What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all x_17, if x_17 were a scientist, then x_17 is a mechanic. For all x_17, x_17 will write a letter or x_17 is a scientist. For all x_17, x_17 will write a letter if and only if x_17 will listen to a song. There is at least one x_17 for which x_17 will not listen to a song.
For all x_17, if x_17 writes a letter, then x_17 is listening to a song can be inferred via the universal biconditional elimination rule. For all x_17, if x_17 listens to a song, then x_17 is writing a letter can be inferred via the universal biconditional elimination rule. There is at least one x_17 for which x_17 will not write a letter can be inferred via the existential biconditional elimination rule.