TSTP Solution File: SEU137+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU137+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 09:20:26 EDT 2024

% Result   : Theorem 0.59s 0.80s
% Output   : Refutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   77 (   7 unt;   0 def)
%            Number of atoms       :  321 (  35 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  388 ( 144   ~; 156   |;  66   &)
%                                         (  11 <=>;  10  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   4 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-3 aty)
%            Number of variables   :  147 ( 129   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f738,plain,
    $false,
    inference(avatar_sat_refutation,[],[f270,f271,f551,f704,f735]) ).

fof(f735,plain,
    ( spl13_3
    | ~ spl13_4
    | ~ spl13_6 ),
    inference(avatar_contradiction_clause,[],[f734]) ).

fof(f734,plain,
    ( $false
    | spl13_3
    | ~ spl13_4
    | ~ spl13_6 ),
    inference(subsumption_resolution,[],[f722,f264]) ).

fof(f264,plain,
    ( ~ in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK10)
    | spl13_3 ),
    inference(avatar_component_clause,[],[f263]) ).

fof(f263,plain,
    ( spl13_3
  <=> in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).

fof(f722,plain,
    ( in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK10)
    | ~ spl13_4
    | ~ spl13_6 ),
    inference(resolution,[],[f269,f557]) ).

fof(f557,plain,
    ( ! [X0] :
        ( ~ in(X0,set_union2(sK9,set_difference(sK10,sK9)))
        | in(X0,sK10) )
    | ~ spl13_6 ),
    inference(resolution,[],[f278,f135]) ).

fof(f135,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK2(X0,X1),X1)
          & in(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f92,f93]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK2(X0,X1),X1)
        & in(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.v0U0G1s4PO/Vampire---4.8_30153',d3_tarski) ).

fof(f278,plain,
    ( subset(set_union2(sK9,set_difference(sK10,sK9)),sK10)
    | ~ spl13_6 ),
    inference(avatar_component_clause,[],[f277]) ).

fof(f277,plain,
    ( spl13_6
  <=> subset(set_union2(sK9,set_difference(sK10,sK9)),sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).

fof(f269,plain,
    ( in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),set_union2(sK9,set_difference(sK10,sK9)))
    | ~ spl13_4 ),
    inference(avatar_component_clause,[],[f267]) ).

fof(f267,plain,
    ( spl13_4
  <=> in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),set_union2(sK9,set_difference(sK10,sK9))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).

fof(f704,plain,
    ( ~ spl13_3
    | spl13_4 ),
    inference(avatar_contradiction_clause,[],[f703]) ).

fof(f703,plain,
    ( $false
    | ~ spl13_3
    | spl13_4 ),
    inference(subsumption_resolution,[],[f702,f265]) ).

fof(f265,plain,
    ( in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK10)
    | ~ spl13_3 ),
    inference(avatar_component_clause,[],[f263]) ).

fof(f702,plain,
    ( ~ in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK10)
    | spl13_4 ),
    inference(subsumption_resolution,[],[f694,f584]) ).

fof(f584,plain,
    ( ~ in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK9)
    | spl13_4 ),
    inference(resolution,[],[f268,f199]) ).

fof(f199,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f130]) ).

fof(f130,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X0)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK1(X0,X1,X2),X1)
              & ~ in(sK1(X0,X1,X2),X0) )
            | ~ in(sK1(X0,X1,X2),X2) )
          & ( in(sK1(X0,X1,X2),X1)
            | in(sK1(X0,X1,X2),X0)
            | in(sK1(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f88,f89]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK1(X0,X1,X2),X1)
            & ~ in(sK1(X0,X1,X2),X0) )
          | ~ in(sK1(X0,X1,X2),X2) )
        & ( in(sK1(X0,X1,X2),X1)
          | in(sK1(X0,X1,X2),X0)
          | in(sK1(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(rectify,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(flattening,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.v0U0G1s4PO/Vampire---4.8_30153',d2_xboole_0) ).

