SET007 Axioms: SET007+463.ax


%------------------------------------------------------------------------------
% File     : SET007+463 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Functors for Alternative Categories
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : functor0 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  172 (   5 unit)
%            Number of atoms       : 1515 ( 116 equality)
%            Maximal formula depth :   28 (  10 average)
%            Number of connectives : 1596 ( 253 ~  ;   1  |; 829  &)
%                                         (  40 <=>; 473 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   55 (   1 propositional; 0-6 arity)
%            Number of functors    :   56 (   6 constant; 0-6 arity)
%            Number of variables   :  655 (   0 singleton; 618 !;  37 ?)
%            Maximal term depth    :    6 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_functor0,axiom,(
    ! [A] :
      ( ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_xboole_0(k2_funct_4(A))
        & v1_relat_1(k2_funct_4(A))
        & v1_funct_1(k2_funct_4(A))
        & v2_funct_1(k2_funct_4(A)) ) ) )).

fof(fc2_functor0,axiom,(
    ! [A,B] :
      ( ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_xboole_0(k15_funct_3(A,B))
        & v1_relat_1(k15_funct_3(A,B))
        & v1_funct_1(k15_funct_3(A,B))
        & v2_funct_1(k15_funct_3(A,B)) ) ) )).

fof(fc3_functor0,axiom,(
    ! [A,B] :
      ( ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_xboole_0(k15_funct_3(B,A))
        & v1_relat_1(k15_funct_3(B,A))
        & v1_funct_1(k15_funct_3(B,A))
        & v2_funct_1(k15_funct_3(B,A)) ) ) )).

fof(fc4_functor0,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ( v1_relat_1(k2_funct_4(A))
        & v1_funct_1(k2_funct_4(A))
        & v1_funcop_1(k2_funct_4(A)) ) ) )).

fof(rc1_functor0,axiom,(
    ! [A,B] :
    ? [C] :
      ( m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
      & v1_relat_1(C)
      & v1_funct_1(C)
      & v1_funct_2(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
      & v1_functor0(C,A,B)
      & v2_functor0(C,A,B) ) )).

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) ) ) )).

fof(rc2_functor0,axiom,(
    ! [A,B] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B) )
     => ? [C] :
          ( l1_functor0(C,A,B)
          & v3_functor0(C,A,B) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) )).

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)) ) ) )).

fof(fc6_functor0,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & v1_altcat_2(B)
        & l1_altcat_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,k1_altcat_1(B,C,C)) )
     => ( v8_functor0(k9_functor0(A,B,C,D),A,B)
        & v9_functor0(k9_functor0(A,B,C,D),A,B)
        & v10_functor0(k9_functor0(A,B,C,D),A,B)
        & v11_functor0(k9_functor0(A,B,C,D),A,B) ) ) )).

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) ) ) )).

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)) ) ) )).

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

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) ) ) ) )).

fof(fc8_functor0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( v8_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v9_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v10_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v11_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v12_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B) ) ) )).

fof(fc9_functor0,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & v1_altcat_2(B)
        & l1_altcat_1(B)
        & m1_subset_1(C,u1_struct_0(B))
        & m1_subset_1(D,k1_altcat_1(B,C,C)) )
     => ( v6_functor0(k9_functor0(A,B,C,D),A,B)
        & v8_functor0(k9_functor0(A,B,C,D),A,B)
        & v9_functor0(k9_functor0(A,B,C,D),A,B)
        & v10_functor0(k9_functor0(A,B,C,D),A,B)
        & v11_functor0(k9_functor0(A,B,C,D),A,B) ) ) )).

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) ) ) )).

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) ) ) )).

fof(fc10_functor0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v12_altcat_1(B)
        & l2_altcat_1(B)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ( v6_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v8_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v9_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v10_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v11_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v13_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B)
        & v14_functor0(k9_functor0(A,B,C,k8_altcat_1(B,C)),A,B) ) ) )).

fof(fc11_functor0,axiom,(
    ! [A,B] :
      ( ( l2_altcat_1(A)
        & m1_altcat_2(B,A) )
     => ( v9_functor0(k10_functor0(A,B),B,A)
        & v10_functor0(k10_functor0(A,B),B,A) ) ) )).

fof(fc12_functor0,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & m1_altcat_2(B,A) )
     => ( v8_functor0(k10_functor0(A,B),B,A)
        & v9_functor0(k10_functor0(A,B),B,A)
        & v10_functor0(k10_functor0(A,B),B,A) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) )).

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

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) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) )).

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) ) ) ) )).

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) ) ) ) )).

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) ) ) ) )).

