%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 10:53:47 EDT 2022

% Result   : Unsatisfiable 0.69s 0.90s
% Output   : CNFRefutation 0.69s
% 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(apply_to_two_arguments,axiom,
    apply_to_two_arguments(Xf,X,Y) = apply(Xf,ordered_pair(X,Y)),
    input ).

fof(apply_to_two_arguments_0,plain,
    ! [X,Xf,Y] :
      ( apply_to_two_arguments(Xf,X,Y) = apply(Xf,ordered_pair(X,Y))
      | $false ),
    inference(orientation,[status(thm)],[apply_to_two_arguments]) ).

cnf(restrict,axiom,
    restrict(X,Y) = intersection(X,cross_product(Y,universal_set)),
    input ).

fof(restrict_0,plain,
    ! [X,Y] :
      ( restrict(X,Y) = intersection(X,cross_product(Y,universal_set))
      | $false ),
    inference(orientation,[status(thm)],[restrict]) ).

cnf(choice1,axiom,
    function(f25),
    input ).

fof(choice1_0,plain,
    ( function(f25)
    | $false ),
    inference(orientation,[status(thm)],[choice1]) ).

cnf(infinity2,axiom,
    member(empty_set,infinity),
    input ).

fof(infinity2_0,plain,
    ( member(empty_set,infinity)
    | $false ),
    inference(orientation,[status(thm)],[infinity2]) ).

cnf(infinity1,axiom,
    little_set(infinity),
    input ).

fof(infinity1_0,plain,
    ( little_set(infinity)
    | $false ),
    inference(orientation,[status(thm)],[infinity1]) ).

cnf(empty_set,axiom,
    ~ member(Z,empty_set),
    input ).

fof(empty_set_0,plain,
    ! [Z] :
      ( ~ member(Z,empty_set)
      | $false ),
    inference(orientation,[status(thm)],[empty_set]) ).

cnf(successor,axiom,
    successor(X) = union(X,singleton_set(X)),
    input ).

fof(successor_0,plain,
    ! [X] :
      ( successor(X) = union(X,singleton_set(X))
      | $false ),
    inference(orientation,[status(thm)],[successor]) ).

cnf(union,axiom,
    union(X,Y) = complement(intersection(complement(X),complement(Y))),
    input ).

fof(union_0,plain,
    ! [X,Y] :
      ( union(X,Y) = complement(intersection(complement(X),complement(Y)))
      | $false ),
    inference(orientation,[status(thm)],[union]) ).

cnf(ordered_pair,axiom,
    ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)),
    input ).

fof(ordered_pair_0,plain,
    ! [X,Y] :
      ( ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y))
      | $false ),
    inference(orientation,[status(thm)],[ordered_pair]) ).

cnf(singleton_set,axiom,
    singleton_set(X) = non_ordered_pair(X,X),
    input ).

fof(singleton_set_0,plain,
    ! [X] :
      ( singleton_set(X) = non_ordered_pair(X,X)
      | $false ),
    inference(orientation,[status(thm)],[singleton_set]) ).

cnf(non_ordered_pair4,axiom,
    little_set(non_ordered_pair(X,Y)),
    input ).

fof(non_ordered_pair4_0,plain,
    ! [X,Y] :
      ( little_set(non_ordered_pair(X,Y))
      | $false ),
    inference(orientation,[status(thm)],[non_ordered_pair4]) ).

fof(def_lhs_atom1,axiom,
    ! [Y,X] :
      ( lhs_atom1(Y,X)
    <=> little_set(non_ordered_pair(X,Y)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_0,plain,
    ! [X,Y] :
      ( lhs_atom1(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[non_ordered_pair4_0,def_lhs_atom1]) ).

fof(def_lhs_atom2,axiom,
    ! [X] :
      ( lhs_atom2(X)
    <=> singleton_set(X) = non_ordered_pair(X,X) ),
    inference(definition,[],]) ).

fof(to_be_clausified_1,plain,
    ! [X] :
      ( lhs_atom2(X)
      | $false ),
    inference(fold_definition,[status(thm)],[singleton_set_0,def_lhs_atom2]) ).

fof(def_lhs_atom3,axiom,
    ! [Y,X] :
      ( lhs_atom3(Y,X)
    <=> ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_2,plain,
    ! [X,Y] :
      ( lhs_atom3(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[ordered_pair_0,def_lhs_atom3]) ).

fof(def_lhs_atom4,axiom,
    ! [Y,X] :
      ( lhs_atom4(Y,X)
    <=> union(X,Y) = complement(intersection(complement(X),complement(Y))) ),
    inference(definition,[],]) ).

fof(to_be_clausified_3,plain,
    ! [X,Y] :
      ( lhs_atom4(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[union_0,def_lhs_atom4]) ).

fof(def_lhs_atom5,axiom,
    ! [X] :
      ( lhs_atom5(X)
    <=> successor(X) = union(X,singleton_set(X)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_4,plain,
    ! [X] :
      ( lhs_atom5(X)
      | $false ),
    inference(fold_definition,[status(thm)],[successor_0,def_lhs_atom5]) ).

fof(def_lhs_atom6,axiom,
    ! [Z] :
      ( lhs_atom6(Z)
    <=> ~ member(Z,empty_set) ),
    inference(definition,[],]) ).

fof(to_be_clausified_5,plain,
    ! [Z] :
      ( lhs_atom6(Z)
      | $false ),
    inference(fold_definition,[status(thm)],[empty_set_0,def_lhs_atom6]) ).

fof(def_lhs_atom7,axiom,
    ( lhs_atom7
  <=> little_set(infinity) ),
    inference(definition,[],]) ).

fof(to_be_clausified_6,plain,
    ( lhs_atom7
    | $false ),
    inference(fold_definition,[status(thm)],[infinity1_0,def_lhs_atom7]) ).

fof(def_lhs_atom8,axiom,
    ( lhs_atom8
  <=> member(empty_set,infinity) ),
    inference(definition,[],]) ).

fof(to_be_clausified_7,plain,
    ( lhs_atom8
    | $false ),
    inference(fold_definition,[status(thm)],[infinity2_0,def_lhs_atom8]) ).

fof(def_lhs_atom9,axiom,
    ( lhs_atom9
  <=> function(f25) ),
    inference(definition,[],]) ).

fof(to_be_clausified_8,plain,
    ( lhs_atom9
    | $false ),
    inference(fold_definition,[status(thm)],[choice1_0,def_lhs_atom9]) ).

fof(def_lhs_atom10,axiom,
    ! [Y,X] :
      ( lhs_atom10(Y,X)
    <=> restrict(X,Y) = intersection(X,cross_product(Y,universal_set)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_9,plain,
    ! [X,Y] :
      ( lhs_atom10(Y,X)
      | $false ),
    inference(fold_definition,[status(thm)],[restrict_0,def_lhs_atom10]) ).

fof(def_lhs_atom11,axiom,
    ! [Y,Xf,X] :
      ( lhs_atom11(Y,Xf,X)
    <=> apply_to_two_arguments(Xf,X,Y) = apply(Xf,ordered_pair(X,Y)) ),
    inference(definition,[],]) ).

fof(to_be_clausified_10,plain,
    ! [X,Xf,Y] :
      ( lhs_atom11(Y,Xf,X)
      | $false ),
    inference(fold_definition,[status(thm)],[apply_to_two_arguments_0,def_lhs_atom11]) ).

% Start CNF derivation
fof(c_0_0,axiom,
    ! [X1,X4,X2] :
      ( lhs_atom11(X1,X4,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_10) ).

fof(c_0_1,axiom,
    ! [X1,X2] :
      ( lhs_atom10(X1,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_9) ).

fof(c_0_2,axiom,
    ! [X1,X2] :
      ( lhs_atom4(X1,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_3) ).

fof(c_0_3,axiom,
    ! [X1,X2] :
      ( lhs_atom3(X1,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_2) ).

fof(c_0_4,axiom,
    ! [X1,X2] :
      ( lhs_atom1(X1,X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_0) ).

fof(c_0_5,axiom,
    ! [X3] :
      ( lhs_atom6(X3)
      | ~ $true ),
    file('<stdin>',to_be_clausified_5) ).

fof(c_0_6,axiom,
    ! [X2] :
      ( lhs_atom5(X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_4) ).

fof(c_0_7,axiom,
    ! [X2] :
      ( lhs_atom2(X2)
      | ~ $true ),
    file('<stdin>',to_be_clausified_1) ).

fof(c_0_8,axiom,
    ( lhs_atom9
    | ~ $true ),
    file('<stdin>',to_be_clausified_8) ).

fof(c_0_9,axiom,
    ( lhs_atom8
    | ~ $true ),
    file('<stdin>',to_be_clausified_7) ).

fof(c_0_10,axiom,
    ( lhs_atom7
    | ~ $true ),
    file('<stdin>',to_be_clausified_6) ).

fof(c_0_11,plain,
    ! [X1,X4,X2] : lhs_atom11(X1,X4,X2),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_12,plain,
    ! [X1,X2] : lhs_atom10(X1,X2),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_13,plain,
    ! [X1,X2] : lhs_atom4(X1,X2),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_14,plain,
    ! [X1,X2] : lhs_atom3(X1,X2),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_15,plain,
    ! [X1,X2] : lhs_atom1(X1,X2),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_16,plain,
    ! [X3] : lhs_atom6(X3),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_17,plain,
    ! [X2] : lhs_atom5(X2),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_18,plain,
    ! [X2] : lhs_atom2(X2),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_19,plain,
    lhs_atom9,
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_20,plain,
    lhs_atom8,
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_21,plain,
    lhs_atom7,
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_22,plain,
    ! [X5,X6,X7] : lhs_atom11(X5,X6,X7),
    inference(variable_rename,[status(thm)],[c_0_11]) ).

fof(c_0_23,plain,
    ! [X3,X4] : lhs_atom10(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_12]) ).

fof(c_0_24,plain,
    ! [X3,X4] : lhs_atom4(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_13]) ).

fof(c_0_25,plain,
    ! [X3,X4] : lhs_atom3(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_14]) ).

fof(c_0_26,plain,
    ! [X3,X4] : lhs_atom1(X3,X4),
    inference(variable_rename,[status(thm)],[c_0_15]) ).

fof(c_0_27,plain,
    ! [X4] : lhs_atom6(X4),
    inference(variable_rename,[status(thm)],[c_0_16]) ).

fof(c_0_28,plain,
    ! [X3] : lhs_atom5(X3),
    inference(variable_rename,[status(thm)],[c_0_17]) ).

fof(c_0_29,plain,
    ! [X3] : lhs_atom2(X3),
    inference(variable_rename,[status(thm)],[c_0_18]) ).

fof(c_0_30,plain,
    lhs_atom9,
    c_0_19 ).

fof(c_0_31,plain,
    lhs_atom8,
    c_0_20 ).

fof(c_0_32,plain,
    lhs_atom7,
    c_0_21 ).

cnf(c_0_33,plain,
    lhs_atom11(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_34,plain,
    lhs_atom10(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_35,plain,
    lhs_atom4(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_36,plain,
    lhs_atom3(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_37,plain,
    lhs_atom1(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_38,plain,
    lhs_atom6(X1),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_39,plain,
    lhs_atom5(X1),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_40,plain,
    lhs_atom2(X1),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_41,plain,
    lhs_atom9,
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_42,plain,
    lhs_atom8,
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_43,plain,
    lhs_atom7,
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_44,plain,
    lhs_atom11(X1,X2,X3),
    c_0_33,
    [final] ).

cnf(c_0_45,plain,
    lhs_atom10(X1,X2),
    c_0_34,
    [final] ).

cnf(c_0_46,plain,
    lhs_atom4(X1,X2),
    c_0_35,
    [final] ).

cnf(c_0_47,plain,
    lhs_atom3(X1,X2),
    c_0_36,
    [final] ).

cnf(c_0_48,plain,
    lhs_atom1(X1,X2),
    c_0_37,
    [final] ).

cnf(c_0_49,plain,
    lhs_atom6(X1),
    c_0_38,
    [final] ).

cnf(c_0_50,plain,
    lhs_atom5(X1),
    c_0_39,
    [final] ).

cnf(c_0_51,plain,
    lhs_atom2(X1),
    c_0_40,
    [final] ).

cnf(c_0_52,plain,
    lhs_atom9,
    c_0_41,
    [final] ).

cnf(c_0_53,plain,
    lhs_atom8,
    c_0_42,
    [final] ).

cnf(c_0_54,plain,
    lhs_atom7,
    c_0_43,
    [final] ).

% End CNF derivation
cnf(c_0_44_0,axiom,
    apply_to_two_arguments(X2,X3,X1) = apply(X2,ordered_pair(X3,X1)),
    inference(unfold_definition,[status(thm)],[c_0_44,def_lhs_atom11]) ).

cnf(c_0_45_0,axiom,
    restrict(X2,X1) = intersection(X2,cross_product(X1,universal_set)),
    inference(unfold_definition,[status(thm)],[c_0_45,def_lhs_atom10]) ).

cnf(c_0_46_0,axiom,
    union(X2,X1) = complement(intersection(complement(X2),complement(X1))),
    inference(unfold_definition,[status(thm)],[c_0_46,def_lhs_atom4]) ).

cnf(c_0_47_0,axiom,
    ordered_pair(X2,X1) = non_ordered_pair(singleton_set(X2),non_ordered_pair(X2,X1)),
    inference(unfold_definition,[status(thm)],[c_0_47,def_lhs_atom3]) ).

cnf(c_0_48_0,axiom,
    little_set(non_ordered_pair(X2,X1)),
    inference(unfold_definition,[status(thm)],[c_0_48,def_lhs_atom1]) ).

cnf(c_0_49_0,axiom,
    ~ member(X1,empty_set),
    inference(unfold_definition,[status(thm)],[c_0_49,def_lhs_atom6]) ).

cnf(c_0_50_0,axiom,
    successor(X1) = union(X1,singleton_set(X1)),
    inference(unfold_definition,[status(thm)],[c_0_50,def_lhs_atom5]) ).

cnf(c_0_51_0,axiom,
    singleton_set(X1) = non_ordered_pair(X1,X1),
    inference(unfold_definition,[status(thm)],[c_0_51,def_lhs_atom2]) ).

cnf(c_0_52_0,axiom,
    function(f25),
    inference(unfold_definition,[status(thm)],[c_0_52,def_lhs_atom9]) ).

cnf(c_0_53_0,axiom,
    member(empty_set,infinity),
    inference(unfold_definition,[status(thm)],[c_0_53,def_lhs_atom8]) ).

cnf(c_0_54_0,axiom,
    little_set(infinity),
    inference(unfold_definition,[status(thm)],[c_0_54,def_lhs_atom7]) ).

% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0_001,axiom,
    ! [X16,X17,X18,X19,X20] :
      ( homomorphism(X18,X17,X20,X16,X19)
      | ~ closed(X17,X20)
      | ~ closed(X16,X19)
      | ~ maps(X18,X17,X16)
      | apply(X18,apply_to_two_arguments(X20,f32(X18,X17,X20,X16,X19),f33(X18,X17,X20,X16,X19))) != apply_to_two_arguments(X19,apply(X18,f32(X18,X17,X20,X16,X19)),apply(X18,f33(X18,X17,X20,X16,X19))) ),
    file('<stdin>',homomorphism7) ).

fof(c_0_1_002,axiom,
    ! [X11,X14,X4,X15] :
      ( inverse(X11,X4,X15,X14)
      | ~ maps(X14,X11,X11)
      | apply_to_two_arguments(X4,apply(X14,f38(X11,X4,X15,X14)),f38(X11,X4,X15,X14)) != X15
      | apply_to_two_arguments(X4,f38(X11,X4,X15,X14),apply(X14,f38(X11,X4,X15,X14))) != X15 ),
    file('<stdin>',inverse5) ).

fof(c_0_2_003,axiom,
    ! [X16,X17,X18,X19,X20] :
      ( homomorphism(X18,X17,X20,X16,X19)
      | ~ closed(X17,X20)
      | ~ closed(X16,X19)
      | ~ maps(X18,X17,X16)
      | member(f32(X18,X17,X20,X16,X19),X17) ),
    file('<stdin>',homomorphism5) ).

fof(c_0_3_004,axiom,
    ! [X16,X17,X18,X19,X20] :
      ( homomorphism(X18,X17,X20,X16,X19)
      | ~ closed(X17,X20)
      | ~ closed(X16,X19)
      | ~ maps(X18,X17,X16)
      | member(f33(X18,X17,X20,X16,X19),X17) ),
    file('<stdin>',homomorphism6) ).

fof(c_0_4_005,axiom,
    ! [X13,X16,X17,X18,X19,X20,X2] :
      ( ~ homomorphism(X18,X17,X20,X16,X19)
      | ~ member(X2,X17)
      | ~ member(X13,X17)
      | apply(X18,apply_to_two_arguments(X20,X2,X13)) = apply_to_two_arguments(X19,apply(X18,X2),apply(X18,X13)) ),
    file('<stdin>',homomorphism4) ).

fof(c_0_5_006,axiom,
    ! [X16,X17,X18,X19,X20] :
      ( ~ homomorphism(X18,X17,X20,X16,X19)
      | maps(X18,X17,X16) ),
    file('<stdin>',homomorphism3) ).

fof(c_0_6_007,axiom,
    ! [X16,X17,X18,X19,X20] :
      ( ~ homomorphism(X18,X17,X20,X16,X19)
      | closed(X17,X20) ),
    file('<stdin>',homomorphism1) ).

fof(c_0_7_008,axiom,
    ! [X16,X17,X18,X19,X20] :
      ( ~ homomorphism(X18,X17,X20,X16,X19)
      | closed(X16,X19) ),
    file('<stdin>',homomorphism2) ).

fof(c_0_8_009,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X11)),f52(X1,X11)),apply_to_two_arguments(plus,f53(X1,X11),f52(X1,X11))),X11)
      | member(X1,X11) ),
    file('<stdin>',times10) ).

fof(c_0_9_010,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X11)),f52(X1,X11)),apply_to_two_arguments(plus,f53(X1,X11),f52(X1,X11))),X11)
      | member(X1,X11) ),
    file('<stdin>',times5) ).

fof(c_0_10_011,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X11)),f47(X1,X11)),successor(f48(X1,X11))),X11)
      | member(X1,X11) ),
    file('<stdin>',plus10) ).

fof(c_0_11_012,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X11)),f47(X1,X11)),successor(f48(X1,X11))),X11)
      | member(X1,X11) ),
    file('<stdin>',plus5) ).

fof(c_0_12_013,axiom,
    ! [X11,X4] :
      ( associative(X11,X4)
      | apply_to_two_arguments(X4,apply_to_two_arguments(X4,f34(X11,X4),f35(X11,X4)),f36(X11,X4)) != apply_to_two_arguments(X4,f34(X11,X4),apply_to_two_arguments(X4,f35(X11,X4),f36(X11,X4))) ),
    file('<stdin>',associative_system5) ).

fof(c_0_13_014,axiom,
    ! [X11,X14,X4,X15] :
      ( inverse(X11,X4,X15,X14)
      | ~ maps(X14,X11,X11)
      | member(f38(X11,X4,X15,X14),X11) ),
    file('<stdin>',inverse4) ).

fof(c_0_14_015,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | member(ordered_pair(ordered_pair(f46(X1,X11),f47(X1,X11)),f48(X1,X11)),X11)
      | member(X1,X11) ),
    file('<stdin>',plus9) ).

fof(c_0_15_016,axiom,
    ! [X11,X4,X15] :
      ( identity(X11,X4,X15)
      | ~ member(X15,X11)
      | apply_to_two_arguments(X4,X15,f37(X11,X4,X15)) != f37(X11,X4,X15)
      | apply_to_two_arguments(X4,f37(X11,X4,X15),X15) != f37(X11,X4,X15) ),
    file('<stdin>',identity5) ).

fof(c_0_16_017,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | member(ordered_pair(ordered_pair(f51(X1,X11),f52(X1,X11)),f53(X1,X11)),X11)
      | member(X1,X11) ),
    file('<stdin>',times9) ).

fof(c_0_17_018,axiom,
    ! [X1,X7,X8,X9] :
      ( member(X1,times)
      | ~ little_set(X1)
      | ~ member(X9,natural_numbers)
      | ~ member(X8,natural_numbers)
      | ~ member(X7,natural_numbers)
      | ~ member(ordered_pair(ordered_pair(X9,X8),X7),f54(X1))
      | member(ordered_pair(ordered_pair(successor(X9),X8),apply_to_two_arguments(plus,X7,X8)),f54(X1)) ),
    file('<stdin>',times13) ).

fof(c_0_18_019,axiom,
    ! [X11,X14,X4,X15] :
      ( group(X11,X4)
      | ~ closed(X11,X4)
      | ~ associative(X11,X4)
      | ~ identity(X11,X4,X15)
      | ~ inverse(X11,X4,X15,X14) ),
    file('<stdin>',group5) ).

fof(c_0_19_020,axiom,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | member(ordered_pair(f29(X1,X4,X14),f31(X1,X4,X14)),X4) ),
    file('<stdin>',compose5) ).

fof(c_0_20_021,axiom,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | member(ordered_pair(f31(X1,X4,X14),f30(X1,X4,X14)),X14) ),
    file('<stdin>',compose6) ).

fof(c_0_21_022,axiom,
    ! [X11,X14,X4,X15,X2] :
      ( ~ inverse(X11,X4,X15,X14)
      | ~ member(X2,X11)
      | apply_to_two_arguments(X4,apply(X14,X2),X2) = X15 ),
    file('<stdin>',inverse2) ).

fof(c_0_22_023,axiom,
    ! [X11,X14,X4,X15,X2] :
      ( ~ inverse(X11,X4,X15,X14)
      | ~ member(X2,X11)
      | apply_to_two_arguments(X4,X2,apply(X14,X2)) = X15 ),
    file('<stdin>',inverse3) ).

fof(c_0_23_024,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | member(f46(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',plus6) ).

fof(c_0_24_025,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | member(f47(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',plus7) ).

fof(c_0_25_026,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | member(f48(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',plus8) ).

fof(c_0_26_027,axiom,
    ! [X11,X14,X4,X15] :
      ( ~ inverse(X11,X4,X15,X14)
      | maps(X14,X11,X11) ),
    file('<stdin>',inverse1) ).

fof(c_0_27_028,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | member(ordered_pair(ordered_pair(f46(X1,X11),f47(X1,X11)),f48(X1,X11)),X11)
      | member(X1,X11) ),
    file('<stdin>',plus4) ).

fof(c_0_28_029,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | member(ordered_pair(ordered_pair(f51(X1,X11),f52(X1,X11)),f53(X1,X11)),X11)
      | member(X1,X11) ),
    file('<stdin>',times4) ).

fof(c_0_29_030,axiom,
    ! [X1,X13,X11,X4,X2] :
      ( ~ associative(X11,X4)
      | ~ member(X2,X11)
      | ~ member(X13,X11)
      | ~ member(X1,X11)
      | apply_to_two_arguments(X4,apply_to_two_arguments(X4,X2,X13),X1) = apply_to_two_arguments(X4,X2,apply_to_two_arguments(X4,X13,X1)) ),
    file('<stdin>',associative_system1) ).

fof(c_0_30_031,axiom,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2) ),
    file('<stdin>',rotate_right5) ).

fof(c_0_31_032,axiom,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2) ),
    file('<stdin>',flip_range5) ).

fof(c_0_32_033,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | member(f51(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',times6) ).

fof(c_0_33_034,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | member(f52(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',times7) ).

fof(c_0_34_035,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | member(f53(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',times8) ).

fof(c_0_35_036,axiom,
    ! [X1,X7,X8,X12] :
      ( member(X1,plus)
      | ~ little_set(X1)
      | ~ member(X12,natural_numbers)
      | ~ member(X8,natural_numbers)
      | ~ member(X7,natural_numbers)
      | ~ member(ordered_pair(ordered_pair(X12,X8),X7),f49(X1))
      | member(ordered_pair(ordered_pair(successor(X12),X8),successor(X7)),f49(X1)) ),
    file('<stdin>',plus13) ).

fof(c_0_36_037,axiom,
    ! [X11,X4] :
      ( commutes(X11,X4)
      | apply_to_two_arguments(X4,f41(X11,X4),f42(X11,X4)) != apply_to_two_arguments(X4,f42(X11,X4),f41(X11,X4)) ),
    file('<stdin>',commutes4) ).

fof(c_0_37_038,axiom,
    ! [X11,X4] :
      ( ~ group(X11,X4)
      | inverse(X11,X4,f39(X11,X4),f40(X11,X4)) ),
    file('<stdin>',group4) ).

fof(c_0_38_039,axiom,
    ! [X1,X4,X2] :
      ( ~ member(X1,image(X2,X4))
      | member(first(f22(X1,X2,X4)),X2) ),
    file('<stdin>',image_and_substitution3) ).

fof(c_0_39_040,axiom,
    ! [X1,X13,X4] :
      ( ~ member(X1,apply(X4,X13))
      | member(X1,second(f28(X1,X4,X13))) ),
    file('<stdin>',apply4) ).

fof(c_0_40_041,axiom,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | X1 = ordered_pair(f29(X1,X4,X14),f30(X1,X4,X14)) ),
    file('<stdin>',compose4) ).

fof(c_0_41_042,axiom,
    ! [X1,X2,X21,X5,X6] :
      ( member(X1,rotate_right(X2))
      | ~ little_set(X1)
      | ~ little_set(X6)
      | ~ little_set(X5)
      | ~ little_set(X21)
      | X1 != ordered_pair(X6,ordered_pair(X5,X21))
      | ~ member(ordered_pair(X5,ordered_pair(X21,X6)),X2) ),
    file('<stdin>',rotate_right6) ).

fof(c_0_42_043,axiom,
    ! [X1,X2,X21,X5,X6] :
      ( member(X1,flip_range_of(X2))
      | ~ little_set(X1)
      | ~ little_set(X6)
      | ~ little_set(X5)
      | ~ little_set(X21)
      | X1 != ordered_pair(X6,ordered_pair(X5,X21))
      | ~ member(ordered_pair(X6,ordered_pair(X21,X5)),X2) ),
    file('<stdin>',flip_range6) ).

fof(c_0_43_044,axiom,
    ! [X1,X13,X14,X4,X2,X21] :
      ( member(X1,compose(X4,X14))
      | ~ little_set(X1)
      | ~ little_set(X2)
      | ~ little_set(X13)
      | ~ little_set(X21)
      | X1 != ordered_pair(X2,X13)
      | ~ member(ordered_pair(X2,X21),X4)
      | ~ member(ordered_pair(X21,X13),X14) ),
    file('<stdin>',compose7) ).

fof(c_0_44_045,axiom,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | X1 = ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2))) ),
    file('<stdin>',rotate_right4) ).

fof(c_0_45_046,axiom,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | X1 = ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2))) ),
    file('<stdin>',flip_range4) ).

fof(c_0_46_047,axiom,
    ! [X11,X4,X15] :
      ( identity(X11,X4,X15)
      | ~ member(X15,X11)
      | member(f37(X11,X4,X15),X11) ),
    file('<stdin>',identity4) ).

fof(c_0_47_048,axiom,
    ! [X1,X5,X6] :
      ( ~ member(X1,prime_numbers)
      | ~ member(X6,natural_numbers)
      | ~ member(X5,natural_numbers)
      | apply_to_two_arguments(times,X6,X5) != X1
      | member(X6,non_ordered_pair(successor(empty_set),X1)) ),
    file('<stdin>',prime_numbers4) ).

fof(c_0_48_049,axiom,
    ! [X1,X4,X2] :
      ( ~ member(X1,image(X2,X4))
      | member(f22(X1,X2,X4),X4) ),
    file('<stdin>',image_and_substitution2) ).

fof(c_0_49_050,axiom,
    ! [X1,X13,X4] :
      ( ~ member(X1,apply(X4,X13))
      | member(f28(X1,X4,X13),X4) ),
    file('<stdin>',apply2) ).

fof(c_0_50_051,axiom,
    ! [X13,X11,X4,X2] :
      ( ~ commutes(X11,X4)
      | ~ member(X2,X11)
      | ~ member(X13,X11)
      | apply_to_two_arguments(X4,X2,X13) = apply_to_two_arguments(X4,X13,X2) ),
    file('<stdin>',commutes1) ).

fof(c_0_51_052,axiom,
    ! [X1,X11] :
      ( ~ member(X1,natural_numbers)
      | ~ little_set(X11)
      | ~ member(empty_set,X11)
      | ~ member(successor(f43(X1,X11)),X11)
      | member(X1,X11) ),
    file('<stdin>',natural_numbers2) ).

fof(c_0_52_053,axiom,
    ! [X1,X4,X2] :
      ( ~ member(X1,image(X2,X4))
      | second(f22(X1,X2,X4)) = X1 ),
    file('<stdin>',image_and_substitution4) ).

fof(c_0_53_054,axiom,
    ! [X1,X13,X4] :
      ( ~ member(X1,apply(X4,X13))
      | first(f28(X1,X4,X13)) = X13 ),
    file('<stdin>',apply3) ).

fof(c_0_54_055,axiom,
    ! [X1,X4,X2] :
      ( ~ member(X1,image(X2,X4))
      | ordered_pair_predicate(f22(X1,X2,X4)) ),
    file('<stdin>',image_and_substitution1) ).

fof(c_0_55,axiom,
    ! [X1,X13,X4] :
      ( ~ member(X1,apply(X4,X13))
      | ordered_pair_predicate(f28(X1,X4,X13)) ),
    file('<stdin>',apply1) ).

fof(c_0_56,axiom,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | little_set(f29(X1,X4,X14)) ),
    file('<stdin>',compose1) ).

fof(c_0_57,axiom,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | little_set(f30(X1,X4,X14)) ),
    file('<stdin>',compose2) ).

fof(c_0_58,axiom,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | little_set(f31(X1,X4,X14)) ),
    file('<stdin>',compose3) ).

fof(c_0_59,axiom,
    ! [X11,X4,X15,X2] :
      ( ~ identity(X11,X4,X15)
      | ~ member(X2,X11)
      | apply_to_two_arguments(X4,X15,X2) = X2 ),
    file('<stdin>',identity2) ).

fof(c_0_60,axiom,
    ! [X11,X4,X15,X2] :
      ( ~ identity(X11,X4,X15)
      | ~ member(X2,X11)
      | apply_to_two_arguments(X4,X2,X15) = X2 ),
    file('<stdin>',identity3) ).

fof(c_0_61,axiom,
    ! [X2,X21,X5,X6] :
      ( ~ single_valued_set(X2)
      | ~ little_set(X6)
      | ~ little_set(X5)
      | ~ little_set(X21)
      | ~ member(ordered_pair(X6,X5),X2)
      | ~ member(ordered_pair(X6,X21),X2)
      | X5 = X21 ),
    file('<stdin>',single_valued_set1) ).

fof(c_0_62,axiom,
    ! [X11,X4] :
      ( closed(X11,X4)
      | ~ little_set(X11)
      | ~ little_set(X4)
      | ~ maps(X4,cross_product(X11,X11),X11) ),
    file('<stdin>',closed4) ).

fof(c_0_63,axiom,
    ! [X1,X2] :
      ( member(X1,even_numbers)
      | ~ member(X1,natural_numbers)
      | ~ member(X2,natural_numbers)
      | apply_to_two_arguments(plus,X2,X2) != X1 ),
    file('<stdin>',even_numbers4) ).

fof(c_0_64,axiom,
    ! [X1,X2] :
      ( member(X1,converse(X2))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X1)
      | ~ member(ordered_pair(second(X1),first(X1)),X2) ),
    file('<stdin>',converse3) ).

fof(c_0_65,axiom,
    ! [X1,X10] :
      ( member(X1,plus)
      | ~ little_set(X1)
      | ~ member(X10,natural_numbers)
      | member(ordered_pair(ordered_pair(empty_set,X10),X10),f49(X1)) ),
    file('<stdin>',plus12) ).

fof(c_0_66,axiom,
    ! [X1,X10] :
      ( member(X1,times)
      | ~ little_set(X1)
      | ~ member(X10,natural_numbers)
      | member(ordered_pair(ordered_pair(empty_set,X10),empty_set),f54(X1)) ),
    file('<stdin>',times12) ).

fof(c_0_67,axiom,
    ! [X13,X2] :
      ( ~ member(f1(X2,X13),X2)
      | ~ member(f1(X2,X13),X13)
      | X2 = X13 ),
    file('<stdin>',extensionality3) ).

fof(c_0_68,axiom,
    ! [X3,X4,X2] :
      ( finite(X2)
      | ~ member(X3,natural_numbers)
      | ~ maps(X4,X3,X2)
      | range_of(X4) != X2
      | ~ one_to_one_function(X4) ),
    file('<stdin>',finite5) ).

fof(c_0_69,axiom,
    ! [X1] :
      ( member(X1,prime_numbers)
      | ~ member(X1,natural_numbers)
      | X1 = empty_set
      | X1 = successor(empty_set)
      | ~ member(f55(X1),non_ordered_pair(successor(empty_set),X1)) ),
    file('<stdin>',prime_numbers8) ).

fof(c_0_70,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | member(f46(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',plus1) ).

fof(c_0_71,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | member(f47(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',plus2) ).

fof(c_0_72,axiom,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | member(f48(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',plus3) ).

fof(c_0_73,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | member(f51(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',times1) ).

fof(c_0_74,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | member(f52(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',times2) ).

fof(c_0_75,axiom,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | member(f53(X1,X11),natural_numbers)
      | member(X1,X11) ),
    file('<stdin>',times3) ).

fof(c_0_76,axiom,
    ! [X1,X13,X2] :
      ( member(X1,cross_product(X2,X13))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X1)
      | ~ member(first(X1),X2)
      | ~ member(second(X1),X13) ),
    file('<stdin>',cross_product4) ).

fof(c_0_77,axiom,
    ! [X1,X13,X4,X2] :
      ( member(X1,image(X2,X4))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X13)
      | ~ member(X13,X4)
      | ~ member(first(X13),X2)
      | second(X13) != X1 ),
    file('<stdin>',image_and_substitution5) ).

fof(c_0_78,axiom,
    ! [X1,X13,X4,X21] :
      ( member(X1,apply(X4,X13))
      | ~ ordered_pair_predicate(X21)
      | ~ member(X21,X4)
      | first(X21) != X13
      | ~ member(X1,second(X21)) ),
    file('<stdin>',apply5) ).

fof(c_0_79,axiom,
    ! [X13,X4,X2] :
      ( ~ maps(X4,X2,X13)
      | subset(range_of(X4),X13) ),
    file('<stdin>',maps3) ).

fof(c_0_80,axiom,
    ! [X1] :
      ( member(X1,prime_numbers)
      | ~ member(X1,natural_numbers)
      | X1 = empty_set
      | X1 = successor(empty_set)
      | apply_to_two_arguments(times,f55(X1),f56(X1)) = X1 ),
    file('<stdin>',prime_numbers7) ).

fof(c_0_81,axiom,
    ! [X11,X4] :
      ( ~ closed(X11,X4)
      | maps(X4,cross_product(X11,X11),X11) ),
    file('<stdin>',closed3) ).

fof(c_0_82,axiom,
    ! [X11,X4] :
      ( ~ group(X11,X4)
      | identity(X11,X4,f39(X11,X4)) ),
    file('<stdin>',group3) ).

fof(c_0_83,axiom,
    ! [X13,X4,X2] :
      ( maps(X4,X2,X13)
      | ~ function(X4)
      | domain_of(X4) != X2
      | ~ subset(range_of(X4),X13) ),
    file('<stdin>',maps4) ).

fof(c_0_84,axiom,
    ! [X1,X11] :
      ( ~ member(X1,natural_numbers)
      | ~ little_set(X11)
      | ~ member(empty_set,X11)
      | member(f43(X1,X11),X11)
      | member(X1,X11) ),
    file('<stdin>',natural_numbers1) ).

fof(c_0_85,axiom,
    ! [X11,X4,X15] :
      ( ~ identity(X11,X4,X15)
      | member(X15,X11) ),
    file('<stdin>',identity1) ).

fof(c_0_86,axiom,
    ! [X1,X2] :
      ( ~ member(X1,first(X2))
      | X2 = ordered_pair(f4(X1,X2),f5(X1,X2)) ),
    file('<stdin>',first3) ).

fof(c_0_87,axiom,
    ! [X1,X2] :
      ( ~ member(X1,second(X2))
      | X2 = ordered_pair(f6(X1,X2),f7(X1,X2)) ),
    file('<stdin>',second3) ).

fof(c_0_88,axiom,
    ! [X1,X2] :
      ( ~ member(X1,converse(X2))
      | member(ordered_pair(second(X1),first(X1)),X2) ),
    file('<stdin>',converse2) ).

fof(c_0_89,axiom,
    ! [X13,X4,X2] :
      ( ~ maps(X4,X2,X13)
      | domain_of(X4) = X2 ),
    file('<stdin>',maps2) ).

fof(c_0_90,axiom,
    ! [X13,X4,X2] :
      ( ~ maps(X4,X2,X13)
      | function(X4) ),
    file('<stdin>',maps1) ).

fof(c_0_91,axiom,
    ! [X1] :
      ( ~ member(X1,even_numbers)
      | apply_to_two_arguments(plus,f59(X1),f59(X1)) = X1 ),
    file('<stdin>',even_numbers3) ).

fof(c_0_92,axiom,
    ! [X1,X13,X2] :
      ( member(X1,intersection(X2,X13))
      | ~ member(X1,X2)
      | ~ member(X1,X13) ),
    file('<stdin>',intersection3) ).

fof(c_0_93,axiom,
    ! [X1,X13,X2] :
      ( ~ member(X1,cross_product(X2,X13))
      | member(first(X1),X2) ),
    file('<stdin>',cross_product2) ).

fof(c_0_94,axiom,
    ! [X1,X13,X2] :
      ( ~ member(X1,cross_product(X2,X13))
      | member(second(X1),X13) ),
    file('<stdin>',cross_product3) ).

fof(c_0_95,axiom,
    ! [X13,X2] :
      ( member(f1(X2,X13),X2)
      | member(f1(X2,X13),X13)
      | X2 = X13 ),
    file('<stdin>',extensionality2) ).

fof(c_0_96,axiom,
    ! [X1] :
      ( member(X1,twin_prime_numbers)
      | ~ member(X1,prime_numbers)
      | ~ member(successor(successor(X1)),prime_numbers) ),
    file('<stdin>',twin_primes3) ).

fof(c_0_97,axiom,
    ! [X1,X2,X5,X6] :
      ( member(X1,first(X2))
      | ~ little_set(X6)
      | ~ little_set(X5)
      | X2 != ordered_pair(X6,X5)
      | ~ member(X1,X6) ),
    file('<stdin>',first5) ).

fof(c_0_98,axiom,
    ! [X1,X2,X5,X6] :
      ( member(X1,second(X2))
      | ~ little_set(X6)
      | ~ little_set(X5)
      | X2 != ordered_pair(X6,X5)
      | ~ member(X1,X5) ),
    file('<stdin>',second5) ).

fof(c_0_99,axiom,
    ! [X1,X7] :
      ( member(X1,natural_numbers)
      | ~ little_set(X1)
      | ~ member(X7,f44(X1))
      | member(successor(X7),f44(X1)) ),
    file('<stdin>',natural_numbers5) ).

fof(c_0_100,axiom,
    ! [X1,X13,X2] :
      ( ~ member(X1,intersection(X2,X13))
      | member(X1,X2) ),
    file('<stdin>',intersection1) ).

fof(c_0_101,axiom,
    ! [X1,X13,X2] :
      ( ~ member(X1,intersection(X2,X13))
      | member(X1,X13) ),
    file('<stdin>',intersection2) ).

fof(c_0_102,axiom,
    ! [X13,X2] :
      ( subset(X2,X13)
      | ~ member(f17(X2,X13),X13) ),
    file('<stdin>',subset3) ).

fof(c_0_103,axiom,
    ! [X2] :
      ( ~ finite(X2)
      | maps(f58(X2),f57(X2),X2) ),
    file('<stdin>',finite2) ).

fof(c_0_104,axiom,
    ! [X1,X2] :
      ( ~ member(X1,first(X2))
      | member(X1,f4(X1,X2)) ),
    file('<stdin>',first4) ).

fof(c_0_105,axiom,
    ! [X1,X2] :
      ( ~ member(X1,second(X2))
      | member(X1,f7(X1,X2)) ),
    file('<stdin>',second4) ).

fof(c_0_106,axiom,
    ! [X1,X2] :
      ( ~ member(X1,domain_of(X2))
      | member(f8(X1,X2),X2) ),
    file('<stdin>',domain2) ).

fof(c_0_107,axiom,
    ! [X1,X2] :
      ( ~ member(X1,sigma(X2))
      | member(f16(X1,X2),X2) ),
    file('<stdin>',sigma1) ).

fof(c_0_108,axiom,
    ! [X1,X2] :
      ( ~ member(X1,sigma(X2))
      | member(X1,f16(X1,X2)) ),
    file('<stdin>',sigma2) ).

fof(c_0_109,axiom,
    ! [X1,X2] :
      ( ~ member(X1,range_of(X2))
      | member(f27(X1,X2),X2) ),
    file('<stdin>',range_of2) ).

fof(c_0_110,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | member(ordered_pair(f19(X2),f20(X2)),X2) ),
    file('<stdin>',single_valued_set5) ).

fof(c_0_111,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | member(ordered_pair(f19(X2),f21(X2)),X2) ),
    file('<stdin>',single_valued_set6) ).

fof(c_0_112,axiom,
    ! [X1] :
      ( member(X1,estin)
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X1)
      | ~ member(first(X1),second(X1)) ),
    file('<stdin>',element_relation3) ).

fof(c_0_113,axiom,
    ! [X13,X2,X6] :
      ( ~ disjoint(X2,X13)
      | ~ member(X6,X2)
      | ~ member(X6,X13) ),
    file('<stdin>',disjoint1) ).

fof(c_0_114,axiom,
    ! [X13,X2,X6] :
      ( ~ member(X6,non_ordered_pair(X2,X13))
      | X6 = X2
      | X6 = X13 ),
    file('<stdin>',non_ordered_pair1) ).

fof(c_0_115,axiom,
    ! [X1,X13,X2] :
      ( ~ member(X1,cross_product(X2,X13))
      | ordered_pair_predicate(X1) ),
    file('<stdin>',cross_product1) ).

fof(c_0_116,axiom,
    ! [X1,X22,X2] :
      ( member(X1,domain_of(X2))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X22)
      | ~ member(X22,X2)
      | X1 != first(X22) ),
    file('<stdin>',domain4) ).

fof(c_0_117,axiom,
    ! [X1,X13,X2] :
      ( member(X1,sigma(X2))
      | ~ member(X13,X2)
      | ~ member(X1,X13) ),
    file('<stdin>',sigma3) ).

fof(c_0_118,axiom,
    ! [X1,X22,X2] :
      ( member(X1,range_of(X2))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X22)
      | ~ member(X22,X2)
      | X1 != second(X22) ),
    file('<stdin>',range_of4) ).

fof(c_0_119,axiom,
    ! [X1,X2] :
      ( ~ member(X1,domain_of(X2))
      | X1 = first(f8(X1,X2)) ),
    file('<stdin>',domain3) ).

