%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM181-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 01:38:44 PM UTC 2026
% Result : Unsatisfiable 103.35s 13.59s
% Output : CNFRefutation 103.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 126 ( 32 unt; 0 def)
% Number of atoms : 254 ( 64 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 223 ( 95 ~; 128 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 161 ( 161 !; 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(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(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),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(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [X] :
( inductive(X)
| ~ subclass(image(successor_relation,X),X)
| ~ member(null_class,X) ),
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(f138,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f139,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
member(null_class,limit_ordinals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f161,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f163,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f164,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f168,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f169,plain,
! [X0,X1,X2] :
( X2 = X0
| ~ member(X0,unordered_pair(X2,X1))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f170,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f171,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f174,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f175,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f187,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f189,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f190,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X2,X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,intersection(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f192,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f193,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f194,plain,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f215,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f217,plain,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f234,plain,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f235,plain,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f322,plain,
kind_1_ordinals = union(singleton(null_class),image(successor_relation,ordinal_numbers)),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f323,plain,
limit_ordinals = intersection(complement(kind_1_ordinals),ordinal_numbers),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f347,plain,
member(null_class,limit_ordinals),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f354,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f175,f174]) ).
fof(f356,plain,
! [X0,X1] :
( X1 = X0
| ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f175,f169]) ).
fof(f357,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f356]) ).
fof(f367,plain,
! [X0] :
( null_class = singleton(X0)
| X0 = regular(singleton(X0)) ),
inference(resolution,[status(thm)],[f234,f357]) ).
fof(f393,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| null_class = intersection(X0,X1) ),
inference(resolution,[status(thm)],[f188,f234]) ).
fof(f396,plain,
! [X0] :
( ~ member(X0,limit_ordinals)
| member(X0,complement(kind_1_ordinals)) ),
inference(paramodulation,[status(thm)],[f323,f188]) ).
fof(f398,plain,
! [X0] :
( ~ member(not_subclass_element(X0,complement(kind_1_ordinals)),limit_ordinals)
| subclass(X0,complement(kind_1_ordinals)) ),
inference(resolution,[status(thm)],[f396,f163]) ).
fof(f399,plain,
! [X0] :
( ~ member(X0,kind_1_ordinals)
| ~ member(X0,limit_ordinals) ),
inference(resolution,[status(thm)],[f396,f192]) ).
fof(f414,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| X0 = not_subclass_element(singleton(X0),X1) ),
inference(resolution,[status(thm)],[f162,f357]) ).
fof(f424,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class ),
inference(resolution,[status(thm)],[f190,f234]) ).
fof(f427,plain,
! [X0] :
( member(X0,ordinal_numbers)
| ~ member(X0,limit_ordinals) ),
inference(paramodulation,[status(thm)],[f323,f190]) ).
fof(f431,plain,
member(null_class,ordinal_numbers),
inference(resolution,[status(thm)],[f427,f347]) ).
fof(f439,plain,
! [X0] :
( null_class = singleton(X0)
| null_class = singleton(X0)
| null_class = intersection(singleton(X0),X0) ),
inference(paramodulation,[status(thm)],[f367,f235]) ).
fof(f440,plain,
! [X0] :
( null_class = singleton(X0)
| null_class = singleton(X0)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f367,f234]) ).
fof(f441,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f440]) ).
fof(f442,plain,
! [X0] :
( singleton(X0) = null_class
| intersection(singleton(X0),X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f439]) ).
fof(f453,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f175,f171]) ).
fof(f477,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f161,f164]) ).
fof(f569,plain,
! [X0,X1,X2] :
( ~ member(X0,singleton(X2))
| X2 = not_subclass_element(singleton(X2),X1)
| member(X0,X1) ),
inference(resolution,[status(thm)],[f414,f161]) ).
fof(f607,plain,
! [X0,X1,X2] :
( member(X0,intersection(complement(X1),complement(X2)))
| member(X0,union(X1,X2))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f194,f193]) ).
