TSTP Solution File: LCL950_17 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : LCL950_17 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 02:40:21 EDT 2024

% Result   : Theorem 1.78s 1.11s
% Output   : CNFRefutation 1.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   52 (  14 unt;   0 typ;   0 def)
%            Number of atoms       :  598 (   0 equ)
%            Maximal formula atoms :   26 (  11 avg)
%            Number of connectives :  580 ( 178   ~; 150   |; 181   &)
%                                         (   0 <=>;  71  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (  10 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  144 ( 144 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  17 usr;  11 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :  323 (  12 sgn 162   !; 108   ?; 197   :)

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

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

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

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

tff(f10,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'] :
                        ( '$ki_accessible'(X2,X4)
                       => ( ? [X5] :
                              ( ! [X6: '$ki_world'] :
                                  ( '$ki_accessible'(X4,X6)
                                 => member(X6,X5,X3) )
                              & ! [X7: '$ki_world'] :
                                  ( '$ki_accessible'(X4,X7)
                                 => member(X7,X5,X1) )
                              & '$ki_exists_in_world_$i'(X4,X5) )
                         => ! [X8: '$ki_world'] :
                              ( '$ki_accessible'(X4,X8)
                             => intersect(X8,X1,X3) ) ) )
                    & ! [X9: '$ki_world'] :
                        ( '$ki_accessible'(X2,X9)
                       => ( ! [X10: '$ki_world'] :
                              ( '$ki_accessible'(X9,X10)
                             => intersect(X10,X1,X3) )
                         => ? [X11] :
                              ( ! [X12: '$ki_world'] :
                                  ( '$ki_accessible'(X9,X12)
                                 => member(X12,X11,X3) )
                              & ! [X13: '$ki_world'] :
                                  ( '$ki_accessible'(X9,X13)
                                 => member(X13,X11,X1) )
                              & '$ki_exists_in_world_$i'(X9,X11) ) ) ) ) ) ) ) ),
    inference(rectify,[],[f4]) ).

tff(f12,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(f13,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ( ! [X4: '$ki_world'] :
                        ( ! [X8: '$ki_world'] :
                            ( intersect(X8,X1,X3)
                            | ~ '$ki_accessible'(X4,X8) )
                        | ! [X5] :
                            ( ? [X6: '$ki_world'] :
                                ( ~ member(X6,X5,X3)
                                & '$ki_accessible'(X4,X6) )
                            | ? [X7: '$ki_world'] :
                                ( ~ member(X7,X5,X1)
                                & '$ki_accessible'(X4,X7) )
                            | ~ '$ki_exists_in_world_$i'(X4,X5) )
                        | ~ '$ki_accessible'(X2,X4) )
                    & ! [X9: '$ki_world'] :
                        ( ? [X11] :
                            ( ! [X12: '$ki_world'] :
                                ( member(X12,X11,X3)
                                | ~ '$ki_accessible'(X9,X12) )
                            & ! [X13: '$ki_world'] :
                                ( member(X13,X11,X1)
                                | ~ '$ki_accessible'(X9,X13) )
                            & '$ki_exists_in_world_$i'(X9,X11) )
                        | ? [X10: '$ki_world'] :
                            ( ~ intersect(X10,X1,X3)
                            & '$ki_accessible'(X9,X10) )
                        | ~ '$ki_accessible'(X2,X9) ) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f10]) ).

