Consider the following premises. forall z: ~T(z). forall z: T(z) -> W_1(z). exists z: Q(z) -> W_1(z). forall z: T(z) <-> W_1(z). Can we infer forall z: Q(z) from them? If possible, name the inference rules being used at each step.
 From forall z: T(z) <-> W_1(z) we can infer forall z: W_1(z) -> T(z) via universal biconditional elimination. From forall z: T(z) -> W_1(z), forall z: W_1(z) -> T(z) we can infer forall z: T(z) <-> W_1(z) via universal biconditional introduction. From forall z: T(z) <-> W_1(z), forall z: ~T(z) we can infer forall z: ~W_1(z) via universal biconditional elimination. Finally, from exists z: Q(z) -> W_1(z), forall z: ~W_1(z) we can infer exists z: ~Q(z) via existential modus tollens, which contradicts forall z: Q(z). Therefore, the answer is no.