Skip to main content
Springer Nature Link
Log in

MACE4 and SEM: A Comparison of Finite Model Generators

  • Chapter
Automated Reasoning and Mathematics

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7788))

Abstract

This article has three objectives: (1) Promote Mace4, a program developed by Bill McCune that searches for finite models of first-order formulas and that is the best way to remember Bill. (2) Promote the research on model generation of first-order formulas. Mace4 remains one of the best model generation programs and we need newcomers who can take over Bill’s torch, because model generation is very important to automated reasoning and has many applications. (3) Compare Mace4 with SEM in detail so that the users of these tools or new model generator developers will understand the strengths and weaknesses of both systems and take advantage from this study.

Supported in part by NSFs of China and USA.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Audemard, G., Benhamou, B.: Reasoning by Symmetry and Function Ordering in Finite Model Generation. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, p. 226. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Audemard, G., Benhamou, B., Henocque, L.: Predicting and Detecting Symmetries in FOL Finite Model Search. Journal of Automated Reasoning 36(3), 177–212 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Audemard, G., Henocque, L.: The eXtended Least Number Heuristic. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 427–442. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solver. In: Twenty-First International Joint Conference on Artificial Intelligence, IJCAI 2009 (2009)

    Google Scholar 

  5. Baumgartner, P., Fuchs, A., De Nivelle, H., Tinelli, C.: Computing finite models by reduction to function-free clause logic. J. of Applied Logic 7(1), 58–74 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Baumgartner, P., Tinelli, C.: The Model Evolution Calculus. In: Baader, F. (ed.) CADE-19. LNCS (LNAI), vol. 2741, pp. 350–364. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Benhamou, B., Henocque, L.: A new method for finite model search in equational theories: FMSET system. Fundamenta Informaticae 39(1,2), 21–38 (1999)

    MathSciNet  MATH  Google Scholar 

  8. Bennett, F.E., Du, B., Zhang, H.: Existence of conjugate orthogonal diagonal Latin squares. J. Combin. Designs 5, 449–461 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bennett, F.E., Du, B., Zhang, H.: Existence of self-orthogonal diagonal Latin squares with a missing subsquare. Discrete Math. 261, 69–86 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bennett, F.E., Zhu, L.: Conjugate-orthogonal Latin squares and related structures. In: Dinitz, J., Stinson, D. (eds.) Contemporary Design Theory: A Collection of Surveys, pp. 41–96. Wiley, New York (1992)

    Google Scholar 

  11. Boy de la Tour, T.: Up-to-Isomorphism Enumeration of Finite Models - The Monadic Case. In: Bonacina, M.P., Furbach, U. (eds.) International Workshop First-Order Theorem Proving (FTP 1997). RISC-Linz Report Series No. 97-50, pp. 29–33. Schloss Hagenberg by Linz, Austria (1997)

    Google Scholar 

  12. Boy de la Tour, T.: Some Techniques of Isomorph-Free Search. In: Campbell, J., Roanes-Lozano, E. (eds.) AISC 2000. LNCS (LNAI), vol. 1930, pp. 240–252. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Bürckert, H.-J., Herold, A., Kapur, D., Siekmann, J.H., Stickel, M., Tepp, M., Zhang, H.: Opening the AC-unification race. J. of Automated Reasoning (4), 465–474 (1988)

    Google Scholar 

  14. Burris, S., Yeats, K.: The saga of the high school identities. Algebra Universalis 52, 325–342 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Caferra, R., Leitsch, A., Peltier, N.: Automated Model Building. Applied Logic Series, vol. 31. Kluwer Academic Publisher (2004)

    Google Scholar 

  16. Caferra, R., Zabel, N.: Extending Resolution for Model Construction. In: van Eijck, J. (ed.) JELIA 1990. LNCS, vol. 478, pp. 153–169. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  17. Claessen, K., Sörensson, N.: New techniques that improve Mace-style finite model finding. In: Model Computation – Principles, Algorithms, Applications, CADE-19 Workshop W4, Miami, Florida, USA (2003)

