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This is probably too dependent on Hellcarver Demon , you literally can't do anything of worth until you have a 6 mana creature on the field.
A lot of the cards interfere with this, too. While casting Cruel Ultimatum with Hellcarver Demon is lolpowerful, there's literally no other way to cast this card in this deck, since there's no red mana. Once you draw Cruel Ultimatum out of the deck it is entirely worthless, since it can only be played from the library by Hellcarver. Having 4, it's going to be drawn a lot and is really going to interfere with getting the mana you need to play Hellcarver.
Liliana is somewhat similar, though her tutor ability is handy. The problem is that if you have one on the field already, you likely won't cast any drawn with Hellcarver since it would destroy the one you have. While it might be nice to tutor other cards with her, again she ends up taking up space. Since you don't have much to defend her with, either, she's never going to be able to cast her -8.
Try adding some cards to stall for time while you build your mana pool. Royal Assassin can really slow the game down in your favor and keep your opponent from attacking (or at least keep them from hurting you too badly).
I'd still leave 1 or 2 Liliana, the tutoring can be pretty handy.
Some tricks to get more mana would be handy to get your game winners on the field faster. Can't think of any standard legal ones off the top of my head, but I'm not an expert. Anything that lets you play an extra land early on is good.
Ponder is super handy. 4x is right on.
The win condition for this is basically playing Emrakul or Cruel Ultimatum with Hellcarver. There's got to be some substitute that can be made that's blue or black for Cruel Ultimatum. Obviously it won't be as devastating, but I think it would work out better.
A sprinkle of removal would probably be good. A well placed Doom Blade from Hellcarver would be the perfect icing on the cake of playing 6 free cards. That and it can be helpful to keep your opponent busy if it's in your hand.
It seems like it would be REAL awkward if you actually ever draw Cruel Ultimatum , being you have no way of actually casting it from hand. Maybe you can add some red mana sources and make this a full-out Grixis deck? Double Red seems hard to hit if you only splash Red. Maybe just taking it out all together would be a good option too. Inkwell Leviathan fits your colors, and is a game-winner for sure when you hit it off of Hellcarver Demon .