TPTP Problem File: LCL974_1.006.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : LCL974_1.006 : TPTP v9.0.0. Released v9.0.0.
% Domain   : Syntactic
% Problem  : Pigeonhole formula 6
% Version  : Especial.
% English  :

% 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    : k4d_ph_p.0006 [Nal22]

% Status   : Theorem
% Rating   : 1.00 v9.0.0
% Syntax   : Number of formulae    :   86 (   0 unt;  85 typ;   0 def)
%            Number of atoms       :  884 (   0 equ)
%            Maximal formula atoms :  884 ( 884 avg)
%            Number of connectives : 3010 ( 548   ~; 456   |; 427   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (1579 {.};   0 {#})
%            Maximal formula depth :  139 ( 139 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  :   85 (  85 usr;  85 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('k4d_ph_p.0006',logic,
    $modal == 
      [ $modalities == $modal_system_D4 ] ).

tff(p101_decl,type,
    p101: $o ).

tff(p102_decl,type,
    p102: $o ).

tff(p103_decl,type,
    p103: $o ).

tff(p104_decl,type,
    p104: $o ).

tff(p105_decl,type,
    p105: $o ).

tff(p106_decl,type,
    p106: $o ).

tff(p201_decl,type,
    p201: $o ).

tff(p202_decl,type,
    p202: $o ).

tff(p203_decl,type,
    p203: $o ).

tff(p204_decl,type,
    p204: $o ).

tff(p205_decl,type,
    p205: $o ).

tff(p206_decl,type,
    p206: $o ).

tff(p301_decl,type,
    p301: $o ).

tff(p302_decl,type,
    p302: $o ).

tff(p303_decl,type,
    p303: $o ).

tff(p304_decl,type,
    p304: $o ).

tff(p305_decl,type,
    p305: $o ).

tff(p306_decl,type,
    p306: $o ).

tff(p401_decl,type,
    p401: $o ).

tff(p402_decl,type,
    p402: $o ).

tff(p403_decl,type,
    p403: $o ).

tff(p404_decl,type,
    p404: $o ).

tff(p405_decl,type,
    p405: $o ).

tff(p406_decl,type,
    p406: $o ).

tff(p501_decl,type,
    p501: $o ).

tff(p502_decl,type,
    p502: $o ).

tff(p503_decl,type,
    p503: $o ).

tff(p504_decl,type,
    p504: $o ).

tff(p505_decl,type,
    p505: $o ).

tff(p506_decl,type,
    p506: $o ).

tff(p601_decl,type,
    p601: $o ).

tff(p602_decl,type,
    p602: $o ).

tff(p603_decl,type,
    p603: $o ).

tff(p604_decl,type,
    p604: $o ).

tff(p605_decl,type,
    p605: $o ).

tff(p606_decl,type,
    p606: $o ).

tff(p701_decl,type,
    p701: $o ).

tff(p702_decl,type,
    p702: $o ).

tff(p703_decl,type,
    p703: $o ).

tff(p704_decl,type,
    p704: $o ).

tff(p705_decl,type,
    p705: $o ).

tff(p706_decl,type,
    p706: $o ).

tff(x0_decl,type,
    x0: $o ).

tff(z101_decl,type,
    z101: $o ).

tff(z102_decl,type,
    z102: $o ).

tff(z103_decl,type,
    z103: $o ).

tff(z104_decl,type,
    z104: $o ).

tff(z105_decl,type,
    z105: $o ).

tff(z106_decl,type,
    z106: $o ).

tff(z201_decl,type,
    z201: $o ).

tff(z202_decl,type,
    z202: $o ).

tff(z203_decl,type,
    z203: $o ).

tff(z204_decl,type,
    z204: $o ).

tff(z205_decl,type,
    z205: $o ).

tff(z206_decl,type,
    z206: $o ).

tff(z301_decl,type,
    z301: $o ).

tff(z302_decl,type,
    z302: $o ).

tff(z303_decl,type,
    z303: $o ).

tff(z304_decl,type,
    z304: $o ).

tff(z305_decl,type,
    z305: $o ).

tff(z306_decl,type,
    z306: $o ).

tff(z401_decl,type,
    z401: $o ).

tff(z402_decl,type,
    z402: $o ).

tff(z403_decl,type,
    z403: $o ).

tff(z404_decl,type,
    z404: $o ).

tff(z405_decl,type,
    z405: $o ).

tff(z406_decl,type,
    z406: $o ).

tff(z501_decl,type,
    z501: $o ).

tff(z502_decl,type,
    z502: $o ).

tff(z503_decl,type,
    z503: $o ).

tff(z504_decl,type,
    z504: $o ).

tff(z505_decl,type,
    z505: $o ).

tff(z506_decl,type,
    z506: $o ).

tff(z601_decl,type,
    z601: $o ).

tff(z602_decl,type,
    z602: $o ).

