branch for universe

[helm.git] / matita / tests / paramodulation / BOO075-1.ma

diff --git a/matita/tests/paramodulation/BOO075-1.ma b/matita/tests/paramodulation/BOO075-1.ma
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+
+
+inductive eq (A:Type) (x:A) : A \to Prop \def refl_eq : eq A x x.
+
+theorem sym_eq : \forall A:Type.\forall x,y:A. eq A x y \to eq A y x.
+intros.elim H. apply refl_eq.
+qed.
+
+theorem eq_elim_r:
+ \forall A:Type.\forall x:A. \forall P: A \to Prop.
+   P x \to \forall y:A. eq A y x \to P y.
+intros. elim (sym_eq ? ? ? H1).assumption.
+qed.
+
+theorem eq_elim_r':
+ \forall A:Type.\forall x:A. \forall P: A \to Set.
+   P x \to \forall y:A. eq A y x \to P y.
+intros. elim (sym_eq ? ? ? H).assumption.
+qed.
+
+theorem eq_elim_r'':
+ \forall A:Type.\forall x:A. \forall P: A \to Type.
+   P x \to \forall y:A. eq A y x \to P y.
+intros. elim (sym_eq ? ? ? H).assumption.
+qed.
+
+theorem trans_eq : 
+    \forall A:Type.\forall x,y,z:A. eq A x y \to eq A y z \to eq A x z.
+intros.elim H1.assumption.
+qed.
+
+default "equality"
+ cic:/matita/tests/paramodulation/BOO075-1/eq.ind
+ cic:/matita/tests/paramodulation/BOO075-1/sym_eq.con
+ cic:/matita/tests/paramodulation/BOO075-1/trans_eq.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_ind.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_elim_r.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_rec.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_elim_r'.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_rect.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_elim_r''.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_f.con
+ cic:/matita/tests/paramodulation/BOO075-1/eq_f1.con.
+
+theorem eq_f: \forall  A,B:Type.\forall f:A\to B.
+  \forall x,y:A. eq A x y \to eq B (f x) (f y).
+intros.elim H.reflexivity.
+qed.
+
+theorem eq_f1: \forall  A,B:Type.\forall f:A\to B.
+  \forall x,y:A. eq A x y \to eq B (f y) (f x).
+intros.elim H.reflexivity.
+qed.
+
+inductive ex (A:Type) (P:A \to Prop) : Prop \def
+    ex_intro: \forall x:A. P x \to ex A P.
+interpretation "exists" 'exists \eta.x =
+  (cic:/matita/tests/paramodulation/BOO075-1/ex.ind#xpointer(1/1) _ x).
+
+notation < "hvbox(\exists ident i opt (: ty) break . p)"
+  right associative with precedence 20
+for @{ 'exists ${default
+  @{\lambda ${ident i} : $ty. $p)}
+  @{\lambda ${ident i} . $p}}}.
+
+
+(* Inclusion of: BOO075-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO075-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Sh-1 is a single axiom for Boolean algebra, part 1 *)
+(*  Version  : [EF+02] axioms. *)
+(*  English  :  *)
+(*  Refs     : [EF+02] Ernst et al. (2002), More First-order Test Problems in *)
+(*           : [MV+02] McCune et al. (2002), Short Single Axioms for Boolean *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  Syntax   : Number of clauses     :    2 (   0 non-Horn;   2 unit;   1 RR) *)
+(*             Number of atoms       :    2 (   2 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    3 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   1 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of BOO039-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_meredith_2_basis_1:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall nand:Univ\rarr Univ\rarr Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a
+.
+intros.
+autobatch paramodulation timeout=600;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)