The argument here is a classic apples and oranges proposition.
The crematoria at Auschwitz and Birkenau were all typical cremation ovens. That is, they were designed to take a body (at maximum shrouded, but NOT in a coffin) which would be inserted singly onto a kind of grill and then be cremated by the super-heated air generated elsewhere in the oven. Even today, cremations are carried out in this manner: the actual fire (from whatever source) is not supposed to contact the body.
The proposed Topf patent is NOT for a cremation oven, but rather for an incinerator. That is, you build a fire, let it develop over a period of time (in this case, two days), and then start throwing material in it -- that is, right on the fire -- to burn.
But you cannot apply this method to the AB crematoria because the bodies were not thrown directly on the fire, but were burned by indirect heat, like all cremation ovens. This simply means that the cremating bodies could not have contributed fuel (in the form of fat) to the ongoing fire, which would need tending on its own. And this is where the coke usage comes in.
True, there were probably attempts to put multiple bodies in the muffles. Perhaps two or three at a time, the dimensions of these particular muffles would not allow for more. But if it takes X to burn one body, it will take 3 X to burn three, and again, if it takes 30 minutes to reduce a body to the size of a football, 30 minutes with three bodies will not produce three football sized remains.
True also, the fat from burning bodies will allow the middle stage of cremation to proceed more or less on its own. But not at the end. High heat is required at the beginning of the cremation cycle, to ignite, and at the end, to reduce the remainder of the body proteins (minus the burnt off fat) to ash.
Even incinerators are not perfect thermal systems: they continue to require fuel for burning, and not just the fuel they are burning. The most efficient incinerators of, say, animal waste, still require external BTU's to keep going far in excess of 3.5 kg per, say, 70 kg (hypothetical human body), and incidentally require far more than 15 minutes per 70 kg, in fact, the going rate for state of the art incinerators is about 40 seconds per kg, IOW, 70 x 40 / 60 = 47 minutes to INCINERATE 70 kg of remains.
CREMATIONS, as opposed to INCINERATIONS, take longer. According to the only SCIENTIFIC data ever done on this matter, by the British Cremation Society, it takes 40 minutes to reduce a body to bone, and another 20-30 minutes to reduce the bone to ash. Furthermore, there is a thermal barrier to these processes of under 40 minutes that it is not possible to go beneath (too much heat or too little heat both turn the body to a kind of hard black tootsie roll substance). Meanwhile, the same study says that after 30 minutes, the body can only be reduced to the size of a football.
Now this is REAL scientific data. It wasn't produced by revisionists or exterminationists, but rather by people who do cremations for a living. Such data obviously trumps such things as the 15 minute per body memo (which has many odd features indicating probable forgery), or the Gusen timesheet, which, only under a charitable interpretation can support the alleged 27 minute cremation time cited therein.
Unless someone comes up with real SCIENTIFIC data to contradict the British Cremation Society, the real conclusions are that:
1) Bodies cannot be cremated in 15 minutes or even 30 minutes, but less than one hour times are conceivable for incomplete multiple cremations,
2) Bodies cannot be CREMATED using 3.5 kg of coke, in fact, they cannot even be INCINERATED using 3.5 kg of coke, although, in both cremation ovens and incinerators, combustible material, such as fat, can assist the burning process.
3) The real rate of burn at the Birkenau crematoria was about 500 a day.
https://archive.is/CrYAa
This is of course just a basic "in a nutshell" outline of the cremation process. I also suggest reading the more detailed studies by Carlo Mattogno as well for more details.