This alternate end occurs right after Spike sees the proof for the first time.
Twilight showed Spike her proof. “See? It's perfect! With this, I've disproved the existence of magic!”
“...So?”
“So what?” Twilight asked.
“So just because you've 'proved' it doesn't make it true,” said Spike. “I mean, there are multiple 'proofs' that claim 1 equals 0. Does that make it true?”
“No, I guess not,” said Twilight. “I guess disproving something like magic is impossible.”
As soon as she said that, the parchment in her hooves vanished into nothing. Twilight and Spike stared bug-eyed at where it had been. “Did it just...?” Spike started.
“...I don't even know. I'm going to bed.”
This one appeals to me the most. In fact I remember arguing with my math teacher over that proof as well. Skipping the step of verifying your work doesn't make it true.
By starting from a single false premise, you can prove absolutely anything. For instance, if you assume that 1=2, then it follows that I am God.
Proof: Consider the elements of the set {I, God}. Since 1=2, those two elements are one, and thus, I am God. Q.E.D.
5855151 Or, for those who don't know sets: I have created 0 known non-fictional universes. For all known non-fictional universes, God has created that universe. Since 0 = 1, I have created 1 known non-fictional universe. The statement to be proven follows directly from this.
6674133 You can prove a negative, but only under the assumption that every variable is accounted for (and there could well be variables that nobody knows existed, such as before physicists knew about quantum). To prove a negative statement, it's common to assume that the opposite holds (assume magic is possible), then using known facts reduce the problem to a contradiction. Often like: "using these facts, X is true; using these other facts, X is not true". There are other methods, but it's important not to assume the thing you're trying to prove in order to come to something known to be true.
Jeez. I just love Spike's reaction to this one.