%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET411-6 : 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 : n012.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 02:12:01 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET411-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n012.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 05:15:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f1,axiom,(
% 0.10/0.40 (![X,Y,U]: (( ~ subclass(X,Y)| ~ member(U,X)| member(U,Y) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f2,axiom,(
% 0.10/0.40 (![X,Y]: (( member(not_subclass_element(X,Y),X)| subclass(X,Y) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f4,axiom,(
% 0.10/0.40 (![X]: (subclass(X,universal_class) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f7,axiom,(
% 0.10/0.40 (![X,Y]: (( ~ subclass(X,Y)| ~ subclass(Y,X)| X = Y ) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f14,axiom,(
% 0.10/0.40 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(U,X) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f16,axiom,(
% 0.10/0.40 (![U,X,V,Y]: (( ~ member(U,X)| ~ member(V,Y)| member(ordered_pair(U,V),cross_product(X,Y)) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f19,axiom,(
% 0.10/0.40 (![X,Y]: (( ~ member(ordered_pair(X,Y),element_relation)| member(X,Y) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f22,axiom,(
% 0.10/0.40 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,Y) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f52,axiom,(
% 0.10/0.40 member(omega,universal_class) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f104,axiom,(
% 0.10/0.40 intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f113,negated_conjecture,(
% 0.10/0.40 member(ordered_pair(x,y),singleton_relation) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f114,negated_conjecture,(
% 0.10/0.40 ~ member(x,universal_class) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f115,plain,(
% 0.10/0.40 ![Y,U]: ((![X]: (~subclass(X,Y)|~member(U,X)))|member(U,Y))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f1])).
% 0.10/0.40 fof(f116,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f115])).
% 0.10/0.40 fof(f117,plain,(
% 0.10/0.40 ![X0,X1]: (member(not_subclass_element(X0,X1),X0)|subclass(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.40 fof(f119,plain,(
% 0.10/0.40 ![X0]: (subclass(X0,universal_class))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.40 fof(f122,plain,(
% 0.10/0.40 ![X0,X1]: (~subclass(X0,X1)|~subclass(X1,X0)|X0=X1)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.10/0.40 fof(f132,plain,(
% 0.10/0.40 ![U,X]: ((![V,Y]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(U,X))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f14])).
% 0.10/0.40 fof(f133,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X0,X2))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f132])).
% 0.10/0.40 fof(f136,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X2,X3)|member(ordered_pair(X0,X2),cross_product(X1,X3)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f16])).
% 0.10/0.40 fof(f140,plain,(
% 0.10/0.40 ![X0,X1]: (~member(ordered_pair(X0,X1),element_relation)|member(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f19])).
% 0.10/0.40 fof(f144,plain,(
% 0.10/0.40 ![Z,Y]: ((![X]: ~member(Z,intersection(X,Y)))|member(Z,Y))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f22])).
% 0.10/0.40 fof(f145,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f144])).
% 0.10/0.40 fof(f175,plain,(
% 0.10/0.40 member(omega,universal_class)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f52])).
% 0.10/0.40 fof(f232,plain,(
% 0.10/0.40 intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)=singleton_relation),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f104])).
% 0.10/0.40 fof(f246,plain,(
% 0.10/0.40 member(ordered_pair(x,y),singleton_relation)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f113])).
% 0.10/0.40 fof(f247,plain,(
% 0.10/0.40 ~member(x,universal_class)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f114])).
% 0.10/0.40 fof(f253,plain,(
% 0.10/0.40 ![X0,X1]: (~member(X0,X1)|member(X0,universal_class))),
% 0.10/0.40 inference(resolution,[status(thm)],[f119,f116])).
% 0.10/0.40 fof(f267,plain,(
% 0.10/0.40 ![X0]: (~subclass(universal_class,X0)|universal_class=X0)),
% 0.10/0.40 inference(resolution,[status(thm)],[f122,f119])).
% 0.10/0.40 fof(f284,definition,(
% 0.10/0.40 sQ1_spl <=> (universal_class=null_class)),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f285,plain,(
% 0.10/0.40 universal_class=null_class|~sQ1_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f284])).
% 0.10/0.40 fof(f286,plain,(
% 0.10/0.40 ~universal_class=null_class|sQ1_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f284])).
% 0.10/0.40 fof(f324,plain,(
% 0.10/0.40 ~member(x,null_class)|~sQ1_spl),
% 0.10/0.40 inference(backward_demodulation,[status(thm)],[f285,f247])).
% 0.10/0.40 fof(f328,plain,(
% 0.10/0.40 member(omega,null_class)|~sQ1_spl),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f285,f175])).
% 0.10/0.40 fof(f339,plain,(
% 0.10/0.40 ![X0]: (~subclass(null_class,X0)|universal_class=X0|~sQ1_spl)),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f285,f267])).
% 0.10/0.40 fof(f340,plain,(
% 0.10/0.40 ![X0]: (~subclass(null_class,X0)|null_class=X0|~sQ1_spl)),
% 0.10/0.40 inference(forward_demodulation,[status(thm)],[f285,f339])).
