TSTP Solution File: LCL950_17 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : LCL950_17 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n011.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 : Mon May 22 15:38:43 EDT 2023

% Result   : Theorem 1.23s 0.53s
% Output   : Refutation 1.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   81 (  14 unt;  18 typ;   0 def)
%            Number of atoms       :  617 (   0 equ)
%            Maximal formula atoms :   26 (   9 avg)
%            Number of connectives :  683 ( 223   ~; 195   |; 177   &)
%                                         (   0 <=>;  88  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (  11 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   94 (  94 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   29 (  11   >;  18   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   4 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-3 aty)
%            Number of variables   :  394 (; 290   !; 104   ?; 309   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    '$ki_world': $tType ).

tff(func_def_0,type,
    '$ki_local_world': '$ki_world' ).

tff(func_def_1,type,
    sK1: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_2,type,
    sK2: '$ki_world' ).

tff(func_def_4,type,
    sK4: '$ki_world' ).

tff(func_def_6,type,
    sK6: '$ki_world' ).

tff(func_def_8,type,
    sK8: '$ki_world' ).

tff(func_def_9,type,
    sK9: '$ki_world' ).

tff(func_def_10,type,
    sK10: '$ki_world' > $i ).

tff(func_def_11,type,
    sK11: ( $i * $i * '$ki_world' ) > $i ).

tff(func_def_12,type,
    sK12: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_13,type,
    sK13: ( $i * '$ki_world' * $i ) > '$ki_world' ).

tff(func_def_14,type,
    sK14: ( $i * '$ki_world' * $i ) > '$ki_world' ).

tff(pred_def_1,type,
    '$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).

tff(pred_def_2,type,
    intersect: ( '$ki_world' * $i * $i ) > $o ).

tff(pred_def_3,type,
    member: ( '$ki_world' * $i * $i ) > $o ).

tff(pred_def_4,type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff(pred_def_5,type,
    sP0: ( $i * $i * '$ki_world' ) > $o ).

tff(f124,plain,
    $false,
    inference(resolution,[],[f121,f56]) ).

tff(f56,plain,
    ~ intersect(sK9,sK5,sK7),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ( '$ki_accessible'(sK4,sK6)
    & '$ki_accessible'(sK6,sK8)
    & ! [X7: '$ki_world'] :
        ( member(X7,sK3,sK7)
        | ~ '$ki_accessible'(sK8,X7) )
    & ! [X8: '$ki_world'] :
        ( member(X8,sK3,sK5)
        | ~ '$ki_accessible'(sK8,X8) )
    & ~ intersect(sK9,sK5,sK7)
    & '$ki_accessible'(sK8,sK9)
    & '$ki_exists_in_world_$i'(sK6,sK7)
    & '$ki_exists_in_world_$i'(sK4,sK5)
    & '$ki_accessible'(sK2,sK4)
    & '$ki_exists_in_world_$i'(sK2,sK3)
    & '$ki_accessible'('$ki_local_world',sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9])],[f19,f33,f32,f31,f30,f29,f28,f27,f26]) ).

tff(f26,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1] :
            ( ? [X2: '$ki_world'] :
                ( ? [X3] :
                    ( ? [X4: '$ki_world'] :
                        ( '$ki_accessible'(X2,X4)
                        & ? [X5] :
                            ( ? [X6: '$ki_world'] :
                                ( '$ki_accessible'(X4,X6)
                                & ! [X7: '$ki_world'] :
                                    ( member(X7,X1,X5)
                                    | ~ '$ki_accessible'(X6,X7) )
                                & ! [X8: '$ki_world'] :
                                    ( member(X8,X1,X3)
                                    | ~ '$ki_accessible'(X6,X8) )
                                & ? [X9: '$ki_world'] :
                                    ( ~ intersect(X9,X3,X5)
                                    & '$ki_accessible'(X6,X9) ) )
                            & '$ki_exists_in_world_$i'(X4,X5) ) )
                    & '$ki_exists_in_world_$i'(X2,X3) )
                & '$ki_accessible'(X0,X2) )
            & '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ? [X3] :
                  ( ? [X4: '$ki_world'] :
                      ( '$ki_accessible'(X2,X4)
                      & ? [X5] :
                          ( ? [X6: '$ki_world'] :
                              ( '$ki_accessible'(X4,X6)
                              & ! [X7: '$ki_world'] :
                                  ( member(X7,X1,X5)
                                  | ~ '$ki_accessible'(X6,X7) )
                              & ! [X8: '$ki_world'] :
                                  ( member(X8,X1,X3)
                                  | ~ '$ki_accessible'(X6,X8) )
                              & ? [X9: '$ki_world'] :
                                  ( ~ intersect(X9,X3,X5)
                                  & '$ki_accessible'(X6,X9) ) )
                          & '$ki_exists_in_world_$i'(X4,X5) ) )
                  & '$ki_exists_in_world_$i'(X2,X3) )
              & '$ki_accessible'(sK2,X2) )
          & '$ki_exists_in_world_$i'(sK2,X1) )
      & '$ki_accessible'('$ki_local_world',sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f27,plain,
    ( ? [X1] :
        ( ? [X2: '$ki_world'] :
            ( ? [X3] :
                ( ? [X4: '$ki_world'] :
                    ( '$ki_accessible'(X2,X4)
                    & ? [X5] :
                        ( ? [X6: '$ki_world'] :
                            ( '$ki_accessible'(X4,X6)
                            & ! [X7: '$ki_world'] :
                                ( member(X7,X1,X5)
                                | ~ '$ki_accessible'(X6,X7) )
                            & ! [X8: '$ki_world'] :
                                ( member(X8,X1,X3)
                                | ~ '$ki_accessible'(X6,X8) )
                            & ? [X9: '$ki_world'] :
                                ( ~ intersect(X9,X3,X5)
                                & '$ki_accessible'(X6,X9) ) )
                        & '$ki_exists_in_world_$i'(X4,X5) ) )
                & '$ki_exists_in_world_$i'(X2,X3) )
            & '$ki_accessible'(sK2,X2) )
        & '$ki_exists_in_world_$i'(sK2,X1) )
   => ( ? [X2: '$ki_world'] :
          ( ? [X3] :
              ( ? [X4: '$ki_world'] :
                  ( '$ki_accessible'(X2,X4)
                  & ? [X5] :
                      ( ? [X6: '$ki_world'] :
                          ( '$ki_accessible'(X4,X6)
                          & ! [X7: '$ki_world'] :
                              ( member(X7,sK3,X5)
                              | ~ '$ki_accessible'(X6,X7) )
                          & ! [X8: '$ki_world'] :
                              ( member(X8,sK3,X3)
                              | ~ '$ki_accessible'(X6,X8) )
                          & ? [X9: '$ki_world'] :
                              ( ~ intersect(X9,X3,X5)
                              & '$ki_accessible'(X6,X9) ) )
                      & '$ki_exists_in_world_$i'(X4,X5) ) )
              & '$ki_exists_in_world_$i'(X2,X3) )
          & '$ki_accessible'(sK2,X2) )
      & '$ki_exists_in_world_$i'(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