fof(c_0_120,axiom,
    ! [X1,X2] :
      ( ~ member(X1,range_of(X2))
      | X1 = second(f27(X1,X2)) ),
    file('<stdin>',range_of3) ).

fof(c_0_121,axiom,
    ! [X1,X2] :
      ( ~ member(X1,first(X2))
      | little_set(f4(X1,X2)) ),
    file('<stdin>',first1) ).

fof(c_0_122,axiom,
    ! [X1,X2] :
      ( ~ member(X1,first(X2))
      | little_set(f5(X1,X2)) ),
    file('<stdin>',first2) ).

fof(c_0_123,axiom,
    ! [X1,X2] :
      ( ~ member(X1,second(X2))
      | little_set(f6(X1,X2)) ),
    file('<stdin>',second1) ).

fof(c_0_124,axiom,
    ! [X1,X2] :
      ( ~ member(X1,second(X2))
      | little_set(f7(X1,X2)) ),
    file('<stdin>',second2) ).

fof(c_0_125,axiom,
    ! [X1,X2] :
      ( ~ member(X1,domain_of(X2))
      | ordered_pair_predicate(f8(X1,X2)) ),
    file('<stdin>',domain1) ).

fof(c_0_126,axiom,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | little_set(f9(X1,X2)) ),
    file('<stdin>',rotate_right1) ).

fof(c_0_127,axiom,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | little_set(f10(X1,X2)) ),
    file('<stdin>',rotate_right2) ).

fof(c_0_128,axiom,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | little_set(f11(X1,X2)) ),
    file('<stdin>',rotate_right3) ).

fof(c_0_129,axiom,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | little_set(f12(X1,X2)) ),
    file('<stdin>',flip_range1) ).

fof(c_0_130,axiom,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | little_set(f13(X1,X2)) ),
    file('<stdin>',flip_range2) ).

fof(c_0_131,axiom,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | little_set(f14(X1,X2)) ),
    file('<stdin>',flip_range3) ).

fof(c_0_132,axiom,
    ! [X1,X2] :
      ( ~ member(X1,range_of(X2))
      | ordered_pair_predicate(f27(X1,X2)) ),
    file('<stdin>',range_of1) ).

fof(c_0_133,axiom,
    ! [X13,X2,X6] :
      ( ~ subset(X2,X13)
      | ~ member(X6,X2)
      | member(X6,X13) ),
    file('<stdin>',subset1) ).

fof(c_0_134,axiom,
    ! [X2] :
      ( ~ little_set(X2)
      | X2 = empty_set
      | member(ordered_pair(X2,f26(X2)),f25) ),
    file('<stdin>',choice3) ).

fof(c_0_135,axiom,
    ! [X1] :
      ( member(X1,prime_numbers)
      | ~ member(X1,natural_numbers)
      | X1 = empty_set
      | X1 = successor(empty_set)
      | member(f55(X1),natural_numbers) ),
    file('<stdin>',prime_numbers5) ).

fof(c_0_136,axiom,
    ! [X1] :
      ( member(X1,prime_numbers)
      | ~ member(X1,natural_numbers)
      | X1 = empty_set
      | X1 = successor(empty_set)
      | member(f56(X1),natural_numbers) ),
    file('<stdin>',prime_numbers6) ).

fof(c_0_137,axiom,
    ! [X1,X2] :
      ( ~ member(X1,complement(X2))
      | ~ member(X1,X2) ),
    file('<stdin>',complement1) ).

fof(c_0_138,axiom,
    ! [X13,X2] :
      ( subset(X2,X13)
      | member(f17(X2,X13),X2) ),
    file('<stdin>',subset2) ).

fof(c_0_139,axiom,
    ! [X13,X2] :
      ( disjoint(X2,X13)
      | member(f23(X2,X13),X2) ),
    file('<stdin>',disjoint2) ).

fof(c_0_140,axiom,
    ! [X13,X2] :
      ( disjoint(X2,X13)
      | member(f23(X2,X13),X13) ),
    file('<stdin>',disjoint3) ).

fof(c_0_141,axiom,
    ! [X11,X4] :
      ( associative(X11,X4)
      | member(f34(X11,X4),X11) ),
    file('<stdin>',associative_system2) ).

fof(c_0_142,axiom,
    ! [X11,X4] :
      ( associative(X11,X4)
      | member(f35(X11,X4),X11) ),
    file('<stdin>',associative_system3) ).

fof(c_0_143,axiom,
    ! [X11,X4] :
      ( associative(X11,X4)
      | member(f36(X11,X4),X11) ),
    file('<stdin>',associative_system4) ).

fof(c_0_144,axiom,
    ! [X11,X4] :
      ( commutes(X11,X4)
      | member(f41(X11,X4),X11) ),
    file('<stdin>',commutes2) ).

fof(c_0_145,axiom,
    ! [X11,X4] :
      ( commutes(X11,X4)
      | member(f42(X11,X4),X11) ),
    file('<stdin>',commutes3) ).

fof(c_0_146,axiom,
    ! [X1] :
      ( ~ member(X1,twin_prime_numbers)
      | member(successor(successor(X1)),prime_numbers) ),
    file('<stdin>',twin_primes2) ).

fof(c_0_147,axiom,
    ! [X13,X2,X6] :
      ( member(X6,non_ordered_pair(X2,X13))
      | ~ little_set(X6)
      | X6 != X2 ),
    file('<stdin>',non_ordered_pair2) ).

fof(c_0_148,axiom,
    ! [X13,X2,X6] :
      ( member(X6,non_ordered_pair(X2,X13))
      | ~ little_set(X6)
      | X6 != X13 ),
    file('<stdin>',non_ordered_pair3) ).

fof(c_0_149,axiom,
    ! [X1,X2] :
      ( member(X1,powerset(X2))
      | ~ little_set(X1)
      | ~ subset(X1,X2) ),
    file('<stdin>',powerset2) ).

fof(c_0_150,axiom,
    ! [X1] :
      ( ~ member(X1,estin)
      | member(first(X1),second(X1)) ),
    file('<stdin>',element_relation2) ).

fof(c_0_151,axiom,
    ! [X1,X2] :
      ( ~ member(X1,powerset(X2))
      | subset(X1,X2) ),
    file('<stdin>',powerset1) ).

fof(c_0_152,axiom,
    ! [X1] :
      ( member(X1,natural_numbers)
      | ~ member(X1,f44(X1)) ),
    file('<stdin>',natural_numbers6) ).

fof(c_0_153,axiom,
    ! [X1] :
      ( member(X1,plus)
      | ~ member(X1,f49(X1)) ),
    file('<stdin>',plus14) ).

fof(c_0_154,axiom,
    ! [X1] :
      ( member(X1,times)
      | ~ member(X1,f54(X1)) ),
    file('<stdin>',times14) ).

fof(c_0_155,axiom,
    ! [X4,X2] :
      ( ~ little_set(X2)
      | ~ function(X4)
      | little_set(image(X2,X4)) ),
    file('<stdin>',image_and_substitution6) ).

fof(c_0_156,axiom,
    ! [X1,X13,X2] :
      ( ordered_pair_predicate(X2)
      | ~ little_set(X13)
      | ~ little_set(X1)
      | X2 != ordered_pair(X13,X1) ),
    file('<stdin>',ordered_pair_predicate4) ).

fof(c_0_157,axiom,
    ! [X1,X2] :
      ( member(X1,complement(X2))
      | ~ little_set(X1)
      | member(X1,X2) ),
    file('<stdin>',complement2) ).

fof(c_0_158,axiom,
    ! [X1] :
      ( member(X1,identity_relation)
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X1)
      | first(X1) != second(X1) ),
    file('<stdin>',identity_relation3) ).

fof(c_0_159,axiom,
    ! [X13,X2] :
      ( proper_subset(X2,X13)
      | ~ subset(X2,X13)
      | X2 = X13 ),
    file('<stdin>',proper_subset3) ).

fof(c_0_160,axiom,
    ! [X2] :
      ( ~ member(X2,infinity)
      | member(successor(X2),infinity) ),
    file('<stdin>',infinity3) ).

fof(c_0_161,axiom,
    ! [X1] :
      ( ~ member(X1,even_numbers)
      | member(f59(X1),natural_numbers) ),
    file('<stdin>',even_numbers2) ).

fof(c_0_162,axiom,
    ! [X1] :
      ( member(X1,natural_numbers)
      | ~ little_set(X1)
      | member(empty_set,f44(X1)) ),
    file('<stdin>',natural_numbers4) ).

fof(c_0_163,axiom,
    ! [X13,X2] :
      ( ~ proper_subset(X2,X13)
      | subset(X2,X13) ),
    file('<stdin>',proper_subset1) ).

fof(c_0_164,axiom,
    ! [X11,X4] :
      ( ~ group(X11,X4)
      | closed(X11,X4) ),
    file('<stdin>',group1) ).

fof(c_0_165,axiom,
    ! [X11,X4] :
      ( ~ group(X11,X4)
      | associative(X11,X4) ),
    file('<stdin>',group2) ).

fof(c_0_166,axiom,
    ! [X1,X2] :
      ( ~ member(X1,converse(X2))
      | ordered_pair_predicate(X1) ),
    file('<stdin>',converse1) ).

fof(c_0_167,axiom,
    ! [X2] :
      ( ~ ordered_pair_predicate(X2)
      | X2 = ordered_pair(f2(X2),f3(X2)) ),
    file('<stdin>',ordered_pair_predicate3) ).

fof(c_0_168,axiom,
    ! [X1,X2] :
      ( ~ relation(X1)
      | ~ member(X2,X1)
      | ordered_pair_predicate(X2) ),
    file('<stdin>',relation1) ).

fof(c_0_169,axiom,
    ! [X1] :
      ( ~ member(X1,prime_numbers)
      | member(X1,natural_numbers) ),
    file('<stdin>',prime_numbers1) ).

fof(c_0_170,axiom,
    ! [X1] :
      ( ~ member(X1,twin_prime_numbers)
      | member(X1,prime_numbers) ),
    file('<stdin>',twin_primes1) ).

fof(c_0_171,axiom,
    ! [X1] :
      ( ~ member(X1,even_numbers)
      | member(X1,natural_numbers) ),
    file('<stdin>',even_numbers1) ).

fof(c_0_172,axiom,
    ! [X13,X2] :
      ( little_set(f1(X2,X13))
      | X2 = X13 ),
    file('<stdin>',extensionality1) ).

fof(c_0_173,axiom,
    ! [X1] :
      ( member(X1,natural_numbers)
      | ~ little_set(X1)
      | little_set(f44(X1)) ),
    file('<stdin>',natural_numbers3) ).

fof(c_0_174,axiom,
    ! [X1] :
      ( member(X1,plus)
      | ~ little_set(X1)
      | little_set(f49(X1)) ),
    file('<stdin>',plus11) ).

fof(c_0_175,axiom,
    ! [X1] :
      ( member(X1,times)
      | ~ little_set(X1)
      | little_set(f54(X1)) ),
    file('<stdin>',times11) ).

fof(c_0_176,axiom,
    ! [X2] :
      ( ~ little_set(X2)
      | X2 = empty_set
      | member(f26(X2),X2) ),
    file('<stdin>',choice2) ).

fof(c_0_177,axiom,
    ! [X1] :
      ( ~ member(X1,identity_relation)
      | first(X1) = second(X1) ),
    file('<stdin>',identity_relation2) ).

fof(c_0_178,axiom,
    ! [X4] :
      ( one_to_one_function(X4)
      | ~ function(X4)
      | ~ function(converse(X4)) ),
    file('<stdin>',one_to_one_function3) ).

fof(c_0_179,axiom,
    ! [X13,X2] :
      ( ~ member(X2,X13)
      | little_set(X2) ),
    file('<stdin>',a2) ).

fof(c_0_180,axiom,
    ! [X11,X4] :
      ( ~ closed(X11,X4)
      | little_set(X11) ),
    file('<stdin>',closed1) ).

fof(c_0_181,axiom,
    ! [X11,X4] :
      ( ~ closed(X11,X4)
      | little_set(X4) ),
    file('<stdin>',closed2) ).

fof(c_0_182,axiom,
    ! [X13,X2] :
      ( ~ proper_subset(X2,X13)
      | X2 != X13 ),
    file('<stdin>',proper_subset2) ).

fof(c_0_183,axiom,
    ! [X1] :
      ( ~ member(X1,prime_numbers)
      | X1 != successor(empty_set) ),
    file('<stdin>',prime_numbers3) ).

fof(c_0_184,axiom,
    ! [X2] :
      ( ~ finite(X2)
      | member(f57(X2),natural_numbers) ),
    file('<stdin>',finite1) ).

fof(c_0_185,axiom,
    ! [X1] :
      ( relation(X1)
      | member(f18(X1),X1) ),
    file('<stdin>',relation2) ).

fof(c_0_186,axiom,
    ! [X1] :
      ( ~ member(X1,estin)
      | ordered_pair_predicate(X1) ),
    file('<stdin>',element_relation1) ).

fof(c_0_187,axiom,
    ! [X1] :
      ( ~ member(X1,identity_relation)
      | ordered_pair_predicate(X1) ),
    file('<stdin>',identity_relation1) ).

fof(c_0_188,axiom,
    ! [X1] :
      ( ~ member(X1,prime_numbers)
      | X1 != empty_set ),
    file('<stdin>',prime_numbers2) ).

fof(c_0_189,axiom,
    ! [X2] :
      ( X2 = empty_set
      | member(f24(X2),X2) ),
    file('<stdin>',regularity1) ).

fof(c_0_190,axiom,
    ! [X2] :
      ( X2 = empty_set
      | disjoint(f24(X2),X2) ),
    file('<stdin>',regularity2) ).

fof(c_0_191,axiom,
    ! [X1] :
      ( relation(X1)
      | ~ ordered_pair_predicate(f18(X1)) ),
    file('<stdin>',relation3) ).

fof(c_0_192,axiom,
    ! [X1] :
      ( member(X1,universal_set)
      | ~ little_set(X1) ),
    file('<stdin>',universal_set) ).

fof(c_0_193,axiom,
    ! [X4] :
      ( function(X4)
      | ~ relation(X4)
      | ~ single_valued_set(X4) ),
    file('<stdin>',function3) ).

fof(c_0_194,axiom,
    ! [X2] :
      ( ~ finite(X2)
      | range_of(f58(X2)) = X2 ),
    file('<stdin>',finite3) ).

fof(c_0_195,axiom,
    ! [X2] :
      ( ~ ordered_pair_predicate(X2)
      | little_set(f2(X2)) ),
    file('<stdin>',ordered_pair_predicate1) ).

fof(c_0_196,axiom,
    ! [X2] :
      ( ~ ordered_pair_predicate(X2)
      | little_set(f3(X2)) ),
    file('<stdin>',ordered_pair_predicate2) ).

fof(c_0_197,axiom,
    ! [X6] :
      ( ~ little_set(X6)
      | little_set(sigma(X6)) ),
    file('<stdin>',sigma4) ).

fof(c_0_198,axiom,
    ! [X6] :
      ( ~ little_set(X6)
      | little_set(powerset(X6)) ),
    file('<stdin>',powerset3) ).

fof(c_0_199,axiom,
    ! [X4] :
      ( ~ one_to_one_function(X4)
      | function(converse(X4)) ),
    file('<stdin>',one_to_one_function2) ).

fof(c_0_200,axiom,
    ! [X2] :
      ( ~ finite(X2)
      | one_to_one_function(f58(X2)) ),
    file('<stdin>',finite4) ).

fof(c_0_201,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | f20(X2) != f21(X2) ),
    file('<stdin>',single_valued_set7) ).

fof(c_0_202,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | little_set(f19(X2)) ),
    file('<stdin>',single_valued_set2) ).

fof(c_0_203,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | little_set(f20(X2)) ),
    file('<stdin>',single_valued_set3) ).

fof(c_0_204,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | little_set(f21(X2)) ),
    file('<stdin>',single_valued_set4) ).

fof(c_0_205,axiom,
    ! [X4] :
      ( ~ function(X4)
      | relation(X4) ),
    file('<stdin>',function1) ).

fof(c_0_206,axiom,
    ! [X4] :
      ( ~ function(X4)
      | single_valued_set(X4) ),
    file('<stdin>',function2) ).

fof(c_0_207,axiom,
    ! [X4] :
      ( ~ one_to_one_function(X4)
      | function(X4) ),
    file('<stdin>',one_to_one_function1) ).

fof(c_0_208,plain,
    ! [X16,X17,X18,X19,X20] :
      ( homomorphism(X18,X17,X20,X16,X19)
      | ~ closed(X17,X20)
      | ~ closed(X16,X19)
      | ~ maps(X18,X17,X16)
      | apply(X18,apply_to_two_arguments(X20,f32(X18,X17,X20,X16,X19),f33(X18,X17,X20,X16,X19))) != apply_to_two_arguments(X19,apply(X18,f32(X18,X17,X20,X16,X19)),apply(X18,f33(X18,X17,X20,X16,X19))) ),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_209,plain,
    ! [X11,X14,X4,X15] :
      ( inverse(X11,X4,X15,X14)
      | ~ maps(X14,X11,X11)
      | apply_to_two_arguments(X4,apply(X14,f38(X11,X4,X15,X14)),f38(X11,X4,X15,X14)) != X15
      | apply_to_two_arguments(X4,f38(X11,X4,X15,X14),apply(X14,f38(X11,X4,X15,X14))) != X15 ),
    inference(fof_simplification,[status(thm)],[c_0_1]) ).

fof(c_0_210,plain,
    ! [X16,X17,X18,X19,X20] :
      ( homomorphism(X18,X17,X20,X16,X19)
      | ~ closed(X17,X20)
      | ~ closed(X16,X19)
      | ~ maps(X18,X17,X16)
      | member(f32(X18,X17,X20,X16,X19),X17) ),
    inference(fof_simplification,[status(thm)],[c_0_2]) ).

fof(c_0_211,plain,
    ! [X16,X17,X18,X19,X20] :
      ( homomorphism(X18,X17,X20,X16,X19)
      | ~ closed(X17,X20)
      | ~ closed(X16,X19)
      | ~ maps(X18,X17,X16)
      | member(f33(X18,X17,X20,X16,X19),X17) ),
    inference(fof_simplification,[status(thm)],[c_0_3]) ).

fof(c_0_212,plain,
    ! [X13,X16,X17,X18,X19,X20,X2] :
      ( ~ homomorphism(X18,X17,X20,X16,X19)
      | ~ member(X2,X17)
      | ~ member(X13,X17)
      | apply(X18,apply_to_two_arguments(X20,X2,X13)) = apply_to_two_arguments(X19,apply(X18,X2),apply(X18,X13)) ),
    inference(fof_simplification,[status(thm)],[c_0_4]) ).

fof(c_0_213,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ homomorphism(X18,X17,X20,X16,X19)
      | maps(X18,X17,X16) ),
    inference(fof_simplification,[status(thm)],[c_0_5]) ).

fof(c_0_214,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ homomorphism(X18,X17,X20,X16,X19)
      | closed(X17,X20) ),
    inference(fof_simplification,[status(thm)],[c_0_6]) ).

fof(c_0_215,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ homomorphism(X18,X17,X20,X16,X19)
      | closed(X16,X19) ),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_216,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X11)),f52(X1,X11)),apply_to_two_arguments(plus,f53(X1,X11),f52(X1,X11))),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_8]) ).

fof(c_0_217,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X11)),f52(X1,X11)),apply_to_two_arguments(plus,f53(X1,X11),f52(X1,X11))),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_9]) ).

fof(c_0_218,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X11)),f47(X1,X11)),successor(f48(X1,X11))),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_10]) ).

fof(c_0_219,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X11)),f47(X1,X11)),successor(f48(X1,X11))),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_11]) ).

fof(c_0_220,axiom,
    ! [X11,X4] :
      ( associative(X11,X4)
      | apply_to_two_arguments(X4,apply_to_two_arguments(X4,f34(X11,X4),f35(X11,X4)),f36(X11,X4)) != apply_to_two_arguments(X4,f34(X11,X4),apply_to_two_arguments(X4,f35(X11,X4),f36(X11,X4))) ),
    c_0_12 ).

fof(c_0_221,plain,
    ! [X11,X14,X4,X15] :
      ( inverse(X11,X4,X15,X14)
      | ~ maps(X14,X11,X11)
      | member(f38(X11,X4,X15,X14),X11) ),
    inference(fof_simplification,[status(thm)],[c_0_13]) ).

fof(c_0_222,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | member(ordered_pair(ordered_pair(f46(X1,X11),f47(X1,X11)),f48(X1,X11)),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_223,plain,
    ! [X11,X4,X15] :
      ( identity(X11,X4,X15)
      | ~ member(X15,X11)
      | apply_to_two_arguments(X4,X15,f37(X11,X4,X15)) != f37(X11,X4,X15)
      | apply_to_two_arguments(X4,f37(X11,X4,X15),X15) != f37(X11,X4,X15) ),
    inference(fof_simplification,[status(thm)],[c_0_15]) ).

fof(c_0_224,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | member(ordered_pair(ordered_pair(f51(X1,X11),f52(X1,X11)),f53(X1,X11)),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_16]) ).

fof(c_0_225,plain,
    ! [X1,X7,X8,X9] :
      ( member(X1,times)
      | ~ little_set(X1)
      | ~ member(X9,natural_numbers)
      | ~ member(X8,natural_numbers)
      | ~ member(X7,natural_numbers)
      | ~ member(ordered_pair(ordered_pair(X9,X8),X7),f54(X1))
      | member(ordered_pair(ordered_pair(successor(X9),X8),apply_to_two_arguments(plus,X7,X8)),f54(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_17]) ).

fof(c_0_226,plain,
    ! [X11,X14,X4,X15] :
      ( group(X11,X4)
      | ~ closed(X11,X4)
      | ~ associative(X11,X4)
      | ~ identity(X11,X4,X15)
      | ~ inverse(X11,X4,X15,X14) ),
    inference(fof_simplification,[status(thm)],[c_0_18]) ).

fof(c_0_227,plain,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | member(ordered_pair(f29(X1,X4,X14),f31(X1,X4,X14)),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_228,plain,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | member(ordered_pair(f31(X1,X4,X14),f30(X1,X4,X14)),X14) ),
    inference(fof_simplification,[status(thm)],[c_0_20]) ).

fof(c_0_229,plain,
    ! [X11,X14,X4,X15,X2] :
      ( ~ inverse(X11,X4,X15,X14)
      | ~ member(X2,X11)
      | apply_to_two_arguments(X4,apply(X14,X2),X2) = X15 ),
    inference(fof_simplification,[status(thm)],[c_0_21]) ).

fof(c_0_230,plain,
    ! [X11,X14,X4,X15,X2] :
      ( ~ inverse(X11,X4,X15,X14)
      | ~ member(X2,X11)
      | apply_to_two_arguments(X4,X2,apply(X14,X2)) = X15 ),
    inference(fof_simplification,[status(thm)],[c_0_22]) ).

fof(c_0_231,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | member(f46(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_23]) ).

fof(c_0_232,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | member(f47(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_24]) ).

fof(c_0_233,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X11)),f45(X1,X11)),X11)
      | member(f48(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_234,plain,
    ! [X11,X14,X4,X15] :
      ( ~ inverse(X11,X4,X15,X14)
      | maps(X14,X11,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_26]) ).

fof(c_0_235,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | member(ordered_pair(ordered_pair(f46(X1,X11),f47(X1,X11)),f48(X1,X11)),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_236,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | member(ordered_pair(ordered_pair(f51(X1,X11),f52(X1,X11)),f53(X1,X11)),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_28]) ).

fof(c_0_237,plain,
    ! [X1,X13,X11,X4,X2] :
      ( ~ associative(X11,X4)
      | ~ member(X2,X11)
      | ~ member(X13,X11)
      | ~ member(X1,X11)
      | apply_to_two_arguments(X4,apply_to_two_arguments(X4,X2,X13),X1) = apply_to_two_arguments(X4,X2,apply_to_two_arguments(X4,X13,X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_238,plain,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_239,plain,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_31]) ).

fof(c_0_240,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | member(f51(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_32]) ).

fof(c_0_241,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | member(f52(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_33]) ).

fof(c_0_242,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X11)),empty_set),X11)
      | member(f53(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_34]) ).

fof(c_0_243,plain,
    ! [X1,X7,X8,X12] :
      ( member(X1,plus)
      | ~ little_set(X1)
      | ~ member(X12,natural_numbers)
      | ~ member(X8,natural_numbers)
      | ~ member(X7,natural_numbers)
      | ~ member(ordered_pair(ordered_pair(X12,X8),X7),f49(X1))
      | member(ordered_pair(ordered_pair(successor(X12),X8),successor(X7)),f49(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_35]) ).

fof(c_0_244,axiom,
    ! [X11,X4] :
      ( commutes(X11,X4)
      | apply_to_two_arguments(X4,f41(X11,X4),f42(X11,X4)) != apply_to_two_arguments(X4,f42(X11,X4),f41(X11,X4)) ),
    c_0_36 ).

fof(c_0_245,plain,
    ! [X11,X4] :
      ( ~ group(X11,X4)
      | inverse(X11,X4,f39(X11,X4),f40(X11,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_37]) ).

fof(c_0_246,plain,
    ! [X1,X4,X2] :
      ( ~ member(X1,image(X2,X4))
      | member(first(f22(X1,X2,X4)),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_38]) ).

fof(c_0_247,plain,
    ! [X1,X13,X4] :
      ( ~ member(X1,apply(X4,X13))
      | member(X1,second(f28(X1,X4,X13))) ),
    inference(fof_simplification,[status(thm)],[c_0_39]) ).

fof(c_0_248,plain,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | X1 = ordered_pair(f29(X1,X4,X14),f30(X1,X4,X14)) ),
    inference(fof_simplification,[status(thm)],[c_0_40]) ).

fof(c_0_249,plain,
    ! [X1,X2,X21,X5,X6] :
      ( member(X1,rotate_right(X2))
      | ~ little_set(X1)
      | ~ little_set(X6)
      | ~ little_set(X5)
      | ~ little_set(X21)
      | X1 != ordered_pair(X6,ordered_pair(X5,X21))
      | ~ member(ordered_pair(X5,ordered_pair(X21,X6)),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_41]) ).

fof(c_0_250,plain,
    ! [X1,X2,X21,X5,X6] :
      ( member(X1,flip_range_of(X2))
      | ~ little_set(X1)
      | ~ little_set(X6)
      | ~ little_set(X5)
      | ~ little_set(X21)
      | X1 != ordered_pair(X6,ordered_pair(X5,X21))
      | ~ member(ordered_pair(X6,ordered_pair(X21,X5)),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_42]) ).

fof(c_0_251,plain,
    ! [X1,X13,X14,X4,X2,X21] :
      ( member(X1,compose(X4,X14))
      | ~ little_set(X1)
      | ~ little_set(X2)
      | ~ little_set(X13)
      | ~ little_set(X21)
      | X1 != ordered_pair(X2,X13)
      | ~ member(ordered_pair(X2,X21),X4)
      | ~ member(ordered_pair(X21,X13),X14) ),
    inference(fof_simplification,[status(thm)],[c_0_43]) ).

fof(c_0_252,plain,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | X1 = ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2))) ),
    inference(fof_simplification,[status(thm)],[c_0_44]) ).

fof(c_0_253,plain,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | X1 = ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2))) ),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_254,plain,
    ! [X11,X4,X15] :
      ( identity(X11,X4,X15)
      | ~ member(X15,X11)
      | member(f37(X11,X4,X15),X11) ),
    inference(fof_simplification,[status(thm)],[c_0_46]) ).

fof(c_0_255,plain,
    ! [X1,X5,X6] :
      ( ~ member(X1,prime_numbers)
      | ~ member(X6,natural_numbers)
      | ~ member(X5,natural_numbers)
      | apply_to_two_arguments(times,X6,X5) != X1
      | member(X6,non_ordered_pair(successor(empty_set),X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_47]) ).

fof(c_0_256,plain,
    ! [X1,X4,X2] :
      ( ~ member(X1,image(X2,X4))
      | member(f22(X1,X2,X4),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_48]) ).

fof(c_0_257,plain,
    ! [X1,X13,X4] :
      ( ~ member(X1,apply(X4,X13))
      | member(f28(X1,X4,X13),X4) ),
    inference(fof_simplification,[status(thm)],[c_0_49]) ).

fof(c_0_258,plain,
    ! [X13,X11,X4,X2] :
      ( ~ commutes(X11,X4)
      | ~ member(X2,X11)
      | ~ member(X13,X11)
      | apply_to_two_arguments(X4,X2,X13) = apply_to_two_arguments(X4,X13,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_50]) ).

fof(c_0_259,plain,
    ! [X1,X11] :
      ( ~ member(X1,natural_numbers)
      | ~ little_set(X11)
      | ~ member(empty_set,X11)
      | ~ member(successor(f43(X1,X11)),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_51]) ).

fof(c_0_260,plain,
    ! [X1,X4,X2] :
      ( ~ member(X1,image(X2,X4))
      | second(f22(X1,X2,X4)) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_52]) ).

fof(c_0_261,plain,
    ! [X1,X13,X4] :
      ( ~ member(X1,apply(X4,X13))
      | first(f28(X1,X4,X13)) = X13 ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_262,plain,
    ! [X1,X4,X2] :
      ( ~ member(X1,image(X2,X4))
      | ordered_pair_predicate(f22(X1,X2,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_54]) ).

fof(c_0_263,plain,
    ! [X1,X13,X4] :
      ( ~ member(X1,apply(X4,X13))
      | ordered_pair_predicate(f28(X1,X4,X13)) ),
    inference(fof_simplification,[status(thm)],[c_0_55]) ).

fof(c_0_264,plain,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | little_set(f29(X1,X4,X14)) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_265,plain,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | little_set(f30(X1,X4,X14)) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_266,plain,
    ! [X1,X14,X4] :
      ( ~ member(X1,compose(X4,X14))
      | little_set(f31(X1,X4,X14)) ),
    inference(fof_simplification,[status(thm)],[c_0_58]) ).

fof(c_0_267,plain,
    ! [X11,X4,X15,X2] :
      ( ~ identity(X11,X4,X15)
      | ~ member(X2,X11)
      | apply_to_two_arguments(X4,X15,X2) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_59]) ).

fof(c_0_268,plain,
    ! [X11,X4,X15,X2] :
      ( ~ identity(X11,X4,X15)
      | ~ member(X2,X11)
      | apply_to_two_arguments(X4,X2,X15) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_60]) ).

fof(c_0_269,plain,
    ! [X2,X21,X5,X6] :
      ( ~ single_valued_set(X2)
      | ~ little_set(X6)
      | ~ little_set(X5)
      | ~ little_set(X21)
      | ~ member(ordered_pair(X6,X5),X2)
      | ~ member(ordered_pair(X6,X21),X2)
      | X5 = X21 ),
    inference(fof_simplification,[status(thm)],[c_0_61]) ).

fof(c_0_270,plain,
    ! [X11,X4] :
      ( closed(X11,X4)
      | ~ little_set(X11)
      | ~ little_set(X4)
      | ~ maps(X4,cross_product(X11,X11),X11) ),
    inference(fof_simplification,[status(thm)],[c_0_62]) ).

fof(c_0_271,plain,
    ! [X1,X2] :
      ( member(X1,even_numbers)
      | ~ member(X1,natural_numbers)
      | ~ member(X2,natural_numbers)
      | apply_to_two_arguments(plus,X2,X2) != X1 ),
    inference(fof_simplification,[status(thm)],[c_0_63]) ).

fof(c_0_272,plain,
    ! [X1,X2] :
      ( member(X1,converse(X2))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X1)
      | ~ member(ordered_pair(second(X1),first(X1)),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_64]) ).

fof(c_0_273,plain,
    ! [X1,X10] :
      ( member(X1,plus)
      | ~ little_set(X1)
      | ~ member(X10,natural_numbers)
      | member(ordered_pair(ordered_pair(empty_set,X10),X10),f49(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_65]) ).

fof(c_0_274,plain,
    ! [X1,X10] :
      ( member(X1,times)
      | ~ little_set(X1)
      | ~ member(X10,natural_numbers)
      | member(ordered_pair(ordered_pair(empty_set,X10),empty_set),f54(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_66]) ).

fof(c_0_275,plain,
    ! [X13,X2] :
      ( ~ member(f1(X2,X13),X2)
      | ~ member(f1(X2,X13),X13)
      | X2 = X13 ),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_276,plain,
    ! [X3,X4,X2] :
      ( finite(X2)
      | ~ member(X3,natural_numbers)
      | ~ maps(X4,X3,X2)
      | range_of(X4) != X2
      | ~ one_to_one_function(X4) ),
    inference(fof_simplification,[status(thm)],[c_0_68]) ).

fof(c_0_277,plain,
    ! [X1] :
      ( member(X1,prime_numbers)
      | ~ member(X1,natural_numbers)
      | X1 = empty_set
      | X1 = successor(empty_set)
      | ~ member(f55(X1),non_ordered_pair(successor(empty_set),X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_69]) ).

fof(c_0_278,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | member(f46(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_70]) ).

fof(c_0_279,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | member(f47(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_71]) ).

fof(c_0_280,plain,
    ! [X1,X11] :
      ( ~ member(X1,plus)
      | ~ little_set(X11)
      | member(f45(X1,X11),natural_numbers)
      | member(f48(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_72]) ).

fof(c_0_281,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | member(f51(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_282,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | member(f52(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_74]) ).

fof(c_0_283,plain,
    ! [X1,X11] :
      ( ~ member(X1,times)
      | ~ little_set(X11)
      | member(f50(X1,X11),natural_numbers)
      | member(f53(X1,X11),natural_numbers)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_75]) ).

fof(c_0_284,plain,
    ! [X1,X13,X2] :
      ( member(X1,cross_product(X2,X13))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X1)
      | ~ member(first(X1),X2)
      | ~ member(second(X1),X13) ),
    inference(fof_simplification,[status(thm)],[c_0_76]) ).

fof(c_0_285,plain,
    ! [X1,X13,X4,X2] :
      ( member(X1,image(X2,X4))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X13)
      | ~ member(X13,X4)
      | ~ member(first(X13),X2)
      | second(X13) != X1 ),
    inference(fof_simplification,[status(thm)],[c_0_77]) ).

fof(c_0_286,plain,
    ! [X1,X13,X4,X21] :
      ( member(X1,apply(X4,X13))
      | ~ ordered_pair_predicate(X21)
      | ~ member(X21,X4)
      | first(X21) != X13
      | ~ member(X1,second(X21)) ),
    inference(fof_simplification,[status(thm)],[c_0_78]) ).

fof(c_0_287,plain,
    ! [X13,X4,X2] :
      ( ~ maps(X4,X2,X13)
      | subset(range_of(X4),X13) ),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_288,plain,
    ! [X1] :
      ( member(X1,prime_numbers)
      | ~ member(X1,natural_numbers)
      | X1 = empty_set
      | X1 = successor(empty_set)
      | apply_to_two_arguments(times,f55(X1),f56(X1)) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_80]) ).

fof(c_0_289,plain,
    ! [X11,X4] :
      ( ~ closed(X11,X4)
      | maps(X4,cross_product(X11,X11),X11) ),
    inference(fof_simplification,[status(thm)],[c_0_81]) ).

fof(c_0_290,plain,
    ! [X11,X4] :
      ( ~ group(X11,X4)
      | identity(X11,X4,f39(X11,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_82]) ).

fof(c_0_291,plain,
    ! [X13,X4,X2] :
      ( maps(X4,X2,X13)
      | ~ function(X4)
      | domain_of(X4) != X2
      | ~ subset(range_of(X4),X13) ),
    inference(fof_simplification,[status(thm)],[c_0_83]) ).

fof(c_0_292,plain,
    ! [X1,X11] :
      ( ~ member(X1,natural_numbers)
      | ~ little_set(X11)
      | ~ member(empty_set,X11)
      | member(f43(X1,X11),X11)
      | member(X1,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_84]) ).

fof(c_0_293,plain,
    ! [X11,X4,X15] :
      ( ~ identity(X11,X4,X15)
      | member(X15,X11) ),
    inference(fof_simplification,[status(thm)],[c_0_85]) ).

fof(c_0_294,plain,
    ! [X1,X2] :
      ( ~ member(X1,first(X2))
      | X2 = ordered_pair(f4(X1,X2),f5(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_86]) ).

fof(c_0_295,plain,
    ! [X1,X2] :
      ( ~ member(X1,second(X2))
      | X2 = ordered_pair(f6(X1,X2),f7(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_87]) ).

fof(c_0_296,plain,
    ! [X1,X2] :
      ( ~ member(X1,converse(X2))
      | member(ordered_pair(second(X1),first(X1)),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_88]) ).

fof(c_0_297,plain,
    ! [X13,X4,X2] :
      ( ~ maps(X4,X2,X13)
      | domain_of(X4) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_89]) ).

fof(c_0_298,plain,
    ! [X13,X4,X2] :
      ( ~ maps(X4,X2,X13)
      | function(X4) ),
    inference(fof_simplification,[status(thm)],[c_0_90]) ).

fof(c_0_299,plain,
    ! [X1] :
      ( ~ member(X1,even_numbers)
      | apply_to_two_arguments(plus,f59(X1),f59(X1)) = X1 ),
    inference(fof_simplification,[status(thm)],[c_0_91]) ).

fof(c_0_300,plain,
    ! [X1,X13,X2] :
      ( member(X1,intersection(X2,X13))
      | ~ member(X1,X2)
      | ~ member(X1,X13) ),
    inference(fof_simplification,[status(thm)],[c_0_92]) ).

fof(c_0_301,plain,
    ! [X1,X13,X2] :
      ( ~ member(X1,cross_product(X2,X13))
      | member(first(X1),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_93]) ).

fof(c_0_302,plain,
    ! [X1,X13,X2] :
      ( ~ member(X1,cross_product(X2,X13))
      | member(second(X1),X13) ),
    inference(fof_simplification,[status(thm)],[c_0_94]) ).

fof(c_0_303,axiom,
    ! [X13,X2] :
      ( member(f1(X2,X13),X2)
      | member(f1(X2,X13),X13)
      | X2 = X13 ),
    c_0_95 ).

fof(c_0_304,plain,
    ! [X1] :
      ( member(X1,twin_prime_numbers)
      | ~ member(X1,prime_numbers)
      | ~ member(successor(successor(X1)),prime_numbers) ),
    inference(fof_simplification,[status(thm)],[c_0_96]) ).

fof(c_0_305,plain,
    ! [X1,X2,X5,X6] :
      ( member(X1,first(X2))
      | ~ little_set(X6)
      | ~ little_set(X5)
      | X2 != ordered_pair(X6,X5)
      | ~ member(X1,X6) ),
    inference(fof_simplification,[status(thm)],[c_0_97]) ).

fof(c_0_306,plain,
    ! [X1,X2,X5,X6] :
      ( member(X1,second(X2))
      | ~ little_set(X6)
      | ~ little_set(X5)
      | X2 != ordered_pair(X6,X5)
      | ~ member(X1,X5) ),
    inference(fof_simplification,[status(thm)],[c_0_98]) ).

fof(c_0_307,plain,
    ! [X1,X7] :
      ( member(X1,natural_numbers)
      | ~ little_set(X1)
      | ~ member(X7,f44(X1))
      | member(successor(X7),f44(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_99]) ).

fof(c_0_308,plain,
    ! [X1,X13,X2] :
      ( ~ member(X1,intersection(X2,X13))
      | member(X1,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_100]) ).

fof(c_0_309,plain,
    ! [X1,X13,X2] :
      ( ~ member(X1,intersection(X2,X13))
      | member(X1,X13) ),
    inference(fof_simplification,[status(thm)],[c_0_101]) ).

fof(c_0_310,plain,
    ! [X13,X2] :
      ( subset(X2,X13)
      | ~ member(f17(X2,X13),X13) ),
    inference(fof_simplification,[status(thm)],[c_0_102]) ).

fof(c_0_311,plain,
    ! [X2] :
      ( ~ finite(X2)
      | maps(f58(X2),f57(X2),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_103]) ).

fof(c_0_312,plain,
    ! [X1,X2] :
      ( ~ member(X1,first(X2))
      | member(X1,f4(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_104]) ).

fof(c_0_313,plain,
    ! [X1,X2] :
      ( ~ member(X1,second(X2))
      | member(X1,f7(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_105]) ).

fof(c_0_314,plain,
    ! [X1,X2] :
      ( ~ member(X1,domain_of(X2))
      | member(f8(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_106]) ).

fof(c_0_315,plain,
    ! [X1,X2] :
      ( ~ member(X1,sigma(X2))
      | member(f16(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_107]) ).

fof(c_0_316,plain,
    ! [X1,X2] :
      ( ~ member(X1,sigma(X2))
      | member(X1,f16(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_108]) ).

fof(c_0_317,plain,
    ! [X1,X2] :
      ( ~ member(X1,range_of(X2))
      | member(f27(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_109]) ).

fof(c_0_318,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | member(ordered_pair(f19(X2),f20(X2)),X2) ),
    c_0_110 ).

fof(c_0_319,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | member(ordered_pair(f19(X2),f21(X2)),X2) ),
    c_0_111 ).

fof(c_0_320,plain,
    ! [X1] :
      ( member(X1,estin)
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X1)
      | ~ member(first(X1),second(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_321,plain,
    ! [X13,X2,X6] :
      ( ~ disjoint(X2,X13)
      | ~ member(X6,X2)
      | ~ member(X6,X13) ),
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_322,plain,
    ! [X13,X2,X6] :
      ( ~ member(X6,non_ordered_pair(X2,X13))
      | X6 = X2
      | X6 = X13 ),
    inference(fof_simplification,[status(thm)],[c_0_114]) ).

fof(c_0_323,plain,
    ! [X1,X13,X2] :
      ( ~ member(X1,cross_product(X2,X13))
      | ordered_pair_predicate(X1) ),
    inference(fof_simplification,[status(thm)],[c_0_115]) ).

fof(c_0_324,plain,
    ! [X1,X22,X2] :
      ( member(X1,domain_of(X2))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X22)
      | ~ member(X22,X2)
      | X1 != first(X22) ),
    inference(fof_simplification,[status(thm)],[c_0_116]) ).

fof(c_0_325,plain,
    ! [X1,X13,X2] :
      ( member(X1,sigma(X2))
      | ~ member(X13,X2)
      | ~ member(X1,X13) ),
    inference(fof_simplification,[status(thm)],[c_0_117]) ).

fof(c_0_326,plain,
    ! [X1,X22,X2] :
      ( member(X1,range_of(X2))
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X22)
      | ~ member(X22,X2)
      | X1 != second(X22) ),
    inference(fof_simplification,[status(thm)],[c_0_118]) ).

fof(c_0_327,plain,
    ! [X1,X2] :
      ( ~ member(X1,domain_of(X2))
      | X1 = first(f8(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_119]) ).

fof(c_0_328,plain,
    ! [X1,X2] :
      ( ~ member(X1,range_of(X2))
      | X1 = second(f27(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_120]) ).

fof(c_0_329,plain,
    ! [X1,X2] :
      ( ~ member(X1,first(X2))
      | little_set(f4(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_121]) ).

fof(c_0_330,plain,
    ! [X1,X2] :
      ( ~ member(X1,first(X2))
      | little_set(f5(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_122]) ).

fof(c_0_331,plain,
    ! [X1,X2] :
      ( ~ member(X1,second(X2))
      | little_set(f6(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_123]) ).

