Consider the following premises. For all x_7, x_7 is an electrician or x_7 will play squash. For all x_7, x_7 is a carpenter. For all x_7, if x_7 plays squash, then x_7 is happy. There is at least one x_7 for which if x_7 were an electrician, then x_7 is happy. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, either x_7 is happy or x_7 is a carpenter are not true.
 From the fact that there is at least one x_7 for which if x_7 were an electrician, then x_7 is happy, that for all x_7, if x_7 plays squash, then x_7 is happy, and that for all x_7, x_7 is an electrician or x_7 will play squash we can infer that there is at least one x_7 for which x_7 is happy via existential disjunction elimination. Finally, from the fact that there is at least one x_7 for which x_7 is happy, and that for all x_7, x_7 is a carpenter we can infer that there is at least one x_7 for which x_7 is happy and x_7 is a carpenter via existential conjunction, which contradicts that For all x_7, either x_7 is happy or x_7 is a carpenter are not true. Therefore, the answer is no.