Automated theorem proving (English Wikipedia)

Frege, Gottlob (1884). Die Grundlagen der Arithmetik (PDF). Breslau: Wilhelm Kobner. Archived from the original (PDF) on 2007-09-26. Retrieved 2012-09-02.

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Bos, Johan. "Wide-coverage semantic analysis with boxer." Semantics in text processing. step 2008 conference proceedings. 2008.

archive.org (Global: 6^th place; English: 6^th place)

Russell, Bertrand; Whitehead, Alfred North (1910–1913). Principia Mathematica (1st ed.). Cambridge University Press.
Russell, Bertrand; Whitehead, Alfred North (1927). Principia Mathematica (2nd ed.). Cambridge University Press.

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gallica.bnf.fr

Frege, Gottlob (1879). Begriffsschrift. Verlag Louis Neuert.

cambridge.org (Global: 209^th place; English: 151^st place)

Boolos, George S.; Burgess, John P.; Jeffrey, Richard C. (2002). Computability and Logic (4 ed.). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139164931. ISBN 978-0-521-80975-7.

doi.org (Global: 2^nd place; English: 2^nd place)

Boolos, George S.; Burgess, John P.; Jeffrey, Richard C. (2002). Computability and Logic (4 ed.). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139164931. ISBN 978-0-521-80975-7.
Chowdhary, K.R. (2025). "Theory of Computation". SpringerLink. doi:10.1007/978-981-97-6234-7. ISBN 978-981-97-6233-0.{{cite journal}}: CS1 maint: periodical has ISBN (link)
Gilmore, Paul (1960). "A proof procedure for quantification theory: its justification and realisation". IBM Journal of Research and Development. 4: 28–35. doi:10.1147/rd.41.0028.
McCune, W. W. (1997). "Solution of the Robbins Problem". Journal of Automated Reasoning. 19 (3): 263–276. doi:10.1023/A:1005843212881. S2CID 30847540.
Goel, Shilpi; Ray, Sandip (2022), "Microprocessor Assurance and the Role of Theorem Proving", in Chattopadhyay, Anupam (ed.), Handbook of Computer Architecture, Singapore: Springer Nature Singapore, pp. 1–43, doi:10.1007/978-981-15-6401-7_38-1, ISBN 978-981-15-6401-7, retrieved 2024-02-10
Meng, Jia; Paulson, Lawrence C. (2008-01-01). "Translating Higher-Order Clauses to First-Order Clauses". Journal of Automated Reasoning. 40 (1): 35–60. doi:10.1007/s10817-007-9085-y. ISSN 1573-0670. S2CID 7716709.
Luckham, David C.; Suzuki, Norihisa (Oct 1979). "Verification of Array, Record, and Pointer Operations in Pascal". ACM Transactions on Programming Languages and Systems. 1 (2): 226–244. doi:10.1145/357073.357078. S2CID 10088183.
Loveland, D. W. (1986). "Automated theorem proving: Mapping logic into AI". Proceedings of the ACM SIGART international symposium on Methodologies for intelligent systems. Knoxville, Tennessee, United States: ACM Press. p. 224. doi:10.1145/12808.12833. ISBN 978-0-89791-206-8. S2CID 14361631.
Blanchette, Jasmin Christian; Böhme, Sascha; Paulson, Lawrence C. (2013-06-01). "Extending Sledgehammer with SMT Solvers". Journal of Automated Reasoning. 51 (1): 109–128. doi:10.1007/s10817-013-9278-5. ISSN 1573-0670. S2CID 5389933. ATPs and SMT solvers have complementary strengths. The former handle quantifiers more elegantly, whereas the latter excel on large, mostly ground problems.
Weber, Tjark; Conchon, Sylvain; Déharbe, David; Heizmann, Matthias; Niemetz, Aina; Reger, Giles (2019-01-01). "The SMT Competition 2015–2018". Journal on Satisfiability, Boolean Modeling and Computation. 11 (1): 221–259. doi:10.3233/SAT190123. In recent years, we have seen a blurring of lines between SMT-COMP and CASC with SMT solvers competing in CASC and ATPs competing in SMT-COMP.

dtic.mil (Global: 934^th place; English: 530^th place)

apps.dtic.mil

Luckham, David C.; Suzuki, Norihisa (Mar 1976). Automatic Program Verification V: Verification-Oriented Proof Rules for Arrays, Records, and Pointers (Technical Report AD-A027 455). Defense Technical Information Center. Archived from the original on August 12, 2021.

ed.ac.uk (Global: 1,867^th place; English: 1,129^th place)

era.lib.ed.ac.uk

Bundy, Alan (1999). The automation of proof by mathematical induction (PDF) (Technical report). Informatics Research Report. Vol. 2. Division of Informatics, University of Edinburgh. hdl:1842/3394.

