## TPTP Problem File: SEV042^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV042^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM600
% Version  : Especial.
% English  : Existence of a symmetric, transitive closure (PER closure).

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0533 [Bro09]
%          : THM600 [TPS]

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   48 (   0 equality;  48 variable)
%            Maximal formula depth :   17 (  17 average)
%            Number of connectives :   47 (   0   ~;   0   |;   7   &;  32   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :   19 (   0 sgn;  18   !;   1   ?;   0   ^)
%                                         (  19   :;   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(cTHM600_pme,conjecture,(
! [Xr: \$i > \$i > \$o] :
? [Xs: \$i > \$i > \$o] :
( ! [Xa: \$i,Xb: \$i] :
( ( Xr @ Xa @ Xb )
=> ( Xs @ Xa @ Xb ) )
& ! [Xx: \$i,Xy: \$i] :
( ( Xs @ Xx @ Xy )
=> ( Xs @ Xy @ Xx ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( Xs @ Xx @ Xy )
& ( Xs @ Xy @ Xz ) )
=> ( Xs @ Xx @ Xz ) )
& ! [Xt: \$i > \$i > \$o] :
( ( ! [Xa: \$i,Xb: \$i] :
( ( Xr @ Xa @ Xb )
=> ( Xt @ Xa @ Xb ) )
& ! [Xx: \$i,Xy: \$i] :
( ( Xt @ Xx @ Xy )
=> ( Xt @ Xy @ Xx ) )
& ! [Xx: \$i,Xy: \$i,Xz: \$i] :
( ( ( Xt @ Xx @ Xy )
& ( Xt @ Xy @ Xz ) )
=> ( Xt @ Xx @ Xz ) ) )
=> ! [Xa: \$i,Xb: \$i] :
( ( Xs @ Xa @ Xb )
=> ( Xt @ Xa @ Xb ) ) ) ) )).

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