## TPTP Problem File: RAL031^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : RAL031^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Functions)
% Problem  : International Mathematical Olympiad, 1978, Problem 3
% Version  : [Mat16] axioms : Especial.
% English  : The set of all positive integers is the union of two disjoint
%            subsets {f(1), f(2), ..., f(n), ...}, {g(1), g(2), ..., g(n),
%            ...}, where f(1) < f(2) < cdots < f(n) < ... g(1) < g(2) < ... <
%            g(n) < ..., and g(n) = f(f(n)) + 1 for all n >= 1.
%            Determine f(240).

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : IMO-1978-3.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45364 (2215 equality;22735 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39648 ( 105   ~; 234   |;1180   &;35997   @)
%                                         (1095 <=>;1037  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2410 (2410   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1247 (1199   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8066 (  66 sgn;7092   !; 432   ?; 406   ^)
%                                         (8066   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1984 (   6 prd;   9 fun;  24 num;1945 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: ZF; Score: 8; Author: Takuya Matsuzaki;
%            Generated: 2015-01-24
%            ^ [V_f240_dot_0: \$int] : ( V_f240_dot_0 = 388 ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p_qustion,conjecture,
( 'find/1' @ \$int
@ ^ [V_f240: \$int] :
? [V_f: ( \$int > \$int ),V_g: ( \$int > \$int )] :
( ! [V_m_dot_0: \$int,V_n_dot_4: \$int] :
( ( ( \$lesseq @ 1 @ V_m_dot_0 )
& ( \$lesseq @ 1 @ V_n_dot_4 ) )
=> ( ( V_f @ V_m_dot_0 )
!= ( V_g @ V_n_dot_4 ) ) )
& ! [V_n_dot_3: \$int] :
( ( \$lesseq @ 1 @ V_n_dot_3 )
=> ? [V_m: \$int] :
( ( ( V_f @ V_m )
= V_n_dot_3 )
| ( ( V_g @ V_m )
= V_n_dot_3 ) ) )
& ! [V_n_dot_2: \$int] :
( ( \$lesseq @ 1 @ V_n_dot_2 )
=> ( \$less @ ( V_f @ V_n_dot_2 ) @ ( V_f @ ( \$sum @ V_n_dot_2 @ 1 ) ) ) )
& ! [V_n_dot_1: \$int] :
( ( \$lesseq @ 1 @ V_n_dot_1 )
=> ( \$less @ ( V_g @ V_n_dot_1 ) @ ( V_g @ ( \$sum @ V_n_dot_1 @ 1 ) ) ) )
& ! [V_n_dot_0: \$int] :
( ( \$lesseq @ 1 @ V_n_dot_0 )
=> ( ( V_g @ V_n_dot_0 )
= ( \$sum @ ( V_f @ ( V_f @ V_n_dot_0 ) ) @ 1 ) ) )
& ! [V_n: \$int] :
( ( \$lesseq @ V_n @ 0 )
=> ( ( ( V_f @ V_n )
= 0 )
& ( ( V_g @ V_n )
= 0 ) ) )
& ( V_f240
= ( V_f @ 240 ) ) ) )).

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