Premises:
1) IF God were willing to prevent evil but unable to do so, God would be impotent.
2) IF God were able to prevent evil but unwilling to do so, God would be malevolent.
3) IF evil exists, then God is either unwilling or unable to prevent it.
4) There is evil.
5) IF God exists, God is neither impotent nor malevolent.
Conclusion: God exists only if he is both unwilling and unable to prevent evil.

W = Willing to prevent evil
A = Able to prevent evil
I = God is impotent
M = God is malevolent
E = Evil exists
G = God exists
(1) = W ^ ~A -> I
(2) = A ^ ~W -> M
(3) = E -> ~W V ~A
(5) = G -> ~I ^ ~M

Since we only care about the instances where E is true, I deleted the false cases. (Premise 4)
**** - All premises are met and God does not exist.
!!!! - All premises are met and God does exist.
	W	A	I	M	E	G	(1)	(2)	(3)	(5)
	t	t	t	t	t	t	t	t	F	F
	t	t	t	t	t	F	t	t	F	t
	t	t	t	F	t	t	t	t	F	F
	t	t	t	F	t	F	t	t	F	t
	t	t	F	t	t	t	t	t	F	F
	t	t	F	t	t	F	t	t	F	t
	t	t	F	F	t	t	t	t	F	t
	t	t	F	F	t	F	t	t	F	t
	t	F	t	t	t	t	t	t	t	F
****	t	F	t	t	t	(F)	(t  &	t   &	t   &	t)
	t	F	t	F	t	t	t	t	t	F
****	t	F	t	F	t	(F)	(t  &	t   &	t   &	t)
	t	F	F	t	t	t	F	t	t	F
	t	F	F	t	t	F	F	t	t	t
	t	F	F	F	t	t	F	t	t	t
	t	F	F	F	t	F	F	t	t	t
	F	t	t	t	t	t	t	t	t	F
****	F	t	t	t	t	(F)	(t  &	t   &	t   &	t)
	F	t	t	F	t	t	t	F	t	F
	F	t	t	F	t	F	t	F	t	t
	F	t	F	t	t	t	t	t	t	F
****	F	t	F	t	t	(F)	(t  &	t   &	t   &	t)
	F	t	F	F	t	t	t	F	t	t
	F	t	F	F	t	F	t	F	t	t
	F	F	t	t	t	t	t	t	t	F
****	F	F	t	t	t	(F)	(t  &	t   &	t   &	t)
	F	F	t	F	t	t	t	t	t	F
****	F	F	t	F	t	(F)	(t  &	t   &	t   &	t)
	F	F	F	t	t	t	t	t	t	F
****	F	F	F	t	t	(F)	(t  &	t   &	t   &	t)
!!!!	F	F	F	F	t	(t)	(t  &	t   &	t   &	t)
****	F	F	F	F	t	(F)	(t  &	t   &	t   &	t)

In the one case in which God exists, it is only because of reasonable doubt.
So, with reasonable doubt, God exists. However, it is heavily weighted to the conclusion 
that God does not exist.