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Abstract

We introduce a class of restrictions for the
ordered paramodulation and superposition calculi (inspired by the {\em basic\/}
strategy for narrowing), in which paramodulation inferences are forbidden at
terms introduced by substitutions from previous inference steps.
In addition we introduce restrictions based on term selection rules and
redex orderings, which are general criteria for delimiting the terms
which are available for inferences. These refinements are compatible
with standard ordering restrictions and are complete without paramodulation
into variables or using functional reflexivity axioms.
We prove refutational completeness in the context of deletion rules,
such as simplification by rewriting (demodulation) and subsumption,
and of techniques for eliminating redundant inferences.