Consider the following premises. forall z_3: ~S(z_3). exists z_3: S_2(z_3) -> U(z_3). forall z_3: S_2(z_3) -> S(z_3). forall z_3: U(z_3) -> S_2(z_3). Can we infer forall z_3: U(z_3) from them?
 From forall z_3: S_2(z_3) -> S(z_3), forall z_3: ~S(z_3) we can infer forall z_3: ~S_2(z_3). From forall z_3: U(z_3) -> S_2(z_3), exists z_3: S_2(z_3) -> U(z_3) we can infer exists z_3: U(z_3) <-> S_2(z_3). Finally, from exists z_3: U(z_3) <-> S_2(z_3), forall z_3: ~S_2(z_3) we can infer exists z_3: ~U(z_3), which contradicts forall z_3: U(z_3). Therefore, the answer is no.