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Question on Logic: Resolution Refutation.

Willem F Esterhuyse
in Analysis and Calculus

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A text says that to prove a formula A we have to refute GA (which must reduce to the negation of A). It says that for each sub-formula of the form B OR C to include the following clauses in GA:

{xB OR C, ~xB}, {xB OR C, ~xC}, {xB, xC, ~xB OR C}.

Shouldn't there be two ~xB OR C's and one xB OR C? As stated it resolves to xB OR C  and not it's negation. If not, why not?

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