## TPTP Problem File: SEV175^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV175^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem THM144A
% Version  : Especial.
% English  : A lemma for the Injective Cantor Theorem X5309.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0230 [Bro09]
%          : THM144A [TPS]

% Status   : Theorem
% Rating   : 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   14 (   2 equality;  12 variable)
%            Maximal formula depth :   12 (  12 average)
%            Number of connectives :   11 (   2   ~;   0   |;   2   &;   7   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :    4 (   0 sgn;   1   !;   2   ?;   1   ^)
%                                         (   4   :;   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(cTHM144A_pme,conjecture,(
! [Xh: ( \$i > \$o ) > \$i] :
? [Xt: \$i > \$o] :
( ~ ( Xt @ ( Xh @ Xt ) )
& ( ( Xh
@ ^ [Xz: \$i] :
? [Xt0: \$i > \$o] :
( ~ ( Xt0 @ ( Xh @ Xt0 ) )
& ( Xz
= ( Xh @ Xt0 ) ) ) )
= ( Xh @ Xt ) ) ) )).

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