%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET506-6 : 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 : n014.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 02:12:07 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET506-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n014.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:22:34 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.17/0.51 % Refutation found
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.51 fof(f1,axiom,(
% 0.17/0.51 (![X,Y,U]: (( ~ subclass(X,Y)| ~ member(U,X)| member(U,Y) ) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f2,axiom,(
% 0.17/0.51 (![X,Y]: (( member(not_subclass_element(X,Y),X)| subclass(X,Y) ) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f4,axiom,(
% 0.17/0.51 (![X]: (subclass(X,universal_class) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f7,axiom,(
% 0.17/0.51 (![X,Y]: (( ~ subclass(X,Y)| ~ subclass(Y,X)| X = Y ) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f11,axiom,(
% 0.17/0.51 (![X,Y]: (member(unordered_pair(X,Y),universal_class) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f14,axiom,(
% 0.17/0.51 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(U,X) ) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f16,axiom,(
% 0.17/0.51 (![U,X,V,Y]: (( ~ member(U,X)| ~ member(V,Y)| member(ordered_pair(U,V),cross_product(X,Y)) ) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f24,axiom,(
% 0.17/0.51 (![Z,X]: (( ~ member(Z,complement(X))| ~ member(Z,X) ) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f47,axiom,(
% 0.17/0.51 (![X]: (( ~ inductive(X)| member(null_class,X) ) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f50,axiom,(
% 0.17/0.51 inductive(omega) ),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f54,axiom,(
% 0.17/0.51 (![X]: (( ~ member(X,universal_class)| member(sum_class(X),universal_class) ) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f66,axiom,(
% 0.17/0.51 (![X]: (( X = null_class| member(regular(X),X) ) ))),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f113,negated_conjecture,(
% 0.17/0.51 universal_class = null_class ),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f114,plain,(
% 0.17/0.51 ![Y,U]: ((![X]: (~subclass(X,Y)|~member(U,X)))|member(U,Y))),
% 0.17/0.51 inference(miniscoping,[status(thm)],[f1])).
% 0.17/0.51 fof(f115,plain,(
% 0.17/0.51 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f114])).
% 0.17/0.51 fof(f116,plain,(
% 0.17/0.51 ![X0,X1]: (member(not_subclass_element(X0,X1),X0)|subclass(X0,X1))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f2])).
% 0.17/0.51 fof(f118,plain,(
% 0.17/0.51 ![X0]: (subclass(X0,universal_class))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f4])).
% 0.17/0.51 fof(f121,plain,(
% 0.17/0.51 ![X0,X1]: (~subclass(X0,X1)|~subclass(X1,X0)|X0=X1)),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f7])).
% 0.17/0.51 fof(f128,plain,(
% 0.17/0.51 ![X0,X1]: (member(unordered_pair(X0,X1),universal_class))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f11])).
% 0.17/0.51 fof(f131,plain,(
% 0.17/0.51 ![U,X]: ((![V,Y]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(U,X))),
% 0.17/0.51 inference(miniscoping,[status(thm)],[f14])).
% 0.17/0.51 fof(f132,plain,(
% 0.17/0.51 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X0,X2))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f131])).
% 0.17/0.51 fof(f135,plain,(
% 0.17/0.51 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X2,X3)|member(ordered_pair(X0,X2),cross_product(X1,X3)))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f16])).
% 0.17/0.51 fof(f146,plain,(
% 0.17/0.51 ![X0,X1]: (~member(X0,complement(X1))|~member(X0,X1))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f24])).
% 0.17/0.51 fof(f169,plain,(
% 0.17/0.51 ![X0]: (~inductive(X0)|member(null_class,X0))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f47])).
% 0.17/0.51 fof(f172,plain,(
% 0.17/0.51 inductive(omega)),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f50])).
% 0.17/0.51 fof(f176,plain,(
% 0.17/0.51 ![X0]: (~member(X0,universal_class)|member(sum_class(X0),universal_class))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f54])).
% 0.17/0.51 fof(f188,plain,(
% 0.17/0.51 ![X0]: (X0=null_class|member(regular(X0),X0))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f66])).
