%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET222-6 : 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 : n009.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 02:11:48 PM UTC 2026
% Result : Unsatisfiable 112.68s 14.69s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET222-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:02:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 112.68/14.69 % Refutation found
% 112.68/14.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 112.68/14.69 % SZS output start CNFRefutation for theBenchmark
% 112.68/14.69 fof(f1,axiom,(
% 112.68/14.69 (![X,Y,U]: (( ~ subclass(X,Y)| ~ member(U,X)| member(U,Y) ) ))),
% 112.68/14.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.69 fof(f2,axiom,(
% 112.68/14.69 (![X,Y]: (( member(not_subclass_element(X,Y),X)| subclass(X,Y) ) ))),
% 112.68/14.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.69 fof(f3,axiom,(
% 112.68/14.69 (![X,Y]: (( ~ member(not_subclass_element(X,Y),Y)| subclass(X,Y) ) ))),
% 112.68/14.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.69 fof(f14,axiom,(
% 112.68/14.69 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(U,X) ) ))),
% 112.68/14.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.69 fof(f15,axiom,(
% 112.68/14.69 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(V,Y) ) ))),
% 112.68/14.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.69 fof(f16,axiom,(
% 112.68/14.69 (![U,X,V,Y]: (( ~ member(U,X)| ~ member(V,Y)| member(ordered_pair(U,V),cross_product(X,Y)) ) ))),
% 112.68/14.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.70 fof(f17,axiom,(
% 112.68/14.70 (![Z,X,Y]: (( ~ member(Z,cross_product(X,Y))| ordered_pair(first(Z),second(Z)) = Z ) ))),
% 112.68/14.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.70 fof(f18,axiom,(
% 112.68/14.70 subclass(element_relation,cross_product(universal_class,universal_class)) ),
% 112.68/14.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.70 fof(f21,axiom,(
% 112.68/14.70 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,X) ) ))),
% 112.68/14.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.70 fof(f22,axiom,(
% 112.68/14.70 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,Y) ) ))),
% 112.68/14.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.70 fof(f28,axiom,(
% 112.68/14.70 (![Xr,X,Y]: (intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ))),
% 112.68/14.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.70 fof(f29,axiom,(
% 112.68/14.70 (![X,Y,Xr]: (intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ))),
% 112.68/14.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.70 fof(f113,negated_conjecture,(
% 112.68/14.70 ~ subclass(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z)) ),
% 112.68/14.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 112.68/14.70 fof(f114,plain,(
% 112.68/14.70 ![Y,U]: ((![X]: (~subclass(X,Y)|~member(U,X)))|member(U,Y))),
% 112.68/14.70 inference(miniscoping,[status(thm)],[f1])).
% 112.68/14.70 fof(f115,plain,(
% 112.68/14.70 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f114])).
% 112.68/14.70 fof(f116,plain,(
% 112.68/14.70 ![X0,X1]: (member(not_subclass_element(X0,X1),X0)|subclass(X0,X1))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f2])).
% 112.68/14.70 fof(f117,plain,(
% 112.68/14.70 ![X0,X1]: (~member(not_subclass_element(X0,X1),X1)|subclass(X0,X1))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f3])).
% 112.68/14.70 fof(f131,plain,(
% 112.68/14.70 ![U,X]: ((![V,Y]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(U,X))),
% 112.68/14.70 inference(miniscoping,[status(thm)],[f14])).
% 112.68/14.70 fof(f132,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X0,X2))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f131])).
% 112.68/14.70 fof(f133,plain,(
% 112.68/14.70 ![V,Y]: ((![U,X]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(V,Y))),
% 112.68/14.70 inference(miniscoping,[status(thm)],[f15])).
% 112.68/14.70 fof(f134,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X1,X3))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f133])).
% 112.68/14.70 fof(f135,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X2,X3)|member(ordered_pair(X0,X2),cross_product(X1,X3)))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f16])).
% 112.68/14.70 fof(f136,plain,(
% 112.68/14.70 ![Z]: ((![X,Y]: ~member(Z,cross_product(X,Y)))|ordered_pair(first(Z),second(Z))=Z)),
% 112.68/14.70 inference(miniscoping,[status(thm)],[f17])).
% 112.68/14.70 fof(f137,plain,(
% 112.68/14.70 ![X0,X1,X2]: (~member(X0,cross_product(X1,X2))|ordered_pair(first(X0),second(X0))=X0)),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f136])).
