%------------------------------------------------------------------------------
% File : GRA076_1.017 : TPTP v9.0.0. Released v9.0.0.
% Domain : Syntactic
% Problem : Adjacent vertices in a polygon with 17 black or white vertices
% Version : Especial.
% English : If a polygon with n black or white vertices, then two adjacent
% vertices have the same color. If n is odd this is provable in
% CPC.
% 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 : k_poly_n.0017 [Nal22]
% Status : CounterSatisfiable
% Rating : 0.50 v9.0.0
% Syntax : Number of formulae : 82 ( 0 unt; 81 typ; 0 def)
% Number of atoms : 263 ( 0 equ)
% Maximal formula atoms : 263 ( 263 avg)
% Number of connectives : 1905 ( 55 ~; 106 |; 104 &)
% ( 52 <=>; 0 =>; 0 <=; 0 <~>)
% (1588 {.}; 0 {#})
% Maximal formula depth : 112 ( 112 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 : 81 ( 81 usr; 81 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 :
%------------------------------------------------------------------------------
tff('k_poly_n.0017',logic,
$modal ==
[ $modalities == $modal_system_K ] ).
tff(false_decl,type,
false: $o ).
tff(p1_decl,type,
p1: $o ).
tff(p10_decl,type,
p10: $o ).
tff(p100_decl,type,
p100: $o ).
tff(p102_decl,type,
p102: $o ).
tff(p104_decl,type,
p104: $o ).
tff(p106_decl,type,
p106: $o ).
tff(p11_decl,type,
p11: $o ).
tff(p12_decl,type,
p12: $o ).
tff(p13_decl,type,
p13: $o ).
tff(p14_decl,type,
p14: $o ).
tff(p15_decl,type,
p15: $o ).
tff(p16_decl,type,
p16: $o ).
tff(p17_decl,type,
p17: $o ).
tff(p18_decl,type,
p18: $o ).
tff(p19_decl,type,
p19: $o ).
tff(p2_decl,type,
p2: $o ).
tff(p20_decl,type,
p20: $o ).
tff(p21_decl,type,
p21: $o ).
tff(p22_decl,type,
p22: $o ).
tff(p23_decl,type,
p23: $o ).
tff(p24_decl,type,
p24: $o ).
tff(p25_decl,type,
p25: $o ).
tff(p26_decl,type,
p26: $o ).
tff(p27_decl,type,
p27: $o ).
tff(p28_decl,type,
p28: $o ).
tff(p29_decl,type,
p29: $o ).
tff(p3_decl,type,
p3: $o ).
tff(p30_decl,type,
p30: $o ).
tff(p31_decl,type,
p31: $o ).
tff(p32_decl,type,
p32: $o ).
tff(p33_decl,type,
p33: $o ).
tff(p34_decl,type,
p34: $o ).
tff(p35_decl,type,
p35: $o ).
tff(p36_decl,type,
p36: $o ).
tff(p37_decl,type,
p37: $o ).
tff(p38_decl,type,
p38: $o ).
tff(p39_decl,type,
p39: $o ).
tff(p4_decl,type,
p4: $o ).
tff(p40_decl,type,
p40: $o ).
tff(p41_decl,type,
p41: $o ).
tff(p42_decl,type,
p42: $o ).
tff(p43_decl,type,
p43: $o ).
tff(p44_decl,type,
p44: $o ).
tff(p45_decl,type,
p45: $o ).
tff(p46_decl,type,
p46: $o ).
tff(p47_decl,type,
p47: $o ).
tff(p48_decl,type,
p48: $o ).
tff(p49_decl,type,
p49: $o ).
tff(p5_decl,type,
p5: $o ).
tff(p50_decl,type,
p50: $o ).
tff(p51_decl,type,
p51: $o ).
tff(p52_decl,type,
p52: $o ).
tff(p53_decl,type,
p53: $o ).
tff(p54_decl,type,
p54: $o ).
tff(p56_decl,type,
p56: $o ).
tff(p58_decl,type,
p58: $o ).
tff(p6_decl,type,
p6: $o ).
tff(p60_decl,type,
p60: $o ).
tff(p62_decl,type,
p62: $o ).
tff(p64_decl,type,
p64: $o ).
tff(p66_decl,type,
p66: $o ).
tff(p68_decl,type,
p68: $o ).
tff(p7_decl,type,
p7: $o ).
tff(p70_decl,type,
p70: $o ).
tff(p72_decl,type,
p72: $o ).
tff(p74_decl,type,
p74: $o ).
tff(p76_decl,type,
p76: $o ).
tff(p78_decl,type,
p78: $o ).
tff(p8_decl,type,
p8: $o ).
tff(p80_decl,type,
p80: $o ).
tff(p82_decl,type,
p82: $o ).
tff(p84_decl,type,
p84: $o ).
tff(p86_decl,type,
p86: $o ).
tff(p88_decl,type,
p88: $o ).
tff(p9_decl,type,
p9: $o ).
