TSTP Solution File: NLP266_23 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NLP266_23 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May  3 02:45:38 EDT 2024

% Result   : Theorem 1.12s 1.19s
% Output   : CNFRefutation 1.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   69 (  14 unt;   0 typ;   0 def)
%            Number of atoms       :  553 (   0 equ)
%            Maximal formula atoms :   26 (   8 avg)
%            Number of connectives :  540 ( 213   ~; 192   |;  91   &)
%                                         (   0 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  157 ( 157 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   20 (  19 usr;   7 prp; 0-4 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  278 (  13 sgn 127   !;  45   ?;  80   :)

% Comments : 
%------------------------------------------------------------------------------
tff(f1,axiom,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).

tff(f2,axiom,
    ! [X0: '$ki_world',X2] : '$ki_exists_in_world_$i'(X0,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

tff(f4,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ? [X3] :
          ( ! [X4: '$ki_world'] :
              ( '$ki_accessible'(X0,X4)
             => ( string(X4,X3)
                & userid(X4,u,X3) ) )
          & '$ki_exists_in_world_$i'(X0,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

tff(f5,axiom,
    ? [X5] :
      ( ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ( number(X0,X5,one)
            & entry_box(X0,X5) ) )
      & '$ki_exists_in_world_$i'('$ki_local_world',X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

tff(f6,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X6] :
          ( '$ki_exists_in_world_$i'(X0,X6)
         => ! [X3] :
              ( '$ki_exists_in_world_$i'(X0,X3)
             => ! [X5] :
                  ( '$ki_exists_in_world_$i'(X0,X5)
                 => ( ( entry_box(X0,X5)
                      & string(X0,X3) )
                   => ? [X7] :
                        ( ! [X4: '$ki_world'] :
                            ( '$ki_accessible'(X0,X4)
                           => ! [X8] :
                                ( '$ki_exists_in_world_$i'(X4,X8)
                               => ( do(X4,X6,X7,X8)
                                 => in(X4,X3,X5,X8) ) ) )
                        & '$ki_exists_in_world_$i'(X0,X7) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

tff(f7,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ? [X3] :
          ( ? [X5] :
              ( ? [X7] :
                  ( ? [X6] :
                      ( ! [X4: '$ki_world'] :
                          ( '$ki_accessible'(X0,X4)
                         => ! [X8] :
                              ( '$ki_exists_in_world_$i'(X4,X8)
                             => ( do(X4,X6,X7,X8)
                               => in(X4,X3,X5,X8) ) ) )
                      & ! [X4: '$ki_world'] :
                          ( '$ki_accessible'(X0,X4)
                         => ( number(X4,X5,one)
                            & entry_box(X4,X5)
                            & userid(X4,u,X3) ) )
                      & '$ki_exists_in_world_$i'(X0,X6) )
                  & '$ki_exists_in_world_$i'(X0,X7) )
              & '$ki_exists_in_world_$i'(X0,X5) )
          & '$ki_exists_in_world_$i'(X0,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f8,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ? [X3] :
            ( ? [X5] :
                ( ? [X7] :
                    ( ? [X6] :
                        ( ! [X4: '$ki_world'] :
                            ( '$ki_accessible'(X0,X4)
                           => ! [X8] :
                                ( '$ki_exists_in_world_$i'(X4,X8)
                               => ( do(X4,X6,X7,X8)
                                 => in(X4,X3,X5,X8) ) ) )
                        & ! [X4: '$ki_world'] :
                            ( '$ki_accessible'(X0,X4)
                           => ( number(X4,X5,one)
                              & entry_box(X4,X5)
                              & userid(X4,u,X3) ) )
                        & '$ki_exists_in_world_$i'(X0,X6) )
                    & '$ki_exists_in_world_$i'(X0,X7) )
                & '$ki_exists_in_world_$i'(X0,X5) )
            & '$ki_exists_in_world_$i'(X0,X3) ) ),
    inference(negated_conjecture,[],[f7]) ).

tff(f9,plain,
    ! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
    inference(rectify,[],[f2]) ).

tff(f11,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ? [X1] :
          ( ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => ( string(X2,X1)
                & userid(X2,u,X1) ) )
          & '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

tff(f12,plain,
    ? [X0] :
      ( ! [X1: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X1)
         => ( number(X1,X0,one)
            & entry_box(X1,X0) ) )
      & '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
    inference(rectify,[],[f5]) ).

