1' @ ( 'cons/2' @ \$real @ ( \$sum @ ( \$sum @ ( '^/2' @ V_k @ 2.0 ) @ ( \$product @ 3.0 @ V_k ) ) @ -9.0 ) @ ( 'cons/2' @ \$real @ V_k @ ( 'cons/2' @ \$real @ 1.0 @ ( 'nil/0' @ \$real ) ) ) ) ) )
& ( 'is-solution-of/2' @ V_x @ V_f ) ) ) )).
%------------------------------------------------------------------------------
```