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1. O & I
2. O -> (S v G)
3. I -> ~G / :. S
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4. I & O 1 Commutation
5. O 1 Simplification
6. I 4 Simplification
7. ~G 3,6 Modus Ponens
8. S v G 2,5 Modus Ponens
9. S 8,7 Disjunctive Syllogism