TSTP Solution File: SEU298+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU298+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:22:02 EDT 2024

% Result   : Theorem 0.56s 0.76s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  103 (   5 unt;   0 def)
%            Number of atoms       :  532 ( 130 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  640 ( 211   ~; 238   |; 153   &)
%                                         (  19 <=>;  17  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   18 (  16 usr;  13 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   2 con; 0-3 aty)
%            Number of variables   :  233 ( 136   !;  97   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f485,plain,
    $false,
    inference(avatar_sat_refutation,[],[f320,f324,f347,f360,f362,f397,f402,f407,f412,f445,f478,f481,f484]) ).

fof(f484,plain,
    ( ~ spl29_9
    | spl29_27 ),
    inference(avatar_contradiction_clause,[],[f482]) ).

fof(f482,plain,
    ( $false
    | ~ spl29_9
    | spl29_27 ),
    inference(resolution,[],[f477,f371]) ).

fof(f371,plain,
    ( in(sK3(sK26(sK1,sK2)),sK26(sK1,sK2))
    | ~ spl29_9 ),
    inference(factoring,[],[f365]) ).

fof(f365,plain,
    ( ! [X0] :
        ( in(sK3(X0),sK26(sK1,sK2))
        | in(sK3(X0),X0) )
    | ~ spl29_9 ),
    inference(duplicate_literal_removal,[],[f363]) ).

fof(f363,plain,
    ( ! [X0] :
        ( in(sK3(X0),X0)
        | in(sK3(X0),sK26(sK1,sK2))
        | in(sK3(X0),X0) )
    | ~ spl29_9 ),
    inference(resolution,[],[f346,f129]) ).

fof(f129,plain,
    ! [X2] :
      ( in(sK3(X2),powerset(sK1))
      | in(sK3(X2),X2) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ( ! [X2] :
        ( ( ! [X4] :
              ( set_difference(X4,singleton(sK1)) != sK3(X2)
              | ~ in(X4,sK2) )
          | ~ in(sK3(X2),powerset(sK1))
          | ~ in(sK3(X2),X2) )
        & ( ( sK3(X2) = set_difference(sK4(X2),singleton(sK1))
            & in(sK4(X2),sK2)
            & in(sK3(X2),powerset(sK1)) )
          | in(sK3(X2),X2) ) )
    & element(sK2,powerset(powerset(succ(sK1))))
    & ordinal(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f79,f82,f81,f80]) ).

fof(f80,plain,
    ( ? [X0,X1] :
        ( ! [X2] :
          ? [X3] :
            ( ( ! [X4] :
                  ( set_difference(X4,singleton(X0)) != X3
                  | ~ in(X4,X1) )
              | ~ in(X3,powerset(X0))
              | ~ in(X3,X2) )
            & ( ( ? [X5] :
                    ( set_difference(X5,singleton(X0)) = X3
                    & in(X5,X1) )
                & in(X3,powerset(X0)) )
              | in(X3,X2) ) )
        & element(X1,powerset(powerset(succ(X0))))
        & ordinal(X0) )
   => ( ! [X2] :
        ? [X3] :
          ( ( ! [X4] :
                ( set_difference(X4,singleton(sK1)) != X3
                | ~ in(X4,sK2) )
            | ~ in(X3,powerset(sK1))
            | ~ in(X3,X2) )
          & ( ( ? [X5] :
                  ( set_difference(X5,singleton(sK1)) = X3
                  & in(X5,sK2) )
              & in(X3,powerset(sK1)) )
            | in(X3,X2) ) )
      & element(sK2,powerset(powerset(succ(sK1))))
      & ordinal(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ! [X2] :
      ( ? [X3] :
          ( ( ! [X4] :
                ( set_difference(X4,singleton(sK1)) != X3
                | ~ in(X4,sK2) )
            | ~ in(X3,powerset(sK1))
            | ~ in(X3,X2) )
          & ( ( ? [X5] :
                  ( set_difference(X5,singleton(sK1)) = X3
                  & in(X5,sK2) )
              & in(X3,powerset(sK1)) )
            | in(X3,X2) ) )
     => ( ( ! [X4] :
              ( set_difference(X4,singleton(sK1)) != sK3(X2)
              | ~ in(X4,sK2) )
          | ~ in(sK3(X2),powerset(sK1))
          | ~ in(sK3(X2),X2) )
        & ( ( ? [X5] :
                ( set_difference(X5,singleton(sK1)) = sK3(X2)
                & in(X5,sK2) )
            & in(sK3(X2),powerset(sK1)) )
          | in(sK3(X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ! [X2] :
      ( ? [X5] :
          ( set_difference(X5,singleton(sK1)) = sK3(X2)
          & in(X5,sK2) )
     => ( sK3(X2) = set_difference(sK4(X2),singleton(sK1))
        & in(sK4(X2),sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ? [X0,X1] :
      ( ! [X2] :
        ? [X3] :
          ( ( ! [X4] :
                ( set_difference(X4,singleton(X0)) != X3
                | ~ in(X4,X1) )
            | ~ in(X3,powerset(X0))
            | ~ in(X3,X2) )
          & ( ( ? [X5] :
                  ( set_difference(X5,singleton(X0)) = X3
                  & in(X5,X1) )
              & in(X3,powerset(X0)) )
            | in(X3,X2) ) )
      & element(X1,powerset(powerset(succ(X0))))
      & ordinal(X0) ),
    inference(rectify,[],[f78]) ).

