%------------------------------------------------------------------------------
% File : GRA080_1.006 : TPTP v9.0.0. Released v9.0.0.
% Domain : Syntactic
% Problem : Adjacent vertices in a polygon with 6 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 : s5_poly_p.0006 [Nal22]
% Status : Theorem
% Rating : 1.00 v9.0.0
% Syntax : Number of formulae : 95 ( 0 unt; 94 typ; 0 def)
% Number of atoms : 677 ( 0 equ)
% Maximal formula atoms : 677 ( 677 avg)
% Number of connectives : 1969 ( 349 ~; 328 |; 348 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% ( 944 {.}; 0 {#})
% Maximal formula depth : 90 ( 90 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 : 94 ( 94 usr; 94 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('s5_poly_p.0006',logic,
$modal ==
[ $modalities == $modal_system_S5 ] ).
tff(p1_decl,type,
p1: $o ).
tff(p10_decl,type,
p10: $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(p24_decl,type,
p24: $o ).
tff(p26_decl,type,
p26: $o ).
tff(p28_decl,type,
p28: $o ).
tff(p3_decl,type,
p3: $o ).
tff(p30_decl,type,
p30: $o ).
tff(p32_decl,type,
p32: $o ).
tff(p34_decl,type,
p34: $o ).
tff(p36_decl,type,
p36: $o ).
tff(p38_decl,type,
p38: $o ).
tff(p4_decl,type,
p4: $o ).
tff(p40_decl,type,
p40: $o ).
tff(p5_decl,type,
p5: $o ).
tff(p6_decl,type,
p6: $o ).
tff(p7_decl,type,
p7: $o ).
tff(p8_decl,type,
p8: $o ).
tff(p9_decl,type,
p9: $o ).
tff(x0_decl,type,
x0: $o ).
tff(y1_decl,type,
y1: $o ).
tff(y10_decl,type,
y10: $o ).
tff(y11_decl,type,
y11: $o ).
tff(y12_decl,type,
y12: $o ).
tff(y13_decl,type,
y13: $o ).
tff(y14_decl,type,
y14: $o ).
tff(y15_decl,type,
y15: $o ).
tff(y16_decl,type,
y16: $o ).
tff(y17_decl,type,
y17: $o ).
tff(y18_decl,type,
y18: $o ).
tff(y19_decl,type,
y19: $o ).
tff(y2_decl,type,
y2: $o ).
tff(y20_decl,type,
y20: $o ).
tff(y21_decl,type,
y21: $o ).
tff(y22_decl,type,
y22: $o ).
tff(y24_decl,type,
y24: $o ).
tff(y26_decl,type,
y26: $o ).
tff(y28_decl,type,
y28: $o ).
tff(y3_decl,type,
y3: $o ).
tff(y30_decl,type,
y30: $o ).
tff(y32_decl,type,
y32: $o ).
tff(y34_decl,type,
y34: $o ).
tff(y36_decl,type,
y36: $o ).
tff(y38_decl,type,
y38: $o ).
tff(y4_decl,type,
y4: $o ).
tff(y40_decl,type,
y40: $o ).
tff(y5_decl,type,
y5: $o ).
tff(y6_decl,type,
y6: $o ).
tff(y7_decl,type,
y7: $o ).
tff(y8_decl,type,
y8: $o ).
tff(y9_decl,type,
y9: $o ).
tff(z1_decl,type,
z1: $o ).
tff(z10_decl,type,
z10: $o ).
tff(z11_decl,type,
z11: $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(z24_decl,type,
z24: $o ).
tff(z26_decl,type,
z26: $o ).
tff(z28_decl,type,
z28: $o ).
tff(z3_decl,type,
z3: $o ).
tff(z30_decl,type,
z30: $o ).
tff(z32_decl,type,
z32: $o ).
tff(z34_decl,type,
z34: $o ).
tff(z36_decl,type,
z36: $o ).
