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Providing a clean procedural semanticsof the ’’Negation As Failure rule‘‘ in Logic Programming hasbeen an open problem for some time now. This rule has been treatedas a technique in nonmonotonic reasoning, not as a rule in classicallogic. This paper contains a demonstration of the negation asfailure rule as a resolution procedure in first-order logic.We present a sound and complete resolution scheme for negationas failure rule for the larger class of constraint logic programs.The approach is to consider a canonical partition of the completionof a definite (constraint) program into the \Ifand the \FI programs. We show that a negated goal,provable from the completed definite program is provable fromjust the \FI part. The clauses in this program havea structure dual to that of definite Horn clauses. We describea sound and complete linear resolution rule for this fragment,and show that a resolution proof of the negated goal from the\FI part corresponds to a finite failure tree resultingfrom classical linear resolution applied to the goal on the \Ifpart of the original definite program. Our work shows that negationas failure rule can be computationally efficient in the sensethat the SLD-resolution on the \If part of a definiteprogram along with the negation as failure rule is more efficientthan a direct resolution procedure on the completion of thatprogram.