tff(z603_decl,type,
    z603: $o ).

tff(z604_decl,type,
    z604: $o ).

tff(z605_decl,type,
    z605: $o ).

tff(z606_decl,type,
    z606: $o ).

tff(z701_decl,type,
    z701: $o ).

tff(z702_decl,type,
    z702: $o ).

tff(z703_decl,type,
    z703: $o ).

tff(z704_decl,type,
    z704: $o ).

tff(z705_decl,type,
    z705: $o ).

tff(z706_decl,type,
    z706: $o ).

tff(prove,conjecture,
    ~ ( ( [.] x0
        & [.] ~ x0 )
      | ( <.> ( ( p101
                | ( [.] z101
                  & <.> <.> [.] <.> ~ z101 )
                | [.] ( p102
                      | ( [.] z102
                        & <.> <.> [.] <.> ~ z102 ) )
                | [.] ( p103
                      | ( [.] z103
                        & <.> <.> [.] <.> ~ z103 ) )
                | [.] ( p104
                      | ( [.] z104
                        & <.> <.> [.] <.> ~ z104 ) )
                | [.] ( p105
                      | ( [.] z105
                        & <.> <.> [.] <.> ~ z105 ) )
                | [.] ( p106
                      | ( [.] z106
                        & <.> <.> [.] <.> ~ z106 ) ) )
              & ( p201
                | ( [.] z201
                  & <.> <.> [.] <.> ~ z201 )
                | p202
                | ( [.] z202
                  & <.> <.> [.] <.> ~ z202 )
                | [.] ( p203
                      | ( [.] z203
                        & <.> <.> [.] <.> ~ z203 ) )
                | [.] ( p204
                      | ( [.] z204
                        & <.> <.> [.] <.> ~ z204 ) )
                | [.] ( p205
                      | ( [.] z205
                        & <.> <.> [.] <.> ~ z205 ) )
                | [.] ( p206
                      | ( [.] z206
                        & <.> <.> [.] <.> ~ z206 ) ) )
              & ( p301
                | ( [.] z301
                  & <.> <.> [.] <.> ~ z301 )
                | p302
                | ( [.] z302
                  & <.> <.> [.] <.> ~ z302 )
                | p303
                | ( [.] z303
                  & <.> <.> [.] <.> ~ z303 )
                | [.] ( p304
                      | ( [.] z304
                        & <.> <.> [.] <.> ~ z304 ) )
                | [.] ( p305
                      | ( [.] z305
                        & <.> <.> [.] <.> ~ z305 ) )
                | [.] ( p306
                      | ( [.] z306
                        & <.> <.> [.] <.> ~ z306 ) ) )
              & ( p401
                | ( [.] z401
                  & <.> <.> [.] <.> ~ z401 )
                | p402
                | ( [.] z402
                  & <.> <.> [.] <.> ~ z402 )
                | p403
                | ( [.] z403
                  & <.> <.> [.] <.> ~ z403 )
                | p404
                | ( [.] z404
                  & <.> <.> [.] <.> ~ z404 )
                | [.] ( p405
                      | ( [.] z405
                        & <.> <.> [.] <.> ~ z405 ) )
                | [.] ( p406
                      | ( [.] z406
                        & <.> <.> [.] <.> ~ z406 ) ) )
              & ( p501
                | ( [.] z501
                  & <.> <.> [.] <.> ~ z501 )
                | p502
                | ( [.] z502
                  & <.> <.> [.] <.> ~ z502 )
                | p503
                | ( [.] z503
                  & <.> <.> [.] <.> ~ z503 )
                | p504
                | ( [.] z504
                  & <.> <.> [.] <.> ~ z504 )
                | p505
                | ( [.] z505
                  & <.> <.> [.] <.> ~ z505 )
                | [.] ( p506
                      | ( [.] z506
                        & <.> <.> [.] <.> ~ z506 ) ) )
              & ( p601
                | ( [.] z601
                  & <.> <.> [.] <.> ~ z601 )
                | p602
                | ( [.] z602
                  & <.> <.> [.] <.> ~ z602 )
                | p603
                | ( [.] z603
                  & <.> <.> [.] <.> ~ z603 )
                | p604
                | ( [.] z604
                  & <.> <.> [.] <.> ~ z604 )
                | p605
                | ( [.] z605
                  & <.> <.> [.] <.> ~ z605 )
                | p606
                | ( [.] z606
                  & <.> <.> [.] <.> ~ z606 ) )
              & ( p701
                | ( [.] z701
                  & <.> <.> [.] <.> ~ z701 )
                | p702
                | ( [.] z702
                  & <.> <.> [.] <.> ~ z702 )
                | p703
                | ( [.] z703
                  & <.> <.> [.] <.> ~ z703 )
                | p704
