Proving Definite Clauses without Explicit Use of Inductions

We propose an algorithm to prove a definite clause is modeled by an intended minimal model of a set of definite clauses. In the algorithm, no induction scheme will be used explicitly, although in effect a mathematical induction is implied. This algorithm corresponds to an inductionless induction method using the Knuth-Bendix algorithm in an equation problem. It resembles the completion algorithm, but in fact it is a completely different algorithm.