%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : SET098-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n003.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 : Tue Jul 19 02:10:23 EDT 2022

% Result   : Unsatisfiable 0.86s 1.14s
% Output   : CNFRefutation 0.96s
% 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(null_class_in_its_singleton,axiom,
    member(null_class,singleton(null_class)),
    input ).

fof(null_class_in_its_singleton_0,plain,
    ( member(null_class,singleton(null_class))
    | $false ),
    inference(orientation,[status(thm)],[null_class_in_its_singleton]) ).

cnf(corollary_1_to_singletons_are_sets,axiom,
    member(singleton(Y),unordered_pair(X,singleton(Y))),
    input ).

fof(corollary_1_to_singletons_are_sets_0,plain,
    ! [X,Y] :
      ( member(singleton(Y),unordered_pair(X,singleton(Y)))
      | $false ),
    inference(orientation,[status(thm)],[corollary_1_to_singletons_are_sets]) ).

cnf(singletons_are_sets,axiom,
    member(singleton(X),universal_class),
    input ).

fof(singletons_are_sets_0,plain,
    ! [X] :
      ( member(singleton(X),universal_class)
      | $false ),
    inference(orientation,[status(thm)],[singletons_are_sets]) ).

cnf(singleton_in_unordered_pair2,axiom,
    subclass(singleton(Y),unordered_pair(X,Y)),
    input ).

fof(singleton_in_unordered_pair2_0,plain,
    ! [X,Y] :
      ( subclass(singleton(Y),unordered_pair(X,Y))
      | $false ),
    inference(orientation,[status(thm)],[singleton_in_unordered_pair2]) ).

cnf(singleton_in_unordered_pair1,axiom,
    subclass(singleton(X),unordered_pair(X,Y)),
    input ).

fof(singleton_in_unordered_pair1_0,plain,
    ! [X,Y] :
      ( subclass(singleton(X),unordered_pair(X,Y))
      | $false ),
    inference(orientation,[status(thm)],[singleton_in_unordered_pair1]) ).

cnf(commutativity_of_unordered_pair,axiom,
    unordered_pair(X,Y) = unordered_pair(Y,X),
    input ).

fof(commutativity_of_unordered_pair_0,plain,
    ! [X,Y] :
      ( unordered_pair(X,Y) = unordered_pair(Y,X)
      | $false ),
    inference(orientation,[status(thm)],[commutativity_of_unordered_pair]) ).

cnf(null_class_is_a_set,axiom,
    member(null_class,universal_class),
    input ).

fof(null_class_is_a_set_0,plain,
    ( member(null_class,universal_class)
    | $false ),
    inference(orientation,[status(thm)],[null_class_is_a_set]) ).

cnf(null_class_is_subclass,axiom,
    subclass(null_class,X),
    input ).

fof(null_class_is_subclass_0,plain,
    ! [X] :
      ( subclass(null_class,X)
      | $false ),
    inference(orientation,[status(thm)],[null_class_is_subclass]) ).

cnf(existence_of_null_class,axiom,
    ~ member(Z,null_class),
    input ).

fof(existence_of_null_class_0,plain,
    ! [Z] :
      ( ~ member(Z,null_class)
      | $false ),
    inference(orientation,[status(thm)],[existence_of_null_class]) ).

cnf(special_classes_lemma,axiom,
    ~ member(Y,intersection(complement(X),X)),
    input ).

fof(special_classes_lemma_0,plain,
    ! [X,Y] :
      ( ~ member(Y,intersection(complement(X),X))
      | $false ),
    inference(orientation,[status(thm)],[special_classes_lemma]) ).

cnf(subclass_is_reflexive,axiom,
    subclass(X,X),
    input ).

fof(subclass_is_reflexive_0,plain,
    ! [X] :
      ( subclass(X,X)
      | $false ),
    inference(orientation,[status(thm)],[subclass_is_reflexive]) ).

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(X,X) ),
    inference(definition,[],]) ).

fof(to_be_clausified_29,plain,
    ! [X] :
      ( lhs_atom30(X)
      | $false ),
    inference(fold_definition,[status(thm)],[subclass_is_reflexive_0,def_lhs_atom30]) ).

fof(def_lhs_atom31,axiom,
    ! [Y,X] :
      ( lhs_atom31(Y,X)
    <=> ~ member(Y,intersection(complement(X),X)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_30,plain,
    ! [X,Y] :
      ( lhs_atom31(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[special_classes_lemma_0,def_lhs_atom31]) ).

fof(def_lhs_atom32,axiom,
    ! [Z] :
      ( lhs_atom32(Z)
    <=> ~ member(Z,null_class) ),
    inference(definition,[],]) ).

fof(to_be_clausified_31,plain,
    ! [Z] :
      ( lhs_atom32(Z)
      | $false ),
    inference(fold_definition,[status(thm)],[existence_of_null_class_0,def_lhs_atom32]) ).

fof(def_lhs_atom33,axiom,
    ! [X] :
      ( lhs_atom33(X)
    <=> subclass(null_class,X) ),
    inference(definition,[],]) ).

fof(to_be_clausified_32,plain,
    ! [X] :
      ( lhs_atom33(X)
      | $false ),
    inference(fold_definition,[status(thm)],[null_class_is_subclass_0,def_lhs_atom33]) ).

fof(def_lhs_atom34,axiom,
    ( lhs_atom34
  <=> member(null_class,universal_class) ),
    inference(definition,[],]) ).

fof(to_be_clausified_33,plain,
    ( lhs_atom34
    | $false ),
    inference(fold_definition,[status(thm)],[null_class_is_a_set_0,def_lhs_atom34]) ).

fof(def_lhs_atom35,axiom,
    ! [Y,X] :
      ( lhs_atom35(Y,X)
    <=> unordered_pair(X,Y) = unordered_pair(Y,X) ),
    inference(definition,[],]) ).

fof(to_be_clausified_34,plain,
    ! [X,Y] :
      ( lhs_atom35(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[commutativity_of_unordered_pair_0,def_lhs_atom35]) ).

fof(def_lhs_atom36,axiom,
    ! [Y,X] :
      ( lhs_atom36(Y,X)
    <=> subclass(singleton(X),unordered_pair(X,Y)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_35,plain,
    ! [X,Y] :
      ( lhs_atom36(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[singleton_in_unordered_pair1_0,def_lhs_atom36]) ).

fof(def_lhs_atom37,axiom,
    ! [Y,X] :
      ( lhs_atom37(Y,X)
    <=> subclass(singleton(Y),unordered_pair(X,Y)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_36,plain,
    ! [X,Y] :
      ( lhs_atom37(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[singleton_in_unordered_pair2_0,def_lhs_atom37]) ).

fof(def_lhs_atom38,axiom,
    ! [X] :
      ( lhs_atom38(X)
    <=> member(singleton(X),universal_class) ),
    inference(definition,[],]) ).

fof(to_be_clausified_37,plain,
    ! [X] :
      ( lhs_atom38(X)
      | $false ),
    inference(fold_definition,[status(thm)],[singletons_are_sets_0,def_lhs_atom38]) ).

fof(def_lhs_atom39,axiom,
    ! [Y,X] :
      ( lhs_atom39(Y,X)
    <=> member(singleton(Y),unordered_pair(X,singleton(Y))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_38,plain,
    ! [X,Y] :
      ( lhs_atom39(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[corollary_1_to_singletons_are_sets_0,def_lhs_atom39]) ).

fof(def_lhs_atom40,axiom,
    ( lhs_atom40
  <=> member(null_class,singleton(null_class)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_39,plain,
    ( lhs_atom40
    | $false ),
    inference(fold_definition,[status(thm)],[null_class_in_its_singleton_0,def_lhs_atom40]) ).

% Start CNF derivation
fof(c_0_0,axiom,
    ! [X4,X2,X1] :
      ( lhs_atom15(X4,X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_14) ).

fof(c_0_1,axiom,
    ! [X4,X2,X1] :
      ( lhs_atom14(X4,X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_13) ).

fof(c_0_2,axiom,
    ! [X2,X3,X1] :
      ( lhs_atom9(X2,X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_8) ).

fof(c_0_3,axiom,
    ! [X2,X3,X1] :
      ( lhs_atom8(X2,X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_7) ).

fof(c_0_4,axiom,
    ! [X2,X1] :
      ( lhs_atom39(X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_38) ).

fof(c_0_5,axiom,
    ! [X2,X1] :
      ( lhs_atom37(X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_36) ).

fof(c_0_6,axiom,
    ! [X2,X1] :
      ( lhs_atom36(X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_35) ).

fof(c_0_7,axiom,
    ! [X2,X1] :
      ( lhs_atom35(X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_34) ).

fof(c_0_8,axiom,
    ! [X2,X1] :
      ( lhs_atom31(X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_30) ).

fof(c_0_9,axiom,
    ! [X2,X6] :
      ( lhs_atom24(X2,X6)
      | ~ $true ),
    file('<stdin>',to_be_clausified_23) ).

fof(c_0_10,axiom,
    ! [X5,X3] :
      ( lhs_atom23(X5,X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_22) ).

fof(c_0_11,axiom,
    ! [X3,X1] :
      ( lhs_atom16(X3,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_15) ).

fof(c_0_12,axiom,
    ! [X2,X1] :
      ( lhs_atom7(X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_6) ).

fof(c_0_13,axiom,
    ! [X2,X1] :
      ( lhs_atom6(X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_5) ).

fof(c_0_14,axiom,
    ! [X2,X1] :
      ( lhs_atom4(X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_3) ).

fof(c_0_15,axiom,
    ! [X2,X1] :
      ( lhs_atom2(X2,X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_1) ).

fof(c_0_16,axiom,
    ! [X1] :
      ( lhs_atom38(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_37) ).

fof(c_0_17,axiom,
    ! [X1] :
      ( lhs_atom33(X1)
      | ~ $true ),
    file('<stdin>',to_be_clausified_32) ).

fof(c_0_18,axiom,
    ! [X4] :
      ( lhs_atom32(X4)
      | ~ $true ),
    file('<stdin>',to_be_clausified_31) ).

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_atom40
    | ~ $true ),
    file('<stdin>',to_be_clausified_39) ).

fof(c_0_32,axiom,
    ( lhs_atom34
    | ~ $true ),
    file('<stdin>',to_be_clausified_33) ).

fof(c_0_33,axiom,
    ( lhs_atom27
    | ~ $true ),
    file('<stdin>',to_be_clausified_26) ).

fof(c_0_34,axiom,
    ( lhs_atom26
    | ~ $true ),
    file('<stdin>',to_be_clausified_25) ).

fof(c_0_35,axiom,
    ( lhs_atom25
    | ~ $true ),
    file('<stdin>',to_be_clausified_24) ).

fof(c_0_36,axiom,
    ( lhs_atom20
    | ~ $true ),
    file('<stdin>',to_be_clausified_19) ).

fof(c_0_37,axiom,
    ( lhs_atom19
    | ~ $true ),
    file('<stdin>',to_be_clausified_18) ).

fof(c_0_38,axiom,
    ( lhs_atom18
    | ~ $true ),
    file('<stdin>',to_be_clausified_17) ).

fof(c_0_39,axiom,
    ( lhs_atom5
    | ~ $true ),
    file('<stdin>',to_be_clausified_4) ).

fof(c_0_40,plain,
    ! [X4,X2,X1] : lhs_atom15(X4,X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_41,plain,
    ! [X4,X2,X1] : lhs_atom14(X4,X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_42,plain,
    ! [X2,X3,X1] : lhs_atom9(X2,X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_43,plain,
    ! [X2,X3,X1] : lhs_atom8(X2,X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_44,plain,
    ! [X2,X1] : lhs_atom39(X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_45,plain,
    ! [X2,X1] : lhs_atom37(X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_46,plain,
    ! [X2,X1] : lhs_atom36(X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_47,plain,
    ! [X2,X1] : lhs_atom35(X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_48,plain,
    ! [X2,X1] : lhs_atom31(X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_49,plain,
    ! [X2,X6] : lhs_atom24(X2,X6),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_50,plain,
    ! [X5,X3] : lhs_atom23(X5,X3),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_51,plain,
    ! [X3,X1] : lhs_atom16(X3,X1),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_52,plain,
    ! [X2,X1] : lhs_atom7(X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_53,plain,
    ! [X2,X1] : lhs_atom6(X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_54,plain,
    ! [X2,X1] : lhs_atom4(X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_55,plain,
    ! [X2,X1] : lhs_atom2(X2,X1),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_56,plain,
    ! [X1] : lhs_atom38(X1),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_57,plain,
    ! [X1] : lhs_atom33(X1),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_58,plain,
    ! [X4] : lhs_atom32(X4),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_59,plain,
    ! [X1] : lhs_atom30(X1),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_60,plain,
    ! [X1] : lhs_atom29(X1),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_61,plain,
    ! [X3] : lhs_atom28(X3),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_62,plain,
    ! [X1] : lhs_atom22(X1),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_63,plain,
    ! [X1] : lhs_atom21(X1),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_64,plain,
    ! [X1] : lhs_atom17(X1),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_65,plain,
    ! [X4] : lhs_atom13(X4),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_66,plain,
    ! [X2] : lhs_atom12(X2),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_67,plain,
    ! [X1] : lhs_atom11(X1),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_68,plain,
    ! [X1] : lhs_atom10(X1),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_69,plain,
    ! [X1] : lhs_atom3(X1),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_70,plain,
    ! [X1] : lhs_atom1(X1),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_71,plain,
    lhs_atom40,
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_72,plain,
    lhs_atom34,
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_73,plain,
    lhs_atom27,
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_74,plain,
    lhs_atom26,
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_75,plain,
    lhs_atom25,
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_76,plain,
    lhs_atom20,
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_77,plain,
    lhs_atom19,
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_78,plain,
    lhs_atom18,
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_79,plain,
    lhs_atom5,
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_80,plain,
    ! [X5,X6,X7] : lhs_atom15(X5,X6,X7),
    inference(variable_rename,[status(thm)],[c_0_40]) ).

fof(c_0_81,plain,
    ! [X5,X6,X7] : lhs_atom14(X5,X6,X7),
    inference(variable_rename,[status(thm)],[c_0_41]) ).

fof(c_0_82,plain,
    ! [X4,X5,X6] : lhs_atom9(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_42]) ).

fof(c_0_83,plain,
    ! [X4,X5,X6] : lhs_atom8(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_43]) ).

fof(c_0_84,plain,
    ! [X3,X4] : lhs_atom39(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_44]) ).

fof(c_0_85,plain,
    ! [X3,X4] : lhs_atom37(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_45]) ).

fof(c_0_86,plain,
    ! [X3,X4] : lhs_atom36(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_46]) ).

fof(c_0_87,plain,
    ! [X3,X4] : lhs_atom35(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_47]) ).

fof(c_0_88,plain,
    ! [X3,X4] : lhs_atom31(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_48]) ).

fof(c_0_89,plain,
    ! [X7,X8] : lhs_atom24(X7,X8),
    inference(variable_rename,[status(thm)],[c_0_49]) ).

fof(c_0_90,plain,
    ! [X6,X7] : lhs_atom23(X6,X7),
    inference(variable_rename,[status(thm)],[c_0_50]) ).

fof(c_0_91,plain,
    ! [X4,X5] : lhs_atom16(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_51]) ).

fof(c_0_92,plain,
    ! [X3,X4] : lhs_atom7(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_52]) ).

fof(c_0_93,plain,
    ! [X3,X4] : lhs_atom6(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_53]) ).

fof(c_0_94,plain,
    ! [X3,X4] : lhs_atom4(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_54]) ).

fof(c_0_95,plain,
    ! [X3,X4] : lhs_atom2(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_55]) ).

fof(c_0_96,plain,
    ! [X2] : lhs_atom38(X2),
    inference(variable_rename,[status(thm)],[c_0_56]) ).

fof(c_0_97,plain,
    ! [X2] : lhs_atom33(X2),
    inference(variable_rename,[status(thm)],[c_0_57]) ).

fof(c_0_98,plain,
    ! [X5] : lhs_atom32(X5),
    inference(variable_rename,[status(thm)],[c_0_58]) ).

fof(c_0_99,plain,
    ! [X2] : lhs_atom30(X2),
    inference(variable_rename,[status(thm)],[c_0_59]) ).

fof(c_0_100,plain,
    ! [X2] : lhs_atom29(X2),
    inference(variable_rename,[status(thm)],[c_0_60]) ).

fof(c_0_101,plain,
    ! [X4] : lhs_atom28(X4),
    inference(variable_rename,[status(thm)],[c_0_61]) ).

fof(c_0_102,plain,
    ! [X2] : lhs_atom22(X2),
    inference(variable_rename,[status(thm)],[c_0_62]) ).

fof(c_0_103,plain,
    ! [X2] : lhs_atom21(X2),
    inference(variable_rename,[status(thm)],[c_0_63]) ).

fof(c_0_104,plain,
    ! [X2] : lhs_atom17(X2),
    inference(variable_rename,[status(thm)],[c_0_64]) ).

fof(c_0_105,plain,
    ! [X5] : lhs_atom13(X5),
    inference(variable_rename,[status(thm)],[c_0_65]) ).

fof(c_0_106,plain,
    ! [X3] : lhs_atom12(X3),
    inference(variable_rename,[status(thm)],[c_0_66]) ).

fof(c_0_107,plain,
    ! [X2] : lhs_atom11(X2),
    inference(variable_rename,[status(thm)],[c_0_67]) ).

fof(c_0_108,plain,
    ! [X2] : lhs_atom10(X2),
    inference(variable_rename,[status(thm)],[c_0_68]) ).

fof(c_0_109,plain,
    ! [X2] : lhs_atom3(X2),
    inference(variable_rename,[status(thm)],[c_0_69]) ).

fof(c_0_110,plain,
    ! [X2] : lhs_atom1(X2),
    inference(variable_rename,[status(thm)],[c_0_70]) ).

fof(c_0_111,plain,
    lhs_atom40,
    c_0_71 ).

fof(c_0_112,plain,
    lhs_atom34,
    c_0_72 ).

fof(c_0_113,plain,
    lhs_atom27,
    c_0_73 ).

fof(c_0_114,plain,
    lhs_atom26,
    c_0_74 ).

fof(c_0_115,plain,
    lhs_atom25,
    c_0_75 ).

fof(c_0_116,plain,
    lhs_atom20,
    c_0_76 ).

fof(c_0_117,plain,
    lhs_atom19,
    c_0_77 ).

fof(c_0_118,plain,
    lhs_atom18,
    c_0_78 ).

fof(c_0_119,plain,
    lhs_atom5,
    c_0_79 ).

cnf(c_0_120,plain,
    lhs_atom15(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

cnf(c_0_121,plain,
    lhs_atom14(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

cnf(c_0_122,plain,
    lhs_atom9(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_82]) ).

cnf(c_0_123,plain,
    lhs_atom8(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_83]) ).

cnf(c_0_124,plain,
    lhs_atom39(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_84]) ).

cnf(c_0_125,plain,
    lhs_atom37(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_126,plain,
    lhs_atom36(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_127,plain,
    lhs_atom35(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

cnf(c_0_128,plain,
    lhs_atom31(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_88]) ).

cnf(c_0_129,plain,
    lhs_atom24(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

cnf(c_0_130,plain,
    lhs_atom23(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_90]) ).

cnf(c_0_131,plain,
    lhs_atom16(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_91]) ).

cnf(c_0_132,plain,
    lhs_atom7(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_92]) ).

cnf(c_0_133,plain,
    lhs_atom6(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_93]) ).

cnf(c_0_134,plain,
    lhs_atom4(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_135,plain,
    lhs_atom2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_95]) ).

cnf(c_0_136,plain,
    lhs_atom38(X1),
    inference(split_conjunct,[status(thm)],[c_0_96]) ).

cnf(c_0_137,plain,
    lhs_atom33(X1),
    inference(split_conjunct,[status(thm)],[c_0_97]) ).

cnf(c_0_138,plain,
    lhs_atom32(X1),
    inference(split_conjunct,[status(thm)],[c_0_98]) ).

cnf(c_0_139,plain,
    lhs_atom30(X1),
    inference(split_conjunct,[status(thm)],[c_0_99]) ).

cnf(c_0_140,plain,
    lhs_atom29(X1),
    inference(split_conjunct,[status(thm)],[c_0_100]) ).

cnf(c_0_141,plain,
    lhs_atom28(X1),
    inference(split_conjunct,[status(thm)],[c_0_101]) ).

cnf(c_0_142,plain,
    lhs_atom22(X1),
    inference(split_conjunct,[status(thm)],[c_0_102]) ).

cnf(c_0_143,plain,
    lhs_atom21(X1),
    inference(split_conjunct,[status(thm)],[c_0_103]) ).

cnf(c_0_144,plain,
    lhs_atom17(X1),
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

cnf(c_0_145,plain,
    lhs_atom13(X1),
    inference(split_conjunct,[status(thm)],[c_0_105]) ).

cnf(c_0_146,plain,
    lhs_atom12(X1),
    inference(split_conjunct,[status(thm)],[c_0_106]) ).

cnf(c_0_147,plain,
    lhs_atom11(X1),
    inference(split_conjunct,[status(thm)],[c_0_107]) ).

cnf(c_0_148,plain,
    lhs_atom10(X1),
    inference(split_conjunct,[status(thm)],[c_0_108]) ).

cnf(c_0_149,plain,
    lhs_atom3(X1),
    inference(split_conjunct,[status(thm)],[c_0_109]) ).

cnf(c_0_150,plain,
    lhs_atom1(X1),
    inference(split_conjunct,[status(thm)],[c_0_110]) ).

cnf(c_0_151,plain,
    lhs_atom40,
    inference(split_conjunct,[status(thm)],[c_0_111]) ).

cnf(c_0_152,plain,
    lhs_atom34,
    inference(split_conjunct,[status(thm)],[c_0_112]) ).

cnf(c_0_153,plain,
    lhs_atom27,
    inference(split_conjunct,[status(thm)],[c_0_113]) ).

cnf(c_0_154,plain,
    lhs_atom26,
    inference(split_conjunct,[status(thm)],[c_0_114]) ).

cnf(c_0_155,plain,
    lhs_atom25,
    inference(split_conjunct,[status(thm)],[c_0_115]) ).

cnf(c_0_156,plain,
    lhs_atom20,
    inference(split_conjunct,[status(thm)],[c_0_116]) ).

cnf(c_0_157,plain,
    lhs_atom19,
    inference(split_conjunct,[status(thm)],[c_0_117]) ).

cnf(c_0_158,plain,
    lhs_atom18,
    inference(split_conjunct,[status(thm)],[c_0_118]) ).