                | ( [.] z704
                  & <.> <.> [.] <.> ~ z704 )
                | p705
                | ( [.] z705
                  & <.> <.> [.] <.> ~ z705 )
                | p706
                | ( [.] z706
                  & <.> <.> [.] <.> ~ z706 ) ) )
        & [.] ( ( ~ p101
                | ( [.] z101
                  & <.> <.> [.] <.> ~ z101 )
                | ~ p201
                | ( [.] z201
                  & <.> <.> [.] <.> ~ z201 ) )
              & ( ~ p101
                | ( [.] z101
                  & <.> <.> [.] <.> ~ z101 )
                | ~ p301
                | ( [.] z301
                  & <.> <.> [.] <.> ~ z301 ) )
              & ( ~ p101
                | ( [.] z101
                  & <.> <.> [.] <.> ~ z101 )
                | ~ p401
                | ( [.] z401
                  & <.> <.> [.] <.> ~ z401 ) )
              & ( ~ p101
                | ( [.] z101
                  & <.> <.> [.] <.> ~ z101 )
                | ~ p501
                | ( [.] z501
                  & <.> <.> [.] <.> ~ z501 ) )
              & ( ~ p101
                | ( [.] z101
                  & <.> <.> [.] <.> ~ z101 )
                | ~ p601
                | ( [.] z601
                  & <.> <.> [.] <.> ~ z601 ) )
              & ( ~ p101
                | ( [.] z101
                  & <.> <.> [.] <.> ~ z101 )
                | ~ p701
                | ( [.] z701
                  & <.> <.> [.] <.> ~ z701 ) )
              & ( ~ p201
                | ( [.] z201
                  & <.> <.> [.] <.> ~ z201 )
                | ~ p301
                | ( [.] z301
                  & <.> <.> [.] <.> ~ z301 ) )
              & ( ~ p201
                | ( [.] z201
                  & <.> <.> [.] <.> ~ z201 )
                | ~ p401
                | ( [.] z401
                  & <.> <.> [.] <.> ~ z401 ) )
              & ( ~ p201
                | ( [.] z201
                  & <.> <.> [.] <.> ~ z201 )
                | ~ p501
                | ( [.] z501
                  & <.> <.> [.] <.> ~ z501 ) )
              & ( ~ p201
                | ( [.] z201
                  & <.> <.> [.] <.> ~ z201 )
                | ~ p601
                | ( [.] z601
                  & <.> <.> [.] <.> ~ z601 ) )
              & ( ~ p201
                | ( [.] z201
                  & <.> <.> [.] <.> ~ z201 )
                | ~ p701
                | ( [.] z701
                  & <.> <.> [.] <.> ~ z701 ) )
              & ( ~ p301
                | ( [.] z301
                  & <.> <.> [.] <.> ~ z301 )
                | ~ p401
                | ( [.] z401
                  & <.> <.> [.] <.> ~ z401 ) )
              & ( ~ p301
                | ( [.] z301
                  & <.> <.> [.] <.> ~ z301 )
                | ~ p501
                | ( [.] z501
                  & <.> <.> [.] <.> ~ z501 ) )
              & ( ~ p301
                | ( [.] z301
                  & <.> <.> [.] <.> ~ z301 )
                | ~ p601
                | ( [.] z601
                  & <.> <.> [.] <.> ~ z601 ) )
              & ( ~ p301
                | ( [.] z301
                  & <.> <.> [.] <.> ~ z301 )
                | ~ p701
                | ( [.] z701
                  & <.> <.> [.] <.> ~ z701 ) )
              & ( ~ p401
                | ( [.] z401
                  & <.> <.> [.] <.> ~ z401 )
                | ~ p501
                | ( [.] z501
                  & <.> <.> [.] <.> ~ z501 ) )
              & ( ~ p401
                | ( [.] z401
                  & <.> <.> [.] <.> ~ z401 )
                | ~ p601
                | ( [.] z601
                  & <.> <.> [.] <.> ~ z601 ) )
              & ( ~ p401
                | ( [.] z401
                  & <.> <.> [.] <.> ~ z401 )
                | ~ p701
                | ( [.] z701
                  & <.> <.> [.] <.> ~ z701 ) )
              & ( ~ p501
                | ( [.] z501
                  & <.> <.> [.] <.> ~ z501 )
                | ~ p601
                | ( [.] z601
                  & <.> <.> [.] <.> ~ z601 ) )
              & ( ~ p501
                | ( [.] z501
                  & <.> <.> [.] <.> ~ z501 )
                | ~ p701
                | ( [.] z701
                  & <.> <.> [.] <.> ~ z701 ) )
              & ( ~ p601
                | ( [.] z601
                  & <.> <.> [.] <.> ~ z601 )
                | ~ p701
                | ( [.] z701
                  & <.> <.> [.] <.> ~ z701 ) )
              & ( <.> ( ~ p102
                      | ( [.] z102
                        & <.> <.> [.] <.> ~ z102 ) )
