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[helm.git] / matita / tests / TPTP / Veloci / ROB002-1.p.ma

diff --git a/matita/tests/TPTP/Veloci/ROB002-1.p.ma b/matita/tests/TPTP/Veloci/ROB002-1.p.ma
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+++ b/matita/tests/TPTP/Veloci/ROB002-1.p.ma
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+
+include "logic/equality.ma".
+(* Inclusion of: ROB002-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB002-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Robbins Algebra *)
+(*  Problem  : --X = X => Boolean *)
+(*  Version  : [Win90] (equality) axioms. *)
+(*  English  : If --X = X then the algebra is Boolean. *)
+(*  Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+(*           : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+(*  Source   : [Win90] *)
+(*  Names    : Lemma 2.1 [Win90] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0 *)
+(*  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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments : Commutativity, associativity, and Huntington's axiom  *)
+(*             axiomatize Boolean algebra. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include axioms for Robbins algebra  *)
+(* Inclusion of: Axioms/ROB001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Robbins algebra *)
+(*  Axioms   : Robbins algebra axioms *)
+(*  Version  : [Win90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+(*           : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+(*  Source   : [OTTER] *)
+(*  Names    : Lemma 2.2 [Win90] *)
+(*  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   :    2 (   0 constant; 1-2 arity) *)
+(*             Number of variables  :    7 (   0 singleton) *)
+(*             Maximal term depth   :    6 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_huntingtons_axiom:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall negate:\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (negate (negate X)) X.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)