%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET505-6 : 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 : n003.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 7.81s 7.00s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET505-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.89 % Computer : n003.cluster.edu
% 0.18/5.89 % Model : x86_64 x86_64
% 0.18/5.89 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.89 % Memory : 8046.5625MB
% 0.18/5.89 % OS : Linux 6.8.0-71-generic
% 0.18/5.89 % CPULimit : 300
% 0.18/5.89 % WCLimit : 300
% 0.18/5.89 % DateTime : Mon Sep 21 05:24:23 UTC 2026
% 0.18/5.89 % CPUTime :
% 0.23/5.92 % Drodi V4.1.1
% 7.81/7.00 % Refutation found
% 7.81/7.00 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.81/7.00 % SZS output start CNFRefutation for theBenchmark
% 7.81/7.00 fof(f1,axiom,(
% 7.81/7.00 (![X,Y,U]: (( ~ subclass(X,Y)| ~ member(U,X)| member(U,Y) ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f4,axiom,(
% 7.81/7.00 (![X]: (subclass(X,universal_class) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f8,axiom,(
% 7.81/7.00 (![U,X,Y]: (( ~ member(U,unordered_pair(X,Y))| U = X| U = Y ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f9,axiom,(
% 7.81/7.00 (![X,Y]: (( ~ member(X,universal_class)| member(X,unordered_pair(X,Y)) ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f10,axiom,(
% 7.81/7.00 (![Y,X]: (( ~ member(Y,universal_class)| member(Y,unordered_pair(X,Y)) ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f12,axiom,(
% 7.81/7.00 (![X]: (unordered_pair(X,X) = singleton(X) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f14,axiom,(
% 7.81/7.00 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(U,X) ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f15,axiom,(
% 7.81/7.00 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(V,Y) ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f16,axiom,(
% 7.81/7.00 (![U,X,V,Y]: (( ~ member(U,X)| ~ member(V,Y)| member(ordered_pair(U,V),cross_product(X,Y)) ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f17,axiom,(
% 7.81/7.00 (![Z,X,Y]: (( ~ member(Z,cross_product(X,Y))| ordered_pair(first(Z),second(Z)) = Z ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f23,axiom,(
% 7.81/7.00 (![Z,X,Y]: (( ~ member(Z,X)| ~ member(Z,Y)| member(Z,intersection(X,Y)) ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f24,axiom,(
% 7.81/7.00 (![Z,X]: (( ~ member(Z,complement(X))| ~ member(Z,X) ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f66,axiom,(
% 7.81/7.00 (![X]: (( X = null_class| member(regular(X),X) ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f67,axiom,(
% 7.81/7.00 (![X]: (( X = null_class| intersection(X,regular(X)) = null_class ) ))),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f113,negated_conjecture,(
% 7.81/7.00 member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class)) ),
% 7.81/7.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.81/7.00 fof(f114,plain,(
% 7.81/7.00 ![Y,U]: ((![X]: (~subclass(X,Y)|~member(U,X)))|member(U,Y))),
% 7.81/7.00 inference(miniscoping,[status(thm)],[f1])).
% 7.81/7.00 fof(f115,plain,(
% 7.81/7.00 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f114])).
% 7.81/7.00 fof(f118,plain,(
% 7.81/7.00 ![X0]: (subclass(X0,universal_class))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f4])).
% 7.81/7.00 fof(f122,plain,(
% 7.81/7.00 ![U,Y]: ((![X]: (~member(U,unordered_pair(X,Y))|U=X))|U=Y)),
% 7.81/7.00 inference(miniscoping,[status(thm)],[f8])).
% 7.81/7.00 fof(f123,plain,(
% 7.81/7.00 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f122])).
% 7.81/7.00 fof(f124,plain,(
% 7.81/7.00 ![X]: (~member(X,universal_class)|(![Y]: member(X,unordered_pair(X,Y))))),
% 7.81/7.00 inference(miniscoping,[status(thm)],[f9])).
% 7.81/7.00 fof(f125,plain,(
% 7.81/7.00 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X0,X1)))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f124])).
% 7.81/7.00 fof(f126,plain,(
% 7.81/7.00 ![Y]: (~member(Y,universal_class)|(![X]: member(Y,unordered_pair(X,Y))))),
% 7.81/7.00 inference(miniscoping,[status(thm)],[f10])).
% 7.81/7.00 fof(f127,plain,(
% 7.81/7.00 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X1,X0)))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f126])).
% 7.81/7.00 fof(f129,plain,(
% 7.81/7.00 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f12])).
