Consider the following premises. forall x: W(x) -> R(x). forall x: T(x) <-> W(x). exists x: ~T_1(x). forall x: R(x) -> T_1(x). Can we infer exists x: ~T(x) from them? If possible, name the inference rules being used at each step.
 From forall x: R(x) -> T_1(x), exists x: ~T_1(x) we can infer exists x: ~R(x) via existential modus tollens. From forall x: W(x) -> R(x), exists x: ~R(x) we can infer exists x: ~W(x) via existential modus tollens. Finally, from forall x: T(x) <-> W(x), exists x: ~W(x) we can infer exists x: ~T(x) via existential biconditional elimination. Therefore, the answer is yes.