cnf(c_0_159,plain,
    lhs_atom5,
    inference(split_conjunct,[status(thm)],[c_0_119]) ).

cnf(c_0_160,plain,
    lhs_atom15(X1,X2,X3),
    c_0_120,
    [final] ).

cnf(c_0_161,plain,
    lhs_atom14(X1,X2,X3),
    c_0_121,
    [final] ).

cnf(c_0_162,plain,
    lhs_atom9(X1,X2,X3),
    c_0_122,
    [final] ).

cnf(c_0_163,plain,
    lhs_atom8(X1,X2,X3),
    c_0_123,
    [final] ).

cnf(c_0_164,plain,
    lhs_atom39(X1,X2),
    c_0_124,
    [final] ).

cnf(c_0_165,plain,
    lhs_atom37(X1,X2),
    c_0_125,
    [final] ).

cnf(c_0_166,plain,
    lhs_atom36(X1,X2),
    c_0_126,
    [final] ).

cnf(c_0_167,plain,
    lhs_atom35(X1,X2),
    c_0_127,
    [final] ).

cnf(c_0_168,plain,
    lhs_atom31(X1,X2),
    c_0_128,
    [final] ).

cnf(c_0_169,plain,
    lhs_atom24(X1,X2),
    c_0_129,
    [final] ).

cnf(c_0_170,plain,
    lhs_atom23(X1,X2),
    c_0_130,
    [final] ).

cnf(c_0_171,plain,
    lhs_atom16(X1,X2),
    c_0_131,
    [final] ).

cnf(c_0_172,plain,
    lhs_atom7(X1,X2),
    c_0_132,
    [final] ).

cnf(c_0_173,plain,
    lhs_atom6(X1,X2),
    c_0_133,
    [final] ).

cnf(c_0_174,plain,
    lhs_atom4(X1,X2),
    c_0_134,
    [final] ).

cnf(c_0_175,plain,
    lhs_atom2(X1,X2),
    c_0_135,
    [final] ).

cnf(c_0_176,plain,
    lhs_atom38(X1),
    c_0_136,
    [final] ).

cnf(c_0_177,plain,
    lhs_atom33(X1),
    c_0_137,
    [final] ).

cnf(c_0_178,plain,
    lhs_atom32(X1),
    c_0_138,
    [final] ).

cnf(c_0_179,plain,
    lhs_atom30(X1),
    c_0_139,
    [final] ).

cnf(c_0_180,plain,
    lhs_atom29(X1),
    c_0_140,
    [final] ).

cnf(c_0_181,plain,
    lhs_atom28(X1),
    c_0_141,
    [final] ).

cnf(c_0_182,plain,
    lhs_atom22(X1),
    c_0_142,
    [final] ).

cnf(c_0_183,plain,
    lhs_atom21(X1),
    c_0_143,
    [final] ).

cnf(c_0_184,plain,
    lhs_atom17(X1),
    c_0_144,
    [final] ).

cnf(c_0_185,plain,
    lhs_atom13(X1),
    c_0_145,
    [final] ).

cnf(c_0_186,plain,
    lhs_atom12(X1),
    c_0_146,
    [final] ).

cnf(c_0_187,plain,
    lhs_atom11(X1),
    c_0_147,
    [final] ).

cnf(c_0_188,plain,
    lhs_atom10(X1),
    c_0_148,
    [final] ).

cnf(c_0_189,plain,
    lhs_atom3(X1),
    c_0_149,
    [final] ).

cnf(c_0_190,plain,
    lhs_atom1(X1),
    c_0_150,
    [final] ).

cnf(c_0_191,plain,
    lhs_atom40,
    c_0_151,
    [final] ).

cnf(c_0_192,plain,
    lhs_atom34,
    c_0_152,
    [final] ).

cnf(c_0_193,plain,
    lhs_atom27,
    c_0_153,
    [final] ).

cnf(c_0_194,plain,
    lhs_atom26,
    c_0_154,
    [final] ).

cnf(c_0_195,plain,
    lhs_atom25,
    c_0_155,
    [final] ).

cnf(c_0_196,plain,
    lhs_atom20,
    c_0_156,
    [final] ).

cnf(c_0_197,plain,
    lhs_atom19,
    c_0_157,
    [final] ).

cnf(c_0_198,plain,
    lhs_atom18,
    c_0_158,
    [final] ).

cnf(c_0_199,plain,
    lhs_atom5,
    c_0_159,
    [final] ).

% End CNF derivation
cnf(c_0_160_0,axiom,
    second(not_subclass_element(restrict(X1,singleton(X3),X2),null_class)) = range(X1,X3,X2),
    inference(unfold_definition,[status(thm)],[c_0_160,def_lhs_atom15]) ).

cnf(c_0_161_0,axiom,
    first(not_subclass_element(restrict(X1,X3,singleton(X2)),null_class)) = domain(X1,X3,X2),
    inference(unfold_definition,[status(thm)],[c_0_161,def_lhs_atom14]) ).

cnf(c_0_162_0,axiom,
    intersection(cross_product(X3,X1),X2) = restrict(X2,X3,X1),
    inference(unfold_definition,[status(thm)],[c_0_162,def_lhs_atom9]) ).

cnf(c_0_163_0,axiom,
    intersection(X2,cross_product(X3,X1)) = restrict(X2,X3,X1),
    inference(unfold_definition,[status(thm)],[c_0_163,def_lhs_atom8]) ).

cnf(c_0_164_0,axiom,
    member(singleton(X1),unordered_pair(X2,singleton(X1))),
    inference(unfold_definition,[status(thm)],[c_0_164,def_lhs_atom39]) ).

cnf(c_0_165_0,axiom,
    subclass(singleton(X1),unordered_pair(X2,X1)),
    inference(unfold_definition,[status(thm)],[c_0_165,def_lhs_atom37]) ).

cnf(c_0_166_0,axiom,
    subclass(singleton(X2),unordered_pair(X2,X1)),
    inference(unfold_definition,[status(thm)],[c_0_166,def_lhs_atom36]) ).

cnf(c_0_167_0,axiom,
    unordered_pair(X2,X1) = unordered_pair(X1,X2),
    inference(unfold_definition,[status(thm)],[c_0_167,def_lhs_atom35]) ).

cnf(c_0_168_0,axiom,
    ~ member(X1,intersection(complement(X2),X2)),
    inference(unfold_definition,[status(thm)],[c_0_168,def_lhs_atom31]) ).

cnf(c_0_169_0,axiom,
    sum_class(image(X2,singleton(X1))) = apply(X2,X1),
    inference(unfold_definition,[status(thm)],[c_0_169,def_lhs_atom24]) ).

cnf(c_0_170_0,axiom,
    subclass(compose(X1,X2),cross_product(universal_class,universal_class)),
    inference(unfold_definition,[status(thm)],[c_0_170,def_lhs_atom23]) ).

cnf(c_0_171_0,axiom,
    range_of(restrict(X1,X2,universal_class)) = image(X1,X2),
    inference(unfold_definition,[status(thm)],[c_0_171,def_lhs_atom16]) ).

cnf(c_0_172_0,axiom,
    intersection(complement(intersection(X2,X1)),complement(intersection(complement(X2),complement(X1)))) = symmetric_difference(X2,X1),
    inference(unfold_definition,[status(thm)],[c_0_172,def_lhs_atom7]) ).

cnf(c_0_173_0,axiom,
    complement(intersection(complement(X2),complement(X1))) = union(X2,X1),
    inference(unfold_definition,[status(thm)],[c_0_173,def_lhs_atom6]) ).

cnf(c_0_174_0,axiom,
    unordered_pair(singleton(X2),unordered_pair(X2,singleton(X1))) = ordered_pair(X2,X1),
    inference(unfold_definition,[status(thm)],[c_0_174,def_lhs_atom4]) ).

cnf(c_0_175_0,axiom,
    member(unordered_pair(X2,X1),universal_class),
    inference(unfold_definition,[status(thm)],[c_0_175,def_lhs_atom2]) ).

cnf(c_0_176_0,axiom,
    member(singleton(X1),universal_class),
    inference(unfold_definition,[status(thm)],[c_0_176,def_lhs_atom38]) ).

cnf(c_0_177_0,axiom,
    subclass(null_class,X1),
    inference(unfold_definition,[status(thm)],[c_0_177,def_lhs_atom33]) ).

cnf(c_0_178_0,axiom,
    ~ member(X1,null_class),
    inference(unfold_definition,[status(thm)],[c_0_178,def_lhs_atom32]) ).

cnf(c_0_179_0,axiom,
    subclass(X1,X1),
    inference(unfold_definition,[status(thm)],[c_0_179,def_lhs_atom30]) ).

cnf(c_0_180_0,axiom,
    intersection(domain_of(X1),diagonalise(compose(inverse(element_relation),X1))) = cantor(X1),
    inference(unfold_definition,[status(thm)],[c_0_180,def_lhs_atom29]) ).

cnf(c_0_181_0,axiom,
    complement(domain_of(intersection(X1,identity_relation))) = diagonalise(X1),
    inference(unfold_definition,[status(thm)],[c_0_181,def_lhs_atom28]) ).

cnf(c_0_182_0,axiom,
    complement(image(element_relation,complement(X1))) = power_class(X1),
    inference(unfold_definition,[status(thm)],[c_0_182,def_lhs_atom22]) ).

cnf(c_0_183_0,axiom,
    domain_of(restrict(element_relation,universal_class,X1)) = sum_class(X1),
    inference(unfold_definition,[status(thm)],[c_0_183,def_lhs_atom21]) ).

cnf(c_0_184_0,axiom,
    union(X1,singleton(X1)) = successor(X1),
    inference(unfold_definition,[status(thm)],[c_0_184,def_lhs_atom17]) ).

cnf(c_0_185_0,axiom,
    domain_of(inverse(X1)) = range_of(X1),
    inference(unfold_definition,[status(thm)],[c_0_185,def_lhs_atom13]) ).

cnf(c_0_186_0,axiom,
    domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    inference(unfold_definition,[status(thm)],[c_0_186,def_lhs_atom12]) ).

cnf(c_0_187_0,axiom,
    subclass(flip(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
    inference(unfold_definition,[status(thm)],[c_0_187,def_lhs_atom11]) ).

cnf(c_0_188_0,axiom,
    subclass(rotate(X1),cross_product(cross_product(universal_class,universal_class),universal_class)),
    inference(unfold_definition,[status(thm)],[c_0_188,def_lhs_atom10]) ).

cnf(c_0_189_0,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    inference(unfold_definition,[status(thm)],[c_0_189,def_lhs_atom3]) ).

cnf(c_0_190_0,axiom,
    subclass(X1,universal_class),
    inference(unfold_definition,[status(thm)],[c_0_190,def_lhs_atom1]) ).

cnf(c_0_191_0,axiom,
    member(null_class,singleton(null_class)),
    inference(unfold_definition,[status(thm)],[c_0_191,def_lhs_atom40]) ).

cnf(c_0_192_0,axiom,
    member(null_class,universal_class),
    inference(unfold_definition,[status(thm)],[c_0_192,def_lhs_atom34]) ).

cnf(c_0_193_0,axiom,
    intersection(inverse(subset_relation),subset_relation) = identity_relation,
    inference(unfold_definition,[status(thm)],[c_0_193,def_lhs_atom27]) ).

cnf(c_0_194_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_194,def_lhs_atom26]) ).

cnf(c_0_195_0,axiom,
    function(choice),
    inference(unfold_definition,[status(thm)],[c_0_195,def_lhs_atom25]) ).

cnf(c_0_196_0,axiom,
    member(omega,universal_class),
    inference(unfold_definition,[status(thm)],[c_0_196,def_lhs_atom20]) ).

cnf(c_0_197_0,axiom,
    inductive(omega),
    inference(unfold_definition,[status(thm)],[c_0_197,def_lhs_atom19]) ).

cnf(c_0_198_0,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    inference(unfold_definition,[status(thm)],[c_0_198,def_lhs_atom18]) ).

cnf(c_0_199_0,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    inference(unfold_definition,[status(thm)],[c_0_199,def_lhs_atom5]) ).

% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
    ! [X6,X7,X8] :
      ( ~ operation(X8)
      | ~ operation(X7)
      | ~ compatible(X6,X8,X7)
      | apply(X7,ordered_pair(apply(X6,not_homomorphism1(X6,X8,X7)),apply(X6,not_homomorphism2(X6,X8,X7)))) != apply(X6,apply(X8,ordered_pair(not_homomorphism1(X6,X8,X7),not_homomorphism2(X6,X8,X7))))
      | homomorphism(X6,X8,X7) ),
    file('<stdin>',homomorphism6) ).

fof(c_0_1_002,axiom,
    ! [X1] :
      ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1))
      | singleton(not_subclass_element(X1,null_class)) = X1
      | X1 = null_class ),
    file('<stdin>',number_of_elements_in_class) ).

fof(c_0_2_003,axiom,
    ! [X6,X7,X8] :
      ( ~ operation(X8)
      | ~ operation(X7)
      | ~ compatible(X6,X8,X7)
      | member(ordered_pair(not_homomorphism1(X6,X8,X7),not_homomorphism2(X6,X8,X7)),domain_of(X8))
      | homomorphism(X6,X8,X7) ),
    file('<stdin>',homomorphism5) ).

fof(c_0_3_004,axiom,
    ! [X1,X12,X5,X3] :
      ( ~ member(ordered_pair(ordered_pair(X5,X12),X3),X1)
      | ~ member(ordered_pair(ordered_pair(X3,X5),X12),cross_product(cross_product(universal_class,universal_class),universal_class))
      | member(ordered_pair(ordered_pair(X3,X5),X12),rotate(X1)) ),
    file('<stdin>',rotate3) ).

fof(c_0_4_005,axiom,
    ! [X1,X12,X5,X3] :
      ( ~ member(ordered_pair(ordered_pair(X5,X3),X12),X1)
      | ~ member(ordered_pair(ordered_pair(X3,X5),X12),cross_product(cross_product(universal_class,universal_class),universal_class))
      | member(ordered_pair(ordered_pair(X3,X5),X12),flip(X1)) ),
    file('<stdin>',flip3) ).

fof(c_0_5_006,axiom,
    ! [X2,X6,X7,X8,X1] :
      ( ~ homomorphism(X6,X8,X7)
      | ~ member(ordered_pair(X1,X2),domain_of(X8))
      | apply(X7,ordered_pair(apply(X6,X1),apply(X6,X2))) = apply(X6,apply(X8,ordered_pair(X1,X2))) ),
    file('<stdin>',homomorphism4) ).

fof(c_0_6_007,axiom,
    ! [X4,X10,X2,X11] :
      ( ~ member(X4,image(X10,image(X11,singleton(X2))))
      | ~ member(ordered_pair(X2,X4),cross_product(universal_class,universal_class))
      | member(ordered_pair(X2,X4),compose(X10,X11)) ),
    file('<stdin>',compose3) ).

fof(c_0_7_008,axiom,
    ! [X1,X12,X5,X3] :
      ( ~ member(ordered_pair(ordered_pair(X3,X5),X12),rotate(X1))
      | member(ordered_pair(ordered_pair(X5,X12),X3),X1) ),
    file('<stdin>',rotate2) ).

fof(c_0_8_009,axiom,
    ! [X1,X12,X5,X3] :
      ( ~ member(ordered_pair(ordered_pair(X3,X5),X12),flip(X1))
      | member(ordered_pair(ordered_pair(X5,X3),X12),X1) ),
    file('<stdin>',flip2) ).

fof(c_0_9_010,axiom,
    ! [X4,X10,X2,X11] :
      ( ~ member(ordered_pair(X2,X4),compose(X10,X11))
      | member(X4,image(X10,image(X11,singleton(X2)))) ),
    file('<stdin>',compose2) ).

fof(c_0_10_011,axiom,
    ! [X9] :
      ( ~ function(X9)
      | cross_product(domain_of(domain_of(X9)),domain_of(domain_of(X9))) != domain_of(X9)
      | ~ subclass(range_of(X9),domain_of(domain_of(X9)))
      | operation(X9) ),
    file('<stdin>',operation4) ).

fof(c_0_11_012,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_12_013,axiom,
    ! [X6,X7,X8] :
      ( ~ function(X6)
      | domain_of(domain_of(X8)) != domain_of(X6)
      | ~ subclass(range_of(X6),domain_of(domain_of(X7)))
      | compatible(X6,X8,X7) ),
    file('<stdin>',compatible4) ).

fof(c_0_13_014,axiom,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X1,X2),cross_product(X3,X5))
      | member(X1,unordered_pair(X1,X2)) ),
    file('<stdin>',corollary_1_to_unordered_pair) ).

fof(c_0_14_015,axiom,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X1,X2),cross_product(X3,X5))
      | member(X2,unordered_pair(X1,X2)) ),
    file('<stdin>',corollary_2_to_unordered_pair) ).

fof(c_0_15_016,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_16_017,axiom,
    ! [X4,X2,X1] :
      ( unordered_pair(X1,X2) != unordered_pair(X1,X4)
      | ~ member(ordered_pair(X2,X4),cross_product(universal_class,universal_class))
      | X2 = X4 ),
    file('<stdin>',left_cancellation) ).

fof(c_0_17_018,axiom,
    ! [X4,X2,X1] :
      ( unordered_pair(X1,X4) != unordered_pair(X2,X4)
      | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
      | X1 = X2 ),
    file('<stdin>',right_cancellation) ).

fof(c_0_18_019,axiom,
    ! [X6,X7,X8] :
      ( ~ homomorphism(X6,X8,X7)
      | compatible(X6,X8,X7) ),
    file('<stdin>',homomorphism3) ).

fof(c_0_19_020,axiom,
    ! [X9] :
      ( ~ subclass(X9,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X9,inverse(X9)),identity_relation)
      | function(X9) ),
    file('<stdin>',function3) ).

fof(c_0_20_021,axiom,
    ! [X2,X1] :
      ( ~ member(not_subclass_element(X1,X2),X2)
      | ~ member(not_subclass_element(X2,X1),X1)
      | X1 = X2 ),
    file('<stdin>',equality4) ).

fof(c_0_21_022,axiom,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X1,X2),cross_product(X3,X5))
      | unordered_pair(X1,X2) != null_class ),
    file('<stdin>',corollary_to_unordered_pair_axiom3) ).

fof(c_0_22_023,axiom,
    ! [X4,X1] :
      ( restrict(X1,singleton(X4),universal_class) != null_class
      | ~ member(X4,domain_of(X1)) ),
    file('<stdin>',domain1) ).

fof(c_0_23_024,axiom,
    ! [X6,X7,X8] :
      ( ~ compatible(X6,X8,X7)
      | subclass(range_of(X6),domain_of(domain_of(X7))) ),
    file('<stdin>',compatible3) ).

fof(c_0_24_025,axiom,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X3,X5),cross_product(X1,X2))
      | member(X3,X1) ),
    file('<stdin>',cartesian_product1) ).

fof(c_0_25_026,axiom,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X3,X5),cross_product(X1,X2))
      | member(X5,X2) ),
    file('<stdin>',cartesian_product2) ).

fof(c_0_26_027,axiom,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X3,X5),cross_product(X1,X2))
      | member(X3,universal_class) ),
    file('<stdin>',corollary_1_to_cartesian_product) ).

fof(c_0_27_028,axiom,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X3,X5),cross_product(X1,X2))
      | member(X5,universal_class) ),
    file('<stdin>',corollary_2_to_cartesian_product) ).

fof(c_0_28_029,axiom,
    ! [X2,X1,X5,X3] :
      ( ~ member(X3,X1)
      | ~ member(X5,X2)
      | member(ordered_pair(X3,X5),cross_product(X1,X2)) ),
    file('<stdin>',cartesian_product3) ).

fof(c_0_29_030,axiom,
    ! [X2,X1] :
      ( ~ member(not_subclass_element(X1,X2),X2)
      | X1 = X2
      | member(not_subclass_element(X2,X1),X2) ),
    file('<stdin>',equality2) ).

fof(c_0_30_031,axiom,
    ! [X2,X1] :
      ( ~ member(not_subclass_element(X2,X1),X1)
      | X1 = X2
      | member(not_subclass_element(X1,X2),X1) ),
    file('<stdin>',equality3) ).

fof(c_0_31_032,axiom,
    ! [X6,X7,X8] :
      ( ~ compatible(X6,X8,X7)
      | domain_of(domain_of(X8)) = domain_of(X6) ),
    file('<stdin>',compatible2) ).

fof(c_0_32_033,axiom,
    ! [X4,X1] :
      ( ~ member(X4,universal_class)
      | restrict(X1,singleton(X4),universal_class) = null_class
      | member(X4,domain_of(X1)) ),
    file('<stdin>',domain2) ).

fof(c_0_33_034,axiom,
    ! [X4,X2,X1] :
      ( ~ member(X4,cross_product(X1,X2))
      | ordered_pair(first(X4),second(X4)) = X4 ),
    file('<stdin>',cartesian_product4) ).

fof(c_0_34_035,axiom,
    ! [X6,X7,X8] :
      ( ~ compatible(X6,X8,X7)
      | function(X6) ),
    file('<stdin>',compatible1) ).

fof(c_0_35_036,axiom,
    ! [X6,X7,X8] :
      ( ~ homomorphism(X6,X8,X7)
      | operation(X8) ),
    file('<stdin>',homomorphism1) ).

fof(c_0_36_037,axiom,
    ! [X6,X7,X8] :
      ( ~ homomorphism(X6,X8,X7)
      | operation(X7) ),
    file('<stdin>',homomorphism2) ).

fof(c_0_37_038,axiom,
    ! [X4,X2,X1] :
      ( ~ member(X4,X1)
      | ~ member(X4,X2)
      | member(X4,intersection(X1,X2)) ),
    file('<stdin>',intersection3) ).

fof(c_0_38_039,axiom,
    ! [X4,X2,X1] :
      ( ~ member(X1,X4)
      | ~ member(X2,X4)
      | subclass(unordered_pair(X1,X2),X4) ),
    file('<stdin>',unordered_pair_is_subset) ).

fof(c_0_39_040,axiom,
    ! [X1] :
      ( ~ subclass(compose(X1,inverse(X1)),identity_relation)
      | single_valued_class(X1) ),
    file('<stdin>',single_valued_class2) ).

fof(c_0_40_041,axiom,
    ! [X1] :
      ( ~ member(null_class,X1)
      | ~ subclass(image(successor_relation,X1),X1)
      | inductive(X1) ),
    file('<stdin>',inductive3) ).

