+include "logic/equality.ma".
+
+(* Inclusion of: LDA007-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LDA007-3 : TPTP v3.7.0. Released v1.0.0. *)
+
+(* Domain : LD-Algebras (Embedding algebras) *)
+
+(* Problem : Let g = cr(t). Show that t(tsg) = tt(ts)(tg) *)
+
+(* Version : [Jec93] axioms : Incomplete > Reduced & Augmented > Incomplete. *)
+
+(* English : *)
+
+(* Refs : [Jec93] Jech (1993), LD-Algebras *)
+
+(* Source : [Jec93] *)
+
+(* Names : Problem 8 [Jec93] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0 *)
+
+(* Syntax : Number of clauses : 7 ( 0 non-Horn; 7 unit; 6 RR) *)
+
+(* Number of atoms : 7 ( 7 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 9 ( 8 constant; 0-2 arity) *)
+
+(* Number of variables : 3 ( 0 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Embedding algebra axioms *)
+
+(* include('Axioms/LDA001-0.ax'). *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----t(tsk) = tt(ts)(tk), where k=crit(t) *)
+ntheorem prove_equation:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀f:∀_:Univ.∀_:Univ.Univ.
+∀k:Univ.
+∀s:Univ.
+∀t:Univ.
+∀tk:Univ.
+∀ts:Univ.
+∀tsk:Univ.
+∀tt:Univ.
+∀tt_ts:Univ.
+∀H0:eq Univ tsk (f ts k).
+∀H1:eq Univ tk (f t k).
+∀H2:eq Univ tt_ts (f tt ts).
+∀H3:eq Univ ts (f t s).
+∀H4:eq Univ tt (f t t).
+∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f t tsk) (f tt_ts tk))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#f ##.
+#k ##.
+#s ##.
+#t ##.
+#tk ##.
+#ts ##.
+#tsk ##.
+#tt ##.
+#tt_ts ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+nauto by H0,H1,H2,H3,H4,H5 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)