X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FCOL044-3.ma;fp=matita%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FCOL044-3.ma;h=111980afb52442463e0755b301b67451ff7cd271;hb=2c01ff6094173915e7023076ea48b5804dca7778;hp=0000000000000000000000000000000000000000;hpb=a050e3f80d7ea084ce0184279af98e8251c7d2a6;p=helm.git diff --git a/matita/matita/contribs/TPTP/HEQ/COL044-3.ma b/matita/matita/contribs/TPTP/HEQ/COL044-3.ma new file mode 100644 index 000000000..111980afb --- /dev/null +++ b/matita/matita/contribs/TPTP/HEQ/COL044-3.ma @@ -0,0 +1,62 @@ +set "baseuri" "cic:/matita/TPTP/COL044-3". +include "logic/equality.ma". + +(* Inclusion of: COL044-3.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL044-3 : TPTP v3.2.0. Released v1.2.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B and N *) + +(* Version : [WM88] (equality) axioms : Augmented > Especial. *) + +(* Theorem formulation : The fixed point is provided and checked. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B and N, where ((Bx)y)z *) + +(* = x(yz), ((Nx)y)z = ((xz)y)z. *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.57 v3.2.0, 0.43 v3.1.0, 0.56 v2.7.0, 0.33 v2.6.0, 0.43 v2.5.0, 0.40 v2.4.0, 0.67 v2.3.0, 0.83 v2.2.1, 0.75 v2.2.0, 0.83 v2.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *) + +(* Number of atoms : 5 ( 3 equality) *) + +(* Maximal clause size : 2 ( 1 average) *) + +(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *) + +(* Number of functors : 4 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 7 ( 0 singleton) *) + +(* Maximal term depth : 12 ( 4 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +theorem prove_strong_fixed_point: + ∀Univ:Set.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀apply:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀fixed_point:∀_:Univ.Prop.∀fixed_pt:Univ.∀n:Univ.∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply n (apply b b))) n))) n)) b)) b) +. +intros. +autobatch depth=5 width=5 size=20 timeout=10; +try assumption. +print proofterm. +qed. + +(* -------------------------------------------------------------------------- *)