Satisfiability of Non-linear (Ir)rational Arithmetic

Abstract. We present a novel way for reasoning about (possibly ir)ratio-nal quantifier-free non-linear arithmetic by a reduction to SAT/SMT. The approach is incomplete and dedicated to satisfiable instances only but is able to produce models for satisfiable problems quickly. These char-acteristics suffice for applications such as termination analysis of rewrite systems. Our prototype implementation, called MiniSmt, is made freely available. Extensive experiments show that it outperforms current SMT solvers especially on rational and irrational domains