TSTP Solution File: SEU061+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU061+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n019.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 May  1 03:49:56 EDT 2024

% Result   : Theorem 0.58s 0.79s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   72 (   4 unt;   0 def)
%            Number of atoms       :  313 (  78 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  380 ( 139   ~; 151   |;  61   &)
%                                         (  15 <=>;  13  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   3 con; 0-3 aty)
%            Number of variables   :  175 ( 135   !;  40   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f287,plain,
    $false,
    inference(avatar_sat_refutation,[],[f133,f134,f255,f285]) ).

fof(f285,plain,
    ( ~ spl12_1
    | ~ spl12_2 ),
    inference(avatar_contradiction_clause,[],[f284]) ).

fof(f284,plain,
    ( $false
    | ~ spl12_1
    | ~ spl12_2 ),
    inference(subsumption_resolution,[],[f283,f122]) ).

fof(f122,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f107]) ).

fof(f107,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK8(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f72,f73]) ).

fof(f73,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK8(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f72,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.0bJ2dReHhI/Vampire---4.8_26449',d1_xboole_0) ).

fof(f283,plain,
    ( in(sK11(sK1,sK0),empty_set)
    | ~ spl12_1
    | ~ spl12_2 ),
    inference(forward_demodulation,[],[f270,f132]) ).

fof(f132,plain,
    ( empty_set = relation_inverse_image(sK1,singleton(sK0))
    | ~ spl12_2 ),
    inference(avatar_component_clause,[],[f130]) ).

fof(f130,plain,
    ( spl12_2
  <=> empty_set = relation_inverse_image(sK1,singleton(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).

fof(f270,plain,
    ( in(sK11(sK1,sK0),relation_inverse_image(sK1,singleton(sK0)))
    | ~ spl12_1 ),
    inference(unit_resulting_resolution,[],[f81,f120,f257,f116]) ).

fof(f116,plain,
    ! [X0,X1,X6,X7] :
      ( ~ in(ordered_pair(X6,X7),X0)
      | ~ in(X7,X1)
      | in(X6,relation_inverse_image(X0,X1))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f89]) ).

fof(f89,plain,
    ! [X2,X0,X1,X6,X7] :
      ( in(X6,X2)
      | ~ in(X7,X1)
      | ~ in(ordered_pair(X6,X7),X0)
      | relation_inverse_image(X0,X1) != X2
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ( ( ! [X4] :
                    ( ~ in(X4,X1)
                    | ~ in(ordered_pair(sK2(X0,X1,X2),X4),X0) )
                | ~ in(sK2(X0,X1,X2),X2) )
              & ( ( in(sK3(X0,X1,X2),X1)
                  & in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X0) )
                | in(sK2(X0,X1,X2),X2) ) ) )
          & ( ! [X6] :
                ( ( in(X6,X2)
                  | ! [X7] :
                      ( ~ in(X7,X1)
                      | ~ in(ordered_pair(X6,X7),X0) ) )
                & ( ( in(sK4(X0,X1,X6),X1)
                    & in(ordered_pair(X6,sK4(X0,X1,X6)),X0) )
                  | ~ in(X6,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f58,f61,f60,f59]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4] :
                ( ~ in(X4,X1)
                | ~ in(ordered_pair(X3,X4),X0) )
            | ~ in(X3,X2) )
          & ( ? [X5] :
                ( in(X5,X1)
                & in(ordered_pair(X3,X5),X0) )
            | in(X3,X2) ) )
     => ( ( ! [X4] :
              ( ~ in(X4,X1)
              | ~ in(ordered_pair(sK2(X0,X1,X2),X4),X0) )
          | ~ in(sK2(X0,X1,X2),X2) )
        & ( ? [X5] :
              ( in(X5,X1)
              & in(ordered_pair(sK2(X0,X1,X2),X5),X0) )
          | in(sK2(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( in(X5,X1)
          & in(ordered_pair(sK2(X0,X1,X2),X5),X0) )
     => ( in(sK3(X0,X1,X2),X1)
        & in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ! [X0,X1,X6] :
      ( ? [X8] :
          ( in(X8,X1)
          & in(ordered_pair(X6,X8),X0) )
     => ( in(sK4(X0,X1,X6),X1)
        & in(ordered_pair(X6,sK4(X0,X1,X6)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ! [X4] :
                      ( ~ in(X4,X1)
                      | ~ in(ordered_pair(X3,X4),X0) )
                  | ~ in(X3,X2) )
                & ( ? [X5] :
                      ( in(X5,X1)
                      & in(ordered_pair(X3,X5),X0) )
                  | in(X3,X2) ) ) )
          & ( ! [X6] :
                ( ( in(X6,X2)
                  | ! [X7] :
                      ( ~ in(X7,X1)
                      | ~ in(ordered_pair(X6,X7),X0) ) )
                & ( ? [X8] :
                      ( in(X8,X1)
                      & in(ordered_pair(X6,X8),X0) )
                  | ~ in(X6,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f57]) ).

