I had a small bug in my code. I found it using my test sample. I would like to share it with you. I have used some extra white space in the boolean expression. I am not sure if it is necessary, you can remove them.

Input:

(NOT  ( (NOT  NOT TRUE ) AND  A) OR (B AND C AND D))    OR E
 3 10 14
 -3 -3
 -3 -1
 -3 3
 -1 1
 0 -2
 2 -1
 2 3
 3 -3
 3 0
 3 2
 -3 -2 A
 -2 -3 A
 -2 -1 A
 -1 -3 D
 -1 -1 Z
 0 -3 C
 0 -1 C
 1 -3 E
 1 0 A
 2 -3 B
 2 0 A
 2 1 E
 3 -1 E
 3 3 B
 0 0
 1 0
 2 0
 3 0
 3 1
 3 2
 2 2
 1 2
 0 2
 -1 2
 -2 2
 -3 2


Output:
0 0
1 0
2 0
3 0
3 -1
3 -2
3 -3
2 -3
1 -3
0 -3
-1 -3
-2 -3
-3 -3
-3 -2
-3 -1
-2 -1
-1 -1
0 -1
1 -1
2 -1
2 0
2 1
2 2
2 3
3 3

This is how the table looks like: (1 means there is a Fork and * means empty cell)
1 A 1 * * * 1
A * A * * * *
D * Z * 1 * *
C 1 C * * * *
E * * A * * *
B * 1 A E * 1
1 * E 1 * 1 B