Automatic Derivation of the Irrationality of e

Abstract

As part of a project on automatic generation of proofs involving both logic and computation, we have automatically generated a proof of the irrationality of e. The proof involves inequalities, bounds on infinite series, type distinctions (between real numbers and natural numbers), a subproof by mathematical induction, and significant mathematical steps, including correct simplification of expressions involving factorials and summing an infinite geometrical series. Metavariables are instantiated by inference rules embodying mathematical knowledge, rather than only by unification. The proof is generated completely automatically, without any interactive component.