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) ) ) ) )).

fof(t1_functor0,axiom,(
    ! [A] :
      ( v1_funct_1(k1_xboole_0)
      & v1_funct_2(k1_xboole_0,A,k1_xboole_0)
      & m2_relset_1(k1_xboole_0,A,k1_xboole_0) ) )).

fof(t2_functor0,axiom,(
    $true )).

fof(t3_functor0,axiom,(
    ! [A,B] :
      ( m1_pboole(B,A)
     => k5_relat_1(k6_partfun1(A),B) = B ) )).

fof(t4_functor0,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => k9_relat_1(B,k6_partfun1(A)) = k9_relat_1(k2_funct_4(B),k6_partfun1(A)) ) )).

fof(t5_functor0,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v2_funct_2(C,A,B)
      <=> v2_funct_2(k16_funct_3(A,A,B,B,C,C),k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) ) ) )).

fof(t6_functor0,axiom,(
    ! [A,B,C] : k2_funct_4(k10_pboole(k2_zfmisc_1(A,B),C)) = k10_pboole(k2_zfmisc_1(B,A),C) )).

fof(t7_functor0,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & v2_funct_1(B) )
           => k2_funct_1(k15_funct_3(A,B)) = k15_funct_3(k2_funct_1(A),k2_funct_1(B)) ) ) ) )).

fof(t8_functor0,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(k15_funct_3(A,A))
       => v2_funct_1(A) ) ) )).

fof(t9_functor0,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => v2_funct_1(k2_funct_4(A)) ) ) )).

fof(t10_functor0,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( v2_funct_1(k2_funct_4(k15_funct_3(A,B)))
           => v2_funct_1(k15_funct_3(B,A)) ) ) ) )).

fof(t11_functor0,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & v2_funct_1(B) )
           => k2_funct_1(k2_funct_4(k15_funct_3(A,B))) = k2_funct_4(k2_funct_1(k15_funct_3(B,A))) ) ) ) )).

fof(t12_functor0,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( v2_funct_2(C,A,B)
       => r1_tarski(k6_partfun1(B),k2_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(A))) ) ) )).

fof(t13_functor0,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_funcop_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ! [C] :
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => k5_relat_1(C,k13_pboole(A,B)) = k13_pboole(k5_relat_1(C,A),k5_relat_1(C,B)) ) ) ) )).

fof(t14_functor0,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m2_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ( v2_funct_2(k1_functor0(A,B,C,D),k2_zfmisc_1(B,A),C)
       => v2_funct_2(D,k2_zfmisc_1(A,B),C) ) ) )).

fof(t15_functor0,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => r1_tarski(k2_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(A)),k6_partfun1(B)) ) ) )).

fof(d1_functor0,axiom,(
    $true )).

fof(d2_functor0,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
        & m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) )
     => ( v1_functor0(C,A,B)
      <=> ? [D] :
            ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B)
            & C = k16_funct_3(A,A,B,B,D,D) ) ) ) )).

fof(d3_functor0,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
        & m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) )
     => ( v2_functor0(C,A,B)
      <=> ? [D] :
            ( v1_funct_1(D)
            & v1_funct_2(D,A,B)
            & m2_relset_1(D,A,B)
            & C = k1_functor0(A,A,k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,D,D)) ) ) ) )).

fof(t16_functor0,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_subset_1(C,B)
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
                & m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) )
             => ( D = k10_pboole(k2_zfmisc_1(A,A),k4_tarski(C,C))
               => ( v1_functor0(D,A,B)
                  & v2_functor0(D,A,B) ) ) ) ) ) )).

fof(t17_functor0,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B))
                & v1_functor0(C,A,B)
                & v2_functor0(C,A,B)
                & m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)) )
             => ? [D] :
                  ( m1_subset_1(D,B)
                  & C = k10_pboole(k2_zfmisc_1(A,A),k4_tarski(D,D)) ) ) ) ) )).

fof(d4_functor0,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] :
          ( m1_pboole(D,A)
         => ! [E] :
              ( m1_pboole(E,B)
             => ! [F] :
                  ( m1_pboole(F,A)
                 => ( ( B != k1_xboole_0
                     => ( m1_functor0(F,A,B,C,D,E)
                      <=> ? [G] :
                            ( ~ v1_xboole_0(G)
                            & ? [H] :
                                ( m1_pboole(H,G)
                                & ? [I] :
                                    ( v1_funct_1(I)
                                    & v1_funct_2(I,A,G)
                                    & m2_relset_1(I,A,G)
                                    & C = I
                                    & E = H
                                    & m3_pboole(F,A,D,k7_pboole(A,G,I,H)) ) ) ) ) )
                    & ( B = k1_xboole_0
                     => ( m1_functor0(F,A,B,C,D,E)
                      <=> r6_pboole(A,F,k1_pboole(A)) ) ) ) ) ) ) ) )).

fof(d5_functor0,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,B)
            & m2_relset_1(C,A,B) )
         => ! [D] :
              ( m1_pboole(D,A)
             => ! [E] :
                  ( m1_pboole(E,B)
                 => ! [F] :
                      ( m1_pboole(F,A)
                     => ( m1_functor0(F,A,B,C,D,E)
                      <=> m3_pboole(F,A,D,k7_pboole(A,B,C,E)) ) ) ) ) ) ) )).

