TPTP Problem File: LCL680+1.005.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : LCL680+1.005 : TPTP v8.1.2. Released v4.0.0.
% Domain   : Logic Calculi (Modal Logic)
% Problem  : In S4, in backward search find a way through box and dia, 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    : s4_md_p [BHS00]

% Status   : Theorem
% Rating   : 0.80 v8.1.0, 0.79 v7.5.0, 0.86 v7.4.0, 0.81 v7.3.0, 0.57 v7.2.0, 0.67 v7.1.0, 0.50 v7.0.0, 0.93 v6.3.0, 0.92 v6.2.0, 0.82 v6.1.0, 1.00 v5.2.0, 0.93 v5.0.0, 0.95 v4.1.0, 0.94 v4.0.1, 0.95 v4.0.0
% Syntax   : Number of formulae    :    3 (   1 unt;   0 def)
%            Number of atoms       :  348 (   0 equ)
%            Maximal formula atoms :  344 ( 116 avg)
%            Number of connectives :  836 ( 491   ~; 331   |;  13   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  104 (  37 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   :  187 ( 186   !;   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] :
        ~ ( p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ( p2(Y)
                    | ~ ! [X] :
                          ( ~ r1(Y,X)
                          | ~ ( p2(X)
                              | ~ ! [Y] :
                                    ( ~ r1(X,Y)
                                    | ~ ( p2(Y)
                                        | ~ ! [X] :
                                              ( ~ r1(Y,X)
                                              | ~ ! [Y] :
                                                    ( ~ r1(X,Y)
                                                    | p2(Y)
                                                    | ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ( p2(X)
                                                              | ~ ! [Y] :
                                                                    ( ~ r1(X,Y)
                                                                    | ~ ( p2(Y)
                                                                        | ~ ! [X] :
                                                                              ( ~ r1(Y,X)
                                                                              | ~ ! [Y] :
                                                                                    ( ~ r1(X,Y)
                                                                                    | p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( p2(X)
                                                                                              | ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ ( p2(Y)
                                                                                                        | ~ ! [X] :
                                                                                                              ( ~ r1(Y,X)
                                                                                                              | ~ ! [Y] :
                                                                                                                    ( ~ r1(X,Y)
                                                                                                                    | p2(Y)
                                                                                                                    | ~ ! [X] :
                                                                                                                          ( ~ r1(Y,X)
                                                                                                                          | ~ ( p2(X)
                                                                                                                              | ~ ! [Y] :
                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                    | ~ ( p2(Y)
                                                                                                                                        | ~ ! [X] :
                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                              | ~ ! [Y] :
                                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                                    | p2(Y)
                                                                                                                                                    | ~ ! [X] :
                                                                                                                                                          ( ~ r1(Y,X)
                                                                                                                                                          | ~ ( p2(X)
                                                                                                                                                              | ~ ! [Y] :
                                                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                                                    | ~ ( p2(Y)
                                                                                                                                                                        | ~ ! [X] :
                                                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                                                              | p1(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          | p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ( p2(Y)
                    | ~ ! [X] :
                          ( ~ r1(Y,X)
                          | ~ ( p2(X)
                              | ~ ! [Y] :
                                    ( ~ r1(X,Y)
                                    | ~ ! [X] :
                                          ( ~ r1(Y,X)
                                          | p2(X)
                                          | ~ ! [Y] :
                                                ( ~ r1(X,Y)
                                                | ~ ( p2(Y)
                                                    | ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ( p2(X)
                                                              | ~ ! [Y] :
                                                                    ( ~ r1(X,Y)
                                                                    | ~ ! [X] :
                                                                          ( ~ r1(Y,X)
                                                                          | p2(X)
                                                                          | ~ ! [Y] :
                                                                                ( ~ r1(X,Y)
                                                                                | ~ ( p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( p2(X)
                                                                                              | ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ ! [X] :
                                                                                                          ( ~ r1(Y,X)
                                                                                                          | p2(X)
                                                                                                          | ~ ! [Y] :
                                                                                                                ( ~ r1(X,Y)
                                                                                                                | ~ ( p2(Y)
                                                                                                                    | ~ ! [X] :
                                                                                                                          ( ~ r1(Y,X)
                                                                                                                          | ~ ( p2(X)
                                                                                                                              | ~ ! [Y] :
                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                    | ~ ( ~ ! [X] :
                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                              | ~ ! [Y] :
                                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                                    | p2(Y)
                                                                                                                                                    | ~ ! [X] :
                                                                                                                                                          ( ~ r1(Y,X)
                                                                                                                                                          | ~ ( p2(X)
                                                                                                                                                              | ~ ! [Y] :
                                                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                                                    | ~ ( p2(Y)
                                                                                                                                                                        | ~ ! [X] :
