Consider the following premises. w. forall x_2: P(x_2) -> T_3(x_2). forall x_2: W_1(x_2) -> T_3(x_2). forall x_2: P(x_2) or W_1(x_2). Can we infer ~w from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.