%------------------------------------------------------------------------------
% File : LCL973_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 : k45_ph_p.0006 [Nal22]
% Status : Theorem
% Rating : 1.00 v9.0.0
% Syntax : Number of formulae : 127 ( 0 unt; 126 typ; 0 def)
% Number of atoms : 1470 ( 0 equ)
% Maximal formula atoms : 1470 (1470 avg)
% Number of connectives : 3887 ( 841 ~; 749 |; 720 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% (1577 {.}; 0 {#})
% Maximal formula depth : 138 ( 138 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 : 126 ( 126 usr; 126 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 (; 0 !; 0 ?; 0 :)
% SPC : NX0_THM_PRP_NEQ_NAR
% Comments :
%------------------------------------------------------------------------------
tff('k45_ph_p.0006',logic,
$modal ==
[ $modalities == $modal_system_K45 ] ).
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(y101_decl,type,
y101: $o ).
tff(y102_decl,type,
y102: $o ).
tff(y103_decl,type,
y103: $o ).
tff(y104_decl,type,
y104: $o ).
tff(y105_decl,type,
y105: $o ).
tff(y106_decl,type,
y106: $o ).
tff(y201_decl,type,
y201: $o ).
tff(y202_decl,type,
y202: $o ).
tff(y203_decl,type,
y203: $o ).
tff(y204_decl,type,
y204: $o ).
tff(y205_decl,type,
y205: $o ).
tff(y206_decl,type,
y206: $o ).
tff(y301_decl,type,
y301: $o ).
tff(y302_decl,type,
y302: $o ).
tff(y303_decl,type,
y303: $o ).
tff(y304_decl,type,
y304: $o ).
tff(y305_decl,type,
y305: $o ).
tff(y306_decl,type,
y306: $o ).
tff(y401_decl,type,
y401: $o ).
tff(y402_decl,type,
y402: $o ).
tff(y403_decl,type,
y403: $o ).
tff(y404_decl,type,
y404: $o ).
tff(y405_decl,type,
y405: $o ).
tff(y406_decl,type,
y406: $o ).
tff(y501_decl,type,
y501: $o ).
tff(y502_decl,type,
y502: $o ).
tff(y503_decl,type,
y503: $o ).
tff(y504_decl,type,
y504: $o ).
tff(y505_decl,type,
y505: $o ).
tff(y506_decl,type,
y506: $o ).
tff(y601_decl,type,
y601: $o ).
tff(y602_decl,type,
y602: $o ).
tff(y603_decl,type,
y603: $o ).
tff(y604_decl,type,
y604: $o ).
tff(y605_decl,type,
y605: $o ).
tff(y606_decl,type,
y606: $o ).
tff(y701_decl,type,
y701: $o ).
tff(y702_decl,type,
y702: $o ).
tff(y703_decl,type,
y703: $o ).
tff(y704_decl,type,
y704: $o ).
tff(y705_decl,type,
y705: $o ).
tff(y706_decl,type,
y706: $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,
~ ( <.> ( ( p101
| ( [.] z101
& <.> [.] y101
& <.> <.> ( ~ z101
| ~ y101 ) )
| [.] ( p102
| ( [.] z102
& <.> [.] y102
& <.> <.> ( ~ z102
| ~ y102 ) ) )
| [.] ( p103
| ( [.] z103
& <.> [.] y103
& <.> <.> ( ~ z103
| ~ y103 ) ) )
| [.] ( p104
| ( [.] z104
& <.> [.] y104
& <.> <.> ( ~ z104
| ~ y104 ) ) )
| [.] ( p105
| ( [.] z105
& <.> [.] y105
& <.> <.> ( ~ z105
| ~ y105 ) ) )
| [.] ( p106
| ( [.] z106
& <.> [.] y106
& <.> <.> ( ~ z106
| ~ y106 ) ) ) )
& ( p201
| ( [.] z201
& <.> [.] y201
& <.> <.> ( ~ z201
| ~ y201 ) )
| p202
| ( [.] z202
& <.> [.] y202
& <.> <.> ( ~ z202
| ~ y202 ) )
| [.] ( p203
| ( [.] z203
& <.> [.] y203
& <.> <.> ( ~ z203
| ~ y203 ) ) )
| [.] ( p204
| ( [.] z204
