Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
Term rewriting and all that
Ordered Semantic Hyper-Linking
Journal of Automated Reasoning
New Directions in Instantiation-Based Theorem Proving
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Comparing Instance Generation Methods for Automated Reasoning
Journal of Automated Reasoning
Logical Engineering with Instance-Based Methods
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
System Description: Spass Version 3.0
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
iProver --- An Instantiation-Based Theorem Prover for First-Order Logic (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Instantiation-Based Automated Reasoning: From Theory to Practice
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Combining instance generation and resolution
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
The decidability of the first-order theory of knuth-bendix order
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
The model evolution calculus with equality
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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We present a new calculus for first-order theorem proving with equality, $ \mathcal{ME}+$ Sup, which generalizes both the Superposition calculus and the Model Evolution calculus (with equality) by integrating their inference rules and redundancy criteria in a non-trivial way. The main motivation is to combine the advantageous features of these two rather complementary calculi in a single framework. In particular, Model Evolution, as a lifted version of the propositional DPLL procedure, contributes a non-ground splitting rule that effectively permits to split a clause into non variable disjoint subclauses. In the paper we present the calculus in detail. Our main result is its completeness under semantically justified redundancy criteria and simplification rules. We also show how under certain assumptions the model representation computed by a (finite and fair) derivation can be queried in an effective way.