TSTP Solution File: SEU203+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU203+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n027.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 : Thu Aug 31 17:56:46 EDT 2023

% Result   : Theorem 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   72 (  14 unt;   0 def)
%            Number of atoms       :  305 (  19 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  363 ( 130   ~; 133   |;  73   &)
%                                         (  14 <=>;  12  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   7 con; 0-3 aty)
%            Number of variables   :  191 (; 140   !;  51   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f312,plain,
    $false,
    inference(subsumption_resolution,[],[f311,f223]) ).

fof(f223,plain,
    in(sK2,sF20),
    inference(subsumption_resolution,[],[f222,f133]) ).

fof(f133,plain,
    ( in(sF21,sK4)
    | in(sK2,sF20) ),
    inference(definition_folding,[],[f81,f129,f132]) ).

fof(f132,plain,
    ordered_pair(sK5,sK2) = sF21,
    introduced(function_definition,[]) ).

fof(f129,plain,
    relation_image(sK4,sK3) = sF20,
    introduced(function_definition,[]) ).

fof(f81,plain,
    ( in(ordered_pair(sK5,sK2),sK4)
    | in(sK2,relation_image(sK4,sK3)) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ( ( ! [X3] :
          ( ~ in(X3,sK3)
          | ~ in(ordered_pair(X3,sK2),sK4)
          | ~ in(X3,relation_dom(sK4)) )
      | ~ in(sK2,relation_image(sK4,sK3)) )
    & ( ( in(sK5,sK3)
        & in(ordered_pair(sK5,sK2),sK4)
        & in(sK5,relation_dom(sK4)) )
      | in(sK2,relation_image(sK4,sK3)) )
    & relation(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f52,f54,f53]) ).

fof(f53,plain,
    ( ? [X0,X1,X2] :
        ( ( ! [X3] :
              ( ~ in(X3,X1)
              | ~ in(ordered_pair(X3,X0),X2)
              | ~ in(X3,relation_dom(X2)) )
          | ~ in(X0,relation_image(X2,X1)) )
        & ( ? [X4] :
              ( in(X4,X1)
              & in(ordered_pair(X4,X0),X2)
              & in(X4,relation_dom(X2)) )
          | in(X0,relation_image(X2,X1)) )
        & relation(X2) )
   => ( ( ! [X3] :
            ( ~ in(X3,sK3)
            | ~ in(ordered_pair(X3,sK2),sK4)
            | ~ in(X3,relation_dom(sK4)) )
        | ~ in(sK2,relation_image(sK4,sK3)) )
      & ( ? [X4] :
            ( in(X4,sK3)
            & in(ordered_pair(X4,sK2),sK4)
            & in(X4,relation_dom(sK4)) )
        | in(sK2,relation_image(sK4,sK3)) )
      & relation(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ( ? [X4] :
        ( in(X4,sK3)
        & in(ordered_pair(X4,sK2),sK4)
        & in(X4,relation_dom(sK4)) )
   => ( in(sK5,sK3)
      & in(ordered_pair(sK5,sK2),sK4)
      & in(sK5,relation_dom(sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ? [X0,X1,X2] :
      ( ( ! [X3] :
            ( ~ in(X3,X1)
            | ~ in(ordered_pair(X3,X0),X2)
            | ~ in(X3,relation_dom(X2)) )
        | ~ in(X0,relation_image(X2,X1)) )
      & ( ? [X4] :
            ( in(X4,X1)
            & in(ordered_pair(X4,X0),X2)
            & in(X4,relation_dom(X2)) )
        | in(X0,relation_image(X2,X1)) )
      & relation(X2) ),
    inference(rectify,[],[f51]) ).

fof(f51,plain,
    ? [X0,X1,X2] :
      ( ( ! [X3] :
            ( ~ in(X3,X1)
            | ~ in(ordered_pair(X3,X0),X2)
            | ~ in(X3,relation_dom(X2)) )
        | ~ in(X0,relation_image(X2,X1)) )
      & ( ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X3,X0),X2)
            & in(X3,relation_dom(X2)) )
        | in(X0,relation_image(X2,X1)) )
      & relation(X2) ),
    inference(flattening,[],[f50]) ).

fof(f50,plain,
    ? [X0,X1,X2] :
      ( ( ! [X3] :
            ( ~ in(X3,X1)
            | ~ in(ordered_pair(X3,X0),X2)
            | ~ in(X3,relation_dom(X2)) )
        | ~ in(X0,relation_image(X2,X1)) )
      & ( ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X3,X0),X2)
            & in(X3,relation_dom(X2)) )
        | in(X0,relation_image(X2,X1)) )
      & relation(X2) ),
    inference(nnf_transformation,[],[f33]) ).

