Automated deduction by theory resolution
Journal of Automated Reasoning
Theory of linear and integer programming
Theory of linear and integer programming
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
Proving termination with multiset orderings
Communications of the ACM
A Resolution Principle for Clauses with Constraints
Proceedings of the 10th International Conference on Automated Deduction
Incremental Closure of Free Variable Tableaux
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Journal of Automated Reasoning
Differential Dynamic Logic for Hybrid Systems
Journal of 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
Beyond quantifier-free interpolation in extensions of Presburger arithmetic
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Model evolution with equality modulo built-in theories
CADE'11 Proceedings of the 23rd international conference on Automated deduction
An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic
Journal of Automated Reasoning
Ranking function synthesis for bit-vector relations
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Linear quantifier elimination as an abstract decision procedure
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
An interpolating sequent calculus for quantifier-free presburger arithmetic
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
E-Matching with free variables
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
The TPTP typed first-order form with arithmetic
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Structural counter abstraction
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Hierarchic superposition with weak abstraction
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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First-order logic modulo the theory of integer arithmetic is the basis for reasoning in many areas, including deductive software verification and software model checking. While satisfiability checking for ground formulae in this logic is well understood, it is still an open question how the general case of quantified formulae can be handled in an efficient and systematic way. As a possible answer, we introduce a sequent calculus that combines ideas from free-variable constraint tableaux with the Omega quantifier elimination procedure. The calculus is complete for theorems of first-order logic (without functions, but with arbitrary uninterpreted predicates), can decide Presburger arithmetic, and is complete for a substantial fragment of the combination of both.