fof(f78,plain,
    ? [X0,X1] :
      ( ! [X2] :
        ? [X3] :
          ( ( ! [X4] :
                ( set_difference(X4,singleton(X0)) != X3
                | ~ in(X4,X1) )
            | ~ in(X3,powerset(X0))
            | ~ in(X3,X2) )
          & ( ( ? [X4] :
                  ( set_difference(X4,singleton(X0)) = X3
                  & in(X4,X1) )
              & in(X3,powerset(X0)) )
            | in(X3,X2) ) )
      & element(X1,powerset(powerset(succ(X0))))
      & ordinal(X0) ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ? [X0,X1] :
      ( ! [X2] :
        ? [X3] :
          ( ( ! [X4] :
                ( set_difference(X4,singleton(X0)) != X3
                | ~ in(X4,X1) )
            | ~ in(X3,powerset(X0))
            | ~ in(X3,X2) )
          & ( ( ? [X4] :
                  ( set_difference(X4,singleton(X0)) = X3
                  & in(X4,X1) )
              & in(X3,powerset(X0)) )
            | in(X3,X2) ) )
      & element(X1,powerset(powerset(succ(X0))))
      & ordinal(X0) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ? [X0,X1] :
      ( ! [X2] :
        ? [X3] :
          ( in(X3,X2)
        <~> ( ? [X4] :
                ( set_difference(X4,singleton(X0)) = X3
                & in(X4,X1) )
            & in(X3,powerset(X0)) ) )
      & element(X1,powerset(powerset(succ(X0))))
      & ordinal(X0) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ? [X0,X1] :
      ( ! [X2] :
        ? [X3] :
          ( in(X3,X2)
        <~> ( ? [X4] :
                ( set_difference(X4,singleton(X0)) = X3
                & in(X4,X1) )
            & in(X3,powerset(X0)) ) )
      & element(X1,powerset(powerset(succ(X0))))
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( element(X1,powerset(powerset(succ(X0))))
          & ordinal(X0) )
       => ? [X2] :
          ! [X3] :
            ( in(X3,X2)
          <=> ( ? [X4] :
                  ( set_difference(X4,singleton(X0)) = X3
                  & in(X4,X1) )
              & in(X3,powerset(X0)) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ! [X0,X1] :
      ( ( element(X1,powerset(powerset(succ(X0))))
        & ordinal(X0) )
     => ? [X2] :
        ! [X3] :
          ( in(X3,X2)
        <=> ( ? [X4] :
                ( set_difference(X4,singleton(X0)) = X3
                & in(X4,X1) )
            & in(X3,powerset(X0)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.PxwB9m59L4/Vampire---4.8_8293',s1_xboole_0__e4_27_3_1__finset_1) ).

fof(f346,plain,
    ( ! [X0] :
        ( ~ in(sK3(X0),powerset(sK1))
        | in(sK3(X0),X0)
        | in(sK3(X0),sK26(sK1,sK2)) )
    | ~ spl29_9 ),
    inference(avatar_component_clause,[],[f345]) ).

fof(f345,plain,
    ( spl29_9
  <=> ! [X0] :
        ( in(sK3(X0),X0)
        | ~ in(sK3(X0),powerset(sK1))
        | in(sK3(X0),sK26(sK1,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_9])]) ).

fof(f477,plain,
    ( ~ in(sK3(sK26(sK1,sK2)),sK26(sK1,sK2))
    | spl29_27 ),
    inference(avatar_component_clause,[],[f475]) ).

