Consider the following premises. ~q_1. q_4 -> q_1. q_3 -> q_4. Can we infer q_3 from them? If possible, name the inference rules being used at each step.
 From q_4 -> q_1, ~q_1 we can infer ~q_4 via modus tollens. Finally, from q_3 -> q_4, ~q_4 we can infer ~q_3 via modus tollens, which contradicts q_3. Therefore, the answer is no.