Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / RNG023-6.ma

diff --git a/matita/matita/contribs/ng_TPTP/RNG023-6.ma b/matita/matita/contribs/ng_TPTP/RNG023-6.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: RNG023-6.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : RNG023-6 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Ring Theory (Alternative) *)
+
+(*  Problem  : Left alternative *)
+
+(*  Version  : [Ste87] (equality) axioms. *)
+
+(*             Theorem formulation : In terms of associators *)
+
+(*  English  :  *)
+
+(*  Refs     : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+
+(*           : [Ste92] Stevens (1992), Unpublished Note *)
+
+(*  Source   : [Ste92] *)
+
+(*  Names    : - [Ste87] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.1.0, 0.13 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    :    8 (   3 constant; 0-3 arity) *)
+
+(*             Number of variables   :   27 (   2 singleton) *)
+
+(*             Maximal term depth    :    5 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include nonassociative ring axioms  *)
+
+(* Inclusion of: Axioms/RNG003-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Ring Theory (Alternative) *)
+
+(*  Axioms   : Alternative ring theory (equality) axioms *)
+
+(*  Version  : [Ste87] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+
+(*  Source   : [Ste87] *)
+
+(*  Names    :  *)
+
+(*  Status   :  *)
+
+(*  Syntax   : Number of clauses    :   15 (   0 non-Horn;  15 unit;   0 RR) *)
+
+(*             Number of atoms      :   15 (  15 equality) *)
+
+(*             Maximal clause size  :    1 (   1 average) *)
+
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors   :    6 (   1 constant; 0-3 arity) *)
+
+(*             Number of variables  :   27 (   2 singleton) *)
+
+(*             Maximal term depth   :    5 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----There exists an additive identity element  *)
+
+(* ----Multiplicative zero  *)
+
+(* ----Existence of left additive additive_inverse  *)
+
+(* ----Inverse of additive_inverse of X is X  *)
+
+(* ----Distributive property of product over sum  *)
+
+(* ----Commutativity for addition  *)
+
+(* ----Associativity for addition  *)
+
+(* ----Right alternative law  *)
+
+(* ----Left alternative law  *)
+
+(* ----Associator  *)
+
+(* ----Commutator  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_left_alternative:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀add:∀_:Univ.∀_:Univ.Univ.
+∀additive_identity:Univ.
+∀additive_inverse:∀_:Univ.Univ.
+∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ.
+∀commutator:∀_:Univ.∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀x:Univ.
+∀y:Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))).
+∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)).
+∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
+∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).
+∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+∀H8:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+∀H9:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+∀H10:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+∀H13:∀X:Univ.eq Univ (add X additive_identity) X.
+∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (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 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)