TPTP Problem File: SYP092_1.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SYP092_1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Syntactic
% Problem  : Logic KD, problem k_ph, 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_ph_n/10.p

% Status   : CounterSatisfiable
% Rating   : 1.00 v9.3.0
% Syntax   : Number of formulae    :  111 (   0 unt; 110 typ;   0 def)
%            Number of atoms       : 1210 (   0 equ)
%            Maximal formula atoms : 1210 (1210 avg)
%            Number of connectives : 1716 (  10   ~; 648   |; 560   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         ( 497 {.};   0 {#})
%            Maximal formula depth :  554 ( 554 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  :  110 ( 110 usr; 110 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)
% SPC      : NX0_CSA_PRP_NEQ_NAR_NDT

% Comments :
%------------------------------------------------------------------------------
tff(simple_k,logic,
    $modal == 
      [ $domains == $constant,
        $designation == $rigid,
        $terms == $local,
        $modalities == $modal_system_D ] ).

tff(p402_type,type,
    p402: $o ).

tff(p207_type,type,
    p207: $o ).

tff(p110_type,type,
    p110: $o ).

tff(p510_type,type,
    p510: $o ).

tff(p610_type,type,
    p610: $o ).

tff(p810_type,type,
    p810: $o ).

tff(p905_type,type,
    p905: $o ).

tff(p604_type,type,
    p604: $o ).

tff(p705_type,type,
    p705: $o ).

tff(p1106_type,type,
    p1106: $o ).

tff(p104_type,type,
    p104: $o ).

tff(p504_type,type,
    p504: $o ).

tff(p1001_type,type,
    p1001: $o ).

tff(p809_type,type,
    p809: $o ).

tff(p208_type,type,
    p208: $o ).

tff(p509_type,type,
    p509: $o ).

tff(p309_type,type,
    p309: $o ).

tff(p808_type,type,
    p808: $o ).

tff(p1102_type,type,
    p1102: $o ).

tff(p408_type,type,
    p408: $o ).

tff(p1002_type,type,
    p1002: $o ).

tff(p804_type,type,
    p804: $o ).

tff(p1009_type,type,
    p1009: $o ).

tff(p410_type,type,
    p410: $o ).

tff(p301_type,type,
    p301: $o ).

tff(p910_type,type,
    p910: $o ).

tff(p306_type,type,
    p306: $o ).

tff(p908_type,type,
    p908: $o ).

tff(p609_type,type,
    p609: $o ).

tff(p107_type,type,
    p107: $o ).

tff(p508_type,type,
    p508: $o ).

tff(p102_type,type,
    p102: $o ).

tff(p209_type,type,
    p209: $o ).

tff(p1101_type,type,
    p1101: $o ).

tff(p903_type,type,
    p903: $o ).

tff(p805_type,type,
    p805: $o ).

tff(p603_type,type,
    p603: $o ).

tff(p203_type,type,
    p203: $o ).

tff(p906_type,type,
    p906: $o ).

tff(p210_type,type,
    p210: $o ).

tff(p304_type,type,
    p304: $o ).

tff(p503_type,type,
    p503: $o ).

tff(p1108_type,type,
    p1108: $o ).

tff(p205_type,type,
    p205: $o ).

tff(p704_type,type,
    p704: $o ).

tff(p607_type,type,
    p607: $o ).

tff(p1003_type,type,
    p1003: $o ).

tff(p708_type,type,
    p708: $o ).

tff(p1109_type,type,
    p1109: $o ).

tff(p407_type,type,
    p407: $o ).

tff(p103_type,type,
    p103: $o ).

tff(p204_type,type,
    p204: $o ).

tff(p506_type,type,
    p506: $o ).

tff(p108_type,type,
    p108: $o ).

tff(p902_type,type,
    p902: $o ).

tff(p1006_type,type,
    p1006: $o ).

tff(p701_type,type,
    p701: $o ).

tff(p403_type,type,
    p403: $o ).

tff(p801_type,type,
    p801: $o ).

