set(auto2).

formulas(sos).
% axioms for theorem 8

all x all G ((Object(x) & Property(G)) -> (IsAFormOf(x,G) <-> Ex1(A,x,W) & (all F (Property(F) -> (Enc(x,F) <-> Implies(G,F)))))).

all x all G (IsAFormOf(x,G) -> Object(x) & Property(G)).

all x all y ((Object(x) & Object(y) & Ex1(A,x,W) & Ex1(A,y,W)) -> ((all F (Property(F) -> (Enc(x,F) <-> Enc(y,F)))) ->  x = y)). 

all F all G ((Property(F) & Property(G)) -> (Implies(F,G) <-> (all x all w (Point(w) -> (Ex1(F,x,w) -> Ex1(G,x,w)))))).

all x all G ((Object(x) & Property(G)) -> (IsTheFormOf(x,G) <-> (IsAFormOf(x,G)  & (all y (IsAFormOf(y,G) -> y=x))))). 

all x all y ((Object(x) & Object(y)) -> (PartPH(x,y) <-> (exists F (Property(F) & IsTheFormOf(y,F) & Enc(x,F))))).

all x (Object(x) -> (Form(x) <-> (exists G (Property(G) & IsAFormOf(x,G))))).

all x (Form(x) -> Object(x)).

% theorem 
-(all x (Form(x) -> PartPH(x,x))).
end_of_list.
