Abstract: 
In this paper I provide a very short but decisive proof that P ≠ NP, anf NP=EXPTIME
in the context of the ZF set theory and deterministic Turing machines. We discuss also the
subtle implications of considering the P versus NP problem, in different axiomatic theories!
The results of the current paper definitely solve the 3rd Clay Millennium problem P versus
NP, in a simple and transparent away that the general scientific community, but also the
experts of the area, can follow, understand and therefore become able to accept.
