Automated Discovery of Inductive Theorems

Abstract

Inductive mathematical theorems have, as a rule, historically been quite difficult to prove – both for mathematics students and for auto- mated theorem provers. That said, there has been considerable progress over the past several years, within the automated reasoning community, towards proving some of these theorems. However, little work has been done thus far towards automatically discovering them. In this paper we present our methods of discovering (as well as proving) inductive theorems, within an automated system. These methods have been tested over the natural num- bers, with regards to addition and multiplication, as well as to exponents of group elements.