TSTP Solution File: SEU297+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU297+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_sat --cores 0 -t %d %s

% Computer : n028.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 18:33:04 EDT 2022

% Result   : Theorem 0.18s 0.52s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  101 (  11 unt;   0 def)
%            Number of atoms       :  479 (  66 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  583 ( 205   ~; 231   |; 117   &)
%                                         (  14 <=>;  14  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   7 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   7 con; 0-3 aty)
%            Number of variables   :  203 ( 142   !;  61   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f639,plain,
    $false,
    inference(avatar_sat_refutation,[],[f520,f549,f580,f592,f600,f610,f638]) ).

fof(f638,plain,
    ( ~ spl30_15
    | ~ spl30_19
    | ~ spl30_20
    | ~ spl30_21 ),
    inference(avatar_contradiction_clause,[],[f637]) ).

fof(f637,plain,
    ( $false
    | ~ spl30_15
    | ~ spl30_19
    | ~ spl30_20
    | ~ spl30_21 ),
    inference(subsumption_resolution,[],[f636,f558]) ).

fof(f558,plain,
    ( in(sK6(sK23(sK3,sK5)),sK23(sK3,sK5))
    | ~ spl30_15 ),
    inference(factoring,[],[f516]) ).

fof(f516,plain,
    ( ! [X0] :
        ( in(sK6(X0),sK23(sK3,sK5))
        | in(sK6(X0),X0) )
    | ~ spl30_15 ),
    inference(avatar_component_clause,[],[f515]) ).

fof(f515,plain,
    ( spl30_15
  <=> ! [X0] :
        ( in(sK6(X0),sK23(sK3,sK5))
        | in(sK6(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl30_15])]) ).

fof(f636,plain,
    ( ~ in(sK6(sK23(sK3,sK5)),sK23(sK3,sK5))
    | ~ spl30_19
    | ~ spl30_20
    | ~ spl30_21 ),
    inference(subsumption_resolution,[],[f633,f611]) ).

fof(f611,plain,
    ( in(sK6(sK23(sK3,sK5)),sF27)
    | ~ spl30_19
    | ~ spl30_21 ),
    inference(forward_demodulation,[],[f609,f591]) ).

fof(f591,plain,
    ( sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
    | ~ spl30_19 ),
    inference(avatar_component_clause,[],[f589]) ).

fof(f589,plain,
    ( spl30_19
  <=> sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl30_19])]) ).

fof(f609,plain,
    ( in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),sF27)
    | ~ spl30_21 ),
    inference(avatar_component_clause,[],[f607]) ).

fof(f607,plain,
    ( spl30_21
  <=> in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),sF27) ),
    introduced(avatar_definition,[new_symbols(naming,[spl30_21])]) ).

fof(f633,plain,
    ( ~ in(sK6(sK23(sK3,sK5)),sF27)
    | ~ in(sK6(sK23(sK3,sK5)),sK23(sK3,sK5))
    | ~ spl30_20 ),
    inference(resolution,[],[f599,f213]) ).

fof(f213,plain,
    ! [X3] :
      ( ~ in(relation_image(sK3,sK6(X3)),sK5)
      | ~ in(sK6(X3),sF27)
      | ~ in(sK6(X3),X3) ),
    inference(definition_folding,[],[f146,f212,f211]) ).

fof(f211,plain,
    sF26 = relation_dom(sK3),
    introduced(function_definition,[]) ).

fof(f212,plain,
    sF27 = powerset(sF26),
    introduced(function_definition,[]) ).

fof(f146,plain,
    ! [X3] :
      ( ~ in(sK6(X3),X3)
      | ~ in(sK6(X3),powerset(relation_dom(sK3)))
      | ~ in(relation_image(sK3,sK6(X3)),sK5) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ( ! [X3] :
        ( ( ~ in(sK6(X3),X3)
          | ~ in(sK6(X3),powerset(relation_dom(sK3)))
          | ~ in(relation_image(sK3,sK6(X3)),sK5) )
        & ( in(sK6(X3),X3)
          | ( in(sK6(X3),powerset(relation_dom(sK3)))
            & in(relation_image(sK3,sK6(X3)),sK5) ) ) )
    & function(sK3)
    & relation(sK3)
    & element(sK5,powerset(powerset(sK4))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f82,f84,f83]) ).

