Theory of linear and integer programming
Theory of linear and integer programming
Superposition and Chaining for Totally Ordered Divisible Abelian Groups
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Combining superposition, sorts and splitting
Handbook of automated reasoning
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
SAT modulo the theory of linear arithmetic: exact, inexact and commercial solvers
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
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
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
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
Superposition-based analysis of first-order probabilistic timed automata
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Model evolution with equality modulo built-in theories
CADE'11 Proceedings of the 23rd international conference on Automated deduction
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
Superposition modulo non-linear arithmetic
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Linear quantifier elimination as an abstract decision procedure
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Automatic generation of invariants for circular derivations in SUP(LA)
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and 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
Combination of disjoint theories: beyond decidability
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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
A Resolution Calculus for First-order Schemata
Fundamenta Informaticae
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The hierarchical superposition based theorem proving calculus of Bachmair, Ganzinger, and Waldmann enables the hierarchic combination of a theory with full first-order logic. If a clause set of the combination enjoys a sufficient completeness criterion, the calculus is even complete. We instantiate the calculus for the theory of linear arithmetic. In particular, we develop new effective versions for the standard superposition redundancy criteria taking the linear arithmetic theory into account. The resulting calculus is implemented in SPASS(LA) and extends the state of the art in proving properties of first-order formulas over linear arithmetic.