Kiesl, B., Suda, M., Seidl, M., Tompits, H., & Biere, A. (2017). Blocked Clauses in First-Order Logic. In T. Eiter & D. Sands (Eds.), LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning. EasyChair. https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:3-3121
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 whose elimination can improve the performance of modern theorem provers, especially on satisfiable problem instances.
