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Drodi---4.1.1.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : SET099-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 02:09:20 PM UTC 2026

% Result   : Unsatisfiable 4.70s 1.08s
% Output   : CNFRefutation 4.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  113 (  28 unt;   0 def)
%            Number of atoms       :  226 (  66 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  188 (  75   ~; 113   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :  141 ( 141   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y,U] :
      ( member(U,Y)
      | ~ member(U,X)
      | ~ subclass(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
      | member(not_subclass_element(X,Y),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
      | ~ member(not_subclass_element(X,Y),Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X] : subclass(X,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y] :
      ( X = Y
      | ~ subclass(Y,X)
      | ~ subclass(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [U,X,Y] :
      ( U = Y
      | U = X
      | ~ member(U,unordered_pair(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y] :
      ( member(X,unordered_pair(X,Y))
      | ~ member(X,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X] : unordered_pair(X,X) = singleton(X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [Z,X,Y] :
      ( member(Z,X)
      | ~ member(Z,intersection(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [Z,X,Y] :
      ( member(Z,Y)
      | ~ member(Z,intersection(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [Z,X,Y] :
      ( member(Z,intersection(X,Y))
      | ~ member(Z,Y)
      | ~ member(Z,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ! [Z,X] :
      ( ~ member(Z,X)
      | ~ member(Z,complement(X)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ! [Z,X] :
      ( member(Z,X)
      | member(Z,complement(X))
      | ~ member(Z,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f66,axiom,
    ! [X] :
      ( member(regular(X),X)
      | X = null_class ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f67,axiom,
    ! [X] :
      ( intersection(X,regular(X)) = null_class
      | X = null_class ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f92,negated_conjecture,
    not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f93,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f94,negated_conjecture,
    x != null_class,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f95,plain,
    ! [Y,U] :
      ( member(U,Y)
      | ! [X] :
          ( ~ member(U,X)
          | ~ subclass(X,Y) ) ),
    inference(miniscoping,[status(thm)],[f1]) ).

fof(f96,plain,
    ! [X0,X1,X2] :
      ( member(X2,X1)
      | ~ member(X2,X0)
      | ~ subclass(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f95]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    inference(cnf_transformation,[status(thm)],[f2]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    inference(cnf_transformation,[status(thm)],[f3]) ).

fof(f99,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(thm)],[f4]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subclass(X1,X0)
      | ~ subclass(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f7]) ).

fof(f103,plain,
    ! [U,Y] :
      ( U = Y
      | ! [X] :
          ( U = X
          | ~ member(U,unordered_pair(X,Y)) ) ),
    inference(miniscoping,[status(thm)],[f8]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( X0 = X2
      | X0 = X1
      | ~ member(X0,unordered_pair(X1,X2)) ),
    inference(cnf_transformation,[status(thm)],[f103]) ).

fof(f105,plain,
    ! [X] :
      ( ! [Y] : member(X,unordered_pair(X,Y))
      | ~ member(X,universal_class) ),
    inference(miniscoping,[status(thm)],[f9]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( member(X0,unordered_pair(X0,X1))
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[status(thm)],[f105]) ).

fof(f110,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(thm)],[f12]) ).

fof(f122,plain,
    ! [Z,X] :
      ( member(Z,X)
      | ! [Y] : ~ member(Z,intersection(X,Y)) ),
    inference(miniscoping,[status(thm)],[f21]) ).

fof(f123,plain,
    ! [X0,X1,X2] :
      ( member(X0,X1)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[status(thm)],[f122]) ).

fof(f124,plain,
    ! [Z,Y] :
      ( member(Z,Y)
      | ! [X] : ~ member(Z,intersection(X,Y)) ),
    inference(miniscoping,[status(thm)],[f22]) ).

fof(f125,plain,
    ! [X0,X1,X2] :
      ( member(X0,X2)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[status(thm)],[f124]) ).

fof(f126,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X2)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f23]) ).

fof(f127,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | ~ member(X0,complement(X1)) ),
    inference(cnf_transformation,[status(thm)],[f24]) ).

fof(f128,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | member(X0,complement(X1))
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[status(thm)],[f25]) ).