tff(f13,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ! [X2] :
              ( '$ki_exists_in_world_$i'(X0,X2)
             => ! [X3] :
                  ( '$ki_exists_in_world_$i'(X0,X3)
                 => ( ( entry_box(X0,X3)
                      & string(X0,X2) )
                   => ? [X4] :
                        ( ! [X5: '$ki_world'] :
                            ( '$ki_accessible'(X0,X5)
                           => ! [X6] :
                                ( '$ki_exists_in_world_$i'(X5,X6)
                               => ( do(X5,X1,X4,X6)
                                 => in(X5,X2,X3,X6) ) ) )
                        & '$ki_exists_in_world_$i'(X0,X4) ) ) ) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f14,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ! [X5: '$ki_world'] :
                            ( '$ki_accessible'(X0,X5)
                           => ! [X6] :
                                ( '$ki_exists_in_world_$i'(X5,X6)
                               => ( do(X5,X4,X3,X6)
                                 => in(X5,X1,X2,X6) ) ) )
                        & ! [X7: '$ki_world'] :
                            ( '$ki_accessible'(X0,X7)
                           => ( number(X7,X2,one)
                              & entry_box(X7,X2)
                              & userid(X7,u,X1) ) )
                        & '$ki_exists_in_world_$i'(X0,X4) )
                    & '$ki_exists_in_world_$i'(X0,X3) )
                & '$ki_exists_in_world_$i'(X0,X2) )
            & '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(rectify,[],[f8]) ).

tff(f15,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( ! [X2: '$ki_world'] :
              ( ( string(X2,X1)
                & userid(X2,u,X1) )
              | ~ '$ki_accessible'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f11]) ).

tff(f16,plain,
    ? [X0] :
      ( ! [X1: '$ki_world'] :
          ( ( number(X1,X0,one)
            & entry_box(X1,X0) )
          | ~ '$ki_accessible'('$ki_local_world',X1) )
      & '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f12]) ).

tff(f17,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ? [X4] :
                      ( ! [X5: '$ki_world'] :
                          ( ! [X6] :
                              ( in(X5,X2,X3,X6)
                              | ~ do(X5,X1,X4,X6)
                              | ~ '$ki_exists_in_world_$i'(X5,X6) )
                          | ~ '$ki_accessible'(X0,X5) )
                      & '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ entry_box(X0,X3)
                  | ~ string(X0,X2)
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f13]) ).

tff(f18,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ? [X4] :
                      ( ! [X5: '$ki_world'] :
                          ( ! [X6] :
                              ( in(X5,X2,X3,X6)
                              | ~ do(X5,X1,X4,X6)
                              | ~ '$ki_exists_in_world_$i'(X5,X6) )
                          | ~ '$ki_accessible'(X0,X5) )
                      & '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ entry_box(X0,X3)
                  | ~ string(X0,X2)
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f17]) ).

tff(f19,plain,
    ? [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ? [X5: '$ki_world'] :
                          ( ? [X6] :
                              ( ~ in(X5,X1,X2,X6)
                              & do(X5,X4,X3,X6)
                              & '$ki_exists_in_world_$i'(X5,X6) )
                          & '$ki_accessible'(X0,X5) )
                      | ? [X7: '$ki_world'] :
                          ( ( ~ number(X7,X2,one)
                            | ~ entry_box(X7,X2)
                            | ~ userid(X7,u,X1) )
                          & '$ki_accessible'(X0,X7) )
                      | ~ '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f14]) ).

tff(f20,plain,
    ? [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ? [X5: '$ki_world'] :
                          ( ? [X6] :
                              ( ~ in(X5,X1,X2,X6)
                              & do(X5,X4,X3,X6)
                              & '$ki_exists_in_world_$i'(X5,X6) )
                          & '$ki_accessible'(X0,X5) )
                      | ? [X7: '$ki_world'] :
                          ( ( ~ number(X7,X2,one)
                            | ~ entry_box(X7,X2)
                            | ~ userid(X7,u,X1) )
                          & '$ki_accessible'(X0,X7) )
                      | ~ '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f19]) ).

