%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET132-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 02:11:38 PM UTC 2026
% Result : Unsatisfiable 0.27s 0.82s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET132-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 04:58:36 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.27/0.82 % Refutation found
% 0.27/0.82 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.27/0.82 % SZS output start CNFRefutation for theBenchmark
% 0.27/0.82 fof(f1,axiom,(
% 0.27/0.82 (![X,Y,U]: (( ~ subclass(X,Y)| ~ member(U,X)| member(U,Y) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f4,axiom,(
% 0.27/0.82 (![X]: (subclass(X,universal_class) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f8,axiom,(
% 0.27/0.82 (![U,X,Y]: (( ~ member(U,unordered_pair(X,Y))| U = X| U = Y ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f9,axiom,(
% 0.27/0.82 (![X,Y]: (( ~ member(X,universal_class)| member(X,unordered_pair(X,Y)) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f12,axiom,(
% 0.27/0.82 (![X]: (unordered_pair(X,X) = singleton(X) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f15,axiom,(
% 0.27/0.82 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(V,Y) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f16,axiom,(
% 0.27/0.82 (![U,X,V,Y]: (( ~ member(U,X)| ~ member(V,Y)| member(ordered_pair(U,V),cross_product(X,Y)) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f17,axiom,(
% 0.27/0.82 (![Z,X,Y]: (( ~ member(Z,cross_product(X,Y))| ordered_pair(first(Z),second(Z)) = Z ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f21,axiom,(
% 0.27/0.82 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,X) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f22,axiom,(
% 0.27/0.82 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,Y) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f24,axiom,(
% 0.27/0.82 (![Z,X]: (( ~ member(Z,complement(X))| ~ member(Z,X) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f25,axiom,(
% 0.27/0.82 (![Z,X]: (( ~ member(Z,universal_class)| member(Z,complement(X))| member(Z,X) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f26,axiom,(
% 0.27/0.82 (![X,Y]: (complement(intersection(complement(X),complement(Y))) = union(X,Y) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f47,axiom,(
% 0.27/0.82 (![X]: (( ~ inductive(X)| member(null_class,X) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f49,axiom,(
% 0.27/0.82 (![X]: (( ~ member(null_class,X)| ~ subclass(image(successor_relation,X),X)| inductive(X) ) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f50,axiom,(
% 0.27/0.82 inductive(omega) ),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f92,axiom,(
% 0.27/0.82 (![X,Y]: (union(singleton(X),Y) = set_builder(X,Y) ))),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f93,negated_conjecture,(
% 0.27/0.82 member(u,universal_class) ),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f94,negated_conjecture,(
% 0.27/0.82 ~ member(u,set_builder(x,set_builder(y,set_builder(u,null_class)))) ),
% 0.27/0.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.27/0.82 fof(f95,plain,(
% 0.27/0.82 ![Y,U]: ((![X]: (~subclass(X,Y)|~member(U,X)))|member(U,Y))),
% 0.27/0.82 inference(miniscoping,[status(thm)],[f1])).
% 0.27/0.82 fof(f96,plain,(
% 0.27/0.82 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f95])).
% 0.27/0.82 fof(f99,plain,(
% 0.27/0.82 ![X0]: (subclass(X0,universal_class))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f4])).
% 0.27/0.82 fof(f103,plain,(
% 0.27/0.82 ![U,Y]: ((![X]: (~member(U,unordered_pair(X,Y))|U=X))|U=Y)),
% 0.27/0.82 inference(miniscoping,[status(thm)],[f8])).
% 0.27/0.82 fof(f104,plain,(
% 0.27/0.82 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f103])).
% 0.27/0.82 fof(f105,plain,(
% 0.27/0.82 ![X]: (~member(X,universal_class)|(![Y]: member(X,unordered_pair(X,Y))))),
% 0.27/0.82 inference(miniscoping,[status(thm)],[f9])).
% 0.27/0.82 fof(f106,plain,(
% 0.27/0.82 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X0,X1)))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f105])).
