TSTP Solution File: SEU225+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU225+3 : TPTP v8.1.2. Released v3.2.0.
% 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 : 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 : Thu Aug 31 17:57:05 EDT 2023

% Result   : Theorem 0.22s 0.45s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   85 (  12 unt;   0 def)
%            Number of atoms       :  329 (  87 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  402 ( 158   ~; 158   |;  55   &)
%                                         (  16 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :  118 (; 105   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1031,plain,
    $false,
    inference(avatar_sat_refutation,[],[f354,f390,f713,f1024,f1030]) ).

fof(f1030,plain,
    ( ~ spl18_10
    | ~ spl18_8 ),
    inference(avatar_split_clause,[],[f715,f351,f387]) ).

fof(f387,plain,
    ( spl18_10
  <=> empty_set = sF17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).

fof(f351,plain,
    ( spl18_8
  <=> empty_set = sF16 ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).

fof(f715,plain,
    ( empty_set != sF17
    | ~ spl18_8 ),
    inference(backward_demodulation,[],[f203,f353]) ).

fof(f353,plain,
    ( empty_set = sF16
    | ~ spl18_8 ),
    inference(avatar_component_clause,[],[f351]) ).

fof(f203,plain,
    sF16 != sF17,
    inference(definition_folding,[],[f122,f202,f201,f200]) ).

fof(f200,plain,
    relation_dom_restriction(sK2,sK0) = sF15,
    introduced(function_definition,[]) ).

fof(f201,plain,
    apply(sF15,sK1) = sF16,
    introduced(function_definition,[]) ).

fof(f202,plain,
    apply(sK2,sK1) = sF17,
    introduced(function_definition,[]) ).

fof(f122,plain,
    apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ( apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1)
    & in(sK1,sK0)
    & function(sK2)
    & relation(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f54,f87]) ).

fof(f87,plain,
    ( ? [X0,X1,X2] :
        ( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
        & in(X1,X0)
        & function(X2)
        & relation(X2) )
   => ( apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1)
      & in(sK1,sK0)
      & function(sK2)
      & relation(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ? [X0,X1,X2] :
      ( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
      & in(X1,X0)
      & function(X2)
      & relation(X2) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ? [X0,X1,X2] :
      ( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
      & in(X1,X0)
      & function(X2)
      & relation(X2) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( function(X2)
          & relation(X2) )
       => ( in(X1,X0)
         => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( in(X1,X0)
       => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KcBhzXIHmg/Vampire---4.8_25893',t72_funct_1) ).

fof(f1024,plain,
    ( spl18_7
    | ~ spl18_9 ),
    inference(avatar_contradiction_clause,[],[f1023]) ).

fof(f1023,plain,
    ( $false
    | spl18_7
    | ~ spl18_9 ),
    inference(subsumption_resolution,[],[f1022,f348]) ).

fof(f348,plain,
    ( ~ in(sK1,relation_dom(sF15))
    | spl18_7 ),
    inference(avatar_component_clause,[],[f347]) ).

fof(f347,plain,
    ( spl18_7
  <=> in(sK1,relation_dom(sF15)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).

fof(f1022,plain,
    ( in(sK1,relation_dom(sF15))
    | ~ spl18_9 ),
    inference(forward_demodulation,[],[f1019,f200]) ).

fof(f1019,plain,
    ( in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
    | ~ spl18_9 ),
    inference(resolution,[],[f397,f121]) ).

fof(f121,plain,
    in(sK1,sK0),
    inference(cnf_transformation,[],[f88]) ).

fof(f397,plain,
    ( ! [X0] :
        ( ~ in(sK1,X0)
        | in(sK1,relation_dom(relation_dom_restriction(sK2,X0))) )
    | ~ spl18_9 ),
    inference(subsumption_resolution,[],[f396,f119]) ).

fof(f119,plain,
    relation(sK2),
    inference(cnf_transformation,[],[f88]) ).

fof(f396,plain,
    ( ! [X0] :
        ( ~ in(sK1,X0)
        | in(sK1,relation_dom(relation_dom_restriction(sK2,X0)))
        | ~ relation(sK2) )
    | ~ spl18_9 ),
    inference(subsumption_resolution,[],[f391,f120]) ).

fof(f120,plain,
    function(sK2),
    inference(cnf_transformation,[],[f88]) ).

fof(f391,plain,
    ( ! [X0] :
        ( ~ in(sK1,X0)
        | in(sK1,relation_dom(relation_dom_restriction(sK2,X0)))
        | ~ function(sK2)
        | ~ relation(sK2) )
    | ~ spl18_9 ),
    inference(resolution,[],[f385,f174]) ).

fof(f174,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,relation_dom(X2))
      | ~ in(X1,X0)
      | in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
          | ~ in(X1,X0)
          | ~ in(X1,relation_dom(X2)) )
        & ( ( in(X1,X0)
            & in(X1,relation_dom(X2)) )
          | ~ in(X1,relation_dom(relation_dom_restriction(X2,X0))) ) )
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(flattening,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
          | ~ in(X1,X0)
          | ~ in(X1,relation_dom(X2)) )
        & ( ( in(X1,X0)
            & in(X1,relation_dom(X2)) )
          | ~ in(X1,relation_dom(relation_dom_restriction(X2,X0))) ) )
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(nnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      <=> ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) )
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      <=> ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) )
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      <=> ( in(X1,X0)
          & in(X1,relation_dom(X2)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KcBhzXIHmg/Vampire---4.8_25893',l82_funct_1) ).