fof(c_0_332,plain,
    ! [X1,X2] :
      ( ~ member(X1,second(X2))
      | little_set(f7(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_333,plain,
    ! [X1,X2] :
      ( ~ member(X1,domain_of(X2))
      | ordered_pair_predicate(f8(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_125]) ).

fof(c_0_334,plain,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | little_set(f9(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_126]) ).

fof(c_0_335,plain,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | little_set(f10(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_127]) ).

fof(c_0_336,plain,
    ! [X1,X2] :
      ( ~ member(X1,rotate_right(X2))
      | little_set(f11(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_128]) ).

fof(c_0_337,plain,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | little_set(f12(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_129]) ).

fof(c_0_338,plain,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | little_set(f13(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_130]) ).

fof(c_0_339,plain,
    ! [X1,X2] :
      ( ~ member(X1,flip_range_of(X2))
      | little_set(f14(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_131]) ).

fof(c_0_340,plain,
    ! [X1,X2] :
      ( ~ member(X1,range_of(X2))
      | ordered_pair_predicate(f27(X1,X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_132]) ).

fof(c_0_341,plain,
    ! [X13,X2,X6] :
      ( ~ subset(X2,X13)
      | ~ member(X6,X2)
      | member(X6,X13) ),
    inference(fof_simplification,[status(thm)],[c_0_133]) ).

fof(c_0_342,plain,
    ! [X2] :
      ( ~ little_set(X2)
      | X2 = empty_set
      | member(ordered_pair(X2,f26(X2)),f25) ),
    inference(fof_simplification,[status(thm)],[c_0_134]) ).

fof(c_0_343,plain,
    ! [X1] :
      ( member(X1,prime_numbers)
      | ~ member(X1,natural_numbers)
      | X1 = empty_set
      | X1 = successor(empty_set)
      | member(f55(X1),natural_numbers) ),
    inference(fof_simplification,[status(thm)],[c_0_135]) ).

fof(c_0_344,plain,
    ! [X1] :
      ( member(X1,prime_numbers)
      | ~ member(X1,natural_numbers)
      | X1 = empty_set
      | X1 = successor(empty_set)
      | member(f56(X1),natural_numbers) ),
    inference(fof_simplification,[status(thm)],[c_0_136]) ).

fof(c_0_345,plain,
    ! [X1,X2] :
      ( ~ member(X1,complement(X2))
      | ~ member(X1,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_346,axiom,
    ! [X13,X2] :
      ( subset(X2,X13)
      | member(f17(X2,X13),X2) ),
    c_0_138 ).

fof(c_0_347,axiom,
    ! [X13,X2] :
      ( disjoint(X2,X13)
      | member(f23(X2,X13),X2) ),
    c_0_139 ).

fof(c_0_348,axiom,
    ! [X13,X2] :
      ( disjoint(X2,X13)
      | member(f23(X2,X13),X13) ),
    c_0_140 ).

fof(c_0_349,axiom,
    ! [X11,X4] :
      ( associative(X11,X4)
      | member(f34(X11,X4),X11) ),
    c_0_141 ).

fof(c_0_350,axiom,
    ! [X11,X4] :
      ( associative(X11,X4)
      | member(f35(X11,X4),X11) ),
    c_0_142 ).

fof(c_0_351,axiom,
    ! [X11,X4] :
      ( associative(X11,X4)
      | member(f36(X11,X4),X11) ),
    c_0_143 ).

fof(c_0_352,axiom,
    ! [X11,X4] :
      ( commutes(X11,X4)
      | member(f41(X11,X4),X11) ),
    c_0_144 ).

fof(c_0_353,axiom,
    ! [X11,X4] :
      ( commutes(X11,X4)
      | member(f42(X11,X4),X11) ),
    c_0_145 ).

fof(c_0_354,plain,
    ! [X1] :
      ( ~ member(X1,twin_prime_numbers)
      | member(successor(successor(X1)),prime_numbers) ),
    inference(fof_simplification,[status(thm)],[c_0_146]) ).

fof(c_0_355,plain,
    ! [X13,X2,X6] :
      ( member(X6,non_ordered_pair(X2,X13))
      | ~ little_set(X6)
      | X6 != X2 ),
    inference(fof_simplification,[status(thm)],[c_0_147]) ).

fof(c_0_356,plain,
    ! [X13,X2,X6] :
      ( member(X6,non_ordered_pair(X2,X13))
      | ~ little_set(X6)
      | X6 != X13 ),
    inference(fof_simplification,[status(thm)],[c_0_148]) ).

fof(c_0_357,plain,
    ! [X1,X2] :
      ( member(X1,powerset(X2))
      | ~ little_set(X1)
      | ~ subset(X1,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_149]) ).

fof(c_0_358,plain,
    ! [X1] :
      ( ~ member(X1,estin)
      | member(first(X1),second(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_150]) ).

fof(c_0_359,plain,
    ! [X1,X2] :
      ( ~ member(X1,powerset(X2))
      | subset(X1,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_151]) ).

fof(c_0_360,plain,
    ! [X1] :
      ( member(X1,natural_numbers)
      | ~ member(X1,f44(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_152]) ).

fof(c_0_361,plain,
    ! [X1] :
      ( member(X1,plus)
      | ~ member(X1,f49(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_153]) ).

fof(c_0_362,plain,
    ! [X1] :
      ( member(X1,times)
      | ~ member(X1,f54(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_154]) ).

fof(c_0_363,plain,
    ! [X4,X2] :
      ( ~ little_set(X2)
      | ~ function(X4)
      | little_set(image(X2,X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_155]) ).

fof(c_0_364,plain,
    ! [X1,X13,X2] :
      ( ordered_pair_predicate(X2)
      | ~ little_set(X13)
      | ~ little_set(X1)
      | X2 != ordered_pair(X13,X1) ),
    inference(fof_simplification,[status(thm)],[c_0_156]) ).

fof(c_0_365,plain,
    ! [X1,X2] :
      ( member(X1,complement(X2))
      | ~ little_set(X1)
      | member(X1,X2) ),
    inference(fof_simplification,[status(thm)],[c_0_157]) ).

fof(c_0_366,plain,
    ! [X1] :
      ( member(X1,identity_relation)
      | ~ little_set(X1)
      | ~ ordered_pair_predicate(X1)
      | first(X1) != second(X1) ),
    inference(fof_simplification,[status(thm)],[c_0_158]) ).

fof(c_0_367,plain,
    ! [X13,X2] :
      ( proper_subset(X2,X13)
      | ~ subset(X2,X13)
      | X2 = X13 ),
    inference(fof_simplification,[status(thm)],[c_0_159]) ).

fof(c_0_368,plain,
    ! [X2] :
      ( ~ member(X2,infinity)
      | member(successor(X2),infinity) ),
    inference(fof_simplification,[status(thm)],[c_0_160]) ).

fof(c_0_369,plain,
    ! [X1] :
      ( ~ member(X1,even_numbers)
      | member(f59(X1),natural_numbers) ),
    inference(fof_simplification,[status(thm)],[c_0_161]) ).

fof(c_0_370,plain,
    ! [X1] :
      ( member(X1,natural_numbers)
      | ~ little_set(X1)
      | member(empty_set,f44(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_162]) ).

fof(c_0_371,plain,
    ! [X13,X2] :
      ( ~ proper_subset(X2,X13)
      | subset(X2,X13) ),
    inference(fof_simplification,[status(thm)],[c_0_163]) ).

fof(c_0_372,plain,
    ! [X11,X4] :
      ( ~ group(X11,X4)
      | closed(X11,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_164]) ).

fof(c_0_373,plain,
    ! [X11,X4] :
      ( ~ group(X11,X4)
      | associative(X11,X4) ),
    inference(fof_simplification,[status(thm)],[c_0_165]) ).

fof(c_0_374,plain,
    ! [X1,X2] :
      ( ~ member(X1,converse(X2))
      | ordered_pair_predicate(X1) ),
    inference(fof_simplification,[status(thm)],[c_0_166]) ).

fof(c_0_375,plain,
    ! [X2] :
      ( ~ ordered_pair_predicate(X2)
      | X2 = ordered_pair(f2(X2),f3(X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_167]) ).

fof(c_0_376,plain,
    ! [X1,X2] :
      ( ~ relation(X1)
      | ~ member(X2,X1)
      | ordered_pair_predicate(X2) ),
    inference(fof_simplification,[status(thm)],[c_0_168]) ).

fof(c_0_377,plain,
    ! [X1] :
      ( ~ member(X1,prime_numbers)
      | member(X1,natural_numbers) ),
    inference(fof_simplification,[status(thm)],[c_0_169]) ).

fof(c_0_378,plain,
    ! [X1] :
      ( ~ member(X1,twin_prime_numbers)
      | member(X1,prime_numbers) ),
    inference(fof_simplification,[status(thm)],[c_0_170]) ).

fof(c_0_379,plain,
    ! [X1] :
      ( ~ member(X1,even_numbers)
      | member(X1,natural_numbers) ),
    inference(fof_simplification,[status(thm)],[c_0_171]) ).

fof(c_0_380,axiom,
    ! [X13,X2] :
      ( little_set(f1(X2,X13))
      | X2 = X13 ),
    c_0_172 ).

fof(c_0_381,plain,
    ! [X1] :
      ( member(X1,natural_numbers)
      | ~ little_set(X1)
      | little_set(f44(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_173]) ).

fof(c_0_382,plain,
    ! [X1] :
      ( member(X1,plus)
      | ~ little_set(X1)
      | little_set(f49(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_174]) ).

fof(c_0_383,plain,
    ! [X1] :
      ( member(X1,times)
      | ~ little_set(X1)
      | little_set(f54(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_175]) ).

fof(c_0_384,plain,
    ! [X2] :
      ( ~ little_set(X2)
      | X2 = empty_set
      | member(f26(X2),X2) ),
    inference(fof_simplification,[status(thm)],[c_0_176]) ).

fof(c_0_385,plain,
    ! [X1] :
      ( ~ member(X1,identity_relation)
      | first(X1) = second(X1) ),
    inference(fof_simplification,[status(thm)],[c_0_177]) ).

fof(c_0_386,plain,
    ! [X4] :
      ( one_to_one_function(X4)
      | ~ function(X4)
      | ~ function(converse(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_178]) ).

fof(c_0_387,plain,
    ! [X13,X2] :
      ( ~ member(X2,X13)
      | little_set(X2) ),
    inference(fof_simplification,[status(thm)],[c_0_179]) ).

fof(c_0_388,plain,
    ! [X11,X4] :
      ( ~ closed(X11,X4)
      | little_set(X11) ),
    inference(fof_simplification,[status(thm)],[c_0_180]) ).

fof(c_0_389,plain,
    ! [X11,X4] :
      ( ~ closed(X11,X4)
      | little_set(X4) ),
    inference(fof_simplification,[status(thm)],[c_0_181]) ).

fof(c_0_390,plain,
    ! [X13,X2] :
      ( ~ proper_subset(X2,X13)
      | X2 != X13 ),
    inference(fof_simplification,[status(thm)],[c_0_182]) ).

fof(c_0_391,plain,
    ! [X1] :
      ( ~ member(X1,prime_numbers)
      | X1 != successor(empty_set) ),
    inference(fof_simplification,[status(thm)],[c_0_183]) ).

fof(c_0_392,plain,
    ! [X2] :
      ( ~ finite(X2)
      | member(f57(X2),natural_numbers) ),
    inference(fof_simplification,[status(thm)],[c_0_184]) ).

fof(c_0_393,axiom,
    ! [X1] :
      ( relation(X1)
      | member(f18(X1),X1) ),
    c_0_185 ).

fof(c_0_394,plain,
    ! [X1] :
      ( ~ member(X1,estin)
      | ordered_pair_predicate(X1) ),
    inference(fof_simplification,[status(thm)],[c_0_186]) ).

fof(c_0_395,plain,
    ! [X1] :
      ( ~ member(X1,identity_relation)
      | ordered_pair_predicate(X1) ),
    inference(fof_simplification,[status(thm)],[c_0_187]) ).

fof(c_0_396,plain,
    ! [X1] :
      ( ~ member(X1,prime_numbers)
      | X1 != empty_set ),
    inference(fof_simplification,[status(thm)],[c_0_188]) ).

fof(c_0_397,axiom,
    ! [X2] :
      ( X2 = empty_set
      | member(f24(X2),X2) ),
    c_0_189 ).

fof(c_0_398,axiom,
    ! [X2] :
      ( X2 = empty_set
      | disjoint(f24(X2),X2) ),
    c_0_190 ).

fof(c_0_399,plain,
    ! [X1] :
      ( relation(X1)
      | ~ ordered_pair_predicate(f18(X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_191]) ).

fof(c_0_400,plain,
    ! [X1] :
      ( member(X1,universal_set)
      | ~ little_set(X1) ),
    inference(fof_simplification,[status(thm)],[c_0_192]) ).

fof(c_0_401,plain,
    ! [X4] :
      ( function(X4)
      | ~ relation(X4)
      | ~ single_valued_set(X4) ),
    inference(fof_simplification,[status(thm)],[c_0_193]) ).

fof(c_0_402,plain,
    ! [X2] :
      ( ~ finite(X2)
      | range_of(f58(X2)) = X2 ),
    inference(fof_simplification,[status(thm)],[c_0_194]) ).

fof(c_0_403,plain,
    ! [X2] :
      ( ~ ordered_pair_predicate(X2)
      | little_set(f2(X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_195]) ).

fof(c_0_404,plain,
    ! [X2] :
      ( ~ ordered_pair_predicate(X2)
      | little_set(f3(X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_196]) ).

fof(c_0_405,plain,
    ! [X6] :
      ( ~ little_set(X6)
      | little_set(sigma(X6)) ),
    inference(fof_simplification,[status(thm)],[c_0_197]) ).

fof(c_0_406,plain,
    ! [X6] :
      ( ~ little_set(X6)
      | little_set(powerset(X6)) ),
    inference(fof_simplification,[status(thm)],[c_0_198]) ).

fof(c_0_407,plain,
    ! [X4] :
      ( ~ one_to_one_function(X4)
      | function(converse(X4)) ),
    inference(fof_simplification,[status(thm)],[c_0_199]) ).

fof(c_0_408,plain,
    ! [X2] :
      ( ~ finite(X2)
      | one_to_one_function(f58(X2)) ),
    inference(fof_simplification,[status(thm)],[c_0_200]) ).

fof(c_0_409,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | f20(X2) != f21(X2) ),
    c_0_201 ).

fof(c_0_410,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | little_set(f19(X2)) ),
    c_0_202 ).

fof(c_0_411,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | little_set(f20(X2)) ),
    c_0_203 ).

fof(c_0_412,axiom,
    ! [X2] :
      ( single_valued_set(X2)
      | little_set(f21(X2)) ),
    c_0_204 ).

fof(c_0_413,plain,
    ! [X4] :
      ( ~ function(X4)
      | relation(X4) ),
    inference(fof_simplification,[status(thm)],[c_0_205]) ).

fof(c_0_414,plain,
    ! [X4] :
      ( ~ function(X4)
      | single_valued_set(X4) ),
    inference(fof_simplification,[status(thm)],[c_0_206]) ).

fof(c_0_415,plain,
    ! [X4] :
      ( ~ one_to_one_function(X4)
      | function(X4) ),
    inference(fof_simplification,[status(thm)],[c_0_207]) ).

fof(c_0_416,plain,
    ! [X21,X22,X23,X24,X25] :
      ( homomorphism(X23,X22,X25,X21,X24)
      | ~ closed(X22,X25)
      | ~ closed(X21,X24)
      | ~ maps(X23,X22,X21)
      | apply(X23,apply_to_two_arguments(X25,f32(X23,X22,X25,X21,X24),f33(X23,X22,X25,X21,X24))) != apply_to_two_arguments(X24,apply(X23,f32(X23,X22,X25,X21,X24)),apply(X23,f33(X23,X22,X25,X21,X24))) ),
    inference(variable_rename,[status(thm)],[c_0_208]) ).

fof(c_0_417,plain,
    ! [X16,X17,X18,X19] :
      ( inverse(X16,X18,X19,X17)
      | ~ maps(X17,X16,X16)
      | apply_to_two_arguments(X18,apply(X17,f38(X16,X18,X19,X17)),f38(X16,X18,X19,X17)) != X19
      | apply_to_two_arguments(X18,f38(X16,X18,X19,X17),apply(X17,f38(X16,X18,X19,X17))) != X19 ),
    inference(variable_rename,[status(thm)],[c_0_209]) ).

fof(c_0_418,plain,
    ! [X21,X22,X23,X24,X25] :
      ( homomorphism(X23,X22,X25,X21,X24)
      | ~ closed(X22,X25)
      | ~ closed(X21,X24)
      | ~ maps(X23,X22,X21)
      | member(f32(X23,X22,X25,X21,X24),X22) ),
    inference(variable_rename,[status(thm)],[c_0_210]) ).

fof(c_0_419,plain,
    ! [X21,X22,X23,X24,X25] :
      ( homomorphism(X23,X22,X25,X21,X24)
      | ~ closed(X22,X25)
      | ~ closed(X21,X24)
      | ~ maps(X23,X22,X21)
      | member(f33(X23,X22,X25,X21,X24),X22) ),
    inference(variable_rename,[status(thm)],[c_0_211]) ).

fof(c_0_420,plain,
    ! [X21,X22,X23,X24,X25,X26,X27] :
      ( ~ homomorphism(X24,X23,X26,X22,X25)
      | ~ member(X27,X23)
      | ~ member(X21,X23)
      | apply(X24,apply_to_two_arguments(X26,X27,X21)) = apply_to_two_arguments(X25,apply(X24,X27),apply(X24,X21)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_212])])]) ).

fof(c_0_421,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ homomorphism(X23,X22,X25,X21,X24)
      | maps(X23,X22,X21) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_213])])]) ).

fof(c_0_422,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ homomorphism(X23,X22,X25,X21,X24)
      | closed(X22,X25) ),
    inference(variable_rename,[status(thm)],[c_0_214]) ).

fof(c_0_423,plain,
    ! [X21,X22,X23,X24,X25] :
      ( ~ homomorphism(X23,X22,X25,X21,X24)
      | closed(X21,X24) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_215])])]) ).

fof(c_0_424,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X12,X13)),empty_set),X13)
      | ~ member(ordered_pair(ordered_pair(successor(f51(X12,X13)),f52(X12,X13)),apply_to_two_arguments(plus,f53(X12,X13),f52(X12,X13))),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_216])])]) ).

fof(c_0_425,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | member(f50(X12,X13),natural_numbers)
      | ~ member(ordered_pair(ordered_pair(successor(f51(X12,X13)),f52(X12,X13)),apply_to_two_arguments(plus,f53(X12,X13),f52(X12,X13))),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_217])])]) ).

fof(c_0_426,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X12,X13)),f45(X12,X13)),X13)
      | ~ member(ordered_pair(ordered_pair(successor(f46(X12,X13)),f47(X12,X13)),successor(f48(X12,X13))),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_218])])]) ).

fof(c_0_427,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | member(f45(X12,X13),natural_numbers)
      | ~ member(ordered_pair(ordered_pair(successor(f46(X12,X13)),f47(X12,X13)),successor(f48(X12,X13))),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_219])])]) ).

fof(c_0_428,plain,
    ! [X12,X13] :
      ( associative(X12,X13)
      | apply_to_two_arguments(X13,apply_to_two_arguments(X13,f34(X12,X13),f35(X12,X13)),f36(X12,X13)) != apply_to_two_arguments(X13,f34(X12,X13),apply_to_two_arguments(X13,f35(X12,X13),f36(X12,X13))) ),
    inference(variable_rename,[status(thm)],[c_0_220]) ).

fof(c_0_429,plain,
    ! [X16,X17,X18,X19] :
      ( inverse(X16,X18,X19,X17)
      | ~ maps(X17,X16,X16)
      | member(f38(X16,X18,X19,X17),X16) ),
    inference(variable_rename,[status(thm)],[c_0_221]) ).

fof(c_0_430,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X12,X13)),f45(X12,X13)),X13)
      | member(ordered_pair(ordered_pair(f46(X12,X13),f47(X12,X13)),f48(X12,X13)),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_222])])]) ).

fof(c_0_431,plain,
    ! [X16,X17,X18] :
      ( identity(X16,X17,X18)
      | ~ member(X18,X16)
      | apply_to_two_arguments(X17,X18,f37(X16,X17,X18)) != f37(X16,X17,X18)
      | apply_to_two_arguments(X17,f37(X16,X17,X18),X18) != f37(X16,X17,X18) ),
    inference(variable_rename,[status(thm)],[c_0_223]) ).

fof(c_0_432,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X12,X13)),empty_set),X13)
      | member(ordered_pair(ordered_pair(f51(X12,X13),f52(X12,X13)),f53(X12,X13)),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_224])])]) ).

fof(c_0_433,plain,
    ! [X10,X11,X12,X13] :
      ( member(X10,times)
      | ~ little_set(X10)
      | ~ member(X13,natural_numbers)
      | ~ member(X12,natural_numbers)
      | ~ member(X11,natural_numbers)
      | ~ member(ordered_pair(ordered_pair(X13,X12),X11),f54(X10))
      | member(ordered_pair(ordered_pair(successor(X13),X12),apply_to_two_arguments(plus,X11,X12)),f54(X10)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_225])])]) ).

fof(c_0_434,plain,
    ! [X16,X17,X18,X19] :
      ( group(X16,X18)
      | ~ closed(X16,X18)
      | ~ associative(X16,X18)
      | ~ identity(X16,X18,X19)
      | ~ inverse(X16,X18,X19,X17) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_226])])]) ).

fof(c_0_435,plain,
    ! [X15,X16,X17] :
      ( ~ member(X15,compose(X17,X16))
      | member(ordered_pair(f29(X15,X17,X16),f31(X15,X17,X16)),X17) ),
    inference(variable_rename,[status(thm)],[c_0_227]) ).

fof(c_0_436,plain,
    ! [X15,X16,X17] :
      ( ~ member(X15,compose(X17,X16))
      | member(ordered_pair(f31(X15,X17,X16),f30(X15,X17,X16)),X16) ),
    inference(variable_rename,[status(thm)],[c_0_228]) ).

fof(c_0_437,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ inverse(X16,X18,X19,X17)
      | ~ member(X20,X16)
      | apply_to_two_arguments(X18,apply(X17,X20),X20) = X19 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_229])])]) ).

fof(c_0_438,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ~ inverse(X16,X18,X19,X17)
      | ~ member(X20,X16)
      | apply_to_two_arguments(X18,X20,apply(X17,X20)) = X19 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_230])])]) ).

fof(c_0_439,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X12,X13)),f45(X12,X13)),X13)
      | member(f46(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_231])])]) ).

fof(c_0_440,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X12,X13)),f45(X12,X13)),X13)
      | member(f47(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_232])])]) ).

fof(c_0_441,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f45(X12,X13)),f45(X12,X13)),X13)
      | member(f48(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_233])])]) ).

fof(c_0_442,plain,
    ! [X16,X17,X18,X19] :
      ( ~ inverse(X16,X18,X19,X17)
      | maps(X17,X16,X16) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_234])])]) ).

fof(c_0_443,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | member(f45(X12,X13),natural_numbers)
      | member(ordered_pair(ordered_pair(f46(X12,X13),f47(X12,X13)),f48(X12,X13)),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_235])])]) ).

fof(c_0_444,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | member(f50(X12,X13),natural_numbers)
      | member(ordered_pair(ordered_pair(f51(X12,X13),f52(X12,X13)),f53(X12,X13)),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_236])])]) ).

fof(c_0_445,plain,
    ! [X14,X15,X16,X17,X18] :
      ( ~ associative(X16,X17)
      | ~ member(X18,X16)
      | ~ member(X15,X16)
      | ~ member(X14,X16)
      | apply_to_two_arguments(X17,apply_to_two_arguments(X17,X18,X15),X14) = apply_to_two_arguments(X17,X18,apply_to_two_arguments(X17,X15,X14)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_237])])]) ).

fof(c_0_446,plain,
    ! [X3,X4] :
      ( ~ member(X3,rotate_right(X4))
      | member(ordered_pair(f10(X3,X4),ordered_pair(f11(X3,X4),f9(X3,X4))),X4) ),
    inference(variable_rename,[status(thm)],[c_0_238]) ).

fof(c_0_447,plain,
    ! [X3,X4] :
      ( ~ member(X3,flip_range_of(X4))
      | member(ordered_pair(f12(X3,X4),ordered_pair(f14(X3,X4),f13(X3,X4))),X4) ),
    inference(variable_rename,[status(thm)],[c_0_239]) ).

fof(c_0_448,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X12,X13)),empty_set),X13)
      | member(f51(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_240])])]) ).

fof(c_0_449,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X12,X13)),empty_set),X13)
      | member(f52(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_241])])]) ).

fof(c_0_450,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | ~ member(ordered_pair(ordered_pair(empty_set,f50(X12,X13)),empty_set),X13)
      | member(f53(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_242])])]) ).

fof(c_0_451,plain,
    ! [X13,X14,X15,X16] :
      ( member(X13,plus)
      | ~ little_set(X13)
      | ~ member(X16,natural_numbers)
      | ~ member(X15,natural_numbers)
      | ~ member(X14,natural_numbers)
      | ~ member(ordered_pair(ordered_pair(X16,X15),X14),f49(X13))
      | member(ordered_pair(ordered_pair(successor(X16),X15),successor(X14)),f49(X13)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_243])])]) ).

fof(c_0_452,plain,
    ! [X12,X13] :
      ( commutes(X12,X13)
      | apply_to_two_arguments(X13,f41(X12,X13),f42(X12,X13)) != apply_to_two_arguments(X13,f42(X12,X13),f41(X12,X13)) ),
    inference(variable_rename,[status(thm)],[c_0_244]) ).

fof(c_0_453,plain,
    ! [X12,X13] :
      ( ~ group(X12,X13)
      | inverse(X12,X13,f39(X12,X13),f40(X12,X13)) ),
    inference(variable_rename,[status(thm)],[c_0_245]) ).

fof(c_0_454,plain,
    ! [X5,X6,X7] :
      ( ~ member(X5,image(X7,X6))
      | member(first(f22(X5,X7,X6)),X7) ),
    inference(variable_rename,[status(thm)],[c_0_246]) ).

fof(c_0_455,plain,
    ! [X14,X15,X16] :
      ( ~ member(X14,apply(X16,X15))
      | member(X14,second(f28(X14,X16,X15))) ),
    inference(variable_rename,[status(thm)],[c_0_247]) ).

fof(c_0_456,plain,
    ! [X15,X16,X17] :
      ( ~ member(X15,compose(X17,X16))
      | X15 = ordered_pair(f29(X15,X17,X16),f30(X15,X17,X16)) ),
    inference(variable_rename,[status(thm)],[c_0_248]) ).

fof(c_0_457,plain,
    ! [X22,X23,X24,X25,X26] :
      ( member(X22,rotate_right(X23))
      | ~ little_set(X22)
      | ~ little_set(X26)
      | ~ little_set(X25)
      | ~ little_set(X24)
      | X22 != ordered_pair(X26,ordered_pair(X25,X24))
      | ~ member(ordered_pair(X25,ordered_pair(X24,X26)),X23) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_249])])]) ).

fof(c_0_458,plain,
    ! [X22,X23,X24,X25,X26] :
      ( member(X22,flip_range_of(X23))
      | ~ little_set(X22)
      | ~ little_set(X26)
      | ~ little_set(X25)
      | ~ little_set(X24)
      | X22 != ordered_pair(X26,ordered_pair(X25,X24))
      | ~ member(ordered_pair(X26,ordered_pair(X24,X25)),X23) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_250])])]) ).

fof(c_0_459,plain,
    ! [X22,X23,X24,X25,X26,X27] :
      ( member(X22,compose(X25,X24))
      | ~ little_set(X22)
      | ~ little_set(X26)
      | ~ little_set(X23)
      | ~ little_set(X27)
      | X22 != ordered_pair(X26,X23)
      | ~ member(ordered_pair(X26,X27),X25)
      | ~ member(ordered_pair(X27,X23),X24) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_251])])]) ).

fof(c_0_460,plain,
    ! [X3,X4] :
      ( ~ member(X3,rotate_right(X4))
      | X3 = ordered_pair(f9(X3,X4),ordered_pair(f10(X3,X4),f11(X3,X4))) ),
    inference(variable_rename,[status(thm)],[c_0_252]) ).

fof(c_0_461,plain,
    ! [X3,X4] :
      ( ~ member(X3,flip_range_of(X4))
      | X3 = ordered_pair(f12(X3,X4),ordered_pair(f13(X3,X4),f14(X3,X4))) ),
    inference(variable_rename,[status(thm)],[c_0_253]) ).

fof(c_0_462,plain,
    ! [X16,X17,X18] :
      ( identity(X16,X17,X18)
      | ~ member(X18,X16)
      | member(f37(X16,X17,X18),X16) ),
    inference(variable_rename,[status(thm)],[c_0_254]) ).

fof(c_0_463,plain,
    ! [X7,X8,X9] :
      ( ~ member(X7,prime_numbers)
      | ~ member(X9,natural_numbers)
      | ~ member(X8,natural_numbers)
      | apply_to_two_arguments(times,X9,X8) != X7
      | member(X9,non_ordered_pair(successor(empty_set),X7)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_255])])]) ).

fof(c_0_464,plain,
    ! [X5,X6,X7] :
      ( ~ member(X5,image(X7,X6))
      | member(f22(X5,X7,X6),X6) ),
    inference(variable_rename,[status(thm)],[c_0_256]) ).

fof(c_0_465,plain,
    ! [X14,X15,X16] :
      ( ~ member(X14,apply(X16,X15))
      | member(f28(X14,X16,X15),X16) ),
    inference(variable_rename,[status(thm)],[c_0_257]) ).

fof(c_0_466,plain,
    ! [X14,X15,X16,X17] :
      ( ~ commutes(X15,X16)
      | ~ member(X17,X15)
      | ~ member(X14,X15)
      | apply_to_two_arguments(X16,X17,X14) = apply_to_two_arguments(X16,X14,X17) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_258])])]) ).

fof(c_0_467,plain,
    ! [X12,X13] :
      ( ~ member(X12,natural_numbers)
      | ~ little_set(X13)
      | ~ member(empty_set,X13)
      | ~ member(successor(f43(X12,X13)),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_259])])]) ).

fof(c_0_468,plain,
    ! [X5,X6,X7] :
      ( ~ member(X5,image(X7,X6))
      | second(f22(X5,X7,X6)) = X5 ),
    inference(variable_rename,[status(thm)],[c_0_260]) ).

fof(c_0_469,plain,
    ! [X14,X15,X16] :
      ( ~ member(X14,apply(X16,X15))
      | first(f28(X14,X16,X15)) = X15 ),
    inference(variable_rename,[status(thm)],[c_0_261]) ).

fof(c_0_470,plain,
    ! [X5,X6,X7] :
      ( ~ member(X5,image(X7,X6))
      | ordered_pair_predicate(f22(X5,X7,X6)) ),
    inference(variable_rename,[status(thm)],[c_0_262]) ).

fof(c_0_471,plain,
    ! [X14,X15,X16] :
      ( ~ member(X14,apply(X16,X15))
      | ordered_pair_predicate(f28(X14,X16,X15)) ),
    inference(variable_rename,[status(thm)],[c_0_263]) ).

fof(c_0_472,plain,
    ! [X15,X16,X17] :
      ( ~ member(X15,compose(X17,X16))
      | little_set(f29(X15,X17,X16)) ),
    inference(variable_rename,[status(thm)],[c_0_264]) ).

fof(c_0_473,plain,
    ! [X15,X16,X17] :
      ( ~ member(X15,compose(X17,X16))
      | little_set(f30(X15,X17,X16)) ),
    inference(variable_rename,[status(thm)],[c_0_265]) ).

fof(c_0_474,plain,
    ! [X15,X16,X17] :
      ( ~ member(X15,compose(X17,X16))
      | little_set(f31(X15,X17,X16)) ),
    inference(variable_rename,[status(thm)],[c_0_266]) ).

fof(c_0_475,plain,
    ! [X16,X17,X18,X19] :
      ( ~ identity(X16,X17,X18)
      | ~ member(X19,X16)
      | apply_to_two_arguments(X17,X18,X19) = X19 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_267])])]) ).

fof(c_0_476,plain,
    ! [X16,X17,X18,X19] :
      ( ~ identity(X16,X17,X18)
      | ~ member(X19,X16)
      | apply_to_two_arguments(X17,X19,X18) = X19 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_268])])]) ).

fof(c_0_477,plain,
    ! [X22,X23,X24,X25] :
      ( ~ single_valued_set(X22)
      | ~ little_set(X25)
      | ~ little_set(X24)
      | ~ little_set(X23)
      | ~ member(ordered_pair(X25,X24),X22)
      | ~ member(ordered_pair(X25,X23),X22)
      | X24 = X23 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_269])])]) ).

fof(c_0_478,plain,
    ! [X12,X13] :
      ( closed(X12,X13)
      | ~ little_set(X12)
      | ~ little_set(X13)
      | ~ maps(X13,cross_product(X12,X12),X12) ),
    inference(variable_rename,[status(thm)],[c_0_270]) ).

fof(c_0_479,plain,
    ! [X3,X4] :
      ( member(X3,even_numbers)
      | ~ member(X3,natural_numbers)
      | ~ member(X4,natural_numbers)
      | apply_to_two_arguments(plus,X4,X4) != X3 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_271])])]) ).

fof(c_0_480,plain,
    ! [X3,X4] :
      ( member(X3,converse(X4))
      | ~ little_set(X3)
      | ~ ordered_pair_predicate(X3)
      | ~ member(ordered_pair(second(X3),first(X3)),X4) ),
    inference(variable_rename,[status(thm)],[c_0_272]) ).

fof(c_0_481,plain,
    ! [X11,X12] :
      ( member(X11,plus)
      | ~ little_set(X11)
      | ~ member(X12,natural_numbers)
      | member(ordered_pair(ordered_pair(empty_set,X12),X12),f49(X11)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_273])])]) ).

fof(c_0_482,plain,
    ! [X11,X12] :
      ( member(X11,times)
      | ~ little_set(X11)
      | ~ member(X12,natural_numbers)
      | member(ordered_pair(ordered_pair(empty_set,X12),empty_set),f54(X11)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_274])])]) ).

fof(c_0_483,plain,
    ! [X14,X15] :
      ( ~ member(f1(X15,X14),X15)
      | ~ member(f1(X15,X14),X14)
      | X15 = X14 ),
    inference(variable_rename,[status(thm)],[c_0_275]) ).

fof(c_0_484,plain,
    ! [X5,X6,X7] :
      ( finite(X7)
      | ~ member(X5,natural_numbers)
      | ~ maps(X6,X5,X7)
      | range_of(X6) != X7
      | ~ one_to_one_function(X6) ),
    inference(variable_rename,[status(thm)],[c_0_276]) ).

fof(c_0_485,plain,
    ! [X2] :
      ( member(X2,prime_numbers)
      | ~ member(X2,natural_numbers)
      | X2 = empty_set
      | X2 = successor(empty_set)
      | ~ member(f55(X2),non_ordered_pair(successor(empty_set),X2)) ),
    inference(variable_rename,[status(thm)],[c_0_277]) ).

fof(c_0_486,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | member(f45(X12,X13),natural_numbers)
      | member(f46(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_278])])]) ).

fof(c_0_487,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | member(f45(X12,X13),natural_numbers)
      | member(f47(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_279])])]) ).

fof(c_0_488,plain,
    ! [X12,X13] :
      ( ~ member(X12,plus)
      | ~ little_set(X13)
      | member(f45(X12,X13),natural_numbers)
      | member(f48(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_280])])]) ).

fof(c_0_489,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | member(f50(X12,X13),natural_numbers)
      | member(f51(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_281])])]) ).

fof(c_0_490,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | member(f50(X12,X13),natural_numbers)
      | member(f52(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_282])])]) ).

fof(c_0_491,plain,
    ! [X12,X13] :
      ( ~ member(X12,times)
      | ~ little_set(X13)
      | member(f50(X12,X13),natural_numbers)
      | member(f53(X12,X13),natural_numbers)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_283])])]) ).

fof(c_0_492,plain,
    ! [X14,X15,X16] :
      ( member(X14,cross_product(X16,X15))
      | ~ little_set(X14)
      | ~ ordered_pair_predicate(X14)
      | ~ member(first(X14),X16)
      | ~ member(second(X14),X15) ),
    inference(variable_rename,[status(thm)],[c_0_284]) ).

fof(c_0_493,plain,
    ! [X14,X15,X16,X17] :
      ( member(X14,image(X17,X16))
      | ~ little_set(X14)
      | ~ ordered_pair_predicate(X15)
      | ~ member(X15,X16)
      | ~ member(first(X15),X17)
      | second(X15) != X14 ),
    inference(variable_rename,[status(thm)],[c_0_285]) ).

fof(c_0_494,plain,
    ! [X22,X23,X24,X25] :
      ( member(X22,apply(X24,X23))
      | ~ ordered_pair_predicate(X25)
      | ~ member(X25,X24)
      | first(X25) != X23
      | ~ member(X22,second(X25)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_286])])]) ).

fof(c_0_495,plain,
    ! [X14,X15,X16] :
      ( ~ maps(X15,X16,X14)
      | subset(range_of(X15),X14) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_287])])]) ).

fof(c_0_496,plain,
    ! [X2] :
      ( member(X2,prime_numbers)
      | ~ member(X2,natural_numbers)
      | X2 = empty_set
      | X2 = successor(empty_set)
      | apply_to_two_arguments(times,f55(X2),f56(X2)) = X2 ),
    inference(variable_rename,[status(thm)],[c_0_288]) ).

fof(c_0_497,plain,
    ! [X12,X13] :
      ( ~ closed(X12,X13)
      | maps(X13,cross_product(X12,X12),X12) ),
    inference(variable_rename,[status(thm)],[c_0_289]) ).

fof(c_0_498,plain,
    ! [X12,X13] :
      ( ~ group(X12,X13)
      | identity(X12,X13,f39(X12,X13)) ),
    inference(variable_rename,[status(thm)],[c_0_290]) ).

fof(c_0_499,plain,
    ! [X14,X15,X16] :
      ( maps(X15,X16,X14)
      | ~ function(X15)
      | domain_of(X15) != X16
      | ~ subset(range_of(X15),X14) ),
    inference(variable_rename,[status(thm)],[c_0_291]) ).

fof(c_0_500,plain,
    ! [X12,X13] :
      ( ~ member(X12,natural_numbers)
      | ~ little_set(X13)
      | ~ member(empty_set,X13)
      | member(f43(X12,X13),X13)
      | member(X12,X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_292])])]) ).

fof(c_0_501,plain,
    ! [X16,X17,X18] :
      ( ~ identity(X16,X17,X18)
      | member(X18,X16) ),
    inference(variable_rename,[status(thm)],[c_0_293]) ).

fof(c_0_502,plain,
    ! [X3,X4] :
      ( ~ member(X3,first(X4))
      | X4 = ordered_pair(f4(X3,X4),f5(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_294]) ).

fof(c_0_503,plain,
    ! [X3,X4] :
      ( ~ member(X3,second(X4))
      | X4 = ordered_pair(f6(X3,X4),f7(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_295]) ).

fof(c_0_504,plain,
    ! [X3,X4] :
      ( ~ member(X3,converse(X4))
      | member(ordered_pair(second(X3),first(X3)),X4) ),
    inference(variable_rename,[status(thm)],[c_0_296]) ).

fof(c_0_505,plain,
    ! [X14,X15,X16] :
      ( ~ maps(X15,X16,X14)
      | domain_of(X15) = X16 ),
    inference(variable_rename,[status(thm)],[c_0_297]) ).

fof(c_0_506,plain,
    ! [X14,X15,X16] :
      ( ~ maps(X15,X16,X14)
      | function(X15) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_298])])]) ).

fof(c_0_507,plain,
    ! [X2] :
      ( ~ member(X2,even_numbers)
      | apply_to_two_arguments(plus,f59(X2),f59(X2)) = X2 ),
    inference(variable_rename,[status(thm)],[c_0_299]) ).

fof(c_0_508,plain,
    ! [X14,X15,X16] :
      ( member(X14,intersection(X16,X15))
      | ~ member(X14,X16)
      | ~ member(X14,X15) ),
    inference(variable_rename,[status(thm)],[c_0_300]) ).

fof(c_0_509,plain,
    ! [X14,X15,X16] :
      ( ~ member(X14,cross_product(X16,X15))
      | member(first(X14),X16) ),
    inference(variable_rename,[status(thm)],[c_0_301]) ).

fof(c_0_510,plain,
    ! [X14,X15,X16] :
      ( ~ member(X14,cross_product(X16,X15))
      | member(second(X14),X15) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_302])])]) ).

fof(c_0_511,plain,
    ! [X14,X15] :
      ( member(f1(X15,X14),X15)
      | member(f1(X15,X14),X14)
      | X15 = X14 ),
    inference(variable_rename,[status(thm)],[c_0_303]) ).

fof(c_0_512,plain,
    ! [X2] :
      ( member(X2,twin_prime_numbers)
      | ~ member(X2,prime_numbers)
      | ~ member(successor(successor(X2)),prime_numbers) ),
    inference(variable_rename,[status(thm)],[c_0_304]) ).

fof(c_0_513,plain,
    ! [X7,X8,X9,X10] :
      ( member(X7,first(X8))
      | ~ little_set(X10)
      | ~ little_set(X9)
      | X8 != ordered_pair(X10,X9)
      | ~ member(X7,X10) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_305])])]) ).

fof(c_0_514,plain,
    ! [X7,X8,X9,X10] :
      ( member(X7,second(X8))
      | ~ little_set(X10)
      | ~ little_set(X9)
      | X8 != ordered_pair(X10,X9)
      | ~ member(X7,X9) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_306])])]) ).

fof(c_0_515,plain,
    ! [X8,X9] :
      ( member(X8,natural_numbers)
      | ~ little_set(X8)
      | ~ member(X9,f44(X8))
      | member(successor(X9),f44(X8)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_307])])]) ).

fof(c_0_516,plain,
    ! [X14,X15,X16] :
      ( ~ member(X14,intersection(X16,X15))
      | member(X14,X16) ),
    inference(variable_rename,[status(thm)],[c_0_308]) ).

fof(c_0_517,plain,
    ! [X14,X15,X16] :
      ( ~ member(X14,intersection(X16,X15))
      | member(X14,X15) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_309])])]) ).

fof(c_0_518,plain,
    ! [X14,X15] :
      ( subset(X15,X14)
      | ~ member(f17(X15,X14),X14) ),
    inference(variable_rename,[status(thm)],[c_0_310]) ).

fof(c_0_519,plain,
    ! [X3] :
      ( ~ finite(X3)
      | maps(f58(X3),f57(X3),X3) ),
    inference(variable_rename,[status(thm)],[c_0_311]) ).

fof(c_0_520,plain,
    ! [X3,X4] :
      ( ~ member(X3,first(X4))
      | member(X3,f4(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_312]) ).

fof(c_0_521,plain,
    ! [X3,X4] :
      ( ~ member(X3,second(X4))
      | member(X3,f7(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_313]) ).

fof(c_0_522,plain,
    ! [X3,X4] :
      ( ~ member(X3,domain_of(X4))
      | member(f8(X3,X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_314]) ).