tff(f23,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( ! [X2: '$ki_world'] :
              ( ( string(X2,X1)
                & userid(X2,u,X1) )
              | ~ '$ki_accessible'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
     => ( ! [X2: '$ki_world'] :
            ( ( string(X2,sK1(X0))
              & userid(X2,u,sK1(X0)) )
            | ~ '$ki_accessible'(X0,X2) )
        & '$ki_exists_in_world_$i'(X0,sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f24,plain,
    ! [X0: '$ki_world'] :
      ( ( ! [X2: '$ki_world'] :
            ( ( string(X2,sK1(X0))
              & userid(X2,u,sK1(X0)) )
            | ~ '$ki_accessible'(X0,X2) )
        & '$ki_exists_in_world_$i'(X0,sK1(X0)) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f23]) ).

tff(f25,plain,
    ( ? [X0] :
        ( ! [X1: '$ki_world'] :
            ( ( number(X1,X0,one)
              & entry_box(X1,X0) )
            | ~ '$ki_accessible'('$ki_local_world',X1) )
        & '$ki_exists_in_world_$i'('$ki_local_world',X0) )
   => ( ! [X1: '$ki_world'] :
          ( ( number(X1,sK2,one)
            & entry_box(X1,sK2) )
          | ~ '$ki_accessible'('$ki_local_world',X1) )
      & '$ki_exists_in_world_$i'('$ki_local_world',sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f26,plain,
    ( ! [X1: '$ki_world'] :
        ( ( number(X1,sK2,one)
          & entry_box(X1,sK2) )
        | ~ '$ki_accessible'('$ki_local_world',X1) )
    & '$ki_exists_in_world_$i'('$ki_local_world',sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f16,f25]) ).

tff(f27,plain,
    ! [X0: '$ki_world',X1,X2,X3] :
      ( ? [X4] :
          ( ! [X5: '$ki_world'] :
              ( ! [X6] :
                  ( in(X5,X2,X3,X6)
                  | ~ do(X5,X1,X4,X6)
                  | ~ '$ki_exists_in_world_$i'(X5,X6) )
              | ~ '$ki_accessible'(X0,X5) )
          & '$ki_exists_in_world_$i'(X0,X4) )
     => ( ! [X5: '$ki_world'] :
            ( ! [X6] :
                ( in(X5,X2,X3,X6)
                | ~ do(X5,X1,sK3(X0,X1,X2,X3),X6)
                | ~ '$ki_exists_in_world_$i'(X5,X6) )
            | ~ '$ki_accessible'(X0,X5) )
        & '$ki_exists_in_world_$i'(X0,sK3(X0,X1,X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

tff(f28,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ! [X5: '$ki_world'] :
                        ( ! [X6] :
                            ( in(X5,X2,X3,X6)
                            | ~ do(X5,X1,sK3(X0,X1,X2,X3),X6)
                            | ~ '$ki_exists_in_world_$i'(X5,X6) )
                        | ~ '$ki_accessible'(X0,X5) )
                    & '$ki_exists_in_world_$i'(X0,sK3(X0,X1,X2,X3)) )
                  | ~ entry_box(X0,X3)
                  | ~ string(X0,X2)
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f18,f27]) ).