fof(f385,plain,
    ( in(sK1,relation_dom(sK2))
    | ~ spl18_9 ),
    inference(avatar_component_clause,[],[f383]) ).

fof(f383,plain,
    ( spl18_9
  <=> in(sK1,relation_dom(sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).

fof(f713,plain,
    ~ spl18_7,
    inference(avatar_contradiction_clause,[],[f712]) ).

fof(f712,plain,
    ( $false
    | ~ spl18_7 ),
    inference(subsumption_resolution,[],[f709,f203]) ).

fof(f709,plain,
    ( sF16 = sF17
    | ~ spl18_7 ),
    inference(backward_demodulation,[],[f202,f694]) ).

fof(f694,plain,
    ( apply(sK2,sK1) = sF16
    | ~ spl18_7 ),
    inference(forward_demodulation,[],[f692,f201]) ).

fof(f692,plain,
    ( apply(sK2,sK1) = apply(sF15,sK1)
    | ~ spl18_7 ),
    inference(resolution,[],[f556,f349]) ).

fof(f349,plain,
    ( in(sK1,relation_dom(sF15))
    | ~ spl18_7 ),
    inference(avatar_component_clause,[],[f347]) ).

fof(f556,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF15))
      | apply(sK2,X0) = apply(sF15,X0) ),
    inference(forward_demodulation,[],[f555,f200]) ).

fof(f555,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF15))
      | apply(sK2,X0) = apply(relation_dom_restriction(sK2,sK0),X0) ),
    inference(subsumption_resolution,[],[f554,f119]) ).

fof(f554,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF15))
      | apply(sK2,X0) = apply(relation_dom_restriction(sK2,sK0),X0)
      | ~ relation(sK2) ),
    inference(subsumption_resolution,[],[f552,f120]) ).

fof(f552,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF15))
      | apply(sK2,X0) = apply(relation_dom_restriction(sK2,sK0),X0)
      | ~ function(sK2)
      | ~ relation(sK2) ),
    inference(superposition,[],[f523,f200]) ).

fof(f523,plain,
    ! [X2,X0,X4] :
      ( ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
      | apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
      | ~ function(X2)
      | ~ relation(X2) ),
    inference(subsumption_resolution,[],[f522,f156]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( relation(X0)
     => relation(relation_dom_restriction(X0,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.KcBhzXIHmg/Vampire---4.8_25893',dt_k7_relat_1) ).

fof(f522,plain,
    ! [X2,X0,X4] :
      ( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
      | ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ relation(relation_dom_restriction(X2,X0)) ),
    inference(subsumption_resolution,[],[f198,f163]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( function(relation_dom_restriction(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KcBhzXIHmg/Vampire---4.8_25893',fc4_funct_1) ).

fof(f198,plain,
    ! [X2,X0,X4] :
      ( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
      | ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(relation_dom_restriction(X2,X0))
      | ~ relation(relation_dom_restriction(X2,X0)) ),
    inference(equality_resolution,[],[f165]) ).

fof(f165,plain,
    ! [X2,X0,X1,X4] :
      ( apply(X1,X4) = apply(X2,X4)
      | ~ in(X4,relation_dom(X1))
      | relation_dom_restriction(X2,X0) != X1
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ( apply(X1,sK6(X1,X2)) != apply(X2,sK6(X1,X2))
                & in(sK6(X1,X2),relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X4] :
                    ( apply(X1,X4) = apply(X2,X4)
                    | ~ in(X4,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f98,f99]) ).

fof(f99,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( apply(X1,X3) != apply(X2,X3)
          & in(X3,relation_dom(X1)) )
     => ( apply(X1,sK6(X1,X2)) != apply(X2,sK6(X1,X2))
        & in(sK6(X1,X2),relation_dom(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ? [X3] :
                  ( apply(X1,X3) != apply(X2,X3)
                  & in(X3,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X4] :
                    ( apply(X1,X4) = apply(X2,X4)
                    | ~ in(X4,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(rectify,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ? [X3] :
                  ( apply(X1,X3) != apply(X2,X3)
                  & in(X3,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X3] :
                    ( apply(X1,X3) = apply(X2,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ? [X3] :
                  ( apply(X1,X3) != apply(X2,X3)
                  & in(X3,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X3] :
                    ( apply(X1,X3) = apply(X2,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_dom_restriction(X2,X0) = X1
          <=> ( ! [X3] :
                  ( apply(X1,X3) = apply(X2,X3)
                  | ~ in(X3,relation_dom(X1)) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_dom_restriction(X2,X0) = X1
          <=> ( ! [X3] :
                  ( apply(X1,X3) = apply(X2,X3)
                  | ~ in(X3,relation_dom(X1)) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( relation_dom_restriction(X2,X0) = X1
          <=> ( ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X1,X3) = apply(X2,X3) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KcBhzXIHmg/Vampire---4.8_25893',t68_funct_1) ).