fof(f649,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,null_class)
| singleton(X1) = null_class
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f442,f191]) ).
fof(f652,plain,
! [X0] :
( ~ member(X0,complement(kind_1_ordinals))
| member(X0,limit_ordinals)
| ~ member(X0,ordinal_numbers) ),
inference(paramodulation,[status(thm)],[f323,f191]) ).
fof(f668,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,kind_1_ordinals)
| member(X0,limit_ordinals)
| ~ member(X0,ordinal_numbers) ),
inference(resolution,[status(thm)],[f652,f193]) ).
fof(f669,plain,
! [X0] :
( member(X0,kind_1_ordinals)
| member(X0,limit_ordinals)
| ~ member(X0,ordinal_numbers) ),
inference(forward_subsumption_resolution,[status(thm)],[f668,f477]) ).
fof(f784,plain,
! [X0] :
( null_class = intersection(kind_1_ordinals,X0)
| ~ member(regular(intersection(kind_1_ordinals,X0)),limit_ordinals) ),
inference(resolution,[status(thm)],[f393,f399]) ).
fof(f794,plain,
! [X0,X1] :
( regular(intersection(singleton(X0),X1)) = X0
| intersection(singleton(X0),X1) = null_class ),
inference(resolution,[status(thm)],[f393,f357]) ).
fof(f844,plain,
( null_class = intersection(kind_1_ordinals,limit_ordinals)
| intersection(kind_1_ordinals,limit_ordinals) = null_class ),
inference(resolution,[status(thm)],[f424,f784]) ).
fof(f859,plain,
! [X0] :
( null_class = intersection(X0,kind_1_ordinals)
| ~ member(regular(intersection(X0,kind_1_ordinals)),limit_ordinals) ),
inference(resolution,[status(thm)],[f424,f399]) ).
fof(f881,plain,
intersection(kind_1_ordinals,limit_ordinals) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f844]) ).
fof(f888,plain,
! [X0] :
( member(X0,limit_ordinals)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f881,f190]) ).
fof(f889,plain,
! [X0] :
( member(X0,kind_1_ordinals)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f881,f188]) ).
fof(f899,plain,
! [X0] :
( ~ member(X0,limit_ordinals)
| ~ member(X0,null_class) ),
inference(resolution,[status(thm)],[f889,f399]) ).
fof(f901,plain,
! [X0,X1] :
( singleton(X1) = null_class
| ~ member(X0,singleton(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f649,f902]) ).
fof(f902,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f899,f888]) ).
fof(f1152,plain,
! [X0] :
( ~ member(X0,universal_class)
| singleton(X0) = null_class
| ~ member(X0,X0) ),
inference(resolution,[status(thm)],[f901,f453]) ).
fof(f1155,plain,
! [X0] :
( ~ member(X0,X0)
| null_class = singleton(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1152,f477]) ).
fof(f1163,plain,
! [X0] :
( ~ member(universal_class,X0)
| null_class = singleton(universal_class) ),
inference(resolution,[status(thm)],[f1155,f477]) ).
fof(f1176,plain,
( singleton(universal_class) = null_class
| null_class = singleton(universal_class) ),
inference(resolution,[status(thm)],[f1163,f441]) ).
fof(f1184,plain,
null_class = singleton(universal_class),
inference(duplicate_literals_removal,[status(thm)],[f1176]) ).
fof(f1206,plain,
member(null_class,universal_class),
inference(paramodulation,[status(thm)],[f1184,f354]) ).
fof(f1781,plain,
( inductive(universal_class)
| ~ member(null_class,universal_class) ),
inference(resolution,[status(thm)],[f217,f164]) ).
fof(f1782,plain,
inductive(universal_class),
inference(forward_subsumption_resolution,[status(thm)],[f1781,f1206]) ).