fof(f83,plain,
    ( ? [X0,X1,X2] :
        ( ! [X3] :
          ? [X4] :
            ( ( ~ in(X4,X3)
              | ~ in(X4,powerset(relation_dom(X0)))
              | ~ in(relation_image(X0,X4),X2) )
            & ( in(X4,X3)
              | ( in(X4,powerset(relation_dom(X0)))
                & in(relation_image(X0,X4),X2) ) ) )
        & function(X0)
        & relation(X0)
        & element(X2,powerset(powerset(X1))) )
   => ( ! [X3] :
        ? [X4] :
          ( ( ~ in(X4,X3)
            | ~ in(X4,powerset(relation_dom(sK3)))
            | ~ in(relation_image(sK3,X4),sK5) )
          & ( in(X4,X3)
            | ( in(X4,powerset(relation_dom(sK3)))
              & in(relation_image(sK3,X4),sK5) ) ) )
      & function(sK3)
      & relation(sK3)
      & element(sK5,powerset(powerset(sK4))) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ! [X3] :
      ( ? [X4] :
          ( ( ~ in(X4,X3)
            | ~ in(X4,powerset(relation_dom(sK3)))
            | ~ in(relation_image(sK3,X4),sK5) )
          & ( in(X4,X3)
            | ( in(X4,powerset(relation_dom(sK3)))
              & in(relation_image(sK3,X4),sK5) ) ) )
     => ( ( ~ in(sK6(X3),X3)
          | ~ in(sK6(X3),powerset(relation_dom(sK3)))
          | ~ in(relation_image(sK3,sK6(X3)),sK5) )
        & ( in(sK6(X3),X3)
          | ( in(sK6(X3),powerset(relation_dom(sK3)))
            & in(relation_image(sK3,sK6(X3)),sK5) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ? [X0,X1,X2] :
      ( ! [X3] :
        ? [X4] :
          ( ( ~ in(X4,X3)
            | ~ in(X4,powerset(relation_dom(X0)))
            | ~ in(relation_image(X0,X4),X2) )
          & ( in(X4,X3)
            | ( in(X4,powerset(relation_dom(X0)))
              & in(relation_image(X0,X4),X2) ) ) )
      & function(X0)
      & relation(X0)
      & element(X2,powerset(powerset(X1))) ),
    inference(flattening,[],[f81]) ).

fof(f81,plain,
    ? [X0,X1,X2] :
      ( ! [X3] :
        ? [X4] :
          ( ( ~ in(X4,X3)
            | ~ in(X4,powerset(relation_dom(X0)))
            | ~ in(relation_image(X0,X4),X2) )
          & ( in(X4,X3)
            | ( in(X4,powerset(relation_dom(X0)))
              & in(relation_image(X0,X4),X2) ) ) )
      & function(X0)
      & relation(X0)
      & element(X2,powerset(powerset(X1))) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f56,plain,
    ? [X0,X1,X2] :
      ( ! [X3] :
        ? [X4] :
          ( ( in(X4,powerset(relation_dom(X0)))
            & in(relation_image(X0,X4),X2) )
        <~> in(X4,X3) )
      & function(X0)
      & relation(X0)
      & element(X2,powerset(powerset(X1))) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ? [X0,X2,X1] :
      ( ! [X3] :
        ? [X4] :
          ( ( in(X4,powerset(relation_dom(X0)))
            & in(relation_image(X0,X4),X2) )
        <~> in(X4,X3) )
      & function(X0)
      & relation(X0)
      & element(X2,powerset(powerset(X1))) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,plain,
    ~ ! [X0,X2,X1] :
        ( ( function(X0)
          & relation(X0)
          & element(X2,powerset(powerset(X1))) )
       => ? [X3] :
          ! [X4] :
            ( in(X4,X3)
          <=> ( in(X4,powerset(relation_dom(X0)))
              & in(relation_image(X0,X4),X2) ) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ! [X2,X0,X1] :
        ( ( relation(X2)
          & element(X1,powerset(powerset(X0)))
          & function(X2) )
       => ? [X3] :
          ! [X4] :
            ( ( in(X4,powerset(relation_dom(X2)))
              & in(relation_image(X2,X4),X1) )
          <=> in(X4,X3) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ! [X2,X0,X1] :
      ( ( relation(X2)
        & element(X1,powerset(powerset(X0)))
        & function(X2) )
     => ? [X3] :
        ! [X4] :
          ( ( in(X4,powerset(relation_dom(X2)))
            & in(relation_image(X2,X4),X1) )
        <=> in(X4,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).