fof(f169,plain,
    ! [X0] :
      ( member(regular(X0),X0)
      | X0 = null_class ),
    inference(cnf_transformation,[status(thm)],[f66]) ).

fof(f170,plain,
    ! [X0] :
      ( intersection(X0,regular(X0)) = null_class
      | X0 = null_class ),
    inference(cnf_transformation,[status(thm)],[f67]) ).

fof(f200,plain,
    not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
    inference(cnf_transformation,[status(thm)],[f92]) ).

fof(f201,plain,
    singleton(not_subclass_element(x,null_class)) != x,
    inference(cnf_transformation,[status(thm)],[f93]) ).

fof(f202,plain,
    x != null_class,
    inference(cnf_transformation,[status(thm)],[f94]) ).

fof(f210,plain,
    ( subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class)
    | member(not_subclass_element(x,null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
    inference(paramodulation,[status(thm)],[f200,f97]) ).

fof(f214,plain,
    ( subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class)
    | member(not_subclass_element(x,null_class),complement(singleton(not_subclass_element(x,null_class)))) ),
    inference(resolution,[status(thm)],[f123,f210]) ).

fof(f215,plain,
    ! [X0,X1,X2] :
      ( subclass(intersection(X0,X1),X2)
      | member(not_subclass_element(intersection(X0,X1),X2),X0) ),
    inference(resolution,[status(thm)],[f123,f97]) ).

fof(f216,plain,
    ( subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class)
    | member(not_subclass_element(x,null_class),x) ),
    inference(resolution,[status(thm)],[f125,f210]) ).

fof(f217,plain,
    ! [X0,X1,X2] :
      ( subclass(intersection(X0,X1),X2)
      | member(not_subclass_element(intersection(X0,X1),X2),X1) ),
    inference(resolution,[status(thm)],[f125,f97]) ).

fof(f219,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),intersection(X2,X0))
      | ~ member(not_subclass_element(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f126,f97]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( subclass(intersection(X0,X1),X0)
      | subclass(intersection(X0,X1),X0) ),
    inference(resolution,[status(thm)],[f215,f98]) ).

fof(f228,plain,
    ! [X0,X1] : subclass(intersection(X0,X1),X0),
    inference(duplicate_literals_removal,[status(thm)],[f221]) ).

fof(f229,plain,
    ! [X0,X1] :
      ( subclass(intersection(X0,X1),X1)
      | subclass(intersection(X0,X1),X1) ),
    inference(resolution,[status(thm)],[f217,f98]) ).

fof(f236,plain,
    ! [X0,X1] : subclass(intersection(X0,X1),X1),
    inference(duplicate_literals_removal,[status(thm)],[f229]) ).

fof(f237,plain,
    ! [X0,X1] :
      ( subclass(X0,intersection(X1,X0))
      | subclass(X0,intersection(X1,X0))
      | ~ member(not_subclass_element(X0,intersection(X1,X0)),X1) ),
    inference(resolution,[status(thm)],[f219,f98]) ).

fof(f242,plain,
    ! [X0,X1] :
      ( subclass(X0,intersection(X1,X0))
      | ~ member(not_subclass_element(X0,intersection(X1,X0)),X1) ),
    inference(duplicate_literals_removal,[status(thm)],[f237]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( member(X0,universal_class)
      | ~ member(X0,X1) ),
    inference(resolution,[status(thm)],[f96,f99]) ).

fof(f276,plain,
    ! [X0,X1] :
      ( X0 = intersection(X1,X0)
      | ~ subclass(X0,intersection(X1,X0)) ),
    inference(resolution,[status(thm)],[f102,f236]) ).

fof(f277,plain,
    ! [X0,X1] :
      ( X0 = intersection(X0,X1)
      | ~ subclass(X0,intersection(X0,X1)) ),
    inference(resolution,[status(thm)],[f102,f228]) ).

fof(f287,plain,
    ! [X0,X1] :
      ( X0 = X1
      | X0 = X1
      | ~ member(X0,singleton(X1)) ),
    inference(paramodulation,[status(thm)],[f110,f104]) ).

fof(f288,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(X0,singleton(X1)) ),
    inference(duplicate_literals_removal,[status(thm)],[f287]) ).