                | ~ p202
                | ( [.] z202
                  & <.> <.> [.] <.> ~ z202 ) )
              & ( <.> ( ~ p102
                      | ( [.] z102
                        & <.> <.> [.] <.> ~ z102 ) )
                | ~ p302
                | ( [.] z302
                  & <.> <.> [.] <.> ~ z302 ) )
              & ( <.> ( ~ p102
                      | ( [.] z102
                        & <.> <.> [.] <.> ~ z102 ) )
                | ~ p402
                | ( [.] z402
                  & <.> <.> [.] <.> ~ z402 ) )
              & ( <.> ( ~ p102
                      | ( [.] z102
                        & <.> <.> [.] <.> ~ z102 ) )
                | ~ p502
                | ( [.] z502
                  & <.> <.> [.] <.> ~ z502 ) )
              & ( <.> ( ~ p102
                      | ( [.] z102
                        & <.> <.> [.] <.> ~ z102 ) )
                | ~ p602
                | ( [.] z602
                  & <.> <.> [.] <.> ~ z602 ) )
              & ( <.> ( ~ p102
                      | ( [.] z102
                        & <.> <.> [.] <.> ~ z102 ) )
                | ~ p702
                | ( [.] z702
                  & <.> <.> [.] <.> ~ z702 ) )
              & ( ~ p202
                | ( [.] z202
                  & <.> <.> [.] <.> ~ z202 )
                | ~ p302
                | ( [.] z302
                  & <.> <.> [.] <.> ~ z302 ) )
              & ( ~ p202
                | ( [.] z202
                  & <.> <.> [.] <.> ~ z202 )
                | ~ p402
                | ( [.] z402
                  & <.> <.> [.] <.> ~ z402 ) )
              & ( ~ p202
                | ( [.] z202
                  & <.> <.> [.] <.> ~ z202 )
                | ~ p502
                | ( [.] z502
                  & <.> <.> [.] <.> ~ z502 ) )
              & ( ~ p202
                | ( [.] z202
                  & <.> <.> [.] <.> ~ z202 )
                | ~ p602
                | ( [.] z602
                  & <.> <.> [.] <.> ~ z602 ) )
              & ( ~ p202
                | ( [.] z202
                  & <.> <.> [.] <.> ~ z202 )
                | ~ p702
                | ( [.] z702
                  & <.> <.> [.] <.> ~ z702 ) )
              & ( ~ p302
                | ( [.] z302
                  & <.> <.> [.] <.> ~ z302 )
                | ~ p402
                | ( [.] z402
                  & <.> <.> [.] <.> ~ z402 ) )
              & ( ~ p302
                | ( [.] z302
                  & <.> <.> [.] <.> ~ z302 )
                | ~ p502
                | ( [.] z502
                  & <.> <.> [.] <.> ~ z502 ) )
              & ( ~ p302
                | ( [.] z302
                  & <.> <.> [.] <.> ~ z302 )
                | ~ p602
                | ( [.] z602
                  & <.> <.> [.] <.> ~ z602 ) )
              & ( ~ p302
                | ( [.] z302
                  & <.> <.> [.] <.> ~ z302 )
                | ~ p702
                | ( [.] z702
                  & <.> <.> [.] <.> ~ z702 ) )
              & ( ~ p402
                | ( [.] z402
                  & <.> <.> [.] <.> ~ z402 )
                | ~ p502
                | ( [.] z502
                  & <.> <.> [.] <.> ~ z502 ) )
              & ( ~ p402
                | ( [.] z402
                  & <.> <.> [.] <.> ~ z402 )
                | ~ p602
                | ( [.] z602
                  & <.> <.> [.] <.> ~ z602 ) )
              & ( ~ p402
                | ( [.] z402
                  & <.> <.> [.] <.> ~ z402 )
                | ~ p702
                | ( [.] z702
                  & <.> <.> [.] <.> ~ z702 ) )
              & ( ~ p502
                | ( [.] z502
                  & <.> <.> [.] <.> ~ z502 )
                | ~ p602
                | ( [.] z602
                  & <.> <.> [.] <.> ~ z602 ) )
              & ( ~ p502
                | ( [.] z502
                  & <.> <.> [.] <.> ~ z502 )
                | ~ p702
                | ( [.] z702
                  & <.> <.> [.] <.> ~ z702 ) )
              & ( ~ p602
                | ( [.] z602
                  & <.> <.> [.] <.> ~ z602 )
                | ~ p702
                | ( [.] z702
                  & <.> <.> [.] <.> ~ z702 ) )
              & ( <.> ( ~ p103
                      | ( [.] z103
                        & <.> <.> [.] <.> ~ z103 ) )
                | <.> ( ~ p203
                      | ( [.] z203
                        & <.> <.> [.] <.> ~ z203 ) ) )
              & ( <.> ( ~ p103
                      | ( [.] z103
                        & <.> <.> [.] <.> ~ z103 ) )
