TSTP Solution File: NUM250-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM250-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 : Wed Jul 27 13:07:52 EDT 2022
% Result : Unknown 5.25s 5.38s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM250-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 09:57:35 EDT 2022
% 0.14/0.34 % CPUTime :
% 4.65/5.23 ----- Otter 3.3f, August 2004 -----
% 4.65/5.23 The process was started by sandbox on n012.cluster.edu,
% 4.65/5.23 Wed Jul 27 09:57:35 2022
% 4.65/5.23 The command was "./otter". The process ID is 13979.
% 4.65/5.23
% 4.65/5.23 set(prolog_style_variables).
% 4.65/5.23 set(auto).
% 4.65/5.23 dependent: set(auto1).
% 4.65/5.23 dependent: set(process_input).
% 4.65/5.23 dependent: clear(print_kept).
% 4.65/5.23 dependent: clear(print_new_demod).
% 4.65/5.23 dependent: clear(print_back_demod).
% 4.65/5.23 dependent: clear(print_back_sub).
% 4.65/5.23 dependent: set(control_memory).
% 4.65/5.23 dependent: assign(max_mem, 12000).
% 4.65/5.23 dependent: assign(pick_given_ratio, 4).
% 4.65/5.23 dependent: assign(stats_level, 1).
% 4.65/5.23 dependent: assign(max_seconds, 10800).
% 4.65/5.23 clear(print_given).
% 4.65/5.23
% 4.65/5.23 list(usable).
% 4.65/5.23 0 [] A=A.
% 4.65/5.23 0 [] -subclass(X,Y)| -member(U,X)|member(U,Y).
% 4.65/5.23 0 [] member(not_subclass_element(X,Y),X)|subclass(X,Y).
% 4.65/5.23 0 [] -member(not_subclass_element(X,Y),Y)|subclass(X,Y).
% 4.65/5.23 0 [] subclass(X,universal_class).
% 4.65/5.23 0 [] X!=Y|subclass(X,Y).
% 4.65/5.23 0 [] X!=Y|subclass(Y,X).
% 4.65/5.23 0 [] -subclass(X,Y)| -subclass(Y,X)|X=Y.
% 4.65/5.23 0 [] -member(U,unordered_pair(X,Y))|U=X|U=Y.
% 4.65/5.23 0 [] -member(X,universal_class)|member(X,unordered_pair(X,Y)).
% 4.65/5.23 0 [] -member(Y,universal_class)|member(Y,unordered_pair(X,Y)).
% 4.65/5.23 0 [] member(unordered_pair(X,Y),universal_class).
% 4.65/5.23 0 [] unordered_pair(X,X)=singleton(X).
% 4.65/5.23 0 [] unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))=ordered_pair(X,Y).
% 4.65/5.23 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(U,X).
% 4.65/5.23 0 [] -member(ordered_pair(U,V),cross_product(X,Y))|member(V,Y).
% 4.65/5.23 0 [] -member(U,X)| -member(V,Y)|member(ordered_pair(U,V),cross_product(X,Y)).
% 4.65/5.23 0 [] -member(Z,cross_product(X,Y))|ordered_pair(first(Z),second(Z))=Z.
% 4.65/5.23 0 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 4.65/5.23 0 [] -member(ordered_pair(X,Y),element_relation)|member(X,Y).
% 4.65/5.23 0 [] -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))| -member(X,Y)|member(ordered_pair(X,Y),element_relation).
% 4.65/5.23 0 [] -member(Z,intersection(X,Y))|member(Z,X).
% 4.65/5.23 0 [] -member(Z,intersection(X,Y))|member(Z,Y).
% 4.65/5.23 0 [] -member(Z,X)| -member(Z,Y)|member(Z,intersection(X,Y)).
% 4.65/5.23 0 [] -member(Z,complement(X))| -member(Z,X).
% 4.65/5.23 0 [] -member(Z,universal_class)|member(Z,complement(X))|member(Z,X).
% 4.65/5.23 0 [] complement(intersection(complement(X),complement(Y)))=union(X,Y).
% 4.65/5.23 0 [] intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y))))=symmetric_difference(X,Y).
% 4.65/5.23 0 [] intersection(Xr,cross_product(X,Y))=restrict(Xr,X,Y).
% 4.65/5.23 0 [] intersection(cross_product(X,Y),Xr)=restrict(Xr,X,Y).
% 4.65/5.23 0 [] restrict(X,singleton(Z),universal_class)!=null_class| -member(Z,domain_of(X)).
% 4.65/5.23 0 [] -member(Z,universal_class)|restrict(X,singleton(Z),universal_class)=null_class|member(Z,domain_of(X)).
% 4.65/5.23 0 [] subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 4.65/5.23 0 [] -member(ordered_pair(ordered_pair(U,V),W),rotate(X))|member(ordered_pair(ordered_pair(V,W),U),X).
% 4.65/5.23 0 [] -member(ordered_pair(ordered_pair(V,W),U),X)| -member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class))|member(ordered_pair(ordered_pair(U,V),W),rotate(X)).
% 4.65/5.23 0 [] subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 4.65/5.23 0 [] -member(ordered_pair(ordered_pair(U,V),W),flip(X))|member(ordered_pair(ordered_pair(V,U),W),X).
% 4.65/5.23 0 [] -member(ordered_pair(ordered_pair(V,U),W),X)| -member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class))|member(ordered_pair(ordered_pair(U,V),W),flip(X)).
% 4.65/5.23 0 [] domain_of(flip(cross_product(Y,universal_class)))=inverse(Y).
% 4.65/5.23 0 [] domain_of(inverse(Z))=range_of(Z).
% 4.65/5.23 0 [] first(not_subclass_element(restrict(Z,X,singleton(Y)),null_class))=domain(Z,X,Y).
% 4.65/5.23 0 [] second(not_subclass_element(restrict(Z,singleton(X),Y),null_class))=range(Z,X,Y).
% 4.65/5.23 0 [] range_of(restrict(Xr,X,universal_class))=image(Xr,X).
% 4.65/5.23 0 [] union(X,singleton(X))=successor(X).
% 4.65/5.23 0 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 4.65/5.23 0 [] -member(ordered_pair(X,Y),successor_relation)|successor(X)=Y.
% 4.65/5.23 0 [] successor(X)!=Y| -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))|member(ordered_pair(X,Y),successor_relation).
% 4.65/5.23 0 [] -inductive(X)|member(null_class,X).
% 4.65/5.23 0 [] -inductive(X)|subclass(image(successor_relation,X),X).
% 4.65/5.23 0 [] -member(null_class,X)| -subclass(image(successor_relation,X),X)|inductive(X).
% 4.65/5.23 0 [] inductive(omega).
% 4.65/5.23 0 [] -inductive(Y)|subclass(omega,Y).
% 4.65/5.23 0 [] member(omega,universal_class).
% 4.65/5.23 0 [] domain_of(restrict(element_relation,universal_class,X))=sum_class(X).
% 4.65/5.23 0 [] -member(X,universal_class)|member(sum_class(X),universal_class).
% 4.65/5.23 0 [] complement(image(element_relation,complement(X)))=power_class(X).
% 4.65/5.23 0 [] -member(U,universal_class)|member(power_class(U),universal_class).
% 4.65/5.23 0 [] subclass(compose(Yr,Xr),cross_product(universal_class,universal_class)).
% 4.65/5.23 0 [] -member(ordered_pair(Y,Z),compose(Yr,Xr))|member(Z,image(Yr,image(Xr,singleton(Y)))).
% 4.65/5.23 0 [] -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)).
% 4.65/5.23 0 [] -single_valued_class(X)|subclass(compose(X,inverse(X)),identity_relation).
% 4.65/5.23 0 [] -subclass(compose(X,inverse(X)),identity_relation)|single_valued_class(X).
% 4.65/5.23 0 [] -function(Xf)|subclass(Xf,cross_product(universal_class,universal_class)).
% 4.65/5.23 0 [] -function(Xf)|subclass(compose(Xf,inverse(Xf)),identity_relation).
% 4.65/5.23 0 [] -subclass(Xf,cross_product(universal_class,universal_class))| -subclass(compose(Xf,inverse(Xf)),identity_relation)|function(Xf).
% 4.65/5.23 0 [] -function(Xf)| -member(X,universal_class)|member(image(Xf,X),universal_class).