fof(f289,plain,
    ( null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x)
    | ~ subclass(null_class,intersection(complement(singleton(not_subclass_element(x,null_class))),x))
    | member(not_subclass_element(x,null_class),x) ),
    inference(resolution,[status(thm)],[f216,f102]) ).

fof(f296,plain,
    ( null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x)
    | ~ subclass(null_class,intersection(complement(singleton(not_subclass_element(x,null_class))),x))
    | member(not_subclass_element(x,null_class),complement(singleton(not_subclass_element(x,null_class)))) ),
    inference(resolution,[status(thm)],[f214,f102]) ).

fof(f413,plain,
    ! [X0,X1] :
      ( subclass(singleton(X0),X1)
      | not_subclass_element(singleton(X0),X1) = X0 ),
    inference(resolution,[status(thm)],[f288,f97]) ).

fof(f418,plain,
    ! [X0,X1] :
      ( member(regular(intersection(X0,X1)),X1)
      | intersection(X0,X1) = null_class ),
    inference(resolution,[status(thm)],[f169,f125]) ).

fof(f428,plain,
    ! [X0,X1,X2] :
      ( member(X0,X2)
      | member(X0,complement(X2))
      | ~ member(X0,X1) ),
    inference(resolution,[status(thm)],[f271,f128]) ).

fof(f508,plain,
    ! [X0] :
      ( X0 = null_class
      | subclass(null_class,X0) ),
    inference(paramodulation,[status(thm)],[f170,f228]) ).

fof(f512,plain,
    ( null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x)
    | member(not_subclass_element(x,null_class),complement(singleton(not_subclass_element(x,null_class)))) ),
    inference(backward_subsumption_resolution,[status(thm)],[f296,f508]) ).

fof(f513,plain,
    ( null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x)
    | member(not_subclass_element(x,null_class),x) ),
    inference(backward_subsumption_resolution,[status(thm)],[f289,f508]) ).

fof(f520,plain,
    ! [X0] :
      ( member(X0,singleton(X0))
      | ~ member(X0,universal_class) ),
    inference(paramodulation,[status(thm)],[f110,f106]) ).

fof(f546,plain,
    ( ~ member(not_subclass_element(x,null_class),singleton(not_subclass_element(x,null_class)))
    | null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x) ),
    inference(resolution,[status(thm)],[f512,f127]) ).

fof(f565,plain,
    ! [X0] :
      ( null_class = intersection(null_class,X0)
      | intersection(null_class,X0) = null_class ),
    inference(resolution,[status(thm)],[f508,f277]) ).

fof(f567,plain,
    ! [X0] :
      ( X0 = null_class
      | ~ subclass(X0,null_class)
      | X0 = null_class ),
    inference(resolution,[status(thm)],[f508,f102]) ).

fof(f569,plain,
    ! [X0] : intersection(null_class,X0) = null_class,
    inference(duplicate_literals_removal,[status(thm)],[f565]) ).

fof(f573,plain,
    ! [X0] :
      ( ~ subclass(X0,null_class)
      | X0 = null_class ),
    inference(duplicate_literals_removal,[status(thm)],[f567]) ).

fof(f597,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(X0,null_class) ),
    inference(paramodulation,[status(thm)],[f569,f125]) ).

fof(f695,plain,
    ( null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x)
    | ~ member(not_subclass_element(x,null_class),universal_class) ),
    inference(resolution,[status(thm)],[f520,f546]) ).

fof(f698,plain,
    ! [X0,X1] :
      ( member(X0,intersection(X1,singleton(X0)))
      | ~ member(X0,X1)
      | ~ member(X0,universal_class) ),
    inference(resolution,[status(thm)],[f520,f126]) ).

fof(f700,plain,
    ! [X0,X1] :
      ( member(X0,intersection(X1,singleton(X0)))
      | ~ member(X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f698,f271]) ).

fof(f791,plain,
    ! [X0] :
      ( ~ member(not_subclass_element(x,null_class),X0)
      | null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x) ),
    inference(resolution,[status(thm)],[f695,f271]) ).

fof(f792,plain,
    null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x),
    inference(backward_subsumption_resolution,[status(thm)],[f513,f791]) ).

