Consider the following premises. forall x_12: Q_12(x_12) -> Q_6(x_12). exists x_12: R_6(x_12) -> R_2(x_12). forall x_12: Q_6(x_12) -> R_6(x_12). forall x_12: W_3(x_12) <-> Q_12(x_12). Can we infer forall x_12: ~(W_3(x_12) -> R_2(x_12)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.