Consider the following premises. s or ~t. q_1 -> s. s -> q_1. Can we infer ~(t -> q_1) from them?
 From q_1 -> s, s -> q_1 we can infer q_1 <-> s. From q_1 <-> s we can infer s -> q_1. From s or ~t we can infer t -> s. Finally, from t -> s, s -> q_1 we can infer t -> q_1, which contradicts ~(t -> q_1). Therefore, the answer is no.