% 4.65/5.23 0 [] X=null_class|member(regular(X),X).
% 4.65/5.23 0 [] X=null_class|intersection(X,regular(X))=null_class.
% 4.65/5.23 0 [] sum_class(image(Xf,singleton(Y)))=apply(Xf,Y).
% 4.65/5.23 0 [] function(choice).
% 4.65/5.23 0 [] -member(Y,universal_class)|Y=null_class|member(apply(choice,Y),Y).
% 4.65/5.23 0 [] -one_to_one(Xf)|function(Xf).
% 4.65/5.23 0 [] -one_to_one(Xf)|function(inverse(Xf)).
% 4.65/5.23 0 [] -function(inverse(Xf))| -function(Xf)|one_to_one(Xf).
% 4.65/5.23 0 [] intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))))=subset_relation.
% 4.65/5.24 0 [] intersection(inverse(subset_relation),subset_relation)=identity_relation.
% 4.65/5.24 0 [] complement(domain_of(intersection(Xr,identity_relation)))=diagonalise(Xr).
% 4.65/5.24 0 [] intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X)))=cantor(X).
% 4.65/5.24 0 [] -operation(Xf)|function(Xf).
% 4.65/5.24 0 [] -operation(Xf)|cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf)))=domain_of(Xf).
% 4.65/5.24 0 [] -operation(Xf)|subclass(range_of(Xf),domain_of(domain_of(Xf))).
% 4.65/5.24 0 [] -function(Xf)|cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf)))!=domain_of(Xf)| -subclass(range_of(Xf),domain_of(domain_of(Xf)))|operation(Xf).
% 4.65/5.24 0 [] -compatible(Xh,Xf1,Xf2)|function(Xh).
% 4.65/5.24 0 [] -compatible(Xh,Xf1,Xf2)|domain_of(domain_of(Xf1))=domain_of(Xh).
% 4.65/5.24 0 [] -compatible(Xh,Xf1,Xf2)|subclass(range_of(Xh),domain_of(domain_of(Xf2))).
% 4.65/5.24 0 [] -function(Xh)|domain_of(domain_of(Xf1))!=domain_of(Xh)| -subclass(range_of(Xh),domain_of(domain_of(Xf2)))|compatible(Xh,Xf1,Xf2).
% 4.65/5.24 0 [] -homomorphism(Xh,Xf1,Xf2)|operation(Xf1).
% 4.65/5.24 0 [] -homomorphism(Xh,Xf1,Xf2)|operation(Xf2).
% 4.65/5.24 0 [] -homomorphism(Xh,Xf1,Xf2)|compatible(Xh,Xf1,Xf2).
% 4.65/5.24 0 [] -homomorphism(Xh,Xf1,Xf2)| -member(ordered_pair(X,Y),domain_of(Xf1))|apply(Xf2,ordered_pair(apply(Xh,X),apply(Xh,Y)))=apply(Xh,apply(Xf1,ordered_pair(X,Y))).
% 4.65/5.24 0 [] -operation(Xf1)| -operation(Xf2)| -compatible(Xh,Xf1,Xf2)|member(ordered_pair(not_homomorphism1(Xh,Xf1,Xf2),not_homomorphism2(Xh,Xf1,Xf2)),domain_of(Xf1))|homomorphism(Xh,Xf1,Xf2).
% 4.65/5.24 0 [] -operation(Xf1)| -operation(Xf2)| -compatible(Xh,Xf1,Xf2)|apply(Xf2,ordered_pair(apply(Xh,not_homomorphism1(Xh,Xf1,Xf2)),apply(Xh,not_homomorphism2(Xh,Xf1,Xf2))))!=apply(Xh,apply(Xf1,ordered_pair(not_homomorphism1(Xh,Xf1,Xf2),not_homomorphism2(Xh,Xf1,Xf2))))|homomorphism(Xh,Xf1,Xf2).
% 4.65/5.24 0 [] subclass(compose_class(X),cross_product(universal_class,universal_class)).
% 4.65/5.24 0 [] -member(ordered_pair(Y,Z),compose_class(X))|compose(X,Y)=Z.
% 4.65/5.24 0 [] -member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))|compose(X,Y)!=Z|member(ordered_pair(Y,Z),compose_class(X)).
% 4.65/5.24 0 [] subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))).
% 4.65/5.24 0 [] -member(ordered_pair(X,ordered_pair(Y,Z)),composition_function)|compose(X,Y)=Z.
% 4.65/5.24 0 [] -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))|member(ordered_pair(X,ordered_pair(Y,compose(X,Y))),composition_function).
% 4.65/5.24 0 [] subclass(domain_relation,cross_product(universal_class,universal_class)).
% 4.65/5.24 0 [] -member(ordered_pair(X,Y),domain_relation)|domain_of(X)=Y.
% 4.65/5.24 0 [] -member(X,universal_class)|member(ordered_pair(X,domain_of(X)),domain_relation).
% 4.65/5.24 0 [] first(not_subclass_element(compose(X,inverse(X)),identity_relation))=single_valued1(X).
% 4.65/5.24 0 [] second(not_subclass_element(compose(X,inverse(X)),identity_relation))=single_valued2(X).
% 4.65/5.24 0 [] domain(X,image(inverse(X),singleton(single_valued1(X))),single_valued2(X))=single_valued3(X).
% 4.65/5.24 0 [] intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)=singleton_relation.
% 4.65/5.24 0 [] subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))).
% 4.65/5.24 0 [] -member(ordered_pair(X,ordered_pair(Y,Z)),application_function)|member(Y,domain_of(X)).
% 4.65/5.24 0 [] -member(ordered_pair(X,ordered_pair(Y,Z)),application_function)|apply(X,Y)=Z.
% 4.65/5.24 0 [] -member(ordered_pair(X,ordered_pair(Y,Z)),cross_product(universal_class,cross_product(universal_class,universal_class)))| -member(Y,domain_of(X))|member(ordered_pair(X,ordered_pair(Y,apply(X,Y))),application_function).
% 4.65/5.24 0 [] -maps(Xf,X,Y)|function(Xf).
% 4.65/5.24 0 [] -maps(Xf,X,Y)|domain_of(Xf)=X.
% 4.65/5.24 0 [] -maps(Xf,X,Y)|subclass(range_of(Xf),Y).
% 4.65/5.24 0 [] -function(Xf)| -subclass(range_of(Xf),Y)|maps(Xf,domain_of(Xf),Y).
% 4.65/5.24 0 [] union(X,inverse(X))=symmetrization_of(X).
% 4.65/5.24 0 [] -irreflexive(X,Y)|subclass(restrict(X,Y,Y),complement(identity_relation)).
% 4.65/5.24 0 [] -subclass(restrict(X,Y,Y),complement(identity_relation))|irreflexive(X,Y).
% 4.65/5.24 0 [] -connected(X,Y)|subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X))).
% 4.65/5.24 0 [] -subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))|connected(X,Y).
% 4.65/5.24 0 [] -transitive(Xr,Y)|subclass(compose(restrict(Xr,Y,Y),restrict(Xr,Y,Y)),restrict(Xr,Y,Y)).
% 4.65/5.24 0 [] -subclass(compose(restrict(Xr,Y,Y),restrict(Xr,Y,Y)),restrict(Xr,Y,Y))|transitive(Xr,Y).
% 4.65/5.24 0 [] -asymmetric(Xr,Y)|restrict(intersection(Xr,inverse(Xr)),Y,Y)=null_class.
% 4.65/5.24 0 [] restrict(intersection(Xr,inverse(Xr)),Y,Y)!=null_class|asymmetric(Xr,Y).
% 4.65/5.24 0 [] segment(Xr,Y,Z)=domain_of(restrict(Xr,Y,singleton(Z))).
% 4.65/5.24 0 [] -well_ordering(X,Y)|connected(X,Y).
% 4.65/5.24 0 [] -well_ordering(Xr,Y)| -subclass(U,Y)|U=null_class|member(least(Xr,U),U).
% 4.65/5.24 0 [] -well_ordering(Xr,Y)| -subclass(U,Y)| -member(V,U)|member(least(Xr,U),U).
% 4.65/5.24 0 [] -well_ordering(Xr,Y)| -subclass(U,Y)|segment(Xr,U,least(Xr,U))=null_class.
