▁be ▁as ▁compact ▁in ▁the ▁number ▁of ▁cla uses ▁as ▁list ▁representations ▁and ▁they ▁also ▁store ▁struct ural ▁information ▁regarding ▁which ▁cla uses ▁were ▁resolved ▁to ▁derive ▁each ▁resol vent . ▁ ▁A ▁simple ▁example ▁▁ ▁In ▁plain ▁language : ▁Suppose ▁ ▁is ▁false . ▁In ▁order ▁for ▁the ▁prem ise ▁ ▁to ▁be ▁true , ▁ ▁must ▁be ▁true . ▁Alternatively , ▁suppose ▁ ▁is ▁true . ▁In ▁order ▁for ▁the ▁prem ise ▁ ▁to ▁be ▁true , ▁ ▁must ▁be ▁true . ▁Therefore , ▁regardless ▁of ▁false hood ▁or ▁ver acity ▁of ▁, ▁if ▁both ▁prem ises ▁hold , ▁then ▁the ▁conclusion ▁ ▁is ▁true . ▁ ▁Resol ution ▁in ▁first ▁order ▁logic ▁▁ ▁Resol ution ▁rule ▁can ▁be ▁generalized ▁to ▁first - order ▁logic ▁to : ▁ ▁where ▁ ▁is ▁a ▁most ▁general ▁un ifier ▁of ▁ ▁and ▁, ▁and ▁ ▁and ▁ ▁have ▁no ▁common ▁variables . ▁ ▁Example ▁ ▁The ▁cla uses ▁ ▁and ▁ ▁can ▁apply ▁this ▁rule ▁with ▁ ▁as ▁un ifier . ▁ ▁Here ▁x ▁is ▁a ▁variable ▁and ▁b ▁is ▁a ▁constant . ▁ ▁Here ▁we ▁see ▁that ▁▁ ▁The ▁cla uses ▁▁ ▁and ▁ ▁are ▁the ▁inference ' s ▁prem ises ▁▁ ▁( the ▁resol vent ▁of ▁the ▁prem ises ) ▁is ▁its ▁conclusion . ▁ ▁The ▁literal ▁ ▁is ▁the ▁left ▁resolved ▁literal , ▁ ▁The ▁literal ▁ ▁is ▁the ▁right ▁resolved ▁literal , ▁▁ ▁is ▁the ▁resolved ▁atom ▁or ▁pivot . ▁▁ ▁is ▁the ▁most ▁general ▁un ifier ▁of ▁the ▁resolved