%------------------------------------------------------------------------------
% File : GRA079_1.002 : TPTP v9.0.0. Released v9.0.0.
% Domain : Syntactic
% Problem : Adjacent vertices in a polygon with 2 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 : k45_poly_p.0002 [Nal22]
% Status : Theorem
% Rating : 1.00 v9.0.0
% Syntax : Number of formulae : 40 ( 0 unt; 39 typ; 0 def)
% Number of atoms : 255 ( 0 equ)
% Maximal formula atoms : 255 ( 255 avg)
% Number of connectives : 699 ( 132 ~; 123 |; 131 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% ( 313 {.}; 0 {#})
% Maximal formula depth : 34 ( 34 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 : 39 ( 39 usr; 39 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('k45_poly_p.0002',logic,
$modal ==
[ $modalities == $modal_system_K45 ] ).
tff(p1_decl,type,
p1: $o ).
tff(p10_decl,type,
p10: $o ).
tff(p12_decl,type,
p12: $o ).
tff(p14_decl,type,
p14: $o ).
tff(p16_decl,type,
p16: $o ).
tff(p2_decl,type,
p2: $o ).
tff(p3_decl,type,
p3: $o ).
tff(p4_decl,type,
p4: $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(y1_decl,type,
y1: $o ).
tff(y10_decl,type,
y10: $o ).
tff(y12_decl,type,
y12: $o ).
tff(y14_decl,type,
y14: $o ).
tff(y16_decl,type,
y16: $o ).
tff(y2_decl,type,
y2: $o ).
tff(y3_decl,type,
y3: $o ).
tff(y4_decl,type,
y4: $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(z12_decl,type,
z12: $o ).
tff(z14_decl,type,
z14: $o ).
tff(z16_decl,type,
z16: $o ).
tff(z2_decl,type,
z2: $o ).
tff(z3_decl,type,
z3: $o ).
tff(z4_decl,type,
z4: $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,
~ ( <.> <.> <.> <.> <.> <.> <.> <.> ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) )
| ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) )
| ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) )
| ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| ~ p7
| ( [.] z7
& <.> [.] y7
& <.> <.> ( ~ z7
| ~ y7 ) )
| ~ p8
| ( [.] z8
& <.> [.] y8
& <.> <.> ( ~ z8
| ~ y8 ) ) )
& [.] ( [.] ( [.] ( [.] ( [.] ( [.] ( [.] [.] ( ( ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) )
| ( ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) )
& ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) ) )
& <.> ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) )
& [.] [.] ( ( ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) )
& ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) )
| ( ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) )
& ( ~ p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) ) ) ) ) )
& <.> ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) )
& [.] [.] [.] ( ( ( p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) )
& ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) )
| ( ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) )
& ( ~ p3
| ( [.] z3
& <.> [.] y3
& <.> <.> ( ~ z3
| ~ y3 ) ) ) ) ) )
& <.> ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) )
& [.] [.] [.] [.] ( ( ( p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) )
& ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) )
| ( ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) )
& ( ~ p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) ) ) ) ) )
& <.> ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) )
& [.] [.] [.] [.] [.] ( ( ( p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) )
& ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) )
| ( ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) )
& ( ~ p5
| ( [.] z5
& <.> [.] y5
& <.> <.> ( ~ z5
| ~ y5 ) ) ) ) ) )
& <.> ( ~ p7
| ( [.] z7
& <.> [.] y7
& <.> <.> ( ~ z7
| ~ y7 ) ) )
& [.] [.] [.] [.] [.] [.] ( ( ( p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) )
& ( ~ p7
| ( [.] z7
& <.> [.] y7
& <.> <.> ( ~ z7
| ~ y7 ) ) ) )
| ( ( p7
| ( [.] z7
& <.> [.] y7
& <.> <.> ( ~ z7
| ~ y7 ) ) )
& ( ~ p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) ) ) ) ) )
& <.> ( ~ p8
| ( [.] z8
& <.> [.] y8
& <.> <.> ( ~ z8
| ~ y8 ) ) )
& [.] [.] [.] [.] [.] [.] [.] ( ( ( p7
| ( [.] z7
& <.> [.] y7
& <.> <.> ( ~ z7
| ~ y7 ) ) )
& ( ~ p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) ) )
| ( ( p1
| ( [.] z1
& <.> [.] y1
& <.> <.> ( ~ z1
| ~ y1 ) ) )
& ( ~ p7
| ( [.] z7
& <.> [.] y7
& <.> <.> ( ~ z7
| ~ y7 ) ) ) ) ) )
& <.> ( ~ p9
| ( [.] z9
& <.> [.] y9
& <.> <.> ( ~ z9
| ~ y9 ) ) )
& <.> <.> <.> <.> <.> <.> <.> <.> ( p2
| ( [.] z2
& <.> [.] y2
& <.> <.> ( ~ z2
| ~ y2 ) )
| p4
| ( [.] z4
& <.> [.] y4
& <.> <.> ( ~ z4
| ~ y4 ) )
| p6
| ( [.] z6
& <.> [.] y6
& <.> <.> ( ~ z6
| ~ y6 ) )
| p8
| ( [.] z8
& <.> [.] y8
& <.> <.> ( ~ z8
| ~ y8 ) )
| p10
| ( [.] z10
& <.> [.] y10
& <.> <.> ( ~ z10
| ~ y10 ) )
| p12
| ( [.] z12
& <.> [.] y12
& <.> <.> ( ~ z12
| ~ y12 ) )
| p14
| ( [.] z14
& <.> [.] y14
& <.> <.> ( ~ z14
| ~ y14 ) )
| p16
| ( [.] z16
& <.> [.] y16
& <.> <.> ( ~ z16
| ~ y16 ) ) ) ) ).
%------------------------------------------------------------------------------