TSTP Solution File: SEU341+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU341+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n025.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 : Wed Aug 31 18:29:02 EDT 2022

% Result   : Theorem 0.19s 0.53s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  102 (  18 unt;   0 def)
%            Number of atoms       :  342 (  12 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  395 ( 155   ~; 133   |;  67   &)
%                                         (  17 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   24 (  22 usr;  15 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  106 (  91   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f607,plain,
    $false,
    inference(avatar_sat_refutation,[],[f203,f374,f383,f406,f420,f422,f424,f469,f471,f508,f510,f551,f579,f584,f601]) ).

fof(f601,plain,
    ~ spl9_33,
    inference(avatar_contradiction_clause,[],[f599]) ).

fof(f599,plain,
    ( $false
    | ~ spl9_33 ),
    inference(resolution,[],[f577,f132]) ).

fof(f132,plain,
    ~ point_neighbourhood(sK1,sK0,sK2),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ( ~ empty_carrier(sK0)
    & topological_space(sK0)
    & element(sK1,powerset(the_carrier(sK0)))
    & open_subset(sK1,sK0)
    & ~ point_neighbourhood(sK1,sK0,sK2)
    & element(sK2,the_carrier(sK0))
    & in(sK2,sK1)
    & top_str(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f99,f108,f107,f106]) ).

fof(f106,plain,
    ( ? [X0] :
        ( ~ empty_carrier(X0)
        & topological_space(X0)
        & ? [X1] :
            ( element(X1,powerset(the_carrier(X0)))
            & ? [X2] :
                ( open_subset(X1,X0)
                & ~ point_neighbourhood(X1,X0,X2)
                & element(X2,the_carrier(X0))
                & in(X2,X1) ) )
        & top_str(X0) )
   => ( ~ empty_carrier(sK0)
      & topological_space(sK0)
      & ? [X1] :
          ( element(X1,powerset(the_carrier(sK0)))
          & ? [X2] :
              ( open_subset(X1,sK0)
              & ~ point_neighbourhood(X1,sK0,X2)
              & element(X2,the_carrier(sK0))
              & in(X2,X1) ) )
      & top_str(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ( ? [X1] :
        ( element(X1,powerset(the_carrier(sK0)))
        & ? [X2] :
            ( open_subset(X1,sK0)
            & ~ point_neighbourhood(X1,sK0,X2)
            & element(X2,the_carrier(sK0))
            & in(X2,X1) ) )
   => ( element(sK1,powerset(the_carrier(sK0)))
      & ? [X2] :
          ( open_subset(sK1,sK0)
          & ~ point_neighbourhood(sK1,sK0,X2)
          & element(X2,the_carrier(sK0))
          & in(X2,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ( ? [X2] :
        ( open_subset(sK1,sK0)
        & ~ point_neighbourhood(sK1,sK0,X2)
        & element(X2,the_carrier(sK0))
        & in(X2,sK1) )
   => ( open_subset(sK1,sK0)
      & ~ point_neighbourhood(sK1,sK0,sK2)
      & element(sK2,the_carrier(sK0))
      & in(sK2,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ~ empty_carrier(X0)
      & topological_space(X0)
      & ? [X1] :
          ( element(X1,powerset(the_carrier(X0)))
          & ? [X2] :
              ( open_subset(X1,X0)
              & ~ point_neighbourhood(X1,X0,X2)
              & element(X2,the_carrier(X0))
              & in(X2,X1) ) )
      & top_str(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ point_neighbourhood(X1,X0,X2)
              & open_subset(X1,X0)
              & in(X2,X1)
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & topological_space(X0)
      & top_str(X0)
      & ~ empty_carrier(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,negated_conjecture,
    ~ ! [X0] :
        ( ( topological_space(X0)
          & top_str(X0)
          & ~ empty_carrier(X0) )
       => ! [X1] :
            ( element(X1,powerset(the_carrier(X0)))
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => ( ( open_subset(X1,X0)
                    & in(X2,X1) )
                 => point_neighbourhood(X1,X0,X2) ) ) ) ),
    inference(negated_conjecture,[],[f41]) ).

fof(f41,conjecture,
    ! [X0] :
      ( ( topological_space(X0)
        & top_str(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( ( open_subset(X1,X0)
                  & in(X2,X1) )
               => point_neighbourhood(X1,X0,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_connsp_2) ).

