Solving quantified verification conditions using satisfiability modulo theories

Yeting Ge, Clark Barrett, Cesare Tinelli

Research output: Chapter in Book/Report/Conference proceedingConference contribution


First order logic provides a convenient formalism for describing a wide variety of verification conditions. Two main approaches to checking such conditions are pure first order automated theorem proving (ATP) and automated theorem proving based on satisfiability modulo theories (SMT). Traditional ATP systems are designed to handle quantifiers easily, but often have difficulty reasoning with respect to theories. SMT systems, on the other hand, have built-in support for many useful theories, but have a much more difficult time with quantifiers. One clue on how to get the best of both worlds can be found in the legacy system Simplify which combines built-in theory reasoning with quantifier instantiation heuristics. Inspired by Simplify and motivated by a desire to provide a competitive alternative to ATP systems, this paper describes a methodology for reasoning about quantifiers in SMT systems. We present the methodology in the context of the Abstract DPLL Modulo Theories framework. Besides adapting many of Simplify's techniques, we also introduce a number of new heuristics. Most important is the notion of instantiation level which provides an effective mechanism for prioritizing and managing the large search space inherent in quantifier instantiation techniques. These techniques have been implemented in the SMT system CVC3. Experimental results show that our methodology enables CVC3 to solve a significant number of benchmarks that were not solvable with any previous approach.

Original languageEnglish (US)
Title of host publicationAutomated Deduction - CADE-21 - 21st International Conference on Automated Deduction, Proceedings
PublisherSpringer Verlag
Number of pages16
ISBN (Print)3540735941, 9783540735946
StatePublished - 2007
Event21st International Conference on Automated Deduction, CADE-21 2007 - Bremen, Germany
Duration: Jul 17 2007Jul 20 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4603 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other21st International Conference on Automated Deduction, CADE-21 2007

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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