Consider the following premises. ~w_2 or w. forall x_1: W_1(x_1) -> T(x_1). w_2 or T(j_4). forall x_1: ~W_1(x_1). forall x_1: T(x_1) -> W_1(x_1). Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From forall x_1: T(x_1) -> W_1(x_1), forall x_1: W_1(x_1) -> T(x_1) we can infer forall x_1: T(x_1) <-> W_1(x_1) via universal biconditional introduction. From forall x_1: T(x_1) <-> W_1(x_1), forall x_1: ~W_1(x_1) we can infer forall x_1: ~T(x_1) via universal biconditional elimination. From forall x_1: ~T(x_1) we can infer ~T(j_4) via universal instantiation. From w_2 or T(j_4), ~w_2 or w we can infer T(j_4) or w via resolution. Finally, from T(j_4) or w, ~T(j_4) we can infer w via disjunctive syllogism, which contradicts ~w. Therefore, the answer is no.