%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM181-1 : 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 01:42:20 PM UTC 2026
% Result : Unsatisfiable 63.58s 8.64s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM181-1 : 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 02:13:51 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 63.58/8.64 % Refutation found
% 63.58/8.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 63.58/8.64 % SZS output start CNFRefutation for theBenchmark
% 63.58/8.64 fof(f1,axiom,(
% 63.58/8.64 (![X,Y,U]: (( ~ subclass(X,Y)| ~ member(U,X)| member(U,Y) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f4,axiom,(
% 63.58/8.64 (![X]: (subclass(X,universal_class) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f9,axiom,(
% 63.58/8.64 (![X,Y]: (( ~ member(X,universal_class)| member(X,unordered_pair(X,Y)) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f12,axiom,(
% 63.58/8.64 (![X]: (unordered_pair(X,X) = singleton(X) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f21,axiom,(
% 63.58/8.64 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,X) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f22,axiom,(
% 63.58/8.64 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,Y) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f24,axiom,(
% 63.58/8.64 (![Z,X]: (( ~ member(Z,complement(X))| ~ member(Z,X) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f25,axiom,(
% 63.58/8.64 (![Z,X]: (( ~ member(Z,universal_class)| member(Z,complement(X))| member(Z,X) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f26,axiom,(
% 63.58/8.64 (![X,Y]: (complement(intersection(complement(X),complement(Y))) = union(X,Y) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f47,axiom,(
% 63.58/8.64 (![X]: (( ~ inductive(X)| member(null_class,X) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f50,axiom,(
% 63.58/8.64 inductive(omega) ),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f134,axiom,(
% 63.58/8.64 (![X]: (( ~ member(X,ordinal_numbers)| well_ordering(element_relation,X) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f135,axiom,(
% 63.58/8.64 (![X]: (( ~ member(X,ordinal_numbers)| subclass(sum_class(X),X) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f136,axiom,(
% 63.58/8.64 (![X]: (( ~ well_ordering(element_relation,X)| ~ subclass(sum_class(X),X)| ~ member(X,universal_class)| member(X,ordinal_numbers) ) ))),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f138,axiom,(
% 63.58/8.64 union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals ),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f139,axiom,(
% 63.58/8.64 intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals ),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f159,negated_conjecture,(
% 63.58/8.64 member(null_class,limit_ordinals) ),
% 63.58/8.64 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 63.58/8.64 fof(f160,plain,(
% 63.58/8.64 ![Y,U]: ((![X]: (~subclass(X,Y)|~member(U,X)))|member(U,Y))),
% 63.58/8.64 inference(miniscoping,[status(thm)],[f1])).
% 63.58/8.64 fof(f161,plain,(
% 63.58/8.64 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f160])).
% 63.58/8.64 fof(f164,plain,(
% 63.58/8.64 ![X0]: (subclass(X0,universal_class))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f4])).
% 63.58/8.64 fof(f170,plain,(
% 63.58/8.64 ![X]: (~member(X,universal_class)|(![Y]: member(X,unordered_pair(X,Y))))),
% 63.58/8.64 inference(miniscoping,[status(thm)],[f9])).
% 63.58/8.64 fof(f171,plain,(
% 63.58/8.64 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X0,X1)))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f170])).
% 63.58/8.64 fof(f175,plain,(
% 63.58/8.64 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f12])).
% 63.58/8.64 fof(f187,plain,(
% 63.58/8.64 ![Z,X]: ((![Y]: ~member(Z,intersection(X,Y)))|member(Z,X))),
% 63.58/8.64 inference(miniscoping,[status(thm)],[f21])).
% 63.58/8.64 fof(f188,plain,(
% 63.58/8.64 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f187])).
% 63.58/8.64 fof(f189,plain,(
% 63.58/8.64 ![Z,Y]: ((![X]: ~member(Z,intersection(X,Y)))|member(Z,Y))),
% 63.58/8.64 inference(miniscoping,[status(thm)],[f22])).
% 63.58/8.64 fof(f190,plain,(
% 63.58/8.64 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f189])).
% 63.58/8.64 fof(f192,plain,(
% 63.58/8.64 ![X0,X1]: (~member(X0,complement(X1))|~member(X0,X1))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f24])).
% 63.58/8.64 fof(f193,plain,(
% 63.58/8.64 ![X0,X1]: (~member(X0,universal_class)|member(X0,complement(X1))|member(X0,X1))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f25])).
