(* -------------------------------------------------------------------------- *)
-(* File : RNG008-3 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : RNG008-3 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Ring Theory *)
(* Status : Unsatisfiable *)
-(* Rating : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(* Rating : 0.00 v3.3.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
(* Syntax : Number of clauses : 19 ( 0 non-Horn; 19 unit; 3 RR) *)
(* -------------------------------------------------------------------------- *)
-(* File : RNG002-0 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : RNG002-0 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Ring Theory *)
(* Syntax : Number of clauses : 14 ( 0 non-Horn; 14 unit; 1 RR) *)
-(* Number of literals : 14 ( 14 equality) *)
+(* Number of atoms : 14 ( 14 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* ----Right identity and inverse are dependent lemmas *)
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.
∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
∀H16:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
-∀H17:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c
+∀H17:∀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.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#b ##.
+#c ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##;
+ntry (nassumption) ##;
nqed.
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