%------------------------------------------------------------------------------
% File     : LCL687+1.001 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Logic Calculi (Modal Logic)
% Problem  : In S4, formula not provable in S5 embedding, 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    : s4_s5_n [BHS00]

% Status   : CounterSatisfiable
% Rating   : 0.33 v8.2.0, 0.00 v7.4.0, 0.33 v7.3.0, 0.00 v7.0.0, 0.33 v6.4.0, 0.00 v6.2.0, 0.22 v6.1.0, 0.10 v6.0.0, 0.00 v5.5.0, 0.29 v5.4.0, 0.60 v5.3.0, 0.62 v5.2.0, 0.25 v5.0.0, 0.56 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    3 (   1 unt;   0 def)
%            Number of atoms       :   12 (   0 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :   20 (  11   ~;   7   |;   1   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   3 usr;   0 prp; 1-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   10 (   9   !;   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(transitivity,axiom,
    ! [X,Y,Z] :
      ( ( r1(X,Y)
        & r1(Y,Z) )
     => r1(X,Z) ) ).

fof(main,conjecture,
    ~ ? [X] :
        ~ ( ! [Y] :
              ( ~ r1(X,Y)
              | ~ p6(Y)
              | ! [X] :
                  ( ~ r1(Y,X)
                  | ~ p1(X) ) )
          | ! [Y] :
              ( ~ r1(X,Y)
              | ~ ! [X] :
                    ( ~ r1(Y,X)
                    | ~ ! [Y] :
                          ( ~ r1(X,Y)
                          | p6(Y) ) ) ) ) ).

%------------------------------------------------------------------------------