Experiments with discrimination-tree indexing and path indexing for term retrieval
Journal of Automated Reasoning
Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
Term rewriting and all that
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Journal of Automated Reasoning
Ordered Semantic Hyper-Linking
Journal of Automated Reasoning
Integration of Equality Reasoning into the Disconnection Calculus
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
FDPLL - A First Order Davis-Putnam-Longeman-Loveland Procedure
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Handbook of automated reasoning
Handbook of automated reasoning
New Directions in Instantiation-Based Theorem Proving
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
AI Communications
AI Communications - CASC
The design and implementation of VAMPIRE
AI Communications - CASC
AI Communications - CASC
The model evolution calculus as a first-order DPLL method
Artificial Intelligence
Logical Engineering with Instance-Based Methods
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
System Description: E- KRHyper
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
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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
Superposition and Model Evolution Combined
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Instantiation-Based Automated Reasoning: From Theory to Practice
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Geometric resolution: a proof procedure based on finite model search
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
The model evolution calculus with equality
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
The TPTP typed first-order form with arithmetic
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Journal of Automated Reasoning
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In many theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this paper, we show how to integrate a modern treatment of equality in the Model Evolution calculus (ME), a first-order version of the propositional DPLL procedure. The new calculus, ME"E, is a proper extension of the ME calculus without equality. Like ME it maintains an explicit candidate model, which is searched for by DPLL-style splitting. For equational reasoning ME"E uses an adapted version of the superposition inference rule, where equations used for superposition are drawn (only) from the candidate model. The calculus also features a generic, semantically justified simplification rule which covers many simplification techniques known from superposition-style theorem proving. Our main theoretical result is the correctness of the ME"E calculus in the presence of very general redundancy elimination criteria. We also describe our implementation of the calculus, the E-Darwin system, and we report on practical experiments with it on the TPTP problem library.