tff(z38_decl,type,
z38: $o ).
tff(z4_decl,type,
z4: $o ).
tff(z40_decl,type,
z40: $o ).
tff(z5_decl,type,
z5: $o ).
tff(z6_decl,type,
z6: $o ).
tff(z7_decl,type,
z7: $o ).
tff(z8_decl,type,
z8: $o ).
tff(z9_decl,type,
z9: $o ).
tff(prove,conjecture,
~ ( ( x0
& [.] ~ x0 )
| ( <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p1
| ( ~ y1
& [.] y1 )
| ( ~ z1
& <.> <.> <.> [.] z1 )
| ~ p2
| ( ~ y2
& [.] y2 )
| ( ~ z2
& <.> <.> <.> [.] z2 )
| ~ p3
| ( ~ y3
& [.] y3 )
| ( ~ z3
& <.> <.> <.> [.] z3 )
| ~ p4
| ( ~ y4
& [.] y4 )
| ( ~ z4
& <.> <.> <.> [.] z4 )
| ~ p5
| ( ~ y5
& [.] y5 )
| ( ~ z5
& <.> <.> <.> [.] z5 )
| ~ p6
| ( ~ y6
& [.] y6 )
| ( ~ z6
& <.> <.> <.> [.] z6 )
| ~ p7
| ( ~ y7
& [.] y7 )
| ( ~ z7
& <.> <.> <.> [.] z7 )
| ~ p8
| ( ~ y8
& [.] y8 )
| ( ~ z8
& <.> <.> <.> [.] z8 )
| ~ p9
| ( ~ y9
& [.] y9 )
| ( ~ z9
& <.> <.> <.> [.] z9 )
| ~ p10
| ( ~ y10
& [.] y10 )
| ( ~ z10
& <.> <.> <.> [.] z10 )
| ~ p11
| ( ~ y11
& [.] y11 )
| ( ~ z11
& <.> <.> <.> [.] z11 )
| ~ p12
| ( ~ y12
& [.] y12 )
| ( ~ z12
& <.> <.> <.> [.] z12 )
| ~ p13
| ( ~ y13
& [.] y13 )
| ( ~ z13
& <.> <.> <.> [.] z13 )
| ~ p14
| ( ~ y14
& [.] y14 )
| ( ~ z14
& <.> <.> <.> [.] z14 )
| ~ p15
| ( ~ y15
& [.] y15 )
| ( ~ z15
& <.> <.> <.> [.] z15 )
| ~ p16
| ( ~ y16
& [.] y16 )
| ( ~ z16
& <.> <.> <.> [.] z16 )
| ~ p17
| ( ~ y17
& [.] y17 )
| ( ~ z17
& <.> <.> <.> [.] z17 )
| ~ p18
| ( ~ y18
& [.] y18 )
| ( ~ z18
& <.> <.> <.> [.] z18 )
| ~ p19
| ( ~ y19
& [.] y19 )
| ( ~ z19
& <.> <.> <.> [.] z19 )
| ~ p20
| ( ~ y20
& [.] y20 )
| ( ~ z20
& <.> <.> <.> [.] z20 ) )
& [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] [.] ( ( ( p1
| ( ~ y1
& [.] y1 )
| ( ~ z1
& <.> <.> <.> [.] z1 ) )
& ( ~ p2
| ( ~ y2
& [.] y2 )
| ( ~ z2
& <.> <.> <.> [.] z2 ) ) )
| ( ( p2
| ( ~ y2
& [.] y2 )
| ( ~ z2
& <.> <.> <.> [.] z2 ) )
& ( ~ p1
| ( ~ y1
& [.] y1 )
| ( ~ z1
& <.> <.> <.> [.] z1 ) ) ) )
& <.> ( ~ p3
| ( ~ y3
& [.] y3 )
| ( ~ z3
& <.> <.> <.> [.] z3 ) )
& [.] [.] ( ( ( p2
| ( ~ y2
& [.] y2 )
| ( ~ z2
& <.> <.> <.> [.] z2 ) )