fof(f57,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ! [X4] :
                      ( ~ in(X4,X1)
                      | ~ in(ordered_pair(X3,X4),X0) )
                  | ~ in(X3,X2) )
                & ( ? [X4] :
                      ( in(X4,X1)
                      & in(ordered_pair(X3,X4),X0) )
                  | in(X3,X2) ) ) )
          & ( ! [X3] :
                ( ( in(X3,X2)
                  | ! [X4] :
                      ( ~ in(X4,X1)
                      | ~ in(ordered_pair(X3,X4),X0) ) )
                & ( ? [X4] :
                      ( in(X4,X1)
                      & in(ordered_pair(X3,X4),X0) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X3,X4),X0) ) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1,X2] :
          ( relation_inverse_image(X0,X1) = X2
        <=> ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(X4,X1)
                  & in(ordered_pair(X3,X4),X0) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0bJ2dReHhI/Vampire---4.8_26449',d14_relat_1) ).

fof(f257,plain,
    ( in(ordered_pair(sK11(sK1,sK0),sK0),sK1)
    | ~ spl12_1 ),
    inference(unit_resulting_resolution,[],[f81,f127,f124]) ).

fof(f124,plain,
    ! [X0,X5] :
      ( ~ in(X5,relation_rng(X0))
      | in(ordered_pair(sK11(X0,X5),X5),X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f112]) ).

fof(f112,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(sK11(X0,X5),X5),X0)
      | ~ in(X5,X1)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(X3,sK9(X0,X1)),X0)
                | ~ in(sK9(X0,X1),X1) )
              & ( in(ordered_pair(sK10(X0,X1),sK9(X0,X1)),X0)
                | in(sK9(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( in(ordered_pair(sK11(X0,X5),X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f76,f79,f78,f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X4,X2),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(X3,sK9(X0,X1)),X0)
          | ~ in(sK9(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(X4,sK9(X0,X1)),X0)
          | in(sK9(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(X4,sK9(X0,X1)),X0)
     => in(ordered_pair(sK10(X0,X1),sK9(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X7,X5),X0)
     => in(ordered_pair(sK11(X0,X5),X5),X0) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X4,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
                & ( ? [X7] : in(ordered_pair(X7,X5),X0)
                  | ~ in(X5,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_rng(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0bJ2dReHhI/Vampire---4.8_26449',d5_relat_1) ).

fof(f127,plain,
    ( in(sK0,relation_rng(sK1))
    | ~ spl12_1 ),
    inference(avatar_component_clause,[],[f126]) ).

fof(f126,plain,
    ( spl12_1
  <=> in(sK0,relation_rng(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f120,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f119]) ).

fof(f119,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f95]) ).

fof(f95,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK5(X0,X1) != X0
            | ~ in(sK5(X0,X1),X1) )
          & ( sK5(X0,X1) = X0
            | in(sK5(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f64,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK5(X0,X1) != X0
          | ~ in(sK5(X0,X1),X1) )
        & ( sK5(X0,X1) = X0
          | in(sK5(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/tmp/tmp.0bJ2dReHhI/Vampire---4.8_26449',d1_tarski) ).

