## TPTP Problem File: SEU466^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU466^1 : TPTP v7.1.0. Released v3.6.0.
% Domain   : Set Theory (Binary relations)
% Problem  : The transitive closure operator is idempotent
% Version  : [Nei08] axioms.
% English  :

% Refs     : [BN99]  Baader & Nipkow (1999), Term Rewriting and All That
%          : [Nei08] Neis (2008), Email to Geoff Sutcliffe
% Source   : [Nei08]
% Names    :

% Status   : Theorem
% Rating   : 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.60 v5.3.0, 0.80 v5.2.0, 0.60 v4.1.0, 0.67 v4.0.0, 1.00 v3.7.0
% Syntax   : Number of formulae    :   59 (   0 unit;  29 type;  29 defn)
%            Number of atoms       :  251 (  33 equality; 158 variable)
%            Maximal formula depth :   12 (   7 average)
%            Number of connectives :  159 (   4   ~;   4   |;  12   &; 123   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  197 ( 197   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  29   :;   0   =)
%            Number of variables   :   86 (   0 sgn;  38   !;   5   ?;  43   ^)
%                                         (  86   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : Some proofs can be found in chapter 2 of [BN99]
%          :
%------------------------------------------------------------------------------
%----Include axioms of binary relations
include('Axioms/SET009^0.ax').
%------------------------------------------------------------------------------
thf(transitive_closure_op_is_idempotent,conjecture,
( idem @ tc )).

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