%------------------------------------------------------------------------------
% File     : LCL672+1.001 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Logic Calculi (Modal Logic)
% Problem  : In S4, A5{box p0/p0} & box A5{~p0/p0} -> A5, 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_45_p [BHS00]

% Status   : Theorem
% Rating   : 0.00 v6.1.0, 0.12 v6.0.0, 0.25 v5.4.0, 0.26 v5.3.0, 0.30 v5.2.0, 0.14 v5.0.0, 0.15 v4.1.0, 0.17 v4.0.1, 0.21 v4.0.0
% Syntax   : Number of formulae    :    3 (   1 unt;   0 def)
%            Number of atoms       :   53 (   0 equ)
%            Maximal formula atoms :   49 (  17 avg)
%            Number of connectives :  110 (  60   ~;  37   |;  12   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (  11 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   35 (  34   !;   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)
                  | p2(Y) )
            & ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ ( ~ ! [X] :
                            ( ~ r1(Y,X)
                            | ~ ! [Y] :
                                  ( ~ r1(X,Y)
                                  | ~ p1(Y) ) )
                      & p1(Y) ) )
            & ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | p1(Y) ) )
          | ( ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | p2(Y) )
            & ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | ! [X] :
                      ( ~ r1(Y,X)
                      | ~ ( ~ ! [Y] :
                                ( ~ r1(X,Y)
                                | ~ ! [X] :
                                      ( ~ r1(Y,X)
                                      | p1(X) ) )
                          & ~ ! [Y] :
                                ( ~ r1(X,Y)
                                | p1(Y) ) ) ) )
            & ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | p1(Y) ) )
          | ( ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | p2(Y) )
            & ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ ( ~ ! [X] :
                            ( ~ r1(Y,X)
                            | ~ ! [Y] :
                                  ( ~ r1(X,Y)
                                  | ~ ! [X] :
                                        ( ~ r1(Y,X)
                                        | p1(X) ) ) )
                      & ~ ! [X] :
                            ( ~ r1(Y,X)
                            | ~ ! [Y] :
                                  ( ~ r1(X,Y)
                                  | p1(Y) ) ) ) )
            & ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | p1(Y) ) )
          | ( ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | p2(Y) )
            & ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ ! [X] :
                        ( ~ r1(Y,X)
                        | $false ) )
            & ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | p1(Y) ) )
          | ! [Y] :
              ( ~ r1(X,Y)
              | p2(Y) )
          | ! [Y] :
              ( ~ r1(X,Y)
              | ! [X] :
                  ( ~ r1(Y,X)
                  | ~ ! [Y] :
                        ( ~ r1(X,Y)
                        | p1(Y) ) )
              | ! [X] :
                  ( ~ r1(Y,X)
                  | p1(X) ) )
          | ! [Y] :
              ( ~ r1(X,Y)
              | p1(Y) ) ) ).

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