-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / BOO006-2.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/BOO006-2.ma b/helm/software/matita/contribs/ng_TPTP/BOO006-2.ma
new file mode 100644 (file)
index 0000000..73227bf
--- /dev/null
+++ b/helm/software/matita/contribs/ng_TPTP/BOO006-2.ma
@@ -0,0 +1,140 @@
+include "logic/equality.ma".
+
+(* Inclusion of: BOO006-2.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : BOO006-2 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Boolean Algebra *)
+
+(*  Problem  : Multiplication is bounded (X * 0 = 0) *)
+
+(*  Version  : [ANL] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     :  *)
+
+(*  Source   : [ANL] *)
+
+(*  Names    : prob3_part2.ver2.in [ANL] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.1.0, 0.38 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :   15 (   0 non-Horn;  15 unit;   1 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 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :   24 (   0 singleton) *)
+
+(*             Maximal term depth    :    3 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include boolean algebra axioms for equality formulation  *)
+
+(* Inclusion of: Axioms/BOO003-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : BOO003-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Boolean Algebra *)
+
+(*  Axioms   : Boolean algebra (equality) axioms *)
+
+(*  Version  : [ANL] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     :  *)
+
+(*  Source   : [ANL] *)
+
+(*  Names    :  *)
+
+(*  Status   :  *)
+
+(*  Syntax   : Number of clauses    :   14 (   0 non-Horn;  14 unit;   0 RR) *)
+
+(*             Number of literals   :   14 (  14 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  :   24 (   0 singleton) *)
+
+(*             Maximal term depth   :    3 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_right_identity:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀add:∀_:Univ.∀_:Univ.Univ.
+∀additive_identity:Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiplicative_identity:Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀X:Univ.eq Univ (add additive_identity X) X.
+∀H1:∀X:Univ.eq Univ (add X additive_identity) X.
+∀H2:∀X:Univ.eq Univ (multiply multiplicative_identity X) X.
+∀H3:∀X:Univ.eq Univ (multiply X multiplicative_identity) X.
+∀H4:∀X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+∀H5:∀X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+∀H6:∀X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+∀H7:∀X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a additive_identity) additive_identity
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#a.
+#add.
+#additive_identity.
+#inverse.
+#multiplicative_identity.
+#multiply.
+#H0.
+#H1.
+#H2.
+#H3.
+#H4.
+#H5.
+#H6.
+#H7.
+#H8.
+#H9.
+#H10.
+#H11.
+#H12.
+#H13.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13;
+nqed.
+
+(* -------------------------------------------------------------------------- *)