fof(c_0_41_042,axiom,
    ! [X2,X1] :
      ( X1 = X2
      | member(not_subclass_element(X1,X2),X1)
      | member(not_subclass_element(X2,X1),X2) ),
    file('<stdin>',equality1) ).

fof(c_0_42_043,axiom,
    ! [X2,X1] :
      ( ~ member(not_subclass_element(X1,X2),X2)
      | subclass(X1,X2) ),
    file('<stdin>',not_subclass_members2) ).

fof(c_0_43_044,axiom,
    ! [X4,X2,X1] :
      ( ~ member(X4,intersection(X1,X2))
      | member(X4,X1) ),
    file('<stdin>',intersection1) ).

fof(c_0_44_045,axiom,
    ! [X4,X2,X1] :
      ( ~ member(X4,intersection(X1,X2))
      | member(X4,X2) ),
    file('<stdin>',intersection2) ).

fof(c_0_45_046,axiom,
    ! [X2,X1] :
      ( ~ member(ordered_pair(X1,X2),element_relation)
      | member(X1,X2) ),
    file('<stdin>',element_relation2) ).

fof(c_0_46_047,axiom,
    ! [X2,X1,X3] :
      ( ~ member(X3,unordered_pair(X1,X2))
      | X3 = X1
      | X3 = X2 ),
    file('<stdin>',unordered_pair_member) ).

fof(c_0_47_048,axiom,
    ! [X2,X1] :
      ( ~ member(ordered_pair(X1,X2),successor_relation)
      | successor(X1) = X2 ),
    file('<stdin>',successor_relation2) ).

fof(c_0_48_049,axiom,
    ! [X9,X1] :
      ( ~ function(X9)
      | ~ member(X1,universal_class)
      | member(image(X9,X1),universal_class) ),
    file('<stdin>',replacement) ).

fof(c_0_49_050,axiom,
    ! [X9] :
      ( ~ operation(X9)
      | cross_product(domain_of(domain_of(X9)),domain_of(domain_of(X9))) = domain_of(X9) ),
    file('<stdin>',operation2) ).

fof(c_0_50_051,axiom,
    ! [X2,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X1,X2)) ),
    file('<stdin>',unordered_pair2) ).

fof(c_0_51_052,axiom,
    ! [X2,X1] :
      ( ~ member(X2,universal_class)
      | member(X2,unordered_pair(X1,X2)) ),
    file('<stdin>',unordered_pair3) ).

fof(c_0_52_053,axiom,
    ! [X2,X1,X3] :
      ( ~ subclass(X1,X2)
      | ~ member(X3,X1)
      | member(X3,X2) ),
    file('<stdin>',subclass_members) ).

fof(c_0_53_054,axiom,
    ! [X4,X2,X1] :
      ( ~ subclass(X1,X2)
      | ~ subclass(X2,X4)
      | subclass(X1,X4) ),
    file('<stdin>',transitivity_of_subclass) ).

fof(c_0_54_055,axiom,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | X2 = null_class
      | member(apply(choice,X2),X2) ),
    file('<stdin>',choice2) ).

fof(c_0_55_056,axiom,
    ! [X1] :
      ( ~ single_valued_class(X1)
      | subclass(compose(X1,inverse(X1)),identity_relation) ),
    file('<stdin>',single_valued_class1) ).

fof(c_0_56_057,axiom,
    ! [X9] :
      ( ~ function(X9)
      | subclass(compose(X9,inverse(X9)),identity_relation) ),
    file('<stdin>',function2) ).

fof(c_0_57_058,axiom,
    ! [X4,X1] :
      ( ~ member(X4,universal_class)
      | member(X4,complement(X1))
      | member(X4,X1) ),
    file('<stdin>',complement2) ).

fof(c_0_58_059,axiom,
    ! [X4,X1] :
      ( ~ member(X4,complement(X1))
      | ~ member(X4,X1) ),
    file('<stdin>',complement1) ).

fof(c_0_59_060,axiom,
    ! [X2,X1] :
      ( member(not_subclass_element(X1,X2),X1)
      | subclass(X1,X2) ),
    file('<stdin>',not_subclass_members1) ).

fof(c_0_60_061,axiom,
    ! [X4,X2,X1] :
      ( unordered_pair(X2,X4) != singleton(X1)
      | ~ member(X1,universal_class)
      | X1 = X2
      | X1 = X4 ),
    file('<stdin>',singleton_in_unordered_pair3) ).

fof(c_0_61_062,axiom,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(member_of(singleton(X2)),universal_class) ),
    file('<stdin>',member_exists1) ).

fof(c_0_62_063,axiom,
    ! [X2,X1] :
      ( ~ subclass(X1,X2)
      | ~ subclass(X2,X1)
      | X1 = X2 ),
    file('<stdin>',subclass_implies_equal) ).

fof(c_0_63_064,axiom,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | singleton(member_of(singleton(X2))) = singleton(X2) ),
    file('<stdin>',member_exists2) ).

fof(c_0_64_065,axiom,
    ! [X9] :
      ( ~ operation(X9)
      | subclass(range_of(X9),domain_of(domain_of(X9))) ),
    file('<stdin>',operation3) ).

fof(c_0_65_066,axiom,
    ! [X2,X1] :
      ( singleton(member_of(X1)) != X1
      | ~ member(X2,X1)
      | member_of(X1) = X2 ),
    file('<stdin>',property_of_singletons1) ).

fof(c_0_66_067,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(image(successor_relation,X1),X1) ),
    file('<stdin>',inductive2) ).

fof(c_0_67_068,axiom,
    ! [X2,X1] :
      ( ~ member(X1,X2)
      | subclass(singleton(X1),X2) ),
    file('<stdin>',property_of_singletons2) ).

fof(c_0_68_069,axiom,
    ! [X2,X1] :
      ( ~ member(X1,universal_class)
      | unordered_pair(X1,X2) != null_class ),
    file('<stdin>',corollary_to_unordered_pair_axiom1) ).

fof(c_0_69_070,axiom,
    ! [X2,X1] :
      ( ~ member(X2,universal_class)
      | unordered_pair(X1,X2) != null_class ),
    file('<stdin>',corollary_to_unordered_pair_axiom2) ).

fof(c_0_70_071,axiom,
    ! [X9] :
      ( ~ function(X9)
      | subclass(X9,cross_product(universal_class,universal_class)) ),
    file('<stdin>',function1) ).

fof(c_0_71_072,axiom,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | member(X1,singleton(X1)) ),
    file('<stdin>',set_in_its_singleton) ).

fof(c_0_72_073,axiom,
    ! [X2,X1] :
      ( unordered_pair(X1,X2) = null_class
      | member(X1,universal_class)
      | member(X2,universal_class) ),
    file('<stdin>',null_unordered_pair) ).

fof(c_0_73_074,axiom,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | member(sum_class(X1),universal_class) ),
    file('<stdin>',sum_class2) ).

fof(c_0_74_075,axiom,
    ! [X3] :
      ( ~ member(X3,universal_class)
      | member(power_class(X3),universal_class) ),
    file('<stdin>',power_class2) ).

fof(c_0_75_076,axiom,
    ! [X2,X1] :
      ( ~ subclass(X1,singleton(X2))
      | X1 = null_class
      | singleton(X2) = X1 ),
    file('<stdin>',two_subsets_of_singleton) ).

fof(c_0_76_077,axiom,
    ! [X4] :
      ( X4 = null_class
      | member(not_subclass_element(X4,null_class),X4) ),
    file('<stdin>',null_class_is_unique) ).

fof(c_0_77_078,axiom,
    ! [X2,X1] :
      ( singleton(X1) != singleton(X2)
      | ~ member(X1,universal_class)
      | X1 = X2 ),
    file('<stdin>',singleton_identified_by_element1) ).

fof(c_0_78_079,axiom,
    ! [X2,X1] :
      ( singleton(X1) != singleton(X2)
      | ~ member(X2,universal_class)
      | X1 = X2 ),
    file('<stdin>',singleton_identified_by_element2) ).

fof(c_0_79_080,axiom,
    ! [X2,X1] :
      ( ~ member(X2,singleton(X1))
      | X2 = X1 ),
    file('<stdin>',only_member_in_singleton) ).

fof(c_0_80_081,axiom,
    ! [X3] :
      ( ~ member(X3,universal_class)
      | member_of(singleton(X3)) = X3 ),
    file('<stdin>',member_of_singleton_is_unique) ).

fof(c_0_81_082,axiom,
    ! [X2,X1] :
      ( member(X2,universal_class)
      | unordered_pair(X1,X2) = singleton(X1) ),
    file('<stdin>',unordered_pair_equals_singleton1) ).

fof(c_0_82_083,axiom,
    ! [X2,X1] :
      ( member(X1,universal_class)
      | unordered_pair(X1,X2) = singleton(X2) ),
    file('<stdin>',unordered_pair_equals_singleton2) ).

fof(c_0_83_084,axiom,
    ! [X1] :
      ( singleton(member_of(X1)) != X1
      | member(X1,universal_class) ),
    file('<stdin>',corollary_2_to_singletons_are_sets) ).

fof(c_0_84_085,axiom,
    ! [X9] :
      ( ~ function(inverse(X9))
      | ~ function(X9)
      | one_to_one(X9) ),
    file('<stdin>',one_to_one3) ).

fof(c_0_85_086,axiom,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | singleton(X1) != null_class ),
    file('<stdin>',corollary_to_set_in_its_singleton) ).

fof(c_0_86_087,axiom,
    ! [X1] :
      ( member(member_of(X1),universal_class)
      | member_of(X1) = X1 ),
    file('<stdin>',member_exists3) ).

fof(c_0_87_088,axiom,
    ! [X1] :
      ( member(member_of1(X1),universal_class)
      | member_of(X1) = X1 ),
    file('<stdin>',member_of_non_singleton_unique1) ).

fof(c_0_88_089,axiom,
    ! [X1] :
      ( X1 = null_class
      | member(regular(X1),X1) ),
    file('<stdin>',regularity1) ).

fof(c_0_89_090,axiom,
    ! [X1] :
      ( X1 = null_class
      | intersection(X1,regular(X1)) = null_class ),
    file('<stdin>',regularity2) ).

fof(c_0_90_091,axiom,
    ! [X1] :
      ( ~ subclass(X1,null_class)
      | X1 = null_class ),
    file('<stdin>',corollary_of_null_class_is_subclass) ).

fof(c_0_91_092,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | member(null_class,X1) ),
    file('<stdin>',inductive1) ).

fof(c_0_92_093,axiom,
    ! [X2] :
      ( ~ inductive(X2)
      | subclass(omega,X2) ),
    file('<stdin>',omega_is_inductive2) ).

fof(c_0_93_094,axiom,
    ! [X2,X1] :
      ( X1 != X2
      | subclass(X1,X2) ),
    file('<stdin>',equal_implies_subclass1) ).

fof(c_0_94_095,axiom,
    ! [X2,X1] :
      ( X1 != X2
      | subclass(X2,X1) ),
    file('<stdin>',equal_implies_subclass2) ).

fof(c_0_95_096,axiom,
    ! [X9] :
      ( ~ one_to_one(X9)
      | function(inverse(X9)) ),
    file('<stdin>',one_to_one2) ).

fof(c_0_96_097,axiom,
    ! [X1] :
      ( member(X1,universal_class)
      | singleton(X1) = null_class ),
    file('<stdin>',singleton_is_null_class) ).

fof(c_0_97_098,axiom,
    ! [X1] :
      ( singleton(member_of(X1)) = X1
      | member_of(X1) = X1 ),
    file('<stdin>',member_exists4) ).

fof(c_0_98_099,axiom,
    ! [X1] :
      ( singleton(member_of1(X1)) = X1
      | member_of(X1) = X1 ),
    file('<stdin>',member_of_non_singleton_unique2) ).

fof(c_0_99_100,axiom,
    ! [X9] :
      ( ~ one_to_one(X9)
      | function(X9) ),
    file('<stdin>',one_to_one1) ).

fof(c_0_100_101,axiom,
    ! [X9] :
      ( ~ operation(X9)
      | function(X9) ),
    file('<stdin>',operation1) ).

fof(c_0_101_102,plain,
    ! [X6,X7,X8] :
      ( ~ operation(X8)
      | ~ operation(X7)
      | ~ compatible(X6,X8,X7)
      | apply(X7,ordered_pair(apply(X6,not_homomorphism1(X6,X8,X7)),apply(X6,not_homomorphism2(X6,X8,X7)))) != apply(X6,apply(X8,ordered_pair(not_homomorphism1(X6,X8,X7),not_homomorphism2(X6,X8,X7))))
      | homomorphism(X6,X8,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_102_103,axiom,
    ! [X1] :
      ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1))
      | singleton(not_subclass_element(X1,null_class)) = X1
      | X1 = null_class ),
    c_0_1 ).

fof(c_0_103_104,plain,
    ! [X6,X7,X8] :
      ( ~ operation(X8)
      | ~ operation(X7)
      | ~ compatible(X6,X8,X7)
      | member(ordered_pair(not_homomorphism1(X6,X8,X7),not_homomorphism2(X6,X8,X7)),domain_of(X8))
      | homomorphism(X6,X8,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_104_105,plain,
    ! [X1,X12,X5,X3] :
      ( ~ member(ordered_pair(ordered_pair(X5,X12),X3),X1)
      | ~ member(ordered_pair(ordered_pair(X3,X5),X12),cross_product(cross_product(universal_class,universal_class),universal_class))
      | member(ordered_pair(ordered_pair(X3,X5),X12),rotate(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_105_106,plain,
    ! [X1,X12,X5,X3] :
      ( ~ member(ordered_pair(ordered_pair(X5,X3),X12),X1)
      | ~ member(ordered_pair(ordered_pair(X3,X5),X12),cross_product(cross_product(universal_class,universal_class),universal_class))
      | member(ordered_pair(ordered_pair(X3,X5),X12),flip(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_106_107,plain,
    ! [X2,X6,X7,X8,X1] :
      ( ~ homomorphism(X6,X8,X7)
      | ~ member(ordered_pair(X1,X2),domain_of(X8))
      | apply(X7,ordered_pair(apply(X6,X1),apply(X6,X2))) = apply(X6,apply(X8,ordered_pair(X1,X2))) ),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_107_108,plain,
    ! [X4,X10,X2,X11] :
      ( ~ member(X4,image(X10,image(X11,singleton(X2))))
      | ~ member(ordered_pair(X2,X4),cross_product(universal_class,universal_class))
      | member(ordered_pair(X2,X4),compose(X10,X11)) ),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_108_109,plain,
    ! [X1,X12,X5,X3] :
      ( ~ member(ordered_pair(ordered_pair(X3,X5),X12),rotate(X1))
      | member(ordered_pair(ordered_pair(X5,X12),X3),X1) ),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_109_110,plain,
    ! [X1,X12,X5,X3] :
      ( ~ member(ordered_pair(ordered_pair(X3,X5),X12),flip(X1))
      | member(ordered_pair(ordered_pair(X5,X3),X12),X1) ),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_110_111,plain,
    ! [X4,X10,X2,X11] :
      ( ~ member(ordered_pair(X2,X4),compose(X10,X11))
      | member(X4,image(X10,image(X11,singleton(X2)))) ),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_111_112,plain,
    ! [X9] :
      ( ~ function(X9)
      | cross_product(domain_of(domain_of(X9)),domain_of(domain_of(X9))) != domain_of(X9)
      | ~ subclass(range_of(X9),domain_of(domain_of(X9)))
      | operation(X9) ),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_112_113,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_11]) ).

fof(c_0_113_114,plain,
    ! [X6,X7,X8] :
      ( ~ function(X6)
      | domain_of(domain_of(X8)) != domain_of(X6)
      | ~ subclass(range_of(X6),domain_of(domain_of(X7)))
      | compatible(X6,X8,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_12]) ).

fof(c_0_114_115,plain,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X1,X2),cross_product(X3,X5))
      | member(X1,unordered_pair(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_115_116,plain,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X1,X2),cross_product(X3,X5))
      | member(X2,unordered_pair(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_116_117,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_15]) ).

fof(c_0_117_118,plain,
    ! [X4,X2,X1] :
      ( unordered_pair(X1,X2) != unordered_pair(X1,X4)
      | ~ member(ordered_pair(X2,X4),cross_product(universal_class,universal_class))
      | X2 = X4 ),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_118_119,plain,
    ! [X4,X2,X1] :
      ( unordered_pair(X1,X4) != unordered_pair(X2,X4)
      | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
      | X1 = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_119_120,plain,
    ! [X6,X7,X8] :
      ( ~ homomorphism(X6,X8,X7)
      | compatible(X6,X8,X7) ),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_120_121,plain,
    ! [X9] :
      ( ~ subclass(X9,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X9,inverse(X9)),identity_relation)
      | function(X9) ),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_121_122,plain,
    ! [X2,X1] :
      ( ~ member(not_subclass_element(X1,X2),X2)
      | ~ member(not_subclass_element(X2,X1),X1)
      | X1 = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_122_123,plain,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X1,X2),cross_product(X3,X5))
      | unordered_pair(X1,X2) != null_class ),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_123_124,plain,
    ! [X4,X1] :
      ( restrict(X1,singleton(X4),universal_class) != null_class
      | ~ member(X4,domain_of(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_124_125,plain,
    ! [X6,X7,X8] :
      ( ~ compatible(X6,X8,X7)
      | subclass(range_of(X6),domain_of(domain_of(X7))) ),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_125_126,plain,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X3,X5),cross_product(X1,X2))
      | member(X3,X1) ),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_126_127,plain,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X3,X5),cross_product(X1,X2))
      | member(X5,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_127_128,plain,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X3,X5),cross_product(X1,X2))
      | member(X3,universal_class) ),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_128_129,plain,
    ! [X2,X1,X5,X3] :
      ( ~ member(ordered_pair(X3,X5),cross_product(X1,X2))
      | member(X5,universal_class) ),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_129_130,plain,
    ! [X2,X1,X5,X3] :
      ( ~ member(X3,X1)
      | ~ member(X5,X2)
      | member(ordered_pair(X3,X5),cross_product(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_130_131,plain,
    ! [X2,X1] :
      ( ~ member(not_subclass_element(X1,X2),X2)
      | X1 = X2
      | member(not_subclass_element(X2,X1),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_131_132,plain,
    ! [X2,X1] :
      ( ~ member(not_subclass_element(X2,X1),X1)
      | X1 = X2
      | member(not_subclass_element(X1,X2),X1) ),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_132_133,plain,
    ! [X6,X7,X8] :
      ( ~ compatible(X6,X8,X7)
      | domain_of(domain_of(X8)) = domain_of(X6) ),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_133_134,plain,
    ! [X4,X1] :
      ( ~ member(X4,universal_class)
      | restrict(X1,singleton(X4),universal_class) = null_class
      | member(X4,domain_of(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_134_135,plain,
    ! [X4,X2,X1] :
      ( ~ member(X4,cross_product(X1,X2))
      | ordered_pair(first(X4),second(X4)) = X4 ),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_135_136,plain,
    ! [X6,X7,X8] :
      ( ~ compatible(X6,X8,X7)
      | function(X6) ),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_136_137,plain,
    ! [X6,X7,X8] :
      ( ~ homomorphism(X6,X8,X7)
      | operation(X8) ),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_137_138,plain,
    ! [X6,X7,X8] :
      ( ~ homomorphism(X6,X8,X7)
      | operation(X7) ),
    inference(fof_simplification,[status(thm)],[c_0_36]) ).

fof(c_0_138_139,plain,
    ! [X4,X2,X1] :
      ( ~ member(X4,X1)
      | ~ member(X4,X2)
      | member(X4,intersection(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_139_140,plain,
    ! [X4,X2,X1] :
      ( ~ member(X1,X4)
      | ~ member(X2,X4)
      | subclass(unordered_pair(X1,X2),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_140_141,plain,
    ! [X1] :
      ( ~ subclass(compose(X1,inverse(X1)),identity_relation)
      | single_valued_class(X1) ),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_141_142,plain,
    ! [X1] :
      ( ~ member(null_class,X1)
      | ~ subclass(image(successor_relation,X1),X1)
      | inductive(X1) ),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_142_143,axiom,
    ! [X2,X1] :
      ( X1 = X2
      | member(not_subclass_element(X1,X2),X1)
      | member(not_subclass_element(X2,X1),X2) ),
    c_0_41 ).

fof(c_0_143_144,plain,
    ! [X2,X1] :
      ( ~ member(not_subclass_element(X1,X2),X2)
      | subclass(X1,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_144_145,plain,
    ! [X4,X2,X1] :
      ( ~ member(X4,intersection(X1,X2))
      | member(X4,X1) ),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_145_146,plain,
    ! [X4,X2,X1] :
      ( ~ member(X4,intersection(X1,X2))
      | member(X4,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_146_147,plain,
    ! [X2,X1] :
      ( ~ member(ordered_pair(X1,X2),element_relation)
      | member(X1,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_147_148,plain,
    ! [X2,X1,X3] :
      ( ~ member(X3,unordered_pair(X1,X2))
      | X3 = X1
      | X3 = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_148_149,plain,
    ! [X2,X1] :
      ( ~ member(ordered_pair(X1,X2),successor_relation)
      | successor(X1) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_149_150,plain,
    ! [X9,X1] :
      ( ~ function(X9)
      | ~ member(X1,universal_class)
      | member(image(X9,X1),universal_class) ),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_150_151,plain,
    ! [X9] :
      ( ~ operation(X9)
      | cross_product(domain_of(domain_of(X9)),domain_of(domain_of(X9))) = domain_of(X9) ),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_151_152,plain,
    ! [X2,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_152_153,plain,
    ! [X2,X1] :
      ( ~ member(X2,universal_class)
      | member(X2,unordered_pair(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_153_154,plain,
    ! [X2,X1,X3] :
      ( ~ subclass(X1,X2)
      | ~ member(X3,X1)
      | member(X3,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_154_155,plain,
    ! [X4,X2,X1] :
      ( ~ subclass(X1,X2)
      | ~ subclass(X2,X4)
      | subclass(X1,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_155_156,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | X2 = null_class
      | member(apply(choice,X2),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_156_157,plain,
    ! [X1] :
      ( ~ single_valued_class(X1)
      | subclass(compose(X1,inverse(X1)),identity_relation) ),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_157_158,plain,
    ! [X9] :
      ( ~ function(X9)
      | subclass(compose(X9,inverse(X9)),identity_relation) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_158_159,plain,
    ! [X4,X1] :
      ( ~ member(X4,universal_class)
      | member(X4,complement(X1))
      | member(X4,X1) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_159_160,plain,
    ! [X4,X1] :
      ( ~ member(X4,complement(X1))
      | ~ member(X4,X1) ),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_160_161,axiom,
    ! [X2,X1] :
      ( member(not_subclass_element(X1,X2),X1)
      | subclass(X1,X2) ),
    c_0_59 ).