% 63.58/8.64 fof(f194,plain,(
% 63.58/8.64 ![X0,X1]: (complement(intersection(complement(X0),complement(X1)))=union(X0,X1))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f26])).
% 63.58/8.64 fof(f215,plain,(
% 63.58/8.64 ![X0]: (~inductive(X0)|member(null_class,X0))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f47])).
% 63.58/8.64 fof(f218,plain,(
% 63.58/8.64 inductive(omega)),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f50])).
% 63.58/8.64 fof(f318,plain,(
% 63.58/8.64 ![X0]: (~member(X0,ordinal_numbers)|well_ordering(element_relation,X0))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f134])).
% 63.58/8.64 fof(f319,plain,(
% 63.58/8.64 ![X0]: (~member(X0,ordinal_numbers)|subclass(sum_class(X0),X0))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f135])).
% 63.58/8.64 fof(f320,plain,(
% 63.58/8.64 ![X0]: (~well_ordering(element_relation,X0)|~subclass(sum_class(X0),X0)|~member(X0,universal_class)|member(X0,ordinal_numbers))),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f136])).
% 63.58/8.64 fof(f322,plain,(
% 63.58/8.64 union(singleton(null_class),image(successor_relation,ordinal_numbers))=kind_1_ordinals),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f138])).
% 63.58/8.64 fof(f323,plain,(
% 63.58/8.64 intersection(complement(kind_1_ordinals),ordinal_numbers)=limit_ordinals),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f139])).
% 63.58/8.64 fof(f347,plain,(
% 63.58/8.64 member(null_class,limit_ordinals)),
% 63.58/8.64 inference(cnf_transformation,[status(thm)],[f159])).
% 63.58/8.64 fof(f364,plain,(
% 63.58/8.64 ![X0]: (~member(X0,limit_ordinals)|member(X0,complement(kind_1_ordinals)))),
% 63.58/8.64 inference(paramodulation,[status(thm)],[f323,f188])).
% 63.58/8.64 fof(f367,plain,(
% 63.58/8.64 ![X0]: (~member(X0,limit_ordinals)|member(X0,ordinal_numbers))),
% 63.58/8.64 inference(paramodulation,[status(thm)],[f323,f190])).
% 63.58/8.64 fof(f381,plain,(
% 63.58/8.64 ![X0]: (~member(X0,kind_1_ordinals)|~member(X0,limit_ordinals))),
% 63.58/8.64 inference(resolution,[status(thm)],[f192,f364])).
% 63.58/8.64 fof(f390,plain,(
% 63.58/8.64 ![X0,X1,X2]: (member(X0,unordered_pair(X0,X1))|~subclass(X2,universal_class)|~member(X0,X2))),
% 63.58/8.64 inference(resolution,[status(thm)],[f171,f161])).
% 63.58/8.64 fof(f391,plain,(
% 63.58/8.64 ![X0,X1,X2]: (member(X0,unordered_pair(X0,X1))|~member(X0,X2))),
% 63.58/8.64 inference(forward_subsumption_resolution,[status(thm)],[f390,f164])).
% 63.58/8.64 fof(f393,plain,(
% 63.58/8.64 ![X0,X1]: (member(X0,singleton(X0))|~member(X0,X1))),
% 63.58/8.64 inference(paramodulation,[status(thm)],[f175,f391])).
% 63.58/8.64 fof(f435,plain,(
% 63.58/8.64 ![X0,X1,X2]: (member(X0,complement(X1))|member(X0,X1)|~subclass(X2,universal_class)|~member(X0,X2))),
% 63.58/8.64 inference(resolution,[status(thm)],[f193,f161])).
% 63.58/8.64 fof(f436,plain,(
% 63.58/8.64 ![X0,X1,X2]: (member(X0,complement(X1))|member(X0,X1)|~member(X0,X2))),
% 63.58/8.64 inference(forward_subsumption_resolution,[status(thm)],[f435,f164])).
% 63.58/8.64 fof(f442,plain,(
% 63.58/8.64 ![X0,X1,X2,X3]: (member(X0,union(X1,X2))|member(X0,intersection(complement(X1),complement(X2)))|~member(X0,X3))),
% 63.58/8.64 inference(paramodulation,[status(thm)],[f194,f436])).
% 63.58/8.64 fof(f560,plain,(
% 63.58/8.64 member(null_class,omega)),
% 63.58/8.64 inference(resolution,[status(thm)],[f218,f215])).
