% Mizar problem: t21_functor3,functor3,993,40 
fof(t21_functor3,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] : 
              ( ( v15_functor0(C,B,A)
                & m2_functor0(C,B,A) )
             => ! [D] : 
                  ( ( v15_functor0(D,B,A)
                    & m2_functor0(D,B,A) )
                 => ! [E] : 
                      ( m1_functor2(E,B,A,C,D)
                     => ( r1_functor2(B,A,C,D)
                       => r6_pboole(u1_struct_0(B),k6_functor3(B,B,A,C,D,k12_functor0(B),E),E) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v9_functor0,antisymmetry_r2_hidden,cc1_funct_1,cc1_funct_2,cc1_functor0,cc1_functor2,cc1_relset_1,cc2_funct_1,cc2_functor0,cc2_functor2,cc3_functor0,cc3_functor2,cc5_funct_2,cc5_functor0,cc6_funct_2,d1_binop_1,d2_functor3,d4_functor2,d6_functor0,dt_g2_functor0,dt_k11_functor0,dt_k12_functor0,dt_k13_functor0,dt_k1_altcat_1,dt_k1_binop_1,dt_k1_funct_1,dt_k1_functor3,dt_k1_mcart_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_binop_1,dt_k2_functor2,dt_k2_zfmisc_1,dt_k3_functor0,dt_k4_tarski,dt_k6_functor3,dt_l1_altcat_1,dt_l1_functor0,dt_l1_struct_0,dt_l2_altcat_1,dt_l2_functor0,dt_m1_functor0,dt_m1_functor2,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_functor0,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_altcat_1,existence_l2_functor0,existence_m1_functor0,existence_m1_functor2,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_functor0,existence_m2_relset_1,fc13_functor0,fc14_functor0,fc15_functor0,fc16_functor0,fc1_altcat_4,fc1_functor3,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc20_functor0,fc21_functor0,fc4_subset_1,fc7_funcop_1,fc7_functor0,free_g2_functor0,rc11_functor0,rc1_funcop_1,rc1_funct_1,rc1_funct_2,rc1_subset_1,rc1_xboole_0,rc2_funct_1,rc2_subset_1,rc2_xboole_0,rc3_funct_1,rc3_functor0,rc3_struct_0,rc4_functor0,rc4_pboole,rc5_struct_0,rc7_functor0,rc8_functor0,rc9_functor0,redefinition_k12_functor0,redefinition_k1_functor3,redefinition_k2_binop_1,redefinition_m2_relset_1,redefinition_r6_pboole,reflexivity_r1_functor2,reflexivity_r1_tarski,reflexivity_r6_pboole,symmetry_r6_pboole,t1_subset,t2_subset,t30_functor0,t3_pboole,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(functor3,t21_functor3)]).

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_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_functor2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ! [C] : 
          ( m2_functor0(C,A,B)
         => ( v8_functor0(C,A,B)
            & v12_functor0(C,A,B) ) ) ) ),
    file(functor2,cc1_functor2),
    []).

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_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(cc2_functor2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ! [C] : 
          ( m2_functor0(C,A,B)
         => ( v15_functor0(C,A,B)
           => ( v6_functor0(C,A,B)
              & v8_functor0(C,A,B)
              & v10_functor0(C,A,B)
              & v12_functor0(C,A,B)
              & v13_functor0(C,A,B) ) ) ) ) ),
    file(functor2,cc2_functor2),
    []).

fof(cc3_functor0,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B) )
     => ! [C] : 
          ( l1_functor0(C,A,B)
         => ( v10_functor0(C,A,B)
           => v6_functor0(C,A,B) ) ) ) ),
    file(functor0,cc3_functor0),
    []).

fof(cc3_functor2,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ! [C] : 
          ( m2_functor0(C,A,B)
         => ( ( v10_functor0(C,A,B)
              & v13_functor0(C,A,B) )
           => ( v6_functor0(C,A,B)
              & v8_functor0(C,A,B)
              & v12_functor0(C,A,B)
              & v15_functor0(C,A,B) ) ) ) ) ),
    file(functor2,cc3_functor2),
    []).

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(cc5_functor0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ! [C] : 
          ( m2_functor0(C,A,B)
         => ( v15_functor0(C,A,B)
           => v6_functor0(C,A,B) ) ) ) ),
    file(functor0,cc5_functor0),
    []).

