TSTP Solution File: NUM066-1 by iProverMo---2.5-0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : NUM066-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n004.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 : 600s
% DateTime : Mon Jul 18 10:54:11 EDT 2022
% Result : Unsatisfiable 18.96s 19.16s
% Output : CNFRefutation 18.99s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
cnf(ordinal_multiplication,axiom,
recursion(null_class,apply(add_relation,X),union_of_range_map) = ordinal_multiply(X,Y),
input ).
fof(ordinal_multiplication_0,plain,
! [X,Y] :
( ordinal_multiply(X,Y) = recursion(null_class,apply(add_relation,X),union_of_range_map)
| $false ),
inference(orientation,[status(thm)],[ordinal_multiplication]) ).
cnf(ordinal_addition,axiom,
apply(recursion(X,successor_relation,union_of_range_map),Y) = ordinal_add(X,Y),
input ).
fof(ordinal_addition_0,plain,
! [X,Y] :
( apply(recursion(X,successor_relation,union_of_range_map),Y) = ordinal_add(X,Y)
| $false ),
inference(orientation,[status(thm)],[ordinal_addition]) ).
cnf(union_of_range_map1,axiom,
subclass(union_of_range_map,cross_product(universal_class,universal_class)),
input ).
fof(union_of_range_map1_0,plain,
( subclass(union_of_range_map,cross_product(universal_class,universal_class))
| $false ),
inference(orientation,[status(thm)],[union_of_range_map1]) ).
cnf(rest_relation1,axiom,
subclass(rest_relation,cross_product(universal_class,universal_class)),
input ).
fof(rest_relation1_0,plain,
( subclass(rest_relation,cross_product(universal_class,universal_class))
| $false ),
inference(orientation,[status(thm)],[rest_relation1]) ).
cnf(rest_of1,axiom,
subclass(rest_of(X),cross_product(universal_class,universal_class)),
input ).
fof(rest_of1_0,plain,
! [X] :
( subclass(rest_of(X),cross_product(universal_class,universal_class))
| $false ),
inference(orientation,[status(thm)],[rest_of1]) ).
cnf(limit_ordinals,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
input ).
fof(limit_ordinals_0,plain,
( intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals
| $false ),
inference(orientation,[status(thm)],[limit_ordinals]) ).
cnf(kind_1_ordinals,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
input ).
fof(kind_1_ordinals_0,plain,
( union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals
| $false ),
inference(orientation,[status(thm)],[kind_1_ordinals]) ).
cnf(segment,axiom,
segment(Xr,Y,Z) = domain_of(restrict(Xr,Y,singleton(Z))),
input ).
fof(segment_0,plain,
! [Xr,Y,Z] :
( segment(Xr,Y,Z) = domain_of(restrict(Xr,Y,singleton(Z)))
| $false ),
inference(orientation,[status(thm)],[segment]) ).
cnf(symmetrization,axiom,
union(X,inverse(X)) = symmetrization_of(X),
input ).
fof(symmetrization_0,plain,
! [X] :
( union(X,inverse(X)) = symmetrization_of(X)
| $false ),
inference(orientation,[status(thm)],[symmetrization]) ).
cnf(application_function_defn1,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
input ).
fof(application_function_defn1_0,plain,
( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| $false ),
inference(orientation,[status(thm)],[application_function_defn1]) ).
cnf(compose_can_define_singleton,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
input ).
fof(compose_can_define_singleton_0,plain,
( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
| $false ),
inference(orientation,[status(thm)],[compose_can_define_singleton]) ).
cnf(single_valued_term_defn3,axiom,
domain(X,image(inverse(X),singleton(single_valued1(X))),single_valued2(X)) = single_valued3(X),
input ).
fof(single_valued_term_defn3_0,plain,
! [X] :
( domain(X,image(inverse(X),singleton(single_valued1(X))),single_valued2(X)) = single_valued3(X)
| $false ),
inference(orientation,[status(thm)],[single_valued_term_defn3]) ).
cnf(single_valued_term_defn2,axiom,
second(not_subclass_element(compose(X,inverse(X)),identity_relation)) = single_valued2(X),
input ).
fof(single_valued_term_defn2_0,plain,
! [X] :
( second(not_subclass_element(compose(X,inverse(X)),identity_relation)) = single_valued2(X)
| $false ),
inference(orientation,[status(thm)],[single_valued_term_defn2]) ).
cnf(single_valued_term_defn1,axiom,
first(not_subclass_element(compose(X,inverse(X)),identity_relation)) = single_valued1(X),
input ).
fof(single_valued_term_defn1_0,plain,
! [X] :
( first(not_subclass_element(compose(X,inverse(X)),identity_relation)) = single_valued1(X)
| $false ),
inference(orientation,[status(thm)],[single_valued_term_defn1]) ).
cnf(definition_of_domain_relation1,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
input ).
fof(definition_of_domain_relation1_0,plain,
( subclass(domain_relation,cross_product(universal_class,universal_class))
| $false ),
inference(orientation,[status(thm)],[definition_of_domain_relation1]) ).
cnf(definition_of_composition_function1,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
input ).
fof(definition_of_composition_function1_0,plain,
( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| $false ),
inference(orientation,[status(thm)],[definition_of_composition_function1]) ).
cnf(compose_class_definition1,axiom,
subclass(compose_class(X),cross_product(universal_class,universal_class)),
input ).
fof(compose_class_definition1_0,plain,
! [X] :
( subclass(compose_class(X),cross_product(universal_class,universal_class))
| $false ),
inference(orientation,[status(thm)],[compose_class_definition1]) ).
cnf(cantor_class,axiom,
intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))) = cantor(X),
input ).
fof(cantor_class_0,plain,
! [X] :
( intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))) = cantor(X)
| $false ),
inference(orientation,[status(thm)],[cantor_class]) ).
cnf(diagonalisation,axiom,
complement(domain_of(intersection(Xr,identity_relation))) = diagonalise(Xr),
input ).
fof(diagonalisation_0,plain,
! [Xr] :
( complement(domain_of(intersection(Xr,identity_relation))) = diagonalise(Xr)
| $false ),
inference(orientation,[status(thm)],[diagonalisation]) ).
cnf(identity_relation,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
input ).
fof(identity_relation_0,plain,
( intersection(inverse(subset_relation),subset_relation) = identity_relation
| $false ),
inference(orientation,[status(thm)],[identity_relation]) ).
cnf(subset_relation,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
input ).
fof(subset_relation_0,plain,
( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation
| $false ),
inference(orientation,[status(thm)],[subset_relation]) ).
cnf(choice1,axiom,
function(choice),
input ).
fof(choice1_0,plain,
( function(choice)
| $false ),
inference(orientation,[status(thm)],[choice1]) ).
cnf(apply,axiom,
sum_class(image(Xf,singleton(Y))) = apply(Xf,Y),
input ).
fof(apply_0,plain,
! [Xf,Y] :
( sum_class(image(Xf,singleton(Y))) = apply(Xf,Y)
| $false ),
inference(orientation,[status(thm)],[apply]) ).
cnf(compose1,axiom,
subclass(compose(Yr,Xr),cross_product(universal_class,universal_class)),
input ).
fof(compose1_0,plain,
! [Xr,Yr] :
( subclass(compose(Yr,Xr),cross_product(universal_class,universal_class))
| $false ),
inference(orientation,[status(thm)],[compose1]) ).
cnf(power_class_definition,axiom,
complement(image(element_relation,complement(X))) = power_class(X),
input ).
fof(power_class_definition_0,plain,
! [X] :
( complement(image(element_relation,complement(X))) = power_class(X)
| $false ),
inference(orientation,[status(thm)],[power_class_definition]) ).
cnf(sum_class_definition,axiom,
domain_of(restrict(element_relation,universal_class,X)) = sum_class(X),
input ).
fof(sum_class_definition_0,plain,
! [X] :
( domain_of(restrict(element_relation,universal_class,X)) = sum_class(X)
| $false ),
inference(orientation,[status(thm)],[sum_class_definition]) ).
cnf(omega_in_universal,axiom,
member(omega,universal_class),
input ).
fof(omega_in_universal_0,plain,
( member(omega,universal_class)
| $false ),
inference(orientation,[status(thm)],[omega_in_universal]) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
input ).
fof(omega_is_inductive1_0,plain,
( inductive(omega)
| $false ),
inference(orientation,[status(thm)],[omega_is_inductive1]) ).
cnf(successor_relation1,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
input ).
fof(successor_relation1_0,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| $false ),
inference(orientation,[status(thm)],[successor_relation1]) ).
cnf(successor,axiom,
union(X,singleton(X)) = successor(X),
input ).
fof(successor_0,plain,
! [X] :
( union(X,singleton(X)) = successor(X)
| $false ),
inference(orientation,[status(thm)],[successor]) ).
cnf(image,axiom,
range_of(restrict(Xr,X,universal_class)) = image(Xr,X),
input ).
fof(image_0,plain,
! [X,Xr] :
( range_of(restrict(Xr,X,universal_class)) = image(Xr,X)
| $false ),
inference(orientation,[status(thm)],[image]) ).
cnf(range,axiom,
second(not_subclass_element(restrict(Z,singleton(X),Y),null_class)) = range(Z,X,Y),
input ).
fof(range_0,plain,
! [X,Y,Z] :
( second(not_subclass_element(restrict(Z,singleton(X),Y),null_class)) = range(Z,X,Y)
| $false ),
inference(orientation,[status(thm)],[range]) ).
cnf(domain,axiom,
first(not_subclass_element(restrict(Z,X,singleton(Y)),null_class)) = domain(Z,X,Y),
input ).
fof(domain_0,plain,
! [X,Y,Z] :
( first(not_subclass_element(restrict(Z,X,singleton(Y)),null_class)) = domain(Z,X,Y)
| $false ),
inference(orientation,[status(thm)],[domain]) ).
cnf(range_of,axiom,
domain_of(inverse(Z)) = range_of(Z),
input ).
fof(range_of_0,plain,
! [Z] :
( domain_of(inverse(Z)) = range_of(Z)
| $false ),
inference(orientation,[status(thm)],[range_of]) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(Y,universal_class))) = inverse(Y),
input ).
fof(inverse_0,plain,
! [Y] :
( domain_of(flip(cross_product(Y,universal_class))) = inverse(Y)
| $false ),
inference(orientation,[status(thm)],[inverse]) ).
cnf(flip1,axiom,
subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)),
input ).
fof(flip1_0,plain,
! [X] :
( subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))
| $false ),
inference(orientation,[status(thm)],[flip1]) ).
cnf(rotate1,axiom,
subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)),
input ).
fof(rotate1_0,plain,
! [X] :
( subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))
| $false ),
inference(orientation,[status(thm)],[rotate1]) ).
cnf(restriction2,axiom,
intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
input ).
fof(restriction2_0,plain,
! [X,Xr,Y] :
( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y)
| $false ),
inference(orientation,[status(thm)],[restriction2]) ).
cnf(restriction1,axiom,
intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
input ).
fof(restriction1_0,plain,
! [X,Xr,Y] :
( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y)
| $false ),
inference(orientation,[status(thm)],[restriction1]) ).
cnf(symmetric_difference,axiom,
intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y)))) = symmetric_difference(X,Y),
input ).
fof(symmetric_difference_0,plain,
! [X,Y] :
( intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y)))) = symmetric_difference(X,Y)
| $false ),
inference(orientation,[status(thm)],[symmetric_difference]) ).
cnf(union,axiom,
complement(intersection(complement(X),complement(Y))) = union(X,Y),
input ).
fof(union_0,plain,
! [X,Y] :
( complement(intersection(complement(X),complement(Y))) = union(X,Y)
| $false ),
inference(orientation,[status(thm)],[union]) ).
cnf(element_relation1,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
input ).
fof(element_relation1_0,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| $false ),
inference(orientation,[status(thm)],[element_relation1]) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
input ).
fof(ordered_pair_0,plain,
! [X,Y] :
( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y)
| $false ),
inference(orientation,[status(thm)],[ordered_pair]) ).
cnf(singleton_set,axiom,
unordered_pair(X,X) = singleton(X),
input ).
fof(singleton_set_0,plain,
! [X] :
( unordered_pair(X,X) = singleton(X)
| $false ),
inference(orientation,[status(thm)],[singleton_set]) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X,Y),universal_class),
input ).
fof(unordered_pairs_in_universal_0,plain,
! [X,Y] :
( member(unordered_pair(X,Y),universal_class)
| $false ),
inference(orientation,[status(thm)],[unordered_pairs_in_universal]) ).
cnf(class_elements_are_sets,axiom,
subclass(X,universal_class),
input ).
fof(class_elements_are_sets_0,plain,
! [X] :
( subclass(X,universal_class)
| $false ),
inference(orientation,[status(thm)],[class_elements_are_sets]) ).
fof(def_lhs_atom1,axiom,
! [X] :
( lhs_atom1(X)
<=> subclass(X,universal_class) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
! [X] :
( lhs_atom1(X)
| $false ),
inference(fold_definition,[status(thm)],[class_elements_are_sets_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
! [Y,X] :
( lhs_atom2(Y,X)
<=> member(unordered_pair(X,Y),universal_class) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
! [X,Y] :
( lhs_atom2(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[unordered_pairs_in_universal_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [X] :
( lhs_atom3(X)
<=> unordered_pair(X,X) = singleton(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [X] :
( lhs_atom3(X)
| $false ),
inference(fold_definition,[status(thm)],[singleton_set_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [Y,X] :
( lhs_atom4(Y,X)
<=> unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [X,Y] :
( lhs_atom4(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[ordered_pair_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
( lhs_atom5
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
( lhs_atom5
| $false ),
inference(fold_definition,[status(thm)],[element_relation1_0,def_lhs_atom5]) ).
fof(def_lhs_atom6,axiom,
! [Y,X] :
( lhs_atom6(Y,X)
<=> complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_5,plain,
! [X,Y] :
( lhs_atom6(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[union_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
! [Y,X] :
( lhs_atom7(Y,X)
<=> intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y)))) = symmetric_difference(X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [X,Y] :
( lhs_atom7(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[symmetric_difference_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
! [Y,Xr,X] :
( lhs_atom8(Y,Xr,X)
<=> intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_7,plain,
! [X,Xr,Y] :
( lhs_atom8(Y,Xr,X)
| $false ),
inference(fold_definition,[status(thm)],[restriction1_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [Y,Xr,X] :
( lhs_atom9(Y,Xr,X)
<=> intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
! [X,Xr,Y] :
( lhs_atom9(Y,Xr,X)
| $false ),
inference(fold_definition,[status(thm)],[restriction2_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
! [X] :
( lhs_atom10(X)
<=> subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
! [X] :
( lhs_atom10(X)
| $false ),
inference(fold_definition,[status(thm)],[rotate1_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
! [X] :
( lhs_atom11(X)
<=> subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [X] :
( lhs_atom11(X)
| $false ),
inference(fold_definition,[status(thm)],[flip1_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
! [Y] :
( lhs_atom12(Y)
<=> domain_of(flip(cross_product(Y,universal_class))) = inverse(Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
! [Y] :
( lhs_atom12(Y)
| $false ),
inference(fold_definition,[status(thm)],[inverse_0,def_lhs_atom12]) ).
fof(def_lhs_atom13,axiom,
! [Z] :
( lhs_atom13(Z)
<=> domain_of(inverse(Z)) = range_of(Z) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
! [Z] :
( lhs_atom13(Z)
| $false ),
inference(fold_definition,[status(thm)],[range_of_0,def_lhs_atom13]) ).
fof(def_lhs_atom14,axiom,
! [Z,Y,X] :
( lhs_atom14(Z,Y,X)
<=> first(not_subclass_element(restrict(Z,X,singleton(Y)),null_class)) = domain(Z,X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
! [X,Y,Z] :
( lhs_atom14(Z,Y,X)
| $false ),
inference(fold_definition,[status(thm)],[domain_0,def_lhs_atom14]) ).
fof(def_lhs_atom15,axiom,
! [Z,Y,X] :
( lhs_atom15(Z,Y,X)
<=> second(not_subclass_element(restrict(Z,singleton(X),Y),null_class)) = range(Z,X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_14,plain,
! [X,Y,Z] :
( lhs_atom15(Z,Y,X)
| $false ),
inference(fold_definition,[status(thm)],[range_0,def_lhs_atom15]) ).
fof(def_lhs_atom16,axiom,
! [Xr,X] :
( lhs_atom16(Xr,X)
<=> range_of(restrict(Xr,X,universal_class)) = image(Xr,X) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
! [X,Xr] :
( lhs_atom16(Xr,X)
| $false ),
inference(fold_definition,[status(thm)],[image_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [X] :
( lhs_atom17(X)
<=> union(X,singleton(X)) = successor(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_16,plain,
! [X] :
( lhs_atom17(X)
| $false ),
inference(fold_definition,[status(thm)],[successor_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
( lhs_atom18
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
( lhs_atom18
| $false ),
inference(fold_definition,[status(thm)],[successor_relation1_0,def_lhs_atom18]) ).
fof(def_lhs_atom19,axiom,
( lhs_atom19
<=> inductive(omega) ),
inference(definition,[],]) ).
fof(to_be_clausified_18,plain,
( lhs_atom19
| $false ),
inference(fold_definition,[status(thm)],[omega_is_inductive1_0,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
( lhs_atom20
<=> member(omega,universal_class) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
( lhs_atom20
| $false ),
inference(fold_definition,[status(thm)],[omega_in_universal_0,def_lhs_atom20]) ).
fof(def_lhs_atom21,axiom,
! [X] :
( lhs_atom21(X)
<=> domain_of(restrict(element_relation,universal_class,X)) = sum_class(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_20,plain,
! [X] :
( lhs_atom21(X)
| $false ),
inference(fold_definition,[status(thm)],[sum_class_definition_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [X] :
( lhs_atom22(X)
<=> complement(image(element_relation,complement(X))) = power_class(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_21,plain,
! [X] :
( lhs_atom22(X)
| $false ),
inference(fold_definition,[status(thm)],[power_class_definition_0,def_lhs_atom22]) ).
fof(def_lhs_atom23,axiom,
! [Yr,Xr] :
( lhs_atom23(Yr,Xr)
<=> subclass(compose(Yr,Xr),cross_product(universal_class,universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_22,plain,
! [Xr,Yr] :
( lhs_atom23(Yr,Xr)
| $false ),
inference(fold_definition,[status(thm)],[compose1_0,def_lhs_atom23]) ).
fof(def_lhs_atom24,axiom,
! [Y,Xf] :
( lhs_atom24(Y,Xf)
<=> sum_class(image(Xf,singleton(Y))) = apply(Xf,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_23,plain,
! [Xf,Y] :
( lhs_atom24(Y,Xf)
| $false ),
inference(fold_definition,[status(thm)],[apply_0,def_lhs_atom24]) ).
fof(def_lhs_atom25,axiom,
( lhs_atom25
<=> function(choice) ),
inference(definition,[],]) ).
fof(to_be_clausified_24,plain,
( lhs_atom25
| $false ),
inference(fold_definition,[status(thm)],[choice1_0,def_lhs_atom25]) ).
fof(def_lhs_atom26,axiom,
( lhs_atom26
<=> intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
( lhs_atom26
| $false ),
inference(fold_definition,[status(thm)],[subset_relation_0,def_lhs_atom26]) ).
fof(def_lhs_atom27,axiom,
( lhs_atom27
<=> intersection(inverse(subset_relation),subset_relation) = identity_relation ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
( lhs_atom27
| $false ),
inference(fold_definition,[status(thm)],[identity_relation_0,def_lhs_atom27]) ).
fof(def_lhs_atom28,axiom,
! [Xr] :
( lhs_atom28(Xr)
<=> complement(domain_of(intersection(Xr,identity_relation))) = diagonalise(Xr) ),
inference(definition,[],]) ).
fof(to_be_clausified_27,plain,
! [Xr] :
( lhs_atom28(Xr)
| $false ),
inference(fold_definition,[status(thm)],[diagonalisation_0,def_lhs_atom28]) ).
fof(def_lhs_atom29,axiom,
! [X] :
( lhs_atom29(X)
<=> intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))) = cantor(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_28,plain,
! [X] :
( lhs_atom29(X)
| $false ),
inference(fold_definition,[status(thm)],[cantor_class_0,def_lhs_atom29]) ).
fof(def_lhs_atom30,axiom,
! [X] :
( lhs_atom30(X)
<=> subclass(compose_class(X),cross_product(universal_class,universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
! [X] :
( lhs_atom30(X)
| $false ),
inference(fold_definition,[status(thm)],[compose_class_definition1_0,def_lhs_atom30]) ).
fof(def_lhs_atom31,axiom,
( lhs_atom31
<=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(definition,[],]) ).
fof(to_be_clausified_30,plain,
( lhs_atom31
| $false ),
inference(fold_definition,[status(thm)],[definition_of_composition_function1_0,def_lhs_atom31]) ).
fof(def_lhs_atom32,axiom,
( lhs_atom32
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
( lhs_atom32
| $false ),
inference(fold_definition,[status(thm)],[definition_of_domain_relation1_0,def_lhs_atom32]) ).
fof(def_lhs_atom33,axiom,
! [X] :
( lhs_atom33(X)
<=> first(not_subclass_element(compose(X,inverse(X)),identity_relation)) = single_valued1(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
! [X] :
( lhs_atom33(X)
| $false ),
inference(fold_definition,[status(thm)],[single_valued_term_defn1_0,def_lhs_atom33]) ).
fof(def_lhs_atom34,axiom,
! [X] :
( lhs_atom34(X)
<=> second(not_subclass_element(compose(X,inverse(X)),identity_relation)) = single_valued2(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_33,plain,
! [X] :
( lhs_atom34(X)
| $false ),
inference(fold_definition,[status(thm)],[single_valued_term_defn2_0,def_lhs_atom34]) ).
fof(def_lhs_atom35,axiom,
! [X] :
( lhs_atom35(X)
<=> domain(X,image(inverse(X),singleton(single_valued1(X))),single_valued2(X)) = single_valued3(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_34,plain,
! [X] :
( lhs_atom35(X)
| $false ),
inference(fold_definition,[status(thm)],[single_valued_term_defn3_0,def_lhs_atom35]) ).
fof(def_lhs_atom36,axiom,
( lhs_atom36
<=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
inference(definition,[],]) ).
fof(to_be_clausified_35,plain,
( lhs_atom36
| $false ),
inference(fold_definition,[status(thm)],[compose_can_define_singleton_0,def_lhs_atom36]) ).
fof(def_lhs_atom37,axiom,
( lhs_atom37
<=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(definition,[],]) ).
fof(to_be_clausified_36,plain,
( lhs_atom37
| $false ),
inference(fold_definition,[status(thm)],[application_function_defn1_0,def_lhs_atom37]) ).
fof(def_lhs_atom38,axiom,
! [X] :
( lhs_atom38(X)
<=> union(X,inverse(X)) = symmetrization_of(X) ),
inference(definition,[],]) ).
fof(to_be_clausified_37,plain,
! [X] :
( lhs_atom38(X)
| $false ),
inference(fold_definition,[status(thm)],[symmetrization_0,def_lhs_atom38]) ).
fof(def_lhs_atom39,axiom,
! [Z,Y,Xr] :
( lhs_atom39(Z,Y,Xr)
<=> segment(Xr,Y,Z) = domain_of(restrict(Xr,Y,singleton(Z))) ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
! [Xr,Y,Z] :
( lhs_atom39(Z,Y,Xr)
| $false ),
inference(fold_definition,[status(thm)],[segment_0,def_lhs_atom39]) ).
fof(def_lhs_atom40,axiom,
( lhs_atom40
<=> union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals ),
inference(definition,[],]) ).
fof(to_be_clausified_39,plain,
( lhs_atom40
| $false ),
inference(fold_definition,[status(thm)],[kind_1_ordinals_0,def_lhs_atom40]) ).
fof(def_lhs_atom41,axiom,
( lhs_atom41
<=> intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals ),
inference(definition,[],]) ).
fof(to_be_clausified_40,plain,
( lhs_atom41
| $false ),
inference(fold_definition,[status(thm)],[limit_ordinals_0,def_lhs_atom41]) ).
fof(def_lhs_atom42,axiom,
! [X] :
( lhs_atom42(X)
<=> subclass(rest_of(X),cross_product(universal_class,universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_41,plain,
! [X] :
( lhs_atom42(X)
| $false ),
inference(fold_definition,[status(thm)],[rest_of1_0,def_lhs_atom42]) ).
fof(def_lhs_atom43,axiom,
( lhs_atom43
<=> subclass(rest_relation,cross_product(universal_class,universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_42,plain,
( lhs_atom43
| $false ),
inference(fold_definition,[status(thm)],[rest_relation1_0,def_lhs_atom43]) ).
fof(def_lhs_atom44,axiom,
( lhs_atom44
<=> subclass(union_of_range_map,cross_product(universal_class,universal_class)) ),
inference(definition,[],]) ).
fof(to_be_clausified_43,plain,
( lhs_atom44
| $false ),
inference(fold_definition,[status(thm)],[union_of_range_map1_0,def_lhs_atom44]) ).
fof(def_lhs_atom45,axiom,
! [Y,X] :
( lhs_atom45(Y,X)
<=> apply(recursion(X,successor_relation,union_of_range_map),Y) = ordinal_add(X,Y) ),
inference(definition,[],]) ).
fof(to_be_clausified_44,plain,
! [X,Y] :
( lhs_atom45(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[ordinal_addition_0,def_lhs_atom45]) ).
fof(def_lhs_atom46,axiom,
! [Y,X] :
( lhs_atom46(Y,X)
<=> ordinal_multiply(X,Y) = recursion(null_class,apply(add_relation,X),union_of_range_map) ),
inference(definition,[],]) ).
fof(to_be_clausified_45,plain,
! [X,Y] :
( lhs_atom46(Y,X)
| $false ),
inference(fold_definition,[status(thm)],[ordinal_multiplication_0,def_lhs_atom46]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X4,X2,X3] :
( lhs_atom39(X4,X2,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_1,axiom,
! [X4,X2,X1] :
( lhs_atom15(X4,X2,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_2,axiom,
! [X4,X2,X1] :
( lhs_atom14(X4,X2,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_3,axiom,
! [X2,X3,X1] :
( lhs_atom9(X2,X3,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_4,axiom,
! [X2,X3,X1] :
( lhs_atom8(X2,X3,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_5,axiom,
! [X2,X1] :
( lhs_atom46(X2,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_45) ).
fof(c_0_6,axiom,
! [X2,X1] :
( lhs_atom45(X2,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_44) ).
