% Mizar problem: t30_ordinal4,ordinal4,1196,34 
fof(t30_ordinal4,conjecture,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => k16_ordinal2(A,k14_ordinal2(B,C)) = k15_ordinal2(k16_ordinal2(A,C),k16_ordinal2(A,B)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_arytm_3,cc1_funct_1,cc1_ordinal1,cc2_arytm_3,cc2_funct_1,cc2_ordinal1,cc3_ordinal1,connectedness_r1_ordinal1,d14_ordinal2,d1_ordinal4,d4_ordinal2,d5_ordinal3,dt_k12_ordinal2,dt_k14_ordinal2,dt_k15_ordinal2,dt_k16_ordinal2,dt_k1_funct_1,dt_k1_ordinal1,dt_k1_ordinal4,dt_k1_relat_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_ordinal2,dt_k4_ordinal3,dt_m1_subset_1,existence_m1_subset_1,fc1_arytm_3,fc1_ordinal1,fc2_arytm_3,fc2_ordinal1,fc2_ordinal4,fc3_arytm_3,fc3_ordinal1,fc3_ordinal2,fc5_arytm_3,fc5_ordinal1,rc1_arytm_3,rc1_funct_1,rc1_ordinal1,rc1_ordinal2,rc2_funct_1,rc2_ordinal1,rc2_ordinal2,rc3_funct_1,rc3_ordinal1,rc4_funct_1,rc4_ordinal1,redefinition_r1_ordinal1,reflexivity_r1_ordinal1,reflexivity_r1_tarski,s1_ordinal2__e5_37__ordinal4,s3_ordinal2__e3_37_2__ordinal4,s3_ordinal2__e5_37_2__ordinal4,s3_ordinal2__e9_37_2__ordinal4,t1_subset,t21_ordinal4,t27_ordinal3,t29_ordinal3,t2_subset,t32_ordinal3,t3_ordinal4,t3_subset,t44_ordinal2,t45_ordinal2,t49_ordinal2,t4_subset,t56_ordinal2,t58_ordinal3,t5_ordinal4,t5_subset,t60_ordinal2,t61_ordinal2,t62_ordinal2,t6_boole,t7_boole,t8_boole]),
    [file(ordinal4,t30_ordinal4)]).

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_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

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_funct_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    []).

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

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

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(d14_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ( ? [B] : 
            ( v3_ordinal1(B)
            & r1_ordinal2(B,A) )
       => ! [B] : 
            ( v3_ordinal1(B)
           => ( B = k12_ordinal2(A)
            <=> r1_ordinal2(B,A) ) ) ) ) ),
    file(ordinal2,d14_ordinal2),
    []).

fof(d1_ordinal4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v5_ordinal1(C) )
             => ( C = k1_ordinal4(A,B)
              <=> ( k1_relat_1(C) = k14_ordinal2(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ( r2_hidden(D,k1_relat_1(A))
                       => k1_funct_1(C,D) = k1_funct_1(A,D) ) )
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ( r2_hidden(D,k1_relat_1(B))
                       => k1_funct_1(C,k14_ordinal2(k1_relat_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) ),
    file(ordinal4,d1_ordinal4),
    []).

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

fof(d5_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B)
            & v1_ordinal2(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v5_ordinal1(C)
                & v1_ordinal2(C) )
             => ( C = k4_ordinal3(A,B)
              <=> ( k1_relat_1(C) = k1_relat_1(B)
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ( r2_hidden(D,k1_relat_1(B))
                       => k1_funct_1(C,D) = k15_ordinal2(k1_funct_1(B,D),A) ) ) ) ) ) ) ) ),
    file(ordinal3,d5_ordinal3),
    []).

fof(dt_k12_ordinal2,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => v3_ordinal1(k12_ordinal2(A)) ) ),
    file(ordinal2,k12_ordinal2),
    []).

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_k16_ordinal2,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => v3_ordinal1(k16_ordinal2(A,B)) ) ),
    file(ordinal2,k16_ordinal2),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

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

fof(dt_k1_ordinal4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v5_ordinal1(B) )
     => ( v1_relat_1(k1_ordinal4(A,B))
        & v1_funct_1(k1_ordinal4(A,B))
        & v5_ordinal1(k1_ordinal4(A,B)) ) ) ),
    file(ordinal4,k1_ordinal4),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

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_k4_ordinal2,axiom,
    ( v3_ordinal1(k4_ordinal2)
    & ~ v1_xboole_0(k4_ordinal2) ),
    file(ordinal2,k4_ordinal2),
    []).

fof(dt_k4_ordinal3,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v5_ordinal1(B)
        & v1_ordinal2(B) )
     => ( v1_relat_1(k4_ordinal3(A,B))
        & v1_funct_1(k4_ordinal3(A,B))
        & v5_ordinal1(k4_ordinal3(A,B))
        & v1_ordinal2(k4_ordinal3(A,B)) ) ) ),
    file(ordinal3,k4_ordinal3),
    []).