% 4.65/5.24 0 [] -well_ordering(Xr,Y)| -subclass(U,Y)| -member(V,U)| -member(ordered_pair(V,least(Xr,U)),Xr).
% 4.65/5.24 0 [] -connected(Xr,Y)|not_well_ordering(Xr,Y)!=null_class|well_ordering(Xr,Y).
% 4.65/5.24 0 [] -connected(Xr,Y)|subclass(not_well_ordering(Xr,Y),Y)|well_ordering(Xr,Y).
% 4.65/5.24 0 [] -member(V,not_well_ordering(Xr,Y))|segment(Xr,not_well_ordering(Xr,Y),V)!=null_class| -connected(Xr,Y)|well_ordering(Xr,Y).
% 4.65/5.24 0 [] -section(Xr,Y,Z)|subclass(Y,Z).
% 4.65/5.24 0 [] -section(Xr,Y,Z)|subclass(domain_of(restrict(Xr,Z,Y)),Y).
% 4.65/5.24 0 [] -subclass(Y,Z)| -subclass(domain_of(restrict(Xr,Z,Y)),Y)|section(Xr,Y,Z).
% 4.65/5.24 0 [] -member(X,ordinal_numbers)|well_ordering(element_relation,X).
% 4.65/5.24 0 [] -member(X,ordinal_numbers)|subclass(sum_class(X),X).
% 4.65/5.24 0 [] -well_ordering(element_relation,X)| -subclass(sum_class(X),X)| -member(X,universal_class)|member(X,ordinal_numbers).
% 4.65/5.24 0 [] -well_ordering(element_relation,X)| -subclass(sum_class(X),X)|member(X,ordinal_numbers)|X=ordinal_numbers.
% 4.65/5.24 0 [] union(singleton(null_class),image(successor_relation,ordinal_numbers))=kind_1_ordinals.
% 4.65/5.24 0 [] intersection(complement(kind_1_ordinals),ordinal_numbers)=limit_ordinals.
% 4.65/5.24 0 [] subclass(rest_of(X),cross_product(universal_class,universal_class)).
% 4.65/5.24 0 [] -member(ordered_pair(U,V),rest_of(X))|member(U,domain_of(X)).
% 4.65/5.24 0 [] -member(ordered_pair(U,V),rest_of(X))|restrict(X,U,universal_class)=V.
% 4.65/5.24 0 [] -member(U,domain_of(X))|restrict(X,U,universal_class)!=V|member(ordered_pair(U,V),rest_of(X)).
% 4.65/5.24 0 [] subclass(rest_relation,cross_product(universal_class,universal_class)).
% 4.65/5.24 0 [] -member(ordered_pair(X,Y),rest_relation)|rest_of(X)=Y.
% 4.65/5.24 0 [] -member(X,universal_class)|member(ordered_pair(X,rest_of(X)),rest_relation).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))|function(Z).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))|function(X).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))|member(domain_of(X),ordinal_numbers).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))|compose(Z,rest_of(X))=X.
% 4.65/5.24 0 [] -function(Z)| -function(X)| -member(domain_of(X),ordinal_numbers)|compose(Z,rest_of(X))!=X|member(X,recursion_e_quation_functions(Z)).
% 4.65/5.24 0 [] subclass(union_of_range_map,cross_product(universal_class,universal_class)).
% 4.65/5.24 0 [] -member(ordered_pair(X,Y),union_of_range_map)|sum_class(range_of(X))=Y.
% 4.65/5.24 0 [] -member(ordered_pair(X,Y),cross_product(universal_class,universal_class))|sum_class(range_of(X))!=Y|member(ordered_pair(X,Y),union_of_range_map).
% 4.65/5.24 0 [] apply(recursion(X,successor_relation,union_of_range_map),Y)=ordinal_add(X,Y).
% 4.65/5.24 0 [] recursion(null_class,apply(add_relation,X),union_of_range_map)=ordinal_multiply(X,Y).
% 4.65/5.24 0 [] -member(X,omega)|integer_of(X)=X.
% 4.65/5.24 0 [] member(X,omega)|integer_of(X)=null_class.
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))|subclass(domain_of(intersection(complement(Y),X)),ordinal_numbers).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))| -member(ordered_pair(U,V),X)| -member(U,least(element_relation,domain_of(intersection(complement(Y),X))))|member(ordered_pair(U,V),Y).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))| -member(ordered_pair(U,V),Y)| -member(U,least(element_relation,domain_of(intersection(complement(Y),X))))|subclass(X,Y)|member(ordered_pair(U,V),X).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))|subclass(X,Y)|restrict(X,least(element_relation,domain_of(intersection(complement(Y),X))),universal_class)=restrict(Y,least(element_relation,domain_of(intersection(complement(Y),X))),universal_class).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))| -member(domain_of(X),domain_of(Y))|subclass(X,Y)|apply(Y,least(element_relation,domain_of(intersection(complement(Y),X))))=apply(X,least(element_relation,domain_of(intersection(complement(Y),X)))).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))| -member(domain_of(X),domain_of(Y))|subclass(X,Y)|member(ordered_pair(least(element_relation,domain_of(intersection(complement(Y),X))),apply(Y,least(element_relation,domain_of(intersection(complement(Y),X))))),Y).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))| -member(domain_of(X),domain_of(Y))|subclass(X,Y).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))|member(union(X,Y),recursion_e_quation_functions(Z)).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))|function(union(X,Y)).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))| -member(domain_of(X),domain_of(Y))| -member(U,domain_of(X))|restrict(X,U,universal_class)=restrict(Y,U,universal_class).
% 4.65/5.24 0 [] -member(X,recursion_e_quation_functions(Z))| -member(Y,recursion_e_quation_functions(Z))| -member(domain_of(X),domain_of(Y))|subclass(rest_of(X),rest_of(Y)).
% 4.65/5.24 0 [] -member(Z,universal_class)|image(image(composition_function,singleton(Z)),image(rest_relation,recursion_e_quation_functions(Z)))=recursion_e_quation_functions(Z).
% 4.65/5.24 0 [] image(comp(Z),image(rest_relation,recursion_e_quation_functions(Z)))=recursion_e_quation_functions(Z).
% 4.65/5.24 0 [] -function(X)| -function(Y)|domain_of(X)!=ordinal_numbers|domain_of(Y)!=ordinal_numbers|X=Y|restrict(X,least(element_relation,domain_of(intersection(complement(X),Y))),universal_class)=restrict(Y,least(element_relation,domain_of(intersection(complement(X),Y))),universal_class).
% 5.13/5.24 0 [] -function(X)|compose(Z,rest_of(X))!=X|domain_of(X)!=ordinal_numbers|subclass(sum_class(recursion_e_quation_functions(Z)),X)|apply(sum_class(recursion_e_quation_functions(Z)),least(element_relation,domain_of(intersection(complement(X),sum_class(recursion_e_quation_functions(Z))))))=apply(X,least(element_relation,domain_of(intersection(complement(X),sum_class(recursion_e_quation_functions(Z)))))).
% 5.13/5.24 0 [] -function(X)|compose(Z,rest_of(X))!=X|domain_of(X)!=ordinal_numbers| -member(ordered_pair(least(element_relation,domain_of(intersection(complement(X),sum_class(recursion_e_quation_functions(Z))))),apply(sum_class(recursion_e_quation_functions(Z)),least(element_relation,domain_of(intersection(complement(X),sum_class(recursion_e_quation_functions(Z))))))),intersection(complement(X),sum_class(recursion_e_quation_functions(Z))))|subclass(sum_class(recursion_e_quation_functions(Z)),X).
% 5.13/5.24 0 [] -subclass(image(domain_relation,recursion_e_quation_functions(z)),ordinal_numbers).
% 5.13/5.24 end_of_list.
% 5.13/5.24
% 5.13/5.24 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 5.13/5.24
% 5.13/5.24 This ia a non-Horn set with equality. The strategy will be
% 5.13/5.24 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 5.13/5.24 deletion, with positive clauses in sos and nonpositive
% 5.13/5.24 clauses in usable.
% 5.13/5.24
% 5.13/5.24 dependent: set(knuth_bendix).
% 5.13/5.24 dependent: set(anl_eq).
% 5.13/5.24 dependent: set(para_from).
% 5.13/5.24 dependent: set(para_into).