fof(f577,plain,
    ( point_neighbourhood(sK1,sK0,sK2)
    | ~ spl9_33 ),
    inference(avatar_component_clause,[],[f575]) ).

fof(f575,plain,
    ( spl9_33
  <=> point_neighbourhood(sK1,sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_33])]) ).

fof(f584,plain,
    ~ spl9_17,
    inference(avatar_contradiction_clause,[],[f581]) ).

fof(f581,plain,
    ( $false
    | ~ spl9_17 ),
    inference(resolution,[],[f373,f211]) ).

fof(f211,plain,
    ~ empty(sK1),
    inference(resolution,[],[f146,f130]) ).

fof(f130,plain,
    in(sK2,sK1),
    inference(cnf_transformation,[],[f109]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ~ empty(X0)
      | ~ in(X1,X0) ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ! [X1,X0] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X1,X0] :
      ~ ( in(X0,X1)
        & empty(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f373,plain,
    ( empty(sK1)
    | ~ spl9_17 ),
    inference(avatar_component_clause,[],[f371]) ).

fof(f371,plain,
    ( spl9_17
  <=> empty(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).

fof(f579,plain,
    ( ~ spl9_16
    | spl9_33
    | ~ spl9_18
    | ~ spl9_25
    | ~ spl9_27 ),
    inference(avatar_split_clause,[],[f561,f506,f466,f376,f575,f367]) ).

fof(f367,plain,
    ( spl9_16
  <=> in(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).

fof(f376,plain,
    ( spl9_18
  <=> in(sK2,the_carrier(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).

fof(f466,plain,
    ( spl9_25
  <=> sK1 = interior(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).

fof(f506,plain,
    ( spl9_27
  <=> ! [X10] :
        ( ~ in(X10,interior(sK0,sK1))
        | ~ element(X10,the_carrier(sK0))
        | point_neighbourhood(sK1,sK0,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).

fof(f561,plain,
    ( point_neighbourhood(sK1,sK0,sK2)
    | ~ in(sK2,sK1)
    | ~ spl9_18
    | ~ spl9_25
    | ~ spl9_27 ),
    inference(resolution,[],[f557,f553]) ).

fof(f553,plain,
    ( element(sK2,the_carrier(sK0))
    | ~ spl9_18 ),
    inference(resolution,[],[f378,f188]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | element(X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

fof(f378,plain,
    ( in(sK2,the_carrier(sK0))
    | ~ spl9_18 ),
    inference(avatar_component_clause,[],[f376]) ).

fof(f557,plain,
    ( ! [X10] :
        ( ~ element(X10,the_carrier(sK0))
        | point_neighbourhood(sK1,sK0,X10)
        | ~ in(X10,sK1) )
    | ~ spl9_25
    | ~ spl9_27 ),
    inference(forward_demodulation,[],[f507,f468]) ).

fof(f468,plain,
    ( sK1 = interior(sK0,sK1)
    | ~ spl9_25 ),
    inference(avatar_component_clause,[],[f466]) ).

fof(f507,plain,
    ( ! [X10] :
        ( point_neighbourhood(sK1,sK0,X10)
        | ~ element(X10,the_carrier(sK0))
        | ~ in(X10,interior(sK0,sK1)) )
    | ~ spl9_27 ),
    inference(avatar_component_clause,[],[f506]) ).

fof(f551,plain,
    ~ spl9_21,
    inference(avatar_contradiction_clause,[],[f550]) ).

fof(f550,plain,
    ( $false
    | ~ spl9_21 ),
    inference(resolution,[],[f405,f130]) ).

fof(f405,plain,
    ( ! [X3] : ~ in(X3,sK1)
    | ~ spl9_21 ),
    inference(avatar_component_clause,[],[f404]) ).

fof(f404,plain,
    ( spl9_21
  <=> ! [X3] : ~ in(X3,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).

fof(f510,plain,
    ~ spl9_26,
    inference(avatar_contradiction_clause,[],[f509]) ).

fof(f509,plain,
    ( $false
    | ~ spl9_26 ),
    inference(resolution,[],[f504,f136]) ).

fof(f136,plain,
    ~ empty_carrier(sK0),
    inference(cnf_transformation,[],[f109]) ).

fof(f504,plain,
    ( empty_carrier(sK0)
    | ~ spl9_26 ),
    inference(avatar_component_clause,[],[f502]) ).

