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, if x goes running, then x is writing a letter. For all x, x will play tennis or x will listen to a song. For all x, if x writes a letter, then x is playing tennis. For all x, if x plays squash, then x is running. For all x, if x plays tennis, then x is writing a letter. There is at least one x for which if x listens to a song, then x is playing squash.
For all x, if x goes running, then x is playing tennis can be inferred via the universal transitivity rule. For all x, if x plays squash, then x is writing a letter can be inferred via the universal transitivity rule. There is at least one x for which if x listens to a song, then x is running can be inferred via the existential transitivity rule. For all x, x will write a letter if and only if x will play tennis can be inferred via the universal biconditional introduction rule. For all x, x will play tennis if and only if x will write a letter can be inferred via the universal biconditional introduction rule.