% Mizar problem: t65_normform,normform,711,46 
fof(t65_normform,conjecture,(
    ! [A,B] : 
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] : 
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ~ ( r2_hidden(B,C)
              & ! [D] : 
                  ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                 => ~ ( r1_normform(k5_finsub_1(A),k5_finsub_1(A),D,B)
                      & r2_hidden(D,k9_normform(A,C)) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finsub_1,cc1_relset_1,cc2_finsub_1,cc3_finsub_1,d10_normform,d8_normform,d9_normform,dt_k1_mcart_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_domain_1,dt_k2_mcart_1,dt_k2_zfmisc_1,dt_k3_domain_1,dt_k5_finsub_1,dt_k7_normform,dt_k8_normform,dt_k9_normform,dt_m1_subset_1,dt_m2_subset_1,existence_m1_subset_1,existence_m2_subset_1,fc1_finsub_1,fc1_subset_1,fc1_xboole_0,fc2_finsub_1,fc2_normform,fc3_normform,fc4_subset_1,fraenkel_a_1_0_normform,fraenkel_a_1_1_normform,fraenkel_a_2_0_normform,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,redefinition_k2_domain_1,redefinition_k3_domain_1,redefinition_m2_subset_1,reflexivity_r1_normform,reflexivity_r1_tarski,s23_fraenkel__e4_49__normform,symmetry_r1_xboole_0,t1_subset,t2_subset,t2_tarski,t3_subset,t4_normform,t4_subset,t5_normform,t5_subset,t61_normform,t6_boole,t7_boole,t8_boole]),
    [file(normform,t65_normform)]).

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

fof(cc1_finsub_1,axiom,(
    ! [A] : 
      ( v4_finsub_1(A)
     => ( v1_finsub_1(A)
        & v3_finsub_1(A) ) ) ),
    file(finsub_1,cc1_finsub_1),
    []).

fof(cc1_relset_1,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    []).

fof(cc2_finsub_1,axiom,(
    ! [A] : 
      ( ( v1_finsub_1(A)
        & v3_finsub_1(A) )
     => v4_finsub_1(A) ) ),
    file(finsub_1,cc2_finsub_1),
    []).

fof(cc3_finsub_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(A))
     => v1_finset_1(B) ) ),
    file(finsub_1,cc3_finsub_1),
    []).

fof(d10_normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => k9_normform(A,B) = a_2_0_normform(A,B) ) ),
    file(normform,d10_normform),
    []).

fof(d8_normform,axiom,(
    ! [A] : k7_normform(A) = a_1_0_normform(A) ),
    file(normform,d8_normform),
    []).

fof(d9_normform,axiom,(
    ! [A] : k8_normform(A) = a_1_1_normform(A) ),
    file(normform,d9_normform),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_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_k2_domain_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k2_domain_1(A,B,C),A) ) ),
    file(domain_1,k2_domain_1),
    []).

fof(dt_k2_mcart_1,axiom,(
    $true ),
    file(mcart_1,k2_mcart_1),
    []).

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

fof(dt_k3_domain_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => m1_subset_1(k3_domain_1(A,B,C),B) ) ),
    file(domain_1,k3_domain_1),
    []).

fof(dt_k5_finsub_1,axiom,(
    ! [A] : v4_finsub_1(k5_finsub_1(A)) ),
    file(finsub_1,k5_finsub_1),
    []).

fof(dt_k7_normform,axiom,(
    ! [A] : m1_subset_1(k7_normform(A),k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))) ),
    file(normform,k7_normform),
    []).

fof(dt_k8_normform,axiom,(
    ! [A] : m1_subset_1(k8_normform(A),k1_zfmisc_1(k5_finsub_1(k7_normform(A)))) ),
    file(normform,k8_normform),
    []).

fof(dt_k9_normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => m2_subset_1(k9_normform(A,B),k5_finsub_1(k7_normform(A)),k8_normform(A)) ) ),
    file(normform,k9_normform),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_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_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_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_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_zfmisc_1(A))
      & v1_finsub_1(k1_zfmisc_1(A))
      & v3_finsub_1(k1_zfmisc_1(A))
      & v4_finsub_1(k1_zfmisc_1(A)) ) ),
    file(finsub_1,fc1_finsub_1),
    []).

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(fc2_finsub_1,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finsub_1(A))
      & v1_finsub_1(k5_finsub_1(A))
      & v3_finsub_1(k5_finsub_1(A))
      & v4_finsub_1(k5_finsub_1(A)) ) ),
    file(finsub_1,fc2_finsub_1),
    []).

fof(fc2_normform,axiom,(
    ! [A] : 
      ( v1_relat_1(k7_normform(A))
      & ~ v1_xboole_0(k7_normform(A)) ) ),
    file(normform,fc2_normform),
    []).

fof(fc3_normform,axiom,(
    ! [A] : ~ v1_xboole_0(k8_normform(A)) ),
    file(normform,fc3_normform),
    []).