% 0.27/0.82 fof(f110,plain,(
% 0.27/0.82 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f12])).
% 0.27/0.82 fof(f114,plain,(
% 0.27/0.82 ![V,Y]: ((![U,X]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(V,Y))),
% 0.27/0.82 inference(miniscoping,[status(thm)],[f15])).
% 0.27/0.82 fof(f115,plain,(
% 0.27/0.82 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X1,X3))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f114])).
% 0.27/0.82 fof(f116,plain,(
% 0.27/0.82 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X2,X3)|member(ordered_pair(X0,X2),cross_product(X1,X3)))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f16])).
% 0.27/0.82 fof(f117,plain,(
% 0.27/0.82 ![Z]: ((![X,Y]: ~member(Z,cross_product(X,Y)))|ordered_pair(first(Z),second(Z))=Z)),
% 0.27/0.82 inference(miniscoping,[status(thm)],[f17])).
% 0.27/0.82 fof(f118,plain,(
% 0.27/0.82 ![X0,X1,X2]: (~member(X0,cross_product(X1,X2))|ordered_pair(first(X0),second(X0))=X0)),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f117])).
% 0.27/0.82 fof(f122,plain,(
% 0.27/0.82 ![Z,X]: ((![Y]: ~member(Z,intersection(X,Y)))|member(Z,X))),
% 0.27/0.82 inference(miniscoping,[status(thm)],[f21])).
% 0.27/0.82 fof(f123,plain,(
% 0.27/0.82 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f122])).
% 0.27/0.82 fof(f124,plain,(
% 0.27/0.82 ![Z,Y]: ((![X]: ~member(Z,intersection(X,Y)))|member(Z,Y))),
% 0.27/0.82 inference(miniscoping,[status(thm)],[f22])).
% 0.27/0.82 fof(f125,plain,(
% 0.27/0.82 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f124])).
% 0.27/0.82 fof(f127,plain,(
% 0.27/0.82 ![X0,X1]: (~member(X0,complement(X1))|~member(X0,X1))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f24])).
% 0.27/0.82 fof(f128,plain,(
% 0.27/0.82 ![X0,X1]: (~member(X0,universal_class)|member(X0,complement(X1))|member(X0,X1))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f25])).
% 0.27/0.82 fof(f129,plain,(
% 0.27/0.82 ![X0,X1]: (complement(intersection(complement(X0),complement(X1)))=union(X0,X1))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f26])).
% 0.27/0.82 fof(f150,plain,(
% 0.27/0.82 ![X0]: (~inductive(X0)|member(null_class,X0))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f47])).
% 0.27/0.82 fof(f152,plain,(
% 0.27/0.82 ![X0]: (~member(null_class,X0)|~subclass(image(successor_relation,X0),X0)|inductive(X0))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f49])).
% 0.27/0.82 fof(f153,plain,(
% 0.27/0.82 inductive(omega)),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f50])).
% 0.27/0.82 fof(f200,plain,(
% 0.27/0.82 ![X0,X1]: (union(singleton(X0),X1)=set_builder(X0,X1))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f92])).
% 0.27/0.82 fof(f201,plain,(
% 0.27/0.82 member(u,universal_class)),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f93])).
% 0.27/0.82 fof(f202,plain,(
% 0.27/0.82 ~member(u,set_builder(x,set_builder(y,set_builder(u,null_class))))),
% 0.27/0.82 inference(cnf_transformation,[status(thm)],[f94])).
% 0.27/0.82 fof(f210,plain,(
% 0.27/0.82 ![X0,X1]: (~member(X0,X1)|member(X0,universal_class))),
% 0.27/0.82 inference(resolution,[status(thm)],[f99,f96])).
% 0.27/0.82 fof(f217,plain,(
% 0.27/0.82 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1|X0=X1)),
% 0.27/0.82 inference(paramodulation,[status(thm)],[f110,f104])).
% 0.27/0.82 fof(f218,plain,(
% 0.27/0.82 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 0.27/0.82 inference(duplicate_literals_removal,[status(thm)],[f217])).
