%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET016-6 : 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 : n005.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 02:11:12 PM UTC 2026
% Result : Unsatisfiable 3.95s 0.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:42:33 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 3.95/0.98 % Refutation found
% 3.95/0.98 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.95/0.98 % SZS output start CNFRefutation for theBenchmark
% 3.95/0.98 fof(f8,axiom,(
% 3.95/0.98 (![U,X,Y]: (( ~ member(U,unordered_pair(X,Y))| U = X| U = Y ) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f9,axiom,(
% 3.95/0.98 (![X,Y]: (( ~ member(X,universal_class)| member(X,unordered_pair(X,Y)) ) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f10,axiom,(
% 3.95/0.98 (![Y,X]: (( ~ member(Y,universal_class)| member(Y,unordered_pair(X,Y)) ) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f11,axiom,(
% 3.95/0.98 (![X,Y]: (member(unordered_pair(X,Y),universal_class) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f12,axiom,(
% 3.95/0.98 (![X]: (unordered_pair(X,X) = singleton(X) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f13,axiom,(
% 3.95/0.98 (![X,Y]: (unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f14,axiom,(
% 3.95/0.98 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(U,X) ) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f15,axiom,(
% 3.95/0.98 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(V,Y) ) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f16,axiom,(
% 3.95/0.98 (![U,X,V,Y]: (( ~ member(U,X)| ~ member(V,Y)| member(ordered_pair(U,V),cross_product(X,Y)) ) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f66,axiom,(
% 3.95/0.98 (![X]: (( X = null_class| member(regular(X),X) ) ))),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f92,negated_conjecture,(
% 3.95/0.98 ordered_pair(w,x) = ordered_pair(y,z) ),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f93,negated_conjecture,(
% 3.95/0.98 member(w,universal_class) ),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f94,negated_conjecture,(
% 3.95/0.98 w != y ),
% 3.95/0.98 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.95/0.98 fof(f103,plain,(
% 3.95/0.98 ![U,Y]: ((![X]: (~member(U,unordered_pair(X,Y))|U=X))|U=Y)),
% 3.95/0.98 inference(miniscoping,[status(thm)],[f8])).
% 3.95/0.98 fof(f104,plain,(
% 3.95/0.98 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f103])).
% 3.95/0.98 fof(f105,plain,(
% 3.95/0.98 ![X]: (~member(X,universal_class)|(![Y]: member(X,unordered_pair(X,Y))))),
% 3.95/0.98 inference(miniscoping,[status(thm)],[f9])).
% 3.95/0.98 fof(f106,plain,(
% 3.95/0.98 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X0,X1)))),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f105])).
% 3.95/0.98 fof(f107,plain,(
% 3.95/0.98 ![Y]: (~member(Y,universal_class)|(![X]: member(Y,unordered_pair(X,Y))))),
% 3.95/0.98 inference(miniscoping,[status(thm)],[f10])).
% 3.95/0.98 fof(f108,plain,(
% 3.95/0.98 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X1,X0)))),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f107])).
% 3.95/0.98 fof(f109,plain,(
% 3.95/0.98 ![X0,X1]: (member(unordered_pair(X0,X1),universal_class))),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f11])).
% 3.95/0.98 fof(f110,plain,(
% 3.95/0.98 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f12])).
% 3.95/0.98 fof(f111,plain,(
% 3.95/0.98 ![X0,X1]: (unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1)))=ordered_pair(X0,X1))),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f13])).
% 3.95/0.98 fof(f112,plain,(
% 3.95/0.98 ![U,X]: ((![V,Y]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(U,X))),
% 3.95/0.98 inference(miniscoping,[status(thm)],[f14])).
% 3.95/0.98 fof(f113,plain,(
% 3.95/0.98 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X0,X2))),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f112])).
% 3.95/0.98 fof(f114,plain,(
% 3.95/0.98 ![V,Y]: ((![U,X]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(V,Y))),
% 3.95/0.98 inference(miniscoping,[status(thm)],[f15])).
% 3.95/0.98 fof(f115,plain,(
% 3.95/0.98 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X1,X3))),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f114])).
