% Mizar problem: t59_altcat_4,altcat_4,3644,32 
fof(t59_altcat_4,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => k5_altcat_4(k4_altcat_4(A)) = k5_altcat_4(A) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v6_altcat_1,antisymmetry_r2_hidden,cc1_altcat_1,cc1_altcat_2,cc1_relset_1,cc2_functor0,cc3_altcat_2,cc3_pboole,cc4_altcat_2,commutativity_k2_tarski,d10_xboole_0,d11_altcat_2,d1_binop_1,d2_altcat_1,d2_altcat_2,d3_tarski,d4_altcat_4,d5_altcat_4,d5_tarski,dt_g2_altcat_1,dt_k1_altcat_1,dt_k1_altcat_3,dt_k1_binop_1,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_altcat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_altcat_1,dt_k3_zfmisc_1,dt_k4_altcat_4,dt_k4_tarski,dt_k5_altcat_4,dt_l1_altcat_1,dt_l1_struct_0,dt_l2_altcat_1,dt_m1_altcat_2,dt_m1_pboole,dt_m1_subset_1,dt_m3_pboole,dt_u1_altcat_1,dt_u1_struct_0,dt_u2_altcat_1,existence_l1_altcat_1,existence_l1_struct_0,existence_l2_altcat_1,existence_m1_altcat_2,existence_m1_pboole,existence_m1_subset_1,existence_m3_pboole,fc1_altcat_4,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc2_altcat_1,fc2_subset_1,fc3_altcat_1,fc3_subset_1,fc4_subset_1,fc5_subset_1,fc7_altcat_4,fc7_funcop_1,fc8_altcat_4,free_g2_altcat_1,rc10_altcat_2,rc1_funcop_1,rc1_subset_1,rc1_xboole_0,rc2_altcat_1,rc2_altcat_2,rc2_subset_1,rc2_xboole_0,rc3_altcat_1,rc3_altcat_2,rc3_struct_0,rc4_altcat_2,rc4_pboole,rc5_altcat_2,rc5_struct_0,rc6_altcat_1,rc6_altcat_2,rc7_functor0,redefinition_r2_altcat_2,reflexivity_r1_altcat_2,reflexivity_r1_tarski,reflexivity_r2_altcat_2,t103_zfmisc_1,t1_subset,t1_xboole_1,t22_altcat_2,t25_altcat_2,t26_altcat_2,t2_subset,t32_altcat_2,t3_pboole,t3_subset,t3_xboole_1,t40_altcat_4,t42_altcat_4,t4_subset,t52_altcat_4,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(altcat_4,t59_altcat_4)]).

fof(abstractness_v6_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( v6_altcat_1(A)
       => A = g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) ) ) ),
    file(altcat_1,v6_altcat_1),
    []).

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

fof(cc1_altcat_1,axiom,(
    ! [A] : 
      ( v1_fraenkel(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_fraenkel(B) ) ) ),
    file(altcat_1,cc1_altcat_1),
    []).

fof(cc1_altcat_2,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v12_altcat_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_altcat_2(A) ) ) ) ),
    file(altcat_2,cc1_altcat_2),
    []).

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_functor0,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v12_altcat_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_altcat_2(A) ) ) ) ),
    file(functor0,cc2_functor0),
    []).

fof(cc3_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B) )
           => ( ~ v3_struct_0(B)
              & v11_altcat_1(B) ) ) ) ) ),
    file(altcat_2,cc3_altcat_2),
    []).

fof(cc3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => v1_funcop_1(D) ) ) ),
    file(pboole,cc3_pboole),
    []).

fof(cc4_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v3_altcat_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v12_altcat_1(B)
              & v1_altcat_2(B) ) ) ) ) ),
    file(altcat_2,cc4_altcat_2),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

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_altcat_2,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ! [B] : 
          ( l2_altcat_1(B)
         => ( m1_altcat_2(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
              & r2_altcat_2(k3_zfmisc_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(B)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),u2_altcat_1(B),u2_altcat_1(A)) ) ) ) ) ),
    file(altcat_2,d11_altcat_2),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d2_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_altcat_1(A,B,C) = k1_binop_1(u1_altcat_1(A),B,C) ) ) ) ),
    file(altcat_1,d2_altcat_1),
    []).

fof(d2_altcat_2,axiom,(
    ! [A,B,C] : 
      ( m1_pboole(C,A)
     => ! [D] : 
          ( m1_pboole(D,B)
         => ( r2_altcat_2(A,B,C,D)
          <=> ( r1_tarski(A,B)
              & ! [E] : 
                  ( r2_hidden(E,A)
                 => r1_tarski(k1_funct_1(C,E),k1_funct_1(D,E)) ) ) ) ) ) ),
    file(altcat_2,d2_altcat_2),
    []).