& ( ~ p3
| ( ~ y3
& [.] y3 )
| ( ~ z3
& <.> <.> <.> [.] z3 ) ) )
| ( ( p3
| ( ~ y3
& [.] y3 )
| ( ~ z3
& <.> <.> <.> [.] z3 ) )
& ( ~ p2
| ( ~ y2
& [.] y2 )
| ( ~ z2
& <.> <.> <.> [.] z2 ) ) ) ) )
& <.> ( ~ p4
| ( ~ y4
& [.] y4 )
| ( ~ z4
& <.> <.> <.> [.] z4 ) )
& [.] [.] [.] ( ( ( p3
| ( ~ y3
& [.] y3 )
| ( ~ z3
& <.> <.> <.> [.] z3 ) )
& ( ~ p4
| ( ~ y4
& [.] y4 )
| ( ~ z4
& <.> <.> <.> [.] z4 ) ) )
| ( ( p4
| ( ~ y4
& [.] y4 )
| ( ~ z4
& <.> <.> <.> [.] z4 ) )
& ( ~ p3
| ( ~ y3
& [.] y3 )
| ( ~ z3
& <.> <.> <.> [.] z3 ) ) ) ) )
& <.> ( ~ p5
| ( ~ y5
& [.] y5 )
| ( ~ z5
& <.> <.> <.> [.] z5 ) )
& [.] [.] [.] [.] ( ( ( p4
| ( ~ y4
& [.] y4 )
| ( ~ z4
& <.> <.> <.> [.] z4 ) )
& ( ~ p5
| ( ~ y5
& [.] y5 )
| ( ~ z5
& <.> <.> <.> [.] z5 ) ) )
| ( ( p5
| ( ~ y5
& [.] y5 )
| ( ~ z5
& <.> <.> <.> [.] z5 ) )
& ( ~ p4
| ( ~ y4
& [.] y4 )
| ( ~ z4
& <.> <.> <.> [.] z4 ) ) ) ) )
& <.> ( ~ p6
| ( ~ y6
& [.] y6 )
| ( ~ z6
& <.> <.> <.> [.] z6 ) )
& [.] [.] [.] [.] [.] ( ( ( p5
| ( ~ y5
& [.] y5 )
| ( ~ z5
& <.> <.> <.> [.] z5 ) )
& ( ~ p6
| ( ~ y6
& [.] y6 )
| ( ~ z6
& <.> <.> <.> [.] z6 ) ) )
| ( ( p6
| ( ~ y6
& [.] y6 )
| ( ~ z6
& <.> <.> <.> [.] z6 ) )
& ( ~ p5
| ( ~ y5
& [.] y5 )
| ( ~ z5
& <.> <.> <.> [.] z5 ) ) ) ) )
& <.> ( ~ p7
| ( ~ y7
& [.] y7 )
| ( ~ z7
& <.> <.> <.> [.] z7 ) )
& [.] [.] [.] [.] [.] [.] ( ( ( p6
| ( ~ y6
& [.] y6 )
| ( ~ z6
& <.> <.> <.> [.] z6 ) )
& ( ~ p7
| ( ~ y7
& [.] y7 )
| ( ~ z7
& <.> <.> <.> [.] z7 ) ) )
| ( ( p7
| ( ~ y7
& [.] y7 )
| ( ~ z7
& <.> <.> <.> [.] z7 ) )
& ( ~ p6
| ( ~ y6
& [.] y6 )
| ( ~ z6
& <.> <.> <.> [.] z6 ) ) ) ) )
& <.> ( ~ p8
| ( ~ y8
& [.] y8 )
| ( ~ z8
& <.> <.> <.> [.] z8 ) )
& [.] [.] [.] [.] [.] [.] [.] ( ( ( p7
| ( ~ y7
& [.] y7 )
| ( ~ z7
& <.> <.> <.> [.] z7 ) )
& ( ~ p8
| ( ~ y8
& [.] y8 )
| ( ~ z8
& <.> <.> <.> [.] z8 ) ) )
| ( ( p8
| ( ~ y8
& [.] y8 )
| ( ~ z8
& <.> <.> <.> [.] z8 ) )
& ( ~ p7
| ( ~ y7
& [.] y7 )
| ( ~ z7
& <.> <.> <.> [.] z7 ) ) ) ) )
& <.> ( ~ p9
| ( ~ y9
& [.] y9 )
| ( ~ z9
