Consider the following premises. forall x_8: P_8(x_8) -> R(x_8). forall x_8: P_8(x_8) <-> U(x_8). forall x_8: U(x_8) -> P_8(x_8). Can we infer exists x_8: ~(U(x_8) -> R(x_8)) from them?
 From forall x_8: P_8(x_8) <-> U(x_8) we can infer forall x_8: P_8(x_8) -> U(x_8). From forall x_8: U(x_8) -> P_8(x_8), forall x_8: P_8(x_8) -> U(x_8) we can infer forall x_8: U(x_8) <-> P_8(x_8). From forall x_8: U(x_8) <-> P_8(x_8) we can infer forall x_8: U(x_8) -> P_8(x_8). Finally, from forall x_8: U(x_8) -> P_8(x_8), forall x_8: P_8(x_8) -> R(x_8) we can infer forall x_8: U(x_8) -> R(x_8), which contradicts exists x_8: ~(U(x_8) -> R(x_8)). Therefore, the answer is no.