(* -------------------------------------------------------------------------- *)
-(* File : COL051-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : COL051-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Combinatory Logic *)
(* ---- FAx -[response(x,x) = x]. *)
ntheorem prove_the_bird_exists:
- ∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.
+ (∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.
∀compose:∀_:Univ.∀_:Univ.Univ.
∀mocking_bird:Univ.
∀response:∀_:Univ.∀_:Univ.Univ.
∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).
-∀H1:∀Y:Univ.eq Univ (response mocking_bird Y) (response Y Y).∃X:Univ.eq Univ (response X X) X
+∀H1:∀Y:Univ.eq Univ (response mocking_bird Y) (response Y Y).∃X:Univ.eq Univ (response X X) X)
.
-#Univ.
-#W.
-#X.
-#Y.
-#compose.
-#mocking_bird.
-#response.
-#H0.
-#H1.
-napply ex_intro[
-nid2:
-nauto by H0,H1;
-nid|
-skip]
+#Univ ##.
+#W ##.
+#X ##.
+#Y ##.
+#compose ##.
+#mocking_bird ##.
+#response ##.
+#H0 ##.
+#H1 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
nqed.
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