branch for universe

[helm.git] / matita / tests / TPTP / Veloci / BOO003-2.p.ma

diff --git a/matita/tests/TPTP/Veloci/BOO003-2.p.ma b/matita/tests/TPTP/Veloci/BOO003-2.p.ma
new file mode 100644 (file)
index 0000000..f41c21a
--- /dev/null
+++ b/matita/tests/TPTP/Veloci/BOO003-2.p.ma
@@ -0,0 +1,75 @@
+
+include "logic/equality.ma".
+(* Inclusion of: BOO003-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO003-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Multiplication is idempotent (X * X = X) *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob2_part1.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 v3.1.1. 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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_times_a_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)