                                                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                                                              | ~ ( p2(X)
                                                                                                                                                                                  | ~ ! [Y] :
                                                                                                                                                                                        ( ~ r1(X,Y)
                                                                                                                                                                                        | ~ p1(Y) ) ) ) ) ) ) ) ) )
                                                                                                                                        & ~ p2(Y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          | p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ( p2(Y)
                    | ~ ! [X] :
                          ( ~ r1(Y,X)
                          | ~ ( p2(X)
                              | ~ ! [Y] :
                                    ( ~ r1(X,Y)
                                    | ~ ! [X] :
                                          ( ~ r1(Y,X)
                                          | p2(X)
                                          | ~ ! [Y] :
                                                ( ~ r1(X,Y)
                                                | ~ ( p2(Y)
                                                    | ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ( p2(X)
                                                              | ~ ! [Y] :
                                                                    ( ~ r1(X,Y)
                                                                    | ~ ! [X] :
                                                                          ( ~ r1(Y,X)
                                                                          | p2(X)
                                                                          | ~ ! [Y] :
                                                                                ( ~ r1(X,Y)
                                                                                | ~ ( p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( p2(X)
                                                                                              | ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ ! [X] :
                                                                                                          ( ~ r1(Y,X)
                                                                                                          | p2(X)
                                                                                                          | ~ ! [Y] :
                                                                                                                ( ~ r1(X,Y)
                                                                                                                | ~ ( p2(Y)
                                                                                                                    | ~ ! [X] :
                                                                                                                          ( ~ r1(Y,X)
                                                                                                                          | ~ ( p2(X)
                                                                                                                              | ~ ! [Y] :
                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                    | ~ ( ~ ! [X] :
                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                              | ~ ! [Y] :
                                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                                    | p2(Y)
                                                                                                                                                    | ~ ! [X] :
                                                                                                                                                          ( ~ r1(Y,X)
                                                                                                                                                          | ~ ( p2(X)
                                                                                                                                                              | ~ ! [Y] :
                                                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                                                    | ~ ( p2(Y)
                                                                                                                                                                        | ~ ! [X] :
                                                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                                                              | ~ ( p2(X)
                                                                                                                                                                                  | ~ ! [Y] :
                                                                                                                                                                                        ( ~ r1(X,Y)
                                                                                                                                                                                        | ~ p1(Y) ) ) ) ) ) ) ) ) )
                                                                                                                                        & ~ p1(Y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          | p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ( p2(Y)
                    | ~ ! [X] :
                          ( ~ r1(Y,X)
                          | ~ ( p2(X)
                              | ~ ! [Y] :
                                    ( ~ r1(X,Y)
                                    | ~ ! [X] :
                                          ( ~ r1(Y,X)
                                          | p2(X)
                                          | ~ ! [Y] :
                                                ( ~ r1(X,Y)
                                                | ~ ( p2(Y)
                                                    | ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ( p2(X)
                                                              | ~ ! [Y] :
                                                                    ( ~ r1(X,Y)
                                                                    | ~ ! [X] :
                                                                          ( ~ r1(Y,X)
                                                                          | p2(X)
                                                                          | ~ ! [Y] :
                                                                                ( ~ r1(X,Y)
                                                                                | ~ ( p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( p2(X)
                                                                                              | ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ ! [X] :
                                                                                                          ( ~ r1(Y,X)
                                                                                                          | p2(X)
                                                                                                          | ~ ! [Y] :
                                                                                                                ( ~ r1(X,Y)
                                                                                                                | ~ ( p2(Y)
                                                                                                                    | ~ ! [X] :
                                                                                                                          ( ~ r1(Y,X)
                                                                                                                          | ~ ( p2(X)
                                                                                                                              | ~ ! [Y] :
                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                    | ~ ( ~ ! [X] :
                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                              | ~ ! [Y] :
                                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                                    | p2(Y)
                                                                                                                                                    | ~ ! [X] :
                                                                                                                                                          ( ~ r1(Y,X)
                                                                                                                                                          | ~ ( p2(X)