tff(f28,plain,
    ( ? [X2: '$ki_world'] :
        ( ? [X3] :
            ( ? [X4: '$ki_world'] :
                ( '$ki_accessible'(X2,X4)
                & ? [X5] :
                    ( ? [X6: '$ki_world'] :
                        ( '$ki_accessible'(X4,X6)
                        & ! [X7: '$ki_world'] :
                            ( member(X7,sK3,X5)
                            | ~ '$ki_accessible'(X6,X7) )
                        & ! [X8: '$ki_world'] :
                            ( member(X8,sK3,X3)
                            | ~ '$ki_accessible'(X6,X8) )
                        & ? [X9: '$ki_world'] :
                            ( ~ intersect(X9,X3,X5)
                            & '$ki_accessible'(X6,X9) ) )
                    & '$ki_exists_in_world_$i'(X4,X5) ) )
            & '$ki_exists_in_world_$i'(X2,X3) )
        & '$ki_accessible'(sK2,X2) )
   => ( ? [X3] :
          ( ? [X4: '$ki_world'] :
              ( '$ki_accessible'(sK4,X4)
              & ? [X5] :
                  ( ? [X6: '$ki_world'] :
                      ( '$ki_accessible'(X4,X6)
                      & ! [X7: '$ki_world'] :
                          ( member(X7,sK3,X5)
                          | ~ '$ki_accessible'(X6,X7) )
                      & ! [X8: '$ki_world'] :
                          ( member(X8,sK3,X3)
                          | ~ '$ki_accessible'(X6,X8) )
                      & ? [X9: '$ki_world'] :
                          ( ~ intersect(X9,X3,X5)
                          & '$ki_accessible'(X6,X9) ) )
                  & '$ki_exists_in_world_$i'(X4,X5) ) )
          & '$ki_exists_in_world_$i'(sK4,X3) )
      & '$ki_accessible'(sK2,sK4) ) ),
    introduced(choice_axiom,[]) ).

