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_11, if x_11 were a mechanic, then x_11 is listening to a song. For all x_11, if x_11 works, then x_11 is a mechanic. There is at least one x_11 for which x_11 will work if and only if x_11 is a mechanic. For all x_11, if x_11 listens to a song, then x_11 is working.
For all x_11, if x_11 were a mechanic, then x_11 is working can be inferred via the universal transitivity rule. For all x_11, if x_11 works, then x_11 is listening to a song can be inferred via the universal transitivity rule. For all x_11, if x_11 listens to a song, then x_11 is a mechanic can be inferred via the universal transitivity rule. There is at least one x_11 for which if x_11 works, then x_11 is a mechanic can be inferred via the existential biconditional elimination rule. There is at least one x_11 for which if x_11 were a mechanic, then x_11 is working can be inferred via the existential biconditional elimination rule.