Equational Reasoning in Saturation-Based Theorem Proving

5 Rewriting Techniques for Equational Reasoning 9 5.1 Knuth-Bendix Completion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.1.1 Basic Concepts in Term Rewriting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.1.2 The Completion Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.1.3 Ordered Rewriting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.1.4 Ordered Completion and Proof Orderings . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.2 Superposition for Horn Clauses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

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