fof(c_0_7,axiom,
! [X2,X6] :
( lhs_atom24(X2,X6)
| ~ $true ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_8,axiom,
! [X5,X3] :
( lhs_atom23(X5,X3)
| ~ $true ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_9,axiom,
! [X3,X1] :
( lhs_atom16(X3,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_10,axiom,
! [X2,X1] :
( lhs_atom7(X2,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_11,axiom,
! [X2,X1] :
( lhs_atom6(X2,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_12,axiom,
! [X2,X1] :
( lhs_atom4(X2,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_13,axiom,
! [X2,X1] :
( lhs_atom2(X2,X1)
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_14,axiom,
! [X1] :
( lhs_atom42(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_15,axiom,
! [X1] :
( lhs_atom38(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_16,axiom,
! [X1] :
( lhs_atom35(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_17,axiom,
! [X1] :
( lhs_atom34(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_18,axiom,
! [X1] :
( lhs_atom33(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_19,axiom,
! [X1] :
( lhs_atom30(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_20,axiom,
! [X1] :
( lhs_atom29(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_21,axiom,
! [X3] :
( lhs_atom28(X3)
| ~ $true ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_22,axiom,
! [X1] :
( lhs_atom22(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_23,axiom,
! [X1] :
( lhs_atom21(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_24,axiom,
! [X1] :
( lhs_atom17(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_25,axiom,
! [X4] :
( lhs_atom13(X4)
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_26,axiom,
! [X2] :
( lhs_atom12(X2)
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_27,axiom,
! [X1] :
( lhs_atom11(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_28,axiom,
! [X1] :
( lhs_atom10(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_29,axiom,
! [X1] :
( lhs_atom3(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_30,axiom,
! [X1] :
( lhs_atom1(X1)
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_31,axiom,
( lhs_atom44
| ~ $true ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_32,axiom,
( lhs_atom43
| ~ $true ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_33,axiom,
( lhs_atom41
| ~ $true ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_34,axiom,
( lhs_atom40
| ~ $true ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_35,axiom,
( lhs_atom37
| ~ $true ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_36,axiom,
( lhs_atom36
| ~ $true ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_37,axiom,
( lhs_atom32
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_38,axiom,
( lhs_atom31
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_39,axiom,
( lhs_atom27
| ~ $true ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_40,axiom,
( lhs_atom26
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_41,axiom,
( lhs_atom25
| ~ $true ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_42,axiom,
( lhs_atom20
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_43,axiom,
( lhs_atom19
| ~ $true ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_44,axiom,
( lhs_atom18
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_45,axiom,
( lhs_atom5
| ~ $true ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_46,plain,
! [X4,X2,X3] : lhs_atom39(X4,X2,X3),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_47,plain,
! [X4,X2,X1] : lhs_atom15(X4,X2,X1),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_48,plain,
! [X4,X2,X1] : lhs_atom14(X4,X2,X1),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_49,plain,
! [X2,X3,X1] : lhs_atom9(X2,X3,X1),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_50,plain,
! [X2,X3,X1] : lhs_atom8(X2,X3,X1),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_51,plain,
! [X2,X1] : lhs_atom46(X2,X1),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_52,plain,
! [X2,X1] : lhs_atom45(X2,X1),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_53,plain,
! [X2,X6] : lhs_atom24(X2,X6),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_54,plain,
! [X5,X3] : lhs_atom23(X5,X3),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_55,plain,
! [X3,X1] : lhs_atom16(X3,X1),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_56,plain,
! [X2,X1] : lhs_atom7(X2,X1),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_57,plain,
! [X2,X1] : lhs_atom6(X2,X1),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_58,plain,
! [X2,X1] : lhs_atom4(X2,X1),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_59,plain,
! [X2,X1] : lhs_atom2(X2,X1),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_60,plain,
! [X1] : lhs_atom42(X1),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_61,plain,
! [X1] : lhs_atom38(X1),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_62,plain,
! [X1] : lhs_atom35(X1),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_63,plain,
! [X1] : lhs_atom34(X1),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_64,plain,
! [X1] : lhs_atom33(X1),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_65,plain,
! [X1] : lhs_atom30(X1),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_66,plain,
! [X1] : lhs_atom29(X1),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_67,plain,
! [X3] : lhs_atom28(X3),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_68,plain,
! [X1] : lhs_atom22(X1),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_69,plain,
! [X1] : lhs_atom21(X1),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_70,plain,
! [X1] : lhs_atom17(X1),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_71,plain,
! [X4] : lhs_atom13(X4),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_72,plain,
! [X2] : lhs_atom12(X2),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_73,plain,
! [X1] : lhs_atom11(X1),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_74,plain,
! [X1] : lhs_atom10(X1),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_75,plain,
! [X1] : lhs_atom3(X1),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_76,plain,
! [X1] : lhs_atom1(X1),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_77,plain,
lhs_atom44,
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_78,plain,
lhs_atom43,
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_79,plain,
lhs_atom41,
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_80,plain,
lhs_atom40,
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_81,plain,
lhs_atom37,
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_82,plain,
lhs_atom36,
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_83,plain,
lhs_atom32,
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_84,plain,
lhs_atom31,
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_85,plain,
lhs_atom27,
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_86,plain,
lhs_atom26,
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_87,plain,
lhs_atom25,
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_88,plain,
lhs_atom20,
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_89,plain,
lhs_atom19,
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_90,plain,
lhs_atom18,
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_91,plain,
lhs_atom5,
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_92,plain,
! [X5,X6,X7] : lhs_atom39(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_46]) ).
fof(c_0_93,plain,
! [X5,X6,X7] : lhs_atom15(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_47]) ).
fof(c_0_94,plain,
! [X5,X6,X7] : lhs_atom14(X5,X6,X7),
inference(variable_rename,[status(thm)],[c_0_48]) ).
fof(c_0_95,plain,
! [X4,X5,X6] : lhs_atom9(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_49]) ).
fof(c_0_96,plain,
! [X4,X5,X6] : lhs_atom8(X4,X5,X6),
inference(variable_rename,[status(thm)],[c_0_50]) ).
fof(c_0_97,plain,
! [X3,X4] : lhs_atom46(X3,X4),
inference(variable_rename,[status(thm)],[c_0_51]) ).
fof(c_0_98,plain,
! [X3,X4] : lhs_atom45(X3,X4),
inference(variable_rename,[status(thm)],[c_0_52]) ).
fof(c_0_99,plain,
! [X7,X8] : lhs_atom24(X7,X8),
inference(variable_rename,[status(thm)],[c_0_53]) ).
fof(c_0_100,plain,
! [X6,X7] : lhs_atom23(X6,X7),
inference(variable_rename,[status(thm)],[c_0_54]) ).
fof(c_0_101,plain,
! [X4,X5] : lhs_atom16(X4,X5),
inference(variable_rename,[status(thm)],[c_0_55]) ).
fof(c_0_102,plain,
! [X3,X4] : lhs_atom7(X3,X4),
inference(variable_rename,[status(thm)],[c_0_56]) ).
fof(c_0_103,plain,
! [X3,X4] : lhs_atom6(X3,X4),
inference(variable_rename,[status(thm)],[c_0_57]) ).
fof(c_0_104,plain,
! [X3,X4] : lhs_atom4(X3,X4),
inference(variable_rename,[status(thm)],[c_0_58]) ).
fof(c_0_105,plain,
! [X3,X4] : lhs_atom2(X3,X4),
inference(variable_rename,[status(thm)],[c_0_59]) ).
fof(c_0_106,plain,
! [X2] : lhs_atom42(X2),
inference(variable_rename,[status(thm)],[c_0_60]) ).
fof(c_0_107,plain,
! [X2] : lhs_atom38(X2),
inference(variable_rename,[status(thm)],[c_0_61]) ).
fof(c_0_108,plain,
! [X2] : lhs_atom35(X2),
inference(variable_rename,[status(thm)],[c_0_62]) ).
fof(c_0_109,plain,
! [X2] : lhs_atom34(X2),
inference(variable_rename,[status(thm)],[c_0_63]) ).
fof(c_0_110,plain,
! [X2] : lhs_atom33(X2),
inference(variable_rename,[status(thm)],[c_0_64]) ).
fof(c_0_111,plain,
! [X2] : lhs_atom30(X2),
inference(variable_rename,[status(thm)],[c_0_65]) ).
fof(c_0_112,plain,
! [X2] : lhs_atom29(X2),
inference(variable_rename,[status(thm)],[c_0_66]) ).
fof(c_0_113,plain,
! [X4] : lhs_atom28(X4),
inference(variable_rename,[status(thm)],[c_0_67]) ).
fof(c_0_114,plain,
! [X2] : lhs_atom22(X2),
inference(variable_rename,[status(thm)],[c_0_68]) ).
fof(c_0_115,plain,
! [X2] : lhs_atom21(X2),
inference(variable_rename,[status(thm)],[c_0_69]) ).
fof(c_0_116,plain,
! [X2] : lhs_atom17(X2),
inference(variable_rename,[status(thm)],[c_0_70]) ).
fof(c_0_117,plain,
! [X5] : lhs_atom13(X5),
inference(variable_rename,[status(thm)],[c_0_71]) ).
fof(c_0_118,plain,
! [X3] : lhs_atom12(X3),
inference(variable_rename,[status(thm)],[c_0_72]) ).
fof(c_0_119,plain,
! [X2] : lhs_atom11(X2),
inference(variable_rename,[status(thm)],[c_0_73]) ).
fof(c_0_120,plain,
! [X2] : lhs_atom10(X2),
inference(variable_rename,[status(thm)],[c_0_74]) ).
fof(c_0_121,plain,
! [X2] : lhs_atom3(X2),
inference(variable_rename,[status(thm)],[c_0_75]) ).
fof(c_0_122,plain,
! [X2] : lhs_atom1(X2),
inference(variable_rename,[status(thm)],[c_0_76]) ).
fof(c_0_123,plain,
lhs_atom44,
c_0_77 ).
fof(c_0_124,plain,
lhs_atom43,
c_0_78 ).
fof(c_0_125,plain,
lhs_atom41,
c_0_79 ).
fof(c_0_126,plain,
lhs_atom40,
c_0_80 ).
fof(c_0_127,plain,
lhs_atom37,
c_0_81 ).
fof(c_0_128,plain,
lhs_atom36,
c_0_82 ).
fof(c_0_129,plain,
lhs_atom32,
c_0_83 ).
fof(c_0_130,plain,
lhs_atom31,
c_0_84 ).
fof(c_0_131,plain,
lhs_atom27,
c_0_85 ).
fof(c_0_132,plain,
lhs_atom26,
c_0_86 ).
fof(c_0_133,plain,
lhs_atom25,
c_0_87 ).
fof(c_0_134,plain,
lhs_atom20,
c_0_88 ).
fof(c_0_135,plain,
lhs_atom19,
c_0_89 ).
fof(c_0_136,plain,
lhs_atom18,
c_0_90 ).
fof(c_0_137,plain,
lhs_atom5,
c_0_91 ).
cnf(c_0_138,plain,
lhs_atom39(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_139,plain,
lhs_atom15(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_140,plain,
lhs_atom14(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_141,plain,
lhs_atom9(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_142,plain,
lhs_atom8(X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_143,plain,
lhs_atom46(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_144,plain,
lhs_atom45(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_145,plain,
lhs_atom24(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_146,plain,
lhs_atom23(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_147,plain,
lhs_atom16(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_148,plain,
lhs_atom7(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_149,plain,
lhs_atom6(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_150,plain,
lhs_atom4(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_151,plain,
lhs_atom2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_152,plain,
lhs_atom42(X1),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_153,plain,
lhs_atom38(X1),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_154,plain,
lhs_atom35(X1),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_155,plain,
lhs_atom34(X1),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_156,plain,
lhs_atom33(X1),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_157,plain,
lhs_atom30(X1),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_158,plain,
lhs_atom29(X1),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_159,plain,
lhs_atom28(X1),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_160,plain,
lhs_atom22(X1),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_161,plain,
lhs_atom21(X1),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_162,plain,
lhs_atom17(X1),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_163,plain,
lhs_atom13(X1),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_164,plain,
lhs_atom12(X1),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_165,plain,
lhs_atom11(X1),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_166,plain,
lhs_atom10(X1),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_167,plain,
lhs_atom3(X1),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_168,plain,
lhs_atom1(X1),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_169,plain,
lhs_atom44,
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_170,plain,
lhs_atom43,
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_171,plain,
lhs_atom41,
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_172,plain,
lhs_atom40,
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_173,plain,
lhs_atom37,
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_174,plain,
lhs_atom36,
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_175,plain,
lhs_atom32,
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_176,plain,
lhs_atom31,
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_177,plain,
lhs_atom27,
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_178,plain,
lhs_atom26,
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_179,plain,
lhs_atom25,
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_180,plain,
lhs_atom20,
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_181,plain,
lhs_atom19,
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_182,plain,
lhs_atom18,
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_183,plain,
lhs_atom5,
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_184,plain,
lhs_atom39(X1,X2,X3),
c_0_138,
[final] ).
cnf(c_0_185,plain,
lhs_atom15(X1,X2,X3),
c_0_139,
[final] ).
cnf(c_0_186,plain,
lhs_atom14(X1,X2,X3),
c_0_140,
[final] ).
cnf(c_0_187,plain,
lhs_atom9(X1,X2,X3),
c_0_141,
[final] ).
cnf(c_0_188,plain,
lhs_atom8(X1,X2,X3),
c_0_142,
[final] ).
cnf(c_0_189,plain,
lhs_atom46(X1,X2),
c_0_143,
[final] ).
cnf(c_0_190,plain,
lhs_atom45(X1,X2),
c_0_144,
[final] ).
cnf(c_0_191,plain,
lhs_atom24(X1,X2),
c_0_145,
[final] ).
cnf(c_0_192,plain,
lhs_atom23(X1,X2),
c_0_146,
[final] ).
cnf(c_0_193,plain,
lhs_atom16(X1,X2),
c_0_147,
[final] ).
cnf(c_0_194,plain,
lhs_atom7(X1,X2),
c_0_148,
[final] ).
cnf(c_0_195,plain,
lhs_atom6(X1,X2),
c_0_149,
[final] ).
cnf(c_0_196,plain,
lhs_atom4(X1,X2),
c_0_150,
[final] ).
cnf(c_0_197,plain,
lhs_atom2(X1,X2),
c_0_151,
[final] ).
cnf(c_0_198,plain,
lhs_atom42(X1),
c_0_152,
[final] ).
cnf(c_0_199,plain,
lhs_atom38(X1),
c_0_153,
[final] ).
cnf(c_0_200,plain,
lhs_atom35(X1),
c_0_154,
[final] ).
cnf(c_0_201,plain,
lhs_atom34(X1),
c_0_155,
[final] ).
cnf(c_0_202,plain,
lhs_atom33(X1),
c_0_156,
[final] ).
cnf(c_0_203,plain,
lhs_atom30(X1),
c_0_157,
[final] ).
cnf(c_0_204,plain,
lhs_atom29(X1),
c_0_158,
[final] ).
cnf(c_0_205,plain,
lhs_atom28(X1),
c_0_159,
[final] ).
cnf(c_0_206,plain,
lhs_atom22(X1),
c_0_160,
[final] ).
cnf(c_0_207,plain,
lhs_atom21(X1),
c_0_161,
[final] ).
cnf(c_0_208,plain,
lhs_atom17(X1),
c_0_162,
[final] ).
cnf(c_0_209,plain,
lhs_atom13(X1),
c_0_163,
[final] ).
cnf(c_0_210,plain,
lhs_atom12(X1),
c_0_164,
[final] ).
cnf(c_0_211,plain,
lhs_atom11(X1),
c_0_165,
[final] ).
cnf(c_0_212,plain,
lhs_atom10(X1),
c_0_166,
[final] ).
cnf(c_0_213,plain,
lhs_atom3(X1),
c_0_167,
[final] ).
cnf(c_0_214,plain,
lhs_atom1(X1),
c_0_168,
[final] ).
cnf(c_0_215,plain,
lhs_atom44,
c_0_169,
[final] ).
cnf(c_0_216,plain,
lhs_atom43,
c_0_170,
[final] ).
cnf(c_0_217,plain,
lhs_atom41,
c_0_171,
[final] ).
cnf(c_0_218,plain,
lhs_atom40,
c_0_172,
[final] ).
cnf(c_0_219,plain,
lhs_atom37,
c_0_173,
[final] ).
cnf(c_0_220,plain,
lhs_atom36,
c_0_174,
[final] ).
cnf(c_0_221,plain,
lhs_atom32,
c_0_175,
[final] ).
cnf(c_0_222,plain,
lhs_atom31,
c_0_176,
[final] ).
cnf(c_0_223,plain,
lhs_atom27,
c_0_177,
[final] ).
cnf(c_0_224,plain,
lhs_atom26,
c_0_178,
[final] ).
cnf(c_0_225,plain,
lhs_atom25,
c_0_179,
[final] ).
cnf(c_0_226,plain,
lhs_atom20,
c_0_180,
[final] ).
cnf(c_0_227,plain,
lhs_atom19,
c_0_181,
[final] ).
cnf(c_0_228,plain,
lhs_atom18,
c_0_182,
[final] ).
cnf(c_0_229,plain,
lhs_atom5,
c_0_183,
[final] ).
% End CNF derivation
cnf(c_0_184_0,axiom,
segment(X3,X2,X1) = domain_of(restrict(X3,X2,singleton(X1))),
inference(unfold_definition,[status(thm)],[c_0_184,def_lhs_atom39]) ).
cnf(c_0_185_0,axiom,
second(not_subclass_element(restrict(X1,singleton(X3),X2),null_class)) = range(X1,X3,X2),
inference(unfold_definition,[status(thm)],[c_0_185,def_lhs_atom15]) ).
cnf(c_0_186_0,axiom,
first(not_subclass_element(restrict(X1,X3,singleton(X2)),null_class)) = domain(X1,X3,X2),
inference(unfold_definition,[status(thm)],[c_0_186,def_lhs_atom14]) ).
cnf(c_0_187_0,axiom,
intersection(cross_product(X3,X1),X2) = restrict(X2,X3,X1),
inference(unfold_definition,[status(thm)],[c_0_187,def_lhs_atom9]) ).
cnf(c_0_188_0,axiom,
intersection(X2,cross_product(X3,X1)) = restrict(X2,X3,X1),
inference(unfold_definition,[status(thm)],[c_0_188,def_lhs_atom8]) ).
cnf(c_0_189_0,axiom,
ordinal_multiply(X2,X1) = recursion(null_class,apply(add_relation,X2),union_of_range_map),
inference(unfold_definition,[status(thm)],[c_0_189,def_lhs_atom46]) ).
cnf(c_0_190_0,axiom,
apply(recursion(X2,successor_relation,union_of_range_map),X1) = ordinal_add(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_190,def_lhs_atom45]) ).
cnf(c_0_191_0,axiom,
sum_class(image(X2,singleton(X1))) = apply(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_191,def_lhs_atom24]) ).
cnf(c_0_192_0,axiom,
subclass(compose(X1,X2),cross_product(universal_class,universal_class)),
inference(unfold_definition,[status(thm)],[c_0_192,def_lhs_atom23]) ).
cnf(c_0_193_0,axiom,
range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
inference(unfold_definition,[status(thm)],[c_0_193,def_lhs_atom16]) ).
cnf(c_0_194_0,axiom,
intersection(complement(intersection(X2,X1)),complement(intersection(complement(X2),complement(X1)))) = symmetric_difference(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_194,def_lhs_atom7]) ).
cnf(c_0_195_0,axiom,
complement(intersection(complement(X2),complement(X1))) = union(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_195,def_lhs_atom6]) ).
cnf(c_0_196_0,axiom,
unordered_pair(singleton(X2),unordered_pair(X2,singleton(X1))) = ordered_pair(X2,X1),
inference(unfold_definition,[status(thm)],[c_0_196,def_lhs_atom4]) ).
cnf(c_0_197_0,axiom,
member(unordered_pair(X2,X1),universal_class),
inference(unfold_definition,[status(thm)],[c_0_197,def_lhs_atom2]) ).
cnf(c_0_198_0,axiom,
subclass(rest_of(X1),cross_product(universal_class,universal_class)),
inference(unfold_definition,[status(thm)],[c_0_198,def_lhs_atom42]) ).
cnf(c_0_199_0,axiom,
union(X1,inverse(X1)) = symmetrization_of(X1),
inference(unfold_definition,[status(thm)],[c_0_199,def_lhs_atom38]) ).
cnf(c_0_200_0,axiom,
domain(X1,image(inverse(X1),singleton(single_valued1(X1))),single_valued2(X1)) = single_valued3(X1),
inference(unfold_definition,[status(thm)],[c_0_200,def_lhs_atom35]) ).
cnf(c_0_201_0,axiom,
second(not_subclass_element(compose(X1,inverse(X1)),identity_relation)) = single_valued2(X1),
inference(unfold_definition,[status(thm)],[c_0_201,def_lhs_atom34]) ).
cnf(c_0_202_0,axiom,
first(not_subclass_element(compose(X1,inverse(X1)),identity_relation)) = single_valued1(X1),
inference(unfold_definition,[status(thm)],[c_0_202,def_lhs_atom33]) ).
cnf(c_0_203_0,axiom,
subclass(compose_class(X1),cross_product(universal_class,universal_class)),
inference(unfold_definition,[status(thm)],[c_0_203,def_lhs_atom30]) ).
cnf(c_0_204_0,axiom,
intersection(domain_of(X1),diagonalise(compose(inverse(element_relation),X1))) = cantor(X1),
inference(unfold_definition,[status(thm)],[c_0_204,def_lhs_atom29]) ).
cnf(c_0_205_0,axiom,
complement(domain_of(intersection(X1,identity_relation))) = diagonalise(X1),
inference(unfold_definition,[status(thm)],[c_0_205,def_lhs_atom28]) ).
cnf(c_0_206_0,axiom,
complement(image(element_relation,complement(X1))) = power_class(X1),
inference(unfold_definition,[status(thm)],[c_0_206,def_lhs_atom22]) ).
cnf(c_0_207_0,axiom,
domain_of(restrict(element_relation,universal_class,X1)) = sum_class(X1),
inference(unfold_definition,[status(thm)],[c_0_207,def_lhs_atom21]) ).
cnf(c_0_208_0,axiom,
union(X1,singleton(X1)) = successor(X1),
inference(unfold_definition,[status(thm)],[c_0_208,def_lhs_atom17]) ).
cnf(c_0_209_0,axiom,
domain_of(inverse(X1)) = range_of(X1),
inference(unfold_definition,[status(thm)],[c_0_209,def_lhs_atom13]) ).
cnf(c_0_210_0,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inference(unfold_definition,[status(thm)],[c_0_210,def_lhs_atom12]) ).
cnf(c_0_211_0,axiom,
subclass(flip(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(unfold_definition,[status(thm)],[c_0_211,def_lhs_atom11]) ).
cnf(c_0_212_0,axiom,
subclass(rotate(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(unfold_definition,[status(thm)],[c_0_212,def_lhs_atom10]) ).
cnf(c_0_213_0,axiom,
unordered_pair(X1,X1) = singleton(X1),
inference(unfold_definition,[status(thm)],[c_0_213,def_lhs_atom3]) ).
cnf(c_0_214_0,axiom,
subclass(X1,universal_class),
inference(unfold_definition,[status(thm)],[c_0_214,def_lhs_atom1]) ).
cnf(c_0_215_0,axiom,
subclass(union_of_range_map,cross_product(universal_class,universal_class)),
inference(unfold_definition,[status(thm)],[c_0_215,def_lhs_atom44]) ).
cnf(c_0_216_0,axiom,
subclass(rest_relation,cross_product(universal_class,universal_class)),
inference(unfold_definition,[status(thm)],[c_0_216,def_lhs_atom43]) ).
cnf(c_0_217_0,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
inference(unfold_definition,[status(thm)],[c_0_217,def_lhs_atom41]) ).
cnf(c_0_218_0,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
inference(unfold_definition,[status(thm)],[c_0_218,def_lhs_atom40]) ).
cnf(c_0_219_0,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
inference(unfold_definition,[status(thm)],[c_0_219,def_lhs_atom37]) ).
cnf(c_0_220_0,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
inference(unfold_definition,[status(thm)],[c_0_220,def_lhs_atom36]) ).
cnf(c_0_221_0,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
inference(unfold_definition,[status(thm)],[c_0_221,def_lhs_atom32]) ).
cnf(c_0_222_0,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
inference(unfold_definition,[status(thm)],[c_0_222,def_lhs_atom31]) ).
cnf(c_0_223_0,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(unfold_definition,[status(thm)],[c_0_223,def_lhs_atom27]) ).
cnf(c_0_224_0,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(unfold_definition,[status(thm)],[c_0_224,def_lhs_atom26]) ).
cnf(c_0_225_0,axiom,
function(choice),
inference(unfold_definition,[status(thm)],[c_0_225,def_lhs_atom25]) ).
cnf(c_0_226_0,axiom,
member(omega,universal_class),
inference(unfold_definition,[status(thm)],[c_0_226,def_lhs_atom20]) ).
cnf(c_0_227_0,axiom,
inductive(omega),
inference(unfold_definition,[status(thm)],[c_0_227,def_lhs_atom19]) ).
cnf(c_0_228_0,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(unfold_definition,[status(thm)],[c_0_228,def_lhs_atom18]) ).
cnf(c_0_229_0,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(unfold_definition,[status(thm)],[c_0_229,def_lhs_atom5]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
! [X8,X9,X10] :
( ~ operation(X10)
| ~ operation(X9)
| ~ compatible(X8,X10,X9)
| apply(X9,ordered_pair(apply(X8,not_homomorphism1(X8,X10,X9)),apply(X8,not_homomorphism2(X8,X10,X9)))) != apply(X8,apply(X10,ordered_pair(not_homomorphism1(X8,X10,X9),not_homomorphism2(X8,X10,X9))))
| homomorphism(X8,X10,X9) ),
file('<stdin>',homomorphism6) ).
fof(c_0_1_002,axiom,
! [X2,X6] :
( ~ subclass(compose(restrict(X6,X2,X2),restrict(X6,X2,X2)),restrict(X6,X2,X2))
| transitive(X6,X2) ),
file('<stdin>',transitive2) ).
fof(c_0_2_003,axiom,
! [X8,X9,X10] :
( ~ operation(X10)
| ~ operation(X9)
| ~ compatible(X8,X10,X9)
| member(ordered_pair(not_homomorphism1(X8,X10,X9),not_homomorphism2(X8,X10,X9)),domain_of(X10))
| homomorphism(X8,X10,X9) ),
file('<stdin>',homomorphism5) ).
fof(c_0_3_004,axiom,
! [X2,X6] :
( ~ transitive(X6,X2)
| subclass(compose(restrict(X6,X2,X2),restrict(X6,X2,X2)),restrict(X6,X2,X2)) ),
file('<stdin>',transitive1) ).
fof(c_0_4_005,axiom,
! [X1,X12,X4,X5] :
( ~ member(ordered_pair(ordered_pair(X4,X12),X5),X1)
| ~ member(ordered_pair(ordered_pair(X5,X4),X12),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X5,X4),X12),rotate(X1)) ),
file('<stdin>',rotate3) ).
fof(c_0_5_006,axiom,
! [X1,X12,X4,X5] :
( ~ member(ordered_pair(ordered_pair(X4,X5),X12),X1)
| ~ member(ordered_pair(ordered_pair(X5,X4),X12),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X5,X4),X12),flip(X1)) ),
file('<stdin>',flip3) ).
fof(c_0_6_007,axiom,
! [X3,X2,X1] :
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(X2,domain_of(X1))
| member(ordered_pair(X1,ordered_pair(X2,apply(X1,X2))),application_function) ),
file('<stdin>',application_function_defn4) ).
fof(c_0_7_008,axiom,
! [X3,X2,X6] :
( ~ subclass(X2,X3)
| ~ subclass(domain_of(restrict(X6,X3,X2)),X2)
| section(X6,X2,X3) ),
file('<stdin>',section3) ).
fof(c_0_8_009,axiom,
! [X2,X8,X9,X10,X1] :
( ~ homomorphism(X8,X10,X9)
| ~ member(ordered_pair(X1,X2),domain_of(X10))
| apply(X9,ordered_pair(apply(X8,X1),apply(X8,X2))) = apply(X8,apply(X10,ordered_pair(X1,X2))) ),
file('<stdin>',homomorphism4) ).
fof(c_0_9_010,axiom,
! [X3,X11,X2,X6] :
( ~ member(X3,image(X11,image(X6,singleton(X2))))
| ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class))
| member(ordered_pair(X2,X3),compose(X11,X6)) ),
file('<stdin>',compose3) ).
fof(c_0_10_011,axiom,
! [X3,X2,X6] :
( ~ section(X6,X2,X3)
| subclass(domain_of(restrict(X6,X3,X2)),X2) ),
file('<stdin>',section2) ).
fof(c_0_11_012,axiom,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,ordered_pair(X2,compose(X1,X2))),composition_function) ),
file('<stdin>',definition_of_composition_function3) ).
