Introducing Quantified Cuts in Logic with Equality

  • Stefan Hetzl
  • Alexander Leitsch
  • Giselle Reis
  • Janos Tapolczai
  • Daniel Weller
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8562)


Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form ∀ x.A (for quantifier-free A) to a method generating lemmas of the form ∀ x 1 … ∀ x n .A. Moreover, we extend the original method to predicate logic with equality. The new method was implemented and applied to the TSTP proof database. It is shown that the extension of the method to handle equality and quantifier-blocks leads to a substantial improvement of the old algorithm.


Automate Reasoning Conjunctive Normal Form Ground Term Canonical Solution Proof Check 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Stefan Hetzl
    • 1
  • Alexander Leitsch
    • 2
  • Giselle Reis
    • 2
  • Janos Tapolczai
    • 1
  • Daniel Weller
    • 1
  1. 1.Institut für Diskrete Mathematik und GeometrieTechnische Universität WienAustria
  2. 2.Institut für ComputersprachenTechnische Universität WienAustria

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