tff(f14,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ( ! [X4: '$ki_world'] :
                        ( ! [X8: '$ki_world'] :
                            ( intersect(X8,X1,X3)
                            | ~ '$ki_accessible'(X4,X8) )
                        | ! [X5] :
                            ( ? [X6: '$ki_world'] :
                                ( ~ member(X6,X5,X3)
                                & '$ki_accessible'(X4,X6) )
                            | ? [X7: '$ki_world'] :
                                ( ~ member(X7,X5,X1)
                                & '$ki_accessible'(X4,X7) )
                            | ~ '$ki_exists_in_world_$i'(X4,X5) )
                        | ~ '$ki_accessible'(X2,X4) )
                    & ! [X9: '$ki_world'] :
                        ( ? [X11] :
                            ( ! [X12: '$ki_world'] :
                                ( member(X12,X11,X3)
                                | ~ '$ki_accessible'(X9,X12) )
                            & ! [X13: '$ki_world'] :
                                ( member(X13,X11,X1)
                                | ~ '$ki_accessible'(X9,X13) )
                            & '$ki_exists_in_world_$i'(X9,X11) )
                        | ? [X10: '$ki_world'] :
                            ( ~ intersect(X10,X1,X3)
                            & '$ki_accessible'(X9,X10) )
                        | ~ '$ki_accessible'(X2,X9) ) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f13]) ).

tff(f17,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,[],[f12]) ).

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(flattening,[],[f17]) ).

tff(f19,plain,
    ! [X3,X1,X2: '$ki_world'] :
      ( ! [X9: '$ki_world'] :
          ( ? [X11] :
              ( ! [X12: '$ki_world'] :
                  ( member(X12,X11,X3)
                  | ~ '$ki_accessible'(X9,X12) )
              & ! [X13: '$ki_world'] :
                  ( member(X13,X11,X1)
                  | ~ '$ki_accessible'(X9,X13) )
              & '$ki_exists_in_world_$i'(X9,X11) )
          | ? [X10: '$ki_world'] :
              ( ~ intersect(X10,X1,X3)
              & '$ki_accessible'(X9,X10) )
          | ~ '$ki_accessible'(X2,X9) )
      | ~ sP0(X3,X1,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f20,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ( ! [X4: '$ki_world'] :
                        ( ! [X8: '$ki_world'] :
                            ( intersect(X8,X1,X3)
                            | ~ '$ki_accessible'(X4,X8) )
                        | ! [X5] :
                            ( ? [X6: '$ki_world'] :
                                ( ~ member(X6,X5,X3)
                                & '$ki_accessible'(X4,X6) )
                            | ? [X7: '$ki_world'] :
                                ( ~ member(X7,X5,X1)
                                & '$ki_accessible'(X4,X7) )
                            | ~ '$ki_exists_in_world_$i'(X4,X5) )
                        | ~ '$ki_accessible'(X2,X4) )
                    & sP0(X3,X1,X2) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(definition_folding,[],[f14,f19]) ).

tff(f28,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ( ! [X4: '$ki_world'] :
                        ( ! [X5: '$ki_world'] :
                            ( intersect(X5,X1,X3)
                            | ~ '$ki_accessible'(X4,X5) )
                        | ! [X6] :
                            ( ? [X7: '$ki_world'] :
                                ( ~ member(X7,X6,X3)
                                & '$ki_accessible'(X4,X7) )
                            | ? [X8: '$ki_world'] :
                                ( ~ member(X8,X6,X1)
                                & '$ki_accessible'(X4,X8) )
                            | ~ '$ki_exists_in_world_$i'(X4,X6) )
                        | ~ '$ki_accessible'(X2,X4) )
                    & sP0(X3,X1,X2) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(rectify,[],[f20]) ).

tff(f29,plain,
    ! [X3,X4: '$ki_world',X6] :
      ( ? [X7: '$ki_world'] :
          ( ~ member(X7,X6,X3)
          & '$ki_accessible'(X4,X7) )
     => ( ~ member(sK4(X3,X4,X6),X6,X3)
        & '$ki_accessible'(X4,sK4(X3,X4,X6)) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ! [X1,X4: '$ki_world',X6] :
      ( ? [X8: '$ki_world'] :
          ( ~ member(X8,X6,X1)
          & '$ki_accessible'(X4,X8) )
     => ( ~ member(sK5(X1,X4,X6),X6,X1)
        & '$ki_accessible'(X4,sK5(X1,X4,X6)) ) ),
    introduced(choice_axiom,[]) ).

