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, x_11 will play tennis if and only if x_11 will listen to a song. Susan is a writer. Robert is not listening to a song. If it is late, then Susan is not a writer.
It is not late can be inferred via the modus tollens rule. Susan is a writer and Robert is not listening to a song can be inferred via the conjunction rule. Robert is not listening to a song and Susan is a writer can be inferred via the conjunction rule. For all x_11, if x_11 plays tennis, then x_11 is listening to a song can be inferred via the universal biconditional elimination rule. For all x_11, if x_11 listens to a song, then x_11 is playing tennis can be inferred via the universal biconditional elimination rule.