Consider the following premises. exists z_2: T(z_2) -> S_1(z_2). forall z_2: Q(z_2) -> T(z_2). forall z_2: S_1(z_2) -> Q(z_2). Can we infer exists z_2: T(z_2) -> S_1(z_2) from them?
That is one of the premises. Therefore, the answer is yes.