Cassez, Franck; Raskin, Jean-François
Extensionality axioms are common when reasoning about data collections, such as arrays and functions in program analysis, or sets in mathematics. An extensionality axiom asserts that two collections are equal if they consist of the same elements at the same indices. Using extensionality is often required to show that two collections are equal. A typical example is the set theory theorem (∀x)(∀y)x∪y = y ∪x. Interestingly, while humans have no problem with proving such set identities using extensionality, they are very hard for superposition theorem provers because of the calculi they use. In this paper we show how addition of a new inference rule, called extensionality resolution, allows first-order theorem provers to easily solve problems no modern first-order theorem prover can solve. We illustrate this by running the VAMPIRE theorem prover with extensionality resolution on a number of set theory and array problems. Extensionality resolution helps VAMPIRE to solve problems from the TPTP library of first-order problems that were never solved before by any prover.
This research was supported in part by the Austrian National Research Network RiSE (S11410-N23).
185 - 200
ATVA: Automated Technology for Verification and Analysis
2014-11-03 – 2014-11-07
Gupta A, Kovács L, Kragl B, Voronkov A. Extensional crisis and proving identity. In: Cassez F, Raskin J-F, eds. ATVA 2014. Vol 8837. Springer; 2014:185-200. doi:10.1007/978-3-319-11936-6_14
Gupta, A., Kovács, L., Kragl, B., & Voronkov, A. (2014). Extensional crisis and proving identity. In F. Cassez & J.-F. Raskin (Eds.), ATVA 2014 (Vol. 8837, pp. 185–200). Sydney, Australia: Springer. https://doi.org/10.1007/978-3-319-11936-6_14
Gupta, Ashutosh, Laura Kovács, Bernhard Kragl, and Andrei Voronkov. “Extensional Crisis and Proving Identity.” In ATVA 2014, edited by Franck Cassez and Jean-François Raskin, 8837:185–200. Springer, 2014. https://doi.org/10.1007/978-3-319-11936-6_14.
A. Gupta, L. Kovács, B. Kragl, and A. Voronkov, “Extensional crisis and proving identity,” in ATVA 2014, Sydney, Australia, 2014, vol. 8837, pp. 185–200.
Gupta A, Kovács L, Kragl B, Voronkov A. 2014. Extensional crisis and proving identity. ATVA 2014. ATVA: Automated Technology for Verification and Analysis, LNCS, vol. 8837. 185–200.
Gupta, Ashutosh, et al. “Extensional Crisis and Proving Identity.” ATVA 2014, edited by Franck Cassez and Jean-François Raskin, vol. 8837, Springer, 2014, pp. 185–200, doi:10.1007/978-3-319-11936-6_14.