fof(t18_functor0,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ~ v1_xboole_0(C)
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,C)
                    & m2_relset_1(E,B,C) )
                 => ! [F] :
                      ( m1_pboole(F,B)
                     => ! [G] :
                          ( m1_pboole(G,C)
                         => ! [H] :
                              ( m1_functor0(H,B,C,E,F,G)
                             => m1_functor0(k7_pboole(A,B,D,H),A,C,k7_funct_2(A,B,C,D,E),k7_pboole(A,B,D,F),G) ) ) ) ) ) ) ) )).

fof(t20_functor0,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( ~ v1_xboole_0(C)
         => ! [D] :
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,B)
                & m2_relset_1(D,A,B) )
             => ! [E] :
                  ( ( v1_funct_1(E)
                    & v1_funct_2(E,B,C)
                    & m2_relset_1(E,B,C) )
                 => ! [F] :
                      ( m1_pboole(F,A)
                     => ! [G] :
                          ( m1_pboole(G,B)
                         => ! [H] :
                              ( m1_pboole(H,C)
                             => ! [I] :
                                  ( m1_functor0(I,A,B,D,F,G)
                                 => ! [J] :
                                      ( m1_functor0(J,A,C,k7_funct_2(A,B,C,D,E),k7_pboole(A,B,D,G),H)
                                     => ( ! [K] :
                                            ~ ( r2_hidden(K,A)
                                              & k1_funct_1(k7_pboole(A,B,D,G),K) = k1_xboole_0
                                              & k1_funct_1(F,K) != k1_xboole_0
                                              & k1_funct_1(k7_pboole(A,C,k7_funct_2(A,B,C,D,E),H),K) != k1_xboole_0 )
                                       => m1_functor0(k13_pboole(I,J),A,C,k7_funct_2(A,B,C,D,E),F,H) ) ) ) ) ) ) ) ) ) ) )).

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)) ) ) ) ) )).

fof(d7_functor0,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( v4_functor0(C,A,B)
              <=> v2_funct_1(u1_functor0(A,B,C)) ) ) ) ) )).

fof(d8_functor0,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( v5_functor0(C,A,B)
              <=> v2_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))) ) ) ) ) )).

fof(d9_functor0,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( v6_functor0(C,A,B)
              <=> r1_tarski(k2_funct_2(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),k6_partfun1(u1_struct_0(A))),k6_partfun1(u1_struct_0(B))) ) ) ) ) )).

fof(d10_functor0,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( v7_functor0(C,A,B)
              <=> r1_tarski(k6_partfun1(u1_struct_0(B)),k2_funct_2(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),k6_partfun1(u1_struct_0(A)))) ) ) ) ) )).

fof(d11_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)
             => ( v6_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => 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) = k4_tarski(k3_functor0(A,B,C,D),k3_functor0(A,B,C,D)) ) ) ) ) ) )).

fof(t21_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_altcat_2(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( v7_functor0(C,A,B)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & k3_functor0(A,B,C,E) = D ) ) ) ) ) ) )).

fof(d12_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)
             => ( v8_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                            & k1_funct_1(u1_altcat_1(B),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,E)) = k1_xboole_0 ) ) ) ) ) ) ) )).

fof(d13_functor0,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( v10_functor0(C,A,B)
              <=> v1_functor0(u1_functor0(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) )).

fof(d14_functor0,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( v11_functor0(C,A,B)
              <=> v2_functor0(u1_functor0(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) )).

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) ) ) ) ) ) )).

fof(d16_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v10_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                          & k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) != k1_xboole_0
                          & ~ ! [F] :
                                ( m1_subset_1(F,k1_altcat_1(A,D,E))
                               => k6_functor0(A,B,C,D,E,F) = k1_funct_1(k5_functor0(A,B,C,D,E),F) ) ) ) ) ) ) ) )).

fof(d17_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v11_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                          & k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) != k1_xboole_0
                          & ~ ! [F] :
                                ( m1_subset_1(F,k1_altcat_1(A,D,E))
                               => k8_functor0(A,B,C,D,E,F) = k1_funct_1(k7_functor0(A,B,C,D,E),F) ) ) ) ) ) ) ) )).

fof(t22_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] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k3_functor0(A,B,k9_functor0(A,B,C,D),E) = C ) ) ) ) ) ) )).

fof(t23_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v10_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => 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,E) = k4_tarski(k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) ) ) ) ) ) )).

fof(d19_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v10_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( v8_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                            & k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)) = k1_xboole_0 ) ) ) ) ) ) ) )).

fof(t24_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v11_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => 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,E) = k4_tarski(k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) ) ) ) ) ) )).

fof(d20_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( ( v11_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( v8_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                            & k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)) = k1_xboole_0 ) ) ) ) ) ) ) )).

fof(d21_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v12_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_funct_1(k4_functor0(A,B,C,D,D),k8_altcat_1(A,D)) = k8_altcat_1(B,k3_functor0(A,B,C,D)) ) ) ) ) ) )).