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(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_ordinal4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v5_ordinal1(B)
        & v1_ordinal2(B) )
     => ( v1_relat_1(k1_ordinal4(A,B))
        & v1_funct_1(k1_ordinal4(A,B))
        & v5_ordinal1(k1_ordinal4(A,B))
        & v1_ordinal2(k1_ordinal4(A,B)) ) ) ),
    file(ordinal4,fc2_ordinal4),
    []).

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_ordinal2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A)
        & v3_ordinal1(B) )
     => ( v1_ordinal1(k1_funct_1(A,B))
        & v2_ordinal1(k1_funct_1(A,B))
        & v3_ordinal1(k1_funct_1(A,B)) ) ) ),
    file(ordinal2,fc3_ordinal2),
    []).

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(fc5_ordinal1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A) )
     => ( v1_ordinal1(k1_relat_1(A))
        & v2_ordinal1(k1_relat_1(A))
        & v3_ordinal1(k1_relat_1(A)) ) ) ),
    file(ordinal1,fc5_ordinal1),
    []).

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_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

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(rc2_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    []).

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_ordinal2,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A)
      & v1_ordinal2(A) ) ),
    file(ordinal2,rc2_ordinal2),
    []).

fof(rc3_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    []).

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

fof(rc4_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    []).

fof(rc4_ordinal1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v5_ordinal1(A) ) ),
    file(ordinal1,rc4_ordinal1),
    []).

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(s1_ordinal2__e5_37__ordinal4,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ( ( k16_ordinal2(A,k14_ordinal2(B,k1_xboole_0)) = k15_ordinal2(k16_ordinal2(A,k1_xboole_0),k16_ordinal2(A,B))
          & ! [C] : 
              ( v3_ordinal1(C)
             => ( k16_ordinal2(A,k14_ordinal2(B,C)) = k15_ordinal2(k16_ordinal2(A,C),k16_ordinal2(A,B))
               => k16_ordinal2(A,k14_ordinal2(B,k1_ordinal1(C))) = k15_ordinal2(k16_ordinal2(A,k1_ordinal1(C)),k16_ordinal2(A,B)) ) )
          & ! [C] : 
              ( v3_ordinal1(C)
             => ( ( v4_ordinal1(C)
                  & ! [D] : 
                      ( v3_ordinal1(D)
                     => ( r2_hidden(D,C)
                       => k16_ordinal2(A,k14_ordinal2(B,D)) = k15_ordinal2(k16_ordinal2(A,D),k16_ordinal2(A,B)) ) ) )
               => ( C = k1_xboole_0
                  | k16_ordinal2(A,k14_ordinal2(B,C)) = k15_ordinal2(k16_ordinal2(A,C),k16_ordinal2(A,B)) ) ) ) )
       => ! [C] : 
            ( v3_ordinal1(C)
           => k16_ordinal2(A,k14_ordinal2(B,C)) = k15_ordinal2(k16_ordinal2(A,C),k16_ordinal2(A,B)) ) ) ) ),
    file(ordinal4,s1_ordinal2__e5_37__ordinal4),
    []).

fof(s3_ordinal2__e3_37_2__ordinal4,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v5_ordinal1(C)
          & v1_ordinal2(C)
          & k1_relat_1(C) = B
          & ! [D] : 
              ( v3_ordinal1(D)
             => ( r2_hidden(D,B)
               => k1_funct_1(C,D) = k16_ordinal2(A,D) ) ) ) ) ),
    file(ordinal4,s3_ordinal2__e3_37_2__ordinal4),
    []).

fof(s3_ordinal2__e5_37_2__ordinal4,axiom,(
    ! [A,B,C] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B)
        & v3_ordinal1(C) )
     => ? [D] : 
          ( v1_relat_1(D)
          & v1_funct_1(D)
          & v5_ordinal1(D)
          & v1_ordinal2(D)
          & k1_relat_1(D) = k14_ordinal2(B,C)
          & ! [E] : 
              ( v3_ordinal1(E)
             => ( r2_hidden(E,k14_ordinal2(B,C))
               => k1_funct_1(D,E) = k16_ordinal2(A,E) ) ) ) ) ),
    file(ordinal4,s3_ordinal2__e5_37_2__ordinal4),
    []).

fof(s3_ordinal2__e9_37_2__ordinal4,axiom,(
    ! [A,B] : 
      ( ( v3_ordinal1(A)
        & v3_ordinal1(B) )
     => ? [C] : 
          ( v1_relat_1(C)
          & v1_funct_1(C)
          & v5_ordinal1(C)
          & v1_ordinal2(C)
          & k1_relat_1(C) = B
          & ! [D] : 
              ( v3_ordinal1(D)
             => ( r2_hidden(D,B)
               => k1_funct_1(C,D) = k16_ordinal2(A,D) ) ) ) ) ),
    file(ordinal4,s3_ordinal2__e9_37_2__ordinal4),
    []).

