It seems to me that they ARE trying to disprove God using the Law of Contradiction.
Yes, but I also think they realise that it isn't
really possible to disprove God.
then it is in reality the only way TO disprove God
Nah, there's no way. God has magic powers so he can't be held to any law. Even if he is self-contradicting, he can still exist.
And like jar typed, even if we do find a way to disprove the existence of god, if he does exists, he'll still exist even if we disprovce his existence (meaning...we were wrong).