TSTP Solution File: LCL953_8 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : LCL953_8 : 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 : n022.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 15:38:44 EDT 2023

% Result   : Theorem 0.21s 0.53s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   83 (  10 unt;  18 typ;   0 def)
%            Number of atoms       :  509 (   0 equ)
%            Maximal formula atoms :   20 (   7 avg)
%            Number of connectives :  513 ( 201   ~; 160   |;  94   &)
%                                         (   5 <=>;  53  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :  132 ( 132 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   27 (  12   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  13 usr;   8 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :  199 (; 134   !;  65   ?; 165   :)

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

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

tff(func_def_2,type,
    sK0: '$ki_world' ).

tff(func_def_4,type,
    sK2: '$ki_world' ).

tff(func_def_6,type,
    sK4: '$ki_world' ).

tff(func_def_7,type,
    sK5: '$ki_world' > '$ki_world' ).

tff(func_def_8,type,
    sK6: '$ki_world' ).

tff(func_def_9,type,
    sK7: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_10,type,
    sK8: '$ki_world' > $i ).

tff(func_def_11,type,
    sK9: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_14,type,
    sK12: '$ki_world' > '$ki_world' ).

tff(func_def_15,type,
    sK13: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_16,type,
    sK14: ( $i * $i * '$ki_world' ) > '$ki_world' ).

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

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

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

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

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

tff(f381,plain,
    $false,
    inference(avatar_sat_refutation,[],[f82,f86,f368,f373,f377,f380]) ).

tff(f380,plain,
    ( spl15_2
    | ~ spl15_51 ),
    inference(avatar_split_clause,[],[f379,f366,f80]) ).

tff(f80,plain,
    ( spl15_2
  <=> ! [X0: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X0,sK1)
        | ~ '$ki_accessible'(X0,sK2)
        | ~ '$ki_accessible'('$ki_local_world',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).

tff(f366,plain,
    ( spl15_51
  <=> ! [X0: '$ki_world',X1: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X0,sK1)
        | ~ '$ki_accessible'(X0,X1)
        | ~ '$ki_accessible'('$ki_local_world',X0)
        | ~ '$ki_accessible'(X1,sK4)
        | ~ '$ki_exists_in_world_$i'(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_51])]) ).

tff(f379,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'(X0,sK2)
        | ~ '$ki_accessible'('$ki_local_world',X0)
        | ~ '$ki_exists_in_world_$i'(X0,sK1) )
    | ~ spl15_51 ),
    inference(subsumption_resolution,[],[f378,f52]) ).

tff(f52,plain,
    '$ki_accessible'(sK2,sK4),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,plain,
    ( '$ki_exists_in_world_$i'(sK2,sK3)
    & ! [X5: '$ki_world'] :
        ( ~ '$ki_accessible'(sK4,X5)
        | ( ~ in(sK5(X5),sK1,sK3)
          & '$ki_accessible'(X5,sK5(X5)) ) )
    & ~ disjoint(sK6,singleton(sK1),sK3)
    & '$ki_accessible'(sK4,sK6)
    & '$ki_accessible'(sK2,sK4)
    & '$ki_accessible'(sK0,sK2)
    & '$ki_exists_in_world_$i'(sK0,sK1)
    & '$ki_accessible'('$ki_local_world',sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f21,f32,f31,f30,f29,f28,f27,f26]) ).

