Satallax: An Automatic Higher-Order Prover

  • Chad E. Brown
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)


Satallax is an automatic higher-order theorem prover that generates propositional clauses encoding (ground) tableau rules and uses MiniSat to test for unsatisfiability. We describe the implementation, focusing on flags that control search and examples that illustrate how the search proceeds.


higher-order logic simple type theory higher-order theorem proving 


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  1. 1.
    Backes, J., Brown, C.E.: Analytic Tableaux for Higher-Order Logic with Choice. Journal of Automated Reasoning 47(4), 451–479 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Benzmüller, C.: Equality and Extensionality in Automated Higher-Order Theorem Proving. PhD thesis, Universität des Saarlandes (1999)Google Scholar
  3. 3.
    Benzmüller, C., Paulson, L.C., Theiss, F., Fietzke, A.: LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 162–170. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Blanchette, J.C., Böhme, S., Paulson, L.C.: Extending Sledgehammer with SMT Solvers. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 116–130. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Brown, C.E.: Solving for Set Variables in Higher-Order Theorem Proving. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 408–422. Springer, Heidelberg (2002)Google Scholar
  6. 6.
    Brown, C.E.: Reducing Higher-Order Theorem Proving to a Sequence of SAT Problems. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 147–161. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    De Moura, L., Bjørner, N.: Satisfiability modulo theories: introduction and applications. Commununications of the ACM 54(9), 69–77 (2011)CrossRefGoogle Scholar
  8. 8.
    Eén, N., Sörensson, N.: An Extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    McCarthy, J.: A Tough Nut for Proof Procedures. Stanford Artificial Intelligence Memo No. 16 (July 1964)Google Scholar
  10. 10.
    Sutcliffe, G.: The TPTP Problem Library and Associated Infrastructure: The FOF and CNF Parts, v3.5.0. Journal of Automated Reasoning 43(4), 337–362 (2009)zbMATHCrossRefGoogle Scholar
  11. 11.
    Sutcliffe, G.: The CADE-23 Automated Theorem Proving System Competition - CASC-23. AI Communications 25(1), 49–63 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chad E. Brown
    • 1
  1. 1.Saarland UniversitySaarbrückenGermany

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