% Mizar problem: t9_functor2,functor2,388,32 
fof(t9_functor2,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,A,B)
                & m2_functor0(C,A,B) )
             => r2_functor2(A,B,C,C) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_functor2,cc2_functor0,cc2_functor2,cc3_functor0,cc3_functor2,cc5_functor0,d1_binop_1,d2_altcat_1,d6_functor2,dt_k1_altcat_1,dt_k1_binop_1,dt_k1_funct_1,dt_k1_functor2,dt_k1_xboole_0,dt_k2_functor2,dt_k2_zfmisc_1,dt_k3_functor0,dt_k4_tarski,dt_k5_altcat_1,dt_k6_functor0,dt_l1_altcat_1,dt_l1_functor0,dt_l1_struct_0,dt_l2_altcat_1,dt_l2_functor0,dt_m1_functor2,dt_m1_pboole,dt_m1_subset_1,dt_m2_functor0,dt_u1_altcat_1,dt_u1_struct_0,existence_l1_altcat_1,existence_l1_functor0,existence_l1_struct_0,existence_l2_altcat_1,existence_l2_functor0,existence_m1_functor2,existence_m1_pboole,existence_m1_subset_1,existence_m2_functor0,fc1_struct_0,fc1_xboole_0,fc4_subset_1,l15_functor2,rc11_functor0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc4_functor0,rc7_functor0,rc8_functor0,reflexivity_r1_functor2,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole]),
    [file(functor2,t9_functor2)]).

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

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(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_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(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(d6_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) )
                 => ( r2_functor2(A,B,C,D)
                  <=> ( 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,u1_struct_0(A))
                                 => ( k1_altcat_1(A,F,G) != k1_xboole_0
                                   => ! [H] : 
                                        ( m1_subset_1(H,k1_altcat_1(A,F,G))
                                       => k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,G),k3_functor0(A,B,D,G),k6_functor0(A,B,C,F,G,H),k2_functor2(A,B,C,D,E,G)) = k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F),k3_functor0(A,B,D,G),k2_functor2(A,B,C,D,E,F),k6_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) ) ) ),
    file(functor2,d6_functor2),
    []).

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_functor2,axiom,(
    ! [A,B,C] : 
      ( ( ~ 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) )
     => m1_functor2(k1_functor2(A,B,C),A,B,C,C) ) ),
    file(functor2,k1_functor2),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

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_k5_altcat_1,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(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,u1_struct_0(A))
        & m1_subset_1(E,k1_altcat_1(A,B,C))
        & m1_subset_1(F,k1_altcat_1(A,C,D)) )
     => m1_subset_1(k5_altcat_1(A,B,C,D,E,F),k1_altcat_1(A,B,D)) ) ),
    file(altcat_1,k5_altcat_1),
    []).

fof(dt_k6_functor0,axiom,(
    ! [A,B,C,D,E,F] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & v10_functor0(C,A,B)
        & l2_functor0(C,A,B)
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(A))
        & m1_subset_1(F,k1_altcat_1(A,D,E)) )
     => m1_subset_1(k6_functor0(A,B,C,D,E,F),k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E))) ) ),
    file(functor0,k6_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_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_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_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_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(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_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_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(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_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_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(l15_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) )
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( k1_altcat_1(A,E,F) != k1_xboole_0
                           => ! [G] : 
                                ( m1_subset_1(G,k1_altcat_1(A,E,F))
                               => k5_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),k3_functor0(A,B,C,F),k6_functor0(A,B,C,E,F,G),k2_functor2(A,B,C,C,k1_functor2(A,B,C),F)) = k5_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),k2_functor2(A,B,C,C,k1_functor2(A,B,C),E),k6_functor0(A,B,C,E,F,G)) ) ) ) ) ) ) ) ) ),
    file(functor2,l15_functor2),
    []).

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_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

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(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(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(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(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),
    []).