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Herbrand, J. (1930). Recherches sur la théorie de la démonstration (PhD) (in French). University of Paris.

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Benzmüller, Christoph, et al. "LEO-II-a cooperative automatic theorem prover for classical higher-order logic (system description)." International Joint Conference on Automated Reasoning. Berlin, Germany and Heidelberg: Springer, 2008.

ghostarchive.org (Global: 64^th place; English: 28^th place)

Bibel, Wolfgang (2007). "Early History and Perspectives of Automated Deduction" (PDF). Ki 2007. LNAI (4667). Springer: 2–18. Archived (PDF) from the original on 2022-10-09. Retrieved 2 September 2012.

hdl.handle.net (Global: 66^th place; English: 34^th place)

Bundy, Alan (1999). The automation of proof by mathematical induction (PDF) (Technical report). Informatics Research Report. Vol. 2. Division of Informatics, University of Edinburgh. hdl:1842/3394.

intellektik.de (Global: low place; English: low place)

Bibel, Wolfgang (2007). "Early History and Perspectives of Automated Deduction" (PDF). Ki 2007. LNAI (4667). Springer: 2–18. Archived (PDF) from the original on 2022-10-09. Retrieved 2 September 2012.

mpg.de (Global: 1,722^nd place; English: 1,710^th place)

pure.mpg.de

Gabbay, Dov M., and Hans Jürgen Ohlbach. "Quantifier elimination in second-order predicate logic." (1992).

nytimes.com (Global: 7^th place; English: 7^th place)

Kolata, Gina (December 10, 1996). "Computer Math Proof Shows Reasoning Power". The New York Times. Retrieved 2008-10-11.

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cs.nyu.edu

Davis, Martin (2001). "The Early History of Automated Deduction". Robinson & Voronkov 2001. Archived from the original on 2012-07-28. Retrieved 2012-09-08. Robinson, Alan; Voronkov, Andrei, eds. (2001). Handbook of Automated Reasoning. Vol. I. Elsevier, MIT Press. ISBN 9780080532790. II ISBN 9780262182232.

philarchive.org (Global: low place; English: 7,457^th place)

Russell, Bertrand (1931). Principles of Mathematics. New York: W.W. Norton & Company.
Muskens, Reinhard. "Combining Montague semantics and discourse representation." Linguistics and philosophy (1996): 143-186.

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Kleene, Stephen Cole (1967). Mathematical Logic. Mineola, N.Y.: Dover Publications.

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"Computational Complexity: A Modern Approach / Sanjeev Arora and Boaz Barak". theory.cs.princeton.edu. Retrieved 2026-01-25.

psu.edu (Global: 299^th place; English: 159^th place)

citeseerx.ist.psu.edu

Basin, D.; Deville, Y.; Flener, P.; Hamfelt, A.; Fischer Nilsson, J. (2004). "Synthesis of programs in computational logic". In M. Bruynooghe and K.-K. Lau (ed.). Program Development in Computational Logic. LNCS. Vol. 3049. Springer. pp. 30–65. CiteSeerX 10.1.1.62.4976. {{cite book}}: Cite uses deprecated parameter |citeseerx= (help)

scientificamerican.com (Global: 1,110^th place; English: 817^th place)

Howlett, Joseph. "AI just solved an 80-year-old 'Erdős problem,' and mathematicians are amazed". Scientific American. Retrieved 2026-06-07.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

