--- /dev/null
+
+include "logic/equality.ma".
+(* Inclusion of: COL064-8.p *)
+(* -------------------------------------------------------------------------- *)
+(* File : COL064-8 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(* Domain : Combinatory Logic *)
+(* Problem : Find combinator equivalent to V 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 V does, where ((Bx)y)z = x(yz), (Tx)y = yx, *)
+(* ((Vx)y)z = (zx)y. *)
+(* 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, 0.22 v2.2.0, 0.29 v2.1.0, 0.71 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 : 11 ( 4 average) *)
+(* Comments : *)
+(* Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the V equivalent *)
+theorem prove_v_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall 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 (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b t) t)) x) y) z) (apply (apply z x) y)
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)