%--------------------------------------------------------------------------
% File     : SET707+4 : TPTP v8.2.0. Released v2.2.0.
% Domain   : Set Theory (Naive)
% Problem  : Components of equal ordered pairs are equal
% Version  : [Pas99] axioms.
% English  : If {{A},{A,B}} = {{U},{U,V}} then A = U and B = V.

% Refs     : [Pas99] Pastre (1999), Email to G. Sutcliffe
% Source   : [Pas99]
% Names    :

% Status   : Theorem
% Rating   : 0.47 v7.5.0, 0.53 v7.4.0, 0.43 v7.3.0, 0.52 v7.1.0, 0.48 v7.0.0, 0.50 v6.4.0, 0.58 v6.3.0, 0.54 v6.2.0, 0.68 v6.1.0, 0.80 v6.0.0, 0.78 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0, 0.70 v5.1.0, 0.71 v5.0.0, 0.67 v4.1.0, 0.65 v4.0.1, 0.70 v4.0.0, 0.71 v3.7.0, 0.75 v3.5.0, 0.74 v3.3.0, 0.71 v3.2.0, 0.64 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.86 v2.5.0, 0.88 v2.4.0, 0.75 v2.3.0, 0.67 v2.2.1
% Syntax   : Number of formulae    :   12 (   1 unt;   0 def)
%            Number of atoms       :   32 (   5 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   22 (   2   ~;   2   |;   5   &)
%                                         (  10 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   0 prp; 2-2 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :   32 (  31   !;   1   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Include set theory definitions
include('Axioms/SET006+0.ax').
%--------------------------------------------------------------------------
fof(thI50,conjecture,
    ! [A,B,U,V] :
      ( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
     => ( A = U
        & B = V ) ) ).

%--------------------------------------------------------------------------