TPTP Problem File: LCL680+1.005.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : LCL680+1.005 : TPTP v7.4.0. 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   : 0.86 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 unit)
%            Number of atoms       :  348 (   0 equality)
%            Maximal formula depth :  104 (  37 average)
%            Number of connectives :  836 ( 491   ~; 331   |;  13   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    3 (   0 propositional; 1-2 arity)
%            Number of functors    :    0 (   0 constant; --- arity)
%            Number of variables   :  187 (   0 sgn; 186   !;   1   ?)
%            Maximal term depth    :    1 (   1 average)
% 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) ) ) )).

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