fof(c_0_161_162,plain,
    ! [X4,X2,X1] :
      ( unordered_pair(X2,X4) != singleton(X1)
      | ~ member(X1,universal_class)
      | X1 = X2
      | X1 = X4 ),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_162_163,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(member_of(singleton(X2)),universal_class) ),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_163_164,plain,
    ! [X2,X1] :
      ( ~ subclass(X1,X2)
      | ~ subclass(X2,X1)
      | X1 = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_164_165,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | singleton(member_of(singleton(X2))) = singleton(X2) ),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_165_166,plain,
    ! [X9] :
      ( ~ operation(X9)
      | subclass(range_of(X9),domain_of(domain_of(X9))) ),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_166_167,plain,
    ! [X2,X1] :
      ( singleton(member_of(X1)) != X1
      | ~ member(X2,X1)
      | member_of(X1) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_167_168,plain,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(image(successor_relation,X1),X1) ),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_168_169,plain,
    ! [X2,X1] :
      ( ~ member(X1,X2)
      | subclass(singleton(X1),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_169_170,plain,
    ! [X2,X1] :
      ( ~ member(X1,universal_class)
      | unordered_pair(X1,X2) != null_class ),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_170_171,plain,
    ! [X2,X1] :
      ( ~ member(X2,universal_class)
      | unordered_pair(X1,X2) != null_class ),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_171_172,plain,
    ! [X9] :
      ( ~ function(X9)
      | subclass(X9,cross_product(universal_class,universal_class)) ),
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_172_173,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | member(X1,singleton(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_173_174,axiom,
    ! [X2,X1] :
      ( unordered_pair(X1,X2) = null_class
      | member(X1,universal_class)
      | member(X2,universal_class) ),
    c_0_72 ).

fof(c_0_174_175,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | member(sum_class(X1),universal_class) ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_175_176,plain,
    ! [X3] :
      ( ~ member(X3,universal_class)
      | member(power_class(X3),universal_class) ),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_176_177,plain,
    ! [X2,X1] :
      ( ~ subclass(X1,singleton(X2))
      | X1 = null_class
      | singleton(X2) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_177_178,axiom,
    ! [X4] :
      ( X4 = null_class
      | member(not_subclass_element(X4,null_class),X4) ),
    c_0_76 ).

fof(c_0_178_179,plain,
    ! [X2,X1] :
      ( singleton(X1) != singleton(X2)
      | ~ member(X1,universal_class)
      | X1 = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_179_180,plain,
    ! [X2,X1] :
      ( singleton(X1) != singleton(X2)
      | ~ member(X2,universal_class)
      | X1 = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_180_181,plain,
    ! [X2,X1] :
      ( ~ member(X2,singleton(X1))
      | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_181_182,plain,
    ! [X3] :
      ( ~ member(X3,universal_class)
      | member_of(singleton(X3)) = X3 ),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_182_183,axiom,
    ! [X2,X1] :
      ( member(X2,universal_class)
      | unordered_pair(X1,X2) = singleton(X1) ),
    c_0_81 ).

fof(c_0_183_184,axiom,
    ! [X2,X1] :
      ( member(X1,universal_class)
      | unordered_pair(X1,X2) = singleton(X2) ),
    c_0_82 ).

fof(c_0_184_185,axiom,
    ! [X1] :
      ( singleton(member_of(X1)) != X1
      | member(X1,universal_class) ),
    c_0_83 ).

fof(c_0_185_186,plain,
    ! [X9] :
      ( ~ function(inverse(X9))
      | ~ function(X9)
      | one_to_one(X9) ),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_186_187,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | singleton(X1) != null_class ),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_187_188,axiom,
    ! [X1] :
      ( member(member_of(X1),universal_class)
      | member_of(X1) = X1 ),
    c_0_86 ).

fof(c_0_188_189,axiom,
    ! [X1] :
      ( member(member_of1(X1),universal_class)
      | member_of(X1) = X1 ),
    c_0_87 ).

fof(c_0_189_190,axiom,
    ! [X1] :
      ( X1 = null_class
      | member(regular(X1),X1) ),
    c_0_88 ).

fof(c_0_190_191,axiom,
    ! [X1] :
      ( X1 = null_class
      | intersection(X1,regular(X1)) = null_class ),
    c_0_89 ).

fof(c_0_191_192,plain,
    ! [X1] :
      ( ~ subclass(X1,null_class)
      | X1 = null_class ),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_192_193,plain,
    ! [X1] :
      ( ~ inductive(X1)
      | member(null_class,X1) ),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_193_194,plain,
    ! [X2] :
      ( ~ inductive(X2)
      | subclass(omega,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_194_195,axiom,
    ! [X2,X1] :
      ( X1 != X2
      | subclass(X1,X2) ),
    c_0_93 ).

fof(c_0_195_196,axiom,
    ! [X2,X1] :
      ( X1 != X2
      | subclass(X2,X1) ),
    c_0_94 ).

fof(c_0_196_197,plain,
    ! [X9] :
      ( ~ one_to_one(X9)
      | function(inverse(X9)) ),
    inference(fof_simplification,[status(thm)],[c_0_95]) ).

fof(c_0_197_198,axiom,
    ! [X1] :
      ( member(X1,universal_class)
      | singleton(X1) = null_class ),
    c_0_96 ).

fof(c_0_198_199,axiom,
    ! [X1] :
      ( singleton(member_of(X1)) = X1
      | member_of(X1) = X1 ),
    c_0_97 ).

fof(c_0_199_200,axiom,
    ! [X1] :
      ( singleton(member_of1(X1)) = X1
      | member_of(X1) = X1 ),
    c_0_98 ).

fof(c_0_200,plain,
    ! [X9] :
      ( ~ one_to_one(X9)
      | function(X9) ),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_201,plain,
    ! [X9] :
      ( ~ operation(X9)
      | function(X9) ),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_202,plain,
    ! [X9,X10,X11] :
      ( ~ operation(X11)
      | ~ operation(X10)
      | ~ compatible(X9,X11,X10)
      | apply(X10,ordered_pair(apply(X9,not_homomorphism1(X9,X11,X10)),apply(X9,not_homomorphism2(X9,X11,X10)))) != apply(X9,apply(X11,ordered_pair(not_homomorphism1(X9,X11,X10),not_homomorphism2(X9,X11,X10))))
      | homomorphism(X9,X11,X10) ),
    inference(variable_rename,[status(thm)],[c_0_101]) ).

fof(c_0_203,plain,
    ! [X2] :
      ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X2,null_class))),X2),null_class),intersection(complement(singleton(not_subclass_element(X2,null_class))),X2))
      | singleton(not_subclass_element(X2,null_class)) = X2
      | X2 = null_class ),
    inference(variable_rename,[status(thm)],[c_0_102]) ).

fof(c_0_204,plain,
    ! [X9,X10,X11] :
      ( ~ operation(X11)
      | ~ operation(X10)
      | ~ compatible(X9,X11,X10)
      | member(ordered_pair(not_homomorphism1(X9,X11,X10),not_homomorphism2(X9,X11,X10)),domain_of(X11))
      | homomorphism(X9,X11,X10) ),
    inference(variable_rename,[status(thm)],[c_0_103]) ).

fof(c_0_205,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_104]) ).

fof(c_0_206,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_105]) ).

fof(c_0_207,plain,
    ! [X9,X10,X11,X12,X13] :
      ( ~ homomorphism(X10,X12,X11)
      | ~ member(ordered_pair(X13,X9),domain_of(X12))
      | apply(X11,ordered_pair(apply(X10,X13),apply(X10,X9))) = apply(X10,apply(X12,ordered_pair(X13,X9))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_106])])]) ).

fof(c_0_208,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_107]) ).

fof(c_0_209,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_108]) ).

fof(c_0_210,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_109]) ).

fof(c_0_211,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_110]) ).

fof(c_0_212,plain,
    ! [X10] :
      ( ~ function(X10)
      | cross_product(domain_of(domain_of(X10)),domain_of(domain_of(X10))) != domain_of(X10)
      | ~ subclass(range_of(X10),domain_of(domain_of(X10)))
      | operation(X10) ),
    inference(variable_rename,[status(thm)],[c_0_111]) ).

fof(c_0_213,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_112]) ).

fof(c_0_214,plain,
    ! [X9,X10,X11] :
      ( ~ function(X9)
      | domain_of(domain_of(X11)) != domain_of(X9)
      | ~ subclass(range_of(X9),domain_of(domain_of(X10)))
      | compatible(X9,X11,X10) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_113])])]) ).

fof(c_0_215,plain,
    ! [X6,X7,X8,X9] :
      ( ~ member(ordered_pair(X7,X6),cross_product(X9,X8))
      | member(X7,unordered_pair(X7,X6)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_114])])]) ).

fof(c_0_216,plain,
    ! [X6,X7,X8,X9] :
      ( ~ member(ordered_pair(X7,X6),cross_product(X9,X8))
      | member(X6,unordered_pair(X7,X6)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_115])])]) ).

fof(c_0_217,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_116]) ).

fof(c_0_218,plain,
    ! [X5,X6,X7] :
      ( unordered_pair(X7,X6) != unordered_pair(X7,X5)
      | ~ member(ordered_pair(X6,X5),cross_product(universal_class,universal_class))
      | X6 = X5 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_117])])]) ).

fof(c_0_219,plain,
    ! [X5,X6,X7] :
      ( unordered_pair(X7,X5) != unordered_pair(X6,X5)
      | ~ member(ordered_pair(X7,X6),cross_product(universal_class,universal_class))
      | X7 = X6 ),
    inference(variable_rename,[status(thm)],[c_0_118]) ).

fof(c_0_220,plain,
    ! [X9,X10,X11] :
      ( ~ homomorphism(X9,X11,X10)
      | compatible(X9,X11,X10) ),
    inference(variable_rename,[status(thm)],[c_0_119]) ).

fof(c_0_221,plain,
    ! [X10] :
      ( ~ subclass(X10,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X10,inverse(X10)),identity_relation)
      | function(X10) ),
    inference(variable_rename,[status(thm)],[c_0_120]) ).

fof(c_0_222,plain,
    ! [X3,X4] :
      ( ~ member(not_subclass_element(X4,X3),X3)
      | ~ member(not_subclass_element(X3,X4),X4)
      | X4 = X3 ),
    inference(variable_rename,[status(thm)],[c_0_121]) ).

fof(c_0_223,plain,
    ! [X6,X7,X8,X9] :
      ( ~ member(ordered_pair(X7,X6),cross_product(X9,X8))
      | unordered_pair(X7,X6) != null_class ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_122])])]) ).

fof(c_0_224,plain,
    ! [X5,X6] :
      ( restrict(X6,singleton(X5),universal_class) != null_class
      | ~ member(X5,domain_of(X6)) ),
    inference(variable_rename,[status(thm)],[c_0_123]) ).

fof(c_0_225,plain,
    ! [X9,X10,X11] :
      ( ~ compatible(X9,X11,X10)
      | subclass(range_of(X9),domain_of(domain_of(X10))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_124])])]) ).

fof(c_0_226,plain,
    ! [X6,X7,X8,X9] :
      ( ~ member(ordered_pair(X9,X8),cross_product(X7,X6))
      | member(X9,X7) ),
    inference(variable_rename,[status(thm)],[c_0_125]) ).

fof(c_0_227,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_126])])]) ).

fof(c_0_228,plain,
    ! [X6,X7,X8,X9] :
      ( ~ member(ordered_pair(X9,X8),cross_product(X7,X6))
      | member(X9,universal_class) ),
    inference(variable_rename,[status(thm)],[c_0_127]) ).

fof(c_0_229,plain,
    ! [X6,X7,X8,X9] :
      ( ~ member(ordered_pair(X9,X8),cross_product(X7,X6))
      | member(X8,universal_class) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_128])])]) ).

fof(c_0_230,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_129]) ).

fof(c_0_231,plain,
    ! [X3,X4] :
      ( ~ member(not_subclass_element(X4,X3),X3)
      | X4 = X3
      | member(not_subclass_element(X3,X4),X3) ),
    inference(variable_rename,[status(thm)],[c_0_130]) ).

fof(c_0_232,plain,
    ! [X3,X4] :
      ( ~ member(not_subclass_element(X3,X4),X4)
      | X4 = X3
      | member(not_subclass_element(X4,X3),X4) ),
    inference(variable_rename,[status(thm)],[c_0_131]) ).

fof(c_0_233,plain,
    ! [X9,X10,X11] :
      ( ~ compatible(X9,X11,X10)
      | domain_of(domain_of(X11)) = domain_of(X9) ),
    inference(variable_rename,[status(thm)],[c_0_132]) ).

fof(c_0_234,plain,
    ! [X5,X6] :
      ( ~ member(X5,universal_class)
      | restrict(X6,singleton(X5),universal_class) = null_class
      | member(X5,domain_of(X6)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_133])])]) ).

fof(c_0_235,plain,
    ! [X5,X6,X7] :
      ( ~ member(X5,cross_product(X7,X6))
      | ordered_pair(first(X5),second(X5)) = X5 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_134])])]) ).

fof(c_0_236,plain,
    ! [X9,X10,X11] :
      ( ~ compatible(X9,X11,X10)
      | function(X9) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_135])])]) ).

fof(c_0_237,plain,
    ! [X9,X10,X11] :
      ( ~ homomorphism(X9,X11,X10)
      | operation(X11) ),
    inference(variable_rename,[status(thm)],[c_0_136]) ).

fof(c_0_238,plain,
    ! [X9,X10,X11] :
      ( ~ homomorphism(X9,X11,X10)
      | operation(X10) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_137])])]) ).

fof(c_0_239,plain,
    ! [X5,X6,X7] :
      ( ~ member(X5,X7)
      | ~ member(X5,X6)
      | member(X5,intersection(X7,X6)) ),
    inference(variable_rename,[status(thm)],[c_0_138]) ).

fof(c_0_240,plain,
    ! [X5,X6,X7] :
      ( ~ member(X7,X5)
      | ~ member(X6,X5)
      | subclass(unordered_pair(X7,X6),X5) ),
    inference(variable_rename,[status(thm)],[c_0_139]) ).

fof(c_0_241,plain,
    ! [X2] :
      ( ~ subclass(compose(X2,inverse(X2)),identity_relation)
      | single_valued_class(X2) ),
    inference(variable_rename,[status(thm)],[c_0_140]) ).

fof(c_0_242,plain,
    ! [X2] :
      ( ~ member(null_class,X2)
      | ~ subclass(image(successor_relation,X2),X2)
      | inductive(X2) ),
    inference(variable_rename,[status(thm)],[c_0_141]) ).

fof(c_0_243,plain,
    ! [X3,X4] :
      ( X4 = X3
      | member(not_subclass_element(X4,X3),X4)
      | member(not_subclass_element(X3,X4),X3) ),
    inference(variable_rename,[status(thm)],[c_0_142]) ).

fof(c_0_244,plain,
    ! [X3,X4] :
      ( ~ member(not_subclass_element(X4,X3),X3)
      | subclass(X4,X3) ),
    inference(variable_rename,[status(thm)],[c_0_143]) ).

fof(c_0_245,plain,
    ! [X5,X6,X7] :
      ( ~ member(X5,intersection(X7,X6))
      | member(X5,X7) ),
    inference(variable_rename,[status(thm)],[c_0_144]) ).

fof(c_0_246,plain,
    ! [X5,X6,X7] :
      ( ~ member(X5,intersection(X7,X6))
      | member(X5,X6) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_145])])]) ).

fof(c_0_247,plain,
    ! [X3,X4] :
      ( ~ member(ordered_pair(X4,X3),element_relation)
      | member(X4,X3) ),
    inference(variable_rename,[status(thm)],[c_0_146]) ).

fof(c_0_248,plain,
    ! [X4,X5,X6] :
      ( ~ member(X6,unordered_pair(X5,X4))
      | X6 = X5
      | X6 = X4 ),
    inference(variable_rename,[status(thm)],[c_0_147]) ).

fof(c_0_249,plain,
    ! [X3,X4] :
      ( ~ member(ordered_pair(X4,X3),successor_relation)
      | successor(X4) = X3 ),
    inference(variable_rename,[status(thm)],[c_0_148]) ).

fof(c_0_250,plain,
    ! [X10,X11] :
      ( ~ function(X10)
      | ~ member(X11,universal_class)
      | member(image(X10,X11),universal_class) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_149])])]) ).

fof(c_0_251,plain,
    ! [X10] :
      ( ~ operation(X10)
      | cross_product(domain_of(domain_of(X10)),domain_of(domain_of(X10))) = domain_of(X10) ),
    inference(variable_rename,[status(thm)],[c_0_150]) ).

fof(c_0_252,plain,
    ! [X3,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,unordered_pair(X4,X3)) ),
    inference(variable_rename,[status(thm)],[c_0_151]) ).

fof(c_0_253,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_152])])]) ).

fof(c_0_254,plain,
    ! [X4,X5,X6] :
      ( ~ subclass(X5,X4)
      | ~ member(X6,X5)
      | member(X6,X4) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_153])])]) ).

fof(c_0_255,plain,
    ! [X5,X6,X7] :
      ( ~ subclass(X7,X6)
      | ~ subclass(X6,X5)
      | subclass(X7,X5) ),
    inference(variable_rename,[status(thm)],[c_0_154]) ).

fof(c_0_256,plain,
    ! [X3] :
      ( ~ member(X3,universal_class)
      | X3 = null_class
      | member(apply(choice,X3),X3) ),
    inference(variable_rename,[status(thm)],[c_0_155]) ).

fof(c_0_257,plain,
    ! [X2] :
      ( ~ single_valued_class(X2)
      | subclass(compose(X2,inverse(X2)),identity_relation) ),
    inference(variable_rename,[status(thm)],[c_0_156]) ).

fof(c_0_258,plain,
    ! [X10] :
      ( ~ function(X10)
      | subclass(compose(X10,inverse(X10)),identity_relation) ),
    inference(variable_rename,[status(thm)],[c_0_157]) ).

fof(c_0_259,plain,
    ! [X5,X6] :
      ( ~ member(X5,universal_class)
      | member(X5,complement(X6))
      | member(X5,X6) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_158])])]) ).

fof(c_0_260,plain,
    ! [X5,X6] :
      ( ~ member(X5,complement(X6))
      | ~ member(X5,X6) ),
    inference(variable_rename,[status(thm)],[c_0_159]) ).

fof(c_0_261,plain,
    ! [X3,X4] :
      ( member(not_subclass_element(X4,X3),X4)
      | subclass(X4,X3) ),
    inference(variable_rename,[status(thm)],[c_0_160]) ).

fof(c_0_262,plain,
    ! [X5,X6,X7] :
      ( unordered_pair(X6,X5) != singleton(X7)
      | ~ member(X7,universal_class)
      | X7 = X6
      | X7 = X5 ),
    inference(variable_rename,[status(thm)],[c_0_161]) ).

fof(c_0_263,plain,
    ! [X3] :
      ( ~ member(X3,universal_class)
      | member(member_of(singleton(X3)),universal_class) ),
    inference(variable_rename,[status(thm)],[c_0_162]) ).

fof(c_0_264,plain,
    ! [X3,X4] :
      ( ~ subclass(X4,X3)
      | ~ subclass(X3,X4)
      | X4 = X3 ),
    inference(variable_rename,[status(thm)],[c_0_163]) ).

fof(c_0_265,plain,
    ! [X3] :
      ( ~ member(X3,universal_class)
      | singleton(member_of(singleton(X3))) = singleton(X3) ),
    inference(variable_rename,[status(thm)],[c_0_164]) ).

fof(c_0_266,plain,
    ! [X10] :
      ( ~ operation(X10)
      | subclass(range_of(X10),domain_of(domain_of(X10))) ),
    inference(variable_rename,[status(thm)],[c_0_165]) ).

fof(c_0_267,plain,
    ! [X3,X4] :
      ( singleton(member_of(X4)) != X4
      | ~ member(X3,X4)
      | member_of(X4) = X3 ),
    inference(variable_rename,[status(thm)],[c_0_166]) ).

fof(c_0_268,plain,
    ! [X2] :
      ( ~ inductive(X2)
      | subclass(image(successor_relation,X2),X2) ),
    inference(variable_rename,[status(thm)],[c_0_167]) ).

fof(c_0_269,plain,
    ! [X3,X4] :
      ( ~ member(X4,X3)
      | subclass(singleton(X4),X3) ),
    inference(variable_rename,[status(thm)],[c_0_168]) ).

fof(c_0_270,plain,
    ! [X3,X4] :
      ( ~ member(X4,universal_class)
      | unordered_pair(X4,X3) != null_class ),
    inference(variable_rename,[status(thm)],[c_0_169]) ).

fof(c_0_271,plain,
    ! [X3,X4] :
      ( ~ member(X3,universal_class)
      | unordered_pair(X4,X3) != null_class ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_170])])]) ).

fof(c_0_272,plain,
    ! [X10] :
      ( ~ function(X10)
      | subclass(X10,cross_product(universal_class,universal_class)) ),
    inference(variable_rename,[status(thm)],[c_0_171]) ).

fof(c_0_273,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(X2,singleton(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_172]) ).

fof(c_0_274,plain,
    ! [X3,X4] :
      ( unordered_pair(X4,X3) = null_class
      | member(X4,universal_class)
      | member(X3,universal_class) ),
    inference(variable_rename,[status(thm)],[c_0_173]) ).

fof(c_0_275,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(sum_class(X2),universal_class) ),
    inference(variable_rename,[status(thm)],[c_0_174]) ).

fof(c_0_276,plain,
    ! [X4] :
      ( ~ member(X4,universal_class)
      | member(power_class(X4),universal_class) ),
    inference(variable_rename,[status(thm)],[c_0_175]) ).

fof(c_0_277,plain,
    ! [X3,X4] :
      ( ~ subclass(X4,singleton(X3))
      | X4 = null_class
      | singleton(X3) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_176]) ).

fof(c_0_278,plain,
    ! [X5] :
      ( X5 = null_class
      | member(not_subclass_element(X5,null_class),X5) ),
    inference(variable_rename,[status(thm)],[c_0_177]) ).

fof(c_0_279,plain,
    ! [X3,X4] :
      ( singleton(X4) != singleton(X3)
      | ~ member(X4,universal_class)
      | X4 = X3 ),
    inference(variable_rename,[status(thm)],[c_0_178]) ).

