TSTP Solution File: SET504-6 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET504-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 20:39:46 EDT 2024
% Result : Unsatisfiable 19.92s 2.90s
% Output : CNFRefutation 20.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET504-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n024.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Apr 29 21:37:51 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % Drodi V3.6.0
% 19.92/2.90 % Refutation found
% 19.92/2.90 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 19.92/2.90 % SZS output start CNFRefutation for theBenchmark
% 19.92/2.90 fof(f1,axiom,(
% 19.92/2.90 (![X,Y,U]: (( ~ subclass(X,Y)| ~ member(U,X)| member(U,Y) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f2,axiom,(
% 19.92/2.90 (![X,Y]: (( member(not_subclass_element(X,Y),X)| subclass(X,Y) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f3,axiom,(
% 19.92/2.90 (![X,Y]: (( ~ member(not_subclass_element(X,Y),Y)| subclass(X,Y) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f4,axiom,(
% 19.92/2.90 (![X]: (subclass(X,universal_class) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f5,axiom,(
% 19.92/2.90 (![X,Y]: (( X != Y| subclass(X,Y) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f7,axiom,(
% 19.92/2.90 (![X,Y]: (( ~ subclass(X,Y)| ~ subclass(Y,X)| X = Y ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f8,axiom,(
% 19.92/2.90 (![U,X,Y]: (( ~ member(U,unordered_pair(X,Y))| U = X| U = Y ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f9,axiom,(
% 19.92/2.90 (![X,Y]: (( ~ member(X,universal_class)| member(X,unordered_pair(X,Y)) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f10,axiom,(
% 19.92/2.90 (![Y,X]: (( ~ member(Y,universal_class)| member(Y,unordered_pair(X,Y)) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f11,axiom,(
% 19.92/2.90 (![X,Y]: (member(unordered_pair(X,Y),universal_class) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f12,axiom,(
% 19.92/2.90 (![X]: (unordered_pair(X,X) = singleton(X) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f13,axiom,(
% 19.92/2.90 (![X,Y]: (unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f14,axiom,(
% 19.92/2.90 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(U,X) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f15,axiom,(
% 19.92/2.90 (![U,V,X,Y]: (( ~ member(ordered_pair(U,V),cross_product(X,Y))| member(V,Y) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f16,axiom,(
% 19.92/2.90 (![U,X,V,Y]: (( ~ member(U,X)| ~ member(V,Y)| member(ordered_pair(U,V),cross_product(X,Y)) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f17,axiom,(
% 19.92/2.90 (![Z,X,Y]: (( ~ member(Z,cross_product(X,Y))| ordered_pair(first(Z),second(Z)) = Z ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f19,axiom,(
% 19.92/2.90 (![X,Y]: (( ~ member(ordered_pair(X,Y),element_relation)| member(X,Y) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f20,axiom,(
% 19.92/2.90 (![X,Y]: (( ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))| ~ member(X,Y)| member(ordered_pair(X,Y),element_relation) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f21,axiom,(
% 19.92/2.90 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,X) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f22,axiom,(
% 19.92/2.90 (![Z,X,Y]: (( ~ member(Z,intersection(X,Y))| member(Z,Y) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f23,axiom,(
% 19.92/2.90 (![Z,X,Y]: (( ~ member(Z,X)| ~ member(Z,Y)| member(Z,intersection(X,Y)) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f24,axiom,(
% 19.92/2.90 (![Z,X]: (( ~ member(Z,complement(X))| ~ member(Z,X) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f25,axiom,(
% 19.92/2.90 (![Z,X]: (( ~ member(Z,universal_class)| member(Z,complement(X))| member(Z,X) ) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f26,axiom,(
% 19.92/2.90 (![X,Y]: (complement(intersection(complement(X),complement(Y))) = union(X,Y) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f27,axiom,(
% 19.92/2.90 (![X,Y]: (intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y)))) = symmetric_difference(X,Y) ))),
% 19.92/2.90 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.90 fof(f30,axiom,(
% 19.92/2.90 (![X,Z]: (( restrict(X,singleton(Z),universal_class) != null_class| ~ member(Z,domain_of(X)) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f31,axiom,(
% 19.92/2.92 (![Z,X]: (( ~ member(Z,universal_class)| restrict(X,singleton(Z),universal_class) = null_class| member(Z,domain_of(X)) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f33,axiom,(
% 19.92/2.92 (![U,V,W,X]: (( ~ member(ordered_pair(ordered_pair(U,V),W),rotate(X))| member(ordered_pair(ordered_pair(V,W),U),X) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f36,axiom,(
% 19.92/2.92 (![U,V,W,X]: (( ~ member(ordered_pair(ordered_pair(U,V),W),flip(X))| member(ordered_pair(ordered_pair(V,U),W),X) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f45,axiom,(
% 19.92/2.92 (![X,Y]: (( ~ member(ordered_pair(X,Y),successor_relation)| successor(X) = Y ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f47,axiom,(
% 19.92/2.92 (![X]: (( ~ inductive(X)| member(null_class,X) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f48,axiom,(
% 19.92/2.92 (![X]: (( ~ inductive(X)| subclass(image(successor_relation,X),X) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f49,axiom,(
% 19.92/2.92 (![X]: (( ~ member(null_class,X)| ~ subclass(image(successor_relation,X),X)| inductive(X) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f50,axiom,(
% 19.92/2.92 inductive(omega) ),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f51,axiom,(
% 19.92/2.92 (![Y]: (( ~ inductive(Y)| subclass(omega,Y) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f52,axiom,(
% 19.92/2.92 member(omega,universal_class) ),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f58,axiom,(
% 19.92/2.92 (![Y,Z,Yr,Xr]: (( ~ member(ordered_pair(Y,Z),compose(Yr,Xr))| member(Z,image(Yr,image(Xr,singleton(Y)))) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f59,axiom,(
% 19.92/2.92 (![Z,Yr,Xr,Y]: (( ~ member(Z,image(Yr,image(Xr,singleton(Y))))| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))| member(ordered_pair(Y,Z),compose(Yr,Xr)) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f66,axiom,(
% 19.92/2.92 (![X]: (( X = null_class| member(regular(X),X) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f67,axiom,(
% 19.92/2.92 (![X]: (( X = null_class| intersection(X,regular(X)) = null_class ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f70,axiom,(
% 19.92/2.92 (![Y]: (( ~ member(Y,universal_class)| Y = null_class| member(apply(choice,Y),Y) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f75,axiom,(
% 19.92/2.92 intersection(inverse(subset_relation),subset_relation) = identity_relation ),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f93,axiom,(
% 19.92/2.92 (![Y,Z,X]: (( ~ member(ordered_pair(Y,Z),compose_class(X))| compose(X,Y) = Z ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f96,axiom,(
% 19.92/2.92 (![X,Y,Z]: (( ~ member(ordered_pair(X,ordered_pair(Y,Z)),composition_function)| compose(X,Y) = Z ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f99,axiom,(
% 19.92/2.92 (![X,Y]: (( ~ member(ordered_pair(X,Y),domain_relation)| domain_of(X) = Y ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f104,axiom,(
% 19.92/2.92 intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f106,axiom,(
% 19.92/2.92 (![X,Y,Z]: (( ~ member(ordered_pair(X,ordered_pair(Y,Z)),application_function)| member(Y,domain_of(X)) ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f107,axiom,(
% 19.92/2.92 (![X,Y,Z]: (( ~ member(ordered_pair(X,ordered_pair(Y,Z)),application_function)| apply(X,Y) = Z ) ))),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f113,negated_conjecture,(
% 19.92/2.92 member(ordered_pair(x,universal_class),cross_product(universal_class,universal_class)) ),
% 19.92/2.92 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 19.92/2.92 fof(f114,plain,(
% 19.92/2.92 ![Y,U]: ((![X]: (~subclass(X,Y)|~member(U,X)))|member(U,Y))),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f1])).
% 19.92/2.92 fof(f115,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~subclass(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f114])).
% 19.92/2.92 fof(f116,plain,(
% 19.92/2.92 ![X0,X1]: (member(not_subclass_element(X0,X1),X0)|subclass(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f2])).
% 19.92/2.92 fof(f117,plain,(
% 19.92/2.92 ![X0,X1]: (~member(not_subclass_element(X0,X1),X1)|subclass(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f3])).
% 19.92/2.92 fof(f118,plain,(
% 19.92/2.92 ![X0]: (subclass(X0,universal_class))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f4])).
% 19.92/2.92 fof(f119,plain,(
% 19.92/2.92 ![X0,X1]: (~X0=X1|subclass(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f5])).
% 19.92/2.92 fof(f121,plain,(
% 19.92/2.92 ![X0,X1]: (~subclass(X0,X1)|~subclass(X1,X0)|X0=X1)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f7])).
% 19.92/2.92 fof(f122,plain,(
% 19.92/2.92 ![U,Y]: ((![X]: (~member(U,unordered_pair(X,Y))|U=X))|U=Y)),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f8])).
% 19.92/2.92 fof(f123,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f122])).
% 19.92/2.92 fof(f124,plain,(
% 19.92/2.92 ![X]: (~member(X,universal_class)|(![Y]: member(X,unordered_pair(X,Y))))),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f9])).
% 19.92/2.92 fof(f125,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X0,X1)))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f124])).
% 19.92/2.92 fof(f126,plain,(
% 19.92/2.92 ![Y]: (~member(Y,universal_class)|(![X]: member(Y,unordered_pair(X,Y))))),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f10])).
% 19.92/2.92 fof(f127,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,universal_class)|member(X0,unordered_pair(X1,X0)))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f126])).
% 19.92/2.92 fof(f128,plain,(
% 19.92/2.92 ![X0,X1]: (member(unordered_pair(X0,X1),universal_class))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f11])).
% 19.92/2.92 fof(f129,plain,(
% 19.92/2.92 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f12])).
% 19.92/2.92 fof(f130,plain,(
% 19.92/2.92 ![X0,X1]: (unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1)))=ordered_pair(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f13])).
% 19.92/2.92 fof(f131,plain,(
% 19.92/2.92 ![U,X]: ((![V,Y]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(U,X))),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f14])).
% 19.92/2.92 fof(f132,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X0,X2))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f131])).
% 19.92/2.92 fof(f133,plain,(
% 19.92/2.92 ![V,Y]: ((![U,X]: ~member(ordered_pair(U,V),cross_product(X,Y)))|member(V,Y))),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f15])).
% 19.92/2.92 fof(f134,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(X2,X3))|member(X1,X3))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f133])).
% 19.92/2.92 fof(f135,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X2,X3)|member(ordered_pair(X0,X2),cross_product(X1,X3)))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f16])).
% 19.92/2.92 fof(f136,plain,(
% 19.92/2.92 ![Z]: ((![X,Y]: ~member(Z,cross_product(X,Y)))|ordered_pair(first(Z),second(Z))=Z)),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f17])).
% 19.92/2.92 fof(f137,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,cross_product(X1,X2))|ordered_pair(first(X0),second(X0))=X0)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f136])).
% 19.92/2.92 fof(f139,plain,(
% 19.92/2.92 ![X0,X1]: (~member(ordered_pair(X0,X1),element_relation)|member(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f19])).
% 19.92/2.92 fof(f140,plain,(
% 19.92/2.92 ![X0,X1]: (~member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))|~member(X0,X1)|member(ordered_pair(X0,X1),element_relation))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f20])).
% 19.92/2.92 fof(f141,plain,(
% 19.92/2.92 ![Z,X]: ((![Y]: ~member(Z,intersection(X,Y)))|member(Z,X))),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f21])).
% 19.92/2.92 fof(f142,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f141])).
% 19.92/2.92 fof(f143,plain,(
% 19.92/2.92 ![Z,Y]: ((![X]: ~member(Z,intersection(X,Y)))|member(Z,Y))),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f22])).
% 19.92/2.92 fof(f144,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f143])).
% 19.92/2.92 fof(f145,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,X1)|~member(X0,X2)|member(X0,intersection(X1,X2)))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f23])).
% 19.92/2.92 fof(f146,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,complement(X1))|~member(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f24])).
% 19.92/2.92 fof(f147,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,universal_class)|member(X0,complement(X1))|member(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f25])).
% 19.92/2.92 fof(f148,plain,(
% 19.92/2.92 ![X0,X1]: (complement(intersection(complement(X0),complement(X1)))=union(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f26])).
% 19.92/2.92 fof(f149,plain,(
% 19.92/2.92 ![X0,X1]: (intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1))))=symmetric_difference(X0,X1))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f27])).
% 19.92/2.92 fof(f152,plain,(
% 19.92/2.92 ![X0,X1]: (~restrict(X0,singleton(X1),universal_class)=null_class|~member(X1,domain_of(X0)))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f30])).
% 19.92/2.92 fof(f153,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,universal_class)|restrict(X1,singleton(X0),universal_class)=null_class|member(X0,domain_of(X1)))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f31])).
% 19.92/2.92 fof(f155,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(ordered_pair(ordered_pair(X0,X1),X2),rotate(X3))|member(ordered_pair(ordered_pair(X1,X2),X0),X3))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f33])).
% 19.92/2.92 fof(f158,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))|member(ordered_pair(ordered_pair(X1,X0),X2),X3))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f36])).
% 19.92/2.92 fof(f167,plain,(
% 19.92/2.92 ![X0,X1]: (~member(ordered_pair(X0,X1),successor_relation)|successor(X0)=X1)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f45])).
% 19.92/2.92 fof(f169,plain,(
% 19.92/2.92 ![X0]: (~inductive(X0)|member(null_class,X0))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f47])).
% 19.92/2.92 fof(f170,plain,(
% 19.92/2.92 ![X0]: (~inductive(X0)|subclass(image(successor_relation,X0),X0))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f48])).
% 19.92/2.92 fof(f171,plain,(
% 19.92/2.92 ![X0]: (~member(null_class,X0)|~subclass(image(successor_relation,X0),X0)|inductive(X0))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f49])).
% 19.92/2.92 fof(f172,plain,(
% 19.92/2.92 inductive(omega)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f50])).
% 19.92/2.92 fof(f173,plain,(
% 19.92/2.92 ![X0]: (~inductive(X0)|subclass(omega,X0))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f51])).
% 19.92/2.92 fof(f174,plain,(
% 19.92/2.92 member(omega,universal_class)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f52])).
% 19.92/2.92 fof(f180,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),compose(X2,X3))|member(X1,image(X2,image(X3,singleton(X0)))))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f58])).
% 19.92/2.92 fof(f181,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,image(X1,image(X2,singleton(X3))))|~member(ordered_pair(X3,X0),cross_product(universal_class,universal_class))|member(ordered_pair(X3,X0),compose(X1,X2)))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f59])).
% 19.92/2.92 fof(f188,plain,(
% 19.92/2.92 ![X0]: (X0=null_class|member(regular(X0),X0))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f66])).
% 19.92/2.92 fof(f189,plain,(
% 19.92/2.92 ![X0]: (X0=null_class|intersection(X0,regular(X0))=null_class)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f67])).
% 19.92/2.92 fof(f192,plain,(
% 19.92/2.92 ![X0]: (~member(X0,universal_class)|X0=null_class|member(apply(choice,X0),X0))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f70])).
% 19.92/2.92 fof(f197,plain,(
% 19.92/2.92 intersection(inverse(subset_relation),subset_relation)=identity_relation),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f75])).
