%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM548+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n010.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 12:27:38 EDT 2022

% Result   : Theorem 0.18s 0.46s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   27 (  14 unt;   0 def)
%            Number of atoms       :   60 (   5 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   59 (  26   ~;  19   |;   9   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :    8 (   0 sgn   7   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mCardNum,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) ) ) ).

fof(m__2202,hypothesis,
    aElementOf0(xk,szNzAzT0) ).

fof(m__2270,hypothesis,
    ( aSet0(xQ)
    & ! [W0] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xS) )
    & aSubsetOf0(xQ,xS)
    & sbrdtbr0(xQ) = xk
    & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ) ).

fof(m__,conjecture,
    isFinite0(xQ) ).

fof(subgoal_0,plain,
    isFinite0(xQ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ isFinite0(xQ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ( ~ aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> ~ isFinite0(W0) ) ),
    inference(canonicalize,[],[mCardNum]) ).

fof(normalize_0_1,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ( ~ aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> ~ isFinite0(W0) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [W0] :
      ( ( ~ aElementOf0(sbrdtbr0(W0),szNzAzT0)
        | ~ aSet0(W0)
        | isFinite0(W0) )
      & ( ~ aSet0(W0)
        | ~ isFinite0(W0)
        | aElementOf0(sbrdtbr0(W0),szNzAzT0) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [W0] :
      ( ~ aElementOf0(sbrdtbr0(W0),szNzAzT0)
      | ~ aSet0(W0)
      | isFinite0(W0) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ( sbrdtbr0(xQ) = xk
    & aElementOf0(xQ,slbdtsldtrb0(xS,xk))
    & aSet0(xQ)
    & aSubsetOf0(xQ,xS)
    & ! [W0] :
        ( ~ aElementOf0(W0,xQ)
        | aElementOf0(W0,xS) ) ),
    inference(canonicalize,[],[m__2270]) ).

fof(normalize_0_5,plain,
    sbrdtbr0(xQ) = xk,
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    aElementOf0(xk,szNzAzT0),
    inference(canonicalize,[],[m__2202]) ).

fof(normalize_0_7,plain,
    aSet0(xQ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_8,plain,
    ~ isFinite0(xQ),
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    ( ~ aElementOf0(sbrdtbr0(W0),szNzAzT0)
    | ~ aSet0(W0)
    | isFinite0(W0) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ aElementOf0(sbrdtbr0(xQ),szNzAzT0)
    | ~ aSet0(xQ)
    | isFinite0(xQ) ),
    inference(subst,[],[refute_0_0:[bind(W0,$fot(xQ))]]) ).

cnf(refute_0_2,plain,
    sbrdtbr0(xQ) = xk,
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
    ( sbrdtbr0(xQ) != xk
    | ~ aElementOf0(xk,szNzAzT0)
    | aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),
    introduced(tautology,[equality,[$cnf( ~ aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),[0],$fot(xk)]]) ).

cnf(refute_0_4,plain,
    ( ~ aElementOf0(xk,szNzAzT0)
    | aElementOf0(sbrdtbr0(xQ),szNzAzT0) ),
    inference(resolve,[$cnf( $equal(sbrdtbr0(xQ),xk) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ aElementOf0(xk,szNzAzT0)
    | ~ aSet0(xQ)
    | isFinite0(xQ) ),
    inference(resolve,[$cnf( aElementOf0(sbrdtbr0(xQ),szNzAzT0) )],[refute_0_4,refute_0_1]) ).

cnf(refute_0_6,plain,
    aElementOf0(xk,szNzAzT0),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_7,plain,
    ( ~ aSet0(xQ)
    | isFinite0(xQ) ),
    inference(resolve,[$cnf( aElementOf0(xk,szNzAzT0) )],[refute_0_6,refute_0_5]) ).

cnf(refute_0_8,plain,
    aSet0(xQ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_9,plain,
    isFinite0(xQ),
    inference(resolve,[$cnf( aSet0(xQ) )],[refute_0_8,refute_0_7]) ).

cnf(refute_0_10,plain,
    ~ isFinite0(xQ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( isFinite0(xQ) )],[refute_0_9,refute_0_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : NUM548+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n010.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  : 600
% 0.12/0.33  % DateTime : Thu Jul  7 02:10:31 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.46  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46  
% 0.18/0.46  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.46  
%------------------------------------------------------------------------------