## TPTP Problem File: SEV069^6.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV069^6 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM575
% Version  : Especial.
% English  : Existence of transitive closure.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0500 [Bro09]
%          : THM575 [TPS]
%          : tps_0449 [Bro09]
%          : THM275A [TPS]

% Status   : Theorem
% Rating   : 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, 0.80 v5.4.0, 0.75 v5.1.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   36 (   0 equality;  36 variable)
%            Maximal formula depth :   15 (  15 average)
%            Number of connectives :   35 (   0   ~;   0   |;   5   &;  24   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :   15 (   0 sgn;  14   !;   1   ?;   0   ^)
%                                         (  15   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%          : Polymorphic definitions expanded.
%          :
%          : Renamed from SEV073^5
%------------------------------------------------------------------------------
thf(cTHM575_pme,conjecture,(
! [Xr: \$i > \$i > \$o] :
? [Xs: \$i > \$i > \$o] :
( ! [Xa: \$i,Xb: \$i] :
( ( Xr @ Xa @ Xb )
=> ( Xs @ Xa @ Xb ) )
& ! [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,Xz: \$i] :
( ( ( Xt @ Xx @ Xy )
& ( Xt @ Xy @ Xz ) )
=> ( Xt @ Xx @ Xz ) ) )
=> ! [Xa: \$i,Xb: \$i] :
( ( Xs @ Xa @ Xb )
=> ( Xt @ Xa @ Xb ) ) ) ) )).

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