% Mizar problem: t18_yellow18,yellow18,2202,56 
fof(t18_yellow18,conjecture,(
    ! [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)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v2_altcat_1(C)
                & v11_altcat_1(C)
                & v12_altcat_1(C)
                & l2_altcat_1(C) )
             => ( r2_yellow18(A,B)
               => ( r1_functor0(A,C)
                <=> r2_functor0(B,C) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v9_functor0,antisymmetry_r2_hidden,cc1_altcat_2,cc1_funct_1,cc1_funct_2,cc1_functor0,cc1_functor2,cc1_pboole,cc1_relat_1,cc1_relset_1,cc2_funct_1,cc2_functor0,cc2_functor2,cc2_pboole,cc3_functor0,cc3_functor2,cc4_functor0,cc4_functor2,cc5_funct_2,cc5_functor0,cc5_functor2,cc6_funct_2,cc6_functor0,d40_functor0,d41_functor0,dt_g2_functor0,dt_k13_functor0,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_functor3,dt_k2_yellow18,dt_k2_zfmisc_1,dt_k3_functor3,dt_l1_altcat_1,dt_l1_functor0,dt_l1_struct_0,dt_l2_altcat_1,dt_l2_functor0,dt_m1_functor0,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_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_functor0,existence_m2_relset_1,fc12_relat_1,fc16_functor0,fc17_functor0,fc18_functor0,fc19_functor0,fc1_struct_0,fc1_subset_1,fc20_functor0,fc21_functor0,fc4_relat_1,fc4_subset_1,fc7_functor0,free_g2_functor0,rc10_functor0,rc11_functor0,rc1_funcop_1,rc1_funct_1,rc1_funct_2,rc1_pboole,rc1_relat_1,rc1_subset_1,rc2_altcat_2,rc2_funct_1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc3_altcat_2,rc3_funct_1,rc3_functor0,rc3_pboole,rc3_relat_1,rc3_struct_0,rc4_funct_1,rc4_functor0,rc4_pboole,rc5_funct_1,rc5_functor0,rc5_struct_0,rc6_functor0,rc7_functor0,rc8_functor0,rc9_functor0,redefinition_k2_functor3,redefinition_k3_functor3,redefinition_m2_relset_1,reflexivity_r1_functor0,reflexivity_r1_tarski,symmetry_r1_functor0,symmetry_r2_functor0,symmetry_r2_yellow18,t13_functor1,t16_yellow18,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t7_boole,t8_boole]),
    [file(yellow18,t18_yellow18)]).

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_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_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_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_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(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(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(cc4_functor0,axiom,(
    ! [A,B] : 
      ( ( l1_struct_0(A)
        & ~ v3_struct_0(B)
        & l1_struct_0(B) )
     => ! [C] : 
          ( l1_functor0(C,A,B)
         => ( v11_functor0(C,A,B)
           => v6_functor0(C,A,B) ) ) ) ),
    file(functor0,cc4_functor0),
    []).

fof(cc4_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)
         => ( v16_functor0(C,A,B)
           => ( v6_functor0(C,A,B)
              & v8_functor0(C,A,B)
              & v11_functor0(C,A,B)
              & v12_functor0(C,A,B)
              & v14_functor0(C,A,B) ) ) ) ) ),
    file(functor2,cc4_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(cc5_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)
         => ( ( v11_functor0(C,A,B)
              & v14_functor0(C,A,B) )
           => ( v6_functor0(C,A,B)
              & v8_functor0(C,A,B)
              & v12_functor0(C,A,B)
              & v16_functor0(C,A,B) ) ) ) ) ),
    file(functor2,cc5_functor2),
    []).

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(cc6_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)
         => ( v16_functor0(C,A,B)
           => v6_functor0(C,A,B) ) ) ) ),
    file(functor0,cc6_functor0),
    []).

fof(d40_functor0,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) )
         => ( r1_functor0(A,B)
          <=> ? [C] : 
                ( m2_functor0(C,A,B)
                & v21_functor0(C,A,B)
                & v15_functor0(C,A,B) ) ) ) ) ),
    file(functor0,d40_functor0),
    []).

fof(d41_functor0,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) )
         => ( r2_functor0(A,B)
          <=> ? [C] : 
                ( m2_functor0(C,A,B)
                & v21_functor0(C,A,B)
                & v16_functor0(C,A,B) ) ) ) ) ),
    file(functor0,d41_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_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_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_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)
        & v16_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v16_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => ( v9_functor0(k2_functor3(A,B,C,D,E),A,C)
        & v15_functor0(k2_functor3(A,B,C,D,E),A,C)
        & m2_functor0(k2_functor3(A,B,C,D,E),A,C) ) ) ),
    file(functor3,k2_functor3),
    []).

fof(dt_k2_yellow18,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v2_altcat_1(B)
        & v11_altcat_1(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B) )
     => ( v9_functor0(k2_yellow18(A,B),A,B)
        & v16_functor0(k2_yellow18(A,B),A,B)
        & m2_functor0(k2_yellow18(A,B),A,B) ) ) ),
    file(yellow18,k2_yellow18),
    []).