& <.> <.> <.> [.] z9 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p8
| ( ~ y8
& [.] y8 )
| ( ~ z8
& <.> <.> <.> [.] z8 ) )
& ( ~ p9
| ( ~ y9
& [.] y9 )
| ( ~ z9
& <.> <.> <.> [.] z9 ) ) )
| ( ( p9
| ( ~ y9
& [.] y9 )
| ( ~ z9
& <.> <.> <.> [.] z9 ) )
& ( ~ p8
| ( ~ y8
& [.] y8 )
| ( ~ z8
& <.> <.> <.> [.] z8 ) ) ) ) )
& <.> ( ~ p10
| ( ~ y10
& [.] y10 )
| ( ~ z10
& <.> <.> <.> [.] z10 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p9
| ( ~ y9
& [.] y9 )
| ( ~ z9
& <.> <.> <.> [.] z9 ) )
& ( ~ p10
| ( ~ y10
& [.] y10 )
| ( ~ z10
& <.> <.> <.> [.] z10 ) ) )
| ( ( p10
| ( ~ y10
& [.] y10 )
| ( ~ z10
& <.> <.> <.> [.] z10 ) )
& ( ~ p9
| ( ~ y9
& [.] y9 )
| ( ~ z9
& <.> <.> <.> [.] z9 ) ) ) ) )
& <.> ( ~ p11
| ( ~ y11
& [.] y11 )
| ( ~ z11
& <.> <.> <.> [.] z11 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p10
| ( ~ y10
& [.] y10 )
| ( ~ z10
& <.> <.> <.> [.] z10 ) )
& ( ~ p11
| ( ~ y11
& [.] y11 )
| ( ~ z11
& <.> <.> <.> [.] z11 ) ) )
| ( ( p11
| ( ~ y11
& [.] y11 )
| ( ~ z11
& <.> <.> <.> [.] z11 ) )
& ( ~ p10
| ( ~ y10
& [.] y10 )
| ( ~ z10
& <.> <.> <.> [.] z10 ) ) ) ) )
& <.> ( ~ p12
| ( ~ y12
& [.] y12 )
| ( ~ z12
& <.> <.> <.> [.] z12 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p11
| ( ~ y11
& [.] y11 )
| ( ~ z11
& <.> <.> <.> [.] z11 ) )
& ( ~ p12
| ( ~ y12
& [.] y12 )
| ( ~ z12
& <.> <.> <.> [.] z12 ) ) )
| ( ( p12
| ( ~ y12
& [.] y12 )
| ( ~ z12
& <.> <.> <.> [.] z12 ) )
& ( ~ p11
| ( ~ y11
& [.] y11 )
| ( ~ z11
& <.> <.> <.> [.] z11 ) ) ) ) )
& <.> ( ~ p13
| ( ~ y13
& [.] y13 )
| ( ~ z13
& <.> <.> <.> [.] z13 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p12
| ( ~ y12
& [.] y12 )
| ( ~ z12
& <.> <.> <.> [.] z12 ) )
& ( ~ p13
| ( ~ y13
& [.] y13 )
| ( ~ z13
& <.> <.> <.> [.] z13 ) ) )
| ( ( p13
| ( ~ y13
& [.] y13 )
| ( ~ z13
& <.> <.> <.> [.] z13 ) )
& ( ~ p12
| ( ~ y12
& [.] y12 )
| ( ~ z12
& <.> <.> <.> [.] z12 ) ) ) ) )
& <.> ( ~ p14
| ( ~ y14
& [.] y14 )
| ( ~ z14
& <.> <.> <.> [.] z14 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p13
| ( ~ y13
& [.] y13 )
| ( ~ z13
