%------------------------------------------------------------------------------
% File : GRA078_1.018 : TPTP v9.0.0. Released v9.0.0.
% Domain : Syntactic
% Problem : Adjacent vertices in a polygon with 18 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 : k4d_poly_p.0018 [Nal22]
% Status : Theorem
% Rating : 1.00 v9.0.0
% Syntax : Number of formulae : 172 ( 0 unt; 171 typ; 0 def)
% Number of atoms : 1163 ( 0 equ)
% Maximal formula atoms : 1163 (1163 avg)
% Number of connectives : 5471 ( 610 ~; 553 |; 609 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% (3699 {.}; 0 {#})
% Maximal formula depth : 179 ( 179 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 : 171 ( 171 usr; 171 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_poly_p.0018',logic,
$modal ==
[ $modalities == $modal_system_D4 ] ).
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(p108_decl,type,
p108: $o ).
tff(p11_decl,type,
p11: $o ).
tff(p110_decl,type,
p110: $o ).
tff(p112_decl,type,
p112: $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(p55_decl,type,
p55: $o ).
tff(p56_decl,type,
p56: $o ).
tff(p57_decl,type,
p57: $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(x0_decl,type,
x0: $o ).
tff(z1_decl,type,
z1: $o ).
tff(z10_decl,type,
z10: $o ).
tff(z100_decl,type,
z100: $o ).
tff(z102_decl,type,
z102: $o ).
tff(z104_decl,type,
z104: $o ).
tff(z106_decl,type,
z106: $o ).
tff(z108_decl,type,
z108: $o ).
tff(z11_decl,type,
z11: $o ).
tff(z110_decl,type,
z110: $o ).
tff(z112_decl,type,
z112: $o ).
tff(z12_decl,type,
z12: $o ).
tff(z13_decl,type,
z13: $o ).
tff(z14_decl,type,
z14: $o ).
tff(z15_decl,type,
z15: $o ).
tff(z16_decl,type,
z16: $o ).
tff(z17_decl,type,
z17: $o ).
tff(z18_decl,type,
z18: $o ).
tff(z19_decl,type,
z19: $o ).
tff(z2_decl,type,
z2: $o ).
tff(z20_decl,type,
z20: $o ).
tff(z21_decl,type,
z21: $o ).
tff(z22_decl,type,
z22: $o ).
tff(z23_decl,type,
z23: $o ).
tff(z24_decl,type,
z24: $o ).
tff(z25_decl,type,
z25: $o ).
tff(z26_decl,type,
z26: $o ).
tff(z27_decl,type,
z27: $o ).
tff(z28_decl,type,
z28: $o ).
tff(z29_decl,type,
z29: $o ).
tff(z3_decl,type,
z3: $o ).
tff(z30_decl,type,
z30: $o ).
tff(z31_decl,type,
z31: $o ).
tff(z32_decl,type,
z32: $o ).
tff(z33_decl,type,
z33: $o ).
tff(z34_decl,type,
z34: $o ).
tff(z35_decl,type,
z35: $o ).
tff(z36_decl,type,
z36: $o ).
tff(z37_decl,type,
z37: $o ).
tff(z38_decl,type,
z38: $o ).
tff(z39_decl,type,
z39: $o ).
tff(z4_decl,type,
z4: $o ).
tff(z40_decl,type,
z40: $o ).
tff(z41_decl,type,
z41: $o ).
tff(z42_decl,type,
z42: $o ).
tff(z43_decl,type,
z43: $o ).
tff(z44_decl,type,
z44: $o ).
tff(z45_decl,type,
z45: $o ).
tff(z46_decl,type,
z46: $o ).
tff(z47_decl,type,
z47: $o ).
tff(z48_decl,type,
z48: $o ).
tff(z49_decl,type,
z49: $o ).
tff(z5_decl,type,
z5: $o ).
tff(z50_decl,type,
z50: $o ).
tff(z51_decl,type,
z51: $o ).
tff(z52_decl,type,
z52: $o ).
tff(z53_decl,type,
z53: $o ).
tff(z54_decl,type,
z54: $o ).
tff(z55_decl,type,
z55: $o ).
tff(z56_decl,type,
z56: $o ).
tff(z57_decl,type,
z57: $o ).
tff(z58_decl,type,
z58: $o ).
tff(z6_decl,type,
z6: $o ).
tff(z60_decl,type,
z60: $o ).
tff(z62_decl,type,
z62: $o ).
tff(z64_decl,type,
z64: $o ).
tff(z66_decl,type,
z66: $o ).
tff(z68_decl,type,
z68: $o ).
tff(z7_decl,type,
z7: $o ).
