Handbook of theoretical computer science (vol. B)
Journal of Automated Reasoning
Basic Paramodulation and Superposition
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
New Directions in Instantiation-Based Theorem Proving
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
The design and implementation of VAMPIRE
AI Communications - CASC
AI Communications - CASC
The model evolution calculus as a first-order DPLL method
Artificial Intelligence
Logical Engineering with Instance-Based Methods
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
CAV'07 Proceedings of the 19th international conference on Computer aided verification
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Integrating linear arithmetic into superposition calculus
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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We give a method for extending efficient SMT solvers to handle quantifiers, using Superposition inference rules. In our method, the input formula is converted into CNF as in traditional first order logic theorem provers. The ground clauses are given to the SMT solver, which runs a DPLL method to build partial models. The partial model is passed to a Congruence Closure procedure, as is normally done in SMT. Congruence Closure calculates all reduced (dis)equations in the partial model and passes them to a Superposition procedure, along with a justification. The Superposition procedure then performs an inference rule, which we call Justified Superposition, between the (dis)equations and the nonground clauses, plus usual Superposition rules with the nonground clauses. Any resulting ground clauses are provided to the DPLL engine. We prove the completeness of this method, using a nontrivial modification of Bachmair and Ganzinger's model generation technique. We believe this combination uses the best of both worlds, an SMT process to handle ground clauses efficiently, and a Superposition procedure which uses orderings to handle the nonground clauses.