Consider the following premises. exists x_10: T_2(x_10) -> W_3(x_10). forall x_10: W_3(x_10) -> T(x_10). forall x_10: P_10(x_10). forall x_10: P_10(x_10) -> T_2(x_10). Can we infer exists x_10: T(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> T_2(x_10), forall x_10: P_10(x_10) we can infer forall x_10: T_2(x_10) via universal modus ponens. From exists x_10: T_2(x_10) -> W_3(x_10), forall x_10: T_2(x_10) we can infer exists x_10: W_3(x_10) via existential modus ponens. Finally, from forall x_10: W_3(x_10) -> T(x_10), exists x_10: W_3(x_10) we can infer exists x_10: T(x_10) via existential modus ponens. Therefore, the answer is yes.