We prove an exponential lower bound on the size of static
Lovasz-Schrijver calculus refutations of
Tseitin tautologies.
We use several techniques, namely, translating static LS proof into
Positivstellensatz proof of Grigoriev et al.,
extracting a "good" expander out of a given graph by
removing edges and vertices of Alekhnovich et al.,
and proving linear lower bound on the degree of Positivstellensatz
proofs for Tseitin tautologies.
This work was done in cooperation with Arist Kojevnikov.