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During the push
there MUST be some deformation of the wall.
That deformation may be very small,
but then the forces are very large.
Energy is stored in the deformed
wall BUT came from the person.
As the wall rebounds there is a force
(perhaps quite large)
that acts through a displacement (perhaps quite small)
that will account for the change in KE of the person.
In the end analysis,
the energy does come from the person, but was temporarily stored in the
wall.
There will also be dissipative losses, but we can imagine those being
minimized.
I'm having trouble with
the mechanism by which the energy stored as chemical PE ultimately becomes
KE of the CM through only internal conversions.