                | ~ p303
                | ( [.] z303
                  & <.> <.> [.] <.> ~ z303 ) )
              & ( <.> ( ~ p103
                      | ( [.] z103
                        & <.> <.> [.] <.> ~ z103 ) )
                | ~ p403
                | ( [.] z403
                  & <.> <.> [.] <.> ~ z403 ) )
              & ( <.> ( ~ p103
                      | ( [.] z103
                        & <.> <.> [.] <.> ~ z103 ) )
                | ~ p503
                | ( [.] z503
                  & <.> <.> [.] <.> ~ z503 ) )
              & ( <.> ( ~ p103
                      | ( [.] z103
                        & <.> <.> [.] <.> ~ z103 ) )
                | ~ p603
                | ( [.] z603
                  & <.> <.> [.] <.> ~ z603 ) )
              & ( <.> ( ~ p103
                      | ( [.] z103
                        & <.> <.> [.] <.> ~ z103 ) )
                | ~ p703
                | ( [.] z703
                  & <.> <.> [.] <.> ~ z703 ) )
              & ( <.> ( ~ p203
                      | ( [.] z203
                        & <.> <.> [.] <.> ~ z203 ) )
                | ~ p303
                | ( [.] z303
                  & <.> <.> [.] <.> ~ z303 ) )
              & ( <.> ( ~ p203
                      | ( [.] z203
                        & <.> <.> [.] <.> ~ z203 ) )
                | ~ p403
                | ( [.] z403
                  & <.> <.> [.] <.> ~ z403 ) )
              & ( <.> ( ~ p203
                      | ( [.] z203
                        & <.> <.> [.] <.> ~ z203 ) )
                | ~ p503
                | ( [.] z503
                  & <.> <.> [.] <.> ~ z503 ) )
              & ( <.> ( ~ p203
                      | ( [.] z203
                        & <.> <.> [.] <.> ~ z203 ) )
                | ~ p603
                | ( [.] z603
                  & <.> <.> [.] <.> ~ z603 ) )
              & ( <.> ( ~ p203
                      | ( [.] z203
                        & <.> <.> [.] <.> ~ z203 ) )
                | ~ p703
                | ( [.] z703
                  & <.> <.> [.] <.> ~ z703 ) )
              & ( ~ p303
                | ( [.] z303
                  & <.> <.> [.] <.> ~ z303 )
                | ~ p403
                | ( [.] z403
                  & <.> <.> [.] <.> ~ z403 ) )
              & ( ~ p303
                | ( [.] z303
                  & <.> <.> [.] <.> ~ z303 )
                | ~ p503
                | ( [.] z503
                  & <.> <.> [.] <.> ~ z503 ) )
              & ( ~ p303
                | ( [.] z303
                  & <.> <.> [.] <.> ~ z303 )
                | ~ p603
                | ( [.] z603
                  & <.> <.> [.] <.> ~ z603 ) )
              & ( ~ p303
                | ( [.] z303
                  & <.> <.> [.] <.> ~ z303 )
                | ~ p703
                | ( [.] z703
                  & <.> <.> [.] <.> ~ z703 ) )
              & ( ~ p403
                | ( [.] z403
                  & <.> <.> [.] <.> ~ z403 )
                | ~ p503
                | ( [.] z503
                  & <.> <.> [.] <.> ~ z503 ) )
              & ( ~ p403
                | ( [.] z403
                  & <.> <.> [.] <.> ~ z403 )
                | ~ p603
                | ( [.] z603
                  & <.> <.> [.] <.> ~ z603 ) )
              & ( ~ p403
                | ( [.] z403
                  & <.> <.> [.] <.> ~ z403 )
                | ~ p703
                | ( [.] z703
                  & <.> <.> [.] <.> ~ z703 ) )
              & ( ~ p503
                | ( [.] z503
                  & <.> <.> [.] <.> ~ z503 )
                | ~ p603
                | ( [.] z603
                  & <.> <.> [.] <.> ~ z603 ) )
              & ( ~ p503
                | ( [.] z503
                  & <.> <.> [.] <.> ~ z503 )
                | ~ p703
                | ( [.] z703
                  & <.> <.> [.] <.> ~ z703 ) )
              & ( ~ p603
                | ( [.] z603
                  & <.> <.> [.] <.> ~ z603 )
                | ~ p703
                | ( [.] z703
                  & <.> <.> [.] <.> ~ z703 ) )
              & ( <.> ( ~ p104
                      | ( [.] z104
                        & <.> <.> [.] <.> ~ z104 ) )
                | <.> ( ~ p204
                      | ( [.] z204
                        & <.> <.> [.] <.> ~ z204 ) ) )
              & ( <.> ( ~ p104
                      | ( [.] z104
                        & <.> <.> [.] <.> ~ z104 ) )
                | <.> ( ~ p304
                      | ( [.] z304
                        & <.> <.> [.] <.> ~ z304 ) ) )
