Problem with the Proof:
Step 2 of the proof ("You do the opposite of what it prints on the paper") assumes that it is possible for you to not do what the computer said. In other words, it assumes you have free will. By assuming the goal of the proof, you committed a fallacy called Begging the Question.

Where to go from here
I good place to start is always the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy. Both sources are peer-reviewed and do not take sides, so they are very trustworthy. They can get rather technical depending at times, but they usually lay things out well enough for a general audience to follow.

Problem with the Proof:
Step 2 of the proof ("You do the opposite of what it prints on the paper") assumes that it is possible for you to not do what the computer said. In other words, it assumes you have free will. By assuming the goal of the proof, you committed a fallacy called Begging the Question.

Where to go from here
I good place to start is always the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy. Both sources are peer-reviewed and do not take sides, so they are very trustworthy. They can get rather technical at times, but they usually lay things out well enough for a general audience to follow.