Consider the following premises. S_17(a_17) -> t. p_4 <-> t. T(a_17) -> t. forall x_17: T(x_17) or S_17(x_17). Can we infer ~p_4 from them? If possible, name the inference rules being used at each step.
 From forall x_17: T(x_17) or S_17(x_17) we can infer T(a_17) or S_17(a_17) via universal instantiation. From T(a_17) -> t, S_17(a_17) -> t, T(a_17) or S_17(a_17) we can infer t via disjunction elimination. From p_4 <-> t we can infer t -> p_4 via biconditional elimination. Finally, from t -> p_4, t we can infer p_4 via modus ponens, which contradicts ~p_4. Therefore, the answer is no.