Deduction, D. Bonevac, Blackwell Publishing, 2003, 8.3 problem 1

A simple argument and a two-step proof:

Jones's killer weighed over 200 pounds. Smith weighs less than 200 pounds. So, Smith isn't Jones's killer.

Regarding the translation, if we take 'Wx' for 'x weighed over 200 pounds', then 'weighs less than 200 pounds' can be translated as a negation of the former, that is 'It is not the case that Smith weighs over 200 pounds'.

1. (x)(Kxj ⊃Wx)
2. ¬ Ws
3. ∴¬ Ksj
4. Ksj ⊃Ws ......... 1UI x/s
5. ¬ Ksj ......... 2,4MT