Consider the following premises. forall x_6: P_6(x_6) or P(x_6). forall x_6: ~P_6(x_6) or S(x_6). forall x_6: ~P(x_6). Can we infer ~S(a) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) or P(x_6), forall x_6: ~P_6(x_6) or S(x_6) we can infer forall x_6: P(x_6) or S(x_6) via universal resolution. Finally, from forall x_6: P(x_6) or S(x_6), forall x_6: ~P(x_6) we can infer forall x_6: S(x_6) via universal disjunctive syllogism, which contradicts ~S(a). Therefore, the answer is no.