fof(c_0_12_013,axiom,
! [X1,X12,X4,X5] :
( ~ member(ordered_pair(ordered_pair(X5,X4),X12),rotate(X1))
| member(ordered_pair(ordered_pair(X4,X12),X5),X1) ),
file('<stdin>',rotate2) ).
fof(c_0_13_014,axiom,
! [X1,X12,X4,X5] :
( ~ member(ordered_pair(ordered_pair(X5,X4),X12),flip(X1))
| member(ordered_pair(ordered_pair(X4,X5),X12),X1) ),
file('<stdin>',flip2) ).
fof(c_0_14_015,axiom,
! [X2,X6,X4] :
( ~ member(X4,not_well_ordering(X6,X2))
| segment(X6,not_well_ordering(X6,X2),X4) != null_class
| ~ connected(X6,X2)
| well_ordering(X6,X2) ),
file('<stdin>',well_ordering8) ).
fof(c_0_15_016,axiom,
! [X3,X11,X2,X6] :
( ~ member(ordered_pair(X2,X3),compose(X11,X6))
| member(X3,image(X11,image(X6,singleton(X2)))) ),
file('<stdin>',compose2) ).
fof(c_0_16_017,axiom,
! [X2,X6,X4,X5] :
( ~ well_ordering(X6,X2)
| ~ subclass(X5,X2)
| ~ member(X4,X5)
| ~ member(ordered_pair(X4,least(X6,X5)),X6) ),
file('<stdin>',well_ordering5) ).
fof(c_0_17_018,axiom,
! [X2,X1] :
( ~ subclass(restrict(X1,X2,X2),complement(identity_relation))
| irreflexive(X1,X2) ),
file('<stdin>',irreflexive2) ).
fof(c_0_18_019,axiom,
! [X3,X2,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class))
| compose(X1,X2) != X3
| member(ordered_pair(X2,X3),compose_class(X1)) ),
file('<stdin>',compose_class_definition3) ).
fof(c_0_19_020,axiom,
! [X1,X4,X5] :
( ~ member(X5,domain_of(X1))
| restrict(X1,X5,universal_class) != X4
| member(ordered_pair(X5,X4),rest_of(X1)) ),
file('<stdin>',rest_of4) ).
fof(c_0_20_021,axiom,
! [X3,X2,X1] :
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),application_function)
| member(X2,domain_of(X1)) ),
file('<stdin>',application_function_defn2) ).
fof(c_0_21_022,axiom,
! [X2,X6] :
( restrict(intersection(X6,inverse(X6)),X2,X2) != null_class
| asymmetric(X6,X2) ),
file('<stdin>',asymmetric2) ).
fof(c_0_22_023,axiom,
! [X7] :
( ~ function(X7)
| cross_product(domain_of(domain_of(X7)),domain_of(domain_of(X7))) != domain_of(X7)
| ~ subclass(range_of(X7),domain_of(domain_of(X7)))
| operation(X7) ),
file('<stdin>',operation4) ).
fof(c_0_23_024,axiom,
! [X3,X2,X1] :
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),composition_function)
| compose(X1,X2) = X3 ),
file('<stdin>',definition_of_composition_function2) ).
fof(c_0_24_025,axiom,
! [X3,X2,X1] :
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),application_function)
| apply(X1,X2) = X3 ),
file('<stdin>',application_function_defn3) ).
fof(c_0_25_026,axiom,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2)
| member(ordered_pair(X1,X2),element_relation) ),
file('<stdin>',element_relation3) ).
fof(c_0_26_027,axiom,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| sum_class(range_of(X1)) != X2
| member(ordered_pair(X1,X2),union_of_range_map) ),
file('<stdin>',union_of_range_map3) ).
fof(c_0_27_028,axiom,
! [X2,X1] :
( ~ irreflexive(X1,X2)
| subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
file('<stdin>',irreflexive1) ).
fof(c_0_28_029,axiom,
! [X8,X9,X10] :
( ~ function(X8)
| domain_of(domain_of(X10)) != domain_of(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X9)))
| compatible(X8,X10,X9) ),
file('<stdin>',compatible4) ).
fof(c_0_29_030,axiom,
! [X2,X1] :
( successor(X1) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),successor_relation) ),
file('<stdin>',successor_relation3) ).
fof(c_0_30_031,axiom,
! [X8,X9,X10] :
( ~ homomorphism(X8,X10,X9)
| compatible(X8,X10,X9) ),
file('<stdin>',homomorphism3) ).
fof(c_0_31_032,axiom,
! [X7] :
( ~ subclass(X7,cross_product(universal_class,universal_class))
| ~ subclass(compose(X7,inverse(X7)),identity_relation)
| function(X7) ),
file('<stdin>',function3) ).
fof(c_0_32_033,axiom,
! [X2,X1] :
( ~ subclass(cross_product(X2,X2),union(identity_relation,symmetrization_of(X1)))
| connected(X1,X2) ),
file('<stdin>',connected2) ).
fof(c_0_33_034,axiom,
! [X1,X4,X5] :
( ~ member(ordered_pair(X5,X4),rest_of(X1))
| restrict(X1,X5,universal_class) = X4 ),
file('<stdin>',rest_of3) ).
fof(c_0_34_035,axiom,
! [X2,X6,X5] :
( ~ well_ordering(X6,X2)
| ~ subclass(X5,X2)
| segment(X6,X5,least(X6,X5)) = null_class ),
file('<stdin>',well_ordering4) ).
fof(c_0_35_036,axiom,
! [X3,X1] :
( restrict(X1,singleton(X3),universal_class) != null_class
| ~ member(X3,domain_of(X1)) ),
file('<stdin>',domain1) ).
fof(c_0_36_037,axiom,
! [X8,X9,X10] :
( ~ compatible(X8,X10,X9)
| subclass(range_of(X8),domain_of(domain_of(X9))) ),
file('<stdin>',compatible3) ).
fof(c_0_37_038,axiom,
! [X2,X1,X4,X5] :
( ~ member(ordered_pair(X5,X4),cross_product(X1,X2))
| member(X5,X1) ),
file('<stdin>',cartesian_product1) ).
fof(c_0_38_039,axiom,
! [X2,X1,X4,X5] :
( ~ member(ordered_pair(X5,X4),cross_product(X1,X2))
| member(X4,X2) ),
file('<stdin>',cartesian_product2) ).
fof(c_0_39_040,axiom,
! [X2,X6] :
( ~ asymmetric(X6,X2)
| restrict(intersection(X6,inverse(X6)),X2,X2) = null_class ),
file('<stdin>',asymmetric1) ).
fof(c_0_40_041,axiom,
! [X2,X1,X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X2)
| member(ordered_pair(X5,X4),cross_product(X1,X2)) ),
file('<stdin>',cartesian_product3) ).
fof(c_0_41_042,axiom,
! [X2,X6,X4,X5] :
( ~ well_ordering(X6,X2)
| ~ subclass(X5,X2)
| ~ member(X4,X5)
| member(least(X6,X5),X5) ),
file('<stdin>',well_ordering3) ).
fof(c_0_42_043,axiom,
! [X2,X7,X1] :
( ~ maps(X7,X1,X2)
| subclass(range_of(X7),X2) ),
file('<stdin>',maps3) ).
fof(c_0_43_044,axiom,
! [X8,X9,X10] :
( ~ compatible(X8,X10,X9)
| domain_of(domain_of(X10)) = domain_of(X8) ),
file('<stdin>',compatible2) ).
fof(c_0_44_045,axiom,
! [X3,X2,X6] :
( ~ section(X6,X2,X3)
| subclass(X2,X3) ),
file('<stdin>',section1) ).
fof(c_0_45_046,axiom,
! [X2,X7] :
( ~ function(X7)
| ~ subclass(range_of(X7),X2)
| maps(X7,domain_of(X7),X2) ),
file('<stdin>',maps4) ).
fof(c_0_46_047,axiom,
! [X3,X1] :
( ~ member(X3,universal_class)
| restrict(X1,singleton(X3),universal_class) = null_class
| member(X3,domain_of(X1)) ),
file('<stdin>',domain2) ).
fof(c_0_47_048,axiom,
! [X3,X1] :
( ~ function(X3)
| ~ function(X1)
| ~ member(domain_of(X1),ordinal_numbers)
| compose(X3,rest_of(X1)) != X1
| member(X1,recursion_equation_functions(X3)) ),
file('<stdin>',recursion_equation_functions5) ).
fof(c_0_48_049,axiom,
! [X2,X1] :
( ~ connected(X1,X2)
| subclass(cross_product(X2,X2),union(identity_relation,symmetrization_of(X1))) ),
file('<stdin>',connected1) ).
fof(c_0_49_050,axiom,
! [X1,X4,X5] :
( ~ member(ordered_pair(X5,X4),rest_of(X1))
| member(X5,domain_of(X1)) ),
file('<stdin>',rest_of2) ).
fof(c_0_50_051,axiom,
! [X2,X7,X1] :
( ~ maps(X7,X1,X2)
| domain_of(X7) = X1 ),
file('<stdin>',maps2) ).
fof(c_0_51_052,axiom,
! [X3,X2,X1] :
( ~ member(X3,cross_product(X1,X2))
| ordered_pair(first(X3),second(X3)) = X3 ),
file('<stdin>',cartesian_product4) ).
fof(c_0_52_053,axiom,
! [X8,X9,X10] :
( ~ compatible(X8,X10,X9)
| function(X8) ),
file('<stdin>',compatible1) ).
fof(c_0_53_054,axiom,
! [X8,X9,X10] :
( ~ homomorphism(X8,X10,X9)
| operation(X10) ),
file('<stdin>',homomorphism1) ).
fof(c_0_54_055,axiom,
! [X8,X9,X10] :
( ~ homomorphism(X8,X10,X9)
| operation(X9) ),
file('<stdin>',homomorphism2) ).
fof(c_0_55_056,axiom,
! [X2,X7,X1] :
( ~ maps(X7,X1,X2)
| function(X7) ),
file('<stdin>',maps1) ).
fof(c_0_56_057,axiom,
! [X3,X2,X1] :
( ~ member(ordered_pair(X2,X3),compose_class(X1))
| compose(X1,X2) = X3 ),
file('<stdin>',compose_class_definition2) ).
fof(c_0_57_058,axiom,
! [X2,X6,X5] :
( ~ well_ordering(X6,X2)
| ~ subclass(X5,X2)
| X5 = null_class
| member(least(X6,X5),X5) ),
file('<stdin>',well_ordering2) ).
fof(c_0_58_059,axiom,
! [X1] :
( ~ well_ordering(element_relation,X1)
| ~ subclass(sum_class(X1),X1)
| ~ member(X1,universal_class)
| member(X1,ordinal_numbers) ),
file('<stdin>',ordinal_numbers3) ).
fof(c_0_59_060,axiom,
! [X3,X2,X1] :
( ~ member(X3,X1)
| ~ member(X3,X2)
| member(X3,intersection(X1,X2)) ),
file('<stdin>',intersection3) ).
fof(c_0_60_061,axiom,
! [X1] :
( ~ subclass(compose(X1,inverse(X1)),identity_relation)
| single_valued_class(X1) ),
file('<stdin>',single_valued_class2) ).
fof(c_0_61_062,axiom,
! [X1] :
( ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1)
| inductive(X1) ),
file('<stdin>',inductive3) ).
fof(c_0_62_063,axiom,
! [X2,X1] :
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
file('<stdin>',not_subclass_members2) ).
fof(c_0_63_064,axiom,
! [X3,X2,X1] :
( ~ member(X3,intersection(X1,X2))
| member(X3,X1) ),
file('<stdin>',intersection1) ).
fof(c_0_64_065,axiom,
! [X3,X2,X1] :
( ~ member(X3,intersection(X1,X2))
| member(X3,X2) ),
file('<stdin>',intersection2) ).
fof(c_0_65_066,axiom,
! [X2,X6] :
( ~ connected(X6,X2)
| subclass(not_well_ordering(X6,X2),X2)
| well_ordering(X6,X2) ),
file('<stdin>',well_ordering7) ).
fof(c_0_66_067,axiom,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),element_relation)
| member(X1,X2) ),
file('<stdin>',element_relation2) ).
fof(c_0_67_068,axiom,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),union_of_range_map)
| sum_class(range_of(X1)) = X2 ),
file('<stdin>',union_of_range_map2) ).
fof(c_0_68_069,axiom,
! [X1] :
( ~ member(X1,universal_class)
| member(ordered_pair(X1,domain_of(X1)),domain_relation) ),
file('<stdin>',definition_of_domain_relation3) ).
fof(c_0_69_070,axiom,
! [X1] :
( ~ member(X1,universal_class)
| member(ordered_pair(X1,rest_of(X1)),rest_relation) ),
file('<stdin>',rest_relation3) ).
fof(c_0_70_071,axiom,
! [X2,X1,X5] :
( ~ member(X5,unordered_pair(X1,X2))
| X5 = X1
| X5 = X2 ),
file('<stdin>',unordered_pair_member) ).
fof(c_0_71_072,axiom,
! [X1] :
( ~ well_ordering(element_relation,X1)
| ~ subclass(sum_class(X1),X1)
| member(X1,ordinal_numbers)
| X1 = ordinal_numbers ),
file('<stdin>',ordinal_numbers4) ).
fof(c_0_72_073,axiom,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),successor_relation)
| successor(X1) = X2 ),
file('<stdin>',successor_relation2) ).
fof(c_0_73_074,axiom,
! [X7,X1] :
( ~ function(X7)
| ~ member(X1,universal_class)
| member(image(X7,X1),universal_class) ),
file('<stdin>',replacement) ).
fof(c_0_74_075,axiom,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),domain_relation)
| domain_of(X1) = X2 ),
file('<stdin>',definition_of_domain_relation2) ).
fof(c_0_75_076,axiom,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),rest_relation)
| rest_of(X1) = X2 ),
file('<stdin>',rest_relation2) ).
fof(c_0_76_077,axiom,
! [X7] :
( ~ operation(X7)
| cross_product(domain_of(domain_of(X7)),domain_of(domain_of(X7))) = domain_of(X7) ),
file('<stdin>',operation2) ).
fof(c_0_77_078,axiom,
! [X2,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
file('<stdin>',unordered_pair2) ).
fof(c_0_78_079,axiom,
! [X2,X1] :
( ~ member(X2,universal_class)
| member(X2,unordered_pair(X1,X2)) ),
file('<stdin>',unordered_pair3) ).
fof(c_0_79_080,axiom,
! [X2,X1,X5] :
( ~ subclass(X1,X2)
| ~ member(X5,X1)
| member(X5,X2) ),
file('<stdin>',subclass_members) ).
fof(c_0_80_081,axiom,
! [X2,X6] :
( ~ connected(X6,X2)
| not_well_ordering(X6,X2) != null_class
| well_ordering(X6,X2) ),
file('<stdin>',well_ordering6) ).
fof(c_0_81_082,axiom,
! [X2] :
( ~ member(X2,universal_class)
| X2 = null_class
| member(apply(choice,X2),X2) ),
file('<stdin>',choice2) ).
fof(c_0_82_083,axiom,
! [X1] :
( ~ single_valued_class(X1)
| subclass(compose(X1,inverse(X1)),identity_relation) ),
file('<stdin>',single_valued_class1) ).
fof(c_0_83_084,axiom,
! [X7] :
( ~ function(X7)
| subclass(compose(X7,inverse(X7)),identity_relation) ),
file('<stdin>',function2) ).
fof(c_0_84_085,axiom,
! [X3,X1] :
( ~ member(X3,universal_class)
| member(X3,complement(X1))
| member(X3,X1) ),
file('<stdin>',complement2) ).
fof(c_0_85_086,axiom,
! [X3,X1] :
( ~ member(X3,complement(X1))
| ~ member(X3,X1) ),
file('<stdin>',complement1) ).
fof(c_0_86_087,axiom,
! [X2,X1] :
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
file('<stdin>',not_subclass_members1) ).
fof(c_0_87_088,axiom,
! [X3,X1] :
( ~ member(X1,recursion_equation_functions(X3))
| compose(X3,rest_of(X1)) = X1 ),
file('<stdin>',recursion_equation_functions4) ).
fof(c_0_88_089,axiom,
! [X3,X1] :
( ~ member(X1,recursion_equation_functions(X3))
| member(domain_of(X1),ordinal_numbers) ),
file('<stdin>',recursion_equation_functions3) ).
fof(c_0_89_090,axiom,
! [X2,X1] :
( ~ subclass(X1,X2)
| ~ subclass(X2,X1)
| X1 = X2 ),
file('<stdin>',subclass_implies_equal) ).
fof(c_0_90_091,axiom,
! [X7] :
( ~ operation(X7)
| subclass(range_of(X7),domain_of(domain_of(X7))) ),
file('<stdin>',operation3) ).
fof(c_0_91_092,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(image(successor_relation,X1),X1) ),
file('<stdin>',inductive2) ).
fof(c_0_92_093,axiom,
! [X7] :
( ~ function(X7)
| subclass(X7,cross_product(universal_class,universal_class)) ),
file('<stdin>',function1) ).
fof(c_0_93_094,axiom,
! [X1] :
( ~ member(X1,ordinal_numbers)
| subclass(sum_class(X1),X1) ),
file('<stdin>',ordinal_numbers2) ).
fof(c_0_94_095,axiom,
! [X1] :
( ~ member(X1,universal_class)
| member(sum_class(X1),universal_class) ),
file('<stdin>',sum_class2) ).
fof(c_0_95_096,axiom,
! [X5] :
( ~ member(X5,universal_class)
| member(power_class(X5),universal_class) ),
file('<stdin>',power_class2) ).
fof(c_0_96_097,axiom,
! [X2,X1] :
( ~ well_ordering(X1,X2)
| connected(X1,X2) ),
file('<stdin>',well_ordering1) ).
fof(c_0_97_098,axiom,
! [X3,X1] :
( ~ member(X1,recursion_equation_functions(X3))
| function(X3) ),
file('<stdin>',recursion_equation_functions1) ).
fof(c_0_98_099,axiom,
! [X3,X1] :
( ~ member(X1,recursion_equation_functions(X3))
| function(X1) ),
file('<stdin>',recursion_equation_functions2) ).
fof(c_0_99_100,axiom,
! [X1] :
( ~ member(X1,ordinal_numbers)
| well_ordering(element_relation,X1) ),
file('<stdin>',ordinal_numbers1) ).
fof(c_0_100_101,axiom,
! [X7] :
( ~ function(inverse(X7))
| ~ function(X7)
| one_to_one(X7) ),
file('<stdin>',one_to_one3) ).
fof(c_0_101_102,axiom,
! [X1] :
( ~ member(X1,omega)
| integer_of(X1) = X1 ),
file('<stdin>',integer_function1) ).
fof(c_0_102_103,axiom,
! [X1] :
( X1 = null_class
| member(regular(X1),X1) ),
file('<stdin>',regularity1) ).
fof(c_0_103_104,axiom,
! [X1] :
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('<stdin>',regularity2) ).
fof(c_0_104_105,axiom,
! [X1] :
( ~ inductive(X1)
| member(null_class,X1) ),
file('<stdin>',inductive1) ).
fof(c_0_105_106,axiom,
! [X2] :
( ~ inductive(X2)
| subclass(omega,X2) ),
file('<stdin>',omega_is_inductive2) ).
fof(c_0_106_107,axiom,
! [X2,X1] :
( X1 != X2
| subclass(X1,X2) ),
file('<stdin>',equal_implies_subclass1) ).
fof(c_0_107_108,axiom,
! [X2,X1] :
( X1 != X2
| subclass(X2,X1) ),
file('<stdin>',equal_implies_subclass2) ).
fof(c_0_108_109,axiom,
! [X7] :
( ~ one_to_one(X7)
| function(inverse(X7)) ),
file('<stdin>',one_to_one2) ).
fof(c_0_109_110,axiom,
! [X1] :
( member(X1,omega)
| integer_of(X1) = null_class ),
file('<stdin>',integer_function2) ).
fof(c_0_110_111,axiom,
! [X7] :
( ~ one_to_one(X7)
| function(X7) ),
file('<stdin>',one_to_one1) ).
fof(c_0_111_112,axiom,
! [X7] :
( ~ operation(X7)
| function(X7) ),
file('<stdin>',operation1) ).
fof(c_0_112_113,plain,
! [X8,X9,X10] :
( ~ operation(X10)
| ~ operation(X9)
| ~ compatible(X8,X10,X9)
| apply(X9,ordered_pair(apply(X8,not_homomorphism1(X8,X10,X9)),apply(X8,not_homomorphism2(X8,X10,X9)))) != apply(X8,apply(X10,ordered_pair(not_homomorphism1(X8,X10,X9),not_homomorphism2(X8,X10,X9))))
| homomorphism(X8,X10,X9) ),
inference(fof_simplification,[status(thm)],[c_0_0]) ).
fof(c_0_113_114,plain,
! [X2,X6] :
( ~ subclass(compose(restrict(X6,X2,X2),restrict(X6,X2,X2)),restrict(X6,X2,X2))
| transitive(X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_114_115,plain,
! [X8,X9,X10] :
( ~ operation(X10)
| ~ operation(X9)
| ~ compatible(X8,X10,X9)
| member(ordered_pair(not_homomorphism1(X8,X10,X9),not_homomorphism2(X8,X10,X9)),domain_of(X10))
| homomorphism(X8,X10,X9) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
fof(c_0_115_116,plain,
! [X2,X6] :
( ~ transitive(X6,X2)
| subclass(compose(restrict(X6,X2,X2),restrict(X6,X2,X2)),restrict(X6,X2,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_116_117,plain,
! [X1,X12,X4,X5] :
( ~ member(ordered_pair(ordered_pair(X4,X12),X5),X1)
| ~ member(ordered_pair(ordered_pair(X5,X4),X12),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X5,X4),X12),rotate(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_117_118,plain,
! [X1,X12,X4,X5] :
( ~ member(ordered_pair(ordered_pair(X4,X5),X12),X1)
| ~ member(ordered_pair(ordered_pair(X5,X4),X12),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X5,X4),X12),flip(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_118_119,plain,
! [X3,X2,X1] :
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(X2,domain_of(X1))
| member(ordered_pair(X1,ordered_pair(X2,apply(X1,X2))),application_function) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_119_120,plain,
! [X3,X2,X6] :
( ~ subclass(X2,X3)
| ~ subclass(domain_of(restrict(X6,X3,X2)),X2)
| section(X6,X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
fof(c_0_120_121,plain,
! [X2,X8,X9,X10,X1] :
( ~ homomorphism(X8,X10,X9)
| ~ member(ordered_pair(X1,X2),domain_of(X10))
| apply(X9,ordered_pair(apply(X8,X1),apply(X8,X2))) = apply(X8,apply(X10,ordered_pair(X1,X2))) ),
inference(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_121_122,plain,
! [X3,X11,X2,X6] :
( ~ member(X3,image(X11,image(X6,singleton(X2))))
| ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class))
| member(ordered_pair(X2,X3),compose(X11,X6)) ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_122_123,plain,
! [X3,X2,X6] :
( ~ section(X6,X2,X3)
| subclass(domain_of(restrict(X6,X3,X2)),X2) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
fof(c_0_123_124,plain,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,ordered_pair(X2,compose(X1,X2))),composition_function) ),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
fof(c_0_124_125,plain,
! [X1,X12,X4,X5] :
( ~ member(ordered_pair(ordered_pair(X5,X4),X12),rotate(X1))
| member(ordered_pair(ordered_pair(X4,X12),X5),X1) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
fof(c_0_125_126,plain,
! [X1,X12,X4,X5] :
( ~ member(ordered_pair(ordered_pair(X5,X4),X12),flip(X1))
| member(ordered_pair(ordered_pair(X4,X5),X12),X1) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
fof(c_0_126_127,plain,
! [X2,X6,X4] :
( ~ member(X4,not_well_ordering(X6,X2))
| segment(X6,not_well_ordering(X6,X2),X4) != null_class
| ~ connected(X6,X2)
| well_ordering(X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_127_128,plain,
! [X3,X11,X2,X6] :
( ~ member(ordered_pair(X2,X3),compose(X11,X6))
| member(X3,image(X11,image(X6,singleton(X2)))) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_128_129,plain,
! [X2,X6,X4,X5] :
( ~ well_ordering(X6,X2)
| ~ subclass(X5,X2)
| ~ member(X4,X5)
| ~ member(ordered_pair(X4,least(X6,X5)),X6) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_129_130,plain,
! [X2,X1] :
( ~ subclass(restrict(X1,X2,X2),complement(identity_relation))
| irreflexive(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_130_131,plain,
! [X3,X2,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class))
| compose(X1,X2) != X3
| member(ordered_pair(X2,X3),compose_class(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_18]) ).
fof(c_0_131_132,plain,
! [X1,X4,X5] :
( ~ member(X5,domain_of(X1))
| restrict(X1,X5,universal_class) != X4
| member(ordered_pair(X5,X4),rest_of(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_132_133,plain,
! [X3,X2,X1] :
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),application_function)
| member(X2,domain_of(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
fof(c_0_133_134,axiom,
! [X2,X6] :
( restrict(intersection(X6,inverse(X6)),X2,X2) != null_class
| asymmetric(X6,X2) ),
c_0_21 ).
fof(c_0_134_135,plain,
! [X7] :
( ~ function(X7)
| cross_product(domain_of(domain_of(X7)),domain_of(domain_of(X7))) != domain_of(X7)
| ~ subclass(range_of(X7),domain_of(domain_of(X7)))
| operation(X7) ),
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_135_136,plain,
! [X3,X2,X1] :
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),composition_function)
| compose(X1,X2) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_136_137,plain,
! [X3,X2,X1] :
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),application_function)
| apply(X1,X2) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_137_138,plain,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2)
| member(ordered_pair(X1,X2),element_relation) ),
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_138_139,plain,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| sum_class(range_of(X1)) != X2
| member(ordered_pair(X1,X2),union_of_range_map) ),
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_139_140,plain,
! [X2,X1] :
( ~ irreflexive(X1,X2)
| subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_140_141,plain,
! [X8,X9,X10] :
( ~ function(X8)
| domain_of(domain_of(X10)) != domain_of(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X9)))
| compatible(X8,X10,X9) ),
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_141_142,plain,
! [X2,X1] :
( successor(X1) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),successor_relation) ),
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_142_143,plain,
! [X8,X9,X10] :
( ~ homomorphism(X8,X10,X9)
| compatible(X8,X10,X9) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_143_144,plain,
! [X7] :
( ~ subclass(X7,cross_product(universal_class,universal_class))
| ~ subclass(compose(X7,inverse(X7)),identity_relation)
| function(X7) ),
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_144_145,plain,
! [X2,X1] :
( ~ subclass(cross_product(X2,X2),union(identity_relation,symmetrization_of(X1)))
| connected(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_145_146,plain,
! [X1,X4,X5] :
( ~ member(ordered_pair(X5,X4),rest_of(X1))
| restrict(X1,X5,universal_class) = X4 ),
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_146_147,plain,
! [X2,X6,X5] :
( ~ well_ordering(X6,X2)
| ~ subclass(X5,X2)
| segment(X6,X5,least(X6,X5)) = null_class ),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_147_148,plain,
! [X3,X1] :
( restrict(X1,singleton(X3),universal_class) != null_class
| ~ member(X3,domain_of(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_148_149,plain,
! [X8,X9,X10] :
( ~ compatible(X8,X10,X9)
| subclass(range_of(X8),domain_of(domain_of(X9))) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_149_150,plain,
! [X2,X1,X4,X5] :
( ~ member(ordered_pair(X5,X4),cross_product(X1,X2))
| member(X5,X1) ),
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_150_151,plain,
! [X2,X1,X4,X5] :
( ~ member(ordered_pair(X5,X4),cross_product(X1,X2))
| member(X4,X2) ),
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_151_152,plain,
! [X2,X6] :
( ~ asymmetric(X6,X2)
| restrict(intersection(X6,inverse(X6)),X2,X2) = null_class ),
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_152_153,plain,
! [X2,X1,X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X2)
| member(ordered_pair(X5,X4),cross_product(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_153_154,plain,
! [X2,X6,X4,X5] :
( ~ well_ordering(X6,X2)
| ~ subclass(X5,X2)
| ~ member(X4,X5)
| member(least(X6,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_154_155,plain,
! [X2,X7,X1] :
( ~ maps(X7,X1,X2)
| subclass(range_of(X7),X2) ),
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_155_156,plain,
! [X8,X9,X10] :
( ~ compatible(X8,X10,X9)
| domain_of(domain_of(X10)) = domain_of(X8) ),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_156_157,plain,
! [X3,X2,X6] :
( ~ section(X6,X2,X3)
| subclass(X2,X3) ),
inference(fof_simplification,[status(thm)],[c_0_44]) ).
