The Ifidonlike Conjecture

Based on my discussions with ifidonlike, I think he's making one or both of the following claims, which I respectfully term the "Ifidonlike Conjecture".

First, note that we are talking about real-world engines, transmissions and cars. This means that they must be achievable with today's technology by competent engineers and consistent with laws of physics and principals of engineering.

The statements concern two engines given as black boxes, with only the following data to tell them apart:

Engine 1: Max power P1 @ R1 rpm.
Engine 2: Max power P2 @ R2 rpm.
P1 > P2 by any amount.

[STRONG CONJECTURE]
One can construct two transmissions, suitable for each individual engine, and install them on two cars that have all else equal (weight, aerodynamics etc), such that: Given any objective acceleration performance criterion (e.g. 0-60 time, 5-60 time, etc), car #1 will outperform car #2.

[WEAK CONJECTURE]
Let there be one given objective acceleration performance criterion. Then one can construct two transmissions, suitable for each individual engine, and install them on two cars that have all else equal, such that car #1 will outperform car #2.

Ifidonlike can further clarify whether he claims the stronger version to be true or just the weaker version.

Note that several other people on the board, when making statements such as "don't believe in peak hp figures as they don't necessarily translate into better performance," have been criticized by ifidonlike. It would seem to me that such a broad criticism means that ifidonlike does believe in the strong version of his conjecture. This would be remarkable indeed, if true.

I hold the opinion that even the weaker version is false. This being a real-world situation, and this conjecture ultimately could be reduced to non-falsifiable statements if one so wishes (e.g. "I want to build transmissions that don't slip away any power, how do you know this can't happen, how do you know the 2nd law of thermodynamics has to hold everywhere and every time?"), obviously we can't formally prove or disprove it. But it's quite easy to disprove it beyond reasonable doubt.

But before I present my arguments, maybe people will care to comment?