& <.> [.] y204
& <.> <.> ( ~ z204
| ~ y204 ) ) )
| [.] ( p205
| ( [.] z205
& <.> [.] y205
& <.> <.> ( ~ z205
| ~ y205 ) ) )
| [.] ( p206
| ( [.] z206
& <.> [.] y206
& <.> <.> ( ~ z206
| ~ y206 ) ) ) )
& ( p301
| ( [.] z301
& <.> [.] y301
& <.> <.> ( ~ z301
| ~ y301 ) )
| p302
| ( [.] z302
& <.> [.] y302
& <.> <.> ( ~ z302
| ~ y302 ) )
| p303
| ( [.] z303
& <.> [.] y303
& <.> <.> ( ~ z303
| ~ y303 ) )
| [.] ( p304
| ( [.] z304
& <.> [.] y304
& <.> <.> ( ~ z304
| ~ y304 ) ) )
| [.] ( p305
| ( [.] z305
& <.> [.] y305
& <.> <.> ( ~ z305
| ~ y305 ) ) )
| [.] ( p306
| ( [.] z306
& <.> [.] y306
& <.> <.> ( ~ z306
| ~ y306 ) ) ) )
& ( p401
| ( [.] z401
& <.> [.] y401
& <.> <.> ( ~ z401
| ~ y401 ) )
| p402
| ( [.] z402
& <.> [.] y402
& <.> <.> ( ~ z402
| ~ y402 ) )
| p403
| ( [.] z403
& <.> [.] y403
& <.> <.> ( ~ z403
| ~ y403 ) )
| p404
| ( [.] z404
& <.> [.] y404
& <.> <.> ( ~ z404
| ~ y404 ) )
| [.] ( p405
| ( [.] z405
& <.> [.] y405
& <.> <.> ( ~ z405
| ~ y405 ) ) )
| [.] ( p406
| ( [.] z406
& <.> [.] y406
& <.> <.> ( ~ z406
| ~ y406 ) ) ) )
& ( p501
| ( [.] z501
& <.> [.] y501
& <.> <.> ( ~ z501
| ~ y501 ) )
| p502
| ( [.] z502
& <.> [.] y502
& <.> <.> ( ~ z502
| ~ y502 ) )
| p503
| ( [.] z503
& <.> [.] y503
& <.> <.> ( ~ z503
| ~ y503 ) )
| p504
| ( [.] z504
& <.> [.] y504
& <.> <.> ( ~ z504
| ~ y504 ) )
| p505
| ( [.] z505
& <.> [.] y505
& <.> <.> ( ~ z505
| ~ y505 ) )
| [.] ( p506
| ( [.] z506
& <.> [.] y506
& <.> <.> ( ~ z506
| ~ y506 ) ) ) )
& ( p601
| ( [.] z601
& <.> [.] y601
& <.> <.> ( ~ z601
| ~ y601 ) )
| p602
| ( [.] z602
& <.> [.] y602
& <.> <.> ( ~ z602
| ~ y602 ) )
| p603
| ( [.] z603
& <.> [.] y603
& <.> <.> ( ~ z603
| ~ y603 ) )
| p604
| ( [.] z604
& <.> [.] y604
& <.> <.> ( ~ z604
| ~ y604 ) )
| p605
| ( [.] z605
& <.> [.] y605
& <.> <.> ( ~ z605
| ~ y605 ) )
| p606
| ( [.] z606
& <.> [.] y606
& <.> <.> ( ~ z606
| ~ y606 ) ) )
& ( p701
| ( [.] z701
& <.> [.] y701
& <.> <.> ( ~ z701
| ~ y701 ) )
| p702
| ( [.] z702
& <.> [.] y702
& <.> <.> ( ~ z702
| ~ y702 ) )
| p703
| ( [.] z703
& <.> [.] y703
& <.> <.> ( ~ z703
| ~ y703 ) )
| p704
| ( [.] z704
& <.> [.] y704
& <.> <.> ( ~ z704
| ~ y704 ) )
| p705
| ( [.] z705
& <.> [.] y705
& <.> <.> ( ~ z705
| ~ y705 ) )
| p706
| ( [.] z706
& <.> [.] y706
& <.> <.> ( ~ z706
| ~ y706 ) ) ) )
& [.] ( ( ~ p101
| ( [.] z101
& <.> [.] y101
& <.> <.> ( ~ z101
| ~ y101 ) )
| ~ p201
| ( [.] z201
& <.> [.] y201
& <.> <.> ( ~ z201
| ~ y201 ) ) )
& ( ~ p101
| ( [.] z101
& <.> [.] y101
& <.> <.> ( ~ z101
| ~ y101 ) )
| ~ p301
| ( [.] z301
& <.> [.] y301
& <.> <.> ( ~ z301
| ~ y301 ) ) )
& ( ~ p101
| ( [.] z101
& <.> [.] y101
& <.> <.> ( ~ z101
| ~ y101 ) )
| ~ p401
| ( [.] z401
& <.> [.] y401
& <.> <.> ( ~ z401
| ~ y401 ) ) )
& ( ~ p101
| ( [.] z101
& <.> [.] y101
& <.> <.> ( ~ z101
| ~ y101 ) )
| ~ p501
| ( [.] z501
& <.> [.] y501
& <.> <.> ( ~ z501
| ~ y501 ) ) )
& ( ~ p101
| ( [.] z101
& <.> [.] y101
& <.> <.> ( ~ z101
| ~ y101 ) )
| ~ p601
| ( [.] z601
& <.> [.] y601
& <.> <.> ( ~ z601
| ~ y601 ) ) )
