## TPTP Problem File: MSC007^1.003.004.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : MSC007^1.003.004 : TPTP v7.5.0. Released v5.4.0.
% Domain   : Miscellaneous
% Problem  : Cook pigeon-hole problem, 4 pigeons and 3 holes
% Version  : Especial.
% English  : Suppose there are N holes and more pigeons to put in the
%            holes. Every pigeon is in a hole and no hole contains more
%            than one pigeon. Prove that some pigoen has no hole.

% Refs     : [Bro12] Brown (2012), Email to G. Sutcliffe
% Source   : [Bro12]
% Names    :

% Status   : Theorem
% Rating   : 0.64 v7.5.0, 0.57 v7.4.0, 0.89 v7.2.0, 0.88 v7.1.0, 1.00 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0
% Syntax   : Number of formulae    :   18 (   0 unit;  10 type;   0 defn)
%            Number of atoms       :   34 (   8 equality;   9 variable)
%            Maximal formula depth :    6 (   3 average)
%            Number of connectives :   17 (   7   ~;   0   |;   3   &;   6   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10   :;   0   =)
%            Number of variables   :    4 (   0 sgn;   2   !;   2   ?;   0   ^)
%                                         (   4   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

%------------------------------------------------------------------------------
thf(hole,type,(
hole: \$tType )).

thf(pigeon,type,(
pigeon: \$tType )).

thf(hole1,type,(
hole1: hole )).

thf(hole2,type,(
hole2: hole )).

thf(hole3,type,(
hole3: hole )).

thf(pigeon1,type,(
pigeon1: pigeon )).

thf(pigeon2,type,(
pigeon2: pigeon )).

thf(pigeon3,type,(
pigeon3: pigeon )).

thf(pigeon4,type,(
pigeon4: pigeon )).

thf(pigeon_hole_t,type,(
pigeon_hole: pigeon > hole )).

thf(holecover,axiom,(
! [P: hole > \$o] :
( ( ( P @ hole1 )
& ( P @ hole2 )
& ( P @ hole3 ) )
=> ! [X: hole] :
( P @ X ) ) )).

thf(pigeon1pigeon2,axiom,(
pigeon1 != pigeon2 )).

thf(pigeon1pigeon3,axiom,(
pigeon1 != pigeon3 )).

thf(pigeon2pigeon3,axiom,(
pigeon2 != pigeon3 )).

thf(pigeon1pigeon4,axiom,(
pigeon1 != pigeon4 )).

thf(pigeon2pigeon4,axiom,(
pigeon2 != pigeon4 )).

thf(pigeon3pigeon4,axiom,(
pigeon3 != pigeon4 )).

% thf(one_in_a_hole,axiom,(
%     ! [X: pigeon,Y: pigeon] :
%       ( ( ( pigeon_hole @ X )
%         = ( pigeon_hole @ Y ) )
%      => ( X = Y ) ) )).

thf(sharing_a_hole,conjecture,(
? [X: pigeon,Y: pigeon] :
( ( ( pigeon_hole @ X )
= ( pigeon_hole @ Y ) )
& ( X != Y ) ) )).

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