Consider the following premises. For all x_6, x_6 will not listen to a song or x_6 is rich. There is at least one x_6 for which x_6 will listen to a song or x_6 will play squash. For all x_6, x_6 is rich if and only if x_6 will climb a mountain. For all x_6, if x_6 plays squash, then x_6 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not climb a mountain.
 From the fact that for all x_6, x_6 is rich if and only if x_6 will climb a mountain we can infer that for all x_6, if x_6 were rich, then x_6 is climbing a mountain via universal biconditional elimination. From the fact that there is at least one x_6 for which x_6 will listen to a song or x_6 will play squash, and that for all x_6, x_6 will not listen to a song or x_6 is rich we can infer that there is at least one x_6 for which x_6 will play squash or x_6 is rich via existential resolution. Finally, from the fact that for all x_6, if x_6 plays squash, then x_6 is climbing a mountain, that for all x_6, if x_6 were rich, then x_6 is climbing a mountain, and that there is at least one x_6 for which x_6 will play squash or x_6 is rich we can infer that there is at least one x_6 for which x_6 will climb a mountain via existential disjunction elimination, which contradicts that For all x_6, x_6 will not climb a mountain. Therefore, the answer is no.