(* -------------------------------------------------------------------------- *)
-(* File : RNG031-6 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : RNG031-6 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Ring Theory (Right alternative) *)
(* Status : Satisfiable *)
-(* Rating : 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.6.0, 0.67 v2.5.0, 1.00 v2.0.0 *)
+(* Rating : 0.67 v3.3.0, 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.6.0, 0.67 v2.5.0, 1.00 v2.0.0 *)
(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 1 RR) *)
(* ----Commutator *)
ntheorem prove_conjecture_2:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀add:∀_:Univ.∀_:Univ.Univ.
∀additive_identity:Univ.
∀additive_inverse:∀_:Univ.Univ.
∀H10:∀X:Univ.eq Univ (add X additive_identity) X.
∀H11:∀X:Univ.eq Univ (add additive_identity X) X.
∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
-∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity
+∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#x.
-#y.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#x ##.
+#y ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##;
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)