A-SATCHMORE: SATCHMORE with availability checking
New Generation Computing
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Efficient model generation through compilation
Information and Computation
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Heuristics used by HERBY for semantic tree theorem proving
Annals of Mathematics and Artificial Intelligence
Satchmo - The Compiling and Functional Variants
Journal of Automated Reasoning
Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation
Journal of Automated Reasoning
I-SATCHMO: An Improvement of SATCHMO
Journal of Automated Reasoning
A Comparison of Different Techniques for Grounding Near-Propositional CNF Formulae
Proceedings of the Fifteenth International Florida Artificial Intelligence Research Society Conference
SATCHMO: A Theorem Prover Implemented in Prolog
Proceedings of the 9th International Conference on Automated Deduction
I-SATCHMORE: an improvement of A-SATCHMORE
Journal of Computer Science and Technology
SATCHMOREBID: SATCHMO(RE) with BIDirectional relevancy
New Generation Computing
R-SATCHMO: Refinements on I-SATCHMO
Journal of Logic and Computation
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
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This paper presents an improvement of Herbrand's theorem. We propose a method for specifying a subuniverse of the Herbrand universe of a clause set S for each argument of predicate symbols and function symbols in S. We prove that a clause set S is unsatisfiable if and only if there is a finite unsatisfiable set of ground instances of clauses of S that are derived by only instantiating each variable, which appears as an argument of predicate symbols or function symbols, in S over its corresponding argument's sub-universe of the Herbrand universe of S. Because such sub-universes are usually smaller (sometimes considerably) than the Herbrand universe of S, the number of ground instances may decrease considerably in many cases. We present an algorithm for automatically deriving the sub-universes for arguments in a given clause set, and show the correctness of our improvement. Moreover, we introduce an application of our approach to model generation theorem proving for non-range-restricted problems, show the range-restriction transformation algorithm based on our improvement and provide examples on benchmark problems to demonstrate the power of our approach.