Assume the following situation. Suppose I met an alien called Protoss who can speak English. He said he is from Aiur. Now I want to make the following statement.
There exists (a or the) tallest Protoss in Aiur who can speak English.
In school, I learned that I should use "the" before the superlative. But somehow I feel awkward if I say "there exists the ...".
By the way, I know the existence because I already met one, although I might not be able to find him. Aiur is too far. I wonder if this situation affects the answer.
 Thanks to the suggestion by Damkerng T, I write below what I wanted to know. I was actually writing a math sentence. I thought it would be boring to most people, so I tried to write down something which seems more popular. The above was my attempt.
Assume Condition A. Then there exists (a or the) largest integer k satisfying Condition B.
[edit after looking at two more comments] I am trying to modify the original situation more properly.
Let's say Protoss refers to an alien race, the only alien race known, and we call each member a Protoss as well. Let's call the Protoss I met "Fenix". Fenix was quite tall. I like tall creatures, so I wanted to meet the tallest Protoss and then talk to him. But suddenly Fenix began to say nonsense. He said no such Protoss exists. I want to claim that Fenix is wrong. So I told Fenix the sentence in the first box.
This is also awkward. There should be better interpretation and I need to think about it.