fof(t25_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] :
                        ( 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 ) ) ) ) ) ) ) ) ) )).

fof(d22_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v13_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                                & k1_altcat_1(A,E,F) != k1_xboole_0
                                & ? [G] :
                                    ( m1_subset_1(G,k1_altcat_1(A,D,E))
                                    & ? [H] :
                                        ( m1_subset_1(H,k1_altcat_1(A,E,F))
                                        & ! [I] :
                                            ( m1_subset_1(I,k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)))
                                           => ! [J] :
                                                ( m1_subset_1(J,k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F)))
                                               => ~ ( I = k1_funct_1(k4_functor0(A,B,C,D,E),G)
                                                    & J = k1_funct_1(k4_functor0(A,B,C,E,F),H)
                                                    & k1_funct_1(k4_functor0(A,B,C,D,F),k5_altcat_1(A,D,E,F,G,H)) = k5_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d23_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v14_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                                & k1_altcat_1(A,E,F) != k1_xboole_0
                                & ? [G] :
                                    ( m1_subset_1(G,k1_altcat_1(A,D,E))
                                    & ? [H] :
                                        ( m1_subset_1(H,k1_altcat_1(A,E,F))
                                        & ! [I] :
                                            ( m1_subset_1(I,k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)))
                                           => ! [J] :
                                                ( m1_subset_1(J,k1_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E)))
                                               => ~ ( I = k1_funct_1(k4_functor0(A,B,C,D,E),G)
                                                    & J = k1_funct_1(k4_functor0(A,B,C,E,F),H)
                                                    & k1_funct_1(k4_functor0(A,B,C,D,F),k5_altcat_1(A,D,E,F,G,H)) = k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E),k3_functor0(A,B,C,D),J,I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d24_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v8_functor0(C,A,B)
                & v10_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( v13_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                                & k1_altcat_1(A,E,F) != k1_xboole_0
                                & ~ ! [G] :
                                      ( m1_subset_1(G,k1_altcat_1(A,D,E))
                                     => ! [H] :
                                          ( m1_subset_1(H,k1_altcat_1(A,E,F))
                                         => k6_functor0(A,B,C,D,F,k5_altcat_1(A,D,E,F,G,H)) = k5_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),k6_functor0(A,B,C,D,E,G),k6_functor0(A,B,C,E,F,H)) ) ) ) ) ) ) ) ) ) ) )).

fof(d25_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( v8_functor0(C,A,B)
                & v11_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( v14_functor0(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ~ ( k1_altcat_1(A,D,E) != k1_xboole_0
                                & k1_altcat_1(A,E,F) != k1_xboole_0
                                & ~ ! [G] :
                                      ( m1_subset_1(G,k1_altcat_1(A,D,E))
                                     => ! [H] :
                                          ( m1_subset_1(H,k1_altcat_1(A,E,F))
                                         => k8_functor0(A,B,C,D,F,k5_altcat_1(A,D,E,F,G,H)) = k5_altcat_1(B,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E),k3_functor0(A,B,C,D),k8_functor0(A,B,C,E,F,H),k8_functor0(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t26_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,k1_altcat_1(B,C,C))
                 => ! [E] :
                      ( ( v8_functor0(E,A,B)
                        & v10_functor0(E,A,B)
                        & l2_functor0(E,A,B) )
                     => ( E = k9_functor0(A,B,C,D)
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,k1_altcat_1(A,F,G))
                                   => ( k1_altcat_1(A,F,G) != k1_xboole_0
                                     => k6_functor0(A,B,E,F,G,H) = D ) ) ) ) ) ) ) ) ) ) )).

fof(t27_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [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
                               => k8_functor0(A,B,k9_functor0(A,B,C,D),E,F,G) = D ) ) ) ) ) ) ) ) )).

fof(d26_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( m2_functor0(C,A,B)
              <=> ( v8_functor0(C,A,B)
                  & v12_functor0(C,A,B)
                  & ( ( v10_functor0(C,A,B)
                      & v13_functor0(C,A,B) )
                    | ( v11_functor0(C,A,B)
                      & v14_functor0(C,A,B) ) ) ) ) ) ) ) )).

fof(d27_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( m2_functor0(C,A,B)
             => ( v15_functor0(C,A,B)
              <=> ( v10_functor0(C,A,B)
                  & v13_functor0(C,A,B) ) ) ) ) ) )).

fof(d28_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( m2_functor0(C,A,B)
             => ( v16_functor0(C,A,B)
              <=> ( v11_functor0(C,A,B)
                  & v14_functor0(C,A,B) ) ) ) ) ) )).

fof(d29_functor0,axiom,(
    ! [A] :
      ( l2_altcat_1(A)
     => ! [B] :
          ( m1_altcat_2(B,A)
         => ! [C] :
              ( ( v9_functor0(C,B,A)
                & l2_functor0(C,B,A) )
             => ( C = k10_functor0(A,B)
              <=> ( u1_functor0(B,A,C) = k6_partfun1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
                  & r6_pboole(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u2_functor0(B,A,C),k2_msualg_3(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_altcat_1(B))) ) ) ) ) ) )).