fof(f268,plain,
    ( ~ in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),set_union2(sK9,set_difference(sK10,sK9)))
    | spl13_4 ),
    inference(avatar_component_clause,[],[f267]) ).

fof(f694,plain,
    ( in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK9)
    | ~ in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK10)
    | spl13_4 ),
    inference(resolution,[],[f585,f204]) ).

fof(f204,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_difference(X0,X1))
      | in(X4,X1)
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f146]) ).

fof(f146,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | in(X4,X1)
      | ~ in(X4,X0)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ( ( in(sK4(X0,X1,X2),X1)
            | ~ in(sK4(X0,X1,X2),X0)
            | ~ in(sK4(X0,X1,X2),X2) )
          & ( ( ~ in(sK4(X0,X1,X2),X1)
              & in(sK4(X0,X1,X2),X0) )
            | in(sK4(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( ~ in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f102,f103]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( ~ in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( in(sK4(X0,X1,X2),X1)
          | ~ in(sK4(X0,X1,X2),X0)
          | ~ in(sK4(X0,X1,X2),X2) )
        & ( ( ~ in(sK4(X0,X1,X2),X1)
            & in(sK4(X0,X1,X2),X0) )
          | in(sK4(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( ~ in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(flattening,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ? [X3] :
            ( ( in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) )
            & ( ( ~ in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) ) )
        | set_difference(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2] :
      ( set_difference(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.v0U0G1s4PO/Vampire---4.8_30153',d4_xboole_0) ).

fof(f585,plain,
    ( ~ in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),set_difference(sK10,sK9))
    | spl13_4 ),
    inference(resolution,[],[f268,f198]) ).

fof(f198,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f131]) ).

fof(f131,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f90]) ).

fof(f551,plain,
    spl13_6,
    inference(avatar_contradiction_clause,[],[f550]) ).

fof(f550,plain,
    ( $false
    | spl13_6 ),
    inference(subsumption_resolution,[],[f549,f185]) ).

fof(f185,plain,
    subset(sK9,sK10),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,plain,
    ( sK10 != set_union2(sK9,set_difference(sK10,sK9))
    & subset(sK9,sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f73,f117]) ).

fof(f117,plain,
    ( ? [X0,X1] :
        ( set_union2(X0,set_difference(X1,X0)) != X1
        & subset(X0,X1) )
   => ( sK10 != set_union2(sK9,set_difference(sK10,sK9))
      & subset(sK9,sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ? [X0,X1] :
      ( set_union2(X0,set_difference(X1,X0)) != X1
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => set_union2(X0,set_difference(X1,X0)) = X1 ),
    inference(negated_conjecture,[],[f43]) ).

fof(f43,conjecture,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_union2(X0,set_difference(X1,X0)) = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.v0U0G1s4PO/Vampire---4.8_30153',t45_xboole_1) ).

fof(f549,plain,
    ( ~ subset(sK9,sK10)
    | spl13_6 ),
    inference(subsumption_resolution,[],[f540,f175]) ).

fof(f175,plain,
    ! [X0,X1] : subset(set_difference(X0,X1),X0),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] : subset(set_difference(X0,X1),X0),
    file('/export/starexec/sandbox2/tmp/tmp.v0U0G1s4PO/Vampire---4.8_30153',t36_xboole_1) ).

fof(f540,plain,
    ( ~ subset(set_difference(sK10,sK9),sK10)
    | ~ subset(sK9,sK10)
    | spl13_6 ),
    inference(resolution,[],[f194,f279]) ).

fof(f279,plain,
    ( ~ subset(set_union2(sK9,set_difference(sK10,sK9)),sK10)
    | spl13_6 ),
    inference(avatar_component_clause,[],[f277]) ).

