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_8, x_8 will work if and only if x_8 is a taxi driver. For all x_8, x_8 will not listen to a song. There is at least one x_8 for which if x_8 writes a letter, then x_8 is working. For all x_8, x_8 is a taxi driver if and only if x_8 will listen to a song.
For all x_8, if x_8 works, then x_8 is a taxi driver can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 were a taxi driver, then x_8 is listening to a song can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 were a taxi driver, then x_8 is working can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 listens to a song, then x_8 is a taxi driver can be inferred via the universal biconditional elimination rule. For all x_8, x_8 is not a taxi driver can be inferred via the universal biconditional elimination rule.