fof(c_0_280,plain,
    ! [X3,X4] :
      ( singleton(X4) != singleton(X3)
      | ~ member(X3,universal_class)
      | X4 = X3 ),
    inference(variable_rename,[status(thm)],[c_0_179]) ).

fof(c_0_281,plain,
    ! [X3,X4] :
      ( ~ member(X3,singleton(X4))
      | X3 = X4 ),
    inference(variable_rename,[status(thm)],[c_0_180]) ).

fof(c_0_282,plain,
    ! [X4] :
      ( ~ member(X4,universal_class)
      | member_of(singleton(X4)) = X4 ),
    inference(variable_rename,[status(thm)],[c_0_181]) ).

fof(c_0_283,plain,
    ! [X3,X4] :
      ( member(X3,universal_class)
      | unordered_pair(X4,X3) = singleton(X4) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_182])])]) ).

fof(c_0_284,plain,
    ! [X3,X4] :
      ( member(X4,universal_class)
      | unordered_pair(X4,X3) = singleton(X3) ),
    inference(variable_rename,[status(thm)],[c_0_183]) ).

fof(c_0_285,plain,
    ! [X2] :
      ( singleton(member_of(X2)) != X2
      | member(X2,universal_class) ),
    inference(variable_rename,[status(thm)],[c_0_184]) ).

fof(c_0_286,plain,
    ! [X10] :
      ( ~ function(inverse(X10))
      | ~ function(X10)
      | one_to_one(X10) ),
    inference(variable_rename,[status(thm)],[c_0_185]) ).

fof(c_0_287,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | singleton(X2) != null_class ),
    inference(variable_rename,[status(thm)],[c_0_186]) ).

fof(c_0_288,plain,
    ! [X2] :
      ( member(member_of(X2),universal_class)
      | member_of(X2) = X2 ),
    inference(variable_rename,[status(thm)],[c_0_187]) ).

fof(c_0_289,plain,
    ! [X2] :
      ( member(member_of1(X2),universal_class)
      | member_of(X2) = X2 ),
    inference(variable_rename,[status(thm)],[c_0_188]) ).

fof(c_0_290,plain,
    ! [X2] :
      ( X2 = null_class
      | member(regular(X2),X2) ),
    inference(variable_rename,[status(thm)],[c_0_189]) ).

fof(c_0_291,plain,
    ! [X2] :
      ( X2 = null_class
      | intersection(X2,regular(X2)) = null_class ),
    inference(variable_rename,[status(thm)],[c_0_190]) ).

fof(c_0_292,plain,
    ! [X2] :
      ( ~ subclass(X2,null_class)
      | X2 = null_class ),
    inference(variable_rename,[status(thm)],[c_0_191]) ).

fof(c_0_293,plain,
    ! [X2] :
      ( ~ inductive(X2)
      | member(null_class,X2) ),
    inference(variable_rename,[status(thm)],[c_0_192]) ).

fof(c_0_294,plain,
    ! [X3] :
      ( ~ inductive(X3)
      | subclass(omega,X3) ),
    inference(variable_rename,[status(thm)],[c_0_193]) ).

fof(c_0_295,plain,
    ! [X3,X4] :
      ( X4 != X3
      | subclass(X4,X3) ),
    inference(variable_rename,[status(thm)],[c_0_194]) ).

fof(c_0_296,plain,
    ! [X3,X4] :
      ( X4 != X3
      | subclass(X3,X4) ),
    inference(variable_rename,[status(thm)],[c_0_195]) ).

fof(c_0_297,plain,
    ! [X10] :
      ( ~ one_to_one(X10)
      | function(inverse(X10)) ),
    inference(variable_rename,[status(thm)],[c_0_196]) ).

fof(c_0_298,plain,
    ! [X2] :
      ( member(X2,universal_class)
      | singleton(X2) = null_class ),
    inference(variable_rename,[status(thm)],[c_0_197]) ).

fof(c_0_299,plain,
    ! [X2] :
      ( singleton(member_of(X2)) = X2
      | member_of(X2) = X2 ),
    inference(variable_rename,[status(thm)],[c_0_198]) ).

fof(c_0_300,plain,
    ! [X2] :
      ( singleton(member_of1(X2)) = X2
      | member_of(X2) = X2 ),
    inference(variable_rename,[status(thm)],[c_0_199]) ).

fof(c_0_301,plain,
    ! [X10] :
      ( ~ one_to_one(X10)
      | function(X10) ),
    inference(variable_rename,[status(thm)],[c_0_200]) ).

fof(c_0_302,plain,
    ! [X10] :
      ( ~ operation(X10)
      | function(X10) ),
    inference(variable_rename,[status(thm)],[c_0_201]) ).

cnf(c_0_303,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_202]) ).

cnf(c_0_304,plain,
    ( X1 = null_class
    | singleton(not_subclass_element(X1,null_class)) = X1
    | member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_203]) ).

cnf(c_0_305,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_204]) ).

cnf(c_0_306,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_205]) ).

cnf(c_0_307,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_206]) ).

cnf(c_0_308,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_207]) ).

cnf(c_0_309,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_208]) ).

cnf(c_0_310,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_209]) ).

cnf(c_0_311,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_210]) ).

cnf(c_0_312,plain,
    ( member(X1,image(X2,image(X3,singleton(X4))))
    | ~ member(ordered_pair(X4,X1),compose(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_211]) ).

cnf(c_0_313,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_212]) ).

cnf(c_0_314,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_213]) ).

cnf(c_0_315,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_214]) ).

cnf(c_0_316,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_215]) ).

cnf(c_0_317,plain,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_216]) ).

cnf(c_0_318,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_217]) ).

cnf(c_0_319,plain,
    ( X1 = X2
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | unordered_pair(X3,X1) != unordered_pair(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_218]) ).

cnf(c_0_320,plain,
    ( X1 = X2
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | unordered_pair(X1,X3) != unordered_pair(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_219]) ).

cnf(c_0_321,plain,
    ( compatible(X1,X2,X3)
    | ~ homomorphism(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_220]) ).

cnf(c_0_322,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_221]) ).

cnf(c_0_323,plain,
    ( X1 = X2
    | ~ member(not_subclass_element(X2,X1),X1)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_222]) ).

cnf(c_0_324,plain,
    ( unordered_pair(X1,X2) != null_class
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_223]) ).

cnf(c_0_325,plain,
    ( ~ member(X1,domain_of(X2))
    | restrict(X2,singleton(X1),universal_class) != null_class ),
    inference(split_conjunct,[status(thm)],[c_0_224]) ).

cnf(c_0_326,plain,
    ( subclass(range_of(X1),domain_of(domain_of(X2)))
    | ~ compatible(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_225]) ).

cnf(c_0_327,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_226]) ).

cnf(c_0_328,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_227]) ).

cnf(c_0_329,plain,
    ( member(X1,universal_class)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_228]) ).

cnf(c_0_330,plain,
    ( member(X1,universal_class)
    | ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_229]) ).

cnf(c_0_331,plain,
    ( member(ordered_pair(X1,X2),cross_product(X3,X4))
    | ~ member(X2,X4)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_230]) ).

cnf(c_0_332,plain,
    ( member(not_subclass_element(X1,X2),X1)
    | X2 = X1
    | ~ member(not_subclass_element(X2,X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_231]) ).

cnf(c_0_333,plain,
    ( member(not_subclass_element(X1,X2),X1)
    | X1 = X2
    | ~ member(not_subclass_element(X2,X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_232]) ).

cnf(c_0_334,plain,
    ( domain_of(domain_of(X1)) = domain_of(X2)
    | ~ compatible(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_233]) ).

cnf(c_0_335,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_234]) ).

cnf(c_0_336,plain,
    ( ordered_pair(first(X1),second(X1)) = X1
    | ~ member(X1,cross_product(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_235]) ).

cnf(c_0_337,plain,
    ( function(X1)
    | ~ compatible(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_236]) ).

cnf(c_0_338,plain,
    ( operation(X1)
    | ~ homomorphism(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_237]) ).

cnf(c_0_339,plain,
    ( operation(X1)
    | ~ homomorphism(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_238]) ).

cnf(c_0_340,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_239]) ).

cnf(c_0_341,plain,
    ( subclass(unordered_pair(X1,X2),X3)
    | ~ member(X2,X3)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_240]) ).

cnf(c_0_342,plain,
    ( single_valued_class(X1)
    | ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
    inference(split_conjunct,[status(thm)],[c_0_241]) ).

cnf(c_0_343,plain,
    ( inductive(X1)
    | ~ subclass(image(successor_relation,X1),X1)
    | ~ member(null_class,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_242]) ).

cnf(c_0_344,plain,
    ( member(not_subclass_element(X1,X2),X1)
    | member(not_subclass_element(X2,X1),X2)
    | X2 = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_243]) ).

cnf(c_0_345,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_244]) ).

cnf(c_0_346,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_245]) ).

cnf(c_0_347,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_246]) ).

cnf(c_0_348,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X2),element_relation) ),
    inference(split_conjunct,[status(thm)],[c_0_247]) ).

cnf(c_0_349,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_248]) ).

cnf(c_0_350,plain,
    ( successor(X1) = X2
    | ~ member(ordered_pair(X1,X2),successor_relation) ),
    inference(split_conjunct,[status(thm)],[c_0_249]) ).

cnf(c_0_351,plain,
    ( member(image(X1,X2),universal_class)
    | ~ member(X2,universal_class)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_250]) ).

cnf(c_0_352,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_251]) ).

cnf(c_0_353,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_252]) ).

cnf(c_0_354,plain,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_253]) ).

cnf(c_0_355,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subclass(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_254]) ).

cnf(c_0_356,plain,
    ( subclass(X1,X2)
    | ~ subclass(X3,X2)
    | ~ subclass(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_255]) ).

cnf(c_0_357,plain,
    ( member(apply(choice,X1),X1)
    | X1 = null_class
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_256]) ).

cnf(c_0_358,plain,
    ( subclass(compose(X1,inverse(X1)),identity_relation)
    | ~ single_valued_class(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_257]) ).

cnf(c_0_359,plain,
    ( subclass(compose(X1,inverse(X1)),identity_relation)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_258]) ).

cnf(c_0_360,plain,
    ( member(X1,X2)
    | member(X1,complement(X2))
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_259]) ).

cnf(c_0_361,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,complement(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_260]) ).

cnf(c_0_362,plain,
    ( subclass(X1,X2)
    | member(not_subclass_element(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_261]) ).

cnf(c_0_363,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,universal_class)
    | unordered_pair(X3,X2) != singleton(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_262]) ).

cnf(c_0_364,plain,
    ( member(member_of(singleton(X1)),universal_class)
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_263]) ).

cnf(c_0_365,plain,
    ( X1 = X2
    | ~ subclass(X2,X1)
    | ~ subclass(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_264]) ).

cnf(c_0_366,plain,
    ( singleton(member_of(singleton(X1))) = singleton(X1)
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_265]) ).

cnf(c_0_367,plain,
    ( subclass(range_of(X1),domain_of(domain_of(X1)))
    | ~ operation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_266]) ).

cnf(c_0_368,plain,
    ( member_of(X1) = X2
    | ~ member(X2,X1)
    | singleton(member_of(X1)) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_267]) ).

cnf(c_0_369,plain,
    ( subclass(image(successor_relation,X1),X1)
    | ~ inductive(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_268]) ).

cnf(c_0_370,plain,
    ( subclass(singleton(X1),X2)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_269]) ).

cnf(c_0_371,plain,
    ( unordered_pair(X1,X2) != null_class
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_270]) ).

cnf(c_0_372,plain,
    ( unordered_pair(X1,X2) != null_class
    | ~ member(X2,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_271]) ).

cnf(c_0_373,plain,
    ( subclass(X1,cross_product(universal_class,universal_class))
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_272]) ).

cnf(c_0_374,plain,
    ( member(X1,singleton(X1))
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_273]) ).

cnf(c_0_375,plain,
    ( member(X1,universal_class)
    | member(X2,universal_class)
    | unordered_pair(X2,X1) = null_class ),
    inference(split_conjunct,[status(thm)],[c_0_274]) ).

cnf(c_0_376,plain,
    ( member(sum_class(X1),universal_class)
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_275]) ).

cnf(c_0_377,plain,
    ( member(power_class(X1),universal_class)
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_276]) ).

cnf(c_0_378,plain,
    ( singleton(X1) = X2
    | X2 = null_class
    | ~ subclass(X2,singleton(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_277]) ).

cnf(c_0_379,plain,
    ( member(not_subclass_element(X1,null_class),X1)
    | X1 = null_class ),
    inference(split_conjunct,[status(thm)],[c_0_278]) ).

cnf(c_0_380,plain,
    ( X1 = X2
    | ~ member(X1,universal_class)
    | singleton(X1) != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_279]) ).

cnf(c_0_381,plain,
    ( X1 = X2
    | ~ member(X2,universal_class)
    | singleton(X1) != singleton(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_280]) ).

cnf(c_0_382,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_281]) ).

cnf(c_0_383,plain,
    ( member_of(singleton(X1)) = X1
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_282]) ).

cnf(c_0_384,plain,
    ( unordered_pair(X1,X2) = singleton(X1)
    | member(X2,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_283]) ).

cnf(c_0_385,plain,
    ( unordered_pair(X1,X2) = singleton(X2)
    | member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_284]) ).

cnf(c_0_386,plain,
    ( member(X1,universal_class)
    | singleton(member_of(X1)) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_285]) ).

cnf(c_0_387,plain,
    ( one_to_one(X1)
    | ~ function(X1)
    | ~ function(inverse(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_286]) ).

cnf(c_0_388,plain,
    ( singleton(X1) != null_class
    | ~ member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_287]) ).

cnf(c_0_389,plain,
    ( member_of(X1) = X1
    | member(member_of(X1),universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_288]) ).

cnf(c_0_390,plain,
    ( member_of(X1) = X1
    | member(member_of1(X1),universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_289]) ).

cnf(c_0_391,plain,
    ( member(regular(X1),X1)
    | X1 = null_class ),
    inference(split_conjunct,[status(thm)],[c_0_290]) ).

cnf(c_0_392,plain,
    ( intersection(X1,regular(X1)) = null_class
    | X1 = null_class ),
    inference(split_conjunct,[status(thm)],[c_0_291]) ).

cnf(c_0_393,plain,
    ( X1 = null_class
    | ~ subclass(X1,null_class) ),
    inference(split_conjunct,[status(thm)],[c_0_292]) ).

cnf(c_0_394,plain,
    ( member(null_class,X1)
    | ~ inductive(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_293]) ).

cnf(c_0_395,plain,
    ( subclass(omega,X1)
    | ~ inductive(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_294]) ).

cnf(c_0_396,plain,
    ( subclass(X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_295]) ).

cnf(c_0_397,plain,
    ( subclass(X1,X2)
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_296]) ).

cnf(c_0_398,plain,
    ( function(inverse(X1))
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_297]) ).

cnf(c_0_399,plain,
    ( singleton(X1) = null_class
    | member(X1,universal_class) ),
    inference(split_conjunct,[status(thm)],[c_0_298]) ).

cnf(c_0_400,plain,
    ( member_of(X1) = X1
    | singleton(member_of(X1)) = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_299]) ).

cnf(c_0_401,plain,
    ( member_of(X1) = X1
    | singleton(member_of1(X1)) = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_300]) ).

cnf(c_0_402,plain,
    ( function(X1)
    | ~ one_to_one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_301]) ).

cnf(c_0_403,plain,
    ( function(X1)
    | ~ operation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_302]) ).

cnf(c_0_404,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_303,
    [final] ).

cnf(c_0_405,plain,
    ( X1 = null_class
    | singleton(not_subclass_element(X1,null_class)) = X1
    | member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1)) ),
    c_0_304,
    [final] ).

cnf(c_0_406,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_305,
    [final] ).

cnf(c_0_407,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_306,
    [final] ).

cnf(c_0_408,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_307,
    [final] ).

cnf(c_0_409,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_308,
    [final] ).

cnf(c_0_410,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_309,
    [final] ).

cnf(c_0_411,plain,
    ( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
    | ~ member(ordered_pair(ordered_pair(X3,X1),X2),rotate(X4)) ),
    c_0_310,
    [final] ).

cnf(c_0_412,plain,
    ( member(ordered_pair(ordered_pair(X1,X2),X3),X4)
    | ~ member(ordered_pair(ordered_pair(X2,X1),X3),flip(X4)) ),
    c_0_311,
    [final] ).

cnf(c_0_413,plain,
    ( member(X1,image(X2,image(X3,singleton(X4))))
    | ~ member(ordered_pair(X4,X1),compose(X2,X3)) ),
    c_0_312,
    [final] ).

cnf(c_0_414,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_313,
    [final] ).

cnf(c_0_415,plain,
    ( member(ordered_pair(X1,X2),element_relation)
    | ~ member(X1,X2)
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class)) ),
    c_0_314,
    [final] ).

cnf(c_0_416,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_315,
    [final] ).

cnf(c_0_417,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    c_0_316,
    [final] ).

cnf(c_0_418,plain,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
    c_0_317,
    [final] ).

cnf(c_0_419,plain,
    ( member(ordered_pair(X1,X2),successor_relation)
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | successor(X1) != X2 ),
    c_0_318,
    [final] ).

cnf(c_0_420,plain,
    ( X1 = X2
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | unordered_pair(X3,X1) != unordered_pair(X3,X2) ),
    c_0_319,
    [final] ).

cnf(c_0_421,plain,
    ( X1 = X2
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | unordered_pair(X1,X3) != unordered_pair(X2,X3) ),
    c_0_320,
    [final] ).

cnf(c_0_422,plain,
    ( compatible(X1,X2,X3)
    | ~ homomorphism(X1,X2,X3) ),
    c_0_321,
    [final] ).

cnf(c_0_423,plain,
    ( function(X1)
    | ~ subclass(compose(X1,inverse(X1)),identity_relation)
    | ~ subclass(X1,cross_product(universal_class,universal_class)) ),
    c_0_322,
    [final] ).

cnf(c_0_424,plain,
    ( X1 = X2
    | ~ member(not_subclass_element(X2,X1),X1)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    c_0_323,
    [final] ).

cnf(c_0_425,plain,
    ( unordered_pair(X1,X2) != null_class
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    c_0_324,
    [final] ).

cnf(c_0_426,plain,
    ( ~ member(X1,domain_of(X2))
    | restrict(X2,singleton(X1),universal_class) != null_class ),
    c_0_325,
    [final] ).

cnf(c_0_427,plain,
    ( subclass(range_of(X1),domain_of(domain_of(X2)))
    | ~ compatible(X1,X3,X2) ),
    c_0_326,
    [final] ).

cnf(c_0_428,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
    c_0_327,
    [final] ).

cnf(c_0_429,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
    c_0_328,
    [final] ).

cnf(c_0_430,plain,
    ( member(X1,universal_class)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    c_0_329,
    [final] ).

cnf(c_0_431,plain,
    ( member(X1,universal_class)
    | ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
    c_0_330,
    [final] ).

cnf(c_0_432,plain,
    ( member(ordered_pair(X1,X2),cross_product(X3,X4))
    | ~ member(X2,X4)
    | ~ member(X1,X3) ),
    c_0_331,
    [final] ).

cnf(c_0_433,plain,
    ( member(not_subclass_element(X1,X2),X1)
    | X2 = X1
    | ~ member(not_subclass_element(X2,X1),X1) ),
    c_0_332,
    [final] ).

cnf(c_0_434,plain,
    ( member(not_subclass_element(X1,X2),X1)
    | X1 = X2
    | ~ member(not_subclass_element(X2,X1),X1) ),
    c_0_333,
    [final] ).

cnf(c_0_435,plain,
    ( domain_of(domain_of(X1)) = domain_of(X2)
    | ~ compatible(X2,X1,X3) ),
    c_0_334,
    [final] ).

cnf(c_0_436,plain,
    ( member(X1,domain_of(X2))
    | restrict(X2,singleton(X1),universal_class) = null_class
    | ~ member(X1,universal_class) ),
    c_0_335,
    [final] ).

cnf(c_0_437,plain,
    ( ordered_pair(first(X1),second(X1)) = X1
    | ~ member(X1,cross_product(X2,X3)) ),
    c_0_336,
    [final] ).

cnf(c_0_438,plain,
    ( function(X1)
    | ~ compatible(X1,X2,X3) ),
    c_0_337,
    [final] ).

cnf(c_0_439,plain,
    ( operation(X1)
    | ~ homomorphism(X2,X1,X3) ),
    c_0_338,
    [final] ).

cnf(c_0_440,plain,
    ( operation(X1)
    | ~ homomorphism(X2,X3,X1) ),
    c_0_339,
    [final] ).

cnf(c_0_441,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    c_0_340,
    [final] ).

cnf(c_0_442,plain,
    ( subclass(unordered_pair(X1,X2),X3)
    | ~ member(X2,X3)
    | ~ member(X1,X3) ),
    c_0_341,
    [final] ).

cnf(c_0_443,plain,
    ( single_valued_class(X1)
    | ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
    c_0_342,
    [final] ).

cnf(c_0_444,plain,
    ( inductive(X1)
    | ~ subclass(image(successor_relation,X1),X1)
    | ~ member(null_class,X1) ),
    c_0_343,
    [final] ).

cnf(c_0_445,plain,
    ( member(not_subclass_element(X1,X2),X1)
    | member(not_subclass_element(X2,X1),X2)
    | X2 = X1 ),
    c_0_344,
    [final] ).

cnf(c_0_446,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    c_0_345,
    [final] ).

cnf(c_0_447,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    c_0_346,
    [final] ).

cnf(c_0_448,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    c_0_347,
    [final] ).

cnf(c_0_449,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X2),element_relation) ),
    c_0_348,
    [final] ).

cnf(c_0_450,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X3,X2)) ),
    c_0_349,
    [final] ).

cnf(c_0_451,plain,
    ( successor(X1) = X2
    | ~ member(ordered_pair(X1,X2),successor_relation) ),
    c_0_350,
    [final] ).

cnf(c_0_452,plain,
    ( member(image(X1,X2),universal_class)
    | ~ member(X2,universal_class)
    | ~ function(X1) ),
    c_0_351,
    [final] ).

cnf(c_0_453,plain,
    ( cross_product(domain_of(domain_of(X1)),domain_of(domain_of(X1))) = domain_of(X1)
    | ~ operation(X1) ),
    c_0_352,
    [final] ).

cnf(c_0_454,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    c_0_353,
    [final] ).

