TSTP Solution File: SEU009+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU009+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:31:43 EDT 2022

% Result   : Theorem 0.20s 0.56s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   82 (  18 unt;   0 def)
%            Number of atoms       :  342 (  46 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  437 ( 177   ~; 174   |;  66   &)
%                                         (   9 <=>;   9  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   8 con; 0-2 aty)
%            Number of variables   :  107 (  85   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f374,plain,
    $false,
    inference(subsumption_resolution,[],[f373,f367]) ).

fof(f367,plain,
    ~ in(sF14,sK7),
    inference(subsumption_resolution,[],[f366,f312]) ).

fof(f312,plain,
    ( ~ in(sF14,sK7)
    | ~ in(sK8,sF17) ),
    inference(resolution,[],[f291,f182]) ).

fof(f182,plain,
    ( ~ in(sK8,sF13)
    | ~ in(sK8,sF17)
    | ~ in(sF14,sK7) ),
    inference(definition_folding,[],[f157,f181,f180,f179,f178,f177]) ).

fof(f177,plain,
    sF13 = relation_dom(sK9),
    introduced(function_definition,[]) ).

fof(f178,plain,
    apply(sK9,sK8) = sF14,
    introduced(function_definition,[]) ).

fof(f179,plain,
    sF15 = identity_relation(sK7),
    introduced(function_definition,[]) ).

fof(f180,plain,
    sF16 = relation_composition(sK9,sF15),
    introduced(function_definition,[]) ).

fof(f181,plain,
    sF17 = relation_dom(sF16),
    introduced(function_definition,[]) ).

fof(f157,plain,
    ( ~ in(sK8,relation_dom(sK9))
    | ~ in(apply(sK9,sK8),sK7)
    | ~ in(sK8,relation_dom(relation_composition(sK9,identity_relation(sK7)))) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ( relation(sK9)
    & ( ~ in(sK8,relation_dom(sK9))
      | ~ in(apply(sK9,sK8),sK7)
      | ~ in(sK8,relation_dom(relation_composition(sK9,identity_relation(sK7)))) )
    & ( ( in(sK8,relation_dom(sK9))
        & in(apply(sK9,sK8),sK7) )
      | in(sK8,relation_dom(relation_composition(sK9,identity_relation(sK7)))) )
    & function(sK9) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f102,f103]) ).

fof(f103,plain,
    ( ? [X0,X1,X2] :
        ( relation(X2)
        & ( ~ in(X1,relation_dom(X2))
          | ~ in(apply(X2,X1),X0)
          | ~ in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
        & ( ( in(X1,relation_dom(X2))
            & in(apply(X2,X1),X0) )
          | in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
        & function(X2) )
   => ( relation(sK9)
      & ( ~ in(sK8,relation_dom(sK9))
        | ~ in(apply(sK9,sK8),sK7)
        | ~ in(sK8,relation_dom(relation_composition(sK9,identity_relation(sK7)))) )
      & ( ( in(sK8,relation_dom(sK9))
          & in(apply(sK9,sK8),sK7) )
        | in(sK8,relation_dom(relation_composition(sK9,identity_relation(sK7)))) )
      & function(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ? [X0,X1,X2] :
      ( relation(X2)
      & ( ~ in(X1,relation_dom(X2))
        | ~ in(apply(X2,X1),X0)
        | ~ in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
      & ( ( in(X1,relation_dom(X2))
          & in(apply(X2,X1),X0) )
        | in(X1,relation_dom(relation_composition(X2,identity_relation(X0)))) )
      & function(X2) ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ? [X2,X1,X0] :
      ( relation(X0)
      & ( ~ in(X1,relation_dom(X0))
        | ~ in(apply(X0,X1),X2)
        | ~ in(X1,relation_dom(relation_composition(X0,identity_relation(X2)))) )
      & ( ( in(X1,relation_dom(X0))
          & in(apply(X0,X1),X2) )
        | in(X1,relation_dom(relation_composition(X0,identity_relation(X2)))) )
      & function(X0) ),
    inference(flattening,[],[f100]) ).

