2 include "logic/equality.ma".
3 (* Inclusion of: LAT008-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : LAT008-1 : TPTP v3.1.1. Released v2.2.0. *)
6 (* Domain : Lattice Theory (Distributive lattices) *)
7 (* Problem : Sholander's basis for distributive lattices, part 5 (of 6). *)
8 (* Version : [MP96] (equality) axioms. *)
9 (* English : This is part of the proof that Sholanders 2-basis for *)
10 (* distributive lattices is correct. Here we prove the absorption *)
11 (* law x v (x ^ y) = x. *)
12 (* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *)
13 (* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *)
14 (* Source : [McC98] *)
15 (* Names : LT-3-f [MP96] *)
16 (* Status : Unsatisfiable *)
17 (* Rating : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 *)
18 (* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *)
19 (* Number of atoms : 3 ( 3 equality) *)
20 (* Maximal clause size : 1 ( 1 average) *)
21 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
22 (* Number of functors : 4 ( 2 constant; 0-2 arity) *)
23 (* Number of variables : 5 ( 1 singleton) *)
24 (* Maximal term depth : 3 ( 2 average) *)
26 (* -------------------------------------------------------------------------- *)
27 (* ----Sholander's 2-basis for distributive lattices: *)
28 (* ----Denial of the conclusion: *)
29 theorem prove_absorbtion_dual:
33 \forall join:\forall _:Univ.\forall _:Univ.Univ.
34 \forall meet:\forall _:Univ.\forall _:Univ.Univ.
35 \forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet X (join Y Z)) (join (meet Z X) (meet Y X)).
36 \forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join a (meet a b)) a
39 autobatch paramodulation timeout=100;
43 (* -------------------------------------------------------------------------- *)