Consider the following premises. forall x_6: P_6(x_6) or ~P(x_6). forall x_6: P_6(x_6) -> R(x_6). forall x_6: R(x_6) -> P(x_6). Can we infer exists x_6: ~(R(x_6) <-> P(x_6)) from them?
 From forall x_6: P_6(x_6) or ~P(x_6) we can infer forall x_6: P(x_6) -> P_6(x_6). From forall x_6: P(x_6) -> P_6(x_6), forall x_6: P_6(x_6) -> R(x_6) we can infer forall x_6: P(x_6) -> R(x_6). Finally, from forall x_6: R(x_6) -> P(x_6), forall x_6: P(x_6) -> R(x_6) we can infer forall x_6: R(x_6) <-> P(x_6), which contradicts exists x_6: ~(R(x_6) <-> P(x_6)). Therefore, the answer is no.