tff(f29,plain,
    ( ? [X3] :
        ( ? [X4: '$ki_world'] :
            ( '$ki_accessible'(sK4,X4)
            & ? [X5] :
                ( ? [X6: '$ki_world'] :
                    ( '$ki_accessible'(X4,X6)
                    & ! [X7: '$ki_world'] :
                        ( member(X7,sK3,X5)
                        | ~ '$ki_accessible'(X6,X7) )
                    & ! [X8: '$ki_world'] :
                        ( member(X8,sK3,X3)
                        | ~ '$ki_accessible'(X6,X8) )
                    & ? [X9: '$ki_world'] :
                        ( ~ intersect(X9,X3,X5)
                        & '$ki_accessible'(X6,X9) ) )
                & '$ki_exists_in_world_$i'(X4,X5) ) )
        & '$ki_exists_in_world_$i'(sK4,X3) )
   => ( ? [X4: '$ki_world'] :
          ( '$ki_accessible'(sK4,X4)
          & ? [X5] :
              ( ? [X6: '$ki_world'] :
                  ( '$ki_accessible'(X4,X6)
                  & ! [X7: '$ki_world'] :
                      ( member(X7,sK3,X5)
                      | ~ '$ki_accessible'(X6,X7) )
                  & ! [X8: '$ki_world'] :
                      ( member(X8,sK3,sK5)
                      | ~ '$ki_accessible'(X6,X8) )
                  & ? [X9: '$ki_world'] :
                      ( ~ intersect(X9,sK5,X5)
                      & '$ki_accessible'(X6,X9) ) )
              & '$ki_exists_in_world_$i'(X4,X5) ) )
      & '$ki_exists_in_world_$i'(sK4,sK5) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ( ? [X4: '$ki_world'] :
        ( '$ki_accessible'(sK4,X4)
        & ? [X5] :
            ( ? [X6: '$ki_world'] :
                ( '$ki_accessible'(X4,X6)
                & ! [X7: '$ki_world'] :
                    ( member(X7,sK3,X5)
                    | ~ '$ki_accessible'(X6,X7) )
                & ! [X8: '$ki_world'] :
                    ( member(X8,sK3,sK5)
                    | ~ '$ki_accessible'(X6,X8) )
                & ? [X9: '$ki_world'] :
                    ( ~ intersect(X9,sK5,X5)
                    & '$ki_accessible'(X6,X9) ) )
            & '$ki_exists_in_world_$i'(X4,X5) ) )
   => ( '$ki_accessible'(sK4,sK6)
      & ? [X5] :
          ( ? [X6: '$ki_world'] :
              ( '$ki_accessible'(sK6,X6)
              & ! [X7: '$ki_world'] :
                  ( member(X7,sK3,X5)
                  | ~ '$ki_accessible'(X6,X7) )
              & ! [X8: '$ki_world'] :
                  ( member(X8,sK3,sK5)
                  | ~ '$ki_accessible'(X6,X8) )
              & ? [X9: '$ki_world'] :
                  ( ~ intersect(X9,sK5,X5)
                  & '$ki_accessible'(X6,X9) ) )
          & '$ki_exists_in_world_$i'(sK6,X5) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f31,plain,
    ( ? [X5] :
        ( ? [X6: '$ki_world'] :
            ( '$ki_accessible'(sK6,X6)
            & ! [X7: '$ki_world'] :
                ( member(X7,sK3,X5)
                | ~ '$ki_accessible'(X6,X7) )
            & ! [X8: '$ki_world'] :
                ( member(X8,sK3,sK5)
                | ~ '$ki_accessible'(X6,X8) )
            & ? [X9: '$ki_world'] :
                ( ~ intersect(X9,sK5,X5)
                & '$ki_accessible'(X6,X9) ) )
        & '$ki_exists_in_world_$i'(sK6,X5) )
   => ( ? [X6: '$ki_world'] :
          ( '$ki_accessible'(sK6,X6)
          & ! [X7: '$ki_world'] :
              ( member(X7,sK3,sK7)
              | ~ '$ki_accessible'(X6,X7) )
          & ! [X8: '$ki_world'] :
              ( member(X8,sK3,sK5)
              | ~ '$ki_accessible'(X6,X8) )
          & ? [X9: '$ki_world'] :
              ( ~ intersect(X9,sK5,sK7)
              & '$ki_accessible'(X6,X9) ) )
      & '$ki_exists_in_world_$i'(sK6,sK7) ) ),
    introduced(choice_axiom,[]) ).

tff(f32,plain,
    ( ? [X6: '$ki_world'] :
        ( '$ki_accessible'(sK6,X6)
        & ! [X7: '$ki_world'] :
            ( member(X7,sK3,sK7)
            | ~ '$ki_accessible'(X6,X7) )
        & ! [X8: '$ki_world'] :
            ( member(X8,sK3,sK5)
            | ~ '$ki_accessible'(X6,X8) )
        & ? [X9: '$ki_world'] :
            ( ~ intersect(X9,sK5,sK7)
            & '$ki_accessible'(X6,X9) ) )
   => ( '$ki_accessible'(sK6,sK8)
      & ! [X7: '$ki_world'] :
          ( member(X7,sK3,sK7)
          | ~ '$ki_accessible'(sK8,X7) )
      & ! [X8: '$ki_world'] :
          ( member(X8,sK3,sK5)
          | ~ '$ki_accessible'(sK8,X8) )
      & ? [X9: '$ki_world'] :
          ( ~ intersect(X9,sK5,sK7)
          & '$ki_accessible'(sK8,X9) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f33,plain,
    ( ? [X9: '$ki_world'] :
        ( ~ intersect(X9,sK5,sK7)
        & '$ki_accessible'(sK8,X9) )
   => ( ~ intersect(sK9,sK5,sK7)
      & '$ki_accessible'(sK8,sK9) ) ),
    introduced(choice_axiom,[]) ).

tff(f19,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ? [X3] :
                  ( ? [X4: '$ki_world'] :
                      ( '$ki_accessible'(X2,X4)
                      & ? [X5] :
                          ( ? [X6: '$ki_world'] :
                              ( '$ki_accessible'(X4,X6)
                              & ! [X7: '$ki_world'] :
                                  ( member(X7,X1,X5)
                                  | ~ '$ki_accessible'(X6,X7) )
                              & ! [X8: '$ki_world'] :
                                  ( member(X8,X1,X3)
                                  | ~ '$ki_accessible'(X6,X8) )
                              & ? [X9: '$ki_world'] :
                                  ( ~ intersect(X9,X3,X5)
                                  & '$ki_accessible'(X6,X9) ) )
                          & '$ki_exists_in_world_$i'(X4,X5) ) )
                  & '$ki_exists_in_world_$i'(X2,X3) )
              & '$ki_accessible'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f18]) ).

