## TPTP Problem File: SEV119^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV119^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM252
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0371 [Bro09]
%          : THM252 [TPS]
%          : THM252C [TPS]

% Status   : Theorem
% Rating   : 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   45 (   1 equality;  44 variable)
%            Maximal formula depth :   22 (  12 average)
%            Number of connectives :   42 (   0   ~;   2   |;   4   &;  28   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   19 (   0 sgn;  15   !;   0   ?;   4   ^)
%                                         (  19   :;   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(a_type,type,(
a: \$tType )).

thf(cTHM252_pme,conjecture,(
! [PROP: ( a > a > \$o ) > \$o,R: a > a > \$o,S: a > a > \$o] :
( ( ^ [Xx: a,Xy: a] :
! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ( R @ Xx0 @ Xy0 )
| ( S @ Xx0 @ Xy0 ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) )
= ( ^ [Xx: a,Xy: a] :
! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( ! [Xp0: a > a > \$o] :
( ( ! [Xx1: a,Xy1: a] :
( ( R @ Xx1 @ Xy1 )
=> ( Xp0 @ Xx1 @ Xy1 ) )
& ( PROP @ Xp0 ) )
=> ( Xp0 @ Xx0 @ Xy0 ) )
| ! [Xp0: a > a > \$o] :
( ( ! [Xx1: a,Xy1: a] :
( ( S @ Xx1 @ Xy1 )
=> ( Xp0 @ Xx1 @ Xy1 ) )
& ( PROP @ Xp0 ) )
=> ( Xp0 @ Xx0 @ Xy0 ) ) )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) ) ) )).

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