P is not equal to NP by Modus Tollens

TL;DR

This paper claims to prove that P is not equal to NP by constructing a specific Turing Machine and applying modus tollens logic, challenging the assumption that P equals NP.

Contribution

It introduces a novel Turing Machine algorithm that distinguishes properties under the assumption P=NP versus P≠NP, providing a new proof approach.

Findings

Shows a property of the Turing Machine under P=NP assumption

Demonstrates the property does not hold without the assumption

Concludes P ≠ NP based on logical contradiction

Abstract

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 $\mathcal{P}\neq\mathcal{NP}$ $ $ by modus tollens.