tff(f26,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1] :
            ( ? [X2: '$ki_world'] :
                ( ? [X3] :
                    ( '$ki_exists_in_world_$i'(X2,X3)
                    & ? [X4: '$ki_world'] :
                        ( ! [X5: '$ki_world'] :
                            ( ~ '$ki_accessible'(X4,X5)
                            | ? [X6: '$ki_world'] :
                                ( ~ in(X6,X1,X3)
                                & '$ki_accessible'(X5,X6) ) )
                        & ? [X7: '$ki_world'] :
                            ( ~ disjoint(X7,singleton(X1),X3)
                            & '$ki_accessible'(X4,X7) )
                        & '$ki_accessible'(X2,X4) ) )
                & '$ki_accessible'(X0,X2) )
            & '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ? [X3] :
                  ( '$ki_exists_in_world_$i'(X2,X3)
                  & ? [X4: '$ki_world'] :
                      ( ! [X5: '$ki_world'] :
                          ( ~ '$ki_accessible'(X4,X5)
                          | ? [X6: '$ki_world'] :
                              ( ~ in(X6,X1,X3)
                              & '$ki_accessible'(X5,X6) ) )
                      & ? [X7: '$ki_world'] :
                          ( ~ disjoint(X7,singleton(X1),X3)
                          & '$ki_accessible'(X4,X7) )
                      & '$ki_accessible'(X2,X4) ) )
              & '$ki_accessible'(sK0,X2) )
          & '$ki_exists_in_world_$i'(sK0,X1) )
      & '$ki_accessible'('$ki_local_world',sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f27,plain,
    ( ? [X1] :
        ( ? [X2: '$ki_world'] :
            ( ? [X3] :
                ( '$ki_exists_in_world_$i'(X2,X3)
                & ? [X4: '$ki_world'] :
                    ( ! [X5: '$ki_world'] :
                        ( ~ '$ki_accessible'(X4,X5)
                        | ? [X6: '$ki_world'] :
                            ( ~ in(X6,X1,X3)
                            & '$ki_accessible'(X5,X6) ) )
                    & ? [X7: '$ki_world'] :
                        ( ~ disjoint(X7,singleton(X1),X3)
                        & '$ki_accessible'(X4,X7) )
                    & '$ki_accessible'(X2,X4) ) )
            & '$ki_accessible'(sK0,X2) )
        & '$ki_exists_in_world_$i'(sK0,X1) )
   => ( ? [X2: '$ki_world'] :
          ( ? [X3] :
              ( '$ki_exists_in_world_$i'(X2,X3)
              & ? [X4: '$ki_world'] :
                  ( ! [X5: '$ki_world'] :
                      ( ~ '$ki_accessible'(X4,X5)
                      | ? [X6: '$ki_world'] :
                          ( ~ in(X6,sK1,X3)
                          & '$ki_accessible'(X5,X6) ) )
                  & ? [X7: '$ki_world'] :
                      ( ~ disjoint(X7,singleton(sK1),X3)
                      & '$ki_accessible'(X4,X7) )
                  & '$ki_accessible'(X2,X4) ) )
          & '$ki_accessible'(sK0,X2) )
      & '$ki_exists_in_world_$i'(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f28,plain,
    ( ? [X2: '$ki_world'] :
        ( ? [X3] :
            ( '$ki_exists_in_world_$i'(X2,X3)
            & ? [X4: '$ki_world'] :
                ( ! [X5: '$ki_world'] :
                    ( ~ '$ki_accessible'(X4,X5)
                    | ? [X6: '$ki_world'] :
                        ( ~ in(X6,sK1,X3)
                        & '$ki_accessible'(X5,X6) ) )
                & ? [X7: '$ki_world'] :
                    ( ~ disjoint(X7,singleton(sK1),X3)
                    & '$ki_accessible'(X4,X7) )
                & '$ki_accessible'(X2,X4) ) )
        & '$ki_accessible'(sK0,X2) )
   => ( ? [X3] :
          ( '$ki_exists_in_world_$i'(sK2,X3)
          & ? [X4: '$ki_world'] :
              ( ! [X5: '$ki_world'] :
                  ( ~ '$ki_accessible'(X4,X5)
                  | ? [X6: '$ki_world'] :
                      ( ~ in(X6,sK1,X3)
                      & '$ki_accessible'(X5,X6) ) )
              & ? [X7: '$ki_world'] :
                  ( ~ disjoint(X7,singleton(sK1),X3)
                  & '$ki_accessible'(X4,X7) )
              & '$ki_accessible'(sK2,X4) ) )
      & '$ki_accessible'(sK0,sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f29,plain,
    ( ? [X3] :
        ( '$ki_exists_in_world_$i'(sK2,X3)
        & ? [X4: '$ki_world'] :
            ( ! [X5: '$ki_world'] :
                ( ~ '$ki_accessible'(X4,X5)
                | ? [X6: '$ki_world'] :
                    ( ~ in(X6,sK1,X3)
                    & '$ki_accessible'(X5,X6) ) )
            & ? [X7: '$ki_world'] :
                ( ~ disjoint(X7,singleton(sK1),X3)
                & '$ki_accessible'(X4,X7) )
            & '$ki_accessible'(sK2,X4) ) )
   => ( '$ki_exists_in_world_$i'(sK2,sK3)
      & ? [X4: '$ki_world'] :
          ( ! [X5: '$ki_world'] :
              ( ~ '$ki_accessible'(X4,X5)
              | ? [X6: '$ki_world'] :
                  ( ~ in(X6,sK1,sK3)
                  & '$ki_accessible'(X5,X6) ) )
          & ? [X7: '$ki_world'] :
              ( ~ disjoint(X7,singleton(sK1),sK3)
              & '$ki_accessible'(X4,X7) )
          & '$ki_accessible'(sK2,X4) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ( ? [X4: '$ki_world'] :
        ( ! [X5: '$ki_world'] :
            ( ~ '$ki_accessible'(X4,X5)
            | ? [X6: '$ki_world'] :
                ( ~ in(X6,sK1,sK3)
                & '$ki_accessible'(X5,X6) ) )
        & ? [X7: '$ki_world'] :
            ( ~ disjoint(X7,singleton(sK1),sK3)
            & '$ki_accessible'(X4,X7) )
        & '$ki_accessible'(sK2,X4) )
   => ( ! [X5: '$ki_world'] :
          ( ~ '$ki_accessible'(sK4,X5)
          | ? [X6: '$ki_world'] :
              ( ~ in(X6,sK1,sK3)
              & '$ki_accessible'(X5,X6) ) )
      & ? [X7: '$ki_world'] :
          ( ~ disjoint(X7,singleton(sK1),sK3)
          & '$ki_accessible'(sK4,X7) )
      & '$ki_accessible'(sK2,sK4) ) ),
    introduced(choice_axiom,[]) ).

