Translate the following inference to logic notation: For all x, if x_13 sleeps, then x_13 is rich. There is at least one x for which x_13 is a doctor or x_13 will sleep. For all x, if x_13 were a doctor, then x_13 is rich. For all x, x_13 is happy and x_13 will go running. Therefore there is at least one x for which x_13 is happy and x_13 is rich.
forall x: P(x) -> Q(x). exists x: R(x) or P(x). forall x: R(x) -> Q(x). forall x: S(x) and T(x). Therefore exists x: S(x) and Q(x).