fof(f100,plain,
    ? [X2,X1,X0] :
      ( relation(X0)
      & ( ~ in(X1,relation_dom(X0))
        | ~ in(apply(X0,X1),X2)
        | ~ in(X1,relation_dom(relation_composition(X0,identity_relation(X2)))) )
      & ( ( in(X1,relation_dom(X0))
          & in(apply(X0,X1),X2) )
        | in(X1,relation_dom(relation_composition(X0,identity_relation(X2)))) )
      & function(X0) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f72,plain,
    ? [X2,X1,X0] :
      ( relation(X0)
      & ( in(X1,relation_dom(relation_composition(X0,identity_relation(X2))))
      <~> ( in(X1,relation_dom(X0))
          & in(apply(X0,X1),X2) ) )
      & function(X0) ),
    inference(flattening,[],[f71]) ).

fof(f71,plain,
    ? [X2,X0,X1] :
      ( ( in(X1,relation_dom(relation_composition(X0,identity_relation(X2))))
      <~> ( in(X1,relation_dom(X0))
          & in(apply(X0,X1),X2) ) )
      & relation(X0)
      & function(X0) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,plain,
    ~ ! [X2,X0,X1] :
        ( ( relation(X0)
          & function(X0) )
       => ( in(X1,relation_dom(relation_composition(X0,identity_relation(X2))))
        <=> ( in(X1,relation_dom(X0))
            & in(apply(X0,X1),X2) ) ) ),
    inference(rectify,[],[f32]) ).

fof(f32,negated_conjecture,
    ~ ! [X2,X1,X0] :
        ( ( function(X2)
          & relation(X2) )
       => ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
        <=> ( in(apply(X2,X1),X0)
            & in(X1,relation_dom(X2)) ) ) ),
    inference(negated_conjecture,[],[f31]) ).

fof(f31,conjecture,
    ! [X2,X1,X0] :
      ( ( function(X2)
        & relation(X2) )
     => ( in(X1,relation_dom(relation_composition(X2,identity_relation(X0))))
      <=> ( in(apply(X2,X1),X0)
          & in(X1,relation_dom(X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_1) ).

fof(f291,plain,
    in(sK8,sF13),
    inference(duplicate_literal_removal,[],[f290]) ).

fof(f290,plain,
    ( in(sK8,sF13)
    | in(sK8,sF13) ),
    inference(resolution,[],[f288,f183]) ).

fof(f183,plain,
    ( in(sK8,sF17)
    | in(sK8,sF13) ),
    inference(definition_folding,[],[f156,f181,f180,f179,f177]) ).

fof(f156,plain,
    ( in(sK8,relation_dom(sK9))
    | in(sK8,relation_dom(relation_composition(sK9,identity_relation(sK7)))) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f288,plain,
    ! [X0] :
      ( ~ in(X0,sF17)
      | in(X0,sF13) ),
    inference(forward_demodulation,[],[f287,f177]) ).

fof(f287,plain,
    ! [X0] :
      ( ~ in(X0,sF17)
      | in(X0,relation_dom(sK9)) ),
    inference(forward_demodulation,[],[f286,f181]) ).

fof(f286,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF16))
      | in(X0,relation_dom(sK9)) ),
    inference(subsumption_resolution,[],[f285,f158]) ).

fof(f158,plain,
    relation(sK9),
    inference(cnf_transformation,[],[f104]) ).

fof(f285,plain,
    ! [X0] :
      ( ~ relation(sK9)
      | ~ in(X0,relation_dom(sF16))
      | in(X0,relation_dom(sK9)) ),
    inference(subsumption_resolution,[],[f284,f188]) ).

fof(f188,plain,
    relation(sF15),
    inference(superposition,[],[f136,f179]) ).

fof(f136,plain,
    ! [X0] : relation(identity_relation(X0)),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( function(identity_relation(X0))
      & relation(identity_relation(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).