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(fraenkel_a_1_0_normform,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,a_1_0_normform(B))
    <=> ? [C] : 
          ( m1_subset_1(C,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)))
          & A = C
          & r1_xboole_0(k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),C),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),C)) ) ) ),
    file(normform,a_1_0_normform),
    []).

fof(fraenkel_a_1_1_normform,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,a_1_1_normform(B))
    <=> ? [C] : 
          ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
          & A = C
          & ! [D] : 
              ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
             => ! [E] : 
                  ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
                 => ( ( r2_hidden(D,C)
                      & r2_hidden(E,C)
                      & r1_normform(k5_finsub_1(B),k5_finsub_1(B),D,E) )
                   => D = E ) ) ) ) ) ),
    file(normform,a_1_1_normform),
    []).

fof(fraenkel_a_2_0_normform,axiom,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
     => ( r2_hidden(A,a_2_0_normform(B,C))
      <=> ? [D] : 
            ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
            & A = D
            & ! [E] : 
                ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
               => ( ( r2_hidden(E,C)
                    & r1_normform(k5_finsub_1(B),k5_finsub_1(B),E,D) )
                <=> E = D ) ) ) ) ) ),
    file(normform,a_2_0_normform),
    []).

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_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(redefinition_k2_domain_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => k2_domain_1(A,B,C) = k1_mcart_1(C) ) ),
    file(domain_1,k2_domain_1),
    []).

fof(redefinition_k3_domain_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B)) )
     => k3_domain_1(A,B,C) = k2_mcart_1(C) ) ),
    file(domain_1,k3_domain_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_normform,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & ~ v1_xboole_0(B)
        & v4_finsub_1(B)
        & m1_subset_1(C,k2_zfmisc_1(A,B))
        & m1_subset_1(D,k2_zfmisc_1(A,B)) )
     => r1_normform(A,B,C,C) ) ),
    file(normform,r1_normform),
    []).

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

fof(s23_fraenkel__e4_49__normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ( ( ! [C] : 
              ( m1_subset_1(C,k7_normform(A))
             => r1_normform(k5_finsub_1(A),k5_finsub_1(A),C,C) )
          & ! [C] : 
              ( m1_subset_1(C,k7_normform(A))
             => ! [D] : 
                  ( m1_subset_1(D,k7_normform(A))
                 => ! [E] : 
                      ( m1_subset_1(E,k7_normform(A))
                     => ( ( r1_normform(k5_finsub_1(A),k5_finsub_1(A),C,D)
                          & r1_normform(k5_finsub_1(A),k5_finsub_1(A),D,E) )
                       => r1_normform(k5_finsub_1(A),k5_finsub_1(A),C,E) ) ) ) ) )
       => ! [C] : 
            ( m1_subset_1(C,k7_normform(A))
           => ~ ( r2_hidden(C,B)
                & ! [D] : 
                    ( m1_subset_1(D,k7_normform(A))
                   => ~ ( r2_hidden(D,B)
                        & r1_normform(k5_finsub_1(A),k5_finsub_1(A),D,C)
                        & ! [E] : 
                            ( m1_subset_1(E,k7_normform(A))
                           => ( ( r2_hidden(E,B)
                                & r1_normform(k5_finsub_1(A),k5_finsub_1(A),E,D) )
                             => r1_normform(k5_finsub_1(A),k5_finsub_1(A),D,E) ) ) ) ) ) ) ) ) ),
    file(normform,s23_fraenkel__e4_49__normform),
    []).

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

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

fof(t4_normform,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ( ( r1_normform(A,B,C,D)
                      & r1_normform(A,B,D,C) )
                   => C = D ) ) ) ) ) ),
    file(normform,t4_normform),
    []).

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_normform,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v4_finsub_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,k2_zfmisc_1(A,B))
             => ! [D] : 
                  ( m1_subset_1(D,k2_zfmisc_1(A,B))
                 => ! [E] : 
                      ( m1_subset_1(E,k2_zfmisc_1(A,B))
                     => ( ( r1_normform(A,B,C,D)
                          & r1_normform(A,B,D,E) )
                       => r1_normform(A,B,C,E) ) ) ) ) ) ) ),
    file(normform,t5_normform),
    []).

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(t61_normform,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] : 
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ( ( r2_hidden(B,C)
              & ! [D] : 
                  ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                 => ( ( r2_hidden(D,C)
                      & r1_normform(k5_finsub_1(A),k5_finsub_1(A),D,B) )
                   => D = B ) ) )
           => r2_hidden(B,k9_normform(A,C)) ) ) ) ),
    file(normform,t61_normform),
    []).

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),
    []).