Detecting Unsatisfiability of Nonlinear Constraints Using DISCOVERER

Recent advances in program verification indicate that various verification problems can be reduced to semialgebraic system (SAS for short) solving. An SAS consists of polynomial equations and polynomial inequalities. L.Yang invented new theories and algorithms for SAS solving and partly implemented them as a real symbolic computation tool in Maple named discoverer. In this paper, we first introduce the tool discoverer on solving SASs, and then we describe a method how to apply the techniques on solving semi-algebraic systems to detecting unsatisfiability of conjunction of nonlinear equalities and inequalities.