Also, your conclusion about the first statement is fallacious anyway.
"I think therefore I exist" does not imply "I don't think, therefore I don't exist"
just as
"I am on Southperry, therefore I am on a forum" does not imply "I am not on Southperry, therefore I am not on a forum"
"I think therefore I exist" does not imply "I don't think, therefore I don't exist"
just as
"I am on Southperry, therefore I am on a forum" does not imply "I am not on Southperry, therefore I am not on a forum"