fof(c_0_523,plain,
    ! [X3,X4] :
      ( ~ member(X3,sigma(X4))
      | member(f16(X3,X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_315]) ).

fof(c_0_524,plain,
    ! [X3,X4] :
      ( ~ member(X3,sigma(X4))
      | member(X3,f16(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_316]) ).

fof(c_0_525,plain,
    ! [X3,X4] :
      ( ~ member(X3,range_of(X4))
      | member(f27(X3,X4),X4) ),
    inference(variable_rename,[status(thm)],[c_0_317]) ).

fof(c_0_526,plain,
    ! [X3] :
      ( single_valued_set(X3)
      | member(ordered_pair(f19(X3),f20(X3)),X3) ),
    inference(variable_rename,[status(thm)],[c_0_318]) ).

fof(c_0_527,plain,
    ! [X3] :
      ( single_valued_set(X3)
      | member(ordered_pair(f19(X3),f21(X3)),X3) ),
    inference(variable_rename,[status(thm)],[c_0_319]) ).

fof(c_0_528,plain,
    ! [X2] :
      ( member(X2,estin)
      | ~ little_set(X2)
      | ~ ordered_pair_predicate(X2)
      | ~ member(first(X2),second(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_320]) ).

fof(c_0_529,plain,
    ! [X14,X15,X16] :
      ( ~ disjoint(X15,X14)
      | ~ member(X16,X15)
      | ~ member(X16,X14) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_321])])]) ).

fof(c_0_530,plain,
    ! [X14,X15,X16] :
      ( ~ member(X16,non_ordered_pair(X15,X14))
      | X16 = X15
      | X16 = X14 ),
    inference(variable_rename,[status(thm)],[c_0_322]) ).

fof(c_0_531,plain,
    ! [X14,X15,X16] :
      ( ~ member(X14,cross_product(X16,X15))
      | ordered_pair_predicate(X14) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_323])])]) ).

fof(c_0_532,plain,
    ! [X23,X24,X25] :
      ( member(X23,domain_of(X25))
      | ~ little_set(X23)
      | ~ ordered_pair_predicate(X24)
      | ~ member(X24,X25)
      | X23 != first(X24) ),
    inference(variable_rename,[status(thm)],[c_0_324]) ).

fof(c_0_533,plain,
    ! [X14,X15,X16] :
      ( member(X14,sigma(X16))
      | ~ member(X15,X16)
      | ~ member(X14,X15) ),
    inference(variable_rename,[status(thm)],[c_0_325]) ).

fof(c_0_534,plain,
    ! [X23,X24,X25] :
      ( member(X23,range_of(X25))
      | ~ little_set(X23)
      | ~ ordered_pair_predicate(X24)
      | ~ member(X24,X25)
      | X23 != second(X24) ),
    inference(variable_rename,[status(thm)],[c_0_326]) ).

fof(c_0_535,plain,
    ! [X3,X4] :
      ( ~ member(X3,domain_of(X4))
      | X3 = first(f8(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_327]) ).

fof(c_0_536,plain,
    ! [X3,X4] :
      ( ~ member(X3,range_of(X4))
      | X3 = second(f27(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_328]) ).

fof(c_0_537,plain,
    ! [X3,X4] :
      ( ~ member(X3,first(X4))
      | little_set(f4(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_329]) ).

fof(c_0_538,plain,
    ! [X3,X4] :
      ( ~ member(X3,first(X4))
      | little_set(f5(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_330]) ).

fof(c_0_539,plain,
    ! [X3,X4] :
      ( ~ member(X3,second(X4))
      | little_set(f6(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_331]) ).

fof(c_0_540,plain,
    ! [X3,X4] :
      ( ~ member(X3,second(X4))
      | little_set(f7(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_332]) ).

fof(c_0_541,plain,
    ! [X3,X4] :
      ( ~ member(X3,domain_of(X4))
      | ordered_pair_predicate(f8(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_333]) ).

fof(c_0_542,plain,
    ! [X3,X4] :
      ( ~ member(X3,rotate_right(X4))
      | little_set(f9(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_334]) ).

fof(c_0_543,plain,
    ! [X3,X4] :
      ( ~ member(X3,rotate_right(X4))
      | little_set(f10(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_335]) ).

fof(c_0_544,plain,
    ! [X3,X4] :
      ( ~ member(X3,rotate_right(X4))
      | little_set(f11(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_336]) ).

fof(c_0_545,plain,
    ! [X3,X4] :
      ( ~ member(X3,flip_range_of(X4))
      | little_set(f12(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_337]) ).

fof(c_0_546,plain,
    ! [X3,X4] :
      ( ~ member(X3,flip_range_of(X4))
      | little_set(f13(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_338]) ).

fof(c_0_547,plain,
    ! [X3,X4] :
      ( ~ member(X3,flip_range_of(X4))
      | little_set(f14(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_339]) ).

fof(c_0_548,plain,
    ! [X3,X4] :
      ( ~ member(X3,range_of(X4))
      | ordered_pair_predicate(f27(X3,X4)) ),
    inference(variable_rename,[status(thm)],[c_0_340]) ).

fof(c_0_549,plain,
    ! [X14,X15,X16] :
      ( ~ subset(X15,X14)
      | ~ member(X16,X15)
      | member(X16,X14) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_341])])]) ).

fof(c_0_550,plain,
    ! [X3] :
      ( ~ little_set(X3)
      | X3 = empty_set
      | member(ordered_pair(X3,f26(X3)),f25) ),
    inference(variable_rename,[status(thm)],[c_0_342]) ).

fof(c_0_551,plain,
    ! [X2] :
      ( member(X2,prime_numbers)
      | ~ member(X2,natural_numbers)
      | X2 = empty_set
      | X2 = successor(empty_set)
      | member(f55(X2),natural_numbers) ),
    inference(variable_rename,[status(thm)],[c_0_343]) ).

fof(c_0_552,plain,
    ! [X2] :
      ( member(X2,prime_numbers)
      | ~ member(X2,natural_numbers)
      | X2 = empty_set
      | X2 = successor(empty_set)
      | member(f56(X2),natural_numbers) ),
    inference(variable_rename,[status(thm)],[c_0_344]) ).

fof(c_0_553,plain,
    ! [X3,X4] :
      ( ~ member(X3,complement(X4))
      | ~ member(X3,X4) ),
    inference(variable_rename,[status(thm)],[c_0_345]) ).

fof(c_0_554,plain,
    ! [X14,X15] :
      ( subset(X15,X14)
      | member(f17(X15,X14),X15) ),
    inference(variable_rename,[status(thm)],[c_0_346]) ).

fof(c_0_555,plain,
    ! [X14,X15] :
      ( disjoint(X15,X14)
      | member(f23(X15,X14),X15) ),
    inference(variable_rename,[status(thm)],[c_0_347]) ).

fof(c_0_556,plain,
    ! [X14,X15] :
      ( disjoint(X15,X14)
      | member(f23(X15,X14),X14) ),
    inference(variable_rename,[status(thm)],[c_0_348]) ).

fof(c_0_557,plain,
    ! [X12,X13] :
      ( associative(X12,X13)
      | member(f34(X12,X13),X12) ),
    inference(variable_rename,[status(thm)],[c_0_349]) ).

fof(c_0_558,plain,
    ! [X12,X13] :
      ( associative(X12,X13)
      | member(f35(X12,X13),X12) ),
    inference(variable_rename,[status(thm)],[c_0_350]) ).

fof(c_0_559,plain,
    ! [X12,X13] :
      ( associative(X12,X13)
      | member(f36(X12,X13),X12) ),
    inference(variable_rename,[status(thm)],[c_0_351]) ).

fof(c_0_560,plain,
    ! [X12,X13] :
      ( commutes(X12,X13)
      | member(f41(X12,X13),X12) ),
    inference(variable_rename,[status(thm)],[c_0_352]) ).

fof(c_0_561,plain,
    ! [X12,X13] :
      ( commutes(X12,X13)
      | member(f42(X12,X13),X12) ),
    inference(variable_rename,[status(thm)],[c_0_353]) ).

fof(c_0_562,plain,
    ! [X2] :
      ( ~ member(X2,twin_prime_numbers)
      | member(successor(successor(X2)),prime_numbers) ),
    inference(variable_rename,[status(thm)],[c_0_354]) ).

fof(c_0_563,plain,
    ! [X14,X15,X16] :
      ( member(X16,non_ordered_pair(X15,X14))
      | ~ little_set(X16)
      | X16 != X15 ),
    inference(variable_rename,[status(thm)],[c_0_355]) ).

fof(c_0_564,plain,
    ! [X14,X15,X16] :
      ( member(X16,non_ordered_pair(X15,X14))
      | ~ little_set(X16)
      | X16 != X14 ),
    inference(variable_rename,[status(thm)],[c_0_356]) ).

fof(c_0_565,plain,
    ! [X3,X4] :
      ( member(X3,powerset(X4))
      | ~ little_set(X3)
      | ~ subset(X3,X4) ),
    inference(variable_rename,[status(thm)],[c_0_357]) ).

fof(c_0_566,plain,
    ! [X2] :
      ( ~ member(X2,estin)
      | member(first(X2),second(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_358]) ).

fof(c_0_567,plain,
    ! [X3,X4] :
      ( ~ member(X3,powerset(X4))
      | subset(X3,X4) ),
    inference(variable_rename,[status(thm)],[c_0_359]) ).

fof(c_0_568,plain,
    ! [X2] :
      ( member(X2,natural_numbers)
      | ~ member(X2,f44(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_360]) ).

fof(c_0_569,plain,
    ! [X2] :
      ( member(X2,plus)
      | ~ member(X2,f49(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_361]) ).

fof(c_0_570,plain,
    ! [X2] :
      ( member(X2,times)
      | ~ member(X2,f54(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_362]) ).

fof(c_0_571,plain,
    ! [X5,X6] :
      ( ~ little_set(X6)
      | ~ function(X5)
      | little_set(image(X6,X5)) ),
    inference(variable_rename,[status(thm)],[c_0_363]) ).

fof(c_0_572,plain,
    ! [X14,X15,X16] :
      ( ordered_pair_predicate(X16)
      | ~ little_set(X15)
      | ~ little_set(X14)
      | X16 != ordered_pair(X15,X14) ),
    inference(variable_rename,[status(thm)],[c_0_364]) ).

fof(c_0_573,plain,
    ! [X3,X4] :
      ( member(X3,complement(X4))
      | ~ little_set(X3)
      | member(X3,X4) ),
    inference(variable_rename,[status(thm)],[c_0_365]) ).

fof(c_0_574,plain,
    ! [X2] :
      ( member(X2,identity_relation)
      | ~ little_set(X2)
      | ~ ordered_pair_predicate(X2)
      | first(X2) != second(X2) ),
    inference(variable_rename,[status(thm)],[c_0_366]) ).

fof(c_0_575,plain,
    ! [X14,X15] :
      ( proper_subset(X15,X14)
      | ~ subset(X15,X14)
      | X15 = X14 ),
    inference(variable_rename,[status(thm)],[c_0_367]) ).

fof(c_0_576,plain,
    ! [X3] :
      ( ~ member(X3,infinity)
      | member(successor(X3),infinity) ),
    inference(variable_rename,[status(thm)],[c_0_368]) ).

fof(c_0_577,plain,
    ! [X2] :
      ( ~ member(X2,even_numbers)
      | member(f59(X2),natural_numbers) ),
    inference(variable_rename,[status(thm)],[c_0_369]) ).

fof(c_0_578,plain,
    ! [X2] :
      ( member(X2,natural_numbers)
      | ~ little_set(X2)
      | member(empty_set,f44(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_370]) ).

fof(c_0_579,plain,
    ! [X14,X15] :
      ( ~ proper_subset(X15,X14)
      | subset(X15,X14) ),
    inference(variable_rename,[status(thm)],[c_0_371]) ).

fof(c_0_580,plain,
    ! [X12,X13] :
      ( ~ group(X12,X13)
      | closed(X12,X13) ),
    inference(variable_rename,[status(thm)],[c_0_372]) ).

fof(c_0_581,plain,
    ! [X12,X13] :
      ( ~ group(X12,X13)
      | associative(X12,X13) ),
    inference(variable_rename,[status(thm)],[c_0_373]) ).

fof(c_0_582,plain,
    ! [X3,X4] :
      ( ~ member(X3,converse(X4))
      | ordered_pair_predicate(X3) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_374])])]) ).

fof(c_0_583,plain,
    ! [X3] :
      ( ~ ordered_pair_predicate(X3)
      | X3 = ordered_pair(f2(X3),f3(X3)) ),
    inference(variable_rename,[status(thm)],[c_0_375]) ).

fof(c_0_584,plain,
    ! [X3,X4] :
      ( ~ relation(X3)
      | ~ member(X4,X3)
      | ordered_pair_predicate(X4) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_376])])]) ).

fof(c_0_585,plain,
    ! [X2] :
      ( ~ member(X2,prime_numbers)
      | member(X2,natural_numbers) ),
    inference(variable_rename,[status(thm)],[c_0_377]) ).

fof(c_0_586,plain,
    ! [X2] :
      ( ~ member(X2,twin_prime_numbers)
      | member(X2,prime_numbers) ),
    inference(variable_rename,[status(thm)],[c_0_378]) ).

fof(c_0_587,plain,
    ! [X2] :
      ( ~ member(X2,even_numbers)
      | member(X2,natural_numbers) ),
    inference(variable_rename,[status(thm)],[c_0_379]) ).

fof(c_0_588,plain,
    ! [X14,X15] :
      ( little_set(f1(X15,X14))
      | X15 = X14 ),
    inference(variable_rename,[status(thm)],[c_0_380]) ).

fof(c_0_589,plain,
    ! [X2] :
      ( member(X2,natural_numbers)
      | ~ little_set(X2)
      | little_set(f44(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_381]) ).

fof(c_0_590,plain,
    ! [X2] :
      ( member(X2,plus)
      | ~ little_set(X2)
      | little_set(f49(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_382]) ).

fof(c_0_591,plain,
    ! [X2] :
      ( member(X2,times)
      | ~ little_set(X2)
      | little_set(f54(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_383]) ).

fof(c_0_592,plain,
    ! [X3] :
      ( ~ little_set(X3)
      | X3 = empty_set
      | member(f26(X3),X3) ),
    inference(variable_rename,[status(thm)],[c_0_384]) ).

fof(c_0_593,plain,
    ! [X2] :
      ( ~ member(X2,identity_relation)
      | first(X2) = second(X2) ),
    inference(variable_rename,[status(thm)],[c_0_385]) ).

fof(c_0_594,plain,
    ! [X5] :
      ( one_to_one_function(X5)
      | ~ function(X5)
      | ~ function(converse(X5)) ),
    inference(variable_rename,[status(thm)],[c_0_386]) ).

fof(c_0_595,plain,
    ! [X14,X15] :
      ( ~ member(X15,X14)
      | little_set(X15) ),
    inference(variable_rename,[status(thm)],[c_0_387]) ).

fof(c_0_596,plain,
    ! [X12,X13] :
      ( ~ closed(X12,X13)
      | little_set(X12) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_388])])]) ).

fof(c_0_597,plain,
    ! [X12,X13] :
      ( ~ closed(X12,X13)
      | little_set(X13) ),
    inference(variable_rename,[status(thm)],[c_0_389]) ).

fof(c_0_598,plain,
    ! [X14,X15] :
      ( ~ proper_subset(X15,X14)
      | X15 != X14 ),
    inference(variable_rename,[status(thm)],[c_0_390]) ).

fof(c_0_599,plain,
    ! [X2] :
      ( ~ member(X2,prime_numbers)
      | X2 != successor(empty_set) ),
    inference(variable_rename,[status(thm)],[c_0_391]) ).

fof(c_0_600,plain,
    ! [X3] :
      ( ~ finite(X3)
      | member(f57(X3),natural_numbers) ),
    inference(variable_rename,[status(thm)],[c_0_392]) ).

fof(c_0_601,plain,
    ! [X2] :
      ( relation(X2)
      | member(f18(X2),X2) ),
    inference(variable_rename,[status(thm)],[c_0_393]) ).

fof(c_0_602,plain,
    ! [X2] :
      ( ~ member(X2,estin)
      | ordered_pair_predicate(X2) ),
    inference(variable_rename,[status(thm)],[c_0_394]) ).

fof(c_0_603,plain,
    ! [X2] :
      ( ~ member(X2,identity_relation)
      | ordered_pair_predicate(X2) ),
    inference(variable_rename,[status(thm)],[c_0_395]) ).

fof(c_0_604,plain,
    ! [X2] :
      ( ~ member(X2,prime_numbers)
      | X2 != empty_set ),
    inference(variable_rename,[status(thm)],[c_0_396]) ).

fof(c_0_605,plain,
    ! [X3] :
      ( X3 = empty_set
      | member(f24(X3),X3) ),
    inference(variable_rename,[status(thm)],[c_0_397]) ).

fof(c_0_606,plain,
    ! [X3] :
      ( X3 = empty_set
      | disjoint(f24(X3),X3) ),
    inference(variable_rename,[status(thm)],[c_0_398]) ).

fof(c_0_607,plain,
    ! [X2] :
      ( relation(X2)
      | ~ ordered_pair_predicate(f18(X2)) ),
    inference(variable_rename,[status(thm)],[c_0_399]) ).

fof(c_0_608,plain,
    ! [X2] :
      ( member(X2,universal_set)
      | ~ little_set(X2) ),
    inference(variable_rename,[status(thm)],[c_0_400]) ).

fof(c_0_609,plain,
    ! [X5] :
      ( function(X5)
      | ~ relation(X5)
      | ~ single_valued_set(X5) ),
    inference(variable_rename,[status(thm)],[c_0_401]) ).

fof(c_0_610,plain,
    ! [X3] :
      ( ~ finite(X3)
      | range_of(f58(X3)) = X3 ),
    inference(variable_rename,[status(thm)],[c_0_402]) ).

fof(c_0_611,plain,
    ! [X3] :
      ( ~ ordered_pair_predicate(X3)
      | little_set(f2(X3)) ),
    inference(variable_rename,[status(thm)],[c_0_403]) ).

fof(c_0_612,plain,
    ! [X3] :
      ( ~ ordered_pair_predicate(X3)
      | little_set(f3(X3)) ),
    inference(variable_rename,[status(thm)],[c_0_404]) ).

fof(c_0_613,plain,
    ! [X7] :
      ( ~ little_set(X7)
      | little_set(sigma(X7)) ),
    inference(variable_rename,[status(thm)],[c_0_405]) ).

fof(c_0_614,plain,
    ! [X7] :
      ( ~ little_set(X7)
      | little_set(powerset(X7)) ),
    inference(variable_rename,[status(thm)],[c_0_406]) ).

fof(c_0_615,plain,
    ! [X5] :
      ( ~ one_to_one_function(X5)
      | function(converse(X5)) ),
    inference(variable_rename,[status(thm)],[c_0_407]) ).

fof(c_0_616,plain,
    ! [X3] :
      ( ~ finite(X3)
      | one_to_one_function(f58(X3)) ),
    inference(variable_rename,[status(thm)],[c_0_408]) ).

fof(c_0_617,plain,
    ! [X3] :
      ( single_valued_set(X3)
      | f20(X3) != f21(X3) ),
    inference(variable_rename,[status(thm)],[c_0_409]) ).

fof(c_0_618,plain,
    ! [X3] :
      ( single_valued_set(X3)
      | little_set(f19(X3)) ),
    inference(variable_rename,[status(thm)],[c_0_410]) ).

fof(c_0_619,plain,
    ! [X3] :
      ( single_valued_set(X3)
      | little_set(f20(X3)) ),
    inference(variable_rename,[status(thm)],[c_0_411]) ).

fof(c_0_620,plain,
    ! [X3] :
      ( single_valued_set(X3)
      | little_set(f21(X3)) ),
    inference(variable_rename,[status(thm)],[c_0_412]) ).

fof(c_0_621,plain,
    ! [X5] :
      ( ~ function(X5)
      | relation(X5) ),
    inference(variable_rename,[status(thm)],[c_0_413]) ).

fof(c_0_622,plain,
    ! [X5] :
      ( ~ function(X5)
      | single_valued_set(X5) ),
    inference(variable_rename,[status(thm)],[c_0_414]) ).

fof(c_0_623,plain,
    ! [X5] :
      ( ~ one_to_one_function(X5)
      | function(X5) ),
    inference(variable_rename,[status(thm)],[c_0_415]) ).

cnf(c_0_624,plain,
    ( homomorphism(X1,X3,X2,X4,X5)
    | apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
    | ~ maps(X1,X3,X4)
    | ~ closed(X4,X5)
    | ~ closed(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_416]) ).

cnf(c_0_625,plain,
    ( inverse(X2,X1,X3,X4)
    | apply_to_two_arguments(X1,f38(X2,X1,X3,X4),apply(X4,f38(X2,X1,X3,X4))) != X3
    | apply_to_two_arguments(X1,apply(X4,f38(X2,X1,X3,X4)),f38(X2,X1,X3,X4)) != X3
    | ~ maps(X4,X2,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_417]) ).

cnf(c_0_626,plain,
    ( member(f32(X1,X2,X3,X4,X5),X2)
    | homomorphism(X1,X2,X3,X4,X5)
    | ~ maps(X1,X2,X4)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_418]) ).

cnf(c_0_627,plain,
    ( member(f33(X1,X2,X3,X4,X5),X2)
    | homomorphism(X1,X2,X3,X4,X5)
    | ~ maps(X1,X2,X4)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_419]) ).

cnf(c_0_628,plain,
    ( apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
    | ~ member(X4,X6)
    | ~ member(X3,X6)
    | ~ homomorphism(X1,X6,X2,X7,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_420]) ).

cnf(c_0_629,plain,
    ( maps(X1,X2,X3)
    | ~ homomorphism(X1,X2,X4,X3,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_421]) ).

cnf(c_0_630,plain,
    ( closed(X1,X2)
    | ~ homomorphism(X3,X1,X2,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_422]) ).

cnf(c_0_631,plain,
    ( closed(X1,X2)
    | ~ homomorphism(X3,X4,X5,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_423]) ).

cnf(c_0_632,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_424]) ).

cnf(c_0_633,plain,
    ( member(X1,X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_425]) ).

cnf(c_0_634,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_426]) ).

cnf(c_0_635,plain,
    ( member(X1,X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_427]) ).

cnf(c_0_636,plain,
    ( associative(X2,X1)
    | apply_to_two_arguments(X1,apply_to_two_arguments(X1,f34(X2,X1),f35(X2,X1)),f36(X2,X1)) != apply_to_two_arguments(X1,f34(X2,X1),apply_to_two_arguments(X1,f35(X2,X1),f36(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_428]) ).

cnf(c_0_637,plain,
    ( member(f38(X1,X2,X3,X4),X1)
    | inverse(X1,X2,X3,X4)
    | ~ maps(X4,X1,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_429]) ).

cnf(c_0_638,plain,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_430]) ).

cnf(c_0_639,plain,
    ( identity(X2,X1,X3)
    | apply_to_two_arguments(X1,f37(X2,X1,X3),X3) != f37(X2,X1,X3)
    | apply_to_two_arguments(X1,X3,f37(X2,X1,X3)) != f37(X2,X1,X3)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_431]) ).

cnf(c_0_640,plain,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_432]) ).

cnf(c_0_641,plain,
    ( member(ordered_pair(ordered_pair(successor(X1),X2),apply_to_two_arguments(plus,X3,X2)),f54(X4))
    | member(X4,times)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f54(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_433]) ).

cnf(c_0_642,plain,
    ( group(X1,X2)
    | ~ inverse(X1,X2,X3,X4)
    | ~ identity(X1,X2,X3)
    | ~ associative(X1,X2)
    | ~ closed(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_434]) ).

cnf(c_0_643,plain,
    ( member(ordered_pair(f29(X1,X2,X3),f31(X1,X2,X3)),X2)
    | ~ member(X1,compose(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_435]) ).

cnf(c_0_644,plain,
    ( member(ordered_pair(f31(X1,X2,X3),f30(X1,X2,X3)),X3)
    | ~ member(X1,compose(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_436]) ).

cnf(c_0_645,plain,
    ( apply_to_two_arguments(X1,apply(X2,X3),X3) = X4
    | ~ member(X3,X5)
    | ~ inverse(X5,X1,X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_437]) ).

cnf(c_0_646,plain,
    ( apply_to_two_arguments(X1,X2,apply(X3,X2)) = X4
    | ~ member(X2,X5)
    | ~ inverse(X5,X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_438]) ).

cnf(c_0_647,plain,
    ( member(X1,X2)
    | member(f46(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_439]) ).

cnf(c_0_648,plain,
    ( member(X1,X2)
    | member(f47(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_440]) ).

cnf(c_0_649,plain,
    ( member(X1,X2)
    | member(f48(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_441]) ).

cnf(c_0_650,plain,
    ( maps(X1,X2,X2)
    | ~ inverse(X2,X3,X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_442]) ).

cnf(c_0_651,plain,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_443]) ).

cnf(c_0_652,plain,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_444]) ).

cnf(c_0_653,plain,
    ( apply_to_two_arguments(X1,apply_to_two_arguments(X1,X2,X3),X4) = apply_to_two_arguments(X1,X2,apply_to_two_arguments(X1,X3,X4))
    | ~ member(X4,X5)
    | ~ member(X3,X5)
    | ~ member(X2,X5)
    | ~ associative(X5,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_445]) ).

cnf(c_0_654,plain,
    ( member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2)
    | ~ member(X1,rotate_right(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_446]) ).

cnf(c_0_655,plain,
    ( member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2)
    | ~ member(X1,flip_range_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_447]) ).

cnf(c_0_656,plain,
    ( member(X1,X2)
    | member(f51(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_448]) ).

cnf(c_0_657,plain,
    ( member(X1,X2)
    | member(f52(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_449]) ).

cnf(c_0_658,plain,
    ( member(X1,X2)
    | member(f53(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_450]) ).

cnf(c_0_659,plain,
    ( member(ordered_pair(ordered_pair(successor(X1),X2),successor(X3)),f49(X4))
    | member(X4,plus)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f49(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_451]) ).

cnf(c_0_660,plain,
    ( commutes(X2,X1)
    | apply_to_two_arguments(X1,f41(X2,X1),f42(X2,X1)) != apply_to_two_arguments(X1,f42(X2,X1),f41(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_452]) ).

cnf(c_0_661,plain,
    ( inverse(X1,X2,f39(X1,X2),f40(X1,X2))
    | ~ group(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_453]) ).

cnf(c_0_662,plain,
    ( member(first(f22(X1,X2,X3)),X2)
    | ~ member(X1,image(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_454]) ).

cnf(c_0_663,plain,
    ( member(X1,second(f28(X1,X2,X3)))
    | ~ member(X1,apply(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_455]) ).

cnf(c_0_664,plain,
    ( X1 = ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_456]) ).

cnf(c_0_665,plain,
    ( member(X5,rotate_right(X4))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | X5 != ordered_pair(X3,ordered_pair(X1,X2))
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ little_set(X5) ),
    inference(split_conjunct,[status(thm)],[c_0_457]) ).

cnf(c_0_666,plain,
    ( member(X5,flip_range_of(X4))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | X5 != ordered_pair(X1,ordered_pair(X3,X2))
    | ~ little_set(X2)
    | ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X5) ),
    inference(split_conjunct,[status(thm)],[c_0_458]) ).

cnf(c_0_667,plain,
    ( member(X6,compose(X5,X3))
    | ~ member(ordered_pair(X1,X2),X3)
    | ~ member(ordered_pair(X4,X1),X5)
    | X6 != ordered_pair(X4,X2)
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ little_set(X4)
    | ~ little_set(X6) ),
    inference(split_conjunct,[status(thm)],[c_0_459]) ).

cnf(c_0_668,plain,
    ( X1 = ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2)))
    | ~ member(X1,rotate_right(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_460]) ).

cnf(c_0_669,plain,
    ( X1 = ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2)))
    | ~ member(X1,flip_range_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_461]) ).

cnf(c_0_670,plain,
    ( member(f37(X1,X2,X3),X1)
    | identity(X1,X2,X3)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_462]) ).

cnf(c_0_671,plain,
    ( member(X1,non_ordered_pair(successor(empty_set),X2))
    | apply_to_two_arguments(times,X1,X3) != X2
    | ~ member(X3,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ member(X2,prime_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_463]) ).

cnf(c_0_672,plain,
    ( member(f22(X1,X2,X3),X3)
    | ~ member(X1,image(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_464]) ).

cnf(c_0_673,plain,
    ( member(f28(X1,X2,X3),X2)
    | ~ member(X1,apply(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_465]) ).

cnf(c_0_674,plain,
    ( apply_to_two_arguments(X1,X2,X3) = apply_to_two_arguments(X1,X3,X2)
    | ~ member(X3,X4)
    | ~ member(X2,X4)
    | ~ commutes(X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_466]) ).

cnf(c_0_675,plain,
    ( member(X1,X2)
    | ~ member(successor(f43(X1,X2)),X2)
    | ~ member(empty_set,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_467]) ).

cnf(c_0_676,plain,
    ( second(f22(X1,X2,X3)) = X1
    | ~ member(X1,image(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_468]) ).

cnf(c_0_677,plain,
    ( first(f28(X1,X2,X3)) = X3
    | ~ member(X1,apply(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_469]) ).

cnf(c_0_678,plain,
    ( ordered_pair_predicate(f22(X1,X2,X3))
    | ~ member(X1,image(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_470]) ).

cnf(c_0_679,plain,
    ( ordered_pair_predicate(f28(X1,X2,X3))
    | ~ member(X1,apply(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_471]) ).

cnf(c_0_680,plain,
    ( little_set(f29(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_472]) ).

cnf(c_0_681,plain,
    ( little_set(f30(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_473]) ).

cnf(c_0_682,plain,
    ( little_set(f31(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_474]) ).

cnf(c_0_683,plain,
    ( apply_to_two_arguments(X1,X2,X3) = X3
    | ~ member(X3,X4)
    | ~ identity(X4,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_475]) ).

cnf(c_0_684,plain,
    ( apply_to_two_arguments(X1,X2,X3) = X2
    | ~ member(X2,X4)
    | ~ identity(X4,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_476]) ).

cnf(c_0_685,plain,
    ( X1 = X2
    | ~ member(ordered_pair(X3,X2),X4)
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ single_valued_set(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_477]) ).

cnf(c_0_686,plain,
    ( closed(X2,X1)
    | ~ maps(X1,cross_product(X2,X2),X2)
    | ~ little_set(X1)
    | ~ little_set(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_478]) ).

cnf(c_0_687,plain,
    ( member(X2,even_numbers)
    | apply_to_two_arguments(plus,X1,X1) != X2
    | ~ member(X1,natural_numbers)
    | ~ member(X2,natural_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_479]) ).

cnf(c_0_688,plain,
    ( member(X1,converse(X2))
    | ~ member(ordered_pair(second(X1),first(X1)),X2)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_480]) ).

cnf(c_0_689,plain,
    ( member(ordered_pair(ordered_pair(empty_set,X1),X1),f49(X2))
    | member(X2,plus)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_481]) ).

cnf(c_0_690,plain,
    ( member(ordered_pair(ordered_pair(empty_set,X1),empty_set),f54(X2))
    | member(X2,times)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_482]) ).

cnf(c_0_691,plain,
    ( X1 = X2
    | ~ member(f1(X1,X2),X2)
    | ~ member(f1(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_483]) ).

cnf(c_0_692,plain,
    ( finite(X2)
    | ~ one_to_one_function(X1)
    | range_of(X1) != X2
    | ~ maps(X1,X3,X2)
    | ~ member(X3,natural_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_484]) ).

cnf(c_0_693,plain,
    ( X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(f55(X1),non_ordered_pair(successor(empty_set),X1))
    | ~ member(X1,natural_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_485]) ).

cnf(c_0_694,plain,
    ( member(X1,X2)
    | member(f46(X1,X2),natural_numbers)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_486]) ).

cnf(c_0_695,plain,
    ( member(X1,X2)
    | member(f47(X1,X2),natural_numbers)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_487]) ).

cnf(c_0_696,plain,
    ( member(X1,X2)
    | member(f48(X1,X2),natural_numbers)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(split_conjunct,[status(thm)],[c_0_488]) ).

cnf(c_0_697,plain,
    ( member(X1,X2)
    | member(f51(X1,X2),natural_numbers)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_489]) ).

cnf(c_0_698,plain,
    ( member(X1,X2)
    | member(f52(X1,X2),natural_numbers)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_490]) ).

cnf(c_0_699,plain,
    ( member(X1,X2)
    | member(f53(X1,X2),natural_numbers)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(split_conjunct,[status(thm)],[c_0_491]) ).

cnf(c_0_700,plain,
    ( member(X1,cross_product(X3,X2))
    | ~ member(second(X1),X2)
    | ~ member(first(X1),X3)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_492]) ).

cnf(c_0_701,plain,
    ( member(X2,image(X3,X4))
    | second(X1) != X2
    | ~ member(first(X1),X3)
    | ~ member(X1,X4)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_493]) ).

cnf(c_0_702,plain,
    ( member(X1,apply(X4,X3))
    | ~ member(X1,second(X2))
    | first(X2) != X3
    | ~ member(X2,X4)
    | ~ ordered_pair_predicate(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_494]) ).

cnf(c_0_703,plain,
    ( subset(range_of(X1),X2)
    | ~ maps(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_495]) ).

cnf(c_0_704,plain,
    ( apply_to_two_arguments(times,f55(X1),f56(X1)) = X1
    | X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_496]) ).

cnf(c_0_705,plain,
    ( maps(X1,cross_product(X2,X2),X2)
    | ~ closed(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_497]) ).

cnf(c_0_706,plain,
    ( identity(X1,X2,f39(X1,X2))
    | ~ group(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_498]) ).

cnf(c_0_707,plain,
    ( maps(X1,X3,X2)
    | ~ subset(range_of(X1),X2)
    | domain_of(X1) != X3
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_499]) ).

cnf(c_0_708,plain,
    ( member(X1,X2)
    | member(f43(X1,X2),X2)
    | ~ member(empty_set,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_500]) ).

cnf(c_0_709,plain,
    ( member(X1,X2)
    | ~ identity(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_501]) ).

cnf(c_0_710,plain,
    ( X1 = ordered_pair(f4(X2,X1),f5(X2,X1))
    | ~ member(X2,first(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_502]) ).

cnf(c_0_711,plain,
    ( X1 = ordered_pair(f6(X2,X1),f7(X2,X1))
    | ~ member(X2,second(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_503]) ).

cnf(c_0_712,plain,
    ( member(ordered_pair(second(X1),first(X1)),X2)
    | ~ member(X1,converse(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_504]) ).

cnf(c_0_713,plain,
    ( domain_of(X1) = X2
    | ~ maps(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_505]) ).

cnf(c_0_714,plain,
    ( function(X1)
    | ~ maps(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_506]) ).

cnf(c_0_715,plain,
    ( apply_to_two_arguments(plus,f59(X1),f59(X1)) = X1
    | ~ member(X1,even_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_507]) ).

cnf(c_0_716,plain,
    ( member(X1,intersection(X3,X2))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_508]) ).

cnf(c_0_717,plain,
    ( member(first(X1),X2)
    | ~ member(X1,cross_product(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_509]) ).

cnf(c_0_718,plain,
    ( member(second(X1),X2)
    | ~ member(X1,cross_product(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_510]) ).

cnf(c_0_719,plain,
    ( X1 = X2
    | member(f1(X1,X2),X2)
    | member(f1(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_511]) ).

cnf(c_0_720,plain,
    ( member(X1,twin_prime_numbers)
    | ~ member(successor(successor(X1)),prime_numbers)
    | ~ member(X1,prime_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_512]) ).

cnf(c_0_721,plain,
    ( member(X1,first(X3))
    | ~ member(X1,X2)
    | X3 != ordered_pair(X2,X4)
    | ~ little_set(X4)
    | ~ little_set(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_513]) ).

cnf(c_0_722,plain,
    ( member(X1,second(X3))
    | ~ member(X1,X2)
    | X3 != ordered_pair(X4,X2)
    | ~ little_set(X2)
    | ~ little_set(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_514]) ).

cnf(c_0_723,plain,
    ( member(successor(X1),f44(X2))
    | member(X2,natural_numbers)
    | ~ member(X1,f44(X2))
    | ~ little_set(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_515]) ).

cnf(c_0_724,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_516]) ).

cnf(c_0_725,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_517]) ).

cnf(c_0_726,plain,
    ( subset(X1,X2)
    | ~ member(f17(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_518]) ).

cnf(c_0_727,plain,
    ( maps(f58(X1),f57(X1),X1)
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_519]) ).

cnf(c_0_728,plain,
    ( member(X1,f4(X1,X2))
    | ~ member(X1,first(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_520]) ).

cnf(c_0_729,plain,
    ( member(X1,f7(X1,X2))
    | ~ member(X1,second(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_521]) ).

cnf(c_0_730,plain,
    ( member(f8(X1,X2),X2)
    | ~ member(X1,domain_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_522]) ).

cnf(c_0_731,plain,
    ( member(f16(X1,X2),X2)
    | ~ member(X1,sigma(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_523]) ).

cnf(c_0_732,plain,
    ( member(X1,f16(X1,X2))
    | ~ member(X1,sigma(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_524]) ).

cnf(c_0_733,plain,
    ( member(f27(X1,X2),X2)
    | ~ member(X1,range_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_525]) ).

cnf(c_0_734,plain,
    ( member(ordered_pair(f19(X1),f20(X1)),X1)
    | single_valued_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_526]) ).

cnf(c_0_735,plain,
    ( member(ordered_pair(f19(X1),f21(X1)),X1)
    | single_valued_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_527]) ).

cnf(c_0_736,plain,
    ( member(X1,estin)
    | ~ member(first(X1),second(X1))
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_528]) ).

cnf(c_0_737,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,X3)
    | ~ disjoint(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_529]) ).

cnf(c_0_738,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,non_ordered_pair(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_530]) ).

cnf(c_0_739,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,cross_product(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_531]) ).

cnf(c_0_740,plain,
    ( member(X1,domain_of(X3))
    | X1 != first(X2)
    | ~ member(X2,X3)
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_532]) ).

cnf(c_0_741,plain,
    ( member(X1,sigma(X3))
    | ~ member(X1,X2)
    | ~ member(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_533]) ).

cnf(c_0_742,plain,
    ( member(X1,range_of(X3))
    | X1 != second(X2)
    | ~ member(X2,X3)
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_534]) ).

cnf(c_0_743,plain,
    ( X1 = first(f8(X1,X2))
    | ~ member(X1,domain_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_535]) ).

cnf(c_0_744,plain,
    ( X1 = second(f27(X1,X2))
    | ~ member(X1,range_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_536]) ).

cnf(c_0_745,plain,
    ( little_set(f4(X1,X2))
    | ~ member(X1,first(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_537]) ).

cnf(c_0_746,plain,
    ( little_set(f5(X1,X2))
    | ~ member(X1,first(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_538]) ).

cnf(c_0_747,plain,
    ( little_set(f6(X1,X2))
    | ~ member(X1,second(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_539]) ).

cnf(c_0_748,plain,
    ( little_set(f7(X1,X2))
    | ~ member(X1,second(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_540]) ).

cnf(c_0_749,plain,
    ( ordered_pair_predicate(f8(X1,X2))
    | ~ member(X1,domain_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_541]) ).

cnf(c_0_750,plain,
    ( little_set(f9(X1,X2))
    | ~ member(X1,rotate_right(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_542]) ).

cnf(c_0_751,plain,
    ( little_set(f10(X1,X2))
    | ~ member(X1,rotate_right(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_543]) ).

cnf(c_0_752,plain,
    ( little_set(f11(X1,X2))
    | ~ member(X1,rotate_right(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_544]) ).

cnf(c_0_753,plain,
    ( little_set(f12(X1,X2))
    | ~ member(X1,flip_range_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_545]) ).

cnf(c_0_754,plain,
    ( little_set(f13(X1,X2))
    | ~ member(X1,flip_range_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_546]) ).

cnf(c_0_755,plain,
    ( little_set(f14(X1,X2))
    | ~ member(X1,flip_range_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_547]) ).

cnf(c_0_756,plain,
    ( ordered_pair_predicate(f27(X1,X2))
    | ~ member(X1,range_of(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_548]) ).

cnf(c_0_757,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_549]) ).

cnf(c_0_758,plain,
    ( member(ordered_pair(X1,f26(X1)),f25)
    | X1 = empty_set
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_550]) ).

cnf(c_0_759,plain,
    ( member(f55(X1),natural_numbers)
    | X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_551]) ).

cnf(c_0_760,plain,
    ( member(f56(X1),natural_numbers)
    | X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_552]) ).

cnf(c_0_761,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,complement(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_553]) ).

cnf(c_0_762,plain,
    ( member(f17(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_554]) ).

cnf(c_0_763,plain,
    ( member(f23(X1,X2),X1)
    | disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_555]) ).

cnf(c_0_764,plain,
    ( member(f23(X1,X2),X2)
    | disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_556]) ).

cnf(c_0_765,plain,
    ( member(f34(X1,X2),X1)
    | associative(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_557]) ).

cnf(c_0_766,plain,
    ( member(f35(X1,X2),X1)
    | associative(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_558]) ).

cnf(c_0_767,plain,
    ( member(f36(X1,X2),X1)
    | associative(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_559]) ).

cnf(c_0_768,plain,
    ( member(f41(X1,X2),X1)
    | commutes(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_560]) ).

cnf(c_0_769,plain,
    ( member(f42(X1,X2),X1)
    | commutes(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_561]) ).

cnf(c_0_770,plain,
    ( member(successor(successor(X1)),prime_numbers)
    | ~ member(X1,twin_prime_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_562]) ).

cnf(c_0_771,plain,
    ( member(X1,non_ordered_pair(X2,X3))
    | X1 != X2
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_563]) ).

cnf(c_0_772,plain,
    ( member(X1,non_ordered_pair(X3,X2))
    | X1 != X2
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_564]) ).

cnf(c_0_773,plain,
    ( member(X1,powerset(X2))
    | ~ subset(X1,X2)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_565]) ).

cnf(c_0_774,plain,
    ( member(first(X1),second(X1))
    | ~ member(X1,estin) ),
    inference(split_conjunct,[status(thm)],[c_0_566]) ).

cnf(c_0_775,plain,
    ( subset(X1,X2)
    | ~ member(X1,powerset(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_567]) ).

cnf(c_0_776,plain,
    ( member(X1,natural_numbers)
    | ~ member(X1,f44(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_568]) ).

cnf(c_0_777,plain,
    ( member(X1,plus)
    | ~ member(X1,f49(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_569]) ).

cnf(c_0_778,plain,
    ( member(X1,times)
    | ~ member(X1,f54(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_570]) ).

cnf(c_0_779,plain,
    ( little_set(image(X1,X2))
    | ~ function(X2)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_571]) ).

cnf(c_0_780,plain,
    ( ordered_pair_predicate(X1)
    | X1 != ordered_pair(X2,X3)
    | ~ little_set(X3)
    | ~ little_set(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_572]) ).

cnf(c_0_781,plain,
    ( member(X1,X2)
    | member(X1,complement(X2))
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_573]) ).

