Automated deduction by theory resolution
Journal of Automated Reasoning
Presburger arithmetic with unary predicates is P11 complete
Journal of Symbolic Logic
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
A Hyperresolution-Based Proof Procedure and its Implementation in Prolog
GWAI '87 Proceedings of the 11th German Workshop on Artificial Intelligence
SATCHMO: A Theorem Prover Implemented in Prolog
Proceedings of the 9th International Conference on Automated Deduction
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Solving Quantified Verification Conditions Using Satisfiability Modulo Theories
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Efficient E-Matching for SMT Solvers
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
(LIA) - Model Evolution with Linear Integer Arithmetic Constraints
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Constraint Sequent Calculus for First-Order Logic with Linear Integer Arithmetic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Handbook of Practical Logic and Automated Reasoning
Handbook of Practical Logic and Automated Reasoning
Complete Instantiation for Quantified Formulas in Satisfiabiliby Modulo Theories
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
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
Superposition modulo linear arithmetic SUP(LA)
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Model evolution with equality modulo built-in theories
CADE'11 Proceedings of the 23rd international conference on Automated deduction
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
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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E-matching is the most commonly used technique to handle quantifiers in SMT solvers. It works by identifying characteristic sub-expressions of quantified formulae, named triggers, which are matched during proof search on ground terms to discover relevant instantiations of the quantified formula. E-matching has proven to be an efficient and practical approach to handle quantifiers, in particular because triggers can be provided by the user to guide proof search; however, as it is heuristic in nature, e-matching alone is typically insufficient to establish a complete proof procedure. In contrast, free variable methods in tableau-like calculi are more robust and give rise to complete procedures, e.g., for first-order logic, but are not comparable to e-matching in terms of scalability. This paper discusses how e-matching can be combined with free variable approaches, leading to calculi that enjoy similar completeness properties as pure free variable procedures, but in which it is still possible for a user to provide domain-specific triggers to improve performance.