fof(d30_functor0,axiom,(
    ! [A] :
      ( l1_altcat_1(A)
     => ! [B] :
          ( ( v9_functor0(B,A,A)
            & l2_functor0(B,A,A) )
         => ( B = k11_functor0(A)
          <=> ( u1_functor0(A,A,B) = k6_partfun1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
              & r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u2_functor0(A,A,B),k2_msualg_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A))) ) ) ) ) )).

fof(t28_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_altcat_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k3_functor0(B,A,k10_functor0(A,B),C) = C ) ) ) )).

fof(t29_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & m1_altcat_2(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => r1_tarski(k1_altcat_1(B,C,D),k1_altcat_1(A,k3_functor0(B,A,k10_functor0(A,B),C),k3_functor0(B,A,k10_functor0(A,B),D))) ) ) ) ) )).

fof(d31_functor0,axiom,(
    ! [A] :
      ( l1_altcat_1(A)
     => ! [B] :
          ( l1_altcat_1(B)
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v17_functor0(C,A,B)
              <=> v1_msualg_3(u2_functor0(A,B,C)) ) ) ) ) )).

fof(d32_functor0,axiom,(
    ! [A] :
      ( l1_altcat_1(A)
     => ! [B] :
          ( l1_altcat_1(B)
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v18_functor0(C,A,B)
              <=> ? [D] :
                    ( m1_pboole(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
                    & ? [E] :
                        ( m3_pboole(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),D)
                        & D = k5_relat_1(u1_functor0(A,B,C),u1_altcat_1(B))
                        & r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),E,u2_functor0(A,B,C))
                        & v2_msualg_3(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),D) ) ) ) ) ) ) )).

fof(d33_functor0,axiom,(
    ! [A] :
      ( l1_altcat_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v18_functor0(C,A,B)
              <=> ? [D] :
                    ( m3_pboole(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),k7_pboole(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(B)))
                    & r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),D,u2_functor0(A,B,C))
                    & v2_msualg_3(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),k7_pboole(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(B))) ) ) ) ) ) )).

fof(d34_functor0,axiom,(
    ! [A] :
      ( l1_altcat_1(A)
     => ! [B] :
          ( l1_altcat_1(B)
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v19_functor0(C,A,B)
              <=> ( v4_functor0(C,A,B)
                  & v17_functor0(C,A,B) ) ) ) ) ) )).

fof(d35_functor0,axiom,(
    ! [A] :
      ( l1_altcat_1(A)
     => ! [B] :
          ( l1_altcat_1(B)
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v20_functor0(C,A,B)
              <=> ( v18_functor0(C,A,B)
                  & v5_functor0(C,A,B) ) ) ) ) ) )).

fof(d36_functor0,axiom,(
    ! [A] :
      ( l1_altcat_1(A)
     => ! [B] :
          ( l1_altcat_1(B)
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v21_functor0(C,A,B)
              <=> ( v19_functor0(C,A,B)
                  & v20_functor0(C,A,B) ) ) ) ) ) )).

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 ) ) )).

fof(t31_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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_xboole_0
               => ! [D] :
                    ( m1_subset_1(D,k1_altcat_1(A,B,C))
                   => k1_funct_1(k4_functor0(A,A,k11_functor0(A),B,C),D) = D ) ) ) ) ) )).

fof(t32_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(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_xboole_0
               => ! [D] :
                    ( ( v8_functor0(D,A,A)
                      & v10_functor0(D,A,A)
                      & l2_functor0(D,A,A) )
                   => ( D = k11_functor0(A)
                     => ! [E] :
                          ( m1_subset_1(E,k1_altcat_1(A,B,C))
                         => k6_functor0(A,A,D,B,C,E) = E ) ) ) ) ) ) ) )).

fof(d37_functor0,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)
                     => ! [F] :
                          ( ( v9_functor0(F,A,C)
                            & l2_functor0(F,A,C) )
                         => ( F = k13_functor0(A,B,C,D,E)
                          <=> ( u1_functor0(A,C,F) = k7_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_functor0(A,B,D),u1_functor0(B,C,E))
                              & r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u2_functor0(A,C,F),k3_altcat_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u2_functor0(A,B,D),k7_pboole(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,D),u2_functor0(B,C,E)))) ) ) ) ) ) ) ) ) )).

fof(t33_functor0,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] :
                  ( ( ~ v3_struct_0(D)
                    & v1_altcat_2(D)
                    & l1_altcat_1(D) )
                 => ! [E] :
                      ( ( v8_functor0(E,A,B)
                        & l2_functor0(E,A,B) )
                     => ! [F] :
                          ( ( v8_functor0(F,B,C)
                            & l2_functor0(F,B,C) )
                         => ! [G] :
                              ( l2_functor0(G,C,D)
                             => k13_functor0(A,B,D,E,k13_functor0(B,C,D,F,G)) = k13_functor0(A,C,D,k13_functor0(A,B,C,E,F),G) ) ) ) ) ) ) ) )).

