%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET205-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:11:46 PM UTC 2026
% Result : Unsatisfiable 22.12s 3.29s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET205-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:02:30 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 22.12/3.29 % Refutation found
% 22.12/3.29 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 22.12/3.29 % SZS output start CNFRefutation for theBenchmark
% 22.12/3.29 fof(f2,axiom,(
% 22.12/3.29 (![X,Y]: (( member(not_subclass_element(X,Y),X)| subclass(X,Y) ) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f3,axiom,(
% 22.12/3.29 (![X,Y]: (( ~ member(not_subclass_element(X,Y),Y)| subclass(X,Y) ) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f7,axiom,(
% 22.12/3.29 (![X,Y]: (( ~ subclass(X,Y)| ~ subclass(Y,X)| X = Y ) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f15,axiom,(
% 22.12/3.29 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(V,Y) ) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f17,axiom,(
% 22.12/3.29 (![Z,X,Y]: (( ~ member(Z,cross_product(X,Y))| ordered_pair(first(Z),second(Z)) = Z ) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f21,axiom,(
% 22.12/3.29 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,X) ) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f28,axiom,(
% 22.12/3.29 (![Xr,X,Y]: (intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f30,axiom,(
% 22.12/3.29 (![X,Z]: (( restrict(X,singleton(Z),universal_class) != null_class| ~ member(Z,domain_of(X)) ) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f66,axiom,(
% 22.12/3.29 (![X]: (( X = null_class| member(regular(X),X) ) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f67,axiom,(
% 22.12/3.29 (![X]: (( X = null_class| intersection(X,regular(X)) = null_class ) ))),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f113,negated_conjecture,(
% 22.12/3.29 cross_product(x,null_class) != null_class ),
% 22.12/3.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 22.12/3.29 fof(f116,plain,(
% 22.12/3.29 ![X0,X1]: (member(not_subclass_element(X0,X1),X0)|subclass(X0,X1))),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f2])).
% 22.12/3.29 fof(f117,plain,(
% 22.12/3.29 ![X0,X1]: (~member(not_subclass_element(X0,X1),X1)|subclass(X0,X1))),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f3])).
% 22.12/3.29 fof(f121,plain,(
% 22.12/3.29 ![X0,X1]: (~subclass(X0,X1)|~subclass(X1,X0)|X0=X1)),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f7])).
% 22.12/3.29 fof(f133,plain,(
% 22.12/3.29 ![V,Y]: ((![U,X]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(V,Y))),
% 22.12/3.29 inference(miniscoping,[status(thm)],[f15])).
% 22.12/3.29 fof(f134,plain,(
% 22.12/3.29 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X1,X3))),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f133])).
% 22.12/3.29 fof(f136,plain,(
% 22.12/3.29 ![Z]: ((![X,Y]: ~member(Z,cross_product(X,Y)))|ordered_pair(first(Z),second(Z))=Z)),
% 22.12/3.29 inference(miniscoping,[status(thm)],[f17])).
% 22.12/3.29 fof(f137,plain,(
% 22.12/3.29 ![X0,X1,X2]: (~member(X0,cross_product(X1,X2))|ordered_pair(first(X0),second(X0))=X0)),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f136])).
% 22.12/3.29 fof(f141,plain,(
% 22.12/3.29 ![Z,X]: ((![Y]: ~member(Z,intersection(X,Y)))|member(Z,X))),
% 22.12/3.29 inference(miniscoping,[status(thm)],[f21])).
% 22.12/3.29 fof(f142,plain,(
% 22.12/3.29 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f141])).
% 22.12/3.29 fof(f150,plain,(
% 22.12/3.29 ![X0,X1,X2]: (intersection(X0,cross_product(X1,X2))=restrict(X0,X1,X2))),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f28])).
% 22.12/3.29 fof(f152,plain,(
% 22.12/3.29 ![X0,X1]: (~restrict(X0,singleton(X1),universal_class)=null_class|~member(X1,domain_of(X0)))),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f30])).
% 22.12/3.29 fof(f188,plain,(
% 22.12/3.29 ![X0]: (X0=null_class|member(regular(X0),X0))),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f66])).
% 22.12/3.29 fof(f189,plain,(
% 22.12/3.29 ![X0]: (X0=null_class|intersection(X0,regular(X0))=null_class)),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f67])).
% 22.12/3.29 fof(f245,plain,(
% 22.12/3.29 ~cross_product(x,null_class)=null_class),
% 22.12/3.29 inference(cnf_transformation,[status(thm)],[f113])).
% 22.12/3.29 fof(f427,plain,(
% 22.12/3.29 ![X0,X1,X2]: (member(not_subclass_element(intersection(X0,X1),X2),X0)|subclass(intersection(X0,X1),X2))),
% 22.12/3.29 inference(resolution,[status(thm)],[f142,f116])).
