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Scavenger 0.1: A Theorem Prover Based on Conflict Resolution

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Automated Deduction – CADE 26 (CADE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

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Abstract

This paper introduces Scavenger, the first theorem prover for pure first-order logic without equality based on the new conflict resolution calculus. Conflict resolution has a restricted resolution inference rule that resembles (a first-order generalization of) unit propagation as well as a rule for assuming decision literals and a rule for deriving new clauses by (a first-order generalization of) conflict-driven clause learning.

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Notes

  1. 1.

    Not to be confused with the homonymous calculus for linear rational inequalities [17].

  2. 2.

    In practice, optimizations (e.g. 1UIP) are used, and more sophisticated clauses, which are not just disjunctions of duals of the decision literals involved in the conflict, can be derived. But these optimizations are inessential to the focus of this paper.

  3. 3.

    Because of the isomorphism between implication graphs and subderivations in Conflict Resolution [25], the propagation depth is equal to the corresponding subderivation’s height, where initial axiom clauses and learned clauses have height 0 and the height of the conclusion of a unit-propagating resolution inference is \(k + 1\) where k is the maximum height of its unit premises.

  4. 4.

    The depth of constants and variables is zero and the depth of a complex term is \(k+1\) when k is the maximum depth of its proper subterms.

  5. 5.

    Raw experimental data are available at https://doi.org/10.5281/zenodo.293187.

References

  1. Alagi, G., Weidenbach, C.: NRCL - a model building approach to the Bernays-Schönfinkel fragment. In: Lutz, C., Ranise, S. (eds.) FroCoS 2015. LNCS, vol. 9322, pp. 69–84. Springer, Cham (2015). doi:10.1007/978-3-319-24246-0_5

    Chapter  Google Scholar 

  2. Baumgartner, P.: A first order Davis-Putnam-Longeman-Loveland procedure. In: Proceedings of the 17th International Conference on Automated Deduction (CADE), pp. 200–219 (2000)

    Google Scholar 

  3. Baumgartner, P.: Model evolution-based theorem proving. IEEE Intell. Syst. 29(1), 4–10 (2014). http://dx.doi.org/10.1109/MIS.2013.124

    Article  Google Scholar 

  4. Baumgartner, P., Fuchs, A., Tinelli, C.: Lemma learning in the model evolution calculus. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS, vol. 4246, pp. 572–586. Springer, Heidelberg (2006). doi:10.1007/11916277_39

    Chapter  Google Scholar 

  5. Baumgartner, P., Tinelli, C.: The model evolution calculus. In: Baader, F. (ed.) CADE 2003. LNCS, vol. 2741, pp. 350–364. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45085-6_32

    Chapter  Google Scholar 

  6. Bonacina, M.P., Plaisted, D.A.: Constraint manipulation in SGGS. In: Kutsia, T., Ringeissen, C. (eds.) Proceedings of the Twenty-Eighth Workshop on Unification (UNIF), Seventh International Joint Conference on Automated Reasoning (IJCAR) and Sixth Federated Logic Conference (FLoC), pp. 47–54, Technical reports of the Research Institute for Symbolic Computation, Johannes Kepler Universität Linz (2014). http://vsl2014.at/meetings/UNIF-index.html

  7. Bonacina, M.P., Plaisted, D.A.: SGGS theorem proving: an exposition. In: Schulz, S., Moura, L.D., Konev, B. (eds.) Proceedings of the Fourth Workshop on Practical Aspects in Automated Reasoning (PAAR), Seventh International Joint Conference on Automated Reasoning (IJCAR) and Sixth Federated Logic Conference (FLoC), July 2014. EasyChair Proceedings in Computing (EPiC), vol. 31, pp. 25–38, July 2015

    Google Scholar 

  8. Bonacina, M.P., Plaisted, D.A.: Semantically-guided goal-sensitive reasoning: model representation. J. Autom. Reasoning 56(2), 113–141 (2016). http://dx.doi.org/10.1007/s10817-015-9334-4

    Article  MathSciNet  MATH  Google Scholar 

  9. Bonacina, M.P., Plaisted, D.A.: Semantically-guided goal-sensitive reasoning: Inference system and completeness. J. Autom. Reasoning, 1–54 (2017). http://dx.doi.org/10.1007/s10817-016-9384-2

  10. Boudou, J., Fellner, A., Woltzenlogel Paleo, B.: Skeptik: a proof compression system. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 374–380. Springer, Cham (2014). doi:10.1007/978-3-319-08587-6_29

    Google Scholar 

  11. Brown, C.E.: Satallax: an automatic higher-order prover. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 111–117. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31365-3_11

    Chapter  Google Scholar 

  12. Claessen, K.: The anatomy of Equinox - an extensible automated reasoning tool for first-order logic and beyond (talk abstract). In: Proceedings of the 23rd International Conference on Automated Deduction (CADE-23), pp. 1–3 (2011)

