The number 1 definition of 'can' in the OED on-line dictionary is:
1 Be able to.
When you are referring to someone having the skill and/or knowledge to accomplish a task, 'can' and 'able' are synonymous (as also pointed out by Andrew in a comment to your question). There are other meanings of both words that are not synonymous, but they do not apply to the sentences you provided.
Adding 'just' in your comments totally changes the original sentence, i.e.:
I don't believe he's able to open any safe.
does not mean the same as
I don't believe he's able to open just any safe.
The second implies that he can open some safes but not any safe. Presumably he can only open safes of a particular kind. And, exactly the same problem occurs if you add 'just' to your original second sentence.
I don't believe he can open any safe.
I don't believe he can open just any safe.
Both sentences without 'just' mean the same. Both sentences with 'just' mean the same.
The exact same logic applies to (c) and (d)