{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:13:08Z","timestamp":1761610388536,"version":"build-2065373602"},"reference-count":13,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[1999,1,1]],"date-time":"1999-01-01T00:00:00Z","timestamp":915148800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[1999,1,1]],"date-time":"1999-01-01T00:00:00Z","timestamp":915148800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2013,7,29]],"date-time":"2013-07-29T00:00:00Z","timestamp":1375056000000},"content-version":"vor","delay-in-days":5323,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Electronic Notes in Theoretical Computer Science"],"published-print":{"date-parts":[[1999]]},"DOI":"10.1016\/s1571-0661(05)80613-9","type":"journal-article","created":{"date-parts":[[2005,5,6]],"date-time":"2005-05-06T15:34:43Z","timestamp":1115393683000},"page":"420-439","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"title":["Automatic Derivation of the Irrationality of e"],"prefix":"10.1016","volume":"23","author":[{"given":"Michael","family":"Beeson","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S1571-0661(05)80613-9_BIB1","first-page":"67","article-title":"Automatic Generation of Epsilon-Delta Proofs of Continuity in:","volume":"1476","author":"Beeson","year":"1998"},{"key":"10.1016\/S1571-0661(05)80613-9_BIB2","first-page":"103","article-title":"Unification in lambda-calculus with if-then-else, in:","volume":"1421","author":"Beeson","year":"1998"},{"key":"10.1016\/S1571-0661(05)80613-9_BIB3","series-title":"Computers and Mathematics","first-page":"202","article-title":"Logic and computation in Mathpert: an expert system for learning mathematics","author":"Beeson","year":"1989"},{"key":"10.1016\/S1571-0661(05)80613-9_BIB4","series-title":"Human Interfaces to Symbolic Computation","article-title":"Design Principles of Mathpert: Software to support education in algebra and calculus in:","author":"Beeson","year":"1996"},{"issue":"3","key":"10.1016\/S1571-0661(05)80613-9_BIB5","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1142\/S0129054195000172","article-title":"Using nonstandard analysis to ensure the correctness of symbolic computations","volume":"6","author":"Beeson","year":"1995","journal-title":"International Journal of Foundations of Computer Science"},{"key":"10.1016\/S1571-0661(05)80613-9_BIB6","first-page":"101","article-title":"Some applications of Gentzen's proof theory in automated deduction","volume":"475","author":"Beeson","year":"1991"},{"year":"1979","series-title":"A Computational Logic","author":"Boyer","key":"10.1016\/S1571-0661(05)80613-9_BIB7"},{"key":"10.1016\/S1571-0661(05)80613-9_BIB8","series-title":"Automated Deduction: CADE\ue4f811 Proc. of the 11th International Conference on Automated Deduction","first-page":"761","article-title":"Analytica: A Theorem Prover in Mathematica","author":"Clarke","year":"1992"},{"key":"10.1016\/S1571-0661(05)80613-9_BIB9","series-title":"Algorithms in Real Algebraic Geometry","article-title":"Thom's lemma, the coding of real algebraic numbers, and the computation of the topology of semi-algebraic sets in:","author":"Coste","year":"1988"},{"year":"1998","series-title":"Theorem proving modulo, Rapport de Recherche 3400","author":"Dowek","key":"10.1016\/S1571-0661(05)80613-9_BIB10"},{"key":"10.1016\/S1571-0661(05)80613-9_BIB11","doi-asserted-by":"crossref","unstructured":"Harrison, J., and Thery, L.: Extending the HOL theorem prover with a computer algebra system to reason about the reals, in Higher Order Logic Theorem Proving and its Applications: 6th International Workshop, HUG \u203293, pp. 174\ue4f8184, Lecture Notes in Computer Science 780, Springer-Verlag (1993).","DOI":"10.1007\/3-540-57826-9_134"},{"key":"10.1016\/S1571-0661(05)80613-9_BIB12","series-title":"10th International Conference on Automated Deduction","first-page":"663","article-title":"Otter 2.0","author":"McCune","year":"1990"},{"key":"10.1016\/S1571-0661(05)80613-9_BIB13","series-title":"Transcendental Numbers 16","article-title":"Annals of Mathematics Studies","author":"Siegel","year":"1949"}],"container-title":["Electronic Notes in Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1571066105806139?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1571066105806139?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:08:33Z","timestamp":1761610113000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1571066105806139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1999]]}},"alternative-id":["S1571066105806139"],"URL":"https:\/\/doi.org\/10.1016\/s1571-0661(05)80613-9","relation":{},"ISSN":["1571-0661"],"issn-type":[{"type":"print","value":"1571-0661"}],"subject":[],"published":{"date-parts":[[1999]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Automatic Derivation of the Irrationality of e","name":"articletitle","label":"Article Title"},{"value":"Electronic Notes in Theoretical Computer Science","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S1571-0661(05)80613-9","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 1999 Elsevier B.V.","name":"copyright","label":"Copyright"}]}}