Puzzle #149: Another Murder

I have arranged for another murder. Again, the puzzle comes courtesy of Dan O’Reilly, formerly of the Philosophy department at the University College of the Cariboo (now Thompson Rivers University).

Sherlock Holmes considered the following evidence and then announced correctly who the murderer was. What did Holmes conclude?

The maid was the murderer only if the murder was done neatly. But, it was not done neatly unless it was done with the revolver. The butler was the murderer just in case his affair with the maid needed to be hidden. If the butler didn’t do it, then either the maid did it, the gardener did it, or the cook did it. Neither the gardener nor the cook did it provided that it was done with the revolver. A necessary condition that the murder was done with a knife is that the cook did it. However, it was not done with a knife. Although it was done neatly, the butler’s affair with the maid did not need to be hidden.

Therefore, Holmes concluded that the ___[who]___ did it with the ___[weapon]___ ___[neatly/unneatly]___.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, April 13, 2016 at noon Pacific Time. I will post the answer shortly after.