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

fof(d4_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ( B = k4_altcat_4(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,C,D))
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( k1_altcat_1(A,C,D) != k1_xboole_0
                              & k1_altcat_1(A,D,C) != k1_xboole_0
                              & v2_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) ),
    file(altcat_4,d4_altcat_4),
    []).

fof(d5_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v6_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ( B = k5_altcat_4(A)
          <=> ( u1_struct_0(B) = u1_struct_0(A)
              & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(B),u1_altcat_1(A))
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] : 
                          ( m1_subset_1(E,k1_altcat_1(A,C,D))
                         => ( r2_hidden(E,k1_binop_1(u1_altcat_1(B),C,D))
                          <=> ( k1_altcat_1(A,C,D) != k1_xboole_0
                              & k1_altcat_1(A,D,C) != k1_xboole_0
                              & v3_altcat_3(E,A,C,D) ) ) ) ) ) ) ) ) ) ),
    file(altcat_4,d5_altcat_4),
    []).

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

fof(dt_g2_altcat_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,k2_zfmisc_1(A,A))
        & m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B)) )
     => ( v6_altcat_1(g2_altcat_1(A,B,C))
        & l2_altcat_1(g2_altcat_1(A,B,C)) ) ) ),
    file(altcat_1,g2_altcat_1),
    []).

fof(dt_k1_altcat_1,axiom,(
    $true ),
    file(altcat_1,k1_altcat_1),
    []).

fof(dt_k1_altcat_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,k1_altcat_1(A,B,C)) )
     => m1_subset_1(k1_altcat_3(A,B,C,D),k1_altcat_1(A,C,B)) ) ),
    file(altcat_3,k1_altcat_3),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

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_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_altcat_1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,k2_zfmisc_1(A,A))
     => m1_pboole(k2_altcat_1(A,B),k3_zfmisc_1(A,A,A)) ) ),
    file(altcat_1,k2_altcat_1),
    []).

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k3_altcat_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,k2_zfmisc_1(A,A))
        & m1_pboole(C,k2_zfmisc_1(A,A)) )
     => m1_pboole(k3_altcat_1(A,B,C),k3_zfmisc_1(A,A,A)) ) ),
    file(altcat_1,k3_altcat_1),
    []).

fof(dt_k3_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

fof(dt_k4_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k4_altcat_4(A))
        & v2_altcat_1(k4_altcat_4(A))
        & v6_altcat_1(k4_altcat_4(A))
        & m1_altcat_2(k4_altcat_4(A),A) ) ) ),
    file(altcat_4,k4_altcat_4),
    []).

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

fof(dt_k5_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k5_altcat_4(A))
        & v2_altcat_1(k5_altcat_4(A))
        & v6_altcat_1(k5_altcat_4(A))
        & m1_altcat_2(k5_altcat_4(A),A) ) ) ),
    file(altcat_4,k5_altcat_4),
    []).

fof(dt_l1_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => l1_struct_0(A) ) ),
    file(altcat_1,l1_altcat_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => l1_altcat_1(A) ) ),
    file(altcat_1,l2_altcat_1),
    []).

fof(dt_m1_altcat_2,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => l2_altcat_1(B) ) ) ),
    file(altcat_2,m1_altcat_2),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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

fof(dt_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(pboole,m3_pboole),
    []).

fof(dt_u1_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => m1_pboole(u1_altcat_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ),
    file(altcat_1,u1_altcat_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(dt_u2_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => m3_pboole(u2_altcat_1(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_altcat_1(u1_struct_0(A),u1_altcat_1(A),u1_altcat_1(A)),k2_altcat_1(u1_struct_0(A),u1_altcat_1(A))) ) ),
    file(altcat_1,u2_altcat_1),
    []).

fof(existence_l1_altcat_1,axiom,(
    ? [A] : l1_altcat_1(A) ),
    file(altcat_1,l1_altcat_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_altcat_1,axiom,(
    ? [A] : l2_altcat_1(A) ),
    file(altcat_1,l2_altcat_1),
    []).

