Abstract
Case splitting, with and without backtracking, is compared with straightforward ordered resolution. Both forms of splitting have been implemented for MetiTarski, an automatic theorem prover for real-valued special functions such as \(\exp\), ln , sin, cos and tan − 1. The experimental findings confirm the superiority of true backtracking over the simulation of backtracking through the introduction of new predicate symbols, and the superiority of both over straightforward resolution.
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References
Akbarpour, B., Paulson, L.: MetiTarski: An automatic theorem prover for real-valued special functions. J. Autom. Reason. 44(3), 175–205 (2010). doi:10.1007/s10817-009-9149-2
Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, chap. 2, pp. 19–99. Elsevier, Amsterdam (2001)
Denman, W., Akbarpour, B., Tahar, S., Zaki, M., Paulson, L.C.: Formal verification of analog designs using MetiTarski. In: Biere, A., Pixley, C. (eds.) Formal Methods in Computer Aided Design, pp. 93–100. IEEE, Piscataway (2009). doi:10.1109/FMCAD.2009.5351136
Fietzke, A., Weidenbach, C.: Labelled splitting. Ann. Math. Artif. Intell. 55, 3–34 (2009). doi:10.1007/s10472-009-9150-9
Hurd, J.: Metis first order prover (2007). URL: http://gilith.com/software/metis/
McCune, W., Wos, L.: Otter: The CADE-13 competition incarnations. J. Autom. Reason. 18(2), 211–220 (1997). doi:10.1023/A:1005843632307
Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Appl. Log. 7(1), 41–57 (2009). doi:10.1016/j.jal.2007.07.004
Mitrinović, D.S., Vasić, P.M.: Analytic Inequalities. Springer, New York (1970)
Nivelle, H.: Splitting through new proposition symbols. In: Nieuwenhuis, R., Voronkov, A. (eds.) Logic for Programming, Artificial Intelligence, and Reasoning: 8th International Conference, LPAR, LNCS 2250, pp. 172–185. Springer, New York (2001). doi:10.1007/3-540-45653-8_12
Nonnengart, A., Weidenbach, C.: Computing small clause normal forms. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, chap. 6, pp. 335–367. Elsevier, Amsterdam (2001)
Riazanov, A., Voronkov, A.: Splitting without backtracking. In: International Joint Conference on Artificial Intelligence (IJCAI-17), vol. 1, pp. 611–617 (2001). http://www.cs.man.ac.uk/~voronkov/papers/ijcai01.ps
Sutcliffe, G., Zimmer, J., Schulz, S.: TSTP data-exchange formats for automated theorem proving tools. In: Zhang, W., Sorge, V. (eds.) Distributed Constraint Problem Solving and Reasoning in Multi-Agent Systems, no. 112 in Frontiers in Artificial Intelligence and Applications, pp. 201–215. IOS Press, Amsterdam (2004)
Weidenbach, C.: SPASS - version 0.49. J. Autom. Reason. 18, 247–252 (1997). doi:10.1023/A:1005812220011
Weidenbach, C.: Combining superposition, sorts and splitting. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, chap. 27, pp. 1965–2013. Elsevier, Amsterdam (2001)
Wos, L., Robinson, G.A., Carson, D.F.: Efficiency and completeness of the set of support strategy in theorem proving. J. ACM 12(4), 536–541 (1965). doi:10.1145/321296.321302
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Bridge, J.P., Paulson, L.C. Case Splitting in an Automatic Theorem Prover for Real-Valued Special Functions. J Autom Reasoning 50, 99–117 (2013). https://doi.org/10.1007/s10817-012-9245-6
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DOI: https://doi.org/10.1007/s10817-012-9245-6