Premise 1: W+P
Premise 2:~(W.S)
Premise 3: ~(S.P)
                  Conclusion~(S.U) 

4. ~W+~S               Premise 2, DeMorgan's law
5. ~S+~W               4, commutativity
6. ~S+~P               Premise 3, DeMorgan's law 
7. (~S+~W).(~S+~P)     5,6, conjunction 
8. ~S+(~W.~P)          7, distribution
9. ~S+~(W+P)           8, DeMorgan's law (replacement)
10. ~(W+P)+~S          9, commutativity
11. ~~(W+P)            Premise 1, double negation
12. ~S                10,11, disjunctive syllogism   
13. ~S+~U             12, addition
14. ~(S.U)            13, DeMorgan's law

Edwin