tff(p1105_type,type,
    p1105: $o ).

tff(p1004_type,type,
    p1004: $o ).

tff(p710_type,type,
    p710: $o ).

tff(p1104_type,type,
    p1104: $o ).

tff(p608_type,type,
    p608: $o ).

tff(p405_type,type,
    p405: $o ).

tff(p307_type,type,
    p307: $o ).

tff(p806_type,type,
    p806: $o ).

tff(p707_type,type,
    p707: $o ).

tff(p305_type,type,
    p305: $o ).

tff(p1010_type,type,
    p1010: $o ).

tff(p1107_type,type,
    p1107: $o ).

tff(p303_type,type,
    p303: $o ).

tff(p703_type,type,
    p703: $o ).

tff(p106_type,type,
    p106: $o ).

tff(p907_type,type,
    p907: $o ).

tff(p709_type,type,
    p709: $o ).

tff(p101_type,type,
    p101: $o ).

tff(p606_type,type,
    p606: $o ).

tff(p308_type,type,
    p308: $o ).

tff(p601_type,type,
    p601: $o ).

tff(p507_type,type,
    p507: $o ).

tff(p1007_type,type,
    p1007: $o ).

tff(p505_type,type,
    p505: $o ).

tff(p406_type,type,
    p406: $o ).

tff(p802_type,type,
    p802: $o ).

tff(p109_type,type,
    p109: $o ).

tff(p404_type,type,
    p404: $o ).

tff(p310_type,type,
    p310: $o ).

tff(p202_type,type,
    p202: $o ).

tff(p501_type,type,
    p501: $o ).

tff(p1103_type,type,
    p1103: $o ).

tff(p302_type,type,
    p302: $o ).

tff(p1005_type,type,
    p1005: $o ).

tff(p105_type,type,
    p105: $o ).

tff(p702_type,type,
    p702: $o ).

tff(p904_type,type,
    p904: $o ).

tff(p1110_type,type,
    p1110: $o ).

tff(p807_type,type,
    p807: $o ).

tff(p409_type,type,
    p409: $o ).

tff(p605_type,type,
    p605: $o ).

tff(p901_type,type,
    p901: $o ).

tff(p803_type,type,
    p803: $o ).

tff(p201_type,type,
    p201: $o ).

tff(p502_type,type,
    p502: $o ).

tff(p206_type,type,
    p206: $o ).

tff(p602_type,type,
    p602: $o ).

tff(p1008_type,type,
    p1008: $o ).

tff(p706_type,type,
    p706: $o ).

tff(p909_type,type,
    p909: $o ).

tff(p401_type,type,
    p401: $o ).