fof(f599,plain,
    ( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
    | ~ spl30_20 ),
    inference(avatar_component_clause,[],[f597]) ).

fof(f597,plain,
    ( spl30_20
  <=> in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl30_20])]) ).

fof(f610,plain,
    ( spl30_21
    | spl30_16
    | spl30_14
    | ~ spl30_15 ),
    inference(avatar_split_clause,[],[f605,f515,f511,f518,f607]) ).

fof(f518,plain,
    ( spl30_16
  <=> ! [X1] : ~ element(sK5,powerset(powerset(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl30_16])]) ).

fof(f511,plain,
    ( spl30_14
  <=> sP0(sK5,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl30_14])]) ).

fof(f605,plain,
    ( ! [X0] :
        ( ~ element(sK5,powerset(powerset(X0)))
        | in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),sF27) )
    | spl30_14
    | ~ spl30_15 ),
    inference(forward_demodulation,[],[f604,f212]) ).

fof(f604,plain,
    ( ! [X0] :
        ( in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(sF26))
        | ~ element(sK5,powerset(powerset(X0))) )
    | spl30_14
    | ~ spl30_15 ),
    inference(forward_demodulation,[],[f603,f211]) ).

fof(f603,plain,
    ( ! [X0] :
        ( in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(relation_dom(sK3)))
        | ~ element(sK5,powerset(powerset(X0))) )
    | spl30_14
    | ~ spl30_15 ),
    inference(subsumption_resolution,[],[f602,f512]) ).

fof(f512,plain,
    ( ~ sP0(sK5,sK3)
    | spl30_14 ),
    inference(avatar_component_clause,[],[f511]) ).

fof(f602,plain,
    ( ! [X0] :
        ( sP0(sK5,sK3)
        | ~ element(sK5,powerset(powerset(X0)))
        | in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(relation_dom(sK3))) )
    | ~ spl30_15 ),
    inference(subsumption_resolution,[],[f601,f143]) ).

fof(f143,plain,
    function(sK3),
    inference(cnf_transformation,[],[f85]) ).

fof(f601,plain,
    ( ! [X0] :
        ( ~ function(sK3)
        | ~ element(sK5,powerset(powerset(X0)))
        | sP0(sK5,sK3)
        | in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(relation_dom(sK3))) )
    | ~ spl30_15 ),
    inference(subsumption_resolution,[],[f581,f142]) ).

fof(f142,plain,
    relation(sK3),
    inference(cnf_transformation,[],[f85]) ).

fof(f581,plain,
    ( ! [X0] :
        ( in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(relation_dom(sK3)))
        | ~ relation(sK3)
        | sP0(sK5,sK3)
        | ~ element(sK5,powerset(powerset(X0)))
        | ~ function(sK3) )
    | ~ spl30_15 ),
    inference(resolution,[],[f558,f202]) ).

fof(f202,plain,
    ! [X2,X0,X1,X4] :
      ( ~ in(X4,sK23(X0,X2))
      | sP0(X2,X0)
      | ~ element(X2,powerset(powerset(X1)))
      | in(sK24(X0,X2,X4),powerset(relation_dom(X0)))
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0,X1,X2] :
      ( sP0(X2,X0)
      | ~ element(X2,powerset(powerset(X1)))
      | ~ function(X0)
      | ~ relation(X0)
      | ! [X4] :
          ( ( ( sK24(X0,X2,X4) = X4
              & in(sK24(X0,X2,X4),powerset(relation_dom(X0)))
              & in(relation_image(X0,X4),X2) )
            | ~ in(X4,sK23(X0,X2)) )
          & ( in(X4,sK23(X0,X2))
            | ! [X6] :
                ( X4 != X6
                | ~ in(X6,powerset(relation_dom(X0)))
                | ~ in(relation_image(X0,X4),X2) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f117,f119,f118]) ).