& ( ~ p101
| ( [.] z101
& <.> [.] y101
& <.> <.> ( ~ z101
| ~ y101 ) )
| ~ p701
| ( [.] z701
& <.> [.] y701
& <.> <.> ( ~ z701
| ~ y701 ) ) )
& ( ~ p201
| ( [.] z201
& <.> [.] y201
& <.> <.> ( ~ z201
| ~ y201 ) )
| ~ p301
| ( [.] z301
& <.> [.] y301
& <.> <.> ( ~ z301
| ~ y301 ) ) )
& ( ~ p201
| ( [.] z201
& <.> [.] y201
& <.> <.> ( ~ z201
| ~ y201 ) )
| ~ p401
| ( [.] z401
& <.> [.] y401
& <.> <.> ( ~ z401
| ~ y401 ) ) )
& ( ~ p201
| ( [.] z201
& <.> [.] y201
& <.> <.> ( ~ z201
| ~ y201 ) )
| ~ p501
| ( [.] z501
& <.> [.] y501
& <.> <.> ( ~ z501
| ~ y501 ) ) )
& ( ~ p201
| ( [.] z201
& <.> [.] y201
& <.> <.> ( ~ z201
| ~ y201 ) )
| ~ p601
| ( [.] z601
& <.> [.] y601
& <.> <.> ( ~ z601
| ~ y601 ) ) )
& ( ~ p201
| ( [.] z201
& <.> [.] y201
& <.> <.> ( ~ z201
| ~ y201 ) )
| ~ p701
| ( [.] z701
& <.> [.] y701
& <.> <.> ( ~ z701
| ~ y701 ) ) )
& ( ~ p301
| ( [.] z301
& <.> [.] y301
& <.> <.> ( ~ z301
| ~ y301 ) )
| ~ p401
| ( [.] z401
& <.> [.] y401
& <.> <.> ( ~ z401
| ~ y401 ) ) )
& ( ~ p301
| ( [.] z301
& <.> [.] y301
& <.> <.> ( ~ z301
| ~ y301 ) )
| ~ p501
| ( [.] z501
& <.> [.] y501
& <.> <.> ( ~ z501
| ~ y501 ) ) )
& ( ~ p301
| ( [.] z301
& <.> [.] y301
& <.> <.> ( ~ z301
| ~ y301 ) )
| ~ p601
| ( [.] z601
& <.> [.] y601
& <.> <.> ( ~ z601
| ~ y601 ) ) )
& ( ~ p301
| ( [.] z301
& <.> [.] y301
& <.> <.> ( ~ z301
| ~ y301 ) )
| ~ p701
| ( [.] z701
& <.> [.] y701
& <.> <.> ( ~ z701
| ~ y701 ) ) )
& ( ~ p401
| ( [.] z401
& <.> [.] y401
& <.> <.> ( ~ z401
| ~ y401 ) )
| ~ p501
| ( [.] z501
& <.> [.] y501
& <.> <.> ( ~ z501
| ~ y501 ) ) )
& ( ~ p401
| ( [.] z401
& <.> [.] y401
& <.> <.> ( ~ z401
| ~ y401 ) )
| ~ p601
| ( [.] z601
& <.> [.] y601
& <.> <.> ( ~ z601
| ~ y601 ) ) )
& ( ~ p401
| ( [.] z401
& <.> [.] y401
& <.> <.> ( ~ z401
| ~ y401 ) )
| ~ p701
| ( [.] z701
& <.> [.] y701
& <.> <.> ( ~ z701
| ~ y701 ) ) )
& ( ~ p501
| ( [.] z501
& <.> [.] y501
& <.> <.> ( ~ z501
| ~ y501 ) )
| ~ p601
| ( [.] z601
& <.> [.] y601
& <.> <.> ( ~ z601
| ~ y601 ) ) )
& ( ~ p501
| ( [.] z501
& <.> [.] y501
& <.> <.> ( ~ z501
| ~ y501 ) )
| ~ p701
| ( [.] z701
& <.> [.] y701
& <.> <.> ( ~ z701
| ~ y701 ) ) )
& ( ~ p601
| ( [.] z601
& <.> [.] y601
& <.> <.> ( ~ z601
| ~ y601 ) )
| ~ p701
| ( [.] z701
& <.> [.] y701
& <.> <.> ( ~ z701
| ~ y701 ) ) )
& ( <.> ( ~ p102
| ( [.] z102
& <.> [.] y102
& <.> <.> ( ~ z102
| ~ y102 ) ) )
| ~ p202
| ( [.] z202
& <.> [.] y202
& <.> <.> ( ~ z202
| ~ y202 ) ) )
& ( <.> ( ~ p102
| ( [.] z102
& <.> [.] y102
& <.> <.> ( ~ z102
| ~ y102 ) ) )
| ~ p302
| ( [.] z302
& <.> [.] y302
& <.> <.> ( ~ z302
| ~ y302 ) ) )
& ( <.> ( ~ p102
| ( [.] z102
& <.> [.] y102
& <.> <.> ( ~ z102
| ~ y102 ) ) )
| ~ p402
| ( [.] z402
& <.> [.] y402
& <.> <.> ( ~ z402
| ~ y402 ) ) )
& ( <.> ( ~ p102
| ( [.] z102
& <.> [.] y102
& <.> <.> ( ~ z102
| ~ y102 ) ) )
| ~ p502
| ( [.] z502
& <.> [.] y502
& <.> <.> ( ~ z502
| ~ y502 ) ) )
& ( <.> ( ~ p102
| ( [.] z102
& <.> [.] y102
& <.> <.> ( ~ z102
| ~ y102 ) ) )
| ~ p602
| ( [.] z602
& <.> [.] y602
& <.> <.> ( ~ z602