fof(f804,plain,
    not_subclass_element(null_class,null_class) = not_subclass_element(x,null_class),
    inference(backward_demodulation,[status(thm)],[f792,f200]) ).

fof(f824,plain,
    singleton(not_subclass_element(null_class,null_class)) != x,
    inference(backward_demodulation,[status(thm)],[f804,f201]) ).

fof(f825,plain,
    null_class = intersection(complement(singleton(not_subclass_element(null_class,null_class))),x),
    inference(backward_demodulation,[status(thm)],[f804,f792]) ).

fof(f863,plain,
    ( subclass(x,null_class)
    | member(not_subclass_element(null_class,null_class),x) ),
    inference(paramodulation,[status(thm)],[f804,f97]) ).

fof(f870,plain,
    ! [X0] :
      ( subclass(x,X0)
      | member(not_subclass_element(x,X0),null_class)
      | ~ member(not_subclass_element(x,X0),complement(singleton(not_subclass_element(null_class,null_class)))) ),
    inference(paramodulation,[status(thm)],[f825,f219]) ).

fof(f1144,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(x,X0),singleton(not_subclass_element(null_class,null_class)))
      | ~ member(not_subclass_element(x,X0),X1)
      | subclass(x,X0)
      | member(not_subclass_element(x,X0),null_class) ),
    inference(resolution,[status(thm)],[f870,f428]) ).

fof(f1146,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(x,X0),singleton(not_subclass_element(null_class,null_class)))
      | ~ member(not_subclass_element(x,X0),X1)
      | subclass(x,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1144,f597]) ).

fof(f1150,plain,
    ! [X0,X1] :
      ( not_subclass_element(x,X0) = not_subclass_element(null_class,null_class)
      | ~ member(not_subclass_element(x,X0),X1)
      | subclass(x,X0) ),
    inference(resolution,[status(thm)],[f1146,f288]) ).

fof(f1158,plain,
    ! [X0] :
      ( subclass(x,X0)
      | not_subclass_element(x,X0) = not_subclass_element(null_class,null_class)
      | subclass(x,X0) ),
    inference(resolution,[status(thm)],[f1150,f97]) ).

fof(f1169,plain,
    ! [X0] :
      ( not_subclass_element(x,X0) = not_subclass_element(null_class,null_class)
      | subclass(x,X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f1158]) ).

fof(f1171,plain,
    ! [X0] :
      ( x = intersection(x,X0)
      | not_subclass_element(x,intersection(x,X0)) = not_subclass_element(null_class,null_class) ),
    inference(resolution,[status(thm)],[f1169,f277]) ).

fof(f2472,plain,
    ! [X0] :
      ( x = intersection(x,X0)
      | subclass(x,intersection(x,X0))
      | ~ member(not_subclass_element(null_class,null_class),intersection(x,X0)) ),
    inference(paramodulation,[status(thm)],[f1171,f98]) ).

fof(f2473,plain,
    ! [X0] :
      ( x = intersection(x,X0)
      | subclass(x,intersection(x,X0))
      | member(not_subclass_element(null_class,null_class),x) ),
    inference(paramodulation,[status(thm)],[f1171,f97]) ).

fof(f2481,plain,
    ! [X0] :
      ( x = intersection(x,X0)
      | ~ member(not_subclass_element(null_class,null_class),intersection(x,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2472,f277]) ).

fof(f2482,plain,
    ! [X0] :
      ( x = intersection(x,X0)
      | member(not_subclass_element(null_class,null_class),x) ),
    inference(forward_subsumption_resolution,[status(thm)],[f2473,f277]) ).

fof(f2494,plain,
    ( ~ member(not_subclass_element(null_class,null_class),x)
    | x = intersection(x,singleton(not_subclass_element(null_class,null_class))) ),
    inference(resolution,[status(thm)],[f2481,f700]) ).

fof(f2505,plain,
    x = intersection(x,singleton(not_subclass_element(null_class,null_class))),
    inference(forward_subsumption_resolution,[status(thm)],[f2494,f2482]) ).

fof(f2522,plain,
    ( member(regular(x),singleton(not_subclass_element(null_class,null_class)))
    | intersection(x,singleton(not_subclass_element(null_class,null_class))) = null_class ),
    inference(paramodulation,[status(thm)],[f2505,f418]) ).

