The technique of proof plans, is explained. This technique is used to guide automatic inference in order to avoid a combinatorial explosion. Empirical research is described to test this technique in the domain of theorem proving by mathematical induction. Heuristics, adapted from the work of Boyer and Moore, have been implemented as Prolog programs, called tactics, and used to guide an inductive proof checker, Oyster. These tactics have been partially specified in a meta-logic, and the plan formation program, clam, has been used to reason with these specifications and form plans. These plans are then executed by running their associated tactics and, hence, performing an Oyster proof. Results are presented of the use of this technique on a number of standard theorems from the literature. Searching in the planning space is shown to be considerably cheaper than searching directly in Oyster's search space. The success rate on the standard theorems is high. Keywords Theorem prov...

We describe proof planning: a technique for both describing the hierarchical structure of proofs and then using this structure to guide proof attempts. When such a proof attempt fails, these failures can be analyzed and a patch formulated and applied. We also describe rippling: a powerful proof method used in proof planning. We pose and answer a number of common questions about proof planning and rippling.