A New Class of Automated Theorem-Proving Algorithms

A procedure is defined for deriving from any statement S an infinite sequence of statements S 0 , S 1 , S 2 , S 3 , ··· such that: (a) if there exists an i such that S i is unsatisfiable, then S is unsatisfiable; (b) if S is unsatisfiable, then there exists an i such that S i is unsatisfiable; (c) for all i the Herbrand universe of S i is finite; hence, for each i the satisfiability of S i is decidable. The new algorithms are then based on the idea of generating successive S i in the sequence and testing each S i for satisfiability. Each element in the class of new algorithms is complete.