Heiwa's challenge reminds me of an old story about a psychotic patient who believed he was dead, and the new psychiatrist who decided to cure him of his delusions by logic.
He asked the patient, "Do dead people bleed?" and the patient responded, "No, of course, everyone knows dead people do not bleed, because their blood no longer circulates."
So, the psychiatrist took out a scalpel, and made a small incision on the patient's arm. Blood immediately started welling out.
"There!" said the psychiatrist triumphantly. "You're bleeding, and this proves you're alive!"
"No," the patient responded dolefully, "it just proves that dead people do bleed, after all."
The moral is, if someone is determined to cling to a certain conclusion, no amount of logic or sound scientific argument will persuade them. So, Heiwa's claim that "no one has succeeded in proving the case," is pointless, because there is no proof he will accept.