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