An integral theorem prover and the role of proof planning

An investigation is made into the ways proof planning can enhance the capability of a rule based prover for the theory of integration. The integrals are of the Riemann type and are defined in a way to maximize the theorem proving methods of predicate calculus. Approximately fifty theorems have been proved and several examples are discussed. A major shortcoming was found to be the inability of the system to work with or produce a proof plan. As a result, a planning scheme based on the idea of subgoals or milestones was considered. With user defined plans, there was a substantial increase in performance and capability of the system and, in some cases, proofs which were previously unsuccessful were completed.