(* -------------------------------------------------------------------------- *)
-(* File : RNG009-7 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : RNG009-7 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Ring Theory *)
(* Status : Unsatisfiable *)
-(* Rating : 0.50 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.17 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.56 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0 *)
+(* Rating : 0.56 v3.4.0, 0.62 v3.3.0, 0.50 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.17 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.56 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0 *)
(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 2 RR) *)
(* -------------------------------------------------------------------------- *)
-(* File : RNG005-0 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : RNG005-0 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Ring Theory *)
(* Syntax : Number of clauses : 9 ( 0 non-Horn; 9 unit; 0 RR) *)
-(* Number of literals : 9 ( 9 equality) *)
+(* Number of atoms : 9 ( 9 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* -------------------------------------------------------------------------- *)
ntheorem prove_commutativity:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀add:∀_:Univ.∀_:Univ.Univ.
∀additive_identity:Univ.
∀H7:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
∀H8:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
∀H9:∀X:Univ.eq Univ (add X additive_identity) X.
-∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c
+∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#add.
-#additive_identity.
-#additive_inverse.
-#b.
-#c.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#b ##.
+#c ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##;
+ntry (nassumption) ##;
nqed.
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