Consider the following premises. For all x_6, x_6 will work or x_6 is a musician. For all x_6, x_6 will not work or x_6 is happy. For all x_6, x_6 is a doctor if and only if x_6 is happy. For all x_6, if x_6 were a musician, then x_6 is a doctor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is not a doctor.
 From the fact that for all x_6, x_6 will work or x_6 is a musician, and that for all x_6, x_6 will not work or x_6 is happy we can infer that for all x_6, x_6 is a musician or x_6 is happy via universal resolution. From the fact that for all x_6, x_6 is a doctor if and only if x_6 is happy we can infer that for all x_6, if x_6 were happy, then x_6 is a doctor via universal biconditional elimination. Finally, from the fact that for all x_6, if x_6 were a musician, then x_6 is a doctor, that for all x_6, if x_6 were happy, then x_6 is a doctor, and that for all x_6, x_6 is a musician or x_6 is happy we can infer that for all x_6, x_6 is a doctor via universal disjunction elimination, which contradicts that There is at least one x_6 for which x_6 is not a doctor. Therefore, the answer is no.