Logic Octopus

My logic professor, Dr. Noel Adams, always loved to find great examples of logic in everyday life. Nick was serving lunch the other day, and I think he encountered a particularly awesome one. When he handed the man his lunch and cup of water, the man took the food, leaving the water on the tray, and said:

"You can take the water. I'm not an octopus."

Clearly, this is an awesome statement. I absolutely loved it. It is really quite complicated though, and it took me a while to really unpack the logic inside. Here's my attempt.

(Typical lunch and infamous cup of water)

In predicate and propositional logic, we could represent the situation as follows:

Let Ox stand for "x is an octopus".
Let Wx stand for "x wants water".
Let m stand for "this particular man Nick and I now know"
The symbol "--" in front of anything means "not" or "the negation of".
The symbol "-->" means "implies".

The implied logical argument of the man's statement, which we should have known:
(1) For all x, Wx --> Ox
(2) --Om
(3) Wm-->Om
(4) --Om--> --Wm
(5) --Wm

Explanation:

(1) Only octopi want water. "Only" statements are tricky, but I remembered that they can be translated into "If… then" statements. So, "Only octopi want water" translates to "For all x, if x wants water, then x is an octopus" or "For all x, Wx --> Ox".

(2) We are given the information that the man is not an octopus, i.e. "--Om"

(3) By instantiation from line (1) we can obtain: "Wm-->Om" for our particular man.

(4) Then, from line (3) and the use of the Contrapositive, we can obtain "--Om--> --Wm".

(5) Finally by using lines (2) and (4) and the Arrow Out Rule, we can obtain "-Wm".

Thus, clearly, if we had just remembered (1) our propositional logic, (2) the fact that this man was not an octopus, and (3) that only octopi want water, we would have obviously realized "--Wm", which is what we should have known all along:

He didn't want any water.