% 0.27/0.82 fof(f220,plain,(
% 0.27/0.82 ![X0]: (~member(X0,universal_class)|member(X0,singleton(X0)))),
% 0.27/0.82 inference(paramodulation,[status(thm)],[f110,f106])).
% 0.27/0.82 fof(f221,plain,(
% 0.27/0.82 member(null_class,omega)),
% 0.27/0.82 inference(resolution,[status(thm)],[f150,f153])).
% 0.27/0.82 fof(f238,plain,(
% 0.27/0.82 ![X0,X1,X2,X3]: (ordered_pair(first(ordered_pair(X0,X1)),second(ordered_pair(X0,X1)))=ordered_pair(X0,X1)|~member(X0,X2)|~member(X1,X3))),
% 0.27/0.82 inference(resolution,[status(thm)],[f118,f116])).
% 0.27/0.82 fof(f270,plain,(
% 0.27/0.82 ![X0,X1,X2]: (~member(X0,universal_class)|member(X0,union(X1,X2))|member(X0,intersection(complement(X1),complement(X2))))),
% 0.27/0.82 inference(paramodulation,[status(thm)],[f129,f128])).
% 0.27/0.82 fof(f366,plain,(
% 0.27/0.82 ~member(null_class,universal_class)|inductive(universal_class)),
% 0.27/0.82 inference(resolution,[status(thm)],[f152,f99])).
% 0.27/0.82 fof(f367,plain,(
% 0.27/0.82 ![X0]: (inductive(universal_class)|~member(null_class,X0))),
% 0.27/0.82 inference(resolution,[status(thm)],[f366,f210])).
% 0.27/0.82 fof(f368,plain,(
% 0.27/0.82 inductive(universal_class)),
% 0.27/0.82 inference(resolution,[status(thm)],[f367,f221])).
% 0.27/0.82 fof(f381,plain,(
% 0.27/0.82 member(null_class,universal_class)),
% 0.27/0.82 inference(resolution,[status(thm)],[f368,f150])).
% 0.27/0.82 fof(f671,plain,(
% 0.27/0.82 ![X0,X1]: (ordered_pair(first(ordered_pair(X0,u)),second(ordered_pair(X0,u)))=ordered_pair(X0,u)|~member(X0,X1))),
% 0.27/0.82 inference(resolution,[status(thm)],[f238,f201])).
% 0.27/0.82 fof(f693,plain,(
% 0.27/0.82 ordered_pair(first(ordered_pair(null_class,u)),second(ordered_pair(null_class,u)))=ordered_pair(null_class,u)),
% 0.27/0.85 inference(resolution,[status(thm)],[f671,f381])).
% 0.27/0.85 fof(f793,plain,(
% 0.27/0.85 ![X0,X1]: (~member(ordered_pair(null_class,u),cross_product(X0,X1))|member(second(ordered_pair(null_class,u)),X1))),
% 0.27/0.85 inference(paramodulation,[status(thm)],[f693,f115])).
% 0.27/0.85 fof(f818,plain,(
% 0.27/0.85 ![X0,X1]: (member(second(ordered_pair(null_class,u)),X0)|~member(null_class,X1)|~member(u,X0))),
% 0.27/0.85 inference(resolution,[status(thm)],[f793,f116])).
% 0.27/0.85 fof(f823,plain,(
% 0.27/0.85 ![X0]: (member(second(ordered_pair(null_class,u)),singleton(u))|~member(null_class,X0)|~member(u,universal_class))),
% 0.27/0.85 inference(resolution,[status(thm)],[f818,f220])).
% 0.27/0.85 fof(f831,plain,(
% 0.27/0.85 ![X0]: (member(second(ordered_pair(null_class,u)),singleton(u))|~member(null_class,X0))),
% 0.27/0.85 inference(forward_subsumption_resolution,[status(thm)],[f823,f201])).
% 0.27/0.85 fof(f837,plain,(
% 0.27/0.85 ![X0]: (~member(null_class,X0)|second(ordered_pair(null_class,u))=u)),
% 0.27/0.85 inference(resolution,[status(thm)],[f831,f218])).