McCune, W. W. (1997). "Solution of the Robbins Problem". Journal of Automated Reasoning. 19 (3): 263–276. doi:10.1023/A:1005843212881. S2CID 30847540.
Meng, Jia; Paulson, Lawrence C. (2008-01-01). "Translating Higher-Order Clauses to First-Order Clauses". Journal of Automated Reasoning. 40 (1): 35–60. doi:10.1007/s10817-007-9085-y. ISSN 1573-0670. S2CID 7716709.
Luckham, David C.; Suzuki, Norihisa (Oct 1979). "Verification of Array, Record, and Pointer Operations in Pascal". ACM Transactions on Programming Languages and Systems. 1 (2): 226–244. doi:10.1145/357073.357078. S2CID 10088183.
Loveland, D. W. (1986). "Automated theorem proving: Mapping logic into AI". Proceedings of the ACM SIGART international symposium on Methodologies for intelligent systems. Knoxville, Tennessee, United States: ACM Press. p. 224. doi:10.1145/12808.12833. ISBN 978-0-89791-206-8. S2CID 14361631.
Blanchette, Jasmin Christian; Böhme, Sascha; Paulson, Lawrence C. (2013-06-01). "Extending Sledgehammer with SMT Solvers". Journal of Automated Reasoning. 51 (1): 109–128. doi:10.1007/s10817-013-9278-5. ISSN 1573-0670. S2CID 5389933. ATPs and SMT solvers have complementary strengths. The former handle quantifiers more elegantly, whereas the latter excel on large, mostly ground problems.

springer.com (Global: 182^nd place; English: 172^nd place)

link.springer.com

Chowdhary, K.R. (2025). "Theory of Computation". SpringerLink. doi:10.1007/978-981-97-6234-7. ISBN 978-981-97-6233-0.{{cite journal}}: CS1 maint: periodical has ISBN (link)
Goel, Shilpi; Ray, Sandip (2022), "Microprocessor Assurance and the Role of Theorem Proving", in Chattopadhyay, Anupam (ed.), Handbook of Computer Architecture, Singapore: Springer Nature Singapore, pp. 1–43, doi:10.1007/978-981-15-6401-7_38-1, ISBN 978-981-15-6401-7, retrieved 2024-02-10

stanford.edu (Global: 194^th place; English: 182^nd place)

plato.stanford.edu

Raatikainen, Panu (2026), "Gödel's Incompleteness Theorems", in Zalta, Edward N.; Nodelman, Uri (eds.), The Stanford Encyclopedia of Philosophy (Spring 2026 ed.), Metaphysics Research Lab, Stanford University, retrieved 2026-01-25

exhibits.stanford.edu

Luckham, D.; German, S.; von Henke, F.; Karp, R.; Milne, P.; Oppen, D.; Polak, W.; Scherlis, W. (1979). Stanford Pascal verifier user manual (Technical report). Stanford University. CS-TR-79-731.

theoremprover-museum.github.io (Global: low place; English: low place)

"The Theorem Prover Museum". Michael Kohlhase. Retrieved 2022-11-20.

tptp.org (Global: low place; English: low place)

Sutcliffe, Geoff. "The TPTP Problem Library for Automated Theorem Proving". Retrieved 15 July 2019.

uni-kl.de (Global: low place; English: low place)

kluedo.ub.uni-kl.de

Kerber, Manfred. "How to prove higher order theorems in first order logic." (1999).

vprover.github.io (Global: low place; English: low place)

"History". vprover.github.io.

web.archive.org (Global: 1^st place; English: 1^st place)

Frege, Gottlob (1884). Die Grundlagen der Arithmetik (PDF). Breslau: Wilhelm Kobner. Archived from the original (PDF) on 2007-09-26. Retrieved 2012-09-02.
Davis, Martin (2001). "The Early History of Automated Deduction". Robinson & Voronkov 2001. Archived from the original on 2012-07-28. Retrieved 2012-09-08. Robinson, Alan; Voronkov, Andrei, eds. (2001). Handbook of Automated Reasoning. Vol. I. Elsevier, MIT Press. ISBN 9780080532790. II ISBN 9780262182232.
Luckham, David C.; Suzuki, Norihisa (Mar 1976). Automatic Program Verification V: Verification-Oriented Proof Rules for Arrays, Records, and Pointers (Technical Report AD-A027 455). Defense Technical Information Center. Archived from the original on August 12, 2021.

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Meng, Jia; Paulson, Lawrence C. (2008-01-01). "Translating Higher-Order Clauses to First-Order Clauses". Journal of Automated Reasoning. 40 (1): 35–60. doi:10.1007/s10817-007-9085-y. ISSN 1573-0670. S2CID 7716709.
Blanchette, Jasmin Christian; Böhme, Sascha; Paulson, Lawrence C. (2013-06-01). "Extending Sledgehammer with SMT Solvers". Journal of Automated Reasoning. 51 (1): 109–128. doi:10.1007/s10817-013-9278-5. ISSN 1573-0670. S2CID 5389933. ATPs and SMT solvers have complementary strengths. The former handle quantifiers more elegantly, whereas the latter excel on large, mostly ground problems.

Automated theorem proving (English Wikipedia)

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