%--------------------------------------------------------------------------
% File     : SET021-3 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Set Theory
% Problem  : 2nd is unique when x is an ordered pair of sets
% Version  : [BL+86] axioms : Augmented.
% English  :

% Refs     : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% Source   : [BL+86]
% Names    : Lemma 6 [BL+86]

% Status   : Unsatisfiable
% Rating   : 0.85 v8.2.0, 0.95 v7.5.0, 1.00 v7.3.0, 0.83 v7.0.0, 1.00 v6.4.0, 0.87 v6.3.0, 1.00 v6.0.0, 0.90 v5.5.0, 0.95 v5.3.0, 0.94 v5.2.0, 1.00 v2.0.0
% Syntax   : Number of clauses     :  149 (  14 unt;  20 nHn; 126 RR)
%            Number of literals    :  378 (  56 equ; 213 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   :  335 (  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(two_sets_equal,axiom,
    ( ~ subset(X,Y)
    | ~ subset(Y,X)
    | X = Y ) ).

cnf(property_of_first,axiom,
    ( ~ little_set(X)
    | ~ little_set(Y)
    | first(ordered_pair(X,Y)) = X ) ).

cnf(a_little_set,hypothesis,
    little_set(a) ).

cnf(b_little_set,hypothesis,
    little_set(b) ).

cnf(prove_second_is_second,negated_conjecture,
    second(ordered_pair(a,b)) != b ).

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