Consider the following premises. For all x_11, if x_11 were a carpenter, then x_11 is not listening to a song. For all x_11, x_11 will listen to a song. For all x_11, x_11 will play tennis. For all x_11, x_11 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 is not a scientist.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.