tff(10,conjecture,
    ( <.> ( ( p101
            | [.] p102
            | [.] p103
            | [.] p104
            | [.] p105
            | [.] p106
            | [.] p107
            | [.] p108
            | [.] p109
            | [.] p110 )
          & ( p201
            | p202
            | [.] p203
            | [.] p204
            | [.] p205
            | [.] p206
            | [.] p207
            | [.] p208
            | [.] p209
            | [.] p210 )
          & ( p301
            | p302
            | p303
            | [.] p304
            | [.] p305
            | [.] p306
            | [.] p307
            | [.] p308
            | [.] p309
            | [.] p310 )
          & ( p401
            | p402
            | p403
            | p404
            | [.] p405
            | [.] p406
            | [.] p407
            | [.] p408
            | [.] p409
            | [.] p410 )
          & ( p501
            | p502
            | p503
            | p504
            | p505
            | [.] p506
            | [.] p507
            | [.] p508
            | [.] p509
            | [.] p510 )
          & ( p601
            | p602
            | p603
            | p604
            | p605
            | p606
            | [.] p607
            | [.] p608
            | [.] p609
            | [.] p610 )
          & ( p701
            | p702
            | p703
            | p704
            | p705
            | p706
            | p707
            | [.] p708
            | [.] p709
            | [.] p710 )
          & ( p801
            | p802
            | p803
            | p804
            | p805
            | p806
            | p807
            | p808
            | [.] p809
            | [.] p810 )
          & ( p901
            | p902
            | p903
            | p904
            | p905
            | p906
            | p907
            | p908
            | p909
            | [.] p910 )
          & ( p1001
            | p1002
            | p1003
            | p1004
            | p1005
            | p1006
            | p1007
            | p1008
            | p1009
            | p1010 )
          & ( p1101
            | p1102
            | p1103
            | p1104
            | p1105
            | p1106
            | p1107
            | p1108
            | p1109
            | p1110 ) )
   => <.> ( ( p101
            & p201 )
          | ( p101
            & p301 )
          | ( p101
            & p401 )
          | ( p101
            & p501 )
          | ( p101
            & p601 )
          | ( p101
            & p701 )
          | ( p101
            & p801 )
          | ( p101
            & p901 )
          | ( p101
            & p1001 )
          | ( p101
            & p1101 )
          | ( p201
            & p301 )
          | ( p201
            & p401 )
          | ( p201
            & p501 )
          | ( p201
            & p601 )
          | ( p201
            & p701 )
          | ( p201
            & p801 )
          | ( p201
            & p901 )
          | ( p201
            & p1001 )
          | ( p201
            & p1101 )
          | ( p301
            & p401 )
          | ( p301
            & p501 )
          | ( p301
            & p601 )
          | ( p301
            & p701 )
          | ( p301
            & p801 )
          | ( p301
            & p901 )
          | ( p301
            & p1001 )
          | ( p301
            & p1101 )
          | ( p401
            & p501 )
          | ( p401
            & p601 )
          | ( p401
            & p701 )
          | ( p401
            & p801 )
          | ( p401
            & p901 )
          | ( p401
            & p1001 )
          | ( p401
            & p1101 )
          | ( p501
            & p601 )
          | ( p501
            & p701 )
          | ( p501
            & p801 )
          | ( p501
            & p901 )
          | ( p501
            & p1001 )
          | ( p501
            & p1101 )
          | ( p601
            & p701 )
          | ( p601
            & p801 )
          | ( p601
            & p901 )
          | ( p601
            & p1001 )
          | ( p601
            & p1101 )
          | ( p701
            & p801 )
          | ( p701
            & p901 )
          | ( p701
            & p1001 )
          | ( p701
            & p1101 )
          | ( p801
            & p901 )
          | ( p801
            & p1001 )
          | ( p801
