branch for universe

[helm.git] / matita / tests / TPTP / Veloci / RNG011-5.p.ma

diff --git a/matita/tests/TPTP/Veloci/RNG011-5.p.ma b/matita/tests/TPTP/Veloci/RNG011-5.p.ma
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+
+include "logic/equality.ma".
+(* Inclusion of: RNG011-5.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG011-5 : TPTP v3.1.1. 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  *)
+theorem prove_equality:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall additive_inverse:\forall _:Univ.Univ.
+\forall associator:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall commutator:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply (associator X X Y) X) (associator X X Y)) additive_identity.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).
+\forall H9:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+\forall H10:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+\forall H11:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (additive_inverse (add X Y)) (add (additive_inverse X) (additive_inverse Y)).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X (add (additive_inverse X) Y)) Y.
+\forall H14:eq Univ (additive_inverse additive_identity) additive_identity.
+\forall H15:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+\forall H16:\forall X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+\forall H17:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H18:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H19:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H20:\forall X:Univ.\forall 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
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)