Consider the following premises. There is at least one x_17 for which if x_17 were an office clerk, then x_17 is not writing a letter. For all x_17, x_17 is an office clerk and x_17 will play a game. For all x_17, x_17 will write a letter and x_17 is sad. Can we infer the following from them? For all x_17, x_17 is not bored.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.