Consider the following premises. exists y_3: P(y_3) or U_4(y_3). forall y_3: U_4(y_3) -> U(y_3). forall y_3: ~P(y_3) or R_2(y_3). forall y_3: U(y_3) <-> R_2(y_3). Can we infer forall y_3: ~U(y_3) from them?
 From forall y_3: U(y_3) <-> R_2(y_3) we can infer forall y_3: R_2(y_3) -> U(y_3). From exists y_3: P(y_3) or U_4(y_3), forall y_3: ~P(y_3) or R_2(y_3) we can infer exists y_3: U_4(y_3) or R_2(y_3). Finally, from forall y_3: U_4(y_3) -> U(y_3), forall y_3: R_2(y_3) -> U(y_3), exists y_3: U_4(y_3) or R_2(y_3) we can infer exists y_3: U(y_3), which contradicts forall y_3: ~U(y_3). Therefore, the answer is no.