--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: COL063-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL063-4 : TPTP v3.2.0. Bugfixed v1.2.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Find combinator equivalent to F from B and T *)
+
+(* Version : [WM88] (equality) axioms. *)
+
+(* Theorem formulation : The combinator is provided and checked. *)
+
+(* English : Construct from B and T alone a combinator that behaves as the *)
+
+(* combinator F does, where ((Bx)y)z = x(yz), (Tx)y = yx, *)
+
+(* ((Fx)y)z = (zy)x. *)
+
+(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.43 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 : 6 ( 5 constant; 0-2 arity) *)
+
+(* Number of variables : 5 ( 0 singleton) *)
+
+(* Maximal term depth : 9 ( 4 average) *)
+
+(* Comments : *)
+
+(* Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----This is the F equivalent *)
+ntheorem prove_f_combinator:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀t:Univ.
+∀x:Univ.
+∀y:Univ.
+∀z:Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z y) x)
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#apply.
+#b.
+#t.
+#x.
+#y.
+#z.
+#H0.
+#H1.
+nauto by H0,H1;
+nqed.
+
+(* -------------------------------------------------------------------------- *)