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(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_functor3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ! [D] : 
                  ( ( v15_functor0(D,B,C)
                    & m2_functor0(D,B,C) )
                 => ! [E] : 
                      ( ( v15_functor0(E,B,C)
                        & m2_functor0(E,B,C) )
                     => ! [F] : 
                          ( ( v15_functor0(F,A,B)
                            & m2_functor0(F,A,B) )
                         => ! [G] : 
                              ( m1_functor2(G,B,C,D,E)
                             => ( r1_functor2(B,C,D,E)
                               => ! [H] : 
                                    ( m1_functor2(H,A,C,k1_functor3(A,B,C,F,D),k1_functor3(A,B,C,F,E))
                                   => ( H = k6_functor3(A,B,C,D,E,F,G)
                                    <=> ! [I] : 
                                          ( m1_subset_1(I,u1_struct_0(A))
                                         => k1_funct_1(H,I) = k2_functor2(B,C,D,E,G,k3_functor0(A,B,F,I)) ) ) ) ) ) ) ) ) ) ) ) ),
    file(functor3,d2_functor3),
    []).

fof(d4_functor2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] : 
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ! [D] : 
                  ( ( v15_functor0(D,A,B)
                    & m2_functor0(D,A,B) )
                 => ( r1_functor2(A,B,C,D)
                   => ! [E] : 
                        ( m1_functor2(E,A,B,C,D)
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,k1_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F)))
                               => ( G = k2_functor2(A,B,C,D,E,F)
                                <=> G = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ) ),
    file(functor2,d4_functor2),
    []).

fof(d6_functor0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] : 
              ( l1_functor0(C,A,B)
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k3_functor0(A,B,C,D) = k1_mcart_1(k2_binop_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),D,D)) ) ) ) ) ),
    file(functor0,d6_functor0),
    []).

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_k11_functor0,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ( v9_functor0(k11_functor0(A),A,A)
        & l2_functor0(k11_functor0(A),A,A) ) ) ),
    file(functor0,k11_functor0),
    []).

fof(dt_k12_functor0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v9_functor0(k12_functor0(A),A,A)
        & v15_functor0(k12_functor0(A),A,A)
        & m2_functor0(k12_functor0(A),A,A) ) ) ),
    file(functor0,k12_functor0),
    []).

fof(dt_k13_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & v1_altcat_2(B)
        & l1_altcat_1(B)
        & ~ v3_struct_0(C)
        & v1_altcat_2(C)
        & l1_altcat_1(C)
        & v8_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & l2_functor0(E,B,C) )
     => ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
        & l2_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ),
    file(functor0,k13_functor0),
    []).

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_functor3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v15_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => ( v9_functor0(k1_functor3(A,B,C,D,E),A,C)
        & v15_functor0(k1_functor3(A,B,C,D,E),A,C)
        & m2_functor0(k1_functor3(A,B,C,D,E),A,C) ) ) ),
    file(functor3,k1_functor3),
    []).

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_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ),
    file(binop_1,k2_binop_1),
    []).

fof(dt_k2_functor2,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & m1_functor2(E,A,B,C,D)
        & m1_subset_1(F,u1_struct_0(A)) )
     => m1_subset_1(k2_functor2(A,B,C,D,E,F),k1_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F))) ) ),
    file(functor2,k2_functor2),
    []).

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

fof(dt_k3_functor0,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & l1_functor0(C,A,B)
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k3_functor0(A,B,C,D),u1_struct_0(B)) ) ),
    file(functor0,k3_functor0),
    []).

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

fof(dt_k6_functor3,axiom,(
    ! [A,B,C,D,E,F,G] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v2_altcat_1(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,B,C)
        & m2_functor0(D,B,C)
        & v15_functor0(E,B,C)
        & m2_functor0(E,B,C)
        & v15_functor0(F,A,B)
        & m2_functor0(F,A,B)
        & m1_functor2(G,B,C,D,E) )
     => m1_functor2(k6_functor3(A,B,C,D,E,F,G),A,C,k1_functor3(A,B,C,F,D),k1_functor3(A,B,C,F,E)) ) ),
    file(functor3,k6_functor3),
    []).

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_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => l1_altcat_1(A) ) ),
    file(altcat_1,l2_altcat_1),
    []).

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_functor2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => ! [E] : 
          ( m1_functor2(E,A,B,C,D)
         => m1_pboole(E,u1_struct_0(A)) ) ) ),
    file(functor2,m1_functor2),
    []).

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_functor0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ! [C] : 
          ( m2_functor0(C,A,B)
         => l2_functor0(C,A,B) ) ) ),
    file(functor0,m2_functor0),
    []).

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_altcat_1,axiom,(
    ? [A] : l2_altcat_1(A) ),
    file(altcat_1,l2_altcat_1),
    []).

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_functor2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => ? [E] : m1_functor2(E,A,B,C,D) ) ),
    file(functor2,m1_functor2),
    []).

