Translate the following inference to logic notation: For all x, if x_13 plays a game, then x_13 is a scientist. For all x, x_13 is a sailor if and only if x_13 is curious. For all x, if x_13 were a scientist, then x_13 is playing a game. There is at least one x for which x_13 is a carpenter if and only if x_13 is a sailor. For all x, x_13 is not a scientist. For all x, if x_13 were curious, then x_13 is playing a game. Therefore there is at least one x for which x_13 is not a carpenter.
forall x: P(x) -> Q(x). forall x: R(x) <-> S(x). forall x: Q(x) -> P(x). exists x: T(x) <-> R(x). forall x: ~Q(x). forall x: S(x) -> P(x). Therefore exists x: ~T(x).