Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / RNG011-5.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: RNG011-5.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : RNG011-5 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Ring Theory *)
+
+(*  Problem  : In a right alternative ring (((X,X,Y)*X)*(X,X,Y)) = Add Id *)
+
+(*  Version  : [Ove90] (equality) axioms : *)
+
+(*             Incomplete > Augmented > Incomplete. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Ove90] Overbeek (1990), ATP competition announced at CADE-10 *)
+
+(*           : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal  *)
+
+(*           : [LM93]  Lusk & McCune (1993), Uniform Strategies: The CADE-11  *)
+
+(*           : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in *)
+
+(*  Source   : [Ove90] *)
+
+(*  Names    : CADE-11 Competition Eq-10 [Ove90] *)
+
+(*           : THEOREM EQ-10 [LM93] *)
+
+(*           : PROBLEM 10 [Zha93] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :   22 (   0 non-Horn;  22 unit;   2 RR) *)
+
+(*             Number of atoms       :   22 (  22 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   :   37 (   2 singleton) *)
+
+(*             Maximal term depth    :    5 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Commutativity of addition  *)
+
+(* ----Associativity of addition  *)
+
+(* ----Additive identity  *)
+
+(* ----Additive inverse  *)
+
+(* ----Inverse of identity is identity, stupid  *)
+
+(* ----Axiom of Overbeek  *)
+
+(* ----Inverse of (x + y) is additive_inverse(x) + additive_inverse(y),  *)
+
+(* ----Inverse of additive_inverse of X is X  *)
+
+(* ----Behavior of 0 and the multiplication operation  *)
+
+(* ----Axiom of Overbeek  *)
+
+(* ----x * additive_inverse(y) = additive_inverse (x * y),  *)
+
+(* ----Distributive property of product over sum  *)
+
+(* ----Right alternative law  *)
+
+(* ----Associator  *)
+
+(* ----Commutator  *)
+
+(* ----Middle associator identity  *)
+ntheorem prove_equality:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀add:∀_:Univ.∀_:Univ.Univ.
+∀additive_identity:Univ.
+∀additive_inverse:∀_:Univ.Univ.
+∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀commutator:∀_:Univ.∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply (associator X X Y) X) (associator X X Y)) additive_identity.
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+∀H2:∀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)))).
+∀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 (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
+∀H7:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
+∀H8:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).
+∀H9:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+∀H10:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+∀H11:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+∀H12:∀X:Univ.∀Y:Univ.eq Univ (additive_inverse (add X Y)) (add (additive_inverse X) (additive_inverse Y)).
+∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X (add (additive_inverse X) Y)) Y.
+∀H14:eq Univ (additive_inverse additive_identity) additive_identity.
+∀H15:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+∀H16:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+∀H17:∀X:Univ.eq Univ (add additive_identity X) X.
+∀H18:∀X:Univ.eq Univ (add X additive_identity) X.
+∀H19:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+∀H20:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (associator a a b) a) (associator a a b)) additive_identity)
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#b ##.
+#commutator ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+#H18 ##.
+#H19 ##.
+#H20 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)