(* ----Denial of conclusion: *)
ntheorem prove_this:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀b:Univ.
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X (multiply Y Y)) (multiply Y (multiply Y X)).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))) (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b b)))))))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))) (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b b))))))))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#multiply.
-#H0.
-#H1.
-nauto by H0,H1;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+nauto by H0,H1 ##;
nqed.
(* -------------------------------------------------------------------------- *)