Disproving False Conjectures

Abstract

For automatic theorem provers it is as important to disprove false conjectures as it is to prove true ones, especially if it is not known ahead of time if a formula is derivable inside a particular inference system. Situations of this kind occur frequently in inductive theorem proving systems where failure is a common mode of operation. This paper describes an abstraction mechanism for first-order logic over an arbitrary but fixed term algebra to second-order monadic logic with 0 successor functions. The decidability of second-order monadic logic together with our notion of abstraction yields an elegant criterion that characterizes a subclass of unprovable conjectures.