fof(f502,plain,
    ( spl9_26
  <=> empty_carrier(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).

fof(f508,plain,
    ( spl9_26
    | ~ spl9_23
    | ~ spl9_22
    | spl9_27 ),
    inference(avatar_split_clause,[],[f495,f506,f413,f417,f502]) ).

fof(f417,plain,
    ( spl9_23
  <=> topological_space(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).

fof(f413,plain,
    ( spl9_22
  <=> top_str(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).

fof(f495,plain,
    ! [X10] :
      ( ~ in(X10,interior(sK0,sK1))
      | point_neighbourhood(sK1,sK0,X10)
      | ~ top_str(sK0)
      | ~ topological_space(sK0)
      | ~ element(X10,the_carrier(sK0))
      | empty_carrier(sK0) ),
    inference(resolution,[],[f191,f134]) ).

fof(f134,plain,
    element(sK1,powerset(the_carrier(sK0))),
    inference(cnf_transformation,[],[f109]) ).

fof(f191,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | point_neighbourhood(X2,X0,X1)
      | ~ in(X1,interior(X0,X2))
      | ~ element(X1,the_carrier(X0))
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( ~ topological_space(X0)
      | empty_carrier(X0)
      | ! [X1] :
          ( ! [X2] :
              ( ~ element(X2,powerset(the_carrier(X0)))
              | ( ( in(X1,interior(X0,X2))
                  | ~ point_neighbourhood(X2,X0,X1) )
                & ( point_neighbourhood(X2,X0,X1)
                  | ~ in(X1,interior(X0,X2)) ) ) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ top_str(X0) ),
    inference(nnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0] :
      ( ~ topological_space(X0)
      | empty_carrier(X0)
      | ! [X1] :
          ( ! [X2] :
              ( ~ element(X2,powerset(the_carrier(X0)))
              | ( in(X1,interior(X0,X2))
              <=> point_neighbourhood(X2,X0,X1) ) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ top_str(X0) ),
    inference(flattening,[],[f96]) ).

fof(f96,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ~ element(X2,powerset(the_carrier(X0)))
              | ( in(X1,interior(X0,X2))
              <=> point_neighbourhood(X2,X0,X1) ) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ topological_space(X0)
      | empty_carrier(X0)
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0] :
      ( ( topological_space(X0)
        & ~ empty_carrier(X0)
        & top_str(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,powerset(the_carrier(X0)))
             => ( in(X1,interior(X0,X2))
              <=> point_neighbourhood(X2,X0,X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_connsp_2) ).

fof(f471,plain,
    spl9_24,
    inference(avatar_contradiction_clause,[],[f470]) ).

fof(f470,plain,
    ( $false
    | spl9_24 ),
    inference(resolution,[],[f464,f133]) ).

fof(f133,plain,
    open_subset(sK1,sK0),
    inference(cnf_transformation,[],[f109]) ).

fof(f464,plain,
    ( ~ open_subset(sK1,sK0)
    | spl9_24 ),
    inference(avatar_component_clause,[],[f462]) ).

fof(f462,plain,
    ( spl9_24
  <=> open_subset(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).

fof(f469,plain,
    ( ~ spl9_24
    | ~ spl9_22
    | spl9_25
    | ~ spl9_1 ),
    inference(avatar_split_clause,[],[f456,f198,f466,f413,f462]) ).

fof(f198,plain,
    ( spl9_1
  <=> ! [X1,X3] :
        ( ~ open_subset(X3,X1)
        | ~ element(X3,powerset(the_carrier(X1)))
        | interior(X1,X3) = X3
        | ~ top_str(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

fof(f456,plain,
    ( sK1 = interior(sK0,sK1)
    | ~ top_str(sK0)
    | ~ open_subset(sK1,sK0)
    | ~ spl9_1 ),
    inference(resolution,[],[f199,f134]) ).

fof(f199,plain,
    ( ! [X3,X1] :
        ( ~ element(X3,powerset(the_carrier(X1)))
        | ~ open_subset(X3,X1)
        | interior(X1,X3) = X3
        | ~ top_str(X1) )
    | ~ spl9_1 ),
    inference(avatar_component_clause,[],[f198]) ).

fof(f424,plain,
    spl9_23,
    inference(avatar_contradiction_clause,[],[f423]) ).

fof(f423,plain,
    ( $false
    | spl9_23 ),
    inference(resolution,[],[f419,f135]) ).