tff(f18,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ? [X3] :
                  ( ? [X4: '$ki_world'] :
                      ( ? [X5] :
                          ( ? [X6: '$ki_world'] :
                              ( ? [X9: '$ki_world'] :
                                  ( ~ intersect(X9,X3,X5)
                                  & '$ki_accessible'(X6,X9) )
                              & ! [X7: '$ki_world'] :
                                  ( member(X7,X1,X5)
                                  | ~ '$ki_accessible'(X6,X7) )
                              & ! [X8: '$ki_world'] :
                                  ( member(X8,X1,X3)
                                  | ~ '$ki_accessible'(X6,X8) )
                              & '$ki_accessible'(X4,X6) )
                          & '$ki_exists_in_world_$i'(X4,X5) )
                      & '$ki_accessible'(X2,X4) )
                  & '$ki_exists_in_world_$i'(X2,X3) )
              & '$ki_accessible'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f9]) ).

tff(f9,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X1] :
            ( '$ki_exists_in_world_$i'(X0,X1)
           => ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => ! [X3] :
                    ( '$ki_exists_in_world_$i'(X2,X3)
                   => ! [X4: '$ki_world'] :
                        ( '$ki_accessible'(X2,X4)
                       => ! [X5] :
                            ( '$ki_exists_in_world_$i'(X4,X5)
                           => ! [X6: '$ki_world'] :
                                ( '$ki_accessible'(X4,X6)
                               => ( ( ! [X7: '$ki_world'] :
                                        ( '$ki_accessible'(X6,X7)
                                       => member(X7,X1,X5) )
                                    & ! [X8: '$ki_world'] :
                                        ( '$ki_accessible'(X6,X8)
                                       => member(X8,X1,X3) ) )
                                 => ! [X9: '$ki_world'] :
                                      ( '$ki_accessible'(X6,X9)
                                     => intersect(X9,X3,X5) ) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X3] :
            ( '$ki_exists_in_world_$i'(X0,X3)
           => ! [X4: '$ki_world'] :
                ( '$ki_accessible'(X0,X4)
               => ! [X5] :
                    ( '$ki_exists_in_world_$i'(X4,X5)
                   => ! [X6: '$ki_world'] :
                        ( '$ki_accessible'(X4,X6)
                       => ! [X8] :
                            ( '$ki_exists_in_world_$i'(X6,X8)
                           => ! [X7: '$ki_world'] :
                                ( '$ki_accessible'(X6,X7)
                               => ( ( ! [X9: '$ki_world'] :
                                        ( '$ki_accessible'(X7,X9)
                                       => member(X9,X3,X8) )
                                    & ! [X9: '$ki_world'] :
                                        ( '$ki_accessible'(X7,X9)
                                       => member(X9,X3,X5) ) )
                                 => ! [X9: '$ki_world'] :
                                      ( '$ki_accessible'(X7,X9)
                                     => intersect(X9,X5,X8) ) ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X3] :
          ( '$ki_exists_in_world_$i'(X0,X3)
         => ! [X4: '$ki_world'] :
              ( '$ki_accessible'(X0,X4)
             => ! [X5] :
                  ( '$ki_exists_in_world_$i'(X4,X5)
                 => ! [X6: '$ki_world'] :
                      ( '$ki_accessible'(X4,X6)
                     => ! [X8] :
                          ( '$ki_exists_in_world_$i'(X6,X8)
                         => ! [X7: '$ki_world'] :
                              ( '$ki_accessible'(X6,X7)
                             => ( ( ! [X9: '$ki_world'] :
                                      ( '$ki_accessible'(X7,X9)
                                     => member(X9,X3,X8) )
                                  & ! [X9: '$ki_world'] :
                                      ( '$ki_accessible'(X7,X9)
                                     => member(X9,X3,X5) ) )
                               => ! [X9: '$ki_world'] :
                                    ( '$ki_accessible'(X7,X9)
                                   => intersect(X9,X5,X8) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f121,plain,
    ! [X10: '$ki_world'] : intersect(X10,sK5,sK7),
    inference(subsumption_resolution,[],[f120,f47]) ).

tff(f47,plain,
    ! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
    inference(cnf_transformation,[],[f22]) ).

tff(f22,plain,
    ! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
    inference(rectify,[],[f8]) ).

tff(f8,plain,
    ! [X1: '$ki_world',X0] : '$ki_exists_in_world_$i'(X1,X0),
    inference(rectify,[],[f2]) ).

