On the Completeness of Arbitrary Selection Strategies for Paramodulation

A crucial way for reducing the search space in automated deduction are the so-called selection strategies: in each clause, the subset of selected literals are the only ones involved in inferences. For first-order Horn clauses without equality, resolution is complete with an arbitrary selection of one single literal in each clause [dN96]. For Horn clauses with built-in equality, i.e., paramodulation-based inference systems, the situation is far more complex. Here we show that if a paramodulation-based inference system is complete with eager selection of negative equations and, moreover, it is compatible with equality constraint inheritance, then it is complete with arbitrary selection strategies. A first important application of this result is the one for paramodulation wrt. non-monotonic orderings, which was left open in [BGNR99].