fof(definefunctiontest,conjecture,elem(fx,fy)=>elem(fx,fy)).
fof(relation,axiom,![Xf]:(relation(Xf)<=>Xf=Xf)).
fof(rightunique,axiom,![Xf]:(rightunique(Xf)<=>Xf=Xf)).
fof(dom,axiom,![Xf]:dom(Xf)=Xf).
fof(apply,axiom,![Xf,Xx]:apply(Xf,Xx)=Xx).
fof(definefunctiontest1,axiom,relation(ff)).
fof(definefunctiontest2,axiom,rightunique(ff)).
fof(definefunctiontest3,axiom,![Xz]:(elem(Xz,fx)=>apply(ff,Xz)=Xz)).
fof(definefunctiontest4,axiom,dom(ff)=fx).