Abstract
First-order translations of large mathematical repositories allow discovery of new proofs by automated reasoning systems. Large amounts of available mathematical knowledge can be re-used by combined AI/ATP systems, possibly in unexpected ways. But automated systems can be also more easily misled by irrelevant knowledge in this setting, and finding deeper proofs is typically more difficult. Both large-theory AI/ATP methods, and translation and data-mining techniques of large formal corpora, have significantly developed recently, providing enough data for an initial comparison of the proofs written by mathematicians and the proofs found automatically. This paper describes such an initial experiment and comparison conducted over the 50000 mathematical theorems from the Mizar Mathematical Library.
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References
Alama, J., Kühlwein, D., Tsivtsivadze, E., Urban, J., Heskes, T.: Premise selection for mathematics by corpus analysis and kernel methods. CoRR, abs/1108.3446
Alama, J., Mamane, L., Urban, J.: Dependencies in formal mathematics. CoRR, abs/1109.3687 (2011), http://arxiv.org/abs/1109.3687
Dahn, I.: Robbins algebras are Boolean: A revision of McCune’s computer-generated solution of Robbins problem. Journal of Algebra 208, 526–532 (1998)
Dosen, K.: Identity of proofs based on normalization and generality. Bulletin of Symbolic Logic 9, 477–503 (2003)
Fitelson, B.: Using Mathematica to understand the computer proof of the Robbins Conjecture. Mathematica In Education and Research 7(1) (1998)
Hales, T.: Mathematics in the age of the Turing Machine. Lecture Notes in Logic in Commemoration of the Centennial of the Birth of Alan Turing (to appear, 2012)
Hoder, K., Voronkov, A.: Sine Qua Non for Large Theory Reasoning. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 299–314. Springer, Heidelberg (2011)
McCune, W.W.: Solution of the Robbins Problem. Journal of Automated Reasoning 19(3), 263–276 (1997)
Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Applied Logic 7(1), 41–57 (2009)
Paulson, L.C., Blanchette, J.: Three years of experience with Sledgehammer, a practical link between automated and interactive theorem provers. In: 8th IWIL (2010)
Phillips, J.D., Stanovský, D.: Automated Theorem Proving in Loop Theory. In: Sutcliffe, G., Colton, S., Schulz, S. (eds.) ESARM. CEUR Workshop Proceedings, vol. 378, pp. 42–53. CEUR-WS.org (2008)
Pudlák, P.: Semantic selection of premisses for automated theorem proving. In: Sutcliffe, G., Urban, J., Schulz, S. (eds.) ESARLT. CEUR Workshop Proceedings, vol. 257. CEUR-WS.org (2007)
Schulz, S.: E – a brainiac theorem prover. J. of AI Communications 15(2-3), 111–126 (2002)
Urban, J.: MPTP 0.2: Design, implementation, and initial experiments. J. Autom. Reasoning 37(1-2), 21–43 (2006)
Urban, J., Hoder, K., Voronkov, A.: Evaluation of Automated Theorem Proving on the Mizar Mathematical Library. In: Fukuda, K., van der Hoeven, J., Joswig, M., Takayama, N. (eds.) ICMS 2010. LNCS, vol. 6327, pp. 155–166. Springer, Heidelberg (2010)
Urban, J., Sutcliffe, G., Pudlák, P., Vyskočil, J.: MaLARea SG1–Machine learner for automated reasoning with semantic guidance. In: IJCAR, pp. 441–456 (2008)
Urban, J., Vyskočil, J., Štěpánek, P.: MaLeCoP Machine Learning Connection Prover. In: Brünnler, K., Metcalfe, G. (eds.) TABLEAUX 2011. LNCS, vol. 6793, pp. 263–277. Springer, Heidelberg (2011)
Vyskočil, J., Stanovský, D., Urban, J.: Automated Proof Compression by Invention of New Definitions. In: Clarke, E.M., Voronkov, A. (eds.) LPAR-16 2010. LNCS, vol. 6355, pp. 447–462. Springer, Heidelberg (2010)
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Alama, J., Kühlwein, D., Urban, J. (2012). Automated and Human Proofs in General Mathematics: An Initial Comparison. In: Bjørner, N., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2012. Lecture Notes in Computer Science, vol 7180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28717-6_6
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DOI: https://doi.org/10.1007/978-3-642-28717-6_6
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