tff(f31,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ( ! [X4: '$ki_world'] :
                        ( ! [X5: '$ki_world'] :
                            ( intersect(X5,X1,X3)
                            | ~ '$ki_accessible'(X4,X5) )
                        | ! [X6] :
                            ( ( ~ member(sK4(X3,X4,X6),X6,X3)
                              & '$ki_accessible'(X4,sK4(X3,X4,X6)) )
                            | ( ~ member(sK5(X1,X4,X6),X6,X1)
                              & '$ki_accessible'(X4,sK5(X1,X4,X6)) )
                            | ~ '$ki_exists_in_world_$i'(X4,X6) )
                        | ~ '$ki_accessible'(X2,X4) )
                    & sP0(X3,X1,X2) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f28,f30,f29]) ).

tff(f35,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ? [X3] :
                  ( ? [X4: '$ki_world'] :
                      ( ? [X5] :
                          ( ? [X6: '$ki_world'] :
                              ( ? [X7: '$ki_world'] :
                                  ( ~ intersect(X7,X3,X5)
                                  & '$ki_accessible'(X6,X7) )
                              & ! [X8: '$ki_world'] :
                                  ( member(X8,X1,X5)
                                  | ~ '$ki_accessible'(X6,X8) )
                              & ! [X9: '$ki_world'] :
                                  ( member(X9,X1,X3)
                                  | ~ '$ki_accessible'(X6,X9) )
                              & '$ki_accessible'(X4,X6) )
                          & '$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(rectify,[],[f18]) ).

tff(f36,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1] :
            ( ? [X2: '$ki_world'] :
                ( ? [X3] :
                    ( ? [X4: '$ki_world'] :
                        ( ? [X5] :
                            ( ? [X6: '$ki_world'] :
                                ( ? [X7: '$ki_world'] :
                                    ( ~ intersect(X7,X3,X5)
                                    & '$ki_accessible'(X6,X7) )
                                & ! [X8: '$ki_world'] :
                                    ( member(X8,X1,X5)
                                    | ~ '$ki_accessible'(X6,X8) )
                                & ! [X9: '$ki_world'] :
                                    ( member(X9,X1,X3)
                                    | ~ '$ki_accessible'(X6,X9) )
                                & '$ki_accessible'(X4,X6) )
                            & '$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'('$ki_local_world',X0) )
   => ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ? [X3] :
                  ( ? [X4: '$ki_world'] :
                      ( ? [X5] :
                          ( ? [X6: '$ki_world'] :
                              ( ? [X7: '$ki_world'] :
                                  ( ~ intersect(X7,X3,X5)
                                  & '$ki_accessible'(X6,X7) )
                              & ! [X8: '$ki_world'] :
                                  ( member(X8,X1,X5)
                                  | ~ '$ki_accessible'(X6,X8) )
                              & ! [X9: '$ki_world'] :
                                  ( member(X9,X1,X3)
                                  | ~ '$ki_accessible'(X6,X9) )
                              & '$ki_accessible'(X4,X6) )
                          & '$ki_exists_in_world_$i'(X4,X5) )
                      & '$ki_accessible'(X2,X4) )
                  & '$ki_exists_in_world_$i'(X2,X3) )
              & '$ki_accessible'(sK7,X2) )
          & '$ki_exists_in_world_$i'(sK7,X1) )
      & '$ki_accessible'('$ki_local_world',sK7) ) ),
    introduced(choice_axiom,[]) ).

