Consider the following premises. For all x_15, x_15 is a poet or x_15 is not a musician. For all x_15, if x_15 were a bartender, then x_15 is writing a letter. There is at least one x_15 for which x_15 will write a letter if and only if x_15 is a musician. For all x_15, if x_15 were a poet, then x_15 is a bartender. Can we infer the following from them? For all x_15, if is not true that x_15 is a musician if and only if x_15 will write a letter.
 From the fact that for all x_15, x_15 is a poet or x_15 is not a musician we can infer that for all x_15, if x_15 were a musician, then x_15 is a poet. From the fact that for all x_15, if x_15 were a musician, then x_15 is a poet, and that for all x_15, if x_15 were a poet, then x_15 is a bartender we can infer that for all x_15, if x_15 were a musician, then x_15 is a bartender. From the fact that there is at least one x_15 for which x_15 will write a letter if and only if x_15 is a musician we can infer that there is at least one x_15 for which if x_15 writes a letter, then x_15 is a musician. From the fact that for all x_15, if x_15 were a musician, then x_15 is a bartender, and that for all x_15, if x_15 were a bartender, then x_15 is writing a letter we can infer that for all x_15, if x_15 were a musician, then x_15 is writing a letter. Finally, from the fact that for all x_15, if x_15 were a musician, then x_15 is writing a letter, and that there is at least one x_15 for which if x_15 writes a letter, then x_15 is a musician we can infer that there is at least one x_15 for which x_15 is a musician if and only if x_15 will write a letter, which contradicts that For all x_15, if is not true that x_15 is a musician if and only if x_15 will write a letter. Therefore, the answer is no.