%--------------------------------------------------------------------------
% File     : SET016-6 : TPTP v9.1.0. Bugfixed v2.1.0.
% Domain   : Set Theory
% Problem  : First components of equal ordered pairs are equal
% Version  : [Qua92] axioms.
% English  :

% Refs     : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% Source   : [Quaife]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.23 v9.1.0, 0.25 v8.2.0, 0.24 v8.1.0, 0.16 v7.5.0, 0.37 v7.4.0, 0.29 v7.3.0, 0.33 v7.1.0, 0.25 v7.0.0, 0.47 v6.3.0, 0.36 v6.2.0, 0.50 v6.1.0, 0.57 v6.0.0, 0.60 v5.5.0, 0.75 v5.3.0, 0.83 v5.2.0, 0.75 v5.1.0, 0.82 v5.0.0, 0.79 v4.1.0, 0.77 v4.0.1, 0.73 v4.0.0, 0.82 v3.7.0, 0.60 v3.5.0, 0.64 v3.4.0, 0.58 v3.3.0, 0.57 v3.2.0, 0.54 v3.1.0, 0.64 v2.7.0, 0.67 v2.6.0, 0.44 v2.5.0, 0.64 v2.4.0, 0.50 v2.2.1, 0.83 v2.2.0, 0.67 v2.1.0
% Syntax   : Number of clauses     :   94 (  32 unt;   8 nHn;  65 RR)
%            Number of literals    :  184 (  41 equ;  85 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :   10 (   9 usr;   0 prp; 1-3 aty)
%            Number of functors    :   42 (  42 usr;  12 con; 0-3 aty)
%            Number of variables   :  176 (  25 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments : OP4 uses an extra antecedent, not used in OP10. This is the
%            OP10 version.
% Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
%--------------------------------------------------------------------------
%----Include von Neuman-Bernays-Godel set theory axioms
include('Axioms/SET004-0.ax').
%--------------------------------------------------------------------------
cnf(prove_ordered_pair_determines_components1_1,negated_conjecture,
    ordered_pair(w,x) = ordered_pair(y,z) ).

cnf(prove_ordered_pair_determines_components1_2,negated_conjecture,
    member(w,universal_class) ).

%----This is the extra clause from [Qua92] for OP4
% input_clause(prove_ordered_pair_determines_components1_2a,negated_conjecture,
%     [++member(y,universal_class)]).

cnf(prove_ordered_pair_determines_components1_3,negated_conjecture,
    w != y ).

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