fof(f5416,plain,
! [X0,X1] :
( X0 = not_subclass_element(singleton(X0),X1)
| ~ member(X0,universal_class)
| member(X0,X1) ),
inference(resolution,[status(thm)],[f569,f453]) ).
fof(f5612,plain,
! [X0] :
( not_subclass_element(singleton(null_class),X0) = null_class
| member(null_class,X0) ),
inference(resolution,[status(thm)],[f5416,f1206]) ).
fof(f5649,plain,
not_subclass_element(singleton(null_class),null_class) = null_class,
inference(resolution,[status(thm)],[f5612,f902]) ).
fof(f5706,plain,
( member(null_class,singleton(null_class))
| subclass(singleton(null_class),null_class) ),
inference(paramodulation,[status(thm)],[f5649,f162]) ).
fof(f6164,plain,
! [X0] :
( member(X0,null_class)
| ~ member(X0,singleton(null_class))
| member(null_class,singleton(null_class)) ),
inference(resolution,[status(thm)],[f5706,f161]) ).
fof(f6167,plain,
! [X0] :
( member(null_class,singleton(null_class))
| ~ member(X0,singleton(null_class)) ),
inference(forward_subsumption_resolution,[status(thm)],[f6164,f902]) ).
fof(f7138,plain,
! [X0] :
( intersection(singleton(X0),kind_1_ordinals) = null_class
| null_class = intersection(singleton(X0),kind_1_ordinals)
| ~ member(X0,limit_ordinals) ),
inference(paramodulation,[status(thm)],[f794,f859]) ).
fof(f7141,plain,
! [X0,X1] :
( intersection(singleton(X0),X1) = null_class
| member(X0,X1)
| intersection(singleton(X0),X1) = null_class ),
inference(paramodulation,[status(thm)],[f794,f424]) ).
fof(f7170,plain,
! [X0,X1] :
( intersection(singleton(X0),X1) = null_class
| member(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f7141]) ).
fof(f7172,plain,
! [X0] :
( ~ member(X0,limit_ordinals)
| null_class = intersection(singleton(X0),kind_1_ordinals) ),
inference(duplicate_literals_removal,[status(thm)],[f7138]) ).
fof(f7328,plain,
! [X0,X1] :
( intersection(singleton(X0),complement(X1)) = null_class
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f7170,f192]) ).
fof(f7490,plain,
intersection(singleton(null_class),kind_1_ordinals) = null_class,
inference(resolution,[status(thm)],[f7172,f347]) ).
fof(f7518,plain,
! [X0] :
( ~ member(X0,singleton(null_class))
| member(X0,null_class)
| ~ member(X0,kind_1_ordinals) ),
inference(paramodulation,[status(thm)],[f7490,f191]) ).
fof(f7524,plain,
! [X0] :
( ~ member(X0,kind_1_ordinals)
| ~ member(X0,singleton(null_class)) ),
inference(forward_subsumption_resolution,[status(thm)],[f7518,f902]) ).
fof(f7542,plain,
! [X0] :
( member(X0,limit_ordinals)
| ~ member(X0,singleton(null_class))
| ~ member(X0,ordinal_numbers) ),
inference(resolution,[status(thm)],[f7524,f669]) ).
fof(f7858,plain,
null_class = intersection(singleton(null_class),complement(ordinal_numbers)),
inference(resolution,[status(thm)],[f7328,f431]) ).
fof(f7918,plain,
! [X0] :
( ~ member(X0,singleton(null_class))
| member(X0,null_class)
| ~ member(X0,complement(ordinal_numbers)) ),
inference(paramodulation,[status(thm)],[f7858,f191]) ).
fof(f7924,plain,
! [X0] :
( ~ member(X0,singleton(null_class))
| ~ member(X0,complement(ordinal_numbers)) ),
inference(forward_subsumption_resolution,[status(thm)],[f7918,f902]) ).
fof(f7966,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,ordinal_numbers)
| ~ member(X0,singleton(null_class)) ),
inference(resolution,[status(thm)],[f7924,f193]) ).