fof(f284,plain,
    ! [X0] :
      ( ~ relation(sF15)
      | ~ in(X0,relation_dom(sF16))
      | ~ relation(sK9)
      | in(X0,relation_dom(sK9)) ),
    inference(subsumption_resolution,[],[f283,f187]) ).

fof(f187,plain,
    function(sF15),
    inference(superposition,[],[f137,f179]) ).

fof(f137,plain,
    ! [X0] : function(identity_relation(X0)),
    inference(cnf_transformation,[],[f12]) ).

fof(f283,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF16))
      | ~ function(sF15)
      | in(X0,relation_dom(sK9))
      | ~ relation(sK9)
      | ~ relation(sF15) ),
    inference(subsumption_resolution,[],[f280,f154]) ).

fof(f154,plain,
    function(sK9),
    inference(cnf_transformation,[],[f104]) ).

fof(f280,plain,
    ! [X0] :
      ( ~ function(sK9)
      | in(X0,relation_dom(sK9))
      | ~ relation(sF15)
      | ~ in(X0,relation_dom(sF16))
      | ~ function(sF15)
      | ~ relation(sK9) ),
    inference(superposition,[],[f148,f180]) ).

fof(f148,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,relation_dom(relation_composition(X2,X0)))
      | ~ relation(X0)
      | in(X1,relation_dom(X2))
      | ~ relation(X2)
      | ~ function(X0)
      | ~ function(X2) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ relation(X2)
          | ( ( in(X1,relation_dom(relation_composition(X2,X0)))
              | ~ in(apply(X2,X1),relation_dom(X0))
              | ~ in(X1,relation_dom(X2)) )
            & ( ( in(apply(X2,X1),relation_dom(X0))
                & in(X1,relation_dom(X2)) )
              | ~ in(X1,relation_dom(relation_composition(X2,X0))) ) )
          | ~ function(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f96]) ).

fof(f96,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ relation(X2)
          | ( ( in(X0,relation_dom(relation_composition(X2,X1)))
              | ~ in(apply(X2,X0),relation_dom(X1))
              | ~ in(X0,relation_dom(X2)) )
            & ( ( in(apply(X2,X0),relation_dom(X1))
                & in(X0,relation_dom(X2)) )
              | ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
          | ~ function(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f95]) ).

fof(f95,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ relation(X2)
          | ( ( in(X0,relation_dom(relation_composition(X2,X1)))
              | ~ in(apply(X2,X0),relation_dom(X1))
              | ~ in(X0,relation_dom(X2)) )
            & ( ( in(apply(X2,X0),relation_dom(X1))
                & in(X0,relation_dom(X2)) )
              | ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
          | ~ function(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ relation(X2)
          | ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) )
          | ~ function(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) )
          | ~ relation(X2)
          | ~ function(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X1,X0] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).

fof(f366,plain,
    ( ~ in(sF14,sK7)
    | in(sK8,sF17) ),
    inference(forward_demodulation,[],[f365,f181]) ).

fof(f365,plain,
    ( in(sK8,relation_dom(sF16))
    | ~ in(sF14,sK7) ),
    inference(forward_demodulation,[],[f364,f236]) ).

fof(f236,plain,
    sK7 = relation_dom(sF15),
    inference(subsumption_resolution,[],[f235,f187]) ).

fof(f235,plain,
    ( ~ function(sF15)
    | sK7 = relation_dom(sF15) ),
    inference(superposition,[],[f185,f179]) ).

fof(f185,plain,
    ! [X1] :
      ( ~ function(identity_relation(X1))
      | relation_dom(identity_relation(X1)) = X1 ),
    inference(subsumption_resolution,[],[f173,f136]) ).

