Translate the following inference to logic notation: For all x, x_11 is a poet and x_11 is a bartender. For all x, x_11 will take a plane if and only if x_11 will go running. For all x, if x_11 takes a plane, then x_11 is not a poet. There is at least one x for which x_11 will go running if and only if x_11 is sad. Therefore there is at least one x for which x_11 is not sad.
forall x: P(x) and Q(x). forall x: R(x) <-> S(x). forall x: R(x) -> ~P(x). exists x: S(x) <-> T(x). Therefore exists x: ~T(x).