The Unit Proof and the Input Proof in Theorem Proving

Abstract

A resolution in which one of the two parent clauses is a unit clause is called a unit resolution, whereas a resolution in which one of the two parent clauses is an original input clause is called an input resolution. A unit (input) proof is a deduction of the empty clause □ such that every resolution in the deduction is a unit (input) resolution. It is proved in the paper that a set S of clauses containing its unit factors has a unit proof if and only if S has an input proof. A LISP program implementing unit resolution is described and results of experiments are given.