fof(c_0_157_158,plain,
! [X2,X7] :
( ~ function(X7)
| ~ subclass(range_of(X7),X2)
| maps(X7,domain_of(X7),X2) ),
inference(fof_simplification,[status(thm)],[c_0_45]) ).
fof(c_0_158_159,plain,
! [X3,X1] :
( ~ member(X3,universal_class)
| restrict(X1,singleton(X3),universal_class) = null_class
| member(X3,domain_of(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_46]) ).
fof(c_0_159_160,plain,
! [X3,X1] :
( ~ function(X3)
| ~ function(X1)
| ~ member(domain_of(X1),ordinal_numbers)
| compose(X3,rest_of(X1)) != X1
| member(X1,recursion_equation_functions(X3)) ),
inference(fof_simplification,[status(thm)],[c_0_47]) ).
fof(c_0_160_161,plain,
! [X2,X1] :
( ~ connected(X1,X2)
| subclass(cross_product(X2,X2),union(identity_relation,symmetrization_of(X1))) ),
inference(fof_simplification,[status(thm)],[c_0_48]) ).
fof(c_0_161_162,plain,
! [X1,X4,X5] :
( ~ member(ordered_pair(X5,X4),rest_of(X1))
| member(X5,domain_of(X1)) ),
inference(fof_simplification,[status(thm)],[c_0_49]) ).
fof(c_0_162_163,plain,
! [X2,X7,X1] :
( ~ maps(X7,X1,X2)
| domain_of(X7) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_50]) ).
fof(c_0_163_164,plain,
! [X3,X2,X1] :
( ~ member(X3,cross_product(X1,X2))
| ordered_pair(first(X3),second(X3)) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_51]) ).
fof(c_0_164_165,plain,
! [X8,X9,X10] :
( ~ compatible(X8,X10,X9)
| function(X8) ),
inference(fof_simplification,[status(thm)],[c_0_52]) ).
fof(c_0_165_166,plain,
! [X8,X9,X10] :
( ~ homomorphism(X8,X10,X9)
| operation(X10) ),
inference(fof_simplification,[status(thm)],[c_0_53]) ).
fof(c_0_166_167,plain,
! [X8,X9,X10] :
( ~ homomorphism(X8,X10,X9)
| operation(X9) ),
inference(fof_simplification,[status(thm)],[c_0_54]) ).
fof(c_0_167_168,plain,
! [X2,X7,X1] :
( ~ maps(X7,X1,X2)
| function(X7) ),
inference(fof_simplification,[status(thm)],[c_0_55]) ).
fof(c_0_168_169,plain,
! [X3,X2,X1] :
( ~ member(ordered_pair(X2,X3),compose_class(X1))
| compose(X1,X2) = X3 ),
inference(fof_simplification,[status(thm)],[c_0_56]) ).
fof(c_0_169_170,plain,
! [X2,X6,X5] :
( ~ well_ordering(X6,X2)
| ~ subclass(X5,X2)
| X5 = null_class
| member(least(X6,X5),X5) ),
inference(fof_simplification,[status(thm)],[c_0_57]) ).
fof(c_0_170_171,plain,
! [X1] :
( ~ well_ordering(element_relation,X1)
| ~ subclass(sum_class(X1),X1)
| ~ member(X1,universal_class)
| member(X1,ordinal_numbers) ),
inference(fof_simplification,[status(thm)],[c_0_58]) ).
fof(c_0_171_172,plain,
! [X3,X2,X1] :
( ~ member(X3,X1)
| ~ member(X3,X2)
| member(X3,intersection(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_59]) ).
fof(c_0_172_173,plain,
! [X1] :
( ~ subclass(compose(X1,inverse(X1)),identity_relation)
| single_valued_class(X1) ),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
fof(c_0_173_174,plain,
! [X1] :
( ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1)
| inductive(X1) ),
inference(fof_simplification,[status(thm)],[c_0_61]) ).
fof(c_0_174_175,plain,
! [X2,X1] :
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_175_176,plain,
! [X3,X2,X1] :
( ~ member(X3,intersection(X1,X2))
| member(X3,X1) ),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
fof(c_0_176_177,plain,
! [X3,X2,X1] :
( ~ member(X3,intersection(X1,X2))
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[c_0_64]) ).
fof(c_0_177_178,plain,
! [X2,X6] :
( ~ connected(X6,X2)
| subclass(not_well_ordering(X6,X2),X2)
| well_ordering(X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_65]) ).
fof(c_0_178_179,plain,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),element_relation)
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_66]) ).
fof(c_0_179_180,plain,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),union_of_range_map)
| sum_class(range_of(X1)) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_67]) ).
fof(c_0_180_181,plain,
! [X1] :
( ~ member(X1,universal_class)
| member(ordered_pair(X1,domain_of(X1)),domain_relation) ),
inference(fof_simplification,[status(thm)],[c_0_68]) ).
fof(c_0_181_182,plain,
! [X1] :
( ~ member(X1,universal_class)
| member(ordered_pair(X1,rest_of(X1)),rest_relation) ),
inference(fof_simplification,[status(thm)],[c_0_69]) ).
fof(c_0_182_183,plain,
! [X2,X1,X5] :
( ~ member(X5,unordered_pair(X1,X2))
| X5 = X1
| X5 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_70]) ).
fof(c_0_183_184,plain,
! [X1] :
( ~ well_ordering(element_relation,X1)
| ~ subclass(sum_class(X1),X1)
| member(X1,ordinal_numbers)
| X1 = ordinal_numbers ),
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_184_185,plain,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),successor_relation)
| successor(X1) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_72]) ).
fof(c_0_185_186,plain,
! [X7,X1] :
( ~ function(X7)
| ~ member(X1,universal_class)
| member(image(X7,X1),universal_class) ),
inference(fof_simplification,[status(thm)],[c_0_73]) ).
fof(c_0_186_187,plain,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),domain_relation)
| domain_of(X1) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_74]) ).
fof(c_0_187_188,plain,
! [X2,X1] :
( ~ member(ordered_pair(X1,X2),rest_relation)
| rest_of(X1) = X2 ),
inference(fof_simplification,[status(thm)],[c_0_75]) ).
fof(c_0_188_189,plain,
! [X7] :
( ~ operation(X7)
| cross_product(domain_of(domain_of(X7)),domain_of(domain_of(X7))) = domain_of(X7) ),
inference(fof_simplification,[status(thm)],[c_0_76]) ).
fof(c_0_189_190,plain,
! [X2,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_77]) ).
fof(c_0_190_191,plain,
! [X2,X1] :
( ~ member(X2,universal_class)
| member(X2,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[c_0_78]) ).
fof(c_0_191_192,plain,
! [X2,X1,X5] :
( ~ subclass(X1,X2)
| ~ member(X5,X1)
| member(X5,X2) ),
inference(fof_simplification,[status(thm)],[c_0_79]) ).
fof(c_0_192_193,plain,
! [X2,X6] :
( ~ connected(X6,X2)
| not_well_ordering(X6,X2) != null_class
| well_ordering(X6,X2) ),
inference(fof_simplification,[status(thm)],[c_0_80]) ).
fof(c_0_193_194,plain,
! [X2] :
( ~ member(X2,universal_class)
| X2 = null_class
| member(apply(choice,X2),X2) ),
inference(fof_simplification,[status(thm)],[c_0_81]) ).
fof(c_0_194_195,plain,
! [X1] :
( ~ single_valued_class(X1)
| subclass(compose(X1,inverse(X1)),identity_relation) ),
inference(fof_simplification,[status(thm)],[c_0_82]) ).
fof(c_0_195_196,plain,
! [X7] :
( ~ function(X7)
| subclass(compose(X7,inverse(X7)),identity_relation) ),
inference(fof_simplification,[status(thm)],[c_0_83]) ).
fof(c_0_196_197,plain,
! [X3,X1] :
( ~ member(X3,universal_class)
| member(X3,complement(X1))
| member(X3,X1) ),
inference(fof_simplification,[status(thm)],[c_0_84]) ).
fof(c_0_197_198,plain,
! [X3,X1] :
( ~ member(X3,complement(X1))
| ~ member(X3,X1) ),
inference(fof_simplification,[status(thm)],[c_0_85]) ).
fof(c_0_198_199,axiom,
! [X2,X1] :
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
c_0_86 ).
fof(c_0_199_200,plain,
! [X3,X1] :
( ~ member(X1,recursion_equation_functions(X3))
| compose(X3,rest_of(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_87]) ).
fof(c_0_200_201,plain,
! [X3,X1] :
( ~ member(X1,recursion_equation_functions(X3))
| member(domain_of(X1),ordinal_numbers) ),
inference(fof_simplification,[status(thm)],[c_0_88]) ).
fof(c_0_201_202,plain,
! [X2,X1] :
( ~ subclass(X1,X2)
| ~ subclass(X2,X1)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[c_0_89]) ).
fof(c_0_202_203,plain,
! [X7] :
( ~ operation(X7)
| subclass(range_of(X7),domain_of(domain_of(X7))) ),
inference(fof_simplification,[status(thm)],[c_0_90]) ).
fof(c_0_203_204,plain,
! [X1] :
( ~ inductive(X1)
| subclass(image(successor_relation,X1),X1) ),
inference(fof_simplification,[status(thm)],[c_0_91]) ).
fof(c_0_204_205,plain,
! [X7] :
( ~ function(X7)
| subclass(X7,cross_product(universal_class,universal_class)) ),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
fof(c_0_205_206,plain,
! [X1] :
( ~ member(X1,ordinal_numbers)
| subclass(sum_class(X1),X1) ),
inference(fof_simplification,[status(thm)],[c_0_93]) ).
fof(c_0_206_207,plain,
! [X1] :
( ~ member(X1,universal_class)
| member(sum_class(X1),universal_class) ),
inference(fof_simplification,[status(thm)],[c_0_94]) ).
fof(c_0_207_208,plain,
! [X5] :
( ~ member(X5,universal_class)
| member(power_class(X5),universal_class) ),
inference(fof_simplification,[status(thm)],[c_0_95]) ).
fof(c_0_208_209,plain,
! [X2,X1] :
( ~ well_ordering(X1,X2)
| connected(X1,X2) ),
inference(fof_simplification,[status(thm)],[c_0_96]) ).
fof(c_0_209_210,plain,
! [X3,X1] :
( ~ member(X1,recursion_equation_functions(X3))
| function(X3) ),
inference(fof_simplification,[status(thm)],[c_0_97]) ).
fof(c_0_210_211,plain,
! [X3,X1] :
( ~ member(X1,recursion_equation_functions(X3))
| function(X1) ),
inference(fof_simplification,[status(thm)],[c_0_98]) ).
fof(c_0_211_212,plain,
! [X1] :
( ~ member(X1,ordinal_numbers)
| well_ordering(element_relation,X1) ),
inference(fof_simplification,[status(thm)],[c_0_99]) ).
fof(c_0_212_213,plain,
! [X7] :
( ~ function(inverse(X7))
| ~ function(X7)
| one_to_one(X7) ),
inference(fof_simplification,[status(thm)],[c_0_100]) ).
fof(c_0_213_214,plain,
! [X1] :
( ~ member(X1,omega)
| integer_of(X1) = X1 ),
inference(fof_simplification,[status(thm)],[c_0_101]) ).
fof(c_0_214_215,axiom,
! [X1] :
( X1 = null_class
| member(regular(X1),X1) ),
c_0_102 ).
fof(c_0_215_216,axiom,
! [X1] :
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
c_0_103 ).
fof(c_0_216_217,plain,
! [X1] :
( ~ inductive(X1)
| member(null_class,X1) ),
inference(fof_simplification,[status(thm)],[c_0_104]) ).
fof(c_0_217_218,plain,
! [X2] :
( ~ inductive(X2)
| subclass(omega,X2) ),
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_218_219,axiom,
! [X2,X1] :
( X1 != X2
| subclass(X1,X2) ),
c_0_106 ).
fof(c_0_219_220,axiom,
! [X2,X1] :
( X1 != X2
| subclass(X2,X1) ),
c_0_107 ).
fof(c_0_220_221,plain,
! [X7] :
( ~ one_to_one(X7)
| function(inverse(X7)) ),
inference(fof_simplification,[status(thm)],[c_0_108]) ).
fof(c_0_221_222,axiom,
! [X1] :
( member(X1,omega)
| integer_of(X1) = null_class ),
c_0_109 ).
fof(c_0_222_223,plain,
! [X7] :
( ~ one_to_one(X7)
| function(X7) ),
inference(fof_simplification,[status(thm)],[c_0_110]) ).
fof(c_0_223_224,plain,
! [X7] :
( ~ operation(X7)
| function(X7) ),
inference(fof_simplification,[status(thm)],[c_0_111]) ).
fof(c_0_224_225,plain,
! [X11,X12,X13] :
( ~ operation(X13)
| ~ operation(X12)
| ~ compatible(X11,X13,X12)
| apply(X12,ordered_pair(apply(X11,not_homomorphism1(X11,X13,X12)),apply(X11,not_homomorphism2(X11,X13,X12)))) != apply(X11,apply(X13,ordered_pair(not_homomorphism1(X11,X13,X12),not_homomorphism2(X11,X13,X12))))
| homomorphism(X11,X13,X12) ),
inference(variable_rename,[status(thm)],[c_0_112]) ).
fof(c_0_225_226,plain,
! [X7,X8] :
( ~ subclass(compose(restrict(X8,X7,X7),restrict(X8,X7,X7)),restrict(X8,X7,X7))
| transitive(X8,X7) ),
inference(variable_rename,[status(thm)],[c_0_113]) ).
fof(c_0_226_227,plain,
! [X11,X12,X13] :
( ~ operation(X13)
| ~ operation(X12)
| ~ compatible(X11,X13,X12)
| member(ordered_pair(not_homomorphism1(X11,X13,X12),not_homomorphism2(X11,X13,X12)),domain_of(X13))
| homomorphism(X11,X13,X12) ),
inference(variable_rename,[status(thm)],[c_0_114]) ).
fof(c_0_227_228,plain,
! [X7,X8] :
( ~ transitive(X8,X7)
| subclass(compose(restrict(X8,X7,X7),restrict(X8,X7,X7)),restrict(X8,X7,X7)) ),
inference(variable_rename,[status(thm)],[c_0_115]) ).
fof(c_0_228_229,plain,
! [X13,X14,X15,X16] :
( ~ member(ordered_pair(ordered_pair(X15,X14),X16),X13)
| ~ member(ordered_pair(ordered_pair(X16,X15),X14),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X16,X15),X14),rotate(X13)) ),
inference(variable_rename,[status(thm)],[c_0_116]) ).
fof(c_0_229_230,plain,
! [X13,X14,X15,X16] :
( ~ member(ordered_pair(ordered_pair(X15,X16),X14),X13)
| ~ member(ordered_pair(ordered_pair(X16,X15),X14),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X16,X15),X14),flip(X13)) ),
inference(variable_rename,[status(thm)],[c_0_117]) ).
fof(c_0_230,plain,
! [X4,X5,X6] :
( ~ member(ordered_pair(X6,ordered_pair(X5,X4)),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(X5,domain_of(X6))
| member(ordered_pair(X6,ordered_pair(X5,apply(X6,X5))),application_function) ),
inference(variable_rename,[status(thm)],[c_0_118]) ).
fof(c_0_231,plain,
! [X7,X8,X9] :
( ~ subclass(X8,X7)
| ~ subclass(domain_of(restrict(X9,X7,X8)),X8)
| section(X9,X8,X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_119])])]) ).
fof(c_0_232,plain,
! [X11,X12,X13,X14,X15] :
( ~ homomorphism(X12,X14,X13)
| ~ member(ordered_pair(X15,X11),domain_of(X14))
| apply(X13,ordered_pair(apply(X12,X15),apply(X12,X11))) = apply(X12,apply(X14,ordered_pair(X15,X11))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_120])])]) ).
fof(c_0_233,plain,
! [X12,X13,X14,X15] :
( ~ member(X12,image(X13,image(X15,singleton(X14))))
| ~ member(ordered_pair(X14,X12),cross_product(universal_class,universal_class))
| member(ordered_pair(X14,X12),compose(X13,X15)) ),
inference(variable_rename,[status(thm)],[c_0_121]) ).
fof(c_0_234,plain,
! [X7,X8,X9] :
( ~ section(X9,X8,X7)
| subclass(domain_of(restrict(X9,X7,X8)),X8) ),
inference(variable_rename,[status(thm)],[c_0_122]) ).
fof(c_0_235,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),cross_product(universal_class,universal_class))
| member(ordered_pair(X4,ordered_pair(X3,compose(X4,X3))),composition_function) ),
inference(variable_rename,[status(thm)],[c_0_123]) ).
fof(c_0_236,plain,
! [X13,X14,X15,X16] :
( ~ member(ordered_pair(ordered_pair(X16,X15),X14),rotate(X13))
| member(ordered_pair(ordered_pair(X15,X14),X16),X13) ),
inference(variable_rename,[status(thm)],[c_0_124]) ).
fof(c_0_237,plain,
! [X13,X14,X15,X16] :
( ~ member(ordered_pair(ordered_pair(X16,X15),X14),flip(X13))
| member(ordered_pair(ordered_pair(X15,X16),X14),X13) ),
inference(variable_rename,[status(thm)],[c_0_125]) ).
fof(c_0_238,plain,
! [X7,X8,X9] :
( ~ member(X9,not_well_ordering(X8,X7))
| segment(X8,not_well_ordering(X8,X7),X9) != null_class
| ~ connected(X8,X7)
| well_ordering(X8,X7) ),
inference(variable_rename,[status(thm)],[c_0_126]) ).
fof(c_0_239,plain,
! [X12,X13,X14,X15] :
( ~ member(ordered_pair(X14,X12),compose(X13,X15))
| member(X12,image(X13,image(X15,singleton(X14)))) ),
inference(variable_rename,[status(thm)],[c_0_127]) ).
fof(c_0_240,plain,
! [X7,X8,X9,X10] :
( ~ well_ordering(X8,X7)
| ~ subclass(X10,X7)
| ~ member(X9,X10)
| ~ member(ordered_pair(X9,least(X8,X10)),X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_128])])]) ).
fof(c_0_241,plain,
! [X3,X4] :
( ~ subclass(restrict(X4,X3,X3),complement(identity_relation))
| irreflexive(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_129]) ).
fof(c_0_242,plain,
! [X4,X5,X6] :
( ~ member(ordered_pair(X5,X4),cross_product(universal_class,universal_class))
| compose(X6,X5) != X4
| member(ordered_pair(X5,X4),compose_class(X6)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_130])])]) ).
fof(c_0_243,plain,
! [X6,X7,X8] :
( ~ member(X8,domain_of(X6))
| restrict(X6,X8,universal_class) != X7
| member(ordered_pair(X8,X7),rest_of(X6)) ),
inference(variable_rename,[status(thm)],[c_0_131]) ).
fof(c_0_244,plain,
! [X4,X5,X6] :
( ~ member(ordered_pair(X6,ordered_pair(X5,X4)),application_function)
| member(X5,domain_of(X6)) ),
inference(variable_rename,[status(thm)],[c_0_132]) ).
fof(c_0_245,plain,
! [X7,X8] :
( restrict(intersection(X8,inverse(X8)),X7,X7) != null_class
| asymmetric(X8,X7) ),
inference(variable_rename,[status(thm)],[c_0_133]) ).
fof(c_0_246,plain,
! [X8] :
( ~ function(X8)
| cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) != domain_of(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| operation(X8) ),
inference(variable_rename,[status(thm)],[c_0_134]) ).
fof(c_0_247,plain,
! [X4,X5,X6] :
( ~ member(ordered_pair(X6,ordered_pair(X5,X4)),composition_function)
| compose(X6,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_135]) ).
fof(c_0_248,plain,
! [X4,X5,X6] :
( ~ member(ordered_pair(X6,ordered_pair(X5,X4)),application_function)
| apply(X6,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_136]) ).
fof(c_0_249,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),cross_product(universal_class,universal_class))
| ~ member(X4,X3)
| member(ordered_pair(X4,X3),element_relation) ),
inference(variable_rename,[status(thm)],[c_0_137]) ).
fof(c_0_250,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),cross_product(universal_class,universal_class))
| sum_class(range_of(X4)) != X3
| member(ordered_pair(X4,X3),union_of_range_map) ),
inference(variable_rename,[status(thm)],[c_0_138]) ).
fof(c_0_251,plain,
! [X3,X4] :
( ~ irreflexive(X4,X3)
| subclass(restrict(X4,X3,X3),complement(identity_relation)) ),
inference(variable_rename,[status(thm)],[c_0_139]) ).
fof(c_0_252,plain,
! [X11,X12,X13] :
( ~ function(X11)
| domain_of(domain_of(X13)) != domain_of(X11)
| ~ subclass(range_of(X11),domain_of(domain_of(X12)))
| compatible(X11,X13,X12) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_140])])]) ).
fof(c_0_253,plain,
! [X3,X4] :
( successor(X4) != X3
| ~ member(ordered_pair(X4,X3),cross_product(universal_class,universal_class))
| member(ordered_pair(X4,X3),successor_relation) ),
inference(variable_rename,[status(thm)],[c_0_141]) ).
fof(c_0_254,plain,
! [X11,X12,X13] :
( ~ homomorphism(X11,X13,X12)
| compatible(X11,X13,X12) ),
inference(variable_rename,[status(thm)],[c_0_142]) ).
fof(c_0_255,plain,
! [X8] :
( ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation)
| function(X8) ),
inference(variable_rename,[status(thm)],[c_0_143]) ).
fof(c_0_256,plain,
! [X3,X4] :
( ~ subclass(cross_product(X3,X3),union(identity_relation,symmetrization_of(X4)))
| connected(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_144]) ).
fof(c_0_257,plain,
! [X6,X7,X8] :
( ~ member(ordered_pair(X8,X7),rest_of(X6))
| restrict(X6,X8,universal_class) = X7 ),
inference(variable_rename,[status(thm)],[c_0_145]) ).
fof(c_0_258,plain,
! [X7,X8,X9] :
( ~ well_ordering(X8,X7)
| ~ subclass(X9,X7)
| segment(X8,X9,least(X8,X9)) = null_class ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_146])])]) ).
fof(c_0_259,plain,
! [X4,X5] :
( restrict(X5,singleton(X4),universal_class) != null_class
| ~ member(X4,domain_of(X5)) ),
inference(variable_rename,[status(thm)],[c_0_147]) ).
fof(c_0_260,plain,
! [X11,X12,X13] :
( ~ compatible(X11,X13,X12)
| subclass(range_of(X11),domain_of(domain_of(X12))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_148])])]) ).
fof(c_0_261,plain,
! [X6,X7,X8,X9] :
( ~ member(ordered_pair(X9,X8),cross_product(X7,X6))
| member(X9,X7) ),
inference(variable_rename,[status(thm)],[c_0_149]) ).
fof(c_0_262,plain,
! [X6,X7,X8,X9] :
( ~ member(ordered_pair(X9,X8),cross_product(X7,X6))
| member(X8,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_150])])]) ).
fof(c_0_263,plain,
! [X7,X8] :
( ~ asymmetric(X8,X7)
| restrict(intersection(X8,inverse(X8)),X7,X7) = null_class ),
inference(variable_rename,[status(thm)],[c_0_151]) ).
fof(c_0_264,plain,
! [X6,X7,X8,X9] :
( ~ member(X9,X7)
| ~ member(X8,X6)
| member(ordered_pair(X9,X8),cross_product(X7,X6)) ),
inference(variable_rename,[status(thm)],[c_0_152]) ).
fof(c_0_265,plain,
! [X7,X8,X9,X10] :
( ~ well_ordering(X8,X7)
| ~ subclass(X10,X7)
| ~ member(X9,X10)
| member(least(X8,X10),X10) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_153])])]) ).
fof(c_0_266,plain,
! [X8,X9,X10] :
( ~ maps(X9,X10,X8)
| subclass(range_of(X9),X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_154])])]) ).
fof(c_0_267,plain,
! [X11,X12,X13] :
( ~ compatible(X11,X13,X12)
| domain_of(domain_of(X13)) = domain_of(X11) ),
inference(variable_rename,[status(thm)],[c_0_155]) ).
fof(c_0_268,plain,
! [X7,X8,X9] :
( ~ section(X9,X8,X7)
| subclass(X8,X7) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_156])])]) ).
fof(c_0_269,plain,
! [X8,X9] :
( ~ function(X9)
| ~ subclass(range_of(X9),X8)
| maps(X9,domain_of(X9),X8) ),
inference(variable_rename,[status(thm)],[c_0_157]) ).
fof(c_0_270,plain,
! [X4,X5] :
( ~ member(X4,universal_class)
| restrict(X5,singleton(X4),universal_class) = null_class
| member(X4,domain_of(X5)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_158])])]) ).
fof(c_0_271,plain,
! [X4,X5] :
( ~ function(X4)
| ~ function(X5)
| ~ member(domain_of(X5),ordinal_numbers)
| compose(X4,rest_of(X5)) != X5
| member(X5,recursion_equation_functions(X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_159])])]) ).
fof(c_0_272,plain,
! [X3,X4] :
( ~ connected(X4,X3)
| subclass(cross_product(X3,X3),union(identity_relation,symmetrization_of(X4))) ),
inference(variable_rename,[status(thm)],[c_0_160]) ).
fof(c_0_273,plain,
! [X6,X7,X8] :
( ~ member(ordered_pair(X8,X7),rest_of(X6))
| member(X8,domain_of(X6)) ),
inference(variable_rename,[status(thm)],[c_0_161]) ).
fof(c_0_274,plain,
! [X8,X9,X10] :
( ~ maps(X9,X10,X8)
| domain_of(X9) = X10 ),
inference(variable_rename,[status(thm)],[c_0_162]) ).
fof(c_0_275,plain,
! [X4,X5,X6] :
( ~ member(X4,cross_product(X6,X5))
| ordered_pair(first(X4),second(X4)) = X4 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_163])])]) ).
fof(c_0_276,plain,
! [X11,X12,X13] :
( ~ compatible(X11,X13,X12)
| function(X11) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_164])])]) ).
fof(c_0_277,plain,
! [X11,X12,X13] :
( ~ homomorphism(X11,X13,X12)
| operation(X13) ),
inference(variable_rename,[status(thm)],[c_0_165]) ).
fof(c_0_278,plain,
! [X11,X12,X13] :
( ~ homomorphism(X11,X13,X12)
| operation(X12) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_166])])]) ).
fof(c_0_279,plain,
! [X8,X9,X10] :
( ~ maps(X9,X10,X8)
| function(X9) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_167])])]) ).
fof(c_0_280,plain,
! [X4,X5,X6] :
( ~ member(ordered_pair(X5,X4),compose_class(X6))
| compose(X6,X5) = X4 ),
inference(variable_rename,[status(thm)],[c_0_168]) ).
fof(c_0_281,plain,
! [X7,X8,X9] :
( ~ well_ordering(X8,X7)
| ~ subclass(X9,X7)
| X9 = null_class
| member(least(X8,X9),X9) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_169])])]) ).
