Only if you have a finite set of theories. If you have infinitely many theories that could explain a phenomenon, eliminating some swath of them brings you 0 new

Only if you have a finite set of theories. If you have infinitely many theories that could explain a phenomenon, eliminating some swath of them brings you 0 new information, in information theoretical terms. The problem with SUSY and String theory and other similar physical theories is that they have many free parameters that can have any value that hasn't yet been ruled out by experiment. So if you build a collider twice as large and find nothing, you'll find that your parameter that today has possible range [n, +Inf) will now be known to have range [2n, +Inf). That doesn't actually mean anything at all, though. That doesn't actually tell you anything: you'll need infinitely more experiments to know what's the value of that parameter.