## TPTP Problem File: SEV011^5.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SEV011^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM260-B
% Version  : Especial.
% English  : An equivalence relation defines a partition.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0541 [Bro09]
%          : THM260-B [TPS]

% Status   : Theorem
% Rating   : 0.38 v7.1.0, 0.62 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   39 (   1 equality;  38 variable)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :   36 (   0   ~;   0   |;   6   &;  22   @)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   14 (   0 sgn;  13   !;   1   ?;   0   ^)
%                                         (  14   :;   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(cTHM260_B_pme,conjecture,(
! [R: a > a > \$o] :
( ( ! [Xx: a] :
( R @ Xx @ Xx )
& ! [Xx: a,Xy: a] :
( ( R @ Xx @ Xy )
=> ( R @ Xy @ Xx ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) )
=> ! [Xx: a] :
? [Xp: a > \$o] :
( ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ! [Xy: a] :
( ( Xp @ Xy )
<=> ( R @ Xx0 @ Xy ) ) )
& ( Xp @ Xx )
& ! [Xq: a > \$o] :
( ( ! [Xx0: a] :
( ( Xq @ Xx0 )
=> ! [Xy: a] :
( ( Xq @ Xy )
<=> ( R @ Xx0 @ Xy ) ) )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) ) ) )).

%------------------------------------------------------------------------------