% 19.92/2.92 fof(f220,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(ordered_pair(X0,X1),compose_class(X2))|compose(X2,X0)=X1)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f93])).
% 19.92/2.92 fof(f223,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(ordered_pair(X0,ordered_pair(X1,X2)),composition_function)|compose(X0,X1)=X2)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f96])).
% 19.92/2.92 fof(f226,plain,(
% 19.92/2.92 ![X0,X1]: (~member(ordered_pair(X0,X1),domain_relation)|domain_of(X0)=X1)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f99])).
% 19.92/2.92 fof(f231,plain,(
% 19.92/2.92 intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)=singleton_relation),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f104])).
% 19.92/2.92 fof(f233,plain,(
% 19.92/2.92 ![X,Y]: ((![Z]: ~member(ordered_pair(X,ordered_pair(Y,Z)),application_function))|member(Y,domain_of(X)))),
% 19.92/2.92 inference(miniscoping,[status(esa)],[f106])).
% 19.92/2.92 fof(f234,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(ordered_pair(X0,ordered_pair(X1,X2)),application_function)|member(X1,domain_of(X0)))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f233])).
% 19.92/2.92 fof(f235,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(ordered_pair(X0,ordered_pair(X1,X2)),application_function)|apply(X0,X1)=X2)),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f107])).
% 19.92/2.92 fof(f245,plain,(
% 19.92/2.92 member(ordered_pair(x,universal_class),cross_product(universal_class,universal_class))),
% 19.92/2.92 inference(cnf_transformation,[status(esa)],[f113])).
% 19.92/2.92 fof(f246,plain,(
% 19.92/2.92 ![X0]: (subclass(X0,X0))),
% 19.92/2.92 inference(destructive_equality_resolution,[status(esa)],[f119])).
% 19.92/2.92 fof(f250,plain,(
% 19.92/2.92 ![X0]: (member(singleton(X0),universal_class))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f129,f128])).
% 19.92/2.92 fof(f251,plain,(
% 19.92/2.92 ![X0]: (~subclass(X0,omega)|X0=omega|~inductive(X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f121,f173])).
% 19.92/2.92 fof(f252,plain,(
% 19.92/2.92 ![X0]: (~subclass(universal_class,X0)|universal_class=X0)),
% 19.92/2.92 inference(resolution,[status(thm)],[f121,f118])).
% 19.92/2.92 fof(f254,plain,(
% 19.92/2.92 ![X0]: (universal_class=X0|~member(not_subclass_element(universal_class,X0),X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f252,f117])).
% 19.92/2.92 fof(f264,plain,(
% 19.92/2.92 ![X0]: (~member(null_class,X0)|~inductive(complement(X0)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f146,f169])).
% 19.92/2.92 fof(f266,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,X1)|~subclass(X2,complement(X1))|~member(X0,X2))),
% 19.92/2.92 inference(resolution,[status(thm)],[f146,f115])).
% 19.92/2.92 fof(f267,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(ordered_pair(X2,X0),cross_product(X3,complement(X1))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f146,f134])).
% 19.92/2.92 fof(f268,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(ordered_pair(X0,X2),cross_product(complement(X1),X3)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f146,f132])).
% 19.92/2.92 fof(f273,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|X0=X2|~member(ordered_pair(X3,X0),cross_product(X4,unordered_pair(X1,X2))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f123,f134])).
% 19.92/2.92 fof(f274,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|X0=X2|~member(ordered_pair(X0,X3),cross_product(unordered_pair(X1,X2),X4)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f123,f132])).
% 19.92/2.92 fof(f277,plain,(
% 19.92/2.92 ![X0]: (~member(X0,universal_class)|member(X0,singleton(X0)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f129,f125])).
% 19.92/2.92 fof(f283,plain,(
% 19.92/2.92 spl0_2 <=> ~member(X0,X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f284,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,X1)|~spl0_2)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f283])).
% 19.92/2.92 fof(f310,plain,(
% 19.92/2.92 $false|~spl0_2),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f250,f284])).
% 19.92/2.92 fof(f311,plain,(
% 19.92/2.92 ~spl0_2),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f310])).
% 19.92/2.92 fof(f324,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (X0=X1|X0=X1|~member(ordered_pair(X2,X0),cross_product(X3,singleton(X1))))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f129,f273])).
% 19.92/2.92 fof(f325,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (X0=X1|~member(ordered_pair(X2,X0),cross_product(X3,singleton(X1))))),
% 19.92/2.92 inference(duplicate_literals_removal,[status(esa)],[f324])).
% 19.92/2.92 fof(f326,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (X0=X1|X0=X1|~member(ordered_pair(X0,X2),cross_product(singleton(X1),X3)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f129,f274])).
% 19.92/2.92 fof(f327,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (X0=X1|~member(ordered_pair(X0,X2),cross_product(singleton(X1),X3)))),
% 19.92/2.92 inference(duplicate_literals_removal,[status(esa)],[f326])).
% 19.92/2.92 fof(f343,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,X1)|member(ordered_pair(X0,omega),cross_product(X1,universal_class)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f174,f135])).
% 19.92/2.92 fof(f356,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,X1)|member(ordered_pair(X0,singleton(X2)),cross_product(X1,universal_class)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f250,f135])).
% 19.92/2.92 fof(f370,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=singleton(X1)|X0=unordered_pair(X1,singleton(X2))|~member(ordered_pair(X0,X3),cross_product(ordered_pair(X1,X2),X4)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f130,f274])).
% 19.92/2.92 fof(f371,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=singleton(X1)|X0=unordered_pair(X1,singleton(X2))|~member(ordered_pair(X3,X0),cross_product(X4,ordered_pair(X1,X2))))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f130,f273])).
% 19.92/2.92 fof(f372,plain,(
% 19.92/2.92 member(null_class,omega)),
% 19.92/2.92 inference(resolution,[status(thm)],[f169,f172])).
% 19.92/2.92 fof(f440,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,X1)|member(ordered_pair(X0,unordered_pair(X2,X3)),cross_product(X1,universal_class)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f128,f135])).
% 19.92/2.92 fof(f455,plain,(
% 19.92/2.92 ![X0,X1,X2]: (X0=null_class|~member(X1,X2)|member(ordered_pair(X1,regular(X0)),cross_product(X2,X0)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f188,f135])).
% 19.92/2.92 fof(f496,plain,(
% 19.92/2.92 subclass(image(successor_relation,omega),omega)),
% 19.92/2.92 inference(resolution,[status(thm)],[f170,f172])).
% 19.92/2.92 fof(f560,plain,(
% 19.92/2.92 spl0_14 <=> member(null_class,universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f561,plain,(
% 19.92/2.92 member(null_class,universal_class)|~spl0_14),
% 19.92/2.92 inference(component_clause,[status(thm)],[f560])).
% 19.92/2.92 fof(f562,plain,(
% 19.92/2.92 ~member(null_class,universal_class)|spl0_14),
% 19.92/2.92 inference(component_clause,[status(thm)],[f560])).
% 19.92/2.92 fof(f579,plain,(
% 19.92/2.92 spl0_17 <=> null_class=null_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f617,plain,(
% 19.92/2.92 spl0_18 <=> member(x,universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f619,plain,(
% 19.92/2.92 ~member(x,universal_class)|spl0_18),
% 19.92/2.92 inference(component_clause,[status(thm)],[f617])).
% 19.92/2.92 fof(f620,plain,(
% 19.92/2.92 spl0_19 <=> member(ordered_pair(x,universal_class),element_relation)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f623,plain,(
% 19.92/2.92 ~member(x,universal_class)|member(ordered_pair(x,universal_class),element_relation)),
% 19.92/2.92 inference(resolution,[status(thm)],[f245,f140])).
% 19.92/2.92 fof(f624,plain,(
% 19.92/2.92 ~spl0_18|spl0_19),
% 19.92/2.92 inference(split_clause,[status(thm)],[f623,f617,f620])).
% 19.92/2.92 fof(f625,plain,(
% 19.92/2.92 member(x,universal_class)),
% 19.92/2.92 inference(resolution,[status(thm)],[f245,f132])).
% 19.92/2.92 fof(f626,plain,(
% 19.92/2.92 member(universal_class,universal_class)),
% 19.92/2.92 inference(resolution,[status(thm)],[f245,f134])).
% 19.92/2.92 fof(f627,plain,(
% 19.92/2.92 ordered_pair(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class)))=ordered_pair(x,universal_class)),
% 19.92/2.92 inference(resolution,[status(thm)],[f245,f137])).
% 19.92/2.92 fof(f631,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,X1)|member(ordered_pair(X0,ordered_pair(x,universal_class)),cross_product(X1,cross_product(universal_class,universal_class))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f245,f135])).
% 19.92/2.92 fof(f634,plain,(
% 19.92/2.92 member(ordered_pair(x,omega),cross_product(universal_class,universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f625,f343])).
% 19.92/2.92 fof(f639,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,X1)|member(ordered_pair(X0,universal_class),cross_product(X1,universal_class)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f626,f135])).
% 19.92/2.92 fof(f662,plain,(
% 19.92/2.92 spl0_22 <=> member(ordered_pair(x,universal_class),cross_product(universal_class,universal_class))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f664,plain,(
% 19.92/2.92 ~member(ordered_pair(x,universal_class),cross_product(universal_class,universal_class))|spl0_22),
% 19.92/2.92 inference(component_clause,[status(thm)],[f662])).
% 19.92/2.92 fof(f665,plain,(
% 19.92/2.92 spl0_23 <=> member(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class)))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f666,plain,(
% 19.92/2.92 member(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class)))|~spl0_23),
% 19.92/2.92 inference(component_clause,[status(thm)],[f665])).
% 19.92/2.92 fof(f668,plain,(
% 19.92/2.92 spl0_24 <=> member(ordered_pair(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class))),element_relation)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f671,plain,(
% 19.92/2.92 ~member(ordered_pair(x,universal_class),cross_product(universal_class,universal_class))|~member(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class)))|member(ordered_pair(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class))),element_relation)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f140])).
% 19.92/2.92 fof(f672,plain,(
% 19.92/2.92 ~spl0_22|~spl0_23|spl0_24),
% 19.92/2.92 inference(split_clause,[status(thm)],[f671,f662,f665,f668])).
% 19.92/2.92 fof(f673,plain,(
% 19.92/2.92 ~member(ordered_pair(x,universal_class),element_relation)|member(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f139])).
% 19.92/2.92 fof(f674,plain,(
% 19.92/2.92 ~spl0_19|spl0_23),
% 19.92/2.92 inference(split_clause,[status(thm)],[f673,f620,f665])).
% 19.92/2.92 fof(f681,plain,(
% 19.92/2.92 ![X0,X1,X2]: (first(ordered_pair(x,universal_class))=X0|first(ordered_pair(x,universal_class))=X1|~member(ordered_pair(x,universal_class),cross_product(unordered_pair(X0,X1),X2)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f274])).
% 19.92/2.92 fof(f683,plain,(
% 19.92/2.92 ![X0,X1,X2]: (second(ordered_pair(x,universal_class))=X0|second(ordered_pair(x,universal_class))=X1|~member(ordered_pair(x,universal_class),cross_product(X2,unordered_pair(X0,X1))))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f273])).
% 19.92/2.92 fof(f684,plain,(
% 19.92/2.92 ![X0,X1]: (~member(first(ordered_pair(x,universal_class)),X0)|~member(ordered_pair(x,universal_class),cross_product(complement(X0),X1)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f268])).
% 19.92/2.92 fof(f686,plain,(
% 19.92/2.92 ![X0,X1]: (~member(ordered_pair(x,universal_class),cross_product(X0,X1))|member(first(ordered_pair(x,universal_class)),X0))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f132])).
% 19.92/2.92 fof(f687,plain,(
% 19.92/2.92 ![X0,X1]: (~member(ordered_pair(x,universal_class),cross_product(X0,X1))|member(second(ordered_pair(x,universal_class)),X1))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f134])).
% 19.92/2.92 fof(f688,plain,(
% 19.92/2.92 $false|spl0_22),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f664,f245])).
% 19.92/2.92 fof(f689,plain,(
% 19.92/2.92 spl0_22),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f688])).
% 19.92/2.92 fof(f791,plain,(
% 19.92/2.92 spl0_29 <=> member(unordered_pair(X2,X3),universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f794,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,X1)|member(unordered_pair(X2,X3),universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f440,f134])).
% 19.92/2.92 fof(f795,plain,(
% 19.92/2.92 spl0_2|spl0_29),
% 19.92/2.92 inference(split_clause,[status(thm)],[f794,f283,f791])).
% 19.92/2.92 fof(f803,plain,(
% 19.92/2.92 spl0_30 <=> X0=null_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f804,plain,(
% 19.92/2.92 ![X0]: (X0=null_class|~spl0_30)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f803])).
% 19.92/2.92 fof(f813,plain,(
% 19.92/2.92 spl0_32 <=> universal_class=null_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f814,plain,(
% 19.92/2.92 universal_class=null_class|~spl0_32),
% 19.92/2.92 inference(component_clause,[status(thm)],[f813])).
% 19.92/2.92 fof(f815,plain,(
% 19.92/2.92 ~universal_class=null_class|spl0_32),
% 19.92/2.92 inference(component_clause,[status(thm)],[f813])).
% 19.92/2.92 fof(f821,plain,(
% 19.92/2.92 spl0_34 <=> ~member(X1,ordered_pair(X2,X3))|X1=singleton(X2)|X1=unordered_pair(X2,singleton(X3))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f824,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (X0=null_class|~member(X1,ordered_pair(X2,X3))|X1=singleton(X2)|X1=unordered_pair(X2,singleton(X3)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f370])).
% 19.92/2.92 fof(f825,plain,(
% 19.92/2.92 spl0_30|spl0_34),
% 19.92/2.92 inference(split_clause,[status(thm)],[f824,f803,f821])).
% 19.92/2.92 fof(f826,plain,(
% 19.92/2.92 spl0_35 <=> ~member(X1,singleton(X2))|X1=X2),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f831,plain,(
% 19.92/2.92 spl0_36 <=> ~member(X1,unordered_pair(X2,X3))|X1=X2|X1=X3),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f836,plain,(
% 19.92/2.92 spl0_37 <=> ~member(X1,complement(X2))|~member(X1,X2)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f841,plain,(
% 19.92/2.92 spl0_38 <=> ordered_pair(X0,X1)=null_class|regular(ordered_pair(X0,X1))=singleton(X0)|regular(ordered_pair(X0,X1))=unordered_pair(X0,singleton(X1))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f844,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (ordered_pair(X0,X1)=null_class|~member(X2,X3)|regular(ordered_pair(X0,X1))=singleton(X0)|regular(ordered_pair(X0,X1))=unordered_pair(X0,singleton(X1)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f371])).
% 19.92/2.92 fof(f845,plain,(
% 19.92/2.92 spl0_38|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f844,f841,f283])).
% 19.92/2.92 fof(f846,plain,(
% 19.92/2.92 spl0_39 <=> singleton(X0)=null_class|regular(singleton(X0))=X0),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f849,plain,(
% 19.92/2.92 ![X0,X1,X2]: (singleton(X0)=null_class|~member(X1,X2)|regular(singleton(X0))=X0)),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f325])).
% 19.92/2.92 fof(f850,plain,(
% 19.92/2.92 spl0_39|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f849,f846,f283])).
