Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: P is not equal to NP by Modus Tollens   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.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con