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

fof(t21_ordinal4,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v4_ordinal1(A)
           => ( A = k1_xboole_0
              | ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C)
                    & v5_ordinal1(C)
                    & v1_ordinal2(C) )
                 => ( ( k1_relat_1(C) = A
                      & ! [D] : 
                          ( v3_ordinal1(D)
                         => ( r2_hidden(D,A)
                           => k1_funct_1(C,D) = k16_ordinal2(B,D) ) ) )
                   => r1_ordinal2(k16_ordinal2(B,A),C) ) ) ) ) ) ) ),
    file(ordinal4,t21_ordinal4),
    []).

fof(t27_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( r1_ordinal1(A,k14_ordinal2(A,B))
            & r1_ordinal1(B,k14_ordinal2(A,B)) ) ) ) ),
    file(ordinal3,t27_ordinal3),
    []).

fof(t29_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( k14_ordinal2(A,B) = k1_xboole_0
           => ( A = k1_xboole_0
              & B = k1_xboole_0 ) ) ) ) ),
    file(ordinal3,t29_ordinal3),
    []).

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

fof(t32_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v4_ordinal1(A)
           => ( A = k1_xboole_0
              | v4_ordinal1(k14_ordinal2(B,A)) ) ) ) ) ),
    file(ordinal3,t32_ordinal3),
    []).

fof(t3_ordinal4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v5_ordinal1(B)
            & v1_ordinal2(B) )
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal2(C,A)
               => r1_ordinal2(C,k1_ordinal4(B,A)) ) ) ) ) ),
    file(ordinal4,t3_ordinal4),
    []).

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

fof(t44_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k14_ordinal2(A,k1_xboole_0) = A ) ),
    file(ordinal2,t44_ordinal2),
    []).

fof(t45_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => k14_ordinal2(A,k1_ordinal1(B)) = k1_ordinal1(k14_ordinal2(A,B)) ) ) ),
    file(ordinal2,t45_ordinal2),
    []).

fof(t49_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r2_hidden(A,B)
               => r2_hidden(k14_ordinal2(C,A),k14_ordinal2(C,B)) ) ) ) ) ),
    file(ordinal2,t49_ordinal2),
    []).

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(t58_ordinal3,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => k15_ordinal2(k15_ordinal2(A,B),C) = k15_ordinal2(A,k15_ordinal2(B,C)) ) ) ) ),
    file(ordinal3,t58_ordinal3),
    []).

fof(t5_ordinal4,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v5_ordinal1(A)
        & v1_ordinal2(A) )
     => ! [B] : 
          ( v3_ordinal1(B)
         => ! [C] : 
              ( v3_ordinal1(C)
             => ( r1_ordinal2(B,A)
               => r1_ordinal2(k15_ordinal2(B,C),k4_ordinal3(C,A)) ) ) ) ) ),
    file(ordinal4,t5_ordinal4),
    []).

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(t60_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => k16_ordinal2(A,k1_xboole_0) = k4_ordinal2 ) ),
    file(ordinal2,t60_ordinal2),
    []).

fof(t61_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => k16_ordinal2(A,k1_ordinal1(B)) = k15_ordinal2(A,k16_ordinal2(A,B)) ) ) ),
    file(ordinal2,t61_ordinal2),
    []).

fof(t62_ordinal2,axiom,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( v3_ordinal1(B)
         => ( v4_ordinal1(A)
           => ( A = k1_xboole_0
              | ! [C] : 
                  ( ( v1_relat_1(C)
                    & v1_funct_1(C)
                    & v5_ordinal1(C)
                    & v1_ordinal2(C) )
                 => ( ( k1_relat_1(C) = A
                      & ! [D] : 
                          ( v3_ordinal1(D)
                         => ( r2_hidden(D,A)
                           => k1_funct_1(C,D) = k16_ordinal2(B,D) ) ) )
                   => k16_ordinal2(B,A) = k12_ordinal2(C) ) ) ) ) ) ) ),
    file(ordinal2,t62_ordinal2),
    []).

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

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

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