Symmetry Avoidance in MACE-Style Finite Model Finding

Abstract

This work considers the MACE-style approach to finite model finding for (multi-sorted) first-order logic. This existing approach iteratively assumes increasing domain sizes and encodes the corresponding model existence problem as a SAT problem. The original MACE tool and its successors have considered techniques for avoiding introducing symmetries in the resulting SAT problem, but this has never been the focus of the previous work and has not received concentrated attention. In this work we formalise the symmetry avoiding problem, characterise the notion of a sound symmetry breaking heuristic, propose a number of such heuristics and evaluate them experimentally with an implementation in the Vampire theorem prover. Our results demonstrate that these new heuristics improve performance on a number of benchmarks taken from SMT-LIB and TPTP. Finally, we show that direct symmetry breaking techniques could be used to improve finite model finding, but that their cost means that symmetry avoidance is still the preferable approach.