Efficient instance retrieval with standard and relational path indexing

Backward demodulation is a simplification technique used in saturation-based theorem proving with superposition and ordered paramodulation. It requires instance retrieval, i.e., search for instances of some term in a typically large set of terms. Path indexing is a family of indexing techniques that can be used to solve this problem efficiently. We propose a number of powerful optimisations to standard path indexing. We also describe a novel framework that combines path indexing with relational joins. The main advantage of the proposed scheme is flexibility, which we illustrate by sketching how to adapt the scheme to instance retrieval modulo commutativity and backward subsumption on multi-literal clauses.