Consider the following premises. forall x_12: U(x_12) <-> S_3(x_12). exists x_12: W(x_12) -> T(x_12). forall x_12: S_3(x_12) -> Q_6(x_12). forall x_12: Q_6(x_12) -> W(x_12). Can we infer forall x_12: ~(U(x_12) -> T(x_12)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.