cnf(c_0_455,plain,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    c_0_354,
    [final] ).

cnf(c_0_456,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subclass(X3,X2) ),
    c_0_355,
    [final] ).

cnf(c_0_457,plain,
    ( subclass(X1,X2)
    | ~ subclass(X3,X2)
    | ~ subclass(X1,X3) ),
    c_0_356,
    [final] ).

cnf(c_0_458,plain,
    ( member(apply(choice,X1),X1)
    | X1 = null_class
    | ~ member(X1,universal_class) ),
    c_0_357,
    [final] ).

cnf(c_0_459,plain,
    ( subclass(compose(X1,inverse(X1)),identity_relation)
    | ~ single_valued_class(X1) ),
    c_0_358,
    [final] ).

cnf(c_0_460,plain,
    ( subclass(compose(X1,inverse(X1)),identity_relation)
    | ~ function(X1) ),
    c_0_359,
    [final] ).

cnf(c_0_461,plain,
    ( member(X1,X2)
    | member(X1,complement(X2))
    | ~ member(X1,universal_class) ),
    c_0_360,
    [final] ).

cnf(c_0_462,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,complement(X2)) ),
    c_0_361,
    [final] ).

cnf(c_0_463,plain,
    ( subclass(X1,X2)
    | member(not_subclass_element(X1,X2),X1) ),
    c_0_362,
    [final] ).

cnf(c_0_464,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,universal_class)
    | unordered_pair(X3,X2) != singleton(X1) ),
    c_0_363,
    [final] ).

cnf(c_0_465,plain,
    ( member(member_of(singleton(X1)),universal_class)
    | ~ member(X1,universal_class) ),
    c_0_364,
    [final] ).

cnf(c_0_466,plain,
    ( X1 = X2
    | ~ subclass(X2,X1)
    | ~ subclass(X1,X2) ),
    c_0_365,
    [final] ).

cnf(c_0_467,plain,
    ( singleton(member_of(singleton(X1))) = singleton(X1)
    | ~ member(X1,universal_class) ),
    c_0_366,
    [final] ).

cnf(c_0_468,plain,
    ( subclass(range_of(X1),domain_of(domain_of(X1)))
    | ~ operation(X1) ),
    c_0_367,
    [final] ).

cnf(c_0_469,plain,
    ( member_of(X1) = X2
    | ~ member(X2,X1)
    | singleton(member_of(X1)) != X1 ),
    c_0_368,
    [final] ).

cnf(c_0_470,plain,
    ( subclass(image(successor_relation,X1),X1)
    | ~ inductive(X1) ),
    c_0_369,
    [final] ).

cnf(c_0_471,plain,
    ( subclass(singleton(X1),X2)
    | ~ member(X1,X2) ),
    c_0_370,
    [final] ).

cnf(c_0_472,plain,
    ( unordered_pair(X1,X2) != null_class
    | ~ member(X1,universal_class) ),
    c_0_371,
    [final] ).

cnf(c_0_473,plain,
    ( unordered_pair(X1,X2) != null_class
    | ~ member(X2,universal_class) ),
    c_0_372,
    [final] ).

cnf(c_0_474,plain,
    ( subclass(X1,cross_product(universal_class,universal_class))
    | ~ function(X1) ),
    c_0_373,
    [final] ).

cnf(c_0_475,plain,
    ( member(X1,singleton(X1))
    | ~ member(X1,universal_class) ),
    c_0_374,
    [final] ).

cnf(c_0_476,plain,
    ( member(X1,universal_class)
    | member(X2,universal_class)
    | unordered_pair(X2,X1) = null_class ),
    c_0_375,
    [final] ).

cnf(c_0_477,plain,
    ( member(sum_class(X1),universal_class)
    | ~ member(X1,universal_class) ),
    c_0_376,
    [final] ).

cnf(c_0_478,plain,
    ( member(power_class(X1),universal_class)
    | ~ member(X1,universal_class) ),
    c_0_377,
    [final] ).

cnf(c_0_479,plain,
    ( singleton(X1) = X2
    | X2 = null_class
    | ~ subclass(X2,singleton(X1)) ),
    c_0_378,
    [final] ).

cnf(c_0_480,plain,
    ( member(not_subclass_element(X1,null_class),X1)
    | X1 = null_class ),
    c_0_379,
    [final] ).

cnf(c_0_481,plain,
    ( X1 = X2
    | ~ member(X1,universal_class)
    | singleton(X1) != singleton(X2) ),
    c_0_380,
    [final] ).

cnf(c_0_482,plain,
    ( X1 = X2
    | ~ member(X2,universal_class)
    | singleton(X1) != singleton(X2) ),
    c_0_381,
    [final] ).

cnf(c_0_483,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    c_0_382,
    [final] ).

cnf(c_0_484,plain,
    ( member_of(singleton(X1)) = X1
    | ~ member(X1,universal_class) ),
    c_0_383,
    [final] ).

cnf(c_0_485,plain,
    ( unordered_pair(X1,X2) = singleton(X1)
    | member(X2,universal_class) ),
    c_0_384,
    [final] ).

cnf(c_0_486,plain,
    ( unordered_pair(X1,X2) = singleton(X2)
    | member(X1,universal_class) ),
    c_0_385,
    [final] ).

cnf(c_0_487,plain,
    ( member(X1,universal_class)
    | singleton(member_of(X1)) != X1 ),
    c_0_386,
    [final] ).

cnf(c_0_488,plain,
    ( one_to_one(X1)
    | ~ function(X1)
    | ~ function(inverse(X1)) ),
    c_0_387,
    [final] ).

cnf(c_0_489,plain,
    ( singleton(X1) != null_class
    | ~ member(X1,universal_class) ),
    c_0_388,
    [final] ).

cnf(c_0_490,plain,
    ( member_of(X1) = X1
    | member(member_of(X1),universal_class) ),
    c_0_389,
    [final] ).

cnf(c_0_491,plain,
    ( member_of(X1) = X1
    | member(member_of1(X1),universal_class) ),
    c_0_390,
    [final] ).

cnf(c_0_492,plain,
    ( member(regular(X1),X1)
    | X1 = null_class ),
    c_0_391,
    [final] ).

cnf(c_0_493,plain,
    ( intersection(X1,regular(X1)) = null_class
    | X1 = null_class ),
    c_0_392,
    [final] ).

cnf(c_0_494,plain,
    ( X1 = null_class
    | ~ subclass(X1,null_class) ),
    c_0_393,
    [final] ).

cnf(c_0_495,plain,
    ( member(null_class,X1)
    | ~ inductive(X1) ),
    c_0_394,
    [final] ).

cnf(c_0_496,plain,
    ( subclass(omega,X1)
    | ~ inductive(X1) ),
    c_0_395,
    [final] ).

cnf(c_0_497,plain,
    ( subclass(X1,X2)
    | X1 != X2 ),
    c_0_396,
    [final] ).

cnf(c_0_498,plain,
    ( subclass(X1,X2)
    | X2 != X1 ),
    c_0_397,
    [final] ).

cnf(c_0_499,plain,
    ( function(inverse(X1))
    | ~ one_to_one(X1) ),
    c_0_398,
    [final] ).

cnf(c_0_500,plain,
    ( singleton(X1) = null_class
    | member(X1,universal_class) ),
    c_0_399,
    [final] ).

cnf(c_0_501,plain,
    ( member_of(X1) = X1
    | singleton(member_of(X1)) = X1 ),
    c_0_400,
    [final] ).

cnf(c_0_502,plain,
    ( member_of(X1) = X1
    | singleton(member_of1(X1)) = X1 ),
    c_0_401,
    [final] ).

cnf(c_0_503,plain,
    ( function(X1)
    | ~ one_to_one(X1) ),
    c_0_402,
    [final] ).

cnf(c_0_504,plain,
    ( function(X1)
    | ~ operation(X1) ),
    c_0_403,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_404_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_404]) ).

cnf(c_0_404_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_404]) ).

cnf(c_0_404_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_404]) ).

cnf(c_0_404_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_404]) ).

cnf(c_0_404_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_404]) ).

cnf(c_0_405_0,axiom,
    ( X1 = null_class
    | singleton(not_subclass_element(X1,null_class)) = X1
    | member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_405]) ).

cnf(c_0_405_1,axiom,
    ( singleton(not_subclass_element(X1,null_class)) = X1
    | X1 = null_class
    | member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_405]) ).

cnf(c_0_405_2,axiom,
    ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1))
    | singleton(not_subclass_element(X1,null_class)) = X1
    | X1 = null_class ),
    inference(literals_permutation,[status(thm)],[c_0_405]) ).

cnf(c_0_406_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_406]) ).

cnf(c_0_406_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_406]) ).

cnf(c_0_406_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_406]) ).

cnf(c_0_406_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_406]) ).

cnf(c_0_406_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_406]) ).

cnf(c_0_407_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_407]) ).

cnf(c_0_407_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_407]) ).

cnf(c_0_407_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_407]) ).

cnf(c_0_408_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_408]) ).

cnf(c_0_408_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_408]) ).

cnf(c_0_408_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_408]) ).

cnf(c_0_409_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_409]) ).

cnf(c_0_409_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_409]) ).

cnf(c_0_409_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_409]) ).

cnf(c_0_410_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_410]) ).

cnf(c_0_410_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_410]) ).

cnf(c_0_410_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_410]) ).

cnf(c_0_411_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_411]) ).

cnf(c_0_411_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_411]) ).

cnf(c_0_412_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_412]) ).

cnf(c_0_412_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_412]) ).

cnf(c_0_413_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_413]) ).

cnf(c_0_413_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_413]) ).

cnf(c_0_414_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_414]) ).

cnf(c_0_414_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_414]) ).

cnf(c_0_414_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_414]) ).

cnf(c_0_414_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_414]) ).

cnf(c_0_415_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_415]) ).

cnf(c_0_415_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_415]) ).

cnf(c_0_415_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_415]) ).

cnf(c_0_416_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_416]) ).

cnf(c_0_416_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_416]) ).

cnf(c_0_416_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_416]) ).

cnf(c_0_416_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_416]) ).

cnf(c_0_417_0,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_417]) ).

cnf(c_0_417_1,axiom,
    ( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
    | member(X1,unordered_pair(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_417]) ).

cnf(c_0_418_0,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_418]) ).

cnf(c_0_418_1,axiom,
    ( ~ member(ordered_pair(X2,X1),cross_product(X3,X4))
    | member(X1,unordered_pair(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_418]) ).

cnf(c_0_419_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_419]) ).

cnf(c_0_419_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_419]) ).

cnf(c_0_419_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_419]) ).

cnf(c_0_420_0,axiom,
    ( X1 = X2
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | unordered_pair(X3,X1) != unordered_pair(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_420]) ).

cnf(c_0_420_1,axiom,
    ( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | X1 = X2
    | unordered_pair(X3,X1) != unordered_pair(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_420]) ).

cnf(c_0_420_2,axiom,
    ( unordered_pair(X3,X1) != unordered_pair(X3,X2)
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_420]) ).

cnf(c_0_421_0,axiom,
    ( X1 = X2
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | unordered_pair(X1,X3) != unordered_pair(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_421]) ).

cnf(c_0_421_1,axiom,
    ( ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | X1 = X2
    | unordered_pair(X1,X3) != unordered_pair(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_421]) ).

cnf(c_0_421_2,axiom,
    ( unordered_pair(X1,X3) != unordered_pair(X2,X3)
    | ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_421]) ).

cnf(c_0_422_0,axiom,
    ( compatible(X1,X2,X3)
    | ~ homomorphism(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_422]) ).

cnf(c_0_422_1,axiom,
    ( ~ homomorphism(X1,X2,X3)
    | compatible(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_422]) ).

cnf(c_0_423_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_423]) ).

cnf(c_0_423_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_423]) ).

cnf(c_0_423_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_423]) ).

cnf(c_0_424_0,axiom,
    ( X1 = X2
    | ~ member(not_subclass_element(X2,X1),X1)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_424]) ).

cnf(c_0_424_1,axiom,
    ( ~ member(not_subclass_element(X2,X1),X1)
    | X1 = X2
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_424]) ).

cnf(c_0_424_2,axiom,
    ( ~ member(not_subclass_element(X1,X2),X2)
    | ~ member(not_subclass_element(X2,X1),X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_424]) ).

cnf(c_0_425_0,axiom,
    ( unordered_pair(X1,X2) != null_class
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_425]) ).

cnf(c_0_425_1,axiom,
    ( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
    | unordered_pair(X1,X2) != null_class ),
    inference(literals_permutation,[status(thm)],[c_0_425]) ).

cnf(c_0_426_0,axiom,
    ( ~ member(X1,domain_of(X2))
    | restrict(X2,singleton(X1),universal_class) != null_class ),
    inference(literals_permutation,[status(thm)],[c_0_426]) ).

cnf(c_0_426_1,axiom,
    ( restrict(X2,singleton(X1),universal_class) != null_class
    | ~ member(X1,domain_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_426]) ).

cnf(c_0_427_0,axiom,
    ( subclass(range_of(X1),domain_of(domain_of(X2)))
    | ~ compatible(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_427]) ).

cnf(c_0_427_1,axiom,
    ( ~ compatible(X1,X3,X2)
    | subclass(range_of(X1),domain_of(domain_of(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_427]) ).

cnf(c_0_428_0,axiom,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_428]) ).

cnf(c_0_428_1,axiom,
    ( ~ member(ordered_pair(X1,X3),cross_product(X2,X4))
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_428]) ).

cnf(c_0_429_0,axiom,
    ( member(X1,X2)
    | ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_429]) ).

cnf(c_0_429_1,axiom,
    ( ~ member(ordered_pair(X3,X1),cross_product(X4,X2))
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_429]) ).

cnf(c_0_430_0,axiom,
    ( member(X1,universal_class)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_430]) ).

cnf(c_0_430_1,axiom,
    ( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
    | member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_430]) ).

cnf(c_0_431_0,axiom,
    ( member(X1,universal_class)
    | ~ member(ordered_pair(X2,X1),cross_product(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_431]) ).

cnf(c_0_431_1,axiom,
    ( ~ member(ordered_pair(X2,X1),cross_product(X3,X4))
    | member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_431]) ).

cnf(c_0_432_0,axiom,
    ( member(ordered_pair(X1,X2),cross_product(X3,X4))
    | ~ member(X2,X4)
    | ~ member(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_432]) ).

cnf(c_0_432_1,axiom,
    ( ~ member(X2,X4)
    | member(ordered_pair(X1,X2),cross_product(X3,X4))
    | ~ member(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_432]) ).

cnf(c_0_432_2,axiom,
    ( ~ member(X1,X3)
    | ~ member(X2,X4)
    | member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_432]) ).

cnf(c_0_433_0,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | X2 = X1
    | ~ member(not_subclass_element(X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_433]) ).

cnf(c_0_433_1,axiom,
    ( X2 = X1
    | member(not_subclass_element(X1,X2),X1)
    | ~ member(not_subclass_element(X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_433]) ).

cnf(c_0_433_2,axiom,
    ( ~ member(not_subclass_element(X2,X1),X1)
    | X2 = X1
    | member(not_subclass_element(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_433]) ).

cnf(c_0_434_0,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | X1 = X2
    | ~ member(not_subclass_element(X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_434]) ).

cnf(c_0_434_1,axiom,
    ( X1 = X2
    | member(not_subclass_element(X1,X2),X1)
    | ~ member(not_subclass_element(X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_434]) ).

cnf(c_0_434_2,axiom,
    ( ~ member(not_subclass_element(X2,X1),X1)
    | X1 = X2
    | member(not_subclass_element(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_434]) ).

cnf(c_0_435_0,axiom,
    ( domain_of(domain_of(X1)) = domain_of(X2)
    | ~ compatible(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_435]) ).

cnf(c_0_435_1,axiom,
    ( ~ compatible(X2,X1,X3)
    | domain_of(domain_of(X1)) = domain_of(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_435]) ).

cnf(c_0_436_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_436]) ).

cnf(c_0_436_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_436]) ).

cnf(c_0_436_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_436]) ).

cnf(c_0_437_0,axiom,
    ( ordered_pair(first(X1),second(X1)) = X1
    | ~ member(X1,cross_product(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_437]) ).

cnf(c_0_437_1,axiom,
    ( ~ member(X1,cross_product(X2,X3))
    | ordered_pair(first(X1),second(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_437]) ).

cnf(c_0_438_0,axiom,
    ( function(X1)
    | ~ compatible(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_438]) ).

cnf(c_0_438_1,axiom,
    ( ~ compatible(X1,X2,X3)
    | function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_438]) ).

cnf(c_0_439_0,axiom,
    ( operation(X1)
    | ~ homomorphism(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_439]) ).

cnf(c_0_439_1,axiom,
    ( ~ homomorphism(X2,X1,X3)
    | operation(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_439]) ).

cnf(c_0_440_0,axiom,
    ( operation(X1)
    | ~ homomorphism(X2,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_440]) ).

cnf(c_0_440_1,axiom,
    ( ~ homomorphism(X2,X3,X1)
    | operation(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_440]) ).

cnf(c_0_441_0,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_441]) ).

cnf(c_0_441_1,axiom,
    ( ~ member(X1,X3)
    | member(X1,intersection(X2,X3))
    | ~ member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_441]) ).

cnf(c_0_441_2,axiom,
    ( ~ member(X1,X2)
    | ~ member(X1,X3)
    | member(X1,intersection(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_441]) ).

cnf(c_0_442_0,axiom,
    ( subclass(unordered_pair(X1,X2),X3)
    | ~ member(X2,X3)
    | ~ member(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_442]) ).

cnf(c_0_442_1,axiom,
    ( ~ member(X2,X3)
    | subclass(unordered_pair(X1,X2),X3)
    | ~ member(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_442]) ).

cnf(c_0_442_2,axiom,
    ( ~ member(X1,X3)
    | ~ member(X2,X3)
    | subclass(unordered_pair(X1,X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_442]) ).

cnf(c_0_443_0,axiom,
    ( single_valued_class(X1)
    | ~ subclass(compose(X1,inverse(X1)),identity_relation) ),
    inference(literals_permutation,[status(thm)],[c_0_443]) ).

cnf(c_0_443_1,axiom,
    ( ~ subclass(compose(X1,inverse(X1)),identity_relation)
    | single_valued_class(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_443]) ).

cnf(c_0_444_0,axiom,
    ( inductive(X1)
    | ~ subclass(image(successor_relation,X1),X1)
    | ~ member(null_class,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_444]) ).

cnf(c_0_444_1,axiom,
    ( ~ subclass(image(successor_relation,X1),X1)
    | inductive(X1)
    | ~ member(null_class,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_444]) ).

cnf(c_0_444_2,axiom,
    ( ~ member(null_class,X1)
    | ~ subclass(image(successor_relation,X1),X1)
    | inductive(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_444]) ).

cnf(c_0_445_0,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | member(not_subclass_element(X2,X1),X2)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_445]) ).

cnf(c_0_445_1,axiom,
    ( member(not_subclass_element(X2,X1),X2)
    | member(not_subclass_element(X1,X2),X1)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_445]) ).

cnf(c_0_445_2,axiom,
    ( X2 = X1
    | member(not_subclass_element(X2,X1),X2)
    | member(not_subclass_element(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_445]) ).

cnf(c_0_446_0,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_446]) ).

cnf(c_0_446_1,axiom,
    ( ~ member(not_subclass_element(X1,X2),X2)
    | subclass(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_446]) ).

cnf(c_0_447_0,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_447]) ).

cnf(c_0_447_1,axiom,
    ( ~ member(X1,intersection(X2,X3))
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_447]) ).

cnf(c_0_448_0,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_448]) ).

cnf(c_0_448_1,axiom,
    ( ~ member(X1,intersection(X3,X2))
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_448]) ).

cnf(c_0_449_0,axiom,
    ( member(X1,X2)
    | ~ member(ordered_pair(X1,X2),element_relation) ),
    inference(literals_permutation,[status(thm)],[c_0_449]) ).

cnf(c_0_449_1,axiom,
    ( ~ member(ordered_pair(X1,X2),element_relation)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_449]) ).

cnf(c_0_450_0,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_450]) ).

cnf(c_0_450_1,axiom,
    ( X1 = X3
    | X1 = X2
    | ~ member(X1,unordered_pair(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_450]) ).

cnf(c_0_450_2,axiom,
    ( ~ member(X1,unordered_pair(X3,X2))
    | X1 = X3
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_450]) ).

cnf(c_0_451_0,axiom,
    ( successor(X1) = X2
    | ~ member(ordered_pair(X1,X2),successor_relation) ),
    inference(literals_permutation,[status(thm)],[c_0_451]) ).

cnf(c_0_451_1,axiom,
    ( ~ member(ordered_pair(X1,X2),successor_relation)
    | successor(X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_451]) ).

cnf(c_0_452_0,axiom,
    ( member(image(X1,X2),universal_class)
    | ~ member(X2,universal_class)
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_452]) ).

cnf(c_0_452_1,axiom,
    ( ~ member(X2,universal_class)
    | member(image(X1,X2),universal_class)
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_452]) ).

cnf(c_0_452_2,axiom,
    ( ~ function(X1)
    | ~ member(X2,universal_class)
    | member(image(X1,X2),universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_452]) ).

cnf(c_0_453_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_453]) ).

cnf(c_0_453_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_453]) ).

cnf(c_0_454_0,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_454]) ).

cnf(c_0_454_1,axiom,
    ( ~ member(X1,universal_class)
    | member(X1,unordered_pair(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_454]) ).

cnf(c_0_455_0,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_455]) ).

cnf(c_0_455_1,axiom,
    ( ~ member(X1,universal_class)
    | member(X1,unordered_pair(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_455]) ).

cnf(c_0_456_0,axiom,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subclass(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_456]) ).

cnf(c_0_456_1,axiom,
    ( ~ member(X1,X3)
    | member(X1,X2)
    | ~ subclass(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_456]) ).

cnf(c_0_456_2,axiom,
    ( ~ subclass(X3,X2)
    | ~ member(X1,X3)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_456]) ).

cnf(c_0_457_0,axiom,
    ( subclass(X1,X2)
    | ~ subclass(X3,X2)
    | ~ subclass(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_457]) ).

cnf(c_0_457_1,axiom,
    ( ~ subclass(X3,X2)
    | subclass(X1,X2)
    | ~ subclass(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_457]) ).

cnf(c_0_457_2,axiom,
    ( ~ subclass(X1,X3)
    | ~ subclass(X3,X2)
    | subclass(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_457]) ).

