Blocked Clauses in First-Order Logic
Abstract
Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper, we lift the notion of blocked clauses to first-order logic. We introduce two types of blocked clauses, one for first-order logic with equality and the other for first-order logic without equality, and prove their redundancy. In addition, we give a polynomial algorithm for checking whether a clause is blocked. Based on our new notions of blocking, we implemented a novel first-order preprocessing tool. Our experiments showed that many first-order problems in the TPTP library contain a large number of blocked clauses. Moreover, we observed that their elimination can improve the performance of modern theorem provers, especially on satisfiable problem instances.
Cite
@article{arxiv.1702.00847,
title = {Blocked Clauses in First-Order Logic},
author = {Benjamin Kiesl and Martin Suda and Martina Seidl and Hans Tompits and Armin Biere},
journal= {arXiv preprint arXiv:1702.00847},
year = {2017}
}