## TPTP Problem File: SEU940^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU940^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Functions)
% Problem  : TPS problem THM112A
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0389 [Bro09]
%          : THM112A [TPS]
%          : THM112E [TPS]

% Status   : Theorem
% Rating   : 0.90 v7.2.0, 0.88 v7.1.0, 0.86 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v5.5.0, 0.60 v5.4.0, 0.75 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   15 (   0 equality;  15 variable)
%            Maximal formula depth :   12 (  12 average)
%            Number of connectives :   14 (   0   ~;   0   |;   3   &;   9   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :    7 (   0 sgn;   4   !;   1   ?;   2   ^)
%                                         (   7   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_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(cTHM112A_pme,conjecture,(
! [P: \$i > \$o] :
? [M: ( \$i > \$i ) > \$o] :
( ( M
@ ^ [Xx: \$i] : Xx )
& ! [G: \$i > \$i,H: \$i > \$i] :
( ( ( M @ G )
& ( M @ H ) )
=> ( ( M
@ ^ [Xx: \$i] :
( G @ ( H @ Xx ) ) )
& ! [Y: \$i] :
( ( P @ Y )
=> ( P @ ( G @ Y ) ) ) ) ) ) )).

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