              & ( <.> ( ~ p104
                      | ( [.] z104
                        & <.> <.> [.] <.> ~ z104 ) )
                | ~ p404
                | ( [.] z404
                  & <.> <.> [.] <.> ~ z404 ) )
              & ( <.> ( ~ p104
                      | ( [.] z104
                        & <.> <.> [.] <.> ~ z104 ) )
                | ~ p504
                | ( [.] z504
                  & <.> <.> [.] <.> ~ z504 ) )
              & ( <.> ( ~ p104
                      | ( [.] z104
                        & <.> <.> [.] <.> ~ z104 ) )
                | ~ p604
                | ( [.] z604
                  & <.> <.> [.] <.> ~ z604 ) )
              & ( <.> ( ~ p104
                      | ( [.] z104
                        & <.> <.> [.] <.> ~ z104 ) )
                | ~ p704
                | ( [.] z704
                  & <.> <.> [.] <.> ~ z704 ) )
              & ( <.> ( ~ p204
                      | ( [.] z204
                        & <.> <.> [.] <.> ~ z204 ) )
                | <.> ( ~ p304
                      | ( [.] z304
                        & <.> <.> [.] <.> ~ z304 ) ) )
              & ( <.> ( ~ p204
                      | ( [.] z204
                        & <.> <.> [.] <.> ~ z204 ) )
                | ~ p404
                | ( [.] z404
                  & <.> <.> [.] <.> ~ z404 ) )
              & ( <.> ( ~ p204
                      | ( [.] z204
                        & <.> <.> [.] <.> ~ z204 ) )
                | ~ p504
                | ( [.] z504
                  & <.> <.> [.] <.> ~ z504 ) )
              & ( <.> ( ~ p204
                      | ( [.] z204
                        & <.> <.> [.] <.> ~ z204 ) )
                | ~ p604
                | ( [.] z604
                  & <.> <.> [.] <.> ~ z604 ) )
              & ( <.> ( ~ p204
                      | ( [.] z204
                        & <.> <.> [.] <.> ~ z204 ) )
                | ~ p704
                | ( [.] z704
                  & <.> <.> [.] <.> ~ z704 ) )
              & ( <.> ( ~ p304
                      | ( [.] z304
                        & <.> <.> [.] <.> ~ z304 ) )
                | ~ p404
                | ( [.] z404
                  & <.> <.> [.] <.> ~ z404 ) )
              & ( <.> ( ~ p304
                      | ( [.] z304
                        & <.> <.> [.] <.> ~ z304 ) )
                | ~ p504
                | ( [.] z504
                  & <.> <.> [.] <.> ~ z504 ) )
              & ( <.> ( ~ p304
                      | ( [.] z304
                        & <.> <.> [.] <.> ~ z304 ) )
                | ~ p604
                | ( [.] z604
                  & <.> <.> [.] <.> ~ z604 ) )
              & ( <.> ( ~ p304
                      | ( [.] z304
                        & <.> <.> [.] <.> ~ z304 ) )
                | ~ p704
                | ( [.] z704
                  & <.> <.> [.] <.> ~ z704 ) )
              & ( ~ p404
                | ( [.] z404
                  & <.> <.> [.] <.> ~ z404 )
                | ~ p504
                | ( [.] z504
                  & <.> <.> [.] <.> ~ z504 ) )
              & ( ~ p404
                | ( [.] z404
                  & <.> <.> [.] <.> ~ z404 )
                | ~ p604
                | ( [.] z604
                  & <.> <.> [.] <.> ~ z604 ) )
              & ( ~ p404
                | ( [.] z404
                  & <.> <.> [.] <.> ~ z404 )
                | ~ p704
                | ( [.] z704
                  & <.> <.> [.] <.> ~ z704 ) )
              & ( ~ p504
                | ( [.] z504
                  & <.> <.> [.] <.> ~ z504 )
                | ~ p604
                | ( [.] z604
                  & <.> <.> [.] <.> ~ z604 ) )
              & ( ~ p504
                | ( [.] z504
                  & <.> <.> [.] <.> ~ z504 )
                | ~ p704
                | ( [.] z704
                  & <.> <.> [.] <.> ~ z704 ) )
              & ( ~ p604
                | ( [.] z604
                  & <.> <.> [.] <.> ~ z604 )
                | ~ p704
                | ( [.] z704
                  & <.> <.> [.] <.> ~ z704 ) )
              & ( <.> ( ~ p105
                      | ( [.] z105
                        & <.> <.> [.] <.> ~ z105 ) )
                | <.> ( ~ p205
                      | ( [.] z205
                        & <.> <.> [.] <.> ~ z205 ) ) )
              & ( <.> ( ~ p105
                      | ( [.] z105
                        & <.> <.> [.] <.> ~ z105 ) )
                | <.> ( ~ p305
                      | ( [.] z305
