%------------------------------------------------------------------------------
% File     : LCL637+1.001 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Logic Calculi (Modal Logic)
% Problem  : In K, the branching formula, size 1
% 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_branch_n [BHS00]

% Status   : CounterSatisfiable
% Rating   : 0.00 v6.0.0, 0.14 v5.5.0, 0.00 v5.4.0, 0.13 v5.3.0, 0.15 v5.2.0, 0.12 v5.0.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :   67 (   0 equ)
%            Maximal formula atoms :   67 (  67 avg)
%            Number of connectives :  123 (  57   ~;  39   |;  27   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  16 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   6 usr;   0 prp; 1-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   14 (  13   !;   1   ?)
% SPC      : FOF_CSA_RFO_NEQ

% Comments : A naive relational encoding of the modal logic problem into
%            first-order logic.
%------------------------------------------------------------------------------
fof(main,conjecture,
    ~ ? [X] :
        ( ! [Y] :
            ( ~ r1(X,Y)
            | ( ( ( ~ ! [X] :
                        ( ~ r1(Y,X)
                        | ~ ( ~ p2(X)
                            & ~ p102(X)
                            & p101(X) ) )
                  & ~ ! [X] :
                        ( ~ r1(Y,X)
                        | ~ ( p2(X)
                            & ~ p102(X)
                            & p101(X) ) ) )
                | ~ ( ~ p101(Y)
                    & p100(Y) ) )
              & ( ( ( ! [X] :
                        ( ~ r1(Y,X)
                        | ~ p2(X)
                        | ~ p101(X) )
                    | p2(Y) )
                  & ( ! [X] :
                        ( ~ r1(Y,X)
                        | p2(X)
                        | ~ p101(X) )
                    | ~ p2(Y) ) )
                | ~ p101(Y) )
              & ( ( ( ! [X] :
                        ( ~ r1(Y,X)
                        | ~ p1(X)
                        | ~ p100(X) )
                    | p1(Y) )
                  & ( ! [X] :
                        ( ~ r1(Y,X)
                        | p1(X)
                        | ~ p100(X) )
                    | ~ p1(Y) ) )
                | ~ p100(Y) )
              & ( p101(Y)
                | ~ p102(Y) )
              & ( p100(Y)
                | ~ p101(Y) ) ) )
        & ( ( ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ ( ~ p2(Y)
                      & ~ p102(Y)
                      & p101(Y) ) )
            & ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ ( p2(Y)
                      & ~ p102(Y)
                      & p101(Y) ) ) )
          | ~ ( ~ p101(X)
              & p100(X) ) )
        & ( ( ( ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ p2(Y)
                  | ~ p101(Y) )
              | p2(X) )
            & ( ! [Y] :
                  ( ~ r1(X,Y)
                  | p2(Y)
                  | ~ p101(Y) )
              | ~ p2(X) ) )
          | ~ p101(X) )
        & ( ( ( ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ p1(Y)
                  | ~ p100(Y) )
              | p1(X) )
            & ( ! [Y] :
                  ( ~ r1(X,Y)
                  | p1(Y)
                  | ~ p100(Y) )
              | ~ p1(X) ) )
          | ~ p100(X) )
        & ( p101(X)
          | ~ p102(X) )
        & ( p100(X)
          | ~ p101(X) )
        & ~ p101(X)
        & p100(X) ) ).

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