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Towards the Compression of First-Order Resolution Proofs by Lowering Unit Clauses

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Automated Deduction - CADE-25 (CADE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

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Abstract

The recently developed LowerUnits algorithm compresses propositional resolution proofs generated by SAT- and SMT-solvers by postponing and lowering resolution inferences involving unit clauses, which have exactly one literal. This paper describes a generalization of this algorithm to the case of first-order resolution proofs generated by automated theorem provers. An empirical evaluation of a simplified version of this algorithm on hundreds of proofs shows promising results.

J. Gorzny—Supported by the Google Summer of Code 2014 program.

B. Woltzenlogel Paleo—Stipendiat der Österreichischen Akademie der Wissenschaften (APART).

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References

  1. Clarke, E.M., Voronkov, A. (eds.): LPAR-16 2010. LNCS, vol. 6355. Springer, Heidelberg (2010)

    MATH  Google Scholar 

  2. Bar-Ilan, O., Fuhrmann, O., Hoory, S., Shacham, O., Strichman, O.: Linear-time reductions of resolution proofs. In: Chockler, H., Hu, A.J. (eds.) HVC 2008. LNCS, vol. 5394, pp. 114–128. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. 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, Heidelberg (2014)

    Google Scholar 

  4. Boudou, J., Woltzenlogel Paleo, B.: Compression of propositional resolution proofs by lowering subproofs. In: Galmiche, D., Larchey-Wendling, D. (eds.) TABLEAUX 2013. LNCS, vol. 8123, pp. 59–73. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  5. Fontaine, P., Merz, S., Woltzenlogel Paleo, B.: Exploring and exploiting algebraic and graphical properties of resolution. In: 8th International Workshop on SMT, Edinburgh (2010)

    Google Scholar 

  6. Fontaine, P., Merz, S., Woltzenlogel Paleo, B.: Compression of propositional resolution proofs via partial regularization. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 237–251. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  7. Hetzl, S., Leitsch, A., Reis, G., Weller, D.: Algorithmic introduction of quantified cuts. Theor. Comput. Sci. 549, 1–16 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hetzl, S., Leitsch, A., Weller, D., Woltzenlogel Paleo, B.: Herbrand sequent extraction. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds.) AISC 2008, Calculemus 2008, and MKM 2008. LNCS (LNAI), vol. 5144, pp. 462–477. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Woltzenlogel Paleo, B.: Atomic cut introduction by resolution: proof structuring and compression. In: Clarke, E.M., Voronkov, A. (eds.) LPAR-16 2010. LNCS, vol. 6355, pp. 463–480. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Rollini, S.F., Bruttomesso, R., Sharygina, N.: An efficient and flexible approach to resolution proof reduction. In: Raz, O. (ed.) HVC 2010. LNCS, vol. 6504, pp. 182–196. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. 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 

  12. 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)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Victoria, Victoria, Canada

    Jan Gorzny

  2. Vienna University of Technology, Vienna, Austria

    Bruno Woltzenlogel Paleo

Authors
  1. Jan Gorzny
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  2. Bruno Woltzenlogel Paleo
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Corresponding author

Correspondence to Jan Gorzny .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

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Gorzny, J., Woltzenlogel Paleo, B. (2015). Towards the Compression of First-Order Resolution Proofs by Lowering Unit Clauses. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_24

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  • DOI: https://doi.org/10.1007/978-3-319-21401-6_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21400-9

  • Online ISBN: 978-3-319-21401-6

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