▁compare ▁( 5 ) ▁and ▁( 1 0 ), ▁which ▁both ▁resolve ▁( 1 ) ▁and ▁( 2 ) ▁on ▁. ▁ ▁Murray ' s ▁rule ▁introduced ▁ 3 ▁new ▁dis j unction ▁symbols : ▁in ▁( 5 ), ▁( 6 ), ▁and ▁( 7 ), ▁while ▁Tra ug ott ' s ▁rule ▁didn ' t ▁introduce ▁any ▁new ▁symbol ; ▁in ▁this ▁sense , ▁Tra ug ott ' s ▁intermediate ▁formulas ▁res emble ▁the ▁user ' s ▁style ▁more ▁closely ▁than ▁Murray ' s . ▁ ▁Due ▁to ▁the ▁latter ▁issue , ▁Tra ug ott ' s ▁rule ▁can ▁take ▁advantage ▁of ▁the ▁imp lication ▁in ▁assumption ▁( 4 ), ▁using ▁as ▁ ▁the ▁non - atomic ▁formula ▁ ▁in ▁step ▁( 1 2 ). ▁Using ▁Murray ' s ▁rules , ▁the ▁sem ant ically ▁equivalent ▁formula ▁ ▁was ▁obtained ▁as ▁( 7 ), ▁however , ▁it ▁could ▁not ▁be ▁used ▁as ▁ ▁due ▁to ▁its ▁s ynt actic ▁form . ▁ ▁Non - c laus al ▁resolution ▁in ▁first - order ▁logic ▁For ▁first - order ▁predicate ▁logic , ▁Murray ' s ▁rule ▁is ▁generalized ▁to ▁allow ▁distinct , ▁but ▁un ifiable , ▁sub form ulas ▁ ▁and ▁ ▁of ▁ ▁and ▁, ▁respectively . ▁If ▁ ▁is ▁the ▁most ▁general ▁un ifier ▁of ▁ ▁and ▁, ▁then ▁the ▁generalized ▁resol vent ▁is ▁. ▁While ▁the ▁rule ▁remains ▁sound ▁if ▁a ▁more ▁special ▁substitution ▁ ▁is ▁used , ▁no ▁such ▁rule ▁applications ▁are ▁needed ▁to ▁achieve ▁comple ten ess . ▁