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

tff(f120,plain,
    ! [X10: '$ki_world',X9: '$ki_world'] :
      ( intersect(X10,sK5,sK7)
      | ~ '$ki_exists_in_world_$i'(X9,sK7) ),
    inference(subsumption_resolution,[],[f119,f47]) ).

tff(f119,plain,
    ! [X10: '$ki_world',X8: '$ki_world',X9: '$ki_world'] :
      ( intersect(X10,sK5,sK7)
      | ~ '$ki_exists_in_world_$i'(X8,sK5)
      | ~ '$ki_exists_in_world_$i'(X9,sK7) ),
    inference(resolution,[],[f110,f84]) ).

tff(f84,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( ~ intersect(sK1(X1,X3,X4),X1,X3)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | intersect(X5,X3,X1) ),
    inference(subsumption_resolution,[],[f83,f73]) ).

tff(f73,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    inference(cnf_transformation,[],[f46]) ).

tff(f46,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    inference(rectify,[],[f10]) ).

tff(f10,plain,
    ! [X1: '$ki_world',X0: '$ki_world'] : '$ki_accessible'(X1,X0),
    inference(rectify,[],[f1]) ).

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

tff(f83,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( ~ intersect(sK1(X1,X3,X4),X1,X3)
      | ~ '$ki_accessible'(X2,X4)
      | intersect(X5,X3,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_exists_in_world_$i'(X2,X3) ),
    inference(subsumption_resolution,[],[f82,f73]) ).

tff(f82,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( ~ intersect(sK1(X1,X3,X4),X1,X3)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_accessible'(X2,X4)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | intersect(X5,X3,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1) ),
    inference(subsumption_resolution,[],[f81,f73]) ).

tff(f81,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( intersect(X5,X3,X1)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'(X2,X4)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | ~ intersect(sK1(X1,X3,X4),X1,X3)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f48,f73]) ).

tff(f48,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( ~ intersect(sK1(X1,X3,X4),X1,X3)
      | ~ '$ki_accessible'(X4,X5)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | intersect(X5,X3,X1)
      | ~ '$ki_accessible'(X2,X4)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_exists_in_world_$i'(X2,X3) ),
    inference(cnf_transformation,[],[f25]) ).

tff(f25,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ~ '$ki_exists_in_world_$i'(X2,X3)
                  | ! [X4: '$ki_world'] :
                      ( ~ '$ki_accessible'(X2,X4)
                      | ! [X5: '$ki_world'] :
                          ( ~ '$ki_accessible'(X4,X5)
                          | intersect(X5,X3,X1) )
                      | ( '$ki_accessible'(X4,sK1(X1,X3,X4))
                        & ~ intersect(sK1(X1,X3,X4),X1,X3) ) ) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f23,f24]) ).

tff(f24,plain,
    ! [X1,X3,X4: '$ki_world'] :
      ( ? [X6: '$ki_world'] :
          ( '$ki_accessible'(X4,X6)
          & ~ intersect(X6,X1,X3) )
     => ( '$ki_accessible'(X4,sK1(X1,X3,X4))
        & ~ intersect(sK1(X1,X3,X4),X1,X3) ) ),
    introduced(choice_axiom,[]) ).

tff(f23,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ~ '$ki_exists_in_world_$i'(X2,X3)
                  | ! [X4: '$ki_world'] :
                      ( ~ '$ki_accessible'(X2,X4)
                      | ! [X5: '$ki_world'] :
                          ( ~ '$ki_accessible'(X4,X5)
                          | intersect(X5,X3,X1) )
                      | ? [X6: '$ki_world'] :
                          ( '$ki_accessible'(X4,X6)
                          & ~ intersect(X6,X1,X3) ) ) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(rectify,[],[f15]) ).

tff(f15,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ~ '$ki_exists_in_world_$i'(X2,X3)
                  | ! [X4: '$ki_world'] :
                      ( ~ '$ki_accessible'(X2,X4)
                      | ! [X6: '$ki_world'] :
                          ( ~ '$ki_accessible'(X4,X6)
                          | intersect(X6,X3,X1) )
                      | ? [X5: '$ki_world'] :
                          ( '$ki_accessible'(X4,X5)
                          & ~ intersect(X5,X1,X3) ) ) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(flattening,[],[f14]) ).

tff(f14,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ! [X4: '$ki_world'] :
                      ( ! [X6: '$ki_world'] :
                          ( ~ '$ki_accessible'(X4,X6)
                          | intersect(X6,X3,X1) )
                      | ? [X5: '$ki_world'] :
                          ( '$ki_accessible'(X4,X5)
                          & ~ intersect(X5,X1,X3) )
                      | ~ '$ki_accessible'(X2,X4) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f11]) ).

tff(f11,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => ! [X3] :
                  ( '$ki_exists_in_world_$i'(X2,X3)
                 => ! [X4: '$ki_world'] :
                      ( '$ki_accessible'(X2,X4)
                     => ( ! [X5: '$ki_world'] :
                            ( '$ki_accessible'(X4,X5)
                           => intersect(X5,X1,X3) )
                       => ! [X6: '$ki_world'] :
                            ( '$ki_accessible'(X4,X6)
                           => intersect(X6,X3,X1) ) ) ) ) ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X3] :
          ( '$ki_exists_in_world_$i'(X0,X3)
         => ! [X4: '$ki_world'] :
              ( '$ki_accessible'(X0,X4)
             => ! [X5] :
                  ( '$ki_exists_in_world_$i'(X4,X5)
                 => ! [X6: '$ki_world'] :
                      ( '$ki_accessible'(X4,X6)
                     => ( ! [X7: '$ki_world'] :
                            ( '$ki_accessible'(X6,X7)
                           => intersect(X7,X3,X5) )
                       => ! [X7: '$ki_world'] :
                            ( '$ki_accessible'(X6,X7)
                           => intersect(X7,X5,X3) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_intersect) ).