% 19.92/2.92 fof(f851,plain,(
% 19.92/2.92 spl0_40 <=> unordered_pair(X0,X1)=null_class|regular(unordered_pair(X0,X1))=X0|regular(unordered_pair(X0,X1))=X1),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f854,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (unordered_pair(X0,X1)=null_class|~member(X2,X3)|regular(unordered_pair(X0,X1))=X0|regular(unordered_pair(X0,X1))=X1)),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f273])).
% 19.92/2.92 fof(f855,plain,(
% 19.92/2.92 spl0_40|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f854,f851,f283])).
% 19.92/2.92 fof(f856,plain,(
% 19.92/2.92 spl0_41 <=> complement(X0)=null_class|~member(regular(complement(X0)),X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f859,plain,(
% 19.92/2.92 ![X0,X1,X2]: (complement(X0)=null_class|~member(X1,X2)|~member(regular(complement(X0)),X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f267])).
% 19.92/2.92 fof(f860,plain,(
% 19.92/2.92 spl0_41|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f859,f856,f283])).
% 19.92/2.92 fof(f861,plain,(
% 19.92/2.92 spl0_42 <=> ~member(X1,X2)|member(X1,X2)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f864,plain,(
% 19.92/2.92 ![X0,X1,X2]: (X0=null_class|~member(X1,X2)|member(X1,X2))),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f132])).
% 19.92/2.92 fof(f865,plain,(
% 19.92/2.92 spl0_30|spl0_42),
% 19.92/2.92 inference(split_clause,[status(thm)],[f864,f803,f861])).
% 19.92/2.92 fof(f866,plain,(
% 19.92/2.92 spl0_43 <=> X0=null_class|member(regular(X0),X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f869,plain,(
% 19.92/2.92 ![X0,X1,X2]: (X0=null_class|~member(X1,X2)|member(regular(X0),X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f134])).
% 19.92/2.92 fof(f870,plain,(
% 19.92/2.92 spl0_43|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f869,f866,f283])).
% 19.92/2.92 fof(f891,plain,(
% 19.92/2.92 spl0_46 <=> subclass(omega,omega)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f893,plain,(
% 19.92/2.92 ~subclass(omega,omega)|spl0_46),
% 19.92/2.92 inference(component_clause,[status(thm)],[f891])).
% 19.92/2.92 fof(f894,plain,(
% 19.92/2.92 spl0_47 <=> omega=omega),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f897,plain,(
% 19.92/2.92 ~subclass(omega,omega)|omega=omega),
% 19.92/2.92 inference(resolution,[status(thm)],[f251,f172])).
% 19.92/2.92 fof(f898,plain,(
% 19.92/2.92 ~spl0_46|spl0_47),
% 19.92/2.92 inference(split_clause,[status(thm)],[f897,f891,f894])).
% 19.92/2.92 fof(f899,plain,(
% 19.92/2.92 $false|spl0_46),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f893,f246])).
% 19.92/2.92 fof(f900,plain,(
% 19.92/2.92 spl0_46),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f899])).
% 19.92/2.92 fof(f919,plain,(
% 19.92/2.92 ![X0]: (member(not_subclass_element(universal_class,X0),universal_class)|universal_class=X0)),
% 19.92/2.92 inference(resolution,[status(thm)],[f116,f252])).
% 19.92/2.92 fof(f978,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (~member(X0,X1)|~member(X0,X2)|~member(X3,X4)|member(ordered_pair(X3,X0),cross_product(X4,intersection(X1,X2))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f145,f135])).
% 19.92/2.92 fof(f986,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,universal_class)|member(X0,X1)|~member(X2,X3)|member(ordered_pair(X2,X0),cross_product(X3,complement(X1))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f147,f135])).
% 19.92/2.92 fof(f994,plain,(
% 19.92/2.92 $false|spl0_18),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f619,f625])).
% 19.92/2.92 fof(f995,plain,(
% 19.92/2.92 spl0_18),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f994])).
% 19.92/2.92 fof(f1016,plain,(
% 19.92/2.92 ![X0,X1]: (X0=X1|~spl0_30)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f804,f804])).
% 19.92/2.92 fof(f1022,plain,(
% 19.92/2.92 ![X0]: (member(X0,universal_class)|~spl0_14|~spl0_30)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f804,f561])).
% 19.92/2.92 fof(f1039,plain,(
% 19.92/2.92 ![X0,X1]: (member(X0,X1)|~spl0_14|~spl0_30)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f1016,f1022])).
% 19.92/2.92 fof(f1044,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(ordered_pair(X0,X1),cross_product(complement(X2),X3))|~spl0_14|~spl0_30)),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f268,f1039])).
% 19.92/2.92 fof(f1045,plain,(
% 19.92/2.92 $false|~spl0_14|~spl0_30),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f1044,f1039])).
% 19.92/2.92 fof(f1046,plain,(
% 19.92/2.92 ~spl0_14|~spl0_30),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f1045])).
% 19.92/2.92 fof(f1058,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 19.92/2.92 inference(resolution,[status(thm)],[f440,f274])).
% 19.92/2.92 fof(f1079,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,singleton(X1))|~member(X2,X3)|X0=X1)),
% 19.92/2.92 inference(resolution,[status(thm)],[f135,f327])).
% 19.92/2.92 fof(f1080,plain,(
% 19.92/2.92 spl0_35|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1079,f826,f283])).
% 19.92/2.92 fof(f1138,plain,(
% 19.92/2.92 spl0_62 <=> complement(universal_class)=null_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1139,plain,(
% 19.92/2.92 complement(universal_class)=null_class|~spl0_62),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1138])).
% 19.92/2.92 fof(f1171,plain,(
% 19.92/2.92 ![X0,X1]: (~member(first(ordered_pair(x,universal_class)),X0)|~member(second(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X0,X1)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f135])).
% 19.92/2.92 fof(f1191,plain,(
% 19.92/2.92 spl0_66 <=> ~member(X0,X1)|~member(X0,X2)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1192,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,X1)|~member(X0,X2)|~spl0_66)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1191])).
% 19.92/2.92 fof(f1196,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(second(ordered_pair(x,universal_class)),X0)|~member(second(ordered_pair(x,universal_class)),X1)|~member(first(ordered_pair(x,universal_class)),X2)|member(ordered_pair(x,universal_class),cross_product(X2,intersection(X0,X1))))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f978])).
% 19.92/2.92 fof(f1205,plain,(
% 19.92/2.92 spl0_68 <=> member(second(ordered_pair(x,universal_class)),universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1206,plain,(
% 19.92/2.92 member(second(ordered_pair(x,universal_class)),universal_class)|~spl0_68),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1205])).
% 19.92/2.92 fof(f1207,plain,(
% 19.92/2.92 ~member(second(ordered_pair(x,universal_class)),universal_class)|spl0_68),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1205])).
% 19.92/2.92 fof(f1208,plain,(
% 19.92/2.92 spl0_69 <=> member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,complement(X0)))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1209,plain,(
% 19.92/2.92 ![X0,X1]: (member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,complement(X0)))|~spl0_69)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1208])).
% 19.92/2.92 fof(f1211,plain,(
% 19.92/2.92 ![X0,X1]: (~member(second(ordered_pair(x,universal_class)),universal_class)|member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,complement(X0))))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f986])).
% 19.92/2.92 fof(f1212,plain,(
% 19.92/2.92 ~spl0_68|spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1211,f1205,f1208])).
% 19.92/2.92 fof(f1254,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,intersection(X1,unordered_pair(X2,X3)))|X0=X2|X0=X3)),
% 19.92/2.92 inference(resolution,[status(thm)],[f144,f1058])).
% 19.92/2.92 fof(f1261,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,intersection(complement(X1),X2))|~member(X0,X1))),
% 19.92/2.92 inference(resolution,[status(thm)],[f142,f146])).
% 19.92/2.92 fof(f1263,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,intersection(unordered_pair(X1,X2),X3))|X0=X1|X0=X2)),
% 19.92/2.92 inference(resolution,[status(thm)],[f142,f1058])).
% 19.92/2.92 fof(f1265,plain,(
% 19.92/2.92 ![X0]: (~member(not_subclass_element(universal_class,X0),X0)|universal_class=X0)),
% 19.92/2.92 inference(resolution,[status(thm)],[f117,f252])).
% 19.92/2.92 fof(f1269,plain,(
% 19.92/2.92 spl0_74 <=> universal_class=universal_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1297,plain,(
% 19.92/2.92 ![X0,X1,X2]: (universal_class=X0|~member(ordered_pair(X1,not_subclass_element(universal_class,X0)),cross_product(X2,X0)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f254,f134])).
% 19.92/2.92 fof(f1310,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~restrict(X0,singleton(X1),universal_class)=null_class|~member(ordered_pair(X2,X1),cross_product(X3,domain_of(X0))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f152,f134])).
% 19.92/2.92 fof(f1341,plain,(
% 19.92/2.92 ![X0]: (~member(X0,universal_class)|~spl0_66)),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f277,f1192])).
% 19.92/2.92 fof(f1390,plain,(
% 19.92/2.92 $false|~spl0_66),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f128,f1341])).
% 19.92/2.92 fof(f1391,plain,(
% 19.92/2.92 ~spl0_66),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f1390])).
% 19.92/2.92 fof(f1440,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,intersection(singleton(X1),X2))|X0=X1|X0=X1)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f129,f1263])).
% 19.92/2.92 fof(f1441,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,intersection(singleton(X1),X2))|X0=X1)),
% 19.92/2.92 inference(duplicate_literals_removal,[status(esa)],[f1440])).
% 19.92/2.92 fof(f1442,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,intersection(X1,singleton(X2)))|X0=X2|X0=X2)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f129,f1254])).
% 19.92/2.92 fof(f1443,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,intersection(X1,singleton(X2)))|X0=X2)),
% 19.92/2.92 inference(duplicate_literals_removal,[status(esa)],[f1442])).
% 19.92/2.92 fof(f1464,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4,X5]: (member(ordered_pair(ordered_pair(X0,X1),X2),X3)|~member(ordered_pair(ordered_pair(ordered_pair(X2,X0),X1),X4),cross_product(rotate(X3),X5)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f155,f132])).
% 19.92/2.92 fof(f1538,plain,(
% 19.92/2.92 ![X0,X1]: (~member(first(ordered_pair(x,universal_class)),X0)|~member(second(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X0,X1)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f135])).
% 19.92/2.92 fof(f1539,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|~member(ordered_pair(X0,X2),cross_product(intersection(singleton(X1),X3),X4)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1441,f132])).
% 19.92/2.92 fof(f1540,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|~member(ordered_pair(X2,X0),cross_product(X3,intersection(singleton(X1),X4))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1441,f134])).
% 19.92/2.92 fof(f1541,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|~member(ordered_pair(X0,X2),cross_product(intersection(X3,singleton(X1)),X4)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1443,f132])).
% 19.92/2.92 fof(f1542,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|~member(ordered_pair(X2,X0),cross_product(X3,intersection(X4,singleton(X1)))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1443,f134])).
% 19.92/2.92 fof(f1572,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X0,complement(X1))|~member(X2,X3))),
% 19.92/2.92 inference(resolution,[status(thm)],[f268,f135])).
% 19.92/2.92 fof(f1573,plain,(
% 19.92/2.92 spl0_37|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1572,f836,f283])).
% 19.92/2.92 fof(f1596,plain,(
% 19.92/2.92 ![X0]: (~member(universal_class,X0)|~inductive(complement(X0))|~spl0_32)),
% 19.92/2.92 inference(forward_demodulation,[status(thm)],[f814,f264])).
% 19.92/2.92 fof(f1608,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4,X5]: (member(ordered_pair(ordered_pair(X0,X1),X2),X3)|~member(ordered_pair(ordered_pair(ordered_pair(X1,X0),X2),X4),cross_product(flip(X3),X5)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f158,f132])).
% 19.92/2.92 fof(f1635,plain,(
% 19.92/2.92 spl0_83 <=> complement(universal_class)=universal_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1636,plain,(
% 19.92/2.92 complement(universal_class)=universal_class|~spl0_83),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1635])).
% 19.92/2.92 fof(f1640,plain,(
% 19.92/2.92 spl0_84 <=> member(universal_class,universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1642,plain,(
% 19.92/2.92 ~member(universal_class,universal_class)|spl0_84),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1640])).
% 19.92/2.92 fof(f1643,plain,(
% 19.92/2.92 spl0_85 <=> inductive(universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1660,plain,(
% 19.92/2.92 ~member(universal_class,universal_class)|~inductive(universal_class)|~spl0_32|~spl0_83),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f1636,f1596])).
% 19.92/2.92 fof(f1661,plain,(
% 19.92/2.92 ~spl0_84|~spl0_85|~spl0_32|~spl0_83),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1660,f1640,f1643,f813,f1635])).
% 19.92/2.92 fof(f1701,plain,(
% 19.92/2.92 $false|spl0_84),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f626,f1642])).
% 19.92/2.92 fof(f1702,plain,(
% 19.92/2.92 spl0_84),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f1701])).
% 19.92/2.92 fof(f1716,plain,(
% 19.92/2.92 spl0_86 <=> first(ordered_pair(x,universal_class))=X0|first(ordered_pair(x,universal_class))=X1|~member(x,unordered_pair(X0,X1))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1719,plain,(
% 19.92/2.92 spl0_87 <=> ~member(universal_class,X2)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1720,plain,(
% 19.92/2.92 ![X0]: (~member(universal_class,X0)|~spl0_87)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1719])).
% 19.92/2.92 fof(f1722,plain,(
% 19.92/2.92 ![X0,X1,X2]: (first(ordered_pair(x,universal_class))=X0|first(ordered_pair(x,universal_class))=X1|~member(x,unordered_pair(X0,X1))|~member(universal_class,X2))),
% 19.92/2.92 inference(resolution,[status(thm)],[f681,f135])).
% 19.92/2.92 fof(f1723,plain,(
% 19.92/2.92 spl0_86|spl0_87),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1722,f1716,f1719])).
% 19.92/2.92 fof(f1740,plain,(
% 19.92/2.92 ![X0,X1]: (~member(second(ordered_pair(x,universal_class)),X0)|~member(ordered_pair(x,universal_class),cross_product(X1,complement(X0))))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f267])).
% 19.92/2.92 fof(f1745,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|X0=X2|~member(X0,unordered_pair(X1,X2))|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f274,f135])).
% 19.92/2.92 fof(f1746,plain,(
% 19.92/2.92 spl0_36|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1745,f831,f283])).
% 19.92/2.92 fof(f1784,plain,(
% 19.92/2.92 $false|~spl0_87),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f626,f1720])).
% 19.92/2.92 fof(f1785,plain,(
% 19.92/2.92 ~spl0_87),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f1784])).
% 19.92/2.92 fof(f1830,plain,(
% 19.92/2.92 spl0_88 <=> member(first(ordered_pair(x,universal_class)),universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1832,plain,(
% 19.92/2.92 ~member(first(ordered_pair(x,universal_class)),universal_class)|spl0_88),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1830])).
% 19.92/2.92 fof(f1857,plain,(
% 19.92/2.92 spl0_89 <=> second(ordered_pair(x,universal_class))=X0|second(ordered_pair(x,universal_class))=X1|~member(universal_class,unordered_pair(X0,X1))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1860,plain,(
% 19.92/2.92 spl0_90 <=> ~member(x,X2)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1861,plain,(
% 19.92/2.92 ![X0]: (~member(x,X0)|~spl0_90)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1860])).
