%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET064-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 03:32:05 EDT 2022

% Result   : Unsatisfiable 3.44s 3.65s
% Output   : CNFRefutation 3.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   5 unt;   2 nHn;   8 RR)
%            Number of literals    :   13 (   4 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :    3 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(not_subclass_members1,axiom,
    ( member(not_subclass_element(X,Y),X)
    | subclass(X,Y) ) ).

cnf(corollary_of_null_class_is_subclass,axiom,
    ( ~ subclass(X,null_class)
    | X = null_class ) ).

cnf(prove_null_class_is_unique_1,negated_conjecture,
    z != null_class ).

cnf(prove_null_class_is_unique_2,negated_conjecture,
    ~ member(not_subclass_element(z,null_class),z) ).

cnf(refute_0_0,plain,
    ( ~ subclass(z,null_class)
    | z = null_class ),
    inference(subst,[],[corollary_of_null_class_is_subclass:[bind(X,$fot(z))]]) ).

cnf(refute_0_1,plain,
    ( member(not_subclass_element(z,null_class),z)
    | subclass(z,null_class) ),
    inference(subst,[],[not_subclass_members1:[bind(X,$fot(z)),bind(Y,$fot(null_class))]]) ).

cnf(refute_0_2,plain,
    subclass(z,null_class),
    inference(resolve,[$cnf( member(not_subclass_element(z,null_class),z) )],[refute_0_1,prove_null_class_is_unique_2]) ).

cnf(refute_0_3,plain,
    z = null_class,
    inference(resolve,[$cnf( subclass(z,null_class) )],[refute_0_2,refute_0_0]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( $equal(z,null_class) )],[refute_0_3,prove_null_class_is_unique_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET064-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n009.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 03:08:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.44/3.65  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.44/3.65  
% 3.44/3.65  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.44/3.65  
%------------------------------------------------------------------------------