Automating Boolean Set Operations in Mizar Proof Checking with the Aid of an External SAT Solver

Abstract

In this paper we present the results of an experiment with employing an external SAT solver to strengthen the notion of obviousness of the Mizar proof checker. The presented extension of the Mizar system is based on a version of MiniSAT, called Logic2CNF. The SAT-enhanced Mizar checker is programmed to automatically spawn a new Logic2CNF process whenever it needs to justify any goal that can be solved by reducing it into a corresponding propositional satisfiability problem (equalities based on Boolean operations or set inclusion). The external tool is interfaced within the implementation of Mizar’s requirements directives.

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Correspondence to Adam Naumowicz.

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To the memory of Andrzej Trybulec

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Naumowicz, A. Automating Boolean Set Operations in Mizar Proof Checking with the Aid of an External SAT Solver. J Autom Reasoning 55, 285–294 (2015). https://doi.org/10.1007/s10817-015-9332-6

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Keywords

  • Mizar
  • SAT solvers
  • Proof assistants
  • Boolean operations