cnf(c_0_458_0,axiom,
    ( member(apply(choice,X1),X1)
    | X1 = null_class
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_458]) ).

cnf(c_0_458_1,axiom,
    ( X1 = null_class
    | member(apply(choice,X1),X1)
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_458]) ).

cnf(c_0_458_2,axiom,
    ( ~ member(X1,universal_class)
    | X1 = null_class
    | member(apply(choice,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_458]) ).

cnf(c_0_459_0,axiom,
    ( subclass(compose(X1,inverse(X1)),identity_relation)
    | ~ single_valued_class(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_459]) ).

cnf(c_0_459_1,axiom,
    ( ~ single_valued_class(X1)
    | subclass(compose(X1,inverse(X1)),identity_relation) ),
    inference(literals_permutation,[status(thm)],[c_0_459]) ).

cnf(c_0_460_0,axiom,
    ( subclass(compose(X1,inverse(X1)),identity_relation)
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_460]) ).

cnf(c_0_460_1,axiom,
    ( ~ function(X1)
    | subclass(compose(X1,inverse(X1)),identity_relation) ),
    inference(literals_permutation,[status(thm)],[c_0_460]) ).

cnf(c_0_461_0,axiom,
    ( member(X1,X2)
    | member(X1,complement(X2))
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_461]) ).

cnf(c_0_461_1,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_461]) ).

cnf(c_0_461_2,axiom,
    ( ~ member(X1,universal_class)
    | member(X1,complement(X2))
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_461]) ).

cnf(c_0_462_0,axiom,
    ( ~ member(X1,X2)
    | ~ member(X1,complement(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_462]) ).

cnf(c_0_462_1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_462]) ).

cnf(c_0_463_0,axiom,
    ( subclass(X1,X2)
    | member(not_subclass_element(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_463]) ).

cnf(c_0_463_1,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_463]) ).

cnf(c_0_464_0,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,universal_class)
    | unordered_pair(X3,X2) != singleton(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_464]) ).

cnf(c_0_464_1,axiom,
    ( X1 = X3
    | X1 = X2
    | ~ member(X1,universal_class)
    | unordered_pair(X3,X2) != singleton(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_464]) ).

cnf(c_0_464_2,axiom,
    ( ~ member(X1,universal_class)
    | X1 = X3
    | X1 = X2
    | unordered_pair(X3,X2) != singleton(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_464]) ).

cnf(c_0_464_3,axiom,
    ( unordered_pair(X3,X2) != singleton(X1)
    | ~ member(X1,universal_class)
    | X1 = X3
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_464]) ).

cnf(c_0_465_0,axiom,
    ( member(member_of(singleton(X1)),universal_class)
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_465]) ).

cnf(c_0_465_1,axiom,
    ( ~ member(X1,universal_class)
    | member(member_of(singleton(X1)),universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_465]) ).

cnf(c_0_466_0,axiom,
    ( X1 = X2
    | ~ subclass(X2,X1)
    | ~ subclass(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_466]) ).

cnf(c_0_466_1,axiom,
    ( ~ subclass(X2,X1)
    | X1 = X2
    | ~ subclass(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_466]) ).

cnf(c_0_466_2,axiom,
    ( ~ subclass(X1,X2)
    | ~ subclass(X2,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_466]) ).

cnf(c_0_467_0,axiom,
    ( singleton(member_of(singleton(X1))) = singleton(X1)
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_467]) ).

cnf(c_0_467_1,axiom,
    ( ~ member(X1,universal_class)
    | singleton(member_of(singleton(X1))) = singleton(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_467]) ).

cnf(c_0_468_0,axiom,
    ( subclass(range_of(X1),domain_of(domain_of(X1)))
    | ~ operation(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_468]) ).

cnf(c_0_468_1,axiom,
    ( ~ operation(X1)
    | subclass(range_of(X1),domain_of(domain_of(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_468]) ).

cnf(c_0_469_0,axiom,
    ( member_of(X1) = X2
    | ~ member(X2,X1)
    | singleton(member_of(X1)) != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_469]) ).

cnf(c_0_469_1,axiom,
    ( ~ member(X2,X1)
    | member_of(X1) = X2
    | singleton(member_of(X1)) != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_469]) ).

cnf(c_0_469_2,axiom,
    ( singleton(member_of(X1)) != X1
    | ~ member(X2,X1)
    | member_of(X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_469]) ).

cnf(c_0_470_0,axiom,
    ( subclass(image(successor_relation,X1),X1)
    | ~ inductive(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_470]) ).

cnf(c_0_470_1,axiom,
    ( ~ inductive(X1)
    | subclass(image(successor_relation,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_470]) ).

cnf(c_0_471_0,axiom,
    ( subclass(singleton(X1),X2)
    | ~ member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_471]) ).

cnf(c_0_471_1,axiom,
    ( ~ member(X1,X2)
    | subclass(singleton(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_471]) ).

cnf(c_0_472_0,axiom,
    ( unordered_pair(X1,X2) != null_class
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_472]) ).

cnf(c_0_472_1,axiom,
    ( ~ member(X1,universal_class)
    | unordered_pair(X1,X2) != null_class ),
    inference(literals_permutation,[status(thm)],[c_0_472]) ).

cnf(c_0_473_0,axiom,
    ( unordered_pair(X1,X2) != null_class
    | ~ member(X2,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_473]) ).

cnf(c_0_473_1,axiom,
    ( ~ member(X2,universal_class)
    | unordered_pair(X1,X2) != null_class ),
    inference(literals_permutation,[status(thm)],[c_0_473]) ).

cnf(c_0_474_0,axiom,
    ( subclass(X1,cross_product(universal_class,universal_class))
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_474]) ).

cnf(c_0_474_1,axiom,
    ( ~ function(X1)
    | subclass(X1,cross_product(universal_class,universal_class)) ),
    inference(literals_permutation,[status(thm)],[c_0_474]) ).

cnf(c_0_475_0,axiom,
    ( member(X1,singleton(X1))
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_475]) ).

cnf(c_0_475_1,axiom,
    ( ~ member(X1,universal_class)
    | member(X1,singleton(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_475]) ).

cnf(c_0_476_0,axiom,
    ( member(X1,universal_class)
    | member(X2,universal_class)
    | unordered_pair(X2,X1) = null_class ),
    inference(literals_permutation,[status(thm)],[c_0_476]) ).

cnf(c_0_476_1,axiom,
    ( member(X2,universal_class)
    | member(X1,universal_class)
    | unordered_pair(X2,X1) = null_class ),
    inference(literals_permutation,[status(thm)],[c_0_476]) ).

cnf(c_0_476_2,axiom,
    ( unordered_pair(X2,X1) = null_class
    | member(X2,universal_class)
    | member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_476]) ).

cnf(c_0_477_0,axiom,
    ( member(sum_class(X1),universal_class)
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_477]) ).

cnf(c_0_477_1,axiom,
    ( ~ member(X1,universal_class)
    | member(sum_class(X1),universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_477]) ).

cnf(c_0_478_0,axiom,
    ( member(power_class(X1),universal_class)
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_478]) ).

cnf(c_0_478_1,axiom,
    ( ~ member(X1,universal_class)
    | member(power_class(X1),universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_478]) ).

cnf(c_0_479_0,axiom,
    ( singleton(X1) = X2
    | X2 = null_class
    | ~ subclass(X2,singleton(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_479]) ).

cnf(c_0_479_1,axiom,
    ( X2 = null_class
    | singleton(X1) = X2
    | ~ subclass(X2,singleton(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_479]) ).

cnf(c_0_479_2,axiom,
    ( ~ subclass(X2,singleton(X1))
    | X2 = null_class
    | singleton(X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_479]) ).

cnf(c_0_480_0,axiom,
    ( member(not_subclass_element(X1,null_class),X1)
    | X1 = null_class ),
    inference(literals_permutation,[status(thm)],[c_0_480]) ).

cnf(c_0_480_1,axiom,
    ( X1 = null_class
    | member(not_subclass_element(X1,null_class),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_480]) ).

cnf(c_0_481_0,axiom,
    ( X1 = X2
    | ~ member(X1,universal_class)
    | singleton(X1) != singleton(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_481]) ).

cnf(c_0_481_1,axiom,
    ( ~ member(X1,universal_class)
    | X1 = X2
    | singleton(X1) != singleton(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_481]) ).

cnf(c_0_481_2,axiom,
    ( singleton(X1) != singleton(X2)
    | ~ member(X1,universal_class)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_481]) ).

cnf(c_0_482_0,axiom,
    ( X1 = X2
    | ~ member(X2,universal_class)
    | singleton(X1) != singleton(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_482]) ).

cnf(c_0_482_1,axiom,
    ( ~ member(X2,universal_class)
    | X1 = X2
    | singleton(X1) != singleton(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_482]) ).

cnf(c_0_482_2,axiom,
    ( singleton(X1) != singleton(X2)
    | ~ member(X2,universal_class)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_482]) ).

cnf(c_0_483_0,axiom,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_483]) ).

cnf(c_0_483_1,axiom,
    ( ~ member(X1,singleton(X2))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_483]) ).

cnf(c_0_484_0,axiom,
    ( member_of(singleton(X1)) = X1
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_484]) ).

cnf(c_0_484_1,axiom,
    ( ~ member(X1,universal_class)
    | member_of(singleton(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_484]) ).

cnf(c_0_485_0,axiom,
    ( unordered_pair(X1,X2) = singleton(X1)
    | member(X2,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_485]) ).

cnf(c_0_485_1,axiom,
    ( member(X2,universal_class)
    | unordered_pair(X1,X2) = singleton(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_485]) ).

cnf(c_0_486_0,axiom,
    ( unordered_pair(X1,X2) = singleton(X2)
    | member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_486]) ).

cnf(c_0_486_1,axiom,
    ( member(X1,universal_class)
    | unordered_pair(X1,X2) = singleton(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_486]) ).

cnf(c_0_487_0,axiom,
    ( member(X1,universal_class)
    | singleton(member_of(X1)) != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_487]) ).

cnf(c_0_487_1,axiom,
    ( singleton(member_of(X1)) != X1
    | member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_487]) ).

cnf(c_0_488_0,axiom,
    ( one_to_one(X1)
    | ~ function(X1)
    | ~ function(inverse(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_488]) ).

cnf(c_0_488_1,axiom,
    ( ~ function(X1)
    | one_to_one(X1)
    | ~ function(inverse(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_488]) ).

cnf(c_0_488_2,axiom,
    ( ~ function(inverse(X1))
    | ~ function(X1)
    | one_to_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_488]) ).

cnf(c_0_489_0,axiom,
    ( singleton(X1) != null_class
    | ~ member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_489]) ).

cnf(c_0_489_1,axiom,
    ( ~ member(X1,universal_class)
    | singleton(X1) != null_class ),
    inference(literals_permutation,[status(thm)],[c_0_489]) ).

cnf(c_0_490_0,axiom,
    ( member_of(X1) = X1
    | member(member_of(X1),universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_490]) ).

cnf(c_0_490_1,axiom,
    ( member(member_of(X1),universal_class)
    | member_of(X1) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_490]) ).

cnf(c_0_491_0,axiom,
    ( member_of(X1) = X1
    | member(member_of1(X1),universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_491]) ).

cnf(c_0_491_1,axiom,
    ( member(member_of1(X1),universal_class)
    | member_of(X1) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_491]) ).

cnf(c_0_492_0,axiom,
    ( member(regular(X1),X1)
    | X1 = null_class ),
    inference(literals_permutation,[status(thm)],[c_0_492]) ).

cnf(c_0_492_1,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_492]) ).

cnf(c_0_493_0,axiom,
    ( intersection(X1,regular(X1)) = null_class
    | X1 = null_class ),
    inference(literals_permutation,[status(thm)],[c_0_493]) ).

cnf(c_0_493_1,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    inference(literals_permutation,[status(thm)],[c_0_493]) ).

cnf(c_0_494_0,axiom,
    ( X1 = null_class
    | ~ subclass(X1,null_class) ),
    inference(literals_permutation,[status(thm)],[c_0_494]) ).

cnf(c_0_494_1,axiom,
    ( ~ subclass(X1,null_class)
    | X1 = null_class ),
    inference(literals_permutation,[status(thm)],[c_0_494]) ).

cnf(c_0_495_0,axiom,
    ( member(null_class,X1)
    | ~ inductive(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_495]) ).

cnf(c_0_495_1,axiom,
    ( ~ inductive(X1)
    | member(null_class,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_495]) ).

cnf(c_0_496_0,axiom,
    ( subclass(omega,X1)
    | ~ inductive(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_496]) ).

cnf(c_0_496_1,axiom,
    ( ~ inductive(X1)
    | subclass(omega,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_496]) ).

cnf(c_0_497_0,axiom,
    ( subclass(X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_497]) ).

cnf(c_0_497_1,axiom,
    ( X1 != X2
    | subclass(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_497]) ).

cnf(c_0_498_0,axiom,
    ( subclass(X1,X2)
    | X2 != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_498]) ).

cnf(c_0_498_1,axiom,
    ( X2 != X1
    | subclass(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_498]) ).

cnf(c_0_499_0,axiom,
    ( function(inverse(X1))
    | ~ one_to_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_499]) ).

cnf(c_0_499_1,axiom,
    ( ~ one_to_one(X1)
    | function(inverse(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_499]) ).

cnf(c_0_500_0,axiom,
    ( singleton(X1) = null_class
    | member(X1,universal_class) ),
    inference(literals_permutation,[status(thm)],[c_0_500]) ).

cnf(c_0_500_1,axiom,
    ( member(X1,universal_class)
    | singleton(X1) = null_class ),
    inference(literals_permutation,[status(thm)],[c_0_500]) ).

cnf(c_0_501_0,axiom,
    ( member_of(X1) = X1
    | singleton(member_of(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_501]) ).

cnf(c_0_501_1,axiom,
    ( singleton(member_of(X1)) = X1
    | member_of(X1) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_501]) ).

cnf(c_0_502_0,axiom,
    ( member_of(X1) = X1
    | singleton(member_of1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_502]) ).

cnf(c_0_502_1,axiom,
    ( singleton(member_of1(X1)) = X1
    | member_of(X1) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_502]) ).

cnf(c_0_503_0,axiom,
    ( function(X1)
    | ~ one_to_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_503]) ).

cnf(c_0_503_1,axiom,
    ( ~ one_to_one(X1)
    | function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_503]) ).

cnf(c_0_504_0,axiom,
    ( function(X1)
    | ~ operation(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_504]) ).

cnf(c_0_504_1,axiom,
    ( ~ operation(X1)
    | function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_504]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_201,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    file('<stdin>',prove_corollary_1_to_number_of_elements_in_class_1) ).

fof(c_0_1_202,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    file('<stdin>',prove_corollary_1_to_number_of_elements_in_class_2) ).

fof(c_0_2_203,negated_conjecture,
    x != null_class,
    file('<stdin>',prove_corollary_1_to_number_of_elements_in_class_3) ).

fof(c_0_3_204,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_4_205,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    c_0_1 ).

fof(c_0_5_206,negated_conjecture,
    x != null_class,
    c_0_2 ).

fof(c_0_6_207,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    c_0_3 ).

fof(c_0_7_208,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    c_0_4 ).

fof(c_0_8_209,negated_conjecture,
    x != null_class,
    c_0_5 ).

cnf(c_0_9_210,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10_211,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11_212,negated_conjecture,
    x != null_class,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12_213,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    c_0_9,
    [final] ).

cnf(c_0_13_214,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    c_0_10,
    [final] ).

cnf(c_0_14_215,negated_conjecture,
    x != null_class,
    c_0_11,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_288,negated_conjecture,
    x != null_class,
    file('/export/starexec/sandbox2/tmp/iprover_modulo_4de71a.p',c_0_14) ).

cnf(c_401,negated_conjecture,
    x != null_class,
    inference(copy,[status(esa)],[c_288]) ).

cnf(c_411,negated_conjecture,
    x != null_class,
    inference(copy,[status(esa)],[c_401]) ).

cnf(c_412,negated_conjecture,
    x != null_class,
    inference(copy,[status(esa)],[c_411]) ).

cnf(c_415,negated_conjecture,
    x != null_class,
    inference(copy,[status(esa)],[c_412]) ).

cnf(c_1260,plain,
    x != null_class,
    inference(copy,[status(esa)],[c_415]) ).

cnf(c_5,plain,
    ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0))
    | singleton(not_subclass_element(X0,null_class)) = X0
    | X0 = null_class ),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_4de71a.p',c_0_405_0) ).

cnf(c_717,plain,
    ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0))
    | singleton(not_subclass_element(X0,null_class)) = X0
    | X0 = null_class ),
    inference(copy,[status(esa)],[c_5]) ).

cnf(c_1269,plain,
    ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x))
    | singleton(not_subclass_element(x,null_class)) = x ),
    inference(resolution,[status(thm)],[c_1260,c_717]) ).

cnf(c_1270,plain,
    ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x))
    | singleton(not_subclass_element(x,null_class)) = x ),
    inference(rewriting,[status(thm)],[c_1269]) ).

cnf(c_287,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    file('/export/starexec/sandbox2/tmp/iprover_modulo_4de71a.p',c_0_13) ).

cnf(c_399,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    inference(copy,[status(esa)],[c_287]) ).

cnf(c_410,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    inference(copy,[status(esa)],[c_399]) ).

cnf(c_413,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    inference(copy,[status(esa)],[c_410]) ).

cnf(c_417,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    inference(copy,[status(esa)],[c_413]) ).

cnf(c_1264,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    inference(copy,[status(esa)],[c_417]) ).

cnf(c_286,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_4de71a.p',c_0_12) ).

cnf(c_397,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    inference(copy,[status(esa)],[c_286]) ).

cnf(c_409,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    inference(copy,[status(esa)],[c_397]) ).

cnf(c_414,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    inference(copy,[status(esa)],[c_409]) ).

cnf(c_416,negated_conjecture,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    inference(copy,[status(esa)],[c_414]) ).

cnf(c_1262,plain,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
    inference(copy,[status(esa)],[c_416]) ).

cnf(c_117,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    file('/export/starexec/sandbox2/tmp/iprover_modulo_4de71a.p',c_0_448_0) ).

cnf(c_941,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(copy,[status(esa)],[c_117]) ).

cnf(c_1328,plain,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(X0,x)),
    inference(resolution,[status(thm)],[c_1262,c_941]) ).

cnf(c_1331,plain,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(X0,x)),
    inference(rewriting,[status(thm)],[c_1328]) ).

