▁ ▁Therefore , ▁ ∀ X ▁P ( X ) ▁→ ▁R ( X ) ▁ ▁In ▁C NF , ▁the ▁ante ced ents ▁become : ▁▁▁ ¬ P ( X ) ▁ ∨ ▁Q ( X ) ▁▁ ¬ Q ( Y ) ▁ ∨ ▁R ( Y ) ▁ ▁( Note ▁that ▁the ▁variable ▁in ▁the ▁second ▁clause ▁was ▁renamed ▁to ▁make ▁it ▁clear ▁that ▁variables ▁in ▁different ▁cla uses ▁are ▁distinct .) ▁ ▁Now , ▁un ifying ▁Q ( X ) ▁in ▁the ▁first ▁clause ▁with ▁ ¬ Q ( Y ) ▁in ▁the ▁second ▁clause ▁means ▁that ▁X ▁and ▁Y ▁become ▁the ▁same ▁variable ▁anyway . ▁Sub st itut ing ▁this ▁into ▁the ▁remaining ▁cla uses ▁and ▁combining ▁them ▁gives ▁the ▁conclusion : ▁▁▁ ¬ P ( X ) ▁ ∨ ▁R ( X ) ▁ ▁F actor ing ▁ ▁The ▁resolution ▁rule , ▁as ▁defined ▁by ▁Robinson , ▁also ▁incorpor ated ▁factor ing , ▁which ▁un ifies ▁two ▁liter als ▁in ▁the ▁same ▁clause , ▁before ▁or ▁during ▁the ▁application ▁of ▁resolution ▁as ▁defined ▁above . ▁The ▁resulting ▁inference ▁rule ▁is ▁ref ut ation - complete , ▁in ▁that ▁a ▁set ▁of ▁cla uses ▁is ▁uns atisf i able ▁if ▁and ▁only ▁if ▁there ▁exists ▁a ▁deriv ation ▁of ▁the ▁empty ▁clause ▁using ▁only ▁resolution , ▁en hanced ▁by ▁factor ing . ▁ ▁An ▁example ▁for ▁an ▁uns atisf i able ▁clause ▁set ▁for ▁which ▁factor ing ▁is ▁needed ▁to ▁derive ▁the ▁empty ▁clause ▁is : ▁ ▁Since