>>115301751. Q or P (assumption)
2. Q -> H (assumption)
3. H -> R & Z (assumption)
4. P -> R & Z (assumption)
5. Z & R -> L or M (assumption)
6. Q -> NOT(M or L) (assumption)
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7. Q. (assumption)
8. {2, 7} H (modus ponendo ponens) 2, 7
9. {2, 3, 7} R & Z (modus ponendo ponens) 3, 8
10. {2, 3, 7} R (rule of simplification) 9
11. {2, 3, 7} Z (rule of simplification) 10
12. {2, 3, 7} Z & R (rule of conjunction) 10, 11
13. {2, 3, 5, 7} L or M (modus ponendo ponens) 5, 12
14. L (assumption)
15. {14} M or L (rule of addition) 14
16. M (assumption)
17. {16} M or L (rule of addition) 16
18. {2, 3, 5, 7} M or L (proof by cases) 13, 14-15, 16-17
19. {2, 3, 5, 6, 7} NOT Q (modus tollendo tollens) 6, 18
20. {2, 3, 5, 6} NOT Q (proof by contradiction) 7, 19
21. {1, 2, 3, 5, 6} P (modus tollendo ponens) 1, 20
References:
https://proofwiki.org/wiki/Definition:Natural_Deductionhttps://www.iep.utm.edu/nat-ded/ 
