%------------------------------------------------------------------------------
% File : LCL650+1.005 : TPTP v9.0.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In K, black and white polygon with odd number of vertices, size 5
% Version : Especial.
% English : If we have a polygon with n vertices, and all the vertices are
% either black or white, then two adjacent vertices have the same
% colour.
% Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% Source : [Kam08]
% Names : k_poly_p [BHS00]
% Status : Theorem
% Rating : 0.27 v9.0.0, 0.12 v8.2.0, 0.27 v8.1.0, 0.21 v7.5.0, 0.29 v7.4.0, 0.25 v7.3.0, 0.14 v7.2.0, 0.33 v7.1.0, 0.25 v7.0.0, 0.21 v6.3.0, 0.08 v6.2.0, 0.18 v6.1.0, 0.44 v6.0.0, 0.25 v5.5.0, 0.50 v5.4.0, 0.48 v5.3.0, 0.52 v5.2.0, 0.21 v5.1.0, 0.29 v5.0.0, 0.50 v4.0.1, 0.47 v4.0.0
% Syntax : Number of formulae : 1 ( 0 unt; 0 def)
% Number of atoms : 289 ( 0 equ)
% Maximal formula atoms : 289 ( 289 avg)
% Number of connectives : 578 ( 290 ~; 228 |; 60 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 102 ( 102 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 26 ( 26 usr; 0 prp; 1-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 183 ( 182 !; 1 ?)
% SPC : FOF_THM_RFO_NEQ
% Comments : A naive relational encoding of the modal logic problem into
% first-order logic.
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ( ~ p32(X)
& ~ p30(X)
& ~ p28(X)
& ~ p26(X)
& ~ p24(X)
& ~ p22(X)
& ~ p20(X)
& ~ p18(X)
& ~ p16(X)
& ~ p14(X)
& ~ p12(X)
& ~ p10(X)
& ~ p8(X)
& ~ p6(X)
& ~ p4(X)
& ~ p2(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p17(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p15(X)
& ~ p1(X) )
| ( p1(X)
& p15(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ! [X] :
( ~ r1(Y,X)
| p16(X) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p14(X)
& ~ p15(X) )
| ( p15(X)
& p14(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p15(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p13(X)
& ~ p14(X) )
| ( p14(X)
& p13(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ! [X] :
( ~ r1(Y,X)
| p14(X) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p12(X)
& ~ p13(X) )
| ( p13(X)
& p12(X) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p13(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p11(X)
& ~ p12(X) )
| ( p12(X)
& p11(X) ) ) ) ) ) ) ) ) ) ) ) ) )
| ! [X] :
( ~ r1(Y,X)
| p12(X) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p10(X)
& ~ p11(X) )
| ( p11(X)
& p10(X) ) ) ) ) ) ) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p11(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p9(X)
& ~ p10(X) )
| ( p10(X)
& p9(X) ) ) ) ) ) ) ) ) ) ) )
| ! [X] :
( ~ r1(Y,X)
| p10(X) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p8(X)
& ~ p9(X) )
| ( p9(X)
& p8(X) ) ) ) ) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p9(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p7(X)
& ~ p8(X) )
| ( p8(X)
& p7(X) ) ) ) ) ) ) ) ) )
| ! [X] :
( ~ r1(Y,X)
| p8(X) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p6(X)
& ~ p7(X) )
| ( p7(X)
& p6(X) ) ) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p7(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p5(X)
& ~ p6(X) )
| ( p6(X)
& p5(X) ) ) ) ) ) ) )
| ! [X] :
( ~ r1(Y,X)
| p6(X) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p4(X)
& ~ p5(X) )
| ( p5(X)
& p4(X) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p5(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p3(X)
& ~ p4(X) )
| ( p4(X)
& p3(X) ) ) ) ) )
| ! [X] :
( ~ r1(Y,X)
| p4(X) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p2(X)
& ~ p3(X) )
| ( p3(X)
& p2(X) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p3(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ~ ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p1(X)
& ~ p2(X) )
| ( p2(X)
& p1(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ( p16(X)
& p15(X)
& p14(X)
& p13(X)
& p12(X)
& p11(X)
& p10(X)
& p9(X)
& p8(X)
& p7(X)
& p6(X)
& p5(X)
& p4(X)
& p3(X)
& p2(X)
& p1(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------