Handbook of theoretical computer science (vol. B)
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Automating first-order relational logic
SIGSOFT '00/FSE-8 Proceedings of the 8th ACM SIGSOFT international symposium on Foundations of software engineering: twenty-first century applications
A machine program for theorem-proving
Communications of the ACM
Journal of Automated Reasoning
Partial Instantiation Methods for Inference in First-Order Logic
Journal of Automated Reasoning
Deciding Separation Formulas with SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
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
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
The design and implementation of VAMPIRE
AI Communications - CASC
AI Communications - CASC
The model evolution calculus as a first-order DPLL method
Artificial Intelligence
Encoding First Order Proofs in SAT
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
iProver --- An Instantiation-Based Theorem Prover for First-Order Logic (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Engineering DPLL(T) + Saturation
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Theory decision by decomposition
Journal of Symbolic Computation
The CADE-22 automated theorem proving system competition - CASC-22
AI Communications
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
Combining instance generation and resolution
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Automatic decidability and combinability
Information and Computation
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 consider the problem of checking satisfiability of quantified formulae in First Order Logic with Equality. We propose a new procedure for combining SAT solvers with Superposition Theorem Provers to handle quantified formulae in an efficient and complete way. In our procedure, the input formula is converted into CNF as in traditional first order logic theorem provers. The ground clauses are given to the SAT solver, which runs a DPLL method to build partial models. The partial model is reduced, and then passed to a Superposition procedure, along with justifications of literals. The Superposition procedure then performs an inference rule, which we call Justified Superposition, between the ground literals 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 our procedure, using a nontrivial modification of the Bachmair and Ganzinger's model generation technique. We have implemented a theorem prover based on this idea by reusing state-of-the-art SAT solver and Superposition Theorem Prover. Our theorem prover inherits the best of both worlds: a SAT solver to handle ground clauses efficiently, and a Superposition theorem prover which uses powerful orderings to handle the nonground clauses. Experimental results are promising, and hereby confirm the viability of our method.