Consider the following premises. forall z_4: R_2(z_4) -> U_1(z_4). forall z_4: U_1(z_4) -> R_2(z_4). forall z_4: P_3(z_4) -> S_2(z_4). forall z_4: U_1(z_4) -> P_3(z_4). forall z_4: ~S_2(z_4). Can we infer exists z_4: R_2(z_4) from them?
 From forall z_4: R_2(z_4) -> U_1(z_4), forall z_4: U_1(z_4) -> R_2(z_4) we can infer forall z_4: R_2(z_4) <-> U_1(z_4). From forall z_4: P_3(z_4) -> S_2(z_4), forall z_4: ~S_2(z_4) we can infer forall z_4: ~P_3(z_4). From forall z_4: U_1(z_4) -> P_3(z_4), forall z_4: ~P_3(z_4) we can infer forall z_4: ~U_1(z_4). From forall z_4: R_2(z_4) <-> U_1(z_4) we can infer forall z_4: R_2(z_4) -> U_1(z_4). Finally, from forall z_4: R_2(z_4) -> U_1(z_4), forall z_4: ~U_1(z_4) we can infer forall z_4: ~R_2(z_4), which contradicts exists z_4: R_2(z_4). Therefore, the answer is no.