| ~ y602 ) ) )
& ( <.> ( ~ p102
| ( [.] z102
& <.> [.] y102
& <.> <.> ( ~ z102
| ~ y102 ) ) )
| ~ p702
| ( [.] z702
& <.> [.] y702
& <.> <.> ( ~ z702
| ~ y702 ) ) )
& ( ~ p202
| ( [.] z202
& <.> [.] y202
& <.> <.> ( ~ z202
| ~ y202 ) )
| ~ p302
| ( [.] z302
& <.> [.] y302
& <.> <.> ( ~ z302
| ~ y302 ) ) )
& ( ~ p202
| ( [.] z202
& <.> [.] y202
& <.> <.> ( ~ z202
| ~ y202 ) )
| ~ p402
| ( [.] z402
& <.> [.] y402
& <.> <.> ( ~ z402
| ~ y402 ) ) )
& ( ~ p202
| ( [.] z202
& <.> [.] y202
& <.> <.> ( ~ z202
| ~ y202 ) )
| ~ p502
| ( [.] z502
& <.> [.] y502
& <.> <.> ( ~ z502
| ~ y502 ) ) )
& ( ~ p202
| ( [.] z202
& <.> [.] y202
& <.> <.> ( ~ z202
| ~ y202 ) )
| ~ p602
| ( [.] z602
& <.> [.] y602
& <.> <.> ( ~ z602
| ~ y602 ) ) )
& ( ~ p202
| ( [.] z202
& <.> [.] y202
& <.> <.> ( ~ z202
| ~ y202 ) )
| ~ p702
| ( [.] z702
& <.> [.] y702
& <.> <.> ( ~ z702
| ~ y702 ) ) )
& ( ~ p302
| ( [.] z302
& <.> [.] y302
& <.> <.> ( ~ z302
| ~ y302 ) )
| ~ p402
| ( [.] z402
& <.> [.] y402
& <.> <.> ( ~ z402
| ~ y402 ) ) )
& ( ~ p302
| ( [.] z302
& <.> [.] y302
& <.> <.> ( ~ z302
| ~ y302 ) )
| ~ p502
| ( [.] z502
& <.> [.] y502
& <.> <.> ( ~ z502
| ~ y502 ) ) )
& ( ~ p302
| ( [.] z302
& <.> [.] y302
& <.> <.> ( ~ z302
| ~ y302 ) )
| ~ p602
| ( [.] z602
& <.> [.] y602
& <.> <.> ( ~ z602
| ~ y602 ) ) )
& ( ~ p302
| ( [.] z302
& <.> [.] y302
& <.> <.> ( ~ z302
| ~ y302 ) )
| ~ p702
| ( [.] z702
& <.> [.] y702
& <.> <.> ( ~ z702
| ~ y702 ) ) )
& ( ~ p402
| ( [.] z402
& <.> [.] y402
& <.> <.> ( ~ z402
| ~ y402 ) )
| ~ p502
| ( [.] z502
& <.> [.] y502
& <.> <.> ( ~ z502
| ~ y502 ) ) )
& ( ~ p402
| ( [.] z402
& <.> [.] y402
& <.> <.> ( ~ z402
| ~ y402 ) )
| ~ p602
| ( [.] z602
& <.> [.] y602
& <.> <.> ( ~ z602
| ~ y602 ) ) )
& ( ~ p402
| ( [.] z402
& <.> [.] y402
& <.> <.> ( ~ z402
| ~ y402 ) )
| ~ p702
| ( [.] z702
& <.> [.] y702
& <.> <.> ( ~ z702
| ~ y702 ) ) )
& ( ~ p502
| ( [.] z502
& <.> [.] y502
& <.> <.> ( ~ z502
| ~ y502 ) )
| ~ p602
| ( [.] z602
& <.> [.] y602
& <.> <.> ( ~ z602
| ~ y602 ) ) )
& ( ~ p502
| ( [.] z502
& <.> [.] y502
& <.> <.> ( ~ z502
| ~ y502 ) )
| ~ p702
| ( [.] z702
& <.> [.] y702
& <.> <.> ( ~ z702
| ~ y702 ) ) )
& ( ~ p602
| ( [.] z602
& <.> [.] y602
& <.> <.> ( ~ z602
| ~ y602 ) )
| ~ p702
| ( [.] z702
& <.> [.] y702
& <.> <.> ( ~ z702
| ~ y702 ) ) )
& ( <.> ( ~ p103
| ( [.] z103
& <.> [.] y103
& <.> <.> ( ~ z103
| ~ y103 ) ) )
| <.> ( ~ p203
| ( [.] z203
& <.> [.] y203
& <.> <.> ( ~ z203
| ~ y203 ) ) ) )
& ( <.> ( ~ p103
| ( [.] z103
& <.> [.] y103
& <.> <.> ( ~ z103
| ~ y103 ) ) )
| ~ p303
| ( [.] z303
& <.> [.] y303
& <.> <.> ( ~ z303
| ~ y303 ) ) )
& ( <.> ( ~ p103
| ( [.] z103
& <.> [.] y103
& <.> <.> ( ~ z103
| ~ y103 ) ) )
| ~ p403
| ( [.] z403
& <.> [.] y403
& <.> <.> ( ~ z403
| ~ y403 ) ) )
& ( <.> ( ~ p103
| ( [.] z103
& <.> [.] y103
& <.> <.> ( ~ z103
| ~ y103 ) ) )
| ~ p503
| ( [.] z503
& <.> [.] y503
& <.> <.> ( ~ z503
| ~ y503 ) ) )
& ( <.> ( ~ p103
| ( [.] z103
& <.> [.] y103
& <.> <.> ( ~ z103
| ~ y103 ) ) )
| ~ p603