cnf(c_0_782,plain,
    ( member(X1,identity_relation)
    | first(X1) != second(X1)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_574]) ).

cnf(c_0_783,plain,
    ( X1 = X2
    | proper_subset(X1,X2)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_575]) ).

cnf(c_0_784,plain,
    ( member(successor(X1),infinity)
    | ~ member(X1,infinity) ),
    inference(split_conjunct,[status(thm)],[c_0_576]) ).

cnf(c_0_785,plain,
    ( member(f59(X1),natural_numbers)
    | ~ member(X1,even_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_577]) ).

cnf(c_0_786,plain,
    ( member(empty_set,f44(X1))
    | member(X1,natural_numbers)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_578]) ).

cnf(c_0_787,plain,
    ( subset(X1,X2)
    | ~ proper_subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_579]) ).

cnf(c_0_788,plain,
    ( closed(X1,X2)
    | ~ group(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_580]) ).

cnf(c_0_789,plain,
    ( associative(X1,X2)
    | ~ group(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_581]) ).

cnf(c_0_790,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,converse(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_582]) ).

cnf(c_0_791,plain,
    ( X1 = ordered_pair(f2(X1),f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_583]) ).

cnf(c_0_792,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,X2)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_584]) ).

cnf(c_0_793,plain,
    ( member(X1,natural_numbers)
    | ~ member(X1,prime_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_585]) ).

cnf(c_0_794,plain,
    ( member(X1,prime_numbers)
    | ~ member(X1,twin_prime_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_586]) ).

cnf(c_0_795,plain,
    ( member(X1,natural_numbers)
    | ~ member(X1,even_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_587]) ).

cnf(c_0_796,plain,
    ( X1 = X2
    | little_set(f1(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_588]) ).

cnf(c_0_797,plain,
    ( little_set(f44(X1))
    | member(X1,natural_numbers)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_589]) ).

cnf(c_0_798,plain,
    ( little_set(f49(X1))
    | member(X1,plus)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_590]) ).

cnf(c_0_799,plain,
    ( little_set(f54(X1))
    | member(X1,times)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_591]) ).

cnf(c_0_800,plain,
    ( member(f26(X1),X1)
    | X1 = empty_set
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_592]) ).

cnf(c_0_801,plain,
    ( first(X1) = second(X1)
    | ~ member(X1,identity_relation) ),
    inference(split_conjunct,[status(thm)],[c_0_593]) ).

cnf(c_0_802,plain,
    ( one_to_one_function(X1)
    | ~ function(converse(X1))
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_594]) ).

cnf(c_0_803,plain,
    ( little_set(X1)
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_595]) ).

cnf(c_0_804,plain,
    ( little_set(X1)
    | ~ closed(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_596]) ).

cnf(c_0_805,plain,
    ( little_set(X1)
    | ~ closed(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_597]) ).

cnf(c_0_806,plain,
    ( X1 != X2
    | ~ proper_subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_598]) ).

cnf(c_0_807,plain,
    ( X1 != successor(empty_set)
    | ~ member(X1,prime_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_599]) ).

cnf(c_0_808,plain,
    ( member(f57(X1),natural_numbers)
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_600]) ).

cnf(c_0_809,plain,
    ( member(f18(X1),X1)
    | relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_601]) ).

cnf(c_0_810,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,estin) ),
    inference(split_conjunct,[status(thm)],[c_0_602]) ).

cnf(c_0_811,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,identity_relation) ),
    inference(split_conjunct,[status(thm)],[c_0_603]) ).

cnf(c_0_812,plain,
    ( X1 != empty_set
    | ~ member(X1,prime_numbers) ),
    inference(split_conjunct,[status(thm)],[c_0_604]) ).

cnf(c_0_813,plain,
    ( member(f24(X1),X1)
    | X1 = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_605]) ).

cnf(c_0_814,plain,
    ( disjoint(f24(X1),X1)
    | X1 = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_606]) ).

cnf(c_0_815,plain,
    ( relation(X1)
    | ~ ordered_pair_predicate(f18(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_607]) ).

cnf(c_0_816,plain,
    ( member(X1,universal_set)
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_608]) ).

cnf(c_0_817,plain,
    ( function(X1)
    | ~ single_valued_set(X1)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_609]) ).

cnf(c_0_818,plain,
    ( range_of(f58(X1)) = X1
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_610]) ).

cnf(c_0_819,plain,
    ( little_set(f2(X1))
    | ~ ordered_pair_predicate(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_611]) ).

cnf(c_0_820,plain,
    ( little_set(f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_612]) ).

cnf(c_0_821,plain,
    ( little_set(sigma(X1))
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_613]) ).

cnf(c_0_822,plain,
    ( little_set(powerset(X1))
    | ~ little_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_614]) ).

cnf(c_0_823,plain,
    ( function(converse(X1))
    | ~ one_to_one_function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_615]) ).

cnf(c_0_824,plain,
    ( one_to_one_function(f58(X1))
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_616]) ).

cnf(c_0_825,plain,
    ( single_valued_set(X1)
    | f20(X1) != f21(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_617]) ).

cnf(c_0_826,plain,
    ( little_set(f19(X1))
    | single_valued_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_618]) ).

cnf(c_0_827,plain,
    ( little_set(f20(X1))
    | single_valued_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_619]) ).

cnf(c_0_828,plain,
    ( little_set(f21(X1))
    | single_valued_set(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_620]) ).

cnf(c_0_829,plain,
    ( relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_621]) ).

cnf(c_0_830,plain,
    ( single_valued_set(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_622]) ).

cnf(c_0_831,plain,
    ( function(X1)
    | ~ one_to_one_function(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_623]) ).

cnf(c_0_832,plain,
    ( homomorphism(X1,X3,X2,X4,X5)
    | apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
    | ~ maps(X1,X3,X4)
    | ~ closed(X4,X5)
    | ~ closed(X3,X2) ),
    c_0_624,
    [final] ).

cnf(c_0_833,plain,
    ( inverse(X2,X1,X3,X4)
    | apply_to_two_arguments(X1,f38(X2,X1,X3,X4),apply(X4,f38(X2,X1,X3,X4))) != X3
    | apply_to_two_arguments(X1,apply(X4,f38(X2,X1,X3,X4)),f38(X2,X1,X3,X4)) != X3
    | ~ maps(X4,X2,X2) ),
    c_0_625,
    [final] ).

cnf(c_0_834,plain,
    ( member(f32(X1,X2,X3,X4,X5),X2)
    | homomorphism(X1,X2,X3,X4,X5)
    | ~ maps(X1,X2,X4)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    c_0_626,
    [final] ).

cnf(c_0_835,plain,
    ( member(f33(X1,X2,X3,X4,X5),X2)
    | homomorphism(X1,X2,X3,X4,X5)
    | ~ maps(X1,X2,X4)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    c_0_627,
    [final] ).

cnf(c_0_836,plain,
    ( apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
    | ~ member(X4,X6)
    | ~ member(X3,X6)
    | ~ homomorphism(X1,X6,X2,X7,X5) ),
    c_0_628,
    [final] ).

cnf(c_0_837,plain,
    ( maps(X1,X2,X3)
    | ~ homomorphism(X1,X2,X4,X3,X5) ),
    c_0_629,
    [final] ).

cnf(c_0_838,plain,
    ( closed(X1,X2)
    | ~ homomorphism(X3,X1,X2,X4,X5) ),
    c_0_630,
    [final] ).

cnf(c_0_839,plain,
    ( closed(X1,X2)
    | ~ homomorphism(X3,X4,X5,X1,X2) ),
    c_0_631,
    [final] ).

cnf(c_0_840,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_632,
    [final] ).

cnf(c_0_841,plain,
    ( member(X1,X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_633,
    [final] ).

cnf(c_0_842,plain,
    ( member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_634,
    [final] ).

cnf(c_0_843,plain,
    ( member(X1,X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_635,
    [final] ).

cnf(c_0_844,plain,
    ( associative(X2,X1)
    | apply_to_two_arguments(X1,apply_to_two_arguments(X1,f34(X2,X1),f35(X2,X1)),f36(X2,X1)) != apply_to_two_arguments(X1,f34(X2,X1),apply_to_two_arguments(X1,f35(X2,X1),f36(X2,X1))) ),
    c_0_636,
    [final] ).

cnf(c_0_845,plain,
    ( member(f38(X1,X2,X3,X4),X1)
    | inverse(X1,X2,X3,X4)
    | ~ maps(X4,X1,X1) ),
    c_0_637,
    [final] ).

cnf(c_0_846,plain,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_638,
    [final] ).

cnf(c_0_847,plain,
    ( identity(X2,X1,X3)
    | apply_to_two_arguments(X1,f37(X2,X1,X3),X3) != f37(X2,X1,X3)
    | apply_to_two_arguments(X1,X3,f37(X2,X1,X3)) != f37(X2,X1,X3)
    | ~ member(X3,X2) ),
    c_0_639,
    [final] ).

cnf(c_0_848,plain,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_640,
    [final] ).

cnf(c_0_849,plain,
    ( member(ordered_pair(ordered_pair(successor(X1),X2),apply_to_two_arguments(plus,X3,X2)),f54(X4))
    | member(X4,times)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f54(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    c_0_641,
    [final] ).

cnf(c_0_850,plain,
    ( group(X1,X2)
    | ~ inverse(X1,X2,X3,X4)
    | ~ identity(X1,X2,X3)
    | ~ associative(X1,X2)
    | ~ closed(X1,X2) ),
    c_0_642,
    [final] ).

cnf(c_0_851,plain,
    ( member(ordered_pair(f29(X1,X2,X3),f31(X1,X2,X3)),X2)
    | ~ member(X1,compose(X2,X3)) ),
    c_0_643,
    [final] ).

cnf(c_0_852,plain,
    ( member(ordered_pair(f31(X1,X2,X3),f30(X1,X2,X3)),X3)
    | ~ member(X1,compose(X2,X3)) ),
    c_0_644,
    [final] ).

cnf(c_0_853,plain,
    ( apply_to_two_arguments(X1,apply(X2,X3),X3) = X4
    | ~ member(X3,X5)
    | ~ inverse(X5,X1,X4,X2) ),
    c_0_645,
    [final] ).

cnf(c_0_854,plain,
    ( apply_to_two_arguments(X1,X2,apply(X3,X2)) = X4
    | ~ member(X2,X5)
    | ~ inverse(X5,X1,X4,X3) ),
    c_0_646,
    [final] ).

cnf(c_0_855,plain,
    ( member(X1,X2)
    | member(f46(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_647,
    [final] ).

cnf(c_0_856,plain,
    ( member(X1,X2)
    | member(f47(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_648,
    [final] ).

cnf(c_0_857,plain,
    ( member(X1,X2)
    | member(f48(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_649,
    [final] ).

cnf(c_0_858,plain,
    ( maps(X1,X2,X2)
    | ~ inverse(X2,X3,X4,X1) ),
    c_0_650,
    [final] ).

cnf(c_0_859,plain,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_651,
    [final] ).

cnf(c_0_860,plain,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_652,
    [final] ).

cnf(c_0_861,plain,
    ( apply_to_two_arguments(X1,apply_to_two_arguments(X1,X2,X3),X4) = apply_to_two_arguments(X1,X2,apply_to_two_arguments(X1,X3,X4))
    | ~ member(X4,X5)
    | ~ member(X3,X5)
    | ~ member(X2,X5)
    | ~ associative(X5,X1) ),
    c_0_653,
    [final] ).

cnf(c_0_862,plain,
    ( member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2)
    | ~ member(X1,rotate_right(X2)) ),
    c_0_654,
    [final] ).

cnf(c_0_863,plain,
    ( member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2)
    | ~ member(X1,flip_range_of(X2)) ),
    c_0_655,
    [final] ).

cnf(c_0_864,plain,
    ( member(X1,X2)
    | member(f51(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_656,
    [final] ).

cnf(c_0_865,plain,
    ( member(X1,X2)
    | member(f52(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_657,
    [final] ).

cnf(c_0_866,plain,
    ( member(X1,X2)
    | member(f53(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_658,
    [final] ).

cnf(c_0_867,plain,
    ( member(ordered_pair(ordered_pair(successor(X1),X2),successor(X3)),f49(X4))
    | member(X4,plus)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f49(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    c_0_659,
    [final] ).

cnf(c_0_868,plain,
    ( commutes(X2,X1)
    | apply_to_two_arguments(X1,f42(X2,X1),f41(X2,X1)) != apply_to_two_arguments(X1,f41(X2,X1),f42(X2,X1)) ),
    c_0_660,
    [final] ).

cnf(c_0_869,plain,
    ( inverse(X1,X2,f39(X1,X2),f40(X1,X2))
    | ~ group(X1,X2) ),
    c_0_661,
    [final] ).

cnf(c_0_870,plain,
    ( member(first(f22(X1,X2,X3)),X2)
    | ~ member(X1,image(X2,X3)) ),
    c_0_662,
    [final] ).

cnf(c_0_871,plain,
    ( member(X1,second(f28(X1,X2,X3)))
    | ~ member(X1,apply(X2,X3)) ),
    c_0_663,
    [final] ).

cnf(c_0_872,plain,
    ( ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3)) = X1
    | ~ member(X1,compose(X2,X3)) ),
    c_0_664,
    [final] ).

cnf(c_0_873,plain,
    ( member(X5,rotate_right(X4))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | X5 != ordered_pair(X3,ordered_pair(X1,X2))
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ little_set(X5) ),
    c_0_665,
    [final] ).

cnf(c_0_874,plain,
    ( member(X5,flip_range_of(X4))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | X5 != ordered_pair(X1,ordered_pair(X3,X2))
    | ~ little_set(X2)
    | ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X5) ),
    c_0_666,
    [final] ).

cnf(c_0_875,plain,
    ( member(X6,compose(X5,X3))
    | ~ member(ordered_pair(X1,X2),X3)
    | ~ member(ordered_pair(X4,X1),X5)
    | X6 != ordered_pair(X4,X2)
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ little_set(X4)
    | ~ little_set(X6) ),
    c_0_667,
    [final] ).

cnf(c_0_876,plain,
    ( ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2))) = X1
    | ~ member(X1,rotate_right(X2)) ),
    c_0_668,
    [final] ).

cnf(c_0_877,plain,
    ( ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2))) = X1
    | ~ member(X1,flip_range_of(X2)) ),
    c_0_669,
    [final] ).

cnf(c_0_878,plain,
    ( member(f37(X1,X2,X3),X1)
    | identity(X1,X2,X3)
    | ~ member(X3,X1) ),
    c_0_670,
    [final] ).

cnf(c_0_879,plain,
    ( member(X1,non_ordered_pair(successor(empty_set),X2))
    | apply_to_two_arguments(times,X1,X3) != X2
    | ~ member(X3,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ member(X2,prime_numbers) ),
    c_0_671,
    [final] ).

cnf(c_0_880,plain,
    ( member(f22(X1,X2,X3),X3)
    | ~ member(X1,image(X2,X3)) ),
    c_0_672,
    [final] ).

cnf(c_0_881,plain,
    ( member(f28(X1,X2,X3),X2)
    | ~ member(X1,apply(X2,X3)) ),
    c_0_673,
    [final] ).

cnf(c_0_882,plain,
    ( apply_to_two_arguments(X1,X2,X3) = apply_to_two_arguments(X1,X3,X2)
    | ~ member(X3,X4)
    | ~ member(X2,X4)
    | ~ commutes(X4,X1) ),
    c_0_674,
    [final] ).

cnf(c_0_883,plain,
    ( member(X1,X2)
    | ~ member(successor(f43(X1,X2)),X2)
    | ~ member(empty_set,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    c_0_675,
    [final] ).

cnf(c_0_884,plain,
    ( second(f22(X1,X2,X3)) = X1
    | ~ member(X1,image(X2,X3)) ),
    c_0_676,
    [final] ).

cnf(c_0_885,plain,
    ( first(f28(X1,X2,X3)) = X3
    | ~ member(X1,apply(X2,X3)) ),
    c_0_677,
    [final] ).

cnf(c_0_886,plain,
    ( ordered_pair_predicate(f22(X1,X2,X3))
    | ~ member(X1,image(X2,X3)) ),
    c_0_678,
    [final] ).

cnf(c_0_887,plain,
    ( ordered_pair_predicate(f28(X1,X2,X3))
    | ~ member(X1,apply(X2,X3)) ),
    c_0_679,
    [final] ).

cnf(c_0_888,plain,
    ( little_set(f29(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    c_0_680,
    [final] ).

cnf(c_0_889,plain,
    ( little_set(f30(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    c_0_681,
    [final] ).

cnf(c_0_890,plain,
    ( little_set(f31(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    c_0_682,
    [final] ).

cnf(c_0_891,plain,
    ( apply_to_two_arguments(X1,X2,X3) = X3
    | ~ member(X3,X4)
    | ~ identity(X4,X1,X2) ),
    c_0_683,
    [final] ).

cnf(c_0_892,plain,
    ( apply_to_two_arguments(X1,X2,X3) = X2
    | ~ member(X2,X4)
    | ~ identity(X4,X1,X3) ),
    c_0_684,
    [final] ).

cnf(c_0_893,plain,
    ( X1 = X2
    | ~ member(ordered_pair(X3,X2),X4)
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ single_valued_set(X4) ),
    c_0_685,
    [final] ).

cnf(c_0_894,plain,
    ( closed(X2,X1)
    | ~ maps(X1,cross_product(X2,X2),X2)
    | ~ little_set(X1)
    | ~ little_set(X2) ),
    c_0_686,
    [final] ).

cnf(c_0_895,plain,
    ( member(X2,even_numbers)
    | apply_to_two_arguments(plus,X1,X1) != X2
    | ~ member(X1,natural_numbers)
    | ~ member(X2,natural_numbers) ),
    c_0_687,
    [final] ).

cnf(c_0_896,plain,
    ( member(X1,converse(X2))
    | ~ member(ordered_pair(second(X1),first(X1)),X2)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    c_0_688,
    [final] ).

cnf(c_0_897,plain,
    ( member(ordered_pair(ordered_pair(empty_set,X1),X1),f49(X2))
    | member(X2,plus)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X2) ),
    c_0_689,
    [final] ).

cnf(c_0_898,plain,
    ( member(ordered_pair(ordered_pair(empty_set,X1),empty_set),f54(X2))
    | member(X2,times)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X2) ),
    c_0_690,
    [final] ).

cnf(c_0_899,plain,
    ( X1 = X2
    | ~ member(f1(X1,X2),X2)
    | ~ member(f1(X1,X2),X1) ),
    c_0_691,
    [final] ).

cnf(c_0_900,plain,
    ( finite(X2)
    | ~ one_to_one_function(X1)
    | range_of(X1) != X2
    | ~ maps(X1,X3,X2)
    | ~ member(X3,natural_numbers) ),
    c_0_692,
    [final] ).

cnf(c_0_901,plain,
    ( X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(f55(X1),non_ordered_pair(successor(empty_set),X1))
    | ~ member(X1,natural_numbers) ),
    c_0_693,
    [final] ).

cnf(c_0_902,plain,
    ( member(X1,X2)
    | member(f46(X1,X2),natural_numbers)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_694,
    [final] ).

cnf(c_0_903,plain,
    ( member(X1,X2)
    | member(f47(X1,X2),natural_numbers)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_695,
    [final] ).

cnf(c_0_904,plain,
    ( member(X1,X2)
    | member(f48(X1,X2),natural_numbers)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    c_0_696,
    [final] ).

cnf(c_0_905,plain,
    ( member(X1,X2)
    | member(f51(X1,X2),natural_numbers)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_697,
    [final] ).

cnf(c_0_906,plain,
    ( member(X1,X2)
    | member(f52(X1,X2),natural_numbers)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_698,
    [final] ).

cnf(c_0_907,plain,
    ( member(X1,X2)
    | member(f53(X1,X2),natural_numbers)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    c_0_699,
    [final] ).

cnf(c_0_908,plain,
    ( member(X1,cross_product(X3,X2))
    | ~ member(second(X1),X2)
    | ~ member(first(X1),X3)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    c_0_700,
    [final] ).

cnf(c_0_909,plain,
    ( member(X2,image(X3,X4))
    | second(X1) != X2
    | ~ member(first(X1),X3)
    | ~ member(X1,X4)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X2) ),
    c_0_701,
    [final] ).

cnf(c_0_910,plain,
    ( member(X1,apply(X4,X3))
    | ~ member(X1,second(X2))
    | first(X2) != X3
    | ~ member(X2,X4)
    | ~ ordered_pair_predicate(X2) ),
    c_0_702,
    [final] ).

cnf(c_0_911,plain,
    ( subset(range_of(X1),X2)
    | ~ maps(X1,X3,X2) ),
    c_0_703,
    [final] ).

cnf(c_0_912,plain,
    ( apply_to_two_arguments(times,f55(X1),f56(X1)) = X1
    | X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    c_0_704,
    [final] ).

cnf(c_0_913,plain,
    ( maps(X1,cross_product(X2,X2),X2)
    | ~ closed(X2,X1) ),
    c_0_705,
    [final] ).

cnf(c_0_914,plain,
    ( identity(X1,X2,f39(X1,X2))
    | ~ group(X1,X2) ),
    c_0_706,
    [final] ).

cnf(c_0_915,plain,
    ( maps(X1,X3,X2)
    | ~ subset(range_of(X1),X2)
    | domain_of(X1) != X3
    | ~ function(X1) ),
    c_0_707,
    [final] ).

cnf(c_0_916,plain,
    ( member(X1,X2)
    | member(f43(X1,X2),X2)
    | ~ member(empty_set,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    c_0_708,
    [final] ).

cnf(c_0_917,plain,
    ( member(X1,X2)
    | ~ identity(X2,X3,X1) ),
    c_0_709,
    [final] ).

cnf(c_0_918,plain,
    ( ordered_pair(f4(X2,X1),f5(X2,X1)) = X1
    | ~ member(X2,first(X1)) ),
    c_0_710,
    [final] ).

cnf(c_0_919,plain,
    ( ordered_pair(f6(X2,X1),f7(X2,X1)) = X1
    | ~ member(X2,second(X1)) ),
    c_0_711,
    [final] ).

cnf(c_0_920,plain,
    ( member(ordered_pair(second(X1),first(X1)),X2)
    | ~ member(X1,converse(X2)) ),
    c_0_712,
    [final] ).

cnf(c_0_921,plain,
    ( domain_of(X1) = X2
    | ~ maps(X1,X2,X3) ),
    c_0_713,
    [final] ).

cnf(c_0_922,plain,
    ( function(X1)
    | ~ maps(X1,X2,X3) ),
    c_0_714,
    [final] ).

cnf(c_0_923,plain,
    ( apply_to_two_arguments(plus,f59(X1),f59(X1)) = X1
    | ~ member(X1,even_numbers) ),
    c_0_715,
    [final] ).

cnf(c_0_924,plain,
    ( member(X1,intersection(X3,X2))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    c_0_716,
    [final] ).

cnf(c_0_925,plain,
    ( member(first(X1),X2)
    | ~ member(X1,cross_product(X2,X3)) ),
    c_0_717,
    [final] ).

cnf(c_0_926,plain,
    ( member(second(X1),X2)
    | ~ member(X1,cross_product(X3,X2)) ),
    c_0_718,
    [final] ).

cnf(c_0_927,plain,
    ( X1 = X2
    | member(f1(X1,X2),X2)
    | member(f1(X1,X2),X1) ),
    c_0_719,
    [final] ).

cnf(c_0_928,plain,
    ( member(X1,twin_prime_numbers)
    | ~ member(successor(successor(X1)),prime_numbers)
    | ~ member(X1,prime_numbers) ),
    c_0_720,
    [final] ).

cnf(c_0_929,plain,
    ( member(X1,first(X3))
    | ~ member(X1,X2)
    | X3 != ordered_pair(X2,X4)
    | ~ little_set(X4)
    | ~ little_set(X2) ),
    c_0_721,
    [final] ).

cnf(c_0_930,plain,
    ( member(X1,second(X3))
    | ~ member(X1,X2)
    | X3 != ordered_pair(X4,X2)
    | ~ little_set(X2)
    | ~ little_set(X4) ),
    c_0_722,
    [final] ).

cnf(c_0_931,plain,
    ( member(successor(X1),f44(X2))
    | member(X2,natural_numbers)
    | ~ member(X1,f44(X2))
    | ~ little_set(X2) ),
    c_0_723,
    [final] ).

cnf(c_0_932,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    c_0_724,
    [final] ).

cnf(c_0_933,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    c_0_725,
    [final] ).

cnf(c_0_934,plain,
    ( subset(X1,X2)
    | ~ member(f17(X1,X2),X2) ),
    c_0_726,
    [final] ).

cnf(c_0_935,plain,
    ( maps(f58(X1),f57(X1),X1)
    | ~ finite(X1) ),
    c_0_727,
    [final] ).

cnf(c_0_936,plain,
    ( member(X1,f4(X1,X2))
    | ~ member(X1,first(X2)) ),
    c_0_728,
    [final] ).

cnf(c_0_937,plain,
    ( member(X1,f7(X1,X2))
    | ~ member(X1,second(X2)) ),
    c_0_729,
    [final] ).

cnf(c_0_938,plain,
    ( member(f8(X1,X2),X2)
    | ~ member(X1,domain_of(X2)) ),
    c_0_730,
    [final] ).

cnf(c_0_939,plain,
    ( member(f16(X1,X2),X2)
    | ~ member(X1,sigma(X2)) ),
    c_0_731,
    [final] ).

cnf(c_0_940,plain,
    ( member(X1,f16(X1,X2))
    | ~ member(X1,sigma(X2)) ),
    c_0_732,
    [final] ).

cnf(c_0_941,plain,
    ( member(f27(X1,X2),X2)
    | ~ member(X1,range_of(X2)) ),
    c_0_733,
    [final] ).

cnf(c_0_942,plain,
    ( member(ordered_pair(f19(X1),f20(X1)),X1)
    | single_valued_set(X1) ),
    c_0_734,
    [final] ).

cnf(c_0_943,plain,
    ( member(ordered_pair(f19(X1),f21(X1)),X1)
    | single_valued_set(X1) ),
    c_0_735,
    [final] ).

cnf(c_0_944,plain,
    ( member(X1,estin)
    | ~ member(first(X1),second(X1))
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    c_0_736,
    [final] ).

cnf(c_0_945,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,X3)
    | ~ disjoint(X3,X2) ),
    c_0_737,
    [final] ).

cnf(c_0_946,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,non_ordered_pair(X3,X2)) ),
    c_0_738,
    [final] ).

cnf(c_0_947,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,cross_product(X2,X3)) ),
    c_0_739,
    [final] ).

cnf(c_0_948,plain,
    ( member(X1,domain_of(X3))
    | X1 != first(X2)
    | ~ member(X2,X3)
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    c_0_740,
    [final] ).

cnf(c_0_949,plain,
    ( member(X1,sigma(X3))
    | ~ member(X1,X2)
    | ~ member(X2,X3) ),
    c_0_741,
    [final] ).

cnf(c_0_950,plain,
    ( member(X1,range_of(X3))
    | X1 != second(X2)
    | ~ member(X2,X3)
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    c_0_742,
    [final] ).

cnf(c_0_951,plain,
    ( first(f8(X1,X2)) = X1
    | ~ member(X1,domain_of(X2)) ),
    c_0_743,
    [final] ).

cnf(c_0_952,plain,
    ( second(f27(X1,X2)) = X1
    | ~ member(X1,range_of(X2)) ),
    c_0_744,
    [final] ).

cnf(c_0_953,plain,
    ( little_set(f4(X1,X2))
    | ~ member(X1,first(X2)) ),
    c_0_745,
    [final] ).

cnf(c_0_954,plain,
    ( little_set(f5(X1,X2))
    | ~ member(X1,first(X2)) ),
    c_0_746,
    [final] ).

cnf(c_0_955,plain,
    ( little_set(f6(X1,X2))
    | ~ member(X1,second(X2)) ),
    c_0_747,
    [final] ).

cnf(c_0_956,plain,
    ( little_set(f7(X1,X2))
    | ~ member(X1,second(X2)) ),
    c_0_748,
    [final] ).

cnf(c_0_957,plain,
    ( ordered_pair_predicate(f8(X1,X2))
    | ~ member(X1,domain_of(X2)) ),
    c_0_749,
    [final] ).

cnf(c_0_958,plain,
    ( little_set(f9(X1,X2))
    | ~ member(X1,rotate_right(X2)) ),
    c_0_750,
    [final] ).

cnf(c_0_959,plain,
    ( little_set(f10(X1,X2))
    | ~ member(X1,rotate_right(X2)) ),
    c_0_751,
    [final] ).

cnf(c_0_960,plain,
    ( little_set(f11(X1,X2))
    | ~ member(X1,rotate_right(X2)) ),
    c_0_752,
    [final] ).

cnf(c_0_961,plain,
    ( little_set(f12(X1,X2))
    | ~ member(X1,flip_range_of(X2)) ),
    c_0_753,
    [final] ).

cnf(c_0_962,plain,
    ( little_set(f13(X1,X2))
    | ~ member(X1,flip_range_of(X2)) ),
    c_0_754,
    [final] ).

cnf(c_0_963,plain,
    ( little_set(f14(X1,X2))
    | ~ member(X1,flip_range_of(X2)) ),
    c_0_755,
    [final] ).

cnf(c_0_964,plain,
    ( ordered_pair_predicate(f27(X1,X2))
    | ~ member(X1,range_of(X2)) ),
    c_0_756,
    [final] ).

cnf(c_0_965,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    c_0_757,
    [final] ).

cnf(c_0_966,plain,
    ( member(ordered_pair(X1,f26(X1)),f25)
    | X1 = empty_set
    | ~ little_set(X1) ),
    c_0_758,
    [final] ).

cnf(c_0_967,plain,
    ( member(f55(X1),natural_numbers)
    | X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    c_0_759,
    [final] ).

cnf(c_0_968,plain,
    ( member(f56(X1),natural_numbers)
    | X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    c_0_760,
    [final] ).

cnf(c_0_969,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,complement(X2)) ),
    c_0_761,
    [final] ).

cnf(c_0_970,plain,
    ( member(f17(X1,X2),X1)
    | subset(X1,X2) ),
    c_0_762,
    [final] ).

cnf(c_0_971,plain,
    ( member(f23(X1,X2),X1)
    | disjoint(X1,X2) ),
    c_0_763,
    [final] ).

cnf(c_0_972,plain,
    ( member(f23(X1,X2),X2)
    | disjoint(X1,X2) ),
    c_0_764,
    [final] ).

cnf(c_0_973,plain,
    ( member(f34(X1,X2),X1)
    | associative(X1,X2) ),
    c_0_765,
    [final] ).

cnf(c_0_974,plain,
    ( member(f35(X1,X2),X1)
    | associative(X1,X2) ),
    c_0_766,
    [final] ).

cnf(c_0_975,plain,
    ( member(f36(X1,X2),X1)
    | associative(X1,X2) ),
    c_0_767,
    [final] ).

cnf(c_0_976,plain,
    ( member(f41(X1,X2),X1)
    | commutes(X1,X2) ),
    c_0_768,
    [final] ).

cnf(c_0_977,plain,
    ( member(f42(X1,X2),X1)
    | commutes(X1,X2) ),
    c_0_769,
    [final] ).

cnf(c_0_978,plain,
    ( member(successor(successor(X1)),prime_numbers)
    | ~ member(X1,twin_prime_numbers) ),
    c_0_770,
    [final] ).

cnf(c_0_979,plain,
    ( member(X1,non_ordered_pair(X2,X3))
    | X1 != X2
    | ~ little_set(X1) ),
    c_0_771,
    [final] ).

cnf(c_0_980,plain,
    ( member(X1,non_ordered_pair(X3,X2))
    | X1 != X2
    | ~ little_set(X1) ),
    c_0_772,
    [final] ).

cnf(c_0_981,plain,
    ( member(X1,powerset(X2))
    | ~ subset(X1,X2)
    | ~ little_set(X1) ),
    c_0_773,
    [final] ).

cnf(c_0_982,plain,
    ( member(first(X1),second(X1))
    | ~ member(X1,estin) ),
    c_0_774,
    [final] ).

cnf(c_0_983,plain,
    ( subset(X1,X2)
    | ~ member(X1,powerset(X2)) ),
    c_0_775,
    [final] ).

cnf(c_0_984,plain,
    ( member(X1,natural_numbers)
    | ~ member(X1,f44(X1)) ),
    c_0_776,
    [final] ).

cnf(c_0_985,plain,
    ( member(X1,plus)
    | ~ member(X1,f49(X1)) ),
    c_0_777,
    [final] ).

cnf(c_0_986,plain,
    ( member(X1,times)
    | ~ member(X1,f54(X1)) ),
    c_0_778,
    [final] ).

cnf(c_0_987,plain,
    ( little_set(image(X1,X2))
    | ~ function(X2)
    | ~ little_set(X1) ),
    c_0_779,
    [final] ).

cnf(c_0_988,plain,
    ( ordered_pair_predicate(X1)
    | X1 != ordered_pair(X2,X3)
    | ~ little_set(X3)
    | ~ little_set(X2) ),
    c_0_780,
    [final] ).

cnf(c_0_989,plain,
    ( member(X1,X2)
    | member(X1,complement(X2))
    | ~ little_set(X1) ),
    c_0_781,
    [final] ).

cnf(c_0_990,plain,
    ( member(X1,identity_relation)
    | first(X1) != second(X1)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    c_0_782,
    [final] ).

cnf(c_0_991,plain,
    ( X1 = X2
    | proper_subset(X1,X2)
    | ~ subset(X1,X2) ),
    c_0_783,
    [final] ).

cnf(c_0_992,plain,
    ( member(successor(X1),infinity)
    | ~ member(X1,infinity) ),
    c_0_784,
    [final] ).

cnf(c_0_993,plain,
    ( member(f59(X1),natural_numbers)
    | ~ member(X1,even_numbers) ),
    c_0_785,
    [final] ).

cnf(c_0_994,plain,
    ( member(empty_set,f44(X1))
    | member(X1,natural_numbers)
    | ~ little_set(X1) ),
    c_0_786,
    [final] ).

cnf(c_0_995,plain,
    ( subset(X1,X2)
    | ~ proper_subset(X1,X2) ),
    c_0_787,
    [final] ).

cnf(c_0_996,plain,
    ( closed(X1,X2)
    | ~ group(X1,X2) ),
    c_0_788,
    [final] ).

cnf(c_0_997,plain,
    ( associative(X1,X2)
    | ~ group(X1,X2) ),
    c_0_789,
    [final] ).

cnf(c_0_998,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,converse(X2)) ),
    c_0_790,
    [final] ).

cnf(c_0_999,plain,
    ( ordered_pair(f2(X1),f3(X1)) = X1
    | ~ ordered_pair_predicate(X1) ),
    c_0_791,
    [final] ).

cnf(c_0_1000,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,X2)
    | ~ relation(X2) ),
    c_0_792,
    [final] ).

cnf(c_0_1001,plain,
    ( member(X1,natural_numbers)
    | ~ member(X1,prime_numbers) ),
    c_0_793,
    [final] ).

cnf(c_0_1002,plain,
    ( member(X1,prime_numbers)
    | ~ member(X1,twin_prime_numbers) ),
    c_0_794,
    [final] ).

cnf(c_0_1003,plain,
    ( member(X1,natural_numbers)
    | ~ member(X1,even_numbers) ),
    c_0_795,
    [final] ).

cnf(c_0_1004,plain,
    ( X1 = X2
    | little_set(f1(X1,X2)) ),
    c_0_796,
    [final] ).

cnf(c_0_1005,plain,
    ( little_set(f44(X1))
    | member(X1,natural_numbers)
    | ~ little_set(X1) ),
    c_0_797,
    [final] ).

cnf(c_0_1006,plain,
    ( little_set(f49(X1))
    | member(X1,plus)
    | ~ little_set(X1) ),
    c_0_798,
    [final] ).

cnf(c_0_1007,plain,
    ( little_set(f54(X1))
    | member(X1,times)
    | ~ little_set(X1) ),
    c_0_799,
    [final] ).

cnf(c_0_1008,plain,
    ( member(f26(X1),X1)
    | X1 = empty_set
    | ~ little_set(X1) ),
    c_0_800,
    [final] ).

cnf(c_0_1009,plain,
    ( first(X1) = second(X1)
    | ~ member(X1,identity_relation) ),
    c_0_801,
    [final] ).

cnf(c_0_1010,plain,
    ( one_to_one_function(X1)
    | ~ function(converse(X1))
    | ~ function(X1) ),
    c_0_802,
    [final] ).

cnf(c_0_1011,plain,
    ( little_set(X1)
    | ~ member(X1,X2) ),
    c_0_803,
    [final] ).

cnf(c_0_1012,plain,
    ( little_set(X1)
    | ~ closed(X1,X2) ),
    c_0_804,
    [final] ).

cnf(c_0_1013,plain,
    ( little_set(X1)
    | ~ closed(X2,X1) ),
    c_0_805,
    [final] ).

cnf(c_0_1014,plain,
    ( X1 != X2
    | ~ proper_subset(X1,X2) ),
    c_0_806,
    [final] ).

cnf(c_0_1015,plain,
    ( X1 != successor(empty_set)
    | ~ member(X1,prime_numbers) ),
    c_0_807,
    [final] ).

cnf(c_0_1016,plain,
    ( member(f57(X1),natural_numbers)
    | ~ finite(X1) ),
    c_0_808,
    [final] ).

cnf(c_0_1017,plain,
    ( member(f18(X1),X1)
    | relation(X1) ),
    c_0_809,
    [final] ).

cnf(c_0_1018,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,estin) ),
    c_0_810,
    [final] ).

cnf(c_0_1019,plain,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,identity_relation) ),
    c_0_811,
    [final] ).

cnf(c_0_1020,plain,
    ( X1 != empty_set
    | ~ member(X1,prime_numbers) ),
    c_0_812,
    [final] ).

cnf(c_0_1021,plain,
    ( member(f24(X1),X1)
    | X1 = empty_set ),
    c_0_813,
    [final] ).

cnf(c_0_1022,plain,
    ( disjoint(f24(X1),X1)
    | X1 = empty_set ),
    c_0_814,
    [final] ).

cnf(c_0_1023,plain,
    ( relation(X1)
    | ~ ordered_pair_predicate(f18(X1)) ),
    c_0_815,
    [final] ).

cnf(c_0_1024,plain,
    ( member(X1,universal_set)
    | ~ little_set(X1) ),
    c_0_816,
    [final] ).

cnf(c_0_1025,plain,
    ( function(X1)
    | ~ single_valued_set(X1)
    | ~ relation(X1) ),
    c_0_817,
    [final] ).

cnf(c_0_1026,plain,
    ( range_of(f58(X1)) = X1
    | ~ finite(X1) ),
    c_0_818,
    [final] ).

cnf(c_0_1027,plain,
    ( little_set(f2(X1))
    | ~ ordered_pair_predicate(X1) ),
    c_0_819,
    [final] ).

cnf(c_0_1028,plain,
    ( little_set(f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    c_0_820,
    [final] ).

cnf(c_0_1029,plain,
    ( little_set(sigma(X1))
    | ~ little_set(X1) ),
    c_0_821,
    [final] ).

cnf(c_0_1030,plain,
    ( little_set(powerset(X1))
    | ~ little_set(X1) ),
    c_0_822,
    [final] ).

cnf(c_0_1031,plain,
    ( function(converse(X1))
    | ~ one_to_one_function(X1) ),
    c_0_823,
    [final] ).

cnf(c_0_1032,plain,
    ( one_to_one_function(f58(X1))
    | ~ finite(X1) ),
    c_0_824,
    [final] ).

cnf(c_0_1033,plain,
    ( single_valued_set(X1)
    | f21(X1) != f20(X1) ),
    c_0_825,
    [final] ).

cnf(c_0_1034,plain,
    ( little_set(f19(X1))
    | single_valued_set(X1) ),
    c_0_826,
    [final] ).

cnf(c_0_1035,plain,
    ( little_set(f20(X1))
    | single_valued_set(X1) ),
    c_0_827,
    [final] ).

cnf(c_0_1036,plain,
    ( little_set(f21(X1))
    | single_valued_set(X1) ),
    c_0_828,
    [final] ).

cnf(c_0_1037,plain,
    ( relation(X1)
    | ~ function(X1) ),
    c_0_829,
    [final] ).

cnf(c_0_1038,plain,
    ( single_valued_set(X1)
    | ~ function(X1) ),
    c_0_830,
    [final] ).

cnf(c_0_1039,plain,
    ( function(X1)
    | ~ one_to_one_function(X1) ),
    c_0_831,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_832_0,axiom,
    ( homomorphism(X1,X3,X2,X4,X5)
    | apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
    | ~ maps(X1,X3,X4)
    | ~ closed(X4,X5)
    | ~ closed(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_832]) ).

cnf(c_0_832_1,axiom,
    ( apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
    | homomorphism(X1,X3,X2,X4,X5)
    | ~ maps(X1,X3,X4)
    | ~ closed(X4,X5)
    | ~ closed(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_832]) ).

cnf(c_0_832_2,axiom,
    ( ~ maps(X1,X3,X4)
    | apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
    | homomorphism(X1,X3,X2,X4,X5)
    | ~ closed(X4,X5)
    | ~ closed(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_832]) ).

cnf(c_0_832_3,axiom,
    ( ~ closed(X4,X5)
    | ~ maps(X1,X3,X4)
    | apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
    | homomorphism(X1,X3,X2,X4,X5)
    | ~ closed(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_832]) ).

cnf(c_0_832_4,axiom,
    ( ~ closed(X3,X2)
    | ~ closed(X4,X5)
    | ~ maps(X1,X3,X4)
    | apply(X1,apply_to_two_arguments(X2,f32(X1,X3,X2,X4,X5),f33(X1,X3,X2,X4,X5))) != apply_to_two_arguments(X5,apply(X1,f32(X1,X3,X2,X4,X5)),apply(X1,f33(X1,X3,X2,X4,X5)))
    | homomorphism(X1,X3,X2,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_832]) ).

cnf(c_0_833_0,axiom,
    ( inverse(X2,X1,X3,X4)
    | apply_to_two_arguments(X1,f38(X2,X1,X3,X4),apply(X4,f38(X2,X1,X3,X4))) != X3
    | apply_to_two_arguments(X1,apply(X4,f38(X2,X1,X3,X4)),f38(X2,X1,X3,X4)) != X3
    | ~ maps(X4,X2,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_833]) ).

cnf(c_0_833_1,axiom,
    ( apply_to_two_arguments(X1,f38(X2,X1,X3,X4),apply(X4,f38(X2,X1,X3,X4))) != X3
    | inverse(X2,X1,X3,X4)
    | apply_to_two_arguments(X1,apply(X4,f38(X2,X1,X3,X4)),f38(X2,X1,X3,X4)) != X3
    | ~ maps(X4,X2,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_833]) ).

cnf(c_0_833_2,axiom,
    ( apply_to_two_arguments(X1,apply(X4,f38(X2,X1,X3,X4)),f38(X2,X1,X3,X4)) != X3
    | apply_to_two_arguments(X1,f38(X2,X1,X3,X4),apply(X4,f38(X2,X1,X3,X4))) != X3
    | inverse(X2,X1,X3,X4)
    | ~ maps(X4,X2,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_833]) ).

