Consider the following premises. forall x: W_4(x) -> T(x). exists x: T(x) -> R_2(x). forall x: W_2(x) or ~R_2(x). forall x: ~W_2(x). Can we infer forall x: W_4(x) from them? If possible, name the inference rules being used at each step.
 From forall x: W_2(x) or ~R_2(x) we can infer forall x: R_2(x) -> W_2(x) via universal rewriting. From forall x: W_4(x) -> T(x), exists x: T(x) -> R_2(x) we can infer exists x: W_4(x) -> R_2(x) via existential transitivity. From exists x: W_4(x) -> R_2(x), forall x: R_2(x) -> W_2(x) we can infer exists x: W_4(x) -> W_2(x) via existential transitivity. Finally, from exists x: W_4(x) -> W_2(x), forall x: ~W_2(x) we can infer exists x: ~W_4(x) via existential modus tollens, which contradicts forall x: W_4(x). Therefore, the answer is no.