% 19.92/2.92 fof(f1863,plain,(
% 19.92/2.92 ![X0,X1,X2]: (second(ordered_pair(x,universal_class))=X0|second(ordered_pair(x,universal_class))=X1|~member(x,X2)|~member(universal_class,unordered_pair(X0,X1)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f683,f135])).
% 19.92/2.92 fof(f1864,plain,(
% 19.92/2.92 spl0_89|spl0_90),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1863,f1857,f1860])).
% 19.92/2.92 fof(f1901,plain,(
% 19.92/2.92 spl0_92 <=> ~restrict(X0,singleton(regular(domain_of(X0))),universal_class)=null_class|domain_of(X0)=null_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1904,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~restrict(X0,singleton(regular(domain_of(X0))),universal_class)=null_class|domain_of(X0)=null_class|~member(X1,X2))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1310,f455])).
% 19.92/2.92 fof(f1905,plain,(
% 19.92/2.92 spl0_92|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1904,f1901,f283])).
% 19.92/2.92 fof(f1906,plain,(
% 19.92/2.92 spl0_93 <=> ~restrict(X0,singleton(X1),universal_class)=null_class|~member(X1,domain_of(X0))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1909,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~restrict(X0,singleton(X1),universal_class)=null_class|~member(X2,X3)|~member(X1,domain_of(X0)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1310,f135])).
% 19.92/2.92 fof(f1910,plain,(
% 19.92/2.92 spl0_93|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1909,f1906,f283])).
% 19.92/2.92 fof(f1946,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (member(X0,X1)|~member(ordered_pair(X0,X2),cross_product(intersection(X1,X3),X4)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f142,f132])).
% 19.92/2.92 fof(f1947,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (member(X0,X1)|~member(ordered_pair(X2,X0),cross_product(X3,intersection(X1,X4))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f142,f134])).
% 19.92/2.92 fof(f1952,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (member(X0,X1)|~member(ordered_pair(X0,X2),cross_product(intersection(X3,X1),X4)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f144,f132])).
% 19.92/2.92 fof(f1953,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (member(X0,X1)|~member(ordered_pair(X2,X0),cross_product(X3,intersection(X4,X1))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f144,f134])).
% 19.92/2.92 fof(f1964,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (subclass(X0,X1)|~member(ordered_pair(not_subclass_element(X0,X1),X2),cross_product(X1,X3)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f117,f132])).
% 19.92/2.92 fof(f1965,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (subclass(X0,X1)|~member(ordered_pair(X2,not_subclass_element(X0,X1)),cross_product(X3,X1)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f117,f134])).
% 19.92/2.92 fof(f1966,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (successor(X0)=X1|~member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(successor_relation,X3)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f167,f132])).
% 19.92/2.92 fof(f1978,plain,(
% 19.92/2.92 ~member(null_class,universal_class)|inductive(universal_class)),
% 19.92/2.92 inference(resolution,[status(thm)],[f171,f118])).
% 19.92/2.92 fof(f1979,plain,(
% 19.92/2.92 ~spl0_14|spl0_85),
% 19.92/2.92 inference(split_clause,[status(thm)],[f1978,f560,f1643])).
% 19.92/2.92 fof(f1981,plain,(
% 19.92/2.92 spl0_98 <=> member(null_class,omega)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1983,plain,(
% 19.92/2.92 ~member(null_class,omega)|spl0_98),
% 19.92/2.92 inference(component_clause,[status(thm)],[f1981])).
% 19.92/2.92 fof(f1984,plain,(
% 19.92/2.92 spl0_99 <=> inductive(omega)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f1989,plain,(
% 19.92/2.92 $false|spl0_98),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f1983,f372])).
% 19.92/2.92 fof(f1990,plain,(
% 19.92/2.92 spl0_98),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f1989])).
% 19.92/2.92 fof(f2030,plain,(
% 19.92/2.92 $false|~spl0_90),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f625,f1861])).
% 19.92/2.92 fof(f2031,plain,(
% 19.92/2.92 ~spl0_90),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f2030])).
% 19.92/2.92 fof(f2033,plain,(
% 19.92/2.92 spl0_100 <=> member(second(ordered_pair(x,universal_class)),X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2034,plain,(
% 19.92/2.92 ![X0]: (member(second(ordered_pair(x,universal_class)),X0)|~spl0_100)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f2033])).
% 19.92/2.92 fof(f2036,plain,(
% 19.92/2.92 spl0_101 <=> ~member(first(ordered_pair(x,universal_class)),unordered_pair(X1,X2))|first(ordered_pair(x,universal_class))=X1|first(ordered_pair(x,universal_class))=X2),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2039,plain,(
% 19.92/2.92 ![X0,X1,X2]: (member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),unordered_pair(X1,X2))|first(ordered_pair(x,universal_class))=X1|first(ordered_pair(x,universal_class))=X2|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f681])).
% 19.92/2.92 fof(f2040,plain,(
% 19.92/2.92 spl0_100|spl0_101|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2039,f2033,f2036,f1208])).
% 19.92/2.92 fof(f2041,plain,(
% 19.92/2.92 spl0_102 <=> ~member(first(ordered_pair(x,universal_class)),unordered_pair(X1,X2))|x=X1|x=X2),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2044,plain,(
% 19.92/2.92 ![X0,X1,X2]: (member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),unordered_pair(X1,X2))|x=X1|x=X2|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f274])).
% 19.92/2.92 fof(f2045,plain,(
% 19.92/2.92 spl0_100|spl0_102|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2044,f2033,f2041,f1208])).
% 19.92/2.92 fof(f2046,plain,(
% 19.92/2.92 spl0_103 <=> ~member(first(ordered_pair(x,universal_class)),complement(X1))|~member(x,X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2049,plain,(
% 19.92/2.92 ![X0,X1]: (member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),complement(X1))|~member(x,X1)|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f268])).
% 19.92/2.92 fof(f2050,plain,(
% 19.92/2.92 spl0_100|spl0_103|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2049,f2033,f2046,f1208])).
% 19.92/2.92 fof(f2051,plain,(
% 19.92/2.92 spl0_104 <=> ~member(first(ordered_pair(x,universal_class)),singleton(X1))|x=X1),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2054,plain,(
% 19.92/2.92 ![X0,X1]: (member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),singleton(X1))|x=X1|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f327])).
% 19.92/2.92 fof(f2055,plain,(
% 19.92/2.92 spl0_100|spl0_104|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2054,f2033,f2051,f1208])).
% 19.92/2.92 fof(f2056,plain,(
% 19.92/2.92 spl0_105 <=> member(second(ordered_pair(x,universal_class)),X0)|~member(universal_class,X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2059,plain,(
% 19.92/2.92 spl0_106 <=> ~member(first(ordered_pair(x,universal_class)),X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2060,plain,(
% 19.92/2.92 ![X0]: (~member(first(ordered_pair(x,universal_class)),X0)|~spl0_106)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f2059])).
% 19.92/2.92 fof(f2062,plain,(
% 19.92/2.92 ![X0,X1]: (member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|~member(universal_class,X0)|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f267])).
% 19.92/2.92 fof(f2063,plain,(
% 19.92/2.92 spl0_105|spl0_106|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2062,f2056,f2059,f1208])).
% 19.92/2.92 fof(f2154,plain,(
% 19.92/2.92 spl0_108 <=> ~member(first(ordered_pair(x,universal_class)),X0)|~member(x,complement(X0))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2157,plain,(
% 19.92/2.92 ![X0,X1]: (~member(first(ordered_pair(x,universal_class)),X0)|~member(x,complement(X0))|~member(universal_class,X1))),
% 19.92/2.92 inference(resolution,[status(thm)],[f684,f135])).
% 19.92/2.92 fof(f2158,plain,(
% 19.92/2.92 spl0_108|spl0_87),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2157,f2154,f1719])).
% 19.92/2.92 fof(f2285,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (domain_of(X0)=X1|~member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(domain_relation,X3)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f226,f132])).
% 19.92/2.92 fof(f2302,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4,X5]: (member(X0,image(X1,image(X2,singleton(X3))))|~member(ordered_pair(X4,ordered_pair(X3,X0)),cross_product(X5,compose(X1,X2))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f180,f134])).
% 19.92/2.92 fof(f2306,plain,(
% 19.92/2.92 spl0_117 <=> ~member(second(ordered_pair(x,universal_class)),image(X0,image(X1,singleton(first(ordered_pair(x,universal_class))))))|member(ordered_pair(x,universal_class),compose(X0,X1))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2307,plain,(
% 19.92/2.92 ![X0,X1]: (~member(second(ordered_pair(x,universal_class)),image(X0,image(X1,singleton(first(ordered_pair(x,universal_class))))))|member(ordered_pair(x,universal_class),compose(X0,X1))|~spl0_117)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f2306])).
% 19.92/2.92 fof(f2316,plain,(
% 19.92/2.92 ![X0,X1]: (X0=X1|~member(X0,singleton(X1)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f327,f639])).
% 19.92/2.92 fof(f2416,plain,(
% 19.92/2.92 spl0_120 <=> member(universal_class,X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2417,plain,(
% 19.92/2.92 ![X0]: (member(universal_class,X0)|~spl0_120)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f2416])).
% 19.92/2.92 fof(f2423,plain,(
% 19.92/2.92 spl0_121 <=> ~member(X0,universal_class)|member(X0,X1)|~member(X0,X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2426,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,universal_class)|member(X0,X1)|~member(X2,X3)|~member(X0,X1))),
% 19.92/2.92 inference(resolution,[status(thm)],[f986,f267])).
% 19.92/2.92 fof(f2427,plain,(
% 19.92/2.92 spl0_121|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2426,f2423,f283])).
% 19.92/2.92 fof(f2432,plain,(
% 19.92/2.92 spl0_122 <=> member(ordered_pair(ordered_pair(X0,X1),X2),X3)|~member(ordered_pair(ordered_pair(X2,X0),X1),rotate(X3))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2439,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4,X5]: (member(ordered_pair(ordered_pair(X0,X1),X2),X3)|~member(ordered_pair(ordered_pair(X2,X0),X1),rotate(X3))|~member(X4,X5))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1464,f135])).
% 19.92/2.92 fof(f2440,plain,(
% 19.92/2.92 spl0_122|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2439,f2432,f283])).
% 19.92/2.92 fof(f2480,plain,(
% 19.92/2.92 ![X0]: (~member(universal_class,X0)|~spl0_120)),
% 19.92/2.92 inference(resolution,[status(thm)],[f2417,f146])).
% 19.92/2.92 fof(f2481,plain,(
% 19.92/2.92 spl0_87|~spl0_120),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2480,f1719,f2416])).
% 19.92/2.92 fof(f2504,plain,(
% 19.92/2.92 ![X0]: (~member(second(ordered_pair(x,universal_class)),X0)|~spl0_100)),
% 19.92/2.92 inference(resolution,[status(thm)],[f2034,f146])).
% 19.92/2.92 fof(f2505,plain,(
% 19.92/2.92 $false|~spl0_100),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f2504,f2034])).
% 19.92/2.92 fof(f2506,plain,(
% 19.92/2.92 ~spl0_100),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f2505])).
% 19.92/2.92 fof(f2584,plain,(
% 19.92/2.92 spl0_127 <=> member(ordered_pair(ordered_pair(X0,X1),X2),X3)|~member(ordered_pair(ordered_pair(X1,X0),X2),flip(X3))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2591,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4,X5]: (member(ordered_pair(ordered_pair(X0,X1),X2),X3)|~member(ordered_pair(ordered_pair(X1,X0),X2),flip(X3))|~member(X4,X5))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1608,f135])).
% 19.92/2.92 fof(f2592,plain,(
% 19.92/2.92 spl0_127|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2591,f2584,f283])).
% 19.92/2.92 fof(f2659,plain,(
% 19.92/2.92 $false|~spl0_106|~spl0_23),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f666,f2060])).
% 19.92/2.92 fof(f2660,plain,(
% 19.92/2.92 ~spl0_106|~spl0_23),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f2659])).
% 19.92/2.92 fof(f2788,plain,(
% 19.92/2.92 spl0_133 <=> member(X0,X1)|~member(X0,intersection(X1,X4))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2795,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (member(X0,X1)|~member(X0,intersection(X1,X2))|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1946,f135])).
% 19.92/2.92 fof(f2796,plain,(
% 19.92/2.92 spl0_133|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2795,f2788,f283])).
% 19.92/2.92 fof(f2827,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,X1)|member(X0,universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f115,f118])).
% 19.92/2.92 fof(f2828,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,X1)|member(X0,X2)|member(not_subclass_element(X1,X2),X1))),
% 19.92/2.92 inference(resolution,[status(thm)],[f115,f116])).
% 19.92/2.92 fof(f2830,plain,(
% 19.92/2.92 ![X0]: (~member(first(ordered_pair(x,universal_class)),X0)|spl0_88)),
% 19.92/2.92 inference(resolution,[status(thm)],[f2827,f1832])).
% 19.92/2.92 fof(f2831,plain,(
% 19.92/2.92 spl0_106|spl0_88),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2830,f2059,f1830])).
% 19.92/2.92 fof(f2832,plain,(
% 19.92/2.92 ![X0]: (~member(second(ordered_pair(x,universal_class)),X0)|spl0_68)),
% 19.92/2.92 inference(resolution,[status(thm)],[f2827,f1207])).
% 19.92/2.92 fof(f2833,plain,(
% 19.92/2.92 ![X0]: (~member(null_class,X0)|spl0_14)),
% 19.92/2.92 inference(resolution,[status(thm)],[f2827,f562])).
% 19.92/2.92 fof(f2861,plain,(
% 19.92/2.92 universal_class=universal_class|universal_class=universal_class),
% 19.92/2.92 inference(resolution,[status(thm)],[f919,f1265])).
% 19.92/2.92 fof(f2862,plain,(
% 19.92/2.92 spl0_74),
% 19.92/2.92 inference(split_clause,[status(thm)],[f2861,f1269])).
% 19.92/2.92 fof(f2870,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (member(X0,X1)|~member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(element_relation,X3)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f139,f132])).
% 19.92/2.92 fof(f2899,plain,(
% 19.92/2.92 $false|spl0_14),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f372,f2833])).
% 19.92/2.92 fof(f2900,plain,(
% 19.92/2.92 spl0_14),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f2899])).
% 19.92/2.92 fof(f2960,plain,(
% 19.92/2.92 spl0_141 <=> ~member(regular(complement(universal_class)),X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f2961,plain,(
% 19.92/2.92 ![X0]: (~member(regular(complement(universal_class)),X0)|~spl0_141)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f2960])).
% 19.92/2.92 fof(f3006,plain,(
% 19.92/2.92 spl0_143 <=> member(X0,X1)|~member(X0,X1)|~member(X0,X2)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3009,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (member(X0,X1)|~member(X0,X1)|~member(X0,X2)|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1947,f978])).
% 19.92/2.92 fof(f3010,plain,(
% 19.92/2.92 spl0_143|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3009,f3006,f283])).
% 19.92/2.92 fof(f3027,plain,(
% 19.92/2.92 spl0_144 <=> member(X0,X1)|~member(X0,intersection(X4,X1))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3034,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (member(X0,X1)|~member(X0,intersection(X2,X1))|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1952,f135])).
