▁prefix ▁notation ▁string . ▁For ▁example , ▁if ▁you ▁have ▁four ▁ax i oms ▁a ▁typical ▁proof ▁in ▁D - notation ▁might ▁look ▁like : ▁ ▁D D 1 2 D 3 4 ▁ ▁which ▁shows ▁a ▁cond ensed ▁det achment ▁step ▁using ▁the ▁result ▁of ▁two ▁prior ▁cond ensed ▁det achment ▁steps , ▁the ▁first ▁of ▁which ▁used ▁ax i oms ▁ 1 ▁and ▁ 2 , ▁and ▁the ▁second ▁of ▁which ▁used ▁ax i oms ▁ 3 ▁and ▁ 4 . ▁ ▁This ▁notation , ▁besides ▁being ▁used ▁in ▁some ▁autom ated ▁theorem ▁pro vers , ▁sometimes ▁appears ▁in ▁catalog s ▁of ▁proofs . ▁ ▁Cond ensed ▁det achment ' s ▁use ▁of ▁un ification ▁pred ates ▁the ▁resolution ▁techniques ▁of ▁autom ated ▁theorem ▁prov ing . ▁ ▁Adv antages ▁ ▁For ▁autom ated ▁theorem ▁prov ing ▁cond ensed ▁det achment ▁has ▁a ▁number ▁of ▁advantages ▁over ▁raw ▁mod us ▁pon ens ▁and ▁uniform ▁substitution . ▁ ▁At ▁a ▁Mod us ▁Pon ens ▁and ▁substitution ▁proof ▁you ▁have ▁an ▁infinite ▁number ▁of ▁choices ▁for ▁what ▁you ▁can ▁substitute ▁for ▁variables . ▁This ▁means ▁that ▁you ▁have ▁an ▁infinite ▁number ▁of ▁possible ▁next ▁steps . ▁ ▁With ▁cond ensed ▁det achment ▁there ▁are ▁only ▁a ▁finite ▁number ▁of ▁possible ▁next ▁steps ▁in ▁a ▁proof . ▁ ▁The ▁D - notation ▁for ▁complete ▁cond ensed ▁det achment ▁proofs ▁allows ▁easy ▁description ▁of ▁proofs ▁for ▁catalog ing ▁and ▁search . ▁ ▁A ▁typical ▁complete ▁ 3 0 ▁step ▁proof ▁is ▁less ▁than ▁ 6