%--------------------------------------------------------------------------
% File     : SET015-2 : TPTP v9.0.0. Bugfixed v2.1.0.
% Domain   : Set Theory
% Problem  : The union of sets is commutative
% Version  : [MOW76] axioms : Especial.
%            Theorem formulation : modified.
% English  :

% Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source   : [ANL]
% Names    : union.ver1.in [ANL]

% Status   : Unsatisfiable
% Rating   : 0.55 v9.0.0, 0.42 v8.2.0, 0.29 v8.1.0, 0.14 v7.5.0, 0.17 v7.4.0, 0.33 v7.0.0, 0.38 v6.3.0, 0.29 v6.2.0, 0.11 v6.1.0, 0.14 v6.0.0, 0.43 v5.5.0, 0.38 v5.4.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.36 v5.0.0, 0.64 v4.1.0, 0.38 v4.0.1, 0.40 v4.0.0, 0.57 v3.5.0, 0.71 v3.4.0, 0.75 v3.3.0, 0.67 v3.2.0, 0.33 v3.1.0, 0.50 v2.6.0, 0.67 v2.5.0, 0.20 v2.3.0, 0.33 v2.2.1, 0.33 v2.1.0
% Syntax   : Number of clauses     :   24 (   6 unt;   3 nHn;  18 RR)
%            Number of literals    :   48 (   0 equ;  24 neg)
%            Maximal clause size   :    3 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   0 prp; 2-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   48 (   5 sgn)
% SPC      : CNF_UNS_RFO_NEQ_NHN

% Comments :
% Bugfixes : v2.1.0 - Bugfix in SET002-0.eq
%--------------------------------------------------------------------------
%----Include set axioms
include('Axioms/SET002-0.ax').
%--------------------------------------------------------------------------
cnf(a_union_b_is_c,hypothesis,
    equal_sets(union(as,bs),cs) ).

cnf(b_union_a_is_d,hypothesis,
    equal_sets(union(bs,as),ds) ).

cnf(prove_c_equals_d,negated_conjecture,
    ~ equal_sets(cs,ds) ).

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