Consider the following premises. forall x_10: Q_10(x_10) -> R_10(x_10). P_10(a_5) or t. forall x_10: P_10(x_10) -> Q_10(x_10). forall x_10: ~R_10(x_10). Can we infer ~t from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> R_10(x_10) we can infer forall x_10: P_10(x_10) -> R_10(x_10) via universal transitivity. From forall x_10: P_10(x_10) -> R_10(x_10), forall x_10: ~R_10(x_10) we can infer forall x_10: ~P_10(x_10) via universal modus tollens. From forall x_10: ~P_10(x_10) we can infer ~P_10(a_5) via universal instantiation. Finally, from P_10(a_5) or t, ~P_10(a_5) we can infer t via disjunctive syllogism, which contradicts ~t. Therefore, the answer is no.