fof(f390,plain,
    ( spl18_9
    | spl18_10 ),
    inference(avatar_split_clause,[],[f326,f387,f383]) ).

fof(f326,plain,
    ( empty_set = sF17
    | in(sK1,relation_dom(sK2)) ),
    inference(subsumption_resolution,[],[f325,f119]) ).

fof(f325,plain,
    ( empty_set = sF17
    | in(sK1,relation_dom(sK2))
    | ~ relation(sK2) ),
    inference(subsumption_resolution,[],[f320,f120]) ).

fof(f320,plain,
    ( empty_set = sF17
    | in(sK1,relation_dom(sK2))
    | ~ function(sK2)
    | ~ relation(sK2) ),
    inference(superposition,[],[f195,f202]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( apply(X0,X1) = empty_set
      | in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f143]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( apply(X0,X1) = X2
      | empty_set != X2
      | in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( ( apply(X0,X1) = X2
                | empty_set != X2 )
              & ( empty_set = X2
                | apply(X0,X1) != X2 ) )
            | in(X1,relation_dom(X0)) )
          & ( ( ( apply(X0,X1) = X2
                | ~ in(ordered_pair(X1,X2),X0) )
              & ( in(ordered_pair(X1,X2),X0)
                | apply(X0,X1) != X2 ) )
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( apply(X0,X1) = X2
            <=> empty_set = X2 )
            | in(X1,relation_dom(X0)) )
          & ( ( apply(X0,X1) = X2
            <=> in(ordered_pair(X1,X2),X0) )
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( apply(X0,X1) = X2
            <=> empty_set = X2 )
            | in(X1,relation_dom(X0)) )
          & ( ( apply(X0,X1) = X2
            <=> in(ordered_pair(X1,X2),X0) )
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1,X2] :
          ( ( ~ in(X1,relation_dom(X0))
           => ( apply(X0,X1) = X2
            <=> empty_set = X2 ) )
          & ( in(X1,relation_dom(X0))
           => ( apply(X0,X1) = X2
            <=> in(ordered_pair(X1,X2),X0) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KcBhzXIHmg/Vampire---4.8_25893',d4_funct_1) ).

fof(f354,plain,
    ( spl18_7
    | spl18_8 ),
    inference(avatar_split_clause,[],[f324,f351,f347]) ).

fof(f324,plain,
    ( empty_set = sF16
    | in(sK1,relation_dom(sF15)) ),
    inference(subsumption_resolution,[],[f323,f220]) ).

fof(f220,plain,
    relation(sF15),
    inference(subsumption_resolution,[],[f219,f119]) ).

fof(f219,plain,
    ( relation(sF15)
    | ~ relation(sK2) ),
    inference(superposition,[],[f156,f200]) ).

fof(f323,plain,
    ( empty_set = sF16
    | in(sK1,relation_dom(sF15))
    | ~ relation(sF15) ),
    inference(subsumption_resolution,[],[f319,f269]) ).

fof(f269,plain,
    function(sF15),
    inference(subsumption_resolution,[],[f268,f119]) ).

fof(f268,plain,
    ( function(sF15)
    | ~ relation(sK2) ),
    inference(subsumption_resolution,[],[f267,f120]) ).

fof(f267,plain,
    ( function(sF15)
    | ~ function(sK2)
    | ~ relation(sK2) ),
    inference(superposition,[],[f163,f200]) ).

fof(f319,plain,
    ( empty_set = sF16
    | in(sK1,relation_dom(sF15))
    | ~ function(sF15)
    | ~ relation(sF15) ),
    inference(superposition,[],[f195,f201]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU225+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36  % Computer : n028.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   : Wed Aug 23 21:50:04 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.KcBhzXIHmg/Vampire---4.8_25893
% 0.15/0.36  % (26065)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (26066)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)
% 0.22/0.42  % (26068)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)
% 0.22/0.42  % (26069)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)
% 0.22/0.42  % (26067)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)
% 0.22/0.42  % (26071)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.22/0.42  % (26072)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)
% 0.22/0.42  % (26070)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)
% 0.22/0.45  % (26071)First to succeed.
% 0.22/0.45  % (26071)Refutation found. Thanks to Tanya!
% 0.22/0.45  % SZS status Theorem for Vampire---4
% 0.22/0.45  % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.45  % (26071)------------------------------
% 0.22/0.45  % (26071)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45  % (26071)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45  % (26071)Termination reason: Refutation
% 0.22/0.45  
% 0.22/0.45  % (26071)Memory used [KB]: 6012
% 0.22/0.45  % (26071)Time elapsed: 0.030 s
% 0.22/0.45  % (26071)------------------------------
% 0.22/0.45  % (26071)------------------------------
% 0.22/0.45  % (26065)Success in time 0.09 s
% 0.22/0.45  % Vampire---4.8 exiting
%------------------------------------------------------------------------------