fof(f81,plain,
    relation(sK1),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ( ( empty_set = relation_inverse_image(sK1,singleton(sK0))
      | ~ in(sK0,relation_rng(sK1)) )
    & ( empty_set != relation_inverse_image(sK1,singleton(sK0))
      | in(sK0,relation_rng(sK1)) )
    & relation(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f54,f55]) ).

fof(f55,plain,
    ( ? [X0,X1] :
        ( ( empty_set = relation_inverse_image(X1,singleton(X0))
          | ~ in(X0,relation_rng(X1)) )
        & ( empty_set != relation_inverse_image(X1,singleton(X0))
          | in(X0,relation_rng(X1)) )
        & relation(X1) )
   => ( ( empty_set = relation_inverse_image(sK1,singleton(sK0))
        | ~ in(sK0,relation_rng(sK1)) )
      & ( empty_set != relation_inverse_image(sK1,singleton(sK0))
        | in(sK0,relation_rng(sK1)) )
      & relation(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ? [X0,X1] :
      ( ( empty_set = relation_inverse_image(X1,singleton(X0))
        | ~ in(X0,relation_rng(X1)) )
      & ( empty_set != relation_inverse_image(X1,singleton(X0))
        | in(X0,relation_rng(X1)) )
      & relation(X1) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ? [X0,X1] :
      ( ( empty_set = relation_inverse_image(X1,singleton(X0))
        | ~ in(X0,relation_rng(X1)) )
      & ( empty_set != relation_inverse_image(X1,singleton(X0))
        | in(X0,relation_rng(X1)) )
      & relation(X1) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f42,plain,
    ? [X0,X1] :
      ( ( in(X0,relation_rng(X1))
      <~> empty_set != relation_inverse_image(X1,singleton(X0)) )
      & relation(X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,negated_conjecture,
    ~ ! [X0,X1] :
        ( relation(X1)
       => ( in(X0,relation_rng(X1))
        <=> empty_set != relation_inverse_image(X1,singleton(X0)) ) ),
    inference(negated_conjecture,[],[f32]) ).

fof(f32,conjecture,
    ! [X0,X1] :
      ( relation(X1)
     => ( in(X0,relation_rng(X1))
      <=> empty_set != relation_inverse_image(X1,singleton(X0)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0bJ2dReHhI/Vampire---4.8_26449',t142_funct_1) ).

fof(f255,plain,
    ( spl12_1
    | spl12_2 ),
    inference(avatar_contradiction_clause,[],[f254]) ).

fof(f254,plain,
    ( $false
    | spl12_1
    | spl12_2 ),
    inference(subsumption_resolution,[],[f252,f177]) ).

fof(f177,plain,
    ( ! [X0] : ~ in(ordered_pair(X0,sK0),sK1)
    | spl12_1 ),
    inference(unit_resulting_resolution,[],[f81,f128,f123]) ).

fof(f123,plain,
    ! [X0,X6,X5] :
      ( ~ in(ordered_pair(X6,X5),X0)
      | in(X5,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f113]) ).

fof(f113,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X6,X5),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f128,plain,
    ( ~ in(sK0,relation_rng(sK1))
    | spl12_1 ),
    inference(avatar_component_clause,[],[f126]) ).

fof(f252,plain,
    ( in(ordered_pair(sK2(sK1,singleton(sK0),empty_set),sK0),sK1)
    | spl12_2 ),
    inference(backward_demodulation,[],[f236,f240]) ).

fof(f240,plain,
    ( sK0 = sK3(sK1,singleton(sK0),empty_set)
    | spl12_2 ),
    inference(unit_resulting_resolution,[],[f231,f121]) ).

fof(f121,plain,
    ! [X3,X0] :
      ( X0 = X3
      | ~ in(X3,singleton(X0)) ),
    inference(equality_resolution,[],[f94]) ).

fof(f94,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f66]) ).