fof(existence_m1_altcat_2,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ? [B] : m1_altcat_2(B,A) ) ),
    file(altcat_2,m1_altcat_2),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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

fof(existence_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) ),
    file(pboole,m3_pboole),
    []).

fof(fc1_altcat_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k1_altcat_1(A,B,B)) ) ),
    file(altcat_4,fc1_altcat_4),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

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_altcat_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_finset_1(k1_tarski(A))
        & v1_fraenkel(k1_tarski(A))
        & v1_realset1(k1_tarski(A)) ) ) ),
    file(altcat_1,fc2_altcat_1),
    []).

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

fof(fc3_altcat_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_pboole(B,k2_zfmisc_1(A,A))
        & m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B)) )
     => ( ~ v3_struct_0(g2_altcat_1(A,B,C))
        & v6_altcat_1(g2_altcat_1(A,B,C)) ) ) ),
    file(altcat_1,fc3_altcat_1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_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(fc5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C) )
     => ~ v1_xboole_0(k3_zfmisc_1(A,B,C)) ) ),
    file(subset_1,fc5_subset_1),
    []).

fof(fc7_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k4_altcat_4(A))
        & v2_altcat_1(k4_altcat_4(A))
        & v6_altcat_1(k4_altcat_4(A))
        & v11_altcat_1(k4_altcat_4(A))
        & v12_altcat_1(k4_altcat_4(A))
        & v1_altcat_2(k4_altcat_4(A))
        & v3_altcat_2(k4_altcat_4(A),A) ) ) ),
    file(altcat_4,fc7_altcat_4),
    []).

fof(fc7_funcop_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k1_funct_1(A,B))
        & v1_funct_1(k1_funct_1(A,B)) ) ) ),
    file(funcop_1,fc7_funcop_1),
    []).

fof(fc8_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k5_altcat_4(A))
        & v2_altcat_1(k5_altcat_4(A))
        & v6_altcat_1(k5_altcat_4(A))
        & v11_altcat_1(k5_altcat_4(A))
        & v12_altcat_1(k5_altcat_4(A))
        & v1_altcat_2(k5_altcat_4(A))
        & v3_altcat_2(k5_altcat_4(A),A) ) ) ),
    file(altcat_4,fc8_altcat_4),
    []).

fof(free_g2_altcat_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,k2_zfmisc_1(A,A))
        & m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B)) )
     => ! [D,E,F] : 
          ( g2_altcat_1(A,B,C) = g2_altcat_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) ),
    file(altcat_1,g2_altcat_1),
    []).

fof(rc10_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ? [B] : 
          ( m1_altcat_2(B,A)
          & ~ v3_struct_0(B)
          & v2_altcat_1(B)
          & v11_altcat_1(B)
          & v12_altcat_1(B)
          & v1_altcat_2(B)
          & v3_altcat_2(B,A) ) ) ),
    file(altcat_2,rc10_altcat_2),
    []).

fof(rc1_funcop_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_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(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_altcat_1,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & v6_altcat_1(A) ) ),
    file(altcat_1,rc2_altcat_1),
    []).

fof(rc2_altcat_2,axiom,(
    ? [A] : 
      ( l1_altcat_1(A)
      & ~ v3_struct_0(A)
      & v1_altcat_2(A) ) ),
    file(altcat_2,rc2_altcat_2),
    []).

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_altcat_1,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v6_altcat_1(A) ) ),
    file(altcat_1,rc3_altcat_1),
    []).

fof(rc3_altcat_2,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v1_altcat_2(A) ) ),
    file(altcat_2,rc3_altcat_2),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_altcat_2,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & v3_struct_0(A)
      & v6_altcat_1(A) ) ),
    file(altcat_2,rc4_altcat_2),
    []).

fof(rc4_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B) ) ),
    file(pboole,rc4_pboole),
    []).

fof(rc5_altcat_2,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ? [B] : 
          ( m1_altcat_2(B,A)
          & v6_altcat_1(B) ) ) ),
    file(altcat_2,rc5_altcat_2),
    []).

fof(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(rc6_altcat_1,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v2_altcat_1(A)
      & v6_altcat_1(A)
      & v11_altcat_1(A)
      & v12_altcat_1(A) ) ),
    file(altcat_1,rc6_altcat_1),
    []).

