TPTP Problem File: LCL648+1.005.p

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%------------------------------------------------------------------------------
% 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) ) ) ) ) ).

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