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_12, x_12 will not write a letter. Patricia is curious if and only if Sarah is playing squash. For all x_12, x_12 is poor if and only if x_12 is curious. For all x_12, x_12 will write a letter if and only if x_12 is poor.
If Patricia were curious, then Sarah is playing squash can be inferred via the biconditional elimination rule. If Sarah plays squash, then Patricia is curious can be inferred via the biconditional elimination rule. For all x_12, if x_12 were poor, then x_12 is curious can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 writes a letter, then x_12 is poor can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were curious, then x_12 is poor can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were poor, then x_12 is writing a letter can be inferred via the universal biconditional elimination rule. For all x_12, x_12 is not poor can be inferred via the universal biconditional elimination rule.