branch for universe

[helm.git] / matita / tests / TPTP / Veloci / GRP584-1.p.ma

diff --git a/matita/tests/TPTP/Veloci/GRP584-1.p.ma b/matita/tests/TPTP/Veloci/GRP584-1.p.ma
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+
+include "logic/equality.ma".
+(* Inclusion of: GRP584-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP584-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   1 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    :    6 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP103-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)