2 include "logic/equality.ma".
3 (* Inclusion of: LAT045-1.p *)
4 (* -------------------------------------------------------------------------- *)
5 (* File : LAT045-1 : TPTP v3.1.1. Released v2.5.0. *)
6 (* Domain : Lattice Theory *)
7 (* Problem : Lattice orthomodular law from modular lattice *)
8 (* Version : [McC88] (equality) axioms. *)
10 (* Refs : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
11 (* : [RW01] Rose & Wilkinson (2001), Application of Model Search *)
13 (* Names : eqp-f.in [RW01] *)
14 (* Status : Unsatisfiable *)
15 (* Rating : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.5.0 *)
16 (* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 1 RR) *)
17 (* Number of atoms : 15 ( 15 equality) *)
18 (* Maximal clause size : 1 ( 1 average) *)
19 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
20 (* Number of functors : 7 ( 4 constant; 0-2 arity) *)
21 (* Number of variables : 26 ( 2 singleton) *)
22 (* Maximal term depth : 4 ( 2 average) *)
24 (* -------------------------------------------------------------------------- *)
25 (* ----Include lattice axioms *)
26 (* Inclusion of: Axioms/LAT001-0.ax *)
27 (* -------------------------------------------------------------------------- *)
28 (* File : LAT001-0 : TPTP v3.1.1. Released v1.0.0. *)
29 (* Domain : Lattice Theory *)
30 (* Axioms : Lattice theory (equality) axioms *)
31 (* Version : [McC88] (equality) axioms. *)
33 (* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
34 (* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
35 (* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
36 (* Source : [McC88] *)
39 (* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *)
40 (* Number of literals : 8 ( 8 equality) *)
41 (* Maximal clause size : 1 ( 1 average) *)
42 (* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
43 (* Number of functors : 2 ( 0 constant; 2-2 arity) *)
44 (* Number of variables : 16 ( 2 singleton) *)
45 (* Maximal term depth : 3 ( 2 average) *)
47 (* -------------------------------------------------------------------------- *)
48 (* ----The following 8 clauses characterise lattices *)
49 (* -------------------------------------------------------------------------- *)
50 (* -------------------------------------------------------------------------- *)
51 (* ----Compatibility (6) *)
52 (* ----Invertability (5) *)
53 (* ----Modular law (7) *)
54 (* ----Denial of orthomodular law (8) *)
55 theorem prove_orthomodular_law:
59 \forall complement:\forall _:Univ.Univ.
60 \forall join:\forall _:Univ.\forall _:Univ.Univ.
61 \forall meet:\forall _:Univ.\forall _:Univ.Univ.
64 \forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join X (meet Y (join X Z))) (meet (join X Y) (join X Z)).
65 \forall H1:\forall X:Univ.eq Univ (complement (complement X)) X.
66 \forall H2:\forall X:Univ.eq Univ (meet (complement X) X) n0.
67 \forall H3:\forall X:Univ.eq Univ (join (complement X) X) n1.
68 \forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (complement (meet X Y)) (join (complement X) (complement Y)).
69 \forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (complement (join X Y)) (meet (complement X) (complement Y)).
70 \forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
71 \forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
72 \forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
73 \forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
74 \forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
75 \forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.
76 \forall H12:\forall X:Univ.eq Univ (join X X) X.
77 \forall H13:\forall X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement a) (join a b))) (join a b)
80 autobatch paramodulation timeout=100;
84 (* -------------------------------------------------------------------------- *)