Given a set A = {2,3,5,....} decide if every possible combination with repeated usage of set A makes the following true. Where sum(A) ≠ sum(D), where D = every possible combination with repeated usage.

Edit: D must contain at least 2 multiplicities of an element. For example {2,2,3,5,6...}

Edit: A must consist of ONLY distinct numbers > 1. No repeated elements in A

I think this a special case of subset sum and partitioning, but we're allowed to use elements more than once.

Here's an example where the output would be FALSE

When A = {2,4}, and the counter-result is {2,2,2} . Notice that {2 2 2} = {2 4}, as they both sum up to 6.

Since sum(S) = sum(D), the expression sum(A) ≠ sum(D is not true thus the output is FALSE