some horn+equality problems

[helm.git] / helm / software / matita / contribs / TPTP / HEQ / ROB014-1.ma

diff --git a/helm/software/matita/contribs/TPTP/HEQ/ROB014-1.ma b/helm/software/matita/contribs/TPTP/HEQ/ROB014-1.ma
new file mode 100644 (file)
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+++ b/helm/software/matita/contribs/TPTP/HEQ/ROB014-1.ma
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+set "baseuri" "cic:/matita/TPTP/ROB014-1".
+include "logic/equality.ma".
+
+(* Inclusion of: ROB014-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : ROB014-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Robbins Algebra *)
+
+(*  Problem  : If -(-e + -(d + -e)) = d then -(e + k(d + -(d + -e))) = -e, k=1 *)
+
+(*  Version  : [Win90] (equality) axioms. *)
+
+(*  English  : This is the base step of an induction proof. *)
+
+(*  Refs     : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(*  Source   : [Win90] *)
+
+(*  Names    : Lemma 3.6 [Win90] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.71 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.86 v2.5.0, 1.00 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    9 (   0 non-Horn;   7 unit;   4 RR) *)
+
+(*             Number of atoms       :   11 (   7 equality) *)
+
+(*             Maximal clause size   :    2 (   1 average) *)
+
+(*             Number of predicates  :    2 (   0 propositional; 1-2 arity) *)
+
+(*             Number of functors    :    7 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :   11 (   0 singleton) *)
+
+(*             Maximal term depth    :    8 (   3 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include axioms for Robbins algebra  *)
+
+(* Inclusion of: Axioms/ROB001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : ROB001-0 : TPTP v3.2.0. 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 :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include axioms for numbers in Robbins algebras  *)
+
+(* Inclusion of: Axioms/ROB001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : ROB001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Robbins Algebra *)
+
+(*  Axioms   : Robbins algebra numbers axioms *)
+
+(*  Version  : [Win90] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+
+(*           : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+
+(*  Source   : [Win90] *)
+
+(*  Names    :  *)
+
+(*  Status   :  *)
+
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   2 unit;   2 RR) *)
+
+(*             Number of literals   :    6 (   2 equality) *)
+
+(*             Maximal clause size  :    2 (   2 average) *)
+
+(*             Number of predicates :    2 (   0 propositional; 1-2 arity) *)
+
+(*             Number of functors   :    4 (   1 constant; 0-2 arity) *)
+
+(*             Number of variables  :    4 (   0 singleton) *)
+
+(*             Maximal term depth   :    3 (   2 average) *)
+
+(*  Comments : Requires ROB001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_base_step:
+ ∀Univ:Set.∀V:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀d:Univ.∀e:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀negate:∀_:Univ.Univ.∀one:Univ.∀positive_integer:∀_:Univ.Prop.∀successor:∀_:Univ.Univ.∀H0:eq Univ (negate (add (negate e) (negate (add d (negate e))))) d.∀H1:∀X:Univ.∀_:positive_integer X.positive_integer (successor X).∀H2:positive_integer one.∀H3:∀V:Univ.∀X:Univ.∀_:positive_integer X.eq Univ (multiply (successor V) X) (add X (multiply V X)).∀H4:∀X:Univ.eq Univ (multiply one X) X.∀H5:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add e (multiply one (add d (negate (add d (negate e))))))) (negate e)
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)