%------------------------------------------------------------------------------
% File : PLA057_1.018 : TPTP v9.0.0. Released v9.0.0.
% Domain : Planning
% Problem : Path from the entry to the exit of a labyrinth 18
% Version : Especial.
% English : The formula is the path from the entry to the exit of a
% labyrinth. It makes no difference whether one starts at the
% entry or at the exit.
% Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% : [NH+22] Nalon et al. (2022), Local Reductions for the Modal Cu
% : [Nal22] Nalon (2022), Email to Geoff Sutcliffe
% : [NH+23] Nalon et al. (2023), Buy One Get 14 Free: Evaluating L
% Source : [Nal22]
% Names : k45_path_p.0018 [Nal22]
% Status : Theorem
% Rating : 1.00 v9.0.0
% Syntax : Number of formulae : 19 ( 0 unt; 18 typ; 0 def)
% Number of atoms : 2730 ( 0 equ)
% Maximal formula atoms : 2730 (2730 avg)
% Number of connectives : 9591 (1366 ~;1361 |;1368 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% (5496 {.}; 0 {#})
% Maximal formula depth : 303 ( 303 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 18 usr; 18 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 (; 0 !; 0 ?; 0 :)
% SPC : NX0_THM_PRP_NEQ_NAR
% Comments :
%------------------------------------------------------------------------------
tff('k45_path_p.0018',logic,
$modal ==
[ $modalities == $modal_system_K45 ] ).
tff(p1_decl,type,
p1: $o ).
tff(p2_decl,type,
p2: $o ).
tff(p3_decl,type,
p3: $o ).
tff(p4_decl,type,
p4: $o ).
tff(p5_decl,type,
p5: $o ).
tff(p6_decl,type,
p6: $o ).
tff(y1_decl,type,
y1: $o ).
tff(y2_decl,type,
y2: $o ).
tff(y3_decl,type,
y3: $o ).
tff(y4_decl,type,
y4: $o ).
tff(y5_decl,type,
y5: $o ).
tff(y6_decl,type,
y6: $o ).
tff(z1_decl,type,
z1: $o ).
tff(z2_decl,type,
z2: $o ).
tff(z3_decl,type,
z3: $o ).
tff(z4_decl,type,
z4: $o ).
tff(z5_decl,type,
z5: $o ).
tff(z6_decl,type,
z6: $o ).
tff(prove,conjecture,
~ ( <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) )
& <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) )
& <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) )
& [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| <.> ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
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| ( [.] z3
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| ( [.] z1
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| ( [.] z1
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| ~ y1 ) )
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| ( [.] z5
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| ( [.] z2
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| ~ y2 ) )
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| ( [.] z4
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| ( [.] z3
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| ( [.] z3
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| ( [.] z6
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| ( [.] z2
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| ( [.] z6
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| ( [.] z4
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| ( [.] z2
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| ~ y2 ) )
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| ( [.] z4
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| ~ y4 ) )
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| ( [.] z2
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| ( [.] z4
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| ( [.] z3
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| ~ y3 ) ) )
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| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) ) ).
%------------------------------------------------------------------------------