Theorem-proving with resolution and superposition
Journal of Symbolic Computation
On word problems in horn theories
Journal of Symbolic Computation
Journal of the ACM (JACM)
Presburger arithmetic with unary predicates is P11 complete
Journal of Symbolic Logic
An algorithm for finding canonical sets of ground rewrite rules in polynomial time
Journal of the ACM (JACM)
A fast algorithm for generating reduced ground rewriting systems from a set of ground equations
Journal of Symbolic Computation
Towards a foundation of completion procedures as semidecision procedures
Theoretical Computer Science
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)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Proving termination with multiset orderings
Communications of the ACM
Automated complexity analysis based on ordered resolution
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Extended static checking for Java
PLDI '02 Proceedings of the ACM SIGPLAN 2002 Conference on Programming language design and implementation
Polynomial-time computation via local inference relations
ACM Transactions on Computational Logic (TOCL)
A Maximal-Literal Unit Strategy for Horn Clauses
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
ACM Transactions on Computational Logic (TOCL)
Automated Reasoning in Some Local Extensions of Ordered Structures
ISMVL '07 Proceedings of the 37th International Symposium on Multiple-Valued Logic
Rewrite-Based Satisfiability Procedures for Recursive Data Structures
Electronic Notes in Theoretical Computer Science (ENTCS)
Rewrite-Based Decision Procedures
Electronic Notes in Theoretical Computer Science (ENTCS)
On Variable-inactivity and Polynomial T-Satisfiability Procedures
Journal of Logic and Computation
Model-based Theory Combination
Electronic Notes in Theoretical Computer Science (ENTCS)
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
${\mathcal{T}}$-Decision by Decomposition
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)
On Deciding Satisfiability by DPLL($\Gamma+{\mathcal T}$) and Unsound Theorem Proving
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Automated Inference of Finite Unsatisfiability
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Theory decision by decomposition
Journal of Symbolic Computation
On local reasoning in 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
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
A taxonomy of theorem-proving strategies
Artificial intelligence today
Superposition modulo linear arithmetic SUP(LA)
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Combinations of theories for decidable fragments of first-order logic
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Data structures with arithmetic constraints: a non-disjoint combination
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Combining theories with shared set operations
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
On theorem proving for program checking: historical perspective and recent developments
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
The spec# programming system: an overview
CASSIS'04 Proceedings of the 2004 international conference on Construction and Analysis of Safe, Secure, and Interoperable Smart Devices
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Blocking and other enhancements for bottom-up model generation methods
IJCAR'06 Proceedings of the Third international joint conference on Automated 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
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Data structure specifications via local equality axioms
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Hierarchic reasoning in local theory extensions
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
A decision procedure for monotone functions over bounded and complete lattices
TARSKI'02-05 Proceedings of the 2006 international conference on Theory and Applications of Relational Structures as Knowledge Instruments - Volume 2
A decidable class of nested iterated schemata
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
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
Synthesising terminating tableau calculi for relational logics
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
On interpolation in decision procedures
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Instantiation Schemes for Nested Theories
ACM Transactions on Computational Logic (TOCL)
Hierarchic superposition with weak abstraction
CADE'13 Proceedings of the 24th international conference on Automated Deduction
Superposition for bounded domains
Automated Reasoning and Mathematics
Theorem proving in large formal mathematics as an emerging AI field
Automated Reasoning and Mathematics
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Applications in software verification often require determining the satisfiability of first-order formulae with respect to 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 to be highly scalable, efficient and suitable for integrated theory reasoning. Inference systems with resolution and superposition are strong at reasoning with equalities, universally quantified variables, and Horn clauses. We describe a theorem-proving method that tightly integrates superposition-based inference system and SMT solver. The combination is refutationally complete if background theory symbols only occur in ground formulae, and non-ground clauses are variable-inactive. Termination is enforced by introducing additional axioms as hypotheses. The system detects any unsoundness introduced by these speculative inferences and recovers from it.