% Mizar problem: t25_functor0,functor0,1267,24 
fof(t25_functor0,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ( k1_altcat_1(B,C,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,k1_altcat_1(B,C,C))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,k1_altcat_1(A,E,F))
                               => ( k1_altcat_1(A,E,F) != k1_xboole_0
                                 => k1_funct_1(k4_functor0(A,B,k9_functor0(A,B,C,D),E,F),G) = D ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v9_functor0,antisymmetry_r2_hidden,cc1_altcat_1,cc1_funct_1,cc1_funct_2,cc1_functor0,cc1_pboole,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_pboole,cc5_funct_2,cc6_funct_2,commutativity_k2_tarski,d10_xboole_0,d15_functor0,d18_functor0,d1_binop_1,d2_altcat_1,d3_tarski,d5_tarski,dt_g2_functor0,dt_k10_pboole,dt_k1_altcat_1,dt_k1_binop_1,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k4_functor0,dt_k4_tarski,dt_k9_functor0,dt_l1_altcat_1,dt_l1_functor0,dt_l1_struct_0,dt_l2_functor0,dt_m1_functor0,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_altcat_1,dt_u1_functor0,dt_u1_struct_0,dt_u2_functor0,existence_l1_altcat_1,existence_l1_functor0,existence_l1_struct_0,existence_l2_functor0,existence_m1_functor0,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc12_relat_1,fc1_funcop_1,fc1_struct_0,fc1_subset_1,fc2_altcat_1,fc2_funcop_1,fc2_pboole,fc2_subset_1,fc3_funcop_1,fc3_subset_1,fc4_relat_1,fc4_subset_1,fc5_functor0,fc7_funcop_1,fc7_functor0,fc9_funcop_1,fraenkel_a_4_0_functor0,fraenkel_a_4_3_functor0,free_g2_functor0,rc1_funcop_1,rc1_funct_1,rc1_funct_2,rc1_pboole,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc3_funct_1,rc3_functor0,rc3_pboole,rc3_relat_1,rc3_struct_0,rc4_funct_1,rc4_pboole,rc5_funct_1,rc5_struct_0,redefinition_k10_pboole,redefinition_m2_relset_1,reflexivity_r1_tarski,s1_functor0__e2_57_3__functor0,t13_funcop_1,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(functor0,t25_functor0)]).

fof(abstractness_v9_functor0,axiom,(
    ! [A,B,C] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B)
        & l2_functor0(C,A,B) )
     => ( v9_functor0(C,A,B)
       => C = g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) ) ) ),
    file(functor0,v9_functor0),
    []).

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_funct_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    []).

fof(cc1_funct_2,axiom,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
     => ( ( v1_funct_1(C)
          & v1_partfun1(C,A,B) )
       => ( v1_funct_1(C)
          & v1_funct_2(C,A,B) ) ) ) ),
    file(funct_2,cc1_funct_2),
    []).

fof(cc1_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,A)
        & m1_pboole(E,B) )
     => ! [F] : 
          ( m1_functor0(F,A,B,C,D,E)
         => v1_funcop_1(F) ) ) ),
    file(functor0,cc1_functor0),
    []).

fof(cc1_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v2_relat_1(B)
           => ~ v3_relat_1(B) ) ) ) ),
    file(pboole,cc1_pboole),
    []).

fof(cc1_relat_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_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_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_pboole,axiom,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_pboole(B,A)
         => ( v3_relat_1(B)
           => ~ v2_relat_1(B) ) ) ) ),
    file(pboole,cc2_pboole),
    []).

fof(cc5_funct_2,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc5_funct_2),
    []).

fof(cc6_funct_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ! [C] : 
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_partfun1(C,A,B)
              & v1_funct_2(C,A,B) ) ) ) ) ),
    file(funct_2,cc6_funct_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(d15_functor0,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ! [B] : 
          ( l1_altcat_1(B)
         => ! [C] : 
              ( l2_functor0(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k4_functor0(A,B,C,D,E) = k1_binop_1(u2_functor0(A,B,C),D,E) ) ) ) ) ) ),
    file(functor0,d15_functor0),
    []).

fof(d18_functor0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ( k1_altcat_1(B,C,C) != k1_xboole_0
               => ! [D] : 
                    ( m1_subset_1(D,k1_altcat_1(B,C,C))
                   => ! [E] : 
                        ( ( v9_functor0(E,A,B)
                          & l2_functor0(E,A,B) )
                       => ( E = k9_functor0(A,B,C,D)
                        <=> ( u1_functor0(A,B,E) = k10_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k4_tarski(C,C))
                            & u2_functor0(A,B,E) = a_4_0_functor0(A,B,C,D) ) ) ) ) ) ) ) ) ),
    file(functor0,d18_functor0),
    []).

