Consider the following premises. forall x_15: R_15(x_15) -> S_15(x_15). p_1 -> R_15(a_15). S_15(a_15) <-> p. p_1 or p. Can we infer ~S_15(a_15) from them? If possible, name the inference rules being used at each step.
 From forall x_15: R_15(x_15) -> S_15(x_15) we can infer R_15(a_15) -> S_15(a_15) via universal instantiation. From S_15(a_15) <-> p we can infer p -> S_15(a_15) via biconditional elimination. From p_1 -> R_15(a_15), R_15(a_15) -> S_15(a_15) we can infer p_1 -> S_15(a_15) via transitivity. Finally, from p_1 -> S_15(a_15), p -> S_15(a_15), p_1 or p we can infer S_15(a_15) via disjunction elimination, which contradicts ~S_15(a_15). Therefore, the answer is no.