%------------------------------------------------------------------------------
% File : LCL667+1.005 : TPTP v9.0.0. Released v4.0.0.
% Domain : Logic Calculi (Modal Logic)
% Problem : In KT, pigeonhole formulae missing a conjunct, size 5
% Version : Especial.
% English :
% Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% Source : [Kam08]
% Names : kt_ph_n [BHS00]
% Status : CounterSatisfiable
% Rating : 0.00 v7.0.0, 0.33 v6.4.0, 0.00 v5.5.0, 0.14 v5.4.0, 0.13 v5.3.0, 0.23 v5.2.0, 0.12 v5.0.0, 0.22 v4.1.0, 0.17 v4.0.1, 0.00 v4.0.0
% Syntax : Number of formulae : 2 ( 1 unt; 0 def)
% Number of atoms : 242 ( 0 equ)
% Maximal formula atoms : 241 ( 121 avg)
% Number of connectives : 311 ( 71 ~; 160 |; 80 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 84 ( 43 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 31 ( 31 usr; 0 prp; 1-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 63 ( 62 !; 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)
| ~ ( ( p605(Y)
& p505(Y) )
| ( p605(Y)
& ! [X] :
( ~ r1(Y,X)
| p405(X) ) )
| ( p505(Y)
& ! [X] :
( ~ r1(Y,X)
| p405(X) ) )
| ( p605(Y)
& ! [X] :
( ~ r1(Y,X)
| p305(X) ) )
| ( p505(Y)
& ! [X] :
( ~ r1(Y,X)
| p305(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p405(X) )
& ! [X] :
( ~ r1(Y,X)
| p305(X) ) )
| ( p605(Y)
& ! [X] :
( ~ r1(Y,X)
| p205(X) ) )
| ( p505(Y)
& ! [X] :
( ~ r1(Y,X)
| p205(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p405(X) )
& ! [X] :
( ~ r1(Y,X)
| p205(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p305(X) )
& ! [X] :
( ~ r1(Y,X)
| p205(X) ) )
| ( p605(Y)
& ! [X] :
( ~ r1(Y,X)
| p105(X) ) )
| ( p505(Y)
& ! [X] :
( ~ r1(Y,X)
| p105(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p405(X) )
& ! [X] :
( ~ r1(Y,X)
| p105(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p305(X) )
& ! [X] :
( ~ r1(Y,X)
| p105(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p205(X) )
& ! [X] :
( ~ r1(Y,X)
| p105(X) ) )
| ( p604(Y)
& p504(Y) )
| ( p604(Y)
& ~ p404(Y) )
| ( p504(Y)
& ~ p404(Y) )
| ( p604(Y)
& ! [X] :
( ~ r1(Y,X)
| p304(X) ) )
| ( p504(Y)
& ! [X] :
( ~ r1(Y,X)
| p304(X) ) )
| ( ~ p404(Y)
& ! [X] :
( ~ r1(Y,X)
| p304(X) ) )
| ( p604(Y)
& ! [X] :
( ~ r1(Y,X)
| p204(X) ) )
| ( p504(Y)
& ! [X] :
( ~ r1(Y,X)
| p204(X) ) )
| ( ~ p404(Y)
& ! [X] :
( ~ r1(Y,X)
| p204(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p304(X) )
& ! [X] :
( ~ r1(Y,X)
| p204(X) ) )
| ( p604(Y)
& ! [X] :
( ~ r1(Y,X)
| p104(X) ) )
