Consider the following premises. forall x_16: P_16(x_16). exists x_16: W_1(x_16) -> P_16(x_16). forall x_16: P_16(x_16) -> W_1(x_16). Can we infer exists x_16: W_1(x_16) or R_3(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) -> W_1(x_16), exists x_16: W_1(x_16) -> P_16(x_16) we can infer exists x_16: P_16(x_16) <-> W_1(x_16) via existential biconditional introduction. From exists x_16: P_16(x_16) <-> W_1(x_16) we can infer exists x_16: P_16(x_16) -> W_1(x_16) via existential biconditional elimination. From exists x_16: P_16(x_16) -> W_1(x_16), forall x_16: P_16(x_16) we can infer exists x_16: W_1(x_16) via existential modus ponens. Finally, from exists x_16: W_1(x_16) we can infer exists x_16: W_1(x_16) or R_3(x_16) via existential addition. Therefore, the answer is yes.