fof(f475,plain,
    ( spl29_27
  <=> in(sK3(sK26(sK1,sK2)),sK26(sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_27])]) ).

fof(f481,plain,
    ( ~ spl29_15
    | ~ spl29_17
    | spl29_22 ),
    inference(avatar_contradiction_clause,[],[f479]) ).

fof(f479,plain,
    ( $false
    | ~ spl29_15
    | ~ spl29_17
    | spl29_22 ),
    inference(resolution,[],[f452,f413]) ).

fof(f413,plain,
    ( in(sK3(sK26(sK1,sK2)),powerset(sK1))
    | ~ spl29_15
    | ~ spl29_17 ),
    inference(forward_demodulation,[],[f401,f411]) ).

fof(f411,plain,
    ( sK3(sK26(sK1,sK2)) = sK27(sK1,sK2,sK3(sK26(sK1,sK2)))
    | ~ spl29_17 ),
    inference(avatar_component_clause,[],[f409]) ).

fof(f409,plain,
    ( spl29_17
  <=> sK3(sK26(sK1,sK2)) = sK27(sK1,sK2,sK3(sK26(sK1,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_17])]) ).

fof(f401,plain,
    ( in(sK27(sK1,sK2,sK3(sK26(sK1,sK2))),powerset(sK1))
    | ~ spl29_15 ),
    inference(avatar_component_clause,[],[f399]) ).

fof(f399,plain,
    ( spl29_15
  <=> in(sK27(sK1,sK2,sK3(sK26(sK1,sK2))),powerset(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_15])]) ).

fof(f452,plain,
    ( ~ in(sK3(sK26(sK1,sK2)),powerset(sK1))
    | spl29_22 ),
    inference(avatar_component_clause,[],[f450]) ).

fof(f450,plain,
    ( spl29_22
  <=> in(sK3(sK26(sK1,sK2)),powerset(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_22])]) ).

fof(f478,plain,
    ( ~ spl29_22
    | ~ spl29_27
    | ~ spl29_20 ),
    inference(avatar_split_clause,[],[f473,f443,f475,f450]) ).

fof(f443,plain,
    ( spl29_20
  <=> ! [X0] :
        ( sK3(X0) != sK3(sK26(sK1,sK2))
        | ~ in(sK3(X0),X0)
        | ~ in(sK3(X0),powerset(sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_20])]) ).

fof(f473,plain,
    ( ~ in(sK3(sK26(sK1,sK2)),sK26(sK1,sK2))
    | ~ in(sK3(sK26(sK1,sK2)),powerset(sK1))
    | ~ spl29_20 ),
    inference(equality_resolution,[],[f444]) ).

fof(f444,plain,
    ( ! [X0] :
        ( sK3(X0) != sK3(sK26(sK1,sK2))
        | ~ in(sK3(X0),X0)
        | ~ in(sK3(X0),powerset(sK1)) )
    | ~ spl29_20 ),
    inference(avatar_component_clause,[],[f443]) ).

fof(f445,plain,
    ( ~ spl29_16
    | spl29_20
    | ~ spl29_14 ),
    inference(avatar_split_clause,[],[f438,f394,f443,f404]) ).

fof(f404,plain,
    ( spl29_16
  <=> in(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_16])]) ).

fof(f394,plain,
    ( spl29_14
  <=> sK3(sK26(sK1,sK2)) = set_difference(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),singleton(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_14])]) ).

fof(f438,plain,
    ( ! [X0] :
        ( sK3(X0) != sK3(sK26(sK1,sK2))
        | ~ in(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),sK2)
        | ~ in(sK3(X0),powerset(sK1))
        | ~ in(sK3(X0),X0) )
    | ~ spl29_14 ),
    inference(superposition,[],[f132,f396]) ).

fof(f396,plain,
    ( sK3(sK26(sK1,sK2)) = set_difference(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),singleton(sK1))
    | ~ spl29_14 ),
    inference(avatar_component_clause,[],[f394]) ).

fof(f132,plain,
    ! [X2,X4] :
      ( set_difference(X4,singleton(sK1)) != sK3(X2)
      | ~ in(X4,sK2)
      | ~ in(sK3(X2),powerset(sK1))
      | ~ in(sK3(X2),X2) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f412,plain,
    ( ~ spl29_3
    | ~ spl29_8
    | spl29_7
    | spl29_17
    | ~ spl29_9 ),
    inference(avatar_split_clause,[],[f391,f345,f409,f337,f341,f314]) ).

