Consider the following premises. forall x_14: Q_2(x_14) and S_14(x_14). ~Q_2(a_14). Can we infer q_1 from them? If possible, name the inference rules being used at each step.
 From forall x_14: Q_2(x_14) and S_14(x_14) we can infer Q_2(a_14) and S_14(a_14) via universal instantiation. From Q_2(a_14) and S_14(a_14) we can infer Q_2(a_14) via simplification. From Q_2(a_14) we can infer Q_2(a_14) or q_1 via addition. Finally, from Q_2(a_14) or q_1, ~Q_2(a_14) we can infer q_1 via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.