Consider the following premises. forall z_3: P_2(z_3) <-> S(z_3). forall z_3: P_2(z_3) -> Q_4(z_3). forall z_3: U_4(z_3) or ~Q_4(z_3). exists z_3: U_4(z_3) -> S(z_3). Can we infer exists z_3: S(z_3) <-> Q_4(z_3) from them?
 From forall z_3: U_4(z_3) or ~Q_4(z_3) we can infer forall z_3: Q_4(z_3) -> U_4(z_3). From forall z_3: P_2(z_3) <-> S(z_3) we can infer forall z_3: S(z_3) -> P_2(z_3). From forall z_3: S(z_3) -> P_2(z_3), forall z_3: P_2(z_3) -> Q_4(z_3) we can infer forall z_3: S(z_3) -> Q_4(z_3). From forall z_3: Q_4(z_3) -> U_4(z_3), exists z_3: U_4(z_3) -> S(z_3) we can infer exists z_3: Q_4(z_3) -> S(z_3). Finally, from forall z_3: S(z_3) -> Q_4(z_3), exists z_3: Q_4(z_3) -> S(z_3) we can infer exists z_3: S(z_3) <-> Q_4(z_3). Therefore, the answer is yes.