fof(f314,plain,
    ( spl29_3
  <=> ordinal(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_3])]) ).

fof(f341,plain,
    ( spl29_8
  <=> element(sK2,powerset(powerset(succ(sK1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_8])]) ).

fof(f337,plain,
    ( spl29_7
  <=> sP0(sK1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_7])]) ).

fof(f391,plain,
    ( sK3(sK26(sK1,sK2)) = sK27(sK1,sK2,sK3(sK26(sK1,sK2)))
    | sP0(sK1,sK2)
    | ~ element(sK2,powerset(powerset(succ(sK1))))
    | ~ ordinal(sK1)
    | ~ spl29_9 ),
    inference(resolution,[],[f371,f226]) ).

fof(f226,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,sK26(X0,X1))
      | sK27(X0,X1,X3) = X3
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ! [X3] :
          ( ( in(X3,sK26(X0,X1))
            | ! [X4] :
                ( ! [X5] :
                    ( set_difference(X5,singleton(X0)) != X3
                    | ~ in(X5,X1) )
                | X3 != X4
                | ~ in(X4,powerset(X0)) ) )
          & ( ( set_difference(sK28(X0,X1,X3),singleton(X0)) = X3
              & in(sK28(X0,X1,X3),X1)
              & sK27(X0,X1,X3) = X3
              & in(sK27(X0,X1,X3),powerset(X0)) )
            | ~ in(X3,sK26(X0,X1)) ) )
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27,sK28])],[f122,f125,f124,f123]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( in(X3,X2)
            | ! [X4] :
                ( ! [X5] :
                    ( set_difference(X5,singleton(X0)) != X3
                    | ~ in(X5,X1) )
                | X3 != X4
                | ~ in(X4,powerset(X0)) ) )
          & ( ? [X6] :
                ( ? [X7] :
                    ( set_difference(X7,singleton(X0)) = X3
                    & in(X7,X1) )
                & X3 = X6
                & in(X6,powerset(X0)) )
            | ~ in(X3,X2) ) )
     => ! [X3] :
          ( ( in(X3,sK26(X0,X1))
            | ! [X4] :
                ( ! [X5] :
                    ( set_difference(X5,singleton(X0)) != X3
                    | ~ in(X5,X1) )
                | X3 != X4
                | ~ in(X4,powerset(X0)) ) )
          & ( ? [X6] :
                ( ? [X7] :
                    ( set_difference(X7,singleton(X0)) = X3
                    & in(X7,X1) )
                & X3 = X6
                & in(X6,powerset(X0)) )
            | ~ in(X3,sK26(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ! [X0,X1,X3] :
      ( ? [X6] :
          ( ? [X7] :
              ( set_difference(X7,singleton(X0)) = X3
              & in(X7,X1) )
          & X3 = X6
          & in(X6,powerset(X0)) )
     => ( ? [X7] :
            ( set_difference(X7,singleton(X0)) = X3
            & in(X7,X1) )
        & sK27(X0,X1,X3) = X3
        & in(sK27(X0,X1,X3),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f125,plain,
    ! [X0,X1,X3] :
      ( ? [X7] :
          ( set_difference(X7,singleton(X0)) = X3
          & in(X7,X1) )
     => ( set_difference(sK28(X0,X1,X3),singleton(X0)) = X3
        & in(sK28(X0,X1,X3),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( in(X3,X2)
            | ! [X4] :
                ( ! [X5] :
                    ( set_difference(X5,singleton(X0)) != X3
                    | ~ in(X5,X1) )
                | X3 != X4
                | ~ in(X4,powerset(X0)) ) )
          & ( ? [X6] :
                ( ? [X7] :
                    ( set_difference(X7,singleton(X0)) = X3
                    & in(X7,X1) )
                & X3 = X6
                & in(X6,powerset(X0)) )
            | ~ in(X3,X2) ) )
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(rectify,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ? [X7] :
        ! [X8] :
          ( ( in(X8,X7)
            | ! [X9] :
                ( ! [X10] :
                    ( set_difference(X10,singleton(X0)) != X8
                    | ~ in(X10,X1) )
                | X8 != X9
                | ~ in(X9,powerset(X0)) ) )
          & ( ? [X9] :
                ( ? [X10] :
                    ( set_difference(X10,singleton(X0)) = X8
                    & in(X10,X1) )
                & X8 = X9
                & in(X9,powerset(X0)) )
            | ~ in(X8,X7) ) )
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(nnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ? [X7] :
        ! [X8] :
          ( in(X8,X7)
        <=> ? [X9] :
              ( ? [X10] :
                  ( set_difference(X10,singleton(X0)) = X8
                  & in(X10,X1) )
              & X8 = X9
              & in(X9,powerset(X0)) ) )
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(definition_folding,[],[f74,f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ? [X2,X3,X4] :
          ( X3 != X4
          & ? [X5] :
              ( set_difference(X5,singleton(X0)) = X4
              & in(X5,X1) )
          & X2 = X4
          & ? [X6] :
              ( set_difference(X6,singleton(X0)) = X3
              & in(X6,X1) )
          & X2 = X3 )
      | ~ sP0(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ? [X7] :
        ! [X8] :
          ( in(X8,X7)
        <=> ? [X9] :
              ( ? [X10] :
                  ( set_difference(X10,singleton(X0)) = X8
                  & in(X10,X1) )
              & X8 = X9
              & in(X9,powerset(X0)) ) )
      | ? [X2,X3,X4] :
          ( X3 != X4
          & ? [X5] :
              ( set_difference(X5,singleton(X0)) = X4
              & in(X5,X1) )
          & X2 = X4
          & ? [X6] :
              ( set_difference(X6,singleton(X0)) = X3
              & in(X6,X1) )
          & X2 = X3 )
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ? [X7] :
        ! [X8] :
          ( in(X8,X7)
        <=> ? [X9] :
              ( ? [X10] :
                  ( set_difference(X10,singleton(X0)) = X8
                  & in(X10,X1) )
              & X8 = X9
              & in(X9,powerset(X0)) ) )
      | ? [X2,X3,X4] :
          ( X3 != X4
          & ? [X5] :
              ( set_difference(X5,singleton(X0)) = X4
              & in(X5,X1) )
          & X2 = X4
          & ? [X6] :
              ( set_difference(X6,singleton(X0)) = X3
              & in(X6,X1) )
          & X2 = X3 )
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( element(X1,powerset(powerset(succ(X0))))
        & ordinal(X0) )
     => ( ! [X2,X3,X4] :
            ( ( ? [X5] :
                  ( set_difference(X5,singleton(X0)) = X4
                  & in(X5,X1) )
              & X2 = X4
              & ? [X6] :
                  ( set_difference(X6,singleton(X0)) = X3
                  & in(X6,X1) )
              & X2 = X3 )
           => X3 = X4 )
       => ? [X7] :
          ! [X8] :
            ( in(X8,X7)
          <=> ? [X9] :
                ( ? [X10] :
                    ( set_difference(X10,singleton(X0)) = X8
                    & in(X10,X1) )
                & X8 = X9
                & in(X9,powerset(X0)) ) ) ) ),
    inference(rectify,[],[f43]) ).

