## TPTP Problem File: SEV063^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV063^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM136
% Version  : Especial.
% English  : The transitive closure of a relation is transitive.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0372 [Bro09]
%          : THM136 [TPS]

% Status   : Theorem
% Rating   : 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.2.0, 0.25 v5.1.0, 0.50 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   54 (   0 equality;  54 variable)
%            Maximal formula depth :   17 (  10 average)
%            Number of connectives :   53 (   0   ~;   0   |;   7   &;  36   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   22 (   0 sgn;  22   !;   0   ?;   0   ^)
%                                         (  22   :;   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(a_type,type,(
a: \$tType )).

thf(cTHM136_pme,conjecture,(
! [Xr: a > a > \$o,Xx: a,Xy: a,Xz: a] :
( ( ! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xr @ Xx0 @ Xy0 )
=> ( Xp @ Xx0 @ Xy0 ) )
& ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) ) )
=> ( Xp @ Xx @ Xy ) )
& ! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xr @ Xx0 @ Xy0 )
=> ( Xp @ Xx0 @ Xy0 ) )
& ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) ) )
=> ( Xp @ Xy @ Xz ) ) )
=> ! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xr @ Xx0 @ Xy0 )
=> ( Xp @ Xx0 @ Xy0 ) )
& ! [Xx0: a,Xy0: a,Xz0: a] :
( ( ( Xp @ Xx0 @ Xy0 )
& ( Xp @ Xy0 @ Xz0 ) )
=> ( Xp @ Xx0 @ Xz0 ) ) )
=> ( Xp @ Xx @ Xz ) ) ) )).

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