tff(f31,plain,
    ! [X5: '$ki_world'] :
      ( ? [X6: '$ki_world'] :
          ( ~ in(X6,sK1,sK3)
          & '$ki_accessible'(X5,X6) )
     => ( ~ in(sK5(X5),sK1,sK3)
        & '$ki_accessible'(X5,sK5(X5)) ) ),
    introduced(choice_axiom,[]) ).

tff(f32,plain,
    ( ? [X7: '$ki_world'] :
        ( ~ disjoint(X7,singleton(sK1),sK3)
        & '$ki_accessible'(sK4,X7) )
   => ( ~ disjoint(sK6,singleton(sK1),sK3)
      & '$ki_accessible'(sK4,sK6) ) ),
    introduced(choice_axiom,[]) ).

tff(f21,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ? [X3] :
                  ( '$ki_exists_in_world_$i'(X2,X3)
                  & ? [X4: '$ki_world'] :
                      ( ! [X5: '$ki_world'] :
                          ( ~ '$ki_accessible'(X4,X5)
                          | ? [X6: '$ki_world'] :
                              ( ~ in(X6,X1,X3)
                              & '$ki_accessible'(X5,X6) ) )
                      & ? [X7: '$ki_world'] :
                          ( ~ disjoint(X7,singleton(X1),X3)
                          & '$ki_accessible'(X4,X7) )
                      & '$ki_accessible'(X2,X4) ) )
              & '$ki_accessible'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f20]) ).

tff(f20,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ? [X3] :
                  ( ? [X4: '$ki_world'] :
                      ( ? [X7: '$ki_world'] :
                          ( ~ disjoint(X7,singleton(X1),X3)
                          & '$ki_accessible'(X4,X7) )
                      & ! [X5: '$ki_world'] :
                          ( ~ '$ki_accessible'(X4,X5)
                          | ? [X6: '$ki_world'] :
                              ( ~ in(X6,X1,X3)
                              & '$ki_accessible'(X5,X6) ) )
                      & '$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(ennf_transformation,[],[f10]) ).

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'] :
                        ( '$ki_accessible'(X2,X4)
                       => ( ! [X5: '$ki_world'] :
                              ( '$ki_accessible'(X4,X5)
                             => ~ ! [X6: '$ki_world'] :
                                    ( '$ki_accessible'(X5,X6)
                                   => in(X6,X1,X3) ) )
                         => ! [X7: '$ki_world'] :
                              ( '$ki_accessible'(X4,X7)
                             => disjoint(X7,singleton(X1),X3) ) ) ) ) ) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X2] :
            ( '$ki_exists_in_world_$i'(X0,X2)
           => ! [X3: '$ki_world'] :
                ( '$ki_accessible'(X0,X3)
               => ! [X4] :
                    ( '$ki_exists_in_world_$i'(X3,X4)
                   => ! [X5: '$ki_world'] :
                        ( '$ki_accessible'(X3,X5)
                       => ( ! [X6: '$ki_world'] :
                              ( '$ki_accessible'(X5,X6)
                             => ~ ! [X7: '$ki_world'] :
                                    ( '$ki_accessible'(X6,X7)
                                   => in(X7,X2,X4) ) )
                         => ! [X6: '$ki_world'] :
                              ( '$ki_accessible'(X5,X6)
                             => disjoint(X6,singleton(X2),X4) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f8]) ).

