%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET045+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 : Tue Jul 19 03:31:45 EDT 2022

% Result   : Theorem 0.14s 0.35s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   23 (  11 unt;   0 def)
%            Number of atoms       :   48 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   50 (  25   ~;  17   |;   3   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   37 (   3 sgn  24   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(pel41_1,axiom,
    ! [Z] :
    ? [Y] :
    ! [X] :
      ( element(X,Y)
    <=> ( element(X,Z)
        & ~ element(X,X) ) ) ).

fof(pel41,conjecture,
    ~ ? [Z] :
      ! [X] : element(X,Z) ).

fof(subgoal_0,plain,
    ! [Z] :
      ~ ! [X] : element(X,Z),
    inference(strip,[],[pel41]) ).

fof(negate_0_0,plain,
    ~ ! [Z] :
        ~ ! [X] : element(X,Z),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [Z] :
    ! [X] : element(X,Z),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [X] : element(X,skolemFOFtoCNF_Z),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X] : element(X,skolemFOFtoCNF_Z),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [Z] :
    ? [Y] :
    ! [X] :
      ( ~ element(X,Y)
    <=> ( ~ element(X,Z)
        | element(X,X) ) ),
    inference(canonicalize,[],[pel41_1]) ).

fof(normalize_0_4,plain,
    ! [Z] :
    ? [Y] :
    ! [X] :
      ( ~ element(X,Y)
    <=> ( ~ element(X,Z)
        | element(X,X) ) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [Z,X] :
      ( ~ element(X,skolemFOFtoCNF_Y(Z))
    <=> ( ~ element(X,Z)
        | element(X,X) ) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Z] :
      ( ~ element(X,skolemFOFtoCNF_Y(Z))
    <=> ( ~ element(X,Z)
        | element(X,X) ) ),
    inference(specialize,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Z] :
      ( ( ~ element(X,X)
        | ~ element(X,skolemFOFtoCNF_Y(Z)) )
      & ( ~ element(X,skolemFOFtoCNF_Y(Z))
        | element(X,Z) )
      & ( ~ element(X,Z)
        | element(X,X)
        | element(X,skolemFOFtoCNF_Y(Z)) ) ),
    inference(clausify,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X,Z] :
      ( ~ element(X,Z)
      | element(X,X)
      | element(X,skolemFOFtoCNF_Y(Z)) ),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X,Z] :
      ( ~ element(X,X)
      | ~ element(X,skolemFOFtoCNF_Y(Z)) ),
    inference(conjunct,[],[normalize_0_7]) ).

cnf(refute_0_0,plain,
    element(X,skolemFOFtoCNF_Z),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    element(X_6,skolemFOFtoCNF_Z),
    inference(subst,[],[refute_0_0:[bind(X,$fot(X_6))]]) ).

cnf(refute_0_2,plain,
    ( ~ element(X,Z)
    | element(X,X)
    | element(X,skolemFOFtoCNF_Y(Z)) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_3,plain,
    ( ~ element(X_6,skolemFOFtoCNF_Z)
    | element(X_6,X_6)
    | element(X_6,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z)) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(X_6)),bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).

cnf(refute_0_4,plain,
    ( element(X_6,X_6)
    | element(X_6,skolemFOFtoCNF_Y(skolemFOFtoCNF_Z)) ),
    inference(resolve,[$cnf( element(X_6,skolemFOFtoCNF_Z) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    element(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z),skolemFOFtoCNF_Y(skolemFOFtoCNF_Z)),
    inference(subst,[],[refute_0_4:[bind(X_6,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z)))]]) ).

cnf(refute_0_6,plain,
    ( ~ element(X,X)
    | ~ element(X,skolemFOFtoCNF_Y(Z)) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_7,plain,
    ~ element(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z),skolemFOFtoCNF_Y(skolemFOFtoCNF_Z)),
    inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z))),bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( element(skolemFOFtoCNF_Y(skolemFOFtoCNF_Z),skolemFOFtoCNF_Y(skolemFOFtoCNF_Z)) )],[refute_0_5,refute_0_7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET045+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sun Jul 10 04:16:02 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  
% 0.14/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.35  
%------------------------------------------------------------------------------