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Journal of Automated Reasoning

, Volume 2, Issue 2, pp 191–216 | Cite as

Seventy-five problems for testing automatic theorem provers

  • Francis Jeffry Pelletier
Problem Corner

Keywords

Propositional Logic Predicate Logic Automate Reasoning Automatic Theorem Prove Clause Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. BledsoeW., BoyerR., and HennemanW. (1972) ‘Computer proofs of limit theorems’,Artificial Intelligence,3, 27–60.zbMATHMathSciNetCrossRefGoogle Scholar
  2. CookS. and ReckhowR. (1979) ‘The relative efficiency of propositional proof systems’,J. Symbolic Logic 44, 36–50.zbMATHMathSciNetCrossRefGoogle Scholar
  3. DeChampeauxD. (1979) ‘Sub-problem finder and instance checker: two cooperating preprocessors for theorem provers’IJCAI 6, 191–196.Google Scholar
  4. GalilZ. (1977) ‘On resolution with clauses of bounded size’,SIAM J. Computing 6, 444–459.zbMATHMathSciNetCrossRefGoogle Scholar
  5. Kalish, D. & Montague, R. (1964)Logic: Techniques of Formal Reasoning, World, Harcourt & Brace,Google Scholar
  6. LuskE. and OverbeekR. (1985) ‘Reasoning about equality’,J. Automated Reasoning,1, 209–228.zbMATHMathSciNetGoogle Scholar
  7. McCharenR., OverbeekR., & WosL. (1976) ‘Problems and experiments for and with automated theorem-proving programs’,IEEE Trans. Computers C-25(8), 773–782.zbMATHGoogle Scholar
  8. McCuneW. (1985) ‘Schubert's Steamroller Problem with linked UR-resolution’Assoc. Automated Reasoning Newsletter,4, 4–6.Google Scholar
  9. MontagueR. (1955) ‘On the paradox of grounded classes’J. Symbolic Logic 20, 140.zbMATHMathSciNetCrossRefGoogle Scholar
  10. NewellA., ShawJ., and SimonH. (1957) ‘Empirical explorations with the logic theory machine: a case study in heuristics’. Reprinted in E.Feigenbaum and J.Feldman (eds.)Computers and Thought (McGraw-Hill, N.Y.) pp. 279–293 (1963).Google Scholar
  11. NewellA. and SimonH. (1972)Human Problem Solving, (Prentice-Hall, Englewood Cliffs).Google Scholar
  12. PelletierF. J. (1982) ‘Completely nonclausal, completely heuristically driven automatic theorem proving’, Technical Report TR82-7, (Dept. of Computing Science, Edmonton, Alberta).Google Scholar
  13. PelletierF. J. (1985) ‘Six problems in translational equivalence’,Logique et Analyse 108, 423–434.MathSciNetGoogle Scholar
  14. SiklóssyL., RichA., and MarinovV. (1973) ‘Breadth first search: some surprising results’,Artificial Intelligence 4, 1–27.zbMATHMathSciNetCrossRefGoogle Scholar
  15. StickelM. (1986) ‘Schubert's steamroller problem: formulations and solutions’,J. Automated Reasoning 2, 89–104.zbMATHMathSciNetCrossRefGoogle Scholar
  16. ThomasonR. (1972)Symbolic Logic (Prentice-Hall, Englewood Cliffs).Google Scholar
  17. TseitinG. S. (1968) ‘On the complexity of derivation in propositional calculus’, reprinted in J.Siekmann and G.Wrightson (eds.)Automation of Reasoning (Springer-Verlag, Berlin).Google Scholar
  18. Urquhart, A. (unpublished a) ‘The complexity of Genzen systems for propositional logic’.Google Scholar
  19. Urquhart, A. (unpublished b) ‘Hard examples for resolution’.Google Scholar
  20. WaltherC. (1985) ‘A mechanical solution of Schubert's steamroller by many-sorted resolution’,Artificial Intelligence 26, 217–224.zbMATHMathSciNetCrossRefGoogle Scholar
  21. WhiteheadA. and RussellB. (1910)Principia Mathematica, Vol. I. (Cambridge UP, Cambridge).Google Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Francis Jeffry Pelletier
    • 1
  1. 1.Department of PhilosophyUniversity of AlbertaEdmontonCanada

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