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 ) ) ) ) ) ).
%------------------------------------------------------------------------------