Solving Quantified Verification Conditions Using Satisfiability Modulo Theories
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
(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
Superposition and Model Evolution Combined
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Superposition modulo linear arithmetic SUP(LA)
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
The model evolution calculus with equality
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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
E-Matching with free variables
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Combination of disjoint theories: beyond decidability
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
Hierarchic superposition with weak abstraction
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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Many applications of automated deduction require reasoning modulo background theories, in particular some form of integer arithmetic. Developing corresponding automated reasoning systems that are also able to deal with quantified formulas has recently been an active area of research. We contribute to this line of research and propose a novel instantiation-based method for a large fragment of first-order logic with equality modulo a given complete background theory, such as linear integer arithmetic. The new calculus is an extension of the Model Evolution Calculus with Equality, a first-order logic version of the propositional DPLL procedure, including its ordering-based redundancy criteria. We present a basic version of the calculus and prove it sound and (refutationally) complete under certain conditions.