tff(f29,plain,
    ( ? [X0: '$ki_world'] :
        ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ? [X5: '$ki_world'] :
                            ( ? [X6] :
                                ( ~ in(X5,X1,X2,X6)
                                & do(X5,X4,X3,X6)
                                & '$ki_exists_in_world_$i'(X5,X6) )
                            & '$ki_accessible'(X0,X5) )
                        | ? [X7: '$ki_world'] :
                            ( ( ~ number(X7,X2,one)
                              | ~ entry_box(X7,X2)
                              | ~ userid(X7,u,X1) )
                            & '$ki_accessible'(X0,X7) )
                        | ~ '$ki_exists_in_world_$i'(X0,X4) )
                    | ~ '$ki_exists_in_world_$i'(X0,X3) )
                | ~ '$ki_exists_in_world_$i'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ? [X5: '$ki_world'] :
                          ( ? [X6] :
                              ( ~ in(X5,X1,X2,X6)
                              & do(X5,X4,X3,X6)
                              & '$ki_exists_in_world_$i'(X5,X6) )
                          & '$ki_accessible'(sK4,X5) )
                      | ? [X7: '$ki_world'] :
                          ( ( ~ number(X7,X2,one)
                            | ~ entry_box(X7,X2)
                            | ~ userid(X7,u,X1) )
                          & '$ki_accessible'(sK4,X7) )
                      | ~ '$ki_exists_in_world_$i'(sK4,X4) )
                  | ~ '$ki_exists_in_world_$i'(sK4,X3) )
              | ~ '$ki_exists_in_world_$i'(sK4,X2) )
          | ~ '$ki_exists_in_world_$i'(sK4,X1) )
      & '$ki_accessible'('$ki_local_world',sK4) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ! [X1,X2,X3,X4] :
      ( ? [X5: '$ki_world'] :
          ( ? [X6] :
              ( ~ in(X5,X1,X2,X6)
              & do(X5,X4,X3,X6)
              & '$ki_exists_in_world_$i'(X5,X6) )
          & '$ki_accessible'(sK4,X5) )
     => ( ? [X6] :
            ( ~ in(sK5(X1,X2,X3,X4),X1,X2,X6)
            & do(sK5(X1,X2,X3,X4),X4,X3,X6)
            & '$ki_exists_in_world_$i'(sK5(X1,X2,X3,X4),X6) )
        & '$ki_accessible'(sK4,sK5(X1,X2,X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f31,plain,
    ! [X1,X2,X3,X4] :
      ( ? [X6] :
          ( ~ in(sK5(X1,X2,X3,X4),X1,X2,X6)
          & do(sK5(X1,X2,X3,X4),X4,X3,X6)
          & '$ki_exists_in_world_$i'(sK5(X1,X2,X3,X4),X6) )
     => ( ~ in(sK5(X1,X2,X3,X4),X1,X2,sK6(X1,X2,X3,X4))
        & do(sK5(X1,X2,X3,X4),X4,X3,sK6(X1,X2,X3,X4))
        & '$ki_exists_in_world_$i'(sK5(X1,X2,X3,X4),sK6(X1,X2,X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f32,plain,
    ! [X1,X2] :
      ( ? [X7: '$ki_world'] :
          ( ( ~ number(X7,X2,one)
            | ~ entry_box(X7,X2)
            | ~ userid(X7,u,X1) )
          & '$ki_accessible'(sK4,X7) )
     => ( ( ~ number(sK7(X1,X2),X2,one)
          | ~ entry_box(sK7(X1,X2),X2)
          | ~ userid(sK7(X1,X2),u,X1) )
        & '$ki_accessible'(sK4,sK7(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f33,plain,
    ( ! [X1] :
        ( ! [X2] :
            ( ! [X3] :
                ( ! [X4] :
                    ( ( ~ in(sK5(X1,X2,X3,X4),X1,X2,sK6(X1,X2,X3,X4))
                      & do(sK5(X1,X2,X3,X4),X4,X3,sK6(X1,X2,X3,X4))
                      & '$ki_exists_in_world_$i'(sK5(X1,X2,X3,X4),sK6(X1,X2,X3,X4))
                      & '$ki_accessible'(sK4,sK5(X1,X2,X3,X4)) )
                    | ( ( ~ number(sK7(X1,X2),X2,one)
                        | ~ entry_box(sK7(X1,X2),X2)
                        | ~ userid(sK7(X1,X2),u,X1) )
                      & '$ki_accessible'(sK4,sK7(X1,X2)) )
                    | ~ '$ki_exists_in_world_$i'(sK4,X4) )
                | ~ '$ki_exists_in_world_$i'(sK4,X3) )
            | ~ '$ki_exists_in_world_$i'(sK4,X2) )
        | ~ '$ki_exists_in_world_$i'(sK4,X1) )
    & '$ki_accessible'('$ki_local_world',sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f20,f32,f31,f30,f29]) ).

tff(f34,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    inference(cnf_transformation,[],[f1]) ).

tff(f35,plain,
    ! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
    inference(cnf_transformation,[],[f9]) ).

tff(f38,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( userid(X2,u,sK1(X0))
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f39,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( string(X2,sK1(X0))
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f41,plain,
    ! [X1: '$ki_world'] :
      ( entry_box(X1,sK2)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(cnf_transformation,[],[f26]) ).

tff(f42,plain,
    ! [X1: '$ki_world'] :
      ( number(X1,sK2,one)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(cnf_transformation,[],[f26]) ).

