Consider the following premises. forall x_2: W(x_2) -> W_4(x_2). forall x_2: W_4(x_2) -> W(x_2). S_3(a_10). forall x_2: S_3(x_2) -> W(x_2). Can we infer forall x_2: ~W_4(x_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: W_4(x_2) -> W(x_2), forall x_2: W(x_2) -> W_4(x_2) we can infer forall x_2: W_4(x_2) <-> W(x_2) via universal biconditional introduction. From forall x_2: W_4(x_2) <-> W(x_2) we can infer forall x_2: W(x_2) -> W_4(x_2) via universal biconditional elimination. From S_3(a_10) we can infer exists x_2: S_3(x_2) via existential generalization. From forall x_2: S_3(x_2) -> W(x_2), exists x_2: S_3(x_2) we can infer exists x_2: W(x_2) via existential modus ponens. Finally, from forall x_2: W(x_2) -> W_4(x_2), exists x_2: W(x_2) we can infer exists x_2: W_4(x_2) via existential modus ponens, which contradicts forall x_2: ~W_4(x_2). Therefore, the answer is no.