TPTP Problem File: LCL975_1.005.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : LCL975_1.005 : TPTP v9.0.0. Released v9.0.0.
% Domain : Syntactic
% Problem : Pigeonhole formula 5
% 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 : s4_ph_n.0005 [Nal22]
% Status : CounterSatisfiable
% Rating : 0.67 v9.0.0
% Syntax : Number of formulae : 31 ( 0 unt; 30 typ; 0 def)
% Number of atoms : 180 ( 0 equ)
% Maximal formula atoms : 180 ( 180 avg)
% Number of connectives : 322 ( 7 ~; 98 |; 80 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% ( 136 {.}; 0 {#})
% Maximal formula depth : 82 ( 82 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 : 30 ( 30 usr; 30 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
% Comments :
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tff('s4_ph_n.0005',logic,
$modal ==
[ $modalities == $modal_system_S4 ] ).
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(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(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(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(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(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(prove,conjecture,
~ ~ ( ( ( p101
| [.] p102
| [.] p103
| [.] p104
| [.] p105 )
& ( p201
| p202
| [.] p203
| [.] p204
| [.] p205 )
& ( p301
| p302
| p303
| [.] p304
| [.] p305 )
& ( p401
| p402
| p403
| p404
| [.] p405 )
& ( p501
| p502
| p503
| p504
| p505 )
& ( p601
| p602
| p603
| p604
| p605 ) )
=> <.> ( <.> ( p101
& p201 )
| <.> ( p101
& p301 )
| <.> ( p101
& p401 )
| <.> ( p101
& p501 )
| <.> ( p101
& p601 )
| <.> ( p201
& p301 )
| <.> ( p201
& p401 )
| <.> ( p201
& p501 )
| <.> ( p201
& p601 )
| <.> ( p301
& p401 )
| <.> ( p301
& p501 )
| <.> ( p301
& p601 )
| <.> ( p401
& p501 )
| <.> ( p401
& p601 )
| <.> ( p501
& p601 )
| <.> ( [.] p102
& p202 )
| <.> ( [.] p102
& p302 )
| <.> ( [.] p102
& p402 )
| <.> ( [.] p102
& p502 )
| <.> ( [.] p102
& p602 )
| <.> ( p202
& p302 )
| <.> ( p202
& p402 )
| <.> ( p202
& p502 )
| <.> ( p202
& p602 )
| <.> ( p302
& p402 )
| <.> ( p302
& p502 )
| <.> ( p302
& p602 )
| <.> ( p402
& p502 )
| <.> ( p402
& p602 )
| <.> ( p502
& p602 )
| <.> ( [.] p103
& [.] p203 )
| <.> ( [.] p103
& p303 )
| <.> ( [.] p103
& p403 )
| <.> ( [.] p103
& p503 )
| <.> ( [.] p103
& p603 )
| <.> ( [.] p203
& p303 )
| <.> ( [.] p203
& p403 )
| <.> ( [.] p203
& p503 )
| <.> ( [.] p203
& p603 )
| <.> ( p303
& p403 )
| <.> ( p303
& p503 )
| <.> ( p303
& p603 )
| <.> ( p403
& p503 )
| <.> ( p403
& p603 )
| <.> ( p503
& p603 )
| <.> ( [.] p104
& [.] p204 )
| <.> ( [.] p104
& [.] p304 )
| <.> ( [.] p104
& ~ p404 )
| <.> ( [.] p104
& p504 )
| <.> ( [.] p104
& p604 )
| <.> ( [.] p204
& [.] p304 )
| <.> ( [.] p204
& ~ p404 )
| <.> ( [.] p204
& p504 )
| <.> ( [.] p204
& p604 )
| <.> ( [.] p304
& ~ p404 )
| <.> ( [.] p304
& p504 )
| <.> ( [.] p304
& p604 )
| <.> ( ~ p404
& p504 )
| <.> ( ~ p404
& p604 )
| <.> ( p504
& p604 )
| <.> ( [.] p105
& [.] p205 )
| <.> ( [.] p105
& [.] p305 )
| <.> ( [.] p105
& [.] p405 )
| <.> ( [.] p105
& p505 )
| <.> ( [.] p105
& p605 )
| <.> ( [.] p205
& [.] p305 )
| <.> ( [.] p205
& [.] p405 )
| <.> ( [.] p205
& p505 )
| <.> ( [.] p205
& p605 )
| <.> ( [.] p305
& [.] p405 )
| <.> ( [.] p305
& p505 )
| <.> ( [.] p305
& p605 )
| <.> ( [.] p405
& p505 )
| <.> ( [.] p405
& p605 )
| <.> ( p505
& p605 ) ) ) ).
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