% Mizar problem: t99_arytm_3,arytm_3,1831,46 
fof(t99_arytm_3,conjecture,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(A,k1_zfmisc_1(k6_arytm_3)) )
     => ~ ( r2_hidden(A,k6_arytm_3)
          & ! [B] : 
              ( m1_subset_1(B,k6_arytm_3)
             => ~ ( r2_hidden(B,A)
                  & ! [C] : 
                      ( m1_subset_1(C,k6_arytm_3)
                     => ( r2_hidden(C,A)
                       => r3_arytm_3(C,B) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_ordinal1,cc2_arytm_3,cc2_ordinal1,cc3_arytm_3,cc3_ordinal1,cc4_arytm_3,commutativity_k10_arytm_3,commutativity_k1_arytm_3,commutativity_k2_arytm_3,commutativity_k2_tarski,commutativity_k2_xboole_0,connectedness_r1_ordinal1,connectedness_r3_arytm_3,d10_arytm_3,d12_arytm_3,d1_arytm_3,d1_tarski,d21_ordinal2,d2_tarski,d4_ordinal2,d5_ordinal2,d5_tarski,d6_arytm_3,d6_ordinal3,dt_k10_arytm_3,dt_k12_arytm_3,dt_k13_arytm_3,dt_k14_ordinal2,dt_k15_ordinal2,dt_k1_arytm_3,dt_k1_ordinal1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_arytm_3,dt_k2_tarski,dt_k2_xboole_0,dt_k4_ordinal2,dt_k4_tarski,dt_k4_xboole_0,dt_k5_ordinal2,dt_k5_ordinal3,dt_k6_arytm_3,dt_k7_arytm_3,dt_k8_arytm_3,dt_k9_arytm_3,dt_m1_subset_1,existence_m1_subset_1,fc1_arytm_3,fc1_ordinal1,fc1_ordinal2,fc1_subset_1,fc1_xboole_0,fc1_zfmisc_1,fc2_arytm_3,fc2_ordinal1,fc2_subset_1,fc2_xboole_0,fc3_arytm_3,fc3_ordinal1,fc3_subset_1,fc3_xboole_0,fc4_arytm_3,fc5_arytm_3,fc8_arytm_3,fraenkel_a_0_0_arytm_3,fraenkel_a_0_1_arytm_3,idempotence_k2_xboole_0,rc1_arytm_3,rc1_ordinal1,rc1_ordinal2,rc1_subset_1,rc1_xboole_0,rc2_arytm_3,rc2_ordinal1,rc2_subset_1,rc2_xboole_0,rc3_arytm_3,rc3_ordinal1,redefinition_k12_arytm_3,redefinition_k13_arytm_3,redefinition_k1_arytm_3,redefinition_k2_arytm_3,redefinition_r1_ordinal1,reflexivity_r1_ordinal1,reflexivity_r1_tarski,symmetry_r1_arytm_3,t10_ordinal1,t10_ordinal3,t1_boole,t1_subset,t23_ordinal1,t2_subset,t2_tarski,t34_arytm_3,t34_ordinal1,t35_arytm_3,t3_boole,t3_subset,t42_ordinal1,t4_boole,t4_subset,t56_ordinal2,t5_subset,t64_arytm_3,t6_boole,t7_arytm_3,t7_boole,t7_ordinal1,t8_boole]),
    [file(arytm_3,t99_arytm_3)]).

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_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A) ) ) ),
    file(ordinal1,cc1_ordinal1),
    []).

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(cc2_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_ordinal1(A)
        & v2_ordinal1(A) )
     => v3_ordinal1(A) ) ),
    file(ordinal1,cc2_ordinal1),
    []).

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(cc3_ordinal1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A) ) ) ),
    file(ordinal1,cc3_ordinal1),
    []).

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(commutativity_k10_arytm_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_arytm_3)
        & m1_subset_1(B,k6_arytm_3) )
     => k10_arytm_3(A,B) = k10_arytm_3(B,A) ) ),
    file(arytm_3,k10_arytm_3),
    []).

fof(commutativity_k1_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => k1_arytm_3(A,B) = k1_arytm_3(B,A) ) ),
    file(arytm_3,k1_arytm_3),
    []).

fof(commutativity_k2_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => k2_arytm_3(A,B) = k2_arytm_3(B,A) ) ),
    file(arytm_3,k2_arytm_3),
    []).

