Congruence Closure with Free Variables

Many verification techniques nowadays successfully rely on SMT solvers as back-ends to automatically discharge proof obligations. These solvers generally rely on various instantiation techniques to handle quantifiers. We here show that the major instantiation techniques in SMT solving can be cast in a unifying framework for handling quantified formulas with equality and uninterpreted functions. This framework is based on the problem of E-ground (dis)unification, a variation of the classic rigid E -unification problem. We introduce a sound and complete calculus to solve this problem in practice: Congruence Closure with Free Variables (CCFV). Experimental evaluations of implementations of CCFV in the state-of-the-art solver CVC4 and in the solver veriT exhibit improvements in the former and makes the latter competitive with stateof-the-art solvers in several benchmark libraries stemming from verifica-