            & p1101 )
          | ( p901
            & p1001 )
          | ( p901
            & p1101 )
          | ( p1001
            & p1101 )
          | ( [.] p102
            & p202 )
          | ( [.] p102
            & p302 )
          | ( [.] p102
            & p402 )
          | ( [.] p102
            & p502 )
          | ( [.] p102
            & p602 )
          | ( [.] p102
            & p702 )
          | ( [.] p102
            & p802 )
          | ( [.] p102
            & p902 )
          | ( [.] p102
            & p1002 )
          | ( [.] p102
            & p1102 )
          | ( p202
            & p302 )
          | ( p202
            & p402 )
          | ( p202
            & p502 )
          | ( p202
            & p602 )
          | ( p202
            & p702 )
          | ( p202
            & p802 )
          | ( p202
            & p902 )
          | ( p202
            & p1002 )
          | ( p202
            & p1102 )
          | ( p302
            & p402 )
          | ( p302
            & p502 )
          | ( p302
            & p602 )
          | ( p302
            & p702 )
          | ( p302
            & p802 )
          | ( p302
            & p902 )
          | ( p302
            & p1002 )
          | ( p302
            & p1102 )
          | ( p402
            & p502 )
          | ( p402
            & p602 )
          | ( p402
            & p702 )
          | ( p402
            & p802 )
          | ( p402
            & p902 )
          | ( p402
            & p1002 )
          | ( p402
            & p1102 )
          | ( p502
            & p602 )
          | ( p502
            & p702 )
          | ( p502
            & p802 )
          | ( p502
            & p902 )
          | ( p502
            & p1002 )
          | ( p502
            & p1102 )
          | ( p602
            & p702 )
          | ( p602
            & p802 )
          | ( p602
            & p902 )
          | ( p602
            & p1002 )
          | ( p602
            & p1102 )
          | ( p702
            & p802 )
          | ( p702
            & p902 )
          | ( p702
            & p1002 )
          | ( p702
            & p1102 )
          | ( p802
            & p902 )
          | ( p802
            & p1002 )
          | ( p802
            & p1102 )
          | ( p902
            & p1002 )
          | ( p902
            & p1102 )
          | ( p1002
            & p1102 )
          | ( [.] p103
            & [.] p203 )
          | ( [.] p103
            & p303 )
          | ( [.] p103
            & p403 )
          | ( [.] p103
            & p503 )
          | ( [.] p103
            & p603 )
          | ( [.] p103
            & p703 )
          | ( [.] p103
            & p803 )
          | ( [.] p103
            & p903 )
          | ( [.] p103
            & p1003 )
          | ( [.] p103
            & p1103 )
          | ( [.] p203
            & p303 )
          | ( [.] p203
            & p403 )
          | ( [.] p203
            & p503 )
          | ( [.] p203
            & p603 )
          | ( [.] p203
            & p703 )
          | ( [.] p203
            & p803 )
          | ( [.] p203
            & p903 )
          | ( [.] p203
            & p1003 )
          | ( [.] p203
            & p1103 )
          | ( p303
            & p403 )
          | ( p303
            & p503 )
          | ( p303
            & p603 )
          | ( p303
            & p703 )
          | ( p303
            & p803 )
          | ( p303
            & p903 )
          | ( p303
            & p1003 )
          | ( p303
            & p1103 )
          | ( p403
            & p503 )
          | ( p403
            & p603 )
          | ( p403
            & p703 )
          | ( p403
            & p803 )
          | ( p403
            & p903 )
          | ( p403
            & p1003 )
          | ( p403
            & p1103 )
          | ( p503
            & p603 )
          | ( p503
            & p703 )
          | ( p503
            & p803 )
          | ( p503
            & p903 )
          | ( p503
            & p1003 )
          | ( p503
            & p1103 )
          | ( p603
            & p703 )
          | ( p603
            & p803 )
          | ( p603
            & p903 )
          | ( p603
            & p1003 )
          | ( p603
            & p1103 )
          | ( p703
            & p803 )
          | ( p703
            & p903 )
          | ( p703
