It is possible for a valid argument to have a false conclusion. It is not possible for two false statements to be inconsistent with each other. An valid argument with a false conclusion must have at least one false reason.
Giraffes are taller than human babies, and human babies are taller than ants.
Thus giraffes are taller than ants. If the moon is made of blue cheese then it is edible. And the moon is in fact edible. Therefore, the moon is made of blue cheese. Elephants are bigger than lions, and elephants are bigger than chickens.