fof(f173,plain,
    ! [X1] :
      ( ~ relation(identity_relation(X1))
      | ~ function(identity_relation(X1))
      | relation_dom(identity_relation(X1)) = X1 ),
    inference(equality_resolution,[],[f163]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( relation_dom(X0) = X1
      | identity_relation(X1) != X0
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ( ( ( relation_dom(X0) = X1
            & ! [X2] :
                ( ~ in(X2,X1)
                | apply(X0,X2) = X2 ) )
          | identity_relation(X1) != X0 )
        & ( identity_relation(X1) = X0
          | relation_dom(X0) != X1
          | ( in(sK10(X0,X1),X1)
            & apply(X0,sK10(X0,X1)) != sK10(X0,X1) ) ) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f108,f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X1)
          & apply(X0,X3) != X3 )
     => ( in(sK10(X0,X1),X1)
        & apply(X0,sK10(X0,X1)) != sK10(X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ( ( ( relation_dom(X0) = X1
            & ! [X2] :
                ( ~ in(X2,X1)
                | apply(X0,X2) = X2 ) )
          | identity_relation(X1) != X0 )
        & ( identity_relation(X1) = X0
          | relation_dom(X0) != X1
          | ? [X3] :
              ( in(X3,X1)
              & apply(X0,X3) != X3 ) ) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(rectify,[],[f107]) ).

fof(f107,plain,
    ! [X1,X0] :
      ( ( ( ( relation_dom(X1) = X0
            & ! [X2] :
                ( ~ in(X2,X0)
                | apply(X1,X2) = X2 ) )
          | identity_relation(X0) != X1 )
        & ( identity_relation(X0) = X1
          | relation_dom(X1) != X0
          | ? [X2] :
              ( in(X2,X0)
              & apply(X1,X2) != X2 ) ) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(flattening,[],[f106]) ).

fof(f106,plain,
    ! [X1,X0] :
      ( ( ( ( relation_dom(X1) = X0
            & ! [X2] :
                ( ~ in(X2,X0)
                | apply(X1,X2) = X2 ) )
          | identity_relation(X0) != X1 )
        & ( identity_relation(X0) = X1
          | relation_dom(X1) != X0
          | ? [X2] :
              ( in(X2,X0)
              & apply(X1,X2) != X2 ) ) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(nnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X1,X0] :
      ( ( ( relation_dom(X1) = X0
          & ! [X2] :
              ( ~ in(X2,X0)
              | apply(X1,X2) = X2 ) )
      <=> identity_relation(X0) = X1 )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(flattening,[],[f60]) ).

fof(f60,plain,
    ! [X1,X0] :
      ( ( ( relation_dom(X1) = X0
          & ! [X2] :
              ( ~ in(X2,X0)
              | apply(X1,X2) = X2 ) )
      <=> identity_relation(X0) = X1 )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X1,X0] :
      ( ( function(X1)
        & relation(X1) )
     => ( ( ! [X2] :
              ( in(X2,X0)
             => apply(X1,X2) = X2 )
          & relation_dom(X1) = X0 )
      <=> identity_relation(X0) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).

fof(f364,plain,
    ( ~ in(sF14,relation_dom(sF15))
    | in(sK8,relation_dom(sF16)) ),
    inference(subsumption_resolution,[],[f363,f188]) ).

fof(f363,plain,
    ( ~ relation(sF15)
    | ~ in(sF14,relation_dom(sF15))
    | in(sK8,relation_dom(sF16)) ),
    inference(subsumption_resolution,[],[f354,f187]) ).

fof(f354,plain,
    ( ~ in(sF14,relation_dom(sF15))
    | ~ function(sF15)
    | ~ relation(sF15)
    | in(sK8,relation_dom(sF16)) ),
    inference(superposition,[],[f328,f180]) ).

fof(f328,plain,
    ! [X0] :
      ( in(sK8,relation_dom(relation_composition(sK9,X0)))
      | ~ relation(X0)
      | ~ function(X0)
      | ~ in(sF14,relation_dom(X0)) ),
    inference(subsumption_resolution,[],[f327,f291]) ).

fof(f327,plain,
    ! [X0] :
      ( in(sK8,relation_dom(relation_composition(sK9,X0)))
      | ~ in(sK8,sF13)
      | ~ function(X0)
      | ~ in(sF14,relation_dom(X0))
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f326,f177]) ).

