## TPTP Problem File: SEV167^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV167^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM189
% Version  : Especial.
% English  : Basic theorem about pairing.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0493 [Bro09]
%          : THM189 [TPS]

% Status   : Theorem
% Rating   : 0.64 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.71 v6.1.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   23 (   3 equality;  20 variable)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :   16 (   0   ~;   0   |;   1   &;  12   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   15 (   4 sgn;   7   !;   0   ?;   8   ^)
%                                         (  15   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cTHM189_pme,conjecture,(
! [Xr: a > a > a > a > \$o] :
( ! [Xp: ( a > a > a ) > a,Xq: ( a > a > a ) > a] :
( ( Xr
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xp
@ ^ [Xx: a,Xy: a] : Xy )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xx )
@ ( Xq
@ ^ [Xx: a,Xy: a] : Xy ) )
=> ( Xp = Xq ) )
=> ! [Xx1: a,Xy1: a,Xx2: a,Xy2: a] :
( ( Xr @ Xx1 @ Xy1 @ Xx2 @ Xy2 )
=> ( ( Xx1 = Xx2 )
& ( Xy1 = Xy2 ) ) ) ) )).

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