The standard notions of tautology and subsumption can be naturally generalized, (so that refutation completeness is preserved with respect to the associated deletion), within the context of (a specified set of) modified deduction rules for binary clausal resolution-refutation which build-in the reflexivity, symmetry, transitivity and predicate substitutivity axioms for equality. The generalized notions of subsumption and tautology, \Sigma 0 -subsumption and \Sigma 0 -tautology , respectively, are presented, and EPC! , a binary clausal system which provides an adequate deductive context for refutation completeness under deletion with respect to these generalized notions, is introduced. Additionally, some refutation completeness preserving clause "normalization" techniques including generalized forms of replacement factoring and a form of demodulation, are presented. Some refinements for the rules are offered, as well as a possible further generalization for subsumption, and a generaliz..