| ( p504(Y)
& ! [X] :
( ~ r1(Y,X)
| p104(X) ) )
| ( ~ p404(Y)
& ! [X] :
( ~ r1(Y,X)
| p104(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p304(X) )
& ! [X] :
( ~ r1(Y,X)
| p104(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p204(X) )
& ! [X] :
( ~ r1(Y,X)
| p104(X) ) )
| ( p603(Y)
& p503(Y) )
| ( p603(Y)
& p403(Y) )
| ( p503(Y)
& p403(Y) )
| ( p603(Y)
& p303(Y) )
| ( p503(Y)
& p303(Y) )
| ( p403(Y)
& p303(Y) )
| ( p603(Y)
& ! [X] :
( ~ r1(Y,X)
| p203(X) ) )
| ( p503(Y)
& ! [X] :
( ~ r1(Y,X)
| p203(X) ) )
| ( p403(Y)
& ! [X] :
( ~ r1(Y,X)
| p203(X) ) )
| ( p303(Y)
& ! [X] :
( ~ r1(Y,X)
| p203(X) ) )
| ( p603(Y)
& ! [X] :
( ~ r1(Y,X)
| p103(X) ) )
| ( p503(Y)
& ! [X] :
( ~ r1(Y,X)
| p103(X) ) )
| ( p403(Y)
& ! [X] :
( ~ r1(Y,X)
| p103(X) ) )
| ( p303(Y)
& ! [X] :
( ~ r1(Y,X)
| p103(X) ) )
| ( ! [X] :
( ~ r1(Y,X)
| p203(X) )
& ! [X] :
( ~ r1(Y,X)
| p103(X) ) )
| ( p602(Y)
& p502(Y) )
| ( p602(Y)
& p402(Y) )
| ( p502(Y)
& p402(Y) )
| ( p602(Y)
& p302(Y) )
| ( p502(Y)
& p302(Y) )
| ( p402(Y)
& p302(Y) )
| ( p602(Y)
& p202(Y) )
| ( p502(Y)
& p202(Y) )
| ( p402(Y)
& p202(Y) )
| ( p302(Y)
& p202(Y) )
| ( p602(Y)
& ! [X] :
( ~ r1(Y,X)
| p102(X) ) )
| ( p502(Y)
& ! [X] :
( ~ r1(Y,X)
| p102(X) ) )
| ( p402(Y)
& ! [X] :
( ~ r1(Y,X)
| p102(X) ) )
| ( p302(Y)
& ! [X] :
( ~ r1(Y,X)
| p102(X) ) )
| ( p202(Y)
& ! [X] :
( ~ r1(Y,X)
| p102(X) ) )
| ( p601(Y)
& p501(Y) )
| ( p601(Y)
& p401(Y) )
| ( p501(Y)
& p401(Y) )
| ( p601(Y)
& p301(Y) )
| ( p501(Y)
& p301(Y) )
| ( p401(Y)
& p301(Y) )
| ( p601(Y)
& p201(Y) )
| ( p501(Y)
& p201(Y) )
| ( p401(Y)
& p201(Y) )
| ( p301(Y)
& p201(Y) )
| ( p601(Y)
& p101(Y) )
| ( p501(Y)
& p101(Y) )
| ( p401(Y)
& p101(Y) )
| ( p301(Y)
& p101(Y) )
| ( p201(Y)
& p101(Y) ) ) )
| ~ ( ( p605(X)
| p604(X)
| p603(X)
| p602(X)
| p601(X) )
& ( p505(X)
| p504(X)
| p503(X)
| p502(X)
| p501(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p405(Y) )
| p404(X)
| p403(X)
| p402(X)
| p401(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p305(Y) )
| ! [Y] :
( ~ r1(X,Y)
| p304(Y) )
| p303(X)
| p302(X)
| p301(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p205(Y) )
| ! [Y] :
( ~ r1(X,Y)
| p204(Y) )
| ! [Y] :
( ~ r1(X,Y)
| p203(Y) )
| p202(X)
| p201(X) )
& ( ! [Y] :
( ~ r1(X,Y)
| p105(Y) )
| ! [Y] :
( ~ r1(X,Y)
| p104(Y) )
| ! [Y] :
( ~ r1(X,Y)
| p103(Y) )
| ! [Y] :
( ~ r1(X,Y)
| p102(Y) )
| p101(X) ) ) ) ).
%------------------------------------------------------------------------------