Consider the following premises. For all x_14, if x_14 were bored, then x_14 is sad. For all x_14, x_14 is a scientist or x_14 is a sailor. For all x_14, if x_14 were a scientist, then x_14 is sad. For all x_14, if x_14 were a sailor, then x_14 is writing a letter. For all x_14, x_14 is bored or x_14 will not write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 is sad or x_14 will make tea.
 From the fact that for all x_14, x_14 is bored or x_14 will not write a letter we can infer that for all x_14, if x_14 writes a letter, then x_14 is bored via universal rewriting. From the fact that for all x_14, if x_14 were a sailor, then x_14 is writing a letter, and that for all x_14, if x_14 writes a letter, then x_14 is bored we can infer that for all x_14, if x_14 were a sailor, then x_14 is bored via universal transitivity. From the fact that for all x_14, if x_14 were a sailor, then x_14 is bored, and that for all x_14, if x_14 were bored, then x_14 is sad we can infer that for all x_14, if x_14 were a sailor, then x_14 is sad via universal transitivity. From the fact that for all x_14, if x_14 were a scientist, then x_14 is sad, that for all x_14, if x_14 were a sailor, then x_14 is sad, and that for all x_14, x_14 is a scientist or x_14 is a sailor we can infer that for all x_14, x_14 is sad via universal disjunction elimination. Finally, from the fact that for all x_14, x_14 is sad we can infer that for all x_14, x_14 is sad or x_14 will make tea via universal addition. Therefore, the answer is yes.