fof(f43,axiom,
    ! [X0,X1] :
      ( ( element(X1,powerset(powerset(succ(X0))))
        & ordinal(X0) )
     => ( ! [X2,X3,X4] :
            ( ( ? [X6] :
                  ( set_difference(X6,singleton(X0)) = X4
                  & in(X6,X1) )
              & X2 = X4
              & ? [X5] :
                  ( set_difference(X5,singleton(X0)) = X3
                  & in(X5,X1) )
              & X2 = X3 )
           => X3 = X4 )
       => ? [X2] :
          ! [X3] :
            ( in(X3,X2)
          <=> ? [X4] :
                ( ? [X7] :
                    ( set_difference(X7,singleton(X0)) = X3
                    & in(X7,X1) )
                & X3 = X4
                & in(X4,powerset(X0)) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.PxwB9m59L4/Vampire---4.8_8293',s1_tarski__e4_27_3_1__finset_1__1) ).

fof(f407,plain,
    ( ~ spl29_3
    | ~ spl29_8
    | spl29_7
    | spl29_16
    | ~ spl29_9 ),
    inference(avatar_split_clause,[],[f390,f345,f404,f337,f341,f314]) ).

fof(f390,plain,
    ( in(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),sK2)
    | sP0(sK1,sK2)
    | ~ element(sK2,powerset(powerset(succ(sK1))))
    | ~ ordinal(sK1)
    | ~ spl29_9 ),
    inference(resolution,[],[f371,f227]) ).