fof(rc6_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ? [B] : 
          ( m1_altcat_2(B,A)
          & ~ v3_struct_0(B)
          & v2_altcat_1(B)
          & v6_altcat_1(B) ) ) ),
    file(altcat_2,rc6_altcat_2),
    []).

fof(rc7_functor0,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v1_altcat_2(A) ) ),
    file(functor0,rc7_functor0),
    []).

fof(redefinition_r2_altcat_2,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_pboole(C,A)
        & m1_pboole(D,B) )
     => ( r2_altcat_2(A,B,C,D)
      <=> r1_altcat_2(C,D) ) ) ),
    file(altcat_2,r2_altcat_2),
    []).

fof(reflexivity_r1_altcat_2,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => r1_altcat_2(A,A) ) ),
    file(altcat_2,r1_altcat_2),
    []).

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

fof(reflexivity_r2_altcat_2,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_pboole(C,A)
        & m1_pboole(D,B) )
     => r2_altcat_2(A,B,C,C) ) ),
    file(altcat_2,r2_altcat_2),
    []).

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

fof(t1_xboole_1,axiom,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    []).

fof(t22_altcat_2,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ! [B] : 
          ( l2_altcat_1(B)
         => ! [C] : 
              ( l2_altcat_1(C)
             => ( ( m1_altcat_2(A,B)
                  & m1_altcat_2(B,C) )
               => m1_altcat_2(A,C) ) ) ) ) ),
    file(altcat_2,t22_altcat_2),
    []).

fof(t25_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & m1_altcat_2(B,A) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & m1_altcat_2(C,A) )
             => ( ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
                  & r2_altcat_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_altcat_1(B),u1_altcat_1(C)) )
               => m1_altcat_2(B,C) ) ) ) ) ),
    file(altcat_2,t25_altcat_2),
    []).

fof(t26_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => ( ( u1_struct_0(B) = u1_struct_0(A)
              & u1_altcat_1(B) = u1_altcat_1(A) )
           => g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) = g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) ) ) ) ),
    file(altcat_2,t26_altcat_2),
    []).

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_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & m1_altcat_2(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( C = E
                              & D = F )
                           => r1_tarski(k1_altcat_1(B,E,F),k1_altcat_1(A,C,D)) ) ) ) ) ) ) ) ),
    file(altcat_2,t32_altcat_2),
    []).

fof(t3_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ! [D] : 
                ( r2_hidden(D,A)
               => k1_funct_1(B,D) = k1_funct_1(C,D) )
           => B = C ) ) ) ),
    file(pboole,t3_pboole),
    []).

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

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

fof(t40_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v3_altcat_2(B,A)
            & m1_altcat_2(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_altcat_1(A,C,D))
                             => ! [H] : 
                                  ( m1_subset_1(H,k1_altcat_1(B,E,F))
                                 => ( ( E = C
                                      & F = D
                                      & G = H )
                                   => ( k1_altcat_1(B,E,F) = k1_xboole_0
                                      | k1_altcat_1(B,F,E) = k1_xboole_0
                                      | ( ( v1_altcat_3(H,B,E,F)
                                         => v1_altcat_3(G,A,C,D) )
                                        & ( v2_altcat_3(H,B,E,F)
                                         => v2_altcat_3(G,A,C,D) )
                                        & ( v3_altcat_3(H,B,E,F)
                                         => v3_altcat_3(G,A,C,D) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(altcat_4,t40_altcat_4),
    []).

fof(t42_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( ~ v3_struct_0(k5_altcat_4(A))
        & v2_altcat_1(k5_altcat_4(A))
        & v3_altcat_2(k5_altcat_4(A),k4_altcat_4(A))
        & m1_altcat_2(k5_altcat_4(A),k4_altcat_4(A)) ) ) ),
    file(altcat_4,t42_altcat_4),
    []).

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(t52_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k5_altcat_4(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_altcat_4(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_altcat_1(k5_altcat_4(A),B,C))
                 => ( k1_altcat_1(k5_altcat_4(A),B,C) != k1_xboole_0
                   => ( v3_altcat_3(D,k5_altcat_4(A),B,C)
                      & r2_hidden(k1_altcat_3(k5_altcat_4(A),B,C,D),k1_altcat_1(k5_altcat_4(A),C,B)) ) ) ) ) ) ) ),
    file(altcat_4,t52_altcat_4),
    []).

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(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),
    []).