I’m confused by that question. Let’s say we have eight players {A,B,C,D,E,F,G,H}. A wins all matches, B wins all but against A, and so on. So, the scores are {7,6,5,4,3,2,1,0}. This satisfies the two conditions of different scores and B’s score being the sum of scores EFGH. But this answer is the first thing every single person will try. So maybe I misunderstood the question…
Edit: Maybe you are asking to prove that rank 5 cannot win or draw vs rank 4, in which case, I guess more work is required.
Yes, that shows that in this particular scenario #4 wins against #5. I guess I left it out in the question, but the goal is to show that this is the case in all possible scenarios satisfying the two conditions above.
Except in the case of the ship of theseus, the question is if over time you replace the ship piece by piece, eventually ending up with a ship that has no original parts, is it still the same ship? birdman’s answer would suggest that the guy was potentially replacing components of the fork a little bit at a time. As that did not happen, the answer to the question “are the forks the same” remains clearly no.
I had a metaphysics professor. Hed hold a key in his hand, and say “I have a key in my hand. I also have a lump of metal in my hand. Do I have one thing, or two things in my hand? Does the key really exist, or just the lump of metal?” Things along those lines.
I was in the mid way through the process of writing a lengthy philosophical response but then decided that I could just say, there’s no practical reason for asking the question, but it kinda gets to the heart of what you gotta do to really git gud at this sort of game - questioning all the underlying assumptions of the given information, deciding what’s relevant and what isn’t, deciding how to think about statements and truth.