Consider the following premises. For all x_23, x_23 will not go running. John is not excited. Linda is a politician if and only if John is excited. For all x_23, x_23 will go running. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not writing a letter.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.