Consider the following premises. forall x_12: P_12(x_12) <-> P(x_12). forall x_12: P_6(x_12) -> P_12(x_12). exists x_12: P(x_12) <-> P_6(x_12). Can we infer forall x_12: ~(P(x_12) <-> P_6(x_12)) from them?
That contradicts the premises. Therefore the answer is no.