                                                                                                                                                              | ~ ! [Y] :
                                                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                                                    | ~ ( p2(Y)
                                                                                                                                                                        | ~ ! [X] :
                                                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                                                              | ~ ( p2(X)
                                                                                                                                                                                  | ~ ! [Y] :
                                                                                                                                                                                        ( ~ r1(X,Y)
                                                                                                                                                                                        | ~ p2(Y) ) ) ) ) ) ) ) ) )
                                                                                                                                        & ~ p1(Y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          | p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ( p2(Y)
                    | ~ ! [X] :
                          ( ~ r1(Y,X)
                          | ~ ! [Y] :
                                ( ~ r1(X,Y)
                                | p2(Y)
                                | ~ ! [X] :
                                      ( ~ r1(Y,X)
                                      | ~ ( p2(X)
                                          | ~ ! [Y] :
                                                ( ~ r1(X,Y)
                                                | ~ ( p2(Y)
                                                    | ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ! [Y] :
                                                                ( ~ r1(X,Y)
                                                                | p2(Y)
                                                                | ~ ! [X] :
                                                                      ( ~ r1(Y,X)
                                                                      | ~ ( p2(X)
                                                                          | ~ ! [Y] :
                                                                                ( ~ r1(X,Y)
                                                                                | ~ ( p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ ! [X] :
                                                                                                          ( ~ r1(Y,X)
                                                                                                          | p2(X)
                                                                                                          | ~ ! [Y] :
                                                                                                                ( ~ r1(X,Y)
                                                                                                                | ~ ( p2(Y)
                                                                                                                    | ~ ! [X] :
                                                                                                                          ( ~ r1(Y,X)
                                                                                                                          | ~ ( p2(X)
                                                                                                                              | ~ ! [Y] :
                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                    | ~ ( p2(Y)
                                                                                                                                        | ~ ! [X] :
                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                              | ~ p1(X) ) ) ) ) ) ) ) ) )
                                                                                              & ~ p2(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          | p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ( p2(Y)
                    | ~ ! [X] :
                          ( ~ r1(Y,X)
                          | ~ ! [Y] :
                                ( ~ r1(X,Y)
                                | p2(Y)
                                | ~ ! [X] :
                                      ( ~ r1(Y,X)
                                      | ~ ( p2(X)
                                          | ~ ! [Y] :
                                                ( ~ r1(X,Y)
                                                | ~ ( p2(Y)
                                                    | ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ! [Y] :
                                                                ( ~ r1(X,Y)
                                                                | p2(Y)
                                                                | ~ ! [X] :
                                                                      ( ~ r1(Y,X)
                                                                      | ~ ( p2(X)
                                                                          | ~ ! [Y] :
                                                                                ( ~ r1(X,Y)
                                                                                | ~ ( p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ ! [X] :
                                                                                                          ( ~ r1(Y,X)
                                                                                                          | p2(X)
                                                                                                          | ~ ! [Y] :
                                                                                                                ( ~ r1(X,Y)
                                                                                                                | ~ ( p2(Y)
                                                                                                                    | ~ ! [X] :
                                                                                                                          ( ~ r1(Y,X)
                                                                                                                          | ~ ( p2(X)
                                                                                                                              | ~ ! [Y] :
                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                    | ~ ( p2(Y)
                                                                                                                                        | ~ ! [X] :
                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                              | ~ p1(X) ) ) ) ) ) ) ) ) )
                                                                                              & ~ p1(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          | p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ( p2(Y)
                    | ~ ! [X] :
                          ( ~ r1(Y,X)
                          | ~ ! [Y] :
                                ( ~ r1(X,Y)
                                | p2(Y)
                                | ~ ! [X] :
                                      ( ~ r1(Y,X)
                                      | ~ ( p2(X)
                                          | ~ ! [Y] :
                                                ( ~ r1(X,Y)
                                                | ~ ( p2(Y)
                                                    | ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ! [Y] :
                                                                ( ~ r1(X,Y)
                                                                | p2(Y)
                                                                | ~ ! [X] :
                                                                      ( ~ r1(Y,X)
                                                                      | ~ ( p2(X)
                                                                          | ~ ! [Y] :
                                                                                ( ~ r1(X,Y)
                                                                                | ~ ( p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ ! [X] :
                                                                                                          ( ~ r1(Y,X)
                                                                                                          | p2(X)
                                                                                                          | ~ ! [Y] :
                                                                                                                ( ~ r1(X,Y)