tff(z70_decl,type,
z70: $o ).
tff(z72_decl,type,
z72: $o ).
tff(z74_decl,type,
z74: $o ).
tff(z76_decl,type,
z76: $o ).
tff(z78_decl,type,
z78: $o ).
tff(z8_decl,type,
z8: $o ).
tff(z80_decl,type,
z80: $o ).
tff(z82_decl,type,
z82: $o ).
tff(z84_decl,type,
z84: $o ).
tff(z86_decl,type,
z86: $o ).
tff(z88_decl,type,
z88: $o ).
tff(z9_decl,type,
z9: $o ).
tff(z90_decl,type,
z90: $o ).
tff(z92_decl,type,
z92: $o ).
tff(z94_decl,type,
z94: $o ).
tff(z96_decl,type,
z96: $o ).
tff(z98_decl,type,
z98: $o ).
tff(prove,conjecture,
~ ( ( [.] x0
& [.] ~ x0 )
| ( <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p1
| ( [.] z1
& <.> <.> [.] <.> ~ z1 )
| ~ p2
| ( [.] z2
& <.> <.> [.] <.> ~ z2 )
| ~ p3
| ( [.] z3
& <.> <.> [.] <.> ~ z3 )
| ~ p4
| ( [.] z4
& <.> <.> [.] <.> ~ z4 )
| ~ p5
| ( [.] z5
& <.> <.> [.] <.> ~ z5 )
| ~ p6
| ( [.] z6
& <.> <.> [.] <.> ~ z6 )
| ~ p7
| ( [.] z7
& <.> <.> [.] <.> ~ z7 )
| ~ p8
| ( [.] z8
& <.> <.> [.] <.> ~ z8 )
| ~ p9
| ( [.] z9
& <.> <.> [.] <.> ~ z9 )
| ~ p10
| ( [.] z10
& <.> <.> [.] <.> ~ z10 )
| ~ p11
| ( [.] z11
& <.> <.> [.] <.> ~ z11 )
| ~ p12
| ( [.] z12
& <.> <.> [.] <.> ~ z12 )
| ~ p13
| ( [.] z13
& <.> <.> [.] <.> ~ z13 )
| ~ p14
| ( [.] z14
& <.> <.> [.] <.> ~ z14 )
| ~ p15
| ( [.] z15
& <.> <.> [.] <.> ~ z15 )
| ~ p16
| ( [.] z16
& <.> <.> [.] <.> ~ z16 )
| ~ p17
| ( [.] z17
& <.> <.> [.] <.> ~ z17 )
| ~ p18
| ( [.] z18
& <.> <.> [.] <.> ~ z18 )
| ~ p19
| ( [.] z19
& <.> <.> [.] <.> ~ z19 )
| ~ p20
| ( [.] z20
& <.> <.> [.] <.> ~ z20 )
| ~ p21
| ( [.] z21
& <.> <.> [.] <.> ~ z21 )
| ~ p22
| ( [.] z22
& <.> <.> [.] <.> ~ z22 )
| ~ p23
| ( [.] z23
& <.> <.> [.] <.> ~ z23 )
| ~ p24
| ( [.] z24
& <.> <.> [.] <.> ~ z24 )
| ~ p25
| ( [.] z25
& <.> <.> [.] <.> ~ z25 )
| ~ p26
| ( [.] z26
& <.> <.> [.] <.> ~ z26 )
| ~ p27
| ( [.] z27
& <.> <.> [.] <.> ~ z27 )
| ~ p28
| ( [.] z28
& <.> <.> [.] <.> ~ z28 )
| ~ p29
| ( [.] z29
& <.> <.> [.] <.> ~ z29 )
| ~ p30
| ( [.] z30
& <.> <.> [.] <.> ~ z30 )
| ~ p31
| ( [.] z31
& <.> <.> [.] <.> ~ z31 )
| ~ p32
| ( [.] z32
& <.> <.> [.] <.> ~ z32 )
| ~ p33
| ( [.] z33
& <.> <.> [.] <.> ~ z33 )
| ~ p34
| ( [.] z34
& <.> <.> [.] <.> ~ z34 )
| ~ p35
| ( [.] z35
& <.> <.> [.] <.> ~ z35 )
| ~ p36
| ( [.] z36
& <.> <.> [.] <.> ~ z36 )
| ~ p37
| ( [.] z37
& <.> <.> [.] <.> ~ z37 )
| ~ p38
| ( [.] z38
& <.> <.> [.] <.> ~ z38 )
| ~ p39
| ( [.] z39
& <.> <.> [.] <.> ~ z39 )
| ~ p40
| ( [.] z40
& <.> <.> [.] <.> ~ z40 )
| ~ p41
| ( [.] z41
& <.> <.> [.] <.> ~ z41 )
| ~ p42
| ( [.] z42
& <.> <.> [.] <.> ~ z42 )
| ~ p43
| ( [.] z43
& <.> <.> [.] <.> ~ z43 )
| ~ p44
| ( [.] z44
& <.> <.> [.] <.> ~ z44 )
| ~ p45
| ( [.] z45
& <.> <.> [.] <.> ~ z45 )
| ~ p46
| ( [.] z46
& <.> <.> [.] <.> ~ z46 )
| ~ p47
| ( [.] z47
& <.> <.> [.] <.> ~ z47 )
| ~ p48
