Consider the following premises. For all x_13, x_13 will make tea or x_13 will climb a mountain. For all x_13, if x_13 makes tea, then x_13 is playing squash. For all x_13, if x_13 climbs a mountain, then x_13 is playing squash. Charles is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, either x_13 is a carpenter or x_13 will play squash are not true.
 From the fact that for all x_13, if x_13 makes tea, then x_13 is playing squash, that for all x_13, if x_13 climbs a mountain, then x_13 is playing squash, and that for all x_13, x_13 will make tea or x_13 will climb a mountain we can infer that for all x_13, x_13 will play squash via universal disjunction elimination. From the fact that Charles is a carpenter we can infer that there is at least one x_13 for which x_13 is a carpenter via existential generalization. Finally, from the fact that there is at least one x_13 for which x_13 is a carpenter, and that for all x_13, x_13 will play squash we can infer that some carpenters will play squash via existential conjunction, which contradicts that For all x_13, either x_13 is a carpenter or x_13 will play squash are not true. Therefore, the answer is no.