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_functor0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ? [C] : m2_functor0(C,A,B) ) ),
    file(functor0,m2_functor0),
    []).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc13_functor0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ( v8_functor0(k11_functor0(A),A,A)
        & v9_functor0(k11_functor0(A),A,A)
        & v10_functor0(k11_functor0(A),A,A) ) ) ),
    file(functor0,fc13_functor0),
    []).

fof(fc14_functor0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ( v8_functor0(k11_functor0(A),A,A)
        & v9_functor0(k11_functor0(A),A,A)
        & v10_functor0(k11_functor0(A),A,A)
        & v12_functor0(k11_functor0(A),A,A)
        & v13_functor0(k11_functor0(A),A,A) ) ) ),
    file(functor0,fc14_functor0),
    []).

fof(fc15_functor0,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ( v9_functor0(k11_functor0(A),A,A)
        & v21_functor0(k11_functor0(A),A,A) ) ) ),
    file(functor0,fc15_functor0),
    []).

fof(fc16_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & v1_altcat_2(B)
        & l1_altcat_1(B)
        & ~ v3_struct_0(C)
        & v1_altcat_2(C)
        & l1_altcat_1(C)
        & v8_functor0(D,A,B)
        & v10_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & v10_functor0(E,B,C)
        & l2_functor0(E,B,C) )
     => ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v10_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ),
    file(functor0,fc16_functor0),
    []).

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_functor3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v8_functor0(D,A,B)
        & v10_functor0(D,A,B)
        & v13_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & v8_functor0(E,B,C)
        & v10_functor0(E,B,C)
        & v13_functor0(E,B,C)
        & l2_functor0(E,B,C) )
     => ( v6_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v8_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v9_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v10_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v13_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ),
    file(functor3,fc1_functor3),
    []).

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(fc20_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & v1_altcat_2(B)
        & l1_altcat_1(B)
        & ~ v3_struct_0(C)
        & v1_altcat_2(C)
        & l1_altcat_1(C)
        & v8_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & v8_functor0(E,B,C)
        & l2_functor0(E,B,C) )
     => ( v8_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v9_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ),
    file(functor0,fc20_functor0),
    []).

fof(fc21_functor0,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v6_functor0(D,A,B)
        & v8_functor0(D,A,B)
        & v12_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & v12_functor0(E,B,C)
        & l2_functor0(E,B,C) )
     => ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v12_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ),
    file(functor0,fc21_functor0),
    []).

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(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(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(rc11_functor0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ? [B] : 
          ( l2_functor0(B,A,A)
          & v8_functor0(B,A,A)
          & v10_functor0(B,A,A) ) ) ),
    file(functor0,rc11_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_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_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_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(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_functor0,axiom,(
    ! [A,B] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B) )
     => ? [C] : 
          ( l2_functor0(C,A,B)
          & v10_functor0(C,A,B) ) ) ),
    file(functor0,rc4_functor0),
    []).

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

fof(rc8_functor0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & v1_altcat_2(B)
        & l1_altcat_1(B) )
     => ? [C] : 
          ( l2_functor0(C,A,B)
          & v6_functor0(C,A,B)
          & v8_functor0(C,A,B) ) ) ),
    file(functor0,rc8_functor0),
    []).

fof(rc9_functor0,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ? [C] : 
          ( l2_functor0(C,A,B)
          & v6_functor0(C,A,B)
          & v8_functor0(C,A,B)
          & v9_functor0(C,A,B)
          & v12_functor0(C,A,B) ) ) ),
    file(functor0,rc9_functor0),
    []).

fof(redefinition_k12_functor0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => k12_functor0(A) = k11_functor0(A) ) ),
    file(functor0,k12_functor0),
    []).

fof(redefinition_k1_functor3,axiom,(
    ! [A,B,C,D,E] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & v12_altcat_1(C)
        & l2_altcat_1(C)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v15_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => k1_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) ),
    file(functor3,k1_functor3),
    []).

fof(redefinition_k2_binop_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B) )
     => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ),
    file(binop_1,k2_binop_1),
    []).

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(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

fof(reflexivity_r1_functor2,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & v15_functor0(C,A,B)
        & m2_functor0(C,A,B)
        & v15_functor0(D,A,B)
        & m2_functor0(D,A,B) )
     => r1_functor2(A,B,C,C) ) ),
    file(functor2,r1_functor2),
    []).

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

fof(reflexivity_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

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(t30_functor0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_functor0(A,A,k11_functor0(A),B) = B ) ) ),
    file(functor0,t30_functor0),
    []).

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(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),
    []).