cnf(c_1666,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1270,c_1264,c_1331]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SET098-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12  % Command  : iprover_modulo %s %d
% 0.12/0.32  % Computer : n003.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Sun Jul 10 02:57:29 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  % Running in mono-core mode
% 0.12/0.38  % Orienting using strategy Equiv(ClausalAll)
% 0.12/0.38  % Orientation found
% 0.12/0.38  % 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/sandbox2/tmp/iprover_proof_d5f2d5.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_4de71a.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_75a413 | grep -v "SZS"
% 0.18/0.41  
% 0.18/0.41  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.18/0.41  
% 0.18/0.41  % 
% 0.18/0.41  % ------  iProver source info 
% 0.18/0.41  
% 0.18/0.41  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.18/0.41  % git: non_committed_changes: true
% 0.18/0.41  % git: last_make_outside_of_git: true
% 0.18/0.41  
% 0.18/0.41  % 
% 0.18/0.41  % ------ Input Options
% 0.18/0.41  
% 0.18/0.41  % --out_options                         all
% 0.18/0.41  % --tptp_safe_out                       true
% 0.18/0.41  % --problem_path                        ""
% 0.18/0.41  % --include_path                        ""
% 0.18/0.41  % --clausifier                          .//eprover
% 0.18/0.41  % --clausifier_options                  --tstp-format  
% 0.18/0.41  % --stdin                               false
% 0.18/0.41  % --dbg_backtrace                       false
% 0.18/0.41  % --dbg_dump_prop_clauses               false
% 0.18/0.41  % --dbg_dump_prop_clauses_file          -
% 0.18/0.41  % --dbg_out_stat                        false
% 0.18/0.41  
% 0.18/0.41  % ------ General Options
% 0.18/0.41  
% 0.18/0.41  % --fof                                 false
% 0.18/0.41  % --time_out_real                       150.
% 0.18/0.41  % --time_out_prep_mult                  0.2
% 0.18/0.41  % --time_out_virtual                    -1.
% 0.18/0.41  % --schedule                            none
% 0.18/0.41  % --ground_splitting                    input
% 0.18/0.41  % --splitting_nvd                       16
% 0.18/0.41  % --non_eq_to_eq                        false
% 0.18/0.41  % --prep_gs_sim                         true
% 0.18/0.41  % --prep_unflatten                      false
% 0.18/0.41  % --prep_res_sim                        true
% 0.18/0.41  % --prep_upred                          true
% 0.18/0.41  % --res_sim_input                       true
% 0.18/0.41  % --clause_weak_htbl                    true
% 0.18/0.41  % --gc_record_bc_elim                   false
% 0.18/0.41  % --symbol_type_check                   false
% 0.18/0.41  % --clausify_out                        false
% 0.18/0.41  % --large_theory_mode                   false
% 0.18/0.41  % --prep_sem_filter                     none
% 0.18/0.41  % --prep_sem_filter_out                 false
% 0.18/0.41  % --preprocessed_out                    false
% 0.18/0.41  % --sub_typing                          false
% 0.18/0.41  % --brand_transform                     false
% 0.18/0.41  % --pure_diseq_elim                     true
% 0.18/0.41  % --min_unsat_core                      false
% 0.18/0.41  % --pred_elim                           true
% 0.18/0.41  % --add_important_lit                   false
% 0.18/0.41  % --soft_assumptions                    false
% 0.18/0.41  % --reset_solvers                       false
% 0.18/0.41  % --bc_imp_inh                          []
% 0.18/0.41  % --conj_cone_tolerance                 1.5
% 0.18/0.41  % --prolific_symb_bound                 500
% 0.18/0.41  % --lt_threshold                        2000
% 0.18/0.41  
% 0.18/0.41  % ------ SAT Options
% 0.18/0.41  
% 0.18/0.41  % --sat_mode                            false
% 0.18/0.41  % --sat_fm_restart_options              ""
% 0.18/0.41  % --sat_gr_def                          false
% 0.18/0.41  % --sat_epr_types                       true
% 0.18/0.41  % --sat_non_cyclic_types                false
% 0.18/0.41  % --sat_finite_models                   false
% 0.18/0.41  % --sat_fm_lemmas                       false
% 0.18/0.41  % --sat_fm_prep                         false
% 0.18/0.41  % --sat_fm_uc_incr                      true
% 0.18/0.41  % --sat_out_model                       small
% 0.18/0.41  % --sat_out_clauses                     false
% 0.18/0.41  
% 0.18/0.41  % ------ QBF Options
% 0.18/0.41  
% 0.18/0.41  % --qbf_mode                            false
% 0.18/0.41  % --qbf_elim_univ                       true
% 0.18/0.41  % --qbf_sk_in                           true
% 0.18/0.41  % --qbf_pred_elim                       true
% 0.18/0.41  % --qbf_split                           32
% 0.18/0.41  
% 0.18/0.41  % ------ BMC1 Options
% 0.18/0.41  
% 0.18/0.41  % --bmc1_incremental                    false
% 0.18/0.41  % --bmc1_axioms                         reachable_all
% 0.18/0.41  % --bmc1_min_bound                      0
% 0.18/0.41  % --bmc1_max_bound                      -1
% 0.18/0.41  % --bmc1_max_bound_default              -1
% 0.18/0.41  % --bmc1_symbol_reachability            true
% 0.18/0.41  % --bmc1_property_lemmas                false
% 0.18/0.41  % --bmc1_k_induction                    false
% 0.18/0.41  % --bmc1_non_equiv_states               false
% 0.18/0.41  % --bmc1_deadlock                       false
% 0.18/0.41  % --bmc1_ucm                            false
% 0.18/0.41  % --bmc1_add_unsat_core                 none
% 0.18/0.41  % --bmc1_unsat_core_children            false
% 0.18/0.41  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.18/0.41  % --bmc1_out_stat                       full
% 0.18/0.41  % --bmc1_ground_init                    false
% 0.18/0.41  % --bmc1_pre_inst_next_state            false
% 0.18/0.41  % --bmc1_pre_inst_state                 false
% 0.18/0.41  % --bmc1_pre_inst_reach_state           false
% 0.18/0.41  % --bmc1_out_unsat_core                 false
% 0.18/0.41  % --bmc1_aig_witness_out                false
% 0.18/0.41  % --bmc1_verbose                        false
% 0.18/0.41  % --bmc1_dump_clauses_tptp              false
% 0.86/1.12  % --bmc1_dump_unsat_core_tptp           false
% 0.86/1.12  % --bmc1_dump_file                      -
% 0.86/1.12  % --bmc1_ucm_expand_uc_limit            128
% 0.86/1.12  % --bmc1_ucm_n_expand_iterations        6
% 0.86/1.12  % --bmc1_ucm_extend_mode                1
% 0.86/1.12  % --bmc1_ucm_init_mode                  2
% 0.86/1.12  % --bmc1_ucm_cone_mode                  none
% 0.86/1.12  % --bmc1_ucm_reduced_relation_type      0
% 0.86/1.12  % --bmc1_ucm_relax_model                4
% 0.86/1.12  % --bmc1_ucm_full_tr_after_sat          true
% 0.86/1.12  % --bmc1_ucm_expand_neg_assumptions     false
% 0.86/1.12  % --bmc1_ucm_layered_model              none
% 0.86/1.12  % --bmc1_ucm_max_lemma_size             10
% 0.86/1.12  
% 0.86/1.12  % ------ AIG Options
% 0.86/1.12  
% 0.86/1.12  % --aig_mode                            false
% 0.86/1.12  
% 0.86/1.12  % ------ Instantiation Options
% 0.86/1.12  
% 0.86/1.12  % --instantiation_flag                  true
% 0.86/1.12  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.86/1.12  % --inst_solver_per_active              750
% 0.86/1.12  % --inst_solver_calls_frac              0.5
% 0.86/1.12  % --inst_passive_queue_type             priority_queues
% 0.86/1.12  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.86/1.12  % --inst_passive_queues_freq            [25;2]
% 0.86/1.12  % --inst_dismatching                    true
% 0.86/1.12  % --inst_eager_unprocessed_to_passive   true
% 0.86/1.12  % --inst_prop_sim_given                 true
% 0.86/1.12  % --inst_prop_sim_new                   false
% 0.86/1.12  % --inst_orphan_elimination             true
% 0.86/1.12  % --inst_learning_loop_flag             true
% 0.86/1.12  % --inst_learning_start                 3000
% 0.86/1.12  % --inst_learning_factor                2
% 0.86/1.12  % --inst_start_prop_sim_after_learn     3
% 0.86/1.12  % --inst_sel_renew                      solver
% 0.86/1.12  % --inst_lit_activity_flag              true
% 0.86/1.12  % --inst_out_proof                      true
% 0.86/1.12  
% 0.86/1.12  % ------ Resolution Options
% 0.86/1.12  
% 0.86/1.12  % --resolution_flag                     true
% 0.86/1.12  % --res_lit_sel                         kbo_max
% 0.86/1.12  % --res_to_prop_solver                  none
% 0.86/1.12  % --res_prop_simpl_new                  false
% 0.86/1.12  % --res_prop_simpl_given                false
% 0.86/1.12  % --res_passive_queue_type              priority_queues
% 0.86/1.12  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.86/1.12  % --res_passive_queues_freq             [15;5]
% 0.86/1.12  % --res_forward_subs                    full
% 0.86/1.12  % --res_backward_subs                   full
% 0.86/1.12  % --res_forward_subs_resolution         true
% 0.86/1.12  % --res_backward_subs_resolution        true
% 0.86/1.12  % --res_orphan_elimination              false
% 0.86/1.12  % --res_time_limit                      1000.
% 0.86/1.12  % --res_out_proof                       true
% 0.86/1.12  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_d5f2d5.s
% 0.86/1.12  % --modulo                              true
% 0.86/1.12  
% 0.86/1.12  % ------ Combination Options
% 0.86/1.12  
% 0.86/1.12  % --comb_res_mult                       1000
% 0.86/1.12  % --comb_inst_mult                      300
% 0.86/1.12  % ------ 
% 0.86/1.12  
% 0.86/1.12  % ------ Parsing...% successful
% 0.86/1.12  
% 0.86/1.12  % ------ 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 % 
% 0.86/1.12  
% 0.86/1.12  % ------ Proving...
% 0.86/1.12  % ------ Problem Properties 
% 0.86/1.12  
% 0.86/1.12  % 
% 0.86/1.12  % EPR                                   false
% 0.86/1.12  % Horn                                  false
% 0.86/1.12  % Has equality                          true
% 0.86/1.12  
% 0.86/1.12  % % ------ Input Options Time Limit: Unbounded
% 0.86/1.12  
% 0.86/1.12  
% 0.86/1.12  Compiling...
% 0.86/1.12  Loading plugin: done.
% 0.86/1.12  Compiling...
% 0.86/1.12  Loading plugin: done.
% 0.86/1.12  Compiling...
% 0.86/1.12  Loading plugin: done.
% 0.86/1.12  Compiling...
% 0.86/1.12  Loading plugin: done.
% 0.86/1.12  Compiling...
% 0.86/1.12  Loading plugin: done.
% 0.86/1.12  Compiling...
% 0.86/1.12  Loading plugin: done.
% 0.86/1.12  % % ------ Current options:
% 0.86/1.12  
% 0.86/1.12  % ------ Input Options
% 0.86/1.12  
% 0.86/1.12  % --out_options                         all
% 0.86/1.12  % --tptp_safe_out                       true
% 0.86/1.12  % --problem_path                        ""
% 0.86/1.12  % --include_path                        ""
% 0.86/1.12  % --clausifier                          .//eprover
% 0.86/1.12  % --clausifier_options                  --tstp-format  
% 0.86/1.12  % --stdin                               false
% 0.86/1.12  % --dbg_backtrace                       false
% 0.86/1.12  % --dbg_dump_prop_clauses               false
% 0.86/1.12  % --dbg_dump_prop_clauses_file          -
% 0.86/1.12  % --dbg_out_stat                        false
% 0.86/1.12  
% 0.86/1.12  % ------ General Options
% 0.86/1.12  
% 0.86/1.12  % --fof                                 false
% 0.86/1.12  % --time_out_real                       150.
% 0.86/1.12  % --time_out_prep_mult                  0.2
% 0.86/1.12  % --time_out_virtual                    -1.
% 0.86/1.12  % --schedule                            none
% 0.86/1.13  % --ground_splitting                    input
% 0.86/1.13  % --splitting_nvd                       16
% 0.86/1.13  % --non_eq_to_eq                        false
% 0.86/1.13  % --prep_gs_sim                         true
% 0.86/1.13  % --prep_unflatten                      false
% 0.86/1.13  % --prep_res_sim                        true
% 0.86/1.13  % --prep_upred                          true
% 0.86/1.13  % --res_sim_input                       true
% 0.86/1.13  % --clause_weak_htbl                    true
% 0.86/1.13  % --gc_record_bc_elim                   false
% 0.86/1.13  % --symbol_type_check                   false
% 0.86/1.13  % --clausify_out                        false
% 0.86/1.13  % --large_theory_mode                   false
% 0.86/1.13  % --prep_sem_filter                     none
% 0.86/1.13  % --prep_sem_filter_out                 false
% 0.86/1.13  % --preprocessed_out                    false
% 0.86/1.13  % --sub_typing                          false
% 0.86/1.13  % --brand_transform                     false
% 0.86/1.13  % --pure_diseq_elim                     true
% 0.86/1.13  % --min_unsat_core                      false
% 0.86/1.13  % --pred_elim                           true
% 0.86/1.13  % --add_important_lit                   false
% 0.86/1.13  % --soft_assumptions                    false
% 0.86/1.13  % --reset_solvers                       false
% 0.86/1.13  % --bc_imp_inh                          []
% 0.86/1.13  % --conj_cone_tolerance                 1.5
% 0.86/1.13  % --prolific_symb_bound                 500
% 0.86/1.13  % --lt_threshold                        2000
% 0.86/1.13  
% 0.86/1.13  % ------ SAT Options
% 0.86/1.13  
% 0.86/1.13  % --sat_mode                            false
% 0.86/1.13  % --sat_fm_restart_options              ""
% 0.86/1.13  % --sat_gr_def                          false
% 0.86/1.13  % --sat_epr_types                       true
% 0.86/1.13  % --sat_non_cyclic_types                false
% 0.86/1.13  % --sat_finite_models                   false
% 0.86/1.13  % --sat_fm_lemmas                       false
% 0.86/1.13  % --sat_fm_prep                         false
% 0.86/1.13  % --sat_fm_uc_incr                      true
% 0.86/1.13  % --sat_out_model                       small
% 0.86/1.13  % --sat_out_clauses                     false
% 0.86/1.13  
% 0.86/1.13  % ------ QBF Options
% 0.86/1.13  
% 0.86/1.13  % --qbf_mode                            false
% 0.86/1.13  % --qbf_elim_univ                       true
% 0.86/1.13  % --qbf_sk_in                           true
% 0.86/1.13  % --qbf_pred_elim                       true
% 0.86/1.13  % --qbf_split                           32
% 0.86/1.13  
% 0.86/1.13  % ------ BMC1 Options
% 0.86/1.13  
% 0.86/1.13  % --bmc1_incremental                    false
% 0.86/1.13  % --bmc1_axioms                         reachable_all
% 0.86/1.13  % --bmc1_min_bound                      0
% 0.86/1.13  % --bmc1_max_bound                      -1
% 0.86/1.13  % --bmc1_max_bound_default              -1
% 0.86/1.13  % --bmc1_symbol_reachability            true
% 0.86/1.13  % --bmc1_property_lemmas                false
% 0.86/1.13  % --bmc1_k_induction                    false
% 0.86/1.13  % --bmc1_non_equiv_states               false
% 0.86/1.13  % --bmc1_deadlock                       false
% 0.86/1.13  % --bmc1_ucm                            false
% 0.86/1.13  % --bmc1_add_unsat_core                 none
% 0.86/1.13  % --bmc1_unsat_core_children            false
% 0.86/1.13  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.86/1.13  % --bmc1_out_stat                       full
% 0.86/1.13  % --bmc1_ground_init                    false
% 0.86/1.13  % --bmc1_pre_inst_next_state            false
% 0.86/1.13  % --bmc1_pre_inst_state                 false
% 0.86/1.13  % --bmc1_pre_inst_reach_state           false
% 0.86/1.13  % --bmc1_out_unsat_core                 false
% 0.86/1.13  % --bmc1_aig_witness_out                false
% 0.86/1.13  % --bmc1_verbose                        false
% 0.86/1.13  % --bmc1_dump_clauses_tptp              false
% 0.86/1.13  % --bmc1_dump_unsat_core_tptp           false
% 0.86/1.13  % --bmc1_dump_file                      -
% 0.86/1.13  % --bmc1_ucm_expand_uc_limit            128
% 0.86/1.13  % --bmc1_ucm_n_expand_iterations        6
% 0.86/1.13  % --bmc1_ucm_extend_mode                1
% 0.86/1.13  % --bmc1_ucm_init_mode                  2
% 0.86/1.13  % --bmc1_ucm_cone_mode                  none
% 0.86/1.13  % --bmc1_ucm_reduced_relation_type      0
% 0.86/1.13  % --bmc1_ucm_relax_model                4
% 0.86/1.13  % --bmc1_ucm_full_tr_after_sat          true
% 0.86/1.13  % --bmc1_ucm_expand_neg_assumptions     false
% 0.86/1.13  % --bmc1_ucm_layered_model              none
% 0.86/1.13  % --bmc1_ucm_max_lemma_size             10
% 0.86/1.13  
% 0.86/1.13  % ------ AIG Options
% 0.86/1.13  
% 0.86/1.13  % --aig_mode                            false
% 0.86/1.13  
% 0.86/1.13  % ------ Instantiation Options
% 0.86/1.13  
% 0.86/1.13  % --instantiation_flag                  true
% 0.86/1.13  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.86/1.13  % --inst_solver_per_active              750
% 0.86/1.13  % --inst_solver_calls_frac              0.5
% 0.86/1.13  % --inst_passive_queue_type             priority_queues
% 0.86/1.13  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.86/1.14  % --inst_passive_queues_freq            [25;2]
% 0.86/1.14  % --inst_dismatching                    true
% 0.86/1.14  % --inst_eager_unprocessed_to_passive   true
% 0.86/1.14  % --inst_prop_sim_given                 true
% 0.86/1.14  % --inst_prop_sim_new                   false
% 0.86/1.14  % --inst_orphan_elimination             true
% 0.86/1.14  % --inst_learning_loop_flag             true
% 0.86/1.14  % --inst_learning_start                 3000
% 0.86/1.14  % --inst_learning_factor                2
% 0.86/1.14  % --inst_start_prop_sim_after_learn     3
% 0.86/1.14  % --inst_sel_renew                      solver
% 0.86/1.14  % --inst_lit_activity_flag              true
% 0.86/1.14  % --inst_out_proof                      true
% 0.86/1.14  
% 0.86/1.14  % ------ Resolution Options
% 0.86/1.14  
% 0.86/1.14  % --resolution_flag                     true
% 0.86/1.14  % --res_lit_sel                         kbo_max
% 0.86/1.14  % --res_to_prop_solver                  none
% 0.86/1.14  % --res_prop_simpl_new                  false
% 0.86/1.14  % --res_prop_simpl_given                false
% 0.86/1.14  % --res_passive_queue_type              priority_queues
% 0.86/1.14  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.86/1.14  % --res_passive_queues_freq             [15;5]
% 0.86/1.14  % --res_forward_subs                    full
% 0.86/1.14  % --res_backward_subs                   full
% 0.86/1.14  % --res_forward_subs_resolution         true
% 0.86/1.14  % --res_backward_subs_resolution        true
% 0.86/1.14  % --res_orphan_elimination              false
% 0.86/1.14  % --res_time_limit                      1000.
% 0.86/1.14  % --res_out_proof                       true
% 0.86/1.14  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_d5f2d5.s
% 0.86/1.14  % --modulo                              true
% 0.86/1.14  
% 0.86/1.14  % ------ Combination Options
% 0.86/1.14  
% 0.86/1.14  % --comb_res_mult                       1000
% 0.86/1.14  % --comb_inst_mult                      300
% 0.86/1.14  % ------ 
% 0.86/1.14  
% 0.86/1.14  
% 0.86/1.14  
% 0.86/1.14  % ------ Proving...
% 0.86/1.14  % 
% 0.86/1.14  
% 0.86/1.14  
% 0.86/1.14  %  Resolution empty clause
% 0.86/1.14  
% 0.86/1.14  % ------                             Statistics
% 0.86/1.14  
% 0.86/1.14  % ------ General
% 0.86/1.14  
% 0.86/1.14  % num_of_input_clauses:                 289
% 0.86/1.14  % num_of_input_neg_conjectures:         3
% 0.86/1.14  % num_of_splits:                        0
% 0.86/1.14  % num_of_split_atoms:                   0
% 0.86/1.14  % num_of_sem_filtered_clauses:          0
% 0.86/1.14  % num_of_subtypes:                      0
% 0.86/1.14  % monotx_restored_types:                0
% 0.86/1.14  % sat_num_of_epr_types:                 0
% 0.86/1.14  % sat_num_of_non_cyclic_types:          0
% 0.86/1.14  % sat_guarded_non_collapsed_types:      0
% 0.86/1.14  % is_epr:                               0
% 0.86/1.14  % is_horn:                              0
% 0.86/1.14  % has_eq:                               1
% 0.86/1.14  % num_pure_diseq_elim:                  0
% 0.86/1.14  % simp_replaced_by:                     0
% 0.86/1.14  % res_preprocessed:                     6
% 0.86/1.14  % prep_upred:                           0
% 0.86/1.14  % prep_unflattend:                      0
% 0.86/1.14  % pred_elim_cands:                      0
% 0.86/1.14  % pred_elim:                            0
% 0.86/1.14  % pred_elim_cl:                         0
% 0.86/1.14  % pred_elim_cycles:                     0
% 0.86/1.14  % forced_gc_time:                       0
% 0.86/1.14  % gc_basic_clause_elim:                 0
% 0.86/1.14  % parsing_time:                         0.011
% 0.86/1.14  % sem_filter_time:                      0.
% 0.86/1.14  % pred_elim_time:                       0.
% 0.86/1.14  % out_proof_time:                       0.001
% 0.86/1.14  % monotx_time:                          0.
% 0.86/1.14  % subtype_inf_time:                     0.
% 0.86/1.14  % unif_index_cands_time:                0.
% 0.86/1.14  % unif_index_add_time:                  0.
% 0.86/1.14  % total_time:                           0.748
% 0.86/1.14  % num_of_symbols:                       75
% 0.86/1.14  % num_of_terms:                         1323
% 0.86/1.14  
% 0.86/1.14  % ------ Propositional Solver
% 0.86/1.14  
% 0.86/1.14  % prop_solver_calls:                    1
% 0.86/1.14  % prop_fast_solver_calls:               9
% 0.86/1.14  % prop_num_of_clauses:                  289
% 0.86/1.14  % prop_preprocess_simplified:           867
% 0.86/1.14  % prop_fo_subsumed:                     0
% 0.86/1.14  % prop_solver_time:                     0.
% 0.86/1.14  % prop_fast_solver_time:                0.
% 0.86/1.14  % prop_unsat_core_time:                 0.
% 0.86/1.14  
% 0.86/1.14  % ------ QBF 
% 0.86/1.14  
% 0.86/1.14  % qbf_q_res:                            0
% 0.86/1.14  % qbf_num_tautologies:                  0
% 0.86/1.14  % qbf_prep_cycles:                      0
% 0.86/1.14  
% 0.86/1.14  % ------ BMC1
% 0.86/1.14  
% 0.86/1.14  % bmc1_current_bound:                   -1
% 0.86/1.14  % bmc1_last_solved_bound:               -1
% 0.86/1.14  % bmc1_unsat_core_size:                 -1
% 0.86/1.14  % bmc1_unsat_core_parents_size:         -1
% 0.86/1.14  % bmc1_merge_next_fun:                  0
% 0.86/1.14  % bmc1_unsat_core_clauses_time:         0.
% 0.86/1.14  
% 0.86/1.14  % ------ Instantiation
% 0.86/1.14  
% 0.86/1.14  % inst_num_of_clauses:                  289
% 0.86/1.14  % inst_num_in_passive:                  0
% 0.86/1.14  % inst_num_in_active:                   0
% 0.86/1.14  % inst_num_in_unprocessed:              289
% 0.86/1.14  % inst_num_of_loops:                    0
% 0.86/1.14  % inst_num_of_learning_restarts:        0
% 0.86/1.14  % inst_num_moves_active_passive:        0
% 0.86/1.14  % inst_lit_activity:                    0
% 0.86/1.14  % inst_lit_activity_moves:              0
% 0.86/1.14  % inst_num_tautologies:                 0
% 0.86/1.14  % inst_num_prop_implied:                0
% 0.86/1.14  % inst_num_existing_simplified:         0
% 0.86/1.14  % inst_num_eq_res_simplified:           0
% 0.86/1.14  % inst_num_child_elim:                  0
% 0.86/1.14  % inst_num_of_dismatching_blockings:    0
% 0.86/1.14  % inst_num_of_non_proper_insts:         0
% 0.86/1.14  % inst_num_of_duplicates:               0
% 0.86/1.14  % inst_inst_num_from_inst_to_res:       0
% 0.86/1.14  % inst_dismatching_checking_time:       0.
% 0.86/1.14  
% 0.86/1.14  % ------ Resolution
% 0.86/1.14  
% 0.86/1.14  % res_num_of_clauses:                   472
% 0.86/1.14  % res_num_in_passive:                   136
% 0.86/1.14  % res_num_in_active:                    157
% 0.86/1.14  % res_num_of_loops:                     27
% 0.86/1.14  % res_forward_subset_subsumed:          140
% 0.86/1.14  % res_backward_subset_subsumed:         0
% 0.86/1.14  % res_forward_subsumed:                 7
% 0.86/1.14  % res_backward_subsumed:                0
% 0.86/1.14  % res_forward_subsumption_resolution:   4
% 0.86/1.14  % res_backward_subsumption_resolution:  0
% 0.86/1.14  % res_clause_to_clause_subsumption:     47
% 0.86/1.14  % res_orphan_elimination:               0
% 0.86/1.14  % res_tautology_del:                    0
% 0.86/1.14  % res_num_eq_res_simplified:            0
% 0.86/1.14  % res_num_sel_changes:                  0
% 0.86/1.14  % res_moves_from_active_to_pass:        0
% 0.86/1.14  
% 0.86/1.14  % Status Unsatisfiable
% 0.86/1.14  % SZS status Unsatisfiable
% 0.86/1.14  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------