Looks like they (SATNet) are not incorporating a real (exact) SAT solver but their differentiable "SAT solver" is a MAXSAT estimator which gives an approximation of the maximum number of clauses that can be made true.
Looks like they (SATNet) are not incorporating a real (exact) SAT solver but their differentiable "SAT solver" is a MAXSAT estimator which gives an approximation of the maximum number of clauses that can be made true.