| ( [.] z48
& <.> <.> [.] <.> ~ z48 )
| ~ p49
| ( [.] z49
& <.> <.> [.] <.> ~ z49 )
| ~ p50
| ( [.] z50
& <.> <.> [.] <.> ~ z50 )
| ~ p51
| ( [.] z51
& <.> <.> [.] <.> ~ z51 )
| ~ p52
| ( [.] z52
& <.> <.> [.] <.> ~ z52 )
| ~ p53
| ( [.] z53
& <.> <.> [.] <.> ~ z53 )
| ~ p54
| ( [.] z54
& <.> <.> [.] <.> ~ z54 )
| ~ p55
| ( [.] z55
& <.> <.> [.] <.> ~ z55 )
| ~ p56
| ( [.] z56
& <.> <.> [.] <.> ~ z56 ) )
& [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] [.] ( ( ( p1
| ( [.] z1
& <.> <.> [.] <.> ~ z1 ) )
& ( ~ p2
| ( [.] z2
& <.> <.> [.] <.> ~ z2 ) ) )
| ( ( p2
| ( [.] z2
& <.> <.> [.] <.> ~ z2 ) )
& ( ~ p1
| ( [.] z1
& <.> <.> [.] <.> ~ z1 ) ) ) )
& <.> ( ~ p3
| ( [.] z3
& <.> <.> [.] <.> ~ z3 ) )
& [.] [.] ( ( ( p2
| ( [.] z2
& <.> <.> [.] <.> ~ z2 ) )
& ( ~ p3
| ( [.] z3
& <.> <.> [.] <.> ~ z3 ) ) )
| ( ( p3
| ( [.] z3
& <.> <.> [.] <.> ~ z3 ) )
& ( ~ p2
| ( [.] z2
& <.> <.> [.] <.> ~ z2 ) ) ) ) )
& <.> ( ~ p4
| ( [.] z4
& <.> <.> [.] <.> ~ z4 ) )
& [.] [.] [.] ( ( ( p3
| ( [.] z3
& <.> <.> [.] <.> ~ z3 ) )
& ( ~ p4
| ( [.] z4
& <.> <.> [.] <.> ~ z4 ) ) )
| ( ( p4
| ( [.] z4
& <.> <.> [.] <.> ~ z4 ) )
& ( ~ p3
| ( [.] z3
& <.> <.> [.] <.> ~ z3 ) ) ) ) )
& <.> ( ~ p5
| ( [.] z5
& <.> <.> [.] <.> ~ z5 ) )
& [.] [.] [.] [.] ( ( ( p4
| ( [.] z4
& <.> <.> [.] <.> ~ z4 ) )
& ( ~ p5
| ( [.] z5
& <.> <.> [.] <.> ~ z5 ) ) )
| ( ( p5
| ( [.] z5
& <.> <.> [.] <.> ~ z5 ) )
& ( ~ p4
| ( [.] z4
& <.> <.> [.] <.> ~ z4 ) ) ) ) )
& <.> ( ~ p6
| ( [.] z6
& <.> <.> [.] <.> ~ z6 ) )
& [.] [.] [.] [.] [.] ( ( ( p5
| ( [.] z5
& <.> <.> [.] <.> ~ z5 ) )
& ( ~ p6
| ( [.] z6
& <.> <.> [.] <.> ~ z6 ) ) )
| ( ( p6
| ( [.] z6
& <.> <.> [.] <.> ~ z6 ) )
& ( ~ p5
| ( [.] z5
& <.> <.> [.] <.> ~ z5 ) ) ) ) )
& <.> ( ~ p7
| ( [.] z7
& <.> <.> [.] <.> ~ z7 ) )
& [.] [.] [.] [.] [.] [.] ( ( ( p6
| ( [.] z6
& <.> <.> [.] <.> ~ z6 ) )
& ( ~ p7
| ( [.] z7
& <.> <.> [.] <.> ~ z7 ) ) )
| ( ( p7
| ( [.] z7
& <.> <.> [.] <.> ~ z7 ) )
& ( ~ p6
| ( [.] z6
& <.> <.> [.] <.> ~ z6 ) ) ) ) )
& <.> ( ~ p8
| ( [.] z8
& <.> <.> [.] <.> ~ z8 ) )
& [.] [.] [.] [.] [.] [.] [.] ( ( ( p7
| ( [.] z7
& <.> <.> [.] <.> ~ z7 ) )
& ( ~ p8
| ( [.] z8
& <.> <.> [.] <.> ~ z8 ) ) )
| ( ( p8
| ( [.] z8
& <.> <.> [.] <.> ~ z8 ) )
& ( ~ p7
| ( [.] z7
& <.> <.> [.] <.> ~ z7 ) ) ) ) )
& <.> ( ~ p9
| ( [.] z9
& <.> <.> [.] <.> ~ z9 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p8
| ( [.] z8
& <.> <.> [.] <.> ~ z8 ) )
& ( ~ p9
| ( [.] z9
& <.> <.> [.] <.> ~ z9 ) ) )
| ( ( p9
| ( [.] z9
& <.> <.> [.] <.> ~ z9 ) )
& ( ~ p8
| ( [.] z8
& <.> <.> [.] <.> ~ z8 ) ) ) ) )
& <.> ( ~ p10
| ( [.] z10
& <.> <.> [.] <.> ~ z10 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p9
| ( [.] z9
& <.> <.> [.] <.> ~ z9 ) )
& ( ~ p10
| ( [.] z10
& <.> <.> [.] <.> ~ z10 ) ) )