tff(f37,plain,
    ( ? [X1] :
        ( ? [X2: '$ki_world'] :
            ( ? [X3] :
                ( ? [X4: '$ki_world'] :
                    ( ? [X5] :
                        ( ? [X6: '$ki_world'] :
                            ( ? [X7: '$ki_world'] :
                                ( ~ intersect(X7,X3,X5)
                                & '$ki_accessible'(X6,X7) )
                            & ! [X8: '$ki_world'] :
                                ( member(X8,X1,X5)
                                | ~ '$ki_accessible'(X6,X8) )
                            & ! [X9: '$ki_world'] :
                                ( member(X9,X1,X3)
                                | ~ '$ki_accessible'(X6,X9) )
                            & '$ki_accessible'(X4,X6) )
                        & '$ki_exists_in_world_$i'(X4,X5) )
                    & '$ki_accessible'(X2,X4) )
                & '$ki_exists_in_world_$i'(X2,X3) )
            & '$ki_accessible'(sK7,X2) )
        & '$ki_exists_in_world_$i'(sK7,X1) )
   => ( ? [X2: '$ki_world'] :
          ( ? [X3] :
              ( ? [X4: '$ki_world'] :
                  ( ? [X5] :
                      ( ? [X6: '$ki_world'] :
                          ( ? [X7: '$ki_world'] :
                              ( ~ intersect(X7,X3,X5)
                              & '$ki_accessible'(X6,X7) )
                          & ! [X8: '$ki_world'] :
                              ( member(X8,sK8,X5)
                              | ~ '$ki_accessible'(X6,X8) )
                          & ! [X9: '$ki_world'] :
                              ( member(X9,sK8,X3)
                              | ~ '$ki_accessible'(X6,X9) )
                          & '$ki_accessible'(X4,X6) )
                      & '$ki_exists_in_world_$i'(X4,X5) )
                  & '$ki_accessible'(X2,X4) )
              & '$ki_exists_in_world_$i'(X2,X3) )
          & '$ki_accessible'(sK7,X2) )
      & '$ki_exists_in_world_$i'(sK7,sK8) ) ),
    introduced(choice_axiom,[]) ).

tff(f38,plain,
    ( ? [X2: '$ki_world'] :
        ( ? [X3] :
            ( ? [X4: '$ki_world'] :
                ( ? [X5] :
                    ( ? [X6: '$ki_world'] :
                        ( ? [X7: '$ki_world'] :
                            ( ~ intersect(X7,X3,X5)
                            & '$ki_accessible'(X6,X7) )
                        & ! [X8: '$ki_world'] :
                            ( member(X8,sK8,X5)
                            | ~ '$ki_accessible'(X6,X8) )
                        & ! [X9: '$ki_world'] :
                            ( member(X9,sK8,X3)
                            | ~ '$ki_accessible'(X6,X9) )
                        & '$ki_accessible'(X4,X6) )
                    & '$ki_exists_in_world_$i'(X4,X5) )
                & '$ki_accessible'(X2,X4) )
            & '$ki_exists_in_world_$i'(X2,X3) )
        & '$ki_accessible'(sK7,X2) )
   => ( ? [X3] :
          ( ? [X4: '$ki_world'] :
              ( ? [X5] :
                  ( ? [X6: '$ki_world'] :
                      ( ? [X7: '$ki_world'] :
                          ( ~ intersect(X7,X3,X5)
                          & '$ki_accessible'(X6,X7) )
                      & ! [X8: '$ki_world'] :
                          ( member(X8,sK8,X5)
                          | ~ '$ki_accessible'(X6,X8) )
                      & ! [X9: '$ki_world'] :
                          ( member(X9,sK8,X3)
                          | ~ '$ki_accessible'(X6,X9) )
                      & '$ki_accessible'(X4,X6) )
                  & '$ki_exists_in_world_$i'(X4,X5) )
              & '$ki_accessible'(sK9,X4) )
          & '$ki_exists_in_world_$i'(sK9,X3) )
      & '$ki_accessible'(sK7,sK9) ) ),
    introduced(choice_axiom,[]) ).