tff(f110,plain,
    ! [X1: '$ki_world'] : intersect(X1,sK7,sK5),
    inference(resolution,[],[f104,f79]) ).

tff(f79,plain,
    ! [X7: '$ki_world'] : member(X7,sK3,sK7),
    inference(subsumption_resolution,[],[f58,f73]) ).

tff(f58,plain,
    ! [X7: '$ki_world'] :
      ( member(X7,sK3,sK7)
      | ~ '$ki_accessible'(sK8,X7) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f104,plain,
    ! [X2: '$ki_world',X3: '$ki_world',X1: $i] :
      ( ~ member(sK13(X1,X3,sK3),sK3,X1)
      | intersect(X2,X1,sK5) ),
    inference(subsumption_resolution,[],[f103,f47]) ).

tff(f103,plain,
    ! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: $i] :
      ( ~ member(sK13(X1,X3,sK3),sK3,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | intersect(X2,X1,sK5) ),
    inference(subsumption_resolution,[],[f102,f47]) ).

tff(f102,plain,
    ! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: $i] :
      ( ~ '$ki_exists_in_world_$i'(X3,sK3)
      | ~ member(sK13(X1,X3,sK3),sK3,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | intersect(X2,X1,sK5) ),
    inference(subsumption_resolution,[],[f100,f47]) ).

tff(f100,plain,
    ! [X2: '$ki_world',X3: '$ki_world',X0: '$ki_world',X1: $i,X4: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(X4,sK5)
      | intersect(X2,X1,sK5)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ member(sK13(X1,X3,sK3),sK3,X1)
      | ~ '$ki_exists_in_world_$i'(X3,sK3) ),
    inference(resolution,[],[f77,f78]) ).

tff(f78,plain,
    ! [X8: '$ki_world'] : member(X8,sK3,sK5),
    inference(subsumption_resolution,[],[f57,f73]) ).

tff(f57,plain,
    ! [X8: '$ki_world'] :
      ( ~ '$ki_accessible'(sK8,X8)
      | member(X8,sK3,sK5) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f77,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( ~ member(sK14(X3,X4,X6),X6,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | intersect(X5,X1,X3)
      | ~ member(sK13(X1,X4,X6),X6,X1)
      | ~ '$ki_exists_in_world_$i'(X4,X6)
      | ~ '$ki_exists_in_world_$i'(X2,X3) ),
    inference(subsumption_resolution,[],[f76,f73]) ).

tff(f76,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | ~ member(sK13(X1,X4,X6),X6,X1)
      | ~ member(sK14(X3,X4,X6),X6,X3)
      | intersect(X5,X1,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_exists_in_world_$i'(X4,X6) ),
    inference(subsumption_resolution,[],[f75,f73]) ).

tff(f75,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( ~ member(sK14(X3,X4,X6),X6,X3)
      | ~ '$ki_accessible'(X2,X4)
      | ~ member(sK13(X1,X4,X6),X6,X1)
      | intersect(X5,X1,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_exists_in_world_$i'(X4,X6)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_exists_in_world_$i'(X2,X3) ),
    inference(subsumption_resolution,[],[f74,f73]) ).

tff(f74,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X4,X6)
      | ~ '$ki_accessible'(X2,X4)
      | ~ member(sK13(X1,X4,X6),X6,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | intersect(X5,X1,X3)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | ~ member(sK14(X3,X4,X6),X6,X3) ),
    inference(subsumption_resolution,[],[f70,f73]) ).

tff(f70,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( ~ '$ki_accessible'(X4,X5)
      | ~ member(sK14(X3,X4,X6),X6,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | intersect(X5,X1,X3)
      | ~ '$ki_accessible'(X2,X4)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_exists_in_world_$i'(X4,X6)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | ~ member(sK13(X1,X4,X6),X6,X1) ),
    inference(cnf_transformation,[],[f45]) ).

tff(f45,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X0,X2)
              | ! [X3] :
                  ( ~ '$ki_exists_in_world_$i'(X2,X3)
                  | ( sP0(X1,X3,X2)
                    & ! [X4: '$ki_world'] :
                        ( ! [X5: '$ki_world'] :
                            ( ~ '$ki_accessible'(X4,X5)
                            | intersect(X5,X1,X3) )
                        | ~ '$ki_accessible'(X2,X4)
                        | ! [X6] :
                            ( ( ~ member(sK13(X1,X4,X6),X6,X1)
                              & '$ki_accessible'(X4,sK13(X1,X4,X6)) )
                            | ( '$ki_accessible'(X4,sK14(X3,X4,X6))
                              & ~ member(sK14(X3,X4,X6),X6,X3) )
                            | ~ '$ki_exists_in_world_$i'(X4,X6) ) ) ) ) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f42,f44,f43]) ).