% 3.95/0.98 fof(f116,plain,(
% 3.95/0.98 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X2,X3)|member(ordered_pair(X0,X2),cross_product(X1,X3)))),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f16])).
% 3.95/0.98 fof(f169,plain,(
% 3.95/0.98 ![X0]: (X0=null_class|member(regular(X0),X0))),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f66])).
% 3.95/0.98 fof(f200,plain,(
% 3.95/0.98 ordered_pair(w,x)=ordered_pair(y,z)),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f92])).
% 3.95/0.98 fof(f201,plain,(
% 3.95/0.98 member(w,universal_class)),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f93])).
% 3.95/0.98 fof(f202,plain,(
% 3.95/0.98 ~w=y),
% 3.95/0.98 inference(cnf_transformation,[status(thm)],[f94])).
% 3.95/0.98 fof(f224,plain,(
% 3.95/0.98 ![X0]: (~member(X0,universal_class)|member(X0,singleton(X0)))),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f110,f108])).
% 3.95/0.98 fof(f226,plain,(
% 3.95/0.98 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1|X0=X1)),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f110,f104])).
% 3.95/0.98 fof(f227,plain,(
% 3.95/0.98 ![X0]: (member(singleton(X0),universal_class))),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f110,f109])).
% 3.95/0.98 fof(f228,plain,(
% 3.95/0.98 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 3.95/0.98 inference(duplicate_literals_removal,[status(thm)],[f226])).
% 3.95/0.98 fof(f244,plain,(
% 3.95/0.98 ![X0,X1]: (~member(y,X0)|~member(z,X1)|member(ordered_pair(w,x),cross_product(X0,X1)))),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f200,f116])).
% 3.95/0.98 fof(f249,plain,(
% 3.95/0.98 ![X0,X1]: (~member(singleton(X0),universal_class)|member(singleton(X0),ordered_pair(X0,X1)))),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f111,f106])).
% 3.95/0.98 fof(f254,plain,(
% 3.95/0.98 ![X0,X1]: (member(singleton(X0),ordered_pair(X0,X1)))),
% 3.95/0.98 inference(forward_subsumption_resolution,[status(thm)],[f249,f227])).
% 3.95/0.98 fof(f257,plain,(
% 3.95/0.98 ![X0,X1]: (~member(ordered_pair(w,x),cross_product(X0,X1))|member(y,X0))),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f200,f113])).
% 3.95/0.98 fof(f261,plain,(
% 3.95/0.98 ![X0,X1]: (member(y,X0)|~member(w,X0)|~member(x,X1))),
% 3.95/0.98 inference(resolution,[status(thm)],[f257,f116])).
% 3.95/0.98 fof(f263,plain,(
% 3.95/0.98 ![X0,X1]: (~member(w,singleton(X0))|~member(x,X1)|y=X0)),
% 3.95/0.98 inference(resolution,[status(thm)],[f261,f228])).
% 3.95/0.98 fof(f268,plain,(
% 3.95/0.98 ![X0]: (~member(x,X0)|y=w|~member(w,universal_class))),
% 3.95/0.98 inference(resolution,[status(thm)],[f263,f224])).
% 3.95/0.98 fof(f270,plain,(
% 3.95/0.98 ![X0]: (~member(x,X0)|~member(w,universal_class))),
% 3.95/0.98 inference(forward_subsumption_resolution,[status(thm)],[f268,f202])).
% 3.95/0.98 fof(f271,plain,(
% 3.95/0.98 ![X0]: (~member(x,X0))),
% 3.95/0.98 inference(resolution,[status(thm)],[f270,f201])).
% 3.95/0.98 fof(f283,plain,(
% 3.95/0.98 ![X0,X1]: (~member(y,X0)|~member(z,X1)|member(x,X1))),
% 3.95/0.98 inference(resolution,[status(thm)],[f244,f115])).
% 3.95/0.98 fof(f285,plain,(
% 3.95/0.98 ![X0,X1]: (~member(y,X0)|~member(z,X1))),
% 3.95/0.98 inference(forward_subsumption_resolution,[status(thm)],[f283,f271])).