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

fof(dt_k3_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)
        & v16_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => ( v9_functor0(k3_functor3(A,B,C,D,E),A,C)
        & v16_functor0(k3_functor3(A,B,C,D,E),A,C)
        & m2_functor0(k3_functor3(A,B,C,D,E),A,C) ) ) ),
    file(functor3,k3_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_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_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(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(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(fc17_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)
        & v11_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)
        & v11_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ),
    file(functor0,fc17_functor0),
    []).

fof(fc18_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)
        & v11_functor0(E,B,C)
        & l2_functor0(E,B,C) )
     => ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
        & v11_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ),
    file(functor0,fc18_functor0),
    []).

fof(fc19_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)
        & v11_functor0(D,A,B)
        & l2_functor0(D,A,B)
        & v11_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,fc19_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_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    []).

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_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(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(rc10_functor0,axiom,(
    ! [A,B] : 
      ( ( ~ 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) )
     => ? [C] : 
          ( m2_functor0(C,A,B)
          & v8_functor0(C,A,B)
          & v9_functor0(C,A,B)
          & v15_functor0(C,A,B)
          & v16_functor0(C,A,B) ) ) ),
    file(functor0,rc10_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_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_altcat_2,axiom,(
    ? [A] : 
      ( l1_altcat_1(A)
      & ~ v3_struct_0(A)
      & v1_altcat_2(A) ) ),
    file(altcat_2,rc2_altcat_2),
    []).

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_altcat_2,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v1_altcat_2(A) ) ),
    file(altcat_2,rc3_altcat_2),
    []).

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

fof(rc5_functor0,axiom,(
    ! [A,B] : 
      ( ( l1_altcat_1(A)
        & l1_altcat_1(B) )
     => ? [C] : 
          ( l2_functor0(C,A,B)
          & v11_functor0(C,A,B) ) ) ),
    file(functor0,rc5_functor0),
    []).

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_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)
          & v8_functor0(C,A,B)
          & v10_functor0(C,A,B)
          & v11_functor0(C,A,B) ) ) ),
    file(functor0,rc6_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(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_k2_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)
        & v16_functor0(D,A,B)
        & m2_functor0(D,A,B)
        & v16_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => k2_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) ),
    file(functor3,k2_functor3),
    []).

fof(redefinition_k3_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)
        & v16_functor0(E,B,C)
        & m2_functor0(E,B,C) )
     => k3_functor3(A,B,C,D,E) = k13_functor0(A,B,C,D,E) ) ),
    file(functor3,k3_functor3),
    []).

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_functor0,axiom,(
    ! [A,B] : 
      ( ( ~ 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) )
     => r1_functor0(A,A) ) ),
    file(functor0,r1_functor0),
    []).

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

fof(symmetry_r1_functor0,axiom,(
    ! [A,B] : 
      ( ( ~ 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) )
     => ( r1_functor0(A,B)
       => r1_functor0(B,A) ) ) ),
    file(functor0,r1_functor0),
    []).

fof(symmetry_r2_functor0,axiom,(
    ! [A,B] : 
      ( ( ~ 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) )
     => ( r2_functor0(A,B)
       => r2_functor0(B,A) ) ) ),
    file(functor0,r2_functor0),
    []).

fof(symmetry_r2_yellow18,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & l2_altcat_1(B) )
     => ( r2_yellow18(A,B)
       => r2_yellow18(B,A) ) ) ),
    file(yellow18,r2_yellow18),
    []).

fof(t13_functor1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l1_altcat_1(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & v1_altcat_2(C)
                & l1_altcat_1(C) )
             => ! [D] : 
                  ( ( v8_functor0(D,A,B)
                    & l2_functor0(D,A,B) )
                 => ! [E] : 
                      ( l2_functor0(E,B,C)
                     => ( ( v21_functor0(D,A,B)
                          & v21_functor0(E,B,C) )
                       => v21_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ) ) ) ) ),
    file(functor1,t13_functor1),
    []).

fof(t16_yellow18,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)
            & v11_altcat_1(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ( r2_yellow18(A,B)
           => v21_functor0(k2_yellow18(A,B),A,B) ) ) ) ),
    file(yellow18,t16_yellow18),
    []).

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(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),
    []).