TPTP Problem File: RAL034^1.p

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```%------------------------------------------------------------------------------
% File     : RAL034^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Real Algebra (Functions)
% Problem  : International Mathematical Olympiad, 1988, Problem 3
% Version  : [Mat16] axioms : Especial.
% English  : A function f is defined on the positive integers by
%            f(1) = 1, f(3) = 3,f(2n) = f(n), f(4n + 1) = 2f(2n + 1) - f(n),
%            f(4n + 3) = 3f(2n + 1) - 2f(n), for all positive integers n.
%            Determine the number of positive integers n, less than or equal
%            to 1988, for which f(n) = n.

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : IMO-1988-3.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45368 (2216 equality;22725 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39649 ( 104   ~; 233   |;1178   &;36006   @)
%                                         (1095 <=>;1033  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 2409 (2409   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1246 (1199   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   : 8060 (  66 sgn;7087   !; 430   ?; 407   ^)
%                                         (8060   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1978 (   6 prd;   9 fun;  23 num;1940 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: ZF; Score: 7; Author: Yiyang Zhan;
%            Generated: 2015-02-02
%            ^ [V_ans_dot_0: \$int] : ( V_ans_dot_0 = 92 ) )
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p_qustion,conjecture,
( 'find/1' @ \$int
@ ^ [V_ans: \$int] :
? [V_f: ( \$int > \$int )] :
( ! [V_n_dot_1: \$int] :
( ( \$lesseq @ V_n_dot_1 @ 0 )
=> ( ( V_f @ V_n_dot_1 )
= 0 ) )
& ( ( V_f @ 1 )
= 1 )
& ( ( V_f @ 3 )
= 3 )
& ! [V_n_dot_0: \$int] :
( ( \$greater @ V_n_dot_0 @ 0 )
=> ( ( ( V_f @ ( \$product @ 2 @ V_n_dot_0 ) )
= ( V_f @ V_n_dot_0 ) )
& ( ( V_f @ ( \$sum @ ( \$product @ 4 @ V_n_dot_0 ) @ 1 ) )
= ( \$difference @ ( \$product @ 2 @ ( V_f @ ( \$sum @ ( \$product @ 2 @ V_n_dot_0 ) @ 1 ) ) ) @ ( V_f @ V_n_dot_0 ) ) )
& ( ( V_f @ ( \$sum @ ( \$product @ 4 @ V_n_dot_0 ) @ 3 ) )
= ( \$difference @ ( \$product @ 3 @ ( V_f @ ( \$sum @ ( \$product @ 2 @ V_n_dot_0 ) @ 1 ) ) ) @ ( \$product @ 2 @ ( V_f @ V_n_dot_0 ) ) ) ) ) )
& ( V_ans
= ( 'int.cardinality-of/1'
@ ( 'set-by-def/1' @ \$int
@ ^ [V_n: \$int] :
( ( V_f @ V_n )
= V_n ) ) ) ) ) )).

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