tff(f39,plain,
    ( ? [X3] :
        ( ? [X4: '$ki_world'] :
            ( ? [X5] :
                ( ? [X6: '$ki_world'] :
                    ( ? [X7: '$ki_world'] :
                        ( ~ intersect(X7,X3,X5)
                        & '$ki_accessible'(X6,X7) )
                    & ! [X8: '$ki_world'] :
                        ( member(X8,sK8,X5)
                        | ~ '$ki_accessible'(X6,X8) )
                    & ! [X9: '$ki_world'] :
                        ( member(X9,sK8,X3)
                        | ~ '$ki_accessible'(X6,X9) )
                    & '$ki_accessible'(X4,X6) )
                & '$ki_exists_in_world_$i'(X4,X5) )
            & '$ki_accessible'(sK9,X4) )
        & '$ki_exists_in_world_$i'(sK9,X3) )
   => ( ? [X4: '$ki_world'] :
          ( ? [X5] :
              ( ? [X6: '$ki_world'] :
                  ( ? [X7: '$ki_world'] :
                      ( ~ intersect(X7,sK10,X5)
                      & '$ki_accessible'(X6,X7) )
                  & ! [X8: '$ki_world'] :
                      ( member(X8,sK8,X5)
                      | ~ '$ki_accessible'(X6,X8) )
                  & ! [X9: '$ki_world'] :
                      ( member(X9,sK8,sK10)
                      | ~ '$ki_accessible'(X6,X9) )
                  & '$ki_accessible'(X4,X6) )
              & '$ki_exists_in_world_$i'(X4,X5) )
          & '$ki_accessible'(sK9,X4) )
      & '$ki_exists_in_world_$i'(sK9,sK10) ) ),
    introduced(choice_axiom,[]) ).

tff(f40,plain,
    ( ? [X4: '$ki_world'] :
        ( ? [X5] :
            ( ? [X6: '$ki_world'] :
                ( ? [X7: '$ki_world'] :
                    ( ~ intersect(X7,sK10,X5)
                    & '$ki_accessible'(X6,X7) )
                & ! [X8: '$ki_world'] :
                    ( member(X8,sK8,X5)
                    | ~ '$ki_accessible'(X6,X8) )
                & ! [X9: '$ki_world'] :
                    ( member(X9,sK8,sK10)
                    | ~ '$ki_accessible'(X6,X9) )
                & '$ki_accessible'(X4,X6) )
            & '$ki_exists_in_world_$i'(X4,X5) )
        & '$ki_accessible'(sK9,X4) )
   => ( ? [X5] :
          ( ? [X6: '$ki_world'] :
              ( ? [X7: '$ki_world'] :
                  ( ~ intersect(X7,sK10,X5)
                  & '$ki_accessible'(X6,X7) )
              & ! [X8: '$ki_world'] :
                  ( member(X8,sK8,X5)
                  | ~ '$ki_accessible'(X6,X8) )
              & ! [X9: '$ki_world'] :
                  ( member(X9,sK8,sK10)
                  | ~ '$ki_accessible'(X6,X9) )
              & '$ki_accessible'(sK11,X6) )
          & '$ki_exists_in_world_$i'(sK11,X5) )
      & '$ki_accessible'(sK9,sK11) ) ),
    introduced(choice_axiom,[]) ).

tff(f41,plain,
    ( ? [X5] :
        ( ? [X6: '$ki_world'] :
            ( ? [X7: '$ki_world'] :
                ( ~ intersect(X7,sK10,X5)
                & '$ki_accessible'(X6,X7) )
            & ! [X8: '$ki_world'] :
                ( member(X8,sK8,X5)
                | ~ '$ki_accessible'(X6,X8) )
            & ! [X9: '$ki_world'] :
                ( member(X9,sK8,sK10)
                | ~ '$ki_accessible'(X6,X9) )
            & '$ki_accessible'(sK11,X6) )
        & '$ki_exists_in_world_$i'(sK11,X5) )
   => ( ? [X6: '$ki_world'] :
          ( ? [X7: '$ki_world'] :
              ( ~ intersect(X7,sK10,sK12)
              & '$ki_accessible'(X6,X7) )
          & ! [X8: '$ki_world'] :
              ( member(X8,sK8,sK12)
              | ~ '$ki_accessible'(X6,X8) )
          & ! [X9: '$ki_world'] :
              ( member(X9,sK8,sK10)
              | ~ '$ki_accessible'(X6,X9) )
          & '$ki_accessible'(sK11,X6) )
      & '$ki_exists_in_world_$i'(sK11,sK12) ) ),
    introduced(choice_axiom,[]) ).

