[bryanrasmussen]

>There is a way to disprove that the statement: "There is no god" by simply showing a counterfactual god.

that both parties to the argument agree is a god.

>Likewise, there is a way to disprove the statement: "LLMs cannot be successfully used for X application." By showing that LLMs have been used in X application.

Again there the point of argumentation will be the word "successfully", the LLM would have to be such an overwhelming success at what it is trying to do that one cannot weasel out of it with "successfully".