% 5.13/5.24 dependent: clear(para_from_right).
% 5.13/5.24 dependent: clear(para_into_right).
% 5.13/5.24 dependent: set(para_from_vars).
% 5.13/5.24 dependent: set(eq_units_both_ways).
% 5.13/5.24 dependent: set(dynamic_demod_all).
% 5.13/5.24 dependent: set(dynamic_demod).
% 5.13/5.24 dependent: set(order_eq).
% 5.13/5.24 dependent: set(back_demod).
% 5.13/5.24 dependent: set(lrpo).
% 5.13/5.24 dependent: set(hyper_res).
% 5.13/5.24 dependent: set(unit_deletion).
% 5.13/5.24 dependent: set(factor).
% 5.13/5.24
% 5.13/5.24 ------------> process usable:
% 5.13/5.24 ** KEPT (pick-wt=9): 1 [] -subclass(A,B)| -member(C,A)|member(C,B).
% 5.13/5.24 ** KEPT (pick-wt=8): 2 [] -member(not_subclass_element(A,B),B)|subclass(A,B).
% 5.13/5.24 ** KEPT (pick-wt=6): 3 [] A!=B|subclass(A,B).
% 5.13/5.24 ** KEPT (pick-wt=6): 4 [] A!=B|subclass(B,A).
% 5.13/5.24 ** KEPT (pick-wt=9): 5 [] -subclass(A,B)| -subclass(B,A)|A=B.
% 5.13/5.24 ** KEPT (pick-wt=11): 6 [] -member(A,unordered_pair(B,C))|A=B|A=C.
% 5.13/5.24 ** KEPT (pick-wt=8): 7 [] -member(A,universal_class)|member(A,unordered_pair(A,B)).
% 5.13/5.24 ** KEPT (pick-wt=8): 8 [] -member(A,universal_class)|member(A,unordered_pair(B,A)).
% 5.13/5.24 ** KEPT (pick-wt=10): 9 [] -member(ordered_pair(A,B),cross_product(C,D))|member(A,C).
% 5.13/5.24 ** KEPT (pick-wt=10): 10 [] -member(ordered_pair(A,B),cross_product(C,D))|member(B,D).
% 5.13/5.24 ** KEPT (pick-wt=13): 11 [] -member(A,B)| -member(C,D)|member(ordered_pair(A,C),cross_product(B,D)).
% 5.13/5.24 ** KEPT (pick-wt=12): 12 [] -member(A,cross_product(B,C))|ordered_pair(first(A),second(A))=A.
% 5.13/5.24 ** KEPT (pick-wt=8): 13 [] -member(ordered_pair(A,B),element_relation)|member(A,B).
% 5.13/5.24 ** KEPT (pick-wt=15): 14 [] -member(ordered_pair(A,B),cross_product(universal_class,universal_class))| -member(A,B)|member(ordered_pair(A,B),element_relation).
% 5.13/5.24 ** KEPT (pick-wt=8): 15 [] -member(A,intersection(B,C))|member(A,B).
% 5.13/5.24 ** KEPT (pick-wt=8): 16 [] -member(A,intersection(B,C))|member(A,C).
% 5.13/5.24 ** KEPT (pick-wt=11): 17 [] -member(A,B)| -member(A,C)|member(A,intersection(B,C)).
% 5.13/5.24 ** KEPT (pick-wt=7): 18 [] -member(A,complement(B))| -member(A,B).
% 5.13/5.24 ** KEPT (pick-wt=10): 19 [] -member(A,universal_class)|member(A,complement(B))|member(A,B).
% 5.13/5.24 ** KEPT (pick-wt=11): 20 [] restrict(A,singleton(B),universal_class)!=null_class| -member(B,domain_of(A)).
% 5.13/5.24 ** KEPT (pick-wt=14): 21 [] -member(A,universal_class)|restrict(B,singleton(A),universal_class)=null_class|member(A,domain_of(B)).
% 5.13/5.24 ** KEPT (pick-wt=15): 22 [] -member(ordered_pair(ordered_pair(A,B),C),rotate(D))|member(ordered_pair(ordered_pair(B,C),A),D).
% 5.13/5.24 ** KEPT (pick-wt=26): 23 [] -member(ordered_pair(ordered_pair(A,B),C),D)| -member(ordered_pair(ordered_pair(C,A),B),cross_product(cross_product(universal_class,universal_class),universal_class))|member(ordered_pair(ordered_pair(C,A),B),rotate(D)).
% 5.13/5.24 ** KEPT (pick-wt=15): 24 [] -member(ordered_pair(ordered_pair(A,B),C),flip(D))|member(ordered_pair(ordered_pair(B,A),C),D).
% 5.13/5.24 ** KEPT (pick-wt=26): 25 [] -member(ordered_pair(ordered_pair(A,B),C),D)| -member(ordered_pair(ordered_pair(B,A),C),cross_product(cross_product(universal_class,universal_class),universal_class))|member(ordered_pair(ordered_pair(B,A),C),flip(D)).
% 5.13/5.24 ** KEPT (pick-wt=9): 26 [] -member(ordered_pair(A,B),successor_relation)|successor(A)=B.
% 5.13/5.24 ** KEPT (pick-wt=16): 27 [] successor(A)!=B| -member(ordered_pair(A,B),cross_product(universal_class,universal_class))|member(ordered_pair(A,B),successor_relation).
% 5.13/5.24 ** KEPT (pick-wt=5): 28 [] -inductive(A)|member(null_class,A).
% 5.13/5.24 ** KEPT (pick-wt=7): 29 [] -inductive(A)|subclass(image(successor_relation,A),A).
% 5.13/5.24 ** KEPT (pick-wt=10): 30 [] -member(null_class,A)| -subclass(image(successor_relation,A),A)|inductive(A).
% 5.13/5.24 ** KEPT (pick-wt=5): 31 [] -inductive(A)|subclass(omega,A).
% 5.13/5.24 ** KEPT (pick-wt=7): 32 [] -member(A,universal_class)|member(sum_class(A),universal_class).
% 5.13/5.24 ** KEPT (pick-wt=7): 33 [] -member(A,universal_class)|member(power_class(A),universal_class).
% 5.13/5.24 ** KEPT (pick-wt=15): 34 [] -member(ordered_pair(A,B),compose(C,D))|member(B,image(C,image(D,singleton(A)))).
% 5.13/5.24 ** KEPT (pick-wt=22): 35 [] -member(A,image(B,image(C,singleton(D))))| -member(ordered_pair(D,A),cross_product(universal_class,universal_class))|member(ordered_pair(D,A),compose(B,C)).
% 5.13/5.24 ** KEPT (pick-wt=8): 36 [] -single_valued_class(A)|subclass(compose(A,inverse(A)),identity_relation).
% 5.13/5.24 ** KEPT (pick-wt=8): 37 [] -subclass(compose(A,inverse(A)),identity_relation)|single_valued_class(A).
% 5.13/5.24 ** KEPT (pick-wt=7): 38 [] -function(A)|subclass(A,cross_product(universal_class,universal_class)).
% 5.13/5.24 ** KEPT (pick-wt=8): 39 [] -function(A)|subclass(compose(A,inverse(A)),identity_relation).
% 5.13/5.24 ** KEPT (pick-wt=13): 40 [] -subclass(A,cross_product(universal_class,universal_class))| -subclass(compose(A,inverse(A)),identity_relation)|function(A).
% 5.13/5.24 ** KEPT (pick-wt=10): 41 [] -function(A)| -member(B,universal_class)|member(image(A,B),universal_class).
% 5.13/5.24 ** KEPT (pick-wt=11): 42 [] -member(A,universal_class)|A=null_class|member(apply(choice,A),A).
% 5.13/5.24 ** KEPT (pick-wt=4): 43 [] -one_to_one(A)|function(A).
% 5.13/5.24 ** KEPT (pick-wt=5): 44 [] -one_to_one(A)|function(inverse(A)).
% 5.13/5.24 ** KEPT (pick-wt=7): 45 [] -function(inverse(A))| -function(A)|one_to_one(A).
% 5.13/5.24 ** KEPT (pick-wt=4): 46 [] -operation(A)|function(A).
% 5.13/5.24 ** KEPT (pick-wt=12): 47 [] -operation(A)|cross_product(domain_of(domain_of(A)),domain_of(domain_of(A)))=domain_of(A).
