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+include "logic/equality.ma".
+
+(* Inclusion of: GRP189-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : GRP189-1 : TPTP v3.7.0. Bugfixed v1.2.1. *)
+
+(*  Domain   : Group Theory (Lattice Ordered) *)
+
+(*  Problem  : Consequence of lattice theory *)
+
+(*  Version  : [Fuc94] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :   16 (   0 non-Horn;  16 unit;   1 RR) *)
+
+(*             Number of atoms       :   16 (  16 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    7 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :   33 (   2 singleton) *)
+
+(*             Maximal term depth    :    3 (   2 average) *)
+
+(*  Comments : ORDERING LPO greatest_lower_bound > least_upper_bound > *)
+
+(*             inverse > product > identity > a > b *)
+
+(*           : This is a standardized version of the problem that appears in *)
+
+(*             [Sch95]. *)
+
+(*  Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include equality group theory axioms  *)
+
+(* Inclusion of: Axioms/GRP004-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : GRP004-0 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Group Theory *)
+
+(*  Axioms   : Group theory (equality) axioms *)
+
+(*  Version  : [MOW76] (equality) axioms :  *)
+
+(*             Reduced > Complete. *)
+
+(*  English  :  *)
+
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+
+(*  Source   : [ANL] *)
+
+(*  Names    :  *)
+
+(*  Status   :  *)
+
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+
+(*             Number of atoms      :    3 (   3 equality) *)
+
+(*             Maximal clause size  :    1 (   1 average) *)
+
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+
+(*             Number of variables  :    5 (   0 singleton) *)
+
+(*             Maximal term depth   :    3 (   2 average) *)
+
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+
+(*             right_inverse axioms. *)
+
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+
+(*             right_identity and right_inverse. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+
+(* ----is needed here since this is an instance of reflexivity  *)
+
+(* ----There exists an identity element  *)
+
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+
+(* ----= identity. *)
+
+(* ----The operation '*' is associative  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Lattice ordered group (equality) axioms *)
+
+(* Inclusion of: Axioms/GRP004-2.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *)
+
+(*  Domain   : Group Theory (Lattice Ordered) *)
+
+(*  Axioms   : Lattice ordered group (equality) axioms *)
+
+(*  Version  : [Fuc94] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+
+(*  Source   : [Sch95] *)
+
+(*  Names    :  *)
+
+(*  Status   :  *)
+
+(*  Syntax   : Number of clauses    :   12 (   0 non-Horn;  12 unit;   0 RR) *)
+
+(*             Number of atoms      :   12 (  12 equality) *)
+
+(*             Maximal clause size  :    1 (   1 average) *)
+
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors   :    3 (   0 constant; 2-2 arity) *)
+
+(*             Number of variables  :   28 (   2 singleton) *)
+
+(*             Maximal term depth   :    3 (   2 average) *)
+
+(*  Comments : Requires GRP004-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Specification of the least upper bound and greatest lower bound *)
+
+(* ----Monotony of multiply *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_p38b:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀b:Univ.
+∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ.
+∀identity:Univ.
+∀inverse:∀_:Univ.Univ.
+∀least_upper_bound:∀_:Univ.∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+∀H4:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+∀H6:∀X:Univ.eq Univ (greatest_lower_bound X X) X.
+∀H7:∀X:Univ.eq Univ (least_upper_bound X X) X.
+∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+∀H10:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+∀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 b (least_upper_bound a b)) b)
+.
+#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.
+
+(* -------------------------------------------------------------------------- *)