∃!(x,y)x∈{A,B,C,D,E} ∧ y∈{X,Y,Z}.
⊢{X,Y,Z}::G(s)
find S(s)..._::G(s) of known F(s) so that if x∈P does that x = y∈R.
Form and test hypothesises ϖF()◇→G()∨H()⇝G()::do this; H():: do that...
Cross check with own G to not do anything stupid...