| ( [.] z603
& <.> [.] y603
& <.> <.> ( ~ z603
| ~ y603 ) ) )
& ( <.> ( ~ p103
| ( [.] z103
& <.> [.] y103
& <.> <.> ( ~ z103
| ~ y103 ) ) )
| ~ p703
| ( [.] z703
& <.> [.] y703
& <.> <.> ( ~ z703
| ~ y703 ) ) )
& ( <.> ( ~ p203
| ( [.] z203
& <.> [.] y203
& <.> <.> ( ~ z203
| ~ y203 ) ) )
| ~ p303
| ( [.] z303
& <.> [.] y303
& <.> <.> ( ~ z303
| ~ y303 ) ) )
& ( <.> ( ~ p203
| ( [.] z203
& <.> [.] y203
& <.> <.> ( ~ z203
| ~ y203 ) ) )
| ~ p403
| ( [.] z403
& <.> [.] y403
& <.> <.> ( ~ z403
| ~ y403 ) ) )
& ( <.> ( ~ p203
| ( [.] z203
& <.> [.] y203
& <.> <.> ( ~ z203
| ~ y203 ) ) )
| ~ p503
| ( [.] z503
& <.> [.] y503
& <.> <.> ( ~ z503
| ~ y503 ) ) )
& ( <.> ( ~ p203
| ( [.] z203
& <.> [.] y203
& <.> <.> ( ~ z203
| ~ y203 ) ) )
| ~ p603
| ( [.] z603
& <.> [.] y603
& <.> <.> ( ~ z603
| ~ y603 ) ) )
& ( <.> ( ~ p203
| ( [.] z203
& <.> [.] y203
& <.> <.> ( ~ z203
| ~ y203 ) ) )
| ~ p703
| ( [.] z703
& <.> [.] y703
& <.> <.> ( ~ z703
| ~ y703 ) ) )
& ( ~ p303
| ( [.] z303
& <.> [.] y303
& <.> <.> ( ~ z303
| ~ y303 ) )
| ~ p403
| ( [.] z403
& <.> [.] y403
& <.> <.> ( ~ z403
| ~ y403 ) ) )
& ( ~ p303
| ( [.] z303
& <.> [.] y303
& <.> <.> ( ~ z303
| ~ y303 ) )
| ~ p503
| ( [.] z503
& <.> [.] y503
& <.> <.> ( ~ z503
| ~ y503 ) ) )
& ( ~ p303
| ( [.] z303
& <.> [.] y303
& <.> <.> ( ~ z303
| ~ y303 ) )
| ~ p603
| ( [.] z603
& <.> [.] y603
& <.> <.> ( ~ z603
| ~ y603 ) ) )
& ( ~ p303
| ( [.] z303
& <.> [.] y303
& <.> <.> ( ~ z303
| ~ y303 ) )
| ~ p703
| ( [.] z703
& <.> [.] y703
& <.> <.> ( ~ z703
| ~ y703 ) ) )
& ( ~ p403
| ( [.] z403
& <.> [.] y403
& <.> <.> ( ~ z403
| ~ y403 ) )
| ~ p503
| ( [.] z503
& <.> [.] y503
& <.> <.> ( ~ z503
| ~ y503 ) ) )
& ( ~ p403
| ( [.] z403
& <.> [.] y403
& <.> <.> ( ~ z403
| ~ y403 ) )
| ~ p603
| ( [.] z603
& <.> [.] y603
& <.> <.> ( ~ z603
| ~ y603 ) ) )
& ( ~ p403
| ( [.] z403
& <.> [.] y403
& <.> <.> ( ~ z403
| ~ y403 ) )
| ~ p703
| ( [.] z703
& <.> [.] y703
& <.> <.> ( ~ z703
| ~ y703 ) ) )
& ( ~ p503
| ( [.] z503
& <.> [.] y503
& <.> <.> ( ~ z503
| ~ y503 ) )
| ~ p603
| ( [.] z603
& <.> [.] y603
& <.> <.> ( ~ z603
| ~ y603 ) ) )
& ( ~ p503
| ( [.] z503
& <.> [.] y503
& <.> <.> ( ~ z503
| ~ y503 ) )
| ~ p703
| ( [.] z703
& <.> [.] y703
& <.> <.> ( ~ z703
| ~ y703 ) ) )
& ( ~ p603
| ( [.] z603
& <.> [.] y603
& <.> <.> ( ~ z603
| ~ y603 ) )
| ~ p703
| ( [.] z703
& <.> [.] y703
& <.> <.> ( ~ z703
| ~ y703 ) ) )
& ( <.> ( ~ p104
| ( [.] z104
& <.> [.] y104
& <.> <.> ( ~ z104
| ~ y104 ) ) )
| <.> ( ~ p204
| ( [.] z204
& <.> [.] y204
& <.> <.> ( ~ z204
| ~ y204 ) ) ) )
& ( <.> ( ~ p104
| ( [.] z104
& <.> [.] y104
& <.> <.> ( ~ z104
| ~ y104 ) ) )
| <.> ( ~ p304
| ( [.] z304
& <.> [.] y304
& <.> <.> ( ~ z304
| ~ y304 ) ) ) )
& ( <.> ( ~ p104
| ( [.] z104
& <.> [.] y104
& <.> <.> ( ~ z104
| ~ y104 ) ) )
| ~ p404
| ( [.] z404
& <.> [.] y404
& <.> <.> ( ~ z404
| ~ y404 ) ) )
& ( <.> ( ~ p104
| ( [.] z104
& <.> [.] y104
& <.> <.> ( ~ z104
| ~ y104 ) ) )
| ~ p504
| ( [.] z504
& <.> [.] y504
& <.> <.> ( ~ z504
| ~ y504 ) ) )
