Consider the following premises. forall x_2: W_2(x_2) -> Q_2(x_2). exists x_2: Q_2(x_2) -> R_2(x_2). forall x_2: R_2(x_2) -> R(x_2). Can we infer forall x_2: ~(W_2(x_2) -> R(x_2)) from them?
That contradicts the premises. Therefore the answer is no.