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-(* File : GRP582-1 : TPTP v3.2.0. Released v2.6.0. *)
+(* File : GRP582-1 : TPTP v3.7.0. Released v2.6.0. *)
(* Domain : Group Theory (Abelian) *)
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ntheorem prove_these_axioms_2:
- ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.
+ (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.
∀a2:Univ.
∀double_divide:∀_:Univ.∀_:Univ.Univ.
∀identity:Univ.
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2)
.
-#Univ.
-#A.
-#B.
-#C.
-#a2.
-#double_divide.
-#identity.
-#inverse.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-nauto by H0,H1,H2,H3;
+#Univ ##.
+#A ##.
+#B ##.
+#C ##.
+#a2 ##.
+#double_divide ##.
+#identity ##.
+#inverse ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+nauto by H0,H1,H2,H3 ##;
+ntry (nassumption) ##;
nqed.
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