(* -------------------------------------------------------------------------- *)
-(* File : COL002-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : COL002-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Combinatory Logic *)
(* Status : Unsatisfiable *)
-(* Rating : 0.00 v2.1.0, 0.13 v2.0.0 *)
+(* Rating : 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v2.1.0, 0.13 v2.0.0 *)
(* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 RR) *)
(* -------------------------------------------------------------------------- *)
ntheorem prove_fixed_point:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀apply:∀_:Univ.∀_:Univ.Univ.
∀b:Univ.
∀c:Univ.
∀H0:∀X:Univ.eq Univ (apply i X) X.
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y).
∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).
-∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply fixed_pt Y)
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply fixed_pt Y))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#apply.
-#b.
-#c.
-#fixed_pt.
-#i.
-#s.
-#H0.
-#H1.
-#H2.
-#H3.
-napply ex_intro[
-nid2:
-nauto by H0,H1,H2,H3;
-nid|
-skip]
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#c ##.
+#fixed_pt ##.
+#i ##.
+#s ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1,H2,H3 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)