Consider the following premises. exists x: T(x) or W(x). forall x: T(x) -> W_4(x). forall x: W_4(x) -> T(x). forall x: W(x) -> W_4(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_4(x) -> T(x), forall x: T(x) -> W_4(x) we can infer forall x: W_4(x) <-> T(x) via universal biconditional introduction. From forall x: W_4(x) <-> T(x) we can infer forall x: T(x) -> W_4(x) via universal biconditional elimination. Finally, from forall x: T(x) -> W_4(x), forall x: W(x) -> W_4(x), exists x: T(x) or W(x) we can infer exists x: W_4(x) via existential disjunction elimination, which contradicts forall x: ~W_4(x). Therefore, the answer is no.