You made a mistake on line 11. You should have P v Z (not P v S) since the consequent of U -> Z is Z
So continuing with your work...
11. P v Z 2,4,10 Constructive Dilemma
12. ~M 7,11 Modus Ponens
13. ~S 5,12 Modus Tollens
14. ~Y 6,13 Disjunctive Syllogism