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[helm.git] / matita / tests / TPTP / Veloci / GRP001-4.p.ma

diff --git a/matita/tests/TPTP/Veloci/GRP001-4.p.ma b/matita/tests/TPTP/Veloci/GRP001-4.p.ma
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+
+include "logic/equality.ma".
+(* Inclusion of: GRP001-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP001-4 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : X^2 = identity => commutativity *)
+(*  Version  : [Wos65] (equality) axioms : Incomplete. *)
+(*  English  : If the square of every element is the identity, the system  *)
+(*             is commutative. *)
+(*  Refs     : [Wos65] Wos (1965), Unpublished Note *)
+(*           : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au *)
+(*  Source   : [Pel86] *)
+(*  Names    : Pelletier 65 [Pel86] *)
+(*           : x2_quant.in [OTTER] *)
+(*  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     :    5 (   0 non-Horn;   5 unit;   2 RR) *)
+(*             Number of atoms       :    5 (   5 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    5 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : [Pel86] says "... problems, published I think, by Larry Wos  *)
+(*             (but I cannot locate where)." *)
+(* -------------------------------------------------------------------------- *)
+(* ----The operation '*' is associative  *)
+(* ----There exists an identity element 'e' defined below. *)
+theorem prove_b_times_a_is_c:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall identity: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 identity X) X.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b a) c
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)