In my work I commonly encounter large systems of polynomial equations for which it would be useful to know if there is a nontrivial solution over $\mathbb{F}_2$ (and if so, to find such a solution).
This problem can be translated into a SAT solver problem. Treating the values $0,1$ of the variables as F,T respectively, then multiplication of variables translates to conjunction, and addition translates to XOR.
I'm wondering if there is a solver that is optimized for just solving the satisfiability problem for systems of polynomial equations over $\mathbb{F}_2$ directly. The solver z3 allows the use of XOR, but only binary XOR. Perhaps there is another SAT solver that allows more than a binary use of XOR, since there are often many summands in the polynomials I consider.