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[helm.git] / matita / tests / TPTP / Veloci / LCL110-2.p.ma

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+
+include "logic/equality.ma".
+(* Inclusion of: LCL110-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL110-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Many valued sentential) *)
+(*  Problem  : MV-24 depends on the Meredith system *)
+(*  Version  : [LW92] axioms. *)
+(*             Theorem formulation : Wajsberg algebra formulation *)
+(*  English  : An axiomatisation of the many valued sentential calculus  *)
+(*             is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg presented  *)
+(*             an equality axiomatisation. Show that MV-24 depends on the  *)
+(*             Wajsberg axiomatisation. *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*           : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+(*  Source   : [LW92] *)
+(*  Names    : MV1.1 [LW92] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   1 RR) *)
+(*             Number of atoms       :    5 (   5 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   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_mv_24:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not (not x)) x) truth
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)