Redundancy for rigid clausal tableaux

Redundancy is a substantial concept when avoiding endless computation in theorem proving methods. In this paper, we are targeting a special class of tableau calculi, namely rigid clausal tableaux. These tableaux are (1) clausal in the sense that they consist solely of literals, and are (2) rigid in the sense that they employ rigid variables. Such calculi are e.g. rigid hyper tableaux [7] and multi-hyper (hyperS) tableaux [6]. In this paper, we construct a general redundancy concept for rigid clausal tableaux. As a warm-up, we deduce the so-called Sufficient Redundancy Criterion for hyper tableaux [1], in order to demonstrate how rigid variables complicate the redundancy check. Finally, we define what a redundant clause w.r.t. a rigid clausal tableau means, and we prove this redundancy concept to be sound. We show that neither the rigid hyper tableau calculus nor the multi-hyper tableau calculus can employ this redundancy concept, since they do not support the generation of new instances of separate branch clauses. Nevertheless, this fact sets the course to improve the multi-hyper tableau calculus to be applicable in practice.