DS

Let ‘F’ stand for the state of affairs that consists in finite persons possessing and exercising free will. Let ‘p’ stand for ‘God exists’; ‘q’ for ‘F obtains’; ‘r’ for ‘F poses a serious risk of evil’; and ‘s’ for ‘There is no option available to God that counters F.’ With this in place, the argument may be formalized as follows:

(1) [(p & q) & r] → s Premiss

(2) ~s        Premiss

(3) ~[(p & q) & r]   1, 2 MT

(4) ~(p & q) v ~r    3 DM

(5) r         Premiss

(6) ~(p & q)      4, 5 DS

(7) ~p v ~q      6 DM

(3) follows from the conjunction of (1) and (2) by modus tollens; De Morgan’s law applied to (3) yields (4); (4) and (5) together lead to (6) by disjunctive syllogism; and another application of De Morgan’s law takes us from (6) to the final conclusion, according to which either God exists or there is free will (but not both).

You can get the general idea from a recent comment in response to a request from a mother for advice on where to send her DS (Darling Son) to school.