New Techniques that Improve MACE-style Finite Model Finding

Abstract

We describe a new method for nding nite models of unsorted rst-order logic clause sets. The method is a MACE-style method, i.e. it "attens" the rst-order clauses, and for increasing model sizes, instantiates the resulting clauses into propositional clauses which are consecutively solved by a SAT-solver. We enhance the standard method by using 4 novel techniques: term de nitions, which reduce the number of variables in attened clauses, incremental SAT, which enables reuse of search information between consecutive model sizes, static symmetry reduction, which reduces the number of isomorphic models by adding extra constraints to the SAT problem, and sort inference, which allows the symmetry reduction to be applied at a ner grain. All techniques have been implemented in a new model nder, called Paradox, with very promising results