You did miss something, I'm afraid.
You treat "without the laver of regeneration" as something that can be either true or false in and of itself, as if true means it's there and false means it's not. No, you have to operate on the value (T/F) of the proposition in the statement. You have to say: "If it is true/false that justification cannot take place without the laver of regeneration/desire thereof, then..." You have to do this for both propositions to produce a correct result of true or false.
Also, you somehow ended up with the wrong table, the
logical NOR, which produces illogical results when properly used.
The truth table you want is the one for the
logical disjunction. As we continue, you will see that this is the only table that can be correct.
To demonstrate that the table you chose was not the correct one, I will operate on the values of both propositions in this sentence, which follows all the same rules as the decree we've been discussing.
I cannot walk without moving my limbs or stepping.
Now to operate on the value of the propositions in this statement, using the logical NOR table:
F F TIF it is TRUE that I cannot walk without moving my limbs, and
IF it is TRUE that I cannot walk without stepping,
THEN it is FALSE that I cannot walk without moving my limbs or stepping.
Doesn't quite work does it?
Using the truth table for the logical disjunction, we get the correct results across the board, as you can plainly see:
T T T
T F T
F T T
F F FSo, back to justification, using line two in the table for example:
IF it is TRUE that it cannot be effected without the laver of regeneration (as the decree saith), and even IF it is FALSE that it cannot be effected without the desire thereof (as the decree does not say), THEN it is still TRUE that it cannot be effected without the laver of regeneration, or without the desire thereof. That is to say, it is still impossible for it to be effected with one or the other missing (in this case the one that has to be missing is the laver of regeneration).
SO, according to line one in the Table (what the Catholic dogma has been all along since the promulgation of this decree):
SINCE it is TRUE that it cannot be effected without the laver of regeneration (as the decree says), and SINCE it is TRUE that it cannot be effected without the desire thereof (again, as the decree says), THEN it is TRUE that it cannot be effected without the laver of regeneration, or without the desire thereof.
And we are now right back to De Morgan's Law.