cnf(c_0_833_3,axiom,
    ( ~ maps(X4,X2,X2)
    | apply_to_two_arguments(X1,apply(X4,f38(X2,X1,X3,X4)),f38(X2,X1,X3,X4)) != X3
    | apply_to_two_arguments(X1,f38(X2,X1,X3,X4),apply(X4,f38(X2,X1,X3,X4))) != X3
    | inverse(X2,X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_833]) ).

cnf(c_0_834_0,axiom,
    ( member(f32(X1,X2,X3,X4,X5),X2)
    | homomorphism(X1,X2,X3,X4,X5)
    | ~ maps(X1,X2,X4)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_834_1,axiom,
    ( homomorphism(X1,X2,X3,X4,X5)
    | member(f32(X1,X2,X3,X4,X5),X2)
    | ~ maps(X1,X2,X4)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_834_2,axiom,
    ( ~ maps(X1,X2,X4)
    | homomorphism(X1,X2,X3,X4,X5)
    | member(f32(X1,X2,X3,X4,X5),X2)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_834_3,axiom,
    ( ~ closed(X4,X5)
    | ~ maps(X1,X2,X4)
    | homomorphism(X1,X2,X3,X4,X5)
    | member(f32(X1,X2,X3,X4,X5),X2)
    | ~ closed(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_834_4,axiom,
    ( ~ closed(X2,X3)
    | ~ closed(X4,X5)
    | ~ maps(X1,X2,X4)
    | homomorphism(X1,X2,X3,X4,X5)
    | member(f32(X1,X2,X3,X4,X5),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_834]) ).

cnf(c_0_835_0,axiom,
    ( member(f33(X1,X2,X3,X4,X5),X2)
    | homomorphism(X1,X2,X3,X4,X5)
    | ~ maps(X1,X2,X4)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_835]) ).

cnf(c_0_835_1,axiom,
    ( homomorphism(X1,X2,X3,X4,X5)
    | member(f33(X1,X2,X3,X4,X5),X2)
    | ~ maps(X1,X2,X4)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_835]) ).

cnf(c_0_835_2,axiom,
    ( ~ maps(X1,X2,X4)
    | homomorphism(X1,X2,X3,X4,X5)
    | member(f33(X1,X2,X3,X4,X5),X2)
    | ~ closed(X4,X5)
    | ~ closed(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_835]) ).

cnf(c_0_835_3,axiom,
    ( ~ closed(X4,X5)
    | ~ maps(X1,X2,X4)
    | homomorphism(X1,X2,X3,X4,X5)
    | member(f33(X1,X2,X3,X4,X5),X2)
    | ~ closed(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_835]) ).

cnf(c_0_835_4,axiom,
    ( ~ closed(X2,X3)
    | ~ closed(X4,X5)
    | ~ maps(X1,X2,X4)
    | homomorphism(X1,X2,X3,X4,X5)
    | member(f33(X1,X2,X3,X4,X5),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_835]) ).

cnf(c_0_836_0,axiom,
    ( apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
    | ~ member(X4,X6)
    | ~ member(X3,X6)
    | ~ homomorphism(X1,X6,X2,X7,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_836]) ).

cnf(c_0_836_1,axiom,
    ( ~ member(X4,X6)
    | apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
    | ~ member(X3,X6)
    | ~ homomorphism(X1,X6,X2,X7,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_836]) ).

cnf(c_0_836_2,axiom,
    ( ~ member(X3,X6)
    | ~ member(X4,X6)
    | apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4))
    | ~ homomorphism(X1,X6,X2,X7,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_836]) ).

cnf(c_0_836_3,axiom,
    ( ~ homomorphism(X1,X6,X2,X7,X5)
    | ~ member(X3,X6)
    | ~ member(X4,X6)
    | apply(X1,apply_to_two_arguments(X2,X3,X4)) = apply_to_two_arguments(X5,apply(X1,X3),apply(X1,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_836]) ).

cnf(c_0_837_0,axiom,
    ( maps(X1,X2,X3)
    | ~ homomorphism(X1,X2,X4,X3,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_837]) ).

cnf(c_0_837_1,axiom,
    ( ~ homomorphism(X1,X2,X4,X3,X5)
    | maps(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_837]) ).

cnf(c_0_838_0,axiom,
    ( closed(X1,X2)
    | ~ homomorphism(X3,X1,X2,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_838]) ).

cnf(c_0_838_1,axiom,
    ( ~ homomorphism(X3,X1,X2,X4,X5)
    | closed(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_838]) ).

cnf(c_0_839_0,axiom,
    ( closed(X1,X2)
    | ~ homomorphism(X3,X4,X5,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_839]) ).

cnf(c_0_839_1,axiom,
    ( ~ homomorphism(X3,X4,X5,X1,X2)
    | closed(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_839]) ).

cnf(c_0_840_0,axiom,
    ( member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_840]) ).

cnf(c_0_840_1,axiom,
    ( ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_840]) ).

cnf(c_0_840_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_840]) ).

cnf(c_0_840_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_840]) ).

cnf(c_0_840_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_840]) ).

cnf(c_0_841_0,axiom,
    ( member(X1,X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_841]) ).

cnf(c_0_841_1,axiom,
    ( member(f50(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_841]) ).

cnf(c_0_841_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | member(f50(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_841]) ).

cnf(c_0_841_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | member(f50(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_841]) ).

cnf(c_0_841_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(successor(f51(X1,X2)),f52(X1,X2)),apply_to_two_arguments(plus,f53(X1,X2),f52(X1,X2))),X2)
    | member(f50(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_841]) ).

cnf(c_0_842_0,axiom,
    ( member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_842]) ).

cnf(c_0_842_1,axiom,
    ( ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_842]) ).

cnf(c_0_842_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_842]) ).

cnf(c_0_842_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_842]) ).

cnf(c_0_842_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_842]) ).

cnf(c_0_843_0,axiom,
    ( member(X1,X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_843]) ).

cnf(c_0_843_1,axiom,
    ( member(f45(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_843]) ).

cnf(c_0_843_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | member(f45(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_843]) ).

cnf(c_0_843_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | member(f45(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_843]) ).

cnf(c_0_843_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(successor(f46(X1,X2)),f47(X1,X2)),successor(f48(X1,X2))),X2)
    | member(f45(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_843]) ).

cnf(c_0_844_0,axiom,
    ( associative(X2,X1)
    | apply_to_two_arguments(X1,apply_to_two_arguments(X1,f34(X2,X1),f35(X2,X1)),f36(X2,X1)) != apply_to_two_arguments(X1,f34(X2,X1),apply_to_two_arguments(X1,f35(X2,X1),f36(X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_844]) ).

cnf(c_0_844_1,axiom,
    ( apply_to_two_arguments(X1,apply_to_two_arguments(X1,f34(X2,X1),f35(X2,X1)),f36(X2,X1)) != apply_to_two_arguments(X1,f34(X2,X1),apply_to_two_arguments(X1,f35(X2,X1),f36(X2,X1)))
    | associative(X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_844]) ).

cnf(c_0_845_0,axiom,
    ( member(f38(X1,X2,X3,X4),X1)
    | inverse(X1,X2,X3,X4)
    | ~ maps(X4,X1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_845]) ).

cnf(c_0_845_1,axiom,
    ( inverse(X1,X2,X3,X4)
    | member(f38(X1,X2,X3,X4),X1)
    | ~ maps(X4,X1,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_845]) ).

cnf(c_0_845_2,axiom,
    ( ~ maps(X4,X1,X1)
    | inverse(X1,X2,X3,X4)
    | member(f38(X1,X2,X3,X4),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_845]) ).

cnf(c_0_846_0,axiom,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_846]) ).

cnf(c_0_846_1,axiom,
    ( member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_846]) ).

cnf(c_0_846_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_846]) ).

cnf(c_0_846_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_846]) ).

cnf(c_0_846_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_846]) ).

cnf(c_0_847_0,axiom,
    ( identity(X2,X1,X3)
    | apply_to_two_arguments(X1,f37(X2,X1,X3),X3) != f37(X2,X1,X3)
    | apply_to_two_arguments(X1,X3,f37(X2,X1,X3)) != f37(X2,X1,X3)
    | ~ member(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_847]) ).

cnf(c_0_847_1,axiom,
    ( apply_to_two_arguments(X1,f37(X2,X1,X3),X3) != f37(X2,X1,X3)
    | identity(X2,X1,X3)
    | apply_to_two_arguments(X1,X3,f37(X2,X1,X3)) != f37(X2,X1,X3)
    | ~ member(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_847]) ).

cnf(c_0_847_2,axiom,
    ( apply_to_two_arguments(X1,X3,f37(X2,X1,X3)) != f37(X2,X1,X3)
    | apply_to_two_arguments(X1,f37(X2,X1,X3),X3) != f37(X2,X1,X3)
    | identity(X2,X1,X3)
    | ~ member(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_847]) ).

cnf(c_0_847_3,axiom,
    ( ~ member(X3,X2)
    | apply_to_two_arguments(X1,X3,f37(X2,X1,X3)) != f37(X2,X1,X3)
    | apply_to_two_arguments(X1,f37(X2,X1,X3),X3) != f37(X2,X1,X3)
    | identity(X2,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_847]) ).

cnf(c_0_848_0,axiom,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_848]) ).

cnf(c_0_848_1,axiom,
    ( member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_848]) ).

cnf(c_0_848_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_848]) ).

cnf(c_0_848_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_848]) ).

cnf(c_0_848_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_848]) ).

cnf(c_0_849_0,axiom,
    ( member(ordered_pair(ordered_pair(successor(X1),X2),apply_to_two_arguments(plus,X3,X2)),f54(X4))
    | member(X4,times)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f54(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_849]) ).

cnf(c_0_849_1,axiom,
    ( member(X4,times)
    | member(ordered_pair(ordered_pair(successor(X1),X2),apply_to_two_arguments(plus,X3,X2)),f54(X4))
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f54(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_849]) ).

cnf(c_0_849_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(X1,X2),X3),f54(X4))
    | member(X4,times)
    | member(ordered_pair(ordered_pair(successor(X1),X2),apply_to_two_arguments(plus,X3,X2)),f54(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_849]) ).

cnf(c_0_849_3,axiom,
    ( ~ member(X3,natural_numbers)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f54(X4))
    | member(X4,times)
    | member(ordered_pair(ordered_pair(successor(X1),X2),apply_to_two_arguments(plus,X3,X2)),f54(X4))
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_849]) ).

cnf(c_0_849_4,axiom,
    ( ~ member(X2,natural_numbers)
    | ~ member(X3,natural_numbers)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f54(X4))
    | member(X4,times)
    | member(ordered_pair(ordered_pair(successor(X1),X2),apply_to_two_arguments(plus,X3,X2)),f54(X4))
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_849]) ).

cnf(c_0_849_5,axiom,
    ( ~ member(X1,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X3,natural_numbers)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f54(X4))
    | member(X4,times)
    | member(ordered_pair(ordered_pair(successor(X1),X2),apply_to_two_arguments(plus,X3,X2)),f54(X4))
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_849]) ).

cnf(c_0_849_6,axiom,
    ( ~ little_set(X4)
    | ~ member(X1,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X3,natural_numbers)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f54(X4))
    | member(X4,times)
    | member(ordered_pair(ordered_pair(successor(X1),X2),apply_to_two_arguments(plus,X3,X2)),f54(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_849]) ).

cnf(c_0_850_0,axiom,
    ( group(X1,X2)
    | ~ inverse(X1,X2,X3,X4)
    | ~ identity(X1,X2,X3)
    | ~ associative(X1,X2)
    | ~ closed(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_850]) ).

cnf(c_0_850_1,axiom,
    ( ~ inverse(X1,X2,X3,X4)
    | group(X1,X2)
    | ~ identity(X1,X2,X3)
    | ~ associative(X1,X2)
    | ~ closed(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_850]) ).

cnf(c_0_850_2,axiom,
    ( ~ identity(X1,X2,X3)
    | ~ inverse(X1,X2,X3,X4)
    | group(X1,X2)
    | ~ associative(X1,X2)
    | ~ closed(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_850]) ).

cnf(c_0_850_3,axiom,
    ( ~ associative(X1,X2)
    | ~ identity(X1,X2,X3)
    | ~ inverse(X1,X2,X3,X4)
    | group(X1,X2)
    | ~ closed(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_850]) ).

cnf(c_0_850_4,axiom,
    ( ~ closed(X1,X2)
    | ~ associative(X1,X2)
    | ~ identity(X1,X2,X3)
    | ~ inverse(X1,X2,X3,X4)
    | group(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_850]) ).

cnf(c_0_851_0,axiom,
    ( member(ordered_pair(f29(X1,X2,X3),f31(X1,X2,X3)),X2)
    | ~ member(X1,compose(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_851]) ).

cnf(c_0_851_1,axiom,
    ( ~ member(X1,compose(X2,X3))
    | member(ordered_pair(f29(X1,X2,X3),f31(X1,X2,X3)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_851]) ).

cnf(c_0_852_0,axiom,
    ( member(ordered_pair(f31(X1,X2,X3),f30(X1,X2,X3)),X3)
    | ~ member(X1,compose(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_852]) ).

cnf(c_0_852_1,axiom,
    ( ~ member(X1,compose(X2,X3))
    | member(ordered_pair(f31(X1,X2,X3),f30(X1,X2,X3)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_852]) ).

cnf(c_0_853_0,axiom,
    ( apply_to_two_arguments(X1,apply(X2,X3),X3) = X4
    | ~ member(X3,X5)
    | ~ inverse(X5,X1,X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_853]) ).

cnf(c_0_853_1,axiom,
    ( ~ member(X3,X5)
    | apply_to_two_arguments(X1,apply(X2,X3),X3) = X4
    | ~ inverse(X5,X1,X4,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_853]) ).

cnf(c_0_853_2,axiom,
    ( ~ inverse(X5,X1,X4,X2)
    | ~ member(X3,X5)
    | apply_to_two_arguments(X1,apply(X2,X3),X3) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_853]) ).

cnf(c_0_854_0,axiom,
    ( apply_to_two_arguments(X1,X2,apply(X3,X2)) = X4
    | ~ member(X2,X5)
    | ~ inverse(X5,X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_854]) ).

cnf(c_0_854_1,axiom,
    ( ~ member(X2,X5)
    | apply_to_two_arguments(X1,X2,apply(X3,X2)) = X4
    | ~ inverse(X5,X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_854]) ).

cnf(c_0_854_2,axiom,
    ( ~ inverse(X5,X1,X4,X3)
    | ~ member(X2,X5)
    | apply_to_two_arguments(X1,X2,apply(X3,X2)) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_854]) ).

cnf(c_0_855_0,axiom,
    ( member(X1,X2)
    | member(f46(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_855]) ).

cnf(c_0_855_1,axiom,
    ( member(f46(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_855]) ).

cnf(c_0_855_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(f46(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_855]) ).

cnf(c_0_855_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(f46(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_855]) ).

cnf(c_0_855_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(f46(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_855]) ).

cnf(c_0_856_0,axiom,
    ( member(X1,X2)
    | member(f47(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_856]) ).

cnf(c_0_856_1,axiom,
    ( member(f47(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_856]) ).

cnf(c_0_856_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(f47(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_856]) ).

cnf(c_0_856_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(f47(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_856]) ).

cnf(c_0_856_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(f47(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_856]) ).

cnf(c_0_857_0,axiom,
    ( member(X1,X2)
    | member(f48(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_857]) ).

cnf(c_0_857_1,axiom,
    ( member(f48(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_857]) ).

cnf(c_0_857_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(f48(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_857]) ).

cnf(c_0_857_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(f48(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_857]) ).

cnf(c_0_857_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f45(X1,X2)),f45(X1,X2)),X2)
    | member(f48(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_857]) ).

cnf(c_0_858_0,axiom,
    ( maps(X1,X2,X2)
    | ~ inverse(X2,X3,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_858]) ).

cnf(c_0_858_1,axiom,
    ( ~ inverse(X2,X3,X4,X1)
    | maps(X1,X2,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_858]) ).

cnf(c_0_859_0,axiom,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_859]) ).

cnf(c_0_859_1,axiom,
    ( member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(X1,X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_859]) ).

cnf(c_0_859_2,axiom,
    ( member(f45(X1,X2),natural_numbers)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_859]) ).

cnf(c_0_859_3,axiom,
    ( ~ little_set(X2)
    | member(f45(X1,X2),natural_numbers)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_859]) ).

cnf(c_0_859_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | member(f45(X1,X2),natural_numbers)
    | member(ordered_pair(ordered_pair(f46(X1,X2),f47(X1,X2)),f48(X1,X2)),X2)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_859]) ).

cnf(c_0_860_0,axiom,
    ( member(X1,X2)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_860]) ).

cnf(c_0_860_1,axiom,
    ( member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(X1,X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_860]) ).

cnf(c_0_860_2,axiom,
    ( member(f50(X1,X2),natural_numbers)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_860]) ).

cnf(c_0_860_3,axiom,
    ( ~ little_set(X2)
    | member(f50(X1,X2),natural_numbers)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_860]) ).

cnf(c_0_860_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | member(f50(X1,X2),natural_numbers)
    | member(ordered_pair(ordered_pair(f51(X1,X2),f52(X1,X2)),f53(X1,X2)),X2)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_860]) ).

cnf(c_0_861_0,axiom,
    ( apply_to_two_arguments(X1,apply_to_two_arguments(X1,X2,X3),X4) = apply_to_two_arguments(X1,X2,apply_to_two_arguments(X1,X3,X4))
    | ~ member(X4,X5)
    | ~ member(X3,X5)
    | ~ member(X2,X5)
    | ~ associative(X5,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_861]) ).

cnf(c_0_861_1,axiom,
    ( ~ member(X4,X5)
    | apply_to_two_arguments(X1,apply_to_two_arguments(X1,X2,X3),X4) = apply_to_two_arguments(X1,X2,apply_to_two_arguments(X1,X3,X4))
    | ~ member(X3,X5)
    | ~ member(X2,X5)
    | ~ associative(X5,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_861]) ).

cnf(c_0_861_2,axiom,
    ( ~ member(X3,X5)
    | ~ member(X4,X5)
    | apply_to_two_arguments(X1,apply_to_two_arguments(X1,X2,X3),X4) = apply_to_two_arguments(X1,X2,apply_to_two_arguments(X1,X3,X4))
    | ~ member(X2,X5)
    | ~ associative(X5,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_861]) ).

cnf(c_0_861_3,axiom,
    ( ~ member(X2,X5)
    | ~ member(X3,X5)
    | ~ member(X4,X5)
    | apply_to_two_arguments(X1,apply_to_two_arguments(X1,X2,X3),X4) = apply_to_two_arguments(X1,X2,apply_to_two_arguments(X1,X3,X4))
    | ~ associative(X5,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_861]) ).

cnf(c_0_861_4,axiom,
    ( ~ associative(X5,X1)
    | ~ member(X2,X5)
    | ~ member(X3,X5)
    | ~ member(X4,X5)
    | apply_to_two_arguments(X1,apply_to_two_arguments(X1,X2,X3),X4) = apply_to_two_arguments(X1,X2,apply_to_two_arguments(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_861]) ).

cnf(c_0_862_0,axiom,
    ( member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2)
    | ~ member(X1,rotate_right(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_862]) ).

cnf(c_0_862_1,axiom,
    ( ~ member(X1,rotate_right(X2))
    | member(ordered_pair(f10(X1,X2),ordered_pair(f11(X1,X2),f9(X1,X2))),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_862]) ).

cnf(c_0_863_0,axiom,
    ( member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2)
    | ~ member(X1,flip_range_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_863]) ).

cnf(c_0_863_1,axiom,
    ( ~ member(X1,flip_range_of(X2))
    | member(ordered_pair(f12(X1,X2),ordered_pair(f14(X1,X2),f13(X1,X2))),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_863]) ).

cnf(c_0_864_0,axiom,
    ( member(X1,X2)
    | member(f51(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_864]) ).

cnf(c_0_864_1,axiom,
    ( member(f51(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_864]) ).

cnf(c_0_864_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(f51(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_864]) ).

cnf(c_0_864_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(f51(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_864]) ).

cnf(c_0_864_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(f51(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_864]) ).

cnf(c_0_865_0,axiom,
    ( member(X1,X2)
    | member(f52(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_865]) ).

cnf(c_0_865_1,axiom,
    ( member(f52(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_865]) ).

cnf(c_0_865_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(f52(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_865]) ).

cnf(c_0_865_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(f52(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_865]) ).

cnf(c_0_865_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(f52(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_865]) ).

cnf(c_0_866_0,axiom,
    ( member(X1,X2)
    | member(f53(X1,X2),natural_numbers)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_866]) ).

cnf(c_0_866_1,axiom,
    ( member(f53(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_866]) ).

cnf(c_0_866_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(f53(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_866]) ).

cnf(c_0_866_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(f53(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_866]) ).

cnf(c_0_866_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | ~ member(ordered_pair(ordered_pair(empty_set,f50(X1,X2)),empty_set),X2)
    | member(f53(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_866]) ).

cnf(c_0_867_0,axiom,
    ( member(ordered_pair(ordered_pair(successor(X1),X2),successor(X3)),f49(X4))
    | member(X4,plus)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f49(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_867]) ).

cnf(c_0_867_1,axiom,
    ( member(X4,plus)
    | member(ordered_pair(ordered_pair(successor(X1),X2),successor(X3)),f49(X4))
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f49(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_867]) ).

cnf(c_0_867_2,axiom,
    ( ~ member(ordered_pair(ordered_pair(X1,X2),X3),f49(X4))
    | member(X4,plus)
    | member(ordered_pair(ordered_pair(successor(X1),X2),successor(X3)),f49(X4))
    | ~ member(X3,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_867]) ).

cnf(c_0_867_3,axiom,
    ( ~ member(X3,natural_numbers)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f49(X4))
    | member(X4,plus)
    | member(ordered_pair(ordered_pair(successor(X1),X2),successor(X3)),f49(X4))
    | ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_867]) ).

cnf(c_0_867_4,axiom,
    ( ~ member(X2,natural_numbers)
    | ~ member(X3,natural_numbers)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f49(X4))
    | member(X4,plus)
    | member(ordered_pair(ordered_pair(successor(X1),X2),successor(X3)),f49(X4))
    | ~ member(X1,natural_numbers)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_867]) ).

cnf(c_0_867_5,axiom,
    ( ~ member(X1,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X3,natural_numbers)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f49(X4))
    | member(X4,plus)
    | member(ordered_pair(ordered_pair(successor(X1),X2),successor(X3)),f49(X4))
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_867]) ).

cnf(c_0_867_6,axiom,
    ( ~ little_set(X4)
    | ~ member(X1,natural_numbers)
    | ~ member(X2,natural_numbers)
    | ~ member(X3,natural_numbers)
    | ~ member(ordered_pair(ordered_pair(X1,X2),X3),f49(X4))
    | member(X4,plus)
    | member(ordered_pair(ordered_pair(successor(X1),X2),successor(X3)),f49(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_867]) ).

cnf(c_0_868_0,axiom,
    ( commutes(X2,X1)
    | apply_to_two_arguments(X1,f42(X2,X1),f41(X2,X1)) != apply_to_two_arguments(X1,f41(X2,X1),f42(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_868]) ).

cnf(c_0_868_1,axiom,
    ( apply_to_two_arguments(X1,f42(X2,X1),f41(X2,X1)) != apply_to_two_arguments(X1,f41(X2,X1),f42(X2,X1))
    | commutes(X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_868]) ).

cnf(c_0_869_0,axiom,
    ( inverse(X1,X2,f39(X1,X2),f40(X1,X2))
    | ~ group(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_869]) ).

cnf(c_0_869_1,axiom,
    ( ~ group(X1,X2)
    | inverse(X1,X2,f39(X1,X2),f40(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_869]) ).

cnf(c_0_870_0,axiom,
    ( member(first(f22(X1,X2,X3)),X2)
    | ~ member(X1,image(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_870]) ).

cnf(c_0_870_1,axiom,
    ( ~ member(X1,image(X2,X3))
    | member(first(f22(X1,X2,X3)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_870]) ).

cnf(c_0_871_0,axiom,
    ( member(X1,second(f28(X1,X2,X3)))
    | ~ member(X1,apply(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_871]) ).

cnf(c_0_871_1,axiom,
    ( ~ member(X1,apply(X2,X3))
    | member(X1,second(f28(X1,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_871]) ).

cnf(c_0_872_0,axiom,
    ( ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3)) = X1
    | ~ member(X1,compose(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_872]) ).

cnf(c_0_872_1,axiom,
    ( ~ member(X1,compose(X2,X3))
    | ordered_pair(f29(X1,X2,X3),f30(X1,X2,X3)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_872]) ).

cnf(c_0_873_0,axiom,
    ( member(X5,rotate_right(X4))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | X5 != ordered_pair(X3,ordered_pair(X1,X2))
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_873]) ).

cnf(c_0_873_1,axiom,
    ( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,rotate_right(X4))
    | X5 != ordered_pair(X3,ordered_pair(X1,X2))
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_873]) ).

cnf(c_0_873_2,axiom,
    ( X5 != ordered_pair(X3,ordered_pair(X1,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,rotate_right(X4))
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_873]) ).

cnf(c_0_873_3,axiom,
    ( ~ little_set(X2)
    | X5 != ordered_pair(X3,ordered_pair(X1,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,rotate_right(X4))
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_873]) ).

cnf(c_0_873_4,axiom,
    ( ~ little_set(X1)
    | ~ little_set(X2)
    | X5 != ordered_pair(X3,ordered_pair(X1,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,rotate_right(X4))
    | ~ little_set(X3)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_873]) ).

cnf(c_0_873_5,axiom,
    ( ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X2)
    | X5 != ordered_pair(X3,ordered_pair(X1,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,rotate_right(X4))
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_873]) ).

cnf(c_0_873_6,axiom,
    ( ~ little_set(X5)
    | ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X2)
    | X5 != ordered_pair(X3,ordered_pair(X1,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,rotate_right(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_873]) ).

cnf(c_0_874_0,axiom,
    ( member(X5,flip_range_of(X4))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | X5 != ordered_pair(X1,ordered_pair(X3,X2))
    | ~ little_set(X2)
    | ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_874]) ).

cnf(c_0_874_1,axiom,
    ( ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,flip_range_of(X4))
    | X5 != ordered_pair(X1,ordered_pair(X3,X2))
    | ~ little_set(X2)
    | ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_874]) ).

cnf(c_0_874_2,axiom,
    ( X5 != ordered_pair(X1,ordered_pair(X3,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,flip_range_of(X4))
    | ~ little_set(X2)
    | ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_874]) ).

cnf(c_0_874_3,axiom,
    ( ~ little_set(X2)
    | X5 != ordered_pair(X1,ordered_pair(X3,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,flip_range_of(X4))
    | ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_874]) ).

cnf(c_0_874_4,axiom,
    ( ~ little_set(X3)
    | ~ little_set(X2)
    | X5 != ordered_pair(X1,ordered_pair(X3,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,flip_range_of(X4))
    | ~ little_set(X1)
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_874]) ).

cnf(c_0_874_5,axiom,
    ( ~ little_set(X1)
    | ~ little_set(X3)
    | ~ little_set(X2)
    | X5 != ordered_pair(X1,ordered_pair(X3,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,flip_range_of(X4))
    | ~ little_set(X5) ),
    inference(literals_permutation,[status(thm)],[c_0_874]) ).

cnf(c_0_874_6,axiom,
    ( ~ little_set(X5)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ little_set(X2)
    | X5 != ordered_pair(X1,ordered_pair(X3,X2))
    | ~ member(ordered_pair(X1,ordered_pair(X2,X3)),X4)
    | member(X5,flip_range_of(X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_874]) ).

cnf(c_0_875_0,axiom,
    ( member(X6,compose(X5,X3))
    | ~ member(ordered_pair(X1,X2),X3)
    | ~ member(ordered_pair(X4,X1),X5)
    | X6 != ordered_pair(X4,X2)
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ little_set(X4)
    | ~ little_set(X6) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_875_1,axiom,
    ( ~ member(ordered_pair(X1,X2),X3)
    | member(X6,compose(X5,X3))
    | ~ member(ordered_pair(X4,X1),X5)
    | X6 != ordered_pair(X4,X2)
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ little_set(X4)
    | ~ little_set(X6) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_875_2,axiom,
    ( ~ member(ordered_pair(X4,X1),X5)
    | ~ member(ordered_pair(X1,X2),X3)
    | member(X6,compose(X5,X3))
    | X6 != ordered_pair(X4,X2)
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ little_set(X4)
    | ~ little_set(X6) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_875_3,axiom,
    ( X6 != ordered_pair(X4,X2)
    | ~ member(ordered_pair(X4,X1),X5)
    | ~ member(ordered_pair(X1,X2),X3)
    | member(X6,compose(X5,X3))
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ little_set(X4)
    | ~ little_set(X6) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_875_4,axiom,
    ( ~ little_set(X1)
    | X6 != ordered_pair(X4,X2)
    | ~ member(ordered_pair(X4,X1),X5)
    | ~ member(ordered_pair(X1,X2),X3)
    | member(X6,compose(X5,X3))
    | ~ little_set(X2)
    | ~ little_set(X4)
    | ~ little_set(X6) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_875_5,axiom,
    ( ~ little_set(X2)
    | ~ little_set(X1)
    | X6 != ordered_pair(X4,X2)
    | ~ member(ordered_pair(X4,X1),X5)
    | ~ member(ordered_pair(X1,X2),X3)
    | member(X6,compose(X5,X3))
    | ~ little_set(X4)
    | ~ little_set(X6) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_875_6,axiom,
    ( ~ little_set(X4)
    | ~ little_set(X2)
    | ~ little_set(X1)
    | X6 != ordered_pair(X4,X2)
    | ~ member(ordered_pair(X4,X1),X5)
    | ~ member(ordered_pair(X1,X2),X3)
    | member(X6,compose(X5,X3))
    | ~ little_set(X6) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_875_7,axiom,
    ( ~ little_set(X6)
    | ~ little_set(X4)
    | ~ little_set(X2)
    | ~ little_set(X1)
    | X6 != ordered_pair(X4,X2)
    | ~ member(ordered_pair(X4,X1),X5)
    | ~ member(ordered_pair(X1,X2),X3)
    | member(X6,compose(X5,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_875]) ).

cnf(c_0_876_0,axiom,
    ( ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2))) = X1
    | ~ member(X1,rotate_right(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_876]) ).

cnf(c_0_876_1,axiom,
    ( ~ member(X1,rotate_right(X2))
    | ordered_pair(f9(X1,X2),ordered_pair(f10(X1,X2),f11(X1,X2))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_876]) ).

cnf(c_0_877_0,axiom,
    ( ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2))) = X1
    | ~ member(X1,flip_range_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_877]) ).

cnf(c_0_877_1,axiom,
    ( ~ member(X1,flip_range_of(X2))
    | ordered_pair(f12(X1,X2),ordered_pair(f13(X1,X2),f14(X1,X2))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_877]) ).

cnf(c_0_878_0,axiom,
    ( member(f37(X1,X2,X3),X1)
    | identity(X1,X2,X3)
    | ~ member(X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_878]) ).

cnf(c_0_878_1,axiom,
    ( identity(X1,X2,X3)
    | member(f37(X1,X2,X3),X1)
    | ~ member(X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_878]) ).

cnf(c_0_878_2,axiom,
    ( ~ member(X3,X1)
    | identity(X1,X2,X3)
    | member(f37(X1,X2,X3),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_878]) ).

cnf(c_0_879_0,axiom,
    ( member(X1,non_ordered_pair(successor(empty_set),X2))
    | apply_to_two_arguments(times,X1,X3) != X2
    | ~ member(X3,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ member(X2,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_879]) ).

cnf(c_0_879_1,axiom,
    ( apply_to_two_arguments(times,X1,X3) != X2
    | member(X1,non_ordered_pair(successor(empty_set),X2))
    | ~ member(X3,natural_numbers)
    | ~ member(X1,natural_numbers)
    | ~ member(X2,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_879]) ).

cnf(c_0_879_2,axiom,
    ( ~ member(X3,natural_numbers)
    | apply_to_two_arguments(times,X1,X3) != X2
    | member(X1,non_ordered_pair(successor(empty_set),X2))
    | ~ member(X1,natural_numbers)
    | ~ member(X2,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_879]) ).

cnf(c_0_879_3,axiom,
    ( ~ member(X1,natural_numbers)
    | ~ member(X3,natural_numbers)
    | apply_to_two_arguments(times,X1,X3) != X2
    | member(X1,non_ordered_pair(successor(empty_set),X2))
    | ~ member(X2,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_879]) ).

cnf(c_0_879_4,axiom,
    ( ~ member(X2,prime_numbers)
    | ~ member(X1,natural_numbers)
    | ~ member(X3,natural_numbers)
    | apply_to_two_arguments(times,X1,X3) != X2
    | member(X1,non_ordered_pair(successor(empty_set),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_879]) ).

cnf(c_0_880_0,axiom,
    ( member(f22(X1,X2,X3),X3)
    | ~ member(X1,image(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_880]) ).

cnf(c_0_880_1,axiom,
    ( ~ member(X1,image(X2,X3))
    | member(f22(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_880]) ).

cnf(c_0_881_0,axiom,
    ( member(f28(X1,X2,X3),X2)
    | ~ member(X1,apply(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_881]) ).

cnf(c_0_881_1,axiom,
    ( ~ member(X1,apply(X2,X3))
    | member(f28(X1,X2,X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_881]) ).

cnf(c_0_882_0,axiom,
    ( apply_to_two_arguments(X1,X2,X3) = apply_to_two_arguments(X1,X3,X2)
    | ~ member(X3,X4)
    | ~ member(X2,X4)
    | ~ commutes(X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_882]) ).

cnf(c_0_882_1,axiom,
    ( ~ member(X3,X4)
    | apply_to_two_arguments(X1,X2,X3) = apply_to_two_arguments(X1,X3,X2)
    | ~ member(X2,X4)
    | ~ commutes(X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_882]) ).

cnf(c_0_882_2,axiom,
    ( ~ member(X2,X4)
    | ~ member(X3,X4)
    | apply_to_two_arguments(X1,X2,X3) = apply_to_two_arguments(X1,X3,X2)
    | ~ commutes(X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_882]) ).

cnf(c_0_882_3,axiom,
    ( ~ commutes(X4,X1)
    | ~ member(X2,X4)
    | ~ member(X3,X4)
    | apply_to_two_arguments(X1,X2,X3) = apply_to_two_arguments(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_882]) ).

cnf(c_0_883_0,axiom,
    ( member(X1,X2)
    | ~ member(successor(f43(X1,X2)),X2)
    | ~ member(empty_set,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_883]) ).

cnf(c_0_883_1,axiom,
    ( ~ member(successor(f43(X1,X2)),X2)
    | member(X1,X2)
    | ~ member(empty_set,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_883]) ).

cnf(c_0_883_2,axiom,
    ( ~ member(empty_set,X2)
    | ~ member(successor(f43(X1,X2)),X2)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_883]) ).

cnf(c_0_883_3,axiom,
    ( ~ little_set(X2)
    | ~ member(empty_set,X2)
    | ~ member(successor(f43(X1,X2)),X2)
    | member(X1,X2)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_883]) ).

cnf(c_0_883_4,axiom,
    ( ~ member(X1,natural_numbers)
    | ~ little_set(X2)
    | ~ member(empty_set,X2)
    | ~ member(successor(f43(X1,X2)),X2)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_883]) ).

cnf(c_0_884_0,axiom,
    ( second(f22(X1,X2,X3)) = X1
    | ~ member(X1,image(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_884]) ).

cnf(c_0_884_1,axiom,
    ( ~ member(X1,image(X2,X3))
    | second(f22(X1,X2,X3)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_884]) ).

cnf(c_0_885_0,axiom,
    ( first(f28(X1,X2,X3)) = X3
    | ~ member(X1,apply(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_885]) ).

cnf(c_0_885_1,axiom,
    ( ~ member(X1,apply(X2,X3))
    | first(f28(X1,X2,X3)) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_885]) ).

cnf(c_0_886_0,axiom,
    ( ordered_pair_predicate(f22(X1,X2,X3))
    | ~ member(X1,image(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_886]) ).

cnf(c_0_886_1,axiom,
    ( ~ member(X1,image(X2,X3))
    | ordered_pair_predicate(f22(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_886]) ).

cnf(c_0_887_0,axiom,
    ( ordered_pair_predicate(f28(X1,X2,X3))
    | ~ member(X1,apply(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_887]) ).

cnf(c_0_887_1,axiom,
    ( ~ member(X1,apply(X2,X3))
    | ordered_pair_predicate(f28(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_887]) ).

cnf(c_0_888_0,axiom,
    ( little_set(f29(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_888]) ).

cnf(c_0_888_1,axiom,
    ( ~ member(X1,compose(X2,X3))
    | little_set(f29(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_888]) ).

cnf(c_0_889_0,axiom,
    ( little_set(f30(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_889]) ).

cnf(c_0_889_1,axiom,
    ( ~ member(X1,compose(X2,X3))
    | little_set(f30(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_889]) ).

cnf(c_0_890_0,axiom,
    ( little_set(f31(X1,X2,X3))
    | ~ member(X1,compose(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_890]) ).

cnf(c_0_890_1,axiom,
    ( ~ member(X1,compose(X2,X3))
    | little_set(f31(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_890]) ).

cnf(c_0_891_0,axiom,
    ( apply_to_two_arguments(X1,X2,X3) = X3
    | ~ member(X3,X4)
    | ~ identity(X4,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_891]) ).

cnf(c_0_891_1,axiom,
    ( ~ member(X3,X4)
    | apply_to_two_arguments(X1,X2,X3) = X3
    | ~ identity(X4,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_891]) ).

cnf(c_0_891_2,axiom,
    ( ~ identity(X4,X1,X2)
    | ~ member(X3,X4)
    | apply_to_two_arguments(X1,X2,X3) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_891]) ).

cnf(c_0_892_0,axiom,
    ( apply_to_two_arguments(X1,X2,X3) = X2
    | ~ member(X2,X4)
    | ~ identity(X4,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_892]) ).

cnf(c_0_892_1,axiom,
    ( ~ member(X2,X4)
    | apply_to_two_arguments(X1,X2,X3) = X2
    | ~ identity(X4,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_892]) ).

cnf(c_0_892_2,axiom,
    ( ~ identity(X4,X1,X3)
    | ~ member(X2,X4)
    | apply_to_two_arguments(X1,X2,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_892]) ).

cnf(c_0_893_0,axiom,
    ( X1 = X2
    | ~ member(ordered_pair(X3,X2),X4)
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ single_valued_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_893]) ).

cnf(c_0_893_1,axiom,
    ( ~ member(ordered_pair(X3,X2),X4)
    | X1 = X2
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ single_valued_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_893]) ).

cnf(c_0_893_2,axiom,
    ( ~ member(ordered_pair(X3,X1),X4)
    | ~ member(ordered_pair(X3,X2),X4)
    | X1 = X2
    | ~ little_set(X2)
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ single_valued_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_893]) ).

cnf(c_0_893_3,axiom,
    ( ~ little_set(X2)
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ member(ordered_pair(X3,X2),X4)
    | X1 = X2
    | ~ little_set(X1)
    | ~ little_set(X3)
    | ~ single_valued_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_893]) ).

cnf(c_0_893_4,axiom,
    ( ~ little_set(X1)
    | ~ little_set(X2)
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ member(ordered_pair(X3,X2),X4)
    | X1 = X2
    | ~ little_set(X3)
    | ~ single_valued_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_893]) ).

cnf(c_0_893_5,axiom,
    ( ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ member(ordered_pair(X3,X2),X4)
    | X1 = X2
    | ~ single_valued_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_893]) ).

cnf(c_0_893_6,axiom,
    ( ~ single_valued_set(X4)
    | ~ little_set(X3)
    | ~ little_set(X1)
    | ~ little_set(X2)
    | ~ member(ordered_pair(X3,X1),X4)
    | ~ member(ordered_pair(X3,X2),X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_893]) ).

cnf(c_0_894_0,axiom,
    ( closed(X2,X1)
    | ~ maps(X1,cross_product(X2,X2),X2)
    | ~ little_set(X1)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_894]) ).

cnf(c_0_894_1,axiom,
    ( ~ maps(X1,cross_product(X2,X2),X2)
    | closed(X2,X1)
    | ~ little_set(X1)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_894]) ).

cnf(c_0_894_2,axiom,
    ( ~ little_set(X1)
    | ~ maps(X1,cross_product(X2,X2),X2)
    | closed(X2,X1)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_894]) ).

cnf(c_0_894_3,axiom,
    ( ~ little_set(X2)
    | ~ little_set(X1)
    | ~ maps(X1,cross_product(X2,X2),X2)
    | closed(X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_894]) ).

cnf(c_0_895_0,axiom,
    ( member(X2,even_numbers)
    | apply_to_two_arguments(plus,X1,X1) != X2
    | ~ member(X1,natural_numbers)
    | ~ member(X2,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_895]) ).

cnf(c_0_895_1,axiom,
    ( apply_to_two_arguments(plus,X1,X1) != X2
    | member(X2,even_numbers)
    | ~ member(X1,natural_numbers)
    | ~ member(X2,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_895]) ).

cnf(c_0_895_2,axiom,
    ( ~ member(X1,natural_numbers)
    | apply_to_two_arguments(plus,X1,X1) != X2
    | member(X2,even_numbers)
    | ~ member(X2,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_895]) ).

cnf(c_0_895_3,axiom,
    ( ~ member(X2,natural_numbers)
    | ~ member(X1,natural_numbers)
    | apply_to_two_arguments(plus,X1,X1) != X2
    | member(X2,even_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_895]) ).

cnf(c_0_896_0,axiom,
    ( member(X1,converse(X2))
    | ~ member(ordered_pair(second(X1),first(X1)),X2)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_896]) ).

cnf(c_0_896_1,axiom,
    ( ~ member(ordered_pair(second(X1),first(X1)),X2)
    | member(X1,converse(X2))
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_896]) ).

cnf(c_0_896_2,axiom,
    ( ~ ordered_pair_predicate(X1)
    | ~ member(ordered_pair(second(X1),first(X1)),X2)
    | member(X1,converse(X2))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_896]) ).

cnf(c_0_896_3,axiom,
    ( ~ little_set(X1)
    | ~ ordered_pair_predicate(X1)
    | ~ member(ordered_pair(second(X1),first(X1)),X2)
    | member(X1,converse(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_896]) ).

cnf(c_0_897_0,axiom,
    ( member(ordered_pair(ordered_pair(empty_set,X1),X1),f49(X2))
    | member(X2,plus)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_897]) ).

cnf(c_0_897_1,axiom,
    ( member(X2,plus)
    | member(ordered_pair(ordered_pair(empty_set,X1),X1),f49(X2))
    | ~ member(X1,natural_numbers)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_897]) ).

cnf(c_0_897_2,axiom,
    ( ~ member(X1,natural_numbers)
    | member(X2,plus)
    | member(ordered_pair(ordered_pair(empty_set,X1),X1),f49(X2))
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_897]) ).

cnf(c_0_897_3,axiom,
    ( ~ little_set(X2)
    | ~ member(X1,natural_numbers)
    | member(X2,plus)
    | member(ordered_pair(ordered_pair(empty_set,X1),X1),f49(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_897]) ).

