## TPTP Problem File: RAL023^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : RAL023^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Simultaneous equations)
% Problem  : International Mathematical Olympiad, 1963, Problem 4
% Version  : [Mat16] axioms : Especial.
% English  : Find all solutions x_1, x_2, x_3, x_4, x_5 of the system
%            x_5 + x_2 = y x_1; x_1 + x_3 = y x_2; x_2 + x_4 = y x_3;
%            x_3 + x_5 = y x_4; x_4 + x_1 = y x_5, where y is a parameter.

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : IMO-1963-4.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3486 (   0 unit;1200 type;   0 defn)
%            Number of atoms       : 45351 (2214 equality;22720 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39637 ( 104   ~; 233   |;1177   &;35997   @)
%                                         (1095 <=>;1031  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2408 (2408   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1247 (1200   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8061 (  66 sgn;7085   !; 434   ?; 406   ^)
%                                         (8061   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1979 (   6 prd;   9 fun;  23 num;1941 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: RCF; Score: 6; Author: Jumma Kudo;
%            Generated: 2014-12-16
%            ^ [V_x1x2x3x4x5_dot_0: ( 'ListOf' @ \$real )] :
%              ( ( ( ( \$difference @ ( \$sum @ ( '^/2' @ 'y/0' @ 2.0 ) @ 'y/0' ) @ 1.0 )
%                  = 0.0 )
%                & ? [V_s_dot_0: \$real,V_t: \$real] :
%                    ( V_x1x2x3x4x5_dot_0
%                    = ( 'cons/2' @ \$real @ V_s_dot_0 @ ( 'cons/2' @ \$real @ V_t @ ( 'cons/2' @ \$real @ ( \$sum @ ( \$uminus @ V_s_dot_0 ) @ ( \$product @ 'y/0' @ V_t ) ) @ ( 'cons/2' @ \$real @ ( \$uminus @ ( \$sum @ ( \$product @ ( \$difference @ ( '^/2' @ 'y/0' @ 2.0 ) @ 1.0 ) @ V_s_dot_0 ) @ ( \$product @ 'y/0' @ V_t ) ) ) @ ( 'cons/2' @ \$real @ ( \$difference @ ( \$product @ 'y/0' @ V_s_dot_0 ) @ V_t ) @ ( 'nil/0' @ \$real ) ) ) ) ) ) ) )
%              | ( ( 'y/0' = 2.0 )
%                & ? [V_s: \$real] :
%                    ( V_x1x2x3x4x5_dot_0
%                    = ( 'cons/2' @ \$real @ V_s @ ( 'cons/2' @ \$real @ V_s @ ( 'cons/2' @ \$real @ V_s @ ( 'cons/2' @ \$real @ V_s @ ( 'cons/2' @ \$real @ V_s @ ( 'nil/0' @ \$real ) ) ) ) ) ) ) )
%              | ( V_x1x2x3x4x5_dot_0
%                = ( 'cons/2' @ \$real @ 0.0 @ ( 'cons/2' @ \$real @ 0.0 @ ( 'cons/2' @ \$real @ 0.0 @ ( 'cons/2' @ \$real @ 0.0 @ ( 'cons/2' @ \$real @ 0.0 @ ( 'nil/0' @ \$real ) ) ) ) ) ) ) ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf('y/0_type',type,(
'y/0': \$real )).

thf(p_qustion,conjecture,
( 'find/1' @ ( 'ListOf' @ \$real )
@ ^ [V_x1x2x3x4x5: ( 'ListOf' @ \$real )] :
? [V_x1: \$real,V_x2: \$real,V_x3: \$real,V_x4: \$real,V_x5: \$real] :
( ( V_x1x2x3x4x5
= ( 'cons/2' @ \$real @ V_x1 @ ( 'cons/2' @ \$real @ V_x2 @ ( 'cons/2' @ \$real @ V_x3 @ ( 'cons/2' @ \$real @ V_x4 @ ( 'cons/2' @ \$real @ V_x5 @ ( 'nil/0' @ \$real ) ) ) ) ) ) )
& ( ( \$sum @ V_x2 @ V_x5 )
= ( \$product @ 'y/0' @ V_x1 ) )
& ( ( \$sum @ V_x1 @ V_x3 )
= ( \$product @ 'y/0' @ V_x2 ) )
& ( ( \$sum @ V_x2 @ V_x4 )
= ( \$product @ 'y/0' @ V_x3 ) )
& ( ( \$sum @ V_x3 @ V_x5 )
= ( \$product @ 'y/0' @ V_x4 ) )
& ( ( \$sum @ V_x4 @ V_x1 )
= ( \$product @ 'y/0' @ V_x5 ) ) ) )).

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