fof(f118,plain,
    ! [X0,X2] :
      ( ? [X3] :
        ! [X4] :
          ( ( ? [X5] :
                ( X4 = X5
                & in(X5,powerset(relation_dom(X0)))
                & in(relation_image(X0,X4),X2) )
            | ~ in(X4,X3) )
          & ( in(X4,X3)
            | ! [X6] :
                ( X4 != X6
                | ~ in(X6,powerset(relation_dom(X0)))
                | ~ in(relation_image(X0,X4),X2) ) ) )
     => ! [X4] :
          ( ( ? [X5] :
                ( X4 = X5
                & in(X5,powerset(relation_dom(X0)))
                & in(relation_image(X0,X4),X2) )
            | ~ in(X4,sK23(X0,X2)) )
          & ( in(X4,sK23(X0,X2))
            | ! [X6] :
                ( X4 != X6
                | ~ in(X6,powerset(relation_dom(X0)))
                | ~ in(relation_image(X0,X4),X2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ! [X0,X2,X4] :
      ( ? [X5] :
          ( X4 = X5
          & in(X5,powerset(relation_dom(X0)))
          & in(relation_image(X0,X4),X2) )
     => ( sK24(X0,X2,X4) = X4
        & in(sK24(X0,X2,X4),powerset(relation_dom(X0)))
        & in(relation_image(X0,X4),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ! [X0,X1,X2] :
      ( sP0(X2,X0)
      | ~ element(X2,powerset(powerset(X1)))
      | ~ function(X0)
      | ~ relation(X0)
      | ? [X3] :
        ! [X4] :
          ( ( ? [X5] :
                ( X4 = X5
                & in(X5,powerset(relation_dom(X0)))
                & in(relation_image(X0,X4),X2) )
            | ~ in(X4,X3) )
          & ( in(X4,X3)
            | ! [X6] :
                ( X4 != X6
                | ~ in(X6,powerset(relation_dom(X0)))
                | ~ in(relation_image(X0,X4),X2) ) ) ) ),
    inference(rectify,[],[f116]) ).

fof(f116,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X2)
      | ~ element(X1,powerset(powerset(X0)))
      | ~ function(X2)
      | ~ relation(X2)
      | ? [X6] :
        ! [X7] :
          ( ( ? [X8] :
                ( X7 = X8
                & in(X8,powerset(relation_dom(X2)))
                & in(relation_image(X2,X7),X1) )
            | ~ in(X7,X6) )
          & ( in(X7,X6)
            | ! [X8] :
                ( X7 != X8
                | ~ in(X8,powerset(relation_dom(X2)))
                | ~ in(relation_image(X2,X7),X1) ) ) ) ),
    inference(nnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X2)
      | ~ element(X1,powerset(powerset(X0)))
      | ~ function(X2)
      | ~ relation(X2)
      | ? [X6] :
        ! [X7] :
          ( ? [X8] :
              ( X7 = X8
              & in(X8,powerset(relation_dom(X2)))
              & in(relation_image(X2,X7),X1) )
        <=> in(X7,X6) ) ),
    inference(definition_folding,[],[f64,f75]) ).

