TSTP Solution File: SEU215+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU215+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Thu Aug 31 17:04:47 EDT 2023

% Result   : Theorem 0.80s 1.16s
% Output   : CNFRefutation 0.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   59 (  13 unt;   0 def)
%            Number of atoms       :  285 (  47 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  368 ( 142   ~; 139   |;  60   &)
%                                         (   9 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   97 (   0 sgn;  69   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,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/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & relation(X0) )
     => relation(relation_composition(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1)
        & function(X0)
        & relation(X0) )
     => ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).

fof(f32,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( in(X0,relation_dom(relation_composition(X2,X1)))
           => apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).

fof(f33,conjecture,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( in(X0,relation_dom(X1))
           => apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).

fof(f34,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( function(X1)
          & relation(X1) )
       => ! [X2] :
            ( ( function(X2)
              & relation(X2) )
           => ( in(X0,relation_dom(X1))
             => apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
    inference(negated_conjecture,[],[f33]) ).

fof(f49,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,[],[f5]) ).

fof(f50,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,[],[f49]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(flattening,[],[f51]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) )
      | ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ( function(relation_composition(X0,X1))
        & relation(relation_composition(X0,X1)) )
      | ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f55]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f64]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
          | ~ in(X0,relation_dom(relation_composition(X2,X1)))
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
          | ~ in(X0,relation_dom(relation_composition(X2,X1)))
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f66]) ).

fof(f68,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0))
          & in(X0,relation_dom(X1))
          & function(X2)
          & relation(X2) )
      & function(X1)
      & relation(X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f69,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0))
          & in(X0,relation_dom(X1))
          & function(X2)
          & relation(X2) )
      & function(X1)
      & relation(X1) ),
    inference(flattening,[],[f68]) ).

fof(f79,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,[],[f50]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ! [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)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f65]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ! [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)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f98]) ).

fof(f100,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( apply(relation_composition(X1,X2),X0) != apply(X2,apply(X1,X0))
            & in(X0,relation_dom(X1))
            & function(X2)
            & relation(X2) )
        & function(X1)
        & relation(X1) )
   => ( ? [X2] :
          ( apply(relation_composition(sK10,X2),sK9) != apply(X2,apply(sK10,sK9))
          & in(sK9,relation_dom(sK10))
          & function(X2)
          & relation(X2) )
      & function(sK10)
      & relation(sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ( ? [X2] :
        ( apply(relation_composition(sK10,X2),sK9) != apply(X2,apply(sK10,sK9))
        & in(sK9,relation_dom(sK10))
        & function(X2)
        & relation(X2) )
   => ( apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9))
      & in(sK9,relation_dom(sK10))
      & function(sK11)
      & relation(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ( apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9))
    & in(sK9,relation_dom(sK10))
    & function(sK11)
    & relation(sK11)
    & function(sK10)
    & relation(sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f69,f101,f100]) ).

fof(f109,plain,
    ! [X2,X0,X1] :
      ( empty_set = X2
      | apply(X0,X1) != X2
      | in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( function(relation_composition(X0,X1))
      | ~ function(X1)
      | ~ relation(X1)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f149,plain,
    ! [X2,X0,X1] :
      ( in(X0,relation_dom(relation_composition(X2,X1)))
      | ~ in(apply(X2,X0),relation_dom(X1))
      | ~ in(X0,relation_dom(X2))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
      | ~ in(X0,relation_dom(relation_composition(X2,X1)))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f151,plain,
    relation(sK10),
    inference(cnf_transformation,[],[f102]) ).

fof(f152,plain,
    function(sK10),
    inference(cnf_transformation,[],[f102]) ).

fof(f153,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f102]) ).

fof(f154,plain,
    function(sK11),
    inference(cnf_transformation,[],[f102]) ).

fof(f155,plain,
    in(sK9,relation_dom(sK10)),
    inference(cnf_transformation,[],[f102]) ).

fof(f156,plain,
    apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9)),
    inference(cnf_transformation,[],[f102]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( apply(X0,X1) = empty_set
      | in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f109]) ).

cnf(c_54,plain,
    ( ~ function(X0)
    | ~ relation(X0)
    | apply(X0,X1) = empty_set
    | in(X1,relation_dom(X0)) ),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_57,plain,
    ( ~ relation(X0)
    | ~ relation(X1)
    | relation(relation_composition(X1,X0)) ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_63,plain,
    ( ~ function(X0)
    | ~ function(X1)
    | ~ relation(X0)
    | ~ relation(X1)
    | function(relation_composition(X1,X0)) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_92,plain,
    ( ~ in(apply(X0,X1),relation_dom(X2))
    | ~ in(X1,relation_dom(X0))
    | ~ function(X0)
    | ~ function(X2)
    | ~ relation(X0)
    | ~ relation(X2)
    | in(X1,relation_dom(relation_composition(X0,X2))) ),
    inference(cnf_transformation,[],[f149]) ).

cnf(c_95,plain,
    ( ~ in(X0,relation_dom(relation_composition(X1,X2)))
    | ~ function(X1)
    | ~ function(X2)
    | ~ relation(X1)
    | ~ relation(X2)
    | apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_96,negated_conjecture,
    apply(relation_composition(sK10,sK11),sK9) != apply(sK11,apply(sK10,sK9)),
    inference(cnf_transformation,[],[f156]) ).

cnf(c_97,negated_conjecture,
    in(sK9,relation_dom(sK10)),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_98,negated_conjecture,
    function(sK11),
    inference(cnf_transformation,[],[f154]) ).