% 0.17/0.51 fof(f245,plain,(
% 0.17/0.51 universal_class=null_class),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f113])).
% 0.17/0.51 fof(f251,plain,(
% 0.17/0.51 ![X0,X1]: (~member(X0,X1)|member(X0,universal_class))),
% 0.17/0.51 inference(resolution,[status(thm)],[f118,f115])).
% 0.17/0.51 fof(f266,plain,(
% 0.17/0.51 ![X0]: (~inductive(X0)|member(universal_class,X0))),
% 0.17/0.52 inference(forward_demodulation,[status(thm)],[f245,f169])).
% 0.17/0.52 fof(f267,plain,(
% 0.17/0.52 member(universal_class,omega)),
% 0.17/0.52 inference(resolution,[status(thm)],[f266,f172])).
% 0.17/0.52 fof(f272,plain,(
% 0.17/0.52 ![X0,X1]: (~member(X0,X1)|member(ordered_pair(universal_class,X0),cross_product(omega,X1)))),
% 0.17/0.52 inference(resolution,[status(thm)],[f135,f267])).
% 0.17/0.52 fof(f281,plain,(
% 0.17/0.52 ![X0,X1]: (member(ordered_pair(universal_class,not_subclass_element(X0,X1)),cross_product(omega,X0))|subclass(X0,X1))),
% 0.17/0.52 inference(resolution,[status(thm)],[f272,f116])).
% 0.17/0.52 fof(f316,plain,(
% 0.17/0.52 ![X0,X1]: (subclass(X0,X1)|member(universal_class,omega))),
% 0.17/0.52 inference(resolution,[status(thm)],[f281,f132])).
% 0.17/0.52 fof(f320,definition,(
% 0.17/0.52 ![X0,X1]: (sQ2_spl <=> (subclass(X0,X1)))),
% 0.17/0.52 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.17/0.52 fof(f321,plain,(
% 0.17/0.52 ![X0,X1]: (subclass(X0,X1)|~sQ2_spl)),
% 0.17/0.52 inference(component_clause,[status(thm)],[f320])).
% 0.17/0.52 fof(f323,definition,(
% 0.17/0.52 sQ3_spl <=> (member(universal_class,omega))),
% 0.17/0.52 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.17/0.52 fof(f324,plain,(
% 0.17/0.52 member(universal_class,omega)|~sQ3_spl),
% 0.17/0.52 inference(component_clause,[status(thm)],[f323])).
% 0.17/0.52 fof(f326,plain,(
% 0.17/0.52 sQ2_spl|sQ3_spl),
% 0.17/0.52 inference(split_clause,[status(thm)],[f316,f320,f323])).
% 0.17/0.52 fof(f327,plain,(
% 0.17/0.52 ![X0,X1]: (~subclass(X0,X1)|X0=X1|~sQ2_spl)),
% 0.17/0.52 inference(backward_subsumption_resolution,[status(thm)],[f121,f321])).
% 0.17/0.52 fof(f328,plain,(
% 0.17/0.52 ![X0,X1,X2]: (~member(X0,X1)|member(X0,X2)|~sQ2_spl)),
% 0.17/0.52 inference(backward_subsumption_resolution,[status(thm)],[f115,f321])).
% 0.17/0.52 fof(f329,plain,(
% 0.17/0.52 ![X0,X1]: (X0=X1|~sQ2_spl)),
% 0.17/0.52 inference(forward_subsumption_resolution,[status(thm)],[f327,f321])).
% 0.17/0.52 fof(f336,plain,(
% 0.17/0.52 ![X0,X1,X2]: (member(unordered_pair(X0,X1),X2)|~sQ2_spl)),
% 0.17/0.52 inference(resolution,[status(thm)],[f328,f128])).
% 0.17/0.52 fof(f341,plain,(
% 0.17/0.52 ![X0,X1]: (member(X0,X1)|~sQ2_spl)),
% 0.17/0.52 inference(paramodulation,[status(thm)],[f329,f336])).