fof(f231,plain,
    ( in(sK3(sK1,singleton(sK0),empty_set),singleton(sK0))
    | spl12_2 ),
    inference(unit_resulting_resolution,[],[f81,f131,f122,f91]) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( relation_inverse_image(X0,X1) = X2
      | in(sK3(X0,X1,X2),X1)
      | in(sK2(X0,X1,X2),X2)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f131,plain,
    ( empty_set != relation_inverse_image(sK1,singleton(sK0))
    | spl12_2 ),
    inference(avatar_component_clause,[],[f130]) ).

fof(f236,plain,
    ( in(ordered_pair(sK2(sK1,singleton(sK0),empty_set),sK3(sK1,singleton(sK0),empty_set)),sK1)
    | spl12_2 ),
    inference(unit_resulting_resolution,[],[f81,f131,f122,f90]) ).

fof(f90,plain,
    ! [X2,X0,X1] :
      ( relation_inverse_image(X0,X1) = X2
      | in(ordered_pair(sK2(X0,X1,X2),sK3(X0,X1,X2)),X0)
      | in(sK2(X0,X1,X2),X2)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f134,plain,
    ( spl12_1
    | ~ spl12_2 ),
    inference(avatar_split_clause,[],[f82,f130,f126]) ).

fof(f82,plain,
    ( empty_set != relation_inverse_image(sK1,singleton(sK0))
    | in(sK0,relation_rng(sK1)) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f133,plain,
    ( ~ spl12_1
    | spl12_2 ),
    inference(avatar_split_clause,[],[f83,f130,f126]) ).

fof(f83,plain,
    ( empty_set = relation_inverse_image(sK1,singleton(sK0))
    | ~ in(sK0,relation_rng(sK1)) ),
    inference(cnf_transformation,[],[f56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SEU061+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12  % 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
% 0.12/0.32  % Computer : n019.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Tue Apr 30 16:13:59 EDT 2024
% 0.12/0.32  % CPUTime    : 
% 0.12/0.32  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.33  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.0bJ2dReHhI/Vampire---4.8_26449
% 0.58/0.78  % (26560)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 (2995ds/51Mi)
% 0.58/0.78  % (26562)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.58/0.78  % (26559)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 (2995ds/34Mi)
% 0.58/0.78  % (26561)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.58/0.78  % (26563)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 (2995ds/34Mi)
% 0.58/0.78  % (26564)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.58/0.78  % (26565)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 (2995ds/83Mi)
% 0.58/0.78  % (26566)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 (2995ds/56Mi)
% 0.58/0.78  % (26564)Refutation not found, incomplete strategy% (26564)------------------------------
% 0.58/0.78  % (26564)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.58/0.78  % (26564)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.78  
% 0.58/0.78  % (26564)Memory used [KB]: 1050
% 0.58/0.78  % (26564)Time elapsed: 0.024 s
% 0.58/0.78  % (26564)Instructions burned: 4 (million)
% 0.58/0.78  % (26564)------------------------------
% 0.58/0.78  % (26564)------------------------------
% 0.58/0.79  % (26562)First to succeed.
% 0.58/0.79  % (26567)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 (2995ds/55Mi)
% 0.58/0.79  % (26562)Refutation found. Thanks to Tanya!
% 0.58/0.79  % SZS status Theorem for Vampire---4
% 0.58/0.79  % SZS output start Proof for Vampire---4
% See solution above
% 0.58/0.79  % (26562)------------------------------
% 0.58/0.79  % (26562)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.58/0.79  % (26562)Termination reason: Refutation
% 0.58/0.79  
% 0.58/0.79  % (26562)Memory used [KB]: 1153
% 0.58/0.79  % (26562)Time elapsed: 0.030 s
% 0.58/0.79  % (26562)Instructions burned: 13 (million)
% 0.58/0.79  % (26562)------------------------------
% 0.58/0.79  % (26562)------------------------------
% 0.58/0.79  % (26556)Success in time 0.465 s
% 0.58/0.79  % Vampire---4.8 exiting
%------------------------------------------------------------------------------