Translate the following inference to logic notation: For all x, y_1 will not go running. For all x, if y_1 goes running, then y_1 is a poet. There is at least one x for which y_1 will cook if and only if y_1 is a poet. For all x, if y_1 were a poet, then y_1 is running. Therefore there is at least one x for which y_1 will not cook.
forall x: ~P(x). forall x: P(x) -> Q(x). exists x: R(x) <-> Q(x). forall x: Q(x) -> P(x). Therefore exists x: ~R(x).