fof(f227,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,sK26(X0,X1))
      | in(sK28(X0,X1,X3),X1)
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f402,plain,
    ( ~ spl29_3
    | ~ spl29_8
    | spl29_7
    | spl29_15
    | ~ spl29_9 ),
    inference(avatar_split_clause,[],[f389,f345,f399,f337,f341,f314]) ).

fof(f389,plain,
    ( in(sK27(sK1,sK2,sK3(sK26(sK1,sK2))),powerset(sK1))
    | sP0(sK1,sK2)
    | ~ element(sK2,powerset(powerset(succ(sK1))))
    | ~ ordinal(sK1)
    | ~ spl29_9 ),
    inference(resolution,[],[f371,f225]) ).

fof(f225,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,sK26(X0,X1))
      | in(sK27(X0,X1,X3),powerset(X0))
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f397,plain,
    ( ~ spl29_3
    | ~ spl29_8
    | spl29_7
    | spl29_14
    | ~ spl29_9 ),
    inference(avatar_split_clause,[],[f388,f345,f394,f337,f341,f314]) ).

fof(f388,plain,
    ( sK3(sK26(sK1,sK2)) = set_difference(sK28(sK1,sK2,sK3(sK26(sK1,sK2))),singleton(sK1))
    | sP0(sK1,sK2)
    | ~ element(sK2,powerset(powerset(succ(sK1))))
    | ~ ordinal(sK1)
    | ~ spl29_9 ),
    inference(resolution,[],[f371,f228]) ).

fof(f228,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,sK26(X0,X1))
      | set_difference(sK28(X0,X1,X3),singleton(X0)) = X3
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f362,plain,
    spl29_8,
    inference(avatar_contradiction_clause,[],[f361]) ).

fof(f361,plain,
    ( $false
    | spl29_8 ),
    inference(resolution,[],[f343,f128]) ).

fof(f128,plain,
    element(sK2,powerset(powerset(succ(sK1)))),
    inference(cnf_transformation,[],[f83]) ).

fof(f343,plain,
    ( ~ element(sK2,powerset(powerset(succ(sK1))))
    | spl29_8 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f360,plain,
    ( ~ spl29_7
    | ~ spl29_7 ),
    inference(avatar_split_clause,[],[f359,f337,f337]) ).

fof(f359,plain,
    ( ~ sP0(sK1,sK2)
    | ~ spl29_7 ),
    inference(trivial_inequality_removal,[],[f358]) ).

fof(f358,plain,
    ( sK22(sK1,sK2) != sK22(sK1,sK2)
    | ~ sP0(sK1,sK2)
    | ~ spl29_7 ),
    inference(superposition,[],[f224,f356]) ).

fof(f356,plain,
    ( sK23(sK1,sK2) = sK22(sK1,sK2)
    | ~ spl29_7 ),
    inference(superposition,[],[f351,f350]) ).

fof(f350,plain,
    ( sK23(sK1,sK2) = sK21(sK1,sK2)
    | ~ spl29_7 ),
    inference(resolution,[],[f339,f221]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | sK21(X0,X1) = sK23(X0,X1) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ( sK22(X0,X1) != sK23(X0,X1)
        & sK23(X0,X1) = set_difference(sK24(X0,X1),singleton(X0))
        & in(sK24(X0,X1),X1)
        & sK21(X0,X1) = sK23(X0,X1)
        & sK22(X0,X1) = set_difference(sK25(X0,X1),singleton(X0))
        & in(sK25(X0,X1),X1)
        & sK21(X0,X1) = sK22(X0,X1) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24,sK25])],[f116,f119,f118,f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ? [X2,X3,X4] :
          ( X3 != X4
          & ? [X5] :
              ( set_difference(X5,singleton(X0)) = X4
              & in(X5,X1) )
          & X2 = X4
          & ? [X6] :
              ( set_difference(X6,singleton(X0)) = X3
              & in(X6,X1) )
          & X2 = X3 )
     => ( sK22(X0,X1) != sK23(X0,X1)
        & ? [X5] :
            ( set_difference(X5,singleton(X0)) = sK23(X0,X1)
            & in(X5,X1) )
        & sK21(X0,X1) = sK23(X0,X1)
        & ? [X6] :
            ( set_difference(X6,singleton(X0)) = sK22(X0,X1)
            & in(X6,X1) )
        & sK21(X0,X1) = sK22(X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( set_difference(X5,singleton(X0)) = sK23(X0,X1)
          & in(X5,X1) )
     => ( sK23(X0,X1) = set_difference(sK24(X0,X1),singleton(X0))
        & in(sK24(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ? [X6] :
          ( set_difference(X6,singleton(X0)) = sK22(X0,X1)
          & in(X6,X1) )
     => ( sK22(X0,X1) = set_difference(sK25(X0,X1),singleton(X0))
        & in(sK25(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ? [X2,X3,X4] :
          ( X3 != X4
          & ? [X5] :
              ( set_difference(X5,singleton(X0)) = X4
              & in(X5,X1) )
          & X2 = X4
          & ? [X6] :
              ( set_difference(X6,singleton(X0)) = X3
              & in(X6,X1) )
          & X2 = X3 )
      | ~ sP0(X0,X1) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f339,plain,
    ( sP0(sK1,sK2)
    | ~ spl29_7 ),
    inference(avatar_component_clause,[],[f337]) ).

