ACL2 Proofs of Nonlinear Inequalities with Imandra

Abstract: We present a proof-producing integration of ACL2 and Imandra for proving nonlinear inequalities. This leverages a new Imandra interface exposing its nonlinear decision procedures. The reasoning takes place over the reals, but the proofs produced are valid over the rationals and may be run in both ACL2 and ACL2(r). The ACL2 proofs Imandra constructs are extracted from Positivstellensatz refutations, a real algebraic analogue of the Nullstellensatz, and are found using convex optimization.