## TPTP Axioms File: SET001-1.ax

```%--------------------------------------------------------------------------
% File     : SET001-1 : TPTP v7.5.0. 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 (   2 non-Horn;   0 unit;   5 RR)
%            Number of atoms      :   20 (   0 equality)
%            Maximal clause size  :    4 (   3 average)
%            Number of predicates :    2 (   0 propositional; 2-3 arity)
%            Number of functors   :    1 (   0 constant; 3-3 arity)
%            Number of variables  :   21 (   2 singleton)
%            Maximal term depth   :    2 (   1 average)
% SPC      :

%--------------------------------------------------------------------------
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) )).

%--------------------------------------------------------------------------
```