P is not equal to NP by Modus Tollens
Joonmo Kim · arXiv (Cornell University) · 2014
An artificially designed Turing Machine algorithm $\mathbf{M}_{}^{o}$ generates the instances of the satisfiability problem, and check their satisfiability. Under the assumption $\mathcal{P}=\mathcal{NP}$, we show that $\mathbf{M}_{}^{o}$ has a certain property, which, without the assumption, $\mathbf{M}_{}^{o}$ does not have. This leads to $\mathcal{P} eq\mathcal{NP}$ $ $ by modus tollens.