%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM564+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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  : 600s
% DateTime : Mon Jul 18 12:27:46 EDT 2022

% Result   : Theorem 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (   6 unt;   1 def)
%            Number of atoms       :   56 (  10 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   68 (  31   ~;  11   |;  17   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   23 (   3 sgn  11   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mDefEmp,definition,
    ! [W0] :
      ( W0 = slcrc0
    <=> ( aSet0(W0)
        & ~ ? [W1] : aElementOf0(W1,W0) ) ) ).

fof(m__,conjecture,
    ( ( aSet0(slcrc0)
      & ~ ? [W0] : aElementOf0(W0,slcrc0) )
   => ( ! [W0] :
          ( aElementOf0(W0,slcrc0)
         => aElementOf0(W0,xS) )
      | aSubsetOf0(slcrc0,xS)
      | aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ) ) ).

fof(subgoal_0,plain,
    ( ( aSet0(slcrc0)
      & ~ ? [W0] : aElementOf0(W0,slcrc0)
      & ~ ! [W0] :
            ( aElementOf0(W0,slcrc0)
           => aElementOf0(W0,xS) )
      & ~ aSubsetOf0(slcrc0,xS) )
   => aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ( ( aSet0(slcrc0)
        & ~ ? [W0] : aElementOf0(W0,slcrc0)
        & ~ ! [W0] :
              ( aElementOf0(W0,slcrc0)
             => aElementOf0(W0,xS) )
        & ~ aSubsetOf0(slcrc0,xS) )
     => aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
    & ~ aSubsetOf0(slcrc0,xS)
    & aSet0(slcrc0)
    & ? [W0] :
        ( ~ aElementOf0(W0,xS)
        & aElementOf0(W0,slcrc0) )
    & ! [W0] : ~ aElementOf0(W0,slcrc0) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ? [W0] :
      ( ~ aElementOf0(W0,xS)
      & aElementOf0(W0,slcrc0) ),
    inference(conjunct,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ( ~ aElementOf0(skolemFOFtoCNF_W0,xS)
    & aElementOf0(skolemFOFtoCNF_W0,slcrc0) ),
    inference(skolemize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    aElementOf0(skolemFOFtoCNF_W0,slcrc0),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [W0] :
      ( W0 != slcrc0
    <=> ( ~ aSet0(W0)
        | ? [W1] : aElementOf0(W1,W0) ) ),
    inference(canonicalize,[],[mDefEmp]) ).

fof(normalize_0_5,plain,
    ! [W0] :
      ( W0 != slcrc0
    <=> ( ~ aSet0(W0)
        | ? [W1] : aElementOf0(W1,W0) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [W0,W1] :
      ( ( W0 != slcrc0
        | ~ aElementOf0(W1,W0) )
      & ( W0 != slcrc0
        | aSet0(W0) )
      & ( ~ aSet0(W0)
        | W0 = slcrc0
        | aElementOf0(skolemFOFtoCNF_W1(W0),W0) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [W0,W1] :
      ( W0 != slcrc0
      | ~ aElementOf0(W1,W0) ),
    inference(conjunct,[],[normalize_0_6]) ).

cnf(refute_0_0,plain,
    aElementOf0(skolemFOFtoCNF_W0,slcrc0),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( W0 != slcrc0
    | ~ aElementOf0(W1,W0) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_2,plain,
    ( slcrc0 != slcrc0
    | ~ aElementOf0(W1,slcrc0) ),
    inference(subst,[],[refute_0_1:[bind(W0,$fot(slcrc0))]]) ).

cnf(refute_0_3,plain,
    slcrc0 = slcrc0,
    introduced(tautology,[refl,[$fot(slcrc0)]]) ).

cnf(refute_0_4,plain,
    ~ aElementOf0(W1,slcrc0),
    inference(resolve,[$cnf( $equal(slcrc0,slcrc0) )],[refute_0_3,refute_0_2]) ).

cnf(refute_0_5,plain,
    ~ aElementOf0(skolemFOFtoCNF_W0,slcrc0),
    inference(subst,[],[refute_0_4:[bind(W1,$fot(skolemFOFtoCNF_W0))]]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W0,slcrc0) )],[refute_0_0,refute_0_5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : NUM564+3 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n013.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jul  7 14:10:14 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48  
% 0.19/0.48  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.48  
%------------------------------------------------------------------------------