& <.> <.> <.> [.] z13 ) )
& ( ~ p14
| ( ~ y14
& [.] y14 )
| ( ~ z14
& <.> <.> <.> [.] z14 ) ) )
| ( ( p14
| ( ~ y14
& [.] y14 )
| ( ~ z14
& <.> <.> <.> [.] z14 ) )
& ( ~ p13
| ( ~ y13
& [.] y13 )
| ( ~ z13
& <.> <.> <.> [.] z13 ) ) ) ) )
& <.> ( ~ p15
| ( ~ y15
& [.] y15 )
| ( ~ z15
& <.> <.> <.> [.] z15 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p14
| ( ~ y14
& [.] y14 )
| ( ~ z14
& <.> <.> <.> [.] z14 ) )
& ( ~ p15
| ( ~ y15
& [.] y15 )
| ( ~ z15
& <.> <.> <.> [.] z15 ) ) )
| ( ( p15
| ( ~ y15
& [.] y15 )
| ( ~ z15
& <.> <.> <.> [.] z15 ) )
& ( ~ p14
| ( ~ y14
& [.] y14 )
| ( ~ z14
& <.> <.> <.> [.] z14 ) ) ) ) )
& <.> ( ~ p16
| ( ~ y16
& [.] y16 )
| ( ~ z16
& <.> <.> <.> [.] z16 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p15
| ( ~ y15
& [.] y15 )
| ( ~ z15
& <.> <.> <.> [.] z15 ) )
& ( ~ p16
| ( ~ y16
& [.] y16 )
| ( ~ z16
& <.> <.> <.> [.] z16 ) ) )
| ( ( p16
| ( ~ y16
& [.] y16 )
| ( ~ z16
& <.> <.> <.> [.] z16 ) )
& ( ~ p15
| ( ~ y15
& [.] y15 )
| ( ~ z15
& <.> <.> <.> [.] z15 ) ) ) ) )
& <.> ( ~ p17
| ( ~ y17
& [.] y17 )
| ( ~ z17
& <.> <.> <.> [.] z17 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p16
| ( ~ y16
& [.] y16 )
| ( ~ z16
& <.> <.> <.> [.] z16 ) )
& ( ~ p17
| ( ~ y17
& [.] y17 )
| ( ~ z17
& <.> <.> <.> [.] z17 ) ) )
| ( ( p17
| ( ~ y17
& [.] y17 )
| ( ~ z17
& <.> <.> <.> [.] z17 ) )
& ( ~ p16
| ( ~ y16
& [.] y16 )
| ( ~ z16
& <.> <.> <.> [.] z16 ) ) ) ) )
& <.> ( ~ p18
| ( ~ y18
& [.] y18 )
| ( ~ z18
& <.> <.> <.> [.] z18 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p17
| ( ~ y17
& [.] y17 )
| ( ~ z17
& <.> <.> <.> [.] z17 ) )
& ( ~ p18
| ( ~ y18
& [.] y18 )
| ( ~ z18
& <.> <.> <.> [.] z18 ) ) )
| ( ( p18
| ( ~ y18
& [.] y18 )
| ( ~ z18
& <.> <.> <.> [.] z18 ) )
& ( ~ p17
| ( ~ y17
& [.] y17 )
| ( ~ z17
& <.> <.> <.> [.] z17 ) ) ) ) )
& <.> ( ~ p19
| ( ~ y19
& [.] y19 )
| ( ~ z19
& <.> <.> <.> [.] z19 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p18
| ( ~ y18
& [.] y18 )
| ( ~ z18
& <.> <.> <.> [.] z18 ) )
& ( ~ p19