fof(c_0_282,plain,
! [X2] :
( ~ well_ordering(element_relation,X2)
| ~ subclass(sum_class(X2),X2)
| ~ member(X2,universal_class)
| member(X2,ordinal_numbers) ),
inference(variable_rename,[status(thm)],[c_0_170]) ).
fof(c_0_283,plain,
! [X4,X5,X6] :
( ~ member(X4,X6)
| ~ member(X4,X5)
| member(X4,intersection(X6,X5)) ),
inference(variable_rename,[status(thm)],[c_0_171]) ).
fof(c_0_284,plain,
! [X2] :
( ~ subclass(compose(X2,inverse(X2)),identity_relation)
| single_valued_class(X2) ),
inference(variable_rename,[status(thm)],[c_0_172]) ).
fof(c_0_285,plain,
! [X2] :
( ~ member(null_class,X2)
| ~ subclass(image(successor_relation,X2),X2)
| inductive(X2) ),
inference(variable_rename,[status(thm)],[c_0_173]) ).
fof(c_0_286,plain,
! [X3,X4] :
( ~ member(not_subclass_element(X4,X3),X3)
| subclass(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_174]) ).
fof(c_0_287,plain,
! [X4,X5,X6] :
( ~ member(X4,intersection(X6,X5))
| member(X4,X6) ),
inference(variable_rename,[status(thm)],[c_0_175]) ).
fof(c_0_288,plain,
! [X4,X5,X6] :
( ~ member(X4,intersection(X6,X5))
| member(X4,X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_176])])]) ).
fof(c_0_289,plain,
! [X7,X8] :
( ~ connected(X8,X7)
| subclass(not_well_ordering(X8,X7),X7)
| well_ordering(X8,X7) ),
inference(variable_rename,[status(thm)],[c_0_177]) ).
fof(c_0_290,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),element_relation)
| member(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_178]) ).
fof(c_0_291,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),union_of_range_map)
| sum_class(range_of(X4)) = X3 ),
inference(variable_rename,[status(thm)],[c_0_179]) ).
fof(c_0_292,plain,
! [X2] :
( ~ member(X2,universal_class)
| member(ordered_pair(X2,domain_of(X2)),domain_relation) ),
inference(variable_rename,[status(thm)],[c_0_180]) ).
fof(c_0_293,plain,
! [X2] :
( ~ member(X2,universal_class)
| member(ordered_pair(X2,rest_of(X2)),rest_relation) ),
inference(variable_rename,[status(thm)],[c_0_181]) ).
fof(c_0_294,plain,
! [X6,X7,X8] :
( ~ member(X8,unordered_pair(X7,X6))
| X8 = X7
| X8 = X6 ),
inference(variable_rename,[status(thm)],[c_0_182]) ).
fof(c_0_295,plain,
! [X2] :
( ~ well_ordering(element_relation,X2)
| ~ subclass(sum_class(X2),X2)
| member(X2,ordinal_numbers)
| X2 = ordinal_numbers ),
inference(variable_rename,[status(thm)],[c_0_183]) ).
fof(c_0_296,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),successor_relation)
| successor(X4) = X3 ),
inference(variable_rename,[status(thm)],[c_0_184]) ).
fof(c_0_297,plain,
! [X8,X9] :
( ~ function(X8)
| ~ member(X9,universal_class)
| member(image(X8,X9),universal_class) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_185])])]) ).
fof(c_0_298,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),domain_relation)
| domain_of(X4) = X3 ),
inference(variable_rename,[status(thm)],[c_0_186]) ).
fof(c_0_299,plain,
! [X3,X4] :
( ~ member(ordered_pair(X4,X3),rest_relation)
| rest_of(X4) = X3 ),
inference(variable_rename,[status(thm)],[c_0_187]) ).
fof(c_0_300,plain,
! [X8] :
( ~ operation(X8)
| cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) = domain_of(X8) ),
inference(variable_rename,[status(thm)],[c_0_188]) ).
fof(c_0_301,plain,
! [X3,X4] :
( ~ member(X4,universal_class)
| member(X4,unordered_pair(X4,X3)) ),
inference(variable_rename,[status(thm)],[c_0_189]) ).
fof(c_0_302,plain,
! [X3,X4] :
( ~ member(X3,universal_class)
| member(X3,unordered_pair(X4,X3)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_190])])]) ).
fof(c_0_303,plain,
! [X6,X7,X8] :
( ~ subclass(X7,X6)
| ~ member(X8,X7)
| member(X8,X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_191])])]) ).
fof(c_0_304,plain,
! [X7,X8] :
( ~ connected(X8,X7)
| not_well_ordering(X8,X7) != null_class
| well_ordering(X8,X7) ),
inference(variable_rename,[status(thm)],[c_0_192]) ).
fof(c_0_305,plain,
! [X3] :
( ~ member(X3,universal_class)
| X3 = null_class
| member(apply(choice,X3),X3) ),
inference(variable_rename,[status(thm)],[c_0_193]) ).
fof(c_0_306,plain,
! [X2] :
( ~ single_valued_class(X2)
| subclass(compose(X2,inverse(X2)),identity_relation) ),
inference(variable_rename,[status(thm)],[c_0_194]) ).
fof(c_0_307,plain,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
inference(variable_rename,[status(thm)],[c_0_195]) ).
fof(c_0_308,plain,
! [X4,X5] :
( ~ member(X4,universal_class)
| member(X4,complement(X5))
| member(X4,X5) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_196])])]) ).
fof(c_0_309,plain,
! [X4,X5] :
( ~ member(X4,complement(X5))
| ~ member(X4,X5) ),
inference(variable_rename,[status(thm)],[c_0_197]) ).
fof(c_0_310,plain,
! [X3,X4] :
( member(not_subclass_element(X4,X3),X4)
| subclass(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_198]) ).
fof(c_0_311,plain,
! [X4,X5] :
( ~ member(X5,recursion_equation_functions(X4))
| compose(X4,rest_of(X5)) = X5 ),
inference(variable_rename,[status(thm)],[c_0_199]) ).
fof(c_0_312,plain,
! [X4,X5] :
( ~ member(X5,recursion_equation_functions(X4))
| member(domain_of(X5),ordinal_numbers) ),
inference(variable_rename,[status(thm)],[c_0_200]) ).
fof(c_0_313,plain,
! [X3,X4] :
( ~ subclass(X4,X3)
| ~ subclass(X3,X4)
| X4 = X3 ),
inference(variable_rename,[status(thm)],[c_0_201]) ).
fof(c_0_314,plain,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
inference(variable_rename,[status(thm)],[c_0_202]) ).
fof(c_0_315,plain,
! [X2] :
( ~ inductive(X2)
| subclass(image(successor_relation,X2),X2) ),
inference(variable_rename,[status(thm)],[c_0_203]) ).
fof(c_0_316,plain,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
inference(variable_rename,[status(thm)],[c_0_204]) ).
fof(c_0_317,plain,
! [X2] :
( ~ member(X2,ordinal_numbers)
| subclass(sum_class(X2),X2) ),
inference(variable_rename,[status(thm)],[c_0_205]) ).
fof(c_0_318,plain,
! [X2] :
( ~ member(X2,universal_class)
| member(sum_class(X2),universal_class) ),
inference(variable_rename,[status(thm)],[c_0_206]) ).
fof(c_0_319,plain,
! [X6] :
( ~ member(X6,universal_class)
| member(power_class(X6),universal_class) ),
inference(variable_rename,[status(thm)],[c_0_207]) ).
fof(c_0_320,plain,
! [X3,X4] :
( ~ well_ordering(X4,X3)
| connected(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_208]) ).
fof(c_0_321,plain,
! [X4,X5] :
( ~ member(X5,recursion_equation_functions(X4))
| function(X4) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_209])])]) ).
fof(c_0_322,plain,
! [X4,X5] :
( ~ member(X5,recursion_equation_functions(X4))
| function(X5) ),
inference(variable_rename,[status(thm)],[c_0_210]) ).
fof(c_0_323,plain,
! [X2] :
( ~ member(X2,ordinal_numbers)
| well_ordering(element_relation,X2) ),
inference(variable_rename,[status(thm)],[c_0_211]) ).
fof(c_0_324,plain,
! [X8] :
( ~ function(inverse(X8))
| ~ function(X8)
| one_to_one(X8) ),
inference(variable_rename,[status(thm)],[c_0_212]) ).
fof(c_0_325,plain,
! [X2] :
( ~ member(X2,omega)
| integer_of(X2) = X2 ),
inference(variable_rename,[status(thm)],[c_0_213]) ).
fof(c_0_326,plain,
! [X2] :
( X2 = null_class
| member(regular(X2),X2) ),
inference(variable_rename,[status(thm)],[c_0_214]) ).
fof(c_0_327,plain,
! [X2] :
( X2 = null_class
| intersection(X2,regular(X2)) = null_class ),
inference(variable_rename,[status(thm)],[c_0_215]) ).
fof(c_0_328,plain,
! [X2] :
( ~ inductive(X2)
| member(null_class,X2) ),
inference(variable_rename,[status(thm)],[c_0_216]) ).
fof(c_0_329,plain,
! [X3] :
( ~ inductive(X3)
| subclass(omega,X3) ),
inference(variable_rename,[status(thm)],[c_0_217]) ).
fof(c_0_330,plain,
! [X3,X4] :
( X4 != X3
| subclass(X4,X3) ),
inference(variable_rename,[status(thm)],[c_0_218]) ).
fof(c_0_331,plain,
! [X3,X4] :
( X4 != X3
| subclass(X3,X4) ),
inference(variable_rename,[status(thm)],[c_0_219]) ).
fof(c_0_332,plain,
! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ),
inference(variable_rename,[status(thm)],[c_0_220]) ).
fof(c_0_333,plain,
! [X2] :
( member(X2,omega)
| integer_of(X2) = null_class ),
inference(variable_rename,[status(thm)],[c_0_221]) ).
fof(c_0_334,plain,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
inference(variable_rename,[status(thm)],[c_0_222]) ).
fof(c_0_335,plain,
! [X8] :
( ~ operation(X8)
| function(X8) ),
inference(variable_rename,[status(thm)],[c_0_223]) ).
cnf(c_0_336,plain,
( homomorphism(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_224]) ).
cnf(c_0_337,plain,
( transitive(X1,X2)
| ~ subclass(compose(restrict(X1,X2,X2),restrict(X1,X2,X2)),restrict(X1,X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_225]) ).
cnf(c_0_338,plain,
( homomorphism(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_339,plain,
( subclass(compose(restrict(X1,X2,X2),restrict(X1,X2,X2)),restrict(X1,X2,X2))
| ~ transitive(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_227]) ).
cnf(c_0_340,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_341,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_342,plain,
( member(ordered_pair(X1,ordered_pair(X2,apply(X1,X2))),application_function)
| ~ member(X2,domain_of(X1))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(split_conjunct,[status(thm)],[c_0_230]) ).
cnf(c_0_343,plain,
( section(X1,X2,X3)
| ~ subclass(domain_of(restrict(X1,X3,X2)),X2)
| ~ subclass(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_231]) ).
cnf(c_0_344,plain,
( apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4)))
| ~ member(ordered_pair(X3,X4),domain_of(X5))
| ~ homomorphism(X2,X5,X1) ),
inference(split_conjunct,[status(thm)],[c_0_232]) ).
cnf(c_0_345,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X2,image(X3,image(X4,singleton(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_346,plain,
( subclass(domain_of(restrict(X1,X2,X3)),X3)
| ~ section(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_234]) ).
cnf(c_0_347,plain,
( member(ordered_pair(X1,ordered_pair(X2,compose(X1,X2))),composition_function)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(split_conjunct,[status(thm)],[c_0_235]) ).
cnf(c_0_348,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4)) ),
inference(split_conjunct,[status(thm)],[c_0_236]) ).
cnf(c_0_349,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4)) ),
inference(split_conjunct,[status(thm)],[c_0_237]) ).
cnf(c_0_350,plain,
( well_ordering(X1,X2)
| ~ connected(X1,X2)
| segment(X1,not_well_ordering(X1,X2),X3) != null_class
| ~ member(X3,not_well_ordering(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_238]) ).
cnf(c_0_351,plain,
( member(X1,image(X2,image(X3,singleton(X4))))
| ~ member(ordered_pair(X4,X1),compose(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_239]) ).
cnf(c_0_352,plain,
( ~ member(ordered_pair(X1,least(X2,X3)),X2)
| ~ member(X1,X3)
| ~ subclass(X3,X4)
| ~ well_ordering(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_240]) ).
cnf(c_0_353,plain,
( irreflexive(X1,X2)
| ~ subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
inference(split_conjunct,[status(thm)],[c_0_241]) ).
cnf(c_0_354,plain,
( member(ordered_pair(X1,X2),compose_class(X3))
| compose(X3,X1) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(split_conjunct,[status(thm)],[c_0_242]) ).
cnf(c_0_355,plain,
( member(ordered_pair(X1,X2),rest_of(X3))
| restrict(X3,X1,universal_class) != X2
| ~ member(X1,domain_of(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_243]) ).
cnf(c_0_356,plain,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X2,ordered_pair(X1,X3)),application_function) ),
inference(split_conjunct,[status(thm)],[c_0_244]) ).
cnf(c_0_357,plain,
( asymmetric(X1,X2)
| restrict(intersection(X1,inverse(X1)),X2,X2) != null_class ),
inference(split_conjunct,[status(thm)],[c_0_245]) ).
cnf(c_0_358,plain,
( operation(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_246]) ).
cnf(c_0_359,plain,
( compose(X1,X2) = X3
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),composition_function) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_360,plain,
( apply(X1,X2) = X3
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),application_function) ),
inference(split_conjunct,[status(thm)],[c_0_248]) ).
cnf(c_0_361,plain,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(X1,X2)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(split_conjunct,[status(thm)],[c_0_249]) ).
cnf(c_0_362,plain,
( member(ordered_pair(X1,X2),union_of_range_map)
| sum_class(range_of(X1)) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(split_conjunct,[status(thm)],[c_0_250]) ).
cnf(c_0_363,plain,
( subclass(restrict(X1,X2,X2),complement(identity_relation))
| ~ irreflexive(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_251]) ).
cnf(c_0_364,plain,
( compatible(X1,X2,X3)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_252]) ).
cnf(c_0_365,plain,
( member(ordered_pair(X1,X2),successor_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| successor(X1) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_253]) ).
cnf(c_0_366,plain,
( compatible(X1,X2,X3)
| ~ homomorphism(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_254]) ).
cnf(c_0_367,plain,
( function(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation)
| ~ subclass(X1,cross_product(universal_class,universal_class)) ),
inference(split_conjunct,[status(thm)],[c_0_255]) ).
cnf(c_0_368,plain,
( connected(X1,X2)
| ~ subclass(cross_product(X2,X2),union(identity_relation,symmetrization_of(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_256]) ).
cnf(c_0_369,plain,
( restrict(X1,X2,universal_class) = X3
| ~ member(ordered_pair(X2,X3),rest_of(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_257]) ).
cnf(c_0_370,plain,
( segment(X1,X2,least(X1,X2)) = null_class
| ~ subclass(X2,X3)
| ~ well_ordering(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_258]) ).
cnf(c_0_371,plain,
( ~ member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) != null_class ),
inference(split_conjunct,[status(thm)],[c_0_259]) ).
cnf(c_0_372,plain,
( subclass(range_of(X1),domain_of(domain_of(X2)))
| ~ compatible(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_260]) ).
cnf(c_0_373,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_261]) ).
cnf(c_0_374,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_375,plain,
( restrict(intersection(X1,inverse(X1)),X2,X2) = null_class
| ~ asymmetric(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_376,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_264]) ).
cnf(c_0_377,plain,
( member(least(X1,X2),X2)
| ~ member(X3,X2)
| ~ subclass(X2,X4)
| ~ well_ordering(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_265]) ).
cnf(c_0_378,plain,
( subclass(range_of(X1),X2)
| ~ maps(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_266]) ).
cnf(c_0_379,plain,
( domain_of(domain_of(X1)) = domain_of(X2)
| ~ compatible(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_267]) ).
cnf(c_0_380,plain,
( subclass(X1,X2)
| ~ section(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_268]) ).
cnf(c_0_381,plain,
( maps(X1,domain_of(X1),X2)
| ~ subclass(range_of(X1),X2)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_269]) ).
cnf(c_0_382,plain,
( member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_270]) ).
cnf(c_0_383,plain,
( member(X1,recursion_equation_functions(X2))
| compose(X2,rest_of(X1)) != X1
| ~ member(domain_of(X1),ordinal_numbers)
| ~ function(X1)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_271]) ).
cnf(c_0_384,plain,
( subclass(cross_product(X1,X1),union(identity_relation,symmetrization_of(X2)))
| ~ connected(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_272]) ).
cnf(c_0_385,plain,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X1,X3),rest_of(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_273]) ).
cnf(c_0_386,plain,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_387,plain,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_275]) ).
cnf(c_0_388,plain,
( function(X1)
| ~ compatible(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_276]) ).
cnf(c_0_389,plain,
( operation(X1)
| ~ homomorphism(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_277]) ).
cnf(c_0_390,plain,
( operation(X1)
| ~ homomorphism(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_278]) ).
cnf(c_0_391,plain,
( function(X1)
| ~ maps(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_279]) ).
cnf(c_0_392,plain,
( compose(X1,X2) = X3
| ~ member(ordered_pair(X2,X3),compose_class(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_280]) ).
cnf(c_0_393,plain,
( member(least(X1,X2),X2)
| X2 = null_class
| ~ subclass(X2,X3)
| ~ well_ordering(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_281]) ).
cnf(c_0_394,plain,
( member(X1,ordinal_numbers)
| ~ member(X1,universal_class)
| ~ subclass(sum_class(X1),X1)
| ~ well_ordering(element_relation,X1) ),
inference(split_conjunct,[status(thm)],[c_0_282]) ).
cnf(c_0_395,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_396,plain,
( single_valued_class(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
inference(split_conjunct,[status(thm)],[c_0_284]) ).
cnf(c_0_397,plain,
( inductive(X1)
| ~ subclass(image(successor_relation,X1),X1)
| ~ member(null_class,X1) ),
inference(split_conjunct,[status(thm)],[c_0_285]) ).
cnf(c_0_398,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_286]) ).
cnf(c_0_399,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_400,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_288]) ).
cnf(c_0_401,plain,
( well_ordering(X1,X2)
| subclass(not_well_ordering(X1,X2),X2)
| ~ connected(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_289]) ).
cnf(c_0_402,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_403,plain,
( sum_class(range_of(X1)) = X2
| ~ member(ordered_pair(X1,X2),union_of_range_map) ),
inference(split_conjunct,[status(thm)],[c_0_291]) ).
cnf(c_0_404,plain,
( member(ordered_pair(X1,domain_of(X1)),domain_relation)
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_405,plain,
( member(ordered_pair(X1,rest_of(X1)),rest_relation)
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_293]) ).
cnf(c_0_406,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_294]) ).
cnf(c_0_407,plain,
( X1 = ordinal_numbers
| member(X1,ordinal_numbers)
| ~ subclass(sum_class(X1),X1)
| ~ well_ordering(element_relation,X1) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_408,plain,
( successor(X1) = X2
| ~ member(ordered_pair(X1,X2),successor_relation) ),
inference(split_conjunct,[status(thm)],[c_0_296]) ).
cnf(c_0_409,plain,
( member(image(X1,X2),universal_class)
| ~ member(X2,universal_class)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_297]) ).
cnf(c_0_410,plain,
( domain_of(X1) = X2
| ~ member(ordered_pair(X1,X2),domain_relation) ),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_411,plain,
( rest_of(X1) = X2
| ~ member(ordered_pair(X1,X2),rest_relation) ),
inference(split_conjunct,[status(thm)],[c_0_299]) ).
cnf(c_0_412,plain,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1)
| ~ operation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_300]) ).
cnf(c_0_413,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_301]) ).
cnf(c_0_414,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_302]) ).
cnf(c_0_415,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subclass(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_303]) ).
cnf(c_0_416,plain,
( well_ordering(X1,X2)
| not_well_ordering(X1,X2) != null_class
| ~ connected(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_304]) ).
cnf(c_0_417,plain,
( member(apply(choice,X1),X1)
| X1 = null_class
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_305]) ).
cnf(c_0_418,plain,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ single_valued_class(X1) ),
inference(split_conjunct,[status(thm)],[c_0_306]) ).
cnf(c_0_419,plain,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_307]) ).
cnf(c_0_420,plain,
( member(X1,X2)
| member(X1,complement(X2))
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_421,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_309]) ).
cnf(c_0_422,plain,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_423,plain,
( compose(X1,rest_of(X2)) = X2
| ~ member(X2,recursion_equation_functions(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_311]) ).
cnf(c_0_424,plain,
( member(domain_of(X1),ordinal_numbers)
| ~ member(X1,recursion_equation_functions(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_312]) ).
cnf(c_0_425,plain,
( X1 = X2
| ~ subclass(X2,X1)
| ~ subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_313]) ).
cnf(c_0_426,plain,
( subclass(range_of(X1),domain_of(domain_of(X1)))
| ~ operation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_314]) ).
cnf(c_0_427,plain,
( subclass(image(successor_relation,X1),X1)
| ~ inductive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_315]) ).
cnf(c_0_428,plain,
( subclass(X1,cross_product(universal_class,universal_class))
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_316]) ).
cnf(c_0_429,plain,
( subclass(sum_class(X1),X1)
| ~ member(X1,ordinal_numbers) ),
inference(split_conjunct,[status(thm)],[c_0_317]) ).
cnf(c_0_430,plain,
( member(sum_class(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_431,plain,
( member(power_class(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_319]) ).
cnf(c_0_432,plain,
( connected(X1,X2)
| ~ well_ordering(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_320]) ).
cnf(c_0_433,plain,
( function(X1)
| ~ member(X2,recursion_equation_functions(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_434,plain,
( function(X1)
| ~ member(X1,recursion_equation_functions(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_322]) ).
cnf(c_0_435,plain,
( well_ordering(element_relation,X1)
| ~ member(X1,ordinal_numbers) ),
inference(split_conjunct,[status(thm)],[c_0_323]) ).
cnf(c_0_436,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ function(inverse(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_324]) ).
cnf(c_0_437,plain,
( integer_of(X1) = X1
| ~ member(X1,omega) ),
inference(split_conjunct,[status(thm)],[c_0_325]) ).
cnf(c_0_438,plain,
( member(regular(X1),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_326]) ).
cnf(c_0_439,plain,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_327]) ).
cnf(c_0_440,plain,
( member(null_class,X1)
| ~ inductive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_328]) ).
cnf(c_0_441,plain,
( subclass(omega,X1)
| ~ inductive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_329]) ).
cnf(c_0_442,plain,
( subclass(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_330]) ).
cnf(c_0_443,plain,
( subclass(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_331]) ).
cnf(c_0_444,plain,
( function(inverse(X1))
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_332]) ).
cnf(c_0_445,plain,
( integer_of(X1) = null_class
| member(X1,omega) ),
inference(split_conjunct,[status(thm)],[c_0_333]) ).
cnf(c_0_446,plain,
( function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_334]) ).
cnf(c_0_447,plain,
( function(X1)
| ~ operation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_335]) ).
cnf(c_0_448,plain,
( homomorphism(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
c_0_336,
[final] ).
cnf(c_0_449,plain,
( transitive(X1,X2)
| ~ subclass(compose(restrict(X1,X2,X2),restrict(X1,X2,X2)),restrict(X1,X2,X2)) ),
c_0_337,
[final] ).
cnf(c_0_450,plain,
( homomorphism(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
c_0_338,
[final] ).
cnf(c_0_451,plain,
( subclass(compose(restrict(X1,X2,X2),restrict(X1,X2,X2)),restrict(X1,X2,X2))
| ~ transitive(X1,X2) ),
c_0_339,
[final] ).
cnf(c_0_452,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4) ),
c_0_340,
[final] ).
cnf(c_0_453,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4) ),
c_0_341,
[final] ).
cnf(c_0_454,plain,
( member(ordered_pair(X1,ordered_pair(X2,apply(X1,X2))),application_function)
| ~ member(X2,domain_of(X1))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
c_0_342,
[final] ).
cnf(c_0_455,plain,
( section(X1,X2,X3)
| ~ subclass(domain_of(restrict(X1,X3,X2)),X2)
| ~ subclass(X2,X3) ),
c_0_343,
[final] ).
cnf(c_0_456,plain,
( apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4)))
| ~ member(ordered_pair(X3,X4),domain_of(X5))
| ~ homomorphism(X2,X5,X1) ),
c_0_344,
[final] ).
cnf(c_0_457,plain,
( member(ordered_pair(X1,X2),compose(X3,X4))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X2,image(X3,image(X4,singleton(X1)))) ),
c_0_345,
[final] ).
cnf(c_0_458,plain,
( subclass(domain_of(restrict(X1,X2,X3)),X3)
| ~ section(X1,X3,X2) ),
c_0_346,
[final] ).
cnf(c_0_459,plain,
( member(ordered_pair(X1,ordered_pair(X2,compose(X1,X2))),composition_function)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
c_0_347,
[final] ).
cnf(c_0_460,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4)) ),
c_0_348,
[final] ).
cnf(c_0_461,plain,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4)) ),
c_0_349,
[final] ).
cnf(c_0_462,plain,
( well_ordering(X1,X2)
| ~ connected(X1,X2)
| segment(X1,not_well_ordering(X1,X2),X3) != null_class
| ~ member(X3,not_well_ordering(X1,X2)) ),
c_0_350,
[final] ).
cnf(c_0_463,plain,
( member(X1,image(X2,image(X3,singleton(X4))))
| ~ member(ordered_pair(X4,X1),compose(X2,X3)) ),
c_0_351,
[final] ).
cnf(c_0_464,plain,
( ~ member(ordered_pair(X1,least(X2,X3)),X2)
| ~ member(X1,X3)
| ~ subclass(X3,X4)
| ~ well_ordering(X2,X4) ),
c_0_352,
[final] ).
cnf(c_0_465,plain,
( irreflexive(X1,X2)
| ~ subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
c_0_353,
[final] ).
cnf(c_0_466,plain,
( member(ordered_pair(X1,X2),compose_class(X3))
| compose(X3,X1) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
c_0_354,
[final] ).
cnf(c_0_467,plain,
( member(ordered_pair(X1,X2),rest_of(X3))
| restrict(X3,X1,universal_class) != X2
| ~ member(X1,domain_of(X3)) ),
c_0_355,
[final] ).
cnf(c_0_468,plain,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X2,ordered_pair(X1,X3)),application_function) ),
c_0_356,
[final] ).
cnf(c_0_469,plain,
( asymmetric(X1,X2)
| restrict(intersection(X1,inverse(X1)),X2,X2) != null_class ),
c_0_357,
[final] ).
cnf(c_0_470,plain,
( operation(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ function(X1) ),
c_0_358,
[final] ).
cnf(c_0_471,plain,
( compose(X1,X2) = X3
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),composition_function) ),
c_0_359,
[final] ).
cnf(c_0_472,plain,
( apply(X1,X2) = X3
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),application_function) ),
c_0_360,
[final] ).
cnf(c_0_473,plain,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(X1,X2)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
c_0_361,
[final] ).
cnf(c_0_474,plain,
( member(ordered_pair(X1,X2),union_of_range_map)
| sum_class(range_of(X1)) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
c_0_362,
[final] ).
cnf(c_0_475,plain,
( subclass(restrict(X1,X2,X2),complement(identity_relation))
| ~ irreflexive(X1,X2) ),
c_0_363,
[final] ).
cnf(c_0_476,plain,
( compatible(X1,X2,X3)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ function(X1) ),
c_0_364,
[final] ).
cnf(c_0_477,plain,
( member(ordered_pair(X1,X2),successor_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| successor(X1) != X2 ),
c_0_365,
[final] ).
cnf(c_0_478,plain,
( compatible(X1,X2,X3)
| ~ homomorphism(X1,X2,X3) ),
c_0_366,
[final] ).
