## TPTP Problem File: SEV010^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV010^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM260
% Version  : Especial.
% English  : An equivalence relation defines a partition.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0512 [Bro09]
%          : THM260 [TPS]

% Status   : Theorem
% Rating   : 0.55 v7.5.0, 0.57 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v6.1.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   54 (   1 equality;  53 variable)
%            Maximal formula depth :   19 (  10 average)
%            Number of connectives :   51 (   0   ~;   0   |;  10   &;  30   @)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   21 (   0 sgn;  16   !;   5   ?;   0   ^)
%                                         (  21   :;   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_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 ) ) )
=> ( ! [Xp: a > \$o] :
( ( ? [Xz: a] :
( Xp @ Xz )
& ! [Xx: a] :
( ( Xp @ Xx )
=> ! [Xy: a] :
( ( Xp @ Xy )
<=> ( R @ Xx @ Xy ) ) ) )
=> ? [Xz: a] :
( Xp @ Xz ) )
& ! [Xx: a] :
? [Xp: a > \$o] :
( ? [Xz: a] :
( Xp @ Xz )
& ! [Xx0: a] :
( ( Xp @ Xx0 )
=> ! [Xy: a] :
( ( Xp @ Xy )
<=> ( R @ Xx0 @ Xy ) ) )
& ( Xp @ Xx )
& ! [Xq: a > \$o] :
( ( ? [Xz: a] :
( Xq @ Xz )
& ! [Xx0: a] :
( ( Xq @ Xx0 )
=> ! [Xy: a] :
( ( Xq @ Xy )
<=> ( R @ Xx0 @ Xy ) ) )
& ( Xq @ Xx ) )
=> ( Xq = Xp ) ) ) ) ) )).

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