& ( <.> ( ~ p104
| ( [.] z104
& <.> [.] y104
& <.> <.> ( ~ z104
| ~ y104 ) ) )
| ~ p604
| ( [.] z604
& <.> [.] y604
& <.> <.> ( ~ z604
| ~ y604 ) ) )
& ( <.> ( ~ p104
| ( [.] z104
& <.> [.] y104
& <.> <.> ( ~ z104
| ~ y104 ) ) )
| ~ p704
| ( [.] z704
& <.> [.] y704
& <.> <.> ( ~ z704
| ~ y704 ) ) )
& ( <.> ( ~ p204
| ( [.] z204
& <.> [.] y204
& <.> <.> ( ~ z204
| ~ y204 ) ) )
| <.> ( ~ p304
| ( [.] z304
& <.> [.] y304
& <.> <.> ( ~ z304
| ~ y304 ) ) ) )
& ( <.> ( ~ p204
| ( [.] z204
& <.> [.] y204
& <.> <.> ( ~ z204
| ~ y204 ) ) )
| ~ p404
| ( [.] z404
& <.> [.] y404
& <.> <.> ( ~ z404
| ~ y404 ) ) )
& ( <.> ( ~ p204
| ( [.] z204
& <.> [.] y204
& <.> <.> ( ~ z204
| ~ y204 ) ) )
| ~ p504
| ( [.] z504
& <.> [.] y504
& <.> <.> ( ~ z504
| ~ y504 ) ) )
& ( <.> ( ~ p204
| ( [.] z204
& <.> [.] y204
& <.> <.> ( ~ z204
| ~ y204 ) ) )
| ~ p604
| ( [.] z604
& <.> [.] y604
& <.> <.> ( ~ z604
| ~ y604 ) ) )
& ( <.> ( ~ p204
| ( [.] z204
& <.> [.] y204
& <.> <.> ( ~ z204
| ~ y204 ) ) )
| ~ p704
| ( [.] z704
& <.> [.] y704
& <.> <.> ( ~ z704
| ~ y704 ) ) )
& ( <.> ( ~ p304
| ( [.] z304
& <.> [.] y304
& <.> <.> ( ~ z304
| ~ y304 ) ) )
| ~ p404
| ( [.] z404
& <.> [.] y404
& <.> <.> ( ~ z404
| ~ y404 ) ) )
& ( <.> ( ~ p304
| ( [.] z304
& <.> [.] y304
& <.> <.> ( ~ z304
| ~ y304 ) ) )
| ~ p504
| ( [.] z504
& <.> [.] y504
& <.> <.> ( ~ z504
| ~ y504 ) ) )
& ( <.> ( ~ p304
| ( [.] z304
& <.> [.] y304
& <.> <.> ( ~ z304
| ~ y304 ) ) )
| ~ p604
| ( [.] z604
& <.> [.] y604
& <.> <.> ( ~ z604
| ~ y604 ) ) )
& ( <.> ( ~ p304
| ( [.] z304
& <.> [.] y304
& <.> <.> ( ~ z304
| ~ y304 ) ) )
| ~ p704
| ( [.] z704
& <.> [.] y704
& <.> <.> ( ~ z704
| ~ y704 ) ) )
& ( ~ p404
| ( [.] z404
& <.> [.] y404
& <.> <.> ( ~ z404
| ~ y404 ) )
| ~ p504
| ( [.] z504
& <.> [.] y504
& <.> <.> ( ~ z504
| ~ y504 ) ) )
& ( ~ p404
| ( [.] z404
& <.> [.] y404
& <.> <.> ( ~ z404
| ~ y404 ) )
| ~ p604
| ( [.] z604
& <.> [.] y604
& <.> <.> ( ~ z604
| ~ y604 ) ) )
& ( ~ p404
| ( [.] z404
& <.> [.] y404
& <.> <.> ( ~ z404
| ~ y404 ) )
| ~ p704
| ( [.] z704
& <.> [.] y704
& <.> <.> ( ~ z704
| ~ y704 ) ) )
& ( ~ p504
| ( [.] z504
& <.> [.] y504
& <.> <.> ( ~ z504
| ~ y504 ) )
| ~ p604
| ( [.] z604
& <.> [.] y604
& <.> <.> ( ~ z604
| ~ y604 ) ) )
& ( ~ p504
| ( [.] z504
& <.> [.] y504
& <.> <.> ( ~ z504
| ~ y504 ) )
| ~ p704
| ( [.] z704
& <.> [.] y704
& <.> <.> ( ~ z704
| ~ y704 ) ) )
& ( ~ p604
| ( [.] z604
& <.> [.] y604
& <.> <.> ( ~ z604
| ~ y604 ) )
| ~ p704
| ( [.] z704
& <.> [.] y704
& <.> <.> ( ~ z704
| ~ y704 ) ) )
& ( <.> ( ~ p105
| ( [.] z105
& <.> [.] y105
& <.> <.> ( ~ z105
| ~ y105 ) ) )
| <.> ( ~ p205
| ( [.] z205
& <.> [.] y205
& <.> <.> ( ~ z205
| ~ y205 ) ) ) )
& ( <.> ( ~ p105
| ( [.] z105
& <.> [.] y105
& <.> <.> ( ~ z105
| ~ y105 ) ) )
| <.> ( ~ p305
| ( [.] z305
& <.> [.] y305
& <.> <.> ( ~ z305
| ~ y305 ) ) ) )
& ( <.> ( ~ p105
| ( [.] z105
& <.> [.] y105
& <.> <.> ( ~ z105
| ~ y105 ) ) )
| <.> ( ~ p405
| ( [.] z405
& <.> [.] y405
& <.> <.> ( ~ z405
| ~ y405 ) ) ) )
& ( <.> ( ~ p105