tff(f42,plain,
    ( ? [X6: '$ki_world'] :
        ( ? [X7: '$ki_world'] :
            ( ~ intersect(X7,sK10,sK12)
            & '$ki_accessible'(X6,X7) )
        & ! [X8: '$ki_world'] :
            ( member(X8,sK8,sK12)
            | ~ '$ki_accessible'(X6,X8) )
        & ! [X9: '$ki_world'] :
            ( member(X9,sK8,sK10)
            | ~ '$ki_accessible'(X6,X9) )
        & '$ki_accessible'(sK11,X6) )
   => ( ? [X7: '$ki_world'] :
          ( ~ intersect(X7,sK10,sK12)
          & '$ki_accessible'(sK13,X7) )
      & ! [X8: '$ki_world'] :
          ( member(X8,sK8,sK12)
          | ~ '$ki_accessible'(sK13,X8) )
      & ! [X9: '$ki_world'] :
          ( member(X9,sK8,sK10)
          | ~ '$ki_accessible'(sK13,X9) )
      & '$ki_accessible'(sK11,sK13) ) ),
    introduced(choice_axiom,[]) ).

tff(f43,plain,
    ( ? [X7: '$ki_world'] :
        ( ~ intersect(X7,sK10,sK12)
        & '$ki_accessible'(sK13,X7) )
   => ( ~ intersect(sK14,sK10,sK12)
      & '$ki_accessible'(sK13,sK14) ) ),
    introduced(choice_axiom,[]) ).

tff(f44,plain,
    ( ~ intersect(sK14,sK10,sK12)
    & '$ki_accessible'(sK13,sK14)
    & ! [X8: '$ki_world'] :
        ( member(X8,sK8,sK12)
        | ~ '$ki_accessible'(sK13,X8) )
    & ! [X9: '$ki_world'] :
        ( member(X9,sK8,sK10)
        | ~ '$ki_accessible'(sK13,X9) )
    & '$ki_accessible'(sK11,sK13)
    & '$ki_exists_in_world_$i'(sK11,sK12)
    & '$ki_accessible'(sK9,sK11)
    & '$ki_exists_in_world_$i'(sK9,sK10)
    & '$ki_accessible'(sK7,sK9)
    & '$ki_exists_in_world_$i'(sK7,sK8)
    & '$ki_accessible'('$ki_local_world',sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14])],[f35,f43,f42,f41,f40,f39,f38,f37,f36]) ).

tff(f45,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    inference(cnf_transformation,[],[f1]) ).

tff(f46,plain,
    ! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
    inference(cnf_transformation,[],[f8]) ).

tff(f58,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X6: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( intersect(X5,X1,X3)
      | ~ '$ki_accessible'(X4,X5)
      | ~ member(sK4(X3,X4,X6),X6,X3)
      | ~ member(sK5(X1,X4,X6),X6,X1)
      | ~ '$ki_exists_in_world_$i'(X4,X6)
      | ~ '$ki_accessible'(X2,X4)
      | ~ '$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(cnf_transformation,[],[f31]) ).