fof(f194,plain,
    ! [X2,X0,X1] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X2,X1)
        & subset(X0,X1) )
     => subset(set_union2(X0,X2),X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.v0U0G1s4PO/Vampire---4.8_30153',t8_xboole_1) ).

fof(f271,plain,
    ( ~ spl13_3
    | ~ spl13_4 ),
    inference(avatar_split_clause,[],[f250,f267,f263]) ).

fof(f250,plain,
    ( ~ in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),set_union2(sK9,set_difference(sK10,sK9)))
    | ~ in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK10) ),
    inference(resolution,[],[f239,f231]) ).

fof(f231,plain,
    ! [X0,X1] :
      ( sQ12_eqProxy(X0,X1)
      | ~ in(sK7(X0,X1),X1)
      | ~ in(sK7(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f172,f207]) ).

fof(f207,plain,
    ! [X0,X1] :
      ( sQ12_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ12_eqProxy])]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ in(sK7(X0,X1),X1)
      | ~ in(sK7(X0,X1),X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK7(X0,X1),X1)
          | ~ in(sK7(X0,X1),X0) )
        & ( in(sK7(X0,X1),X1)
          | in(sK7(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f111,f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK7(X0,X1),X1)
          | ~ in(sK7(X0,X1),X0) )
        & ( in(sK7(X0,X1),X1)
          | in(sK7(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.v0U0G1s4PO/Vampire---4.8_30153',t2_tarski) ).

fof(f239,plain,
    ~ sQ12_eqProxy(sK10,set_union2(sK9,set_difference(sK10,sK9))),
    inference(equality_proxy_replacement,[],[f186,f207]) ).

fof(f186,plain,
    sK10 != set_union2(sK9,set_difference(sK10,sK9)),
    inference(cnf_transformation,[],[f118]) ).

fof(f270,plain,
    ( spl13_3
    | spl13_4 ),
    inference(avatar_split_clause,[],[f249,f267,f263]) ).

fof(f249,plain,
    ( in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),set_union2(sK9,set_difference(sK10,sK9)))
    | in(sK7(sK10,set_union2(sK9,set_difference(sK10,sK9))),sK10) ),
    inference(resolution,[],[f239,f232]) ).

fof(f232,plain,
    ! [X0,X1] :
      ( sQ12_eqProxy(X0,X1)
      | in(sK7(X0,X1),X1)
      | in(sK7(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f171,f207]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( X0 = X1
      | in(sK7(X0,X1),X1)
      | in(sK7(X0,X1),X0) ),
    inference(cnf_transformation,[],[f113]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU137+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri May  3 11:56:38 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.34  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.v0U0G1s4PO/Vampire---4.8_30153
% 0.59/0.79  % (30264)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.59/0.79  % (30263)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)
% 0.59/0.79  % (30269)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)
% 0.59/0.79  % (30266)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)
% 0.59/0.79  % (30265)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)
% 0.59/0.79  % (30268)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)
% 0.59/0.79  % (30267)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)
% 0.59/0.79  % (30262)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)
% 0.59/0.80  % (30266)First to succeed.
% 0.59/0.80  % (30264)Also succeeded, but the first one will report.
% 0.59/0.80  % (30266)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30261"
% 0.59/0.80  % (30266)Refutation found. Thanks to Tanya!
% 0.59/0.80  % SZS status Theorem for Vampire---4
% 0.59/0.80  % SZS output start Proof for Vampire---4
% See solution above
% 0.59/0.80  % (30266)------------------------------
% 0.59/0.80  % (30266)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.59/0.80  % (30266)Termination reason: Refutation
% 0.59/0.80  
% 0.59/0.80  % (30266)Memory used [KB]: 1250
% 0.59/0.80  % (30266)Time elapsed: 0.012 s
% 0.59/0.80  % (30266)Instructions burned: 17 (million)
% 0.59/0.80  % (30261)Success in time 0.463 s
% 0.59/0.81  % Vampire---4.8 exiting
%------------------------------------------------------------------------------