conclusive
Proving something completely so no reasonable doubt is left.
Conclusive means settling something completely, leaving no room for doubt or further argument. When evidence is conclusive, it proves something so clearly that everyone can agree on what happened. If a detective finds conclusive proof that someone committed a crime, the evidence is so strong that there's no question about what happened.
In science, a conclusive experiment answers a question so definitively that other scientists accept the results without needing to keep testing the same thing. When doctors run conclusive tests, they can make a firm diagnosis instead of just guessing what might be wrong.
You might argue about who ate the last cookie until someone finds conclusive evidence like chocolate smudges on your brother's face and an empty wrapper in his pocket.
Something is only conclusive when it's so clear and complete that reasonable people can't disagree anymore. If your teacher says the evidence about who broke the classroom window is “not conclusive,” it means there's still doubt, and more investigation is needed. Conclusive evidence ends the mystery.