You can't prove a negative
It's called proof by contradiction.
No you have it backwards, proof by contradiction is a method of showing something is true by showing that if it were false it would be a contradiction with something known to be true. An example in this case would be to say,
"assume there are purple unicorns, that would imply through a chain of logic that there can not be pink spotted elephants, since we know that pink spotted elephants do exist then purple unicorns can not exist, QED"
since you are likely to have difficulty finding a contradiction that results by assuming that purple unicorns do exist this method of proof it unlikely to helpful in this case.