fof(f135,plain,
    topological_space(sK0),
    inference(cnf_transformation,[],[f109]) ).

fof(f419,plain,
    ( ~ topological_space(sK0)
    | spl9_23 ),
    inference(avatar_component_clause,[],[f417]) ).

fof(f422,plain,
    spl9_22,
    inference(avatar_contradiction_clause,[],[f421]) ).

fof(f421,plain,
    ( $false
    | spl9_22 ),
    inference(resolution,[],[f415,f129]) ).

fof(f129,plain,
    top_str(sK0),
    inference(cnf_transformation,[],[f109]) ).

fof(f415,plain,
    ( ~ top_str(sK0)
    | spl9_22 ),
    inference(avatar_component_clause,[],[f413]) ).

fof(f420,plain,
    ( ~ spl9_22
    | ~ spl9_23
    | ~ spl9_2 ),
    inference(avatar_split_clause,[],[f408,f201,f417,f413]) ).

fof(f201,plain,
    ( spl9_2
  <=> ! [X2,X0] :
        ( ~ top_str(X0)
        | ~ topological_space(X0)
        | ~ element(X2,powerset(the_carrier(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

fof(f408,plain,
    ( ~ topological_space(sK0)
    | ~ top_str(sK0)
    | ~ spl9_2 ),
    inference(resolution,[],[f202,f134]) ).

fof(f202,plain,
    ( ! [X2,X0] :
        ( ~ element(X2,powerset(the_carrier(X0)))
        | ~ top_str(X0)
        | ~ topological_space(X0) )
    | ~ spl9_2 ),
    inference(avatar_component_clause,[],[f201]) ).

fof(f406,plain,
    ( ~ spl9_19
    | spl9_21 ),
    inference(avatar_split_clause,[],[f399,f404,f380]) ).

fof(f380,plain,
    ( spl9_19
  <=> empty(the_carrier(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).

fof(f399,plain,
    ! [X3] :
      ( ~ in(X3,sK1)
      | ~ empty(the_carrier(sK0)) ),
    inference(resolution,[],[f148,f134]) ).

fof(f148,plain,
    ! [X2,X0,X1] :
      ( ~ element(X1,powerset(X2))
      | ~ empty(X2)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0,X1,X2] :
      ( ~ element(X1,powerset(X2))
      | ~ empty(X2)
      | ~ in(X0,X1) ),
    inference(rectify,[],[f104]) ).

fof(f104,plain,
    ! [X0,X2,X1] :
      ( ~ element(X2,powerset(X1))
      | ~ empty(X1)
      | ~ in(X0,X2) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X2,X1,X0] :
      ~ ( element(X2,powerset(X1))
        & in(X0,X2)
        & empty(X1) ),
    inference(rectify,[],[f43]) ).

fof(f43,axiom,
    ! [X0,X2,X1] :
      ~ ( in(X0,X1)
        & element(X1,powerset(X2))
        & empty(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(f383,plain,
    ( spl9_18
    | spl9_19 ),
    inference(avatar_split_clause,[],[f352,f380,f376]) ).

fof(f352,plain,
    ( empty(the_carrier(sK0))
    | in(sK2,the_carrier(sK0)) ),
    inference(resolution,[],[f187,f131]) ).

fof(f131,plain,
    element(sK2,the_carrier(sK0)),
    inference(cnf_transformation,[],[f109]) ).

fof(f187,plain,
    ! [X0,X1] :
      ( ~ element(X1,X0)
      | in(X1,X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( empty(X0)
      | ~ element(X1,X0)
      | in(X1,X0) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X1,X0] :
      ( in(X1,X0)
      | empty(X0)
      | ~ element(X1,X0) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X1,X0] :
      ( element(X1,X0)
     => ( in(X1,X0)
        | empty(X0) ) ),
    inference(rectify,[],[f37]) ).

fof(f37,axiom,
    ! [X1,X0] :
      ( element(X0,X1)
     => ( empty(X1)
        | in(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f374,plain,
    ( spl9_16
    | spl9_17 ),
    inference(avatar_split_clause,[],[f353,f371,f367]) ).

fof(f353,plain,
    ( empty(sK1)
    | in(sK2,sK1) ),
    inference(resolution,[],[f187,f213]) ).

fof(f213,plain,
    element(sK2,sK1),
    inference(resolution,[],[f188,f130]) ).

