Consider the following premises. For all x_14, x_14 will write a letter. For all x_14, if x_14 were sad, then x_14 is not a doctor. For all x_14, x_14 will not write a letter. For all x_14, x_14 is sad if and only if x_14 will listen to a song. Can we infer the following from them? There is at least one x_14 for which x_14 will listen to a song.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.