Consider the following premises. forall x_2: U(x_2) or ~R(x_2). forall x_2: U(x_2) -> P(x_2). exists x_2: P(x_2) -> R(x_2). Can we infer forall x_2: ~(R(x_2) <-> U(x_2)) from them?
 From forall x_2: U(x_2) or ~R(x_2) we can infer forall x_2: R(x_2) -> U(x_2). From forall x_2: U(x_2) -> P(x_2), exists x_2: P(x_2) -> R(x_2) we can infer exists x_2: U(x_2) -> R(x_2). Finally, from forall x_2: R(x_2) -> U(x_2), exists x_2: U(x_2) -> R(x_2) we can infer exists x_2: R(x_2) <-> U(x_2), which contradicts forall x_2: ~(R(x_2) <-> U(x_2)). Therefore, the answer is no.