% 7.81/7.00 fof(f131,plain,(
% 7.81/7.00 ![U,X]: ((![V,Y]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(U,X))),
% 7.81/7.00 inference(miniscoping,[status(thm)],[f14])).
% 7.81/7.00 fof(f132,plain,(
% 7.81/7.00 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X0,X2))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f131])).
% 7.81/7.00 fof(f133,plain,(
% 7.81/7.00 ![V,Y]: ((![U,X]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(V,Y))),
% 7.81/7.00 inference(miniscoping,[status(thm)],[f15])).
% 7.81/7.00 fof(f134,plain,(
% 7.81/7.00 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X1,X3))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f133])).
% 7.81/7.00 fof(f135,plain,(
% 7.81/7.00 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X2,X3)|member(ordered_pair(X0,X2),cross_product(X1,X3)))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f16])).
% 7.81/7.00 fof(f136,plain,(
% 7.81/7.00 ![Z]: ((![X,Y]: ~member(Z,cross_product(X,Y)))|ordered_pair(first(Z),second(Z))=Z)),
% 7.81/7.00 inference(miniscoping,[status(thm)],[f17])).
% 7.81/7.00 fof(f137,plain,(
% 7.81/7.00 ![X0,X1,X2]: (~member(X0,cross_product(X1,X2))|ordered_pair(first(X0),second(X0))=X0)),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f136])).
% 7.81/7.00 fof(f145,plain,(
% 7.81/7.00 ![X0,X1,X2]: (~member(X0,X1)|~member(X0,X2)|member(X0,intersection(X1,X2)))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f23])).
% 7.81/7.00 fof(f146,plain,(
% 7.81/7.00 ![X0,X1]: (~member(X0,complement(X1))|~member(X0,X1))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f24])).
% 7.81/7.00 fof(f188,plain,(
% 7.81/7.00 ![X0]: (X0=null_class|member(regular(X0),X0))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f66])).
% 7.81/7.00 fof(f189,plain,(
% 7.81/7.00 ![X0]: (X0=null_class|intersection(X0,regular(X0))=null_class)),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f67])).
% 7.81/7.00 fof(f245,plain,(
% 7.81/7.00 member(ordered_pair(universal_class,y),cross_product(universal_class,universal_class))),
% 7.81/7.00 inference(cnf_transformation,[status(thm)],[f113])).
% 7.81/7.00 fof(f253,plain,(
% 7.81/7.00 member(universal_class,universal_class)),
% 7.81/7.00 inference(resolution,[status(thm)],[f132,f245])).
% 7.81/7.00 fof(f254,plain,(
% 7.81/7.00 member(y,universal_class)),
% 7.81/7.00 inference(resolution,[status(thm)],[f134,f245])).
% 7.81/7.00 fof(f257,plain,(
% 7.81/7.00 ![X0,X1]: (~member(X0,X1)|member(X0,universal_class))),
% 7.81/7.00 inference(resolution,[status(thm)],[f115,f118])).
% 7.81/7.00 fof(f268,plain,(
% 7.81/7.00 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1|X0=X1)),
% 7.81/7.00 inference(paramodulation,[status(thm)],[f129,f123])).
% 7.81/7.00 fof(f269,plain,(
% 7.81/7.00 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 7.81/7.00 inference(duplicate_literals_removal,[status(thm)],[f268])).
% 7.81/7.01 fof(f274,plain,(
% 7.81/7.01 ![X0]: (singleton(X0)=null_class|regular(singleton(X0))=X0)),
% 7.81/7.01 inference(resolution,[status(thm)],[f188,f269])).
% 7.81/7.01 fof(f277,plain,(
% 7.81/7.01 ![X0]: (~member(X0,universal_class)|member(X0,singleton(X0)))),
% 7.81/7.01 inference(paramodulation,[status(thm)],[f129,f125])).
% 7.81/7.01 fof(f281,plain,(
% 7.81/7.01 ![X0]: (~member(regular(complement(X0)),X0)|complement(X0)=null_class)),
% 7.81/7.01 inference(resolution,[status(thm)],[f146,f188])).
% 7.81/7.01 fof(f322,plain,(
% 7.81/7.01 ordered_pair(first(ordered_pair(universal_class,y)),second(ordered_pair(universal_class,y)))=ordered_pair(universal_class,y)),
% 7.81/7.01 inference(resolution,[status(thm)],[f137,f245])).
% 7.81/7.01 fof(f332,plain,(
% 7.81/7.01 ![X0,X1]: (~member(ordered_pair(universal_class,y),cross_product(X0,X1))|member(second(ordered_pair(universal_class,y)),X1))),
% 7.81/7.01 inference(paramodulation,[status(thm)],[f322,f134])).
