Function ns_lower_bound_witness_gfp 

pub fn ns_lower_bound_witness_gfp(
    f: NsField,
    num_vars: usize,
    clauses: &[Vec<Lit>],
    degree: usize,
) -> Option<Vec<(Mono, u64)>>

ns_lower_bound_witness_polys_gfp for a CNF (signed clause false-indicators as generators). An empty clause is an immediate refutation — no lower bound at any degree.