A bit outside of my area, but I would try creating a column of zeros, Z, rewriting the equation as

Z = -A*F1 - B*F2 + C*F3 + A*C*F4

Then convert it to a JMP formula with parameters and try it in Nonlinear.

Parameter( {A= 1, B = 1, C = 1}, -A * :F1 - B * :F2 + C * :F3 + A * C * :F4) )