% Mizar problem: t76_normform,normform,932,18 
fof(t76_normform,conjecture,(
    ! [A,B] : 
      ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A))
     => ! [C] : 
          ( m2_subset_1(C,k5_finsub_1(k7_normform(A)),k8_normform(A))
         => ! [D] : 
              ( m2_subset_1(D,k5_finsub_1(k7_normform(A)),k8_normform(A))
             => k10_normform(A,B,k10_normform(A,C,D)) = k10_normform(A,k10_normform(A,B,C),D) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_finsub_1,cc1_relset_1,cc2_finsub_1,cc3_finsub_1,commutativity_k1_finsub_1,commutativity_k1_normform,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,d10_xboole_0,d11_normform,d2_normform,d5_tarski,d8_normform,d9_normform,dt_k10_normform,dt_k1_domain_1,dt_k1_finsub_1,dt_k1_mcart_1,dt_k1_normform,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_domain_1,dt_k2_mcart_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_domain_1,dt_k3_xboole_0,dt_k4_tarski,dt_k5_finsub_1,dt_k7_normform,dt_k8_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,fc2_subset_1,fc2_xboole_0,fc3_normform,fc3_subset_1,fc3_xboole_0,fc4_subset_1,fraenkel_a_1_0_normform,fraenkel_a_1_1_normform,fraenkel_a_3_0_normform,idempotence_k1_finsub_1,idempotence_k1_normform,idempotence_k2_xboole_0,idempotence_k3_xboole_0,l77_normform,rc1_subset_1,rc1_xboole_0,rc2_subset_1,rc2_xboole_0,redefinition_k1_domain_1,redefinition_k1_finsub_1,redefinition_k2_domain_1,redefinition_k3_domain_1,redefinition_m2_subset_1,reflexivity_r1_normform,reflexivity_r1_tarski,symmetry_r1_xboole_0,t16_normform,t1_boole,t1_subset,t26_normform,t2_boole,t2_subset,t2_tarski,t3_subset,t45_normform,t4_subset,t55_normform,t56_normform,t5_subset,t6_boole,t72_normform,t7_boole,t8_boole]),
    [file(normform,t76_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(commutativity_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,C) = k1_finsub_1(A,C,B) ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(commutativity_k1_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)) )
     => k1_normform(A,B,C,D) = k1_normform(A,B,D,C) ) ),
    file(normform,k1_normform),
    []).

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(d10_xboole_0,axiom,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    []).

fof(d11_normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] : 
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => k10_normform(A,B,C) = k3_xboole_0(k7_normform(A),a_3_0_normform(A,B,C)) ) ) ),
    file(normform,d11_normform),
    []).

fof(d2_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))
                 => k1_normform(A,B,C,D) = k1_domain_1(A,B,k1_finsub_1(A,k2_domain_1(A,B,C),k2_domain_1(A,B,D)),k1_finsub_1(B,k3_domain_1(A,B,C),k3_domain_1(A,B,D))) ) ) ) ) ),
    file(normform,d2_normform),
    []).

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

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_k10_normform,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
        & m1_subset_1(C,k5_finsub_1(k7_normform(A))) )
     => m1_subset_1(k10_normform(A,B,C),k5_finsub_1(k7_normform(A))) ) ),
    file(normform,k10_normform),
    []).

fof(dt_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(dt_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => m1_subset_1(k1_finsub_1(A,B,C),A) ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(dt_k1_mcart_1,axiom,(
    $true ),
    file(mcart_1,k1_mcart_1),
    []).

fof(dt_k1_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)) )
     => m1_subset_1(k1_normform(A,B,C,D),k2_zfmisc_1(A,B)) ) ),
    file(normform,k1_normform),
    []).

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_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_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_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_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

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

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

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(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_3_0_normform,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(C,k5_finsub_1(k7_normform(B)))
        & m1_subset_1(D,k5_finsub_1(k7_normform(B))) )
     => ( r2_hidden(A,a_3_0_normform(B,C,D))
      <=> ? [E,F] : 
            ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
            & m2_subset_1(F,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B))
            & A = k1_normform(k5_finsub_1(B),k5_finsub_1(B),E,F)
            & r2_hidden(E,C)
            & r2_hidden(F,D) ) ) ) ),
    file(normform,a_3_0_normform),
    []).

fof(idempotence_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,B) = B ) ),
    file(finsub_1,k1_finsub_1),
    []).

fof(idempotence_k1_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)) )
     => k1_normform(A,B,C,C) = C ) ),
    file(normform,k1_normform),
    []).

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(l77_normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] : 
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ( ! [D] : 
                ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
               => ( r2_hidden(D,B)
                 => r2_hidden(D,C) ) )
           => r1_tarski(B,C) ) ) ) ),
    file(normform,l77_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_k1_domain_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(C,A)
        & m1_subset_1(D,B) )
     => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ),
    file(domain_1,k1_domain_1),
    []).

fof(redefinition_k1_finsub_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v4_finsub_1(A)
        & m1_subset_1(B,A)
        & m1_subset_1(C,A) )
     => k1_finsub_1(A,B,C) = k2_xboole_0(B,C) ) ),
    file(finsub_1,k1_finsub_1),
    []).

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

fof(t16_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))
                     => k1_normform(A,B,k1_normform(A,B,C,D),E) = k1_normform(A,B,C,k1_normform(A,B,D,E)) ) ) ) ) ) ),
    file(normform,t16_normform),
    []).

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(t26_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,k1_normform(A,B,C,D))
                    & r1_normform(A,B,D,k1_normform(A,B,C,D)) ) ) ) ) ) ),
    file(normform,t26_normform),
    []).

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

fof(t45_normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
     => ! [C] : 
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ( r1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C)
           => m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) ) ) ) ),
    file(normform,t45_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(t55_normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))
     => ! [C] : 
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => ! [D] : 
              ( m1_subset_1(D,k5_finsub_1(k7_normform(A)))
             => ~ ( r2_hidden(B,k10_normform(A,C,D))
                  & ! [E] : 
                      ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                     => ! [F] : 
                          ( m2_subset_1(F,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
                         => ~ ( r2_hidden(E,C)
                              & r2_hidden(F,D)
                              & B = k1_normform(k5_finsub_1(A),k5_finsub_1(A),E,F) ) ) ) ) ) ) ) ),
    file(normform,t55_normform),
    []).

fof(t56_normform,axiom,(
    ! [A,B] : 
      ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
     => ! [C] : 
          ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A))
         => ! [D] : 
              ( m1_subset_1(D,k5_finsub_1(k7_normform(A)))
             => ! [E] : 
                  ( m1_subset_1(E,k5_finsub_1(k7_normform(A)))
                 => ( ( r2_hidden(B,D)
                      & r2_hidden(C,E)
                      & r2_hidden(k1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C),k7_normform(A)) )
                   => r2_hidden(k1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C),k10_normform(A,D,E)) ) ) ) ) ) ),
    file(normform,t56_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(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t72_normform,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k5_finsub_1(k7_normform(A)))
     => ! [C] : 
          ( m1_subset_1(C,k5_finsub_1(k7_normform(A)))
         => k10_normform(A,B,C) = k10_normform(A,C,B) ) ) ),
    file(normform,t72_normform),
    []).

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),
    []).