Adapting Real Quantifier Elimination Methods for Conflict Set Computation

  • Maximilian Jaroschek
  • Pablo Federico Dobal
  • Pascal Fontaine
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9322)


The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e. obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice.


SMT real quantifier elimination cylindrical algebraic decomposition virtual substitution conflict set 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Maximilian Jaroschek
    • 1
  • Pablo Federico Dobal
    • 1
    • 2
    • 3
  • Pascal Fontaine
    • 3
  1. 1.Max Planck Institute for InformaticsSaarbrückenGermany
  2. 2.Universität des SaarlandesSaarbrückenGermany
  3. 3.INRIA, Université de Lorraine and LORIANancyFrance

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