How to proceed when a mathematical result contradicts existing literature? An author has proven an interesting mathematical result, but notices that this result contradicts existing literature. 

Does the author have to find an explicit error or counter-example to the existing literature before considering submission? Can she submit the proven result to a journal, if she cannot find an error in her own proof?
Certainly the fact that there is a contradiction with previous literature must be prominently advertised; to do otherwise would be scientific misconduct. I would not be confident in publishing such a paper unless I found the mistake in the other paper, or could give a counterexample showing they are wrong.

After having carefully worked out the other paper and my own paper, and asked any experts with whom I have an established connection, I might contact the authors of the contradicting paper (if they are still active). After their response, or lack thereof, I would consider publishing a preprint and after that submitting to a journal. The journal is the slowest and most uncertain way of finding out where the problem is.