                        & <.> <.> [.] <.> ~ z305 ) ) )
              & ( <.> ( ~ p105
                      | ( [.] z105
                        & <.> <.> [.] <.> ~ z105 ) )
                | <.> ( ~ p405
                      | ( [.] z405
                        & <.> <.> [.] <.> ~ z405 ) ) )
              & ( <.> ( ~ p105
                      | ( [.] z105
                        & <.> <.> [.] <.> ~ z105 ) )
                | ~ p505
                | ( [.] z505
                  & <.> <.> [.] <.> ~ z505 ) )
              & ( <.> ( ~ p105
                      | ( [.] z105
                        & <.> <.> [.] <.> ~ z105 ) )
                | ~ p605
                | ( [.] z605
                  & <.> <.> [.] <.> ~ z605 ) )
              & ( <.> ( ~ p105
                      | ( [.] z105
                        & <.> <.> [.] <.> ~ z105 ) )
                | ~ p705
                | ( [.] z705
                  & <.> <.> [.] <.> ~ z705 ) )
              & ( <.> ( ~ p205
                      | ( [.] z205
                        & <.> <.> [.] <.> ~ z205 ) )
                | <.> ( ~ p305
                      | ( [.] z305
                        & <.> <.> [.] <.> ~ z305 ) ) )
              & ( <.> ( ~ p205
                      | ( [.] z205
                        & <.> <.> [.] <.> ~ z205 ) )
                | <.> ( ~ p405
                      | ( [.] z405
                        & <.> <.> [.] <.> ~ z405 ) ) )
              & ( <.> ( ~ p205
                      | ( [.] z205
                        & <.> <.> [.] <.> ~ z205 ) )
                | ~ p505
                | ( [.] z505
                  & <.> <.> [.] <.> ~ z505 ) )
              & ( <.> ( ~ p205
                      | ( [.] z205
                        & <.> <.> [.] <.> ~ z205 ) )
                | ~ p605
                | ( [.] z605
                  & <.> <.> [.] <.> ~ z605 ) )
              & ( <.> ( ~ p205
                      | ( [.] z205
                        & <.> <.> [.] <.> ~ z205 ) )
                | ~ p705
                | ( [.] z705
                  & <.> <.> [.] <.> ~ z705 ) )
              & ( <.> ( ~ p305
                      | ( [.] z305
                        & <.> <.> [.] <.> ~ z305 ) )
                | <.> ( ~ p405
                      | ( [.] z405
                        & <.> <.> [.] <.> ~ z405 ) ) )
              & ( <.> ( ~ p305
                      | ( [.] z305
                        & <.> <.> [.] <.> ~ z305 ) )
                | ~ p505
                | ( [.] z505
                  & <.> <.> [.] <.> ~ z505 ) )
              & ( <.> ( ~ p305
                      | ( [.] z305
                        & <.> <.> [.] <.> ~ z305 ) )
                | ~ p605
                | ( [.] z605
                  & <.> <.> [.] <.> ~ z605 ) )
              & ( <.> ( ~ p305
                      | ( [.] z305
                        & <.> <.> [.] <.> ~ z305 ) )
                | ~ p705
                | ( [.] z705
                  & <.> <.> [.] <.> ~ z705 ) )
              & ( <.> ( ~ p405
                      | ( [.] z405
                        & <.> <.> [.] <.> ~ z405 ) )
                | ~ p505
                | ( [.] z505
                  & <.> <.> [.] <.> ~ z505 ) )
              & ( <.> ( ~ p405
                      | ( [.] z405
                        & <.> <.> [.] <.> ~ z405 ) )
                | ~ p605
                | ( [.] z605
                  & <.> <.> [.] <.> ~ z605 ) )
              & ( <.> ( ~ p405
                      | ( [.] z405
                        & <.> <.> [.] <.> ~ z405 ) )
                | ~ p705
                | ( [.] z705
                  & <.> <.> [.] <.> ~ z705 ) )
              & ( ~ p505
                | ( [.] z505
                  & <.> <.> [.] <.> ~ z505 )
                | ~ p605
                | ( [.] z605
                  & <.> <.> [.] <.> ~ z605 ) )
              & ( ~ p505
                | ( [.] z505
                  & <.> <.> [.] <.> ~ z505 )
                | ~ p705
                | ( [.] z705
                  & <.> <.> [.] <.> ~ z705 ) )
              & ( ~ p605
                | ( [.] z605
                  & <.> <.> [.] <.> ~ z605 )
                | ~ p705
                | ( [.] z705
                  & <.> <.> [.] <.> ~ z705 ) )
              & ( <.> ( ~ p106
                      | ( [.] z106
                        & <.> <.> [.] <.> ~ z106 ) )
                | <.> ( ~ p206
                      | ( [.] z206
                        & <.> <.> [.] <.> ~ z206 ) ) )
              & ( <.> ( ~ p106
                      | ( [.] z106