    Google Scholar 

  13. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. ACM 7, 201–215 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hodgson, K., Slaney, J.K.: System description: SCOTT-5. In: Automated Reasoning, First International Joint Conference, IJCAR 2001, Siena, Italy, June 18–23, 2001, Proceedings, pp. 443–447 (2001). http://dx.doi.org/10.1007/3-540-45744-5_36

  15. Korovin, K.: iProver – an instantiation-based theorem prover for first-order logic (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS, vol. 5195, pp. 292–298. Springer, Heidelberg (2008). doi:10.1007/978-3-540-71070-7_24

    Chapter  Google Scholar 

  16. Korovin, K.: Inst-Gen - a modular approach to instantiation-based automated reasoning. In: Programming Logics, pp. 239–270 (2013)

    Google Scholar 

  17. Korovin, K., Tsiskaridze, N., Voronkov, A.: Conflict resolution. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 509–523. Springer, Heidelberg (2009). doi:10.1007/978-3-642-04244-7_41

    Chapter  Google Scholar 

  18. João Marques-Silva, I.L., Malik, S.: Conflict-driven clause learning SAT solvers. In: Handbook of Satisfiability, pp. 127–149 (2008)

    Google Scholar 

  19. Martin Davis, G.L., Loveland, D.: A machine program for theorem proving. Commun. ACM 57, 394–397 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  20. McCharen, J., Overbeek, R., Wos, L.: Complexity and related enhancements for automated theorem-proving programs. Comput. Math. Appl. 2, 1–16 (1976)

    MATH  Google Scholar 

  21. McCune, W.: Otter 2.0. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol. 449, pp. 663–664. Springer, Heidelberg (1990). doi:10.1007/3-540-52885-7_131

    Google Scholar 

  22. McCune, W.: OTTER 3.3 reference manual. CoRR cs.SC/0310056 (2003),. http://arxiv.org/abs/cs.SC/0310056

  23. Nieuwenhuis, R., Hillenbrand, T., Riazanov, A., Voronkov, A.: On the evaluation of indexing techniques for theorem proving. In: Automated Reasoning, First International Joint Conference, IJCAR 2001, Siena, Italy, June 18–23, 2001, Proceedings, pp. 257–271 (2001). doi:http://dx.doi.org/10.1007/3-540-45744-5_19

  24. Nivelle, H., Meng, J.: Geometric resolution: a proof procedure based on finite model search. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS, vol. 4130, pp. 303–317. Springer, Heidelberg (2006). doi:10.1007/11814771_28

    Chapter  Google Scholar 

  25. Slaney, J., Woltzenlogel Paleo, B.: Conflict resolution: a first-order resolution calculus with decision literals and conflict-driven clause learning. J. Autom. Reasoning, 1–24 (2017). http://dx.doi.org/10.1007/s10817-017-9408-6

  26. Slaney, J.K.: SCOTT: a model-guided theorem prover. In: Bajcsy, R. (ed.) Proceedings of the 13th International Joint Conference on Artificial Intelligence. Chambéry, France, August 28 - September 3, 1993, pp. 109–115. Morgan Kaufmann (1993). http://ijcai.org/Proceedings/93-1/Papers/016.pdf

  27. Stump, A., Sutcliffe, G., Tinelli, C.: StarExec: a cross-community infrastructure for logic solving. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS, vol. 8562, pp. 367–373. Springer, Cham (2014). doi:10.1007/978-3-319-08587-6_28

    Google Scholar 

  28. Sutcliffe, G.: The TPTP problem library and associated infrastructure: the FOF and CNF parts, v3.5.0. J. Autom. Reasoning 43(4), 337–362 (2009)

    Article  MATH  Google Scholar 

  29. Voronkov, A.: AVATAR: the architecture for first-order theorem provers. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 696–710. Springer, Cham (2014). doi:10.1007/978-3-319-08867-9_46

    Google Scholar 

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Acknowledgments

We thank Ezequiel Postan for his implementation of TPTP parsers for Skeptik [10], which we have reused in Scavenger. We are grateful to Albert A.V. Giegerich, Aaron Stump and Geoff Sutcliffe for all their help in setting up our experiments in StarExec. This research was partially funded by the Australian Government through the Australian Research Council and by the Google Summer of Code 2016 program. Daniyar Itegulov was financially supported by the Russian Scientific Foundation (grant 15-14-00066).

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Authors and Affiliations

  1. ITMO University, St. Petersburg, Russia

    Daniyar Itegulov

  2. Australian National University, Canberra, Australia

    John Slaney & Bruno Woltzenlogel Paleo

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  1. Daniyar Itegulov
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  2. John Slaney
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Correspondence to Bruno Woltzenlogel Paleo .

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  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

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Itegulov, D., Slaney, J., Woltzenlogel Paleo, B. (2017). Scavenger 0.1: A Theorem Prover Based on Conflict Resolution. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_21

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  • DOI: https://doi.org/10.1007/978-3-319-63046-5_21

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