Essentially, a connection graph is merely a data structure for a set of clauses indicating possible refutations. The graph itself is not an inference system. To use the graph, one has to introduce operations on the graph. In this paper, we shall describe a method to obtain rewriting rules from the graph, and then to show that these rewriting rules can be used to generate a refutation plan that may correspond to a large number of linear resolution refutations. Using this method, many redundant resolution steps can be avoided. © 1979.