Consider the following premises. forall x_18: W(x_18) -> P_1(x_18). forall x_18: P_1(x_18) -> W(x_18). forall x_18: W(x_18). Can we infer ~P_1(g) from them? If possible, name the inference rules being used at each step.
 From forall x_18: P_1(x_18) -> W(x_18), forall x_18: W(x_18) -> P_1(x_18) we can infer forall x_18: P_1(x_18) <-> W(x_18) via universal biconditional introduction. From forall x_18: P_1(x_18) <-> W(x_18) we can infer forall x_18: W(x_18) -> P_1(x_18) via universal biconditional elimination. Finally, from forall x_18: W(x_18) -> P_1(x_18), forall x_18: W(x_18) we can infer forall x_18: P_1(x_18) via universal modus ponens, which contradicts ~P_1(g). Therefore, the answer is no.