branch for universe

[helm.git] / matita / tests / TPTP / Veloci / GRP001-2.p.ma

diff --git a/matita/tests/TPTP/Veloci/GRP001-2.p.ma b/matita/tests/TPTP/Veloci/GRP001-2.p.ma
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+
+include "logic/equality.ma".
+(* Inclusion of: GRP001-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP001-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : X^2 = identity => commutativity *)
+(*  Version  : [MOW76] (equality) axioms : Augmented. *)
+(*  English  : If the square of every element is the identity, the system  *)
+(*             is commutative. *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [LO85]  Lusk & Overbeek (1985), Reasoning about Equality *)
+(*           : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+(*  Source   : [ANL] *)
+(*  Names    : GP1 [MOW76] *)
+(*           : Problem 1 [LO85] *)
+(*           : GT1 [LW92] *)
+(*           : xsquared.ver2.in [ANL] *)
+(*  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     :    8 (   0 non-Horn;   8 unit;   2 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    :    6 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----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  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Redundant two axioms *)
+theorem prove_b_times_a_is_c:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (multiply a b) c.
+\forall H1:\forall X:Univ.eq Univ (multiply X X) identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X (inverse X)) identity.
+\forall H3:\forall X:Univ.eq Univ (multiply X identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H5:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H6:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply b a) c
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)