1. (K v S) v (T v W)
2. ~S + [T v ~(O v Z)]
3. K > ~(T v ~Z) /∴ T v W
4. | ~(T v W) Assumption for Indirect Proof
5. | (T v W) v (K v S) 1, Commutation
6. | K v S 5,4 Disjunctive Syllogism
7. | S v K 6, Commutation
8. | ~S 2, Simplification
9. | K 7,8, Disjunctive Syllogism
10. | ~(T v ~Z) 3,9, Modus Ponens
11. | ~T + ~~Z 10, DeMorgan's Law
12. | ~T + Z 11, Double Negation
13. | Z + ~T 12, Commutation
14. | Z 13, Simplification
15. | [T v ~(O v Z)] + ~S 2, Commutation
16. | T v ~(O v Z) 15, Simplification
17. | ~T 12, Simplification
18. | ~(O v Z) 16,17, Disjunctive Syllogism
19. | ~O + ~Z 17, DeMorgan's Law
20. | ~Z + ~O 18, Commutation
21. | ~Z 19, Simplification
22. | Z + ~Z 13,19, Conjunction
23. T v W Lines 4-23 Indirect Proof
Edwin