% 3.95/0.98 fof(f297,plain,(
% 3.95/0.98 ![X0]: (singleton(X0)=null_class|regular(singleton(X0))=X0)),
% 3.95/0.98 inference(resolution,[status(thm)],[f169,f228])).
% 3.95/0.98 fof(f302,plain,(
% 3.95/0.98 member(singleton(y),ordered_pair(w,x))),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f200,f254])).
% 3.95/0.98 fof(f324,plain,(
% 3.95/0.98 ![X0]: (singleton(X0)=null_class|member(X0,singleton(X0))|singleton(X0)=null_class)),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f297,f169])).
% 3.95/0.98 fof(f326,plain,(
% 3.95/0.98 ![X0]: (singleton(X0)=null_class|member(X0,singleton(X0)))),
% 3.95/0.98 inference(duplicate_literals_removal,[status(thm)],[f324])).
% 3.95/0.98 fof(f327,plain,(
% 3.95/0.98 ![X0]: (singleton(z)=null_class|~member(y,X0))),
% 3.95/0.98 inference(resolution,[status(thm)],[f326,f285])).
% 3.95/0.98 fof(f328,plain,(
% 3.95/0.98 singleton(x)=null_class),
% 3.95/0.98 inference(resolution,[status(thm)],[f326,f271])).
% 3.95/0.98 fof(f332,plain,(
% 3.95/0.98 ![X0]: (member(null_class,ordered_pair(x,X0)))),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f328,f254])).
% 3.95/0.98 fof(f334,plain,(
% 3.95/0.98 ![X0]: (unordered_pair(singleton(X0),unordered_pair(X0,null_class))=ordered_pair(X0,x))),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f328,f111])).
% 3.95/0.98 fof(f338,plain,(
% 3.95/0.98 member(null_class,universal_class)),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f328,f227])).
% 3.95/0.98 fof(f387,plain,(
% 3.95/0.98 unordered_pair(singleton(null_class),singleton(null_class))=ordered_pair(null_class,x)),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f110,f334])).
% 3.95/0.98 fof(f390,plain,(
% 3.95/0.98 ![X0,X1]: (~member(X0,ordered_pair(X1,x))|X0=singleton(X1)|X0=unordered_pair(X1,null_class))),
% 3.95/0.98 inference(paramodulation,[status(thm)],[f334,f104])).
% 3.95/0.98 fof(f392,plain,(
% 3.95/0.98 singleton(singleton(null_class))=ordered_pair(null_class,x)),
% 3.95/0.98 inference(forward_demodulation,[status(thm)],[f110,f387])).
% 3.95/0.98 fof(f402,plain,(
% 3.95/0.99 ![X0]: (~member(X0,ordered_pair(null_class,x))|X0=singleton(null_class))),
% 3.95/0.99 inference(paramodulation,[status(thm)],[f392,f228])).
% 3.95/0.99 fof(f595,plain,(
% 3.95/0.99 singleton(y)=singleton(w)|singleton(y)=unordered_pair(w,null_class)),
% 3.95/0.99 inference(resolution,[status(thm)],[f390,f302])).
% 3.95/0.99 fof(f623,plain,(
% 3.95/0.99 ~member(null_class,universal_class)|member(null_class,singleton(y))|singleton(y)=singleton(w)),
% 3.95/0.99 inference(paramodulation,[status(thm)],[f595,f108])).
% 3.95/0.99 fof(f627,plain,(
% 3.95/0.99 member(null_class,singleton(y))|singleton(y)=singleton(w)),
% 3.95/0.99 inference(forward_subsumption_resolution,[status(thm)],[f623,f338])).
% 3.95/0.99 fof(f629,plain,(
% 3.95/0.99 singleton(y)=singleton(w)|null_class=y),
% 3.95/0.99 inference(resolution,[status(thm)],[f627,f228])).
% 3.95/0.99 fof(f642,plain,(
% 3.95/0.99 ![X0]: (~member(X0,singleton(w))|X0=y|null_class=y)),
% 3.95/0.99 inference(paramodulation,[status(thm)],[f629,f228])).
