INFOPATH + Formula with If Statements

You can do any logic you want with InfoPath rules, but the syntax and approach is a little different.
1. For your validation field best practice would be to use a boolean or the false rather than good or bad in a text field.  A little bit simpler and faster.
2. There are two approaches to the check.  Put the check on the submit button as an action.    Create a new rule and add a condition.  Field1 equals Duplicate or field2 equals Duplicate or field3 equals duplicate.  Then have the action be a set a fields value
3. The other way is to put a rule on each of the fields to be checked.  If the field equals one of the other fields or duplicate then set the field value to true.  The advantage here is that you can alert the user to bad input sooner rather than at the end and they have to start over.  It is also easier to have messaging as to the exact field which is the problem since it is in context.

so the answer is to use OR statements and conditions. This is often not trivial and takes experimenting to get the correct logic. Such as if you use not equals you have to flip to and statements.  Always do things in small steps and validate before moving on to the next one.