fof(f75,plain,
    ! [X1,X2] :
      ( ? [X5,X4,X3] :
          ( in(relation_image(X2,X3),X1)
          & X3 = X4
          & X4 = X5
          & in(relation_image(X2,X5),X1)
          & X3 != X5 )
      | ~ sP0(X1,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( ? [X5,X4,X3] :
          ( in(relation_image(X2,X3),X1)
          & X3 = X4
          & X4 = X5
          & in(relation_image(X2,X5),X1)
          & X3 != X5 )
      | ~ element(X1,powerset(powerset(X0)))
      | ~ function(X2)
      | ~ relation(X2)
      | ? [X6] :
        ! [X7] :
          ( ? [X8] :
              ( X7 = X8
              & in(X8,powerset(relation_dom(X2)))
              & in(relation_image(X2,X7),X1) )
        <=> in(X7,X6) ) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X2,X1,X0] :
      ( ? [X6] :
        ! [X7] :
          ( ? [X8] :
              ( X7 = X8
              & in(X8,powerset(relation_dom(X2)))
              & in(relation_image(X2,X7),X1) )
        <=> in(X7,X6) )
      | ? [X3,X4,X5] :
          ( X3 != X5
          & X3 = X4
          & in(relation_image(X2,X5),X1)
          & in(relation_image(X2,X3),X1)
          & X4 = X5 )
      | ~ relation(X2)
      | ~ element(X1,powerset(powerset(X0)))
      | ~ function(X2) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X2,X1,X0] :
      ( ( relation(X2)
        & element(X1,powerset(powerset(X0)))
        & function(X2) )
     => ( ! [X3,X4,X5] :
            ( ( X3 = X4
              & in(relation_image(X2,X5),X1)
              & in(relation_image(X2,X3),X1)
              & X4 = X5 )
           => X3 = X5 )
       => ? [X6] :
          ! [X7] :
            ( ? [X8] :
                ( X7 = X8
                & in(X8,powerset(relation_dom(X2)))
                & in(relation_image(X2,X7),X1) )
          <=> in(X7,X6) ) ) ),
    inference(rectify,[],[f38]) ).

fof(f38,axiom,
    ! [X0,X1,X2] :
      ( ( relation(X2)
        & element(X1,powerset(powerset(X0)))
        & function(X2) )
     => ( ! [X5,X3,X4] :
            ( ( X3 = X5
              & in(relation_image(X2,X4),X1)
              & X3 = X4
              & in(relation_image(X2,X5),X1) )
           => X4 = X5 )
       => ? [X3] :
          ! [X4] :
            ( in(X4,X3)
          <=> ? [X5] :
                ( X4 = X5
                & in(X5,powerset(relation_dom(X2)))
                & in(relation_image(X2,X4),X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).

fof(f600,plain,
    ( spl30_16
    | spl30_20
    | spl30_14
    | ~ spl30_15 ),
    inference(avatar_split_clause,[],[f595,f515,f511,f597,f518]) ).

fof(f595,plain,
    ( ! [X2] :
        ( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
        | ~ element(sK5,powerset(powerset(X2))) )
    | spl30_14
    | ~ spl30_15 ),
    inference(subsumption_resolution,[],[f594,f512]) ).

fof(f594,plain,
    ( ! [X2] :
        ( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
        | sP0(sK5,sK3)
        | ~ element(sK5,powerset(powerset(X2))) )
    | ~ spl30_15 ),
    inference(subsumption_resolution,[],[f593,f142]) ).

fof(f593,plain,
    ( ! [X2] :
        ( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
        | ~ relation(sK3)
        | sP0(sK5,sK3)
        | ~ element(sK5,powerset(powerset(X2))) )
    | ~ spl30_15 ),
    inference(subsumption_resolution,[],[f583,f143]) ).

fof(f583,plain,
    ( ! [X2] :
        ( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
        | ~ function(sK3)
        | ~ relation(sK3)
        | sP0(sK5,sK3)
        | ~ element(sK5,powerset(powerset(X2))) )
    | ~ spl30_15 ),
    inference(resolution,[],[f558,f201]) ).

fof(f201,plain,
    ! [X2,X0,X1,X4] :
      ( ~ in(X4,sK23(X0,X2))
      | sP0(X2,X0)
      | ~ relation(X0)
      | ~ function(X0)
      | ~ element(X2,powerset(powerset(X1)))
      | in(relation_image(X0,X4),X2) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f592,plain,
    ( spl30_16
    | spl30_19
    | spl30_14
    | ~ spl30_15 ),
    inference(avatar_split_clause,[],[f587,f515,f511,f589,f518]) ).

fof(f587,plain,
    ( ! [X1] :
        ( sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
        | ~ element(sK5,powerset(powerset(X1))) )
    | spl30_14
    | ~ spl30_15 ),
    inference(subsumption_resolution,[],[f586,f143]) ).