% 0.27/0.85 fof(f879,plain,(
% 0.27/0.85 second(ordered_pair(null_class,u))=u),
% 0.27/0.85 inference(resolution,[status(thm)],[f837,f381])).
% 0.27/0.85 fof(f892,plain,(
% 0.27/0.85 ![X0]: (member(u,singleton(u))|~member(null_class,X0))),
% 0.27/0.85 inference(backward_demodulation,[status(thm)],[f879,f831])).
% 0.27/0.85 fof(f1693,plain,(
% 0.27/0.85 ![X0,X1]: (member(u,union(X0,X1))|member(u,intersection(complement(X0),complement(X1))))),
% 0.27/0.85 inference(resolution,[status(thm)],[f270,f201])).
% 0.27/0.85 fof(f1725,plain,(
% 0.27/0.85 ![X0,X1]: (member(u,union(X0,X1))|member(u,complement(X1)))),
% 0.27/0.85 inference(resolution,[status(thm)],[f1693,f125])).
% 0.27/0.85 fof(f1726,plain,(
% 0.27/0.85 ![X0,X1]: (member(u,union(X0,X1))|member(u,complement(X0)))),
% 0.27/0.85 inference(resolution,[status(thm)],[f1693,f123])).
% 0.27/0.85 fof(f1758,plain,(
% 0.27/0.85 ![X0,X1]: (member(u,set_builder(X0,X1))|member(u,complement(X1)))),
% 0.27/0.85 inference(paramodulation,[status(thm)],[f200,f1725])).
% 0.27/0.85 fof(f1769,plain,(
% 0.27/0.85 ![X0,X1]: (member(u,set_builder(X0,X1))|member(u,complement(singleton(X0))))),
% 0.27/0.85 inference(paramodulation,[status(thm)],[f200,f1726])).
% 0.27/0.85 fof(f1998,plain,(
% 0.27/0.85 member(u,complement(set_builder(y,set_builder(u,null_class))))),
% 0.27/0.85 inference(resolution,[status(thm)],[f1758,f202])).
% 0.27/0.85 fof(f2043,plain,(
% 0.27/0.85 ~member(u,set_builder(y,set_builder(u,null_class)))),
% 0.27/0.85 inference(resolution,[status(thm)],[f1998,f127])).
% 0.27/0.85 fof(f2046,plain,(
% 0.27/0.85 member(u,complement(set_builder(u,null_class)))),
% 0.27/0.85 inference(resolution,[status(thm)],[f2043,f1758])).
% 0.27/0.85 fof(f2047,plain,(
% 0.27/0.85 ~member(u,set_builder(u,null_class))),
% 0.27/0.85 inference(resolution,[status(thm)],[f2046,f127])).
% 0.27/0.85 fof(f2242,plain,(
% 0.27/0.85 member(u,complement(singleton(u)))),
% 0.27/0.85 inference(resolution,[status(thm)],[f1769,f2047])).
% 0.27/0.85 fof(f2251,plain,(
% 0.27/0.85 ~member(u,singleton(u))),
% 0.27/0.85 inference(resolution,[status(thm)],[f2242,f127])).
% 0.27/0.85 fof(f2254,plain,(
% 0.27/0.85 ![X0]: (~member(null_class,X0))),
% 0.27/0.85 inference(backward_subsumption_resolution,[status(thm)],[f892,f2251])).
% 0.27/0.85 fof(f2257,plain,(
% 0.27/0.85 $false),
% 0.27/0.85 inference(backward_subsumption_resolution,[status(thm)],[f381,f2254])).
% 0.27/0.85 % SZS output end CNFRefutation for theBenchmark.p
% 0.27/0.87 % Elapsed time: 0.412847 seconds
% 0.27/0.87 % CPU time: 2.728611 seconds
% 0.27/0.87 % Total memory used: 142.418 MB
% 0.27/0.87 % Net memory used: 138.960 MB
%------------------------------------------------------------------------------