Abstract
The last few years have seen the advent of a new breed of decision procedures for various fragments of rst-order logic based on propositional abstraction. A lazy satisabilit y checker for a given fragment of rst-order logic invokes a theory-specic decision procedure (a theory solver) on a (partial) model for the abstraction. If the model is found to be consistent in the given theory, then a model for the original formula has been found. Otherwise, a renemen t of the propositional abstraction is extracted from the proof of inconsistency and the search is resumed. We describe a theory solver for integer dier ence logic that is eectiv e when the formula to be decided contains equality and disequality (negated equality) constraints so that the decision problem partakes of the nature of the pigeonhole problem. We propose a reduction of the problem to propositional satisabilit y by computing bounds on a sucien t subset of solutions, and present experimental evidence for the eciency of this approach.
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