Consider the following premises. forall x_4: P_4(x_4). exists x_4: P_4(x_4) -> S_2(x_4). forall x_4: S(x_4). Can we infer exists x_4: S(x_4) from them? If possible, name the inference rules being used at each step.
 From exists x_4: P_4(x_4) -> S_2(x_4), forall x_4: P_4(x_4) we can infer exists x_4: S_2(x_4) via existential modus ponens. From forall x_4: S(x_4), exists x_4: S_2(x_4) we can infer exists x_4: S(x_4) and S_2(x_4) via existential conjunction. Finally, from exists x_4: S(x_4) and S_2(x_4) we can infer exists x_4: S(x_4) via existential simplification. Therefore, the answer is yes.