% 5.13/5.24 ** KEPT (pick-wt=8): 48 [] -operation(A)|subclass(range_of(A),domain_of(domain_of(A))).
% 5.13/5.24 ** KEPT (pick-wt=20): 49 [] -function(A)|cross_product(domain_of(domain_of(A)),domain_of(domain_of(A)))!=domain_of(A)| -subclass(range_of(A),domain_of(domain_of(A)))|operation(A).
% 5.13/5.24 ** KEPT (pick-wt=6): 50 [] -compatible(A,B,C)|function(A).
% 5.13/5.24 ** KEPT (pick-wt=10): 51 [] -compatible(A,B,C)|domain_of(domain_of(B))=domain_of(A).
% 5.13/5.24 ** KEPT (pick-wt=10): 52 [] -compatible(A,B,C)|subclass(range_of(A),domain_of(domain_of(C))).
% 5.13/5.24 ** KEPT (pick-wt=18): 53 [] -function(A)|domain_of(domain_of(B))!=domain_of(A)| -subclass(range_of(A),domain_of(domain_of(C)))|compatible(A,B,C).
% 5.13/5.24 ** KEPT (pick-wt=6): 54 [] -homomorphism(A,B,C)|operation(B).
% 5.13/5.24 ** KEPT (pick-wt=6): 55 [] -homomorphism(A,B,C)|operation(C).
% 5.13/5.24 ** KEPT (pick-wt=8): 56 [] -homomorphism(A,B,C)|compatible(A,B,C).
% 5.13/5.24 ** KEPT (pick-wt=27): 57 [] -homomorphism(A,B,C)| -member(ordered_pair(D,E),domain_of(B))|apply(C,ordered_pair(apply(A,D),apply(A,E)))=apply(A,apply(B,ordered_pair(D,E))).
% 5.13/5.24 ** KEPT (pick-wt=24): 58 [] -operation(A)| -operation(B)| -compatible(C,A,B)|member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A))|homomorphism(C,A,B).
% 5.13/5.24 ** KEPT (pick-wt=41): 59 [] -operation(A)| -operation(B)| -compatible(C,A,B)|apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B))))!=apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B))))|homomorphism(C,A,B).
% 5.13/5.24 ** KEPT (pick-wt=11): 60 [] -member(ordered_pair(A,B),compose_class(C))|compose(C,A)=B.
% 5.13/5.24 ** KEPT (pick-wt=18): 61 [] -member(ordered_pair(A,B),cross_product(universal_class,universal_class))|compose(C,A)!=B|member(ordered_pair(A,B),compose_class(C)).
% 5.13/5.24 ** KEPT (pick-wt=12): 62 [] -member(ordered_pair(A,ordered_pair(B,C)),composition_function)|compose(A,B)=C.
% 5.13/5.24 ** KEPT (pick-wt=16): 63 [] -member(ordered_pair(A,B),cross_product(universal_class,universal_class))|member(ordered_pair(A,ordered_pair(B,compose(A,B))),composition_function).
% 5.13/5.24 ** KEPT (pick-wt=9): 64 [] -member(ordered_pair(A,B),domain_relation)|domain_of(A)=B.
% 5.13/5.24 ** KEPT (pick-wt=9): 65 [] -member(A,universal_class)|member(ordered_pair(A,domain_of(A)),domain_relation).
% 5.13/5.24 ** KEPT (pick-wt=11): 66 [] -member(ordered_pair(A,ordered_pair(B,C)),application_function)|member(B,domain_of(A)).
% 5.13/5.24 ** KEPT (pick-wt=12): 67 [] -member(ordered_pair(A,ordered_pair(B,C)),application_function)|apply(A,B)=C.
% 5.13/5.24 ** KEPT (pick-wt=24): 68 [] -member(ordered_pair(A,ordered_pair(B,C)),cross_product(universal_class,cross_product(universal_class,universal_class)))| -member(B,domain_of(A))|member(ordered_pair(A,ordered_pair(B,apply(A,B))),application_function).
% 5.13/5.24 ** KEPT (pick-wt=6): 69 [] -maps(A,B,C)|function(A).
% 5.13/5.24 ** KEPT (pick-wt=8): 70 [] -maps(A,B,C)|domain_of(A)=B.
% 5.13/5.24 ** KEPT (pick-wt=8): 71 [] -maps(A,B,C)|subclass(range_of(A),C).
% 5.13/5.24 ** KEPT (pick-wt=11): 72 [] -function(A)| -subclass(range_of(A),B)|maps(A,domain_of(A),B).
% 5.13/5.24 ** KEPT (pick-wt=10): 73 [] -irreflexive(A,B)|subclass(restrict(A,B,B),complement(identity_relation)).
% 5.13/5.24 ** KEPT (pick-wt=10): 74 [] -subclass(restrict(A,B,B),complement(identity_relation))|irreflexive(A,B).
% 5.13/5.24 ** KEPT (pick-wt=11): 75 [] -connected(A,B)|subclass(cross_product(B,B),union(identity_relation,symmetrization_of(A))).
% 5.13/5.24 ** KEPT (pick-wt=11): 76 [] -subclass(cross_product(A,A),union(identity_relation,symmetrization_of(B)))|connected(B,A).
% 5.13/5.24 ** KEPT (pick-wt=17): 77 [] -transitive(A,B)|subclass(compose(restrict(A,B,B),restrict(A,B,B)),restrict(A,B,B)).
% 5.13/5.24 ** KEPT (pick-wt=17): 78 [] -subclass(compose(restrict(A,B,B),restrict(A,B,B)),restrict(A,B,B))|transitive(A,B).
% 5.13/5.24 ** KEPT (pick-wt=12): 79 [] -asymmetric(A,B)|restrict(intersection(A,inverse(A)),B,B)=null_class.
% 5.13/5.24 ** KEPT (pick-wt=12): 80 [] restrict(intersection(A,inverse(A)),B,B)!=null_class|asymmetric(A,B).
% 5.13/5.24 ** KEPT (pick-wt=6): 81 [] -well_ordering(A,B)|connected(A,B).
% 5.13/5.24 ** KEPT (pick-wt=14): 82 [] -well_ordering(A,B)| -subclass(C,B)|C=null_class|member(least(A,C),C).
% 5.13/5.24 ** KEPT (pick-wt=14): 83 [] -well_ordering(A,B)| -subclass(C,B)| -member(D,C)|member(least(A,C),C).
% 5.13/5.24 ** KEPT (pick-wt=14): 84 [] -well_ordering(A,B)| -subclass(C,B)|segment(A,C,least(A,C))=null_class.
% 5.13/5.24 ** KEPT (pick-wt=16): 85 [] -well_ordering(A,B)| -subclass(C,B)| -member(D,C)| -member(ordered_pair(D,least(A,C)),A).
% 5.13/5.24 ** KEPT (pick-wt=11): 86 [] -connected(A,B)|not_well_ordering(A,B)!=null_class|well_ordering(A,B).
% 5.13/5.24 ** KEPT (pick-wt=11): 87 [] -connected(A,B)|subclass(not_well_ordering(A,B),B)|well_ordering(A,B).
% 5.13/5.24 ** KEPT (pick-wt=19): 88 [] -member(A,not_well_ordering(B,C))|segment(B,not_well_ordering(B,C),A)!=null_class| -connected(B,C)|well_ordering(B,C).
% 5.13/5.24 ** KEPT (pick-wt=7): 89 [] -section(A,B,C)|subclass(B,C).
% 5.13/5.24 ** KEPT (pick-wt=11): 90 [] -section(A,B,C)|subclass(domain_of(restrict(A,C,B)),B).
% 5.13/5.24 ** KEPT (pick-wt=14): 91 [] -subclass(A,B)| -subclass(domain_of(restrict(C,B,A)),A)|section(C,A,B).
% 5.13/5.24 ** KEPT (pick-wt=6): 92 [] -member(A,ordinal_numbers)|well_ordering(element_relation,A).
% 5.13/5.24 ** KEPT (pick-wt=7): 93 [] -member(A,ordinal_numbers)|subclass(sum_class(A),A).
% 5.13/5.24 ** KEPT (pick-wt=13): 94 [] -well_ordering(element_relation,A)| -subclass(sum_class(A),A)| -member(A,universal_class)|member(A,ordinal_numbers).
