TPTP Problem File: SYP102_1.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SYP102_1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Syntactic
% Problem  : Logic KT, problem k_dum, size 10
% Version  : Especial.
% English  :

% Refs     : [BHS98] Balsiger et al. (1998), Logics Workbench 1.0
%          : [Ste24] Steen (2024), Email to Geoff Sutcliffe
% Source   : [Ste24]
% Names    : KT/k_dum_n/10.p

% Status   : Theorem
% Rating   : 0.67 v9.3.0
% Syntax   : Number of formulae    :    2 (   0 unt;   1 typ;   0 def)
%            Number of atoms       :   95 (   0 equ)
%            Maximal formula atoms :   95 (  95 avg)
%            Number of connectives :  274 (   5   ~;  13   |;  16   &)
%                                         (   0 <=>;  65  =>;   0  <=;   0 <~>)
%                                         ( 175 {.};   0 {#})
%            Maximal formula depth :   26 (  26 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    1 (   1 usr;   1 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)
% SPC      : NX0_THM_PRP_NEQ_NAR_NDT

% Comments :
%------------------------------------------------------------------------------
tff(simple_k,logic,
    $modal == 
      [ $domains == $constant,
        $designation == $rigid,
        $terms == $local,
        $modalities == $modal_system_M ] ).

tff(p0_type,type,
    p0: $o ).

tff(10,conjecture,
    ( ( [.] ( [.] ( [.] p0
                 => [.] [.] p0 )
            & ( [.] ( [.] ( p0
                         => [.] p0 )
                   => p0 )
             => ( <.> [.] p0
               => ( p0
                  | [.] p0 ) ) ) )
      & [.] [.] ( [.] ( [.] p0
                     => [.] [.] p0 )
                & ( [.] ( [.] ( p0
                             => [.] p0 )
                       => p0 )
                 => ( <.> [.] p0
                   => ( p0
                      | [.] p0 ) ) ) )
      & [.] [.] [.] ( [.] ( [.] p0
                         => [.] [.] p0 )
                    & ( [.] ( [.] ( p0
                                 => [.] p0 )
                           => p0 )
                     => ( <.> [.] p0
                       => ( p0
                          | [.] p0 ) ) ) )
      & [.] [.] [.] [.] ( [.] ( [.] p0
                             => [.] [.] p0 )
                        & ( [.] ( [.] ( p0
                                     => [.] p0 )
                               => p0 )
                         => ( <.> [.] p0
                           => ( p0
                              | [.] p0 ) ) ) )
      & [.] [.] [.] [.] [.] ( [.] ( [.] p0
                                 => [.] [.] p0 )
                            & ( [.] ( [.] ( p0
                                         => [.] p0 )
                                   => p0 )
                             => ( <.> [.] p0
                               => ( p0
                                  | [.] p0 ) ) ) )
      & ~ [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] [.] ( [.] ( [.] ( p0
                                                                 => [.] p0 )
                                                           => p0 )
                                                     => ( <.> [.] p0
                                                       => p0 ) ) )
   => ( <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> <.> ~ ( ( [.] ( [.] ( p0
                                                                   => [.] p0 )
                                                             => p0 )
                                                       => [.] [.] ( [.] ( p0
                                                                       => [.] p0 )
                                                                 => p0 ) )
                                                      & [.] ( [.] p0
                                                           => [.] [.] p0 )
                                                      & ( [.] ( [.] ( p0
                                                                   => [.] p0 )
                                                             => p0 )
                                                       => ( <.> [.] p0
                                                         => ( p0
                                                            | [.] p0 ) ) )
                                                      & ( [.] ( [.] ( ( p0
                                                                     => [.] p0 )
                                                                   => [.] ( p0
                                                                         => [.] p0 ) )
                                                             => ( p0
                                                               => [.] p0 ) )
                                                       => ( <.> [.] ( p0
                                                                   => [.] p0 )
                                                         => ( ( p0
                                                             => [.] p0 )
                                                            | [.] ( p0
                                                                 => [.] p0 ) ) ) ) )
      | <.> <.> <.> <.> <.> <.> <.> ~ ( [.] ( [.] p0
                                           => [.] [.] p0 )
                                      & ( [.] ( [.] ( p0
                                                   => [.] p0 )
                                             => p0 )
                                       => ( <.> [.] p0
                                         => ( p0
                                            | [.] p0 ) ) ) )
      | <.> <.> <.> <.> <.> <.> <.> <.> ~ ( [.] ( [.] p0
                                               => [.] [.] p0 )
                                          & ( [.] ( [.] ( p0
                                                       => [.] p0 )
                                                 => p0 )
                                           => ( <.> [.] p0
                                             => ( p0
                                                | [.] p0 ) ) ) )
      | <.> <.> <.> <.> <.> <.> <.> <.> <.> ~ ( [.] ( [.] p0
                                                   => [.] [.] p0 )
                                              & ( [.] ( [.] ( p0
                                                           => [.] p0 )
                                                     => p0 )
                                               => ( <.> [.] p0
                                                 => ( p0
                                                    | [.] p0 ) ) ) ) ) ) ).

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