fof(f33,plain,
    ? [X0,X1,X2] :
      ( ( in(X0,relation_image(X2,X1))
      <~> ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X3,X0),X2)
            & in(X3,relation_dom(X2)) ) )
      & relation(X2) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( relation(X2)
       => ( in(X0,relation_image(X2,X1))
        <=> ? [X3] :
              ( in(X3,X1)
              & in(ordered_pair(X3,X0),X2)
              & in(X3,relation_dom(X2)) ) ) ),
    inference(negated_conjecture,[],[f26]) ).

fof(f26,conjecture,
    ! [X0,X1,X2] :
      ( relation(X2)
     => ( in(X0,relation_image(X2,X1))
      <=> ? [X3] :
            ( in(X3,X1)
            & in(ordered_pair(X3,X0),X2)
            & in(X3,relation_dom(X2)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.cf1rV0Jyr6/Vampire---4.8_28523',t143_relat_1) ).

fof(f222,plain,
    ( ~ in(sF21,sK4)
    | in(sK2,sF20) ),
    inference(subsumption_resolution,[],[f220,f131]) ).

fof(f131,plain,
    ( in(sK5,sK3)
    | in(sK2,sF20) ),
    inference(definition_folding,[],[f82,f129]) ).

fof(f82,plain,
    ( in(sK5,sK3)
    | in(sK2,relation_image(sK4,sK3)) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f220,plain,
    ( ~ in(sF21,sK4)
    | ~ in(sK5,sK3)
    | in(sK2,sF20) ),
    inference(superposition,[],[f219,f132]) ).

fof(f219,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),sK4)
      | ~ in(X0,sK3)
      | in(X1,sF20) ),
    inference(resolution,[],[f126,f215]) ).

fof(f215,plain,
    ! [X3] :
      ( sP17(sK4,sK3,X3)
      | in(X3,sF20) ),
    inference(resolution,[],[f125,f170]) ).

fof(f170,plain,
    sP0(sK3,sK4,sF20),
    inference(subsumption_resolution,[],[f169,f79]) ).

fof(f79,plain,
    relation(sK4),
    inference(cnf_transformation,[],[f55]) ).

fof(f169,plain,
    ( sP0(sK3,sK4,sF20)
    | ~ relation(sK4) ),
    inference(superposition,[],[f168,f129]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( sP0(X0,X1,relation_image(X1,X0))
      | ~ relation(X1) ),
    inference(resolution,[],[f124,f100]) ).

fof(f100,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ relation(X0) ),
    inference(definition_folding,[],[f35,f48,f47]) ).

fof(f47,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4] :
              ( in(X4,X1)
              & in(ordered_pair(X4,X3),X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f48,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_image(X0,X1) = X2
        <=> sP0(X1,X0,X2) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f35,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X4,X3),X0) ) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1,X2] :
          ( relation_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X4,X3),X0) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.cf1rV0Jyr6/Vampire---4.8_28523',d13_relat_1) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ~ sP1(X0)
      | sP0(X1,X0,relation_image(X0,X1)) ),
    inference(equality_resolution,[],[f92]) ).

fof(f92,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X0,X2)
      | relation_image(X0,X1) != X2
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_image(X0,X1) = X2
            | ~ sP0(X1,X0,X2) )
          & ( sP0(X1,X0,X2)
            | relation_image(X0,X1) != X2 ) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f125,plain,
    ! [X2,X0,X1,X6] :
      ( ~ sP0(X0,X1,X2)
      | in(X6,X2)
      | sP17(X1,X0,X6) ),
    inference(cnf_transformation,[],[f125_D]) ).

fof(f125_D,plain,
    ! [X6,X0,X1] :
      ( ! [X2] :
          ( ~ sP0(X0,X1,X2)
          | in(X6,X2) )
    <=> ~ sP17(X1,X0,X6) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP17])]) ).

fof(f126,plain,
    ! [X0,X1,X6,X7] :
      ( ~ sP17(X1,X0,X6)
      | ~ in(ordered_pair(X7,X6),X1)
      | ~ in(X7,X0) ),
    inference(general_splitting,[],[f96,f125_D]) ).

