Consider the following premises. forall x_11: W_3(x_11). forall x_11: P_1(x_11). exists x_11: W(x_11). Can we infer exists x_11: W_3(x_11) and P_1(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: W_3(x_11), exists x_11: W(x_11) we can infer exists x_11: W_3(x_11) and W(x_11) via existential conjunction. From exists x_11: W_3(x_11) and W(x_11) we can infer exists x_11: W_3(x_11) via existential simplification. Finally, from exists x_11: W_3(x_11), forall x_11: P_1(x_11) we can infer exists x_11: W_3(x_11) and P_1(x_11) via existential conjunction. Therefore, the answer is yes.