Your thoughtless edit 

When you did this edit, did you read the next following sentence, "If it is discovered that two (or more) of these conditions hold, then all of them hold and ZFC+A1 is inconsistent and ZFC+A2 is inconsistent; in this case, these 'axioms' would no longer be considered large cardinal axioms."? You are supposing that this cannot happen, that is, that none of the "large cardinal axioms" will ever be found to be inconsistent, even though this has repeated happened in the past.