Ordered Chaining for Total Orderings

We propose inference systems based on ordered chaining and a concept of (global) redundancy for clauses and inferences for dealing with total orderings. A key to the practicality of chaining techniques is the extent to which so-called variable chainings can be restricted. We demonstrate that ordering restrictions and the rewrite techniques which account for their completeness considerably restrict variable chaining. For dense total orderings we show that the techniques for eliminating unshielded variables are admissible simplifications so that no variable chaining is needed at all. We also include equality by combining ordered chaining with superposition