% 112.68/14.70 fof(f138,plain,(
% 112.68/14.70 subclass(element_relation,cross_product(universal_class,universal_class))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f18])).
% 112.68/14.70 fof(f141,plain,(
% 112.68/14.70 ![Z,X]: ((![Y]: ~member(Z,intersection(X,Y)))|member(Z,X))),
% 112.68/14.70 inference(miniscoping,[status(thm)],[f21])).
% 112.68/14.70 fof(f142,plain,(
% 112.68/14.70 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f141])).
% 112.68/14.70 fof(f143,plain,(
% 112.68/14.70 ![Z,Y]: ((![X]: ~member(Z,intersection(X,Y)))|member(Z,Y))),
% 112.68/14.70 inference(miniscoping,[status(thm)],[f22])).
% 112.68/14.70 fof(f144,plain,(
% 112.68/14.70 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f143])).
% 112.68/14.70 fof(f150,plain,(
% 112.68/14.70 ![X0,X1,X2]: (intersection(X0,cross_product(X1,X2))=restrict(X0,X1,X2))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f28])).
% 112.68/14.70 fof(f151,plain,(
% 112.68/14.70 ![X0,X1,X2]: (intersection(cross_product(X0,X1),X2)=restrict(X2,X0,X1))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f29])).
% 112.68/14.70 fof(f245,plain,(
% 112.68/14.70 ~subclass(intersection(cross_product(w,x),cross_product(y,z)),cross_product(w,z))),
% 112.68/14.70 inference(cnf_transformation,[status(thm)],[f113])).
% 112.68/14.70 fof(f254,plain,(
% 112.68/14.70 ![X0,X1,X2]: (subclass(intersection(X0,X1),X2)|member(not_subclass_element(intersection(X0,X1),X2),X1))),
% 112.68/14.70 inference(resolution,[status(thm)],[f116,f144])).
% 112.68/14.70 fof(f255,plain,(
% 112.68/14.70 ![X0,X1,X2]: (subclass(intersection(X0,X1),X2)|member(not_subclass_element(intersection(X0,X1),X2),X0))),
% 112.68/14.70 inference(resolution,[status(thm)],[f116,f142])).
% 112.68/14.70 fof(f258,plain,(
% 112.68/14.70 ![X0,X1,X2]: (subclass(X0,X1)|~subclass(X0,X2)|member(not_subclass_element(X0,X1),X2))),
% 112.68/14.70 inference(resolution,[status(thm)],[f116,f115])).
% 112.68/14.70 fof(f264,plain,(
% 112.68/14.70 ~subclass(restrict(cross_product(w,x),y,z),cross_product(w,z))),
% 112.68/14.70 inference(backward_demodulation,[status(thm)],[f150,f245])).
% 112.68/14.70 fof(f269,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (restrict(cross_product(X0,X1),X2,X3)=restrict(cross_product(X2,X3),X0,X1))),
% 112.68/14.70 inference(paramodulation,[status(thm)],[f150,f151])).
% 112.68/14.70 fof(f279,plain,(
% 112.68/14.70 ![X0,X1]: (subclass(intersection(X0,X1),X1)|subclass(intersection(X0,X1),X1))),
% 112.68/14.70 inference(resolution,[status(thm)],[f117,f254])).
% 112.68/14.70 fof(f281,plain,(
% 112.68/14.70 ![X0,X1]: (subclass(intersection(X0,X1),X1))),
% 112.68/14.70 inference(duplicate_literals_removal,[status(thm)],[f279])).
% 112.68/14.70 fof(f285,plain,(
% 112.68/14.70 ![X0,X1,X2]: (subclass(restrict(X0,X1,X2),cross_product(X1,X2)))),
% 112.68/14.70 inference(paramodulation,[status(thm)],[f150,f281])).
% 112.68/14.70 fof(f297,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (subclass(restrict(cross_product(X0,X1),X2,X3),cross_product(X0,X1)))),
% 112.68/14.70 inference(paramodulation,[status(thm)],[f269,f285])).
% 112.68/14.70 fof(f353,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (ordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)))=not_subclass_element(intersection(cross_product(X0,X1),X2),X3)|subclass(intersection(cross_product(X0,X1),X2),X3))),
% 112.68/14.70 inference(resolution,[status(thm)],[f137,f255])).
% 112.68/14.70 fof(f356,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (ordered_pair(first(not_subclass_element(restrict(X0,X1,X2),X3)),second(not_subclass_element(intersection(cross_product(X1,X2),X0),X3)))=not_subclass_element(intersection(cross_product(X1,X2),X0),X3)|subclass(intersection(cross_product(X1,X2),X0),X3))),
% 112.68/14.70 inference(forward_demodulation,[status(thm)],[f151,f353])).
% 112.68/14.70 fof(f357,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (ordered_pair(first(not_subclass_element(restrict(X0,X1,X2),X3)),second(not_subclass_element(restrict(X0,X1,X2),X3)))=not_subclass_element(intersection(cross_product(X1,X2),X0),X3)|subclass(intersection(cross_product(X1,X2),X0),X3))),
% 112.68/14.70 inference(forward_demodulation,[status(thm)],[f151,f356])).
% 112.68/14.70 fof(f358,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (ordered_pair(first(not_subclass_element(restrict(X0,X1,X2),X3)),second(not_subclass_element(restrict(X0,X1,X2),X3)))=not_subclass_element(restrict(X0,X1,X2),X3)|subclass(intersection(cross_product(X1,X2),X0),X3))),
% 112.68/14.70 inference(forward_demodulation,[status(thm)],[f151,f357])).
% 112.68/14.70 fof(f359,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (ordered_pair(first(not_subclass_element(restrict(X0,X1,X2),X3)),second(not_subclass_element(restrict(X0,X1,X2),X3)))=not_subclass_element(restrict(X0,X1,X2),X3)|subclass(restrict(X0,X1,X2),X3))),
% 112.68/14.70 inference(forward_demodulation,[status(thm)],[f151,f358])).
% 112.68/14.70 fof(f407,plain,(
% 112.68/14.70 ![X0]: (subclass(element_relation,X0)|member(not_subclass_element(element_relation,X0),cross_product(universal_class,universal_class)))),
% 112.68/14.70 inference(resolution,[status(thm)],[f258,f138])).
% 112.68/14.70 fof(f408,plain,(
% 112.68/14.70 ![X0,X1,X2,X3,X4]: (subclass(restrict(cross_product(X0,X1),X2,X3),X4)|member(not_subclass_element(restrict(cross_product(X0,X1),X2,X3),X4),cross_product(X0,X1)))),
% 112.68/14.70 inference(resolution,[status(thm)],[f258,f297])).
% 112.68/14.70 fof(f409,plain,(
% 112.68/14.70 ![X0,X1,X2,X3]: (subclass(restrict(X0,X1,X2),X3)|member(not_subclass_element(restrict(X0,X1,X2),X3),cross_product(X1,X2)))),
% 112.68/14.70 inference(resolution,[status(thm)],[f258,f285])).
% 112.68/14.70 fof(f1403,plain,(
% 112.68/14.70 ordered_pair(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))))=not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),
% 112.68/14.70 inference(resolution,[status(thm)],[f359,f264])).
% 112.68/14.70 fof(f1615,plain,(
% 112.68/14.70 ![X0,X1]: (~member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),cross_product(X0,X1))|member(second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),X1))),
% 112.68/14.70 inference(paramodulation,[status(thm)],[f1403,f134])).
% 112.68/14.70 fof(f1616,plain,(
% 112.68/14.70 ![X0,X1]: (~member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),cross_product(X0,X1))|member(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),X0))),
% 112.68/14.70 inference(paramodulation,[status(thm)],[f1403,f132])).
% 112.68/14.70 fof(f1808,plain,(
% 112.68/14.70 subclass(restrict(cross_product(w,x),y,z),cross_product(w,z))|member(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),w)),
% 112.68/14.70 inference(resolution,[status(thm)],[f408,f1616])).
% 112.68/14.70 fof(f1819,definition,(
% 112.68/14.70 sQ57_spl <=> (subclass(restrict(cross_product(w,x),y,z),cross_product(w,z)))),
% 112.68/14.70 introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 112.68/14.70 fof(f1820,plain,(
% 112.68/14.70 subclass(restrict(cross_product(w,x),y,z),cross_product(w,z))|~sQ57_spl),
% 112.68/14.70 inference(component_clause,[status(thm)],[f1819])).
% 112.68/14.70 fof(f1822,definition,(
% 112.68/14.70 sQ58_spl <=> (member(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),w))),
% 112.68/14.70 introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition])).
% 112.68/14.70 fof(f1823,plain,(
% 112.68/14.70 member(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),w)|~sQ58_spl),
% 112.68/14.70 inference(component_clause,[status(thm)],[f1822])).
% 112.68/14.70 fof(f1825,plain,(
% 112.68/14.70 sQ57_spl|sQ58_spl),
% 112.68/14.70 inference(split_clause,[status(thm)],[f1808,f1819,f1822])).
% 112.68/14.70 fof(f1832,plain,(
% 112.68/14.70 $false|~sQ57_spl),
% 112.68/14.70 inference(forward_subsumption_resolution,[status(thm)],[f1820,f264])).
% 112.68/14.70 fof(f1833,plain,(
% 112.68/14.70 ~sQ57_spl),
% 112.68/14.70 inference(contradiction_clause,[status(thm)],[f1832])).
% 112.68/14.70 fof(f1835,plain,(
% 112.68/14.70 subclass(restrict(cross_product(w,x),y,z),cross_product(w,z))|member(second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),z)),
% 112.68/14.70 inference(resolution,[status(thm)],[f409,f1615])).
% 112.68/14.70 fof(f1850,definition,(
% 112.68/14.70 sQ61_spl <=> (member(second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),z))),
% 112.68/14.70 introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition])).
% 112.68/14.70 fof(f1851,plain,(
% 112.68/14.70 member(second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),z)|~sQ61_spl),
% 112.68/14.70 inference(component_clause,[status(thm)],[f1850])).
% 112.68/14.70 fof(f1853,plain,(
% 112.68/14.70 sQ57_spl|sQ61_spl),
% 112.68/14.70 inference(split_clause,[status(thm)],[f1835,f1819,f1850])).
% 112.68/14.70 fof(f2577,plain,(
% 112.68/14.70 ![X0,X1]: (~member(X0,X1)|member(ordered_pair(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),X0),cross_product(w,X1))|~sQ58_spl)),
% 112.68/14.70 inference(resolution,[status(thm)],[f1823,f135])).
% 112.68/14.70 fof(f3264,plain,(
% 112.68/14.70 subclass(element_relation,cross_product(universal_class,universal_class))|subclass(element_relation,cross_product(universal_class,universal_class))),
% 112.68/14.70 inference(resolution,[status(thm)],[f117,f407])).
% 112.68/14.70 fof(f3284,definition,(
% 112.68/14.70 sQ84_spl <=> (subclass(element_relation,cross_product(universal_class,universal_class)))),
% 112.68/14.70 introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition])).
% 112.68/14.70 fof(f3287,plain,(
% 112.68/14.70 sQ84_spl),
% 112.68/14.70 inference(split_clause,[status(thm)],[f3264,f3284])).
% 102.74/14.77 fof(f5516,plain,(
% 102.74/14.77 member(ordered_pair(first(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z))),second(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)))),cross_product(w,z))|~sQ58_spl|~sQ61_spl),
% 102.74/14.77 inference(resolution,[status(thm)],[f2577,f1851])).
% 102.74/14.77 fof(f5577,plain,(
% 102.74/14.77 member(not_subclass_element(restrict(cross_product(w,x),y,z),cross_product(w,z)),cross_product(w,z))|~sQ58_spl|~sQ61_spl),
% 102.74/14.77 inference(forward_demodulation,[status(thm)],[f1403,f5516])).
% 102.74/14.77 fof(f34534,plain,(
% 102.74/14.77 subclass(restrict(cross_product(w,x),y,z),cross_product(w,z))|~sQ58_spl|~sQ61_spl),
% 102.74/14.77 inference(resolution,[status(thm)],[f5577,f117])).
% 102.74/14.77 fof(f34565,plain,(
% 102.74/14.77 sQ57_spl|~sQ58_spl|~sQ61_spl),
% 102.74/14.77 inference(split_clause,[status(thm)],[f34534,f1819,f1822,f1850])).
% 102.74/14.77 fof(f34567,plain,(
% 102.74/14.77 $false),
% 102.74/14.77 inference(sat_refutation,[status(thm)],[f1825,f1833,f1853,f3287,f34565])).
% 102.74/14.77 % SZS output end CNFRefutation for theBenchmark.p
% 21.54/14.84 % Elapsed time: 14.470500 seconds
% 21.54/14.84 % CPU time: 114.370082 seconds
% 21.54/14.84 % Total memory used: 918.634 MB
% 21.54/14.84 % Net memory used: 817.433 MB
%------------------------------------------------------------------------------