Extensional crisis and proving identity
LNCS
Gupta, Ashutosh
Kovács, Laura
Kragl, Bernhard
Voronkov, Andrei
Cassez, Franck
Raskin, Jean-François
ddc:000
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.
Springer
2014
info:eu-repo/semantics/conferenceObject
doc-type:conferenceObject
text
http://purl.org/coar/resource_type/c_5794
https://research-explorer.app.ist.ac.at/record/1872
https://research-explorer.app.ist.ac.at/download/1872/4801
Gupta A, Kovács L, Kragl B, Voronkov A. Extensional crisis and proving identity. In: Cassez F, Raskin J-F, eds. <i>ATVA 2014</i>. Vol 8837. Springer; 2014:185-200. doi:<a href="https://doi.org/10.1007/978-3-319-11936-6_14">10.1007/978-3-319-11936-6_14</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-11936-6_14
info:eu-repo/grantAgreement/EC/FP7/267989
info:eu-repo/grantAgreement/FWF//S11402-N23
info:eu-repo/semantics/openAccess