## TPTP Problem File: SEU950^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU950^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Set Theory (Functions)
% Problem  : TPS problem THM573
% Version  : Especial.
% English  : Challenge from Dana Scott stemming from injective Cantor Theorem.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0576 [Bro09]
%          : THM573 [TPS]

% Status   : Theorem
% Rating   : 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   12 (   3 equality;   7 variable)
%            Maximal formula depth :    7 (   6 average)
%            Number of connectives :    5 (   0   ~;   0   |;   0   &;   3   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    5 (   0 sgn;   3   !;   2   ?;   0   ^)
%                                         (   5   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          : Polymorphic definitions expanded.
%          :
%------------------------------------------------------------------------------
thf(h,type,(
h: ( \$i > \$o ) > \$i )).

thf(cTHM573_pme,conjecture,
( ! [Xx: \$i > \$o,Xy: \$i > \$o] :
( ( ( h @ Xx )
= ( h @ Xy ) )
=> ( Xx = Xy ) )
=> ? [Xg: \$i > \$i > \$o] :
! [Y: \$i > \$o] :
? [X: \$i] :
( ( Xg @ X )
= Y ) )).

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