% 19.92/2.92 fof(f3035,plain,(
% 19.92/2.92 spl0_144|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3034,f3027,f283])).
% 19.92/2.92 fof(f3115,plain,(
% 19.92/2.92 ![X0]: (~member(X0,null_class)|~member(X0,universal_class)|~spl0_62)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f1139,f146])).
% 19.92/2.92 fof(f3116,plain,(
% 19.92/2.92 ![X0]: (~member(X0,null_class)|~spl0_62)),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f3115,f2827])).
% 19.92/2.92 fof(f3120,plain,(
% 19.92/2.92 complement(universal_class)=null_class|~spl0_141),
% 19.92/2.92 inference(resolution,[status(thm)],[f2961,f188])).
% 19.92/2.92 fof(f3120,plain,(
% 19.92/2.92 complement(universal_class)=null_class|~spl0_141),
% 19.92/2.92 inference(resolution,[status(thm)],[f2961,f188])).
% 19.92/2.92 fof(f3139,plain,(
% 19.92/2.92 ![X0]: (~member(X0,null_class)|~member(X0,universal_class)|~spl0_141)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f3120,f146])).
% 19.92/2.92 fof(f3140,plain,(
% 19.92/2.92 ![X0]: (~member(X0,null_class)|~spl0_141)),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f3139,f2827])).
% 19.92/2.92 fof(f3144,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(ordered_pair(X0,X1),cross_product(null_class,X2))|~spl0_141)),
% 19.92/2.92 inference(resolution,[status(thm)],[f3140,f132])).
% 19.92/2.92 fof(f3228,plain,(
% 19.92/2.92 spl0_155 <=> ~member(X2,null_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3229,plain,(
% 19.92/2.92 ![X0]: (~member(X0,null_class)|~spl0_155)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f3228])).
% 19.92/2.92 fof(f3233,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(X0,X1)|~member(X0,X2)|~member(X3,null_class)|~spl0_141)),
% 19.92/2.92 inference(resolution,[status(thm)],[f3144,f978])).
% 19.92/2.92 fof(f3234,plain,(
% 19.92/2.92 spl0_66|spl0_155|~spl0_141),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3233,f1191,f3228,f2960])).
% 19.92/2.92 fof(f3282,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(ordered_pair(X0,X1),cross_product(null_class,X2))|~spl0_62)),
% 19.92/2.92 inference(resolution,[status(thm)],[f3116,f132])).
% 19.92/2.92 fof(f3302,plain,(
% 19.92/2.92 ![X0]: (member(first(ordered_pair(x,universal_class)),X0)|~member(x,X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f686,f639])).
% 19.92/2.92 fof(f3303,plain,(
% 19.92/2.92 spl0_156 <=> member(first(ordered_pair(x,universal_class)),X0)|~member(x,X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3306,plain,(
% 19.92/2.92 ![X0,X1]: (member(first(ordered_pair(x,universal_class)),X0)|~member(universal_class,universal_class)|member(universal_class,X1)|~member(x,X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f686,f986])).
% 19.92/2.92 fof(f3307,plain,(
% 19.92/2.92 spl0_156|~spl0_84|spl0_120),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3306,f3303,f1640,f2416])).
% 19.92/2.92 fof(f3344,plain,(
% 19.92/2.92 spl0_162 <=> member(first(ordered_pair(x,universal_class)),unordered_pair(x,X0))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3347,plain,(
% 19.92/2.92 ![X0]: (member(first(ordered_pair(x,universal_class)),unordered_pair(x,X0))|~member(x,universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f3302,f125])).
% 19.92/2.92 fof(f3348,plain,(
% 19.92/2.92 spl0_162|~spl0_18),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3347,f3344,f617])).
% 19.92/2.92 fof(f3349,plain,(
% 19.92/2.92 spl0_163 <=> member(first(ordered_pair(x,universal_class)),unordered_pair(X0,x))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3352,plain,(
% 19.92/2.92 ![X0]: (member(first(ordered_pair(x,universal_class)),unordered_pair(X0,x))|~member(x,universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f3302,f127])).
% 19.92/2.92 fof(f3353,plain,(
% 19.92/2.92 spl0_163|~spl0_18),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3352,f3349,f617])).
% 19.92/2.92 fof(f3354,plain,(
% 19.92/2.92 spl0_164 <=> member(first(ordered_pair(x,universal_class)),singleton(x))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3362,plain,(
% 19.92/2.92 member(first(ordered_pair(x,universal_class)),singleton(x))|~member(x,universal_class)),
% 19.92/2.92 inference(resolution,[status(thm)],[f3302,f277])).
% 19.92/2.92 fof(f3363,plain,(
% 19.92/2.92 spl0_164|~spl0_18),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3362,f3354,f617])).
% 19.92/2.92 fof(f3384,plain,(
% 19.92/2.92 spl0_168 <=> universal_class=complement(X0)|~member(not_subclass_element(universal_class,complement(X0)),universal_class)|member(not_subclass_element(universal_class,complement(X0)),X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3387,plain,(
% 19.92/2.92 ![X0,X1,X2]: (universal_class=complement(X0)|~member(not_subclass_element(universal_class,complement(X0)),universal_class)|member(not_subclass_element(universal_class,complement(X0)),X0)|~member(X1,X2))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1297,f986])).
% 19.92/2.92 fof(f3388,plain,(
% 19.92/2.92 spl0_168|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3387,f3384,f283])).
% 19.92/2.92 fof(f3389,plain,(
% 19.92/2.92 spl0_169 <=> universal_class=intersection(X0,X1)|~member(not_subclass_element(universal_class,intersection(X0,X1)),X0)|~member(not_subclass_element(universal_class,intersection(X0,X1)),X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3392,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (universal_class=intersection(X0,X1)|~member(not_subclass_element(universal_class,intersection(X0,X1)),X0)|~member(not_subclass_element(universal_class,intersection(X0,X1)),X1)|~member(X2,X3))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1297,f978])).
% 19.92/2.92 fof(f3393,plain,(
% 19.92/2.92 spl0_169|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3392,f3389,f283])).
% 19.92/2.92 fof(f3394,plain,(
% 19.92/2.92 spl0_170 <=> universal_class=X0|~member(not_subclass_element(universal_class,X0),X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3397,plain,(
% 19.92/2.92 ![X0,X1,X2]: (universal_class=X0|~member(X1,X2)|~member(not_subclass_element(universal_class,X0),X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1297,f135])).
% 19.92/2.92 fof(f3398,plain,(
% 19.92/2.92 spl0_170|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3397,f3394,f283])).
% 19.92/2.92 fof(f3426,plain,(
% 19.92/2.92 ![X0,X1,X2]: (member(X0,subset_relation)|~member(ordered_pair(X1,X0),cross_product(X2,identity_relation)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f197,f1953])).
% 19.92/2.92 fof(f3435,plain,(
% 19.92/2.92 spl0_171 <=> subclass(X0,X1)|~member(not_subclass_element(X0,X1),X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3442,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (subclass(X0,X1)|~member(not_subclass_element(X0,X1),X1)|~member(X2,X3))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1964,f135])).
% 19.92/2.92 fof(f3443,plain,(
% 19.92/2.92 spl0_171|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3442,f3435,f283])).
% 19.92/2.92 fof(f3737,plain,(
% 19.92/2.92 ![X0,X1]: (~member(ordered_pair(x,universal_class),cross_product(X0,X1))|spl0_68)),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f687,f2832])).
% 19.92/2.92 fof(f3738,plain,(
% 19.92/2.92 $false|spl0_68),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f245,f3737])).
% 19.92/2.92 fof(f3739,plain,(
% 19.92/2.92 spl0_68),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f3738])).
% 19.92/2.92 fof(f3740,plain,(
% 19.92/2.92 spl0_190 <=> subclass(X0,complement(X1))|~member(not_subclass_element(X0,complement(X1)),universal_class)|member(not_subclass_element(X0,complement(X1)),X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3741,plain,(
% 19.92/2.92 ![X0,X1]: (subclass(X0,complement(X1))|~member(not_subclass_element(X0,complement(X1)),universal_class)|member(not_subclass_element(X0,complement(X1)),X1)|~spl0_190)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f3740])).
% 19.92/2.92 fof(f3743,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (subclass(X0,complement(X1))|~member(not_subclass_element(X0,complement(X1)),universal_class)|member(not_subclass_element(X0,complement(X1)),X1)|~member(X2,X3))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1965,f986])).
% 19.92/2.92 fof(f3744,plain,(
% 19.92/2.92 spl0_190|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3743,f3740,f283])).
% 19.92/2.92 fof(f3745,plain,(
% 19.92/2.92 spl0_191 <=> subclass(X0,intersection(X1,X2))|~member(not_subclass_element(X0,intersection(X1,X2)),X1)|~member(not_subclass_element(X0,intersection(X1,X2)),X2)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3748,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (subclass(X0,intersection(X1,X2))|~member(not_subclass_element(X0,intersection(X1,X2)),X1)|~member(not_subclass_element(X0,intersection(X1,X2)),X2)|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1965,f978])).
% 19.92/2.92 fof(f3749,plain,(
% 19.92/2.92 spl0_191|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3748,f3745,f283])).
% 19.92/2.92 fof(f3802,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (compose(X0,X1)=X2|~member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(compose_class(X0),X4)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f220,f132])).
% 19.92/2.92 fof(f3814,plain,(
% 19.92/2.92 spl0_196 <=> member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(universal_class,complement(X0)))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3817,plain,(
% 19.92/2.92 ![X0,X1]: (member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(universal_class,complement(X0)))|~member(first(ordered_pair(x,universal_class)),X1)|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f2827])).
% 19.92/2.92 fof(f3818,plain,(
% 19.92/2.92 spl0_196|spl0_106|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3817,f3814,f2059,f1208])).
% 19.92/2.92 fof(f3819,plain,(
% 19.92/2.92 spl0_197 <=> member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(unordered_pair(first(ordered_pair(x,universal_class)),X1),complement(X0)))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3822,plain,(
% 19.92/2.92 ![X0,X1]: (member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(unordered_pair(first(ordered_pair(x,universal_class)),X1),complement(X0)))|~member(first(ordered_pair(x,universal_class)),universal_class)|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f125])).
% 19.92/2.92 fof(f3823,plain,(
% 19.92/2.92 spl0_197|~spl0_88|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3822,f3819,f1830,f1208])).
% 19.92/2.92 fof(f3824,plain,(
% 19.92/2.92 spl0_198 <=> member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(unordered_pair(X1,first(ordered_pair(x,universal_class))),complement(X0)))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3827,plain,(
% 19.92/2.92 ![X0,X1]: (member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(unordered_pair(X1,first(ordered_pair(x,universal_class))),complement(X0)))|~member(first(ordered_pair(x,universal_class)),universal_class)|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f127])).
% 19.92/2.92 fof(f3828,plain,(
% 19.92/2.92 spl0_198|~spl0_88|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3827,f3824,f1830,f1208])).
% 19.92/2.92 fof(f3829,plain,(
% 19.92/2.92 spl0_199 <=> member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(singleton(first(ordered_pair(x,universal_class))),complement(X0)))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3832,plain,(
% 19.92/2.92 ![X0]: (member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(singleton(first(ordered_pair(x,universal_class))),complement(X0)))|~member(first(ordered_pair(x,universal_class)),universal_class)|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f277])).
% 19.92/2.92 fof(f3833,plain,(
% 19.92/2.92 spl0_199|~spl0_88|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3832,f3829,f1830,f1208])).
% 19.92/2.92 fof(f3912,plain,(
% 19.92/2.92 spl0_204 <=> ~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,universal_class))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3915,plain,(
% 19.92/2.92 spl0_205 <=> ~member(second(ordered_pair(x,universal_class)),X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3916,plain,(
% 19.92/2.92 ![X0]: (~member(second(ordered_pair(x,universal_class)),X0)|~spl0_205)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f3915])).
% 19.92/2.92 fof(f3918,plain,(
% 19.92/2.92 ![X0,X1]: (~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,universal_class))|~member(second(ordered_pair(x,universal_class)),X1))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1171,f2827])).
% 19.92/2.92 fof(f3919,plain,(
% 19.92/2.92 spl0_204|spl0_205),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3918,f3912,f3915])).
% 19.92/2.92 fof(f3920,plain,(
% 19.92/2.92 spl0_206 <=> ~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,unordered_pair(second(ordered_pair(x,universal_class)),X1)))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3923,plain,(
% 19.92/2.92 ![X0,X1]: (~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,unordered_pair(second(ordered_pair(x,universal_class)),X1)))|~member(second(ordered_pair(x,universal_class)),universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1171,f125])).
% 19.92/2.92 fof(f3924,plain,(
% 19.92/2.92 spl0_206|~spl0_68),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3923,f3920,f1205])).
% 19.92/2.92 fof(f3925,plain,(
% 19.92/2.92 spl0_207 <=> ~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,unordered_pair(X1,second(ordered_pair(x,universal_class)))))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3928,plain,(
% 19.92/2.92 ![X0,X1]: (~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,unordered_pair(X1,second(ordered_pair(x,universal_class)))))|~member(second(ordered_pair(x,universal_class)),universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1171,f127])).
% 19.92/2.92 fof(f3929,plain,(
% 19.92/2.92 spl0_207|~spl0_68),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3928,f3925,f1205])).
% 19.92/2.92 fof(f3930,plain,(
% 19.92/2.92 spl0_208 <=> ~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,singleton(second(ordered_pair(x,universal_class)))))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f3933,plain,(
% 19.92/2.92 ![X0]: (~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,singleton(second(ordered_pair(x,universal_class)))))|~member(second(ordered_pair(x,universal_class)),universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1171,f277])).
% 19.92/2.92 fof(f3934,plain,(
% 19.92/2.92 spl0_208|~spl0_68),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3933,f3930,f1205])).
% 19.92/2.92 fof(f3952,plain,(
% 19.92/2.92 spl0_62|~spl0_141),
% 19.92/2.92 inference(split_clause,[status(thm)],[f3120,f1138,f2960])).
% 19.92/2.92 fof(f4006,plain,(
% 19.92/2.92 spl0_213 <=> member(X0,subset_relation)|~member(X0,identity_relation)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4009,plain,(
% 19.92/2.92 ![X0,X1,X2]: (member(X0,subset_relation)|~member(X1,X2)|~member(X0,identity_relation))),
% 19.92/2.92 inference(resolution,[status(thm)],[f3426,f135])).
% 19.92/2.92 fof(f4010,plain,(
% 19.92/2.92 spl0_213|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4009,f4006,f283])).
% 19.92/2.92 fof(f4026,plain,(
% 19.92/2.92 spl0_216 <=> successor(X0)=X1|~member(ordered_pair(X0,X1),successor_relation)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4033,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (successor(X0)=X1|~member(ordered_pair(X0,X1),successor_relation)|~member(X2,X3))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1966,f135])).
% 19.92/2.92 fof(f4034,plain,(
% 19.92/2.92 spl0_216|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4033,f4026,f283])).
% 19.92/2.92 fof(f4190,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (compose(X0,X1)=X2|~member(ordered_pair(ordered_pair(X0,ordered_pair(X1,X2)),X3),cross_product(composition_function,X4)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f223,f132])).
% 19.92/2.92 fof(f4232,plain,(
% 19.92/2.92 ~member(null_class,universal_class)|null_class=null_class|~spl0_155),
% 19.92/2.92 inference(resolution,[status(thm)],[f3229,f192])).
