%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM568+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n014.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 12:27:49 EDT 2022

% Result   : Theorem 14.00s 14.15s
% Output   : CNFRefutation 14.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   35 (  13 unt;   0 def)
%            Number of atoms       :   74 (  43 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   68 (  29   ~;  31   |;   7   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   22 (   0 sgn   8   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mNatExtra,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( W0 = sz00
        | ? [W1] :
            ( aElementOf0(W1,szNzAzT0)
            & W0 = szszuzczcdt0(W1) ) ) ) ).

fof(m__3418,hypothesis,
    aElementOf0(xK,szNzAzT0) ).

fof(m__3462,hypothesis,
    xK != sz00 ).

fof(m__3520,hypothesis,
    xK != sz00 ).

fof(m__,conjecture,
    ? [W0] :
      ( aElementOf0(W0,szNzAzT0)
      & szszuzczcdt0(W0) = xK ) ).

fof(subgoal_0,plain,
    ? [W0] :
      ( aElementOf0(W0,szNzAzT0)
      & szszuzczcdt0(W0) = xK ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ? [W0] :
        ( aElementOf0(W0,szNzAzT0)
        & szszuzczcdt0(W0) = xK ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    aElementOf0(xK,szNzAzT0),
    inference(canonicalize,[],[m__3418]) ).

fof(normalize_0_1,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | W0 = sz00
      | ? [W1] :
          ( W0 = szszuzczcdt0(W1)
          & aElementOf0(W1,szNzAzT0) ) ),
    inference(canonicalize,[],[mNatExtra]) ).

fof(normalize_0_2,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | W0 = sz00
      | ? [W1] :
          ( W0 = szszuzczcdt0(W1)
          & aElementOf0(W1,szNzAzT0) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [W0] :
      ( ( ~ aElementOf0(W0,szNzAzT0)
        | W0 = sz00
        | W0 = szszuzczcdt0(skolemFOFtoCNF_W1_1(W0)) )
      & ( ~ aElementOf0(W0,szNzAzT0)
        | W0 = sz00
        | aElementOf0(skolemFOFtoCNF_W1_1(W0),szNzAzT0) ) ),
    inference(clausify,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | W0 = sz00
      | W0 = szszuzczcdt0(skolemFOFtoCNF_W1_1(W0)) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    xK != sz00,
    inference(canonicalize,[],[m__3520]) ).

fof(normalize_0_6,plain,
    ! [W0] :
      ( szszuzczcdt0(W0) != xK
      | ~ aElementOf0(W0,szNzAzT0) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_7,plain,
    ! [W0] :
      ( szszuzczcdt0(W0) != xK
      | ~ aElementOf0(W0,szNzAzT0) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [W0] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | W0 = sz00
      | aElementOf0(skolemFOFtoCNF_W1_1(W0),szNzAzT0) ),
    inference(conjunct,[],[normalize_0_3]) ).

cnf(refute_0_0,plain,
    aElementOf0(xK,szNzAzT0),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    ( ~ aElementOf0(W0,szNzAzT0)
    | W0 = sz00
    | W0 = szszuzczcdt0(skolemFOFtoCNF_W1_1(W0)) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_2,plain,
    ( ~ aElementOf0(xK,szNzAzT0)
    | xK = sz00
    | xK = szszuzczcdt0(skolemFOFtoCNF_W1_1(xK)) ),
    inference(subst,[],[refute_0_1:[bind(W0,$fot(xK))]]) ).

cnf(refute_0_3,plain,
    ( xK = sz00
    | xK = szszuzczcdt0(skolemFOFtoCNF_W1_1(xK)) ),
    inference(resolve,[$cnf( aElementOf0(xK,szNzAzT0) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    xK != sz00,
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_5,plain,
    xK = szszuzczcdt0(skolemFOFtoCNF_W1_1(xK)),
    inference(resolve,[$cnf( $equal(xK,sz00) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( szszuzczcdt0(W0) != xK
    | ~ aElementOf0(W0,szNzAzT0) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_7,plain,
    ( szszuzczcdt0(skolemFOFtoCNF_W1_1(xK)) != xK
    | ~ aElementOf0(skolemFOFtoCNF_W1_1(xK),szNzAzT0) ),
    inference(subst,[],[refute_0_6:[bind(W0,$fot(skolemFOFtoCNF_W1_1(xK)))]]) ).

cnf(refute_0_8,plain,
    ( ~ aElementOf0(W0,szNzAzT0)
    | W0 = sz00
    | aElementOf0(skolemFOFtoCNF_W1_1(W0),szNzAzT0) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_9,plain,
    ( ~ aElementOf0(xK,szNzAzT0)
    | xK = sz00
    | aElementOf0(skolemFOFtoCNF_W1_1(xK),szNzAzT0) ),
    inference(subst,[],[refute_0_8:[bind(W0,$fot(xK))]]) ).

cnf(refute_0_10,plain,
    ( xK = sz00
    | aElementOf0(skolemFOFtoCNF_W1_1(xK),szNzAzT0) ),
    inference(resolve,[$cnf( aElementOf0(xK,szNzAzT0) )],[refute_0_0,refute_0_9]) ).

cnf(refute_0_11,plain,
    aElementOf0(skolemFOFtoCNF_W1_1(xK),szNzAzT0),
    inference(resolve,[$cnf( $equal(xK,sz00) )],[refute_0_10,refute_0_4]) ).

cnf(refute_0_12,plain,
    szszuzczcdt0(skolemFOFtoCNF_W1_1(xK)) != xK,
    inference(resolve,[$cnf( aElementOf0(skolemFOFtoCNF_W1_1(xK),szNzAzT0) )],[refute_0_11,refute_0_7]) ).

cnf(refute_0_13,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_14,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_15,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( xK != szszuzczcdt0(skolemFOFtoCNF_W1_1(xK))
    | szszuzczcdt0(skolemFOFtoCNF_W1_1(xK)) = xK ),
    inference(subst,[],[refute_0_15:[bind(X,$fot(xK)),bind(Y,$fot(szszuzczcdt0(skolemFOFtoCNF_W1_1(xK))))]]) ).

cnf(refute_0_17,plain,
    xK != szszuzczcdt0(skolemFOFtoCNF_W1_1(xK)),
    inference(resolve,[$cnf( $equal(szszuzczcdt0(skolemFOFtoCNF_W1_1(xK)),xK) )],[refute_0_16,refute_0_12]) ).

cnf(refute_0_18,plain,
    $false,
    inference(resolve,[$cnf( $equal(xK,szszuzczcdt0(skolemFOFtoCNF_W1_1(xK))) )],[refute_0_5,refute_0_17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM568+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.33  % Computer : n014.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Thu Jul  7 08:43:52 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 14.00/14.15  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.00/14.15  
% 14.00/14.15  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.00/14.15  
%------------------------------------------------------------------------------