X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Ftests%2FTPTP%2FVeloci%2FGRP141-1.p.ma;fp=matita%2Ftests%2FTPTP%2FVeloci%2FGRP141-1.p.ma;h=84e880f7a8dad9ff254ac662bfd293324e0fad58;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1

diff --git a/matita/tests/TPTP/Veloci/GRP141-1.p.ma b/matita/tests/TPTP/Veloci/GRP141-1.p.ma
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+
+include "logic/equality.ma".
+(* Inclusion of: GRP141-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP141-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove greatest lower-bound axiom using a transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original greatest lower-bound axiom *)
+(*             from the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_glb1d [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.14 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    8 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :   33 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : ORDERING LPO inverse > product > greatest_lower_bound >  *)
+(*             least_upper_bound > identity > a > b > c *)
+(*           : ORDERING LPO greatest_lower_bound > least_upper_bound >  *)
+(*             inverse > product > identity > a > b > c *)
+(*  Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include equality group theory axioms  *)
+(* Inclusion of: Axioms/GRP004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Axioms   : Lattice ordered group (equality) axioms *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :   12 (   0 non-Horn;  12 unit;   0 RR) *)
+(*             Number of literals   :   12 (  12 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   0 constant; 2-2 arity) *)
+(*             Number of variables  :   28 (   2 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : Requires GRP004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Specification of the least upper bound and greatest lower bound *)
+(* ----Monotony of multiply *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_glb1d:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound b c) b.
+\forall H1:eq Univ (least_upper_bound a c) a.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) c) c
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)