This just reads like "I can't find a counterexample and can't think of a way to find a counterexample so there must be no way to construct a counterexample so t

This just reads like "I can't find a counterexample and can't think of a way to find a counterexample so there must be no way to construct a counterexample so there are no counterexamples" and there are two points where you can go wrong with that kind of argument