According to reformed theology, does reformed theology fall apart if one removes the doctrine of predestination? Context:

I was recently pondering on why it took me so long to discover reformed theology, and how my beliefs changed before/after reading reformed theology -- and as I traced my thoughts, it seems like a key point I hit was the doctrine of predestination.

Before believing in predestination, my notion of Christianity was something like: God vs Satan is fighting in some huge battle. I get to play a part. I'm important. I choose who to serve, and I can influence other humans in either direction.

After understanding predestination, it was something like: wow, I'm absolutely useless. There's all these angelic beings worshipping God, God really doesn't need me, and I don't have much influence over whether God or Satan wins, and I don't have much influence even other whether people ultimately get saved.

This realization then somehow paved the door for understanding reformed theology -- i.e. the focus of the Bible is about God, rather than humans.

Question:

Thus, is the doctirne of predestination considered a core pillar of reformed theology? Are there any well known doctrines / documents (accepted by reformed theologists) that argue against predestination?
I found this summary of reformed theology very helpful:
http://www.reformedreader.org/t.u.l.i.p.htm

Reformed theology emphasizes the doctrines of grace, best known by the acronym TULIP, though this does not correspond to the best possible names for the five doctrines.
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U stands for unconditional election. An emphasis on election bothers many people, but the problem they feel is not actually with election; it is with depravity. If sinners are as helpless in their depravity as the Bible says they are, unable to know and unwilling to seek God, then the only way they could possibly be saved is for God to take the initiative to change and save them. This is what election means. It is God choosing to save those who, apart from His sovereign choice and subsequent action, certainly would perish.
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As you can see, one of the &quot;pillars&quot; of reformed theology is Unconditional Election (aka predestination).  If you remove that pillar, I don't believe the theological system you have left could be fairly called &quot;reformed.&quot;
For a more verbose introduction to reformed theology, see this series by R.C. Sproul:
http://www.ligonier.org/learn/series/what_is_reformed_theology/