tff(f8,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X2] :
          ( '$ki_exists_in_world_$i'(X0,X2)
         => ! [X3: '$ki_world'] :
              ( '$ki_accessible'(X0,X3)
             => ! [X4] :
                  ( '$ki_exists_in_world_$i'(X3,X4)
                 => ! [X5: '$ki_world'] :
                      ( '$ki_accessible'(X3,X5)
                     => ( ! [X6: '$ki_world'] :
                            ( '$ki_accessible'(X5,X6)
                           => ~ ! [X7: '$ki_world'] :
                                  ( '$ki_accessible'(X6,X7)
                                 => in(X7,X2,X4) ) )
                       => ! [X6: '$ki_world'] :
                            ( '$ki_accessible'(X5,X6)
                           => disjoint(X6,singleton(X2),X4) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f378,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'(sK2,sK4)
        | ~ '$ki_accessible'(X0,sK2)
        | ~ '$ki_exists_in_world_$i'(X0,sK1)
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    | ~ spl15_51 ),
    inference(resolution,[],[f367,f57]) ).

tff(f57,plain,
    '$ki_exists_in_world_$i'(sK2,sK3),
    inference(cnf_transformation,[],[f33]) ).

tff(f367,plain,
    ( ! [X0: '$ki_world',X1: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X1,sK3)
        | ~ '$ki_exists_in_world_$i'(X0,sK1)
        | ~ '$ki_accessible'(X1,sK4)
        | ~ '$ki_accessible'('$ki_local_world',X0)
        | ~ '$ki_accessible'(X0,X1) )
    | ~ spl15_51 ),
    inference(avatar_component_clause,[],[f366]) ).

tff(f377,plain,
    ~ spl15_50,
    inference(avatar_contradiction_clause,[],[f376]) ).

tff(f376,plain,
    ( $false
    | ~ spl15_50 ),
    inference(subsumption_resolution,[],[f374,f53]) ).

tff(f53,plain,
    '$ki_accessible'(sK4,sK6),
    inference(cnf_transformation,[],[f33]) ).

tff(f374,plain,
    ( ~ '$ki_accessible'(sK4,sK6)
    | ~ spl15_50 ),
    inference(resolution,[],[f364,f54]) ).

tff(f54,plain,
    ~ disjoint(sK6,singleton(sK1),sK3),
    inference(cnf_transformation,[],[f33]) ).

tff(f364,plain,
    ( ! [X2: '$ki_world'] :
        ( disjoint(X2,singleton(sK1),sK3)
        | ~ '$ki_accessible'(sK4,X2) )
    | ~ spl15_50 ),
    inference(avatar_component_clause,[],[f363]) ).

tff(f363,plain,
    ( spl15_50
  <=> ! [X2: '$ki_world'] :
        ( ~ '$ki_accessible'(sK4,X2)
        | disjoint(X2,singleton(sK1),sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_50])]) ).

tff(f373,plain,
    ( ~ spl15_1
    | ~ spl15_49 ),
    inference(avatar_contradiction_clause,[],[f372]) ).

tff(f372,plain,
    ( $false
    | ~ spl15_1
    | ~ spl15_49 ),
    inference(subsumption_resolution,[],[f371,f52]) ).

tff(f371,plain,
    ( ~ '$ki_accessible'(sK2,sK4)
    | ~ spl15_1
    | ~ spl15_49 ),
    inference(subsumption_resolution,[],[f370,f53]) ).

tff(f370,plain,
    ( ~ '$ki_accessible'(sK4,sK6)
    | ~ '$ki_accessible'(sK2,sK4)
    | ~ spl15_1
    | ~ spl15_49 ),
    inference(resolution,[],[f369,f78]) ).

tff(f78,plain,
    ( ! [X1: '$ki_world'] :
        ( '$ki_accessible'(X1,sK7(sK1,sK3,X1))
        | ~ '$ki_accessible'(X1,sK6)
        | ~ '$ki_accessible'(sK2,X1) )
    | ~ spl15_1 ),
    inference(avatar_component_clause,[],[f77]) ).