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

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_functor0,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
        & m1_functor0(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),C,u1_altcat_1(A),u1_altcat_1(B)) )
     => ( v9_functor0(g2_functor0(A,B,C,D),A,B)
        & l2_functor0(g2_functor0(A,B,C,D),A,B) ) ) ),
    file(functor0,g2_functor0),
    []).

fof(dt_k10_pboole,axiom,(
    ! [A,B] : 
      ( v1_funct_1(k10_pboole(A,B))
      & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B))
      & m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) ) ),
    file(pboole,k10_pboole),
    []).

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

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_funcop_1,axiom,(
    $true ),
    file(funcop_1,k2_funcop_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_k4_functor0,axiom,(
    $true ),
    file(functor0,k4_functor0),
    []).

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

fof(dt_k9_functor0,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,k1_altcat_1(B,C,C)) )
     => ( v9_functor0(k9_functor0(A,B,C,D),A,B)
        & l2_functor0(k9_functor0(A,B,C,D),A,B) ) ) ),
    file(functor0,k9_functor0),
    []).

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

fof(dt_l1_functor0,axiom,(
    $true ),
    file(functor0,l1_functor0),
    []).

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

fof(dt_l2_functor0,axiom,(
    ! [A,B] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B) )
     => ! [C] : 
          ( l2_functor0(C,A,B)
         => l1_functor0(C,A,B) ) ) ),
    file(functor0,l2_functor0),
    []).

fof(dt_m1_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,A)
        & m1_pboole(E,B) )
     => ! [F] : 
          ( m1_functor0(F,A,B,C,D,E)
         => m1_pboole(F,A) ) ) ),
    file(functor0,m1_functor0),
    []).

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_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

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_functor0,axiom,(
    ! [A,B,C] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & l1_functor0(C,A,B) )
     => ( v1_funct_1(u1_functor0(A,B,C))
        & v1_funct_2(u1_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
        & m2_relset_1(u1_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) ) ) ),
    file(functor0,u1_functor0),
    []).

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

fof(dt_u2_functor0,axiom,(
    ! [A,B,C] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B)
        & l2_functor0(C,A,B) )
     => m1_functor0(u2_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),u1_altcat_1(A),u1_altcat_1(B)) ) ),
    file(functor0,u2_functor0),
    []).

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

fof(existence_l1_functor0,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & l1_struct_0(B) )
     => ? [C] : l1_functor0(C,A,B) ) ),
    file(functor0,l1_functor0),
    []).

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

fof(existence_l2_functor0,axiom,(
    ! [A,B] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B) )
     => ? [C] : l2_functor0(C,A,B) ) ),
    file(functor0,l2_functor0),
    []).

fof(existence_m1_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,A)
        & m1_pboole(E,B) )
     => ? [F] : m1_functor0(F,A,B,C,D,E) ) ),
    file(functor0,m1_functor0),
    []).

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

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k2_funcop_1(A,B))
      & v1_funct_1(k2_funcop_1(A,B)) ) ),
    file(funcop_1,fc1_funcop_1),
    []).

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(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_funcop_1,axiom,(
    ! [A] : 
      ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A))
      & v1_relat_1(k2_funcop_1(k1_xboole_0,A))
      & v1_funct_1(k2_funcop_1(k1_xboole_0,A))
      & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ),
    file(funcop_1,fc2_funcop_1),
    []).

fof(fc2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & v2_relat_1(B)
        & m1_pboole(B,A)
        & m1_subset_1(C,A) )
     => ~ v1_xboole_0(k1_funct_1(B,C)) ) ),
    file(pboole,fc2_pboole),
    []).