% 0.10/0.40 fof(f382,plain,(
% 0.10/0.40 ![X0,X1]: (~member(X0,X1)|member(ordered_pair(ordered_pair(x,y),X0),cross_product(singleton_relation,X1)))),
% 0.10/0.40 inference(resolution,[status(thm)],[f136,f246])).
% 0.10/0.40 fof(f396,plain,(
% 0.10/0.40 ![X0,X1]: (member(ordered_pair(ordered_pair(x,y),not_subclass_element(X0,X1)),cross_product(singleton_relation,X0))|subclass(X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f382,f117])).
% 0.10/0.40 fof(f487,plain,(
% 0.10/0.40 ![X0,X1]: (subclass(X0,X1)|member(ordered_pair(x,y),singleton_relation))),
% 0.10/0.40 inference(resolution,[status(thm)],[f396,f133])).
% 0.10/0.40 fof(f492,definition,(
% 0.10/0.40 ![X0,X1]: (sQ5_spl <=> (subclass(X0,X1)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f493,plain,(
% 0.10/0.40 ![X0,X1]: (subclass(X0,X1)|~sQ5_spl)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f492])).
% 0.10/0.40 fof(f495,definition,(
% 0.10/0.40 sQ6_spl <=> (member(ordered_pair(x,y),singleton_relation))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f496,plain,(
% 0.10/0.40 member(ordered_pair(x,y),singleton_relation)|~sQ6_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f495])).
% 0.10/0.40 fof(f498,plain,(
% 0.10/0.40 sQ5_spl|sQ6_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f487,f492,f495])).
% 0.10/0.40 fof(f509,plain,(
% 0.10/0.40 ![X0]: (null_class=X0|~sQ5_spl|~sQ1_spl)),
% 0.10/0.40 inference(backward_subsumption_resolution,[status(thm)],[f340,f493])).
% 0.10/0.40 fof(f511,plain,(
% 0.10/0.40 ![X0,X1]: (X0=X1|~sQ5_spl|~sQ1_spl)),
% 0.10/0.40 inference(paramodulation,[status(thm)],[f509,f509])).
% 0.10/0.40 fof(f535,plain,(
% 0.10/0.40 ![X0]: (member(omega,X0)|~sQ5_spl|~sQ1_spl)),
% 0.10/0.40 inference(paramodulation,[status(thm)],[f509,f328])).
% 0.10/0.40 fof(f543,plain,(
% 0.10/0.40 ![X0,X1]: (member(X0,X1)|~sQ5_spl|~sQ1_spl)),
% 0.10/0.40 inference(paramodulation,[status(thm)],[f511,f535])).
% 0.10/0.40 fof(f545,plain,(
% 0.10/0.40 $false|~sQ5_spl|~sQ1_spl),
% 0.10/0.40 inference(backward_subsumption_resolution,[status(thm)],[f324,f543])).
% 0.10/0.40 fof(f546,plain,(
% 0.10/0.40 ~sQ5_spl|~sQ1_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f545])).
% 0.10/0.40 fof(f619,plain,(
% 0.10/0.40 ![X0]: (~member(X0,singleton_relation)|member(X0,element_relation))),
% 0.10/0.40 inference(paramodulation,[status(thm)],[f232,f145])).
% 0.10/0.40 fof(f657,plain,(
% 0.10/0.40 member(ordered_pair(x,y),element_relation)|~sQ6_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f619,f496])).
% 0.10/0.40 fof(f671,plain,(
% 0.10/0.40 member(x,y)|~sQ6_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f657,f140])).
% 0.10/0.40 fof(f676,plain,(
% 0.10/0.40 member(x,universal_class)|~sQ6_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f671,f253])).
% 0.10/0.40 fof(f678,plain,(
% 0.10/0.40 $false|~sQ6_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f676,f247])).
% 0.10/0.40 fof(f679,plain,(
% 0.10/0.40 ~sQ6_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f678])).
% 0.10/0.40 fof(f680,plain,(
% 0.10/0.40 ![X0]: (universal_class=X0|~sQ5_spl)),
% 0.10/0.40 inference(backward_subsumption_resolution,[status(thm)],[f267,f493])).
% 0.10/0.40 fof(f681,plain,(
% 0.10/0.40 $false|~sQ5_spl|sQ1_spl),
% 0.10/0.40 inference(backward_subsumption_resolution,[status(thm)],[f286,f680])).
% 0.10/0.40 fof(f697,plain,(
% 0.10/0.40 ~sQ5_spl|sQ1_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f681])).
% 0.10/0.40 fof(f698,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(sat_refutation,[status(thm)],[f498,f546,f679,f697])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.45 % Elapsed time: 0.064530 seconds
% 0.10/0.45 % CPU time: 0.077650 seconds
% 0.10/0.45 % Total memory used: 10.397 MB
% 0.10/0.45 % Net memory used: 10.347 MB
%------------------------------------------------------------------------------