Evolving combinators

One of the many abilities that distinguish a mathematician from an automated deduction system is to be able to offer appropriate expressions based on intuition and experience that are substituted for existentially quantified variables so as to simplify the problem at hand substantially. We propose to simulate this ability with a technique called genetic programming for use in automated deduction. We apply this approach to problems of combinatory logic. Our experimental results show that the approach is viable and actually produces very promising results. A comparison with the renowned theorem prover OTTER underlines the achievements.