Consider the following premises. forall z_4: P(z_4) -> T_3(z_4). forall z_4: P(z_4) -> W_1(z_4). exists z_4: W_1(z_4) -> P(z_4). Can we infer forall z_4: ~(W_1(z_4) -> T_3(z_4)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.