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.

中文翻译：

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扩展树的提取

我们定义了一种新的 CERES 证明挖掘方法（通过分辨率消除切割），该方法涉及在一阶逻辑中提取扩展树（参见 Miller 在 Stud Log 46(4):347–370, 1987）中等式. 在原始的 CERES 方法中，可以从标准形式的证明（没有量化切割的证明）中提取扩展树作为切割消除的后处理。更准确地说，它们是从 ACNF 中提取的，ACNF 是最多原子切割的证明。我们定义了一种避免证明归一化的新方法，并表明可以从分辨率反驳和相应的证明投影中提取扩展树。我们证明新方法渐近优于标准方法（首先计算 ACNF，然后提取扩展树）。最后，我们将新方法的实现与旧方法进行比较；