Consider the following premises. For all y, if y climbs a mountain, then y is happy. Patricia is happy or Richard is not writing a letter. Richard is writing a letter or Patricia is climbing a mountain. Can we infer the following from them? Patricia is not happy.
 From the fact that for all y, if y climbs a mountain, then y is happy we can infer that if Patricia climbs a mountain, then Patricia is happy. From the fact that Patricia is happy or Richard is not writing a letter we can infer that if Richard writes a letter, then Patricia is happy. Finally, from the fact that if Richard writes a letter, then Patricia is happy, that if Patricia climbs a mountain, then Patricia is happy, and that Richard is writing a letter or Patricia is climbing a mountain we can infer that Patricia is happy, which contradicts that Patricia is not happy. Therefore, the answer is no.