Proofs for incremental SAT with inprocessing

Incremental SAT solvers are automated reasoning tools that efficiently solve sequences of related logic problems, making them go-to tools for inherently incremental applications such as model checking, planning, or test generation. Recent advances in incremental solving using inprocessing have led to substantial performance improvements, but it has remained unclear how the resulting solvers could produce verifiable proofs of unsatisfiability. Here we provide a simple approach that enables inprocessing solvers to produce proofs for incremental results. The approach extends the standard DRAT format with clause restoration steps. These are later removed during postprocessing, yielding a standard DRAT proof. Our empirical evaluation shows that our approach is sound and efficient. Proofs can be generated much faster compared to re-solving a problem non-incrementally, but the resulting proofs tend to be larger. Nevertheless, even when taking proof checking into account, our approach is still slightly faster on average. In addition, our technique has the advantage of guaranteeing proof production whereas the non-incremental approach can time out on hard problems.