%------------------------------------------------------------------------------
% File : LCL668+1.001 : TPTP v9.0.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In KT, black and white polygon with odd number of vertices, size 1
% 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 : kt_poly_p [BHS00]
% Status : Theorem
% Rating : 0.13 v9.0.0, 0.00 v7.5.0, 0.14 v7.4.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.2.0, 0.09 v6.1.0, 0.16 v6.0.0, 0.25 v5.5.0, 0.33 v5.4.0, 0.30 v5.2.0, 0.07 v5.0.0, 0.25 v4.1.0, 0.28 v4.0.1, 0.26 v4.0.0
% Syntax : Number of formulae : 2 ( 1 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 84 ( 42 avg)
% Number of connectives : 168 ( 85 ~; 63 |; 20 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 24 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 11 usr; 0 prp; 1-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 49 ( 48 !; 1 ?)
% SPC : FOF_THM_RFO_NEQ
% Comments : A naive relational encoding of the modal logic problem into
% first-order logic.
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X) ).
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)
| ( ~ p12(X)
& ~ p10(X)
& ~ p8(X)
& ~ p6(X)
& ~ p4(X)
& ~ p2(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)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ~ ( ( ~ p5(X)
& ~ p1(X) )
| ( p1(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)
| ! [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)
| ! [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)
| ! [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)
| ! [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)
| ( p6(X)
& p5(X)
& p4(X)
& p3(X)
& p2(X)
& p1(X) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------