fof(f326,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ~ in(sK8,relation_dom(sK9))
      | ~ in(sF14,relation_dom(X0))
      | in(sK8,relation_dom(relation_composition(sK9,X0))) ),
    inference(subsumption_resolution,[],[f325,f154]) ).

fof(f325,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ in(sF14,relation_dom(X0))
      | ~ in(sK8,relation_dom(sK9))
      | ~ function(sK9)
      | ~ relation(X0)
      | in(sK8,relation_dom(relation_composition(sK9,X0))) ),
    inference(subsumption_resolution,[],[f315,f158]) ).

fof(f315,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ in(sK8,relation_dom(sK9))
      | ~ in(sF14,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(sK9)
      | ~ function(sK9)
      | in(sK8,relation_dom(relation_composition(sK9,X0))) ),
    inference(superposition,[],[f150,f178]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( ~ in(apply(X2,X1),relation_dom(X0))
      | ~ relation(X2)
      | ~ in(X1,relation_dom(X2))
      | ~ function(X0)
      | ~ relation(X0)
      | ~ function(X2)
      | in(X1,relation_dom(relation_composition(X2,X0))) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f373,plain,
    in(sF14,sK7),
    inference(forward_demodulation,[],[f369,f178]) ).

fof(f369,plain,
    in(apply(sK9,sK8),sK7),
    inference(resolution,[],[f368,f300]) ).

fof(f300,plain,
    ! [X0] :
      ( ~ in(X0,sF17)
      | in(apply(sK9,X0),sK7) ),
    inference(forward_demodulation,[],[f299,f236]) ).

fof(f299,plain,
    ! [X0] :
      ( in(apply(sK9,X0),relation_dom(sF15))
      | ~ in(X0,sF17) ),
    inference(forward_demodulation,[],[f298,f181]) ).

fof(f298,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF16))
      | in(apply(sK9,X0),relation_dom(sF15)) ),
    inference(subsumption_resolution,[],[f297,f187]) ).

fof(f297,plain,
    ! [X0] :
      ( ~ function(sF15)
      | in(apply(sK9,X0),relation_dom(sF15))
      | ~ in(X0,relation_dom(sF16)) ),
    inference(subsumption_resolution,[],[f296,f188]) ).

fof(f296,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF16))
      | ~ relation(sF15)
      | ~ function(sF15)
      | in(apply(sK9,X0),relation_dom(sF15)) ),
    inference(subsumption_resolution,[],[f295,f154]) ).

fof(f295,plain,
    ! [X0] :
      ( ~ function(sK9)
      | ~ relation(sF15)
      | in(apply(sK9,X0),relation_dom(sF15))
      | ~ function(sF15)
      | ~ in(X0,relation_dom(sF16)) ),
    inference(subsumption_resolution,[],[f294,f158]) ).

fof(f294,plain,
    ! [X0] :
      ( ~ relation(sK9)
      | in(apply(sK9,X0),relation_dom(sF15))
      | ~ function(sF15)
      | ~ in(X0,relation_dom(sF16))
      | ~ function(sK9)
      | ~ relation(sF15) ),
    inference(superposition,[],[f149,f180]) ).

fof(f149,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,relation_dom(relation_composition(X2,X0)))
      | ~ function(X0)
      | in(apply(X2,X1),relation_dom(X0))
      | ~ relation(X0)
      | ~ relation(X2)
      | ~ function(X2) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f368,plain,
    in(sK8,sF17),
    inference(resolution,[],[f367,f184]) ).

fof(f184,plain,
    ( in(sF14,sK7)
    | in(sK8,sF17) ),
    inference(definition_folding,[],[f155,f181,f180,f179,f178]) ).

