Using a Theorem Prover for Reasoning on Constraint Problems

Specifications of constraint problems can be considered logical formulae. As a consequence, it is possible to infer their properties by means of automated reasoning tools, with the goal of automatically synthesizing transformations that can make the solving process more efficient. The purpose of this paper is to link two important technologies: automated theorem proving and constraint programming. We report the results on using ATP technology for checking existence of symmetries, checking whether a given formula breaks a symmetry, and checking existence of functional dependencies in a specification. The output of the reasoning phase is a transformed constraint program, consisting in a reformulated specification and, possibly a search strategy. We show our techniques on problems such as Graph coloring, Sailco inventory and Protein folding.