Consider the following premises. forall z_4: R_2(z_4) -> U(z_4). forall z_4: U(z_4) -> W(z_4). forall z_4: S_4(z_4) -> R_2(z_4). exists z_4: W(z_4) -> S_4(z_4). Can we infer forall z_4: ~(W(z_4) <-> R_2(z_4)) from them?
 From forall z_4: R_2(z_4) -> U(z_4), forall z_4: U(z_4) -> W(z_4) we can infer forall z_4: R_2(z_4) -> W(z_4). From exists z_4: W(z_4) -> S_4(z_4), forall z_4: S_4(z_4) -> R_2(z_4) we can infer exists z_4: W(z_4) -> R_2(z_4). Finally, from exists z_4: W(z_4) -> R_2(z_4), forall z_4: R_2(z_4) -> W(z_4) we can infer exists z_4: W(z_4) <-> R_2(z_4), which contradicts forall z_4: ~(W(z_4) <-> R_2(z_4)). Therefore, the answer is no.