tff(f68,plain,
    ! [X9: '$ki_world'] :
      ( member(X9,sK8,sK10)
      | ~ '$ki_accessible'(sK13,X9) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f69,plain,
    ! [X8: '$ki_world'] :
      ( member(X8,sK8,sK12)
      | ~ '$ki_accessible'(sK13,X8) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f71,plain,
    ~ intersect(sK14,sK10,sK12),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_49,plain,
    '$ki_accessible'(X0_13,X1_13),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_50,plain,
    '$ki_exists_in_world_$i'(X0_13,X0),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_58,plain,
    ( ~ member(sK4(X0,X0_13,X1),X1,X0)
    | ~ member(sK5(X2,X0_13,X1),X1,X2)
    | ~ '$ki_accessible'(X0_13,X2_13)
    | ~ '$ki_accessible'(X1_13,X0_13)
    | ~ '$ki_accessible'(X3_13,X1_13)
    | ~ '$ki_exists_in_world_$i'(X0_13,X1)
    | ~ '$ki_exists_in_world_$i'(X1_13,X0)
    | ~ '$ki_exists_in_world_$i'(X3_13,X2)
    | ~ '$ki_accessible'('$ki_local_world',X3_13)
    | intersect(X2_13,X2,X0) ),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_65,negated_conjecture,
    ~ intersect(sK14,sK10,sK12),
    inference(cnf_transformation,[],[f71]) ).

cnf(c_67,negated_conjecture,
    ( ~ '$ki_accessible'(sK13,X0_13)
    | member(X0_13,sK8,sK12) ),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_68,negated_conjecture,
    ( ~ '$ki_accessible'(sK13,X0_13)
    | member(X0_13,sK8,sK10) ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_121,plain,
    member(X0_13,sK8,sK12),
    inference(backward_subsumption_resolution,[status(thm)],[c_67,c_49]) ).

cnf(c_122,plain,
    member(X0_13,sK8,sK10),
    inference(backward_subsumption_resolution,[status(thm)],[c_68,c_49]) ).

cnf(c_127,plain,
    ( ~ member(sK4(X0,X0_13,X1),X1,X0)
    | ~ member(sK5(X2,X0_13,X1),X1,X2)
    | ~ '$ki_accessible'(X0_13,X1_13)
    | ~ '$ki_accessible'(X2_13,X0_13)
    | ~ '$ki_accessible'(X3_13,X2_13)
    | ~ '$ki_exists_in_world_$i'(X0_13,X1)
    | ~ '$ki_exists_in_world_$i'(X2_13,X0)
    | ~ '$ki_exists_in_world_$i'(X3_13,X2)
    | intersect(X1_13,X2,X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_58,c_49]) ).

cnf(c_128,plain,
    ( ~ member(sK5(X2,X0_13,X1),X1,X2)
    | ~ member(sK4(X0,X0_13,X1),X1,X0)
    | ~ '$ki_accessible'(X2_13,X0_13)
    | ~ '$ki_accessible'(X3_13,X2_13)
    | ~ '$ki_exists_in_world_$i'(X0_13,X1)
    | ~ '$ki_exists_in_world_$i'(X2_13,X0)
    | ~ '$ki_exists_in_world_$i'(X3_13,X2)
    | intersect(X1_13,X2,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_127,c_49,c_127]) ).

cnf(c_129,plain,
    ( ~ member(sK4(X0,X0_13,X1),X1,X0)
    | ~ member(sK5(X2,X0_13,X1),X1,X2)
    | ~ '$ki_accessible'(X1_13,X0_13)
    | ~ '$ki_accessible'(X2_13,X1_13)
    | ~ '$ki_exists_in_world_$i'(X0_13,X1)
    | ~ '$ki_exists_in_world_$i'(X1_13,X0)
    | ~ '$ki_exists_in_world_$i'(X2_13,X2)
    | intersect(X3_13,X2,X0) ),
    inference(renaming,[status(thm)],[c_128]) ).

cnf(c_138,plain,
    ( ~ member(sK4(X0,X0_13,X1),X1,X0)
    | ~ member(sK5(X2,X0_13,X1),X1,X2)
    | ~ '$ki_accessible'(X1_13,X0_13)
    | ~ '$ki_accessible'(X2_13,X1_13)
    | ~ '$ki_exists_in_world_$i'(X1_13,X0)
    | ~ '$ki_exists_in_world_$i'(X2_13,X2)
    | intersect(X3_13,X2,X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_129,c_50]) ).

