  In this paper, we prove Shelukhin's conjecture on the translated points on
any compact contact manifold $(Q,\xi)$ which reads that for any choice of
function $H = H(t,x)$ and contact form $\lambda$ the contactomorphism
$\psi_H^1$ carries a translated point in the sense of Sandon, whenever the
inequality $ \|H\| \leq 2 T(\lambda,M)$ holds the case. Main
geometro-analytical tools are those of bordered contact instantons employed in
the present author's previous papers with Legendrian boundary condition via the
Legendrianization of contact diffeomorphisms. In addition, the usage of the
$\mathbb Z_2$-symmetry of anti-contact involution and the relevant intersection
theory argument for the contact instantons based on the generic mapping and the
evaluation map transversality plays an important role in the proof of the main
theorem. Along the way, we define the notion of contact product and develop
relevant contact Hamiltonian geometry which plays a fundamental role in our
proof in combination with the analysis of contact instantons, which has its own
interest in relation to the systematic study of quantitative contact topology.
