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I don't think there is such a card. The formulation on cards is always search your opponents library for... Not make him search for...

If you want a mono blue mill deck there are enough cards without using the archive trap, and if you play UB (blue/black) you have tons of options.
That said most people search their libraries without you having to force them. You have tons of fetchland available (budget to very expensive), you have lost of people playing green to fetch land using cards like sakura Tribe Elder, Wood Elves, the new green landfall expedition, you name it...
Some people play tutors...

Anyway I don't think you really need to play cards to make them search their libraries.

Yeah I would like to keep it mono. I am not to worried about getting land out Once Jace is down I will be drawing three cards a turn. Even if I don't get the zero cost of archive trap 5mana cost isn't bad and if I can twincast it I will be laughing!

Even if the card just allows them to search their deck that would be fine. Still your right I probably will get by with out it. Path of Exile allows me to do it but it's white.

Thanks for your input!

Sanity Grinding with Twincast and Hedron Crab go a long way already. Cryptic Command isn't very expensive anymore now that it's no longer T2 and that works wonders with Sanity Grinding.

Sanity Grinding
TwinCast
Cryptic Command
Spell Pierce
Jace
Counterspell
Tome Scour

additional:

- Evacuation
- Sunken Hope
- Overburden
- Propaganda

You can even throw in Oona, Queen of the Fae if you don't plan on running overburden. Oona Rules :)

Thanks Seth very nice suggestions I am definately going to try getting my hands on some Sanity Grinding. They are awesome and so is Oona!

"Once Jace is down I will be drawing three cards a turn."

what makes you draw the extra card? are you expecting to use two of Jace's ability in the same turn because that is not allowed. you only get to play one of his ability per turn.

Sorry I meant 2

Add Hive Mind and some tutors or other cards that makes you search your library of course it will backfire on you too, that's why Feldon's Cane and/or Quest for Ancient Secrets are other cards that must be included.

Noble Benefactor is the closest card in mono-blue to what you're looking for. However, it's optional whether or not they search their library. It might be a good card for your deck anyway; if your opponent knows you're running Archive Trap and declines to search you still get to Demonic Tutor.

acrum dagsson is pretty close to what you're looking for as long as your opponent has an artifact creature in play
it's ability is "T:target artifact creature's controller sacrifices it. that player may search his or her library for a non creature artifact card, put it into play, then shuffle his or her library"