‘Set’ is a tool that is used frequently in designing computer programs. Because of the reason, ‘set constraints languages’ have been developed recently. In this research, we introduce ‘(Ab)(Cl) set unification’ problem and implement it using the ‘set equation rewriting in Prolog’. In this research we shows that the set unification, that is considered to be difficult to be implemented in procedural languages, ran be implemented easily using the non-deterministic control structure and the list data structure in logic language like Prolog. Our research uses the Ciao Prolog with GNU GPL, this is compared with other existing implementations which used expensive commercial Prolog, so anyone can use the result freely. Currently the result is being used for implementing a set constraint language.