branch for universe

[helm.git] / matita / tests / TPTP / Veloci / COL063-3.p.ma

diff --git a/matita/tests/TPTP/Veloci/COL063-3.p.ma b/matita/tests/TPTP/Veloci/COL063-3.p.ma
new file mode 100644 (file)
index 0000000..8e5671a
--- /dev/null
+++ b/matita/tests/TPTP/Veloci/COL063-3.p.ma
@@ -0,0 +1,46 @@
+
+include "logic/equality.ma".
+(* Inclusion of: COL063-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL063-3 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to F 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 F does, where ((Bx)y)z = x(yz), (Tx)y = yx,  *)
+(*             ((Fx)y)z = (zy)x. *)
+(*  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, 0.11 v2.2.0, 0.14 v2.1.0, 0.29 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    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the F equivalent *)
+theorem prove_f_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall 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 t)) b)) (apply (apply b b) t)) x) y) z) (apply (apply z y) x)
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)