--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: COL030-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL030-1 : TPTP v3.7.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for S and L *)
+
+(* Version : [WM88] (equality) axioms. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators S and L, where ((Sx)y)z *)
+
+(* = (xz)(yz), (Lx)y = x(yy). *)
+
+(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+
+(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
+
+(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb *)
+
+(* Source : [MW88] *)
+
+(* Names : - [MW88] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 v2.0.0 *)
+
+(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *)
+
+(* Number of atoms : 3 ( 3 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_fixed_point:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀f:∀_:Univ.Univ.
+∀l:Univ.
+∀s:Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#f ##.
+#l ##.
+#s ##.
+#H0 ##.
+#H1 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)