Consider the following premises. forall x: T(x) -> W(x). forall x: ~W(x). exists x: W_2(x) -> T(x). Can we infer exists x: ~W_2(x) from them? If possible, name the inference rules being used at each step.
 From exists x: W_2(x) -> T(x), forall x: T(x) -> W(x) we can infer exists x: W_2(x) -> W(x) via existential transitivity. Finally, from exists x: W_2(x) -> W(x), forall x: ~W(x) we can infer exists x: ~W_2(x) via existential modus tollens. Therefore, the answer is yes.