op(300,prefix,~). set(auto2). clear(fof_reduction). formulas(sos). % Definition: ActualAt(x,d) all x all d (Object(x) & Point(d) -> (ActualAt(x,d) <-> SituationAt(x,d) & (all p (Proposition(p) -> (TrueInAt(p,x,d) ->True(p,d)))))). % Logical Axiom: ~p is a proposition if p is. all p (Proposition(p) -> Proposition(~p)). % Definition: True(~p,d) all d all p ((Point(d) & Proposition(p)) -> (True(~p,d) <-> -True(p,d))). % Definition: WorldAt(x,d) all x all d (Object(x) & Point(d) -> (WorldAt(x,d) <-> SituationAt(x,d) & (exists d2 (Point(d2) & (all p (Proposition(p) -> (TrueInAt(p,x,d2) <-> True(p,d2)))))))). % Logical Theorem (L1): WorldAt(x,d) is rigid. all x (Object(x) -> ((exists d (Point(d) & WorldAt(x,d))) -> (all d (Point(d) -> WorldAt(x,d))))). % Logical Theorem (L2): EncpAt(x,p,d) is rigid. all x all p ((Object(x) & Proposition(p)) -> ((exists d (Point(d) & EncpAt(x,p,d))) -> (all d (Point(d) -> EncpAt(x,p,d))))). all p all x all d ((Object(x) & Proposition(p) & Point(d)) -> (TrueInAt(p,x,d) <-> EncpAt(x,p,d))). % denial of L3 -(all x all d ((Object(x) & Point(d)) -> ((WorldAt(x,d) & ActualAt(x,d)) -> (all p (Proposition(p) -> (TrueInAt(p,x,d) <-> True(p,d))))))). end_of_list.