## TPTP Problem File: SEV138^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV138^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM150
% Version  : Especial.
% English  : The transitive closure TC2 of a relation is transitive.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0495 [Bro09]
%          : tps_1086 [Bro09]
%          : THM150 [TPS]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   42 (   0 equality;  42 variable)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :   41 (   0   ~;   0   |;   7   &;  24   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   16 (   0 sgn;  16   !;   0   ?;   0   ^)
%                                         (  16   :;   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(cTHM150_pme,conjecture,(
! [Xr: a > a > \$o,Xx: a,Xy: a,Xz: a] :
( ( ! [Xq: a > \$o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( Xr @ Xu @ Xv ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xy ) )
& ! [Xq: a > \$o] :
( ( ! [Xw: a] :
( ( Xr @ Xy @ Xw )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( Xr @ Xu @ Xv ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xz ) ) )
=> ! [Xq: a > \$o] :
( ( ! [Xw: a] :
( ( Xr @ Xx @ Xw )
=> ( Xq @ Xw ) )
& ! [Xu: a,Xv: a] :
( ( ( Xq @ Xu )
& ( Xr @ Xu @ Xv ) )
=> ( Xq @ Xv ) ) )
=> ( Xq @ Xz ) ) ) )).

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