  We present an $SU(3)^{}_{c}\times SU(2)^{}_{L}\times SU(2)^{}_{R}\times
U(1)_{L}^{}\times U(1)_{R}^{}\rightarrow SU(3)^{}_{c}\times SU(2)^{}_{L}\times
SU(2)^{}_{R}\times U(1)^{}_{B-L}$ left-right symmetric model with a discrete
parity symmetry to realize a universal seesaw scenario. The model can
simultaneously solve the strong CP problem without resorting to the unobserved
axion and explain the 750 GeV diphoton resonance reported recently by the ATLAS
and CMS collaborations at the LHC. Owing to large suppressions in the two-loop
induced Dirac mass terms, the Majorana mass matrices of left- and right-handed
neutrinos naturally share the same structure. That allows us to quantitatively
study the neutrinoless double beta decay induced by the right-handed currents.