            & p1003 )
          | ( p703
            & p1103 )
          | ( p803
            & p903 )
          | ( p803
            & p1003 )
          | ( p803
            & p1103 )
          | ( p903
            & p1003 )
          | ( p903
            & p1103 )
          | ( p1003
            & p1103 )
          | ( [.] p104
            & [.] p204 )
          | ( [.] p104
            & [.] p304 )
          | ( [.] p104
            & p404 )
          | ( [.] p104
            & p504 )
          | ( [.] p104
            & p604 )
          | ( [.] p104
            & p704 )
          | ( [.] p104
            & p804 )
          | ( [.] p104
            & p904 )
          | ( [.] p104
            & p1004 )
          | ( [.] p104
            & p1104 )
          | ( [.] p204
            & [.] p304 )
          | ( [.] p204
            & p404 )
          | ( [.] p204
            & p504 )
          | ( [.] p204
            & p604 )
          | ( [.] p204
            & p704 )
          | ( [.] p204
            & p804 )
          | ( [.] p204
            & p904 )
          | ( [.] p204
            & p1004 )
          | ( [.] p204
            & p1104 )
          | ( [.] p304
            & p404 )
          | ( [.] p304
            & p504 )
          | ( [.] p304
            & p604 )
          | ( [.] p304
            & p704 )
          | ( [.] p304
            & p804 )
          | ( [.] p304
            & p904 )
          | ( [.] p304
            & p1004 )
          | ( [.] p304
            & p1104 )
          | ( p404
            & p504 )
          | ( p404
            & p604 )
          | ( p404
            & p704 )
          | ( p404
            & p804 )
          | ( p404
            & p904 )
          | ( p404
            & p1004 )
          | ( p404
            & p1104 )
          | ( p504
            & p604 )
          | ( p504
            & p704 )
          | ( p504
            & p804 )
          | ( p504
            & p904 )
          | ( p504
            & p1004 )
          | ( p504
            & p1104 )
          | ( p604
            & p704 )
          | ( p604
            & p804 )
          | ( p604
            & p904 )
          | ( p604
            & p1004 )
          | ( p604
            & p1104 )
          | ( p704
            & p804 )
          | ( p704
            & p904 )
          | ( p704
            & p1004 )
          | ( p704
            & p1104 )
          | ( p804
            & p904 )
          | ( p804
            & p1004 )
          | ( p804
            & p1104 )
          | ( p904
            & p1004 )
          | ( p904
            & p1104 )
          | ( p1004
            & p1104 )
          | ( [.] p105
            & [.] p205 )
          | ( [.] p105
            & [.] p305 )
          | ( [.] p105
            & [.] p405 )
          | ( [.] p105
            & p505 )
          | ( [.] p105
            & p605 )
          | ( [.] p105
            & p705 )
          | ( [.] p105
            & p805 )
          | ( [.] p105
            & p905 )
          | ( [.] p105
            & p1005 )
          | ( [.] p105
            & p1105 )
          | ( [.] p205
            & [.] p305 )
          | ( [.] p205
            & [.] p405 )
          | ( [.] p205
            & p505 )
          | ( [.] p205
            & p605 )
          | ( [.] p205
            & p705 )
          | ( [.] p205
            & p805 )
          | ( [.] p205
            & p905 )
          | ( [.] p205
            & p1005 )
          | ( [.] p205
            & p1105 )
          | ( [.] p305
            & [.] p405 )
          | ( [.] p305
            & p505 )
          | ( [.] p305
            & p605 )
          | ( [.] p305
            & p705 )
          | ( [.] p305
            & p805 )
          | ( [.] p305
            & p905 )
          | ( [.] p305
            & p1005 )
          | ( [.] p305
            & p1105 )
          | ( [.] p405
            & p505 )
          | ( [.] p405
            & p605 )
          | ( [.] p405
            & p705 )
          | ( [.] p405
            & p805 )
          | ( [.] p405
            & p905 )
          | ( [.] p405
            & p1005 )
          | ( [.] p405
            & p1105 )
          | ( p505
            & p605 )
          | ( p505
            & p705 )
          | ( p505
            & p805 )
          | ( p505
            & p905 )
          | ( p505
            & p1005 )
          | ( p505
