## TPTP Problem File: LCL648+1.005.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : LCL648+1.005 : TPTP v8.1.0. Released v4.0.0.
% Domain   : Logic Calculi (Modal Logic)
% Problem  : In K, pigeonhole formulae, 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    : k_ph_p [BHS00]

% Status   : Theorem
% Rating   : 0.27 v8.1.0, 0.21 v7.5.0, 0.29 v7.4.0, 0.12 v7.3.0, 0.14 v7.2.0, 0.17 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.07 v6.3.0, 0.15 v6.2.0, 0.18 v6.1.0, 0.40 v6.0.0, 0.25 v5.5.0, 0.54 v5.4.0, 0.52 v5.3.0, 0.57 v5.2.0, 0.36 v5.1.0, 0.43 v5.0.0, 0.65 v4.1.0, 0.78 v4.0.1, 0.79 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :  242 (   0 equ)
%            Maximal formula atoms :  242 ( 242 avg)
%            Number of connectives :  308 (  67   ~; 161   |;  80   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   84 (  84 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_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)
| ~ ( ( 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) ) ) )
| ! [Y] :
( ~ r1(X,Y)
| ~ ( ( p605(Y)
| p604(Y)
| p603(Y)
| p602(Y)
| p601(Y) )
& ( p505(Y)
| p504(Y)
| p503(Y)
| p502(Y)
| p501(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p405(X) )
| p404(Y)
| p403(Y)
| p402(Y)
| p401(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p305(X) )
| ! [X] :
( ~ r1(Y,X)
| p304(X) )
| p303(Y)
| p302(Y)
| p301(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p205(X) )
| ! [X] :
( ~ r1(Y,X)
| p204(X) )
| ! [X] :
( ~ r1(Y,X)
| p203(X) )
| p202(Y)
| p201(Y) )
& ( ! [X] :
( ~ r1(Y,X)
| p105(X) )
| ! [X] :
( ~ r1(Y,X)
| p104(X) )
| ! [X] :
( ~ r1(Y,X)
| p103(X) )
| ! [X] :
( ~ r1(Y,X)
| p102(X) )
| p101(Y) ) ) ) ) ).

%------------------------------------------------------------------------------
```