-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / COL064-3.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/COL064-3.ma b/helm/software/matita/contribs/ng_TPTP/COL064-3.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: COL064-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL064-3 : TPTP v3.2.0. Bugfixed v1.2.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Find combinator equivalent to V from B and T *)
+
+(*  Version  : [WM88] (equality) axioms. *)
+
+(*             Theorem formulation : The combinator is provided and checked. *)
+
+(*  English  : Construct from B and T alone a combinator that behaves as the  *)
+
+(*             combinator V does, where ((Bx)y)z = x(yz), (Tx)y = yx,  *)
+
+(*             ((Vx)y)z = (zx)y. *)
+
+(*  Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(*           : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to  *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.43 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    3 (   0 non-Horn;   3 unit;   1 RR) *)
+
+(*             Number of atoms       :    3 (   3 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    6 (   5 constant; 0-2 arity) *)
+
+(*             Number of variables   :    5 (   0 singleton) *)
+
+(*             Maximal term depth    :   11 (   4 average) *)
+
+(*  Comments :  *)
+
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----This is the V equivalent *)
+ntheorem prove_v_combinator:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀t:Univ.
+∀x:Univ.
+∀y:Univ.
+∀z:Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b b) t)) x) y) z) (apply (apply z x) y)
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#apply.
+#b.
+#t.
+#x.
+#y.
+#z.
+#H0.
+#H1.
+nauto by H0,H1;
+nqed.
+
+(* -------------------------------------------------------------------------- *)