% 19.92/2.92 fof(f4233,plain,(
% 19.92/2.92 ~spl0_14|spl0_17|~spl0_155),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4232,f560,f579,f3228])).
% 19.92/2.92 fof(f4341,plain,(
% 19.92/2.92 spl0_232 <=> domain_of(X0)=X1|~member(ordered_pair(X0,X1),domain_relation)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4348,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (domain_of(X0)=X1|~member(ordered_pair(X0,X1),domain_relation)|~member(X2,X3))),
% 19.92/2.92 inference(resolution,[status(thm)],[f2285,f135])).
% 19.92/2.92 fof(f4349,plain,(
% 19.92/2.92 spl0_232|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4348,f4341,f283])).
% 19.92/2.92 fof(f4649,plain,(
% 19.92/2.92 spl0_250 <=> X0=X1|~member(X0,intersection(singleton(X1),X4))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4656,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|~member(X0,intersection(singleton(X1),X2))|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1539,f135])).
% 19.92/2.92 fof(f4657,plain,(
% 19.92/2.92 spl0_250|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4656,f4649,f283])).
% 19.92/2.92 fof(f4665,plain,(
% 19.92/2.92 spl0_251 <=> X0=X1|~member(X0,singleton(X1))|~member(X0,X2)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4668,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|~member(X0,singleton(X1))|~member(X0,X2)|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1540,f978])).
% 19.92/2.92 fof(f4669,plain,(
% 19.92/2.92 spl0_251|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4668,f4665,f283])).
% 19.92/2.92 fof(f4687,plain,(
% 19.92/2.92 spl0_252 <=> member(X0,image(X1,image(X2,singleton(X3))))|~member(ordered_pair(X3,X0),compose(X1,X2))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4690,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4,X5]: (member(X0,image(X1,image(X2,singleton(X3))))|~member(X4,X5)|~member(ordered_pair(X3,X0),compose(X1,X2)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f2302,f135])).
% 19.92/2.92 fof(f4691,plain,(
% 19.92/2.92 spl0_252|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4690,f4687,f283])).
% 19.92/2.92 fof(f4746,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,universal_class)|~subclass(X1,null_class)|~member(X0,X1)|~spl0_62)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f1139,f266])).
% 19.92/2.92 fof(f4747,plain,(
% 19.92/2.92 ![X0,X1]: (~subclass(X0,null_class)|~member(X1,X0)|~spl0_62)),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f4746,f2827])).
% 19.92/2.92 fof(f4779,plain,(
% 19.92/2.92 ![X0,X1,X2]: (member(X0,element_relation)|~member(ordered_pair(X1,X0),cross_product(X2,singleton_relation)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f231,f1953])).
% 19.92/2.92 fof(f4787,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (member(X0,domain_of(X1))|~member(ordered_pair(X2,ordered_pair(X1,ordered_pair(X0,X3))),cross_product(X4,application_function)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f234,f134])).
% 19.92/2.92 fof(f4800,plain,(
% 19.92/2.92 spl0_256 <=> ~member(X0,universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4801,plain,(
% 19.92/2.92 ![X0]: (~member(X0,universal_class)|~spl0_256)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f4800])).
% 19.92/2.92 fof(f4877,plain,(
% 19.92/2.92 spl0_268 <=> ~member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,intersection(X0,universal_class)))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4880,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,intersection(X0,universal_class)))|~member(second(ordered_pair(x,universal_class)),X2))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1196,f2827])).
% 19.92/2.92 fof(f4881,plain,(
% 19.92/2.92 spl0_268|spl0_205),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4880,f4877,f3915])).
% 19.92/2.92 fof(f4882,plain,(
% 19.92/2.92 spl0_269 <=> ~member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,intersection(X0,unordered_pair(second(ordered_pair(x,universal_class)),X2))))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4885,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,intersection(X0,unordered_pair(second(ordered_pair(x,universal_class)),X2))))|~member(second(ordered_pair(x,universal_class)),universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1196,f125])).
% 19.92/2.92 fof(f4886,plain,(
% 19.92/2.92 spl0_269|~spl0_68),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4885,f4882,f1205])).
% 19.92/2.92 fof(f4887,plain,(
% 19.92/2.92 spl0_270 <=> ~member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,intersection(X0,unordered_pair(X2,second(ordered_pair(x,universal_class))))))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4890,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,intersection(X0,unordered_pair(X2,second(ordered_pair(x,universal_class))))))|~member(second(ordered_pair(x,universal_class)),universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1196,f127])).
% 19.92/2.92 fof(f4891,plain,(
% 19.92/2.92 spl0_270|~spl0_68),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4890,f4887,f1205])).
% 19.92/2.92 fof(f4892,plain,(
% 19.92/2.92 spl0_271 <=> ~member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,intersection(X0,singleton(second(ordered_pair(x,universal_class))))))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4895,plain,(
% 19.92/2.92 ![X0,X1]: (~member(second(ordered_pair(x,universal_class)),X0)|~member(first(ordered_pair(x,universal_class)),X1)|member(ordered_pair(x,universal_class),cross_product(X1,intersection(X0,singleton(second(ordered_pair(x,universal_class))))))|~member(second(ordered_pair(x,universal_class)),universal_class))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1196,f277])).
% 19.92/2.92 fof(f4896,plain,(
% 19.92/2.92 spl0_271|~spl0_68),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4895,f4892,f1205])).
% 19.92/2.92 fof(f4899,plain,(
% 19.92/2.92 spl0_272 <=> member(X0,element_relation)|~member(X0,singleton_relation)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4902,plain,(
% 19.92/2.92 ![X0,X1,X2]: (member(X0,element_relation)|~member(X1,X2)|~member(X0,singleton_relation))),
% 19.92/2.92 inference(resolution,[status(thm)],[f4779,f135])).
% 19.92/2.92 fof(f4903,plain,(
% 19.92/2.92 spl0_272|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4902,f4899,f283])).
% 19.92/2.92 fof(f4969,plain,(
% 19.92/2.92 spl0_285 <=> X0=X1|~member(X0,intersection(X4,singleton(X1)))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f4976,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (X0=X1|~member(X0,intersection(X2,singleton(X1)))|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f1541,f135])).
% 19.92/2.92 fof(f4977,plain,(
% 19.92/2.92 spl0_285|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f4976,f4969,f283])).
% 19.92/2.92 fof(f5191,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (apply(X0,X1)=X2|~member(ordered_pair(ordered_pair(X0,ordered_pair(X1,X2)),X3),cross_product(application_function,X4)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f235,f132])).
% 19.92/2.92 fof(f5401,plain,(
% 19.92/2.92 spl0_312 <=> member(x,singleton(x))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f5403,plain,(
% 19.92/2.92 ~member(x,singleton(x))|spl0_312),
% 19.92/2.92 inference(component_clause,[status(thm)],[f5401])).
% 19.92/2.92 fof(f5565,plain,(
% 19.92/2.92 spl0_318 <=> member(universal_class,null_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f5566,plain,(
% 19.92/2.92 member(universal_class,null_class)|~spl0_318),
% 19.92/2.92 inference(component_clause,[status(thm)],[f5565])).
% 19.92/2.92 fof(f5681,plain,(
% 19.92/2.92 spl0_321 <=> regular(singleton(universal_class))=universal_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f5682,plain,(
% 19.92/2.92 regular(singleton(universal_class))=universal_class|~spl0_321),
% 19.92/2.92 inference(component_clause,[status(thm)],[f5681])).
% 19.92/2.92 fof(f5737,plain,(
% 19.92/2.92 spl0_323 <=> intersection(singleton(X0),X1)=null_class|regular(intersection(singleton(X0),X1))=X0),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f5740,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (intersection(singleton(X0),X1)=null_class|~member(X2,X3)|regular(intersection(singleton(X0),X1))=X0)),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f1540])).
% 19.92/2.92 fof(f5741,plain,(
% 19.92/2.92 spl0_323|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f5740,f5737,f283])).
% 19.92/2.92 fof(f5742,plain,(
% 19.92/2.92 spl0_324 <=> intersection(X0,singleton(X1))=null_class|regular(intersection(X0,singleton(X1)))=X1),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f5745,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (intersection(X0,singleton(X1))=null_class|~member(X2,X3)|regular(intersection(X0,singleton(X1)))=X1)),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f1542])).
% 19.92/2.92 fof(f5746,plain,(
% 19.92/2.92 spl0_324|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f5745,f5742,f283])).
% 19.92/2.92 fof(f5747,plain,(
% 19.92/2.92 spl0_325 <=> intersection(X0,X1)=null_class|member(regular(intersection(X0,X1)),X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f5750,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (intersection(X0,X1)=null_class|~member(X2,X3)|member(regular(intersection(X0,X1)),X1))),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f1953])).
% 19.92/2.92 fof(f5751,plain,(
% 19.92/2.92 spl0_325|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f5750,f5747,f283])).
% 19.92/2.92 fof(f5752,plain,(
% 19.92/2.92 spl0_326 <=> intersection(X0,X1)=null_class|member(regular(intersection(X0,X1)),X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f5755,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (intersection(X0,X1)=null_class|~member(X2,X3)|member(regular(intersection(X0,X1)),X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f1947])).
% 19.92/2.92 fof(f5756,plain,(
% 19.92/2.92 spl0_326|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f5755,f5752,f283])).
% 19.92/2.92 fof(f5832,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,X1)|~member(X0,regular(X1))|member(X0,null_class)|X1=null_class)),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f189,f145])).
% 19.92/2.92 fof(f5833,plain,(
% 19.92/2.92 ![X0,X1]: (~member(X0,X1)|~member(X0,regular(X1))|X1=null_class|~spl0_155)),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f5832,f3229])).
% 19.92/2.92 fof(f5835,plain,(
% 19.92/2.92 ![X0]: (~member(not_subclass_element(universal_class,complement(X0)),universal_class)|member(not_subclass_element(universal_class,complement(X0)),X0)|universal_class=complement(X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f147,f1265])).
% 19.92/2.92 fof(f5836,plain,(
% 19.92/2.92 ![X0]: (member(not_subclass_element(universal_class,complement(X0)),X0)|universal_class=complement(X0))),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f5835,f919])).
% 19.92/2.92 fof(f5930,plain,(
% 19.92/2.92 ~member(x,universal_class)|spl0_312),
% 19.92/2.92 inference(resolution,[status(thm)],[f5403,f277])).
% 19.92/2.92 fof(f5931,plain,(
% 19.92/2.92 ~spl0_18|spl0_312),
% 19.92/2.92 inference(split_clause,[status(thm)],[f5930,f617,f5401])).
% 19.92/2.92 fof(f5999,plain,(
% 19.92/2.92 spl0_338 <=> member(X0,X1)|~member(ordered_pair(X0,X1),element_relation)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f6011,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (member(X0,X1)|~member(ordered_pair(X0,X1),element_relation)|~member(X2,X3))),
% 19.92/2.92 inference(resolution,[status(thm)],[f2870,f135])).
% 19.92/2.92 fof(f6012,plain,(
% 19.92/2.92 spl0_338|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f6011,f5999,f283])).
% 19.92/2.92 fof(f6089,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (ordered_pair(first(ordered_pair(X0,X1)),second(ordered_pair(X0,X1)))=ordered_pair(X0,X1)|~member(X0,X2)|~member(X1,X3))),
% 19.92/2.92 inference(resolution,[status(thm)],[f137,f135])).
% 19.92/2.92 fof(f6090,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (ordered_pair(first(X0),second(X0))=X0|~member(ordered_pair(X0,X1),cross_product(cross_product(X2,X3),X4)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f137,f132])).
% 19.92/2.92 fof(f6091,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (ordered_pair(first(X0),second(X0))=X0|~member(ordered_pair(X1,X0),cross_product(X2,cross_product(X3,X4))))),
% 19.92/2.92 inference(resolution,[status(thm)],[f137,f134])).
% 19.92/2.92 fof(f6184,plain,(
% 19.92/2.92 spl0_348 <=> member(ordered_pair(x,omega),cross_product(universal_class,universal_class))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f6186,plain,(
% 19.92/2.92 ~member(ordered_pair(x,omega),cross_product(universal_class,universal_class))|spl0_348),
% 19.92/2.92 inference(component_clause,[status(thm)],[f6184])).
% 19.92/2.92 fof(f6192,plain,(
% 19.92/2.92 $false|spl0_348),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f6186,f634])).
% 19.92/2.92 fof(f6193,plain,(
% 19.92/2.92 spl0_348),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f6192])).
% 19.92/2.92 fof(f6194,plain,(
% 19.92/2.92 spl0_349 <=> member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(domain_of(X1),complement(X0)))|restrict(X1,singleton(first(ordered_pair(x,universal_class))),universal_class)=null_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f6197,plain,(
% 19.92/2.92 ![X0,X1]: (member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(domain_of(X1),complement(X0)))|~member(first(ordered_pair(x,universal_class)),universal_class)|restrict(X1,singleton(first(ordered_pair(x,universal_class))),universal_class)=null_class|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f153])).
% 19.92/2.92 fof(f6198,plain,(
% 19.92/2.92 spl0_349|~spl0_88|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f6197,f6194,f1830,f1208])).
% 19.92/2.92 fof(f6199,plain,(
% 19.92/2.92 spl0_350 <=> member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(complement(X1),complement(X0)))|member(first(ordered_pair(x,universal_class)),X1)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f6202,plain,(
% 19.92/2.92 ![X0,X1]: (member(second(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(complement(X1),complement(X0)))|~member(first(ordered_pair(x,universal_class)),universal_class)|member(first(ordered_pair(x,universal_class)),X1)|~spl0_69)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1209,f147])).
% 19.92/2.92 fof(f6203,plain,(
% 19.92/2.92 spl0_350|~spl0_88|~spl0_69),
% 19.92/2.92 inference(split_clause,[status(thm)],[f6202,f6199,f1830,f1208])).
% 19.92/2.92 fof(f6273,plain,(
% 19.92/2.92 spl0_357 <=> member(first(ordered_pair(x,universal_class)),domain_of(X0))|restrict(X0,singleton(x),universal_class)=null_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f6276,plain,(
% 19.92/2.92 ![X0]: (member(first(ordered_pair(x,universal_class)),domain_of(X0))|~member(x,universal_class)|restrict(X0,singleton(x),universal_class)=null_class)),
% 19.92/2.92 inference(resolution,[status(thm)],[f3302,f153])).
% 19.92/2.92 fof(f6277,plain,(
% 19.92/2.92 spl0_357|~spl0_18),
% 19.92/2.92 inference(split_clause,[status(thm)],[f6276,f6273,f617])).
% 19.92/2.92 fof(f6278,plain,(
% 19.92/2.92 spl0_358 <=> member(first(ordered_pair(x,universal_class)),complement(X0))|member(x,X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f6281,plain,(
% 19.92/2.92 ![X0]: (member(first(ordered_pair(x,universal_class)),complement(X0))|~member(x,universal_class)|member(x,X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f3302,f147])).
% 19.92/2.92 fof(f6282,plain,(
% 19.92/2.92 spl0_358|~spl0_18),
% 19.92/2.92 inference(split_clause,[status(thm)],[f6281,f6278,f617])).
