Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / BOO012-4.ma

diff --git a/matita/matita/contribs/ng_TPTP/BOO012-4.ma b/matita/matita/contribs/ng_TPTP/BOO012-4.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: BOO012-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : BOO012-4 : TPTP v3.7.0. Released v1.1.0. *)
+
+(*  Domain   : Boolean Algebra *)
+
+(*  Problem  : Inverse is an involution *)
+
+(*  Version  : [Ver94] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+
+(*  Source   : [Ver94] *)
+
+(*  Names    : TF [Ver94] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    9 (   0 non-Horn;   9 unit;   1 RR) *)
+
+(*             Number of atoms       :    9 (   9 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    6 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :   14 (   0 singleton) *)
+
+(*             Maximal term depth    :    3 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include boolean algebra axioms for equality formulation  *)
+
+(* Inclusion of: Axioms/BOO004-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : BOO004-0 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Boolean Algebra *)
+
+(*  Axioms   : Boolean algebra (equality) axioms *)
+
+(*  Version  : [Ver94] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+
+(*  Source   : [Ver94] *)
+
+(*  Names    :  *)
+
+(*  Status   :  *)
+
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+
+(*             Number of atoms      :    8 (   8 equality) *)
+
+(*             Maximal clause size  :    1 (   1 average) *)
+
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+
+(*             Number of variables  :   14 (   0 singleton) *)
+
+(*             Maximal term depth   :    3 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_inverse_is_an_involution:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀add:∀_:Univ.∀_:Univ.Univ.
+∀additive_identity:Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiplicative_identity:Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀x:Univ.
+∀H0:∀X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+∀H1:∀X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+∀H2:∀X:Univ.eq Univ (multiply X multiplicative_identity) X.
+∀H3:∀X:Univ.eq Univ (add X additive_identity) X.
+∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x)
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#inverse ##.
+#multiplicative_identity ##.
+#multiply ##.
+#x ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)