% Mizar problem: t10_arytm_0,arytm_0,709,28 
fof(t10_arytm_0,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ~ r2_hidden(k5_funct_4(k1_numbers,0,k13_arytm_3,A,B),k1_numbers) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_funct_2,cc2_arytm_3,cc3_arytm_3,cc4_arytm_3,cc5_funct_2,cc6_funct_2,commutativity_k2_tarski,commutativity_k2_xboole_0,connectedness_r3_arytm_3,d1_arytm_2,d1_numbers,d1_tarski,d2_arytm_2,d2_tarski,d2_xboole_0,d4_xboole_0,d5_tarski,d6_arytm_3,dt_k12_arytm_3,dt_k13_arytm_3,dt_k1_arytm_2,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_arytm_2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k4_funct_4,dt_k4_ordinal2,dt_k4_tarski,dt_k4_xboole_0,dt_k5_funct_4,dt_k5_numbers,dt_k5_ordinal2,dt_k6_arytm_3,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc1_arytm_2,fc1_arytm_3,fc1_funct_4,fc1_numbers,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_2,fc2_subset_1,fc2_xboole_0,fc3_subset_1,fc3_xboole_0,fc4_subset_1,fc8_arytm_3,fraenkel_a_0_0_arytm_0,fraenkel_a_0_0_arytm_2,fraenkel_a_0_0_arytm_3,fraenkel_a_0_1_arytm_0,fraenkel_a_0_1_arytm_3,fraenkel_a_0_2_arytm_0,fraenkel_a_0_2_arytm_2,fraenkel_a_1_0_arytm_2,idempotence_k2_xboole_0,l16_arytm_0,rc1_arytm_3,rc1_funct_2,rc1_subset_1,rc1_xboole_0,rc2_arytm_3,rc2_subset_1,rc2_xboole_0,rc3_arytm_3,redefinition_k12_arytm_3,redefinition_k13_arytm_3,redefinition_k5_funct_4,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc0_boole,symmetry_r1_arytm_3,t103_zfmisc_1,t10_ordinal3,t1_boole,t1_subset,t23_ordinal1,t2_subset,t2_tarski,t33_zfmisc_1,t3_boole,t3_subset,t4_boole,t4_subset,t5_subset,t69_enumset1,t6_boole,t71_funct_4,t7_boole,t82_arytm_3,t8_boole,t9_zfmisc_1]),
    [file(arytm_0,t10_arytm_0)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    []).

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc2_arytm_3,axiom,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    []).

fof(cc3_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    []).

fof(cc4_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ( v3_ordinal1(A)
       => ( v1_ordinal1(A)
          & v2_ordinal1(A)
          & v3_ordinal1(A)
          & v4_ordinal2(A) ) ) ) ),
    file(arytm_3,cc4_arytm_3),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_2),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

fof(connectedness_r3_arytm_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_arytm_3)
        & m1_subset_1(B,k6_arytm_3) )
     => ( r3_arytm_3(A,B)
        | r3_arytm_3(B,A) ) ) ),
    file(arytm_3,r3_arytm_3),
    []).

fof(d1_arytm_2,axiom,(
    k1_arytm_2 = k4_xboole_0(a_0_0_arytm_2,k1_tarski(k6_arytm_3)) ),
    file(arytm_2,d1_arytm_2),
    []).

fof(d1_numbers,axiom,(
    k1_numbers = k4_xboole_0(k2_xboole_0(k2_arytm_2,k2_zfmisc_1(k1_tarski(0),k2_arytm_2)),k1_tarski(k4_tarski(0,0))) ),
    file(numbers,d1_numbers),
    []).

fof(d1_tarski,axiom,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    []).

fof(d2_arytm_2,axiom,(
    k2_arytm_2 = k4_xboole_0(k2_xboole_0(k6_arytm_3,k1_arytm_2),a_0_2_arytm_2) ),
    file(arytm_2,d2_arytm_2),
    []).

fof(d2_tarski,axiom,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    []).

fof(d2_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    []).

fof(d4_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(d6_arytm_3,axiom,(
    k6_arytm_3 = k2_xboole_0(k4_xboole_0(a_0_0_arytm_3,a_0_1_arytm_3),k5_ordinal2) ),
    file(arytm_3,d6_arytm_3),
    []).

fof(dt_k12_arytm_3,axiom,
    ( v1_xboole_0(k12_arytm_3)
    & m1_subset_1(k12_arytm_3,k6_arytm_3) ),
    file(arytm_3,k12_arytm_3),
    []).

fof(dt_k13_arytm_3,axiom,
    ( ~ v1_xboole_0(k13_arytm_3)
    & v3_ordinal1(k13_arytm_3)
    & m1_subset_1(k13_arytm_3,k6_arytm_3) ),
    file(arytm_3,k13_arytm_3),
    []).

fof(dt_k1_arytm_2,axiom,(
    m1_subset_1(k1_arytm_2,k1_zfmisc_1(k1_zfmisc_1(k6_arytm_3))) ),
    file(arytm_2,k1_arytm_2),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_arytm_2,axiom,(
    $true ),
    file(arytm_2,k2_arytm_2),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_funct_4,axiom,(
    $true ),
    file(funct_4,k4_funct_4),
    []).

fof(dt_k4_ordinal2,axiom,
    ( v3_ordinal1(k4_ordinal2)
    & ~ v1_xboole_0(k4_ordinal2) ),
    file(ordinal2,k4_ordinal2),
    []).