% 5.13/5.24 ** KEPT (pick-wt=13): 95 [] -well_ordering(element_relation,A)| -subclass(sum_class(A),A)|member(A,ordinal_numbers)|A=ordinal_numbers.
% 5.13/5.24 ** KEPT (pick-wt=10): 96 [] -member(ordered_pair(A,B),rest_of(C))|member(A,domain_of(C)).
% 5.13/5.24 ** KEPT (pick-wt=12): 97 [] -member(ordered_pair(A,B),rest_of(C))|restrict(C,A,universal_class)=B.
% 5.13/5.24 ** KEPT (pick-wt=16): 98 [] -member(A,domain_of(B))|restrict(B,A,universal_class)!=C|member(ordered_pair(A,C),rest_of(B)).
% 5.13/5.24 ** KEPT (pick-wt=9): 99 [] -member(ordered_pair(A,B),rest_relation)|rest_of(A)=B.
% 5.13/5.24 ** KEPT (pick-wt=9): 100 [] -member(A,universal_class)|member(ordered_pair(A,rest_of(A)),rest_relation).
% 5.13/5.24 ** KEPT (pick-wt=6): 101 [] -member(A,recursion_e_quation_functions(B))|function(B).
% 5.13/5.24 ** KEPT (pick-wt=6): 102 [] -member(A,recursion_e_quation_functions(B))|function(A).
% 5.13/5.24 ** KEPT (pick-wt=8): 103 [] -member(A,recursion_e_quation_functions(B))|member(domain_of(A),ordinal_numbers).
% 5.13/5.24 ** KEPT (pick-wt=10): 104 [] -member(A,recursion_e_quation_functions(B))|compose(B,rest_of(A))=A.
% 5.13/5.24 ** KEPT (pick-wt=18): 105 [] -function(A)| -function(B)| -member(domain_of(B),ordinal_numbers)|compose(A,rest_of(B))!=B|member(B,recursion_e_quation_functions(A)).
% 5.13/5.24 ** KEPT (pick-wt=10): 106 [] -member(ordered_pair(A,B),union_of_range_map)|sum_class(range_of(A))=B.
% 5.13/5.24 ** KEPT (pick-wt=17): 107 [] -member(ordered_pair(A,B),cross_product(universal_class,universal_class))|sum_class(range_of(A))!=B|member(ordered_pair(A,B),union_of_range_map).
% 5.13/5.24 ** KEPT (pick-wt=7): 108 [] -member(A,omega)|integer_of(A)=A.
% 5.13/5.24 ** KEPT (pick-wt=15): 109 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))|subclass(domain_of(intersection(complement(C),A)),ordinal_numbers).
% 5.13/5.24 ** KEPT (pick-wt=27): 110 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))| -member(ordered_pair(D,E),A)| -member(D,least(element_relation,domain_of(intersection(complement(C),A))))|member(ordered_pair(D,E),C).
% 5.13/5.24 ** KEPT (pick-wt=30): 111 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))| -member(ordered_pair(D,E),C)| -member(D,least(element_relation,domain_of(intersection(complement(C),A))))|subclass(A,C)|member(ordered_pair(D,E),A).
% 5.13/5.24 ** KEPT (pick-wt=32): 112 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))|subclass(A,C)|restrict(A,least(element_relation,domain_of(intersection(complement(C),A))),universal_class)=restrict(C,least(element_relation,domain_of(intersection(complement(C),A))),universal_class).
% 5.13/5.24 ** KEPT (pick-wt=35): 113 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))| -member(domain_of(A),domain_of(C))|subclass(A,C)|apply(C,least(element_relation,domain_of(intersection(complement(C),A))))=apply(A,least(element_relation,domain_of(intersection(complement(C),A)))).
% 5.13/5.24 ** KEPT (pick-wt=35): 114 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))| -member(domain_of(A),domain_of(C))|subclass(A,C)|member(ordered_pair(least(element_relation,domain_of(intersection(complement(C),A))),apply(C,least(element_relation,domain_of(intersection(complement(C),A))))),C).
% 5.13/5.24 ** KEPT (pick-wt=16): 115 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))| -member(domain_of(A),domain_of(C))|subclass(A,C).
% 5.13/5.24 ** KEPT (pick-wt=14): 116 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))|member(union(A,C),recursion_e_quation_functions(B)).
% 5.13/5.24 ** KEPT (pick-wt=12): 117 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))|function(union(A,C)).
% 5.13/5.24 ** KEPT (pick-wt=26): 118 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))| -member(domain_of(A),domain_of(C))| -member(D,domain_of(A))|restrict(A,D,universal_class)=restrict(C,D,universal_class).
% 5.13/5.24 ** KEPT (pick-wt=18): 119 [] -member(A,recursion_e_quation_functions(B))| -member(C,recursion_e_quation_functions(B))| -member(domain_of(A),domain_of(C))|subclass(rest_of(A),rest_of(C)).
% 5.13/5.24 ** KEPT (pick-wt=15): 120 [] -member(A,universal_class)|image(image(composition_function,singleton(A)),image(rest_relation,recursion_e_quation_functions(A)))=recursion_e_quation_functions(A).
% 5.13/5.24 ** KEPT (pick-wt=36): 121 [] -function(A)| -function(B)|domain_of(A)!=ordinal_numbers|domain_of(B)!=ordinal_numbers|A=B|restrict(A,least(element_relation,domain_of(intersection(complement(A),B))),universal_class)=restrict(B,least(element_relation,domain_of(intersection(complement(A),B))),universal_class).
% 5.13/5.24 ** KEPT (pick-wt=42): 122 [] -function(A)|compose(B,rest_of(A))!=A|domain_of(A)!=ordinal_numbers|subclass(sum_class(recursion_e_quation_functions(B)),A)|apply(sum_class(recursion_e_quation_functions(B)),least(element_relation,domain_of(intersection(complement(A),sum_class(recursion_e_quation_functions(B))))))=apply(A,least(element_relation,domain_of(intersection(complement(A),sum_class(recursion_e_quation_functions(B)))))).
% 5.13/5.25 ** KEPT (pick-wt=47): 123 [] -function(A)|compose(B,rest_of(A))!=A|domain_of(A)!=ordinal_numbers| -member(ordered_pair(least(element_relation,domain_of(intersection(complement(A),sum_class(recursion_e_quation_functions(B))))),apply(sum_class(recursion_e_quation_functions(B)),least(element_relation,domain_of(intersection(complement(A),sum_class(recursion_e_quation_functions(B))))))),intersection(complement(A),sum_class(recursion_e_quation_functions(B))))|subclass(sum_class(recursion_e_quation_functions(B)),A).
% 5.13/5.25 ** KEPT (pick-wt=6): 124 [] -subclass(image(domain_relation,recursion_e_quation_functions(z)),ordinal_numbers).
% 5.13/5.25 115 back subsumes 114.
% 5.13/5.25 115 back subsumes 113.
% 5.13/5.25
% 5.13/5.25 ------------> process sos:
% 5.13/5.25 ** KEPT (pick-wt=3): 145 [] A=A.
% 5.13/5.25 ** KEPT (pick-wt=8): 146 [] member(not_subclass_element(A,B),A)|subclass(A,B).
% 5.13/5.25 ** KEPT (pick-wt=3): 147 [] subclass(A,universal_class).
% 5.13/5.25 ** KEPT (pick-wt=5): 148 [] member(unordered_pair(A,B),universal_class).
% 5.13/5.25 ** KEPT (pick-wt=6): 150 [copy,149,flip.1] singleton(A)=unordered_pair(A,A).
% 5.13/5.25 ---> New Demodulator: 151 [new_demod,150] singleton(A)=unordered_pair(A,A).
% 5.13/5.25 ** KEPT (pick-wt=13): 153 [copy,152,demod,151,151] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 5.13/5.25 ---> New Demodulator: 154 [new_demod,153] unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B)))=ordered_pair(A,B).
% 5.13/5.25 ** KEPT (pick-wt=5): 155 [] subclass(element_relation,cross_product(universal_class,universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=10): 156 [] complement(intersection(complement(A),complement(B)))=union(A,B).
% 5.13/5.25 ---> New Demodulator: 157 [new_demod,156] complement(intersection(complement(A),complement(B)))=union(A,B).
