%------------------------------------------------------------------------------
% File : SYP081_1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Syntactic
% Problem : Logic KD, problem k_branch, size 10
% Version : Especial.
% English :
% Refs : [BHS98] Balsiger et al. (1998), Logics Workbench 1.0
% : [Ste24] Steen (2024), Email to Geoff Sutcliffe
% Source : [Ste24]
% Names : KD/k_branch_p/10.p
% Status : Theorem
% Rating : 0.67 v9.3.0
% Syntax : Number of formulae : 24 ( 0 unt; 23 typ; 0 def)
% Number of atoms : 1972 ( 0 equ)
% Maximal formula atoms : 1972 (1972 avg)
% Number of connectives : 3183 ( 685 ~; 1 |;1134 &)
% ( 0 <=>; 836 =>; 0 <=; 0 <~>)
% ( 527 {.}; 0 {#})
% Maximal formula depth : 93 ( 93 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 : 23 ( 23 usr; 23 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_NDT
% Comments :
%------------------------------------------------------------------------------
tff(simple_k,logic,
$modal ==
[ $domains == $constant,
$designation == $rigid,
$terms == $local,
$modalities == $modal_system_D ] ).
tff(p104_type,type,
p104: $o ).
tff(p10_type,type,
p10: $o ).
tff(p103_type,type,
p103: $o ).
tff(p106_type,type,
p106: $o ).
tff(p101_type,type,
p101: $o ).
tff(p2_type,type,
p2: $o ).
tff(p109_type,type,
p109: $o ).
tff(p0_type,type,
p0: $o ).
tff(p105_type,type,
p105: $o ).
tff(p1_type,type,
p1: $o ).
tff(p4_type,type,
p4: $o ).
tff(p7_type,type,
p7: $o ).
tff(p5_type,type,
p5: $o ).
tff(p107_type,type,
p107: $o ).
tff(p102_type,type,
p102: $o ).
tff(p108_type,type,
p108: $o ).
tff(p3_type,type,
p3: $o ).
tff(p111_type,type,
p111: $o ).
tff(p9_type,type,
p9: $o ).
tff(p100_type,type,
p100: $o ).
tff(p6_type,type,
p6: $o ).
tff(p8_type,type,
p8: $o ).
tff(p110_type,type,
p110: $o ).
tff(10,conjecture,
( ~ ( p100
& ~ p101
& ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) )
& [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) )
& [.] [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) )
& [.] [.] [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) )
& [.] [.] [.] [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) )
& [.] [.] [.] [.] [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) )
& [.] [.] [.] [.] [.] [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( p101
=> p100 )
& ( p102
=> p101 )
& ( p103
=> p102 )
& ( p104
=> p103 )
& ( p105
=> p104 )
& ( p106
=> p105 )
& ( p107
=> p106 )
& ( p108
=> p107 )
& ( p109
=> p108 )
& ( p110
=> p109 )
& ( p111
=> p110 )
& ( p100
=> ( ( p0
=> [.] ( p100
=> p0 ) )
& ( ~ p0
=> [.] ( p100
=> ~ p0 ) ) ) )
& ( p101
=> ( ( p1
=> [.] ( p101
=> p1 ) )
& ( ~ p1
=> [.] ( p101
=> ~ p1 ) ) ) )
& ( p102
=> ( ( p2
=> [.] ( p102
=> p2 ) )
& ( ~ p2
=> [.] ( p102
=> ~ p2 ) ) ) )
& ( p103
=> ( ( p3
=> [.] ( p103
=> p3 ) )
& ( ~ p3
=> [.] ( p103
=> ~ p3 ) ) ) )
& ( p104
=> ( ( p4
=> [.] ( p104
=> p4 ) )
& ( ~ p4
=> [.] ( p104
=> ~ p4 ) ) ) )
& ( p105
=> ( ( p5
=> [.] ( p105
=> p5 ) )
& ( ~ p5
=> [.] ( p105
=> ~ p5 ) ) ) )
& ( p106
=> ( ( p6
=> [.] ( p106
=> p6 ) )
& ( ~ p6
=> [.] ( p106
=> ~ p6 ) ) ) )
& ( p107
=> ( ( p7
=> [.] ( p107
=> p7 ) )
& ( ~ p7
=> [.] ( p107
=> ~ p7 ) ) ) )
& ( p108
=> ( ( p8
=> [.] ( p108
=> p8 ) )
& ( ~ p8
=> [.] ( p108
=> ~ p8 ) ) ) )
& ( p109
=> ( ( p9
=> [.] ( p109
=> p9 ) )
& ( ~ p9
=> [.] ( p109
=> ~ p9 ) ) ) )
& ( p110
=> ( ( p10
=> [.] ( p110
=> p10 ) )
& ( ~ p10
=> [.] ( p110
=> ~ p10 ) ) ) )
& ( ( p100
& ~ p101 )
=> ( <.> ( p101
& ~ p102
& p1 )
& <.> ( p101
& ~ p102
& ~ p1 ) ) )
& ( ( p101
& ~ p102 )
=> ( <.> ( p102
& ~ p103
& p2 )
& <.> ( p102
& ~ p103
& ~ p2 ) ) )
& ( ( p102
& ~ p103 )
=> ( <.> ( p103
& ~ p104
& p3 )
& <.> ( p103
& ~ p104
& ~ p3 ) ) )
& ( ( p103
& ~ p104 )
=> ( <.> ( p104
& ~ p105
& p4 )
& <.> ( p104
& ~ p105
& ~ p4 ) ) )
& ( ( p104
& ~ p105 )
=> ( <.> ( p105
& ~ p106
& p5 )
& <.> ( p105
& ~ p106
& ~ p5 ) ) )
& ( ( p105
& ~ p106 )
=> ( <.> ( p106
& ~ p107
& p6 )
& <.> ( p106
& ~ p107
& ~ p6 ) ) )
& ( ( p106
& ~ p107 )
=> ( <.> ( p107
& ~ p108
& p7 )
& <.> ( p107
& ~ p108
& ~ p7 ) ) )
& ( ( p107
& ~ p108 )
=> ( <.> ( p108
& ~ p109
& p8 )
& <.> ( p108
& ~ p109
& ~ p8 ) ) )
& ( ( p108
& ~ p109 )
=> ( <.> ( p109
& ~ p110
& p9 )
& <.> ( p109
& ~ p110
& ~ p9 ) ) )
& ( ( p109
& ~ p110 )
=> ( <.> ( p110
& ~ p111
& p10 )
& <.> ( p110
& ~ p111
& ~ p10 ) ) ) ) )
| ~ [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] p4 ) ).
%------------------------------------------------------------------------------