% 63.58/8.64 fof(f828,plain,(
% 63.58/8.64 ![X0]: (well_ordering(element_relation,X0)|~member(X0,limit_ordinals))),
% 63.58/8.64 inference(resolution,[status(thm)],[f318,f367])).
% 63.58/8.64 fof(f833,plain,(
% 63.58/8.64 ![X0]: (subclass(sum_class(X0),X0)|~member(X0,limit_ordinals))),
% 63.58/8.64 inference(resolution,[status(thm)],[f319,f367])).
% 63.58/8.64 fof(f846,plain,(
% 63.58/8.64 well_ordering(element_relation,null_class)),
% 63.58/8.64 inference(resolution,[status(thm)],[f828,f347])).
% 63.58/8.64 fof(f873,plain,(
% 63.58/8.64 subclass(sum_class(null_class),null_class)),
% 63.58/8.64 inference(resolution,[status(thm)],[f833,f347])).
% 63.58/8.64 fof(f908,plain,(
% 63.58/8.64 ~subclass(sum_class(null_class),null_class)|~member(null_class,universal_class)|member(null_class,ordinal_numbers)),
% 63.58/8.64 inference(resolution,[status(thm)],[f846,f320])).
% 63.58/8.64 fof(f915,plain,(
% 63.58/8.64 ~member(null_class,universal_class)|member(null_class,ordinal_numbers)),
% 63.58/8.64 inference(forward_subsumption_resolution,[status(thm)],[f908,f873])).
% 63.58/8.64 fof(f919,plain,(
% 63.58/8.64 ![X0]: (member(null_class,ordinal_numbers)|~subclass(X0,universal_class)|~member(null_class,X0))),
% 63.58/8.64 inference(resolution,[status(thm)],[f915,f161])).
% 63.58/8.64 fof(f920,plain,(
% 63.58/8.64 ![X0]: (member(null_class,ordinal_numbers)|~member(null_class,X0))),
% 63.58/8.64 inference(forward_subsumption_resolution,[status(thm)],[f919,f164])).
% 63.58/8.74 fof(f2067,plain,(
% 63.58/8.74 ![X0,X1,X2,X3]: (member(X0,union(X1,X2))|~member(X0,X3)|member(X0,complement(X1)))),
% 63.58/8.74 inference(resolution,[status(thm)],[f442,f188])).
% 63.58/8.74 fof(f2131,plain,(
% 63.58/8.74 ![X0,X1]: (member(X0,kind_1_ordinals)|~member(X0,X1)|member(X0,complement(singleton(null_class))))),
% 63.58/8.74 inference(paramodulation,[status(thm)],[f322,f2067])).
% 63.58/8.74 fof(f2477,plain,(
% 63.58/8.74 ![X0,X1]: (member(X0,kind_1_ordinals)|~member(X0,X1)|~member(X0,singleton(null_class)))),
% 63.58/8.74 inference(resolution,[status(thm)],[f2131,f192])).
% 63.58/8.74 fof(f2485,plain,(
% 63.58/8.74 ![X0,X1]: (member(null_class,kind_1_ordinals)|~member(null_class,X0)|~member(null_class,X1))),
% 63.58/8.74 inference(resolution,[status(thm)],[f2477,f393])).
% 63.58/8.74 fof(f2487,plain,(
% 63.58/8.74 ![X0,X1]: (~member(null_class,X0)|~member(null_class,X1)|~member(null_class,limit_ordinals))),
% 63.58/8.74 inference(resolution,[status(thm)],[f2485,f381])).
% 63.58/8.74 fof(f2489,plain,(
% 63.58/8.74 ![X0]: (~member(null_class,X0))),
% 63.58/8.74 inference(backward_subsumption_resolution,[status(thm)],[f920,f2490])).
% 63.58/8.74 fof(f2490,plain,(
% 63.58/8.74 ![X0,X1]: (~member(null_class,X0)|~member(null_class,X1))),
% 63.58/8.74 inference(forward_subsumption_resolution,[status(thm)],[f2487,f347])).
% 63.58/8.74 fof(f2494,plain,(
% 63.58/8.74 $false),
% 63.58/8.74 inference(backward_subsumption_resolution,[status(thm)],[f560,f2489])).
% 63.58/8.74 % SZS output end CNFRefutation for theBenchmark.p
% 4.34/8.82 % Elapsed time: 8.360536 seconds
% 4.34/8.82 % CPU time: 65.268287 seconds
% 4.34/8.82 % Total memory used: 557.775 MB
% 4.34/8.82 % Net memory used: 498.118 MB
%------------------------------------------------------------------------------