fof(t34_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v1_altcat_2(C)
                & l2_altcat_1(C) )
             => ! [D] :
                  ( ( v6_functor0(D,A,B)
                    & v8_functor0(D,A,B)
                    & l2_functor0(D,A,B) )
                 => ! [E] :
                      ( l2_functor0(E,B,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => k3_functor0(A,C,k13_functor0(A,B,C,D,E),F) = k3_functor0(B,C,E,k3_functor0(A,B,D,F)) ) ) ) ) ) ) )).

fof(t35_functor0,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] :
                  ( ( v6_functor0(D,A,B)
                    & v8_functor0(D,A,B)
                    & l2_functor0(D,A,B) )
                 => ! [E] :
                      ( l2_functor0(E,B,C)
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => k4_functor0(A,C,k13_functor0(A,B,C,D,E),F,F) = k5_relat_1(k4_functor0(A,B,D,F,F),k4_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,F))) ) ) ) ) ) ) )).

fof(d38_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_altcat_2(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v1_altcat_2(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & m1_altcat_2(C,A) )
             => ! [D] :
                  ( l2_functor0(D,A,B)
                 => k14_functor0(A,B,C,D) = k13_functor0(C,A,B,k10_functor0(A,C),D) ) ) ) ) )).

fof(d39_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_altcat_1(B) )
         => ! [C] :
              ( l2_functor0(C,A,B)
             => ( v21_functor0(C,A,B)
               => ! [D] :
                    ( ( v9_functor0(D,B,A)
                      & l2_functor0(D,B,A) )
                   => ( D = k15_functor0(A,B,C)
                    <=> ( u1_functor0(B,A,D) = k2_funct_1(u1_functor0(A,B,C))
                        & ? [E] :
                            ( m3_pboole(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),k7_pboole(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(B)))
                            & r6_pboole(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),E,u2_functor0(A,B,C))
                            & u2_functor0(B,A,D) = k5_relat_1(k2_funct_1(u1_functor0(A,B,C)),k4_msualg_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_altcat_1(A),k7_pboole(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(B)),E)) ) ) ) ) ) ) ) ) )).

fof(t36_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) )
         => ! [C] :
              ( ( v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( v21_functor0(C,A,B)
               => ( v21_functor0(k15_functor0(A,B,C),B,A)
                  & v8_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) ) )).

fof(t37_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) )
         => ! [C] :
              ( ( v6_functor0(C,A,B)
                & v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( ( v21_functor0(C,A,B)
                  & v7_functor0(C,A,B) )
               => v6_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) )).

fof(t38_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) )
         => ! [C] :
              ( ( v6_functor0(C,A,B)
                & v8_functor0(C,A,B)
                & v12_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( ( v21_functor0(C,A,B)
                  & v7_functor0(C,A,B) )
               => v12_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) )).

fof(t39_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) )
         => ! [C] :
              ( ( v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( ( v21_functor0(C,A,B)
                  & v10_functor0(C,A,B) )
               => v10_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) )).

fof(t40_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) )
         => ! [C] :
              ( ( v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( ( v21_functor0(C,A,B)
                  & v11_functor0(C,A,B) )
               => v11_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) )).

fof(t41_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) )
         => ! [C] :
              ( ( v6_functor0(C,A,B)
                & v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( ( v21_functor0(C,A,B)
                  & v7_functor0(C,A,B)
                  & v10_functor0(C,A,B) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,k1_altcat_1(B,D,E))
                           => ( k1_altcat_1(B,D,E) != k1_xboole_0
                             => k1_funct_1(k4_functor0(A,B,C,k3_functor0(B,A,k15_functor0(A,B,C),D),k3_functor0(B,A,k15_functor0(A,B,C),E)),k1_funct_1(k4_functor0(B,A,k15_functor0(A,B,C),D,E),F)) = F ) ) ) ) ) ) ) ) )).

fof(t42_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) )
         => ! [C] :
              ( ( v6_functor0(C,A,B)
                & v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( ( v21_functor0(C,A,B)
                  & v7_functor0(C,A,B)
                  & v11_functor0(C,A,B) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,k1_altcat_1(B,D,E))
                           => ( k1_altcat_1(B,D,E) != k1_xboole_0
                             => k1_funct_1(k4_functor0(A,B,C,k3_functor0(B,A,k15_functor0(A,B,C),E),k3_functor0(B,A,k15_functor0(A,B,C),D)),k1_funct_1(k4_functor0(B,A,k15_functor0(A,B,C),D,E),F)) = F ) ) ) ) ) ) ) ) )).

fof(t43_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) )
         => ! [C] :
              ( ( v6_functor0(C,A,B)
                & v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( ( v21_functor0(C,A,B)
                  & v13_functor0(C,A,B)
                  & v10_functor0(C,A,B)
                  & v7_functor0(C,A,B) )
               => v13_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) )).

