TPTP Problem File: SEV166^5.p

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```%------------------------------------------------------------------------------
% File     : SEV166^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM182
% Version  : Especial.
% English  : Basic theorem about pairing.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0458 [Bro09]
%          : THM182 [TPS]

% Status   : Theorem
% Rating   : 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   13 (   3 equality;  10 variable)
%            Maximal formula depth :   10 (   6 average)
%            Number of connectives :    6 (   0   ~;   0   |;   1   &;   4   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   1   :;   0   =)
%            Number of variables   :    6 (   0 sgn;   4   !;   0   ?;   2   ^)
%                                         (   6   :;   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(cTHM182_pme,conjecture,(
! [Xx: a,Xy: a,Xu: a,Xv: a] :
( ( ( ^ [Xg: a > a > a] :
( Xg @ Xx @ Xy ) )
= ( ^ [Xg: a > a > a] :
( Xg @ Xu @ Xv ) ) )
<=> ( ( Xx = Xu )
& ( Xy = Xv ) ) ) )).

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