Consider the following premises. For all x_13, if x_13 were a writer, then x_13 is a carpenter. For all x_13, if x_13 were happy, then x_13 is a carpenter. For all x_13, x_13 is happy or x_13 is a writer. If Joseph were a carpenter, then it is overcast. Can we infer the following from them? It is overcast.
 From the fact that for all x_13, if x_13 were happy, then x_13 is a carpenter, that for all x_13, if x_13 were a writer, then x_13 is a carpenter, and that for all x_13, x_13 is happy or x_13 is a writer we can infer that for all x_13, x_13 is a carpenter. From the fact that for all x_13, x_13 is a carpenter we can infer that Joseph is a carpenter. Finally, from the fact that if Joseph were a carpenter, then it is overcast, and that Joseph is a carpenter we can infer that it is overcast. Therefore, the answer is yes.