Compatibility and Complexity of Refinements of the Resolution Principle

This paper studies a number of logically complete search strategies (refinements) for improving the performance of automatic theorem-proving programs based on the resolution principle. These strategies restrict the number of deductions generated by the program at the expense of sometimes missing the shortest proof.By considering elementary proof-preserving transformations on resolution proof trees, (i) it is shown that the conjunction of set-of-support, resolution-with-merging, and linear form deduction is again a complete refinement; (ii) bounds are obtained on the possible increase in complexity of the proof trees when the linear form and resolution-with-merging refinements are imposed.Finally, examples are given which demonstrate the savings in time and storage when refinements are used to prove some theorems of moderate difficulty in group theory and ternary boolean algebra.