| ( [.] z105
& <.> [.] y105
& <.> <.> ( ~ z105
| ~ y105 ) ) )
| ~ p505
| ( [.] z505
& <.> [.] y505
& <.> <.> ( ~ z505
| ~ y505 ) ) )
& ( <.> ( ~ p105
| ( [.] z105
& <.> [.] y105
& <.> <.> ( ~ z105
| ~ y105 ) ) )
| ~ p605
| ( [.] z605
& <.> [.] y605
& <.> <.> ( ~ z605
| ~ y605 ) ) )
& ( <.> ( ~ p105
| ( [.] z105
& <.> [.] y105
& <.> <.> ( ~ z105
| ~ y105 ) ) )
| ~ p705
| ( [.] z705
& <.> [.] y705
& <.> <.> ( ~ z705
| ~ y705 ) ) )
& ( <.> ( ~ p205
| ( [.] z205
& <.> [.] y205
& <.> <.> ( ~ z205
| ~ y205 ) ) )
| <.> ( ~ p305
| ( [.] z305
& <.> [.] y305
& <.> <.> ( ~ z305
| ~ y305 ) ) ) )
& ( <.> ( ~ p205
| ( [.] z205
& <.> [.] y205
& <.> <.> ( ~ z205
| ~ y205 ) ) )
| <.> ( ~ p405
| ( [.] z405
& <.> [.] y405
& <.> <.> ( ~ z405
| ~ y405 ) ) ) )
& ( <.> ( ~ p205
| ( [.] z205
& <.> [.] y205
& <.> <.> ( ~ z205
| ~ y205 ) ) )
| ~ p505
| ( [.] z505
& <.> [.] y505
& <.> <.> ( ~ z505
| ~ y505 ) ) )
& ( <.> ( ~ p205
| ( [.] z205
& <.> [.] y205
& <.> <.> ( ~ z205
| ~ y205 ) ) )
| ~ p605
| ( [.] z605
& <.> [.] y605
& <.> <.> ( ~ z605
| ~ y605 ) ) )
& ( <.> ( ~ p205
| ( [.] z205
& <.> [.] y205
& <.> <.> ( ~ z205
| ~ y205 ) ) )
| ~ p705
| ( [.] z705
& <.> [.] y705
& <.> <.> ( ~ z705
| ~ y705 ) ) )
& ( <.> ( ~ p305
| ( [.] z305
& <.> [.] y305
& <.> <.> ( ~ z305
| ~ y305 ) ) )
| <.> ( ~ p405
| ( [.] z405
& <.> [.] y405
& <.> <.> ( ~ z405
| ~ y405 ) ) ) )
& ( <.> ( ~ p305
| ( [.] z305
& <.> [.] y305
& <.> <.> ( ~ z305
| ~ y305 ) ) )
| ~ p505
| ( [.] z505
& <.> [.] y505
& <.> <.> ( ~ z505
| ~ y505 ) ) )
& ( <.> ( ~ p305
| ( [.] z305
& <.> [.] y305
& <.> <.> ( ~ z305
| ~ y305 ) ) )
| ~ p605
| ( [.] z605
& <.> [.] y605
& <.> <.> ( ~ z605
| ~ y605 ) ) )
& ( <.> ( ~ p305
| ( [.] z305
& <.> [.] y305
& <.> <.> ( ~ z305
| ~ y305 ) ) )
| ~ p705
| ( [.] z705
& <.> [.] y705
& <.> <.> ( ~ z705
| ~ y705 ) ) )
& ( <.> ( ~ p405
| ( [.] z405
& <.> [.] y405
& <.> <.> ( ~ z405
| ~ y405 ) ) )
| ~ p505
| ( [.] z505
& <.> [.] y505
& <.> <.> ( ~ z505
| ~ y505 ) ) )
& ( <.> ( ~ p405
| ( [.] z405
& <.> [.] y405
& <.> <.> ( ~ z405
| ~ y405 ) ) )
| ~ p605
| ( [.] z605
& <.> [.] y605
& <.> <.> ( ~ z605
| ~ y605 ) ) )
& ( <.> ( ~ p405
| ( [.] z405
& <.> [.] y405
& <.> <.> ( ~ z405
| ~ y405 ) ) )
| ~ p705
| ( [.] z705
& <.> [.] y705
& <.> <.> ( ~ z705
| ~ y705 ) ) )
& ( ~ p505
| ( [.] z505
& <.> [.] y505
& <.> <.> ( ~ z505
| ~ y505 ) )
| ~ p605
| ( [.] z605
& <.> [.] y605
& <.> <.> ( ~ z605
| ~ y605 ) ) )
& ( ~ p505
| ( [.] z505
& <.> [.] y505
& <.> <.> ( ~ z505
| ~ y505 ) )
| ~ p705
| ( [.] z705
& <.> [.] y705
& <.> <.> ( ~ z705
| ~ y705 ) ) )
& ( ~ p605
| ( [.] z605
& <.> [.] y605
& <.> <.> ( ~ z605
| ~ y605 ) )
| ~ p705
| ( [.] z705
& <.> [.] y705
& <.> <.> ( ~ z705
| ~ y705 ) ) )
& ( <.> ( ~ p106
| ( [.] z106
& <.> [.] y106
& <.> <.> ( ~ z106
| ~ y106 ) ) )
| <.> ( ~ p206
| ( [.] z206
& <.> [.] y206
& <.> <.> ( ~ z206
| ~ y206 ) ) ) )
& ( <.> ( ~ p106
| ( [.] z106
& <.> [.] y106
& <.> <.> ( ~ z106
| ~ y106 ) ) )
| <.> ( ~ p306
| ( [.] z306
& <.> [.] y306
& <.> <.> ( ~ z306
| ~ y306 ) ) ) )