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_k4_xboole_0,axiom,(
    $true ),
    file(xboole_0,k4_xboole_0),
    []).

fof(dt_k5_funct_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => ( v1_funct_1(k5_funct_4(A,B,C,D,E))
        & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A)
        & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) ) ) ),
    file(funct_4,k5_funct_4),
    []).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k6_arytm_3,axiom,(
    $true ),
    file(arytm_3,k6_arytm_3),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc1_arytm_2,axiom,(
    ~ v1_xboole_0(k1_arytm_2) ),
    file(arytm_2,fc1_arytm_2),
    []).

fof(fc1_arytm_3,axiom,
    ( ~ v1_xboole_0(k4_ordinal2)
    & v1_ordinal1(k4_ordinal2)
    & v2_ordinal1(k4_ordinal2)
    & v3_ordinal1(k4_ordinal2)
    & v4_ordinal2(k4_ordinal2) ),
    file(arytm_3,fc1_arytm_3),
    []).

fof(fc1_funct_4,axiom,(
    ! [A,B,C,D] : 
      ( v1_relat_1(k4_funct_4(A,B,C,D))
      & v1_funct_1(k4_funct_4(A,B,C,D)) ) ),
    file(funct_4,fc1_funct_4),
    []).

fof(fc1_numbers,axiom,(
    ~ v1_xboole_0(k1_numbers) ),
    file(numbers,fc1_numbers),
    []).

fof(fc1_ordinal2,axiom,
    ( v1_ordinal1(k5_ordinal2)
    & v2_ordinal1(k5_ordinal2)
    & v3_ordinal1(k5_ordinal2)
    & ~ v1_xboole_0(k5_ordinal2) ),
    file(ordinal2,fc1_ordinal2),
    []).

fof(fc1_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

fof(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc1_zfmisc_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k4_tarski(A,B)) ),
    file(zfmisc_1,fc1_zfmisc_1),
    []).

fof(fc2_arytm_2,axiom,(
    ~ v1_xboole_0(k2_arytm_2) ),
    file(arytm_2,fc2_arytm_2),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc2_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ),
    file(xboole_0,fc2_xboole_0),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(A)
     => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ),
    file(xboole_0,fc3_xboole_0),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(fc8_arytm_3,axiom,(
    ~ v1_xboole_0(k6_arytm_3) ),
    file(arytm_3,fc8_arytm_3),
    []).

fof(fraenkel_a_0_0_arytm_0,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_arytm_0)
    <=> ? [B,C] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & m2_subset_1(C,k1_numbers,k5_numbers)
          & A = k4_tarski(B,C)
          & r1_arytm_3(B,C)
          & C != k12_arytm_3 ) ) ),
    file(arytm_0,a_0_0_arytm_0),
    []).

fof(fraenkel_a_0_0_arytm_2,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_arytm_2)
    <=> ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k6_arytm_3))
          & A = B
          & ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ( r2_hidden(C,B)
               => ( ! [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                     => ( r3_arytm_3(D,C)
                       => r2_hidden(D,B) ) )
                  & ? [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                      & r2_hidden(D,B)
                      & ~ r3_arytm_3(D,C) ) ) ) ) ) ) ),
    file(arytm_2,a_0_0_arytm_2),
    []).

fof(fraenkel_a_0_0_arytm_3,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_0_arytm_3)
    <=> ? [B,C] : 
          ( m1_subset_1(B,k5_ordinal2)
          & m1_subset_1(C,k5_ordinal2)
          & A = k4_tarski(B,C)
          & r1_arytm_3(B,C)
          & C != k1_xboole_0 ) ) ),
    file(arytm_3,a_0_0_arytm_3),
    []).

fof(fraenkel_a_0_1_arytm_0,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_1_arytm_0)
    <=> ? [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k4_tarski(B,k13_arytm_3) ) ) ),
    file(arytm_0,a_0_1_arytm_0),
    []).

fof(fraenkel_a_0_1_arytm_3,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_1_arytm_3)
    <=> ? [B] : 
          ( m1_subset_1(B,k5_ordinal2)
          & A = k4_tarski(B,k4_ordinal2) ) ) ),
    file(arytm_3,a_0_1_arytm_3),
    []).

fof(fraenkel_a_0_2_arytm_0,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_2_arytm_0)
    <=> ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k6_arytm_3))
          & A = B
          & ! [C] : 
              ( m1_subset_1(C,k6_arytm_3)
             => ( r2_hidden(C,B)
               => ( ! [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                     => ( r3_arytm_3(D,C)
                       => r2_hidden(D,B) ) )
                  & ? [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                      & r2_hidden(D,B)
                      & ~ r3_arytm_3(D,C) ) ) ) ) ) ) ),
    file(arytm_0,a_0_2_arytm_0),
    []).