% 7.81/7.01 fof(f333,plain,(
% 7.81/7.01 ![X0,X1]: (~member(ordered_pair(universal_class,y),cross_product(X0,X1))|member(first(ordered_pair(universal_class,y)),X0))),
% 7.81/7.01 inference(paramodulation,[status(thm)],[f322,f132])).
% 7.81/7.01 fof(f337,plain,(
% 7.81/7.01 ![X0,X1]: (member(second(ordered_pair(universal_class,y)),X0)|~member(universal_class,X1)|~member(y,X0))),
% 7.81/7.01 inference(resolution,[status(thm)],[f332,f135])).
% 7.81/7.01 fof(f340,plain,(
% 7.81/7.01 ![X0]: (member(second(ordered_pair(universal_class,y)),X0)|~member(y,X0))),
% 7.81/7.01 inference(resolution,[status(thm)],[f337,f253])).
% 7.81/7.01 fof(f346,plain,(
% 7.81/7.01 ![X0]: (member(second(ordered_pair(universal_class,y)),unordered_pair(X0,y))|~member(y,universal_class))),
% 7.81/7.01 inference(resolution,[status(thm)],[f340,f127])).
% 7.81/7.01 fof(f347,plain,(
% 7.81/7.01 ![X0]: (member(second(ordered_pair(universal_class,y)),unordered_pair(y,X0))|~member(y,universal_class))),
% 7.81/7.01 inference(resolution,[status(thm)],[f340,f125])).
% 7.81/7.01 fof(f348,plain,(
% 7.81/7.01 ![X0]: (member(second(ordered_pair(universal_class,y)),unordered_pair(X0,y)))),
% 7.81/7.01 inference(forward_subsumption_resolution,[status(thm)],[f346,f254])).
% 7.81/7.01 fof(f349,plain,(
% 7.81/7.01 ![X0]: (member(second(ordered_pair(universal_class,y)),unordered_pair(y,X0)))),
% 7.81/7.01 inference(forward_subsumption_resolution,[status(thm)],[f347,f254])).
% 2.74/7.04 fof(f351,plain,(
% 2.74/7.04 member(second(ordered_pair(universal_class,y)),singleton(y))),
% 2.74/7.04 inference(paramodulation,[status(thm)],[f129,f348])).
% 2.74/7.04 fof(f352,plain,(
% 2.74/7.04 second(ordered_pair(universal_class,y))=y),
% 2.74/7.04 inference(resolution,[status(thm)],[f351,f269])).
% 2.74/7.04 fof(f361,plain,(
% 2.74/7.04 ![X0]: (member(y,unordered_pair(y,X0)))),
% 2.74/7.04 inference(backward_demodulation,[status(thm)],[f352,f349])).
% 2.74/7.04 fof(f400,plain,(
% 2.74/7.04 ![X0]: (singleton(X0)=null_class|intersection(singleton(X0),X0)=null_class|singleton(X0)=null_class)),
% 2.74/7.04 inference(paramodulation,[status(thm)],[f274,f189])).
% 2.74/7.04 fof(f401,plain,(
% 2.74/7.04 ![X0]: (singleton(X0)=null_class|member(X0,singleton(X0))|singleton(X0)=null_class)),
% 2.74/7.04 inference(paramodulation,[status(thm)],[f274,f188])).
% 2.74/7.04 fof(f402,plain,(
% 2.74/7.04 ![X0]: (singleton(X0)=null_class|intersection(singleton(X0),X0)=null_class)),
% 2.74/7.04 inference(duplicate_literals_removal,[status(thm)],[f400])).
% 2.74/7.04 fof(f403,plain,(
% 2.74/7.04 ![X0]: (singleton(X0)=null_class|member(X0,singleton(X0)))),
% 2.74/7.04 inference(duplicate_literals_removal,[status(thm)],[f401])).
% 2.74/7.04 fof(f434,plain,(
% 2.74/7.04 ![X0,X1]: (member(first(ordered_pair(universal_class,y)),X0)|~member(universal_class,X0)|~member(y,X1))),
% 2.74/7.04 inference(resolution,[status(thm)],[f333,f135])).
% 2.74/7.04 fof(f447,plain,(
% 2.74/7.04 ![X0]: (member(first(ordered_pair(universal_class,y)),singleton(universal_class))|~member(y,X0)|~member(universal_class,universal_class))),
% 2.74/7.04 inference(resolution,[status(thm)],[f434,f277])).