fof(f7970,plain,
! [X0] :
( ~ member(X0,singleton(null_class))
| member(X0,limit_ordinals) ),
inference(backward_subsumption_resolution,[status(thm)],[f7542,f7971]) ).
fof(f7971,plain,
! [X0] :
( ~ member(X0,singleton(null_class))
| member(X0,ordinal_numbers) ),
inference(forward_subsumption_resolution,[status(thm)],[f7966,f477]) ).
fof(f8026,plain,
! [X0] :
( subclass(singleton(null_class),X0)
| member(not_subclass_element(singleton(null_class),X0),limit_ordinals) ),
inference(resolution,[status(thm)],[f7970,f162]) ).
fof(f11527,plain,
( subclass(singleton(null_class),complement(kind_1_ordinals))
| subclass(singleton(null_class),complement(kind_1_ordinals)) ),
inference(resolution,[status(thm)],[f8026,f398]) ).
fof(f11563,plain,
subclass(singleton(null_class),complement(kind_1_ordinals)),
inference(duplicate_literals_removal,[status(thm)],[f11527]) ).
fof(f11567,plain,
! [X0] :
( ~ member(X0,singleton(null_class))
| member(X0,complement(kind_1_ordinals)) ),
inference(resolution,[status(thm)],[f11563,f161]) ).
fof(f11585,plain,
( ~ member(null_class,universal_class)
| member(null_class,complement(kind_1_ordinals)) ),
inference(resolution,[status(thm)],[f11567,f453]) ).
fof(f11597,plain,
member(null_class,complement(kind_1_ordinals)),
inference(forward_subsumption_resolution,[status(thm)],[f11585,f1206]) ).
fof(f11600,plain,
~ member(null_class,kind_1_ordinals),
inference(resolution,[status(thm)],[f11597,f192]) ).
fof(f13197,plain,
! [X0,X1] :
( ~ inductive(universal_class)
| member(null_class,intersection(complement(X0),complement(X1)))
| member(null_class,union(X0,X1)) ),
inference(resolution,[status(thm)],[f607,f215]) ).
fof(f13209,plain,
! [X0,X1] :
( member(null_class,intersection(complement(X0),complement(X1)))
| member(null_class,union(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f13197,f1782]) ).
fof(f13584,plain,
! [X0,X1] :
( member(null_class,complement(X0))
| member(null_class,union(X0,X1)) ),
inference(resolution,[status(thm)],[f13209,f188]) ).
fof(f13643,plain,
( member(null_class,complement(singleton(null_class)))
| member(null_class,kind_1_ordinals) ),
inference(paramodulation,[status(thm)],[f322,f13584]) ).
fof(f13647,plain,
member(null_class,complement(singleton(null_class))),
inference(forward_subsumption_resolution,[status(thm)],[f13643,f11600]) ).
fof(f13663,plain,
~ member(null_class,singleton(null_class)),
inference(resolution,[status(thm)],[f13647,f192]) ).
fof(f13677,plain,
! [X0] : ~ member(X0,singleton(null_class)),
inference(backward_subsumption_resolution,[status(thm)],[f6167,f13663]) ).
fof(f13697,plain,
~ member(null_class,universal_class),
inference(resolution,[status(thm)],[f13677,f453]) ).
fof(f13730,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f13697,f1206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM181-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n010.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 21 02:10:57 UTC 2026
% 0.19/0.40 % CPUTime :
% 0.19/0.43 % Drodi V4.1.1
% 103.35/13.59 % Refutation found
% 103.35/13.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 103.35/13.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.85/14.04 % Elapsed time: 13.620638 seconds
% 6.85/14.04 % CPU time: 104.950192 seconds
% 6.85/14.04 % Total memory used: 595.568 MB
% 6.85/14.04 % Net memory used: 536.852 MB
%------------------------------------------------------------------------------