%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET064+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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 03:32:04 EDT 2022

% Result   : Theorem 0.18s 0.58s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   20 (   8 unt;   0 def)
%            Number of atoms       :   42 (  17 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   36 (  14   ~;   9   |;  10   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :   21 (   1 sgn  12   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(regularity,axiom,
    ! [X] :
      ( X != null_class
     => ? [U] :
          ( member(U,universal_class)
          & member(U,X)
          & disjoint(U,X) ) ) ).

fof(null_class_is_unique,conjecture,
    ! [Z] :
      ( Z = null_class
      | ? [Y] : member(Y,Z) ) ).

fof(subgoal_0,plain,
    ! [Z] :
      ( Z != null_class
     => ? [Y] : member(Y,Z) ),
    inference(strip,[],[null_class_is_unique]) ).

fof(negate_0_0,plain,
    ~ ! [Z] :
        ( Z != null_class
       => ? [Y] : member(Y,Z) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [Z] :
      ( Z != null_class
      & ! [Y] : ~ member(Y,Z) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( skolemFOFtoCNF_Z != null_class
    & ! [Y] : ~ member(Y,skolemFOFtoCNF_Z) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [Y] : ~ member(Y,skolemFOFtoCNF_Z),
    inference(conjunct,[],[normalize_0_1]) ).

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

fof(normalize_0_4,plain,
    ! [X] :
      ( X = null_class
      | ? [U] :
          ( disjoint(U,X)
          & member(U,X)
          & member(U,universal_class) ) ),
    inference(canonicalize,[],[regularity]) ).

fof(normalize_0_5,plain,
    ! [X] :
      ( X = null_class
      | ? [U] :
          ( disjoint(U,X)
          & member(U,X)
          & member(U,universal_class) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X] :
      ( ( X = null_class
        | disjoint(skolemFOFtoCNF_U_2(X),X) )
      & ( X = null_class
        | member(skolemFOFtoCNF_U_2(X),X) )
      & ( X = null_class
        | member(skolemFOFtoCNF_U_2(X),universal_class) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X] :
      ( X = null_class
      | member(skolemFOFtoCNF_U_2(X),X) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    skolemFOFtoCNF_Z != null_class,
    inference(conjunct,[],[normalize_0_1]) ).

cnf(refute_0_0,plain,
    ~ member(Y,skolemFOFtoCNF_Z),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ~ member(skolemFOFtoCNF_U_2(skolemFOFtoCNF_Z),skolemFOFtoCNF_Z),
    inference(subst,[],[refute_0_0:[bind(Y,$fot(skolemFOFtoCNF_U_2(skolemFOFtoCNF_Z)))]]) ).

cnf(refute_0_2,plain,
    ( X = null_class
    | member(skolemFOFtoCNF_U_2(X),X) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_3,plain,
    ( skolemFOFtoCNF_Z = null_class
    | member(skolemFOFtoCNF_U_2(skolemFOFtoCNF_Z),skolemFOFtoCNF_Z) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).

cnf(refute_0_4,plain,
    skolemFOFtoCNF_Z = null_class,
    inference(resolve,[$cnf( member(skolemFOFtoCNF_U_2(skolemFOFtoCNF_Z),skolemFOFtoCNF_Z) )],[refute_0_3,refute_0_1]) ).

cnf(refute_0_5,plain,
    skolemFOFtoCNF_Z != null_class,
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z,null_class) )],[refute_0_4,refute_0_5]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SET064+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n015.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 : Sun Jul 10 13:56:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.58  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.58  
% 0.18/0.58  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.58  
%------------------------------------------------------------------------------