TPTP Problem File: GRA077_1.010.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : GRA077_1.010 : TPTP v9.0.0. Released v9.0.0.
% Domain : Syntactic
% Problem : Adjacent vertices in a polygon with 10 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 : k4_poly_p.0010 [Nal22]
% Status : Theorem
% Rating : 1.00 v9.0.0
% Syntax : Number of formulae : 99 ( 0 unt; 98 typ; 0 def)
% Number of atoms : 657 ( 0 equ)
% Maximal formula atoms : 657 ( 657 avg)
% Number of connectives : 2280 ( 345 ~; 312 |; 344 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% (1279 {.}; 0 {#})
% Maximal formula depth : 104 ( 104 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 : 98 ( 98 usr; 98 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('k4_poly_p.0010',logic,
$modal ==
[ $modalities == $modal_system_K4 ] ).
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(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(p36_decl,type,
p36: $o ).
tff(p38_decl,type,
p38: $o ).
tff(p4_decl,type,
p4: $o ).
tff(p40_decl,type,
p40: $o ).
tff(p42_decl,type,
p42: $o ).
tff(p44_decl,type,
p44: $o ).
tff(p46_decl,type,
p46: $o ).
tff(p48_decl,type,
p48: $o ).
tff(p5_decl,type,
p5: $o ).
tff(p50_decl,type,
p50: $o ).
tff(p52_decl,type,
p52: $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(p7_decl,type,
p7: $o ).
tff(p8_decl,type,
p8: $o ).
tff(p9_decl,type,
p9: $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(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(z36_decl,type,
z36: $o ).
tff(z38_decl,type,
z38: $o ).
tff(z4_decl,type,
z4: $o ).
tff(z40_decl,type,
z40: $o ).
tff(z42_decl,type,
z42: $o ).
tff(z44_decl,type,
z44: $o ).
tff(z46_decl,type,
z46: $o ).
tff(z48_decl,type,
z48: $o ).
tff(z5_decl,type,
z5: $o ).
tff(z50_decl,type,
z50: $o ).
tff(z52_decl,type,
z52: $o ).
tff(z54_decl,type,
z54: $o ).
tff(z56_decl,type,
z56: $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(z7_decl,type,
z7: $o ).
tff(z8_decl,type,
z8: $o ).
tff(z9_decl,type,
z9: $o ).
tff(prove,conjecture,
~ ( <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( ~ 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 ) )
& [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] [.] ( ( ( 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 ) ) ) ) )
& <.> ( ~ p13
| ( [.] z13
& <.> <.> ~ z13 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p12
| ( [.] z12
& <.> <.> ~ z12 ) )
& ( ~ p13
| ( [.] z13
& <.> <.> ~ z13 ) ) )
| ( ( p13
| ( [.] z13
& <.> <.> ~ z13 ) )
& ( ~ p12
| ( [.] z12
& <.> <.> ~ z12 ) ) ) ) )
& <.> ( ~ p14
| ( [.] z14
& <.> <.> ~ z14 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p13
| ( [.] z13
& <.> <.> ~ z13 ) )
& ( ~ p14
| ( [.] z14
& <.> <.> ~ z14 ) ) )
| ( ( p14
| ( [.] z14
& <.> <.> ~ z14 ) )
& ( ~ p13
| ( [.] z13
& <.> <.> ~ z13 ) ) ) ) )
& <.> ( ~ p15
| ( [.] z15
& <.> <.> ~ z15 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p14
| ( [.] z14
& <.> <.> ~ z14 ) )
& ( ~ p15
| ( [.] z15
& <.> <.> ~ z15 ) ) )
| ( ( p15
| ( [.] z15
& <.> <.> ~ z15 ) )
& ( ~ p14
| ( [.] z14
& <.> <.> ~ z14 ) ) ) ) )
& <.> ( ~ p16
| ( [.] z16
& <.> <.> ~ z16 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p15
| ( [.] z15
& <.> <.> ~ z15 ) )
& ( ~ p16
| ( [.] z16
& <.> <.> ~ z16 ) ) )
| ( ( p16
| ( [.] z16
& <.> <.> ~ z16 ) )
& ( ~ p15
| ( [.] z15
& <.> <.> ~ z15 ) ) ) ) )
& <.> ( ~ p17
| ( [.] z17
& <.> <.> ~ z17 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p16
| ( [.] z16
& <.> <.> ~ z16 ) )
& ( ~ p17
| ( [.] z17
& <.> <.> ~ z17 ) ) )
| ( ( p17
| ( [.] z17
& <.> <.> ~ z17 ) )
& ( ~ p16
| ( [.] z16
& <.> <.> ~ z16 ) ) ) ) )
& <.> ( ~ p18
| ( [.] z18
& <.> <.> ~ z18 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p17
| ( [.] z17
& <.> <.> ~ z17 ) )
& ( ~ p18
| ( [.] z18
& <.> <.> ~ z18 ) ) )
| ( ( p18
| ( [.] z18
& <.> <.> ~ z18 ) )
& ( ~ p17
| ( [.] z17
& <.> <.> ~ z17 ) ) ) ) )
& <.> ( ~ p19
| ( [.] z19