fof(f586,plain,
    ( ! [X1] :
        ( sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
        | ~ element(sK5,powerset(powerset(X1)))
        | ~ function(sK3) )
    | spl30_14
    | ~ spl30_15 ),
    inference(subsumption_resolution,[],[f585,f142]) ).

fof(f585,plain,
    ( ! [X1] :
        ( ~ element(sK5,powerset(powerset(X1)))
        | sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
        | ~ relation(sK3)
        | ~ function(sK3) )
    | spl30_14
    | ~ spl30_15 ),
    inference(subsumption_resolution,[],[f582,f512]) ).

fof(f582,plain,
    ( ! [X1] :
        ( sP0(sK5,sK3)
        | ~ function(sK3)
        | sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
        | ~ relation(sK3)
        | ~ element(sK5,powerset(powerset(X1))) )
    | ~ spl30_15 ),
    inference(resolution,[],[f558,f203]) ).

fof(f203,plain,
    ! [X2,X0,X1,X4] :
      ( ~ in(X4,sK23(X0,X2))
      | ~ relation(X0)
      | ~ element(X2,powerset(powerset(X1)))
      | ~ function(X0)
      | sP0(X2,X0)
      | sK24(X0,X2,X4) = X4 ),
    inference(cnf_transformation,[],[f120]) ).

fof(f580,plain,
    ~ spl30_16,
    inference(avatar_contradiction_clause,[],[f579]) ).

fof(f579,plain,
    ( $false
    | ~ spl30_16 ),
    inference(subsumption_resolution,[],[f578,f217]) ).

fof(f217,plain,
    element(sK5,sF29),
    inference(definition_folding,[],[f141,f216,f215]) ).

fof(f215,plain,
    powerset(sK4) = sF28,
    introduced(function_definition,[]) ).

fof(f216,plain,
    sF29 = powerset(sF28),
    introduced(function_definition,[]) ).

fof(f141,plain,
    element(sK5,powerset(powerset(sK4))),
    inference(cnf_transformation,[],[f85]) ).

fof(f578,plain,
    ( ~ element(sK5,sF29)
    | ~ spl30_16 ),
    inference(forward_demodulation,[],[f576,f216]) ).

fof(f576,plain,
    ( ~ element(sK5,powerset(sF28))
    | ~ spl30_16 ),
    inference(superposition,[],[f519,f215]) ).

fof(f519,plain,
    ( ! [X1] : ~ element(sK5,powerset(powerset(X1)))
    | ~ spl30_16 ),
    inference(avatar_component_clause,[],[f518]) ).

fof(f549,plain,
    ~ spl30_14,
    inference(avatar_contradiction_clause,[],[f548]) ).

fof(f548,plain,
    ( $false
    | ~ spl30_14 ),
    inference(subsumption_resolution,[],[f547,f513]) ).

fof(f513,plain,
    ( sP0(sK5,sK3)
    | ~ spl30_14 ),
    inference(avatar_component_clause,[],[f511]) ).

fof(f547,plain,
    ( ~ sP0(sK5,sK3)
    | ~ spl30_14 ),
    inference(trivial_inequality_removal,[],[f546]) ).

fof(f546,plain,
    ( ~ sP0(sK5,sK3)
    | sK20(sK5,sK3) != sK20(sK5,sK3)
    | ~ spl30_14 ),
    inference(superposition,[],[f195,f523]) ).

fof(f523,plain,
    ( sK22(sK5,sK3) = sK20(sK5,sK3)
    | ~ spl30_14 ),
    inference(backward_demodulation,[],[f521,f522]) ).

fof(f522,plain,
    ( sK20(sK5,sK3) = sK21(sK5,sK3)
    | ~ spl30_14 ),
    inference(resolution,[],[f513,f197]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | sK21(X0,X1) = sK20(X0,X1) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ( in(relation_image(X1,sK22(X0,X1)),X0)
        & sK22(X0,X1) = sK21(X0,X1)
        & sK21(X0,X1) = sK20(X0,X1)
        & in(relation_image(X1,sK20(X0,X1)),X0)
        & sK22(X0,X1) != sK20(X0,X1) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f113,f114]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ? [X2,X3,X4] :
          ( in(relation_image(X1,X4),X0)
          & X3 = X4
          & X2 = X3
          & in(relation_image(X1,X2),X0)
          & X2 != X4 )
     => ( in(relation_image(X1,sK22(X0,X1)),X0)
        & sK22(X0,X1) = sK21(X0,X1)
        & sK21(X0,X1) = sK20(X0,X1)
        & in(relation_image(X1,sK20(X0,X1)),X0)
        & sK22(X0,X1) != sK20(X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( ? [X2,X3,X4] :
          ( in(relation_image(X1,X4),X0)
          & X3 = X4
          & X2 = X3
          & in(relation_image(X1,X2),X0)
          & X2 != X4 )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f112]) ).

