We use the known linear lower bound for Tseitin's tautologies for establishing linear lower bounds on the degree of Nullstellensatz proofs (in the usual boolean setting) for explicitly constructed systems of polynomials of a constant (in our construction 6) degree. It holds over any field of characteristic distinct from 2. Previously, a linear lower bound was proved for an explicitly constructed system of polynomials of a logarithmic degree.
['Dima Grigoriev']
Tseitin's tautologies and lower bounds for Nullstellensatz proofs