%--------------------------------------------------------------------------
% File     : SET126-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Domain   : Set Theory
% Problem  : Relation to singleton
% Version  : [Qua92] axioms.
% English  :

% Refs     : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% Source   : [Quaife]
% Names    : SB3 [Quaife]

% Status   : Unsatisfiable
% Rating   : 0.55 v9.0.0, 0.60 v8.2.0, 0.62 v8.1.0, 0.63 v7.4.0, 0.59 v7.3.0, 0.58 v7.1.0, 0.50 v7.0.0, 0.60 v6.3.0, 0.55 v6.2.0, 0.60 v6.1.0, 0.71 v6.0.0, 0.80 v5.5.0, 0.95 v5.4.0, 0.90 v5.3.0, 0.94 v5.2.0, 0.88 v5.0.0, 0.86 v4.1.0, 0.85 v4.0.1, 0.82 v3.7.0, 0.70 v3.5.0, 0.82 v3.4.0, 0.83 v3.3.0, 0.79 v3.2.0, 0.77 v3.1.0, 0.82 v2.7.0, 0.92 v2.6.0, 0.67 v2.5.0, 0.73 v2.4.0, 0.88 v2.3.0, 1.00 v2.1.0
% Syntax   : Number of clauses     :   93 (  31 unt;   8 nHn;  63 RR)
%            Number of literals    :  183 (  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    :   40 (  40 usr;   9 con; 0-3 aty)
%            Number of variables   :  178 (  25 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments : The 'set builder' problems, of which this is one, do not appear
%            in [Qua92]. In Quaife's development, these problems appear
%            between the SINGLETON and the ORDERED PAIRS problems of [Qu92].
%            However, in order to correspond to the paper, these theorems
%            have not been used in the augmented versions of the subsequent
%            problems in [Qua92].
%          : Not in [Qua92].
%          : Used as a demodulator by Quaife.
% Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
%--------------------------------------------------------------------------
%----Include von Neuman-Bernays-Godel set theory axioms
include('Axioms/SET004-0.ax').
%--------------------------------------------------------------------------
%----(SBDEF1): definition of set builder.
cnf(definition_of_set_builder,axiom,
    union(singleton(X),Y) = set_builder(X,Y) ).

cnf(prove_set_builder_and_singleton_1,negated_conjecture,
    set_builder(x,null_class) != singleton(x) ).

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