(* -------------------------------------------------------------------------- *)
-(* File : COL004-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : COL004-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Combinatory Logic *)
(* Status : Unsatisfiable *)
-(* Rating : 0.50 v3.2.0, 0.57 v3.1.0, 0.67 v2.7.0, 0.55 v2.6.0, 0.17 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 1.00 v2.0.0 *)
+(* Rating : 0.44 v3.4.0, 0.38 v3.3.0, 0.50 v3.2.0, 0.57 v3.1.0, 0.67 v2.7.0, 0.55 v2.6.0, 0.17 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 1.00 v2.0.0 *)
(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *)
(* -------------------------------------------------------------------------- *)
ntheorem prove_u_combinator:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀apply:∀_:Univ.∀_:Univ.Univ.
∀f:∀_:Univ.Univ.
∀g:∀_:Univ.Univ.
∀k:Univ.
∀s:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Z:Univ.eq Univ (apply (apply Z (f Z)) (g Z)) (apply (g Z) (apply (apply (f Z) (f Z)) (g Z)))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Z:Univ.eq Univ (apply (apply Z (f Z)) (g Z)) (apply (g Z) (apply (apply (f Z) (f Z)) (g Z))))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#apply.
-#f.
-#g.
-#k.
-#s.
-#H0.
-#H1.
-napply ex_intro[
-nid2:
-nauto by H0,H1;
-nid|
-skip]
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#f ##.
+#g ##.
+#k ##.
+#s ##.
+#H0 ##.
+#H1 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)