% 2.74/7.04 fof(f452,plain,(
% 2.74/7.04 ![X0]: (member(first(ordered_pair(universal_class,y)),singleton(universal_class))|~member(y,X0))),
% 2.74/7.04 inference(forward_subsumption_resolution,[status(thm)],[f447,f253])).
% 2.74/7.04 fof(f455,plain,(
% 2.74/7.04 ![X0]: (~member(y,X0)|first(ordered_pair(universal_class,y))=universal_class)),
% 2.74/7.04 inference(resolution,[status(thm)],[f452,f269])).
% 2.74/7.04 fof(f457,plain,(
% 2.74/7.04 first(ordered_pair(universal_class,y))=universal_class),
% 2.74/7.04 inference(resolution,[status(thm)],[f455,f361])).
% 2.74/7.04 fof(f469,plain,(
% 2.74/7.04 ![X0]: (member(universal_class,singleton(universal_class))|~member(y,X0))),
% 2.74/7.04 inference(backward_demodulation,[status(thm)],[f457,f452])).
% 2.74/7.04 fof(f982,plain,(
% 2.74/7.04 ![X0]: (complement(universal_class)=null_class|~member(regular(complement(universal_class)),X0))),
% 2.74/7.04 inference(resolution,[status(thm)],[f281,f257])).
% 2.74/7.04 fof(f1027,plain,(
% 2.74/7.04 ![X0,X1]: (~member(X0,singleton(X1))|~member(X0,X1)|member(X0,null_class)|singleton(X1)=null_class)),
% 2.74/7.04 inference(paramodulation,[status(thm)],[f402,f145])).
% 2.74/7.04 fof(f1749,plain,(
% 2.74/7.04 complement(universal_class)=null_class|complement(universal_class)=null_class),
% 2.74/7.04 inference(resolution,[status(thm)],[f982,f188])).
% 2.74/7.04 fof(f1760,plain,(
% 2.74/7.04 complement(universal_class)=null_class),
% 2.74/7.04 inference(duplicate_literals_removal,[status(thm)],[f1749])).
% 2.74/7.04 fof(f1775,plain,(
% 2.74/7.04 ![X0]: (~member(X0,null_class)|~member(X0,universal_class))),
% 2.74/7.04 inference(paramodulation,[status(thm)],[f1760,f146])).
% 2.74/7.04 fof(f1778,plain,(
% 2.74/7.04 ![X0,X1]: (~member(X0,singleton(X1))|~member(X0,X1)|singleton(X1)=null_class)),
% 2.74/7.04 inference(backward_subsumption_resolution,[status(thm)],[f1027,f1780])).
% 2.74/7.04 fof(f1780,plain,(
% 2.74/7.04 ![X0]: (~member(X0,null_class))),
% 2.74/7.04 inference(forward_subsumption_resolution,[status(thm)],[f1775,f257])).
% 2.74/7.04 fof(f2637,plain,(
% 2.74/7.04 ![X0]: (~member(X0,X0)|singleton(X0)=null_class|singleton(X0)=null_class)),
% 2.74/7.04 inference(resolution,[status(thm)],[f1778,f403])).
% 2.74/7.04 fof(f2642,plain,(
% 2.74/7.04 ![X0]: (~member(X0,X0)|singleton(X0)=null_class)),
% 2.74/7.04 inference(duplicate_literals_removal,[status(thm)],[f2637])).
% 2.74/7.04 fof(f2644,plain,(
% 2.74/7.04 singleton(universal_class)=null_class),
% 2.74/7.04 inference(resolution,[status(thm)],[f2642,f253])).
% 2.74/7.04 fof(f2654,plain,(
% 2.74/7.04 ![X0]: (member(universal_class,null_class)|~member(y,X0))),
% 2.74/7.04 inference(backward_demodulation,[status(thm)],[f2644,f469])).
% 2.74/7.04 fof(f2663,plain,(
% 2.74/7.04 ![X0]: (~member(y,X0))),
% 2.74/7.04 inference(forward_subsumption_resolution,[status(thm)],[f2654,f1780])).
% 2.74/7.04 fof(f2664,plain,(
% 2.74/7.04 $false),
% 2.74/7.04 inference(backward_subsumption_resolution,[status(thm)],[f361,f2663])).
% 2.74/7.04 % SZS output end CNFRefutation for theBenchmark.p
% 2.74/7.05 % Elapsed time: 1.139077 seconds
% 2.74/7.05 % CPU time: 8.617300 seconds
% 2.74/7.05 % Total memory used: 195.591 MB
% 2.74/7.05 % Net memory used: 185.170 MB
%------------------------------------------------------------------------------