tff(f43,plain,
    ! [X1,X4: '$ki_world',X6] :
      ( ? [X7: '$ki_world'] :
          ( ~ member(X7,X6,X1)
          & '$ki_accessible'(X4,X7) )
     => ( ~ member(sK13(X1,X4,X6),X6,X1)
        & '$ki_accessible'(X4,sK13(X1,X4,X6)) ) ),
    introduced(choice_axiom,[]) ).

tff(f44,plain,
    ! [X3,X4: '$ki_world',X6] :
      ( ? [X8: '$ki_world'] :
          ( '$ki_accessible'(X4,X8)
          & ~ member(X8,X6,X3) )
     => ( '$ki_accessible'(X4,sK14(X3,X4,X6))
        & ~ member(sK14(X3,X4,X6),X6,X3) ) ),
    introduced(choice_axiom,[]) ).

tff(f42,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X0,X2)
              | ! [X3] :
                  ( ~ '$ki_exists_in_world_$i'(X2,X3)
                  | ( sP0(X1,X3,X2)
                    & ! [X4: '$ki_world'] :
                        ( ! [X5: '$ki_world'] :
                            ( ~ '$ki_accessible'(X4,X5)
                            | intersect(X5,X1,X3) )
                        | ~ '$ki_accessible'(X2,X4)
                        | ! [X6] :
                            ( ? [X7: '$ki_world'] :
                                ( ~ member(X7,X6,X1)
                                & '$ki_accessible'(X4,X7) )
                            | ? [X8: '$ki_world'] :
                                ( '$ki_accessible'(X4,X8)
                                & ~ member(X8,X6,X3) )
                            | ~ '$ki_exists_in_world_$i'(X4,X6) ) ) ) ) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(rectify,[],[f21]) ).

tff(f21,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X0,X2)
              | ! [X3] :
                  ( ~ '$ki_exists_in_world_$i'(X2,X3)
                  | ( sP0(X1,X3,X2)
                    & ! [X9: '$ki_world'] :
                        ( ! [X13: '$ki_world'] :
                            ( ~ '$ki_accessible'(X9,X13)
                            | intersect(X13,X1,X3) )
                        | ~ '$ki_accessible'(X2,X9)
                        | ! [X10] :
                            ( ? [X12: '$ki_world'] :
                                ( ~ member(X12,X10,X1)
                                & '$ki_accessible'(X9,X12) )
                            | ? [X11: '$ki_world'] :
                                ( '$ki_accessible'(X9,X11)
                                & ~ member(X11,X10,X3) )
                            | ~ '$ki_exists_in_world_$i'(X9,X10) ) ) ) ) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(definition_folding,[],[f17,f20]) ).

tff(f20,plain,
    ! [X1,X3,X2: '$ki_world'] :
      ( ! [X4: '$ki_world'] :
          ( ? [X6] :
              ( ! [X8: '$ki_world'] :
                  ( member(X8,X6,X1)
                  | ~ '$ki_accessible'(X4,X8) )
              & '$ki_exists_in_world_$i'(X4,X6)
              & ! [X7: '$ki_world'] :
                  ( ~ '$ki_accessible'(X4,X7)
                  | member(X7,X6,X3) ) )
          | ? [X5: '$ki_world'] :
              ( '$ki_accessible'(X4,X5)
              & ~ intersect(X5,X1,X3) )
          | ~ '$ki_accessible'(X2,X4) )
      | ~ sP0(X1,X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f17,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X0,X2)
              | ! [X3] :
                  ( ~ '$ki_exists_in_world_$i'(X2,X3)
                  | ( ! [X4: '$ki_world'] :
                        ( ? [X6] :
                            ( ! [X8: '$ki_world'] :
                                ( member(X8,X6,X1)
                                | ~ '$ki_accessible'(X4,X8) )
                            & '$ki_exists_in_world_$i'(X4,X6)
                            & ! [X7: '$ki_world'] :
                                ( ~ '$ki_accessible'(X4,X7)
                                | member(X7,X6,X3) ) )
                        | ? [X5: '$ki_world'] :
                            ( '$ki_accessible'(X4,X5)
                            & ~ intersect(X5,X1,X3) )
                        | ~ '$ki_accessible'(X2,X4) )
                    & ! [X9: '$ki_world'] :
                        ( ! [X13: '$ki_world'] :
                            ( ~ '$ki_accessible'(X9,X13)
                            | intersect(X13,X1,X3) )
                        | ~ '$ki_accessible'(X2,X9)
                        | ! [X10] :
                            ( ? [X12: '$ki_world'] :
                                ( ~ member(X12,X10,X1)
                                & '$ki_accessible'(X9,X12) )
                            | ? [X11: '$ki_world'] :
                                ( '$ki_accessible'(X9,X11)
                                & ~ member(X11,X10,X3) )
                            | ~ '$ki_exists_in_world_$i'(X9,X10) ) ) ) ) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(flattening,[],[f16]) ).

