Uniform Derivation of Decision Procedures by Superposition
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
SATCHMO: A Theorem Prover Implemented in Prolog
Proceedings of the 9th International Conference on Automated Deduction
FINDER: Finite Domain Enumerator - System Description
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Soft Typing for Ordered Resolution
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
A Maximal-Literal Unit Strategy for Horn Clauses
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
Combining superposition, sorts and splitting
Handbook of automated reasoning
Computation: finite and infinite machines
Computation: finite and infinite machines
Proof Systems for Effectively Propositional Logic
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)
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
SEM: a system for enumerating models
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Annals of Mathematics and Artificial Intelligence
The Hyper Tableaux Calculus with Equality and an Application to Finite Model Computation
Journal of Logic and Computation
Superposition modulo linear arithmetic SUP(LA)
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
Blocking and other enhancements for bottom-up model generation methods
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Geometric resolution: a proof procedure based on finite model search
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
On superposition-based satisfiability procedures and their combination
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Combination of disjoint theories: beyond decidability
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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Reasoning about bounded domains in resolution calculi is often painful. For explicit and small domains and formulas with a few variables, grounding can be a successful approach. This approach was in particular shown to be effective by Bill McCune. For larger domains or larger formula sets with many variables, there is not much known. In particular, despite general decidability, superposition implementations that can meanwhile deal with large formula sets typically will not necessarily terminate. We start from the observation that lifting can be done more economically here: A variable does not stand anymore for every ground term, but just for the finitely many domain representatives. Thanks to this observation, the inference rules of superposition can drastically be restricted, and redundancy becomes effective. We present one calculus configuration which constitutes a decision procedure for satisfiability modulo the cardinality bound, and hence decides the Bernays-Schönfinkel class as a simple consequence. Finally, our approach also applies to bounded sorts in combination with arbitrary other, potentially infinite sorts in the framework of soft sorts. This frequent combination --- which we recently explored in a combination of Spass and Isabelle --- is an important motivation of our study.