cnf(c_99,negated_conjecture,
    relation(sK11),
    inference(cnf_transformation,[],[f153]) ).

cnf(c_100,negated_conjecture,
    function(sK10),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_101,negated_conjecture,
    relation(sK10),
    inference(cnf_transformation,[],[f151]) ).

cnf(c_1025,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_2207,plain,
    ( apply(relation_composition(sK10,sK11),sK9) != X0
    | apply(sK11,apply(sK10,sK9)) != X0
    | apply(relation_composition(sK10,sK11),sK9) = apply(sK11,apply(sK10,sK9)) ),
    inference(instantiation,[status(thm)],[c_1025]) ).

cnf(c_2208,plain,
    ( apply(relation_composition(sK10,sK11),sK9) != empty_set
    | apply(sK11,apply(sK10,sK9)) != empty_set
    | apply(relation_composition(sK10,sK11),sK9) = apply(sK11,apply(sK10,sK9)) ),
    inference(instantiation,[status(thm)],[c_2207]) ).

cnf(c_2274,plain,
    ( ~ in(apply(sK10,sK9),relation_dom(X0))
    | ~ in(sK9,relation_dom(sK10))
    | ~ function(X0)
    | ~ relation(X0)
    | ~ function(sK10)
    | ~ relation(sK10)
    | in(sK9,relation_dom(relation_composition(sK10,X0))) ),
    inference(instantiation,[status(thm)],[c_92]) ).

cnf(c_2915,plain,
    ( ~ function(sK10)
    | ~ function(sK11)
    | ~ relation(sK10)
    | ~ relation(sK11)
    | function(relation_composition(sK10,sK11)) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_2941,plain,
    ( ~ function(relation_composition(sK10,sK11))
    | ~ relation(relation_composition(sK10,sK11))
    | apply(relation_composition(sK10,sK11),sK9) = empty_set
    | in(sK9,relation_dom(relation_composition(sK10,sK11))) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_4735,plain,
    ( ~ relation(sK10)
    | ~ relation(sK11)
    | relation(relation_composition(sK10,sK11)) ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_4752,plain,
    ( ~ function(sK11)
    | ~ relation(sK11)
    | apply(sK11,apply(sK10,sK9)) = empty_set
    | in(apply(sK10,sK9),relation_dom(sK11)) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_5401,plain,
    ( ~ in(sK9,relation_dom(relation_composition(sK10,sK11)))
    | ~ function(sK10)
    | ~ function(sK11)
    | ~ relation(sK10)
    | ~ relation(sK11)
    | apply(relation_composition(sK10,sK11),sK9) = apply(sK11,apply(sK10,sK9)) ),
    inference(instantiation,[status(thm)],[c_95]) ).

cnf(c_9866,plain,
    ( ~ in(apply(sK10,sK9),relation_dom(sK11))
    | ~ in(sK9,relation_dom(sK10))
    | ~ function(sK10)
    | ~ function(sK11)
    | ~ relation(sK10)
    | ~ relation(sK11)
    | in(sK9,relation_dom(relation_composition(sK10,sK11))) ),
    inference(instantiation,[status(thm)],[c_2274]) ).

cnf(c_9867,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_9866,c_5401,c_4752,c_4735,c_2941,c_2915,c_2208,c_96,c_97,c_98,c_99,c_100,c_101]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU215+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 16:21:58 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.80/1.16  % SZS status Started for theBenchmark.p
% 0.80/1.16  % SZS status Theorem for theBenchmark.p
% 0.80/1.16  
% 0.80/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.80/1.16  
% 0.80/1.16  ------  iProver source info
% 0.80/1.16  
% 0.80/1.16  git: date: 2023-05-31 18:12:56 +0000
% 0.80/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.80/1.16  git: non_committed_changes: false
% 0.80/1.16  git: last_make_outside_of_git: false
% 0.80/1.16  
% 0.80/1.16  ------ Parsing...
% 0.80/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.80/1.16  
% 0.80/1.16  ------ Preprocessing... sup_sim: 2  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 0.80/1.16  
% 0.80/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.80/1.16  
% 0.80/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.80/1.16  ------ Proving...
% 0.80/1.16  ------ Problem Properties 
% 0.80/1.16  
% 0.80/1.16  
% 0.80/1.16  clauses                                 53
% 0.80/1.16  conjectures                             6
% 0.80/1.16  EPR                                     23
% 0.80/1.16  Horn                                    50
% 0.80/1.16  unary                                   25
% 0.80/1.16  binary                                  10
% 0.80/1.16  lits                                    118
% 0.80/1.16  lits eq                                 7
% 0.80/1.16  fd_pure                                 0
% 0.80/1.16  fd_pseudo                               0
% 0.80/1.16  fd_cond                                 1
% 0.80/1.16  fd_pseudo_cond                          2
% 0.80/1.16  AC symbols                              0
% 0.80/1.16  
% 0.80/1.16  ------ Schedule dynamic 5 is on 
% 0.80/1.16  
% 0.80/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.80/1.16  
% 0.80/1.16  
% 0.80/1.16  ------ 
% 0.80/1.16  Current options:
% 0.80/1.16  ------ 
% 0.80/1.16  
% 0.80/1.16  
% 0.80/1.16  
% 0.80/1.16  
% 0.80/1.16  ------ Proving...
% 0.80/1.16  
% 0.80/1.16  
% 0.80/1.16  % SZS status Theorem for theBenchmark.p
% 0.80/1.16  
% 0.80/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.80/1.16  
% 0.80/1.17  
%------------------------------------------------------------------------------