Consider the following premises. For all x_14, x_14 will listen to a song or x_14 will not make tea. There is at least one x_14 for which if x_14 were an electrician, then x_14 is making tea. For all x_14, if x_14 were a poet, then x_14 is running. For all x_14, if x_14 listens to a song, then x_14 is a poet. For all x_14, if x_14 goes running, then x_14 is an electrician. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, if is not true that x_14 will go running if and only if x_14 is an electrician.
 From the fact that for all x_14, if x_14 listens to a song, then x_14 is a poet, and that for all x_14, if x_14 were a poet, then x_14 is running we can infer that for all x_14, if x_14 listens to a song, then x_14 is running via universal transitivity. From the fact that for all x_14, x_14 will listen to a song or x_14 will not make tea we can infer that for all x_14, if x_14 makes tea, then x_14 is listening to a song via universal rewriting. From the fact that for all x_14, if x_14 makes tea, then x_14 is listening to a song, and that for all x_14, if x_14 listens to a song, then x_14 is running we can infer that for all x_14, if x_14 makes tea, then x_14 is running via universal transitivity. From the fact that there is at least one x_14 for which if x_14 were an electrician, then x_14 is making tea, and that for all x_14, if x_14 makes tea, then x_14 is running we can infer that there is at least one x_14 for which if x_14 were an electrician, then x_14 is running via existential transitivity. Finally, from the fact that for all x_14, if x_14 goes running, then x_14 is an electrician, and that there is at least one x_14 for which if x_14 were an electrician, then x_14 is running we can infer that there is at least one x_14 for which x_14 will go running if and only if x_14 is an electrician via existential biconditional introduction, which contradicts that For all x_14, if is not true that x_14 will go running if and only if x_14 is an electrician. Therefore, the answer is no.