Consider the following premises. forall x_3: P(x_3). forall x_3: U(x_3) or U_2(x_3). exists x_3: U(x_3) -> ~P(x_3). Can we infer forall x_3: ~U_2(x_3) from them?
 From exists x_3: U(x_3) -> ~P(x_3), forall x_3: P(x_3) we can infer exists x_3: ~U(x_3). Finally, from forall x_3: U(x_3) or U_2(x_3), exists x_3: ~U(x_3) we can infer exists x_3: U_2(x_3), which contradicts forall x_3: ~U_2(x_3). Therefore, the answer is no.