tff(f44,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
      ( in(X5,X2,X3,X6)
      | ~ do(X5,X1,sK3(X0,X1,X2,X3),X6)
      | ~ '$ki_exists_in_world_$i'(X5,X6)
      | ~ '$ki_accessible'(X0,X5)
      | ~ entry_box(X0,X3)
      | ~ string(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f51,plain,
    ! [X2: $i,X3: $i,X1: $i,X4: $i] :
      ( do(sK5(X1,X2,X3,X4),X4,X3,sK6(X1,X2,X3,X4))
      | ~ number(sK7(X1,X2),X2,one)
      | ~ entry_box(sK7(X1,X2),X2)
      | ~ userid(sK7(X1,X2),u,X1)
      | ~ '$ki_exists_in_world_$i'(sK4,X4)
      | ~ '$ki_exists_in_world_$i'(sK4,X3)
      | ~ '$ki_exists_in_world_$i'(sK4,X2)
      | ~ '$ki_exists_in_world_$i'(sK4,X1) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f53,plain,
    ! [X2: $i,X3: $i,X1: $i,X4: $i] :
      ( ~ in(sK5(X1,X2,X3,X4),X1,X2,sK6(X1,X2,X3,X4))
      | ~ number(sK7(X1,X2),X2,one)
      | ~ entry_box(sK7(X1,X2),X2)
      | ~ userid(sK7(X1,X2),u,X1)
      | ~ '$ki_exists_in_world_$i'(sK4,X4)
      | ~ '$ki_exists_in_world_$i'(sK4,X3)
      | ~ '$ki_exists_in_world_$i'(sK4,X2)
      | ~ '$ki_exists_in_world_$i'(sK4,X1) ),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_49,plain,
    '$ki_accessible'(X0_13,X1_13),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_50,plain,
    '$ki_exists_in_world_$i'(X0_13,X0),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_52,plain,
    ( ~ '$ki_accessible'(X0_13,X1_13)
    | ~ '$ki_accessible'('$ki_local_world',X0_13)
    | string(X1_13,sK1(X0_13)) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_53,plain,
    ( ~ '$ki_accessible'(X0_13,X1_13)
    | ~ '$ki_accessible'('$ki_local_world',X0_13)
    | userid(X1_13,u,sK1(X0_13)) ),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_55,plain,
    ( ~ '$ki_accessible'('$ki_local_world',X0_13)
    | number(X0_13,sK2,one) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_56,plain,
    ( ~ '$ki_accessible'('$ki_local_world',X0_13)
    | entry_box(X0_13,sK2) ),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_58,plain,
    ( ~ do(X0_13,X0,sK3(X1_13,X0,X1,X2),X3)
    | ~ '$ki_accessible'(X1_13,X0_13)
    | ~ string(X1_13,X1)
    | ~ entry_box(X1_13,X2)
    | ~ '$ki_exists_in_world_$i'(X0_13,X3)
    | ~ '$ki_exists_in_world_$i'(X1_13,X0)
    | ~ '$ki_exists_in_world_$i'(X1_13,X1)
    | ~ '$ki_exists_in_world_$i'(X1_13,X2)
    | ~ '$ki_accessible'('$ki_local_world',X1_13)
    | in(X0_13,X1,X2,X3) ),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_60,negated_conjecture,
    ( ~ in(sK5(X0,X1,X2,X3),X0,X1,sK6(X0,X1,X2,X3))
    | ~ number(sK7(X0,X1),X1,one)
    | ~ userid(sK7(X0,X1),u,X0)
    | ~ entry_box(sK7(X0,X1),X1)
    | ~ '$ki_exists_in_world_$i'(sK4,X0)
    | ~ '$ki_exists_in_world_$i'(sK4,X1)
    | ~ '$ki_exists_in_world_$i'(sK4,X2)
    | ~ '$ki_exists_in_world_$i'(sK4,X3) ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_62,negated_conjecture,
    ( ~ number(sK7(X0,X1),X1,one)
    | ~ userid(sK7(X0,X1),u,X0)
    | ~ entry_box(sK7(X0,X1),X1)
    | ~ '$ki_exists_in_world_$i'(sK4,X0)
    | ~ '$ki_exists_in_world_$i'(sK4,X1)
    | ~ '$ki_exists_in_world_$i'(sK4,X2)
    | ~ '$ki_exists_in_world_$i'(sK4,X3)
    | do(sK5(X0,X1,X2,X3),X3,X2,sK6(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_87,plain,
    ( ~ '$ki_accessible'('$ki_local_world',X0_13)
    | string(X1_13,sK1(X0_13)) ),
    inference(global_subsumption_just,[status(thm)],[c_52,c_49,c_52]) ).