& <.> <.> ~ z19 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p18
| ( [.] z18
& <.> <.> ~ z18 ) )
& ( ~ p19
| ( [.] z19
& <.> <.> ~ z19 ) ) )
| ( ( p19
| ( [.] z19
& <.> <.> ~ z19 ) )
& ( ~ p18
| ( [.] z18
& <.> <.> ~ z18 ) ) ) ) )
& <.> ( ~ p20
| ( [.] z20
& <.> <.> ~ z20 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p19
| ( [.] z19
& <.> <.> ~ z19 ) )
& ( ~ p20
| ( [.] z20
& <.> <.> ~ z20 ) ) )
| ( ( p20
| ( [.] z20
& <.> <.> ~ z20 ) )
& ( ~ p19
| ( [.] z19
& <.> <.> ~ z19 ) ) ) ) )
& <.> ( ~ p21
| ( [.] z21
& <.> <.> ~ z21 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p20
| ( [.] z20
& <.> <.> ~ z20 ) )
& ( ~ p21
| ( [.] z21
& <.> <.> ~ z21 ) ) )
| ( ( p21
| ( [.] z21
& <.> <.> ~ z21 ) )
& ( ~ p20
| ( [.] z20
& <.> <.> ~ z20 ) ) ) ) )
& <.> ( ~ p22
| ( [.] z22
& <.> <.> ~ z22 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p21
| ( [.] z21
& <.> <.> ~ z21 ) )
& ( ~ p22
| ( [.] z22
& <.> <.> ~ z22 ) ) )
| ( ( p22
| ( [.] z22
& <.> <.> ~ z22 ) )
& ( ~ p21
| ( [.] z21
& <.> <.> ~ z21 ) ) ) ) )
& <.> ( ~ p23
| ( [.] z23
& <.> <.> ~ z23 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p22
| ( [.] z22
& <.> <.> ~ z22 ) )
& ( ~ p23
| ( [.] z23
& <.> <.> ~ z23 ) ) )
| ( ( p23
| ( [.] z23
& <.> <.> ~ z23 ) )
& ( ~ p22
| ( [.] z22
& <.> <.> ~ z22 ) ) ) ) )
& <.> ( ~ p24
| ( [.] z24
& <.> <.> ~ z24 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p23
| ( [.] z23
& <.> <.> ~ z23 ) )
& ( ~ p24
| ( [.] z24
& <.> <.> ~ z24 ) ) )
| ( ( p24
| ( [.] z24
& <.> <.> ~ z24 ) )
& ( ~ p23
| ( [.] z23
& <.> <.> ~ z23 ) ) ) ) )
& <.> ( ~ p25
| ( [.] z25
& <.> <.> ~ z25 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p24
| ( [.] z24
& <.> <.> ~ z24 ) )
& ( ~ p25
| ( [.] z25
& <.> <.> ~ z25 ) ) )
| ( ( p25
| ( [.] z25
& <.> <.> ~ z25 ) )
& ( ~ p24
| ( [.] z24
& <.> <.> ~ z24 ) ) ) ) )
& <.> ( ~ p26
| ( [.] z26
& <.> <.> ~ z26 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p25
| ( [.] z25
& <.> <.> ~ z25 ) )
& ( ~ p26
| ( [.] z26
& <.> <.> ~ z26 ) ) )
| ( ( p26
| ( [.] z26
& <.> <.> ~ z26 ) )
& ( ~ p25
| ( [.] z25
& <.> <.> ~ z25 ) ) ) ) )
& <.> ( ~ p27
| ( [.] z27
& <.> <.> ~ z27 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p26
| ( [.] z26
& <.> <.> ~ z26 ) )
& ( ~ p27
| ( [.] z27
& <.> <.> ~ z27 ) ) )
| ( ( p27
| ( [.] z27
& <.> <.> ~ z27 ) )
& ( ~ p26
| ( [.] z26
& <.> <.> ~ z26 ) ) ) ) )
& <.> ( ~ p28
| ( [.] z28
& <.> <.> ~ z28 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p27
| ( [.] z27
& <.> <.> ~ z27 ) )
& ( ~ p28
| ( [.] z28
& <.> <.> ~ z28 ) ) )
| ( ( p28
| ( [.] z28
& <.> <.> ~ z28 ) )
& ( ~ p27
| ( [.] z27
& <.> <.> ~ z27 ) ) ) ) )
& <.> ( ~ p29
| ( [.] z29
& <.> <.> ~ z29 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p28
| ( [.] z28
& <.> <.> ~ z28 ) )
& ( ~ p29
| ( [.] z29
& <.> <.> ~ z29 ) ) )
| ( ( p29
| ( [.] z29
& <.> <.> ~ z29 ) )
& ( ~ p28
| ( [.] z28
& <.> <.> ~ z28 ) ) ) ) )
& <.> ( ~ p30
| ( [.] z30
& <.> <.> ~ z30 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p29
| ( [.] z29
& <.> <.> ~ z29 ) )
& ( ~ p30
| ( [.] z30
& <.> <.> ~ z30 ) ) )
| ( ( p30
| ( [.] z30
& <.> <.> ~ z30 ) )
& ( ~ p29
| ( [.] z29
& <.> <.> ~ z29 ) ) ) ) )
& <.> ( ~ p31
| ( [.] z31
& <.> <.> ~ z31 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p30
| ( [.] z30
& <.> <.> ~ z30 ) )
& ( ~ p31
| ( [.] z31
& <.> <.> ~ z31 ) ) )
| ( ( p31
| ( [.] z31
& <.> <.> ~ z31 ) )
& ( ~ p30
| ( [.] z30
& <.> <.> ~ z30 ) ) ) ) )
& <.> ( ~ p32
| ( [.] z32
& <.> <.> ~ z32 ) )
& [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( ( ( p31
| ( [.] z31
& <.> <.> ~ z31 ) )
& ( ~ p1
| ( [.] z1
& <.> <.> ~ z1 ) ) )
| ( ( p1
| ( [.] z1
& <.> <.> ~ z1 ) )
& ( ~ p31
| ( [.] z31
& <.> <.> ~ z31 ) ) ) ) )
& <.> ( ~ p33
| ( [.] z33
& <.> <.> ~ z33 ) )
& <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ( 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 ) ) ) ).
%------------------------------------------------------------------------------