Maximal Models and Refutation Completeness: Semidecision Procedures in Automatic Theorem Proving*

In recent years the idea of using electronic computers to search for proofs of theorems of quantification theory has drawn considerable attention. One of the more successful methods of attack on the problem has stemmed from the work of Quine [12], Gilmore [5], Davis and Putnam [4] and J. Alan Robinson [16]. This paper is concerned with a portion of the theory underlying an extension of this line of development to systems — first-order theories with equality — in which there is a distinguished relation symbol for equality. The field of mathematics upon which we have concentrated our computer experiments in order to study various properties of our procedure is first-order group theory.