Consider the following premises. For all x_12, x_12 will play a game and x_12 will cook. For all x_12, x_12 is a sailor. There is at least one x_12 for which if x_12 were a sailor, then x_12 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, either x_12 will play a game or x_12 will climb a mountain are not true.
That contradicts the premises. Therefore the answer is no.