## TPTP Problem File: SEV273^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV273^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem THM542
% Version  : Especial.
% English  : A well-ordering is reflexive.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0569 [Bro09]
%          : THM542 [TPS]

% Status   : Theorem
% Rating   : 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   22 (   1 equality;  18 variable)
%            Maximal formula depth :   14 (   7 average)
%            Number of connectives :   19 (   0   ~;   0   |;   3   &;  11   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    7 (   0 sgn;   5   !;   2   ?;   0   ^)
%                                         (   7   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_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(cR,type,(
cR: a > a > \$o )).

thf(cTHM542_pme,conjecture,
( ! [X: a > \$o] :
( ? [Xz: a] :
( X @ Xz )
=> ? [Xz: a] :
( ( X @ Xz )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xz @ Xx ) )
& ! [Xy: a] :
( ( ( X @ Xy )
& ! [Xx: a] :
( ( X @ Xx )
=> ( cR @ Xy @ Xx ) ) )
=> ( Xy = Xz ) ) ) )
=> ! [Xx: a] :
( cR @ Xx @ Xx ) )).

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