tff(p90_decl,type,
p90: $o ).
tff(p92_decl,type,
p92: $o ).
tff(p94_decl,type,
p94: $o ).
tff(p96_decl,type,
p96: $o ).
tff(p98_decl,type,
p98: $o ).
tff(prove,conjecture,
~ ~ ( [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( p1
& p2
& p3
& p4
& p5
& p6
& p7
& p8
& p9
& p10
& p11
& p12
& p13
& p14
& p15
& p16
& p17
& p18
& p19
& p20
& p21
& p22
& p23
& p24
& p25
& p26
& p27
& p28
& p29
& p30
& p31
& p32
& p33
& p34
& p35
& p36
& p37
& p38
& p39
& p40
& p41
& p42
& p43
& p44
& p45
& p46
& p47
& p48
& p49
& p50
& p51
& p52
& p53 )
| <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( <.> ( false
| <.> ( p1
<=> p2 ) )
| [.] p3
| <.> <.> ( p2
<=> p3 ) )
| [.] p4
| <.> <.> <.> ( p3
<=> p4 ) )
| [.] p5
| <.> <.> <.> <.> ( p4
<=> p5 ) )
| [.] p6
| <.> <.> <.> <.> <.> ( p5
<=> p6 ) )
| [.] p7
| <.> <.> <.> <.> <.> <.> ( p6
<=> p7 ) )
| [.] p8
| <.> <.> <.> <.> <.> <.> <.> ( p7
<=> p8 ) )
| [.] p9
| <.> <.> <.> <.> <.> <.> <.> <.> ( p8
<=> p9 ) )
| [.] p10
| <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p9
<=> p10 ) )
| [.] p11
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p10
<=> p11 ) )
| [.] p12
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p11
<=> p12 ) )
| [.] p13
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p12
<=> p13 ) )
| [.] p14
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p13
<=> p14 ) )
| [.] p15
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p14
<=> p15 ) )
| [.] p16
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p15
<=> p16 ) )
| [.] p17
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p16
<=> p17 ) )
| [.] p18
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p17
<=> p18 ) )
| [.] p19
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p18
<=> p19 ) )
| [.] p20
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p19
<=> p20 ) )
| [.] p21
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p20
<=> p21 ) )
| [.] p22
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p21
<=> p22 ) )
| [.] p23
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p22
<=> p23 ) )
| [.] p24
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p23
<=> p24 ) )
| [.] p25
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p24
<=> p25 ) )
| [.] p26
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p25
<=> p26 ) )
| [.] p27
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p26
<=> p27 ) )
| [.] p28
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p27
<=> p28 ) )
| [.] p29
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p28
<=> p29 ) )
| [.] p30
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p29
<=> p30 ) )
| [.] p31
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p30
<=> p31 ) )
| [.] p32
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p31
<=> p32 ) )
| [.] p33
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p32
<=> p33 ) )
| [.] p34
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p33
<=> p34 ) )
| [.] p35
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p34
<=> p35 ) )
| [.] p36
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p35
<=> p36 ) )
| [.] p37
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p36
<=> p37 ) )
| [.] p38
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p37
<=> p38 ) )
| [.] p39
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p38
<=> p39 ) )
| [.] p40
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p39
<=> p40 ) )
| [.] p41
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p40
<=> p41 ) )
| [.] p42
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p41
<=> p42 ) )
| [.] p43
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p42
<=> p43 ) )
| [.] p44
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p43
<=> p44 ) )
| [.] p45
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p44
<=> p45 ) )
| [.] p46
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p45
<=> p46 ) )
| [.] p47
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p46
<=> p47 ) )
| [.] p48
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p47
<=> p48 ) )
| [.] p49
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p48
<=> p49 ) )
| [.] p50
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p49
<=> p50 ) )
| [.] p51
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p50
<=> p51 ) )
| [.] p52
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p51
<=> p52 ) )
| [.] p53
| <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p52
<=> p1 ) )
| [.] p54
| [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ~ p2
& ~ p4
& ~ p6
& ~ p8
& ~ p10
& ~ p12
& ~ p14
& ~ p16
& ~ p18
& ~ p20
& ~ p22
& ~ p24
& ~ p26
& ~ p28
& ~ p30
& ~ p32
& ~ p34
& ~ p36
& ~ p38
& ~ p40
& ~ p42
& ~ p44
& ~ p46
& ~ p48
& ~ p50
& ~ p52
& ~ p54
& ~ p56
& ~ p58
& ~ p60
& ~ p62
& ~ p64
& ~ p66
& ~ p68
& ~ p70
& ~ p72
& ~ p74
& ~ p76
& ~ p78
& ~ p80
& ~ p82
& ~ p84
& ~ p86
& ~ p88
& ~ p90
& ~ p92
& ~ p94
& ~ p96
& ~ p98
& ~ p100
& ~ p102
& ~ p104
& ~ p106 ) ) ).
%------------------------------------------------------------------------------