            & p1105 )
          | ( p605
            & p705 )
          | ( p605
            & p805 )
          | ( p605
            & p905 )
          | ( p605
            & p1005 )
          | ( p605
            & p1105 )
          | ( p705
            & p805 )
          | ( p705
            & p905 )
          | ( p705
            & p1005 )
          | ( p705
            & p1105 )
          | ( p805
            & p905 )
          | ( p805
            & p1005 )
          | ( p805
            & p1105 )
          | ( p905
            & p1005 )
          | ( p905
            & p1105 )
          | ( p1005
            & p1105 )
          | ( [.] p106
            & [.] p206 )
          | ( [.] p106
            & [.] p306 )
          | ( [.] p106
            & [.] p406 )
          | ( [.] p106
            & [.] p506 )
          | ( [.] p106
            & p606 )
          | ( [.] p106
            & p706 )
          | ( [.] p106
            & p806 )
          | ( [.] p106
            & p906 )
          | ( [.] p106
            & p1006 )
          | ( [.] p106
            & p1106 )
          | ( [.] p206
            & [.] p306 )
          | ( [.] p206
            & [.] p406 )
          | ( [.] p206
            & [.] p506 )
          | ( [.] p206
            & p606 )
          | ( [.] p206
            & p706 )
          | ( [.] p206
            & p806 )
          | ( [.] p206
            & p906 )
          | ( [.] p206
            & p1006 )
          | ( [.] p206
            & p1106 )
          | ( [.] p306
            & [.] p406 )
          | ( [.] p306
            & [.] p506 )
          | ( [.] p306
            & p606 )
          | ( [.] p306
            & p706 )
          | ( [.] p306
            & p806 )
          | ( [.] p306
            & p906 )
          | ( [.] p306
            & p1006 )
          | ( [.] p306
            & p1106 )
          | ( [.] p406
            & [.] p506 )
          | ( [.] p406
            & p606 )
          | ( [.] p406
            & p706 )
          | ( [.] p406
            & p806 )
          | ( [.] p406
            & p906 )
          | ( [.] p406
            & p1006 )
          | ( [.] p406
            & p1106 )
          | ( [.] p506
            & p606 )
          | ( [.] p506
            & p706 )
          | ( [.] p506
            & p806 )
          | ( [.] p506
            & p906 )
          | ( [.] p506
            & p1006 )
          | ( [.] p506
            & p1106 )
          | ( p606
            & p706 )
          | ( p606
            & p806 )
          | ( p606
            & p906 )
          | ( p606
            & p1006 )
          | ( p606
            & p1106 )
          | ( p706
            & p806 )
          | ( p706
            & p906 )
          | ( p706
            & p1006 )
          | ( p706
            & p1106 )
          | ( p806
            & p906 )
          | ( p806
            & p1006 )
          | ( p806
            & p1106 )
          | ( p906
            & p1006 )
          | ( p906
            & p1106 )
          | ( p1006
            & p1106 )
          | ( [.] p107
            & [.] p207 )
          | ( [.] p107
            & [.] p307 )
          | ( [.] p107
            & [.] p407 )
          | ( [.] p107
            & [.] p507 )
          | ( [.] p107
            & [.] p607 )
          | ( [.] p107
            & ~ p707 )
          | ( [.] p107
            & p807 )
          | ( [.] p107
            & p907 )
          | ( [.] p107
            & p1007 )
          | ( [.] p107
            & p1107 )
          | ( [.] p207
            & [.] p307 )
          | ( [.] p207
            & [.] p407 )
          | ( [.] p207
            & [.] p507 )
          | ( [.] p207
            & [.] p607 )
          | ( [.] p207
            & ~ p707 )
          | ( [.] p207
            & p807 )
          | ( [.] p207
            & p907 )
          | ( [.] p207
            & p1007 )
          | ( [.] p207
            & p1107 )
          | ( [.] p307
            & [.] p407 )
          | ( [.] p307
            & [.] p507 )
          | ( [.] p307
            & [.] p607 )
          | ( [.] p307
            & ~ p707 )
          | ( [.] p307
            & p807 )
          | ( [.] p307
            & p907 )
          | ( [.] p307
            & p1007 )
          | ( [.] p307
            & p1107 )
          | ( [.] p407
            & [.] p507 )
          | ( [.] p407
            & [.] p607 )
          | ( [.] p407
