## TPTP Problem File: SEV433^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV433^1 : TPTP v7.5.0. Released v5.2.0.
% Domain   : Set Theory
% Problem  : There are at most 2 individuals if there is an injection into o
% Version  : Especial.
% English  :

% Refs     : [Bro11] Brown (2011), Email to Geoff Sutcliffe
% Source   : [Bro11]
% Names    : INJO [Bro11]

% Status   : Theorem
% Rating   : 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% Syntax   : Number of formulae    :    3 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   17 (   5 equality;  10 variable)
%            Maximal formula depth :    7 (   5 average)
%            Number of connectives :    5 (   0   ~;   2   |;   0   &;   2   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    5 (   0 sgn;   5   !;   0   ?;   0   ^)
%                                         (   5   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

%------------------------------------------------------------------------------
thf(f,type,(
f: \$i > \$o )).

thf(finj,axiom,(
! [X: \$i,Y: \$i] :
( ( ( f @ X )
= ( f @ Y ) )
=> ( X = Y ) ) )).

thf(less3,conjecture,(
! [X: \$i,Y: \$i,Z: \$i] :
( ( X = Y )
| ( X = Z )
| ( Y = Z ) ) )).

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