& ( <.> ( ~ p106
| ( [.] z106
& <.> [.] y106
& <.> <.> ( ~ z106
| ~ y106 ) ) )
| <.> ( ~ p406
| ( [.] z406
& <.> [.] y406
& <.> <.> ( ~ z406
| ~ y406 ) ) ) )
& ( <.> ( ~ p106
| ( [.] z106
& <.> [.] y106
& <.> <.> ( ~ z106
| ~ y106 ) ) )
| <.> ( ~ p506
| ( [.] z506
& <.> [.] y506
& <.> <.> ( ~ z506
| ~ y506 ) ) ) )
& ( <.> ( ~ p106
| ( [.] z106
& <.> [.] y106
& <.> <.> ( ~ z106
| ~ y106 ) ) )
| ~ p606
| ( [.] z606
& <.> [.] y606
& <.> <.> ( ~ z606
| ~ y606 ) ) )
& ( <.> ( ~ p106
| ( [.] z106
& <.> [.] y106
& <.> <.> ( ~ z106
| ~ y106 ) ) )
| ~ p706
| ( [.] z706
& <.> [.] y706
& <.> <.> ( ~ z706
| ~ y706 ) ) )
& ( <.> ( ~ p206
| ( [.] z206
& <.> [.] y206
& <.> <.> ( ~ z206
| ~ y206 ) ) )
| <.> ( ~ p306
| ( [.] z306
& <.> [.] y306
& <.> <.> ( ~ z306
| ~ y306 ) ) ) )
& ( <.> ( ~ p206
| ( [.] z206
& <.> [.] y206
& <.> <.> ( ~ z206
| ~ y206 ) ) )
| <.> ( ~ p406
| ( [.] z406
& <.> [.] y406
& <.> <.> ( ~ z406
| ~ y406 ) ) ) )
& ( <.> ( ~ p206
| ( [.] z206
& <.> [.] y206
& <.> <.> ( ~ z206
| ~ y206 ) ) )
| <.> ( ~ p506
| ( [.] z506
& <.> [.] y506
& <.> <.> ( ~ z506
| ~ y506 ) ) ) )
& ( <.> ( ~ p206
| ( [.] z206
& <.> [.] y206
& <.> <.> ( ~ z206
| ~ y206 ) ) )
| ~ p606
| ( [.] z606
& <.> [.] y606
& <.> <.> ( ~ z606
| ~ y606 ) ) )
& ( <.> ( ~ p206
| ( [.] z206
& <.> [.] y206
& <.> <.> ( ~ z206
| ~ y206 ) ) )
| ~ p706
| ( [.] z706
& <.> [.] y706
& <.> <.> ( ~ z706
| ~ y706 ) ) )
& ( <.> ( ~ p306
| ( [.] z306
& <.> [.] y306
& <.> <.> ( ~ z306
| ~ y306 ) ) )
| <.> ( ~ p406
| ( [.] z406
& <.> [.] y406
& <.> <.> ( ~ z406
| ~ y406 ) ) ) )
& ( <.> ( ~ p306
| ( [.] z306
& <.> [.] y306
& <.> <.> ( ~ z306
| ~ y306 ) ) )
| <.> ( ~ p506
| ( [.] z506
& <.> [.] y506
& <.> <.> ( ~ z506
| ~ y506 ) ) ) )
& ( <.> ( ~ p306
| ( [.] z306
& <.> [.] y306
& <.> <.> ( ~ z306
| ~ y306 ) ) )
| ~ p606
| ( [.] z606
& <.> [.] y606
& <.> <.> ( ~ z606
| ~ y606 ) ) )
& ( <.> ( ~ p306
| ( [.] z306
& <.> [.] y306
& <.> <.> ( ~ z306
| ~ y306 ) ) )
| ~ p706
| ( [.] z706
& <.> [.] y706
& <.> <.> ( ~ z706
| ~ y706 ) ) )
& ( <.> ( ~ p406
| ( [.] z406
& <.> [.] y406
& <.> <.> ( ~ z406
| ~ y406 ) ) )
| <.> ( ~ p506
| ( [.] z506
& <.> [.] y506
& <.> <.> ( ~ z506
| ~ y506 ) ) ) )
& ( <.> ( ~ p406
| ( [.] z406
& <.> [.] y406
& <.> <.> ( ~ z406
| ~ y406 ) ) )
| ~ p606
| ( [.] z606
& <.> [.] y606
& <.> <.> ( ~ z606
| ~ y606 ) ) )
& ( <.> ( ~ p406
| ( [.] z406
& <.> [.] y406
& <.> <.> ( ~ z406
| ~ y406 ) ) )
| ~ p706
| ( [.] z706
& <.> [.] y706
& <.> <.> ( ~ z706
| ~ y706 ) ) )
& ( <.> ( ~ p506
| ( [.] z506
& <.> [.] y506
& <.> <.> ( ~ z506
| ~ y506 ) ) )
| ~ p606
| ( [.] z606
& <.> [.] y606
& <.> <.> ( ~ z606
| ~ y606 ) ) )
& ( <.> ( ~ p506
| ( [.] z506
& <.> [.] y506
& <.> <.> ( ~ z506
| ~ y506 ) ) )
| ~ p706
| ( [.] z706
& <.> [.] y706
& <.> <.> ( ~ z706
| ~ y706 ) ) )
& ( ~ p606
| ( [.] z606
& <.> [.] y606
& <.> <.> ( ~ z606
| ~ y606 ) )
| ~ p706
| ( [.] z706
& <.> [.] y706
& <.> <.> ( ~ z706
| ~ y706 ) ) ) ) ) ).
%------------------------------------------------------------------------------