                        & <.> <.> [.] <.> ~ z106 ) )
                | <.> ( ~ p306
                      | ( [.] z306
                        & <.> <.> [.] <.> ~ z306 ) ) )
              & ( <.> ( ~ p106
                      | ( [.] z106
                        & <.> <.> [.] <.> ~ z106 ) )
                | <.> ( ~ p406
                      | ( [.] z406
                        & <.> <.> [.] <.> ~ z406 ) ) )
              & ( <.> ( ~ p106
                      | ( [.] z106
                        & <.> <.> [.] <.> ~ z106 ) )
                | <.> ( ~ p506
                      | ( [.] z506
                        & <.> <.> [.] <.> ~ z506 ) ) )
              & ( <.> ( ~ p106
                      | ( [.] z106
                        & <.> <.> [.] <.> ~ z106 ) )
                | ~ p606
                | ( [.] z606
                  & <.> <.> [.] <.> ~ z606 ) )
              & ( <.> ( ~ p106
                      | ( [.] z106
                        & <.> <.> [.] <.> ~ z106 ) )
                | ~ p706
                | ( [.] z706
                  & <.> <.> [.] <.> ~ z706 ) )
              & ( <.> ( ~ p206
                      | ( [.] z206
                        & <.> <.> [.] <.> ~ z206 ) )
                | <.> ( ~ p306
                      | ( [.] z306
                        & <.> <.> [.] <.> ~ z306 ) ) )
              & ( <.> ( ~ p206
                      | ( [.] z206
                        & <.> <.> [.] <.> ~ z206 ) )
                | <.> ( ~ p406
                      | ( [.] z406
                        & <.> <.> [.] <.> ~ z406 ) ) )
              & ( <.> ( ~ p206
                      | ( [.] z206
                        & <.> <.> [.] <.> ~ z206 ) )
                | <.> ( ~ p506
                      | ( [.] z506
                        & <.> <.> [.] <.> ~ z506 ) ) )
              & ( <.> ( ~ p206
                      | ( [.] z206
                        & <.> <.> [.] <.> ~ z206 ) )
                | ~ p606
                | ( [.] z606
                  & <.> <.> [.] <.> ~ z606 ) )
              & ( <.> ( ~ p206
                      | ( [.] z206
                        & <.> <.> [.] <.> ~ z206 ) )
                | ~ p706
                | ( [.] z706
                  & <.> <.> [.] <.> ~ z706 ) )
              & ( <.> ( ~ p306
                      | ( [.] z306
                        & <.> <.> [.] <.> ~ z306 ) )
                | <.> ( ~ p406
                      | ( [.] z406
                        & <.> <.> [.] <.> ~ z406 ) ) )
              & ( <.> ( ~ p306
                      | ( [.] z306
                        & <.> <.> [.] <.> ~ z306 ) )
                | <.> ( ~ p506
                      | ( [.] z506
                        & <.> <.> [.] <.> ~ z506 ) ) )
              & ( <.> ( ~ p306
                      | ( [.] z306
                        & <.> <.> [.] <.> ~ z306 ) )
                | ~ p606
                | ( [.] z606
                  & <.> <.> [.] <.> ~ z606 ) )
              & ( <.> ( ~ p306
                      | ( [.] z306
                        & <.> <.> [.] <.> ~ z306 ) )
                | ~ p706
                | ( [.] z706
                  & <.> <.> [.] <.> ~ z706 ) )
              & ( <.> ( ~ p406
                      | ( [.] z406
                        & <.> <.> [.] <.> ~ z406 ) )
                | <.> ( ~ p506
                      | ( [.] z506
                        & <.> <.> [.] <.> ~ z506 ) ) )
              & ( <.> ( ~ p406
                      | ( [.] z406
                        & <.> <.> [.] <.> ~ z406 ) )
                | ~ p606
                | ( [.] z606
                  & <.> <.> [.] <.> ~ z606 ) )
              & ( <.> ( ~ p406
                      | ( [.] z406
                        & <.> <.> [.] <.> ~ z406 ) )
                | ~ p706
                | ( [.] z706
                  & <.> <.> [.] <.> ~ z706 ) )
              & ( <.> ( ~ p506
                      | ( [.] z506
                        & <.> <.> [.] <.> ~ z506 ) )
                | ~ p606
                | ( [.] z606
                  & <.> <.> [.] <.> ~ z606 ) )
              & ( <.> ( ~ p506
                      | ( [.] z506
                        & <.> <.> [.] <.> ~ z506 ) )
                | ~ p706
                | ( [.] z706
                  & <.> <.> [.] <.> ~ z706 ) )
              & ( ~ p606
                | ( [.] z606
                  & <.> <.> [.] <.> ~ z606 )
                | ~ p706
                | ( [.] z706
                  & <.> <.> [.] <.> ~ z706 ) ) ) ) ) ).

%------------------------------------------------------------------------------