% Mizar problem: t8_wellset1,wellset1,146,59 
fof(t8_wellset1,conjecture,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : ~ ( ! [C] : 
              ( r2_hidden(C,B)
             => ( ~ r2_hidden(k1_funct_1(A,C),C)
                & r2_hidden(k1_funct_1(A,C),k3_tarski(B)) ) )
          & ! [C] : 
              ( v1_relat_1(C)
             => ~ ( r1_tarski(k3_relat_1(C),k3_tarski(B))
                  & v2_wellord1(C)
                  & ~ r2_hidden(k3_relat_1(C),B)
                  & ! [D] : 
                      ( r2_hidden(D,k3_relat_1(C))
                     => ( r2_hidden(k1_wellord1(C,D),B)
                        & k1_funct_1(A,k1_wellord1(C,D)) = D ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_funct_1,cc1_relat_1,cc2_funct_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,d1_relat_2,d1_tarski,d1_wellord1,d2_xboole_0,d2_zfmisc_1,d3_relat_1,d3_tarski,d3_wellord1,d3_xboole_0,d4_relat_2,d4_xboole_0,d5_tarski,d5_wellord1,d6_relat_2,d6_wellord1,d7_xboole_0,d8_relat_2,dt_k1_funct_1,dt_k1_tarski,dt_k1_wellord1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_wellord1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k3_tarski,dt_k3_xboole_0,dt_k4_tarski,dt_k4_xboole_0,dt_m1_subset_1,existence_m1_subset_1,fc12_relat_1,fc1_relat_1,fc1_subset_1,fc2_relat_1,fc2_subset_1,fc3_relat_1,fc3_subset_1,fc4_relat_1,fc4_subset_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,rc1_funct_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,s1_relat_1__e5_6__wellset1,s1_wellset1__e2_6__wellset1,s1_xboole_0__e2_6_1__wellset1,symmetry_r1_xboole_0,t103_zfmisc_1,t10_wellord1,t113_zfmisc_1,t129_zfmisc_1,t16_wellord1,t17_xboole_1,t1_boole,t1_subset,t1_wellset1,t26_xboole_1,t29_wellord1,t2_boole,t2_subset,t2_tarski,t30_relat_1,t31_relat_1,t32_relat_1,t33_relat_1,t33_zfmisc_1,t35_wellord1,t36_xboole_1,t38_wellord1,t3_boole,t3_subset,t3_wellset1,t3_xboole_0,t3_xboole_1,t40_wellord1,t41_enumset1,t4_boole,t4_relat_1,t4_subset,t4_xboole_1,t5_subset,t6_boole,t6_relat_1,t6_wellset1,t7_boole,t7_wellset1,t7_xboole_1,t8_boole,t8_wellord1]),
    [file(wellset1,t8_wellset1)]).

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

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

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    []).

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(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(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(d1_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
        <=> ! [C] : 
              ( r2_hidden(C,B)
             => r2_hidden(k4_tarski(C,C),A) ) ) ) ),
    file(relat_2,d1_relat_2),
    []).

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

fof(d1_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( C = k1_wellord1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ( D != B
                & r2_hidden(k4_tarski(D,B),A) ) ) ) ) ),
    file(wellord1,d1_wellord1),
    []).

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(d2_zfmisc_1,axiom,(
    ! [A,B,C] : 
      ( C = k2_zfmisc_1(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E,F] : 
              ( r2_hidden(E,A)
              & r2_hidden(F,B)
              & D = k4_tarski(E,F) ) ) ) ),
    file(zfmisc_1,d2_zfmisc_1),
    []).

fof(d3_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
               => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d3_relat_1),
    []).

fof(d3_tarski,axiom,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    []).

fof(d3_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_wellord1(A,B)
        <=> ! [C] : ~ ( r1_tarski(C,B)
              & C != k1_xboole_0
              & ! [D] : ~ ( r2_hidden(D,C)
                  & r1_xboole_0(k1_wellord1(A,D),C) ) ) ) ) ),
    file(wellord1,d3_wellord1),
    []).

fof(d3_xboole_0,axiom,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    []).

fof(d4_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r4_relat_2(A,B)
        <=> ! [C,D] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,C),A) )
             => C = D ) ) ) ),
    file(relat_2,d4_relat_2),
    []).