    Google Scholar 

  18. Dénes, J., Keedwell, A.D.: Latin squares and their applications. Academic Press, New York (1974)

    MATH  Google Scholar 

  19. Du, B.: Self-orthogonal diagonal Latin square with missing subsquare. JCMCC 37, 193–203 (2001)

    MathSciNet  MATH  Google Scholar 

  20. Een, N., Svrensson, N.: Minisat: A SAT solver with conflict-clause minimization. In: SAT 2005 (2005) (poster paper)

    Google Scholar 

  21. Fujita, M., Slaney, J., Bennett, F.: Automatic generation of some results in finite algebra. In: Proc. Int’l Joint Conf. on Artificial Intelligence (IJCAI 1993), pp. 52–57 (1993)

    Google Scholar 

  22. Galton, A.: Note on a lemma of Ladkin. Journal of Logic and Computation 6(1), 1–4 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  23. Hasegawa, R., Koshimura, M., Fujita, H.: MGTP: A Parallel Theorem Prover Based on Lazy Model Generation. In: Kapur, D. (ed.) CADE-11. LNCS, vol. 607, pp. 776–780. Springer, Heidelberg (1992)

    Google Scholar 

  24. Huang, Z., Zhang, H., Zhang, J.: Improving first-order model searching by propositional reasoning and lemma learning. In: The Seventh International Conference on Theory and Applications of Satisfiability Testing (SAT 2004), Vancouver, BC, Canada (May 2004)

    Google Scholar 

  25. Jia, X., Zhang, J.: A Powerful Technique to Eliminate Isomorphism in Finite Model Search. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 318–331. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  26. Kapur, D., Zhang, H.: An Overview of RRL: Rewrite Rule Laboratory. In: Dershowitz, N. (ed.) RTA 1989. LNCS, vol. 355, pp. 513–529. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  27. Kim, S., Zhang, H.: ModGen: Theorem proving by model generation. In: Proc. of National Conference of American Association on Artificial Intelligence (AAAI 1994), Seattle, WA, pp. 162–167. MIT Press (1994)

    Google Scholar 

  28. Kumar, V.: Algorithms for constraint satisfaction problems: A survey. AI Magazine 13(1), 32–44 (1992)

    Google Scholar 

  29. Kunen, K.: The structure of conjugacy closed loops. Transactions of the American Mathematical Society 352(6), 2889–2911 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  30. Leech, J.: Skew lattices in rings. Algebra Universalis 26, 48–72 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  31. Manthey, R., Bry, F.: SATCHMO: A Theorem Prover Implemented in Prolog. In: Lusk, E., Overbeek, R. (eds.) CADE 1988. LNCS, vol. 310, pp. 415–434. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  32. McCune, W.: Experiments with discrimination tree indexing and path indexing for term retrieval. J. of Automated Reasoning 9(2), 147–167 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  33. McCune, W.: MACE 2.0 Reference Manual and Guide. Technical Memorandum No. 249, ANL/MCS-TM-249, Argonne National Lab, Argonne, IL, USA (1994), http://www-unix.mcs.anl.gov/AR/mace2/

  34. McCune, W.: Otter 3.3 Reference Manual, Technical Memorandum No. 263, Argonne National Laboratory, Argonne, IL, USA (August 2003), http://www-unix.mcs.anl.gov/AR/otter/otter33.pdf

  35. McCune, W.: Mace4 reference manual and guide, Technical Memorandum No. 264, Argonne National Laboratory, Argonne, IL, USA (August 2003), http://www.cs.unm.edu/~mccune/prover9/

  36. McCune, W.: Library for Automated Deduction Research (2009), http://www.cs.unm.edu/~mccune/prover9/

  37. McCune, W.: Solution of the Robbins problem. J. of Automated Reasoning 19(3), 263–276 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  38. McCune, W., Henschen, L.J.: Experiments with semantic paramodulation. J. of Automated Reasoning 1(3), 231–261 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  39. Nelson, G., Oppen, D.C.: Fast decision procedures based on congruence closure. J. ACM 27(2), 356–364 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  40. Pichler, R.: Algorithms on Atomic Representations of Herbrand Models. In: Dix, J., Fariñas del Cerro, L., Furbach, U. (eds.) JELIA 1998. LNCS (LNAI), vol. 1489, pp. 199–215. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  41. Slaney, J.: Finder: Finite Domain Enumerator. In: Bundy, A. (ed.) CADE-12. LNCS, vol. 814, pp. 798–801. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  42. Slaney, J., Fujita, M., Stickel, M.: Automated reasoning and exhaustive search: Quasigroup existence problems. Computers & Math. with Appl. 29(2), 115–132 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  43. Slaney, J., Lusk, E.L., McCune, W.: SCOTT: Semantically Constrained Otter (System Description). In: Bundy, A. (ed.) CADE-12. LNCS, vol. 814, pp. 764–768. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  44. Spinks, M.: On middle distributivity for Skew lattices. Semigroup Forum 61(3), 341–345 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  45. Stein, S.K.: On the foundations of quasigroups. Trans. Amer. Math. Soc. 85, 228–256 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  46. Tammet, T.: Using Resolution for Deciding Solvable Classes and Building Finite Models. In: Barzdins, J., Bjorner, D. (eds.) Baltic Computer Science. LNCS, vol. 502, pp. 33–64. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  47. Tammet, T.: Finite model building: improvements and comparisons. In: Model Computation – Principles, Algorithms, Applications, CADE-19 Workshop W4, Miami, Florida, USA (2003)

