Before revision:  The sufficient conditions include IMPs arising from systems of linear equations over GF(p), p prime, and also some conditions defined through special kinds of polymorphisms  .
After revision:  The sufficient conditions include IMPs arising from systems of linear equations over GF(p), p prime, and also some conditions defined through special kinds of polymorphisms . Our work has several consequences and applications in terms of bit complexity of sum-of-squares (SOS) proofs and their automatizability, and studying (construction of) theta bodies of combinatorial problems .