## TPTP Problem File: SEV122^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV122^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM530
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0494 [Bro09]
%          : THM530 [TPS]

% Status   : Theorem
% Rating   : 0.09 v7.5.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   23 (   1 equality;  22 variable)
%            Maximal formula depth :   15 (   8 average)
%            Number of connectives :   20 (   0   ~;   0   |;   2   &;  14   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   14 (   1 sgn;   8   !;   2   ?;   4   ^)
%                                         (  14   :;   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(cTHM530_pme,conjecture,(
! [PROP: ( a > a > \$o ) > \$o,F: ( a > a > \$o ) > \$o] :
( ( ^ [Xx: a,Xy: a] :
! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ? [R: a > a > \$o] :
( R @ Xx0 @ Xy0 )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) )
= ( ^ [Xx: a,Xy: a] :
! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ? [R: a > a > \$o] :
( R @ Xx0 @ Xy0 )
=> ( Xp @ Xx0 @ Xy0 ) )
& ( PROP @ Xp ) )
=> ( Xp @ Xx @ Xy ) ) ) ) )).

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