(* -------------------------------------------------------------------------- *)
-(* File : COL066-3 : TPTP v3.2.0. Bugfixed v1.2.0. *)
+(* File : COL066-3 : TPTP v3.7.0. Bugfixed v1.2.0. *)
(* Domain : Combinatory Logic *)
(* Status : Unsatisfiable *)
-(* Rating : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.1.0, 0.29 v2.0.0 *)
+(* Rating : 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.1.0, 0.29 v2.0.0 *)
(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *)
(* ----This is the P equivalent *)
ntheorem prove_p_combinator:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀apply:∀_:Univ.∀_:Univ.Univ.
∀b:Univ.
∀q:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)).
-∀H2:∀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 (apply b (apply w (apply q (apply q q)))) q) x) y) y) z) (apply (apply x y) (apply (apply x y) z))
+∀H2:∀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 (apply b (apply w (apply q (apply q q)))) q) x) y) y) z) (apply (apply x y) (apply (apply x y) z)))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#apply.
-#b.
-#q.
-#w.
-#x.
-#y.
-#z.
-#H0.
-#H1.
-#H2.
-nauto by H0,H1,H2;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#q ##.
+#w ##.
+#x ##.
+#y ##.
+#z ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+nauto by H0,H1,H2 ##;
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)