% 0.17/0.52 fof(f343,plain,(
% 0.17/0.52 $false|~sQ2_spl),
% 0.17/0.52 inference(backward_subsumption_resolution,[status(thm)],[f341,f344])).
% 0.17/0.52 fof(f344,plain,(
% 0.17/0.52 ![X0,X1]: (~member(X0,X1)|~sQ2_spl)),
% 0.17/0.52 inference(forward_subsumption_resolution,[status(thm)],[f146,f341])).
% 0.17/0.52 fof(f345,plain,(
% 0.17/0.52 ~sQ2_spl),
% 0.17/0.52 inference(contradiction_clause,[status(thm)],[f343])).
% 0.17/0.52 fof(f420,plain,(
% 0.17/0.52 ![X0]: (X0=universal_class|member(regular(X0),X0))),
% 0.17/0.52 inference(forward_demodulation,[status(thm)],[f245,f188])).
% 0.17/0.52 fof(f438,plain,(
% 0.17/0.52 ![X0]: (member(regular(X0),universal_class)|X0=universal_class)),
% 0.17/0.52 inference(resolution,[status(thm)],[f251,f420])).
% 0.17/0.52 fof(f461,plain,(
% 0.17/0.52 member(universal_class,universal_class)|~sQ3_spl),
% 0.17/0.52 inference(resolution,[status(thm)],[f251,f324])).
% 0.17/0.52 fof(f590,plain,(
% 0.17/0.52 ![X0]: (~member(regular(complement(X0)),X0)|complement(X0)=universal_class)),
% 0.17/0.52 inference(resolution,[status(thm)],[f146,f420])).
% 0.17/0.52 fof(f609,plain,(
% 0.17/0.52 member(sum_class(universal_class),universal_class)|~sQ3_spl),
% 0.17/0.52 inference(resolution,[status(thm)],[f176,f461])).
% 0.17/0.52 fof(f626,plain,(
% 0.17/0.52 complement(universal_class)=universal_class|complement(universal_class)=universal_class),
% 0.17/0.52 inference(resolution,[status(thm)],[f590,f438])).
% 0.17/0.52 fof(f630,definition,(
% 0.17/0.52 sQ19_spl <=> (complement(universal_class)=universal_class)),
% 0.17/0.52 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.17/0.52 fof(f631,plain,(
% 0.17/0.52 complement(universal_class)=universal_class|~sQ19_spl),
% 0.17/0.52 inference(component_clause,[status(thm)],[f630])).
% 0.17/0.52 fof(f633,plain,(
% 0.17/0.52 sQ19_spl),
% 0.17/0.52 inference(split_clause,[status(thm)],[f626,f630])).
% 0.17/0.52 fof(f642,plain,(
% 0.17/0.52 ![X0]: (~member(X0,universal_class)|~member(X0,universal_class)|~sQ19_spl)),
% 0.17/0.52 inference(paramodulation,[status(thm)],[f631,f146])).
% 0.17/0.52 fof(f650,plain,(
% 0.17/0.52 ![X0]: (~member(X0,universal_class)|~sQ19_spl)),
% 0.17/0.52 inference(duplicate_literals_removal,[status(thm)],[f642])).
% 0.17/0.52 fof(f653,plain,(
% 0.17/0.52 $false|~sQ19_spl|~sQ3_spl),
% 0.17/0.52 inference(backward_subsumption_resolution,[status(thm)],[f609,f650])).
% 0.17/0.52 fof(f662,plain,(
% 0.17/0.52 ~sQ19_spl|~sQ3_spl),
% 0.17/0.52 inference(contradiction_clause,[status(thm)],[f653])).
% 0.17/0.52 fof(f663,plain,(
% 0.17/0.52 $false),
% 0.17/0.52 inference(sat_refutation,[status(thm)],[f326,f345,f633,f662])).
% 0.17/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 0.25/0.54 % Elapsed time: 0.086113 seconds
% 0.25/0.54 % CPU time: 0.363255 seconds
% 0.25/0.54 % Total memory used: 79.648 MB
% 0.25/0.54 % Net memory used: 79.292 MB
%------------------------------------------------------------------------------