| ( ~ y19
& [.] y19 )
| ( ~ z19
& <.> <.> <.> [.] z19 ) ) )
| ( ( p19
| ( ~ y19
& [.] y19 )
| ( ~ z19
& <.> <.> <.> [.] z19 ) )
& ( ~ p18
| ( ~ y18
& [.] y18 )
| ( ~ z18
& <.> <.> <.> [.] z18 ) ) ) ) )
& <.> ( ~ p20
| ( ~ y20
& [.] y20 )
| ( ~ z20
& <.> <.> <.> [.] z20 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p19
| ( ~ y19
& [.] y19 )
| ( ~ z19
& <.> <.> <.> [.] z19 ) )
& ( ~ p1
| ( ~ y1
& [.] y1 )
| ( ~ z1
& <.> <.> <.> [.] z1 ) ) )
| ( ( p1
| ( ~ y1
& [.] y1 )
| ( ~ z1
& <.> <.> <.> [.] z1 ) )
& ( ~ p19
| ( ~ y19
& [.] y19 )
| ( ~ z19
& <.> <.> <.> [.] z19 ) ) ) ) )
& <.> ( ~ p21
| ( ~ y21
& [.] y21 )
| ( ~ z21
& <.> <.> <.> [.] z21 ) )
& <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( p2
| ( ~ y2
& [.] y2 )
| ( ~ z2
& <.> <.> <.> [.] z2 )
| p4
| ( ~ y4
& [.] y4 )
| ( ~ z4
& <.> <.> <.> [.] z4 )
| p6
| ( ~ y6
& [.] y6 )
| ( ~ z6
& <.> <.> <.> [.] z6 )
| p8
| ( ~ y8
& [.] y8 )
| ( ~ z8
& <.> <.> <.> [.] z8 )
| p10
| ( ~ y10
& [.] y10 )
| ( ~ z10
& <.> <.> <.> [.] z10 )
| p12
| ( ~ y12
& [.] y12 )
| ( ~ z12
& <.> <.> <.> [.] z12 )
| p14
| ( ~ y14
& [.] y14 )
| ( ~ z14
& <.> <.> <.> [.] z14 )
| p16
| ( ~ y16
& [.] y16 )
| ( ~ z16
& <.> <.> <.> [.] z16 )
| p18
| ( ~ y18
& [.] y18 )
| ( ~ z18
& <.> <.> <.> [.] z18 )
| p20
| ( ~ y20
& [.] y20 )
| ( ~ z20
& <.> <.> <.> [.] z20 )
| p22
| ( ~ y22
& [.] y22 )
| ( ~ z22
& <.> <.> <.> [.] z22 )
| p24
| ( ~ y24
& [.] y24 )
| ( ~ z24
& <.> <.> <.> [.] z24 )
| p26
| ( ~ y26
& [.] y26 )
| ( ~ z26
& <.> <.> <.> [.] z26 )
| p28
| ( ~ y28
& [.] y28 )
| ( ~ z28
& <.> <.> <.> [.] z28 )
| p30
| ( ~ y30
& [.] y30 )
| ( ~ z30
& <.> <.> <.> [.] z30 )
| p32
| ( ~ y32
& [.] y32 )
| ( ~ z32
& <.> <.> <.> [.] z32 )
| p34
| ( ~ y34
& [.] y34 )
| ( ~ z34
& <.> <.> <.> [.] z34 )
| p36
| ( ~ y36
& [.] y36 )
| ( ~ z36
& <.> <.> <.> [.] z36 )
| p38
| ( ~ y38
& [.] y38 )
| ( ~ z38
& <.> <.> <.> [.] z38 )
| p40
| ( ~ y40
& [.] y40 )
| ( ~ z40
& <.> <.> <.> [.] z40 ) ) ) ) ).
%------------------------------------------------------------------------------