%--------------------------------------------------------------------------
% File     : SET001-1 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Set Theory
% Axioms   : Membership and union
% Version  : [LS74] axioms.
% English  :

% Refs     : [LS74]  Lawrence & Starkey (1974), Experimental tests of resol
% Source   : [SPRFN]
% Names    : Problem 118 [LS74]

% Status   : Satisfiable
% Syntax   : Number of clauses     :    6 (   0 unt;   2 nHn;   5 RR)
%            Number of literals    :   20 (   0 equ;  10 neg)
%            Maximal clause size   :    4 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 2-3 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 3-3 aty)
%            Number of variables   :   21 (   2 sgn)
% SPC      : 

% Comments : Requires SET001-0.ax
%--------------------------------------------------------------------------
cnf(member_of_union_is_member_of_one_set,axiom,
    ( ~ union(Set1,Set2,Union)
    | ~ member(Element,Union)
    | member(Element,Set1)
    | member(Element,Set2) ) ).

cnf(member_of_set1_is_member_of_union,axiom,
    ( ~ union(Set1,Set2,Union)
    | ~ member(Element,Set1)
    | member(Element,Union) ) ).

cnf(member_of_set2_is_member_of_union,axiom,
    ( ~ union(Set1,Set2,Union)
    | ~ member(Element,Set2)
    | member(Element,Union) ) ).

cnf(union_axiom1,axiom,
    ( union(Set1,Set2,Union)
    | member(g(Set1,Set2,Union),Set1)
    | member(g(Set1,Set2,Union),Set2)
    | member(g(Set1,Set2,Union),Union) ) ).

cnf(union_axiom2,axiom,
    ( ~ member(g(Set1,Set2,Union),Set1)
    | ~ member(g(Set1,Set2,Union),Union)
    | union(Set1,Set2,Union) ) ).

cnf(union_axiom3,axiom,
    ( ~ member(g(Set1,Set2,Union),Set2)
    | ~ member(g(Set1,Set2,Union),Union)
    | union(Set1,Set2,Union) ) ).

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