(* -------------------------------------------------------------------------- *)
-(* File : COL066-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : COL066-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Combinatory Logic *)
(* Status : Unsatisfiable *)
-(* Rating : 0.93 v3.1.0, 0.89 v2.7.0, 0.82 v2.6.0, 0.67 v2.5.0, 0.25 v2.4.0, 0.00 v2.3.0, 0.33 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+(* Rating : 0.78 v3.4.0, 0.88 v3.3.0, 0.93 v3.1.0, 0.89 v2.7.0, 0.82 v2.6.0, 0.67 v2.5.0, 0.25 v2.4.0, 0.00 v2.3.0, 0.33 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *)
(* -------------------------------------------------------------------------- *)
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.
∀f:∀_:Univ.Univ.
∀w: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)).∃X:Univ.eq Univ (apply (apply (apply (apply X (f X)) (g X)) (g X)) (h X)) (apply (apply (f X) (g X)) (apply (apply (f X) (g X)) (h X)))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply (apply X (f X)) (g X)) (g X)) (h X)) (apply (apply (f X) (g X)) (apply (apply (f X) (g X)) (h X))))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#apply.
-#b.
-#f.
-#g.
-#h.
-#q.
-#w.
-#H0.
-#H1.
-#H2.
-napply ex_intro[
-nid2:
-nauto by H0,H1,H2;
-nid|
-skip]
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#f ##.
+#g ##.
+#h ##.
+#q ##.
+#w ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1,H2 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)