(* -------------------------------------------------------------------------- *)
-(* File : GRP151-1 : TPTP v3.2.0. Bugfixed v1.2.1. *)
+(* File : GRP151-1 : TPTP v3.7.0. Bugfixed v1.2.1. *)
(* Domain : Group Theory (Lattice Ordered) *)
(* -------------------------------------------------------------------------- *)
-(* File : GRP004-0 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : GRP004-0 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Group Theory *)
(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
-(* Number of literals : 3 ( 3 equality) *)
+(* Number of atoms : 3 ( 3 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* -------------------------------------------------------------------------- *)
-(* File : GRP004-2 : TPTP v3.2.0. Bugfixed v1.2.0. *)
+(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *)
(* Domain : Group Theory (Lattice Ordered) *)
(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *)
-(* Number of literals : 12 ( 12 equality) *)
+(* Number of atoms : 12 ( 12 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* -------------------------------------------------------------------------- *)
ntheorem prove_ax_lub2b:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀b:Univ.
∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ.
∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity.
-∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound a b)) a
+∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound a b)) a)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)