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1. T -> [(A * R) -> (S v ~A)]
2. ~S /(T * R) -> ~A
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3. T -> [~(A * R) v (S v ~A)] 1 Material Implication
4. T -> [(~A v ~R) v (S v ~A)] 3 De Morgan's Law
5. T -> [(~R v ~A) v (~A v S)] 4 Commutation
6. T -> [(~R v (~A v ~A)) v S] 5 Association
7. T -> [(~R v ~A) v S] 6 Tautology
8. T -> [(~A v ~R) v S] 7 Commutation
9. T -> [~A v (~R v S)] 8 Association
10. T -> [A -> (~R v S)] 9 Material Implication
11. (T * A) -> (~R v S) 10 Exportation
12. ~(T * A) v (~R v S) 11 Material Implication
13. (~T v ~A) v (~R v S) 12 De Morgan's Law
14. [(~T v ~A) v ~R] v S 13 Association
15. (~T v ~A) v ~R 14,2 Disjunctive Syllogism
16. ~T v (~A v ~R) 15 Association
17. ~T v (~R v ~A) 16 Commutation
18. (~T v ~R) v ~A 17 Association
19. ~(T * R) v ~A 18 De Morgan's Law
20. (T * R) -> ~A 19 Material Implication
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