fof(f96,plain,
    ! [X2,X0,X1,X6,X7] :
      ( in(X6,X2)
      | ~ in(X7,X0)
      | ~ in(ordered_pair(X7,X6),X1)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ! [X4] :
                ( ~ in(X4,X0)
                | ~ in(ordered_pair(X4,sK9(X0,X1,X2)),X1) )
            | ~ in(sK9(X0,X1,X2),X2) )
          & ( ( in(sK10(X0,X1,X2),X0)
              & in(ordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)),X1) )
            | in(sK9(X0,X1,X2),X2) ) ) )
      & ( ! [X6] :
            ( ( in(X6,X2)
              | ! [X7] :
                  ( ~ in(X7,X0)
                  | ~ in(ordered_pair(X7,X6),X1) ) )
            & ( ( in(sK11(X0,X1,X6),X0)
                & in(ordered_pair(sK11(X0,X1,X6),X6),X1) )
              | ~ in(X6,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f64,f67,f66,f65]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4] :
                ( ~ in(X4,X0)
                | ~ in(ordered_pair(X4,X3),X1) )
            | ~ in(X3,X2) )
          & ( ? [X5] :
                ( in(X5,X0)
                & in(ordered_pair(X5,X3),X1) )
            | in(X3,X2) ) )
     => ( ( ! [X4] :
              ( ~ in(X4,X0)
              | ~ in(ordered_pair(X4,sK9(X0,X1,X2)),X1) )
          | ~ in(sK9(X0,X1,X2),X2) )
        & ( ? [X5] :
              ( in(X5,X0)
              & in(ordered_pair(X5,sK9(X0,X1,X2)),X1) )
          | in(sK9(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( in(X5,X0)
          & in(ordered_pair(X5,sK9(X0,X1,X2)),X1) )
     => ( in(sK10(X0,X1,X2),X0)
        & in(ordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ! [X0,X1,X6] :
      ( ? [X8] :
          ( in(X8,X0)
          & in(ordered_pair(X8,X6),X1) )
     => ( in(sK11(X0,X1,X6),X0)
        & in(ordered_pair(sK11(X0,X1,X6),X6),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ( ! [X4] :
                  ( ~ in(X4,X0)
                  | ~ in(ordered_pair(X4,X3),X1) )
              | ~ in(X3,X2) )
            & ( ? [X5] :
                  ( in(X5,X0)
                  & in(ordered_pair(X5,X3),X1) )
              | in(X3,X2) ) ) )
      & ( ! [X6] :
            ( ( in(X6,X2)
              | ! [X7] :
                  ( ~ in(X7,X0)
                  | ~ in(ordered_pair(X7,X6),X1) ) )
            & ( ? [X8] :
                  ( in(X8,X0)
                  & in(ordered_pair(X8,X6),X1) )
              | ~ in(X6,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ! [X4] :
                  ( ~ in(X4,X1)
                  | ~ in(ordered_pair(X4,X3),X0) )
              | ~ in(X3,X2) )
            & ( ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X4,X3),X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ! [X4] :
                  ( ~ in(X4,X1)
                  | ~ in(ordered_pair(X4,X3),X0) ) )
            & ( ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X4,X3),X0) )
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f311,plain,
    ~ in(sK2,sF20),
    inference(resolution,[],[f308,f249]) ).

fof(f249,plain,
    ! [X3] :
      ( in(sK11(sK3,sK4,X3),sK3)
      | ~ in(X3,sF20) ),
    inference(resolution,[],[f95,f170]) ).

fof(f95,plain,
    ! [X2,X0,X1,X6] :
      ( ~ sP0(X0,X1,X2)
      | ~ in(X6,X2)
      | in(sK11(X0,X1,X6),X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f308,plain,
    ~ in(sK11(sK3,sK4,sK2),sK3),
    inference(subsumption_resolution,[],[f303,f307]) ).

fof(f307,plain,
    in(sK11(sK3,sK4,sK2),sF19),
    inference(forward_demodulation,[],[f306,f128]) ).

fof(f128,plain,
    relation_dom(sK4) = sF19,
    introduced(function_definition,[]) ).

fof(f306,plain,
    in(sK11(sK3,sK4,sK2),relation_dom(sK4)),
    inference(subsumption_resolution,[],[f304,f79]) ).

fof(f304,plain,
    ( in(sK11(sK3,sK4,sK2),relation_dom(sK4))
    | ~ relation(sK4) ),
    inference(resolution,[],[f302,f209]) ).

