▁valid ▁inference ▁rule ▁that ▁produces ▁a ▁new ▁clause ▁imp lied ▁by ▁two ▁cla uses ▁containing ▁complement ary ▁liter als . ▁A ▁literal ▁is ▁a ▁propos itional ▁variable ▁or ▁the ▁neg ation ▁of ▁a ▁propos itional ▁variable . ▁Two ▁liter als ▁are ▁said ▁to ▁be ▁comple ments ▁if ▁one ▁is ▁the ▁neg ation ▁of ▁the ▁other ▁( in ▁the ▁following , ▁ ▁is ▁taken ▁to ▁be ▁the ▁complement ▁to ▁). ▁The ▁resulting ▁clause ▁contains ▁all ▁the ▁liter als ▁that ▁do ▁not ▁have ▁comple ments . ▁Form ally : ▁ ▁where ▁ ▁all ▁, ▁, ▁and ▁ ▁are ▁liter als , ▁ ▁the ▁div iding ▁line ▁stands ▁for ▁" ent ails ". ▁ ▁The ▁above ▁may ▁also ▁be ▁written ▁as : ▁ ▁The ▁clause ▁produced ▁by ▁the ▁resolution ▁rule ▁is ▁called ▁the ▁resol vent ▁of ▁the ▁two ▁input ▁cla uses . ▁It ▁is ▁the ▁principle ▁of ▁cons ensus ▁applied ▁to ▁cla uses ▁rather ▁than ▁terms . ▁ ▁When ▁the ▁two ▁cla uses ▁contain ▁more ▁than ▁one ▁pair ▁of ▁complement ary ▁liter als , ▁the ▁resolution ▁rule ▁can ▁be ▁applied ▁( in dep end ently ) ▁for ▁each ▁such ▁pair ; ▁however , ▁the ▁result ▁is ▁always ▁a ▁t aut ology . ▁ ▁Mod us ▁pon ens ▁can ▁be ▁seen ▁as ▁a ▁special ▁case ▁of ▁resolution ▁( of ▁a ▁one - liter al ▁clause ▁and ▁a ▁two - liter al ▁clause ). ▁ ▁is ▁equivalent ▁to ▁ ▁A ▁resolution ▁technique ▁ ▁When ▁couple d ▁with ▁a ▁complete ▁search ▁algorithm , ▁the ▁resolution ▁rule ▁yields ▁a ▁sound