%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET454-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:09:57 PM UTC 2026
% Result : Unsatisfiable 3.66s 1.17s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 17 unt; 0 def)
% Number of atoms : 37 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f143,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f144,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f150,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f196,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f197,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f245,plain,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f255,plain,
~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)),
inference(resolution,[status(thm)],[f117,f245]) ).
fof(f442,plain,
! [X0] :
( member(X0,subset_relation)
| ~ member(X0,identity_relation) ),
inference(paramodulation,[status(thm)],[f197,f144]) ).
fof(f512,plain,
! [X0,X1,X2,X3] :
( member(X0,cross_product(X2,X3))
| ~ member(X0,restrict(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f150,f144]) ).
fof(f861,plain,
restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class) = subset_relation,
inference(forward_demodulation,[status(thm)],[f151,f196]) ).
fof(f862,plain,
restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class) = subset_relation,
inference(forward_demodulation,[status(thm)],[f151,f861]) ).
fof(f1263,plain,
! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,subset_relation) ),
inference(paramodulation,[status(thm)],[f862,f512]) ).
fof(f1298,plain,
~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),subset_relation),
inference(resolution,[status(thm)],[f1263,f255]) ).
fof(f1304,plain,
~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),identity_relation),
inference(resolution,[status(thm)],[f1298,f442]) ).
fof(f1320,plain,
subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(resolution,[status(thm)],[f1304,f116]) ).
fof(f1324,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1320,f245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET454-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n017.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 05:13:56 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 3.66/1.17 % Refutation found
% 3.66/1.17 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.66/1.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.60/1.21 % Elapsed time: 0.731979 seconds
% 0.60/1.21 % CPU time: 5.128529 seconds
% 0.60/1.21 % Total memory used: 150.789 MB
% 0.60/1.21 % Net memory used: 144.043 MB
%------------------------------------------------------------------------------