begin_problem(Scenario1_Piece2). list_of_descriptions. name({*Qualitative Reasoning About Containers - Case 1, Piece 2*}). author({*Professor Ernest Davis, Angelica Chen*}). status(unsatisfiable). description({*August 13, 2013*}). end_of_list. list_of_symbols. functions[(RUnion,2), (Singleton,1), (Place,2), (Slice,2), (HPlace,1), (Ox1,0), (Ob1,0), (Ta1,0), (Tb1,0), (Rc1,0), (Hc1,0)]. predicates[(Ordered,2), (Time,1), (Region,1), (History,1), (Object,1), (ObjectSet,1), (Lt,2), (Leq,2), (Leq3,3), (P,2), (Cavity,2), (OSPlace,3), (ClosedContainer,3), (CContained,3), (RigidObject,1), (RigidHistory,1), (O,2), (EC,2), (DR,2), (Outside,2), (NoExitCavity,4), (PersistentCavity,4), (NoEntranceCavity,4)]. end_of_list. list_of_formulae(axioms). % Time Ordering % Sortal axioms % TISA formula(forall([x,y], implies(Lt(x,y), and(Time(x), Time(y))))). % TISB formula(forall([x,y], implies(Leq(x,y), and(Time(x), Time(y))))). % TISC formula(forall([x,y], implies(Ordered(x,y), and(Time(x), Time(y))))). % TISD formula(forall([x,y,z], implies(Leq3(x,y,z), and(Time(x), Time(y), Time(z))))). % Space % Basic spatial relations % Sortal axioms % SBSA formula(forall([u,v], implies(or(P(u,v), O(u,v), EC(u,v), DR(u,v)), and(Region(u), Region(v))))). % SBSB formula(forall([u,v], implies(and(Region(u), Region(v)), Region(RUnion(u,v))))). % Spatial Containment % Sortal axioms % SCSA formula(forall([u,v], implies(or(Cavity(u,v), Outside(u,v)), and(Region(u), Region(v))))). % Objects % Object Sets % Sortal axioms % OSSA formula(forall([x], implies(Object(x), ObjectSet(Singleton(x))))). % Objects and Object Sets: Spatio-Temporal % Sortal axioms % OTSA formula(forall([t,o], implies(and(Time(t), Object(o)), Region(Place(t,o))))). % OTSB formula(forall([t,s,r], implies(OSPlace(t,s,r), and(Time(t), ObjectSet(s), Region(r))))). % Objects containing regions % Sortal axiom % ORSA formula(forall([t,s,r], implies(ClosedContainer(t,s,r), and(Time(t), ObjectSet(s), Region(r))))). % Object Containment % Sortal axiom % OCSA formula(forall([t,ox,s], implies(CContained(t,ox,s), and(Time(t), Object(ox), ObjectSet(s))))). % Histories % Sortal axioms % HISA formula(forall([t,h], implies(and(Time(t), History(h)), Region(Slice(t,h))))). % HISC formula(forall([o], implies(Object(o), History(HPlace(o))))). % Evolving cavities % Sortal axioms % HCSA formula(forall([t1,t2,hc,ho], implies(or(NoExitCavity(t1,t2,hc,ho), NoEntranceCavity(t1,t2,hc,ho), PersistentCavity(t1,t2,hc,ho)), and(Time(t1), Time(t2), History(hc), History(ho))))). % Definition % HCDA formula(forall([t1,t2,hc,hb], equiv(PersistentCavity(t1,t2,hc,hb), and(NoExitCavity(t1,t2,hc,hb), NoEntranceCavity(t1,t2,hc,hb))))). % Rigid Objects % Sortal axioms % RGSA formula(forall([o], implies(RigidObject(o), Object(o)))). % RGSB formula(forall([h], implies(RigidHistory(h), History(h)))). % P.2.1 formula(RigidHistory(HPlace(Ob1))). % P.2.2 formula(Cavity(Rc1,Slice(Ta1,HPlace(Ob1)))). % P.2.3 formula(forall([t1,t2,hc,hb], implies(PersistentCavity(t1,t2,hc,hb), NoExitCavity(t1,t2,hc,hb)))). % C1AC formula(Lt(Ta1,Tb1)). % RGAB formula(forall([h,t1,t2,r], implies(and(RigidHistory(h), Cavity(r,Slice(t1,h)), Lt(t1,t2)), exists([hc], and(RigidHistory(hc), PersistentCavity(t1,t2,hc,h), equal(r, Slice(t1,hc))))))). end_of_list. list_of_formulae(conjectures). formula(exists([hc], and(equal(Rc1, Slice(Ta1,hc)), NoExitCavity(Ta1,Tb1,hc,HPlace(Ob1))))). end_of_list. list_of_settings(SPASS). {*set_flag(DocProof,1).*} end_of_list. end_problem.