fof(f351,plain,
    ( sK22(sK1,sK2) = sK21(sK1,sK2)
    | ~ spl29_7 ),
    inference(resolution,[],[f339,f218]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | sK21(X0,X1) = sK22(X0,X1) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f224,plain,
    ! [X0,X1] :
      ( sK22(X0,X1) != sK23(X0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f347,plain,
    ( spl29_7
    | ~ spl29_8
    | spl29_9
    | ~ spl29_4 ),
    inference(avatar_split_clause,[],[f335,f318,f345,f341,f337]) ).

fof(f318,plain,
    ( spl29_4
  <=> ! [X0,X1] :
        ( ~ in(sK3(X0),powerset(sK1))
        | in(sK3(X0),X0)
        | ~ element(X1,powerset(powerset(succ(sK1))))
        | sP0(sK1,X1)
        | in(sK3(X0),sK26(sK1,X1))
        | ~ in(sK4(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl29_4])]) ).

fof(f335,plain,
    ( ! [X0] :
        ( in(sK3(X0),X0)
        | ~ element(sK2,powerset(powerset(succ(sK1))))
        | sP0(sK1,sK2)
        | in(sK3(X0),sK26(sK1,sK2))
        | ~ in(sK3(X0),powerset(sK1)) )
    | ~ spl29_4 ),
    inference(duplicate_literal_removal,[],[f334]) ).

fof(f334,plain,
    ( ! [X0] :
        ( in(sK3(X0),X0)
        | ~ element(sK2,powerset(powerset(succ(sK1))))
        | sP0(sK1,sK2)
        | in(sK3(X0),sK26(sK1,sK2))
        | ~ in(sK3(X0),powerset(sK1))
        | in(sK3(X0),X0) )
    | ~ spl29_4 ),
    inference(resolution,[],[f319,f130]) ).

fof(f130,plain,
    ! [X2] :
      ( in(sK4(X2),sK2)
      | in(sK3(X2),X2) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f319,plain,
    ( ! [X0,X1] :
        ( ~ in(sK4(X0),X1)
        | in(sK3(X0),X0)
        | ~ element(X1,powerset(powerset(succ(sK1))))
        | sP0(sK1,X1)
        | in(sK3(X0),sK26(sK1,X1))
        | ~ in(sK3(X0),powerset(sK1)) )
    | ~ spl29_4 ),
    inference(avatar_component_clause,[],[f318]) ).

fof(f324,plain,
    spl29_3,
    inference(avatar_contradiction_clause,[],[f321]) ).

fof(f321,plain,
    ( $false
    | spl29_3 ),
    inference(resolution,[],[f316,f127]) ).

fof(f127,plain,
    ordinal(sK1),
    inference(cnf_transformation,[],[f83]) ).

fof(f316,plain,
    ( ~ ordinal(sK1)
    | spl29_3 ),
    inference(avatar_component_clause,[],[f314]) ).

fof(f320,plain,
    ( ~ spl29_3
    | spl29_4 ),
    inference(avatar_split_clause,[],[f312,f318,f314]) ).

fof(f312,plain,
    ! [X0,X1] :
      ( ~ in(sK3(X0),powerset(sK1))
      | ~ in(sK4(X0),X1)
      | in(sK3(X0),sK26(sK1,X1))
      | sP0(sK1,X1)
      | ~ element(X1,powerset(powerset(succ(sK1))))
      | ~ ordinal(sK1)
      | in(sK3(X0),X0) ),
    inference(superposition,[],[f231,f131]) ).

