{"conference":{"location":"Sydney, Australia","start_date":"2014-11-03","end_date":"2014-11-07","name":"ATVA: Automated Technology for Verification and Analysis"},"publication":"ATVA 2014","pubrep_id":"641","file":[{"file_id":"4801","date_created":"2018-12-12T10:10:15Z","checksum":"af4bd3fc1f4c93075e4dc5cbf625fe7b","content_type":"application/pdf","date_updated":"2020-07-14T12:45:19Z","file_size":244294,"file_name":"IST-2016-641-v1+1_atva2014.pdf","creator":"system","access_level":"open_access","relation":"main_file"}],"volume":8837,"ec_funded":1,"quality_controlled":"1","page":"185 - 200","oa_version":"Submitted Version","title":"Extensional crisis and proving identity","date_created":"2018-12-11T11:54:28Z","type":"conference","doi":"10.1007/978-3-319-11936-6_14","author":[{"id":"335E5684-F248-11E8-B48F-1D18A9856A87","first_name":"Ashutosh","last_name":"Gupta","full_name":"Gupta, Ashutosh"},{"last_name":"Kovács","first_name":"Laura","full_name":"Kovács, Laura"},{"id":"320FC952-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-7745-9117","last_name":"Kragl","first_name":"Bernhard","full_name":"Kragl, Bernhard"},{"last_name":"Voronkov","full_name":"Voronkov, Andrei","first_name":"Andrei"}],"alternative_title":["LNCS"],"intvolume":"      8837","publisher":"Springer","status":"public","department":[{"_id":"ToHe"}],"project":[{"_id":"25EE3708-B435-11E9-9278-68D0E5697425","name":"Quantitative Reactive Modeling","grant_number":"267989","call_identifier":"FP7"},{"call_identifier":"FWF","grant_number":"S11402-N23","_id":"25F5A88A-B435-11E9-9278-68D0E5697425","name":"Moderne Concurrency Paradigms"}],"_id":"1872","ddc":["000"],"year":"2014","oa":1,"file_date_updated":"2020-07-14T12:45:19Z","date_published":"2014-01-01T00:00:00Z","publication_status":"published","editor":[{"last_name":"Cassez","full_name":"Cassez, Franck","first_name":"Franck"},{"first_name":"Jean-François","last_name":"Raskin","full_name":"Raskin, Jean-François"}],"has_accepted_license":"1","acknowledgement":"This research was supported in part by the Austrian National Research Network RiSE (S11410-N23).","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:53:45Z","day":"01","publist_id":"5226","citation":{"mla":"Gupta, Ashutosh, et al. “Extensional Crisis and Proving Identity.” <i>ATVA 2014</i>, edited by Franck Cassez and Jean-François Raskin, vol. 8837, Springer, 2014, pp. 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>.","apa":"Gupta, A., Kovács, L., Kragl, B., &#38; Voronkov, A. (2014). Extensional crisis and proving identity. In F. Cassez &#38; J.-F. Raskin (Eds.), <i>ATVA 2014</i> (Vol. 8837, pp. 185–200). Sydney, Australia: Springer. <a href=\"https://doi.org/10.1007/978-3-319-11936-6_14\">https://doi.org/10.1007/978-3-319-11936-6_14</a>","ama":"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>","ista":"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.","ieee":"A. Gupta, L. Kovács, B. Kragl, and A. Voronkov, “Extensional crisis and proving identity,” in <i>ATVA 2014</i>, Sydney, Australia, 2014, vol. 8837, pp. 185–200.","chicago":"Gupta, Ashutosh, Laura Kovács, Bernhard Kragl, and Andrei Voronkov. “Extensional Crisis and Proving Identity.” In <i>ATVA 2014</i>, edited by Franck Cassez and Jean-François Raskin, 8837:185–200. Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-11936-6_14\">https://doi.org/10.1007/978-3-319-11936-6_14</a>.","short":"A. Gupta, L. Kovács, B. Kragl, A. Voronkov, in:, F. Cassez, J.-F. Raskin (Eds.), ATVA 2014, Springer, 2014, pp. 185–200."},"scopus_import":1,"language":[{"iso":"eng"}],"month":"01","abstract":[{"text":"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.","lang":"eng"}]}