fof(f155,plain,
    ( in(apply(sK9,sK8),sK7)
    | in(sK8,relation_dom(relation_composition(sK9,identity_relation(sK7)))) ),
    inference(cnf_transformation,[],[f104]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : SEU009+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 14:35:41 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.20/0.49  % (31597)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)
% 0.20/0.49  % (31596)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)
% 0.20/0.49  % (31614)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)
% 0.20/0.50  % (31602)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.50  % (31613)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.50  % (31605)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)
% 0.20/0.50  % (31604)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.50  % (31599)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)
% 0.20/0.51  % (31594)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)
% 0.20/0.52  % (31595)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)
% 0.20/0.52  % (31602)Instruction limit reached!
% 0.20/0.52  % (31602)------------------------------
% 0.20/0.52  % (31602)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (31602)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (31602)Termination reason: Unknown
% 0.20/0.52  % (31602)Termination phase: Preprocessing 1
% 0.20/0.52  
% 0.20/0.52  % (31602)Memory used [KB]: 895
% 0.20/0.52  % (31602)Time elapsed: 0.002 s
% 0.20/0.52  % (31602)Instructions burned: 2 (million)
% 0.20/0.52  % (31602)------------------------------
% 0.20/0.52  % (31602)------------------------------
% 0.20/0.52  % (31624)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)
% 0.20/0.52  % (31595)Refutation not found, incomplete strategy% (31595)------------------------------
% 0.20/0.52  % (31595)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (31623)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.52  % (31620)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.52  % (31612)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.52  % (31600)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)
% 0.20/0.52  % (31598)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  % (31603)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)
% 0.20/0.52  TRYING [1]
% 0.20/0.52  % (31621)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)
% 0.20/0.52  % (31601)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53  TRYING [2]
% 0.20/0.53  % (31615)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)
% 0.20/0.53  % (31617)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)
% 0.20/0.53  TRYING [1]
% 0.20/0.53  TRYING [2]
% 0.20/0.53  % (31616)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.53  TRYING [3]
% 0.20/0.53  TRYING [3]
% 0.20/0.53  % (31611)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53  % (31610)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)
% 0.20/0.53  % (31595)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (31595)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53  
% 0.20/0.53  % (31595)Memory used [KB]: 5500
% 0.20/0.53  % (31595)Time elapsed: 0.125 s
% 0.20/0.53  % (31595)Instructions burned: 4 (million)
% 0.20/0.53  % (31595)------------------------------
% 0.20/0.53  % (31595)------------------------------
% 0.20/0.53  TRYING [1]
% 0.20/0.53  TRYING [2]
% 0.20/0.53  TRYING [3]
% 0.20/0.53  % (31608)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.53  % (31622)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)
% 0.20/0.54  % (31618)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)
% 0.20/0.54  % (31609)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)
% 0.20/0.54  % (31606)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.54  TRYING [4]
% 0.20/0.54  % (31619)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.55  TRYING [4]
% 0.20/0.55  % (31622)First to succeed.
% 0.20/0.55  % (31601)Instruction limit reached!
% 0.20/0.55  % (31601)------------------------------
% 0.20/0.55  % (31601)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (31601)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (31601)Termination reason: Unknown
% 0.20/0.55  % (31601)Termination phase: Saturation
% 0.20/0.55  
% 0.20/0.55  % (31601)Memory used [KB]: 5628
% 0.20/0.55  % (31601)Time elapsed: 0.104 s
% 0.20/0.55  % (31601)Instructions burned: 8 (million)
% 0.20/0.55  % (31601)------------------------------
% 0.20/0.55  % (31601)------------------------------
% 0.20/0.55  % (31597)Instruction limit reached!
% 0.20/0.55  % (31597)------------------------------
% 0.20/0.55  % (31597)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (31622)Refutation found. Thanks to Tanya!
% 0.20/0.56  % SZS status Theorem for theBenchmark
% 0.20/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.56  % (31622)------------------------------
% 0.20/0.56  % (31622)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (31622)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (31622)Termination reason: Refutation
% 0.20/0.56  
% 0.20/0.56  % (31622)Memory used [KB]: 1151
% 0.20/0.56  % (31622)Time elapsed: 0.154 s
% 0.20/0.56  % (31622)Instructions burned: 12 (million)
% 0.20/0.56  % (31622)------------------------------
% 0.20/0.56  % (31622)------------------------------
% 0.20/0.56  % (31590)Success in time 0.216 s
%------------------------------------------------------------------------------