% 5.13/5.25 ** KEPT (pick-wt=12): 159 [copy,158,demod,157] intersection(complement(intersection(A,B)),union(A,B))=symmetric_difference(A,B).
% 5.13/5.25 ---> New Demodulator: 160 [new_demod,159] intersection(complement(intersection(A,B)),union(A,B))=symmetric_difference(A,B).
% 5.13/5.25 ** KEPT (pick-wt=10): 161 [] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 5.13/5.25 ---> New Demodulator: 162 [new_demod,161] intersection(A,cross_product(B,C))=restrict(A,B,C).
% 5.13/5.25 ** KEPT (pick-wt=10): 163 [] intersection(cross_product(A,B),C)=restrict(C,A,B).
% 5.13/5.25 ---> New Demodulator: 164 [new_demod,163] intersection(cross_product(A,B),C)=restrict(C,A,B).
% 5.13/5.25 ** KEPT (pick-wt=8): 165 [] subclass(rotate(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=8): 166 [] subclass(flip(A),cross_product(cross_product(universal_class,universal_class),universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=8): 168 [copy,167,flip.1] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 5.13/5.25 ---> New Demodulator: 169 [new_demod,168] inverse(A)=domain_of(flip(cross_product(A,universal_class))).
% 5.13/5.25 ** KEPT (pick-wt=9): 171 [copy,170,demod,169,flip.1] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 5.13/5.25 ---> New Demodulator: 172 [new_demod,171] range_of(A)=domain_of(domain_of(flip(cross_product(A,universal_class)))).
% 5.13/5.25 ** KEPT (pick-wt=14): 174 [copy,173,demod,151] first(not_subclass_element(restrict(A,B,unordered_pair(C,C)),null_class))=domain(A,B,C).
% 5.13/5.25 ---> New Demodulator: 175 [new_demod,174] first(not_subclass_element(restrict(A,B,unordered_pair(C,C)),null_class))=domain(A,B,C).
% 5.13/5.25 ** KEPT (pick-wt=14): 177 [copy,176,demod,151] second(not_subclass_element(restrict(A,unordered_pair(B,B),C),null_class))=range(A,B,C).
% 5.13/5.25 ---> New Demodulator: 178 [new_demod,177] second(not_subclass_element(restrict(A,unordered_pair(B,B),C),null_class))=range(A,B,C).
% 5.13/5.25 ** KEPT (pick-wt=13): 180 [copy,179,demod,172] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 5.13/5.25 ---> New Demodulator: 181 [new_demod,180] domain_of(domain_of(flip(cross_product(restrict(A,B,universal_class),universal_class))))=image(A,B).
% 5.13/5.25 ** KEPT (pick-wt=8): 183 [copy,182,demod,151,flip.1] successor(A)=union(A,unordered_pair(A,A)).
% 5.13/5.25 ---> New Demodulator: 184 [new_demod,183] successor(A)=union(A,unordered_pair(A,A)).
% 5.13/5.25 ** KEPT (pick-wt=5): 185 [] subclass(successor_relation,cross_product(universal_class,universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=2): 186 [] inductive(omega).
% 5.13/5.25 ** KEPT (pick-wt=3): 187 [] member(omega,universal_class).
% 5.13/5.25 ** KEPT (pick-wt=8): 189 [copy,188,flip.1] sum_class(A)=domain_of(restrict(element_relation,universal_class,A)).
% 5.13/5.25 ---> New Demodulator: 190 [new_demod,189] sum_class(A)=domain_of(restrict(element_relation,universal_class,A)).
% 5.13/5.25 ** KEPT (pick-wt=8): 192 [copy,191,flip.1] power_class(A)=complement(image(element_relation,complement(A))).
% 5.13/5.25 ---> New Demodulator: 193 [new_demod,192] power_class(A)=complement(image(element_relation,complement(A))).
% 5.13/5.25 ** KEPT (pick-wt=7): 194 [] subclass(compose(A,B),cross_product(universal_class,universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=7): 195 [] A=null_class|member(regular(A),A).
% 5.13/5.25 ** KEPT (pick-wt=9): 196 [] A=null_class|intersection(A,regular(A))=null_class.
% 5.13/5.25 ** KEPT (pick-wt=13): 198 [copy,197,demod,151,190] domain_of(restrict(element_relation,universal_class,image(A,unordered_pair(B,B))))=apply(A,B).
% 5.13/5.25 ---> New Demodulator: 199 [new_demod,198] domain_of(restrict(element_relation,universal_class,image(A,unordered_pair(B,B))))=apply(A,B).
% 5.13/5.25 ** KEPT (pick-wt=2): 200 [] function(choice).
% 5.13/5.25 ** KEPT (pick-wt=17): 202 [copy,201,demod,169,164,164] restrict(restrict(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),universal_class,universal_class),universal_class,universal_class)=subset_relation.
% 5.13/5.25 ---> New Demodulator: 203 [new_demod,202] restrict(restrict(complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))),universal_class,universal_class),universal_class,universal_class)=subset_relation.
% 5.13/5.25 ** KEPT (pick-wt=9): 205 [copy,204,demod,169] intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)=identity_relation.
% 5.13/5.25 ---> New Demodulator: 206 [new_demod,205] intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)=identity_relation.
% 5.13/5.25 ** KEPT (pick-wt=8): 207 [] complement(domain_of(intersection(A,identity_relation)))=diagonalise(A).
% 5.13/5.25 ---> New Demodulator: 208 [new_demod,207] complement(domain_of(intersection(A,identity_relation)))=diagonalise(A).
% 5.13/5.25 ** KEPT (pick-wt=14): 210 [copy,209,demod,169] intersection(domain_of(A),diagonalise(compose(domain_of(flip(cross_product(element_relation,universal_class))),A)))=cantor(A).
% 5.13/5.25 ---> New Demodulator: 211 [new_demod,210] intersection(domain_of(A),diagonalise(compose(domain_of(flip(cross_product(element_relation,universal_class))),A)))=cantor(A).
% 5.13/5.25 ** KEPT (pick-wt=6): 212 [] subclass(compose_class(A),cross_product(universal_class,universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=7): 213 [] subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))).
% 5.13/5.25 ** KEPT (pick-wt=5): 214 [] subclass(domain_relation,cross_product(universal_class,universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=13): 216 [copy,215,demod,169,flip.1] single_valued1(A)=first(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation)).
% 5.13/5.25 ---> New Demodulator: 217 [new_demod,216] single_valued1(A)=first(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation)).
% 5.13/5.25 ** KEPT (pick-wt=13): 219 [copy,218,demod,169,flip.1] single_valued2(A)=second(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation)).
% 5.13/5.25 ---> New Demodulator: 220 [new_demod,219] single_valued2(A)=second(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation)).
% 5.13/5.25 ** KEPT (pick-wt=42): 222 [copy,221,demod,169,217,151,220,flip.1] single_valued3(A)=domain(A,image(domain_of(flip(cross_product(A,universal_class))),unordered_pair(first(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation)),first(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation)))),second(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation))).
% 5.13/5.25 ---> New Demodulator: 223 [new_demod,222] single_valued3(A)=domain(A,image(domain_of(flip(cross_product(A,universal_class))),unordered_pair(first(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation)),first(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation)))),second(not_subclass_element(compose(A,domain_of(flip(cross_product(A,universal_class)))),identity_relation))).
% 5.13/5.25 ** KEPT (pick-wt=9): 224 [] intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)=singleton_relation.
% 5.13/5.25 ---> New Demodulator: 225 [new_demod,224] intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)=singleton_relation.
% 5.13/5.25 ** KEPT (pick-wt=7): 226 [] subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))).
% 5.13/5.25 ** KEPT (pick-wt=10): 228 [copy,227,demod,169,flip.1] symmetrization_of(A)=union(A,domain_of(flip(cross_product(A,universal_class)))).
% 5.13/5.25 ---> New Demodulator: 229 [new_demod,228] symmetrization_of(A)=union(A,domain_of(flip(cross_product(A,universal_class)))).
% 5.13/5.25 ** KEPT (pick-wt=12): 231 [copy,230,demod,151,flip.1] domain_of(restrict(A,B,unordered_pair(C,C)))=segment(A,B,C).