tff(f77,plain,
    ( spl15_1
  <=> ! [X1: '$ki_world'] :
        ( '$ki_accessible'(X1,sK7(sK1,sK3,X1))
        | ~ '$ki_accessible'(X1,sK6)
        | ~ '$ki_accessible'(sK2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).

tff(f369,plain,
    ( ~ '$ki_accessible'(sK4,sK7(sK1,sK3,sK4))
    | ~ spl15_49 ),
    inference(resolution,[],[f361,f56]) ).

tff(f56,plain,
    ! [X5: '$ki_world'] :
      ( ~ in(sK5(X5),sK1,sK3)
      | ~ '$ki_accessible'(sK4,X5) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f361,plain,
    ( in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3)
    | ~ spl15_49 ),
    inference(avatar_component_clause,[],[f359]) ).

tff(f359,plain,
    ( spl15_49
  <=> in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_49])]) ).

tff(f368,plain,
    ( spl15_49
    | spl15_50
    | spl15_51
    | ~ spl15_1 ),
    inference(avatar_split_clause,[],[f357,f77,f366,f363,f359]) ).

tff(f357,plain,
    ( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X0,sK1)
        | ~ '$ki_accessible'(X1,sK4)
        | ~ '$ki_accessible'(sK4,X2)
        | ~ '$ki_exists_in_world_$i'(X1,sK3)
        | ~ '$ki_accessible'('$ki_local_world',X0)
        | ~ '$ki_accessible'(X0,X1)
        | in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3)
        | disjoint(X2,singleton(sK1),sK3) )
    | ~ spl15_1 ),
    inference(subsumption_resolution,[],[f356,f53]) ).

tff(f356,plain,
    ( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
        ( ~ '$ki_accessible'(sK4,sK6)
        | in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3)
        | ~ '$ki_exists_in_world_$i'(X0,sK1)
        | ~ '$ki_accessible'(sK4,X2)
        | ~ '$ki_exists_in_world_$i'(X1,sK3)
        | ~ '$ki_accessible'(X1,sK4)
        | ~ '$ki_accessible'('$ki_local_world',X0)
        | disjoint(X2,singleton(sK1),sK3)
        | ~ '$ki_accessible'(X0,X1) )
    | ~ spl15_1 ),
    inference(subsumption_resolution,[],[f355,f52]) ).

tff(f355,plain,
    ( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X0,sK1)
        | ~ '$ki_accessible'(X1,sK4)
        | ~ '$ki_accessible'(X0,X1)
        | ~ '$ki_accessible'(sK2,sK4)
        | ~ '$ki_accessible'(sK4,sK6)
        | ~ '$ki_accessible'(sK4,X2)
        | disjoint(X2,singleton(sK1),sK3)
        | in(sK5(sK7(sK1,sK3,sK4)),sK1,sK3)
        | ~ '$ki_accessible'('$ki_local_world',X0)
        | ~ '$ki_exists_in_world_$i'(X1,sK3) )
    | ~ spl15_1 ),
    inference(resolution,[],[f319,f78]) ).

tff(f319,plain,
    ! [X10: '$ki_world',X11: '$ki_world',X8: '$ki_world',X6: '$ki_world',X9: $i,X7: $i] :
      ( ~ '$ki_accessible'(sK4,sK7(X9,X7,X11))
      | ~ '$ki_exists_in_world_$i'(X10,X9)
      | in(sK5(sK7(X9,X7,X11)),X9,X7)
      | ~ '$ki_accessible'(X10,X6)
      | ~ '$ki_accessible'(X6,X11)
      | disjoint(X8,singleton(X9),X7)
      | ~ '$ki_accessible'(X11,X8)
      | ~ '$ki_accessible'('$ki_local_world',X10)
      | ~ '$ki_exists_in_world_$i'(X6,X7) ),
    inference(resolution,[],[f59,f55]) ).

