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: If Charles were a carpenter, then Thomas is working. For all x_21, x_21 will work if and only if x_21 will play squash. Thomas is not playing squash. Charles is a carpenter if and only if William is listening to a song.
If Charles were a carpenter, then William is listening to a song can be inferred via the biconditional elimination rule. If William listens to a song, then Charles is a carpenter can be inferred via the biconditional elimination rule. For all x_21, if x_21 works, then x_21 is playing squash can be inferred via the universal biconditional elimination rule. For all x_21, if x_21 plays squash, then x_21 is working can be inferred via the universal biconditional elimination rule.