cnf(c_0_898_0,axiom,
    ( member(ordered_pair(ordered_pair(empty_set,X1),empty_set),f54(X2))
    | member(X2,times)
    | ~ member(X1,natural_numbers)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_898]) ).

cnf(c_0_898_1,axiom,
    ( member(X2,times)
    | member(ordered_pair(ordered_pair(empty_set,X1),empty_set),f54(X2))
    | ~ member(X1,natural_numbers)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_898]) ).

cnf(c_0_898_2,axiom,
    ( ~ member(X1,natural_numbers)
    | member(X2,times)
    | member(ordered_pair(ordered_pair(empty_set,X1),empty_set),f54(X2))
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_898]) ).

cnf(c_0_898_3,axiom,
    ( ~ little_set(X2)
    | ~ member(X1,natural_numbers)
    | member(X2,times)
    | member(ordered_pair(ordered_pair(empty_set,X1),empty_set),f54(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_898]) ).

cnf(c_0_899_0,axiom,
    ( X1 = X2
    | ~ member(f1(X1,X2),X2)
    | ~ member(f1(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_899]) ).

cnf(c_0_899_1,axiom,
    ( ~ member(f1(X1,X2),X2)
    | X1 = X2
    | ~ member(f1(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_899]) ).

cnf(c_0_899_2,axiom,
    ( ~ member(f1(X1,X2),X1)
    | ~ member(f1(X1,X2),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_899]) ).

cnf(c_0_900_0,axiom,
    ( finite(X2)
    | ~ one_to_one_function(X1)
    | range_of(X1) != X2
    | ~ maps(X1,X3,X2)
    | ~ member(X3,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_900]) ).

cnf(c_0_900_1,axiom,
    ( ~ one_to_one_function(X1)
    | finite(X2)
    | range_of(X1) != X2
    | ~ maps(X1,X3,X2)
    | ~ member(X3,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_900]) ).

cnf(c_0_900_2,axiom,
    ( range_of(X1) != X2
    | ~ one_to_one_function(X1)
    | finite(X2)
    | ~ maps(X1,X3,X2)
    | ~ member(X3,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_900]) ).

cnf(c_0_900_3,axiom,
    ( ~ maps(X1,X3,X2)
    | range_of(X1) != X2
    | ~ one_to_one_function(X1)
    | finite(X2)
    | ~ member(X3,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_900]) ).

cnf(c_0_900_4,axiom,
    ( ~ member(X3,natural_numbers)
    | ~ maps(X1,X3,X2)
    | range_of(X1) != X2
    | ~ one_to_one_function(X1)
    | finite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_900]) ).

cnf(c_0_901_0,axiom,
    ( X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(f55(X1),non_ordered_pair(successor(empty_set),X1))
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_901]) ).

cnf(c_0_901_1,axiom,
    ( X1 = empty_set
    | X1 = successor(empty_set)
    | member(X1,prime_numbers)
    | ~ member(f55(X1),non_ordered_pair(successor(empty_set),X1))
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_901]) ).

cnf(c_0_901_2,axiom,
    ( member(X1,prime_numbers)
    | X1 = empty_set
    | X1 = successor(empty_set)
    | ~ member(f55(X1),non_ordered_pair(successor(empty_set),X1))
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_901]) ).

cnf(c_0_901_3,axiom,
    ( ~ member(f55(X1),non_ordered_pair(successor(empty_set),X1))
    | member(X1,prime_numbers)
    | X1 = empty_set
    | X1 = successor(empty_set)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_901]) ).

cnf(c_0_901_4,axiom,
    ( ~ member(X1,natural_numbers)
    | ~ member(f55(X1),non_ordered_pair(successor(empty_set),X1))
    | member(X1,prime_numbers)
    | X1 = empty_set
    | X1 = successor(empty_set) ),
    inference(literals_permutation,[status(thm)],[c_0_901]) ).

cnf(c_0_902_0,axiom,
    ( member(X1,X2)
    | member(f46(X1,X2),natural_numbers)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_902]) ).

cnf(c_0_902_1,axiom,
    ( member(f46(X1,X2),natural_numbers)
    | member(X1,X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_902]) ).

cnf(c_0_902_2,axiom,
    ( member(f45(X1,X2),natural_numbers)
    | member(f46(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_902]) ).

cnf(c_0_902_3,axiom,
    ( ~ little_set(X2)
    | member(f45(X1,X2),natural_numbers)
    | member(f46(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_902]) ).

cnf(c_0_902_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | member(f45(X1,X2),natural_numbers)
    | member(f46(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_902]) ).

cnf(c_0_903_0,axiom,
    ( member(X1,X2)
    | member(f47(X1,X2),natural_numbers)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_903]) ).

cnf(c_0_903_1,axiom,
    ( member(f47(X1,X2),natural_numbers)
    | member(X1,X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_903]) ).

cnf(c_0_903_2,axiom,
    ( member(f45(X1,X2),natural_numbers)
    | member(f47(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_903]) ).

cnf(c_0_903_3,axiom,
    ( ~ little_set(X2)
    | member(f45(X1,X2),natural_numbers)
    | member(f47(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_903]) ).

cnf(c_0_903_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | member(f45(X1,X2),natural_numbers)
    | member(f47(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_903]) ).

cnf(c_0_904_0,axiom,
    ( member(X1,X2)
    | member(f48(X1,X2),natural_numbers)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_904]) ).

cnf(c_0_904_1,axiom,
    ( member(f48(X1,X2),natural_numbers)
    | member(X1,X2)
    | member(f45(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_904]) ).

cnf(c_0_904_2,axiom,
    ( member(f45(X1,X2),natural_numbers)
    | member(f48(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_904]) ).

cnf(c_0_904_3,axiom,
    ( ~ little_set(X2)
    | member(f45(X1,X2),natural_numbers)
    | member(f48(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_904]) ).

cnf(c_0_904_4,axiom,
    ( ~ member(X1,plus)
    | ~ little_set(X2)
    | member(f45(X1,X2),natural_numbers)
    | member(f48(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_904]) ).

cnf(c_0_905_0,axiom,
    ( member(X1,X2)
    | member(f51(X1,X2),natural_numbers)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_905]) ).

cnf(c_0_905_1,axiom,
    ( member(f51(X1,X2),natural_numbers)
    | member(X1,X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_905]) ).

cnf(c_0_905_2,axiom,
    ( member(f50(X1,X2),natural_numbers)
    | member(f51(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_905]) ).

cnf(c_0_905_3,axiom,
    ( ~ little_set(X2)
    | member(f50(X1,X2),natural_numbers)
    | member(f51(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_905]) ).

cnf(c_0_905_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | member(f50(X1,X2),natural_numbers)
    | member(f51(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_905]) ).

cnf(c_0_906_0,axiom,
    ( member(X1,X2)
    | member(f52(X1,X2),natural_numbers)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_906]) ).

cnf(c_0_906_1,axiom,
    ( member(f52(X1,X2),natural_numbers)
    | member(X1,X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_906]) ).

cnf(c_0_906_2,axiom,
    ( member(f50(X1,X2),natural_numbers)
    | member(f52(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_906]) ).

cnf(c_0_906_3,axiom,
    ( ~ little_set(X2)
    | member(f50(X1,X2),natural_numbers)
    | member(f52(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_906]) ).

cnf(c_0_906_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | member(f50(X1,X2),natural_numbers)
    | member(f52(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_906]) ).

cnf(c_0_907_0,axiom,
    ( member(X1,X2)
    | member(f53(X1,X2),natural_numbers)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_907]) ).

cnf(c_0_907_1,axiom,
    ( member(f53(X1,X2),natural_numbers)
    | member(X1,X2)
    | member(f50(X1,X2),natural_numbers)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_907]) ).

cnf(c_0_907_2,axiom,
    ( member(f50(X1,X2),natural_numbers)
    | member(f53(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_907]) ).

cnf(c_0_907_3,axiom,
    ( ~ little_set(X2)
    | member(f50(X1,X2),natural_numbers)
    | member(f53(X1,X2),natural_numbers)
    | member(X1,X2)
    | ~ member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_907]) ).

cnf(c_0_907_4,axiom,
    ( ~ member(X1,times)
    | ~ little_set(X2)
    | member(f50(X1,X2),natural_numbers)
    | member(f53(X1,X2),natural_numbers)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_907]) ).

cnf(c_0_908_0,axiom,
    ( member(X1,cross_product(X3,X2))
    | ~ member(second(X1),X2)
    | ~ member(first(X1),X3)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_908]) ).

cnf(c_0_908_1,axiom,
    ( ~ member(second(X1),X2)
    | member(X1,cross_product(X3,X2))
    | ~ member(first(X1),X3)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_908]) ).

cnf(c_0_908_2,axiom,
    ( ~ member(first(X1),X3)
    | ~ member(second(X1),X2)
    | member(X1,cross_product(X3,X2))
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_908]) ).

cnf(c_0_908_3,axiom,
    ( ~ ordered_pair_predicate(X1)
    | ~ member(first(X1),X3)
    | ~ member(second(X1),X2)
    | member(X1,cross_product(X3,X2))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_908]) ).

cnf(c_0_908_4,axiom,
    ( ~ little_set(X1)
    | ~ ordered_pair_predicate(X1)
    | ~ member(first(X1),X3)
    | ~ member(second(X1),X2)
    | member(X1,cross_product(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_908]) ).

cnf(c_0_909_0,axiom,
    ( member(X2,image(X3,X4))
    | second(X1) != X2
    | ~ member(first(X1),X3)
    | ~ member(X1,X4)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_909]) ).

cnf(c_0_909_1,axiom,
    ( second(X1) != X2
    | member(X2,image(X3,X4))
    | ~ member(first(X1),X3)
    | ~ member(X1,X4)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_909]) ).

cnf(c_0_909_2,axiom,
    ( ~ member(first(X1),X3)
    | second(X1) != X2
    | member(X2,image(X3,X4))
    | ~ member(X1,X4)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_909]) ).

cnf(c_0_909_3,axiom,
    ( ~ member(X1,X4)
    | ~ member(first(X1),X3)
    | second(X1) != X2
    | member(X2,image(X3,X4))
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_909]) ).

cnf(c_0_909_4,axiom,
    ( ~ ordered_pair_predicate(X1)
    | ~ member(X1,X4)
    | ~ member(first(X1),X3)
    | second(X1) != X2
    | member(X2,image(X3,X4))
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_909]) ).

cnf(c_0_909_5,axiom,
    ( ~ little_set(X2)
    | ~ ordered_pair_predicate(X1)
    | ~ member(X1,X4)
    | ~ member(first(X1),X3)
    | second(X1) != X2
    | member(X2,image(X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_909]) ).

cnf(c_0_910_0,axiom,
    ( member(X1,apply(X4,X3))
    | ~ member(X1,second(X2))
    | first(X2) != X3
    | ~ member(X2,X4)
    | ~ ordered_pair_predicate(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_910]) ).

cnf(c_0_910_1,axiom,
    ( ~ member(X1,second(X2))
    | member(X1,apply(X4,X3))
    | first(X2) != X3
    | ~ member(X2,X4)
    | ~ ordered_pair_predicate(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_910]) ).

cnf(c_0_910_2,axiom,
    ( first(X2) != X3
    | ~ member(X1,second(X2))
    | member(X1,apply(X4,X3))
    | ~ member(X2,X4)
    | ~ ordered_pair_predicate(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_910]) ).

cnf(c_0_910_3,axiom,
    ( ~ member(X2,X4)
    | first(X2) != X3
    | ~ member(X1,second(X2))
    | member(X1,apply(X4,X3))
    | ~ ordered_pair_predicate(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_910]) ).

cnf(c_0_910_4,axiom,
    ( ~ ordered_pair_predicate(X2)
    | ~ member(X2,X4)
    | first(X2) != X3
    | ~ member(X1,second(X2))
    | member(X1,apply(X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_910]) ).

cnf(c_0_911_0,axiom,
    ( subset(range_of(X1),X2)
    | ~ maps(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_911]) ).

cnf(c_0_911_1,axiom,
    ( ~ maps(X1,X3,X2)
    | subset(range_of(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_911]) ).

cnf(c_0_912_0,axiom,
    ( apply_to_two_arguments(times,f55(X1),f56(X1)) = X1
    | X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_912]) ).

cnf(c_0_912_1,axiom,
    ( X1 = successor(empty_set)
    | apply_to_two_arguments(times,f55(X1),f56(X1)) = X1
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_912]) ).

cnf(c_0_912_2,axiom,
    ( X1 = empty_set
    | X1 = successor(empty_set)
    | apply_to_two_arguments(times,f55(X1),f56(X1)) = X1
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_912]) ).

cnf(c_0_912_3,axiom,
    ( member(X1,prime_numbers)
    | X1 = empty_set
    | X1 = successor(empty_set)
    | apply_to_two_arguments(times,f55(X1),f56(X1)) = X1
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_912]) ).

cnf(c_0_912_4,axiom,
    ( ~ member(X1,natural_numbers)
    | member(X1,prime_numbers)
    | X1 = empty_set
    | X1 = successor(empty_set)
    | apply_to_two_arguments(times,f55(X1),f56(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_912]) ).

cnf(c_0_913_0,axiom,
    ( maps(X1,cross_product(X2,X2),X2)
    | ~ closed(X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_913]) ).

cnf(c_0_913_1,axiom,
    ( ~ closed(X2,X1)
    | maps(X1,cross_product(X2,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_913]) ).

cnf(c_0_914_0,axiom,
    ( identity(X1,X2,f39(X1,X2))
    | ~ group(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_914]) ).

cnf(c_0_914_1,axiom,
    ( ~ group(X1,X2)
    | identity(X1,X2,f39(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_914]) ).

cnf(c_0_915_0,axiom,
    ( maps(X1,X3,X2)
    | ~ subset(range_of(X1),X2)
    | domain_of(X1) != X3
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_915]) ).

cnf(c_0_915_1,axiom,
    ( ~ subset(range_of(X1),X2)
    | maps(X1,X3,X2)
    | domain_of(X1) != X3
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_915]) ).

cnf(c_0_915_2,axiom,
    ( domain_of(X1) != X3
    | ~ subset(range_of(X1),X2)
    | maps(X1,X3,X2)
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_915]) ).

cnf(c_0_915_3,axiom,
    ( ~ function(X1)
    | domain_of(X1) != X3
    | ~ subset(range_of(X1),X2)
    | maps(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_915]) ).

cnf(c_0_916_0,axiom,
    ( member(X1,X2)
    | member(f43(X1,X2),X2)
    | ~ member(empty_set,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_916]) ).

cnf(c_0_916_1,axiom,
    ( member(f43(X1,X2),X2)
    | member(X1,X2)
    | ~ member(empty_set,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_916]) ).

cnf(c_0_916_2,axiom,
    ( ~ member(empty_set,X2)
    | member(f43(X1,X2),X2)
    | member(X1,X2)
    | ~ little_set(X2)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_916]) ).

cnf(c_0_916_3,axiom,
    ( ~ little_set(X2)
    | ~ member(empty_set,X2)
    | member(f43(X1,X2),X2)
    | member(X1,X2)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_916]) ).

cnf(c_0_916_4,axiom,
    ( ~ member(X1,natural_numbers)
    | ~ little_set(X2)
    | ~ member(empty_set,X2)
    | member(f43(X1,X2),X2)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_916]) ).

cnf(c_0_917_0,axiom,
    ( member(X1,X2)
    | ~ identity(X2,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_917]) ).

cnf(c_0_917_1,axiom,
    ( ~ identity(X2,X3,X1)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_917]) ).

cnf(c_0_918_0,axiom,
    ( ordered_pair(f4(X2,X1),f5(X2,X1)) = X1
    | ~ member(X2,first(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_918]) ).

cnf(c_0_918_1,axiom,
    ( ~ member(X2,first(X1))
    | ordered_pair(f4(X2,X1),f5(X2,X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_918]) ).

cnf(c_0_919_0,axiom,
    ( ordered_pair(f6(X2,X1),f7(X2,X1)) = X1
    | ~ member(X2,second(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_919]) ).

cnf(c_0_919_1,axiom,
    ( ~ member(X2,second(X1))
    | ordered_pair(f6(X2,X1),f7(X2,X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_919]) ).

cnf(c_0_920_0,axiom,
    ( member(ordered_pair(second(X1),first(X1)),X2)
    | ~ member(X1,converse(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_920]) ).

cnf(c_0_920_1,axiom,
    ( ~ member(X1,converse(X2))
    | member(ordered_pair(second(X1),first(X1)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_920]) ).

cnf(c_0_921_0,axiom,
    ( domain_of(X1) = X2
    | ~ maps(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_921]) ).

cnf(c_0_921_1,axiom,
    ( ~ maps(X1,X2,X3)
    | domain_of(X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_921]) ).

cnf(c_0_922_0,axiom,
    ( function(X1)
    | ~ maps(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_922]) ).

cnf(c_0_922_1,axiom,
    ( ~ maps(X1,X2,X3)
    | function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_922]) ).

cnf(c_0_923_0,axiom,
    ( apply_to_two_arguments(plus,f59(X1),f59(X1)) = X1
    | ~ member(X1,even_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_923]) ).

cnf(c_0_923_1,axiom,
    ( ~ member(X1,even_numbers)
    | apply_to_two_arguments(plus,f59(X1),f59(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_923]) ).

cnf(c_0_924_0,axiom,
    ( member(X1,intersection(X3,X2))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_924]) ).

cnf(c_0_924_1,axiom,
    ( ~ member(X1,X2)
    | member(X1,intersection(X3,X2))
    | ~ member(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_924]) ).

cnf(c_0_924_2,axiom,
    ( ~ member(X1,X3)
    | ~ member(X1,X2)
    | member(X1,intersection(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_924]) ).

cnf(c_0_925_0,axiom,
    ( member(first(X1),X2)
    | ~ member(X1,cross_product(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_925]) ).

cnf(c_0_925_1,axiom,
    ( ~ member(X1,cross_product(X2,X3))
    | member(first(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_925]) ).

cnf(c_0_926_0,axiom,
    ( member(second(X1),X2)
    | ~ member(X1,cross_product(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_926]) ).

cnf(c_0_926_1,axiom,
    ( ~ member(X1,cross_product(X3,X2))
    | member(second(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_926]) ).

cnf(c_0_927_0,axiom,
    ( X1 = X2
    | member(f1(X1,X2),X2)
    | member(f1(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_927]) ).

cnf(c_0_927_1,axiom,
    ( member(f1(X1,X2),X2)
    | X1 = X2
    | member(f1(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_927]) ).

cnf(c_0_927_2,axiom,
    ( member(f1(X1,X2),X1)
    | member(f1(X1,X2),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_927]) ).

cnf(c_0_928_0,axiom,
    ( member(X1,twin_prime_numbers)
    | ~ member(successor(successor(X1)),prime_numbers)
    | ~ member(X1,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_928]) ).

cnf(c_0_928_1,axiom,
    ( ~ member(successor(successor(X1)),prime_numbers)
    | member(X1,twin_prime_numbers)
    | ~ member(X1,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_928]) ).

cnf(c_0_928_2,axiom,
    ( ~ member(X1,prime_numbers)
    | ~ member(successor(successor(X1)),prime_numbers)
    | member(X1,twin_prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_928]) ).

cnf(c_0_929_0,axiom,
    ( member(X1,first(X3))
    | ~ member(X1,X2)
    | X3 != ordered_pair(X2,X4)
    | ~ little_set(X4)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_929]) ).

cnf(c_0_929_1,axiom,
    ( ~ member(X1,X2)
    | member(X1,first(X3))
    | X3 != ordered_pair(X2,X4)
    | ~ little_set(X4)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_929]) ).

cnf(c_0_929_2,axiom,
    ( X3 != ordered_pair(X2,X4)
    | ~ member(X1,X2)
    | member(X1,first(X3))
    | ~ little_set(X4)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_929]) ).

cnf(c_0_929_3,axiom,
    ( ~ little_set(X4)
    | X3 != ordered_pair(X2,X4)
    | ~ member(X1,X2)
    | member(X1,first(X3))
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_929]) ).

cnf(c_0_929_4,axiom,
    ( ~ little_set(X2)
    | ~ little_set(X4)
    | X3 != ordered_pair(X2,X4)
    | ~ member(X1,X2)
    | member(X1,first(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_929]) ).

cnf(c_0_930_0,axiom,
    ( member(X1,second(X3))
    | ~ member(X1,X2)
    | X3 != ordered_pair(X4,X2)
    | ~ little_set(X2)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_930]) ).

cnf(c_0_930_1,axiom,
    ( ~ member(X1,X2)
    | member(X1,second(X3))
    | X3 != ordered_pair(X4,X2)
    | ~ little_set(X2)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_930]) ).

cnf(c_0_930_2,axiom,
    ( X3 != ordered_pair(X4,X2)
    | ~ member(X1,X2)
    | member(X1,second(X3))
    | ~ little_set(X2)
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_930]) ).

cnf(c_0_930_3,axiom,
    ( ~ little_set(X2)
    | X3 != ordered_pair(X4,X2)
    | ~ member(X1,X2)
    | member(X1,second(X3))
    | ~ little_set(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_930]) ).

cnf(c_0_930_4,axiom,
    ( ~ little_set(X4)
    | ~ little_set(X2)
    | X3 != ordered_pair(X4,X2)
    | ~ member(X1,X2)
    | member(X1,second(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_930]) ).

cnf(c_0_931_0,axiom,
    ( member(successor(X1),f44(X2))
    | member(X2,natural_numbers)
    | ~ member(X1,f44(X2))
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_931]) ).

cnf(c_0_931_1,axiom,
    ( member(X2,natural_numbers)
    | member(successor(X1),f44(X2))
    | ~ member(X1,f44(X2))
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_931]) ).

cnf(c_0_931_2,axiom,
    ( ~ member(X1,f44(X2))
    | member(X2,natural_numbers)
    | member(successor(X1),f44(X2))
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_931]) ).

cnf(c_0_931_3,axiom,
    ( ~ little_set(X2)
    | ~ member(X1,f44(X2))
    | member(X2,natural_numbers)
    | member(successor(X1),f44(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_931]) ).

cnf(c_0_932_0,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_932]) ).

cnf(c_0_932_1,axiom,
    ( ~ member(X1,intersection(X2,X3))
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_932]) ).

cnf(c_0_933_0,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_933]) ).

cnf(c_0_933_1,axiom,
    ( ~ member(X1,intersection(X3,X2))
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_933]) ).

cnf(c_0_934_0,axiom,
    ( subset(X1,X2)
    | ~ member(f17(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_934]) ).

cnf(c_0_934_1,axiom,
    ( ~ member(f17(X1,X2),X2)
    | subset(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_934]) ).

cnf(c_0_935_0,axiom,
    ( maps(f58(X1),f57(X1),X1)
    | ~ finite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_935]) ).

cnf(c_0_935_1,axiom,
    ( ~ finite(X1)
    | maps(f58(X1),f57(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_935]) ).

cnf(c_0_936_0,axiom,
    ( member(X1,f4(X1,X2))
    | ~ member(X1,first(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_936]) ).

cnf(c_0_936_1,axiom,
    ( ~ member(X1,first(X2))
    | member(X1,f4(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_936]) ).

cnf(c_0_937_0,axiom,
    ( member(X1,f7(X1,X2))
    | ~ member(X1,second(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_937]) ).

cnf(c_0_937_1,axiom,
    ( ~ member(X1,second(X2))
    | member(X1,f7(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_937]) ).

cnf(c_0_938_0,axiom,
    ( member(f8(X1,X2),X2)
    | ~ member(X1,domain_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_938]) ).

cnf(c_0_938_1,axiom,
    ( ~ member(X1,domain_of(X2))
    | member(f8(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_938]) ).

cnf(c_0_939_0,axiom,
    ( member(f16(X1,X2),X2)
    | ~ member(X1,sigma(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_939]) ).

cnf(c_0_939_1,axiom,
    ( ~ member(X1,sigma(X2))
    | member(f16(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_939]) ).

cnf(c_0_940_0,axiom,
    ( member(X1,f16(X1,X2))
    | ~ member(X1,sigma(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_940]) ).

cnf(c_0_940_1,axiom,
    ( ~ member(X1,sigma(X2))
    | member(X1,f16(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_940]) ).

cnf(c_0_941_0,axiom,
    ( member(f27(X1,X2),X2)
    | ~ member(X1,range_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_941]) ).

cnf(c_0_941_1,axiom,
    ( ~ member(X1,range_of(X2))
    | member(f27(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_941]) ).

cnf(c_0_942_0,axiom,
    ( member(ordered_pair(f19(X1),f20(X1)),X1)
    | single_valued_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_942]) ).

cnf(c_0_942_1,axiom,
    ( single_valued_set(X1)
    | member(ordered_pair(f19(X1),f20(X1)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_942]) ).

cnf(c_0_943_0,axiom,
    ( member(ordered_pair(f19(X1),f21(X1)),X1)
    | single_valued_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_943]) ).

cnf(c_0_943_1,axiom,
    ( single_valued_set(X1)
    | member(ordered_pair(f19(X1),f21(X1)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_943]) ).

cnf(c_0_944_0,axiom,
    ( member(X1,estin)
    | ~ member(first(X1),second(X1))
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_944]) ).

cnf(c_0_944_1,axiom,
    ( ~ member(first(X1),second(X1))
    | member(X1,estin)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_944]) ).

cnf(c_0_944_2,axiom,
    ( ~ ordered_pair_predicate(X1)
    | ~ member(first(X1),second(X1))
    | member(X1,estin)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_944]) ).

cnf(c_0_944_3,axiom,
    ( ~ little_set(X1)
    | ~ ordered_pair_predicate(X1)
    | ~ member(first(X1),second(X1))
    | member(X1,estin) ),
    inference(literals_permutation,[status(thm)],[c_0_944]) ).

cnf(c_0_945_0,axiom,
    ( ~ member(X1,X2)
    | ~ member(X1,X3)
    | ~ disjoint(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_945]) ).

cnf(c_0_945_1,axiom,
    ( ~ member(X1,X3)
    | ~ member(X1,X2)
    | ~ disjoint(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_945]) ).

cnf(c_0_945_2,axiom,
    ( ~ disjoint(X3,X2)
    | ~ member(X1,X3)
    | ~ member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_945]) ).

cnf(c_0_946_0,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,non_ordered_pair(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_946]) ).

cnf(c_0_946_1,axiom,
    ( X1 = X3
    | X1 = X2
    | ~ member(X1,non_ordered_pair(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_946]) ).

cnf(c_0_946_2,axiom,
    ( ~ member(X1,non_ordered_pair(X3,X2))
    | X1 = X3
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_946]) ).

cnf(c_0_947_0,axiom,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,cross_product(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_947]) ).

cnf(c_0_947_1,axiom,
    ( ~ member(X1,cross_product(X2,X3))
    | ordered_pair_predicate(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_947]) ).

cnf(c_0_948_0,axiom,
    ( member(X1,domain_of(X3))
    | X1 != first(X2)
    | ~ member(X2,X3)
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_948]) ).

cnf(c_0_948_1,axiom,
    ( X1 != first(X2)
    | member(X1,domain_of(X3))
    | ~ member(X2,X3)
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_948]) ).

cnf(c_0_948_2,axiom,
    ( ~ member(X2,X3)
    | X1 != first(X2)
    | member(X1,domain_of(X3))
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_948]) ).

cnf(c_0_948_3,axiom,
    ( ~ ordered_pair_predicate(X2)
    | ~ member(X2,X3)
    | X1 != first(X2)
    | member(X1,domain_of(X3))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_948]) ).

cnf(c_0_948_4,axiom,
    ( ~ little_set(X1)
    | ~ ordered_pair_predicate(X2)
    | ~ member(X2,X3)
    | X1 != first(X2)
    | member(X1,domain_of(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_948]) ).

cnf(c_0_949_0,axiom,
    ( member(X1,sigma(X3))
    | ~ member(X1,X2)
    | ~ member(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_949]) ).

cnf(c_0_949_1,axiom,
    ( ~ member(X1,X2)
    | member(X1,sigma(X3))
    | ~ member(X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_949]) ).

cnf(c_0_949_2,axiom,
    ( ~ member(X2,X3)
    | ~ member(X1,X2)
    | member(X1,sigma(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_949]) ).

cnf(c_0_950_0,axiom,
    ( member(X1,range_of(X3))
    | X1 != second(X2)
    | ~ member(X2,X3)
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_950]) ).

cnf(c_0_950_1,axiom,
    ( X1 != second(X2)
    | member(X1,range_of(X3))
    | ~ member(X2,X3)
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_950]) ).

cnf(c_0_950_2,axiom,
    ( ~ member(X2,X3)
    | X1 != second(X2)
    | member(X1,range_of(X3))
    | ~ ordered_pair_predicate(X2)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_950]) ).

cnf(c_0_950_3,axiom,
    ( ~ ordered_pair_predicate(X2)
    | ~ member(X2,X3)
    | X1 != second(X2)
    | member(X1,range_of(X3))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_950]) ).

cnf(c_0_950_4,axiom,
    ( ~ little_set(X1)
    | ~ ordered_pair_predicate(X2)
    | ~ member(X2,X3)
    | X1 != second(X2)
    | member(X1,range_of(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_950]) ).

cnf(c_0_951_0,axiom,
    ( first(f8(X1,X2)) = X1
    | ~ member(X1,domain_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_951]) ).

cnf(c_0_951_1,axiom,
    ( ~ member(X1,domain_of(X2))
    | first(f8(X1,X2)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_951]) ).

cnf(c_0_952_0,axiom,
    ( second(f27(X1,X2)) = X1
    | ~ member(X1,range_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_952]) ).

cnf(c_0_952_1,axiom,
    ( ~ member(X1,range_of(X2))
    | second(f27(X1,X2)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_952]) ).

cnf(c_0_953_0,axiom,
    ( little_set(f4(X1,X2))
    | ~ member(X1,first(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_953]) ).

cnf(c_0_953_1,axiom,
    ( ~ member(X1,first(X2))
    | little_set(f4(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_953]) ).

cnf(c_0_954_0,axiom,
    ( little_set(f5(X1,X2))
    | ~ member(X1,first(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_954]) ).

cnf(c_0_954_1,axiom,
    ( ~ member(X1,first(X2))
    | little_set(f5(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_954]) ).

cnf(c_0_955_0,axiom,
    ( little_set(f6(X1,X2))
    | ~ member(X1,second(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_955]) ).

cnf(c_0_955_1,axiom,
    ( ~ member(X1,second(X2))
    | little_set(f6(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_955]) ).

cnf(c_0_956_0,axiom,
    ( little_set(f7(X1,X2))
    | ~ member(X1,second(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_956]) ).

cnf(c_0_956_1,axiom,
    ( ~ member(X1,second(X2))
    | little_set(f7(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_956]) ).

cnf(c_0_957_0,axiom,
    ( ordered_pair_predicate(f8(X1,X2))
    | ~ member(X1,domain_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_957]) ).

cnf(c_0_957_1,axiom,
    ( ~ member(X1,domain_of(X2))
    | ordered_pair_predicate(f8(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_957]) ).

cnf(c_0_958_0,axiom,
    ( little_set(f9(X1,X2))
    | ~ member(X1,rotate_right(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_958]) ).

cnf(c_0_958_1,axiom,
    ( ~ member(X1,rotate_right(X2))
    | little_set(f9(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_958]) ).

cnf(c_0_959_0,axiom,
    ( little_set(f10(X1,X2))
    | ~ member(X1,rotate_right(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_959]) ).

cnf(c_0_959_1,axiom,
    ( ~ member(X1,rotate_right(X2))
    | little_set(f10(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_959]) ).

cnf(c_0_960_0,axiom,
    ( little_set(f11(X1,X2))
    | ~ member(X1,rotate_right(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_960]) ).

cnf(c_0_960_1,axiom,
    ( ~ member(X1,rotate_right(X2))
    | little_set(f11(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_960]) ).

cnf(c_0_961_0,axiom,
    ( little_set(f12(X1,X2))
    | ~ member(X1,flip_range_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_961]) ).

cnf(c_0_961_1,axiom,
    ( ~ member(X1,flip_range_of(X2))
    | little_set(f12(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_961]) ).

cnf(c_0_962_0,axiom,
    ( little_set(f13(X1,X2))
    | ~ member(X1,flip_range_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_962]) ).

cnf(c_0_962_1,axiom,
    ( ~ member(X1,flip_range_of(X2))
    | little_set(f13(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_962]) ).

cnf(c_0_963_0,axiom,
    ( little_set(f14(X1,X2))
    | ~ member(X1,flip_range_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_963]) ).

cnf(c_0_963_1,axiom,
    ( ~ member(X1,flip_range_of(X2))
    | little_set(f14(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_963]) ).

cnf(c_0_964_0,axiom,
    ( ordered_pair_predicate(f27(X1,X2))
    | ~ member(X1,range_of(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_964]) ).

cnf(c_0_964_1,axiom,
    ( ~ member(X1,range_of(X2))
    | ordered_pair_predicate(f27(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_964]) ).

cnf(c_0_965_0,axiom,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ subset(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_965]) ).

cnf(c_0_965_1,axiom,
    ( ~ member(X1,X3)
    | member(X1,X2)
    | ~ subset(X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_965]) ).

cnf(c_0_965_2,axiom,
    ( ~ subset(X3,X2)
    | ~ member(X1,X3)
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_965]) ).

cnf(c_0_966_0,axiom,
    ( member(ordered_pair(X1,f26(X1)),f25)
    | X1 = empty_set
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_966]) ).

cnf(c_0_966_1,axiom,
    ( X1 = empty_set
    | member(ordered_pair(X1,f26(X1)),f25)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_966]) ).

cnf(c_0_966_2,axiom,
    ( ~ little_set(X1)
    | X1 = empty_set
    | member(ordered_pair(X1,f26(X1)),f25) ),
    inference(literals_permutation,[status(thm)],[c_0_966]) ).

cnf(c_0_967_0,axiom,
    ( member(f55(X1),natural_numbers)
    | X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_967]) ).

cnf(c_0_967_1,axiom,
    ( X1 = successor(empty_set)
    | member(f55(X1),natural_numbers)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_967]) ).

cnf(c_0_967_2,axiom,
    ( X1 = empty_set
    | X1 = successor(empty_set)
    | member(f55(X1),natural_numbers)
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_967]) ).

cnf(c_0_967_3,axiom,
    ( member(X1,prime_numbers)
    | X1 = empty_set
    | X1 = successor(empty_set)
    | member(f55(X1),natural_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_967]) ).

cnf(c_0_967_4,axiom,
    ( ~ member(X1,natural_numbers)
    | member(X1,prime_numbers)
    | X1 = empty_set
    | X1 = successor(empty_set)
    | member(f55(X1),natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_967]) ).

cnf(c_0_968_0,axiom,
    ( member(f56(X1),natural_numbers)
    | X1 = successor(empty_set)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_968]) ).

cnf(c_0_968_1,axiom,
    ( X1 = successor(empty_set)
    | member(f56(X1),natural_numbers)
    | X1 = empty_set
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_968]) ).

cnf(c_0_968_2,axiom,
    ( X1 = empty_set
    | X1 = successor(empty_set)
    | member(f56(X1),natural_numbers)
    | member(X1,prime_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_968]) ).

cnf(c_0_968_3,axiom,
    ( member(X1,prime_numbers)
    | X1 = empty_set
    | X1 = successor(empty_set)
    | member(f56(X1),natural_numbers)
    | ~ member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_968]) ).

cnf(c_0_968_4,axiom,
    ( ~ member(X1,natural_numbers)
    | member(X1,prime_numbers)
    | X1 = empty_set
    | X1 = successor(empty_set)
    | member(f56(X1),natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_968]) ).

cnf(c_0_969_0,axiom,
    ( ~ member(X1,X2)
    | ~ member(X1,complement(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_969]) ).

cnf(c_0_969_1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_969]) ).

cnf(c_0_970_0,axiom,
    ( member(f17(X1,X2),X1)
    | subset(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_970]) ).

cnf(c_0_970_1,axiom,
    ( subset(X1,X2)
    | member(f17(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_970]) ).

cnf(c_0_971_0,axiom,
    ( member(f23(X1,X2),X1)
    | disjoint(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_971]) ).

cnf(c_0_971_1,axiom,
    ( disjoint(X1,X2)
    | member(f23(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_971]) ).

cnf(c_0_972_0,axiom,
    ( member(f23(X1,X2),X2)
    | disjoint(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_972]) ).

cnf(c_0_972_1,axiom,
    ( disjoint(X1,X2)
    | member(f23(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_972]) ).

cnf(c_0_973_0,axiom,
    ( member(f34(X1,X2),X1)
    | associative(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_973]) ).

cnf(c_0_973_1,axiom,
    ( associative(X1,X2)
    | member(f34(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_973]) ).

cnf(c_0_974_0,axiom,
    ( member(f35(X1,X2),X1)
    | associative(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_974]) ).

cnf(c_0_974_1,axiom,
    ( associative(X1,X2)
    | member(f35(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_974]) ).

cnf(c_0_975_0,axiom,
    ( member(f36(X1,X2),X1)
    | associative(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_975]) ).

cnf(c_0_975_1,axiom,
    ( associative(X1,X2)
    | member(f36(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_975]) ).

cnf(c_0_976_0,axiom,
    ( member(f41(X1,X2),X1)
    | commutes(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_976]) ).

cnf(c_0_976_1,axiom,
    ( commutes(X1,X2)
    | member(f41(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_976]) ).

cnf(c_0_977_0,axiom,
    ( member(f42(X1,X2),X1)
    | commutes(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_977]) ).

cnf(c_0_977_1,axiom,
    ( commutes(X1,X2)
    | member(f42(X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_977]) ).

cnf(c_0_978_0,axiom,
    ( member(successor(successor(X1)),prime_numbers)
    | ~ member(X1,twin_prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_978]) ).

cnf(c_0_978_1,axiom,
    ( ~ member(X1,twin_prime_numbers)
    | member(successor(successor(X1)),prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_978]) ).

cnf(c_0_979_0,axiom,
    ( member(X1,non_ordered_pair(X2,X3))
    | X1 != X2
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_979]) ).

cnf(c_0_979_1,axiom,
    ( X1 != X2
    | member(X1,non_ordered_pair(X2,X3))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_979]) ).

cnf(c_0_979_2,axiom,
    ( ~ little_set(X1)
    | X1 != X2
    | member(X1,non_ordered_pair(X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_979]) ).

cnf(c_0_980_0,axiom,
    ( member(X1,non_ordered_pair(X3,X2))
    | X1 != X2
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_980]) ).

cnf(c_0_980_1,axiom,
    ( X1 != X2
    | member(X1,non_ordered_pair(X3,X2))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_980]) ).

cnf(c_0_980_2,axiom,
    ( ~ little_set(X1)
    | X1 != X2
    | member(X1,non_ordered_pair(X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_980]) ).

cnf(c_0_981_0,axiom,
    ( member(X1,powerset(X2))
    | ~ subset(X1,X2)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_981]) ).

cnf(c_0_981_1,axiom,
    ( ~ subset(X1,X2)
    | member(X1,powerset(X2))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_981]) ).

cnf(c_0_981_2,axiom,
    ( ~ little_set(X1)
    | ~ subset(X1,X2)
    | member(X1,powerset(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_981]) ).

cnf(c_0_982_0,axiom,
    ( member(first(X1),second(X1))
    | ~ member(X1,estin) ),
    inference(literals_permutation,[status(thm)],[c_0_982]) ).

cnf(c_0_982_1,axiom,
    ( ~ member(X1,estin)
    | member(first(X1),second(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_982]) ).

cnf(c_0_983_0,axiom,
    ( subset(X1,X2)
    | ~ member(X1,powerset(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_983]) ).

cnf(c_0_983_1,axiom,
    ( ~ member(X1,powerset(X2))
    | subset(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_983]) ).

cnf(c_0_984_0,axiom,
    ( member(X1,natural_numbers)
    | ~ member(X1,f44(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_984]) ).

cnf(c_0_984_1,axiom,
    ( ~ member(X1,f44(X1))
    | member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_984]) ).

cnf(c_0_985_0,axiom,
    ( member(X1,plus)
    | ~ member(X1,f49(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_985]) ).

cnf(c_0_985_1,axiom,
    ( ~ member(X1,f49(X1))
    | member(X1,plus) ),
    inference(literals_permutation,[status(thm)],[c_0_985]) ).

cnf(c_0_986_0,axiom,
    ( member(X1,times)
    | ~ member(X1,f54(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_986]) ).

cnf(c_0_986_1,axiom,
    ( ~ member(X1,f54(X1))
    | member(X1,times) ),
    inference(literals_permutation,[status(thm)],[c_0_986]) ).

cnf(c_0_987_0,axiom,
    ( little_set(image(X1,X2))
    | ~ function(X2)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_987]) ).

cnf(c_0_987_1,axiom,
    ( ~ function(X2)
    | little_set(image(X1,X2))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_987]) ).

cnf(c_0_987_2,axiom,
    ( ~ little_set(X1)
    | ~ function(X2)
    | little_set(image(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_987]) ).

cnf(c_0_988_0,axiom,
    ( ordered_pair_predicate(X1)
    | X1 != ordered_pair(X2,X3)
    | ~ little_set(X3)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_988]) ).

cnf(c_0_988_1,axiom,
    ( X1 != ordered_pair(X2,X3)
    | ordered_pair_predicate(X1)
    | ~ little_set(X3)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_988]) ).

cnf(c_0_988_2,axiom,
    ( ~ little_set(X3)
    | X1 != ordered_pair(X2,X3)
    | ordered_pair_predicate(X1)
    | ~ little_set(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_988]) ).

cnf(c_0_988_3,axiom,
    ( ~ little_set(X2)
    | ~ little_set(X3)
    | X1 != ordered_pair(X2,X3)
    | ordered_pair_predicate(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_988]) ).

cnf(c_0_989_0,axiom,
    ( member(X1,X2)
    | member(X1,complement(X2))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_989]) ).

cnf(c_0_989_1,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_989]) ).

cnf(c_0_989_2,axiom,
    ( ~ little_set(X1)
    | member(X1,complement(X2))
    | member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_989]) ).

cnf(c_0_990_0,axiom,
    ( member(X1,identity_relation)
    | first(X1) != second(X1)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_990]) ).

cnf(c_0_990_1,axiom,
    ( first(X1) != second(X1)
    | member(X1,identity_relation)
    | ~ ordered_pair_predicate(X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_990]) ).

cnf(c_0_990_2,axiom,
    ( ~ ordered_pair_predicate(X1)
    | first(X1) != second(X1)
    | member(X1,identity_relation)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_990]) ).

cnf(c_0_990_3,axiom,
    ( ~ little_set(X1)
    | ~ ordered_pair_predicate(X1)
    | first(X1) != second(X1)
    | member(X1,identity_relation) ),
    inference(literals_permutation,[status(thm)],[c_0_990]) ).

cnf(c_0_991_0,axiom,
    ( X1 = X2
    | proper_subset(X1,X2)
    | ~ subset(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_991]) ).

cnf(c_0_991_1,axiom,
    ( proper_subset(X1,X2)
    | X1 = X2
    | ~ subset(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_991]) ).

cnf(c_0_991_2,axiom,
    ( ~ subset(X1,X2)
    | proper_subset(X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_991]) ).

