Logic Gamesadvanced series

This puzzle turns on the correct encoding of quantifiers. It is good to use a relation “defeats” to represent the results of the matches. You may also wish to define other expressions in terms of this to represent drawn matches and the like: it’s up to you.

Our annual logic competition came to a final showdown between five teams: the Aces, Buccaneers, Cougars, Demons and Eagles. The contest was a round robin, each team meeting each other team once. At the end, the judges announced:

Every team won at least once, and some team won all its games.
The Buccaneers beat only the Cougars.
Exactly one match was drawn, and it didn’t involve the Cougars.
The Aces defeated every team that the Eagles defeated, but they didn’t defeat the Demons.
Not every team that defeated the Aces defeated every team that the Aces defeated.

With that, they left us to work out the full set of results. Well?

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