After reading this, I feel as though I will win any debate/argument/court case.
In the case of:
All dogs are mammals.
All cats are mammals.
Therefore, all dogs are cats
And assuming you dont know the conclusion is false, we must also assess the validity of the Subjects in each line. IE: Dogs, Cats, and mammals. By working each Subject down to atomic level and finding at least ONE difference between dogs and cats, we therefore prove that the conclusion is false. IE: counterexample.
Wow, with logic, you really dont need to know anything in order to learn everything.