1. Rocky the dog is alive.
2. Rocky the dog is dead.
3. Exactly one of statements 6 and 9 is true.
4. Exactly one of statements 2 and 6 is false.
5. Statements 4, 5 and 10 are all false.
6. Exactly one of statements 1 and 10 is false.
7. Exactly 5 statements are true.
8. Exactly one of statements 3 and 10 is false.
9. Exactly one of statements 6 and 10 is true.
10. Exactly one of statements 1 and 2 is false.
11. Statements 1, 8 and 11 are all false.

Which of the above statements are definitely true? Is Rocky the dog alive or dead?

*** Based on an original problem by Louise Mayor.