Consider the following premises. For all x_6, if x_6 were a cashier, then x_6 is excited. If Jessica were a scientist, then Thomas is a writer. Jessica is a scientist or Thomas is a cashier. For all x_6, if x_6 were excited, then x_6 is a writer. Can we infer the following from them? Thomas is a writer.
 From the fact that for all x_6, if x_6 were a cashier, then x_6 is excited, and that for all x_6, if x_6 were excited, then x_6 is a writer we can infer that for all x_6, if x_6 were a cashier, then x_6 is a writer. From the fact that for all x_6, if x_6 were a cashier, then x_6 is a writer we can infer that if Thomas were a cashier, then Thomas is a writer. Finally, from the fact that if Jessica were a scientist, then Thomas is a writer, that if Thomas were a cashier, then Thomas is a writer, and that Jessica is a scientist or Thomas is a cashier we can infer that Thomas is a writer. Therefore, the answer is yes.