    Google Scholar 

  48. Zhang, H.: Sato: An Efficient Propositional Prover. In: McCune, W. (ed.) CADE-14. LNCS, vol. 1249, pp. 272–275. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  49. Zhang, H.: Specifying Latin squares in propositional logic. In: Veroff, R. (ed.) Automated Reasoning and Its Applications, Essays in Honor of Larry Wos. MIT Press (1997)

    Google Scholar 

  50. Zhang, H.: Combinatorial designs by SAT solvers. In: Biere, A., Heule, M., Van Haaren, H., Walsh, T. (eds.) Handbook of Satisfiability, ch. 17. IOS Press (2009)

    Google Scholar 

  51. Zhang, H., Stickel, M.: Implementing the Davis-Putnam method. J. of Automated Reasoning 24, 277–296 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  52. Zhang, J.: Problems on the Generation of Finite Models. In: Bundy, A. (ed.) CADE-12. LNCS, vol. 814, pp. 753–757. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  53. Zhang, J.: Constructing finite algebras with Falcon. J. of Automated Reasoning 17(1), 1–22 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  54. Zhang, J.: On the relational translation method for propositional modal logics. Technical Report ISCAS-LCS-96-12, Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences (December 1996)

    Google Scholar 

  55. Zhang, J.: Showing the independence of an axiom for temporal intervals by model generation. Association for Automated Reasoning Newsletter, No. 40 (1998), http://www.aarinc.org/Newsletters/040-1998-06.html

  56. Zhang, J.: System Description: MCS: Model-Based Conjecture Searching. In: Ganzinger, H. (ed.) CADE-16. LNCS (LNAI), vol. 1632, pp. 393–397. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  57. Zhang, J.: Test problem and Perl scripts for finite model searching. Association for Automated Reasoning Newsletter, No. 47 (April 2000), http://www.aarinc.org/Newsletters/047-2000-04.html

  58. Zhang, J.: Computer Search for Counterexamples to Wilkie’s Identity. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 441–451. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  59. Zhang, J., Zhang, H.: SEM: a system for enumerating models. In: Proc. 14th Int’l Joint Conf. on Artif. Intel. (IJCAI), pp. 298–303 (1995)

    Google Scholar 

  60. Zhang, J., Zhang, H.: Constraint Propagation in Model Generation. In: Montanari, U., Rossi, F. (eds.) CP 1995. LNCS, vol. 976, pp. 398–414. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  61. Zhang, J., Zhang, H.: Extending Finite Model Searching with Congruence Closure Computation. In: Buchberger, B., Campbell, J. (eds.) AISC 2004. LNCS (LNAI), vol. 3249, pp. 94–102. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  62. Zhang, X.: Incomplete perfect Mendelsohn designs with block size four. Discrete Mathematics 254, 565–597 (2002)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Iowa, Iowa City, IA, 52242, U.S.A.

    Hantao Zhang

  2. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Jian Zhang

Authors
  1. Hantao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Verona, 37134, Verona, Italy

    Maria Paola Bonacina

  2. Artificial Intelligence Center, SRI International, 333 Ravenswood Avenue, 94025, Menlo Park, CA, USA

    Mark E. Stickel

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Zhang, H., Zhang, J. (2013). MACE4 and SEM: A Comparison of Finite Model Generators. In: Bonacina, M.P., Stickel, M.E. (eds) Automated Reasoning and Mathematics. Lecture Notes in Computer Science(), vol 7788. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36675-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36675-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36674-1

  • Online ISBN: 978-3-642-36675-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics