+include "logic/equality.ma".
+
+(* Inclusion of: COL003-20.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-20 : TPTP v3.7.0. Released v2.1.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.21 v3.1.0, 0.22 v2.7.0, 0.36 v2.6.0, 0.33 v2.5.0, 0.00 v2.2.1, 0.62 v2.2.0, 0.80 v2.1.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 2 RR) *)
+
+(* Number of atoms : 4 ( 4 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 5 ( 0 singleton) *)
+
+(* Maximal term depth : 5 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_strong_fixed_point:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀fixed_pt:Univ.
+∀strong_fixed_point:Univ.
+∀w:Univ.
+∀H0:eq Univ strong_fixed_point (apply (apply b (apply w w)) (apply (apply b (apply b w)) (apply (apply b b) b))).
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#fixed_pt ##.
+#strong_fixed_point ##.
+#w ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+nauto by H0,H1,H2 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)