fof(f203,plain,
    ( spl9_1
    | spl9_2 ),
    inference(avatar_split_clause,[],[f190,f201,f198]) ).

fof(f190,plain,
    ! [X2,X3,X0,X1] :
      ( ~ top_str(X0)
      | ~ element(X2,powerset(the_carrier(X0)))
      | ~ open_subset(X3,X1)
      | ~ top_str(X1)
      | interior(X1,X3) = X3
      | ~ topological_space(X0)
      | ~ element(X3,powerset(the_carrier(X1))) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ~ top_str(X0)
      | ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ~ element(X3,powerset(the_carrier(X1)))
                  | ( ( interior(X1,X3) = X3
                      | ~ open_subset(X3,X1) )
                    & ( interior(X0,X2) != X2
                      | open_subset(X2,X0) ) ) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ top_str(X1) )
      | ~ topological_space(X0) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ~ element(X3,powerset(the_carrier(X1)))
                  | ( ( interior(X1,X3) = X3
                      | ~ open_subset(X3,X1) )
                    & ( interior(X0,X2) != X2
                      | open_subset(X2,X0) ) ) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ top_str(X1) )
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,axiom,
    ! [X0] :
      ( ( top_str(X0)
        & topological_space(X0) )
     => ! [X1] :
          ( top_str(X1)
         => ! [X2] :
              ( element(X2,powerset(the_carrier(X0)))
             => ! [X3] :
                  ( element(X3,powerset(the_carrier(X1)))
                 => ( ( interior(X0,X2) = X2
                     => open_subset(X2,X0) )
                    & ( open_subset(X3,X1)
                     => interior(X1,X3) = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_tops_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SEU341+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 15:24:30 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (20195)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50  % (20179)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (20185)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.51  % (20187)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51  % (20187)Instruction limit reached!
% 0.19/0.51  % (20187)------------------------------
% 0.19/0.51  % (20187)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (20187)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (20187)Termination reason: Unknown
% 0.19/0.51  % (20187)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (20187)Memory used [KB]: 1535
% 0.19/0.51  % (20187)Time elapsed: 0.003 s
% 0.19/0.51  % (20187)Instructions burned: 3 (million)
% 0.19/0.51  % (20187)------------------------------
% 0.19/0.51  % (20187)------------------------------
% 0.19/0.52  % (20185)Instruction limit reached!
% 0.19/0.52  % (20185)------------------------------
% 0.19/0.52  % (20185)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (20201)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.19/0.53  % (20201)Instruction limit reached!
% 0.19/0.53  % (20201)------------------------------
% 0.19/0.53  % (20201)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53  % (20201)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (20201)Termination reason: Unknown
% 0.19/0.53  % (20201)Termination phase: Saturation
% 0.19/0.53  
% 0.19/0.53  % (20201)Memory used [KB]: 6140
% 0.19/0.53  % (20201)Time elapsed: 0.110 s
% 0.19/0.53  % (20201)Instructions burned: 8 (million)
% 0.19/0.53  % (20201)------------------------------
% 0.19/0.53  % (20201)------------------------------
% 0.19/0.53  % (20185)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53  % (20185)Termination reason: Unknown
% 0.19/0.53  % (20185)Termination phase: Saturation
% 0.19/0.53  
% 0.19/0.53  % (20185)Memory used [KB]: 1791
% 0.19/0.53  % (20185)Time elapsed: 0.116 s
% 0.19/0.53  % (20185)Instructions burned: 17 (million)
% 0.19/0.53  % (20185)------------------------------
% 0.19/0.53  % (20185)------------------------------
% 0.19/0.53  % (20174)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.53  % (20195)First to succeed.
% 0.19/0.53  % (20195)Refutation found. Thanks to Tanya!
% 0.19/0.53  % SZS status Theorem for theBenchmark
% 0.19/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.54  % (20195)------------------------------
% 0.19/0.54  % (20195)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54  % (20195)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54  % (20195)Termination reason: Refutation
% 0.19/0.54  
% 0.19/0.54  % (20195)Memory used [KB]: 6268
% 0.19/0.54  % (20195)Time elapsed: 0.119 s
% 0.19/0.54  % (20195)Instructions burned: 9 (million)
% 0.19/0.54  % (20195)------------------------------
% 0.19/0.54  % (20195)------------------------------
% 0.19/0.54  % (20172)Success in time 0.18 s
%------------------------------------------------------------------------------