cnf(c_0_479,plain,
( function(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation)
| ~ subclass(X1,cross_product(universal_class,universal_class)) ),
c_0_367,
[final] ).
cnf(c_0_480,plain,
( connected(X1,X2)
| ~ subclass(cross_product(X2,X2),union(identity_relation,symmetrization_of(X1))) ),
c_0_368,
[final] ).
cnf(c_0_481,plain,
( restrict(X1,X2,universal_class) = X3
| ~ member(ordered_pair(X2,X3),rest_of(X1)) ),
c_0_369,
[final] ).
cnf(c_0_482,plain,
( segment(X1,X2,least(X1,X2)) = null_class
| ~ subclass(X2,X3)
| ~ well_ordering(X1,X3) ),
c_0_370,
[final] ).
cnf(c_0_483,plain,
( ~ member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) != null_class ),
c_0_371,
[final] ).
cnf(c_0_484,plain,
( subclass(range_of(X1),domain_of(domain_of(X2)))
| ~ compatible(X1,X3,X2) ),
c_0_372,
[final] ).
cnf(c_0_485,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
c_0_373,
[final] ).
cnf(c_0_486,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
c_0_374,
[final] ).
cnf(c_0_487,plain,
( restrict(intersection(X1,inverse(X1)),X2,X2) = null_class
| ~ asymmetric(X1,X2) ),
c_0_375,
[final] ).
cnf(c_0_488,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
c_0_376,
[final] ).
cnf(c_0_489,plain,
( member(least(X1,X2),X2)
| ~ member(X3,X2)
| ~ subclass(X2,X4)
| ~ well_ordering(X1,X4) ),
c_0_377,
[final] ).
cnf(c_0_490,plain,
( subclass(range_of(X1),X2)
| ~ maps(X1,X3,X2) ),
c_0_378,
[final] ).
cnf(c_0_491,plain,
( domain_of(domain_of(X1)) = domain_of(X2)
| ~ compatible(X2,X1,X3) ),
c_0_379,
[final] ).
cnf(c_0_492,plain,
( subclass(X1,X2)
| ~ section(X3,X1,X2) ),
c_0_380,
[final] ).
cnf(c_0_493,plain,
( maps(X1,domain_of(X1),X2)
| ~ subclass(range_of(X1),X2)
| ~ function(X1) ),
c_0_381,
[final] ).
cnf(c_0_494,plain,
( member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class
| ~ member(X1,universal_class) ),
c_0_382,
[final] ).
cnf(c_0_495,plain,
( member(X1,recursion_equation_functions(X2))
| compose(X2,rest_of(X1)) != X1
| ~ member(domain_of(X1),ordinal_numbers)
| ~ function(X1)
| ~ function(X2) ),
c_0_383,
[final] ).
cnf(c_0_496,plain,
( subclass(cross_product(X1,X1),union(identity_relation,symmetrization_of(X2)))
| ~ connected(X2,X1) ),
c_0_384,
[final] ).
cnf(c_0_497,plain,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X1,X3),rest_of(X2)) ),
c_0_385,
[final] ).
cnf(c_0_498,plain,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
c_0_386,
[final] ).
cnf(c_0_499,plain,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
c_0_387,
[final] ).
cnf(c_0_500,plain,
( function(X1)
| ~ compatible(X1,X2,X3) ),
c_0_388,
[final] ).
cnf(c_0_501,plain,
( operation(X1)
| ~ homomorphism(X2,X1,X3) ),
c_0_389,
[final] ).
cnf(c_0_502,plain,
( operation(X1)
| ~ homomorphism(X2,X3,X1) ),
c_0_390,
[final] ).
cnf(c_0_503,plain,
( function(X1)
| ~ maps(X1,X2,X3) ),
c_0_391,
[final] ).
cnf(c_0_504,plain,
( compose(X1,X2) = X3
| ~ member(ordered_pair(X2,X3),compose_class(X1)) ),
c_0_392,
[final] ).
cnf(c_0_505,plain,
( member(least(X1,X2),X2)
| X2 = null_class
| ~ subclass(X2,X3)
| ~ well_ordering(X1,X3) ),
c_0_393,
[final] ).
cnf(c_0_506,plain,
( member(X1,ordinal_numbers)
| ~ member(X1,universal_class)
| ~ subclass(sum_class(X1),X1)
| ~ well_ordering(element_relation,X1) ),
c_0_394,
[final] ).
cnf(c_0_507,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
c_0_395,
[final] ).
cnf(c_0_508,plain,
( single_valued_class(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
c_0_396,
[final] ).
cnf(c_0_509,plain,
( inductive(X1)
| ~ subclass(image(successor_relation,X1),X1)
| ~ member(null_class,X1) ),
c_0_397,
[final] ).
cnf(c_0_510,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
c_0_398,
[final] ).
cnf(c_0_511,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
c_0_399,
[final] ).
cnf(c_0_512,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
c_0_400,
[final] ).
cnf(c_0_513,plain,
( well_ordering(X1,X2)
| subclass(not_well_ordering(X1,X2),X2)
| ~ connected(X1,X2) ),
c_0_401,
[final] ).
cnf(c_0_514,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
c_0_402,
[final] ).
cnf(c_0_515,plain,
( sum_class(range_of(X1)) = X2
| ~ member(ordered_pair(X1,X2),union_of_range_map) ),
c_0_403,
[final] ).
cnf(c_0_516,plain,
( member(ordered_pair(X1,domain_of(X1)),domain_relation)
| ~ member(X1,universal_class) ),
c_0_404,
[final] ).
cnf(c_0_517,plain,
( member(ordered_pair(X1,rest_of(X1)),rest_relation)
| ~ member(X1,universal_class) ),
c_0_405,
[final] ).
cnf(c_0_518,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X3,X2)) ),
c_0_406,
[final] ).
cnf(c_0_519,plain,
( X1 = ordinal_numbers
| member(X1,ordinal_numbers)
| ~ subclass(sum_class(X1),X1)
| ~ well_ordering(element_relation,X1) ),
c_0_407,
[final] ).
cnf(c_0_520,plain,
( successor(X1) = X2
| ~ member(ordered_pair(X1,X2),successor_relation) ),
c_0_408,
[final] ).
cnf(c_0_521,plain,
( member(image(X1,X2),universal_class)
| ~ member(X2,universal_class)
| ~ function(X1) ),
c_0_409,
[final] ).
cnf(c_0_522,plain,
( domain_of(X1) = X2
| ~ member(ordered_pair(X1,X2),domain_relation) ),
c_0_410,
[final] ).
cnf(c_0_523,plain,
( rest_of(X1) = X2
| ~ member(ordered_pair(X1,X2),rest_relation) ),
c_0_411,
[final] ).
cnf(c_0_524,plain,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1)
| ~ operation(X1) ),
c_0_412,
[final] ).
cnf(c_0_525,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
c_0_413,
[final] ).
cnf(c_0_526,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
c_0_414,
[final] ).
cnf(c_0_527,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subclass(X3,X2) ),
c_0_415,
[final] ).
cnf(c_0_528,plain,
( well_ordering(X1,X2)
| not_well_ordering(X1,X2) != null_class
| ~ connected(X1,X2) ),
c_0_416,
[final] ).
cnf(c_0_529,plain,
( member(apply(choice,X1),X1)
| X1 = null_class
| ~ member(X1,universal_class) ),
c_0_417,
[final] ).
cnf(c_0_530,plain,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ single_valued_class(X1) ),
c_0_418,
[final] ).
cnf(c_0_531,plain,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ function(X1) ),
c_0_419,
[final] ).
cnf(c_0_532,plain,
( member(X1,X2)
| member(X1,complement(X2))
| ~ member(X1,universal_class) ),
c_0_420,
[final] ).
cnf(c_0_533,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_421,
[final] ).
cnf(c_0_534,plain,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
c_0_422,
[final] ).
cnf(c_0_535,plain,
( compose(X1,rest_of(X2)) = X2
| ~ member(X2,recursion_equation_functions(X1)) ),
c_0_423,
[final] ).
cnf(c_0_536,plain,
( member(domain_of(X1),ordinal_numbers)
| ~ member(X1,recursion_equation_functions(X2)) ),
c_0_424,
[final] ).
cnf(c_0_537,plain,
( X1 = X2
| ~ subclass(X2,X1)
| ~ subclass(X1,X2) ),
c_0_425,
[final] ).
cnf(c_0_538,plain,
( subclass(range_of(X1),domain_of(domain_of(X1)))
| ~ operation(X1) ),
c_0_426,
[final] ).
cnf(c_0_539,plain,
( subclass(image(successor_relation,X1),X1)
| ~ inductive(X1) ),
c_0_427,
[final] ).
cnf(c_0_540,plain,
( subclass(X1,cross_product(universal_class,universal_class))
| ~ function(X1) ),
c_0_428,
[final] ).
cnf(c_0_541,plain,
( subclass(sum_class(X1),X1)
| ~ member(X1,ordinal_numbers) ),
c_0_429,
[final] ).
cnf(c_0_542,plain,
( member(sum_class(X1),universal_class)
| ~ member(X1,universal_class) ),
c_0_430,
[final] ).
cnf(c_0_543,plain,
( member(power_class(X1),universal_class)
| ~ member(X1,universal_class) ),
c_0_431,
[final] ).
cnf(c_0_544,plain,
( connected(X1,X2)
| ~ well_ordering(X1,X2) ),
c_0_432,
[final] ).
cnf(c_0_545,plain,
( function(X1)
| ~ member(X2,recursion_equation_functions(X1)) ),
c_0_433,
[final] ).
cnf(c_0_546,plain,
( function(X1)
| ~ member(X1,recursion_equation_functions(X2)) ),
c_0_434,
[final] ).
cnf(c_0_547,plain,
( well_ordering(element_relation,X1)
| ~ member(X1,ordinal_numbers) ),
c_0_435,
[final] ).
cnf(c_0_548,plain,
( one_to_one(X1)
| ~ function(X1)
| ~ function(inverse(X1)) ),
c_0_436,
[final] ).
cnf(c_0_549,plain,
( integer_of(X1) = X1
| ~ member(X1,omega) ),
c_0_437,
[final] ).
cnf(c_0_550,plain,
( member(regular(X1),X1)
| X1 = null_class ),
c_0_438,
[final] ).
cnf(c_0_551,plain,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
c_0_439,
[final] ).
cnf(c_0_552,plain,
( member(null_class,X1)
| ~ inductive(X1) ),
c_0_440,
[final] ).
cnf(c_0_553,plain,
( subclass(omega,X1)
| ~ inductive(X1) ),
c_0_441,
[final] ).
cnf(c_0_554,plain,
( subclass(X1,X2)
| X1 != X2 ),
c_0_442,
[final] ).
cnf(c_0_555,plain,
( subclass(X1,X2)
| X2 != X1 ),
c_0_443,
[final] ).
cnf(c_0_556,plain,
( function(inverse(X1))
| ~ one_to_one(X1) ),
c_0_444,
[final] ).
cnf(c_0_557,plain,
( integer_of(X1) = null_class
| member(X1,omega) ),
c_0_445,
[final] ).
cnf(c_0_558,plain,
( function(X1)
| ~ one_to_one(X1) ),
c_0_446,
[final] ).
cnf(c_0_559,plain,
( function(X1)
| ~ operation(X1) ),
c_0_447,
[final] ).
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_448_0,axiom,
( homomorphism(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_1,axiom,
( apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| homomorphism(X1,X2,X3)
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_2,axiom,
( ~ compatible(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| homomorphism(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_3,axiom,
( ~ operation(X3)
| ~ compatible(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| homomorphism(X1,X2,X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_448_4,axiom,
( ~ operation(X2)
| ~ operation(X3)
| ~ compatible(X1,X2,X3)
| apply(X3,ordered_pair(apply(X1,not_homomorphism1(X1,X2,X3)),apply(X1,not_homomorphism2(X1,X2,X3)))) != apply(X1,apply(X2,ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3))))
| homomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_448]) ).
cnf(c_0_449_0,axiom,
( transitive(X1,X2)
| ~ subclass(compose(restrict(X1,X2,X2),restrict(X1,X2,X2)),restrict(X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_449]) ).
cnf(c_0_449_1,axiom,
( ~ subclass(compose(restrict(X1,X2,X2),restrict(X1,X2,X2)),restrict(X1,X2,X2))
| transitive(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_449]) ).
cnf(c_0_450_0,axiom,
( homomorphism(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_450_1,axiom,
( member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| homomorphism(X1,X2,X3)
| ~ compatible(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_450_2,axiom,
( ~ compatible(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| homomorphism(X1,X2,X3)
| ~ operation(X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_450_3,axiom,
( ~ operation(X3)
| ~ compatible(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| homomorphism(X1,X2,X3)
| ~ operation(X2) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_450_4,axiom,
( ~ operation(X2)
| ~ operation(X3)
| ~ compatible(X1,X2,X3)
| member(ordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism2(X1,X2,X3)),domain_of(X2))
| homomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_450]) ).
cnf(c_0_451_0,axiom,
( subclass(compose(restrict(X1,X2,X2),restrict(X1,X2,X2)),restrict(X1,X2,X2))
| ~ transitive(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_451]) ).
cnf(c_0_451_1,axiom,
( ~ transitive(X1,X2)
| subclass(compose(restrict(X1,X2,X2),restrict(X1,X2,X2)),restrict(X1,X2,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_451]) ).
cnf(c_0_452_0,axiom,
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4) ),
inference(literals_permutation,[status(thm)],[c_0_452]) ).
cnf(c_0_452_1,axiom,
( ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4) ),
inference(literals_permutation,[status(thm)],[c_0_452]) ).
cnf(c_0_452_2,axiom,
( ~ member(ordered_pair(ordered_pair(X2,X3),X1),X4)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_452]) ).
cnf(c_0_453_0,axiom,
( member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_453]) ).
cnf(c_0_453_1,axiom,
( ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4))
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_453]) ).
cnf(c_0_453_2,axiom,
( ~ member(ordered_pair(ordered_pair(X2,X1),X3),X4)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(ordered_pair(ordered_pair(X1,X2),X3),flip(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_453]) ).
cnf(c_0_454_0,axiom,
( member(ordered_pair(X1,ordered_pair(X2,apply(X1,X2))),application_function)
| ~ member(X2,domain_of(X1))
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_454_1,axiom,
( ~ member(X2,domain_of(X1))
| member(ordered_pair(X1,ordered_pair(X2,apply(X1,X2))),application_function)
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_454_2,axiom,
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(X2,domain_of(X1))
| member(ordered_pair(X1,ordered_pair(X2,apply(X1,X2))),application_function) ),
inference(literals_permutation,[status(thm)],[c_0_454]) ).
cnf(c_0_455_0,axiom,
( section(X1,X2,X3)
| ~ subclass(domain_of(restrict(X1,X3,X2)),X2)
| ~ subclass(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_455_1,axiom,
( ~ subclass(domain_of(restrict(X1,X3,X2)),X2)
| section(X1,X2,X3)
| ~ subclass(X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_455_2,axiom,
( ~ subclass(X2,X3)
| ~ subclass(domain_of(restrict(X1,X3,X2)),X2)
| section(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_455]) ).
cnf(c_0_456_0,axiom,
( apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4)))
| ~ member(ordered_pair(X3,X4),domain_of(X5))
| ~ homomorphism(X2,X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_456]) ).
cnf(c_0_456_1,axiom,
( ~ member(ordered_pair(X3,X4),domain_of(X5))
| apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4)))
| ~ homomorphism(X2,X5,X1) ),
inference(literals_permutation,[status(thm)],[c_0_456]) ).
cnf(c_0_456_2,axiom,
( ~ homomorphism(X2,X5,X1)
| ~ member(ordered_pair(X3,X4),domain_of(X5))
| apply(X1,ordered_pair(apply(X2,X3),apply(X2,X4))) = apply(X2,apply(X5,ordered_pair(X3,X4))) ),
inference(literals_permutation,[status(thm)],[c_0_456]) ).
cnf(c_0_457_0,axiom,
( member(ordered_pair(X1,X2),compose(X3,X4))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X2,image(X3,image(X4,singleton(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_457_1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),compose(X3,X4))
| ~ member(X2,image(X3,image(X4,singleton(X1)))) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_457_2,axiom,
( ~ member(X2,image(X3,image(X4,singleton(X1))))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),compose(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_457]) ).
cnf(c_0_458_0,axiom,
( subclass(domain_of(restrict(X1,X2,X3)),X3)
| ~ section(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_458]) ).
cnf(c_0_458_1,axiom,
( ~ section(X1,X3,X2)
| subclass(domain_of(restrict(X1,X2,X3)),X3) ),
inference(literals_permutation,[status(thm)],[c_0_458]) ).
cnf(c_0_459_0,axiom,
( member(ordered_pair(X1,ordered_pair(X2,compose(X1,X2))),composition_function)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_459_1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,ordered_pair(X2,compose(X1,X2))),composition_function) ),
inference(literals_permutation,[status(thm)],[c_0_459]) ).
cnf(c_0_460_0,axiom,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_460_1,axiom,
( ~ member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4))
| member(ordered_pair(ordered_pair(X1,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_460]) ).
cnf(c_0_461_0,axiom,
( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
| ~ member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4)) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_461_1,axiom,
( ~ member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4))
| member(ordered_pair(ordered_pair(X1,X2),X3),X4) ),
inference(literals_permutation,[status(thm)],[c_0_461]) ).
cnf(c_0_462_0,axiom,
( well_ordering(X1,X2)
| ~ connected(X1,X2)
| segment(X1,not_well_ordering(X1,X2),X3) != null_class
| ~ member(X3,not_well_ordering(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_462_1,axiom,
( ~ connected(X1,X2)
| well_ordering(X1,X2)
| segment(X1,not_well_ordering(X1,X2),X3) != null_class
| ~ member(X3,not_well_ordering(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_462_2,axiom,
( segment(X1,not_well_ordering(X1,X2),X3) != null_class
| ~ connected(X1,X2)
| well_ordering(X1,X2)
| ~ member(X3,not_well_ordering(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_462_3,axiom,
( ~ member(X3,not_well_ordering(X1,X2))
| segment(X1,not_well_ordering(X1,X2),X3) != null_class
| ~ connected(X1,X2)
| well_ordering(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_462]) ).
cnf(c_0_463_0,axiom,
( member(X1,image(X2,image(X3,singleton(X4))))
| ~ member(ordered_pair(X4,X1),compose(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_463]) ).
cnf(c_0_463_1,axiom,
( ~ member(ordered_pair(X4,X1),compose(X2,X3))
| member(X1,image(X2,image(X3,singleton(X4)))) ),
inference(literals_permutation,[status(thm)],[c_0_463]) ).
cnf(c_0_464_0,axiom,
( ~ member(ordered_pair(X1,least(X2,X3)),X2)
| ~ member(X1,X3)
| ~ subclass(X3,X4)
| ~ well_ordering(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_464_1,axiom,
( ~ member(X1,X3)
| ~ member(ordered_pair(X1,least(X2,X3)),X2)
| ~ subclass(X3,X4)
| ~ well_ordering(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_464_2,axiom,
( ~ subclass(X3,X4)
| ~ member(X1,X3)
| ~ member(ordered_pair(X1,least(X2,X3)),X2)
| ~ well_ordering(X2,X4) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_464_3,axiom,
( ~ well_ordering(X2,X4)
| ~ subclass(X3,X4)
| ~ member(X1,X3)
| ~ member(ordered_pair(X1,least(X2,X3)),X2) ),
inference(literals_permutation,[status(thm)],[c_0_464]) ).
cnf(c_0_465_0,axiom,
( irreflexive(X1,X2)
| ~ subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
inference(literals_permutation,[status(thm)],[c_0_465]) ).
cnf(c_0_465_1,axiom,
( ~ subclass(restrict(X1,X2,X2),complement(identity_relation))
| irreflexive(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_465]) ).
cnf(c_0_466_0,axiom,
( member(ordered_pair(X1,X2),compose_class(X3))
| compose(X3,X1) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_466]) ).
cnf(c_0_466_1,axiom,
( compose(X3,X1) != X2
| member(ordered_pair(X1,X2),compose_class(X3))
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_466]) ).
cnf(c_0_466_2,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| compose(X3,X1) != X2
| member(ordered_pair(X1,X2),compose_class(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_466]) ).
cnf(c_0_467_0,axiom,
( member(ordered_pair(X1,X2),rest_of(X3))
| restrict(X3,X1,universal_class) != X2
| ~ member(X1,domain_of(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_467_1,axiom,
( restrict(X3,X1,universal_class) != X2
| member(ordered_pair(X1,X2),rest_of(X3))
| ~ member(X1,domain_of(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_467_2,axiom,
( ~ member(X1,domain_of(X3))
| restrict(X3,X1,universal_class) != X2
| member(ordered_pair(X1,X2),rest_of(X3)) ),
inference(literals_permutation,[status(thm)],[c_0_467]) ).
cnf(c_0_468_0,axiom,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X2,ordered_pair(X1,X3)),application_function) ),
inference(literals_permutation,[status(thm)],[c_0_468]) ).
cnf(c_0_468_1,axiom,
( ~ member(ordered_pair(X2,ordered_pair(X1,X3)),application_function)
| member(X1,domain_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_468]) ).
cnf(c_0_469_0,axiom,
( asymmetric(X1,X2)
| restrict(intersection(X1,inverse(X1)),X2,X2) != null_class ),
inference(literals_permutation,[status(thm)],[c_0_469]) ).
cnf(c_0_469_1,axiom,
( restrict(intersection(X1,inverse(X1)),X2,X2) != null_class
| asymmetric(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_469]) ).
cnf(c_0_470_0,axiom,
( operation(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_470_1,axiom,
( ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| operation(X1)
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_470_2,axiom,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| operation(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_470_3,axiom,
( ~ function(X1)
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X1)))
| operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_470]) ).
cnf(c_0_471_0,axiom,
( compose(X1,X2) = X3
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),composition_function) ),
inference(literals_permutation,[status(thm)],[c_0_471]) ).
cnf(c_0_471_1,axiom,
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),composition_function)
| compose(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_471]) ).
cnf(c_0_472_0,axiom,
( apply(X1,X2) = X3
| ~ member(ordered_pair(X1,ordered_pair(X2,X3)),application_function) ),
inference(literals_permutation,[status(thm)],[c_0_472]) ).
cnf(c_0_472_1,axiom,
( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),application_function)
| apply(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_472]) ).
cnf(c_0_473_0,axiom,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(X1,X2)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_1,axiom,
( ~ member(X1,X2)
| member(ordered_pair(X1,X2),element_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_473_2,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2)
| member(ordered_pair(X1,X2),element_relation) ),
inference(literals_permutation,[status(thm)],[c_0_473]) ).
cnf(c_0_474_0,axiom,
( member(ordered_pair(X1,X2),union_of_range_map)
| sum_class(range_of(X1)) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_1,axiom,
( sum_class(range_of(X1)) != X2
| member(ordered_pair(X1,X2),union_of_range_map)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_474_2,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| sum_class(range_of(X1)) != X2
| member(ordered_pair(X1,X2),union_of_range_map) ),
inference(literals_permutation,[status(thm)],[c_0_474]) ).
cnf(c_0_475_0,axiom,
( subclass(restrict(X1,X2,X2),complement(identity_relation))
| ~ irreflexive(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_475_1,axiom,
( ~ irreflexive(X1,X2)
| subclass(restrict(X1,X2,X2),complement(identity_relation)) ),
inference(literals_permutation,[status(thm)],[c_0_475]) ).
cnf(c_0_476_0,axiom,
( compatible(X1,X2,X3)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_1,axiom,
( ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| compatible(X1,X2,X3)
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_2,axiom,
( domain_of(domain_of(X2)) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| compatible(X1,X2,X3)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_476_3,axiom,
( ~ function(X1)
| domain_of(domain_of(X2)) != domain_of(X1)
| ~ subclass(range_of(X1),domain_of(domain_of(X3)))
| compatible(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_476]) ).
cnf(c_0_477_0,axiom,
( member(ordered_pair(X1,X2),successor_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| successor(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_477_1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),successor_relation)
| successor(X1) != X2 ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_477_2,axiom,
( successor(X1) != X2
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X2),successor_relation) ),
inference(literals_permutation,[status(thm)],[c_0_477]) ).
cnf(c_0_478_0,axiom,
( compatible(X1,X2,X3)
| ~ homomorphism(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_478_1,axiom,
( ~ homomorphism(X1,X2,X3)
| compatible(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_478]) ).
cnf(c_0_479_0,axiom,
( function(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation)
| ~ subclass(X1,cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_479_1,axiom,
( ~ subclass(compose(X1,inverse(X1)),identity_relation)
| function(X1)
| ~ subclass(X1,cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_479_2,axiom,
( ~ subclass(X1,cross_product(universal_class,universal_class))
| ~ subclass(compose(X1,inverse(X1)),identity_relation)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_479]) ).
cnf(c_0_480_0,axiom,
( connected(X1,X2)
| ~ subclass(cross_product(X2,X2),union(identity_relation,symmetrization_of(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_480_1,axiom,
( ~ subclass(cross_product(X2,X2),union(identity_relation,symmetrization_of(X1)))
| connected(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_480]) ).
cnf(c_0_481_0,axiom,
( restrict(X1,X2,universal_class) = X3
| ~ member(ordered_pair(X2,X3),rest_of(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_481_1,axiom,
( ~ member(ordered_pair(X2,X3),rest_of(X1))
| restrict(X1,X2,universal_class) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_481]) ).
cnf(c_0_482_0,axiom,
( segment(X1,X2,least(X1,X2)) = null_class
| ~ subclass(X2,X3)
| ~ well_ordering(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_1,axiom,
( ~ subclass(X2,X3)
| segment(X1,X2,least(X1,X2)) = null_class
| ~ well_ordering(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_482_2,axiom,
( ~ well_ordering(X1,X3)
| ~ subclass(X2,X3)
| segment(X1,X2,least(X1,X2)) = null_class ),
inference(literals_permutation,[status(thm)],[c_0_482]) ).
cnf(c_0_483_0,axiom,
( ~ member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) != null_class ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_483_1,axiom,
( restrict(X2,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_483]) ).
cnf(c_0_484_0,axiom,
( subclass(range_of(X1),domain_of(domain_of(X2)))
| ~ compatible(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_484_1,axiom,
( ~ compatible(X1,X3,X2)
| subclass(range_of(X1),domain_of(domain_of(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_484]) ).
cnf(c_0_485_0,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_485]) ).
cnf(c_0_485_1,axiom,
( ~ member(ordered_pair(X1,X3),cross_product(X2,X4))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_485]) ).
cnf(c_0_486_0,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_486]) ).
cnf(c_0_486_1,axiom,
( ~ member(ordered_pair(X3,X1),cross_product(X4,X2))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_486]) ).
cnf(c_0_487_0,axiom,
( restrict(intersection(X1,inverse(X1)),X2,X2) = null_class
| ~ asymmetric(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_487]) ).
cnf(c_0_487_1,axiom,
( ~ asymmetric(X1,X2)
| restrict(intersection(X1,inverse(X1)),X2,X2) = null_class ),
inference(literals_permutation,[status(thm)],[c_0_487]) ).
cnf(c_0_488_0,axiom,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_488]) ).
cnf(c_0_488_1,axiom,
( ~ member(X2,X4)
| member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_488]) ).
cnf(c_0_488_2,axiom,
( ~ member(X1,X3)
| ~ member(X2,X4)
| member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(literals_permutation,[status(thm)],[c_0_488]) ).
cnf(c_0_489_0,axiom,
( member(least(X1,X2),X2)
| ~ member(X3,X2)
| ~ subclass(X2,X4)
| ~ well_ordering(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_489_1,axiom,
( ~ member(X3,X2)
| member(least(X1,X2),X2)
| ~ subclass(X2,X4)
| ~ well_ordering(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_489_2,axiom,
( ~ subclass(X2,X4)
| ~ member(X3,X2)
| member(least(X1,X2),X2)
| ~ well_ordering(X1,X4) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_489_3,axiom,
( ~ well_ordering(X1,X4)
| ~ subclass(X2,X4)
| ~ member(X3,X2)
| member(least(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_489]) ).
