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: There is at least one x for which if x reads a book, then x is taking a plane. For all x, if x reads a book, then x is playing squash. For all x, if x plays squash, then x is reading a book. For all x, if x takes a plane, then x is playing squash.
For all x, if x takes a plane, then x is reading a book can be inferred via the universal transitivity rule. There is at least one x for which if x reads a book, then x is playing squash can be inferred via the existential transitivity rule. There is at least one x for which if x plays squash, then x is taking a plane can be inferred via the existential transitivity rule. For all x, x will read a book if and only if x will play squash can be inferred via the universal biconditional introduction rule. For all x, x will play squash if and only if x will read a book can be inferred via the universal biconditional introduction rule.