A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Ordered Semantic Hyper-Linking
Journal of Automated Reasoning
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
A Decision Procedure for an Extensional Theory of Arrays
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
The Calculus of Computation: Decision Procedures with Applications to Verification
The Calculus of Computation: Decision Procedures with Applications to Verification
On Variable-inactivity and Polynomial T-Satisfiability Procedures
Journal of Logic and Computation
Efficient E-Matching for SMT Solvers
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Automatic Decidability and Combinability Revisited
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Engineering DPLL(T) + Saturation
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Deciding array formulas with frugal axiom instantiation
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
A write-based solver for SAT modulo the theory of arrays
Proceedings of the 2008 International Conference on Formal Methods in Computer-Aided Design
Complete Instantiation for Quantified Formulas in Satisfiabiliby Modulo Theories
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Solving quantified verification conditions using satisfiability modulo theories
Annals of Mathematics and Artificial Intelligence
Decidable fragments of many-sorted logic
Journal of Symbolic Computation
Theory decision by decomposition
Journal of Symbolic Computation
Instantiation of SMT problems modulo integers
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
Automatic combinability of rewriting-based satisfiability procedures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Decidability and undecidability results for nelson-oppen and rewrite-based decision procedures
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Information Processing Letters
Instantiation Schemes for Nested Theories
ACM Transactions on Computational Logic (TOCL)
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State-of-the-art theory solvers generally rely on an instantiation of the axioms of the theory, and depending on the solvers, this instantiation is more or less explicit. This paper introduces a generic instantiation scheme for solving SMT problems, along with syntactic criteria to identify the classes of clauses for which it is complete. The instantiation scheme itself is simple to implement, and we have produced an implementation of the syntactic criteria that guarantee a given set of clauses can be safely instantiated. We used our implementation to test the completeness of our scheme for several theories of interest in the SMT community, some of which are listed in the last section of this paper.