| ( ( p10
| ( [.] z10
& <.> <.> [.] <.> ~ z10 ) )
& ( ~ p9
| ( [.] z9
& <.> <.> [.] <.> ~ z9 ) ) ) ) )
& <.> ( ~ p11
| ( [.] z11
& <.> <.> [.] <.> ~ z11 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p10
| ( [.] z10
& <.> <.> [.] <.> ~ z10 ) )
& ( ~ p11
| ( [.] z11
& <.> <.> [.] <.> ~ z11 ) ) )
| ( ( p11
| ( [.] z11
& <.> <.> [.] <.> ~ z11 ) )
& ( ~ p10
| ( [.] z10
& <.> <.> [.] <.> ~ z10 ) ) ) ) )
& <.> ( ~ p12
| ( [.] z12
& <.> <.> [.] <.> ~ z12 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p11
| ( [.] z11
& <.> <.> [.] <.> ~ z11 ) )
& ( ~ p12
| ( [.] z12
& <.> <.> [.] <.> ~ z12 ) ) )
| ( ( p12
| ( [.] z12
& <.> <.> [.] <.> ~ z12 ) )
& ( ~ p11
| ( [.] z11
& <.> <.> [.] <.> ~ z11 ) ) ) ) )
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& <.> <.> [.] <.> ~ z21 ) )
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& <.> <.> [.] <.> ~ z22 ) )
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& <.> <.> [.] <.> ~ z23 ) )
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| ( [.] z22
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& <.> <.> [.] <.> ~ z24 ) )
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| ( [.] z23
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& ( ~ p23
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& <.> ( ~ p25
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& <.> <.> [.] <.> ~ z25 ) )
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& ( ~ p24
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& <.> ( ~ p26
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& <.> <.> [.] <.> ~ z26 ) )
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& <.> <.> [.] <.> ~ z26 ) )
& ( ~ p25
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& <.> ( ~ p27
| ( [.] z27
& <.> <.> [.] <.> ~ z27 ) )
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& ( ~ p27
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& <.> <.> [.] <.> ~ z27 ) )
& ( ~ p26
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& <.> <.> [.] <.> ~ z28 ) )
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& <.> <.> [.] <.> ~ z28 ) )
& ( ~ p27
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& <.> <.> [.] <.> ~ z27 ) ) ) ) )
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& <.> <.> [.] <.> ~ z29 ) )
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& ( ~ p28
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& <.> <.> [.] <.> ~ z30 ) )
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& ( ~ p29
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& ( ~ p30
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| ( [.] z46
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| ( [.] z55
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| ( [.] z1