cnf(c_192,plain,
    ( ~ member(sK4(X0,X0_13,X1),X1,X0)
    | ~ member(sK5(X2,X0_13,X1),X1,X2)
    | intersect(X1_13,X2,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_138,c_50,c_50,c_49,c_49]) ).

cnf(c_235,plain,
    ( ~ member(sK4(sK12,X0_13,X0),X0,sK12)
    | ~ member(sK5(sK10,X0_13,X0),X0,sK10)
    | intersect(sK14,sK10,sK12) ),
    inference(instantiation,[status(thm)],[c_192]) ).

cnf(c_241,plain,
    ( ~ member(sK4(sK12,X0_13,sK8),sK8,sK12)
    | ~ member(sK5(sK10,X0_13,sK8),sK8,sK10)
    | intersect(sK14,sK10,sK12) ),
    inference(instantiation,[status(thm)],[c_235]) ).

cnf(c_242,plain,
    member(sK4(sK12,X0_13,sK8),sK8,sK12),
    inference(instantiation,[status(thm)],[c_121]) ).

cnf(c_260,plain,
    member(sK5(sK10,X0_13,sK8),sK8,sK10),
    inference(instantiation,[status(thm)],[c_122]) ).

cnf(c_261,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_260,c_242,c_241,c_65]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10  % Problem  : LCL950_17 : TPTP v8.2.0. Released v8.2.0.
% 0.08/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n008.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Thu May  2 19:00:12 EDT 2024
% 0.16/0.31  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.78/1.11  % SZS status Started for theBenchmark.p
% 1.78/1.11  % SZS status Theorem for theBenchmark.p
% 1.78/1.11  
% 1.78/1.11  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.78/1.11  
% 1.78/1.11  ------  iProver source info
% 1.78/1.11  
% 1.78/1.11  git: date: 2024-05-02 19:28:25 +0000
% 1.78/1.11  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.78/1.11  git: non_committed_changes: false
% 1.78/1.11  
% 1.78/1.11  ------ Parsing...
% 1.78/1.11  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.78/1.11  
% 1.78/1.11  
% 1.78/1.11  ------ Preprocessing... pe_s  pe:1:0s pe:2:0s pe_e  pe_s  pe_e 
% 1.78/1.11  
% 1.78/1.11  ------ Preprocessing...------  preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.78/1.11   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.78/1.11  ------ Proving...
% 1.78/1.11  ------ Problem Properties 
% 1.78/1.11  
% 1.78/1.11  
% 1.78/1.11  clauses                                 7
% 1.78/1.11  conjectures                             1
% 1.78/1.11  EPR                                     3
% 1.78/1.11  Horn                                    7
% 1.78/1.11  unary                                   3
% 1.78/1.11  binary                                  3
% 1.78/1.11  lits                                    12
% 1.78/1.11  lits eq                                 0
% 1.78/1.11  fd_pure                                 0
% 1.78/1.11  fd_pseudo                               0
% 1.78/1.11  fd_cond                                 0
% 1.78/1.11  fd_pseudo_cond                          0
% 1.78/1.11  AC symbols                              0
% 1.78/1.11  
% 1.78/1.11  ------ Schedule dynamic 5 is on 
% 1.78/1.11  
% 1.78/1.11  ------ no equalities: superposition off 
% 1.78/1.11  
% 1.78/1.11  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.78/1.11  
% 1.78/1.11  
% 1.78/1.11  ------ 
% 1.78/1.11  Current options:
% 1.78/1.11  ------ 
% 1.78/1.11  
% 1.78/1.11  
% 1.78/1.11  
% 1.78/1.11  
% 1.78/1.11  ------ Proving...
% 1.78/1.11  
% 1.78/1.11  
% 1.78/1.11  % SZS status Theorem for theBenchmark.p
% 1.78/1.11  
% 1.78/1.11  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.78/1.11  
% 1.78/1.11  
%------------------------------------------------------------------------------