(* -------------------------------------------------------------------------- *)
-(* File : COL032-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : COL032-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Combinatory Logic *)
(* Status : Unsatisfiable *)
-(* Rating : 0.14 v3.1.0, 0.22 v2.7.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 v2.0.0 *)
+(* Rating : 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.1.0, 0.22 v2.7.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 v2.0.0 *)
(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 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.
∀f:∀_:Univ.Univ.
∀m:Univ.
∀q:Univ.
∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)).
-∀H1:∀X:Univ.eq Univ (apply m X) (apply X X).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))
+∀H1:∀X:Univ.eq Univ (apply m X) (apply X X).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#apply.
-#f.
-#m.
-#q.
-#H0.
-#H1.
-napply ex_intro[
-nid2:
-nauto by H0,H1;
-nid|
-skip]
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#f ##.
+#m ##.
+#q ##.
+#H0 ##.
+#H1 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)