%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET097-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 0.08s 0.50s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 19 unt; 0 def)
% Number of atoms : 144 ( 38 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 126 ( 52 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 1 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 : 112 ( 112 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/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(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(f128,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f170,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f200,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
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(f206,plain,
subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(resolution,[status(thm)],[f97,f200]) ).
fof(f210,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(f211,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(f218,plain,
! [X0] :
( member(X0,null_class)
| ~ member(X0,intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(resolution,[status(thm)],[f96,f206]) ).
fof(f219,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f96,f99]) ).
fof(f224,plain,
! [X0,X1,X2] :
( subclass(unordered_pair(X0,X1),X2)
| not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0 ),
inference(resolution,[status(thm)],[f104,f97]) ).
fof(f228,plain,
! [X0] :
( ~ member(X0,x)
| ~ member(X0,complement(singleton(not_subclass_element(x,null_class))))
| member(X0,null_class) ),
inference(resolution,[status(thm)],[f218,f126]) ).
fof(f230,plain,
! [X0] :
( member(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(X0,universal_class)
| ~ member(X0,x)
| member(X0,null_class) ),
inference(resolution,[status(thm)],[f228,f128]) ).
fof(f237,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f210,f98]) ).
fof(f244,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f237]) ).
fof(f247,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[f211,f98]) ).
fof(f254,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(duplicate_literals_removal,[status(thm)],[f247]) ).
fof(f255,plain,
! [X0,X1] :
( X0 = intersection(X1,X0)
| ~ subclass(X0,intersection(X1,X0)) ),
inference(resolution,[status(thm)],[f254,f102]) ).
fof(f296,plain,
! [X0,X1] :
( subclass(unordered_pair(X0,X0),X1)
| not_subclass_element(singleton(X0),X1) = X0
| not_subclass_element(unordered_pair(X0,X0),X1) = X0 ),
inference(paramodulation,[status(thm)],[f110,f224]) ).
fof(f304,plain,
! [X0,X1] :
( subclass(unordered_pair(X0,X0),X1)
| not_subclass_element(singleton(X0),X1) = X0
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(forward_demodulation,[status(thm)],[f110,f296]) ).
fof(f305,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),X1) = X0
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(forward_demodulation,[status(thm)],[f110,f304]) ).
fof(f306,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(duplicate_literals_removal,[status(thm)],[f305]) ).
fof(f328,plain,
! [X0] :
( member(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(X0,x)
| member(X0,null_class) ),
inference(backward_subsumption_resolution,[status(thm)],[f230,f219]) ).
fof(f345,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(paramodulation,[status(thm)],[f306,f98]) ).
fof(f349,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f345]) ).
fof(f353,plain,
! [X0,X1] :
( X1 = singleton(X0)
| ~ subclass(X1,singleton(X0))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f349,f102]) ).
fof(f482,plain,
! [X0] :
( X0 = null_class
| subclass(null_class,X0) ),
inference(paramodulation,[status(thm)],[f170,f244]) ).
fof(f489,plain,
! [X0] :
( null_class = intersection(X0,null_class)
| intersection(X0,null_class) = null_class ),
inference(resolution,[status(thm)],[f482,f255]) ).
fof(f491,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class)
| X0 = null_class ),
inference(resolution,[status(thm)],[f482,f102]) ).
fof(f494,plain,
! [X0] : intersection(X0,null_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f489]) ).
fof(f496,plain,
! [X0] :
( ~ subclass(X0,null_class)
| X0 = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f491]) ).
fof(f513,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f494,f123]) ).
fof(f719,plain,
! [X0] :
( member(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(X0,x) ),
inference(backward_subsumption_resolution,[status(thm)],[f328,f513]) ).
fof(f776,plain,
! [X0] :
( subclass(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),x) ),
inference(resolution,[status(thm)],[f719,f98]) ).
fof(f1365,plain,
( subclass(x,singleton(not_subclass_element(x,null_class)))
| subclass(x,singleton(not_subclass_element(x,null_class))) ),
inference(resolution,[status(thm)],[f776,f97]) ).
fof(f1370,plain,
subclass(x,singleton(not_subclass_element(x,null_class))),
inference(duplicate_literals_removal,[status(thm)],[f1365]) ).
fof(f1373,plain,
( x = singleton(not_subclass_element(x,null_class))
| ~ member(not_subclass_element(x,null_class),x) ),
inference(resolution,[status(thm)],[f1370,f353]) ).
fof(f1376,plain,
~ member(not_subclass_element(x,null_class),x),
inference(forward_subsumption_resolution,[status(thm)],[f1373,f201]) ).
fof(f1378,plain,
subclass(x,null_class),
inference(resolution,[status(thm)],[f1376,f97]) ).
fof(f1380,plain,
x = null_class,
inference(resolution,[status(thm)],[f1378,f496]) ).
fof(f1383,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1380,f202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET097-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:51:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.50 % Refutation found
% 0.08/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.80/0.53 % Elapsed time: 0.152429 seconds
% 0.80/0.53 % CPU time: 0.894548 seconds
% 0.80/0.53 % Total memory used: 122.668 MB
% 0.80/0.53 % Net memory used: 120.913 MB
%------------------------------------------------------------------------------