We are given a set of $n$ positive integers.We assume all of them are bounded by a polynomial of $n$.We would like to find a subset $S$ of these $n$ numbers such thatfor any $T_1,T_2\subseteq S$, the sum of numbers in $T_1$ is not equal to that of $T_2$.We want the size of $S$ is maximized.Clearly, the problem is in NP and can be solved in $n^{O(\log n)}$ time (Since $|S|\leq O(\log n)$).Is this problem polynomial time solvable?Is this problem studied before? Any help is appreciated. 
Find the maximum set whose subset sum is unique for every of its subset
cc.complexity theory;ds.algorithms;nt.number theory