Abstract. In incremental SAT solving, information gained from previous similar instances has so far been limited to learned clauses that are still relevant, and heuristic information such as activity weights and scores. In most settings in which incremental satisfiability is applied, many of the instances along the sequence of formulas being solved are unsatisfiable. We show that in such cases, with a P-time analysis of the proof, we can compute a set of literals that are logically implied by the next instance. By adding those literals as assumptions, we accelerate the search.