Consider the following premises. t_2 <-> q_2. ~t_2. forall x_7: S(x_7) <-> S_7(x_7). S_7(a_7) <-> q_2. Can we infer ~S(a_7) from them?
 From t_2 <-> q_2, ~t_2 we can infer ~q_2. From forall x_7: S(x_7) <-> S_7(x_7) we can infer S(a_7) <-> S_7(a_7). From S_7(a_7) <-> q_2, ~q_2 we can infer ~S_7(a_7). Finally, from S(a_7) <-> S_7(a_7), ~S_7(a_7) we can infer ~S(a_7). Therefore, the answer is yes.