            & ~ p707 )
          | ( [.] p407
            & p807 )
          | ( [.] p407
            & p907 )
          | ( [.] p407
            & p1007 )
          | ( [.] p407
            & p1107 )
          | ( [.] p507
            & [.] p607 )
          | ( [.] p507
            & ~ p707 )
          | ( [.] p507
            & p807 )
          | ( [.] p507
            & p907 )
          | ( [.] p507
            & p1007 )
          | ( [.] p507
            & p1107 )
          | ( [.] p607
            & ~ p707 )
          | ( [.] p607
            & p807 )
          | ( [.] p607
            & p907 )
          | ( [.] p607
            & p1007 )
          | ( [.] p607
            & p1107 )
          | ( ~ p707
            & p807 )
          | ( ~ p707
            & p907 )
          | ( ~ p707
            & p1007 )
          | ( ~ p707
            & p1107 )
          | ( p807
            & p907 )
          | ( p807
            & p1007 )
          | ( p807
            & p1107 )
          | ( p907
            & p1007 )
          | ( p907
            & p1107 )
          | ( p1007
            & p1107 )
          | ( [.] p108
            & [.] p208 )
          | ( [.] p108
            & [.] p308 )
          | ( [.] p108
            & [.] p408 )
          | ( [.] p108
            & [.] p508 )
          | ( [.] p108
            & [.] p608 )
          | ( [.] p108
            & [.] p708 )
          | ( [.] p108
            & p808 )
          | ( [.] p108
            & p908 )
          | ( [.] p108
            & p1008 )
          | ( [.] p108
            & p1108 )
          | ( [.] p208
            & [.] p308 )
          | ( [.] p208
            & [.] p408 )
          | ( [.] p208
            & [.] p508 )
          | ( [.] p208
            & [.] p608 )
          | ( [.] p208
            & [.] p708 )
          | ( [.] p208
            & p808 )
          | ( [.] p208
            & p908 )
          | ( [.] p208
            & p1008 )
          | ( [.] p208
            & p1108 )
          | ( [.] p308
            & [.] p408 )
          | ( [.] p308
            & [.] p508 )
          | ( [.] p308
            & [.] p608 )
          | ( [.] p308
            & [.] p708 )
          | ( [.] p308
            & p808 )
          | ( [.] p308
            & p908 )
          | ( [.] p308
            & p1008 )
          | ( [.] p308
            & p1108 )
          | ( [.] p408
            & [.] p508 )
          | ( [.] p408
            & [.] p608 )
          | ( [.] p408
            & [.] p708 )
          | ( [.] p408
            & p808 )
          | ( [.] p408
            & p908 )
          | ( [.] p408
            & p1008 )
          | ( [.] p408
            & p1108 )
          | ( [.] p508
            & [.] p608 )
          | ( [.] p508
            & [.] p708 )
          | ( [.] p508
            & p808 )
          | ( [.] p508
            & p908 )
          | ( [.] p508
            & p1008 )
          | ( [.] p508
            & p1108 )
          | ( [.] p608
            & [.] p708 )
          | ( [.] p608
            & p808 )
          | ( [.] p608
            & p908 )
          | ( [.] p608
            & p1008 )
          | ( [.] p608
            & p1108 )
          | ( [.] p708
            & p808 )
          | ( [.] p708
            & p908 )
          | ( [.] p708
            & p1008 )
          | ( [.] p708
            & p1108 )
          | ( p808
            & p908 )
          | ( p808
            & p1008 )
          | ( p808
            & p1108 )
          | ( p908
            & p1008 )
          | ( p908
            & p1108 )
          | ( p1008
            & p1108 )
          | ( [.] p109
            & [.] p209 )
          | ( [.] p109
            & [.] p309 )
          | ( [.] p109
            & [.] p409 )
          | ( [.] p109
            & [.] p509 )
          | ( [.] p109
            & [.] p609 )
          | ( [.] p109
            & [.] p709 )
          | ( [.] p109
            & [.] p809 )
          | ( [.] p109
            & p909 )
          | ( [.] p109
            & p1009 )
          | ( [.] p109
            & p1109 )
          | ( [.] p209
            & [.] p309 )
          | ( [.] p209
            & [.] p409 )
          | ( [.] p209
            & [.] p509 )
          | ( [.] p209
            & [.] p609 )
          | ( [.] p209
            & [.] p709 )
          | ( [.] p209
            & [.] p809 )
          | ( [.] p209