fof(f112,plain,
    ! [X1,X2] :
      ( ? [X5,X4,X3] :
          ( in(relation_image(X2,X3),X1)
          & X3 = X4
          & X4 = X5
          & in(relation_image(X2,X5),X1)
          & X3 != X5 )
      | ~ sP0(X1,X2) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f521,plain,
    ( sK22(sK5,sK3) = sK21(sK5,sK3)
    | ~ spl30_14 ),
    inference(resolution,[],[f513,f198]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | sK22(X0,X1) = sK21(X0,X1) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( sK22(X0,X1) != sK20(X0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f115]) ).

fof(f520,plain,
    ( spl30_14
    | spl30_15
    | spl30_16 ),
    inference(avatar_split_clause,[],[f509,f518,f515,f511]) ).

fof(f509,plain,
    ! [X0,X1] :
      ( ~ element(sK5,powerset(powerset(X1)))
      | in(sK6(X0),sK23(sK3,sK5))
      | sP0(sK5,sK3)
      | in(sK6(X0),X0) ),
    inference(subsumption_resolution,[],[f508,f214]) ).

fof(f214,plain,
    ! [X3] :
      ( in(sK6(X3),sF27)
      | in(sK6(X3),X3) ),
    inference(definition_folding,[],[f145,f212,f211]) ).

fof(f145,plain,
    ! [X3] :
      ( in(sK6(X3),X3)
      | in(sK6(X3),powerset(relation_dom(sK3))) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f508,plain,
    ! [X0,X1] :
      ( ~ element(sK5,powerset(powerset(X1)))
      | ~ in(sK6(X0),sF27)
      | in(sK6(X0),X0)
      | sP0(sK5,sK3)
      | in(sK6(X0),sK23(sK3,sK5)) ),
    inference(forward_demodulation,[],[f507,f212]) ).

fof(f507,plain,
    ! [X0,X1] :
      ( in(sK6(X0),X0)
      | in(sK6(X0),sK23(sK3,sK5))
      | ~ element(sK5,powerset(powerset(X1)))
      | sP0(sK5,sK3)
      | ~ in(sK6(X0),powerset(sF26)) ),
    inference(forward_demodulation,[],[f506,f211]) ).

fof(f506,plain,
    ! [X0,X1] :
      ( ~ element(sK5,powerset(powerset(X1)))
      | sP0(sK5,sK3)
      | in(sK6(X0),X0)
      | in(sK6(X0),sK23(sK3,sK5))
      | ~ in(sK6(X0),powerset(relation_dom(sK3))) ),
    inference(subsumption_resolution,[],[f505,f143]) ).

fof(f505,plain,
    ! [X0,X1] :
      ( ~ in(sK6(X0),powerset(relation_dom(sK3)))
      | ~ element(sK5,powerset(powerset(X1)))
      | in(sK6(X0),X0)
      | in(sK6(X0),sK23(sK3,sK5))
      | ~ function(sK3)
      | sP0(sK5,sK3) ),
    inference(subsumption_resolution,[],[f502,f142]) ).

fof(f502,plain,
    ! [X0,X1] :
      ( ~ in(sK6(X0),powerset(relation_dom(sK3)))
      | in(sK6(X0),X0)
      | ~ element(sK5,powerset(powerset(X1)))
      | ~ relation(sK3)
      | ~ function(sK3)
      | in(sK6(X0),sK23(sK3,sK5))
      | sP0(sK5,sK3) ),
    inference(resolution,[],[f210,f144]) ).

