## TPTP Problem File: SEV161^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV161^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM183
% Version  : Especial.
% English  : Basic theorem about pairing.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0071 [Bro09]
%          : THM183 [TPS]

% Status   : Theorem
% Rating   : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :    6 (   0 equality;   6 variable)
%            Maximal formula depth :    7 (   4 average)
%            Number of connectives :    5 (   0   ~;   0   |;   0   &;   4   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   3   !;   0   ?;   0   ^)
%                                         (   3   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cTHM183_pme,conjecture,(
! [Xr: a > a > \$o,Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
<=> ( Xr @ Xx @ Xy ) ) )).

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