tff(f55,plain,
    ! [X5: '$ki_world'] :
      ( '$ki_accessible'(X5,sK5(X5))
      | ~ '$ki_accessible'(sK4,X5) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f59,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X7: '$ki_world',X4: '$ki_world',X5: '$ki_world'] :
      ( ~ '$ki_accessible'(sK7(X1,X3,X4),X7)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | disjoint(X5,singleton(X1),X3)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | in(X7,X1,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'(X2,X4)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'(X4,X5) ),
    inference(cnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ~ '$ki_exists_in_world_$i'(X0,X1)
          | ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X0,X2)
              | ! [X3] :
                  ( ! [X4: '$ki_world'] :
                      ( ! [X5: '$ki_world'] :
                          ( disjoint(X5,singleton(X1),X3)
                          | ~ '$ki_accessible'(X4,X5) )
                      | ~ '$ki_accessible'(X2,X4)
                      | ( ! [X7: '$ki_world'] :
                            ( ~ '$ki_accessible'(sK7(X1,X3,X4),X7)
                            | in(X7,X1,X3) )
                        & '$ki_accessible'(X4,sK7(X1,X3,X4)) ) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) ) ) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f34,f35]) ).

tff(f35,plain,
    ! [X1,X3,X4: '$ki_world'] :
      ( ? [X6: '$ki_world'] :
          ( ! [X7: '$ki_world'] :
              ( ~ '$ki_accessible'(X6,X7)
              | in(X7,X1,X3) )
          & '$ki_accessible'(X4,X6) )
     => ( ! [X7: '$ki_world'] :
            ( ~ '$ki_accessible'(sK7(X1,X3,X4),X7)
            | in(X7,X1,X3) )
        & '$ki_accessible'(X4,sK7(X1,X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f34,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ~ '$ki_exists_in_world_$i'(X0,X1)
          | ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X0,X2)
              | ! [X3] :
                  ( ! [X4: '$ki_world'] :
                      ( ! [X5: '$ki_world'] :
                          ( disjoint(X5,singleton(X1),X3)
                          | ~ '$ki_accessible'(X4,X5) )
                      | ~ '$ki_accessible'(X2,X4)
                      | ? [X6: '$ki_world'] :
                          ( ! [X7: '$ki_world'] :
                              ( ~ '$ki_accessible'(X6,X7)
                              | in(X7,X1,X3) )
                          & '$ki_accessible'(X4,X6) ) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) ) ) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(rectify,[],[f23]) ).

tff(f23,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ~ '$ki_exists_in_world_$i'(X0,X1)
          | ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X0,X2)
              | ! [X3] :
                  ( ! [X4: '$ki_world'] :
                      ( ! [X7: '$ki_world'] :
                          ( disjoint(X7,singleton(X1),X3)
                          | ~ '$ki_accessible'(X4,X7) )
                      | ~ '$ki_accessible'(X2,X4)
                      | ? [X5: '$ki_world'] :
                          ( ! [X6: '$ki_world'] :
                              ( ~ '$ki_accessible'(X5,X6)
                              | in(X6,X1,X3) )
                          & '$ki_accessible'(X4,X5) ) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) ) ) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f22]) ).

tff(f22,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ! [X4: '$ki_world'] :
                      ( ! [X7: '$ki_world'] :
                          ( disjoint(X7,singleton(X1),X3)
                          | ~ '$ki_accessible'(X4,X7) )
                      | ? [X5: '$ki_world'] :
                          ( ! [X6: '$ki_world'] :
                              ( ~ '$ki_accessible'(X5,X6)
                              | in(X6,X1,X3) )
                          & '$ki_accessible'(X4,X5) )
                      | ~ '$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,[],[f14]) ).

tff(f14,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'] :
                            ( '$ki_accessible'(X4,X5)
                           => ~ ! [X6: '$ki_world'] :
                                  ( '$ki_accessible'(X5,X6)
                                 => in(X6,X1,X3) ) )
                       => ! [X7: '$ki_world'] :
                            ( '$ki_accessible'(X4,X7)
                           => disjoint(X7,singleton(X1),X3) ) ) ) ) ) ) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X2] :
          ( '$ki_exists_in_world_$i'(X0,X2)
         => ! [X3: '$ki_world'] :
              ( '$ki_accessible'(X0,X3)
             => ! [X4] :
                  ( '$ki_exists_in_world_$i'(X3,X4)
                 => ! [X5: '$ki_world'] :
                      ( '$ki_accessible'(X3,X5)
                     => ( ! [X6: '$ki_world'] :
                            ( '$ki_accessible'(X5,X6)
                           => ~ ! [X7: '$ki_world'] :
                                  ( '$ki_accessible'(X6,X7)
                                 => in(X7,X2,X4) ) )
                       => ! [X6: '$ki_world'] :
                            ( '$ki_accessible'(X5,X6)
                           => disjoint(X6,singleton(X2),X4) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).