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_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
        | r1_ordinal1(B,A) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

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(d10_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => k10_arytm_3(A,B) = k9_arytm_3(k1_arytm_3(k2_arytm_3(k7_arytm_3(A),k8_arytm_3(B)),k2_arytm_3(k7_arytm_3(B),k8_arytm_3(A))),k2_arytm_3(k8_arytm_3(A),k8_arytm_3(B))) ) ) ),
    file(arytm_3,d10_arytm_3),
    []).

fof(d12_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ! [B] : 
          ( m1_subset_1(B,k6_arytm_3)
         => ( r3_arytm_3(A,B)
          <=> ? [C] : 
                ( m1_subset_1(C,k6_arytm_3)
                & B = k10_arytm_3(A,C) ) ) ) ) ),
    file(arytm_3,d12_arytm_3),
    []).

fof(d1_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_arytm_3(A,B)
          <=> ! [C] : 
                ( v3_ordinal1(C)
               => ! [D] : 
                    ( v3_ordinal1(D)
                   => ! [E] : 
                        ( v3_ordinal1(E)
                       => ( ( A = k15_ordinal2(C,D)
                            & B = k15_ordinal2(C,E) )
                         => C = k4_ordinal2 ) ) ) ) ) ) ) ),
    file(arytm_3,d1_arytm_3),
    []).

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

fof(d21_ordinal2,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
    <=> r2_hidden(A,k5_ordinal2) ) ),
    file(ordinal2,d21_ordinal2),
    []).

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(d4_ordinal2,axiom,(
    k4_ordinal2 = k1_ordinal1(k1_xboole_0) ),
    file(ordinal2,d4_ordinal2),
    []).

fof(d5_ordinal2,axiom,(
    ! [A] : 
      ( A = k5_ordinal2
    <=> ( r2_hidden(k1_xboole_0,A)
        & v4_ordinal1(A)
        & v3_ordinal1(A)
        & ! [B] : 
            ( v3_ordinal1(B)
           => ( ( r2_hidden(k1_xboole_0,B)
                & v4_ordinal1(B) )
             => r1_tarski(A,B) ) ) ) ) ),
    file(ordinal2,d5_ordinal2),
    []).

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(d6_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( ( r1_ordinal1(B,A)
                 => ( C = k5_ordinal3(A,B)
                  <=> A = k14_ordinal2(B,C) ) )
                & ( ~ r1_ordinal1(B,A)
                 => ( C = k5_ordinal3(A,B)
                  <=> C = k1_xboole_0 ) ) ) ) ) ) ),
    file(ordinal3,d6_ordinal3),
    []).

fof(dt_k10_arytm_3,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k6_arytm_3)
        & m1_subset_1(B,k6_arytm_3) )
     => m1_subset_1(k10_arytm_3(A,B),k6_arytm_3) ) ),
    file(arytm_3,k10_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_k14_ordinal2,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => v3_ordinal1(k14_ordinal2(A,B)) ) ),
    file(ordinal2,k14_ordinal2),
    []).

fof(dt_k15_ordinal2,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => v3_ordinal1(k15_ordinal2(A,B)) ) ),
    file(ordinal2,k15_ordinal2),
    []).

fof(dt_k1_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => v3_ordinal1(k1_arytm_3(A,B)) ) ),
    file(arytm_3,k1_arytm_3),
    []).

fof(dt_k1_ordinal1,axiom,(
    $true ),
    file(ordinal1,k1_ordinal1),
    []).

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_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => v3_ordinal1(k2_arytm_3(A,B)) ) ),
    file(arytm_3,k2_arytm_3),
    []).

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_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_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k5_ordinal3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => v3_ordinal1(k5_ordinal3(A,B)) ) ),
    file(ordinal3,k5_ordinal3),
    []).

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

fof(dt_k7_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => m1_subset_1(k7_arytm_3(A),k5_ordinal2) ) ),
    file(arytm_3,k7_arytm_3),
    []).

fof(dt_k8_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => m1_subset_1(k8_arytm_3(A),k5_ordinal2) ) ),
    file(arytm_3,k8_arytm_3),
    []).

fof(dt_k9_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => m1_subset_1(k9_arytm_3(A,B),k6_arytm_3) ) ),
    file(arytm_3,k9_arytm_3),
    []).

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

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

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_ordinal1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_ordinal1(A)) ),
    file(ordinal1,fc1_ordinal1),
    []).

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_3,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A) )
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A))
        & v4_ordinal2(k1_ordinal1(A)) ) ) ),
    file(arytm_3,fc2_arytm_3),
    []).

fof(fc2_ordinal1,axiom,
    ( v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_xboole_0(k1_xboole_0)
    & v1_ordinal1(k1_xboole_0)
    & v2_ordinal1(k1_xboole_0)
    & v3_ordinal1(k1_xboole_0) ),
    file(ordinal1,fc2_ordinal1),
    []).

