Given the following axioms:

Question

Axiom 1: Each game is played by two distinct teams
Axiom 2: There are at least four teams
Axiom 3: There are at least six games played
Axiom 4: Each team played at most 4 games.
I need to come up with 1 to 2 more theorems. The first theorem I know is true, the second I'm unsure about and I need help developing a third.

Theorem 1: If there are exactly 4 teams, then there are at most 8 games.
Theorem 2: If there are exactly 6 games, then there are at most 12 teams.

Theorem 3: