TSTP Solution File: NUM078-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM078-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:30:17 EDT 2024
% Result : Unsatisfiable 5.24s 1.04s
% Output : CNFRefutation 5.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM078-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 29 20:09:48 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 5.24/1.04 % Refutation found
% 5.24/1.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.24/1.04 % SZS output start CNFRefutation for theBenchmark
% 5.24/1.04 fof(f1,axiom,(
% 5.24/1.04 (![X,Y,U]: (( ~ subclass(X,Y)| ~ member(U,X)| member(U,Y) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f2,axiom,(
% 5.24/1.04 (![X,Y]: (( member(not_subclass_element(X,Y),X)| subclass(X,Y) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f3,axiom,(
% 5.24/1.04 (![X,Y]: (( ~ member(not_subclass_element(X,Y),Y)| subclass(X,Y) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f4,axiom,(
% 5.24/1.04 (![X]: (subclass(X,universal_class) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f5,axiom,(
% 5.24/1.04 (![X,Y]: (( X != Y| subclass(X,Y) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f7,axiom,(
% 5.24/1.04 (![X,Y]: (( ~ subclass(X,Y)| ~ subclass(Y,X)| X = Y ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f8,axiom,(
% 5.24/1.04 (![U,X,Y]: (( ~ member(U,unordered_pair(X,Y))| U = X| U = Y ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f9,axiom,(
% 5.24/1.04 (![X,Y]: (( ~ member(X,universal_class)| member(X,unordered_pair(X,Y)) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f12,axiom,(
% 5.24/1.04 (![X]: (unordered_pair(X,X) = singleton(X) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f21,axiom,(
% 5.24/1.04 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,X) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f22,axiom,(
% 5.24/1.04 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,Y) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f23,axiom,(
% 5.24/1.04 (![Z,X,Y]: (( ~ member(Z,X)| ~ member(Z,Y)| member(Z,intersection(X,Y)) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f24,axiom,(
% 5.24/1.04 (![Z,X]: (( ~ member(Z,complement(X))| ~ member(Z,X) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f28,axiom,(
% 5.24/1.04 (![Xr,X,Y]: (intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f29,axiom,(
% 5.24/1.04 (![X,Y,Xr]: (intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f47,axiom,(
% 5.24/1.04 (![X]: (( ~ inductive(X)| member(null_class,X) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f50,axiom,(
% 5.24/1.04 inductive(omega) ),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f52,axiom,(
% 5.24/1.04 member(omega,universal_class) ),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f66,axiom,(
% 5.24/1.04 (![X]: (( X = null_class| member(regular(X),X) ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f67,axiom,(
% 5.24/1.04 (![X]: (( X = null_class| intersection(X,regular(X)) = null_class ) ))),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f74,axiom,(
% 5.24/1.04 intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation ),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f160,negated_conjecture,(
% 5.24/1.04 member(u,y) ),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f161,negated_conjecture,(
% 5.24/1.04 member(u,intersection(u,y)) ),
% 5.24/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.24/1.04 fof(f162,plain,(
% 5.24/1.04 ![Y,U]: ((![X]: (~subclass(X,Y)|~member(U,X)))|member(U,Y))),
% 5.24/1.04 inference(miniscoping,[status(esa)],[f1])).
% 5.24/1.04 fof(f163,plain,(
% 5.24/1.04 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 5.24/1.04 inference(cnf_transformation,[status(esa)],[f162])).
% 5.24/1.04 fof(f164,plain,(
% 5.24/1.04 ![X0,X1]: (member(not_subclass_element(X0,X1),X0)|subclass(X0,X1))),
% 5.24/1.04 inference(cnf_transformation,[status(esa)],[f2])).
% 5.24/1.04 fof(f165,plain,(
% 5.24/1.04 ![X0,X1]: (~member(not_subclass_element(X0,X1),X1)|subclass(X0,X1))),
% 5.24/1.04 inference(cnf_transformation,[status(esa)],[f3])).
% 5.24/1.04 fof(f166,plain,(
% 5.24/1.04 ![X0]: (subclass(X0,universal_class))),
% 5.24/1.04 inference(cnf_transformation,[status(esa)],[f4])).
% 5.24/1.05 fof(f167,plain,(
% 5.24/1.05 ![X0,X1]: (~X0=X1|subclass(X0,X1))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f5])).
% 5.24/1.05 fof(f169,plain,(
% 5.24/1.05 ![X0,X1]: (~subclass(X0,X1)|~subclass(X1,X0)|X0=X1)),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f7])).
% 5.24/1.05 fof(f170,plain,(
% 5.24/1.05 ![U,Y]: ((![X]: (~member(U,unordered_pair(X,Y))|U=X))|U=Y)),
% 5.24/1.05 inference(miniscoping,[status(esa)],[f8])).
% 5.24/1.05 fof(f171,plain,(
% 5.24/1.05 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f170])).
% 5.24/1.05 fof(f172,plain,(
% 5.24/1.05 ![X]: (~member(X,universal_class)|(![Y]: member(X,unordered_pair(X,Y))))),
% 5.24/1.05 inference(miniscoping,[status(esa)],[f9])).
% 5.24/1.05 fof(f173,plain,(
% 5.24/1.05 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X0,X1)))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f172])).
% 5.24/1.05 fof(f177,plain,(
% 5.24/1.05 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f12])).
% 5.24/1.05 fof(f189,plain,(
% 5.24/1.05 ![Z,X]: ((![Y]: ~member(Z,intersection(X,Y)))|member(Z,X))),
% 5.24/1.05 inference(miniscoping,[status(esa)],[f21])).
% 5.24/1.05 fof(f190,plain,(
% 5.24/1.05 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f189])).
% 5.24/1.05 fof(f191,plain,(
% 5.24/1.05 ![Z,Y]: ((![X]: ~member(Z,intersection(X,Y)))|member(Z,Y))),
% 5.24/1.05 inference(miniscoping,[status(esa)],[f22])).
% 5.24/1.05 fof(f192,plain,(
% 5.24/1.05 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f191])).
% 5.24/1.05 fof(f193,plain,(
% 5.24/1.05 ![X0,X1,X2]: (~member(X0,X1)|~member(X0,X2)|member(X0,intersection(X1,X2)))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f23])).
% 5.24/1.05 fof(f194,plain,(
% 5.24/1.05 ![X0,X1]: (~member(X0,complement(X1))|~member(X0,X1))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f24])).
% 5.24/1.05 fof(f198,plain,(
% 5.24/1.05 ![X0,X1,X2]: (intersection(X0,cross_product(X1,X2))=restrict(X0,X1,X2))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f28])).
% 5.24/1.05 fof(f199,plain,(
% 5.24/1.05 ![X0,X1,X2]: (intersection(cross_product(X0,X1),X2)=restrict(X2,X0,X1))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f29])).
% 5.24/1.05 fof(f217,plain,(
% 5.24/1.05 ![X0]: (~inductive(X0)|member(null_class,X0))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f47])).
% 5.24/1.05 fof(f220,plain,(
% 5.24/1.05 inductive(omega)),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f50])).
% 5.24/1.05 fof(f222,plain,(
% 5.24/1.05 member(omega,universal_class)),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f52])).
% 5.24/1.05 fof(f236,plain,(
% 5.24/1.05 ![X0]: (X0=null_class|member(regular(X0),X0))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f66])).
% 5.24/1.05 fof(f237,plain,(
% 5.24/1.05 ![X0]: (X0=null_class|intersection(X0,regular(X0))=null_class)),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f67])).
% 5.24/1.05 fof(f244,plain,(
% 5.24/1.05 intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))))=subset_relation),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f74])).
% 5.24/1.05 fof(f350,plain,(
% 5.24/1.05 member(u,y)),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f160])).
% 5.24/1.05 fof(f351,plain,(
% 5.24/1.05 member(u,intersection(u,y))),
% 5.24/1.05 inference(cnf_transformation,[status(esa)],[f161])).
% 5.24/1.05 fof(f352,plain,(
% 5.24/1.05 ![X0]: (subclass(X0,X0))),
% 5.24/1.05 inference(destructive_equality_resolution,[status(esa)],[f167])).
% 5.24/1.05 fof(f358,plain,(
% 5.24/1.05 member(u,u)),
% 5.24/1.05 inference(resolution,[status(thm)],[f190,f351])).
% 5.24/1.05 fof(f366,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|member(u,intersection(X0,u)))),
% 5.24/1.05 inference(resolution,[status(thm)],[f193,f358])).
% 5.24/1.05 fof(f368,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|member(u,intersection(X0,y)))),
% 5.24/1.05 inference(resolution,[status(thm)],[f193,f350])).
% 5.24/1.05 fof(f384,plain,(
% 5.24/1.05 member(null_class,omega)),
% 5.24/1.05 inference(resolution,[status(thm)],[f217,f220])).
% 5.24/1.05 fof(f385,plain,(
% 5.24/1.05 ![X0]: (~member(null_class,X0)|member(null_class,intersection(X0,omega)))),
% 5.24/1.05 inference(resolution,[status(thm)],[f384,f193])).
% 5.24/1.05 fof(f388,plain,(
% 5.24/1.05 ![X0,X1]: (~member(X0,X1)|member(X0,universal_class))),
% 5.24/1.05 inference(resolution,[status(thm)],[f163,f166])).
% 5.24/1.05 fof(f391,plain,(
% 5.24/1.05 ![X0,X1,X2]: (subclass(intersection(X0,X1),X2)|member(not_subclass_element(intersection(X0,X1),X2),X1))),
% 5.24/1.05 inference(resolution,[status(thm)],[f164,f192])).
% 5.24/1.05 fof(f392,plain,(
% 5.24/1.05 ![X0,X1,X2]: (subclass(intersection(X0,X1),X2)|member(not_subclass_element(intersection(X0,X1),X2),X0))),
% 5.24/1.05 inference(resolution,[status(thm)],[f164,f190])).
% 5.24/1.05 fof(f396,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|member(u,intersection(intersection(X0,y),u)))),
% 5.24/1.05 inference(resolution,[status(thm)],[f368,f366])).
% 5.24/1.05 fof(f397,plain,(
% 5.24/1.05 spl0_0 <=> ~member(u,X0)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f398,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|~spl0_0)),
% 5.24/1.05 inference(component_clause,[status(thm)],[f397])).
% 5.24/1.05 fof(f400,plain,(
% 5.24/1.05 spl0_1 <=> member(u,y)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f401,plain,(
% 5.24/1.05 member(u,y)|~spl0_1),
% 5.24/1.05 inference(component_clause,[status(thm)],[f400])).
% 5.24/1.05 fof(f403,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|member(u,y))),
% 5.24/1.05 inference(resolution,[status(thm)],[f368,f192])).
% 5.24/1.05 fof(f404,plain,(
% 5.24/1.05 spl0_0|spl0_1),
% 5.24/1.05 inference(split_clause,[status(thm)],[f403,f397,f400])).
% 5.24/1.05 fof(f407,plain,(
% 5.24/1.05 $false|~spl0_0),
% 5.24/1.05 inference(backward_subsumption_resolution,[status(thm)],[f358,f398])).
% 5.24/1.05 fof(f408,plain,(
% 5.24/1.05 ~spl0_0),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f407])).
% 5.24/1.05 fof(f409,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|member(u,intersection(X0,y))|~spl0_1)),
% 5.24/1.05 inference(resolution,[status(thm)],[f401,f193])).
% 5.24/1.05 fof(f641,plain,(
% 5.24/1.05 member(null_class,intersection(omega,omega))),
% 5.24/1.05 inference(resolution,[status(thm)],[f385,f384])).
% 5.24/1.05 fof(f690,plain,(
% 5.24/1.05 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1|X0=X1)),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f177,f171])).
% 5.24/1.05 fof(f691,plain,(
% 5.24/1.05 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 5.24/1.05 inference(duplicate_literals_removal,[status(esa)],[f690])).
% 5.24/1.05 fof(f703,plain,(
% 5.24/1.05 ![X0]: (member(omega,unordered_pair(omega,X0)))),
% 5.24/1.05 inference(resolution,[status(thm)],[f173,f222])).
% 5.24/1.05 fof(f935,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|member(u,intersection(intersection(intersection(X0,y),u),y))|~spl0_1)),
% 5.24/1.05 inference(resolution,[status(thm)],[f396,f409])).
% 5.24/1.05 fof(f973,plain,(
% 5.24/1.05 ![X0,X1]: (subclass(intersection(X0,X1),X1)|subclass(intersection(X0,X1),X1))),
% 5.24/1.05 inference(resolution,[status(thm)],[f391,f165])).
% 5.24/1.05 fof(f974,plain,(
% 5.24/1.05 ![X0,X1]: (subclass(intersection(X0,X1),X1))),
% 5.24/1.05 inference(duplicate_literals_removal,[status(esa)],[f973])).
% 5.24/1.05 fof(f992,plain,(
% 5.24/1.05 ![X0,X1,X2]: (subclass(restrict(X0,X1,X2),cross_product(X1,X2)))),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f198,f974])).
% 5.24/1.05 fof(f997,plain,(
% 5.24/1.05 ![X0,X1]: (subclass(intersection(X0,X1),X0)|subclass(intersection(X0,X1),X0))),
% 5.24/1.05 inference(resolution,[status(thm)],[f392,f165])).
% 5.24/1.05 fof(f998,plain,(
% 5.24/1.05 ![X0,X1]: (subclass(intersection(X0,X1),X0))),
% 5.24/1.05 inference(duplicate_literals_removal,[status(esa)],[f997])).
% 5.24/1.05 fof(f1054,plain,(
% 5.24/1.05 spl0_42 <=> ~member(omega,X0)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f1055,plain,(
% 5.24/1.05 ![X0]: (~member(omega,X0)|~spl0_42)),
% 5.24/1.05 inference(component_clause,[status(thm)],[f1054])).
% 5.24/1.05 fof(f1167,plain,(
% 5.24/1.05 spl0_62 <=> member(omega,universal_class)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f1169,plain,(
% 5.24/1.05 ~member(omega,universal_class)|spl0_62),
% 5.24/1.05 inference(component_clause,[status(thm)],[f1167])).
% 5.24/1.05 fof(f1175,plain,(
% 5.24/1.05 spl0_64 <=> member(u,universal_class)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f1176,plain,(
% 5.24/1.05 member(u,universal_class)|~spl0_64),
% 5.24/1.05 inference(component_clause,[status(thm)],[f1175])).
% 5.24/1.05 fof(f1177,plain,(
% 5.24/1.05 ~member(u,universal_class)|spl0_64),
% 5.24/1.05 inference(component_clause,[status(thm)],[f1175])).
% 5.24/1.05 fof(f1191,plain,(
% 5.24/1.05 $false|spl0_62),
% 5.24/1.05 inference(forward_subsumption_resolution,[status(thm)],[f1169,f222])).
% 5.24/1.05 fof(f1192,plain,(
% 5.24/1.05 spl0_62),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f1191])).
% 5.24/1.05 fof(f1203,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|spl0_64)),
% 5.24/1.05 inference(resolution,[status(thm)],[f1177,f388])).
% 5.24/1.05 fof(f1204,plain,(
% 5.24/1.05 spl0_0|spl0_64),
% 5.24/1.05 inference(split_clause,[status(thm)],[f1203,f397,f1175])).
% 5.24/1.05 fof(f1207,plain,(
% 5.24/1.05 ![X0]: (member(u,unordered_pair(u,X0))|~spl0_64)),
% 5.24/1.05 inference(resolution,[status(thm)],[f1176,f173])).
% 5.24/1.05 fof(f1220,plain,(
% 5.24/1.05 member(u,singleton(u))|~spl0_64),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f177,f1207])).
% 5.24/1.05 fof(f1223,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|member(u,intersection(X0,singleton(u)))|~spl0_64)),
% 5.24/1.05 inference(resolution,[status(thm)],[f1220,f193])).
% 5.24/1.05 fof(f1229,plain,(
% 5.24/1.05 $false|~spl0_42),
% 5.24/1.05 inference(backward_subsumption_resolution,[status(thm)],[f703,f1055])).
% 5.24/1.05 fof(f1230,plain,(
% 5.24/1.05 ~spl0_42),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f1229])).
% 5.24/1.05 fof(f1333,plain,(
% 5.24/1.05 member(null_class,omega)),
% 5.24/1.05 inference(resolution,[status(thm)],[f641,f192])).
% 5.24/1.05 fof(f1635,plain,(
% 5.24/1.05 ![X0]: (singleton(X0)=null_class|regular(singleton(X0))=X0)),
% 5.24/1.05 inference(resolution,[status(thm)],[f236,f691])).
% 5.24/1.05 fof(f2041,plain,(
% 5.24/1.05 spl0_111 <=> subclass(element_relation,element_relation)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f2043,plain,(
% 5.24/1.05 ~subclass(element_relation,element_relation)|spl0_111),
% 5.24/1.05 inference(component_clause,[status(thm)],[f2041])).
% 5.24/1.05 fof(f2046,plain,(
% 5.24/1.05 $false|spl0_111),
% 5.24/1.05 inference(forward_subsumption_resolution,[status(thm)],[f2043,f352])).
% 5.24/1.05 fof(f2047,plain,(
% 5.24/1.05 spl0_111),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f2046])).
% 5.24/1.05 fof(f2472,plain,(
% 5.24/1.05 spl0_132 <=> subclass(omega,omega)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f2474,plain,(
% 5.24/1.05 ~subclass(omega,omega)|spl0_132),
% 5.24/1.05 inference(component_clause,[status(thm)],[f2472])).
% 5.24/1.05 fof(f2477,plain,(
% 5.24/1.05 $false|spl0_132),
% 5.24/1.05 inference(forward_subsumption_resolution,[status(thm)],[f2474,f352])).
% 5.24/1.05 fof(f2478,plain,(
% 5.24/1.05 spl0_132),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f2477])).
% 5.24/1.05 fof(f2678,plain,(
% 5.24/1.05 spl0_143 <=> null_class=null_class),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f2723,plain,(
% 5.24/1.05 spl0_148 <=> subclass(null_class,null_class)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f2725,plain,(
% 5.24/1.05 ~subclass(null_class,null_class)|spl0_148),
% 5.24/1.05 inference(component_clause,[status(thm)],[f2723])).
% 5.24/1.05 fof(f2728,plain,(
% 5.24/1.05 $false|spl0_148),
% 5.24/1.05 inference(forward_subsumption_resolution,[status(thm)],[f2725,f352])).
% 5.24/1.05 fof(f2729,plain,(
% 5.24/1.05 spl0_148),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f2728])).
% 5.24/1.05 fof(f2905,plain,(
% 5.24/1.05 spl0_162 <=> member(null_class,omega)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f2907,plain,(
% 5.24/1.05 ~member(null_class,omega)|spl0_162),
% 5.24/1.05 inference(component_clause,[status(thm)],[f2905])).
% 5.24/1.05 fof(f2915,plain,(
% 5.24/1.05 $false|spl0_162),
% 5.24/1.05 inference(forward_subsumption_resolution,[status(thm)],[f2907,f1333])).
% 5.24/1.05 fof(f2916,plain,(
% 5.24/1.05 spl0_162),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f2915])).
% 5.24/1.05 fof(f2967,plain,(
% 5.24/1.05 ![X0]: (subclass(null_class,X0)|X0=null_class)),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f237,f998])).
% 5.24/1.05 fof(f2969,plain,(
% 5.24/1.05 ![X0]: (X0=null_class|~subclass(X0,null_class)|X0=null_class)),
% 5.24/1.05 inference(resolution,[status(thm)],[f2967,f169])).
% 5.24/1.05 fof(f2970,plain,(
% 5.24/1.05 ![X0]: (X0=null_class|~subclass(X0,null_class))),
% 5.24/1.05 inference(duplicate_literals_removal,[status(esa)],[f2969])).
% 5.24/1.05 fof(f2973,plain,(
% 5.24/1.05 spl0_170 <=> member(u,singleton(u))),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f2976,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|member(u,singleton(u))|~spl0_64)),
% 5.24/1.05 inference(resolution,[status(thm)],[f1223,f192])).
% 5.24/1.05 fof(f2977,plain,(
% 5.24/1.05 spl0_0|spl0_170|~spl0_64),
% 5.24/1.05 inference(split_clause,[status(thm)],[f2976,f397,f2973,f1175])).
% 5.24/1.05 fof(f3107,plain,(
% 5.24/1.05 spl0_178 <=> ~member(null_class,X0)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f3108,plain,(
% 5.24/1.05 ![X0]: (~member(null_class,X0)|~spl0_178)),
% 5.24/1.05 inference(component_clause,[status(thm)],[f3107])).
% 5.24/1.05 fof(f3132,plain,(
% 5.24/1.05 ![X0]: (intersection(null_class,X0)=null_class)),
% 5.24/1.05 inference(resolution,[status(thm)],[f2970,f998])).
% 5.24/1.05 fof(f3133,plain,(
% 5.24/1.05 ![X0]: (intersection(X0,null_class)=null_class)),
% 5.24/1.05 inference(resolution,[status(thm)],[f2970,f974])).
% 5.24/1.05 fof(f3134,plain,(
% 5.24/1.05 null_class=null_class|null_class=null_class),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f237,f3132])).
% 5.24/1.05 fof(f3135,plain,(
% 5.24/1.05 spl0_143),
% 5.24/1.05 inference(split_clause,[status(thm)],[f3134,f2678])).
% 5.24/1.05 fof(f3137,plain,(
% 5.24/1.05 spl0_183 <=> member(u,null_class)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f3172,plain,(
% 5.24/1.05 spl0_189 <=> member(u,intersection(intersection(null_class,u),y))),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f3173,plain,(
% 5.24/1.05 member(u,intersection(intersection(null_class,u),y))|~spl0_189),
% 5.24/1.05 inference(component_clause,[status(thm)],[f3172])).
% 5.24/1.05 fof(f3174,plain,(
% 5.24/1.05 ~member(u,intersection(intersection(null_class,u),y))|spl0_189),
% 5.24/1.05 inference(component_clause,[status(thm)],[f3172])).
% 5.24/1.05 fof(f3175,plain,(
% 5.24/1.05 ~member(u,null_class)|member(u,intersection(intersection(null_class,u),y))|~spl0_1),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f3132,f935])).
% 5.24/1.05 fof(f3176,plain,(
% 5.24/1.05 ~spl0_183|spl0_189|~spl0_1),
% 5.24/1.05 inference(split_clause,[status(thm)],[f3175,f3137,f3172,f400])).
% 5.24/1.05 fof(f3252,plain,(
% 5.24/1.05 member(u,intersection(null_class,y))|~spl0_189),
% 5.24/1.05 inference(forward_demodulation,[status(thm)],[f3132,f3173])).
% 5.24/1.05 fof(f3253,plain,(
% 5.24/1.05 member(u,null_class)|~spl0_189),
% 5.24/1.05 inference(forward_demodulation,[status(thm)],[f3132,f3252])).
% 5.24/1.05 fof(f3257,plain,(
% 5.24/1.05 ![X0,X1]: (~member(X0,null_class)|member(X0,X1))),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f3132,f192])).
% 5.24/1.05 fof(f3277,plain,(
% 5.24/1.05 spl0_194 <=> member(regular(null_class),X0)),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f3278,plain,(
% 5.24/1.05 ![X0]: (member(regular(null_class),X0)|~spl0_194)),
% 5.24/1.05 inference(component_clause,[status(thm)],[f3277])).
% 5.24/1.05 fof(f3322,plain,(
% 5.24/1.05 ![X0]: (member(u,X0)|~spl0_189)),
% 5.24/1.05 inference(resolution,[status(thm)],[f3253,f3257])).
% 5.24/1.05 fof(f3330,plain,(
% 5.24/1.05 ![X0]: (~member(u,X0)|~spl0_189)),
% 5.24/1.05 inference(resolution,[status(thm)],[f3322,f194])).
% 5.24/1.05 fof(f3331,plain,(
% 5.24/1.05 spl0_0|~spl0_189),
% 5.24/1.05 inference(split_clause,[status(thm)],[f3330,f397,f3172])).
% 5.24/1.05 fof(f3336,plain,(
% 5.24/1.05 ~member(u,intersection(null_class,y))|spl0_189),
% 5.24/1.05 inference(forward_demodulation,[status(thm)],[f3132,f3174])).
% 5.24/1.05 fof(f3337,plain,(
% 5.24/1.05 ~member(u,null_class)|spl0_189),
% 5.24/1.05 inference(forward_demodulation,[status(thm)],[f3132,f3336])).
% 5.24/1.05 fof(f3358,plain,(
% 5.24/1.05 $false|~spl0_178),
% 5.24/1.05 inference(backward_subsumption_resolution,[status(thm)],[f641,f3108])).
% 5.24/1.05 fof(f3359,plain,(
% 5.24/1.05 ~spl0_178),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f3358])).
% 5.24/1.05 fof(f3813,plain,(
% 5.24/1.05 restrict(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),universal_class,universal_class)=subset_relation),
% 5.24/1.05 inference(forward_demodulation,[status(thm)],[f199,f244])).
% 5.24/1.05 fof(f3814,plain,(
% 5.24/1.05 restrict(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),universal_class,universal_class)=subset_relation),
% 5.24/1.05 inference(forward_demodulation,[status(thm)],[f199,f3813])).
% 5.24/1.05 fof(f3891,plain,(
% 5.24/1.05 ![X0]: (~member(regular(null_class),X0)|~spl0_194)),
% 5.24/1.05 inference(resolution,[status(thm)],[f3278,f194])).
% 5.24/1.05 fof(f3892,plain,(
% 5.24/1.05 $false|~spl0_194),
% 5.24/1.05 inference(forward_subsumption_resolution,[status(thm)],[f3891,f3278])).
% 5.24/1.05 fof(f3893,plain,(
% 5.24/1.05 ~spl0_194),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f3892])).
% 5.24/1.05 fof(f4060,plain,(
% 5.24/1.05 subclass(subset_relation,cross_product(universal_class,universal_class))),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f3814,f992])).
% 5.24/1.05 fof(f4285,plain,(
% 5.24/1.05 ![X0]: (singleton(X0)=null_class|intersection(singleton(X0),X0)=null_class|singleton(X0)=null_class)),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f1635,f237])).
% 5.24/1.05 fof(f4286,plain,(
% 5.24/1.05 ![X0]: (singleton(X0)=null_class|intersection(singleton(X0),X0)=null_class)),
% 5.24/1.05 inference(duplicate_literals_removal,[status(esa)],[f4285])).
% 5.24/1.05 fof(f4529,plain,(
% 5.24/1.05 spl0_242 <=> subclass(subset_relation,cross_product(universal_class,universal_class))),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f4531,plain,(
% 5.24/1.05 ~subclass(subset_relation,cross_product(universal_class,universal_class))|spl0_242),
% 5.24/1.05 inference(component_clause,[status(thm)],[f4529])).
% 5.24/1.05 fof(f4552,plain,(
% 5.24/1.05 $false|spl0_242),
% 5.24/1.05 inference(forward_subsumption_resolution,[status(thm)],[f4531,f4060])).
% 5.24/1.05 fof(f4553,plain,(
% 5.24/1.05 spl0_242),
% 5.24/1.05 inference(contradiction_clause,[status(thm)],[f4552])).
% 5.24/1.05 fof(f5855,plain,(
% 5.24/1.05 ![X0]: (subclass(null_class,X0))),
% 5.24/1.05 inference(paramodulation,[status(thm)],[f3133,f998])).
% 5.24/1.05 fof(f6228,plain,(
% 5.24/1.05 spl0_340 <=> subclass(null_class,complement(identity_relation))),
% 5.24/1.05 introduced(split_symbol_definition)).
% 5.24/1.05 fof(f6230,plain,(
% 5.24/1.05 ~subclass(null_class,complement(identity_relation))|spl0_340),
% 5.24/1.05 inference(component_clause,[status(thm)],[f6228])).
% 5.24/1.05 fof(f6246,plain,(
% 5.24/1.05 $false|spl0_340),
% 5.24/1.05 inference(forward_subsumption_resolution,[status(thm)],[f6230,f5855])).
% 5.24/1.05 fof(f6247,plain,(
% 5.24/1.05 spl0_340),
% 5.42/1.06 inference(contradiction_clause,[status(thm)],[f6246])).
% 5.42/1.06 fof(f7054,plain,(
% 5.42/1.06 spl0_397 <=> singleton(u)=null_class),
% 5.42/1.06 introduced(split_symbol_definition)).
% 5.42/1.06 fof(f7055,plain,(
% 5.42/1.06 singleton(u)=null_class|~spl0_397),
% 5.42/1.06 inference(component_clause,[status(thm)],[f7054])).
% 5.42/1.06 fof(f7061,plain,(
% 5.42/1.06 ~member(u,singleton(u))|member(u,null_class)|singleton(u)=null_class),
% 5.42/1.06 inference(paramodulation,[status(thm)],[f4286,f366])).
% 5.42/1.06 fof(f7062,plain,(
% 5.42/1.06 ~spl0_170|spl0_183|spl0_397),
% 5.42/1.06 inference(split_clause,[status(thm)],[f7061,f2973,f3137,f7054])).
% 5.42/1.06 fof(f7199,plain,(
% 5.42/1.06 member(u,null_class)|~spl0_397|~spl0_64),
% 5.42/1.06 inference(backward_demodulation,[status(thm)],[f7055,f1220])).
% 5.42/1.06 fof(f7200,plain,(
% 5.42/1.06 $false|spl0_189|~spl0_397|~spl0_64),
% 5.42/1.06 inference(forward_subsumption_resolution,[status(thm)],[f7199,f3337])).
% 5.42/1.06 fof(f7201,plain,(
% 5.42/1.06 spl0_189|~spl0_397|~spl0_64),
% 5.42/1.06 inference(contradiction_clause,[status(thm)],[f7200])).
% 5.42/1.06 fof(f7202,plain,(
% 5.42/1.06 $false),
% 5.42/1.06 inference(sat_refutation,[status(thm)],[f404,f408,f1192,f1204,f1230,f2047,f2478,f2729,f2916,f2977,f3135,f3176,f3331,f3359,f3893,f4553,f6247,f7062,f7201])).
% 5.42/1.06 % SZS output end CNFRefutation for theBenchmark.p
% 5.42/1.08 % Elapsed time: 0.726878 seconds
% 5.42/1.08 % CPU time: 5.518804 seconds
% 5.42/1.08 % Total memory used: 122.180 MB
% 5.42/1.08 % Net memory used: 119.485 MB
%------------------------------------------------------------------------------