% 22.12/3.29 fof(f971,plain,(
% 22.12/3.29 ![X0,X1]: (cross_product(X0,X1)=null_class|ordered_pair(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))=regular(cross_product(X0,X1)))),
% 22.12/3.31 inference(resolution,[status(thm)],[f188,f137])).
% 22.12/3.31 fof(f3212,plain,(
% 22.12/3.31 ![X0,X1]: (subclass(intersection(X0,X1),X0)|subclass(intersection(X0,X1),X0))),
% 22.12/3.31 inference(resolution,[status(thm)],[f427,f117])).
% 22.12/3.31 fof(f3255,plain,(
% 22.12/3.31 ![X0,X1]: (subclass(intersection(X0,X1),X0))),
% 22.12/3.31 inference(duplicate_literals_removal,[status(thm)],[f3212])).
% 22.12/3.31 fof(f3530,plain,(
% 22.12/3.31 ![X0]: (subclass(null_class,X0)|X0=null_class)),
% 22.12/3.31 inference(paramodulation,[status(thm)],[f189,f3255])).
% 22.12/3.31 fof(f3531,plain,(
% 22.12/3.31 ![X0,X1,X2]: (subclass(restrict(X0,X1,X2),X0))),
% 22.12/3.31 inference(paramodulation,[status(thm)],[f150,f3255])).
% 22.12/3.31 fof(f4117,plain,(
% 22.12/3.31 ![X0]: (X0=null_class|~subclass(X0,null_class)|X0=null_class)),
% 22.12/3.31 inference(resolution,[status(thm)],[f3530,f121])).
% 22.12/3.31 fof(f4118,plain,(
% 22.12/3.31 ![X0]: (X0=null_class|~subclass(X0,null_class))),
% 22.12/3.31 inference(duplicate_literals_removal,[status(thm)],[f4117])).
% 22.12/3.31 fof(f4431,plain,(
% 22.12/3.31 ![X0,X1]: (restrict(null_class,X0,X1)=null_class)),
% 22.12/3.31 inference(resolution,[status(thm)],[f4118,f3531])).
% 22.12/3.31 fof(f4821,plain,(
% 22.12/3.31 ![X0]: (~member(X0,domain_of(null_class)))),
% 22.12/3.31 inference(resolution,[status(thm)],[f4431,f152])).
% 22.12/3.31 fof(f4834,plain,(
% 22.12/3.31 domain_of(null_class)=null_class),
% 22.12/3.31 inference(resolution,[status(thm)],[f4821,f188])).
% 22.12/3.31 fof(f5098,plain,(
% 22.12/3.31 ![X0]: (~member(X0,null_class))),
% 22.12/3.31 inference(backward_demodulation,[status(thm)],[f4834,f4821])).
% 22.12/3.31 fof(f5352,plain,(
% 22.12/3.31 ![X0,X1,X2,X3]: (~member(regular(cross_product(X0,X1)),cross_product(X2,X3))|member(second(regular(cross_product(X0,X1))),X3)|cross_product(X0,X1)=null_class)),
% 22.12/3.31 inference(paramodulation,[status(thm)],[f971,f134])).
% 22.12/3.31 fof(f6415,plain,(
% 22.12/3.31 ![X0,X1]: (member(second(regular(cross_product(X0,X1))),X1)|cross_product(X0,X1)=null_class|cross_product(X0,X1)=null_class)),
% 22.12/3.31 inference(resolution,[status(thm)],[f5352,f188])).
% 22.12/3.31 fof(f6416,plain,(
% 22.12/3.31 ![X0,X1]: (member(second(regular(cross_product(X0,X1))),X1)|cross_product(X0,X1)=null_class)),
% 22.12/3.31 inference(duplicate_literals_removal,[status(thm)],[f6415])).
% 22.12/3.31 fof(f9206,plain,(
% 22.12/3.31 ![X0]: (cross_product(X0,null_class)=null_class)),
% 22.12/3.31 inference(resolution,[status(thm)],[f6416,f5098])).
% 22.12/3.31 fof(f9263,plain,(
% 22.12/3.31 ~null_class=null_class),
% 22.12/3.31 inference(backward_demodulation,[status(thm)],[f9206,f245])).
% 22.12/3.31 fof(f9368,plain,(
% 22.12/3.31 $false),
% 22.12/3.31 inference(trivial_equality_resolution,[status(thm)],[f9263])).
% 22.12/3.31 % SZS output end CNFRefutation for theBenchmark.p
% 10.98/3.33 % Elapsed time: 2.957038 seconds
% 10.98/3.33 % CPU time: 23.059233 seconds
% 10.98/3.33 % Total memory used: 371.827 MB
% 10.98/3.33 % Net memory used: 331.867 MB
%------------------------------------------------------------------------------