Extraction of Expansion Trees

We define a new method for proof mining by CERES (cut-elimination by resolution) that is concerned with the extraction of expansion trees in first-order logic (see Miller in Stud Log 46(4):347-370, 1987) with equality. In the original CERES method expansion trees can be extracted from proofs in normal form (proofs without quantified cuts) as a post-processing of cut-elimination. More precisely they are extracted from an ACNF, a proof with at most atomic cuts. We define a novel method avoiding proof normalization and show that expansion trees can be extracted from the resolution refutation and the corresponding proof projections. We prove that the new method asymptotically outperforms the standard method (which first computes the ACNF and then extracts an expansion tree). Finally we compare an implementation of the new method with the old one; it turns out that the new method is also more efficient in our experiments.