% 3.95/0.99 fof(f758,plain,(
% 3.95/0.99 w=y|null_class=y|~member(w,universal_class)),
% 3.95/0.99 inference(resolution,[status(thm)],[f642,f224])).
% 3.95/0.99 fof(f762,plain,(
% 3.95/0.99 null_class=y|~member(w,universal_class)),
% 3.95/0.99 inference(forward_subsumption_resolution,[status(thm)],[f758,f202])).
% 3.95/0.99 fof(f782,plain,(
% 3.95/0.99 null_class=y),
% 3.95/0.99 inference(resolution,[status(thm)],[f762,f201])).
% 3.95/0.99 fof(f813,plain,(
% 3.95/0.99 ![X0]: (singleton(z)=null_class|~member(null_class,X0))),
% 3.95/0.99 inference(backward_demodulation,[status(thm)],[f782,f327])).
% 3.95/0.99 fof(f819,plain,(
% 3.95/0.99 ordered_pair(w,x)=ordered_pair(null_class,z)),
% 3.95/0.99 inference(backward_demodulation,[status(thm)],[f782,f200])).
% 3.95/0.99 fof(f820,plain,(
% 3.95/0.99 ~w=null_class),
% 3.95/0.99 inference(backward_demodulation,[status(thm)],[f782,f202])).
% 3.95/0.99 fof(f1006,plain,(
% 3.95/0.99 member(singleton(w),ordered_pair(null_class,z))),
% 3.95/0.99 inference(paramodulation,[status(thm)],[f819,f254])).
% 3.95/0.99 fof(f1015,plain,(
% 3.95/0.99 singleton(z)=null_class),
% 3.95/0.99 inference(resolution,[status(thm)],[f813,f332])).
% 3.95/0.99 fof(f1043,plain,(
% 3.95/0.99 ![X0]: (unordered_pair(singleton(X0),unordered_pair(X0,null_class))=ordered_pair(X0,z))),
% 3.95/0.99 inference(paramodulation,[status(thm)],[f1015,f111])).
% 3.95/0.99 fof(f1056,plain,(
% 3.95/0.99 member(singleton(w),ordered_pair(null_class,x))),
% 3.95/0.99 inference(backward_demodulation,[status(thm)],[f1097,f1006])).
% 3.95/0.99 fof(f1097,plain,(
% 3.95/0.99 ![X0]: (ordered_pair(X0,x)=ordered_pair(X0,z))),
% 3.95/0.99 inference(forward_demodulation,[status(thm)],[f334,f1043])).
% 3.95/0.99 fof(f1247,plain,(
% 3.95/0.99 singleton(w)=singleton(null_class)),
% 3.95/0.99 inference(resolution,[status(thm)],[f1056,f402])).
% 3.95/0.99 fof(f1266,plain,(
% 3.95/0.99 ~member(w,universal_class)|member(w,singleton(null_class))),
% 3.95/0.99 inference(paramodulation,[status(thm)],[f1247,f224])).
% 3.95/0.99 fof(f1279,plain,(
% 3.95/0.99 member(w,singleton(null_class))),
% 3.95/0.99 inference(forward_subsumption_resolution,[status(thm)],[f1266,f201])).
% 3.95/0.99 fof(f1280,plain,(
% 3.95/0.99 w=null_class),
% 3.95/0.99 inference(resolution,[status(thm)],[f1279,f228])).
% 3.95/0.99 fof(f1281,plain,(
% 3.95/0.99 $false),
% 3.95/0.99 inference(forward_subsumption_resolution,[status(thm)],[f1280,f820])).
% 3.95/0.99 % SZS output end CNFRefutation for theBenchmark.p
% 0.59/1.01 % Elapsed time: 0.634420 seconds
% 0.59/1.01 % CPU time: 4.707071 seconds
% 0.59/1.01 % Total memory used: 180.260 MB
% 0.59/1.01 % Net memory used: 168.843 MB
%------------------------------------------------------------------------------