tff(f86,plain,
    ~ spl15_2,
    inference(avatar_contradiction_clause,[],[f85]) ).

tff(f85,plain,
    ( $false
    | ~ spl15_2 ),
    inference(subsumption_resolution,[],[f84,f49]) ).

tff(f49,plain,
    '$ki_accessible'('$ki_local_world',sK0),
    inference(cnf_transformation,[],[f33]) ).

tff(f84,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK0)
    | ~ spl15_2 ),
    inference(subsumption_resolution,[],[f83,f51]) ).

tff(f51,plain,
    '$ki_accessible'(sK0,sK2),
    inference(cnf_transformation,[],[f33]) ).

tff(f83,plain,
    ( ~ '$ki_accessible'(sK0,sK2)
    | ~ '$ki_accessible'('$ki_local_world',sK0)
    | ~ spl15_2 ),
    inference(resolution,[],[f81,f50]) ).

tff(f50,plain,
    '$ki_exists_in_world_$i'(sK0,sK1),
    inference(cnf_transformation,[],[f33]) ).

tff(f81,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X0,sK1)
        | ~ '$ki_accessible'(X0,sK2)
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    | ~ spl15_2 ),
    inference(avatar_component_clause,[],[f80]) ).

tff(f82,plain,
    ( spl15_1
    | spl15_2 ),
    inference(avatar_split_clause,[],[f75,f80,f77]) ).

tff(f75,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(X0,sK1)
      | '$ki_accessible'(X1,sK7(sK1,sK3,X1))
      | ~ '$ki_accessible'(sK2,X1)
      | ~ '$ki_accessible'(X1,sK6)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_accessible'(X0,sK2) ),
    inference(resolution,[],[f74,f57]) ).

tff(f74,plain,
    ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(X2,sK3)
      | ~ '$ki_exists_in_world_$i'(X1,sK1)
      | ~ '$ki_accessible'(X1,X2)
      | ~ '$ki_accessible'(X2,X0)
      | '$ki_accessible'(X0,sK7(sK1,sK3,X0))
      | ~ '$ki_accessible'(X0,sK6)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(resolution,[],[f58,f54]) ).

tff(f58,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( disjoint(X5,singleton(X1),X3)
      | ~ '$ki_accessible'(X4,X5)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | ~ '$ki_accessible'(X2,X4)
      | '$ki_accessible'(X4,sK7(X1,X3,X4))
      | ~ '$ki_exists_in_world_$i'(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : LCL953_8 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.35  % Computer : n022.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 22 12:00:30 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.50  % (32451)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.50  % (32465)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.21/0.51  % (32444)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51  % (32455)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.51  % (32454)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.51  % (32448)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.51  % (32446)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.21/0.51  % (32471)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.51  % (32462)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.21/0.51  % (32445)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.52  % (32443)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.52  % (32447)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.52  % (32470)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.21/0.52  TRYING [1]
% 0.21/0.52  TRYING [2]
% 0.21/0.52  % (32448)Instruction limit reached!
% 0.21/0.52  % (32448)------------------------------
% 0.21/0.52  % (32448)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (32448)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (32448)Termination reason: Unknown
% 0.21/0.52  % (32448)Termination phase: Saturation
% 0.21/0.52  
% 0.21/0.52  % (32448)Memory used [KB]: 5628
% 0.21/0.52  % (32448)Time elapsed: 0.073 s
% 0.21/0.52  % (32448)Instructions burned: 8 (million)
% 0.21/0.52  % (32448)------------------------------
% 0.21/0.52  % (32448)------------------------------
% 0.21/0.52  % (32462)First to succeed.
% 0.21/0.53  % (32463)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.53  % (32461)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.53  % (32464)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.53  % (32453)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.53  % (32442)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.53  % (32462)Refutation found. Thanks to Tanya!
% 0.21/0.53  % SZS status Theorem for theBenchmark
% 0.21/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53  % (32462)------------------------------
% 0.21/0.53  % (32462)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (32462)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (32462)Termination reason: Refutation
% 0.21/0.53  
% 0.21/0.53  % (32462)Memory used [KB]: 5756
% 0.21/0.53  % (32462)Time elapsed: 0.124 s
% 0.21/0.53  % (32462)Instructions burned: 9 (million)
% 0.21/0.53  % (32462)------------------------------
% 0.21/0.53  % (32462)------------------------------
% 0.21/0.53  % (32438)Success in time 0.175 s
%------------------------------------------------------------------------------