fof(f209,plain,
    ! [X2,X1] :
      ( ~ in(sF18(X1),X2)
      | in(X1,relation_dom(X2))
      | ~ relation(X2) ),
    inference(superposition,[],[f122,f127]) ).

fof(f127,plain,
    ! [X3] : ordered_pair(X3,sK2) = sF18(X3),
    introduced(function_definition,[]) ).

fof(f122,plain,
    ! [X0,X6,X5] :
      ( ~ in(ordered_pair(X5,X6),X0)
      | in(X5,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X5,X6),X0)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(sK6(X0,X1),X3),X0)
                | ~ in(sK6(X0,X1),X1) )
              & ( in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
                | in(sK6(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( in(ordered_pair(X5,sK8(X0,X5)),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f57,f60,f59,f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X2,X4),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(sK6(X0,X1),X3),X0)
          | ~ in(sK6(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(sK6(X0,X1),X4),X0)
          | in(sK6(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(sK6(X0,X1),X4),X0)
     => in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X5,X7),X0)
     => in(ordered_pair(X5,sK8(X0,X5)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X2,X4),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( ? [X7] : in(ordered_pair(X5,X7),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.cf1rV0Jyr6/Vampire---4.8_28523',d4_relat_1) ).

fof(f302,plain,
    in(sF18(sK11(sK3,sK4,sK2)),sK4),
    inference(forward_demodulation,[],[f300,f127]) ).

fof(f300,plain,
    in(ordered_pair(sK11(sK3,sK4,sK2),sK2),sK4),
    inference(resolution,[],[f299,f223]) ).

fof(f299,plain,
    ! [X3] :
      ( ~ in(X3,sF20)
      | in(ordered_pair(sK11(sK3,sK4,X3),X3),sK4) ),
    inference(resolution,[],[f94,f170]) ).

fof(f94,plain,
    ! [X2,X0,X1,X6] :
      ( ~ sP0(X0,X1,X2)
      | ~ in(X6,X2)
      | in(ordered_pair(sK11(X0,X1,X6),X6),X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f303,plain,
    ( ~ in(sK11(sK3,sK4,sK2),sF19)
    | ~ in(sK11(sK3,sK4,sK2),sK3) ),
    inference(resolution,[],[f302,f224]) ).

fof(f224,plain,
    ! [X3] :
      ( ~ in(sF18(X3),sK4)
      | ~ in(X3,sF19)
      | ~ in(X3,sK3) ),
    inference(subsumption_resolution,[],[f130,f223]) ).

fof(f130,plain,
    ! [X3] :
      ( ~ in(sK2,sF20)
      | ~ in(sF18(X3),sK4)
      | ~ in(X3,sF19)
      | ~ in(X3,sK3) ),
    inference(definition_folding,[],[f83,f129,f128,f127]) ).

fof(f83,plain,
    ! [X3] :
      ( ~ in(X3,sK3)
      | ~ in(ordered_pair(X3,sK2),sK4)
      | ~ in(X3,relation_dom(sK4))
      | ~ in(sK2,relation_image(sK4,sK3)) ),
    inference(cnf_transformation,[],[f55]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU203+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.34  % Computer : n027.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit   : 300
% 0.16/0.34  % WCLimit    : 300
% 0.16/0.34  % DateTime   : Wed Aug 23 12:58:16 EDT 2023
% 0.16/0.34  % CPUTime    : 
% 0.16/0.34  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.34  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.cf1rV0Jyr6/Vampire---4.8_28523
% 0.16/0.35  % (28703)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.40  % (28712)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.19/0.40  % (28716)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.19/0.40  % (28717)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.19/0.40  % (28705)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.19/0.40  % (28721)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.19/0.40  % (28706)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.19/0.40  % (28722)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.19/0.41  % (28722)First to succeed.
% 0.19/0.42  % (28722)Refutation found. Thanks to Tanya!
% 0.19/0.42  % SZS status Theorem for Vampire---4
% 0.19/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.19/0.42  % (28722)------------------------------
% 0.19/0.42  % (28722)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.19/0.42  % (28722)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.19/0.42  % (28722)Termination reason: Refutation
% 0.19/0.42  
% 0.19/0.42  % (28722)Memory used [KB]: 1279
% 0.19/0.42  % (28722)Time elapsed: 0.014 s
% 0.19/0.42  % (28722)------------------------------
% 0.19/0.42  % (28722)------------------------------
% 0.19/0.42  % (28703)Success in time 0.07 s
% 0.19/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------