fof(fraenkel_a_0_2_arytm_2,axiom,(
    ! [A] : 
      ( r2_hidden(A,a_0_2_arytm_2)
    <=> ? [B] : 
          ( m1_subset_1(B,k6_arytm_3)
          & A = a_1_0_arytm_2(B)
          & B != k12_arytm_3 ) ) ),
    file(arytm_2,a_0_2_arytm_2),
    []).

fof(fraenkel_a_1_0_arytm_2,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k6_arytm_3)
     => ( r2_hidden(A,a_1_0_arytm_2(B))
      <=> ? [C] : 
            ( m1_subset_1(C,k6_arytm_3)
            & A = C
            & ~ r3_arytm_3(B,C) ) ) ) ),
    file(arytm_2,a_1_0_arytm_2),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

fof(l16_arytm_0,axiom,(
    ! [A,B,C] : 
      ( k4_tarski(A,B) = k1_tarski(C)
     => ( C = k1_tarski(A)
        & A = B ) ) ),
    file(arytm_0,l16_arytm_0),
    []).

fof(rc1_arytm_3,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_subset_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_arytm_3,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(arytm_3,rc2_arytm_3),
    []).

fof(rc2_subset_1,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_arytm_3,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k6_arytm_3)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc3_arytm_3),
    []).

fof(redefinition_k12_arytm_3,axiom,(
    k12_arytm_3 = k1_xboole_0 ),
    file(arytm_3,k12_arytm_3),
    []).

fof(redefinition_k13_arytm_3,axiom,(
    k13_arytm_3 = k4_ordinal2 ),
    file(arytm_3,k13_arytm_3),
    []).

fof(redefinition_k5_funct_4,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(D,A)
        & m1_subset_1(E,A) )
     => k5_funct_4(A,B,C,D,E) = k4_funct_4(B,C,D,E) ) ),
    file(funct_4,k5_funct_4),
    []).

fof(redefinition_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(spc0_boole,axiom,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    []).

fof(symmetry_r1_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_arytm_3(A,B)
       => r1_arytm_3(B,A) ) ) ),
    file(arytm_3,r1_arytm_3),
    []).

fof(t103_zfmisc_1,axiom,(
    ! [A,B,C,D] : ~ ( r1_tarski(A,k2_zfmisc_1(B,C))
      & r2_hidden(D,A)
      & ! [E,F] : ~ ( r2_hidden(E,B)
          & r2_hidden(F,C)
          & D = k4_tarski(E,F) ) ) ),
    file(zfmisc_1,t103_zfmisc_1),
    []).

fof(t10_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( A != k1_xboole_0
       => r2_hidden(k1_xboole_0,A) ) ) ),
    file(ordinal3,t10_ordinal3),
    []).

fof(t1_boole,axiom,(
    ! [A] : k2_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t1_boole),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t23_ordinal1,axiom,(
    ! [A,B] : 
      ( v3_ordinal1(B)
     => ( r2_hidden(A,B)
       => v3_ordinal1(A) ) ) ),
    file(ordinal1,t23_ordinal1),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t2_tarski,axiom,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    []).

fof(t33_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( k4_tarski(A,B) = k4_tarski(C,D)
     => ( A = C
        & B = D ) ) ),
    file(zfmisc_1,t33_zfmisc_1),
    []).

fof(t3_boole,axiom,(
    ! [A] : k4_xboole_0(A,k1_xboole_0) = A ),
    file(boole,t3_boole),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_boole,axiom,(
    ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ),
    file(boole,t4_boole),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t69_enumset1,axiom,(
    ! [A] : k2_tarski(A,A) = k1_tarski(A) ),
    file(enumset1,t69_enumset1),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t71_funct_4,axiom,(
    ! [A,B,C,D] : 
      ( A != C
     => k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) ) ),
    file(funct_4,t71_funct_4),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t82_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k6_arytm_3))
     => ~ ( ? [B] : 
              ( m1_subset_1(B,k6_arytm_3)
              & r2_hidden(B,A)
              & B != k12_arytm_3 )
          & ! [B] : 
              ( m1_subset_1(B,k6_arytm_3)
             => ! [C] : 
                  ( m1_subset_1(C,k6_arytm_3)
                 => ( ( r2_hidden(B,A)
                      & r3_arytm_3(C,B) )
                   => r2_hidden(C,A) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,k6_arytm_3)
             => ! [C] : 
                  ( m1_subset_1(C,k6_arytm_3)
                 => ! [D] : 
                      ( m1_subset_1(D,k6_arytm_3)
                     => ~ ( r2_hidden(B,A)
                          & r2_hidden(C,A)
                          & r2_hidden(D,A)
                          & B != C
                          & C != D
                          & D != B ) ) ) ) ) ) ),
    file(arytm_3,t82_arytm_3),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).

fof(t9_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( k1_tarski(A) = k2_tarski(B,C)
     => B = C ) ),
    file(zfmisc_1,t9_zfmisc_1),
    []).