Intelligent Use of a Knowledge Base in Automated Theorem Proving

The problem of automatically reasoning using a relatively large knowledge base containing axioms, deenitions and theorems from a rst-order theory has rarely been approached, because of its inherent complexity. However, mathematicians are able to select and use just the right theorem from an enourmous knowledge base when proving theorems. We demonstrate that a natural, well-motivated and simple automated method provides a powerful and successful framework for the selection of theorems from a knowledge base for use in theorem proving. This method is most useful in applications where other methods|such as rewriting procedures|are least successful. The method has been implemented in the IPR prover. We describe the method and give an example of a theorem which is extremely diicult for traditional methods and for which IPR has automatically found the proof in the presence of relatively large knowledge bases of rst-order theorems, axioms and deenitions.