%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : RNG102+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 20:35:58 EDT 2022

% Result   : Theorem 2.53s 2.78s
% Output   : CNFRefutation 2.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   21 (   7 unt;   0 def)
%            Number of atoms       :   46 (  22 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   40 (  15   ~;   8   |;  17   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   11 (   0 sgn   2   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__1933,hypothesis,
    ( ? [W0] :
        ( aElement0(W0)
        & sdtasdt0(xc,W0) = xx )
    & aElementOf0(xx,slsdtgt0(xc))
    & ? [W0] :
        ( aElement0(W0)
        & sdtasdt0(xc,W0) = xy )
    & aElementOf0(xy,slsdtgt0(xc))
    & aElement0(xz) ) ).

fof(m__,conjecture,
    ? [W0] :
      ( aElement0(W0)
      & sdtasdt0(xc,W0) = xy ) ).

fof(subgoal_0,plain,
    ? [W0] :
      ( aElement0(W0)
      & sdtasdt0(xc,W0) = xy ),
    inference(strip,[],[m__]) ).

fof(negate_0_0,plain,
    ~ ? [W0] :
        ( aElement0(W0)
        & sdtasdt0(xc,W0) = xy ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [W0] :
      ( sdtasdt0(xc,W0) != xy
      | ~ aElement0(W0) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [W0] :
      ( sdtasdt0(xc,W0) != xy
      | ~ aElement0(W0) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ( aElement0(xz)
    & aElementOf0(xx,slsdtgt0(xc))
    & aElementOf0(xy,slsdtgt0(xc))
    & ? [W0] :
        ( sdtasdt0(xc,W0) = xx
        & aElement0(W0) )
    & ? [W0] :
        ( sdtasdt0(xc,W0) = xy
        & aElement0(W0) ) ),
    inference(canonicalize,[],[m__1933]) ).

fof(normalize_0_3,plain,
    ? [W0] :
      ( sdtasdt0(xc,W0) = xy
      & aElement0(W0) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ( sdtasdt0(xc,skolemFOFtoCNF_W0_1) = xy
    & aElement0(skolemFOFtoCNF_W0_1) ),
    inference(skolemize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    sdtasdt0(xc,skolemFOFtoCNF_W0_1) = xy,
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    aElement0(skolemFOFtoCNF_W0_1),
    inference(conjunct,[],[normalize_0_4]) ).

cnf(refute_0_0,plain,
    ( sdtasdt0(xc,W0) != xy
    | ~ aElement0(W0) ),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( sdtasdt0(xc,skolemFOFtoCNF_W0_1) != xy
    | ~ aElement0(skolemFOFtoCNF_W0_1) ),
    inference(subst,[],[refute_0_0:[bind(W0,$fot(skolemFOFtoCNF_W0_1))]]) ).

cnf(refute_0_2,plain,
    sdtasdt0(xc,skolemFOFtoCNF_W0_1) = xy,
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
    ( sdtasdt0(xc,skolemFOFtoCNF_W0_1) != xy
    | xy != xy
    | sdtasdt0(xc,skolemFOFtoCNF_W0_1) = xy ),
    introduced(tautology,[equality,[$cnf( ~ $equal(sdtasdt0(xc,skolemFOFtoCNF_W0_1),xy) ),[0],$fot(xy)]]) ).

cnf(refute_0_4,plain,
    ( xy != xy
    | sdtasdt0(xc,skolemFOFtoCNF_W0_1) = xy ),
    inference(resolve,[$cnf( $equal(sdtasdt0(xc,skolemFOFtoCNF_W0_1),xy) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( xy != xy
    | ~ aElement0(skolemFOFtoCNF_W0_1) ),
    inference(resolve,[$cnf( $equal(sdtasdt0(xc,skolemFOFtoCNF_W0_1),xy) )],[refute_0_4,refute_0_1]) ).

cnf(refute_0_6,plain,
    xy = xy,
    introduced(tautology,[refl,[$fot(xy)]]) ).

cnf(refute_0_7,plain,
    ~ aElement0(skolemFOFtoCNF_W0_1),
    inference(resolve,[$cnf( $equal(xy,xy) )],[refute_0_6,refute_0_5]) ).

cnf(refute_0_8,plain,
    aElement0(skolemFOFtoCNF_W0_1),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0_1) )],[refute_0_8,refute_0_7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG102+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n020.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  : 600
% 0.13/0.34  % DateTime : Mon May 30 16:14:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.53/2.78  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.53/2.78  
% 2.53/2.78  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.53/2.78  
%------------------------------------------------------------------------------