%--------------------------------------------------------------------------
% File     : SET019-3 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Set Theory
% Problem  : Two sets that contain one another are equal
% Version  : [BL+86] axioms : Augmented.
% English  :

% Refs     : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% Source   : [BL+86]
% Names    : Lemma 4 [BL+86]

% Status   : Unsatisfiable
% Rating   : 0.45 v9.0.0, 0.50 v8.2.0, 0.48 v8.1.0, 0.47 v7.5.0, 0.53 v7.4.0, 0.59 v7.3.0, 0.58 v7.1.0, 0.50 v7.0.0, 0.40 v6.3.0, 0.36 v6.2.0, 0.30 v6.1.0, 0.43 v6.0.0, 0.50 v5.5.0, 0.60 v5.3.0, 0.61 v5.2.0, 0.56 v5.1.0, 0.59 v5.0.0, 0.50 v4.1.0, 0.38 v4.0.1, 0.36 v3.7.0, 0.20 v3.5.0, 0.27 v3.4.0, 0.50 v3.2.0, 0.31 v3.1.0, 0.36 v2.7.0, 0.33 v2.6.0, 0.30 v2.5.0, 0.42 v2.4.0, 0.33 v2.2.1, 0.44 v2.2.0, 0.33 v2.1.0, 0.56 v2.0.0
% Syntax   : Number of clauses     :  147 (  14 unt;  20 nHn; 124 RR)
%            Number of literals    :  372 (  54 equ; 209 neg)
%            Maximal clause size   :    8 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   14 (  13 usr;   0 prp; 1-5 aty)
%            Number of functors    :   61 (  61 usr;   8 con; 0-5 aty)
%            Number of variables   :  331 (  30 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%--------------------------------------------------------------------------
%----Include Godel's set axioms
include('Axioms/SET003-0.ax').
%--------------------------------------------------------------------------
%----Previously proved lemmas are added at each step
cnf(first_components_are_equal,axiom,
    ( ~ little_set(X)
    | ~ little_set(U)
    | ordered_pair(X,Y) != ordered_pair(U,V)
    | X = U ) ).

cnf(left_cancellation,axiom,
    ( ~ little_set(X)
    | ~ little_set(Y)
    | non_ordered_pair(Z,X) != non_ordered_pair(Z,Y)
    | X = Y ) ).

cnf(second_components_are_equal,axiom,
    ( ~ little_set(X)
    | ~ little_set(Y)
    | ~ little_set(U)
    | ~ little_set(V)
    | ordered_pair(X,Y) != ordered_pair(U,V)
    | Y = V ) ).

cnf(a_contains_b,hypothesis,
    subset(b,a) ).

cnf(b_contains_a,hypothesis,
    subset(a,b) ).

cnf(prove__a_equals_b,negated_conjecture,
    a != b ).

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