%------------------------------------------------------------------------------
% File     : LCL686+1.001 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Logic Calculi (Modal Logic)
% Problem  : In S4, formula 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_p [BHS00]

% Status   : Theorem
% Rating   : 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.17 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.11 v4.0.0
% Syntax   : Number of formulae    :    3 (   1 unt;   0 def)
%            Number of atoms       :   24 (   0 equ)
%            Maximal formula atoms :   20 (   8 avg)
%            Number of connectives :   41 (  20   ~;  15   |;   5   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   9 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   13 (  12   !;   1   ?)
% SPC      : FOF_THM_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)
              | ~ p3(Y)
              | ! [X] :
                  ( ~ r1(Y,X)
                  | ~ p1(X) ) )
          | ! [Y] :
              ( ~ r1(X,Y)
              | ~ ! [X] :
                    ( ~ r1(Y,X)
                    | ~ ( ! [Y] :
                            ( ~ r1(X,Y)
                            | $false )
                        | ~ ! [Y] :
                              ( ~ r1(X,Y)
                              | ~ ( ( p2(Y)
                                    & ~ p1(Y) )
                                  | ( ~ p2(Y)
                                    & p1(Y) ) ) )
                        | ! [Y] :
                            ( ~ r1(X,Y)
                            | p3(Y) )
                        | ! [Y] :
                            ( ~ r1(X,Y)
                            | ( ~ p1(Y)
                              & ~ p2(Y) )
                            | ( p2(Y)
                              & p1(Y) ) ) ) ) ) ) ).

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