Model checking based on Craig's interpolants ultimately relies on efficient engines, such as SMT-Solvers, to log proofs of unsatisfiability and to derive the desired interpolant by means of a set of algorithms known in literature. These algorithms, however, are designed for proofs that do not contain mixed predicates. In this talk I will present a technique for transforming the propositional proof produced by an SMT-Solver in such a way that mixed predicates are eliminated. There exists a number of cases in which mixed predicates arise as a consequence of state-of-the-art solving procedures (e.g., lemma on demand, theory combination, etc.). In such cases our technique can be applied to allow the reuse of known interpolation algorithms. I will then present a new approach to proof reduction, situated among the purely post-processing methods. The main idea is to reduce the proof size by eliminating redundancies of occurrences of pivots along the proof paths. This is achieved by matching and rewriting local contexts into simpler ones. In our approach, rewriting can be easily customized in the way local contexts are matched, in the amount of transformations to be performed, or in the different application of the rewriting rules. I will provide experimental evaluation of our technique on a set of SMT and SAT benchmarks, which shows considerable reduction in the proofs size.