TPTP Axioms File: SET001-2.ax


%--------------------------------------------------------------------------
% File     : SET001-2 : TPTP v8.1.0. Released v1.0.0.
% Domain   : Set Theory
% Axioms   : Membership and intersection
% 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;   4 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_intersection_is_member_of_set1,axiom,
    ( ~ intersection(Set1,Set2,Intersection)
    | ~ member(Element,Intersection)
    | member(Element,Set1) ) ).

cnf(member_of_intersection_is_member_of_set2,axiom,
    ( ~ intersection(Set1,Set2,Intersection)
    | ~ member(Element,Intersection)
    | member(Element,Set2) ) ).

cnf(member_of_both_is_member_of_intersection,axiom,
    ( ~ intersection(Set1,Set2,Intersection)
    | ~ member(Element,Set2)
    | ~ member(Element,Set1)
    | member(Element,Intersection) ) ).

cnf(intersection_axiom1,axiom,
    ( member(h(Set1,Set2,Intersection),Intersection)
    | intersection(Set1,Set2,Intersection)
    | member(h(Set1,Set2,Intersection),Set1) ) ).

cnf(intersection_axiom2,axiom,
    ( member(h(Set1,Set2,Intersection),Intersection)
    | intersection(Set1,Set2,Intersection)
    | member(h(Set1,Set2,Intersection),Set2) ) ).

cnf(intersection_axiom3,axiom,
    ( ~ member(h(Set1,Set2,Intersection),Intersection)
    | ~ member(h(Set1,Set2,Intersection),Set2)
    | ~ member(h(Set1,Set2,Intersection),Set1)
    | intersection(Set1,Set2,Intersection) ) ).

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