--- /dev/null
+
+include "logic/equality.ma".
+(* Inclusion of: COL015-1.p *)
+(* -------------------------------------------------------------------------- *)
+(* File : COL015-1 : TPTP v3.1.1. Released v1.0.0. *)
+(* Domain : Combinatory Logic *)
+(* Problem : Weak fixed point for Q and M *)
+(* Version : [WM88] (equality) axioms. *)
+(* English : The weak fixed point property holds for the set P consisting *)
+(* of the combinators Q and M, where Mx = xx, ((Qx)y)z = y(xz). *)
+(* 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 : 0.00 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 ( 3 constant; 0-2 arity) *)
+(* Number of variables : 5 ( 0 singleton) *)
+(* Maximal term depth : 4 ( 2 average) *)
+(* Comments : *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall combinator:Univ.
+\forall m:Univ.
+\forall q:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)).
+\forall H1:\forall X:Univ.eq Univ (apply m X) (apply X X).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+autobatch paramodulation timeout=100;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)