%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET062+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n012.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 03:31:59 EDT 2022

% Result   : Theorem 2.24s 2.47s
% Output   : CNFRefutation 2.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   21 (  14 unt;   0 def)
%            Number of atoms       :   36 (   0 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   31 (  16   ~;   7   |;   4   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   27 (   3 sgn  18   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( member(U,X)
         => member(U,Y) ) ) ).

fof(null_class_defn,axiom,
    ! [X] : ~ member(X,null_class) ).

fof(null_class_is_subclass,conjecture,
    ! [X] : subclass(null_class,X) ).

fof(subgoal_0,plain,
    ! [X] : subclass(null_class,X),
    inference(strip,[],[null_class_is_subclass]) ).

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

fof(normalize_0_0,plain,
    ? [X] : ~ subclass(null_class,X),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ~ subclass(null_class,skolemFOFtoCNF_X_2),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X] : ~ member(X,null_class),
    inference(canonicalize,[],[null_class_defn]) ).

fof(normalize_0_3,plain,
    ! [X] : ~ member(X,null_class),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ~ subclass(X,Y)
    <=> ? [U] :
          ( ~ member(U,Y)
          & member(U,X) ) ),
    inference(canonicalize,[],[subclass_defn]) ).

fof(normalize_0_5,plain,
    ! [X,Y] :
      ( ~ subclass(X,Y)
    <=> ? [U] :
          ( ~ member(U,Y)
          & member(U,X) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [U,X,Y] :
      ( ( ~ member(skolemFOFtoCNF_U(X,Y),Y)
        | subclass(X,Y) )
      & ( member(skolemFOFtoCNF_U(X,Y),X)
        | subclass(X,Y) )
      & ( ~ member(U,X)
        | ~ subclass(X,Y)
        | member(U,Y) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( member(skolemFOFtoCNF_U(X,Y),X)
      | subclass(X,Y) ),
    inference(conjunct,[],[normalize_0_6]) ).

cnf(refute_0_0,plain,
    ~ subclass(null_class,skolemFOFtoCNF_X_2),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ~ member(X,null_class),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    ~ member(skolemFOFtoCNF_U(null_class,X_261),null_class),
    inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_U(null_class,X_261)))]]) ).

cnf(refute_0_3,plain,
    ( member(skolemFOFtoCNF_U(X,Y),X)
    | subclass(X,Y) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_4,plain,
    ( member(skolemFOFtoCNF_U(null_class,X_261),null_class)
    | subclass(null_class,X_261) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(null_class)),bind(Y,$fot(X_261))]]) ).

cnf(refute_0_5,plain,
    subclass(null_class,X_261),
    inference(resolve,[$cnf( member(skolemFOFtoCNF_U(null_class,X_261),null_class) )],[refute_0_4,refute_0_2]) ).

cnf(refute_0_6,plain,
    subclass(null_class,skolemFOFtoCNF_X_2),
    inference(subst,[],[refute_0_5:[bind(X_261,$fot(skolemFOFtoCNF_X_2))]]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( subclass(null_class,skolemFOFtoCNF_X_2) )],[refute_0_6,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET062+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n012.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 : Sun Jul 10 13:25:58 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.24/2.47  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.24/2.47  
% 2.24/2.47  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.24/2.47  
%------------------------------------------------------------------------------