Consider the following premises. forall x_12: T_3(x_12) -> Q_6(x_12). exists x_12: S(x_12) <-> Q_12(x_12). forall x_12: S(x_12) or ~Q_6(x_12). Can we infer forall x_12: ~(T_3(x_12) -> Q_12(x_12)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.