this is not done yet. If you are interested, refer to the links instead. (and don’t expect what I will randomly write here to exceed these professional materials!)
https://en.wikipedia.org/wiki/Satisfiability_modulo_theories
Roughly SMT = SAT + x, where x can be quantifier logic, integer
arithmetic, string operations, etc.
https://en.wikipedia.org/wiki/Maximum_satisfiability_problem
https://en.wikipedia.org/wiki/Boolean_satisfiability_problem#Extensions_of_SAT
Read along about search like a machine.