fof(f144,plain,
    ! [X3] :
      ( in(sK6(X3),X3)
      | in(relation_image(sK3,sK6(X3)),sK5) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f210,plain,
    ! [X2,X0,X1,X6] :
      ( ~ in(relation_image(X0,X6),X2)
      | ~ relation(X0)
      | ~ in(X6,powerset(relation_dom(X0)))
      | in(X6,sK23(X0,X2))
      | ~ element(X2,powerset(powerset(X1)))
      | sP0(X2,X0)
      | ~ function(X0) ),
    inference(equality_resolution,[],[f200]) ).

fof(f200,plain,
    ! [X2,X0,X1,X6,X4] :
      ( sP0(X2,X0)
      | ~ element(X2,powerset(powerset(X1)))
      | ~ function(X0)
      | ~ relation(X0)
      | in(X4,sK23(X0,X2))
      | X4 != X6
      | ~ in(X6,powerset(relation_dom(X0)))
      | ~ in(relation_image(X0,X4),X2) ),
    inference(cnf_transformation,[],[f120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SEU297+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.32  % Computer : n028.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 15:15:33 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.49  % (9507)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.49  % (9492)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)
% 0.18/0.49  % (9499)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.50  % (9486)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)
% 0.18/0.50  % (9487)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)
% 0.18/0.50  % (9490)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)
% 0.18/0.51  % (9508)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)
% 0.18/0.51  % (9495)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.51  % (9489)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.51  % (9489)Instruction limit reached!
% 0.18/0.51  % (9489)------------------------------
% 0.18/0.51  % (9489)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (9489)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (9489)Termination reason: Unknown
% 0.18/0.51  % (9489)Termination phase: Unused predicate definition removal
% 0.18/0.51  
% 0.18/0.51  % (9489)Memory used [KB]: 895
% 0.18/0.51  % (9489)Time elapsed: 0.003 s
% 0.18/0.51  % (9489)Instructions burned: 2 (million)
% 0.18/0.51  % (9489)------------------------------
% 0.18/0.51  % (9489)------------------------------
% 0.18/0.51  % (9482)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)
% 0.18/0.51  % (9506)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.18/0.51  % (9481)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.18/0.51  % (9485)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.51  % (9500)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)
% 0.18/0.51  % (9503)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)
% 0.18/0.51  % (9483)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)
% 0.18/0.51  % (9488)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.52  % (9484)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)
% 0.18/0.52  % (9493)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.18/0.52  TRYING [1]
% 0.18/0.52  % (9509)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.18/0.52  % (9488)Instruction limit reached!
% 0.18/0.52  % (9488)------------------------------
% 0.18/0.52  % (9488)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (9488)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (9488)Termination reason: Unknown
% 0.18/0.52  % (9488)Termination phase: Saturation
% 0.18/0.52  
% 0.18/0.52  % (9488)Memory used [KB]: 5628
% 0.18/0.52  % (9488)Time elapsed: 0.093 s
% 0.18/0.52  % (9488)Instructions burned: 8 (million)
% 0.18/0.52  % (9488)------------------------------
% 0.18/0.52  % (9488)------------------------------
% 0.18/0.52  % (9504)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)
% 0.18/0.52  % (9498)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.18/0.52  TRYING [2]
% 0.18/0.52  % (9501)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)
% 0.18/0.52  % (9496)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.18/0.52  % (9499)First to succeed.
% 0.18/0.52  % (9511)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.18/0.52  TRYING [1]
% 0.18/0.52  % (9499)Refutation found. Thanks to Tanya!
% 0.18/0.52  % SZS status Theorem for theBenchmark
% 0.18/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52  % (9499)------------------------------
% 0.18/0.52  % (9499)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52  % (9499)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52  % (9499)Termination reason: Refutation
% 0.18/0.52  
% 0.18/0.52  % (9499)Memory used [KB]: 5756
% 0.18/0.52  % (9499)Time elapsed: 0.142 s
% 0.18/0.52  % (9499)Instructions burned: 18 (million)
% 0.18/0.52  % (9499)------------------------------
% 0.18/0.52  % (9499)------------------------------
% 0.18/0.52  % (9480)Success in time 0.187 s
%------------------------------------------------------------------------------