fof(t44_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) )
         => ! [C] :
              ( ( v6_functor0(C,A,B)
                & v8_functor0(C,A,B)
                & l2_functor0(C,A,B) )
             => ( ( v21_functor0(C,A,B)
                  & v14_functor0(C,A,B)
                  & v11_functor0(C,A,B)
                  & v7_functor0(C,A,B) )
               => v14_functor0(k15_functor0(A,B,C),B,A) ) ) ) ) )).

fof(t45_functor0,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( ( v10_functor0(C,A,B)
                  & v5_functor0(C,A,B) )
               => v7_functor0(C,A,B) ) ) ) ) )).

fof(t46_functor0,axiom,(
    ! [A] :
      ( l1_struct_0(A)
     => ! [B] :
          ( l1_struct_0(B)
         => ! [C] :
              ( l1_functor0(C,A,B)
             => ( ( v11_functor0(C,A,B)
                  & v5_functor0(C,A,B) )
               => v7_functor0(C,A,B) ) ) ) ) )).

fof(t47_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( m2_functor0(C,A,B)
             => ( ( v15_functor0(C,A,B)
                  & v5_functor0(C,A,B) )
               => v7_functor0(C,A,B) ) ) ) ) )).

fof(t48_functor0,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v12_altcat_1(B)
            & l2_altcat_1(B) )
         => ! [C] :
              ( m2_functor0(C,A,B)
             => ( ( v16_functor0(C,A,B)
                  & v5_functor0(C,A,B) )
               => v7_functor0(C,A,B) ) ) ) ) )).

fof(t49_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) )
         => ! [C] :
              ( ( v15_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ~ ( v21_functor0(C,A,B)
                  & ! [D] :
                      ( m2_functor0(D,B,A)
                     => ~ ( D = k15_functor0(A,B,C)
                          & v21_functor0(D,B,A)
                          & v15_functor0(D,B,A) ) ) ) ) ) ) )).

fof(t50_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) )
         => ! [C] :
              ( ( v16_functor0(C,A,B)
                & m2_functor0(C,A,B) )
             => ~ ( v21_functor0(C,A,B)
                  & ! [D] :
                      ( m2_functor0(D,B,A)
                     => ~ ( D = k15_functor0(A,B,C)
                          & v21_functor0(D,B,A)
                          & v16_functor0(D,B,A) ) ) ) ) ) ) )).

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) ) ) ) ) )).

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) ) ) ) ) )).

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) ) ) )).

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) ) )).

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) ) ) )).

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) ) )).

fof(dt_l1_functor0,axiom,(
    $true )).

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

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) ) ) )).

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

fof(abstractness_v3_functor0,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & l1_struct_0(B)
        & l1_functor0(C,A,B) )
     => ( v3_functor0(C,A,B)
       => C = g1_functor0(A,B,u1_functor0(A,B,C)) ) ) )).

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)) ) ) )).

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) ) ) )).

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) ) )).

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) ) ) )).

fof(dt_k1_functor0,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => ( v1_funct_1(k1_functor0(A,B,C,D))
        & v1_funct_2(k1_functor0(A,B,C,D),k2_zfmisc_1(B,A),C)
        & m2_relset_1(k1_functor0(A,B,C,D),k2_zfmisc_1(B,A),C) ) ) )).

fof(redefinition_k1_functor0,axiom,(
    ! [A,B,C,D] :
      ( ( v1_funct_1(D)
        & v1_funct_2(D,k2_zfmisc_1(A,B),C)
        & m1_relset_1(D,k2_zfmisc_1(A,B),C) )
     => k1_functor0(A,B,C,D) = k2_funct_4(D) ) )).

fof(dt_k2_functor0,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,k2_zfmisc_1(A,A))
        & m1_pboole(E,k2_zfmisc_1(B,B))
        & m1_functor0(F,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),D,E) )
     => m1_functor0(k2_functor0(A,B,C,D,E,F),k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k1_altcat_2(A,D),k1_altcat_2(B,E)) ) )).

fof(redefinition_k2_functor0,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(B)
        & v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m1_relset_1(C,A,B)
        & m1_pboole(D,k2_zfmisc_1(A,A))
        & m1_pboole(E,k2_zfmisc_1(B,B))
        & m1_functor0(F,k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),D,E) )
     => k2_functor0(A,B,C,D,E,F) = k2_funct_4(F) ) )).

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)) ) )).

fof(dt_k4_functor0,axiom,(
    $true )).

fof(dt_k5_functor0,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ 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)) )
     => ( v1_funct_1(k5_functor0(A,B,C,D,E))
        & v1_funct_2(k5_functor0(A,B,C,D,E),k1_altcat_1(A,D,E),k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E)))
        & m2_relset_1(k5_functor0(A,B,C,D,E),k1_altcat_1(A,D,E),k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E))) ) ) )).

fof(redefinition_k5_functor0,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ 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)) )
     => k5_functor0(A,B,C,D,E) = k4_functor0(A,B,C,D,E) ) )).

