## TPTP Problem File: MSC030^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : MSC030^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Miscellaneous (Pigeon-hole principle)
% Problem  : International Mathematical Olympiad, 1964, Problem 4
% Version  : [Mat16] axioms : Especial.
% English  : Seventeen people correspond by mail with one another - each one
%            with all the rest. In their letters only three different topics
%            are discussed.  Each pair of correspondents deals with only one
%            of these topics.  Prove that there are at least three people who
%            write to each other about the same topic.

% Refs     : [Mat16] Matsuzaki (2016), Email to Geoff Sutcliffe
%          : [MI+16] Matsuzaki et al. (2016), Race against the Teens - Benc
% Source   : [Mat16]
% Names    : IMO-1964-4.p [Mat16]

% Status   : Theorem
% Rating   : ? v7.0.0
% Syntax   : Number of formulae    : 3485 (   0 unit;1199 type;   0 defn)
%            Number of atoms       : 45415 (2210 equality;22741 variable)
%            Maximal formula depth :   35 (   9 average)
%            Number of connectives : 39715 ( 104   ~; 233   |;1184   &;36064   @)
%                                         (1095 <=>;1035  =>;   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   : 8069 (  66 sgn;7091   !; 437   ?; 405   ^)
%                                         (8069   :; 136  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
%            Arithmetic symbols    : 1987 (   6 prd;   9 fun;  24 num;1948 var)
% SPC      : TH1_THM_EQU_ARI

% Comments : Theory: PA(comb); Score: 6; Author: Takuya Matsuzaki;
%            Generated: 2015-01-24
%------------------------------------------------------------------------------
include('Axioms/MAT001^0.ax').
%------------------------------------------------------------------------------
thf(p,conjecture,(
! [V_G: ( 'ListOf' @ ( 'Triple' @ \$int @ \$int @ \$int ) )] :
( ( ! [V_abt: ( 'Triple' @ \$int @ \$int @ \$int )] :
( ( 'member/2' @ ( 'Triple' @ \$int @ \$int @ \$int ) @ V_abt @ V_G )
=> ? [V_a_dot_0: \$int,V_b_dot_0: \$int,V_t_dot_0: \$int] :
( ( V_abt
= ( 'triple/3' @ \$int @ \$int @ \$int @ V_a_dot_0 @ V_b_dot_0 @ V_t_dot_0 ) )
& ( \$lesseq @ 1 @ V_a_dot_0 )
& ( \$less @ V_a_dot_0 @ V_b_dot_0 )
& ( \$lesseq @ V_b_dot_0 @ 17 )
& ( \$lesseq @ 1 @ V_t_dot_0 )
& ( \$lesseq @ V_t_dot_0 @ 3 ) ) )
& ! [V_a: \$int,V_b: \$int] :
( ( ( \$lesseq @ 1 @ V_a )
& ( \$less @ V_a @ V_b )
& ( \$lesseq @ V_b @ 17 ) )
=> ( ? [V_t: \$int] :
( 'member/2' @ ( 'Triple' @ \$int @ \$int @ \$int ) @ ( 'triple/3' @ \$int @ \$int @ \$int @ V_a @ V_b @ V_t ) @ V_G )
& ! [V_t1: \$int,V_t2: \$int] :
( ( ( 'member/2' @ ( 'Triple' @ \$int @ \$int @ \$int ) @ ( 'triple/3' @ \$int @ \$int @ \$int @ V_a @ V_b @ V_t1 ) @ V_G )
& ( 'member/2' @ ( 'Triple' @ \$int @ \$int @ \$int ) @ ( 'triple/3' @ \$int @ \$int @ \$int @ V_a @ V_b @ V_t2 ) @ V_G ) )
=> ( V_t1 = V_t2 ) ) ) ) )
=> ? [V_a_dot_1: \$int,V_b_dot_1: \$int,V_c: \$int,V_t_dot_1: \$int] :
( ( 'member/2' @ ( 'Triple' @ \$int @ \$int @ \$int ) @ ( 'triple/3' @ \$int @ \$int @ \$int @ V_a_dot_1 @ V_b_dot_1 @ V_t_dot_1 ) @ V_G )
& ( 'member/2' @ ( 'Triple' @ \$int @ \$int @ \$int ) @ ( 'triple/3' @ \$int @ \$int @ \$int @ V_b_dot_1 @ V_c @ V_t_dot_1 ) @ V_G )
& ( 'member/2' @ ( 'Triple' @ \$int @ \$int @ \$int ) @ ( 'triple/3' @ \$int @ \$int @ \$int @ V_c @ V_a_dot_1 @ V_t_dot_1 ) @ V_G ) ) ) )).

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