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(d5_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_wellord1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B)
            & r6_relat_2(A,B)
            & r1_wellord1(A,B) ) ) ) ),
    file(wellord1,d5_wellord1),
    []).

fof(d6_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r6_relat_2(A,B)
        <=> ! [C,D] : ~ ( r2_hidden(C,B)
              & r2_hidden(D,B)
              & C != D
              & ~ r2_hidden(k4_tarski(C,D),A)
              & ~ r2_hidden(k4_tarski(D,C),A) ) ) ) ),
    file(relat_2,d6_relat_2),
    []).

fof(d6_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B)) ) ),
    file(wellord1,d6_wellord1),
    []).

fof(d7_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    []).

fof(d8_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
        <=> ! [C,D,E] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(E,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,E),A) )
             => r2_hidden(k4_tarski(C,E),A) ) ) ) ),
    file(relat_2,d8_relat_2),
    []).

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

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

fof(dt_k1_wellord1,axiom,(
    $true ),
    file(wellord1,k1_wellord1),
    []).

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

fof(dt_k2_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k2_wellord1(A,B)) ) ),
    file(wellord1,k2_wellord1),
    []).

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_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    []).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

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_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(fc12_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    []).

fof(fc1_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_1),
    []).

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

fof(fc2_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k2_xboole_0(A,B)) ) ),
    file(relat_1,fc2_relat_1),
    []).

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

fof(fc3_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k4_xboole_0(A,B)) ) ),
    file(relat_1,fc3_relat_1),
    []).

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

fof(fc4_relat_1,axiom,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    []).

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

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

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

fof(rc1_relat_1,axiom,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    []).

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(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_relat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    []).

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(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_relat_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    []).

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

fof(s1_relat_1__e5_6__wellset1,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( v1_relat_1(C)
      & ! [D,E] : 
          ( r2_hidden(k4_tarski(D,E),C)
        <=> ( r2_hidden(D,k3_tarski(A))
            & r2_hidden(E,k3_tarski(A))
            & ? [F] : 
                ( v1_relat_1(F)
                & r2_hidden(k4_tarski(D,E),F)
                & r2_hidden(F,B) ) ) ) ) ),
    file(wellset1,s1_relat_1__e5_6__wellset1),
    []).

fof(s1_wellset1__e2_6__wellset1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ? [C] : 
        ! [D] : 
          ( v1_relat_1(D)
         => ( r2_hidden(D,C)
          <=> ( r2_hidden(D,k1_zfmisc_1(k2_zfmisc_1(k3_tarski(B),k3_tarski(B))))
              & v2_wellord1(D)
              & ! [E] : 
                  ( r2_hidden(E,k3_relat_1(D))
                 => ( r2_hidden(k1_wellord1(D,E),B)
                    & k1_funct_1(A,k1_wellord1(D,E)) = E ) ) ) ) ) ) ),
    file(wellset1,s1_wellset1__e2_6__wellset1),
    []).

fof(s1_xboole_0__e2_6_1__wellset1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => ? [C] : 
        ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,k3_relat_1(A))
            & r2_hidden(D,k3_relat_1(B))
            & k2_wellord1(A,k1_wellord1(A,D)) = k2_wellord1(B,k1_wellord1(B,D)) ) ) ) ),
    file(wellset1,s1_xboole_0__e2_6_1__wellset1),
    []).

fof(symmetry_r1_xboole_0,axiom,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
     => r1_xboole_0(B,A) ) ),
    file(xboole_0,r1_xboole_0),
    []).

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_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
       => ! [B] : ~ ( r1_tarski(B,k3_relat_1(A))
            & B != k1_xboole_0
            & ! [C] : ~ ( r2_hidden(C,B)
                & ! [D] : 
                    ( r2_hidden(D,B)
                   => r2_hidden(k4_tarski(C,D),A) ) ) ) ) ) ),
    file(wellord1,t10_wellord1),
    []).

fof(t113_zfmisc_1,axiom,(
    ! [A,B] : 
      ( k2_zfmisc_1(A,B) = k1_xboole_0
    <=> ( A = k1_xboole_0
        | B = k1_xboole_0 ) ) ),
    file(zfmisc_1,t113_zfmisc_1),
    []).

fof(t129_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D)))
    <=> ( r2_hidden(A,C)
        & B = D ) ) ),
    file(zfmisc_1,t129_zfmisc_1),
    []).

fof(t16_wellord1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(A,k2_wellord1(C,B))
      <=> ( r2_hidden(A,C)
          & r2_hidden(A,k2_zfmisc_1(B,B)) ) ) ) ),
    file(wellord1,t16_wellord1),
    []).

fof(t17_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    []).

