Translate the following inference to logic notation: For all x, x_15 is a sailor if and only if x_15 will cook. For all x, x_15 will not climb a mountain or x_15 will play squash. For all x, if x_15 plays squash, then x_15 is playing a game. For all x, if x_15 were a sailor, then x_15 is bored. For all x, x_15 will climb a mountain or x_15 will cook. There is at least one x for which if x_15 were bored, then x_15 is playing a game. Therefore there is at least one x for which x_15 will play a game.
forall x: P(x) <-> Q(x). forall x: ~R(x) or S(x). forall x: S(x) -> T(x). forall x: P(x) -> U(x). forall x: R(x) or Q(x). exists x: U(x) -> T(x). Therefore exists x: T(x).