Let the predicates D(x, y) mean “team x defeated team y” and P(x, y) mean “team x has played team y”. The quantified formula for the statement that there is a team that has beaten every team it has played, is :
1
∃x∀y (P(x, y) → D(x, y))
2
∀x∃y (P(x, y) → D(x, y))
3
∀y∃x (P(x, y) → D(x, y))
4
∃x∀y (D(x, y) → P(x, y))