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(t1_wellset1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r2_hidden(A,k3_relat_1(B))
      <=> ~ ! [C] : 
              ( ~ r2_hidden(k4_tarski(A,C),B)
              & ~ r2_hidden(k4_tarski(C,A),B) ) ) ) ),
    file(wellset1,t1_wellset1),
    []).

fof(t26_xboole_1,axiom,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) ),
    file(xboole_1,t26_xboole_1),
    []).

fof(t29_wellord1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => k2_wellord1(k2_wellord1(C,B),A) = k2_wellord1(C,A) ) ) ),
    file(wellord1,t29_wellord1),
    []).

fof(t2_boole,axiom,(
    ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ),
    file(boole,t2_boole),
    []).

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(t30_relat_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(k4_tarski(A,B),C)
       => ( r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C)) ) ) ) ),
    file(relat_1,t30_relat_1),
    []).

fof(t31_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => r1_tarski(k3_relat_1(A),k3_relat_1(B)) ) ) ) ),
    file(relat_1,t31_relat_1),
    []).

fof(t32_relat_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( C = k1_tarski(k4_tarski(A,B))
       => k3_relat_1(C) = k2_tarski(A,B) ) ) ),
    file(relat_1,t32_relat_1),
    []).

fof(t33_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)) ) ) ),
    file(relat_1,t33_relat_1),
    []).

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(t35_wellord1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( v2_wellord1(C)
          & r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k1_wellord1(C,A)) )
       => k1_wellord1(k2_wellord1(C,k1_wellord1(C,A)),B) = k1_wellord1(C,B) ) ) ),
    file(wellord1,t35_wellord1),
    []).

fof(t36_xboole_1,axiom,(
    ! [A,B] : r1_tarski(k4_xboole_0(A,B),A) ),
    file(xboole_1,t36_xboole_1),
    []).

fof(t38_wellord1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( v2_wellord1(C)
          & r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C)) )
       => ( r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B))
        <=> ( A = B
            | r2_hidden(A,k1_wellord1(C,B)) ) ) ) ) ),
    file(wellord1,t38_wellord1),
    []).

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(t3_wellset1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( C = k2_zfmisc_1(A,B)
       => ( A = k1_xboole_0
          | B = k1_xboole_0
          | k3_relat_1(C) = k2_xboole_0(A,B) ) ) ) ),
    file(wellset1,t3_wellset1),
    []).

fof(t3_xboole_0,axiom,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    []).

fof(t3_xboole_1,axiom,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    []).

fof(t40_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( v2_wellord1(B)
       => k3_relat_1(k2_wellord1(B,k1_wellord1(B,A))) = k1_wellord1(B,A) ) ) ),
    file(wellord1,t40_wellord1),
    []).

fof(t41_enumset1,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ),
    file(enumset1,t41_enumset1),
    []).

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

fof(t4_relat_1,axiom,(
    ! [A,B] : v1_relat_1(k1_tarski(k4_tarski(A,B))) ),
    file(relat_1,t4_relat_1),
    []).

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(t4_xboole_1,axiom,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    []).

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

fof(t6_relat_1,axiom,(
    ! [A,B] : v1_relat_1(k2_zfmisc_1(A,B)) ),
    file(relat_1,t6_relat_1),
    []).

fof(t6_wellset1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C))
          & v2_wellord1(C) )
       => ( r2_hidden(A,k1_wellord1(C,B))
          | r2_hidden(k4_tarski(B,A),C) ) ) ) ),
    file(wellset1,t6_wellset1),
    []).

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

fof(t7_wellset1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ~ ( r2_hidden(A,k3_relat_1(C))
          & r2_hidden(B,k3_relat_1(C))
          & v2_wellord1(C)
          & r2_hidden(A,k1_wellord1(C,B))
          & r2_hidden(k4_tarski(B,A),C) ) ) ),
    file(wellset1,t7_wellset1),
    []).

fof(t7_xboole_1,axiom,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    []).

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

fof(t8_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( r2_wellord1(A,k3_relat_1(A))
      <=> v2_wellord1(A) ) ) ),
    file(wellord1,t8_wellord1),
    []).