            & p909 )
          | ( [.] p209
            & p1009 )
          | ( [.] p209
            & p1109 )
          | ( [.] p309
            & [.] p409 )
          | ( [.] p309
            & [.] p509 )
          | ( [.] p309
            & [.] p609 )
          | ( [.] p309
            & [.] p709 )
          | ( [.] p309
            & [.] p809 )
          | ( [.] p309
            & p909 )
          | ( [.] p309
            & p1009 )
          | ( [.] p309
            & p1109 )
          | ( [.] p409
            & [.] p509 )
          | ( [.] p409
            & [.] p609 )
          | ( [.] p409
            & [.] p709 )
          | ( [.] p409
            & [.] p809 )
          | ( [.] p409
            & p909 )
          | ( [.] p409
            & p1009 )
          | ( [.] p409
            & p1109 )
          | ( [.] p509
            & [.] p609 )
          | ( [.] p509
            & [.] p709 )
          | ( [.] p509
            & [.] p809 )
          | ( [.] p509
            & p909 )
          | ( [.] p509
            & p1009 )
          | ( [.] p509
            & p1109 )
          | ( [.] p609
            & [.] p709 )
          | ( [.] p609
            & [.] p809 )
          | ( [.] p609
            & p909 )
          | ( [.] p609
            & p1009 )
          | ( [.] p609
            & p1109 )
          | ( [.] p709
            & [.] p809 )
          | ( [.] p709
            & p909 )
          | ( [.] p709
            & p1009 )
          | ( [.] p709
            & p1109 )
          | ( [.] p809
            & p909 )
          | ( [.] p809
            & p1009 )
          | ( [.] p809
            & p1109 )
          | ( p909
            & p1009 )
          | ( p909
            & p1109 )
          | ( p1009
            & p1109 )
          | ( [.] p110
            & [.] p210 )
          | ( [.] p110
            & [.] p310 )
          | ( [.] p110
            & [.] p410 )
          | ( [.] p110
            & [.] p510 )
          | ( [.] p110
            & [.] p610 )
          | ( [.] p110
            & [.] p710 )
          | ( [.] p110
            & [.] p810 )
          | ( [.] p110
            & [.] p910 )
          | ( [.] p110
            & p1010 )
          | ( [.] p110
            & p1110 )
          | ( [.] p210
            & [.] p310 )
          | ( [.] p210
            & [.] p410 )
          | ( [.] p210
            & [.] p510 )
          | ( [.] p210
            & [.] p610 )
          | ( [.] p210
            & [.] p710 )
          | ( [.] p210
            & [.] p810 )
          | ( [.] p210
            & [.] p910 )
          | ( [.] p210
            & p1010 )
          | ( [.] p210
            & p1110 )
          | ( [.] p310
            & [.] p410 )
          | ( [.] p310
            & [.] p510 )
          | ( [.] p310
            & [.] p610 )
          | ( [.] p310
            & [.] p710 )
          | ( [.] p310
            & [.] p810 )
          | ( [.] p310
            & [.] p910 )
          | ( [.] p310
            & p1010 )
          | ( [.] p310
            & p1110 )
          | ( [.] p410
            & [.] p510 )
          | ( [.] p410
            & [.] p610 )
          | ( [.] p410
            & [.] p710 )
          | ( [.] p410
            & [.] p810 )
          | ( [.] p410
            & [.] p910 )
          | ( [.] p410
            & p1010 )
          | ( [.] p410
            & p1110 )
          | ( [.] p510
            & [.] p610 )
          | ( [.] p510
            & [.] p710 )
          | ( [.] p510
            & [.] p810 )
          | ( [.] p510
            & [.] p910 )
          | ( [.] p510
            & p1010 )
          | ( [.] p510
            & p1110 )
          | ( [.] p610
            & [.] p710 )
          | ( [.] p610
            & [.] p810 )
          | ( [.] p610
            & [.] p910 )
          | ( [.] p610
            & p1010 )
          | ( [.] p610
            & p1110 )
          | ( [.] p710
            & [.] p810 )
          | ( [.] p710
            & [.] p910 )
          | ( [.] p710
            & p1010 )
          | ( [.] p710
            & p1110 )
          | ( [.] p810
            & [.] p910 )
          | ( [.] p810
            & p1010 )
          | ( [.] p810
            & p1110 )
          | ( [.] p910
            & p1010 )
          | ( [.] p910
            & p1110 )
          | ( p1010
            & p1110 ) ) ) ).

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