TSTP Solution File: SET454-6 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET454-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:39:42 EDT 2024
% Result : Unsatisfiable 11.58s 1.88s
% Output : CNFRefutation 11.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 65 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 30 ~; 25 |; 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 : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( X != Y
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [Y,U] :
( ! [X] :
( ~ subclass(X,Y)
| ~ member(U,X) )
| member(U,Y) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f119,plain,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f143,plain,
! [Z,Y] :
( ! [X] : ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f143]) ).
fof(f150,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(esa)],[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(esa)],[f74]) ).
fof(f197,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f245,plain,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(esa)],[f113]) ).
fof(f246,plain,
! [X0] : subclass(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f119]) ).
fof(f255,plain,
! [X0,X1,X2] :
( subclass(X0,X1)
| ~ subclass(X2,X1)
| ~ member(not_subclass_element(X0,X1),X2) ),
inference(resolution,[status(thm)],[f117,f115]) ).
fof(f288,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(resolution,[status(thm)],[f255,f246]) ).
fof(f571,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f116,f144]) ).
fof(f591,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[f571,f288]) ).
fof(f592,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(duplicate_literals_removal,[status(esa)],[f591]) ).
fof(f5801,plain,
! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),X0) ),
inference(resolution,[status(thm)],[f245,f255]) ).
fof(f5815,plain,
! [X0,X1] :
( ~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),X0)
| ~ subclass(X1,cross_product(universal_class,universal_class))
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),X1) ),
inference(resolution,[status(thm)],[f5801,f255]) ).
fof(f5839,plain,
! [X0,X1] :
( ~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),intersection(X1,cross_product(universal_class,universal_class))) ),
inference(resolution,[status(thm)],[f5815,f592]) ).
fof(f5910,plain,
! [X0,X1] :
( ~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),intersection(X0,intersection(X1,cross_product(universal_class,universal_class))))
| subclass(intersection(X0,intersection(X1,cross_product(universal_class,universal_class))),cross_product(universal_class,universal_class)) ),
inference(resolution,[status(thm)],[f5839,f571]) ).
fof(f5911,plain,
! [X0,X1] : ~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),intersection(X0,intersection(X1,cross_product(universal_class,universal_class)))),
inference(forward_subsumption_resolution,[status(thm)],[f5910,f5801]) ).
fof(f6899,plain,
! [X0,X1] : ~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),intersection(X0,restrict(X1,universal_class,universal_class))),
inference(forward_demodulation,[status(thm)],[f150,f5911]) ).
fof(f7631,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(f7632,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,f7631]) ).
fof(f7736,plain,
! [X0] : ~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),intersection(X0,subset_relation)),
inference(paramodulation,[status(thm)],[f7632,f6899]) ).
fof(f7740,plain,
~ member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),identity_relation),
inference(paramodulation,[status(thm)],[f197,f7736]) ).
fof(f7742,plain,
subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(resolution,[status(thm)],[f7740,f116]) ).
fof(f7743,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f7742,f245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET454-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 21:38:26 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 11.58/1.88 % Refutation found
% 11.58/1.88 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 11.58/1.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.19/1.92 % Elapsed time: 1.559602 seconds
% 12.19/1.92 % CPU time: 12.195842 seconds
% 12.19/1.92 % Total memory used: 157.834 MB
% 12.19/1.92 % Net memory used: 151.666 MB
%------------------------------------------------------------------------------