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_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => ( v1_ordinal1(k14_ordinal2(A,B))
        & v2_ordinal1(k14_ordinal2(A,B))
        & v3_ordinal1(k14_ordinal2(A,B))
        & v4_ordinal2(k14_ordinal2(A,B)) ) ) ),
    file(arytm_3,fc3_arytm_3),
    []).

fof(fc3_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ v1_xboole_0(k1_ordinal1(A))
        & v1_ordinal1(k1_ordinal1(A))
        & v2_ordinal1(k1_ordinal1(A))
        & v3_ordinal1(k1_ordinal1(A)) ) ) ),
    file(ordinal1,fc3_ordinal1),
    []).

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_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => ( v1_ordinal1(k5_ordinal3(A,B))
        & v2_ordinal1(k5_ordinal3(A,B))
        & v3_ordinal1(k5_ordinal3(A,B))
        & v4_ordinal2(k5_ordinal3(A,B)) ) ) ),
    file(arytm_3,fc4_arytm_3),
    []).

fof(fc5_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => ( v1_ordinal1(k15_ordinal2(A,B))
        & v2_ordinal1(k15_ordinal2(A,B))
        & v3_ordinal1(k15_ordinal2(A,B))
        & v4_ordinal2(k15_ordinal2(A,B)) ) ) ),
    file(arytm_3,fc5_arytm_3),
    []).

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

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_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(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_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_ordinal1,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc1_ordinal1),
    []).

fof(rc1_ordinal2,axiom,(
    ? [A] : 
      ( v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal1(A) ) ),
    file(ordinal2,rc1_ordinal2),
    []).

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_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc2_ordinal1),
    []).

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(rc3_ordinal1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A) ) ),
    file(ordinal1,rc3_ordinal1),
    []).

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_k1_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => k1_arytm_3(A,B) = k14_ordinal2(A,B) ) ),
    file(arytm_3,k1_arytm_3),
    []).

fof(redefinition_k2_arytm_3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v4_ordinal2(A)
        & v3_ordinal1(B)
        & v4_ordinal2(B) )
     => k2_arytm_3(A,B) = k15_ordinal2(A,B) ) ),
    file(arytm_3,k2_arytm_3),
    []).

fof(redefinition_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( r1_ordinal1(A,B)
      <=> r1_tarski(A,B) ) ) ),
    file(ordinal1,r1_ordinal1),
    []).

fof(reflexivity_r1_ordinal1,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => r1_ordinal1(A,A) ) ),
    file(ordinal1,r1_ordinal1),
    []).

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

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(t10_ordinal1,axiom,(
    ! [A] : r2_hidden(A,k1_ordinal1(A)) ),
    file(ordinal1,t10_ordinal1),
    []).

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(t34_arytm_3,axiom,(
    r1_tarski(k5_ordinal2,k6_arytm_3) ),
    file(arytm_3,t34_arytm_3),
    []).

fof(t34_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r2_hidden(A,k1_ordinal1(B))
          <=> r1_ordinal1(A,B) ) ) ) ),
    file(ordinal1,t34_ordinal1),
    []).

fof(t35_arytm_3,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_arytm_3)
     => ~ ( ~ r2_hidden(A,k5_ordinal2)
          & ! [B] : 
              ( m1_subset_1(B,k5_ordinal2)
             => ! [C] : 
                  ( m1_subset_1(C,k5_ordinal2)
                 => ~ ( A = k4_tarski(B,C)
                      & r1_arytm_3(B,C)
                      & C != k1_xboole_0
                      & C != k4_ordinal2 ) ) ) ) ) ),
    file(arytm_3,t35_arytm_3),
    []).

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(t42_ordinal1,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( ~ ( ~ v4_ordinal1(A)
            & ! [B] : 
                ( v3_ordinal1(B)
               => A != k1_ordinal1(B) ) )
        & ~ ( ? [B] : 
                ( v3_ordinal1(B)
                & A = k1_ordinal1(B) )
            & v4_ordinal1(A) ) ) ) ),
    file(ordinal1,t42_ordinal1),
    []).

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(t56_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( k15_ordinal2(k4_ordinal2,A) = A
        & k15_ordinal2(A,k4_ordinal2) = A ) ) ),
    file(ordinal2,t56_ordinal2),
    []).

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(t64_arytm_3,axiom,(
    ! [A] : 
      ( ( v3_ordinal1(A)
        & m1_subset_1(A,k6_arytm_3) )
     => ! [B] : 
          ( ( v3_ordinal1(B)
            & m1_subset_1(B,k6_arytm_3) )
         => k10_arytm_3(A,B) = k1_arytm_3(A,B) ) ) ),
    file(arytm_3,t64_arytm_3),
    []).

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

fof(t7_arytm_3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ( r1_arytm_3(k1_xboole_0,A)
       => A = k4_ordinal2 ) ) ),
    file(arytm_3,t7_arytm_3),
    []).

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

fof(t7_ordinal1,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & r1_tarski(B,A) ) ),
    file(ordinal1,t7_ordinal1),
    []).

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