Consider the following premises. forall x_10: T(x_10) -> S_2(x_10). forall x_10: P(x_10). exists x_10: T(x_10). Can we infer exists x_10: S_2(x_10) from them? If possible, name the inference rules being used at each step.
 From exists x_10: T(x_10), forall x_10: P(x_10) we can infer exists x_10: T(x_10) and P(x_10) via existential conjunction. From exists x_10: T(x_10) and P(x_10) we can infer exists x_10: T(x_10) via existential simplification. Finally, from forall x_10: T(x_10) -> S_2(x_10), exists x_10: T(x_10) we can infer exists x_10: S_2(x_10) via existential modus ponens. Therefore, the answer is yes.