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))) ) )).

fof(dt_k7_functor0,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & v11_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)) )
     => ( v1_funct_1(k7_functor0(A,B,C,D,E))
        & v1_funct_2(k7_functor0(A,B,C,D,E),k1_altcat_1(A,D,E),k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D)))
        & m2_relset_1(k7_functor0(A,B,C,D,E),k1_altcat_1(A,D,E),k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D))) ) ) )).

fof(redefinition_k7_functor0,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & v11_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)) )
     => k7_functor0(A,B,C,D,E) = k4_functor0(A,B,C,D,E) ) )).

fof(dt_k8_functor0,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & v11_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(k8_functor0(A,B,C,D,E,F),k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D))) ) )).

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) ) ) )).

fof(dt_k10_functor0,axiom,(
    ! [A,B] :
      ( ( l2_altcat_1(A)
        & m1_altcat_2(B,A) )
     => ( v9_functor0(k10_functor0(A,B),B,A)
        & l2_functor0(k10_functor0(A,B),B,A) ) ) )).

fof(dt_k11_functor0,axiom,(
    ! [A] :
      ( l1_altcat_1(A)
     => ( v9_functor0(k11_functor0(A),A,A)
        & l2_functor0(k11_functor0(A),A,A) ) ) )).

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) ) ) )).

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) ) )).

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) ) ) )).

fof(dt_k14_functor0,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v1_altcat_2(A)
        & l2_altcat_1(A)
        & ~ v3_struct_0(B)
        & v1_altcat_2(B)
        & l2_altcat_1(B)
        & ~ v3_struct_0(C)
        & m1_altcat_2(C,A)
        & l2_functor0(D,A,B) )
     => l2_functor0(k14_functor0(A,B,C,D),C,B) ) )).

fof(dt_k15_functor0,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_altcat_1(A)
        & ~ v3_struct_0(B)
        & l1_altcat_1(B)
        & l2_functor0(C,A,B) )
     => ( v9_functor0(k15_functor0(A,B,C),B,A)
        & l2_functor0(k15_functor0(A,B,C),B,A) ) ) )).

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))) ) ) )).

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)) ) )).

fof(dt_g1_functor0,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & l1_struct_0(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))) )
     => ( v3_functor0(g1_functor0(A,B,C),A,B)
        & l1_functor0(g1_functor0(A,B,C),A,B) ) ) )).

fof(free_g1_functor0,axiom,(
    ! [A,B,C] :
      ( ( l1_struct_0(A)
        & l1_struct_0(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))) )
     => ! [D,E,F] :
          ( g1_functor0(A,B,C) = g1_functor0(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).

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) ) ) )).

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 ) ) ) )).

fof(t19_functor0,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m1_pboole(C,A)
             => ! [D] :
                  ( m1_pboole(D,B)
                 => ! [E] :
                      ( m1_subset_1(E,B)
                     => ( k1_funct_1(D,E) != k1_xboole_0
                       => ! [F] :
                            ( m1_subset_1(F,k1_funct_1(D,E))
                           => ! [G] :
                                ( ( v1_funct_1(G)
                                  & v1_funct_2(G,A,B)
                                  & m2_relset_1(G,A,B) )
                               => ( G = k10_pboole(A,E)
                                 => m1_functor0(a_6_0_functor0(A,B,C,D,E,F),A,B,G,C,D) ) ) ) ) ) ) ) ) ) )).

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) ) ) ) ) ) ) ) ) )).

fof(s1_functor0,axiom,
    ( ( f2_s1_functor0 = a_0_0_functor0
      & p1_s1_functor0(f3_s1_functor0,f4_s1_functor0) )
   => k1_binop_1(f2_s1_functor0,f3_s1_functor0,f4_s1_functor0) = f5_s1_functor0(f3_s1_functor0,f4_s1_functor0) )).

fof(fraenkel_a_6_0_functor0,axiom,(
    ! [A,B,C,D,E,F,G] :
      ( ( ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & m1_pboole(D,B)
        & m1_pboole(E,C)
        & m1_subset_1(F,C)
        & m1_subset_1(G,k1_funct_1(E,F)) )
     => ( r2_hidden(A,a_6_0_functor0(B,C,D,E,F,G))
      <=> ? [H] :
            ( m1_subset_1(H,B)
            & A = k4_tarski(H,k10_pboole(k1_funct_1(D,H),G)) ) ) ) )).

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)) ) ) ) )).

fof(fraenkel_a_0_0_functor0,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_functor0)
    <=> ? [B,C] :
          ( m1_subset_1(B,f1_s1_functor0)
          & m1_subset_1(C,f1_s1_functor0)
          & A = k4_tarski(k4_tarski(B,C),f5_s1_functor0(B,C))
          & p1_s1_functor0(B,C) ) ) )).
%------------------------------------------------------------------------------