Formal defintion of SET-PARTITION as a language
The set partition problem asks whether there exists a 2-partition of a multi-set such that sum of numbers in one set is equal to the sum of numbers in the other set.

Note the phrase whether there exists; if you are already being given the partition in the input $\langle S,A,B \rangle$ then the problem becomes whether the given partition is valid and sum of elements of $A$ and $B$ are equal. This problem is easy and can be solved in polynomial it time. 

However, Set Partition is NP-Complete, which seems unlikely to be solved in polynomial time.