Something all theists should all keep in mind.

[Darkstar]

What do you mean by "logically sound"? In logic, an argument is "sound" if and only if it is both valid and its premises are true. Under this meaning of "sound", logically "sound" arguments can't be invalid, because they are by definition valid. Since that's a contradiction, I assume it isn't what you meant.

So what did you mean?

I meant when it's premise is false, but the argument is valid.