cnf(c_90,plain,
    ( ~ '$ki_accessible'('$ki_local_world',X0_13)
    | userid(X1_13,u,sK1(X0_13)) ),
    inference(global_subsumption_just,[status(thm)],[c_53,c_49,c_53]) ).

cnf(c_97,plain,
    entry_box(X0_13,sK2),
    inference(backward_subsumption_resolution,[status(thm)],[c_56,c_49]) ).

cnf(c_99,plain,
    number(X0_13,sK2,one),
    inference(backward_subsumption_resolution,[status(thm)],[c_55,c_49]) ).

cnf(c_100,plain,
    string(X0_13,sK1(X1_13)),
    inference(backward_subsumption_resolution,[status(thm)],[c_87,c_49]) ).

cnf(c_101,plain,
    userid(X0_13,u,sK1(X1_13)),
    inference(backward_subsumption_resolution,[status(thm)],[c_90,c_49]) ).

cnf(c_103,plain,
    ( ~ do(X0_13,X0,sK3(X1_13,X0,X1,X2),X3)
    | ~ '$ki_accessible'(X1_13,X0_13)
    | ~ string(X1_13,X1)
    | ~ entry_box(X1_13,X2)
    | ~ '$ki_exists_in_world_$i'(X0_13,X3)
    | ~ '$ki_exists_in_world_$i'(X1_13,X0)
    | ~ '$ki_exists_in_world_$i'(X1_13,X1)
    | ~ '$ki_exists_in_world_$i'(X1_13,X2)
    | in(X0_13,X1,X2,X3) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_58,c_49]) ).

cnf(c_113,plain,
    ( ~ in(sK5(X0,X1,X2,X3),X0,X1,sK6(X0,X1,X2,X3))
    | ~ number(sK7(X0,X1),X1,one)
    | ~ userid(sK7(X0,X1),u,X0)
    | ~ entry_box(sK7(X0,X1),X1)
    | ~ '$ki_exists_in_world_$i'(sK4,X1)
    | ~ '$ki_exists_in_world_$i'(sK4,X2)
    | ~ '$ki_exists_in_world_$i'(sK4,X3) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_60,c_50]) ).

cnf(c_114,plain,
    ( ~ number(sK7(X0,X1),X1,one)
    | ~ userid(sK7(X0,X1),u,X0)
    | ~ entry_box(sK7(X0,X1),X1)
    | ~ '$ki_exists_in_world_$i'(sK4,X1)
    | ~ '$ki_exists_in_world_$i'(sK4,X2)
    | ~ '$ki_exists_in_world_$i'(sK4,X3)
    | do(sK5(X0,X1,X2,X3),X3,X2,sK6(X0,X1,X2,X3)) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_62,c_50]) ).

cnf(c_115,plain,
    ( ~ do(X0_13,X0,sK3(X1_13,X0,X1,X2),X3)
    | ~ '$ki_accessible'(X1_13,X0_13)
    | ~ string(X1_13,X1)
    | ~ entry_box(X1_13,X2)
    | ~ '$ki_exists_in_world_$i'(X1_13,X0)
    | ~ '$ki_exists_in_world_$i'(X1_13,X1)
    | ~ '$ki_exists_in_world_$i'(X1_13,X2)
    | in(X0_13,X1,X2,X3) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_103,c_50]) ).

cnf(c_131,plain,
    ( ~ number(sK7(X0,X1),X1,one)
    | ~ userid(sK7(X0,X1),u,X0)
    | ~ entry_box(sK7(X0,X1),X1)
    | do(sK5(X0,X1,X2,X3),X3,X2,sK6(X0,X1,X2,X3)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_114,c_50,c_50,c_50]) ).

cnf(c_152,plain,
    ( ~ in(sK5(X0,X1,X2,X3),X0,X1,sK6(X0,X1,X2,X3))
    | ~ number(sK7(X0,X1),X1,one)
    | ~ userid(sK7(X0,X1),u,X0)
    | ~ entry_box(sK7(X0,X1),X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_113,c_50,c_50,c_50]) ).

cnf(c_174,plain,
    ( ~ do(X0_13,X0,sK3(X1_13,X0,X1,X2),X3)
    | ~ string(X1_13,X1)
    | ~ entry_box(X1_13,X2)
    | in(X0_13,X1,X2,X3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_115,c_50,c_50,c_50,c_49]) ).