cnf(c_0_490_0,axiom,
( subclass(range_of(X1),X2)
| ~ maps(X1,X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_490_1,axiom,
( ~ maps(X1,X3,X2)
| subclass(range_of(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_490]) ).
cnf(c_0_491_0,axiom,
( domain_of(domain_of(X1)) = domain_of(X2)
| ~ compatible(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_491]) ).
cnf(c_0_491_1,axiom,
( ~ compatible(X2,X1,X3)
| domain_of(domain_of(X1)) = domain_of(X2) ),
inference(literals_permutation,[status(thm)],[c_0_491]) ).
cnf(c_0_492_0,axiom,
( subclass(X1,X2)
| ~ section(X3,X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_492]) ).
cnf(c_0_492_1,axiom,
( ~ section(X3,X1,X2)
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_492]) ).
cnf(c_0_493_0,axiom,
( maps(X1,domain_of(X1),X2)
| ~ subclass(range_of(X1),X2)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_493_1,axiom,
( ~ subclass(range_of(X1),X2)
| maps(X1,domain_of(X1),X2)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_493_2,axiom,
( ~ function(X1)
| ~ subclass(range_of(X1),X2)
| maps(X1,domain_of(X1),X2) ),
inference(literals_permutation,[status(thm)],[c_0_493]) ).
cnf(c_0_494_0,axiom,
( member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_494_1,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_494_2,axiom,
( ~ member(X1,universal_class)
| restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_494]) ).
cnf(c_0_495_0,axiom,
( member(X1,recursion_equation_functions(X2))
| compose(X2,rest_of(X1)) != X1
| ~ member(domain_of(X1),ordinal_numbers)
| ~ function(X1)
| ~ function(X2) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_495_1,axiom,
( compose(X2,rest_of(X1)) != X1
| member(X1,recursion_equation_functions(X2))
| ~ member(domain_of(X1),ordinal_numbers)
| ~ function(X1)
| ~ function(X2) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_495_2,axiom,
( ~ member(domain_of(X1),ordinal_numbers)
| compose(X2,rest_of(X1)) != X1
| member(X1,recursion_equation_functions(X2))
| ~ function(X1)
| ~ function(X2) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_495_3,axiom,
( ~ function(X1)
| ~ member(domain_of(X1),ordinal_numbers)
| compose(X2,rest_of(X1)) != X1
| member(X1,recursion_equation_functions(X2))
| ~ function(X2) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_495_4,axiom,
( ~ function(X2)
| ~ function(X1)
| ~ member(domain_of(X1),ordinal_numbers)
| compose(X2,rest_of(X1)) != X1
| member(X1,recursion_equation_functions(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_495]) ).
cnf(c_0_496_0,axiom,
( subclass(cross_product(X1,X1),union(identity_relation,symmetrization_of(X2)))
| ~ connected(X2,X1) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_496_1,axiom,
( ~ connected(X2,X1)
| subclass(cross_product(X1,X1),union(identity_relation,symmetrization_of(X2))) ),
inference(literals_permutation,[status(thm)],[c_0_496]) ).
cnf(c_0_497_0,axiom,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X1,X3),rest_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_497]) ).
cnf(c_0_497_1,axiom,
( ~ member(ordered_pair(X1,X3),rest_of(X2))
| member(X1,domain_of(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_497]) ).
cnf(c_0_498_0,axiom,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_498_1,axiom,
( ~ maps(X1,X2,X3)
| domain_of(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_498]) ).
cnf(c_0_499_0,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_499]) ).
cnf(c_0_499_1,axiom,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_499]) ).
cnf(c_0_500_0,axiom,
( function(X1)
| ~ compatible(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_500_1,axiom,
( ~ compatible(X1,X2,X3)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_500]) ).
cnf(c_0_501_0,axiom,
( operation(X1)
| ~ homomorphism(X2,X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_501_1,axiom,
( ~ homomorphism(X2,X1,X3)
| operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_501]) ).
cnf(c_0_502_0,axiom,
( operation(X1)
| ~ homomorphism(X2,X3,X1) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_502_1,axiom,
( ~ homomorphism(X2,X3,X1)
| operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_502]) ).
cnf(c_0_503_0,axiom,
( function(X1)
| ~ maps(X1,X2,X3) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_503_1,axiom,
( ~ maps(X1,X2,X3)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_503]) ).
cnf(c_0_504_0,axiom,
( compose(X1,X2) = X3
| ~ member(ordered_pair(X2,X3),compose_class(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_504_1,axiom,
( ~ member(ordered_pair(X2,X3),compose_class(X1))
| compose(X1,X2) = X3 ),
inference(literals_permutation,[status(thm)],[c_0_504]) ).
cnf(c_0_505_0,axiom,
( member(least(X1,X2),X2)
| X2 = null_class
| ~ subclass(X2,X3)
| ~ well_ordering(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_505_1,axiom,
( X2 = null_class
| member(least(X1,X2),X2)
| ~ subclass(X2,X3)
| ~ well_ordering(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_505_2,axiom,
( ~ subclass(X2,X3)
| X2 = null_class
| member(least(X1,X2),X2)
| ~ well_ordering(X1,X3) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_505_3,axiom,
( ~ well_ordering(X1,X3)
| ~ subclass(X2,X3)
| X2 = null_class
| member(least(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_505]) ).
cnf(c_0_506_0,axiom,
( member(X1,ordinal_numbers)
| ~ member(X1,universal_class)
| ~ subclass(sum_class(X1),X1)
| ~ well_ordering(element_relation,X1) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_506_1,axiom,
( ~ member(X1,universal_class)
| member(X1,ordinal_numbers)
| ~ subclass(sum_class(X1),X1)
| ~ well_ordering(element_relation,X1) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_506_2,axiom,
( ~ subclass(sum_class(X1),X1)
| ~ member(X1,universal_class)
| member(X1,ordinal_numbers)
| ~ well_ordering(element_relation,X1) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_506_3,axiom,
( ~ well_ordering(element_relation,X1)
| ~ subclass(sum_class(X1),X1)
| ~ member(X1,universal_class)
| member(X1,ordinal_numbers) ),
inference(literals_permutation,[status(thm)],[c_0_506]) ).
cnf(c_0_507_0,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_507_1,axiom,
( ~ member(X1,X3)
| member(X1,intersection(X2,X3))
| ~ member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_507_2,axiom,
( ~ member(X1,X2)
| ~ member(X1,X3)
| member(X1,intersection(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_507]) ).
cnf(c_0_508_0,axiom,
( single_valued_class(X1)
| ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
inference(literals_permutation,[status(thm)],[c_0_508]) ).
cnf(c_0_508_1,axiom,
( ~ subclass(compose(X1,inverse(X1)),identity_relation)
| single_valued_class(X1) ),
inference(literals_permutation,[status(thm)],[c_0_508]) ).
cnf(c_0_509_0,axiom,
( inductive(X1)
| ~ subclass(image(successor_relation,X1),X1)
| ~ member(null_class,X1) ),
inference(literals_permutation,[status(thm)],[c_0_509]) ).
cnf(c_0_509_1,axiom,
( ~ subclass(image(successor_relation,X1),X1)
| inductive(X1)
| ~ member(null_class,X1) ),
inference(literals_permutation,[status(thm)],[c_0_509]) ).
cnf(c_0_509_2,axiom,
( ~ member(null_class,X1)
| ~ subclass(image(successor_relation,X1),X1)
| inductive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_509]) ).
cnf(c_0_510_0,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
inference(literals_permutation,[status(thm)],[c_0_510]) ).
cnf(c_0_510_1,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_510]) ).
cnf(c_0_511_0,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(literals_permutation,[status(thm)],[c_0_511]) ).
cnf(c_0_511_1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_511]) ).
cnf(c_0_512_0,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_512]) ).
cnf(c_0_512_1,axiom,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_512]) ).
cnf(c_0_513_0,axiom,
( well_ordering(X1,X2)
| subclass(not_well_ordering(X1,X2),X2)
| ~ connected(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_513]) ).
cnf(c_0_513_1,axiom,
( subclass(not_well_ordering(X1,X2),X2)
| well_ordering(X1,X2)
| ~ connected(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_513]) ).
cnf(c_0_513_2,axiom,
( ~ connected(X1,X2)
| subclass(not_well_ordering(X1,X2),X2)
| well_ordering(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_513]) ).
cnf(c_0_514_0,axiom,
( member(X1,X2)
| ~ member(ordered_pair(X1,X2),element_relation) ),
inference(literals_permutation,[status(thm)],[c_0_514]) ).
cnf(c_0_514_1,axiom,
( ~ member(ordered_pair(X1,X2),element_relation)
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_514]) ).
cnf(c_0_515_0,axiom,
( sum_class(range_of(X1)) = X2
| ~ member(ordered_pair(X1,X2),union_of_range_map) ),
inference(literals_permutation,[status(thm)],[c_0_515]) ).
cnf(c_0_515_1,axiom,
( ~ member(ordered_pair(X1,X2),union_of_range_map)
| sum_class(range_of(X1)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_515]) ).
cnf(c_0_516_0,axiom,
( member(ordered_pair(X1,domain_of(X1)),domain_relation)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_516]) ).
cnf(c_0_516_1,axiom,
( ~ member(X1,universal_class)
| member(ordered_pair(X1,domain_of(X1)),domain_relation) ),
inference(literals_permutation,[status(thm)],[c_0_516]) ).
cnf(c_0_517_0,axiom,
( member(ordered_pair(X1,rest_of(X1)),rest_relation)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_517]) ).
cnf(c_0_517_1,axiom,
( ~ member(X1,universal_class)
| member(ordered_pair(X1,rest_of(X1)),rest_relation) ),
inference(literals_permutation,[status(thm)],[c_0_517]) ).
cnf(c_0_518_0,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_518]) ).
cnf(c_0_518_1,axiom,
( X1 = X3
| X1 = X2
| ~ member(X1,unordered_pair(X3,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_518]) ).
cnf(c_0_518_2,axiom,
( ~ member(X1,unordered_pair(X3,X2))
| X1 = X3
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_518]) ).
cnf(c_0_519_0,axiom,
( X1 = ordinal_numbers
| member(X1,ordinal_numbers)
| ~ subclass(sum_class(X1),X1)
| ~ well_ordering(element_relation,X1) ),
inference(literals_permutation,[status(thm)],[c_0_519]) ).
cnf(c_0_519_1,axiom,
( member(X1,ordinal_numbers)
| X1 = ordinal_numbers
| ~ subclass(sum_class(X1),X1)
| ~ well_ordering(element_relation,X1) ),
inference(literals_permutation,[status(thm)],[c_0_519]) ).
cnf(c_0_519_2,axiom,
( ~ subclass(sum_class(X1),X1)
| member(X1,ordinal_numbers)
| X1 = ordinal_numbers
| ~ well_ordering(element_relation,X1) ),
inference(literals_permutation,[status(thm)],[c_0_519]) ).
cnf(c_0_519_3,axiom,
( ~ well_ordering(element_relation,X1)
| ~ subclass(sum_class(X1),X1)
| member(X1,ordinal_numbers)
| X1 = ordinal_numbers ),
inference(literals_permutation,[status(thm)],[c_0_519]) ).
cnf(c_0_520_0,axiom,
( successor(X1) = X2
| ~ member(ordered_pair(X1,X2),successor_relation) ),
inference(literals_permutation,[status(thm)],[c_0_520]) ).
cnf(c_0_520_1,axiom,
( ~ member(ordered_pair(X1,X2),successor_relation)
| successor(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_520]) ).
cnf(c_0_521_0,axiom,
( member(image(X1,X2),universal_class)
| ~ member(X2,universal_class)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_521_1,axiom,
( ~ member(X2,universal_class)
| member(image(X1,X2),universal_class)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_521_2,axiom,
( ~ function(X1)
| ~ member(X2,universal_class)
| member(image(X1,X2),universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_521]) ).
cnf(c_0_522_0,axiom,
( domain_of(X1) = X2
| ~ member(ordered_pair(X1,X2),domain_relation) ),
inference(literals_permutation,[status(thm)],[c_0_522]) ).
cnf(c_0_522_1,axiom,
( ~ member(ordered_pair(X1,X2),domain_relation)
| domain_of(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_522]) ).
cnf(c_0_523_0,axiom,
( rest_of(X1) = X2
| ~ member(ordered_pair(X1,X2),rest_relation) ),
inference(literals_permutation,[status(thm)],[c_0_523]) ).
cnf(c_0_523_1,axiom,
( ~ member(ordered_pair(X1,X2),rest_relation)
| rest_of(X1) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_523]) ).
cnf(c_0_524_0,axiom,
( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1)
| ~ operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_524]) ).
cnf(c_0_524_1,axiom,
( ~ operation(X1)
| cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1) ),
inference(literals_permutation,[status(thm)],[c_0_524]) ).
cnf(c_0_525_0,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_525]) ).
cnf(c_0_525_1,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(literals_permutation,[status(thm)],[c_0_525]) ).
cnf(c_0_526_0,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_526_1,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(literals_permutation,[status(thm)],[c_0_526]) ).
cnf(c_0_527_0,axiom,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subclass(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_527_1,axiom,
( ~ member(X1,X3)
| member(X1,X2)
| ~ subclass(X3,X2) ),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_527_2,axiom,
( ~ subclass(X3,X2)
| ~ member(X1,X3)
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_527]) ).
cnf(c_0_528_0,axiom,
( well_ordering(X1,X2)
| not_well_ordering(X1,X2) != null_class
| ~ connected(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_528]) ).
cnf(c_0_528_1,axiom,
( not_well_ordering(X1,X2) != null_class
| well_ordering(X1,X2)
| ~ connected(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_528]) ).
cnf(c_0_528_2,axiom,
( ~ connected(X1,X2)
| not_well_ordering(X1,X2) != null_class
| well_ordering(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_528]) ).
cnf(c_0_529_0,axiom,
( member(apply(choice,X1),X1)
| X1 = null_class
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_529_1,axiom,
( X1 = null_class
| member(apply(choice,X1),X1)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_529_2,axiom,
( ~ member(X1,universal_class)
| X1 = null_class
| member(apply(choice,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_529]) ).
cnf(c_0_530_0,axiom,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ single_valued_class(X1) ),
inference(literals_permutation,[status(thm)],[c_0_530]) ).
cnf(c_0_530_1,axiom,
( ~ single_valued_class(X1)
| subclass(compose(X1,inverse(X1)),identity_relation) ),
inference(literals_permutation,[status(thm)],[c_0_530]) ).
cnf(c_0_531_0,axiom,
( subclass(compose(X1,inverse(X1)),identity_relation)
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_531]) ).
cnf(c_0_531_1,axiom,
( ~ function(X1)
| subclass(compose(X1,inverse(X1)),identity_relation) ),
inference(literals_permutation,[status(thm)],[c_0_531]) ).
cnf(c_0_532_0,axiom,
( member(X1,X2)
| member(X1,complement(X2))
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_532]) ).
cnf(c_0_532_1,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_532]) ).
cnf(c_0_532_2,axiom,
( ~ member(X1,universal_class)
| member(X1,complement(X2))
| member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_532]) ).
cnf(c_0_533_0,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_533_1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_533]) ).
cnf(c_0_534_0,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
inference(literals_permutation,[status(thm)],[c_0_534]) ).
cnf(c_0_534_1,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_534]) ).
cnf(c_0_535_0,axiom,
( compose(X1,rest_of(X2)) = X2
| ~ member(X2,recursion_equation_functions(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_535]) ).
cnf(c_0_535_1,axiom,
( ~ member(X2,recursion_equation_functions(X1))
| compose(X1,rest_of(X2)) = X2 ),
inference(literals_permutation,[status(thm)],[c_0_535]) ).
cnf(c_0_536_0,axiom,
( member(domain_of(X1),ordinal_numbers)
| ~ member(X1,recursion_equation_functions(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_536]) ).
cnf(c_0_536_1,axiom,
( ~ member(X1,recursion_equation_functions(X2))
| member(domain_of(X1),ordinal_numbers) ),
inference(literals_permutation,[status(thm)],[c_0_536]) ).
cnf(c_0_537_0,axiom,
( X1 = X2
| ~ subclass(X2,X1)
| ~ subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_537]) ).
cnf(c_0_537_1,axiom,
( ~ subclass(X2,X1)
| X1 = X2
| ~ subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_537]) ).
cnf(c_0_537_2,axiom,
( ~ subclass(X1,X2)
| ~ subclass(X2,X1)
| X1 = X2 ),
inference(literals_permutation,[status(thm)],[c_0_537]) ).
cnf(c_0_538_0,axiom,
( subclass(range_of(X1),domain_of(domain_of(X1)))
| ~ operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_538]) ).
cnf(c_0_538_1,axiom,
( ~ operation(X1)
| subclass(range_of(X1),domain_of(domain_of(X1))) ),
inference(literals_permutation,[status(thm)],[c_0_538]) ).
cnf(c_0_539_0,axiom,
( subclass(image(successor_relation,X1),X1)
| ~ inductive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_539]) ).
cnf(c_0_539_1,axiom,
( ~ inductive(X1)
| subclass(image(successor_relation,X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_539]) ).
cnf(c_0_540_0,axiom,
( subclass(X1,cross_product(universal_class,universal_class))
| ~ function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_540]) ).
cnf(c_0_540_1,axiom,
( ~ function(X1)
| subclass(X1,cross_product(universal_class,universal_class)) ),
inference(literals_permutation,[status(thm)],[c_0_540]) ).
cnf(c_0_541_0,axiom,
( subclass(sum_class(X1),X1)
| ~ member(X1,ordinal_numbers) ),
inference(literals_permutation,[status(thm)],[c_0_541]) ).
cnf(c_0_541_1,axiom,
( ~ member(X1,ordinal_numbers)
| subclass(sum_class(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_541]) ).
cnf(c_0_542_0,axiom,
( member(sum_class(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_542]) ).
cnf(c_0_542_1,axiom,
( ~ member(X1,universal_class)
| member(sum_class(X1),universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_542]) ).
cnf(c_0_543_0,axiom,
( member(power_class(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_543]) ).
cnf(c_0_543_1,axiom,
( ~ member(X1,universal_class)
| member(power_class(X1),universal_class) ),
inference(literals_permutation,[status(thm)],[c_0_543]) ).
cnf(c_0_544_0,axiom,
( connected(X1,X2)
| ~ well_ordering(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_544]) ).
cnf(c_0_544_1,axiom,
( ~ well_ordering(X1,X2)
| connected(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_544]) ).
cnf(c_0_545_0,axiom,
( function(X1)
| ~ member(X2,recursion_equation_functions(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_545]) ).
cnf(c_0_545_1,axiom,
( ~ member(X2,recursion_equation_functions(X1))
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_545]) ).
cnf(c_0_546_0,axiom,
( function(X1)
| ~ member(X1,recursion_equation_functions(X2)) ),
inference(literals_permutation,[status(thm)],[c_0_546]) ).
cnf(c_0_546_1,axiom,
( ~ member(X1,recursion_equation_functions(X2))
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_546]) ).
cnf(c_0_547_0,axiom,
( well_ordering(element_relation,X1)
| ~ member(X1,ordinal_numbers) ),
inference(literals_permutation,[status(thm)],[c_0_547]) ).
cnf(c_0_547_1,axiom,
( ~ member(X1,ordinal_numbers)
| well_ordering(element_relation,X1) ),
inference(literals_permutation,[status(thm)],[c_0_547]) ).
cnf(c_0_548_0,axiom,
( one_to_one(X1)
| ~ function(X1)
| ~ function(inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_548]) ).
cnf(c_0_548_1,axiom,
( ~ function(X1)
| one_to_one(X1)
| ~ function(inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_548]) ).
cnf(c_0_548_2,axiom,
( ~ function(inverse(X1))
| ~ function(X1)
| one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_548]) ).
cnf(c_0_549_0,axiom,
( integer_of(X1) = X1
| ~ member(X1,omega) ),
inference(literals_permutation,[status(thm)],[c_0_549]) ).
cnf(c_0_549_1,axiom,
( ~ member(X1,omega)
| integer_of(X1) = X1 ),
inference(literals_permutation,[status(thm)],[c_0_549]) ).
cnf(c_0_550_0,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
inference(literals_permutation,[status(thm)],[c_0_550]) ).
cnf(c_0_550_1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
inference(literals_permutation,[status(thm)],[c_0_550]) ).
cnf(c_0_551_0,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
inference(literals_permutation,[status(thm)],[c_0_551]) ).
cnf(c_0_551_1,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
inference(literals_permutation,[status(thm)],[c_0_551]) ).
cnf(c_0_552_0,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_552]) ).
cnf(c_0_552_1,axiom,
( ~ inductive(X1)
| member(null_class,X1) ),
inference(literals_permutation,[status(thm)],[c_0_552]) ).
cnf(c_0_553_0,axiom,
( subclass(omega,X1)
| ~ inductive(X1) ),
inference(literals_permutation,[status(thm)],[c_0_553]) ).
cnf(c_0_553_1,axiom,
( ~ inductive(X1)
| subclass(omega,X1) ),
inference(literals_permutation,[status(thm)],[c_0_553]) ).
cnf(c_0_554_0,axiom,
( subclass(X1,X2)
| X1 != X2 ),
inference(literals_permutation,[status(thm)],[c_0_554]) ).
cnf(c_0_554_1,axiom,
( X1 != X2
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_554]) ).
cnf(c_0_555_0,axiom,
( subclass(X1,X2)
| X2 != X1 ),
inference(literals_permutation,[status(thm)],[c_0_555]) ).
cnf(c_0_555_1,axiom,
( X2 != X1
| subclass(X1,X2) ),
inference(literals_permutation,[status(thm)],[c_0_555]) ).
cnf(c_0_556_0,axiom,
( function(inverse(X1))
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_556]) ).
cnf(c_0_556_1,axiom,
( ~ one_to_one(X1)
| function(inverse(X1)) ),
inference(literals_permutation,[status(thm)],[c_0_556]) ).
cnf(c_0_557_0,axiom,
( integer_of(X1) = null_class
| member(X1,omega) ),
inference(literals_permutation,[status(thm)],[c_0_557]) ).
cnf(c_0_557_1,axiom,
( member(X1,omega)
| integer_of(X1) = null_class ),
inference(literals_permutation,[status(thm)],[c_0_557]) ).
cnf(c_0_558_0,axiom,
( function(X1)
| ~ one_to_one(X1) ),
inference(literals_permutation,[status(thm)],[c_0_558]) ).
cnf(c_0_558_1,axiom,
( ~ one_to_one(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_558]) ).
cnf(c_0_559_0,axiom,
( function(X1)
| ~ operation(X1) ),
inference(literals_permutation,[status(thm)],[c_0_559]) ).
cnf(c_0_559_1,axiom,
( ~ operation(X1)
| function(X1) ),
inference(literals_permutation,[status(thm)],[c_0_559]) ).
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_231,negated_conjecture,
member(v,least(element_relation,u)),
file('<stdin>',prove_corollary_to_well_ordering_property1_4) ).
fof(c_0_1_232,negated_conjecture,
member(v,u),
file('<stdin>',prove_corollary_to_well_ordering_property1_3) ).
fof(c_0_2_233,negated_conjecture,
subclass(u,y),
file('<stdin>',prove_corollary_to_well_ordering_property1_2) ).
fof(c_0_3_234,negated_conjecture,
well_ordering(element_relation,y),
file('<stdin>',prove_corollary_to_well_ordering_property1_1) ).
fof(c_0_4_235,negated_conjecture,
member(v,least(element_relation,u)),
c_0_0 ).
fof(c_0_5_236,negated_conjecture,
member(v,u),
c_0_1 ).
fof(c_0_6_237,negated_conjecture,
subclass(u,y),
c_0_2 ).
fof(c_0_7_238,negated_conjecture,
well_ordering(element_relation,y),
c_0_3 ).
fof(c_0_8_239,negated_conjecture,
member(v,least(element_relation,u)),
c_0_4 ).
fof(c_0_9_240,negated_conjecture,
member(v,u),
c_0_5 ).
fof(c_0_10_241,negated_conjecture,
subclass(u,y),
c_0_6 ).
fof(c_0_11_242,negated_conjecture,
well_ordering(element_relation,y),
c_0_7 ).
cnf(c_0_12_243,negated_conjecture,
member(v,least(element_relation,u)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13_244,negated_conjecture,
member(v,u),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14_245,negated_conjecture,
subclass(u,y),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15_246,negated_conjecture,
well_ordering(element_relation,y),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16_247,negated_conjecture,
member(v,least(element_relation,u)),
c_0_12,
[final] ).
cnf(c_0_17_248,negated_conjecture,
member(v,u),
c_0_13,
[final] ).
cnf(c_0_18_249,negated_conjecture,
subclass(u,y),
c_0_14,
[final] ).
cnf(c_0_19_250,negated_conjecture,
well_ordering(element_relation,y),
c_0_15,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_109,plain,
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_488_2) ).
cnf(c_594,plain,
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(copy,[status(esa)],[c_109]) ).
cnf(c_751747,plain,
( member(ordered_pair(v,least(element_relation,u)),cross_product(universal_class,universal_class))
| ~ member(least(element_relation,u),universal_class)
| ~ member(v,universal_class) ),
inference(instantiation,[status(thm)],[c_594]) ).
cnf(c_206,plain,
( member(X0,X1)
| ~ member(X0,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_527_2) ).
cnf(c_691,plain,
( member(X0,X1)
| ~ member(X0,X2)
| ~ subclass(X2,X1) ),
inference(copy,[status(esa)],[c_206]) ).
cnf(c_144411,plain,
( ~ subclass(u,X0)
| ~ member(least(element_relation,u),u)
| member(least(element_relation,u),X0) ),
inference(instantiation,[status(thm)],[c_691]) ).
cnf(c_144412,plain,
( ~ subclass(u,universal_class)
| member(least(element_relation,u),universal_class)
| ~ member(least(element_relation,u),u) ),
inference(instantiation,[status(thm)],[c_144411]) ).
cnf(c_46,plain,
( ~ well_ordering(X0,X1)
| ~ subclass(X2,X1)
| ~ member(X3,X2)
| ~ member(ordered_pair(X3,least(X0,X2)),X0) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_464_0) ).
cnf(c_531,plain,
( ~ well_ordering(X0,X1)
| ~ subclass(X2,X1)
| ~ member(X3,X2)
| ~ member(ordered_pair(X3,least(X0,X2)),X0) ),
inference(copy,[status(esa)],[c_46]) ).
cnf(c_47414,plain,
( ~ subclass(X0,y)
| ~ member(ordered_pair(X1,least(element_relation,X0)),element_relation)
| ~ member(X1,X0)
| ~ well_ordering(element_relation,y) ),
inference(instantiation,[status(thm)],[c_531]) ).
cnf(c_143997,plain,
( ~ subclass(u,y)
| ~ member(ordered_pair(v,least(element_relation,u)),element_relation)
| ~ member(v,u)
| ~ well_ordering(element_relation,y) ),
inference(instantiation,[status(thm)],[c_47414]) ).
cnf(c_113,plain,
( member(least(X0,X1),X1)
| ~ member(X2,X1)
| ~ subclass(X1,X3)
| ~ well_ordering(X0,X3) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_489_3) ).
cnf(c_598,plain,
( member(least(X0,X1),X1)
| ~ member(X2,X1)
| ~ subclass(X1,X3)
| ~ well_ordering(X0,X3) ),
inference(copy,[status(esa)],[c_113]) ).
cnf(c_47412,plain,
( ~ subclass(u,X0)
| member(least(X1,u),u)
| ~ member(v,u)
| ~ well_ordering(X1,X0) ),
inference(instantiation,[status(thm)],[c_598]) ).
cnf(c_143981,plain,
( ~ subclass(u,y)
| member(least(element_relation,u),u)
| ~ member(v,u)
| ~ well_ordering(element_relation,y) ),
inference(instantiation,[status(thm)],[c_47412]) ).
cnf(c_291,plain,
subclass(X0,universal_class),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_214_0) ).
cnf(c_776,plain,
subclass(X0,universal_class),
inference(copy,[status(esa)],[c_291]) ).
cnf(c_143731,plain,
subclass(u,universal_class),
inference(instantiation,[status(thm)],[c_776]) ).
cnf(c_143714,plain,
subclass(least(element_relation,u),universal_class),
inference(instantiation,[status(thm)],[c_776]) ).
cnf(c_204,plain,
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_527_0) ).
cnf(c_689,plain,
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(copy,[status(esa)],[c_204]) ).
cnf(c_47270,plain,
( ~ subclass(least(element_relation,u),X0)
| ~ member(v,least(element_relation,u))
| member(v,X0) ),
inference(instantiation,[status(thm)],[c_689]) ).
cnf(c_47271,plain,
( ~ subclass(least(element_relation,u),universal_class)
| member(v,universal_class)
| ~ member(v,least(element_relation,u)) ),
inference(instantiation,[status(thm)],[c_47270]) ).
cnf(c_70,plain,
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_473_0) ).
cnf(c_555,plain,
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation) ),
inference(copy,[status(esa)],[c_70]) ).
cnf(c_47232,plain,
( ~ member(ordered_pair(v,least(element_relation,u)),cross_product(universal_class,universal_class))
| member(ordered_pair(v,least(element_relation,u)),element_relation)
| ~ member(v,least(element_relation,u)) ),
inference(instantiation,[status(thm)],[c_555]) ).
cnf(c_322,negated_conjecture,
member(v,least(element_relation,u)),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_16) ).
cnf(c_323,negated_conjecture,
member(v,u),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_17) ).
cnf(c_324,negated_conjecture,
subclass(u,y),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_18) ).
cnf(c_325,negated_conjecture,
well_ordering(element_relation,y),
file('/export/starexec/sandbox/tmp/iprover_modulo_f57094.p',c_0_19) ).
cnf(contradiction,plain,
$false,
inference(minisat,[status(thm)],[c_751747,c_144412,c_143997,c_143981,c_143731,c_143714,c_47271,c_47232,c_322,c_323,c_324,c_325]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM066-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : iprover_modulo %s %d
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jul 6 17:53:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Running in mono-core mode
% 0.19/0.41 % Orienting using strategy Equiv(ClausalAll)
% 0.19/0.41 % Orientation found
% 0.19/0.41 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_9ef8fa.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_f57094.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_3a74b3 | grep -v "SZS"
% 0.19/0.43
% 0.19/0.43 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.19/0.43
% 0.19/0.43 %
% 0.19/0.43 % ------ iProver source info
% 0.19/0.43
% 0.19/0.43 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.19/0.43 % git: non_committed_changes: true
% 0.19/0.43 % git: last_make_outside_of_git: true
% 0.19/0.43
% 0.19/0.43 %
% 0.19/0.43 % ------ Input Options
% 0.19/0.43
% 0.19/0.43 % --out_options all
% 0.19/0.43 % --tptp_safe_out true
% 0.19/0.43 % --problem_path ""
% 0.19/0.43 % --include_path ""
% 0.19/0.43 % --clausifier .//eprover
% 0.19/0.43 % --clausifier_options --tstp-format
% 0.19/0.43 % --stdin false
% 0.19/0.43 % --dbg_backtrace false
% 0.19/0.43 % --dbg_dump_prop_clauses false
% 0.19/0.43 % --dbg_dump_prop_clauses_file -
% 0.19/0.43 % --dbg_out_stat false
% 0.19/0.43
% 0.19/0.43 % ------ General Options
% 0.19/0.43
% 0.19/0.43 % --fof false
% 0.19/0.43 % --time_out_real 150.
