%------------------------------------------------------------------------------
% File : LCL669+1.001 : TPTP v9.0.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In KT, black and white polygon with even 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_n [BHS00]
% Status : CounterSatisfiable
% Rating : 0.20 v9.0.0, 0.33 v8.2.0, 0.00 v7.5.0, 0.33 v7.4.0, 0.00 v7.1.0, 0.33 v6.4.0, 0.00 v6.2.0, 0.11 v6.1.0, 0.10 v6.0.0, 0.14 v5.4.0, 0.40 v5.3.0, 0.46 v5.2.0, 0.25 v5.0.0, 0.33 v4.1.0, 0.17 v4.0.1, 0.33 v4.0.0
% Syntax : Number of formulae : 2 ( 1 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 66 ( 33 avg)
% Number of connectives : 132 ( 67 ~; 49 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 21 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 9 usr; 0 prp; 1-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 38 ( 37 !; 1 ?)
% SPC : FOF_CSA_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)
| ( ~ p10(Y)
& ~ p8(Y)
& ~ p6(Y)
& ~ p4(Y)
& ~ p2(Y) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p6(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)
| ~ ( ( ~ p4(Y)
& ~ p1(Y) )
| ( p1(Y)
& p4(Y) ) ) ) ) ) ) ) )
| ! [X] :
( ~ r1(Y,X)
| p5(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)
| ~ ( ( ~ p3(Y)
& ~ p4(Y) )
| ( p4(Y)
& p3(Y) ) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| p4(Y) )
| ~ ! [Y] :
( ~ r1(X,Y)
| ~ ( ~ ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ~ ( ( ~ p2(Y)
& ~ p3(Y) )
| ( p3(Y)
& p2(Y) ) ) ) ) ) )
| ! [X] :
( ~ r1(Y,X)
| p3(X) )
| ~ ! [X] :
( ~ r1(Y,X)
| ~ ~ ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ~ ( ( ~ p1(Y)
& ~ p2(Y) )
| ( p2(Y)
& p1(Y) ) ) ) ) ) ) ) ) ) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ! [X] :
( ~ r1(Y,X)
| ! [Y] :
( ~ r1(X,Y)
| ( p5(Y)
& p4(Y)
& p3(Y)
& p2(Y)
& p1(Y) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------