branch for universe

[helm.git] / matita / tests / TPTP / Veloci / COL050-1.p.ma

diff --git a/matita/tests/TPTP/Veloci/COL050-1.p.ma b/matita/tests/TPTP/Veloci/COL050-1.p.ma
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+
+include "logic/equality.ma".
+(* Inclusion of: COL050-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL050-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : The Significance of the Mockingbird *)
+(*  Version  : Especial. *)
+(*  English  : There exists a mocking bird. For all birds x and y, there  *)
+(*             exists a bird z that composes x with y for all birds w. Prove  *)
+(*             that every bird is fond of at least one other bird. *)
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+(*  Source   : [ANL] *)
+(*  Names    : bird1.ver1.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ---- There exists a mocking bird (Mock). *)
+(* ----    TEx FAy [response(x,y) = response(y,y)]. *)
+(* ----    response(Mock,y) = response(y,y). *)
+(* ---- For all birds x and y, there exists a bird z that composes *)
+(* ---- x with y for all birds w. *)
+(* ----    FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))] *)
+(* ----    response(comp(x,y),w) = response(x,response(y,w)).  *)
+(* ---- Hypothesis: Every bird is fond of at least one other bird. *)
+(* ----    -FAx TEy [response(x,y) = y]. *)
+(* ----    TEx FAy -[response(x,y) = y]. *)
+(* ----    Letting A = x, *)
+(* ----    -[response(A,y) = y]. *)
+theorem prove_all_fond_of_another:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall compose:\forall _:Univ.\forall _:Univ.Univ.
+\forall mocking_bird:Univ.
+\forall response:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall W:Univ.\forall X:Univ.\forall Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).
+\forall H1:\forall Y:Univ.eq Univ (response mocking_bird Y) (response Y Y).\exist Y:Univ.eq Univ (response a Y) Y
+.
+intros.
+exists[
+2:
+autobatch paramodulation timeout=100;
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)