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