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| ( [.] z55
& <.> <.> [.] <.> ~ z55 ) ) ) ) )
& <.> ( ~ p57
| ( [.] z57
& <.> <.> [.] <.> ~ z57 ) )
& <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p2
| ( [.] z2
& <.> <.> [.] <.> ~ z2 )
| p4
| ( [.] z4
& <.> <.> [.] <.> ~ z4 )
| p6
| ( [.] z6
& <.> <.> [.] <.> ~ z6 )
| p8
| ( [.] z8
& <.> <.> [.] <.> ~ z8 )
| p10
| ( [.] z10
& <.> <.> [.] <.> ~ z10 )
| p12
| ( [.] z12
& <.> <.> [.] <.> ~ z12 )
| p14
| ( [.] z14
& <.> <.> [.] <.> ~ z14 )
| p16
| ( [.] z16
& <.> <.> [.] <.> ~ z16 )
| p18
| ( [.] z18
& <.> <.> [.] <.> ~ z18 )
| p20
| ( [.] z20
& <.> <.> [.] <.> ~ z20 )
| p22
| ( [.] z22
& <.> <.> [.] <.> ~ z22 )
| p24
| ( [.] z24
& <.> <.> [.] <.> ~ z24 )
| p26
| ( [.] z26
& <.> <.> [.] <.> ~ z26 )
| p28
| ( [.] z28
& <.> <.> [.] <.> ~ z28 )
| p30
| ( [.] z30
& <.> <.> [.] <.> ~ z30 )
| p32
| ( [.] z32
& <.> <.> [.] <.> ~ z32 )
| p34
| ( [.] z34
& <.> <.> [.] <.> ~ z34 )
| p36
| ( [.] z36
& <.> <.> [.] <.> ~ z36 )
| p38
| ( [.] z38
& <.> <.> [.] <.> ~ z38 )
| p40
| ( [.] z40
& <.> <.> [.] <.> ~ z40 )
| p42
| ( [.] z42
& <.> <.> [.] <.> ~ z42 )
| p44
| ( [.] z44
& <.> <.> [.] <.> ~ z44 )
| p46
| ( [.] z46
& <.> <.> [.] <.> ~ z46 )
| p48
| ( [.] z48
& <.> <.> [.] <.> ~ z48 )
| p50
| ( [.] z50
& <.> <.> [.] <.> ~ z50 )
| p52
| ( [.] z52
& <.> <.> [.] <.> ~ z52 )
| p54
| ( [.] z54
& <.> <.> [.] <.> ~ z54 )
| p56
| ( [.] z56
& <.> <.> [.] <.> ~ z56 )
| p58
| ( [.] z58
& <.> <.> [.] <.> ~ z58 )
| p60
| ( [.] z60
& <.> <.> [.] <.> ~ z60 )
| p62
| ( [.] z62
& <.> <.> [.] <.> ~ z62 )
| p64
| ( [.] z64
& <.> <.> [.] <.> ~ z64 )
| p66
| ( [.] z66
& <.> <.> [.] <.> ~ z66 )
| p68
| ( [.] z68
& <.> <.> [.] <.> ~ z68 )
| p70
| ( [.] z70
& <.> <.> [.] <.> ~ z70 )
| p72
| ( [.] z72
& <.> <.> [.] <.> ~ z72 )
| p74
| ( [.] z74
& <.> <.> [.] <.> ~ z74 )
| p76
| ( [.] z76
& <.> <.> [.] <.> ~ z76 )
| p78
| ( [.] z78
& <.> <.> [.] <.> ~ z78 )
| p80
| ( [.] z80
& <.> <.> [.] <.> ~ z80 )
| p82
| ( [.] z82
& <.> <.> [.] <.> ~ z82 )
| p84
| ( [.] z84
& <.> <.> [.] <.> ~ z84 )
| p86
| ( [.] z86
& <.> <.> [.] <.> ~ z86 )
| p88
| ( [.] z88
& <.> <.> [.] <.> ~ z88 )
| p90
| ( [.] z90
& <.> <.> [.] <.> ~ z90 )
| p92
| ( [.] z92
& <.> <.> [.] <.> ~ z92 )
| p94
| ( [.] z94
& <.> <.> [.] <.> ~ z94 )
| p96
| ( [.] z96
& <.> <.> [.] <.> ~ z96 )
| p98
| ( [.] z98
& <.> <.> [.] <.> ~ z98 )
| p100
| ( [.] z100
& <.> <.> [.] <.> ~ z100 )
| p102
| ( [.] z102
& <.> <.> [.] <.> ~ z102 )
| p104
| ( [.] z104
& <.> <.> [.] <.> ~ z104 )
| p106
| ( [.] z106
& <.> <.> [.] <.> ~ z106 )
| p108
| ( [.] z108
& <.> <.> [.] <.> ~ z108 )
| p110
| ( [.] z110
& <.> <.> [.] <.> ~ z110 )
| p112
| ( [.] z112
& <.> <.> [.] <.> ~ z112 ) ) ) ) ).
%------------------------------------------------------------------------------