% 19.92/2.92 fof(f6319,plain,(
% 19.92/2.92 spl0_360 <=> member(ordered_pair(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class))),cross_product(universal_class,universal_class))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f6321,plain,(
% 19.92/2.92 ~member(ordered_pair(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class))),cross_product(universal_class,universal_class))|spl0_360),
% 19.92/2.92 inference(component_clause,[status(thm)],[f6319])).
% 19.92/2.92 fof(f6375,plain,(
% 19.92/2.92 ~member(ordered_pair(x,universal_class),cross_product(universal_class,universal_class))|spl0_360),
% 19.92/2.92 inference(forward_demodulation,[status(thm)],[f627,f6321])).
% 19.92/2.92 fof(f6376,plain,(
% 19.92/2.92 $false|spl0_360),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f6375,f245])).
% 19.92/2.92 fof(f6377,plain,(
% 19.92/2.92 spl0_360),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f6376])).
% 19.92/2.92 fof(f6551,plain,(
% 19.92/2.92 ![X0,X1]: (intersection(complement(intersection(X0,X1)),union(X0,X1))=symmetric_difference(X0,X1))),
% 19.92/2.92 inference(forward_demodulation,[status(thm)],[f148,f149])).
% 19.92/2.92 fof(f6567,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,symmetric_difference(X1,X2))|~member(X0,intersection(X1,X2)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f6551,f1261])).
% 19.92/2.92 fof(f6600,plain,(
% 19.92/2.92 ![X0,X1]: (X0=null_class|~member(X1,null_class)|~spl0_62)),
% 19.92/2.92 inference(resolution,[status(thm)],[f3282,f455])).
% 19.92/2.92 fof(f6601,plain,(
% 19.92/2.92 spl0_30|spl0_155|~spl0_62),
% 19.92/2.92 inference(split_clause,[status(thm)],[f6600,f803,f3228,f1138])).
% 19.92/2.92 fof(f6825,plain,(
% 19.92/2.92 ~member(null_class,omega)|inductive(omega)),
% 19.92/2.92 inference(resolution,[status(thm)],[f171,f496])).
% 19.92/2.92 fof(f6826,plain,(
% 19.92/2.92 ~spl0_98|spl0_99),
% 19.92/2.92 inference(split_clause,[status(thm)],[f6825,f1981,f1984])).
% 19.92/2.92 fof(f6831,plain,(
% 19.92/2.92 ![X0,X1]: (~member(second(ordered_pair(x,universal_class)),image(X0,image(X1,singleton(first(ordered_pair(x,universal_class))))))|~member(ordered_pair(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class))),cross_product(universal_class,universal_class))|member(ordered_pair(x,universal_class),compose(X0,X1)))),
% 19.92/2.92 inference(paramodulation,[status(thm)],[f627,f181])).
% 19.92/2.92 fof(f6832,plain,(
% 19.92/2.92 spl0_117|~spl0_360),
% 19.92/2.92 inference(split_clause,[status(thm)],[f6831,f2306,f6319])).
% 19.92/2.92 fof(f6836,plain,(
% 19.92/2.92 $false|~spl0_205|~spl0_68),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f1206,f3916])).
% 19.92/2.92 fof(f6837,plain,(
% 19.92/2.92 ~spl0_205|~spl0_68),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f6836])).
% 19.92/2.92 fof(f7163,plain,(
% 19.92/2.92 spl0_394 <=> compose(X0,X1)=X2|~member(ordered_pair(X1,X2),compose_class(X0))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f7170,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (compose(X0,X1)=X2|~member(ordered_pair(X1,X2),compose_class(X0))|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f3802,f135])).
% 19.92/2.92 fof(f7171,plain,(
% 19.92/2.92 spl0_394|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f7170,f7163,f283])).
% 19.92/2.92 fof(f7191,plain,(
% 19.92/2.92 ![X0]: (complement(X0)=null_class|~member(regular(complement(X0)),X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f188,f146])).
% 19.92/2.92 fof(f7524,plain,(
% 19.92/2.92 spl0_408 <=> compose(X0,X1)=X2|~member(ordered_pair(X0,ordered_pair(X1,X2)),composition_function)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f7531,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (compose(X0,X1)=X2|~member(ordered_pair(X0,ordered_pair(X1,X2)),composition_function)|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f4190,f135])).
% 19.92/2.92 fof(f7532,plain,(
% 19.92/2.92 spl0_408|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f7531,f7524,f283])).
% 19.92/2.92 fof(f7545,plain,(
% 19.92/2.92 ![X0]: (complement(universal_class)=null_class|~member(regular(complement(universal_class)),X0))),
% 19.92/2.92 inference(resolution,[status(thm)],[f7191,f2827])).
% 19.92/2.92 fof(f7546,plain,(
% 19.92/2.92 spl0_62|spl0_141),
% 19.92/2.92 inference(split_clause,[status(thm)],[f7545,f1138,f2960])).
% 19.92/2.92 fof(f7815,plain,(
% 19.92/2.92 spl0_423 <=> member(regular(null_class),X0)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f7816,plain,(
% 19.92/2.92 ![X0]: (member(regular(null_class),X0)|~spl0_423)),
% 19.92/2.92 inference(component_clause,[status(thm)],[f7815])).
% 19.92/2.92 fof(f7982,plain,(
% 19.92/2.92 ![X0,X1]: (~member(regular(null_class),intersection(X0,X1))|~spl0_423)),
% 19.92/2.92 inference(resolution,[status(thm)],[f7816,f6567])).
% 19.92/2.92 fof(f7983,plain,(
% 19.92/2.92 $false|~spl0_423),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f7982,f7816])).
% 19.92/2.92 fof(f7984,plain,(
% 19.92/2.92 ~spl0_423),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f7983])).
% 19.92/2.92 fof(f8268,plain,(
% 19.92/2.92 spl0_433 <=> member(X0,domain_of(X1))|~member(ordered_pair(X1,ordered_pair(X0,X4)),application_function)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f8271,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (member(X0,domain_of(X1))|~member(X2,X3)|~member(ordered_pair(X1,ordered_pair(X0,X4)),application_function))),
% 19.92/2.92 inference(resolution,[status(thm)],[f4787,f135])).
% 19.92/2.92 fof(f8272,plain,(
% 19.92/2.92 spl0_433|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f8271,f8268,f283])).
% 19.92/2.92 fof(f8286,plain,(
% 19.92/2.92 spl0_434 <=> apply(X0,X1)=X2|~member(ordered_pair(X0,ordered_pair(X1,X2)),application_function)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f8293,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (apply(X0,X1)=X2|~member(ordered_pair(X0,ordered_pair(X1,X2)),application_function)|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f5191,f135])).
% 19.92/2.92 fof(f8294,plain,(
% 19.92/2.92 spl0_434|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f8293,f8286,f283])).
% 19.92/2.92 fof(f8408,plain,(
% 19.92/2.92 ![X0,X1,X2]: (X0=null_class|member(apply(choice,X0),X0)|~member(ordered_pair(X0,X1),cross_product(universal_class,X2)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f192,f132])).
% 19.92/2.92 fof(f8409,plain,(
% 19.92/2.92 ![X0,X1,X2]: (X0=null_class|member(apply(choice,X0),X0)|~member(ordered_pair(X1,X0),cross_product(X2,universal_class)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f192,f134])).
% 19.92/2.92 fof(f8548,plain,(
% 19.92/2.92 spl0_451 <=> subclass(omega,universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f8550,plain,(
% 19.92/2.92 ~subclass(omega,universal_class)|spl0_451),
% 19.92/2.92 inference(component_clause,[status(thm)],[f8548])).
% 19.92/2.92 fof(f8557,plain,(
% 19.92/2.92 $false|spl0_451),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f8550,f118])).
% 19.92/2.92 fof(f8558,plain,(
% 19.92/2.92 spl0_451),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f8557])).
% 19.92/2.92 fof(f9251,plain,(
% 19.92/2.92 spl0_474 <=> ordered_pair(first(X0),second(X0))=X0|~member(X0,cross_product(X3,X4))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f9258,plain,(
% 19.92/2.92 ![X0,X1,X2,X3,X4]: (ordered_pair(first(X0),second(X0))=X0|~member(X0,cross_product(X1,X2))|~member(X3,X4))),
% 19.92/2.92 inference(resolution,[status(thm)],[f6090,f135])).
% 19.92/2.92 fof(f9259,plain,(
% 19.92/2.92 spl0_474|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f9258,f9251,f283])).
% 19.92/2.92 fof(f9271,plain,(
% 19.92/2.92 spl0_477 <=> ordered_pair(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class)))=ordered_pair(x,universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f9274,plain,(
% 19.92/2.92 ![X0,X1]: (ordered_pair(first(ordered_pair(x,universal_class)),second(ordered_pair(x,universal_class)))=ordered_pair(x,universal_class)|~member(X0,X1))),
% 19.92/2.92 inference(resolution,[status(thm)],[f6091,f631])).
% 19.92/2.92 fof(f9275,plain,(
% 19.92/2.92 spl0_477|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f9274,f9271,f283])).
% 19.92/2.92 fof(f9557,plain,(
% 19.92/2.92 spl0_493 <=> cross_product(X0,X1)=null_class|ordered_pair(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))=regular(cross_product(X0,X1))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f9560,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (cross_product(X0,X1)=null_class|~member(X2,X3)|ordered_pair(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))=regular(cross_product(X0,X1)))),
% 19.92/2.92 inference(resolution,[status(thm)],[f455,f6091])).
% 19.92/2.92 fof(f9561,plain,(
% 19.92/2.92 spl0_493|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f9560,f9557,f283])).
% 19.92/2.92 fof(f10212,plain,(
% 19.92/2.92 spl0_515 <=> X0=null_class|member(apply(choice,X0),X0)|~member(X0,universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f10226,plain,(
% 19.92/2.92 ![X0,X1,X2]: (X0=null_class|member(apply(choice,X0),X0)|~member(X0,universal_class)|~member(X1,X2))),
% 19.92/2.92 inference(resolution,[status(thm)],[f8408,f135])).
% 19.92/2.92 fof(f10227,plain,(
% 19.92/2.92 spl0_515|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f10226,f10212,f283])).
% 19.92/2.92 fof(f10280,plain,(
% 19.92/2.92 ![X0,X1,X2]: (~member(X0,singleton(X1))|member(X0,X2)|not_subclass_element(singleton(X1),X2)=X1)),
% 19.92/2.92 inference(resolution,[status(thm)],[f2828,f2316])).
% 19.92/2.92 fof(f10812,plain,(
% 19.92/2.92 spl0_541 <=> singleton(X0)=null_class|member(apply(choice,singleton(X0)),singleton(X0))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f10815,plain,(
% 19.92/2.92 ![X0,X1,X2]: (singleton(X0)=null_class|member(apply(choice,singleton(X0)),singleton(X0))|~member(X1,X2))),
% 19.92/2.92 inference(resolution,[status(thm)],[f8409,f356])).
% 19.92/2.92 fof(f10816,plain,(
% 19.92/2.92 spl0_541|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f10815,f10812,f283])).
% 19.92/2.92 fof(f10817,plain,(
% 19.92/2.92 spl0_542 <=> unordered_pair(X0,X1)=null_class|member(apply(choice,unordered_pair(X0,X1)),unordered_pair(X0,X1))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f10820,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (unordered_pair(X0,X1)=null_class|member(apply(choice,unordered_pair(X0,X1)),unordered_pair(X0,X1))|~member(X2,X3))),
% 19.92/2.92 inference(resolution,[status(thm)],[f8409,f440])).
% 19.92/2.92 fof(f10821,plain,(
% 19.92/2.92 spl0_542|spl0_2),
% 19.92/2.92 inference(split_clause,[status(thm)],[f10820,f10817,f283])).
% 19.92/2.92 fof(f10908,plain,(
% 19.92/2.92 spl0_544 <=> subclass(universal_class,complement(universal_class))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f10909,plain,(
% 19.92/2.92 subclass(universal_class,complement(universal_class))|~spl0_544),
% 19.92/2.92 inference(component_clause,[status(thm)],[f10908])).
% 19.92/2.92 fof(f10911,plain,(
% 19.92/2.92 spl0_545 <=> member(not_subclass_element(universal_class,complement(universal_class)),universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f10914,plain,(
% 19.92/2.92 universal_class=complement(universal_class)|subclass(universal_class,complement(universal_class))|member(not_subclass_element(universal_class,complement(universal_class)),universal_class)|~spl0_190),
% 19.92/2.92 inference(resolution,[status(thm)],[f5836,f3741])).
% 19.92/2.92 fof(f10915,plain,(
% 19.92/2.92 spl0_83|spl0_544|spl0_545|~spl0_190),
% 19.92/2.92 inference(split_clause,[status(thm)],[f10914,f1635,f10908,f10911,f3740])).
% 19.92/2.92 fof(f11017,plain,(
% 19.92/2.92 ![X0]: (universal_class=complement(singleton(X0))|not_subclass_element(universal_class,complement(singleton(X0)))=X0)),
% 19.92/2.92 inference(resolution,[status(thm)],[f5836,f2316])).
% 19.92/2.92 fof(f11045,plain,(
% 19.92/2.92 subclass(universal_class,null_class)|~spl0_62|~spl0_544),
% 19.92/2.92 inference(forward_demodulation,[status(thm)],[f1139,f10909])).
% 19.92/2.92 fof(f11046,plain,(
% 19.92/2.92 null_class=universal_class|~spl0_62|~spl0_83),
% 19.92/2.92 inference(forward_demodulation,[status(thm)],[f1139,f1636])).
% 19.92/2.92 fof(f11047,plain,(
% 19.92/2.92 $false|spl0_32|~spl0_62|~spl0_83),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f11046,f815])).
% 19.92/2.92 fof(f11048,plain,(
% 19.92/2.92 spl0_32|~spl0_62|~spl0_83),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f11047])).
% 19.92/2.92 fof(f11160,plain,(
% 19.92/2.92 $false|~spl0_256|~spl0_68),
% 19.92/2.92 inference(backward_subsumption_resolution,[status(thm)],[f1206,f4801])).
% 19.92/2.92 fof(f11161,plain,(
% 19.92/2.92 ~spl0_256|~spl0_68),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f11160])).
% 19.92/2.92 fof(f11653,plain,(
% 19.92/2.92 ![X0]: (singleton(X0)=null_class|regular(singleton(X0))=X0)),
% 19.92/2.92 inference(resolution,[status(thm)],[f188,f2316])).
% 19.92/2.92 fof(f11777,plain,(
% 19.92/2.92 ![X0]: (~member(X0,universal_class)|~spl0_544|~spl0_62)),
% 19.92/2.92 inference(resolution,[status(thm)],[f11045,f4747])).
% 19.92/2.92 fof(f11778,plain,(
% 19.92/2.92 spl0_256|~spl0_544|~spl0_62),
% 19.92/2.92 inference(split_clause,[status(thm)],[f11777,f4800,f10908,f1138])).
% 19.92/2.92 fof(f11786,plain,(
% 19.92/2.92 spl0_599 <=> subclass(null_class,universal_class)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f11788,plain,(
% 19.92/2.92 ~subclass(null_class,universal_class)|spl0_599),
% 19.92/2.92 inference(component_clause,[status(thm)],[f11786])).
% 19.92/2.92 fof(f11791,plain,(
% 19.92/2.92 $false|spl0_599),
% 19.92/2.92 inference(forward_subsumption_resolution,[status(thm)],[f11788,f118])).
