Sum query on a Multi D array

In reply to warnerrs:

Thanks for your reply.
I am not trying to sum all the columns. Here is my complete constraint.

constraint constraint_c3_c {
        foreach(pipe[i,j]){
            foreach(pipe[k,l]){
                if(({i,j} != {k,l}) && (pipe[i][j] == pipe[k][l])) {
                    //if((i+sumUntil(i,j)) >= (k+sumUntil(k,l))) {
                    //   i+sumUntil(i,j) >= (k+sumUntil(k,l))+int'(pipe[i][j]);
                    //}else {
                    //   i+sumUntil(i,j)+int'(pipe[i][j]) <= (k+sumUntil(k,l));
                    //}
                    if(i+pipe[i].sum with (item.index < j) >= (k+pipe[k].sum with (item.index < l))) {
                       i+pipe[i].sum with (item.index < j) >= k+pipe[k].sum with (item.index < l);
                    }else {
                       i+pipe[i].sum with (item.index < j) +int'(pipe[i][j]) <= k+pipe[k].sum with (item.index < l);
                    }
                }
        }   }
    }

Its basically adding a subset of the array together. The solver hangs if I use commented portion instead.