cnf(c_0_992_0,axiom,
    ( member(successor(X1),infinity)
    | ~ member(X1,infinity) ),
    inference(literals_permutation,[status(thm)],[c_0_992]) ).

cnf(c_0_992_1,axiom,
    ( ~ member(X1,infinity)
    | member(successor(X1),infinity) ),
    inference(literals_permutation,[status(thm)],[c_0_992]) ).

cnf(c_0_993_0,axiom,
    ( member(f59(X1),natural_numbers)
    | ~ member(X1,even_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_993]) ).

cnf(c_0_993_1,axiom,
    ( ~ member(X1,even_numbers)
    | member(f59(X1),natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_993]) ).

cnf(c_0_994_0,axiom,
    ( member(empty_set,f44(X1))
    | member(X1,natural_numbers)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_994]) ).

cnf(c_0_994_1,axiom,
    ( member(X1,natural_numbers)
    | member(empty_set,f44(X1))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_994]) ).

cnf(c_0_994_2,axiom,
    ( ~ little_set(X1)
    | member(X1,natural_numbers)
    | member(empty_set,f44(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_994]) ).

cnf(c_0_995_0,axiom,
    ( subset(X1,X2)
    | ~ proper_subset(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_995]) ).

cnf(c_0_995_1,axiom,
    ( ~ proper_subset(X1,X2)
    | subset(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_995]) ).

cnf(c_0_996_0,axiom,
    ( closed(X1,X2)
    | ~ group(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_996]) ).

cnf(c_0_996_1,axiom,
    ( ~ group(X1,X2)
    | closed(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_996]) ).

cnf(c_0_997_0,axiom,
    ( associative(X1,X2)
    | ~ group(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_997]) ).

cnf(c_0_997_1,axiom,
    ( ~ group(X1,X2)
    | associative(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_997]) ).

cnf(c_0_998_0,axiom,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,converse(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_998]) ).

cnf(c_0_998_1,axiom,
    ( ~ member(X1,converse(X2))
    | ordered_pair_predicate(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_998]) ).

cnf(c_0_999_0,axiom,
    ( ordered_pair(f2(X1),f3(X1)) = X1
    | ~ ordered_pair_predicate(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_999]) ).

cnf(c_0_999_1,axiom,
    ( ~ ordered_pair_predicate(X1)
    | ordered_pair(f2(X1),f3(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_999]) ).

cnf(c_0_1000_0,axiom,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,X2)
    | ~ relation(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1000]) ).

cnf(c_0_1000_1,axiom,
    ( ~ member(X1,X2)
    | ordered_pair_predicate(X1)
    | ~ relation(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1000]) ).

cnf(c_0_1000_2,axiom,
    ( ~ relation(X2)
    | ~ member(X1,X2)
    | ordered_pair_predicate(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1000]) ).

cnf(c_0_1001_0,axiom,
    ( member(X1,natural_numbers)
    | ~ member(X1,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_1001]) ).

cnf(c_0_1001_1,axiom,
    ( ~ member(X1,prime_numbers)
    | member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_1001]) ).

cnf(c_0_1002_0,axiom,
    ( member(X1,prime_numbers)
    | ~ member(X1,twin_prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_1002]) ).

cnf(c_0_1002_1,axiom,
    ( ~ member(X1,twin_prime_numbers)
    | member(X1,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_1002]) ).

cnf(c_0_1003_0,axiom,
    ( member(X1,natural_numbers)
    | ~ member(X1,even_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_1003]) ).

cnf(c_0_1003_1,axiom,
    ( ~ member(X1,even_numbers)
    | member(X1,natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_1003]) ).

cnf(c_0_1004_0,axiom,
    ( X1 = X2
    | little_set(f1(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_1004]) ).

cnf(c_0_1004_1,axiom,
    ( little_set(f1(X1,X2))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1004]) ).

cnf(c_0_1005_0,axiom,
    ( little_set(f44(X1))
    | member(X1,natural_numbers)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1005]) ).

cnf(c_0_1005_1,axiom,
    ( member(X1,natural_numbers)
    | little_set(f44(X1))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1005]) ).

cnf(c_0_1005_2,axiom,
    ( ~ little_set(X1)
    | member(X1,natural_numbers)
    | little_set(f44(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1005]) ).

cnf(c_0_1006_0,axiom,
    ( little_set(f49(X1))
    | member(X1,plus)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1006]) ).

cnf(c_0_1006_1,axiom,
    ( member(X1,plus)
    | little_set(f49(X1))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1006]) ).

cnf(c_0_1006_2,axiom,
    ( ~ little_set(X1)
    | member(X1,plus)
    | little_set(f49(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1006]) ).

cnf(c_0_1007_0,axiom,
    ( little_set(f54(X1))
    | member(X1,times)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1007]) ).

cnf(c_0_1007_1,axiom,
    ( member(X1,times)
    | little_set(f54(X1))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1007]) ).

cnf(c_0_1007_2,axiom,
    ( ~ little_set(X1)
    | member(X1,times)
    | little_set(f54(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1007]) ).

cnf(c_0_1008_0,axiom,
    ( member(f26(X1),X1)
    | X1 = empty_set
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1008]) ).

cnf(c_0_1008_1,axiom,
    ( X1 = empty_set
    | member(f26(X1),X1)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1008]) ).

cnf(c_0_1008_2,axiom,
    ( ~ little_set(X1)
    | X1 = empty_set
    | member(f26(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1008]) ).

cnf(c_0_1009_0,axiom,
    ( first(X1) = second(X1)
    | ~ member(X1,identity_relation) ),
    inference(literals_permutation,[status(thm)],[c_0_1009]) ).

cnf(c_0_1009_1,axiom,
    ( ~ member(X1,identity_relation)
    | first(X1) = second(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1009]) ).

cnf(c_0_1010_0,axiom,
    ( one_to_one_function(X1)
    | ~ function(converse(X1))
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1010]) ).

cnf(c_0_1010_1,axiom,
    ( ~ function(converse(X1))
    | one_to_one_function(X1)
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1010]) ).

cnf(c_0_1010_2,axiom,
    ( ~ function(X1)
    | ~ function(converse(X1))
    | one_to_one_function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1010]) ).

cnf(c_0_1011_0,axiom,
    ( little_set(X1)
    | ~ member(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1011]) ).

cnf(c_0_1011_1,axiom,
    ( ~ member(X1,X2)
    | little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1011]) ).

cnf(c_0_1012_0,axiom,
    ( little_set(X1)
    | ~ closed(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1012]) ).

cnf(c_0_1012_1,axiom,
    ( ~ closed(X1,X2)
    | little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1012]) ).

cnf(c_0_1013_0,axiom,
    ( little_set(X1)
    | ~ closed(X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1013]) ).

cnf(c_0_1013_1,axiom,
    ( ~ closed(X2,X1)
    | little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1013]) ).

cnf(c_0_1014_0,axiom,
    ( X1 != X2
    | ~ proper_subset(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_1014]) ).

cnf(c_0_1014_1,axiom,
    ( ~ proper_subset(X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_1014]) ).

cnf(c_0_1015_0,axiom,
    ( X1 != successor(empty_set)
    | ~ member(X1,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_1015]) ).

cnf(c_0_1015_1,axiom,
    ( ~ member(X1,prime_numbers)
    | X1 != successor(empty_set) ),
    inference(literals_permutation,[status(thm)],[c_0_1015]) ).

cnf(c_0_1016_0,axiom,
    ( member(f57(X1),natural_numbers)
    | ~ finite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1016]) ).

cnf(c_0_1016_1,axiom,
    ( ~ finite(X1)
    | member(f57(X1),natural_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_1016]) ).

cnf(c_0_1017_0,axiom,
    ( member(f18(X1),X1)
    | relation(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1017]) ).

cnf(c_0_1017_1,axiom,
    ( relation(X1)
    | member(f18(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1017]) ).

cnf(c_0_1018_0,axiom,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,estin) ),
    inference(literals_permutation,[status(thm)],[c_0_1018]) ).

cnf(c_0_1018_1,axiom,
    ( ~ member(X1,estin)
    | ordered_pair_predicate(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1018]) ).

cnf(c_0_1019_0,axiom,
    ( ordered_pair_predicate(X1)
    | ~ member(X1,identity_relation) ),
    inference(literals_permutation,[status(thm)],[c_0_1019]) ).

cnf(c_0_1019_1,axiom,
    ( ~ member(X1,identity_relation)
    | ordered_pair_predicate(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1019]) ).

cnf(c_0_1020_0,axiom,
    ( X1 != empty_set
    | ~ member(X1,prime_numbers) ),
    inference(literals_permutation,[status(thm)],[c_0_1020]) ).

cnf(c_0_1020_1,axiom,
    ( ~ member(X1,prime_numbers)
    | X1 != empty_set ),
    inference(literals_permutation,[status(thm)],[c_0_1020]) ).

cnf(c_0_1021_0,axiom,
    ( member(f24(X1),X1)
    | X1 = empty_set ),
    inference(literals_permutation,[status(thm)],[c_0_1021]) ).

cnf(c_0_1021_1,axiom,
    ( X1 = empty_set
    | member(f24(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1021]) ).

cnf(c_0_1022_0,axiom,
    ( disjoint(f24(X1),X1)
    | X1 = empty_set ),
    inference(literals_permutation,[status(thm)],[c_0_1022]) ).

cnf(c_0_1022_1,axiom,
    ( X1 = empty_set
    | disjoint(f24(X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1022]) ).

cnf(c_0_1023_0,axiom,
    ( relation(X1)
    | ~ ordered_pair_predicate(f18(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1023]) ).

cnf(c_0_1023_1,axiom,
    ( ~ ordered_pair_predicate(f18(X1))
    | relation(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1023]) ).

cnf(c_0_1024_0,axiom,
    ( member(X1,universal_set)
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1024]) ).

cnf(c_0_1024_1,axiom,
    ( ~ little_set(X1)
    | member(X1,universal_set) ),
    inference(literals_permutation,[status(thm)],[c_0_1024]) ).

cnf(c_0_1025_0,axiom,
    ( function(X1)
    | ~ single_valued_set(X1)
    | ~ relation(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1025]) ).

cnf(c_0_1025_1,axiom,
    ( ~ single_valued_set(X1)
    | function(X1)
    | ~ relation(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1025]) ).

cnf(c_0_1025_2,axiom,
    ( ~ relation(X1)
    | ~ single_valued_set(X1)
    | function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1025]) ).

cnf(c_0_1026_0,axiom,
    ( range_of(f58(X1)) = X1
    | ~ finite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1026]) ).

cnf(c_0_1026_1,axiom,
    ( ~ finite(X1)
    | range_of(f58(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_1026]) ).

cnf(c_0_1027_0,axiom,
    ( little_set(f2(X1))
    | ~ ordered_pair_predicate(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1027]) ).

cnf(c_0_1027_1,axiom,
    ( ~ ordered_pair_predicate(X1)
    | little_set(f2(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1027]) ).

cnf(c_0_1028_0,axiom,
    ( little_set(f3(X1))
    | ~ ordered_pair_predicate(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1028]) ).

cnf(c_0_1028_1,axiom,
    ( ~ ordered_pair_predicate(X1)
    | little_set(f3(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1028]) ).

cnf(c_0_1029_0,axiom,
    ( little_set(sigma(X1))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1029]) ).

cnf(c_0_1029_1,axiom,
    ( ~ little_set(X1)
    | little_set(sigma(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1029]) ).

cnf(c_0_1030_0,axiom,
    ( little_set(powerset(X1))
    | ~ little_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1030]) ).

cnf(c_0_1030_1,axiom,
    ( ~ little_set(X1)
    | little_set(powerset(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1030]) ).

cnf(c_0_1031_0,axiom,
    ( function(converse(X1))
    | ~ one_to_one_function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1031]) ).

cnf(c_0_1031_1,axiom,
    ( ~ one_to_one_function(X1)
    | function(converse(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1031]) ).

cnf(c_0_1032_0,axiom,
    ( one_to_one_function(f58(X1))
    | ~ finite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1032]) ).

cnf(c_0_1032_1,axiom,
    ( ~ finite(X1)
    | one_to_one_function(f58(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1032]) ).

cnf(c_0_1033_0,axiom,
    ( single_valued_set(X1)
    | f21(X1) != f20(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1033]) ).

cnf(c_0_1033_1,axiom,
    ( f21(X1) != f20(X1)
    | single_valued_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1033]) ).

cnf(c_0_1034_0,axiom,
    ( little_set(f19(X1))
    | single_valued_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1034]) ).

cnf(c_0_1034_1,axiom,
    ( single_valued_set(X1)
    | little_set(f19(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1034]) ).

cnf(c_0_1035_0,axiom,
    ( little_set(f20(X1))
    | single_valued_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1035]) ).

cnf(c_0_1035_1,axiom,
    ( single_valued_set(X1)
    | little_set(f20(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1035]) ).

cnf(c_0_1036_0,axiom,
    ( little_set(f21(X1))
    | single_valued_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1036]) ).

cnf(c_0_1036_1,axiom,
    ( single_valued_set(X1)
    | little_set(f21(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_1036]) ).

cnf(c_0_1037_0,axiom,
    ( relation(X1)
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1037]) ).

cnf(c_0_1037_1,axiom,
    ( ~ function(X1)
    | relation(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1037]) ).

cnf(c_0_1038_0,axiom,
    ( single_valued_set(X1)
    | ~ function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1038]) ).

cnf(c_0_1038_1,axiom,
    ( ~ function(X1)
    | single_valued_set(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1038]) ).

cnf(c_0_1039_0,axiom,
    ( function(X1)
    | ~ one_to_one_function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1039]) ).

cnf(c_0_1039_1,axiom,
    ( ~ one_to_one_function(X1)
    | function(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_1039]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_056,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    file('<stdin>',prove_zero_is_a_natural) ).

fof(c_0_1_057,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    inference(fof_simplification,[status(thm)],[c_0_0]) ).

fof(c_0_2_058,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    c_0_1 ).

cnf(c_0_3_059,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4_060,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    c_0_3,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_636,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1a9afa.p',c_0_4) ).

cnf(c_843,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    inference(copy,[status(esa)],[c_636]) ).

cnf(c_847,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    inference(copy,[status(esa)],[c_843]) ).

cnf(c_848,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    inference(copy,[status(esa)],[c_847]) ).

cnf(c_849,negated_conjecture,
    ~ member(empty_set,natural_numbers),
    inference(copy,[status(esa)],[c_848]) ).

cnf(c_2753,plain,
    ~ member(empty_set,natural_numbers),
    inference(copy,[status(esa)],[c_849]) ).

cnf(c_498,plain,
    ( ~ member(X0,f44(X0))
    | member(X0,natural_numbers) ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1a9afa.p',c_0_984_0) ).

cnf(c_2483,plain,
    ( ~ member(X0,f44(X0))
    | member(X0,natural_numbers) ),
    inference(copy,[status(esa)],[c_498]) ).

cnf(c_2484,plain,
    ( member(X0,natural_numbers)
    | ~ member(X0,f44(X0)) ),
    inference(rewriting,[status(thm)],[c_2483]) ).

cnf(c_2809,plain,
    ~ member(empty_set,f44(empty_set)),
    inference(resolution,[status(thm)],[c_2753,c_2484]) ).

cnf(c_2810,plain,
    ~ member(empty_set,f44(empty_set)),
    inference(rewriting,[status(thm)],[c_2809]) ).

cnf(c_525,plain,
    ( ~ little_set(X0)
    | member(X0,natural_numbers)
    | member(empty_set,f44(X0)) ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1a9afa.p',c_0_994_0) ).

cnf(c_2537,plain,
    ( ~ little_set(X0)
    | member(X0,natural_numbers)
    | member(empty_set,f44(X0)) ),
    inference(copy,[status(esa)],[c_525]) ).

cnf(c_2538,plain,
    ( member(empty_set,f44(X0))
    | member(X0,natural_numbers)
    | ~ little_set(X0) ),
    inference(rewriting,[status(thm)],[c_2537]) ).

cnf(c_3651,plain,
    ( member(empty_set,natural_numbers)
    | ~ little_set(empty_set) ),
    inference(resolution,[status(thm)],[c_2810,c_2538]) ).

cnf(c_3652,plain,
    ( member(empty_set,natural_numbers)
    | ~ little_set(empty_set) ),
    inference(rewriting,[status(thm)],[c_3651]) ).

cnf(c_5755,plain,
    ~ little_set(empty_set),
    inference(forward_subsumption_resolution,[status(thm)],[c_3652,c_2753]) ).

cnf(c_5756,plain,
    ~ little_set(empty_set),
    inference(rewriting,[status(thm)],[c_5755]) ).

cnf(c_566,plain,
    ( ~ member(X0,X1)
    | little_set(X0) ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1a9afa.p',c_0_1011_0) ).

cnf(c_2619,plain,
    ( ~ member(X0,X1)
    | little_set(X0) ),
    inference(copy,[status(esa)],[c_566]) ).

cnf(c_5761,plain,
    ~ member(empty_set,X0),
    inference(resolution,[status(thm)],[c_5756,c_2619]) ).

cnf(c_5762,plain,
    ~ member(empty_set,X0),
    inference(rewriting,[status(thm)],[c_5761]) ).

cnf(c_626,plain,
    member(empty_set,infinity),
    file('/export/starexec/sandbox/tmp/iprover_modulo_1a9afa.p',c_0_53_0) ).

cnf(c_2739,plain,
    member(empty_set,infinity),
    inference(copy,[status(esa)],[c_626]) ).

cnf(c_5776,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_5762,c_2739]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12  % Command  : iprover_modulo %s %d
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Thu Jul  7 12:10:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.34  % Running in mono-core mode
% 0.20/0.43  % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.43  % Orientation found
% 0.20/0.43  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_31f347.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_1a9afa.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_a2f6a1 | grep -v "SZS"
% 0.20/0.46  
% 0.20/0.46  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.46  
% 0.20/0.46  % 
% 0.20/0.46  % ------  iProver source info 
% 0.20/0.46  
% 0.20/0.46  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.46  % git: non_committed_changes: true
% 0.20/0.46  % git: last_make_outside_of_git: true
% 0.20/0.46  
% 0.20/0.46  % 
% 0.20/0.46  % ------ Input Options
% 0.20/0.46  
% 0.20/0.46  % --out_options                         all
% 0.20/0.46  % --tptp_safe_out                       true
% 0.20/0.46  % --problem_path                        ""
% 0.20/0.46  % --include_path                        ""
% 0.20/0.46  % --clausifier                          .//eprover
% 0.20/0.46  % --clausifier_options                  --tstp-format  
% 0.20/0.46  % --stdin                               false
% 0.20/0.46  % --dbg_backtrace                       false
% 0.20/0.46  % --dbg_dump_prop_clauses               false
% 0.20/0.46  % --dbg_dump_prop_clauses_file          -
% 0.20/0.46  % --dbg_out_stat                        false
% 0.20/0.46  
% 0.20/0.46  % ------ General Options
% 0.20/0.46  
% 0.20/0.46  % --fof                                 false
% 0.20/0.46  % --time_out_real                       150.
% 0.20/0.46  % --time_out_prep_mult                  0.2
% 0.20/0.46  % --time_out_virtual                    -1.
% 0.20/0.46  % --schedule                            none
% 0.20/0.46  % --ground_splitting                    input
% 0.20/0.46  % --splitting_nvd                       16
% 0.20/0.46  % --non_eq_to_eq                        false
% 0.20/0.46  % --prep_gs_sim                         true
% 0.20/0.46  % --prep_unflatten                      false
% 0.20/0.46  % --prep_res_sim                        true
% 0.20/0.46  % --prep_upred                          true
% 0.20/0.46  % --res_sim_input                       true
% 0.20/0.46  % --clause_weak_htbl                    true
% 0.20/0.46  % --gc_record_bc_elim                   false
% 0.20/0.46  % --symbol_type_check                   false
% 0.20/0.46  % --clausify_out                        false
% 0.20/0.46  % --large_theory_mode                   false
% 0.20/0.46  % --prep_sem_filter                     none
% 0.20/0.46  % --prep_sem_filter_out                 false
% 0.20/0.46  % --preprocessed_out                    false
% 0.20/0.46  % --sub_typing                          false
% 0.20/0.46  % --brand_transform                     false
% 0.20/0.46  % --pure_diseq_elim                     true
% 0.20/0.46  % --min_unsat_core                      false
% 0.20/0.46  % --pred_elim                           true
% 0.20/0.46  % --add_important_lit                   false
% 0.20/0.46  % --soft_assumptions                    false
% 0.20/0.46  % --reset_solvers                       false
% 0.20/0.46  % --bc_imp_inh                          []
% 0.20/0.46  % --conj_cone_tolerance                 1.5
% 0.20/0.46  % --prolific_symb_bound                 500
% 0.20/0.46  % --lt_threshold                        2000
% 0.20/0.46  
% 0.20/0.46  % ------ SAT Options
% 0.20/0.46  
% 0.20/0.46  % --sat_mode                            false
% 0.20/0.46  % --sat_fm_restart_options              ""
% 0.20/0.46  % --sat_gr_def                          false
% 0.20/0.46  % --sat_epr_types                       true
% 0.20/0.46  % --sat_non_cyclic_types                false
% 0.20/0.46  % --sat_finite_models                   false
% 0.20/0.46  % --sat_fm_lemmas                       false
% 0.20/0.46  % --sat_fm_prep                         false
% 0.20/0.46  % --sat_fm_uc_incr                      true
% 0.20/0.46  % --sat_out_model                       small
% 0.20/0.46  % --sat_out_clauses                     false
% 0.20/0.46  
% 0.20/0.46  % ------ QBF Options
% 0.20/0.46  
% 0.20/0.46  % --qbf_mode                            false
% 0.20/0.46  % --qbf_elim_univ                       true
% 0.20/0.46  % --qbf_sk_in                           true
% 0.20/0.46  % --qbf_pred_elim                       true
% 0.20/0.46  % --qbf_split                           32
% 0.20/0.46  
% 0.20/0.46  % ------ BMC1 Options
% 0.20/0.46  
% 0.20/0.46  % --bmc1_incremental                    false
% 0.20/0.46  % --bmc1_axioms                         reachable_all
% 0.20/0.46  % --bmc1_min_bound                      0
% 0.20/0.46  % --bmc1_max_bound                      -1
% 0.20/0.46  % --bmc1_max_bound_default              -1
% 0.20/0.46  % --bmc1_symbol_reachability            true
% 0.20/0.46  % --bmc1_property_lemmas                false
% 0.20/0.46  % --bmc1_k_induction                    false
% 0.20/0.46  % --bmc1_non_equiv_states               false
% 0.20/0.46  % --bmc1_deadlock                       false
% 0.20/0.46  % --bmc1_ucm                            false
% 0.20/0.46  % --bmc1_add_unsat_core                 none
% 0.20/0.46  % --bmc1_unsat_core_children            false
% 0.20/0.46  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.20/0.46  % --bmc1_out_stat                       full
% 0.20/0.46  % --bmc1_ground_init                    false
% 0.20/0.46  % --bmc1_pre_inst_next_state            false
% 0.20/0.46  % --bmc1_pre_inst_state                 false
% 0.20/0.46  % --bmc1_pre_inst_reach_state           false
% 0.20/0.46  % --bmc1_out_unsat_core                 false
% 0.20/0.46  % --bmc1_aig_witness_out                false
% 0.20/0.46  % --bmc1_verbose                        false
% 0.20/0.46  % --bmc1_dump_clauses_tptp              false
% 0.47/0.76  % --bmc1_dump_unsat_core_tptp           false
% 0.47/0.76  % --bmc1_dump_file                      -
% 0.47/0.76  % --bmc1_ucm_expand_uc_limit            128
% 0.47/0.76  % --bmc1_ucm_n_expand_iterations        6
% 0.47/0.76  % --bmc1_ucm_extend_mode                1
% 0.47/0.76  % --bmc1_ucm_init_mode                  2
% 0.47/0.76  % --bmc1_ucm_cone_mode                  none
% 0.47/0.76  % --bmc1_ucm_reduced_relation_type      0
% 0.47/0.76  % --bmc1_ucm_relax_model                4
% 0.47/0.76  % --bmc1_ucm_full_tr_after_sat          true
% 0.47/0.76  % --bmc1_ucm_expand_neg_assumptions     false
% 0.47/0.76  % --bmc1_ucm_layered_model              none
% 0.47/0.76  % --bmc1_ucm_max_lemma_size             10
% 0.47/0.76  
% 0.47/0.76  % ------ AIG Options
% 0.47/0.76  
% 0.47/0.76  % --aig_mode                            false
% 0.47/0.76  
% 0.47/0.76  % ------ Instantiation Options
% 0.47/0.76  
% 0.47/0.76  % --instantiation_flag                  true
% 0.47/0.76  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.47/0.76  % --inst_solver_per_active              750
% 0.47/0.76  % --inst_solver_calls_frac              0.5
% 0.47/0.76  % --inst_passive_queue_type             priority_queues
% 0.47/0.76  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.47/0.76  % --inst_passive_queues_freq            [25;2]
% 0.47/0.76  % --inst_dismatching                    true
% 0.47/0.76  % --inst_eager_unprocessed_to_passive   true
% 0.47/0.76  % --inst_prop_sim_given                 true
% 0.47/0.76  % --inst_prop_sim_new                   false
% 0.47/0.76  % --inst_orphan_elimination             true
% 0.47/0.76  % --inst_learning_loop_flag             true
% 0.47/0.76  % --inst_learning_start                 3000
% 0.47/0.76  % --inst_learning_factor                2
% 0.47/0.76  % --inst_start_prop_sim_after_learn     3
% 0.47/0.76  % --inst_sel_renew                      solver
% 0.47/0.76  % --inst_lit_activity_flag              true
% 0.47/0.76  % --inst_out_proof                      true
% 0.47/0.76  
% 0.47/0.76  % ------ Resolution Options
% 0.47/0.76  
% 0.47/0.76  % --resolution_flag                     true
% 0.47/0.76  % --res_lit_sel                         kbo_max
% 0.47/0.76  % --res_to_prop_solver                  none
% 0.47/0.76  % --res_prop_simpl_new                  false
% 0.47/0.76  % --res_prop_simpl_given                false
% 0.47/0.76  % --res_passive_queue_type              priority_queues
% 0.47/0.76  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.47/0.76  % --res_passive_queues_freq             [15;5]
% 0.47/0.76  % --res_forward_subs                    full
% 0.47/0.76  % --res_backward_subs                   full
% 0.47/0.76  % --res_forward_subs_resolution         true
% 0.47/0.76  % --res_backward_subs_resolution        true
% 0.47/0.76  % --res_orphan_elimination              false
% 0.47/0.76  % --res_time_limit                      1000.
% 0.47/0.76  % --res_out_proof                       true
% 0.47/0.76  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_31f347.s
% 0.47/0.76  % --modulo                              true
% 0.47/0.76  
% 0.47/0.76  % ------ Combination Options
% 0.47/0.76  
% 0.47/0.76  % --comb_res_mult                       1000
% 0.47/0.76  % --comb_inst_mult                      300
% 0.47/0.76  % ------ 
% 0.47/0.76  
% 0.47/0.76  % ------ Parsing...% successful
% 0.47/0.76  
% 0.47/0.76  % ------ 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 % 
% 0.47/0.76  
% 0.47/0.76  % ------ Proving...
% 0.47/0.76  % ------ Problem Properties 
% 0.47/0.76  
% 0.47/0.76  % 
% 0.47/0.76  % EPR                                   false
% 0.47/0.76  % Horn                                  false
% 0.47/0.76  % Has equality                          true
% 0.47/0.76  
% 0.47/0.76  % % ------ Input Options Time Limit: Unbounded
% 0.47/0.76  
% 0.47/0.76  
% 0.47/0.76  Compiling...
% 0.47/0.76  Loading plugin: done.
% 0.47/0.76  Compiling...
% 0.47/0.76  Loading plugin: done.
% 0.47/0.76  % % ------ Current options:
% 0.47/0.76  
% 0.47/0.76  % ------ Input Options
% 0.47/0.76  
% 0.47/0.76  % --out_options                         all
% 0.47/0.76  % --tptp_safe_out                       true
% 0.47/0.76  % --problem_path                        ""
% 0.47/0.76  % --include_path                        ""
% 0.47/0.76  % --clausifier                          .//eprover
% 0.47/0.76  % --clausifier_options                  --tstp-format  
% 0.47/0.76  % --stdin                               false
% 0.47/0.76  % --dbg_backtrace                       false
% 0.47/0.76  % --dbg_dump_prop_clauses               false
% 0.47/0.76  % --dbg_dump_prop_clauses_file          -
% 0.47/0.76  % --dbg_out_stat                        false
% 0.47/0.76  
% 0.47/0.76  % ------ General Options
% 0.47/0.76  
% 0.47/0.76  % --fof                                 false
% 0.47/0.76  % --time_out_real                       150.
% 0.47/0.76  % --time_out_prep_mult                  0.2
% 0.47/0.76  % --time_out_virtual                    -1.
% 0.47/0.76  % --schedule                            none
% 0.47/0.76  % --ground_splitting                    input
% 0.47/0.76  % --splitting_nvd                       16
% 0.47/0.76  % --non_eq_to_eq                        false
% 0.47/0.76  % --prep_gs_sim                         true
% 0.47/0.76  % --prep_unflatten                      false
% 0.47/0.76  % --prep_res_sim                        true
% 0.47/0.76  % --prep_upred                          true
% 0.47/0.76  % --res_sim_input                       true
% 0.47/0.76  % --clause_weak_htbl                    true
% 0.47/0.76  % --gc_record_bc_elim                   false
% 0.47/0.76  % --symbol_type_check                   false
% 0.47/0.76  % --clausify_out                        false
% 0.47/0.76  % --large_theory_mode                   false
% 0.47/0.76  % --prep_sem_filter                     none
% 0.47/0.76  % --prep_sem_filter_out                 false
% 0.47/0.76  % --preprocessed_out                    false
% 0.47/0.76  % --sub_typing                          false
% 0.47/0.76  % --brand_transform                     false
% 0.47/0.76  % --pure_diseq_elim                     true
% 0.47/0.76  % --min_unsat_core                      false
% 0.47/0.76  % --pred_elim                           true
% 0.47/0.76  % --add_important_lit                   false
% 0.47/0.76  % --soft_assumptions                    false
% 0.47/0.76  % --reset_solvers                       false
% 0.47/0.76  % --bc_imp_inh                          []
% 0.47/0.76  % --conj_cone_tolerance                 1.5
% 0.47/0.76  % --prolific_symb_bound                 500
% 0.47/0.76  % --lt_threshold                        2000
% 0.47/0.76  
% 0.47/0.76  % ------ SAT Options
% 0.47/0.76  
% 0.47/0.76  % --sat_mode                            false
% 0.47/0.76  % --sat_fm_restart_options              ""
% 0.47/0.76  % --sat_gr_def                          false
% 0.47/0.76  % --sat_epr_types                       true
% 0.47/0.76  % --sat_non_cyclic_types                false
% 0.47/0.76  % --sat_finite_models                   false
% 0.47/0.76  % --sat_fm_lemmas                       false
% 0.47/0.76  % --sat_fm_prep                         false
% 0.47/0.76  % --sat_fm_uc_incr                      true
% 0.47/0.76  % --sat_out_model                       small
% 0.47/0.76  % --sat_out_clauses                     false
% 0.47/0.76  
% 0.47/0.76  % ------ QBF Options
% 0.47/0.76  
% 0.47/0.76  % --qbf_mode                            false
% 0.47/0.76  % --qbf_elim_univ                       true
% 0.47/0.76  % --qbf_sk_in                           true
% 0.47/0.76  % --qbf_pred_elim                       true
% 0.47/0.76  % --qbf_split                           32
% 0.47/0.76  
% 0.47/0.76  % ------ BMC1 Options
% 0.47/0.76  
% 0.47/0.76  % --bmc1_incremental                    false
% 0.47/0.76  % --bmc1_axioms                         reachable_all
% 0.47/0.76  % --bmc1_min_bound                      0
% 0.47/0.76  % --bmc1_max_bound                      -1
% 0.47/0.76  % --bmc1_max_bound_default              -1
% 0.47/0.76  % --bmc1_symbol_reachability            true
% 0.47/0.76  % --bmc1_property_lemmas                false
% 0.47/0.76  % --bmc1_k_induction                    false
% 0.47/0.76  % --bmc1_non_equiv_states               false
% 0.47/0.76  % --bmc1_deadlock                       false
% 0.47/0.76  % --bmc1_ucm                            false
% 0.47/0.76  % --bmc1_add_unsat_core                 none
% 0.47/0.76  % --bmc1_unsat_core_children            false
% 0.47/0.76  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.47/0.76  % --bmc1_out_stat                       full
% 0.47/0.76  % --bmc1_ground_init                    false
% 0.47/0.76  % --bmc1_pre_inst_next_state            false
% 0.47/0.76  % --bmc1_pre_inst_state                 false
% 0.47/0.76  % --bmc1_pre_inst_reach_state           false
% 0.47/0.76  % --bmc1_out_unsat_core                 false
% 0.47/0.76  % --bmc1_aig_witness_out                false
% 0.47/0.76  % --bmc1_verbose                        false
% 0.47/0.76  % --bmc1_dump_clauses_tptp              false
% 0.47/0.76  % --bmc1_dump_unsat_core_tptp           false
% 0.47/0.76  % --bmc1_dump_file                      -
% 0.47/0.76  % --bmc1_ucm_expand_uc_limit            128
% 0.47/0.76  % --bmc1_ucm_n_expand_iterations        6
% 0.47/0.76  % --bmc1_ucm_extend_mode                1
% 0.47/0.76  % --bmc1_ucm_init_mode                  2
% 0.47/0.76  % --bmc1_ucm_cone_mode                  none
% 0.47/0.76  % --bmc1_ucm_reduced_relation_type      0
% 0.47/0.76  % --bmc1_ucm_relax_model                4
% 0.47/0.76  % --bmc1_ucm_full_tr_after_sat          true
% 0.47/0.76  % --bmc1_ucm_expand_neg_assumptions     false
% 0.47/0.76  % --bmc1_ucm_layered_model              none
% 0.47/0.76  % --bmc1_ucm_max_lemma_size             10
% 0.47/0.76  
% 0.47/0.76  % ------ AIG Options
% 0.47/0.76  
% 0.47/0.76  % --aig_mode                            false
% 0.47/0.76  
% 0.47/0.76  % ------ Instantiation Options
% 0.47/0.76  
% 0.47/0.76  % --instantiation_flag                  true
% 0.47/0.76  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.47/0.76  % --inst_solver_per_active              750
% 0.47/0.76  % --inst_solver_calls_frac              0.5
% 0.47/0.76  % --inst_passive_queue_type             priority_queues
% 0.47/0.76  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.47/0.76  % --inst_passive_queues_freq            [25;2]
% 0.47/0.76  % --inst_dismatching                    true
% 0.69/0.90  % --inst_eager_unprocessed_to_passive   true
% 0.69/0.90  % --inst_prop_sim_given                 true
% 0.69/0.90  % --inst_prop_sim_new                   false
% 0.69/0.90  % --inst_orphan_elimination             true
% 0.69/0.90  % --inst_learning_loop_flag             true
% 0.69/0.90  % --inst_learning_start                 3000
% 0.69/0.90  % --inst_learning_factor                2
% 0.69/0.90  % --inst_start_prop_sim_after_learn     3
% 0.69/0.90  % --inst_sel_renew                      solver
% 0.69/0.90  % --inst_lit_activity_flag              true
% 0.69/0.90  % --inst_out_proof                      true
% 0.69/0.90  
% 0.69/0.90  % ------ Resolution Options
% 0.69/0.90  
% 0.69/0.90  % --resolution_flag                     true
% 0.69/0.90  % --res_lit_sel                         kbo_max
% 0.69/0.90  % --res_to_prop_solver                  none
% 0.69/0.90  % --res_prop_simpl_new                  false
% 0.69/0.90  % --res_prop_simpl_given                false
% 0.69/0.90  % --res_passive_queue_type              priority_queues
% 0.69/0.90  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.69/0.90  % --res_passive_queues_freq             [15;5]
% 0.69/0.90  % --res_forward_subs                    full
% 0.69/0.90  % --res_backward_subs                   full
% 0.69/0.90  % --res_forward_subs_resolution         true
% 0.69/0.90  % --res_backward_subs_resolution        true
% 0.69/0.90  % --res_orphan_elimination              false
% 0.69/0.90  % --res_time_limit                      1000.
% 0.69/0.90  % --res_out_proof                       true
% 0.69/0.90  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_31f347.s
% 0.69/0.90  % --modulo                              true
% 0.69/0.90  
% 0.69/0.90  % ------ Combination Options
% 0.69/0.90  
% 0.69/0.90  % --comb_res_mult                       1000
% 0.69/0.90  % --comb_inst_mult                      300
% 0.69/0.90  % ------ 
% 0.69/0.90  
% 0.69/0.90  
% 0.69/0.90  
% 0.69/0.90  % ------ Proving...
% 0.69/0.90  % 
% 0.69/0.90  
% 0.69/0.90  
% 0.69/0.90  %  Resolution empty clause
% 0.69/0.90  
% 0.69/0.90  % ------                             Statistics
% 0.69/0.90  
% 0.69/0.90  % ------ General
% 0.69/0.90  
% 0.69/0.90  % num_of_input_clauses:                 637
% 0.69/0.90  % num_of_input_neg_conjectures:         1
% 0.69/0.90  % num_of_splits:                        0
% 0.69/0.90  % num_of_split_atoms:                   0
% 0.69/0.90  % num_of_sem_filtered_clauses:          0
% 0.69/0.90  % num_of_subtypes:                      0
% 0.69/0.90  % monotx_restored_types:                0
% 0.69/0.90  % sat_num_of_epr_types:                 0
% 0.69/0.90  % sat_num_of_non_cyclic_types:          0
% 0.69/0.90  % sat_guarded_non_collapsed_types:      0
% 0.69/0.90  % is_epr:                               0
% 0.69/0.90  % is_horn:                              0
% 0.69/0.90  % has_eq:                               1
% 0.69/0.90  % num_pure_diseq_elim:                  0
% 0.69/0.90  % simp_replaced_by:                     0
% 0.69/0.90  % res_preprocessed:                     2
% 0.69/0.90  % prep_upred:                           0
% 0.69/0.90  % prep_unflattend:                      0
% 0.69/0.90  % pred_elim_cands:                      0
% 0.69/0.90  % pred_elim:                            0
% 0.69/0.90  % pred_elim_cl:                         0
% 0.69/0.90  % pred_elim_cycles:                     0
% 0.69/0.90  % forced_gc_time:                       0
% 0.69/0.90  % gc_basic_clause_elim:                 0
% 0.69/0.90  % parsing_time:                         0.032
% 0.69/0.90  % sem_filter_time:                      0.
% 0.69/0.90  % pred_elim_time:                       0.
% 0.69/0.90  % out_proof_time:                       0.
% 0.69/0.90  % monotx_time:                          0.
% 0.69/0.90  % subtype_inf_time:                     0.
% 0.69/0.90  % unif_index_cands_time:                0.
% 0.69/0.90  % unif_index_add_time:                  0.
% 0.69/0.90  % total_time:                           0.458
% 0.69/0.90  % num_of_symbols:                       135
% 0.69/0.90  % num_of_terms:                         4439
% 0.69/0.90  
% 0.69/0.90  % ------ Propositional Solver
% 0.69/0.90  
% 0.69/0.90  % prop_solver_calls:                    1
% 0.69/0.90  % prop_fast_solver_calls:               3
% 0.69/0.90  % prop_num_of_clauses:                  495
% 0.69/0.90  % prop_preprocess_simplified:           2053
% 0.69/0.90  % prop_fo_subsumed:                     0
% 0.69/0.90  % prop_solver_time:                     0.
% 0.69/0.90  % prop_fast_solver_time:                0.
% 0.69/0.90  % prop_unsat_core_time:                 0.
% 0.69/0.90  
% 0.69/0.90  % ------ QBF 
% 0.69/0.90  
% 0.69/0.90  % qbf_q_res:                            0
% 0.69/0.90  % qbf_num_tautologies:                  0
% 0.69/0.90  % qbf_prep_cycles:                      0
% 0.69/0.90  
% 0.69/0.90  % ------ BMC1
% 0.69/0.90  
% 0.69/0.90  % bmc1_current_bound:                   -1
% 0.69/0.90  % bmc1_last_solved_bound:               -1
% 0.69/0.90  % bmc1_unsat_core_size:                 -1
% 0.69/0.90  % bmc1_unsat_core_parents_size:         -1
% 0.69/0.90  % bmc1_merge_next_fun:                  0
% 0.69/0.90  % bmc1_unsat_core_clauses_time:         0.
% 0.69/0.90  
% 0.69/0.90  % ------ Instantiation
% 0.69/0.90  
% 0.69/0.90  % inst_num_of_clauses:                  637
% 0.69/0.90  % inst_num_in_passive:                  0
% 0.69/0.90  % inst_num_in_active:                   0
% 0.69/0.90  % inst_num_in_unprocessed:              637
% 0.69/0.90  % inst_num_of_loops:                    0
% 0.69/0.90  % inst_num_of_learning_restarts:        0
% 0.69/0.90  % inst_num_moves_active_passive:        0
% 0.69/0.90  % inst_lit_activity:                    0
% 0.69/0.90  % inst_lit_activity_moves:              0
% 0.69/0.90  % inst_num_tautologies:                 0
% 0.69/0.90  % inst_num_prop_implied:                0
% 0.69/0.90  % inst_num_existing_simplified:         0
% 0.69/0.90  % inst_num_eq_res_simplified:           0
% 0.69/0.90  % inst_num_child_elim:                  0
% 0.69/0.90  % inst_num_of_dismatching_blockings:    0
% 0.69/0.90  % inst_num_of_non_proper_insts:         0
% 0.69/0.90  % inst_num_of_duplicates:               0
% 0.69/0.90  % inst_inst_num_from_inst_to_res:       0
% 0.69/0.90  % inst_dismatching_checking_time:       0.
% 0.69/0.90  
% 0.69/0.90  % ------ Resolution
% 0.69/0.90  
% 0.69/0.90  % res_num_of_clauses:                   1982
% 0.69/0.90  % res_num_in_passive:                   1254
% 0.69/0.90  % res_num_in_active:                    250
% 0.69/0.90  % res_num_of_loops:                     58
% 0.69/0.90  % res_forward_subset_subsumed:          423
% 0.69/0.90  % res_backward_subset_subsumed:         14
% 0.69/0.90  % res_forward_subsumed:                 7
% 0.69/0.90  % res_backward_subsumed:                49
% 0.69/0.90  % res_forward_subsumption_resolution:   3
% 0.69/0.90  % res_backward_subsumption_resolution:  1
% 0.69/0.90  % res_clause_to_clause_subsumption:     466
% 0.69/0.90  % res_orphan_elimination:               0
% 0.69/0.90  % res_tautology_del:                    0
% 0.69/0.90  % res_num_eq_res_simplified:            0
% 0.69/0.90  % res_num_sel_changes:                  0
% 0.69/0.90  % res_moves_from_active_to_pass:        0
% 0.69/0.90  
% 0.69/0.90  % Status Unsatisfiable
% 0.69/0.90  % SZS status Unsatisfiable
% 0.69/0.90  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------