% 0.19/0.43 % --time_out_prep_mult 0.2
% 0.19/0.43 % --time_out_virtual -1.
% 0.19/0.43 % --schedule none
% 0.19/0.43 % --ground_splitting input
% 0.19/0.43 % --splitting_nvd 16
% 0.19/0.43 % --non_eq_to_eq false
% 0.19/0.43 % --prep_gs_sim true
% 0.19/0.43 % --prep_unflatten false
% 0.19/0.43 % --prep_res_sim true
% 0.19/0.43 % --prep_upred true
% 0.19/0.43 % --res_sim_input true
% 0.19/0.43 % --clause_weak_htbl true
% 0.19/0.43 % --gc_record_bc_elim false
% 0.19/0.43 % --symbol_type_check false
% 0.19/0.43 % --clausify_out false
% 0.19/0.43 % --large_theory_mode false
% 0.19/0.43 % --prep_sem_filter none
% 0.19/0.43 % --prep_sem_filter_out false
% 0.19/0.43 % --preprocessed_out false
% 0.19/0.43 % --sub_typing false
% 0.19/0.43 % --brand_transform false
% 0.19/0.43 % --pure_diseq_elim true
% 0.19/0.43 % --min_unsat_core false
% 0.19/0.43 % --pred_elim true
% 0.19/0.43 % --add_important_lit false
% 0.19/0.43 % --soft_assumptions false
% 0.19/0.43 % --reset_solvers false
% 0.19/0.43 % --bc_imp_inh []
% 0.19/0.43 % --conj_cone_tolerance 1.5
% 0.19/0.43 % --prolific_symb_bound 500
% 0.19/0.43 % --lt_threshold 2000
% 0.19/0.43
% 0.19/0.43 % ------ SAT Options
% 0.19/0.43
% 0.19/0.43 % --sat_mode false
% 0.19/0.43 % --sat_fm_restart_options ""
% 0.19/0.43 % --sat_gr_def false
% 0.19/0.43 % --sat_epr_types true
% 0.19/0.43 % --sat_non_cyclic_types false
% 0.19/0.43 % --sat_finite_models false
% 0.19/0.43 % --sat_fm_lemmas false
% 0.19/0.43 % --sat_fm_prep false
% 0.19/0.43 % --sat_fm_uc_incr true
% 0.19/0.43 % --sat_out_model small
% 0.19/0.43 % --sat_out_clauses false
% 0.19/0.43
% 0.19/0.43 % ------ QBF Options
% 0.19/0.43
% 0.19/0.43 % --qbf_mode false
% 0.19/0.43 % --qbf_elim_univ true
% 0.19/0.43 % --qbf_sk_in true
% 0.19/0.43 % --qbf_pred_elim true
% 0.19/0.43 % --qbf_split 32
% 0.19/0.43
% 0.19/0.43 % ------ BMC1 Options
% 0.19/0.43
% 0.19/0.43 % --bmc1_incremental false
% 0.19/0.43 % --bmc1_axioms reachable_all
% 0.19/0.43 % --bmc1_min_bound 0
% 0.19/0.43 % --bmc1_max_bound -1
% 0.19/0.43 % --bmc1_max_bound_default -1
% 0.19/0.43 % --bmc1_symbol_reachability true
% 0.19/0.43 % --bmc1_property_lemmas false
% 0.19/0.43 % --bmc1_k_induction false
% 0.19/0.43 % --bmc1_non_equiv_states false
% 0.19/0.43 % --bmc1_deadlock false
% 0.19/0.43 % --bmc1_ucm false
% 0.19/0.43 % --bmc1_add_unsat_core none
% 0.19/0.43 % --bmc1_unsat_core_children false
% 0.19/0.43 % --bmc1_unsat_core_extrapolate_axioms false
% 0.19/0.43 % --bmc1_out_stat full
% 0.19/0.43 % --bmc1_ground_init false
% 0.19/0.43 % --bmc1_pre_inst_next_state false
% 0.19/0.43 % --bmc1_pre_inst_state false
% 0.19/0.43 % --bmc1_pre_inst_reach_state false
% 0.19/0.43 % --bmc1_out_unsat_core false
% 0.19/0.43 % --bmc1_aig_witness_out false
% 0.19/0.43 % --bmc1_verbose false
% 0.19/0.43 % --bmc1_dump_clauses_tptp false
% 1.06/1.39 % --bmc1_dump_unsat_core_tptp false
% 1.06/1.39 % --bmc1_dump_file -
% 1.06/1.39 % --bmc1_ucm_expand_uc_limit 128
% 1.06/1.39 % --bmc1_ucm_n_expand_iterations 6
% 1.06/1.39 % --bmc1_ucm_extend_mode 1
% 1.06/1.39 % --bmc1_ucm_init_mode 2
% 1.06/1.39 % --bmc1_ucm_cone_mode none
% 1.06/1.39 % --bmc1_ucm_reduced_relation_type 0
% 1.06/1.39 % --bmc1_ucm_relax_model 4
% 1.06/1.39 % --bmc1_ucm_full_tr_after_sat true
% 1.06/1.39 % --bmc1_ucm_expand_neg_assumptions false
% 1.06/1.39 % --bmc1_ucm_layered_model none
% 1.06/1.39 % --bmc1_ucm_max_lemma_size 10
% 1.06/1.39
% 1.06/1.39 % ------ AIG Options
% 1.06/1.39
% 1.06/1.39 % --aig_mode false
% 1.06/1.39
% 1.06/1.39 % ------ Instantiation Options
% 1.06/1.39
% 1.06/1.39 % --instantiation_flag true
% 1.06/1.39 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.06/1.39 % --inst_solver_per_active 750
% 1.06/1.39 % --inst_solver_calls_frac 0.5
% 1.06/1.39 % --inst_passive_queue_type priority_queues
% 1.06/1.39 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 1.06/1.39 % --inst_passive_queues_freq [25;2]
% 1.06/1.39 % --inst_dismatching true
% 1.06/1.39 % --inst_eager_unprocessed_to_passive true
% 1.06/1.39 % --inst_prop_sim_given true
% 1.06/1.39 % --inst_prop_sim_new false
% 1.06/1.39 % --inst_orphan_elimination true
% 1.06/1.39 % --inst_learning_loop_flag true
% 1.06/1.39 % --inst_learning_start 3000
% 1.06/1.39 % --inst_learning_factor 2
% 1.06/1.39 % --inst_start_prop_sim_after_learn 3
% 1.06/1.39 % --inst_sel_renew solver
% 1.06/1.39 % --inst_lit_activity_flag true
% 1.06/1.39 % --inst_out_proof true
% 1.06/1.39
% 1.06/1.39 % ------ Resolution Options
% 1.06/1.39
% 1.06/1.39 % --resolution_flag true
% 1.06/1.39 % --res_lit_sel kbo_max
% 1.06/1.39 % --res_to_prop_solver none
% 1.06/1.39 % --res_prop_simpl_new false
% 1.06/1.39 % --res_prop_simpl_given false
% 1.06/1.39 % --res_passive_queue_type priority_queues
% 1.06/1.39 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 1.06/1.39 % --res_passive_queues_freq [15;5]
% 1.06/1.39 % --res_forward_subs full
% 1.06/1.39 % --res_backward_subs full
% 1.06/1.39 % --res_forward_subs_resolution true
% 1.06/1.39 % --res_backward_subs_resolution true
% 1.06/1.39 % --res_orphan_elimination false
% 1.06/1.39 % --res_time_limit 1000.
% 1.06/1.39 % --res_out_proof true
% 1.06/1.39 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_9ef8fa.s
% 1.06/1.39 % --modulo true
% 1.06/1.39
% 1.06/1.39 % ------ Combination Options
% 1.06/1.39
% 1.06/1.39 % --comb_res_mult 1000
% 1.06/1.39 % --comb_inst_mult 300
% 1.06/1.39 % ------
% 1.06/1.39
% 1.06/1.39 % ------ Parsing...% successful
% 1.06/1.39
% 1.06/1.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e pe_s pe_e snvd_s sp: 0 0s snvd_e %
% 1.06/1.39
% 1.06/1.39 % ------ Proving...
% 1.06/1.39 % ------ Problem Properties
% 1.06/1.39
% 1.06/1.39 %
% 1.06/1.39 % EPR false
% 1.06/1.39 % Horn false
% 1.06/1.39 % Has equality true
% 1.06/1.39
% 1.06/1.39 % % ------ Input Options Time Limit: Unbounded
% 1.06/1.39
% 1.06/1.39
% 1.06/1.39 Compiling...
% 1.06/1.39 Loading plugin: done.
% 1.06/1.39 Compiling...
% 1.06/1.39 Loading plugin: done.
% 1.06/1.39 Compiling...
% 1.06/1.39 Loading plugin: done.
% 1.06/1.39 Compiling...
% 1.06/1.39 Loading plugin: done.
% 1.06/1.39 Compiling...
% 1.06/1.39 Loading plugin: done.
% 1.06/1.39 Compiling...
% 1.06/1.39 Loading plugin: done.
% 1.06/1.39 Compiling...
% 1.06/1.39 Loading plugin: done.
% 1.06/1.39 Compiling...
% 1.06/1.39 Loading plugin: done.
% 1.06/1.39 % % ------ Current options:
% 1.06/1.39
% 1.06/1.39 % ------ Input Options
% 1.06/1.39
% 1.06/1.39 % --out_options all
% 1.06/1.39 % --tptp_safe_out true
% 1.06/1.39 % --problem_path ""
% 1.06/1.39 % --include_path ""
% 1.06/1.39 % --clausifier .//eprover
% 1.06/1.39 % --clausifier_options --tstp-format
% 1.06/1.39 % --stdin false
% 1.06/1.39 % --dbg_backtrace false
% 1.06/1.39 % --dbg_dump_prop_clauses false
% 1.06/1.39 % --dbg_dump_prop_clauses_file -
% 1.06/1.39 % --dbg_out_stat false
% 1.06/1.39
% 1.06/1.39 % ------ General Options
% 1.06/1.39
% 1.06/1.39 % --fof false
% 1.06/1.39 % --time_out_real 150.
% 1.06/1.39 % --time_out_prep_mult 0.2
% 1.06/1.39 % --time_out_virtual -1.
% 1.06/1.39 % --schedule none
% 1.06/1.39 % --ground_splitting input
% 1.06/1.39 % --splitting_nvd 16
% 1.06/1.39 % --non_eq_to_eq false
% 1.06/1.39 % --prep_gs_sim true
% 1.06/1.39 % --prep_unflatten false
% 1.06/1.39 % --prep_res_sim true
% 1.06/1.39 % --prep_upred true
% 1.06/1.39 % --res_sim_input true
% 1.06/1.39 % --clause_weak_htbl true
% 1.06/1.39 % --gc_record_bc_elim false
% 1.06/1.39 % --symbol_type_check false
% 1.06/1.39 % --clausify_out false
% 1.06/1.39 % --large_theory_mode false
% 1.06/1.39 % --prep_sem_filter none
% 1.06/1.39 % --prep_sem_filter_out false
% 1.06/1.39 % --preprocessed_out false
% 1.06/1.39 % --sub_typing false
% 1.06/1.39 % --brand_transform false
% 1.06/1.39 % --pure_diseq_elim true
% 1.06/1.39 % --min_unsat_core false
% 1.06/1.39 % --pred_elim true
% 1.06/1.39 % --add_important_lit false
% 1.06/1.39 % --soft_assumptions false
% 1.06/1.39 % --reset_solvers false
% 1.06/1.39 % --bc_imp_inh []
% 1.06/1.39 % --conj_cone_tolerance 1.5
% 1.06/1.39 % --prolific_symb_bound 500
% 1.06/1.39 % --lt_threshold 2000
% 1.06/1.39
% 1.06/1.39 % ------ SAT Options
% 1.06/1.39
% 1.06/1.39 % --sat_mode false
% 1.06/1.39 % --sat_fm_restart_options ""
% 1.06/1.39 % --sat_gr_def false
% 1.06/1.39 % --sat_epr_types true
% 1.06/1.39 % --sat_non_cyclic_types false
% 1.06/1.39 % --sat_finite_models false
% 1.06/1.39 % --sat_fm_lemmas false
% 1.06/1.39 % --sat_fm_prep false
% 1.06/1.39 % --sat_fm_uc_incr true
% 1.06/1.39 % --sat_out_model small
% 1.06/1.39 % --sat_out_clauses false
% 1.06/1.39
% 1.06/1.39 % ------ QBF Options
% 1.06/1.39
% 1.06/1.39 % --qbf_mode false
% 1.06/1.39 % --qbf_elim_univ true
% 1.06/1.39 % --qbf_sk_in true
% 1.06/1.39 % --qbf_pred_elim true
% 1.06/1.39 % --qbf_split 32
% 1.06/1.39
% 1.06/1.39 % ------ BMC1 Options
% 1.06/1.39
% 1.06/1.39 % --bmc1_incremental false
% 1.06/1.39 % --bmc1_axioms reachable_all
% 1.06/1.39 % --bmc1_min_bound 0
% 1.06/1.39 % --bmc1_max_bound -1
% 1.06/1.39 % --bmc1_max_bound_default -1
% 1.06/1.39 % --bmc1_symbol_reachability true
% 1.06/1.39 % --bmc1_property_lemmas false
% 1.06/1.39 % --bmc1_k_induction false
% 1.06/1.39 % --bmc1_non_equiv_states false
% 1.06/1.39 % --bmc1_deadlock false
% 1.06/1.39 % --bmc1_ucm false
% 1.06/1.39 % --bmc1_add_unsat_core none
% 1.06/1.39 % --bmc1_unsat_core_children false
% 1.06/1.39 % --bmc1_unsat_core_extrapolate_axioms false
% 1.06/1.39 % --bmc1_out_stat full
% 1.06/1.39 % --bmc1_ground_init false
% 1.06/1.39 % --bmc1_pre_inst_next_state false
% 1.06/1.39 % --bmc1_pre_inst_state false
% 1.06/1.39 % --bmc1_pre_inst_reach_state false
% 1.06/1.39 % --bmc1_out_unsat_core false
% 1.06/1.39 % --bmc1_aig_witness_out false
% 1.06/1.39 % --bmc1_verbose false
% 1.06/1.39 % --bmc1_dump_clauses_tptp false
% 1.06/1.39 % --bmc1_dump_unsat_core_tptp false
% 1.06/1.39 % --bmc1_dump_file -
% 1.06/1.39 % --bmc1_ucm_expand_uc_limit 128
% 1.06/1.39 % --bmc1_ucm_n_expand_iterations 6
% 1.06/1.39 % --bmc1_ucm_extend_mode 1
% 1.06/1.39 % --bmc1_ucm_init_mode 2
% 1.06/1.39 % --bmc1_ucm_cone_mode none
% 1.06/1.39 % --bmc1_ucm_reduced_relation_type 0
% 1.06/1.39 % --bmc1_ucm_relax_model 4
% 1.06/1.39 % --bmc1_ucm_full_tr_after_sat true
% 1.06/1.39 % --bmc1_ucm_expand_neg_assumptions false
% 1.06/1.39 % --bmc1_ucm_layered_model none
% 1.06/1.39 % --bmc1_ucm_max_lemma_size 10
% 1.06/1.39
% 1.06/1.39 % ------ AIG Options
% 1.06/1.39
% 1.06/1.39 % --aig_mode false
% 1.06/1.39
% 1.06/1.39 % ------ Instantiation Options
% 1.06/1.39
% 1.06/1.39 % --instantiation_flag true
% 1.06/1.39 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 1.06/1.39 % --inst_solver_per_active 750
% 1.06/1.39 % --inst_solver_calls_frac 0.5
% 1.06/1.39 % --inst_passive_queue_type priority_queues
% 18.96/19.15 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 18.96/19.15 % --inst_passive_queues_freq [25;2]
% 18.96/19.15 % --inst_dismatching true
% 18.96/19.15 % --inst_eager_unprocessed_to_passive true
% 18.96/19.15 % --inst_prop_sim_given true
% 18.96/19.15 % --inst_prop_sim_new false
% 18.96/19.15 % --inst_orphan_elimination true
% 18.96/19.15 % --inst_learning_loop_flag true
% 18.96/19.15 % --inst_learning_start 3000
% 18.96/19.15 % --inst_learning_factor 2
% 18.96/19.15 % --inst_start_prop_sim_after_learn 3
% 18.96/19.15 % --inst_sel_renew solver
% 18.96/19.15 % --inst_lit_activity_flag true
% 18.96/19.15 % --inst_out_proof true
% 18.96/19.15
% 18.96/19.15 % ------ Resolution Options
% 18.96/19.15
% 18.96/19.15 % --resolution_flag true
% 18.96/19.15 % --res_lit_sel kbo_max
% 18.96/19.15 % --res_to_prop_solver none
% 18.96/19.15 % --res_prop_simpl_new false
% 18.96/19.15 % --res_prop_simpl_given false
% 18.96/19.15 % --res_passive_queue_type priority_queues
% 18.96/19.15 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 18.96/19.15 % --res_passive_queues_freq [15;5]
% 18.96/19.15 % --res_forward_subs full
% 18.96/19.15 % --res_backward_subs full
% 18.96/19.15 % --res_forward_subs_resolution true
% 18.96/19.15 % --res_backward_subs_resolution true
% 18.96/19.15 % --res_orphan_elimination false
% 18.96/19.15 % --res_time_limit 1000.
% 18.96/19.15 % --res_out_proof true
% 18.96/19.15 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_9ef8fa.s
% 18.96/19.15 % --modulo true
% 18.96/19.15
% 18.96/19.15 % ------ Combination Options
% 18.96/19.15
% 18.96/19.15 % --comb_res_mult 1000
% 18.96/19.15 % --comb_inst_mult 300
% 18.96/19.15 % ------
% 18.96/19.15
% 18.96/19.15
% 18.96/19.15
% 18.96/19.15 % ------ Proving...
% 18.96/19.15 %
% 18.96/19.15
% 18.96/19.15
% 18.96/19.15 % ------ Statistics
% 18.96/19.15
% 18.96/19.15 % ------ General
% 18.96/19.15
% 18.96/19.15 % num_of_input_clauses: 326
% 18.96/19.15 % num_of_input_neg_conjectures: 4
% 18.96/19.15 % num_of_splits: 0
% 18.96/19.15 % num_of_split_atoms: 0
% 18.96/19.15 % num_of_sem_filtered_clauses: 0
% 18.96/19.15 % num_of_subtypes: 0
% 18.96/19.15 % monotx_restored_types: 0
% 18.96/19.15 % sat_num_of_epr_types: 0
% 18.96/19.15 % sat_num_of_non_cyclic_types: 0
% 18.96/19.15 % sat_guarded_non_collapsed_types: 0
% 18.96/19.15 % is_epr: 0
% 18.96/19.15 % is_horn: 0
% 18.96/19.15 % has_eq: 1
% 18.96/19.15 % num_pure_diseq_elim: 0
% 18.96/19.15 % simp_replaced_by: 0
% 18.96/19.15 % res_preprocessed: 8
% 18.96/19.15 % prep_upred: 0
% 18.96/19.15 % prep_unflattend: 0
% 18.96/19.15 % pred_elim_cands: 0
% 18.96/19.15 % pred_elim: 0
% 18.96/19.15 % pred_elim_cl: 0
% 18.96/19.15 % pred_elim_cycles: 0
% 18.96/19.15 % forced_gc_time: 0
% 18.96/19.15 % gc_basic_clause_elim: 0
% 18.96/19.15 % parsing_time: 0.013
% 18.96/19.15 % sem_filter_time: 0.
% 18.96/19.15 % pred_elim_time: 0.
% 18.96/19.15 % out_proof_time: 0.001
% 18.96/19.15 % monotx_time: 0.
% 18.96/19.15 % subtype_inf_time: 0.
% 18.96/19.15 % unif_index_cands_time: 0.099
% 18.96/19.15 % unif_index_add_time: 0.027
% 18.96/19.15 % total_time: 18.741
% 18.96/19.15 % num_of_symbols: 106
% 18.96/19.15 % num_of_terms: 326914
% 18.96/19.15
% 18.96/19.15 % ------ Propositional Solver
% 18.96/19.15
% 18.96/19.15 % prop_solver_calls: 11
% 18.96/19.15 % prop_fast_solver_calls: 12
% 18.96/19.15 % prop_num_of_clauses: 8021
% 18.96/19.15 % prop_preprocess_simplified: 7449
% 18.96/19.15 % prop_fo_subsumed: 0
% 18.96/19.15 % prop_solver_time: 0.003
% 18.96/19.15 % prop_fast_solver_time: 0.
% 18.96/19.15 % prop_unsat_core_time: 0.001
% 18.96/19.15
% 18.96/19.15 % ------ QBF
% 18.96/19.15
% 18.96/19.15 % qbf_q_res: 0
% 18.96/19.15 % qbf_num_tautologies: 0
% 18.96/19.15 % qbf_prep_cycles: 0
% 18.96/19.15
% 18.96/19.15 % ------ BMC1
% 18.96/19.15
% 18.96/19.15 % bmc1_current_bound: -1
% 18.96/19.15 % bmc1_last_solved_bound: -1
% 18.96/19.15 % bmc1_unsat_core_size: -1
% 18.96/19.15 % bmc1_unsat_core_parents_size: -1
% 18.96/19.15 % bmc1_merge_next_fun: 0
% 18.96/19.16 % bmc1_unsat_core_clauses_time: 0.
% 18.96/19.16
% 18.96/19.16 % ------ Instantiation
% 18.96/19.16
% 18.96/19.16 % inst_num_of_clauses: 5134
% 18.96/19.16 % inst_num_in_passive: 2463
% 18.96/19.16 % inst_num_in_active: 1455
% 18.96/19.16 % inst_num_in_unprocessed: 1210
% 18.96/19.16 % inst_num_of_loops: 1650
% 18.96/19.16 % inst_num_of_learning_restarts: 0
% 18.96/19.16 % inst_num_moves_active_passive: 188
% 18.96/19.16 % inst_lit_activity: 1022
% 18.96/19.16 % inst_lit_activity_moves: 2
% 18.96/19.16 % inst_num_tautologies: 4
% 18.96/19.16 % inst_num_prop_implied: 0
% 18.96/19.16 % inst_num_existing_simplified: 0
% 18.96/19.16 % inst_num_eq_res_simplified: 0
% 18.96/19.16 % inst_num_child_elim: 0
% 18.96/19.16 % inst_num_of_dismatching_blockings: 8673
% 18.96/19.16 % inst_num_of_non_proper_insts: 7642
% 18.96/19.16 % inst_num_of_duplicates: 3739
% 18.96/19.16 % inst_inst_num_from_inst_to_res: 0
% 18.96/19.16 % inst_dismatching_checking_time: 0.084
% 18.96/19.16
% 18.96/19.16 % ------ Resolution
% 18.96/19.16
% 18.96/19.16 % res_num_of_clauses: 291165
% 18.96/19.16 % res_num_in_passive: 291565
% 18.96/19.16 % res_num_in_active: 6018
% 18.96/19.16 % res_num_of_loops: 6000
% 18.96/19.16 % res_forward_subset_subsumed: 54600
% 18.96/19.16 % res_backward_subset_subsumed: 6645
% 18.96/19.16 % res_forward_subsumed: 118
% 18.96/19.16 % res_backward_subsumed: 0
% 18.96/19.16 % res_forward_subsumption_resolution: 34
% 18.96/19.16 % res_backward_subsumption_resolution: 0
% 18.96/19.16 % res_clause_to_clause_subsumption: 41152
% 18.96/19.16 % res_orphan_elimination: 0
% 18.96/19.16 % res_tautology_del: 24
% 18.96/19.16 % res_num_eq_res_simplified: 0
% 18.96/19.16 % res_num_sel_changes: 0
% 18.96/19.16 % res_moves_from_active_to_pass: 0
% 18.96/19.16
% 18.96/19.16 % Status Unsatisfiable
% 18.96/19.16 % SZS status Unsatisfiable
% 18.96/19.16 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------