% 5.13/5.25 ---> New Demodulator: 232 [new_demod,231] domain_of(restrict(A,B,unordered_pair(C,C)))=segment(A,B,C).
% 5.13/5.25 ** KEPT (pick-wt=9): 234 [copy,233,demod,151] union(unordered_pair(null_class,null_class),image(successor_relation,ordinal_numbers))=kind_1_ordinals.
% 5.13/5.25 ---> New Demodulator: 235 [new_demod,234] union(unordered_pair(null_class,null_class),image(successor_relation,ordinal_numbers))=kind_1_ordinals.
% 5.13/5.25 ** KEPT (pick-wt=6): 236 [] intersection(complement(kind_1_ordinals),ordinal_numbers)=limit_ordinals.
% 5.13/5.25 ---> New Demodulator: 237 [new_demod,236] intersection(complement(kind_1_ordinals),ordinal_numbers)=limit_ordinals.
% 5.13/5.25 ** KEPT (pick-wt=6): 238 [] subclass(rest_of(A),cross_product(universal_class,universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=5): 239 [] subclass(rest_relation,cross_product(universal_class,universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=5): 240 [] subclass(union_of_range_map,cross_product(universal_class,universal_class)).
% 5.13/5.25 ** KEPT (pick-wt=10): 242 [copy,241,flip.1] ordinal_add(A,B)=apply(recursion(A,successor_relation,union_of_range_map),B).
% 5.13/5.25 ---> New Demodulator: 243 [new_demod,242] ordinal_add(A,B)=apply(recursion(A,successor_relation,union_of_range_map),B).
% 5.13/5.25 ** KEPT (pick-wt=10): 245 [copy,244,flip.1] ordinal_multiply(A,B)=recursion(null_class,apply(add_relation,A),union_of_range_map).
% 5.13/5.25 ---> New Demodulator: 246 [new_demod,245] ordinal_multiply(A,B)=recursion(null_class,apply(add_relation,A),union_of_range_map).
% 5.13/5.25 ** KEPT (pick-wt=7): 247 [] member(A,omega)|integer_of(A)=null_class.
% 5.13/5.25 ** KEPT (pick-wt=10): 248 [] image(comp(A),image(rest_relation,recursion_e_quation_functions(A)))=recursion_e_quation_functions(A).
% 5.13/5.25 ---> New Demodulator: 249 [new_demod,248] image(comp(A),image(rest_relation,recursion_e_quation_functions(A)))=recursion_e_quation_functions(A).
% 5.13/5.25 Following clause subsumed by 145 during input processing: 0 [copy,145,flip.1] A=A.
% 5.13/5.25 145 back subsumes 144.
% 5.13/5.25 145 back subsumes 142.
% 5.13/5.25 145 back subsumes 141.
% 5.13/5.25 145 back subsumes 137.
% 5.13/5.25 145 back subsumes 125.
% 5.13/5.25 >>>> Starting back demodulation with 151.
% 5.13/5.25 >> back demodulating 120 with 151.
% 5.13/5.25 >> back demodulating 35 with 151.
% 5.13/5.25 >> back demodulating 34 with 151.
% 5.13/5.25 >> back demodulating 21 with 151.
% 5.13/5.25 >> back demodulating 20 with 151.
% 5.13/5.25 >>>> Starting back demodulation with 154.
% 5.13/5.25 >>>> Starting back demodulation with 157.
% 5.13/5.25 >>>> Starting back demodulation with 160.
% 5.13/5.25 >>>> Starting back demodulation with 162.
% 5.13/5.25 >>>> Starting back demodulation with 164.
% 5.13/5.25 >>>> Starting back demodulation with 169.
% 5.25/5.38 >> back demodulating 80 with 169.
% 5.25/5.38 >> back demodulating 79 with 169.
% 5.25/5.38 >> back demodulating 45 with 169.
% 5.25/5.38 >> back demodulating 44 with 169.
% 5.25/5.38 >> back demodulating 40 with 169.
% 5.25/5.38 >> back demodulating 39 with 169.
% 5.25/5.38 >> back demodulating 37 with 169.
% 5.25/5.38 >> back demodulating 36 with 169.
% 5.25/5.38 >>>> Starting back demodulation with 172.
% 5.25/5.38 >> back demodulating 107 with 172.
% 5.25/5.38 >> back demodulating 106 with 172.
% 5.25/5.38 >> back demodulating 72 with 172.
% 5.25/5.38 >> back demodulating 71 with 172.
% 5.25/5.38 >> back demodulating 53 with 172.
% 5.25/5.38 >> back demodulating 52 with 172.
% 5.25/5.38 >> back demodulating 49 with 172.
% 5.25/5.38 >> back demodulating 48 with 172.
% 5.25/5.38 >>>> Starting back demodulation with 175.
% 5.25/5.38 >>>> Starting back demodulation with 178.
% 5.25/5.38 >>>> Starting back demodulation with 181.
% 5.25/5.38 >>>> Starting back demodulation with 184.
% 5.25/5.38 >> back demodulating 27 with 184.
% 5.25/5.38 >> back demodulating 26 with 184.
% 5.25/5.38 >>>> Starting back demodulation with 190.
% 5.25/5.38 >> back demodulating 123 with 190.
% 5.25/5.38 >> back demodulating 122 with 190.
% 5.25/5.38 >> back demodulating 95 with 190.
% 5.25/5.38 >> back demodulating 94 with 190.
% 5.25/5.38 >> back demodulating 93 with 190.
% 5.25/5.38 >> back demodulating 32 with 190.
% 5.25/5.38 >>>> Starting back demodulation with 193.
% 5.25/5.38 >> back demodulating 33 with 193.
% 5.25/5.38 >>>> Starting back demodulation with 199.
% 5.25/5.38 >>>> Starting back demodulation with 203.
% 5.25/5.38 >>>> Starting back demodulation with 206.
% 5.25/5.38 >>>> Starting back demodulation with 208.
% 5.25/5.38 >>>> Starting back demodulation with 211.
% 5.25/5.38 >>>> Starting back demodulation with 217.
% 5.25/5.38 >>>> Starting back demodulation with 220.
% 5.25/5.38 >>>> Starting back demodulation with 223.
% 5.25/5.38 >>>> Starting back demodulation with 225.
% 5.25/5.38 >>>> Starting back demodulation with 229.
% 5.25/5.38 >> back demodulating 76 with 229.
% 5.25/5.38 >> back demodulating 75 with 229.
% 5.25/5.38 >>>> Starting back demodulation with 232.
% 5.25/5.38 >>>> Starting back demodulation with 235.
% 5.25/5.38 >>>> Starting back demodulation with 237.
% 5.25/5.38 >>>> Starting back demodulation with 243.
% 5.25/5.38 >>>> Starting back demodulation with 246.
% 5.25/5.38 >>>> Starting back demodulation with 249.
% 5.25/5.38
% 5.25/5.38 ======= end of input processing =======
% 5.25/5.38
% 5.25/5.38 =========== start of search ===========
% 5.25/5.38
% 5.25/5.38
% 5.25/5.38 Resetting weight limit to 5.
% 5.25/5.38
% 5.25/5.38
% 5.25/5.38 Resetting weight limit to 5.
% 5.25/5.38
% 5.25/5.38 sos_size=83
% 5.25/5.38
% 5.25/5.38 Search stopped because sos empty.
% 5.25/5.38
% 5.25/5.38
% 5.25/5.38 Search stopped because sos empty.
% 5.25/5.38
% 5.25/5.38 ============ end of search ============
% 5.25/5.38
% 5.25/5.38 -------------- statistics -------------
% 5.25/5.38 clauses given 106
% 5.25/5.38 clauses generated 7941
% 5.25/5.38 clauses kept 250
% 5.25/5.38 clauses forward subsumed 121
% 5.25/5.38 clauses back subsumed 9
% 5.25/5.38 Kbytes malloced 6835
% 5.25/5.38
% 5.25/5.38 ----------- times (seconds) -----------
% 5.25/5.38 user CPU time 0.15 (0 hr, 0 min, 0 sec)
% 5.25/5.38 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 5.25/5.38 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 5.25/5.38
% 5.25/5.38 Process 13979 finished Wed Jul 27 09:57:40 2022
% 5.25/5.38 Otter interrupted
% 5.25/5.38 PROOF NOT FOUND
%------------------------------------------------------------------------------