3 Answers

@MichaelHuss

As to the first part of your answer, I agree you can use uninterested and disinterested in the same subject (but perhaps in the same sentence).  We have to deal with that later.

Are you sure you can't be interested and disinterested at the same sentence?

"Being a disinterested (impartial) party at the football game, the referee was truly interested as to how the game was played at the Super Bowl."

Disinterested and Uninterested are the same negative. You can be both in the same subject, but you can't use them both in the same sentence. 

You can't be interested and disinterested at the same time, one is positive the other negative. 

@MichaelHuss, again:

"The judge, a disinterested party, was anything but uninterested in the argument between the plaintiff and the defendant." 

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