Quantifier Instantiation Techniques for Finite Model Finding in SMT^*

Andrew Reynolds¹, Cesare Tinelli¹, Amit Goel², Sava Krsti², Morgan Deters³, and Clark Barrett³

¹Department of Computer Science, The University of Iowa, USA

²Strategic CAD Labs, Intel Corporation, USA

³New York University, USA

Abstract. SMT-based applications increasingly rely on SMT solvers being able to deal with quantified formulas. Current work shows that for formulas with quantifiers over uninterpreted sorts counter-models can be obtained by integrating a finite model finding capability into the architecture of a modern SMT solver. We examine various strategies for on-demand quantifier instantiation in this setting. Here, completeness can be achieved by considering all ground instances over the finite domain of each quantifier. However, exhaustive instantiation quickly becomes unfeasible with larger domain sizes. We propose instantiation strategies to identify and consider only a selection of ground instances that suffices to determine the satisfiability of the input formula. We also examine heuristic quantifier instantiation techniques such as E-matching for the purpose of accelerating the search. We give experimental evidence that our approach is practical for use in industrial applications and is competitive with other approaches.

^*The work of the first two authors was partially funded by a grant from Intel Corporation.

LNAI 7898, p. 377 ff.

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