You may ignore a Trap’s alternative cost condition and simply cast it for its normal mana cost. This is true even if its alternative cost condition has been met.

Casting a Trap by paying its alternative cost doesn't change its mana cost or converted mana cost. The only difference is the cost you actually pay.

Effects that increase or reduce the cost to cast a Trap will apply to whichever cost you chose to pay.

Archive Trap checks only whether an opponent searched his or her library. It doesn't matter whether that player found a card during the search.

A spell or ability causes a player to search his or her library only if it specifically contains the word "search" in its text. For example, if a spell or ability lets a player look at the top four cards of his or her library and do something with one of those cards, that's not a search.

If a search effect is affected by Aven Mindcensor's ability (which causes a player to search the top four cards of his or her library instead), that still counts as searching that library.

The opponent you target doesn't have to be the opponent who searched his or her library.

If the targeted opponent has fewer than thirteen cards in his or her library, that player puts his or her entire library into his or her graveyard.