Consider the following premises. For all x_6, if x_6 plays squash, then x_6 is a lawyer. For all x_6, x_6 will go running or x_6 will play squash. There is at least one x_6 for which x_6 is a politician. For all x_6, x_6 will not go running or x_6 is a scientist. For all x_6, if x_6 were a scientist, then x_6 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: Some politicians are lawyers.
 From the fact that for all x_6, x_6 will go running or x_6 will play squash, and that for all x_6, x_6 will not go running or x_6 is a scientist we can infer that for all x_6, x_6 will play squash or x_6 is a scientist via universal resolution. From the fact that for all x_6, if x_6 plays squash, then x_6 is a lawyer, that for all x_6, if x_6 were a scientist, then x_6 is a lawyer, and that for all x_6, x_6 will play squash or x_6 is a scientist we can infer that for all x_6, x_6 is a lawyer via universal disjunction elimination. Finally, from the fact that there is at least one x_6 for which x_6 is a politician, and that for all x_6, x_6 is a lawyer we can infer that some politicians are lawyers via existential conjunction. Therefore, the answer is yes.