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

fof(fc3_funcop_1,axiom,(
    ! [A,B] : 
      ( v1_xboole_0(B)
     => ( v1_xboole_0(k2_funcop_1(B,A))
        & v1_relat_1(k2_funcop_1(B,A))
        & v1_funct_1(k2_funcop_1(B,A))
        & v2_funct_1(k2_funcop_1(B,A)) ) ) ),
    file(funcop_1,fc3_funcop_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(fc5_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B)
        & l2_functor0(C,A,B)
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(A)) )
     => ( v1_relat_1(k4_functor0(A,B,C,D,E))
        & v1_funct_1(k4_functor0(A,B,C,D,E)) ) ) ),
    file(functor0,fc5_functor0),
    []).

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(fc7_functor0,axiom,(
    ! [A,B,C] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B)
        & l2_functor0(C,A,B) )
     => ( v1_relat_1(u2_functor0(A,B,C))
        & v1_funct_1(u2_functor0(A,B,C))
        & v1_funcop_1(u2_functor0(A,B,C)) ) ) ),
    file(functor0,fc7_functor0),
    []).

fof(fc9_funcop_1,axiom,(
    ! [A,B] : 
      ( ~ v1_xboole_0(B)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v2_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B)) ) ) ),
    file(funcop_1,fc9_funcop_1),
    []).

fof(fraenkel_a_4_0_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & ~ v3_struct_0(C)
        & l1_altcat_1(C)
        & m1_subset_1(D,u1_struct_0(C))
        & m1_subset_1(E,k1_altcat_1(C,D,D)) )
     => ( r2_hidden(A,a_4_0_functor0(B,C,D,E))
      <=> ? [F,G] : 
            ( m1_subset_1(F,u1_struct_0(B))
            & m1_subset_1(G,u1_struct_0(B))
            & A = k4_tarski(k4_tarski(F,G),k10_pboole(k1_altcat_1(B,F,G),E)) ) ) ) ),
    file(functor0,a_4_0_functor0),
    []).

fof(fraenkel_a_4_3_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & ~ v3_struct_0(C)
        & l1_altcat_1(C)
        & m1_subset_1(D,u1_struct_0(C))
        & m1_subset_1(E,k1_altcat_1(C,D,D)) )
     => ( r2_hidden(A,a_4_3_functor0(B,C,D,E))
      <=> ? [F,G] : 
            ( m1_subset_1(F,u1_struct_0(B))
            & m1_subset_1(G,u1_struct_0(B))
            & A = k4_tarski(k4_tarski(F,G),k10_pboole(k1_binop_1(u1_altcat_1(B),F,G),E)) ) ) ) ),
    file(functor0,a_4_3_functor0),
    []).

fof(free_g2_functor0,axiom,(
    ! [A,B,C,D] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
        & m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
        & m1_functor0(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),C,u1_altcat_1(A),u1_altcat_1(B)) )
     => ! [E,F,G,H] : 
          ( g2_functor0(A,B,C,D) = g2_functor0(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) ),
    file(functor0,g2_functor0),
    []).

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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(rc1_funct_2,axiom,(
    ! [A,B] : 
    ? [C] : 
      ( m1_relset_1(C,A,B)
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,A,B) ) ),
    file(funct_2,rc1_funct_2),
    []).

fof(rc1_pboole,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(pboole,rc1_pboole),
    []).

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_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v3_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc2_pboole),
    []).

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_functor0,axiom,(
    ! [A,B] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B) )
     => ? [C] : 
          ( l2_functor0(C,A,B)
          & v9_functor0(C,A,B) ) ) ),
    file(functor0,rc3_functor0),
    []).

fof(rc3_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

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

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

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_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_funct_1),
    []).

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(redefinition_k10_pboole,axiom,(
    ! [A,B] : k10_pboole(A,B) = k2_funcop_1(A,B) ),
    file(pboole,k10_pboole),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

fof(s1_functor0__e2_57_3__functor0,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,k1_altcat_1(B,C,C))
        & m1_subset_1(E,u1_struct_0(A))
        & m1_subset_1(F,u1_struct_0(A)) )
     => ( u2_functor0(A,B,k9_functor0(A,B,C,D)) = a_4_3_functor0(A,B,C,D)
       => k1_binop_1(u2_functor0(A,B,k9_functor0(A,B,C,D)),E,F) = k10_pboole(k1_binop_1(u1_altcat_1(A),E,F),D) ) ) ),
    file(functor0,s1_functor0__e2_57_3__functor0),
    []).

fof(t13_funcop_1,axiom,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    []).

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_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_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),
    []).