On Deciding Satisfiability by DPLL($\Gamma+{\mathcal T}$) and Unsound Theorem Proving

  • Authors:

  • Maria Paola Bonacina;Christopher Lynch;Leonardo Moura

  • Affiliations:

  • Dipartimento di Informatica, Università degli Studi di Verona, Verona, Italy I-37134;Department of Mathematics and Computer Science, Clarkson University, Potsdam, U.S.A. NY 13699-5815;Microsoft Research, Redmond, U.S.A. WA 98052

  • Venue:
  • CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
  • Year:
  • 2009

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Abstract

Applications in software verification often require determining the satisfiability of first-order formulæ with respect to some background theories. During development, conjectures are usually false. Therefore, it is desirable to have a theorem prover that terminates on satisfiable instances. Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrated theory reasoning. Superposition-based inference systems are strong at reasoning with equalities, universally quantified variables, and Horn clauses. We describe a calculus that tightly integrates Superposition and SMT solvers. The combination is refutationally complete if background theory symbols only occur in ground formulæ, and non-ground clauses are variable inactive. Termination is enforced by introducing additional axioms as hypotheses. The calculus detects any unsoundness introduced by these axioms and recovers from it.