% 19.92/2.92 fof(f11792,plain,(
% 19.92/2.92 spl0_599),
% 19.92/2.92 inference(contradiction_clause,[status(thm)],[f11791])).
% 19.92/2.92 fof(f12460,plain,(
% 19.92/2.92 spl0_616 <=> ~member(second(ordered_pair(x,universal_class)),image(X0,image(X1,singleton(first(ordered_pair(x,universal_class))))))),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f12463,plain,(
% 19.92/2.92 spl0_617 <=> ordered_pair(first(ordered_pair(X2,ordered_pair(x,universal_class))),second(ordered_pair(X2,ordered_pair(x,universal_class))))=ordered_pair(X2,ordered_pair(x,universal_class))|~member(X2,X3)),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f12466,plain,(
% 19.92/2.92 ![X0,X1,X2,X3]: (~member(second(ordered_pair(x,universal_class)),image(X0,image(X1,singleton(first(ordered_pair(x,universal_class))))))|ordered_pair(first(ordered_pair(X2,ordered_pair(x,universal_class))),second(ordered_pair(X2,ordered_pair(x,universal_class))))=ordered_pair(X2,ordered_pair(x,universal_class))|~member(X2,X3)|~spl0_117)),
% 19.92/2.92 inference(resolution,[status(thm)],[f2307,f6089])).
% 19.92/2.92 fof(f12467,plain,(
% 19.92/2.92 spl0_616|spl0_617|~spl0_117),
% 19.92/2.92 inference(split_clause,[status(thm)],[f12466,f12460,f12463,f2306])).
% 19.92/2.92 fof(f12601,plain,(
% 19.92/2.92 spl0_625 <=> ~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,domain_of(X1)))|restrict(X1,singleton(second(ordered_pair(x,universal_class))),universal_class)=null_class),
% 19.92/2.92 introduced(split_symbol_definition)).
% 19.92/2.92 fof(f12604,plain,(
% 19.92/2.92 ![X0,X1]: (~member(first(ordered_pair(x,universal_class)),X0)|member(ordered_pair(x,universal_class),cross_product(X0,domain_of(X1)))|~member(second(ordered_pair(x,universal_class)),universal_class)|restrict(X1,singleton(second(ordered_pair(x,universal_class))),universal_class)=null_class)),
% 19.92/2.92 inference(resolution,[status(thm)],[f1538,f153])).
% 19.92/2.92 fof(f12605,plain,(
% 19.92/2.92 spl0_625|~spl0_68),
% 19.92/2.92 inference(split_clause,[status(thm)],[f12604,f12601,f1205])).
% 19.92/2.92 fof(f12761,plain,(
% 19.92/2.92 spl0_634 <=> member(not_subclass_element(universal_class,complement(universal_class)),X0)|~member(X1,X2)|member(ordered_pair(X1,not_subclass_element(universal_class,complement(universal_class))),cross_product(X2,complement(X0)))),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f12764,plain,(
% 19.92/2.93 ![X0,X1,X2]: (member(not_subclass_element(universal_class,complement(universal_class)),X0)|~member(X1,X2)|member(ordered_pair(X1,not_subclass_element(universal_class,complement(universal_class))),cross_product(X2,complement(X0)))|universal_class=complement(universal_class))),
% 19.92/2.93 inference(resolution,[status(thm)],[f986,f5836])).
% 19.92/2.93 fof(f12765,plain,(
% 19.92/2.93 spl0_634|spl0_83),
% 19.92/2.93 inference(split_clause,[status(thm)],[f12764,f12761,f1635])).
% 19.92/2.93 fof(f13530,plain,(
% 19.92/2.93 ![X0,X1]: (member(X0,X1)|not_subclass_element(singleton(X0),X1)=X0|~member(X0,universal_class))),
% 19.92/2.93 inference(resolution,[status(thm)],[f10280,f277])).
% 19.92/2.93 fof(f13552,plain,(
% 19.92/2.93 spl0_651 <=> member(not_subclass_element(universal_class,complement(universal_class)),X0)|not_subclass_element(singleton(not_subclass_element(universal_class,complement(universal_class))),X0)=not_subclass_element(universal_class,complement(universal_class))),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f13555,plain,(
% 19.92/2.93 ![X0]: (member(not_subclass_element(universal_class,complement(universal_class)),X0)|not_subclass_element(singleton(not_subclass_element(universal_class,complement(universal_class))),X0)=not_subclass_element(universal_class,complement(universal_class))|universal_class=complement(universal_class))),
% 19.92/2.93 inference(resolution,[status(thm)],[f13530,f5836])).
% 19.92/2.93 fof(f13556,plain,(
% 19.92/2.93 spl0_651|spl0_83),
% 19.92/2.93 inference(split_clause,[status(thm)],[f13555,f13552,f1635])).
% 19.92/2.93 fof(f13562,plain,(
% 19.92/2.93 ![X0,X1,X2]: (member(X0,X1)|not_subclass_element(singleton(X0),X1)=X0|~member(X0,X2))),
% 19.92/2.93 inference(resolution,[status(thm)],[f13530,f2827])).
% 19.92/2.93 fof(f13600,plain,(
% 19.92/2.93 spl0_653 <=> member(ordered_pair(x,universal_class),X0)|not_subclass_element(singleton(ordered_pair(x,universal_class)),X0)=ordered_pair(x,universal_class)),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f13603,plain,(
% 19.92/2.93 ![X0,X1,X2]: (member(ordered_pair(x,universal_class),X0)|not_subclass_element(singleton(ordered_pair(x,universal_class)),X0)=ordered_pair(x,universal_class)|~member(second(ordered_pair(x,universal_class)),image(X1,image(X2,singleton(first(ordered_pair(x,universal_class))))))|~spl0_117)),
% 19.92/2.93 inference(resolution,[status(thm)],[f13562,f2307])).
% 19.92/2.93 fof(f13604,plain,(
% 19.92/2.93 spl0_653|spl0_616|~spl0_117),
% 19.92/2.93 inference(split_clause,[status(thm)],[f13603,f13600,f12460,f2306])).
% 19.92/2.93 fof(f14122,plain,(
% 19.92/2.93 spl0_680 <=> ~member(null_class,singleton(X0))|not_subclass_element(universal_class,complement(singleton(X0)))=X0),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f14125,plain,(
% 19.92/2.93 ![X0]: (~member(null_class,singleton(X0))|~inductive(universal_class)|not_subclass_element(universal_class,complement(singleton(X0)))=X0)),
% 19.92/2.93 inference(paramodulation,[status(thm)],[f11017,f264])).
% 19.92/2.93 fof(f14126,plain,(
% 19.92/2.93 spl0_680|~spl0_85),
% 19.92/2.93 inference(split_clause,[status(thm)],[f14125,f14122,f1643])).
% 19.92/2.93 fof(f14193,plain,(
% 19.92/2.93 spl0_682 <=> ~member(ordered_pair(x,universal_class),cross_product(X1,complement(universal_class)))),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f14196,plain,(
% 19.92/2.93 ![X0,X1]: (~member(second(ordered_pair(x,universal_class)),X0)|~member(ordered_pair(x,universal_class),cross_product(X1,complement(universal_class))))),
% 19.92/2.93 inference(resolution,[status(thm)],[f2827,f1740])).
% 19.92/2.93 fof(f14197,plain,(
% 19.92/2.93 spl0_205|spl0_682),
% 19.92/2.93 inference(split_clause,[status(thm)],[f14196,f3915,f14193])).
% 19.92/2.93 fof(f14213,plain,(
% 19.92/2.93 spl0_683 <=> ~member(ordered_pair(x,universal_class),cross_product(X0,complement(singleton(second(ordered_pair(x,universal_class))))))),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f14216,plain,(
% 19.92/2.93 ![X0]: (~member(second(ordered_pair(x,universal_class)),universal_class)|~member(ordered_pair(x,universal_class),cross_product(X0,complement(singleton(second(ordered_pair(x,universal_class)))))))),
% 19.92/2.93 inference(resolution,[status(thm)],[f277,f1740])).
% 19.92/2.93 fof(f14217,plain,(
% 19.92/2.93 ~spl0_68|spl0_683),
% 19.92/2.93 inference(split_clause,[status(thm)],[f14216,f1205,f14213])).
% 19.92/2.93 fof(f14240,plain,(
% 19.92/2.93 spl0_684 <=> ~member(ordered_pair(x,universal_class),cross_product(X0,complement(unordered_pair(X1,second(ordered_pair(x,universal_class))))))),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f14243,plain,(
% 19.92/2.93 ![X0,X1]: (~member(second(ordered_pair(x,universal_class)),universal_class)|~member(ordered_pair(x,universal_class),cross_product(X0,complement(unordered_pair(X1,second(ordered_pair(x,universal_class)))))))),
% 19.92/2.93 inference(resolution,[status(thm)],[f127,f1740])).
% 19.92/2.93 fof(f14244,plain,(
% 19.92/2.93 ~spl0_68|spl0_684),
% 19.92/2.93 inference(split_clause,[status(thm)],[f14243,f1205,f14240])).
% 19.92/2.93 fof(f14257,plain,(
% 19.92/2.93 spl0_685 <=> ~member(ordered_pair(x,universal_class),cross_product(X0,complement(unordered_pair(second(ordered_pair(x,universal_class)),X1))))),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f14260,plain,(
% 19.92/2.93 ![X0,X1]: (~member(second(ordered_pair(x,universal_class)),universal_class)|~member(ordered_pair(x,universal_class),cross_product(X0,complement(unordered_pair(second(ordered_pair(x,universal_class)),X1)))))),
% 19.92/2.93 inference(resolution,[status(thm)],[f125,f1740])).
% 19.92/2.93 fof(f14261,plain,(
% 19.92/2.93 ~spl0_68|spl0_685),
% 19.92/2.93 inference(split_clause,[status(thm)],[f14260,f1205,f14257])).
% 19.92/2.93 fof(f14348,plain,(
% 19.92/2.93 spl0_691 <=> singleton(universal_class)=null_class),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f14349,plain,(
% 19.92/2.93 singleton(universal_class)=null_class|~spl0_691),
% 19.92/2.93 inference(component_clause,[status(thm)],[f14348])).
% 19.92/2.93 fof(f14350,plain,(
% 19.92/2.93 ~singleton(universal_class)=null_class|spl0_691),
% 19.92/2.93 inference(component_clause,[status(thm)],[f14348])).
% 19.92/2.93 fof(f14373,plain,(
% 19.92/2.93 spl0_696 <=> ~member(X0,singleton(universal_class))|~member(X0,universal_class)),
% 19.92/2.93 introduced(split_symbol_definition)).
% 19.92/2.93 fof(f14374,plain,(
% 19.92/2.93 ![X0]: (~member(X0,singleton(universal_class))|~member(X0,universal_class)|~spl0_696)),
% 19.92/2.93 inference(component_clause,[status(thm)],[f14373])).
% 19.92/2.93 fof(f14376,plain,(
% 19.92/2.93 ![X0]: (~member(X0,singleton(universal_class))|~member(X0,universal_class)|singleton(universal_class)=null_class|~spl0_155|~spl0_321)),
% 19.92/2.93 inference(paramodulation,[status(thm)],[f5682,f5833])).
% 19.92/2.93 fof(f14377,plain,(
% 19.92/2.93 spl0_696|spl0_691|~spl0_155|~spl0_321),
% 19.92/2.93 inference(split_clause,[status(thm)],[f14376,f14373,f14348,f3228,f5681])).
% 19.92/2.93 fof(f14378,plain,(
% 19.92/2.93 ![X0]: (~member(X0,singleton(universal_class))|~spl0_696)),
% 19.92/2.93 inference(forward_subsumption_resolution,[status(thm)],[f14374,f2827])).
% 19.92/2.93 fof(f14387,plain,(
% 19.92/2.93 ~member(universal_class,universal_class)|member(universal_class,null_class)|~spl0_691),
% 19.92/2.93 inference(paramodulation,[status(thm)],[f14349,f277])).
% 19.92/2.93 fof(f14388,plain,(
% 19.92/2.93 ~spl0_84|spl0_318|~spl0_691),
% 19.92/2.93 inference(split_clause,[status(thm)],[f14387,f1640,f5565,f14348])).
% 19.92/2.93 fof(f14489,plain,(
% 19.92/2.93 ~null_class=null_class|regular(singleton(universal_class))=universal_class|spl0_691),
% 19.92/2.93 inference(paramodulation,[status(thm)],[f11653,f14350])).
% 19.92/2.93 fof(f14490,plain,(
% 19.92/2.93 ~spl0_17|spl0_321|spl0_691),
% 19.92/2.93 inference(split_clause,[status(thm)],[f14489,f579,f5681,f14348])).
% 19.92/2.93 fof(f14505,plain,(
% 19.92/2.93 ~member(universal_class,universal_class)|~spl0_696),
% 19.92/2.93 inference(resolution,[status(thm)],[f14378,f277])).
% 19.92/2.93 fof(f14506,plain,(
% 19.92/2.93 ~spl0_84|~spl0_696),
% 19.92/2.93 inference(split_clause,[status(thm)],[f14505,f1640,f14373])).
% 19.92/2.93 fof(f14513,plain,(
% 19.92/2.93 $false|~spl0_155|~spl0_318),
% 19.92/2.93 inference(forward_subsumption_resolution,[status(thm)],[f5566,f3229])).
% 19.92/2.93 fof(f14514,plain,(
% 19.92/2.93 ~spl0_155|~spl0_318),
% 19.92/2.93 inference(contradiction_clause,[status(thm)],[f14513])).
% 19.92/2.93 fof(f14515,plain,(
% 19.92/2.93 $false),
% 19.92/2.93 inference(sat_refutation,[status(thm)],[f311,f624,f672,f674,f689,f795,f825,f845,f850,f855,f860,f865,f870,f898,f900,f995,f1046,f1080,f1212,f1391,f1573,f1661,f1702,f1723,f1746,f1785,f1864,f1905,f1910,f1979,f1990,f2031,f2040,f2045,f2050,f2055,f2063,f2158,f2427,f2440,f2481,f2506,f2592,f2660,f2796,f2831,f2862,f2900,f3010,f3035,f3234,f3307,f3348,f3353,f3363,f3388,f3393,f3398,f3443,f3739,f3744,f3749,f3818,f3823,f3828,f3833,f3919,f3924,f3929,f3934,f3952,f4010,f4034,f4233,f4349,f4657,f4669,f4691,f4881,f4886,f4891,f4896,f4903,f4977,f5741,f5746,f5751,f5756,f5931,f6012,f6193,f6198,f6203,f6277,f6282,f6377,f6601,f6826,f6832,f6837,f7171,f7532,f7546,f7984,f8272,f8294,f8558,f9259,f9275,f9561,f10227,f10816,f10821,f10915,f11048,f11161,f11778,f11792,f12467,f12605,f12765,f13556,f13604,f14126,f14197,f14217,f14244,f14261,f14377,f14388,f14490,f14506,f14514])).
% 20.64/2.94 % SZS output end CNFRefutation for theBenchmark.p
% 20.64/2.96 % Elapsed time: 2.643939 seconds
% 20.64/2.96 % CPU time: 20.764219 seconds
% 20.64/2.96 % Total memory used: 227.146 MB
% 20.64/2.96 % Net memory used: 217.499 MB
%------------------------------------------------------------------------------