Abstract
AbstractResolution and superposition provers rely on the given clause procedure to saturate clause sets. Using Isabelle/HOL, we formally verify four variants of the procedure: the well-known Otter and DISCOUNT loops as well as the newer iProver and Zipperposition loops. For each of the variants, we show that the procedure guarantees saturation, given a fair data structure to store the formulas that wait to be selected. Our formalization of the Zipperposition loop clarifies some fine points previously misunderstood in the literature.
Publisher
Springer Nature Switzerland
Reference19 articles.
1. Lecture Notes in Computer Science;J Avenhaus,1995
2. Bachmair, L., Ganzinger, H.: Rewrite-based equational theorem proving with selection and simplification. J. Log. Comput. 4(3), 217–247 (1994). https://doi.org/10.1093/logcom/4.3.217
3. Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, pp. 19–99. Elsevier and MIT Press (2001). https://doi.org/10.1016/b978-044450813-3/50004-7
4. Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence);A Bentkamp,2021
5. Blanchette, J., Qiu, Q., Tourret, S.: Given clause loops. Archive of Formal Proofs 2023 (2023). https://www.isa-afp.org/entries/Given_Clause_Loops.html