OBJECT A - CASE
OBJECT B - CUSTOM 
                3 Record Types ((A or B) and C)

After Case is created, I am trying to write a validation rule that will lock down all editting until two record types are related to the case ((A or B) and C)

I currently have this formula:
AND(
        $RecordType.DeveloperName = "Case_Record_Type",
        A_Rollup__c = 0, 
        B_Rollup__c = 0,
        C__c = 0,
        NOT(ISNEW())
)

I am using "The Power of One" and the "Rollup__c" fields are just number fields. 

This formula does exactly what I want it to do, other than only requires one of the three records to be related and then will unlock the Case record for editting. I need it to stay locked until the records related are (A and C) or (B and C)
 

OBJECT A - CASE
OBJECT B - CUSTOM 
                3 Record Types ((A or B) and C)

After Case is created, I am trying to write a validation rule that will lock down all editting until two record types are related to the case ((A or B) and C)

I currently have this formula:
AND(
        $RecordType.DeveloperName = "Case_Record_Type",
        A_Rollup__c = 0, 
        B_Rollup__c = 0,
        C__c = 0,
        NOT(ISNEW())
)

I am using "The Power of One" and the "Rollup__c" fields are just number fields. 

This formula does exactly what I want it to do, other than only requires one of the three records to be related and then will unlock the Case record for editting. I need it to stay locked until the records related are (A and C) or (B and C)