fof(f2526,plain,
    ( singleton(not_subclass_element(null_class,null_class)) = intersection(x,singleton(not_subclass_element(null_class,null_class)))
    | ~ subclass(singleton(not_subclass_element(null_class,null_class)),x) ),
    inference(paramodulation,[status(thm)],[f2505,f276]) ).

fof(f2540,plain,
    ( member(regular(x),singleton(not_subclass_element(null_class,null_class)))
    | x = null_class ),
    inference(forward_demodulation,[status(thm)],[f2505,f2522]) ).

fof(f2541,plain,
    member(regular(x),singleton(not_subclass_element(null_class,null_class))),
    inference(forward_subsumption_resolution,[status(thm)],[f2540,f202]) ).

fof(f2547,plain,
    ( singleton(not_subclass_element(null_class,null_class)) = x
    | ~ subclass(singleton(not_subclass_element(null_class,null_class)),x) ),
    inference(forward_demodulation,[status(thm)],[f2505,f2526]) ).

fof(f2548,plain,
    ~ subclass(singleton(not_subclass_element(null_class,null_class)),x),
    inference(forward_subsumption_resolution,[status(thm)],[f2547,f824]) ).

fof(f2577,plain,
    regular(x) = not_subclass_element(null_class,null_class),
    inference(resolution,[status(thm)],[f2541,f288]) ).

fof(f2584,plain,
    ~ subclass(singleton(regular(x)),x),
    inference(backward_demodulation,[status(thm)],[f2577,f2548]) ).

fof(f2585,plain,
    x = intersection(x,singleton(regular(x))),
    inference(backward_demodulation,[status(thm)],[f2577,f2505]) ).

fof(f2610,plain,
    ( subclass(x,null_class)
    | member(regular(x),x) ),
    inference(backward_demodulation,[status(thm)],[f2577,f863]) ).

fof(f2863,plain,
    not_subclass_element(singleton(regular(x)),x) = regular(x),
    inference(resolution,[status(thm)],[f2584,f413]) ).

fof(f2881,plain,
    ( subclass(singleton(regular(x)),intersection(x,singleton(regular(x))))
    | ~ member(not_subclass_element(singleton(regular(x)),x),x) ),
    inference(paramodulation,[status(thm)],[f2585,f242]) ).

fof(f2898,plain,
    ( subclass(singleton(regular(x)),intersection(x,singleton(regular(x))))
    | ~ member(regular(x),x) ),
    inference(forward_demodulation,[status(thm)],[f2863,f2881]) ).

fof(f2899,plain,
    ( subclass(singleton(regular(x)),x)
    | ~ member(regular(x),x) ),
    inference(forward_demodulation,[status(thm)],[f2585,f2898]) ).

fof(f2903,plain,
    subclass(x,null_class),
    inference(backward_subsumption_resolution,[status(thm)],[f2610,f2906]) ).

fof(f2906,plain,
    ~ member(regular(x),x),
    inference(forward_subsumption_resolution,[status(thm)],[f2899,f2584]) ).

fof(f2920,plain,
    x = null_class,
    inference(resolution,[status(thm)],[f2903,f573]) ).

fof(f2923,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f2920,f202]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SET099-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03  % Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35  % Computer : n014.cluster.edu
% 0.08/0.35  % Model    : x86_64 x86_64
% 0.08/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35  % Memory   : 8046.5625MB
% 0.08/0.35  % OS       : Linux 6.8.0-71-generic
% 0.08/0.35  % CPULimit : 300
% 0.08/0.35  % WCLimit  : 300
% 0.08/0.35  % DateTime : Mon Sep 21 04:52:34 UTC 2026
% 0.08/0.35  % CPUTime  : 
% 0.08/0.37  % Drodi V4.1.1
% 4.70/1.08  % Refutation found
% 4.70/1.08  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.70/1.08  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.82/1.11  % Elapsed time: 0.739141 seconds
% 0.82/1.11  % CPU time: 5.446133 seconds
% 0.82/1.11  % Total memory used: 190.868 MB
% 0.82/1.11  % Net memory used: 181.362 MB
%------------------------------------------------------------------------------