%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET163-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:09:32 PM UTC 2026
% Result : Unsatisfiable 17.66s 2.78s
% Output : CNFRefutation 14.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 19 unt; 0 def)
% Number of atoms : 94 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 37 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 76 !; 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(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(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(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [X] : union(X,singleton(X)) = successor(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
union(universal_class,x) != universal_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f115,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f121,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f141,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f142,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f146,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f147,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f148,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f165,plain,
! [X0] : union(X0,singleton(X0)) = successor(X0),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f188,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f245,plain,
union(universal_class,x) != universal_class,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f513,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f115,f118]) ).
fof(f1692,plain,
! [X0] :
( X0 = null_class
| member(regular(X0),universal_class) ),
inference(resolution,[status(thm)],[f513,f188]) ).
fof(f1700,plain,
! [X0] :
( universal_class = X0
| ~ subclass(universal_class,X0) ),
inference(resolution,[status(thm)],[f121,f118]) ).
fof(f4105,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f146,f188]) ).
fof(f4888,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f142,f188]) ).
fof(f5673,plain,
! [X0,X1,X2] :
( member(X0,intersection(complement(X1),complement(X2)))
| member(X0,union(X1,X2))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f148,f147]) ).
fof(f5823,plain,
! [X0,X1,X2] :
( member(X0,complement(X1))
| member(X0,union(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f5673,f142]) ).
fof(f8035,plain,
! [X0,X1] :
( member(X0,complement(X1))
| member(X0,successor(X1))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f165,f5823]) ).
fof(f8146,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,successor(X1))
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f8035,f146]) ).
fof(f8173,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,successor(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f8146,f513]) ).
fof(f8175,plain,
! [X0,X1] :
( subclass(X0,successor(X1))
| ~ member(not_subclass_element(X0,successor(X1)),X1) ),
inference(resolution,[status(thm)],[f8173,f117]) ).
fof(f8192,plain,
! [X0] :
( subclass(X0,successor(X0))
| subclass(X0,successor(X0)) ),
inference(resolution,[status(thm)],[f8175,f116]) ).
fof(f8207,plain,
! [X0] : subclass(X0,successor(X0)),
inference(duplicate_literals_removal,[status(thm)],[f8192]) ).
fof(f8434,plain,
universal_class = successor(universal_class),
inference(resolution,[status(thm)],[f8207,f1700]) ).
fof(f8484,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f4105,f1692]) ).
fof(f8512,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f8484]) ).
fof(f8600,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f8512,f146]) ).
fof(f8680,plain,
! [X0] : complement(intersection(null_class,complement(X0))) = union(universal_class,X0),
inference(paramodulation,[status(thm)],[f8512,f148]) ).
fof(f8692,plain,
! [X0] : ~ member(X0,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f8600,f513]) ).
fof(f12879,plain,
! [X0] : intersection(null_class,X0) = null_class,
inference(resolution,[status(thm)],[f4888,f8692]) ).
fof(f12958,plain,
! [X0] : complement(null_class) = union(universal_class,X0),
inference(backward_demodulation,[status(thm)],[f12879,f8680]) ).
fof(f13077,plain,
complement(null_class) != universal_class,
inference(backward_demodulation,[status(thm)],[f12958,f245]) ).
fof(f13087,plain,
complement(null_class) = successor(universal_class),
inference(paramodulation,[status(thm)],[f165,f12958]) ).
fof(f13164,plain,
complement(null_class) = universal_class,
inference(forward_demodulation,[status(thm)],[f8434,f13087]) ).
fof(f13291,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f13164,f13077]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET163-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n009.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Mon Sep 21 04:57:43 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 17.66/2.78 % Refutation found
% 17.66/2.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 17.66/2.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.65/2.89 % Elapsed time: 2.426953 seconds
% 14.65/2.89 % CPU time: 18.684795 seconds
% 14.65/2.89 % Total memory used: 560.202 MB
% 14.65/2.89 % Net memory used: 552.388 MB
%------------------------------------------------------------------------------