cnf(c_188,plain,
    ( ~ do(X0_13,X0,sK3(X1_13,X0,sK1(X2_13),X1),X2)
    | ~ entry_box(X1_13,X1)
    | in(X0_13,sK1(X2_13),X1,X2) ),
    inference(resolution,[status(thm)],[c_100,c_174]) ).

cnf(c_202,plain,
    ( ~ do(sK5(sK1(X0_13),X0,X1,X2),X3,sK3(X1_13,X3,sK1(X0_13),X0),sK6(sK1(X0_13),X0,X1,X2))
    | ~ userid(sK7(sK1(X0_13),X0),u,sK1(X0_13))
    | ~ number(sK7(sK1(X0_13),X0),X0,one)
    | ~ entry_box(sK7(sK1(X0_13),X0),X0)
    | ~ entry_box(X1_13,X0) ),
    inference(resolution,[status(thm)],[c_152,c_188]) ).

cnf(c_214,plain,
    ( ~ do(sK5(sK1(X0_13),X0,X1,X2),X3,sK3(X1_13,X3,sK1(X0_13),X0),sK6(sK1(X0_13),X0,X1,X2))
    | ~ number(sK7(sK1(X0_13),X0),X0,one)
    | ~ entry_box(sK7(sK1(X0_13),X0),X0)
    | ~ entry_box(X1_13,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_202,c_101]) ).

cnf(c_224,plain,
    ( ~ number(sK7(sK1(X0_13),X0),X0,one)
    | ~ entry_box(sK7(sK1(X0_13),X0),X0)
    | do(sK5(sK1(X0_13),X0,X1,X2),X2,X1,sK6(sK1(X0_13),X0,X1,X2)) ),
    inference(resolution,[status(thm)],[c_101,c_131]) ).

cnf(c_238,plain,
    ( ~ entry_box(sK7(sK1(X0_13),sK2),sK2)
    | do(sK5(sK1(X0_13),sK2,X0,X1),X1,X0,sK6(sK1(X0_13),sK2,X0,X1)) ),
    inference(resolution,[status(thm)],[c_99,c_224]) ).

cnf(c_244,plain,
    do(sK5(sK1(X0_13),sK2,X0,X1),X1,X0,sK6(sK1(X0_13),sK2,X0,X1)),
    inference(forward_subsumption_resolution,[status(thm)],[c_238,c_97]) ).

cnf(c_247,plain,
    ( ~ do(sK5(sK1(X0_13),sK2,X0,X1),X2,sK3(X1_13,X2,sK1(X0_13),sK2),sK6(sK1(X0_13),sK2,X0,X1))
    | ~ entry_box(sK7(sK1(X0_13),sK2),sK2)
    | ~ entry_box(X1_13,sK2) ),
    inference(resolution,[status(thm)],[c_99,c_214]) ).

cnf(c_255,plain,
    ~ do(sK5(sK1(X0_13),sK2,X0,X1),X2,sK3(X1_13,X2,sK1(X0_13),sK2),sK6(sK1(X0_13),sK2,X0,X1)),
    inference(forward_subsumption_resolution,[status(thm)],[c_247,c_97,c_97]) ).

cnf(c_260,plain,
    $false,
    inference(resolution,[status(thm)],[c_244,c_255]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NLP266_23 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 18:27:01 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.12/1.19  % SZS status Started for theBenchmark.p
% 1.12/1.19  % SZS status Theorem for theBenchmark.p
% 1.12/1.19  
% 1.12/1.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.12/1.19  
% 1.12/1.19  ------  iProver source info
% 1.12/1.19  
% 1.12/1.19  git: date: 2024-05-02 19:28:25 +0000
% 1.12/1.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.12/1.19  git: non_committed_changes: false
% 1.12/1.19  
% 1.12/1.19  ------ Parsing...
% 1.12/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.12/1.19  
% 1.12/1.19  
% 1.12/1.19  ------ Preprocessing... pe_s  pe:1:0s pe:2:0s pe:4:0s
% 1.12/1.19  
% 1.12/1.19  % SZS status Theorem for theBenchmark.p
% 1.12/1.19  
% 1.12/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.12/1.19  
% 1.12/1.19  
%------------------------------------------------------------------------------