Here is the logic:
1. 
Rule
1 (Hypothesis)
2. 
Rule 2
(Hypothesis)
3. 
Rule 3
(Hypothesis)
4. 
Fact
1 (Hypothesis)
5. 
Fact
2 (Hypothesis)
6. 
Fact
3 (Hypothesis)
7. 
Fact
4 (Hypothesis)
(Note: Polly is the character name of the actress, who played the witch, in another TV show)
Experiment: 
? Result: 
is true.
8. 
Fact
5 (Hypothesis)
9. 
3;
Universal Instantiation
10. 
9; Universal Instantiation
11. 
8,
4; conjunction
12. 
10,
11; modus ponens
13. 
2;
Universal Instantiation
14. 
13;
Universal Instantiation
15. 
6,
5; conjunction
16. 
15,
12; conjunction
17. 
14,
16; modus ponens
18. 
1;
Universal Instantiation
19. 
17,
7; conjunction
20. 
19,
18; modus ponens
So, we have proved, given the hypotheses, that Polly is a witch. So, it is actually logically correct.