## TPTP Problem File: SEV164^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV164^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM185
% Version  : Especial.
% English  : Basic theorem about representing relations in terms of ordered
%            pairs.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0224 [Bro09]
%          : THM149 [TPS]
%          : THM185 [TPS]

% Status   : Theorem
% Rating   : 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.2.0, 0.50 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :    8 (   0 equality;   8 variable)
%            Maximal formula depth :    9 (   6 average)
%            Number of connectives :    7 (   0   ~;   0   |;   0   &;   6   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    8 (   2 sgn;   1   !;   3   ?;   4   ^)
%                                         (   8   :;   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(cTHM185_pme,conjecture,(
! [Xr: a > a > \$o] :
( ? [Xx: a,Xy: a] :
( Xr @ Xx @ Xy )
<=> ? [Xp: ( a > a > a ) > a] :
( Xr
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy ) ) ) )).

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