▁in ▁the ▁un ified ▁pred ic ates ▁also ▁occur ▁in ▁other ▁pred ic ates ▁in ▁the ▁two ▁cla uses , ▁replace ▁them ▁with ▁their ▁bound ▁values ▁( ter ms ) ▁there ▁as ▁well . ▁ ▁Dis card ▁the ▁un ified ▁pred ic ates , ▁and ▁combine ▁the ▁remaining ▁ones ▁from ▁the ▁two ▁cla uses ▁into ▁a ▁new ▁clause , ▁also ▁joined ▁by ▁the ▁" ∨ " ▁operator . ▁ ▁To ▁apply ▁this ▁rule ▁to ▁the ▁above ▁example , ▁we ▁find ▁the ▁predicate ▁P ▁occurs ▁in ▁neg ated ▁form ▁▁▁ ¬ P ( X ) ▁ ▁in ▁the ▁first ▁clause , ▁and ▁in ▁non - neg ated ▁form ▁▁ ▁P ( a ) ▁ ▁in ▁the ▁second ▁clause . ▁X ▁is ▁an ▁un bound ▁variable , ▁while ▁a ▁is ▁a ▁bound ▁value ▁( term ). ▁Un ifying ▁the ▁two ▁produces ▁the ▁substitution ▁▁ ▁X ▁ ▁a ▁ ▁Dis card ing ▁the ▁un ified ▁pred ic ates , ▁and ▁applying ▁this ▁substitution ▁to ▁the ▁remaining ▁pred ic ates ▁( just ▁Q ( X ), ▁in ▁this ▁case ), ▁produces ▁the ▁conclusion : ▁▁ ▁Q ( a ) ▁ ▁For ▁another ▁example , ▁consider ▁the ▁s yl log istic ▁form ▁▁ ▁All ▁C ret ans ▁are ▁island ers . ▁ ▁All ▁island ers ▁are ▁li ars . ▁ ▁Therefore ▁all ▁C ret ans ▁are ▁li ars . ▁ ▁Or ▁more ▁generally , ▁▁▁ ∀ X ▁P ( X ) ▁→ ▁Q ( X ) ▁▁ ∀ X ▁Q ( X ) ▁→ ▁R ( X )