fof(f131,plain,
    ! [X2] :
      ( sK3(X2) = set_difference(sK4(X2),singleton(sK1))
      | in(sK3(X2),X2) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f231,plain,
    ! [X0,X1,X5] :
      ( ~ in(set_difference(X5,singleton(X0)),powerset(X0))
      | ~ in(X5,X1)
      | in(set_difference(X5,singleton(X0)),sK26(X0,X1))
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(equality_resolution,[],[f230]) ).

fof(f230,plain,
    ! [X0,X1,X4,X5] :
      ( in(set_difference(X5,singleton(X0)),sK26(X0,X1))
      | ~ in(X5,X1)
      | set_difference(X5,singleton(X0)) != X4
      | ~ in(X4,powerset(X0))
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(equality_resolution,[],[f229]) ).

fof(f229,plain,
    ! [X3,X0,X1,X4,X5] :
      ( in(X3,sK26(X0,X1))
      | set_difference(X5,singleton(X0)) != X3
      | ~ in(X5,X1)
      | X3 != X4
      | ~ in(X4,powerset(X0))
      | sP0(X0,X1)
      | ~ element(X1,powerset(powerset(succ(X0))))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f126]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : SEU298+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 11:36:34 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.PxwB9m59L4/Vampire---4.8_8293
% 0.56/0.74  % (8408)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.56/0.74  % (8401)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.56/0.74  % (8403)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.56/0.74  % (8404)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.56/0.74  % (8402)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.56/0.74  % (8406)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.56/0.74  % (8405)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.56/0.74  % (8407)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.56/0.74  % (8408)Refutation not found, incomplete strategy% (8408)------------------------------
% 0.56/0.74  % (8408)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74  % (8408)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74  
% 0.56/0.74  % (8408)Memory used [KB]: 1153
% 0.56/0.74  % (8408)Time elapsed: 0.003 s
% 0.56/0.74  % (8408)Instructions burned: 6 (million)
% 0.56/0.75  % (8408)------------------------------
% 0.56/0.75  % (8408)------------------------------
% 0.56/0.75  % (8409)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.56/0.75  % (8405)Refutation not found, incomplete strategy% (8405)------------------------------
% 0.56/0.75  % (8405)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (8405)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  
% 0.56/0.75  % (8405)Memory used [KB]: 1146
% 0.56/0.75  % (8405)Time elapsed: 0.006 s
% 0.56/0.75  % (8405)Instructions burned: 7 (million)
% 0.56/0.75  % (8401)Refutation not found, incomplete strategy% (8401)------------------------------
% 0.56/0.75  % (8401)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (8401)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  
% 0.56/0.75  % (8401)Memory used [KB]: 1143
% 0.56/0.75  % (8401)Time elapsed: 0.006 s
% 0.56/0.75  % (8401)Instructions burned: 8 (million)
% 0.56/0.75  % (8406)Refutation not found, incomplete strategy% (8406)------------------------------
% 0.56/0.75  % (8406)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (8406)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.75  % (8405)------------------------------
% 0.56/0.75  % (8405)------------------------------
% 0.56/0.75  
% 0.56/0.75  % (8406)Memory used [KB]: 1144
% 0.56/0.75  % (8406)Time elapsed: 0.006 s
% 0.56/0.75  % (8406)Instructions burned: 7 (million)
% 0.56/0.75  % (8401)------------------------------
% 0.56/0.75  % (8401)------------------------------
% 0.56/0.75  % (8406)------------------------------
% 0.56/0.75  % (8406)------------------------------
% 0.56/0.75  % (8410)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.56/0.75  % (8402)First to succeed.
% 0.56/0.75  % (8411)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.56/0.75  % (8412)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.56/0.76  % (8402)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8400"
% 0.56/0.76  % (8402)Refutation found. Thanks to Tanya!
% 0.56/0.76  % SZS status Theorem for Vampire---4
% 0.56/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.56/0.76  % (8402)------------------------------
% 0.56/0.76  % (8402)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.76  % (8402)Termination reason: Refutation
% 0.56/0.76  
% 0.56/0.76  % (8402)Memory used [KB]: 1204
% 0.56/0.76  % (8402)Time elapsed: 0.013 s
% 0.56/0.76  % (8402)Instructions burned: 18 (million)
% 0.56/0.76  % (8400)Success in time 0.387 s
% 0.56/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------