                                                                                                                | ~ ( p2(Y)
                                                                                                                    | ~ ! [X] :
                                                                                                                          ( ~ r1(Y,X)
                                                                                                                          | ~ ( p2(X)
                                                                                                                              | ~ ! [Y] :
                                                                                                                                    ( ~ r1(X,Y)
                                                                                                                                    | ~ ( p2(Y)
                                                                                                                                        | ~ ! [X] :
                                                                                                                                              ( ~ r1(Y,X)
                                                                                                                                              | ~ p2(X) ) ) ) ) ) ) ) ) )
                                                                                              & ~ p1(X) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
          | p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ! [X] :
                      ( ~ r1(Y,X)
                      | p2(X)
                      | ~ ! [Y] :
                            ( ~ r1(X,Y)
                            | ~ ( p2(Y)
                                | ~ ! [X] :
                                      ( ~ r1(Y,X)
                                      | ~ ( p2(X)
                                          | ~ ! [Y] :
                                                ( ~ r1(X,Y)
                                                | ~ ( ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ! [Y] :
                                                                ( ~ r1(X,Y)
                                                                | p2(Y)
                                                                | ~ ! [X] :
                                                                      ( ~ r1(Y,X)
                                                                      | ~ ( p2(X)
                                                                          | ~ ! [Y] :
                                                                                ( ~ r1(X,Y)
                                                                                | ~ ( p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( p2(X)
                                                                                              | ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ p1(Y) ) ) ) ) ) ) ) ) )
                                                    & ~ p2(Y) ) ) ) ) ) ) ) )
          | p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ! [X] :
                      ( ~ r1(Y,X)
                      | p2(X)
                      | ~ ! [Y] :
                            ( ~ r1(X,Y)
                            | ~ ( p2(Y)
                                | ~ ! [X] :
                                      ( ~ r1(Y,X)
                                      | ~ ( p2(X)
                                          | ~ ! [Y] :
                                                ( ~ r1(X,Y)
                                                | ~ ( ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ! [Y] :
                                                                ( ~ r1(X,Y)
                                                                | p2(Y)
                                                                | ~ ! [X] :
                                                                      ( ~ r1(Y,X)
                                                                      | ~ ( p2(X)
                                                                          | ~ ! [Y] :
                                                                                ( ~ r1(X,Y)
                                                                                | ~ ( p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( p2(X)
                                                                                              | ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ p1(Y) ) ) ) ) ) ) ) ) )
                                                    & ~ p1(Y) ) ) ) ) ) ) ) )
          | p2(X)
          | ~ ! [Y] :
                ( ~ r1(X,Y)
                | ~ ! [X] :
                      ( ~ r1(Y,X)
                      | p2(X)
                      | ~ ! [Y] :
                            ( ~ r1(X,Y)
                            | ~ ( p2(Y)
                                | ~ ! [X] :
                                      ( ~ r1(Y,X)
                                      | ~ ( p2(X)
                                          | ~ ! [Y] :
                                                ( ~ r1(X,Y)
                                                | ~ ( ~ ! [X] :
                                                          ( ~ r1(Y,X)
                                                          | ~ ! [Y] :
                                                                ( ~ r1(X,Y)
                                                                | p2(Y)
                                                                | ~ ! [X] :
                                                                      ( ~ r1(Y,X)
                                                                      | ~ ( p2(X)
                                                                          | ~ ! [Y] :
                                                                                ( ~ r1(X,Y)
                                                                                | ~ ( p2(Y)
                                                                                    | ~ ! [X] :
                                                                                          ( ~ r1(Y,X)
                                                                                          | ~ ( p2(X)
                                                                                              | ~ ! [Y] :
                                                                                                    ( ~ r1(X,Y)
                                                                                                    | ~ p2(Y) ) ) ) ) ) ) ) ) )
                                                    & ~ p1(Y) ) ) ) ) ) ) ) )
          | ( ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ ! [X] :
                        ( ~ r1(Y,X)
                        | p2(X)
                        | ~ ! [Y] :
                              ( ~ r1(X,Y)
                              | ~ ( p2(Y)
                                  | ~ ! [X] :
                                        ( ~ r1(Y,X)
                                        | ~ ( p2(X)
                                            | ~ ! [Y] :
                                                  ( ~ r1(X,Y)
                                                  | ~ ( p2(Y)
                                                      | ~ ! [X] :
                                                            ( ~ r1(Y,X)
                                                            | ~ p1(X) ) ) ) ) ) ) ) ) )
            & ~ p2(X) )
          | ( ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ ! [X] :
                        ( ~ r1(Y,X)
                        | p2(X)
                        | ~ ! [Y] :
                              ( ~ r1(X,Y)
                              | ~ ( p2(Y)
                                  | ~ ! [X] :
                                        ( ~ r1(Y,X)
                                        | ~ ( p2(X)
                                            | ~ ! [Y] :
                                                  ( ~ r1(X,Y)
                                                  | ~ ( p2(Y)
                                                      | ~ ! [X] :
                                                            ( ~ r1(Y,X)
                                                            | ~ p1(X) ) ) ) ) ) ) ) ) )
            & ~ p1(X) )
          | ( ~ ! [Y] :
                  ( ~ r1(X,Y)
                  | ~ ! [X] :
                        ( ~ r1(Y,X)
                        | p2(X)
                        | ~ ! [Y] :
                              ( ~ r1(X,Y)
                              | ~ ( p2(Y)
                                  | ~ ! [X] :
                                        ( ~ r1(Y,X)
                                        | ~ ( p2(X)
                                            | ~ ! [Y] :
                                                  ( ~ r1(X,Y)
                                                  | ~ ( p2(Y)
                                                      | ~ ! [X] :
                                                            ( ~ r1(Y,X)
                                                            | ~ p2(X) ) ) ) ) ) ) ) ) )
            & ~ p1(X) )
          | p1(X) ) ).

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