SyMT: finding symmetries in SMT formulas

The QF UF category of the SMT-LIB test set contains many formulas with symmetries, and breaking these symmetries results in an important speedup [8]. This paper presents SyMT, a tool to find and report symmetries in SMT formulas. SyMT is based on the reduction of the problem of detecting symmetries in formulas to finding automorphisms in a graph representation of these formulas. The output of SyMT may be used to improve SMT formulas to enforce the SMT solver to examine only one assignment out of many symmetric ones. We show that the classic propositional symmetry breaking technique can be lifted to SMT and yields a generic technique to break the symmetries found by SyMT. Experiments on a large part of the SMT-LIB show that symmetries are pervasive in most categories.