The Creation and Use of a Knowledge Baseof

IPR is an automatic theorem-proving system intended particularly for use in higher-level mathematics. It discovers the proofs of theorems in mathematics applying known theorems and deenitions. Theorems and deenitions are stored in the knowledge base in the form of sequents rather than formulas or rewrite rules. Because there is more easily-accessible information in a sequent than there is in the formula it represents, a simple algorithm can be used to search the knowledge base for the most useful theorem or deenition to be used in the theorem-proving process. This paper describes how the sequents in the knowledge base are formed from theorems stated by the user and how the knowledge base is used in the theorem-proving process. An example of a theorem proved and the English proof output are also given.