## TPTP Problem File: RAL024^1.p

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```%------------------------------------------------------------------------------
% File     : RAL024^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Simultaneous equations)
% Problem  : International Mathematical Olympiad, 1965, Problem 4
% Version  : [Mat16] axioms : Especial.
% English  : Find all sets of four real numbers x_1, x_2, x_3, x_4 such that
%            the sum of any one and the product of the other three is equal
%            to 2.

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : IMO-1965-4.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45349 (2213 equality;22720 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39637 ( 104   ~; 233   |;1176   &;35998   @)
%                                         (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   : 8060 (  66 sgn;7085   !; 433   ?; 406   ^)
%                                         (8060   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1978 (   6 prd;   9 fun;  23 num;1940 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: RCF; Score: 6; Author: Jumma Kudo;
%            Generated: 2014-12-17
%            ^ [V_xyzw_dot_0: ( 'ListOf' @ \$real )] :
%              ( ( V_xyzw_dot_0
%                = ( 'cons/2' @ \$real @ 1.0 @ ( 'cons/2' @ \$real @ 1.0 @ ( 'cons/2' @ \$real @ 1.0 @ ( 'cons/2' @ \$real @ 1.0 @ ( 'nil/0' @ \$real ) ) ) ) ) )
%              | ( V_xyzw_dot_0
%                = ( 'cons/2' @ \$real @ 3.0 @ ( 'cons/2' @ \$real @ -1.0 @ ( 'cons/2' @ \$real @ -1.0 @ ( 'cons/2' @ \$real @ -1.0 @ ( 'nil/0' @ \$real ) ) ) ) ) )
%              | ( V_xyzw_dot_0
%                = ( 'cons/2' @ \$real @ -1.0 @ ( 'cons/2' @ \$real @ 3.0 @ ( 'cons/2' @ \$real @ -1.0 @ ( 'cons/2' @ \$real @ -1.0 @ ( 'nil/0' @ \$real ) ) ) ) ) )
%              | ( V_xyzw_dot_0
%                = ( 'cons/2' @ \$real @ -1.0 @ ( 'cons/2' @ \$real @ -1.0 @ ( 'cons/2' @ \$real @ 3.0 @ ( 'cons/2' @ \$real @ -1.0 @ ( 'nil/0' @ \$real ) ) ) ) ) )
%              | ( V_xyzw_dot_0
%                = ( 'cons/2' @ \$real @ -1.0 @ ( 'cons/2' @ \$real @ -1.0 @ ( 'cons/2' @ \$real @ -1.0 @ ( 'cons/2' @ \$real @ 3.0 @ ( 'nil/0' @ \$real ) ) ) ) ) ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p_qustion,conjecture,
( 'find/1' @ ( 'ListOf' @ \$real )
@ ^ [V_xyzw: ( 'ListOf' @ \$real )] :
? [V_x: \$real,V_y: \$real,V_z: \$real,V_w: \$real] :
( ( V_xyzw
= ( 'cons/2' @ \$real @ V_x @ ( 'cons/2' @ \$real @ V_y @ ( 'cons/2' @ \$real @ V_z @ ( 'cons/2' @ \$real @ V_w @ ( 'nil/0' @ \$real ) ) ) ) ) )
& ( ( \$sum @ V_x @ ( \$product @ V_y @ ( \$product @ V_z @ V_w ) ) )
= 2.0 )
& ( ( \$sum @ V_y @ ( \$product @ V_x @ ( \$product @ V_z @ V_w ) ) )
= 2.0 )
& ( ( \$sum @ V_z @ ( \$product @ V_y @ ( \$product @ V_x @ V_w ) ) )
= 2.0 )
& ( ( \$sum @ V_w @ ( \$product @ V_y @ ( \$product @ V_z @ V_x ) ) )
= 2.0 ) ) )).

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