tff(f16,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ( ! [X9: '$ki_world'] :
                        ( ! [X13: '$ki_world'] :
                            ( ~ '$ki_accessible'(X9,X13)
                            | intersect(X13,X1,X3) )
                        | ! [X10] :
                            ( ? [X12: '$ki_world'] :
                                ( ~ member(X12,X10,X1)
                                & '$ki_accessible'(X9,X12) )
                            | ? [X11: '$ki_world'] :
                                ( '$ki_accessible'(X9,X11)
                                & ~ member(X11,X10,X3) )
                            | ~ '$ki_exists_in_world_$i'(X9,X10) )
                        | ~ '$ki_accessible'(X2,X9) )
                    & ! [X4: '$ki_world'] :
                        ( ? [X6] :
                            ( ! [X8: '$ki_world'] :
                                ( member(X8,X6,X1)
                                | ~ '$ki_accessible'(X4,X8) )
                            & '$ki_exists_in_world_$i'(X4,X6)
                            & ! [X7: '$ki_world'] :
                                ( ~ '$ki_accessible'(X4,X7)
                                | member(X7,X6,X3) ) )
                        | ? [X5: '$ki_world'] :
                            ( '$ki_accessible'(X4,X5)
                            & ~ intersect(X5,X1,X3) )
                        | ~ '$ki_accessible'(X2,X4) ) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f13]) ).

tff(f13,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => ! [X3] :
                  ( '$ki_exists_in_world_$i'(X2,X3)
                 => ( ! [X9: '$ki_world'] :
                        ( '$ki_accessible'(X2,X9)
                       => ( ? [X10] :
                              ( '$ki_exists_in_world_$i'(X9,X10)
                              & ! [X12: '$ki_world'] :
                                  ( '$ki_accessible'(X9,X12)
                                 => member(X12,X10,X1) )
                              & ! [X11: '$ki_world'] :
                                  ( '$ki_accessible'(X9,X11)
                                 => member(X11,X10,X3) ) )
                         => ! [X13: '$ki_world'] :
                              ( '$ki_accessible'(X9,X13)
                             => intersect(X13,X1,X3) ) ) )
                    & ! [X4: '$ki_world'] :
                        ( '$ki_accessible'(X2,X4)
                       => ( ! [X5: '$ki_world'] :
                              ( '$ki_accessible'(X4,X5)
                             => intersect(X5,X1,X3) )
                         => ? [X6] :
                              ( '$ki_exists_in_world_$i'(X4,X6)
                              & ! [X7: '$ki_world'] :
                                  ( '$ki_accessible'(X4,X7)
                                 => member(X7,X6,X3) )
                              & ! [X8: '$ki_world'] :
                                  ( '$ki_accessible'(X4,X8)
                                 => member(X8,X6,X1) ) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X3] :
          ( '$ki_exists_in_world_$i'(X0,X3)
         => ! [X4: '$ki_world'] :
              ( '$ki_accessible'(X0,X4)
             => ! [X5] :
                  ( '$ki_exists_in_world_$i'(X4,X5)
                 => ( ! [X6: '$ki_world'] :
                        ( '$ki_accessible'(X4,X6)
                       => ( ! [X7: '$ki_world'] :
                              ( '$ki_accessible'(X6,X7)
                             => intersect(X7,X3,X5) )
                         => ? [X8] :
                              ( ! [X7: '$ki_world'] :
                                  ( '$ki_accessible'(X6,X7)
                                 => member(X7,X8,X5) )
                              & ! [X7: '$ki_world'] :
                                  ( '$ki_accessible'(X6,X7)
                                 => member(X7,X8,X3) )
                              & '$ki_exists_in_world_$i'(X6,X8) ) ) )
                    & ! [X6: '$ki_world'] :
                        ( '$ki_accessible'(X4,X6)
                       => ( ? [X8] :
                              ( '$ki_exists_in_world_$i'(X6,X8)
                              & ! [X7: '$ki_world'] :
                                  ( '$ki_accessible'(X6,X7)
                                 => member(X7,X8,X5) )
                              & ! [X7: '$ki_world'] :
                                  ( '$ki_accessible'(X6,X7)
                                 => member(X7,X8,X3) ) )
                         => ! [X7: '$ki_world'] :
                              ( '$ki_accessible'(X6,X7)
                             => intersect(X7,X3,X5) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : LCL950_17 : TPTP v8.2.0. Released v8.2.0.
% 0.08/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n011.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   : Mon May 22 12:00:21 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.22/0.51  % (14276)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.23/0.52  % (14281)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.23/0.52  % (14282)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.23/0.52  % (14284)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.23/0.52  % (14284)First to succeed.
% 1.23/0.53  % (14284)Refutation found. Thanks to Tanya!
% 1.23/0.53  % SZS status Theorem for theBenchmark
% 1.23/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.23/0.53  % (14284)------------------------------
% 1.23/0.53  % (14284)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.23/0.53  % (14284)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.23/0.53  % (14284)Termination reason: Refutation
% 1.23/0.53  
% 1.23/0.53  % (14284)Memory used [KB]: 1023
% 1.23/0.53  % (14284)Time elapsed: 0.105 s
% 1.23/0.53  % (14284)Instructions burned: 3 (million)
% 1.23/0.53  % (14284)------------------------------
% 1.23/0.53  % (14284)------------------------------
% 1.23/0.53  % (14268)Success in time 0.166 s
%------------------------------------------------------------------------------