SET007 Axioms: SET007+647.ax


%------------------------------------------------------------------------------
% File     : SET007+647 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Composition of Macro Instructions of Standard Computers
% 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    : amistd_2 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  160 (   2 unit)
%            Number of atoms       : 1868 (  96 equality)
%            Maximal formula depth :   29 (  12 average)
%            Number of connectives : 2036 ( 328 ~  ;   1  |;1294  &)
%                                         (  25 <=>; 388 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   64 (   1 propositional; 0-3 arity)
%            Number of functors    :   68 (   5 constant; 0-6 arity)
%            Number of variables   :  514 (   0 singleton; 499 !;  15 ?)
%            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_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & ~ v1_xboole_0(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B))
        & ~ v1_xboole_0(k1_funct_4(A,B))
        & v1_setfam_1(k1_funct_4(A,B)) ) ) )).

fof(fc2_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & ~ v1_xboole_0(B) )
     => ( v1_relat_1(k1_funct_4(B,A))
        & v1_funct_1(k1_funct_4(B,A))
        & ~ v1_xboole_0(k1_funct_4(B,A))
        & v1_setfam_1(k1_funct_4(B,A)) ) ) )).

fof(fc3_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finset_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B))
        & v1_finset_1(k1_funct_4(A,B))
        & v1_setfam_1(k1_funct_4(A,B)) ) ) )).

fof(fc4_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k4_xboole_0(A,B))
        & v1_funct_1(k4_xboole_0(A,B))
        & v1_setfam_1(k4_xboole_0(A,B)) ) ) )).

fof(fc5_amistd_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_fraenkel(k4_card_3(A))
        & v1_amistd_2(k4_card_3(A)) ) ) )).

fof(cc1_amistd_2,axiom,(
    ! [A] :
      ( v1_amistd_2(A)
     => ( v1_fraenkel(A)
        & v1_pralg_2(A) ) ) )).

fof(rc1_amistd_2,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_fraenkel(A)
      & v1_pralg_2(A)
      & v1_amistd_2(A) ) )).

fof(cc2_amistd_2,axiom,(
    ! [A,B] :
      ( m1_finseq_2(B,A)
     => v1_fraenkel(B) ) )).

fof(fc6_amistd_2,axiom,(
    ! [A,B] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_fraenkel(k4_finseq_2(A,B))
        & v1_pralg_2(k4_finseq_2(A,B)) ) ) )).

fof(fc7_amistd_2,axiom,(
    ! [A,B] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_fraenkel(k4_finseq_2(A,B))
        & v1_pralg_2(k4_finseq_2(A,B))
        & v1_amistd_2(k4_finseq_2(A,B)) ) ) )).

fof(rc2_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ? [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
          & ~ v1_xboole_0(C)
          & v3_ami_1(C,A,B) ) ) )).

fof(fc8_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( l1_ami_1(B,A)
        & m1_subset_1(C,u3_ami_1(A,B)) )
     => v1_fraenkel(k5_amistd_2(A,B,C)) ) )).

fof(cc3_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( l1_ami_1(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_ami_1(B,A)
              & v5_ami_1(B,A)
              & v8_ami_1(B,A)
              & v4_amistd_1(B,A) )
           => ( ~ v3_struct_0(B)
              & ~ v2_ami_1(B,A)
              & v5_ami_1(B,A)
              & v8_ami_1(B,A)
              & v7_amistd_2(B,A) ) ) ) ) )).

fof(rc3_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ? [B] :
          ( l1_ami_1(B,A)
          & ~ v3_struct_0(B)
          & ~ v2_ami_1(B,A)
          & v5_ami_1(B,A)
          & v8_ami_1(B,A)
          & v3_amistd_1(B,A)
          & v4_amistd_1(B,A)
          & v7_amistd_2(B,A) ) ) )).

fof(fc9_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & v7_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ~ v1_realset1(u2_ami_1(A,B)) ) )).

fof(fc10_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & m1_subset_1(B,u4_ami_1(A,k4_amistd_1(A))) )
     => ( v1_relat_1(k2_amistd_1(A,k4_amistd_1(A),B))
        & v1_xboole_0(k2_amistd_1(A,k4_amistd_1(A),B))
        & v1_finset_1(k2_amistd_1(A,k4_amistd_1(A),B))
        & v1_setfam_1(k2_amistd_1(A,k4_amistd_1(A),B))
        & v1_membered(k2_amistd_1(A,k4_amistd_1(A),B))
        & v2_membered(k2_amistd_1(A,k4_amistd_1(A),B))
        & v3_membered(k2_amistd_1(A,k4_amistd_1(A),B))
        & v4_membered(k2_amistd_1(A,k4_amistd_1(A),B))
        & v5_membered(k2_amistd_1(A,k4_amistd_1(A),B)) ) ) )).

fof(cc4_amistd_2,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ( v8_amistd_2(B,A)
       => v2_amistd_2(B,A) ) ) )).

fof(fc11_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ( ~ v3_struct_0(k4_amistd_1(A))
        & v1_ami_1(k4_amistd_1(A),A)
        & ~ v2_ami_1(k4_amistd_1(A),A)
        & v4_ami_1(k4_amistd_1(A),A)
        & v5_ami_1(k4_amistd_1(A),A)
        & v6_ami_1(k4_amistd_1(A),A)
        & v7_ami_1(k4_amistd_1(A),A)
        & v8_ami_1(k4_amistd_1(A),A)
        & v10_ami_1(k4_amistd_1(A),A)
        & v13_ami_1(k4_amistd_1(A),A)
        & v3_amistd_1(k4_amistd_1(A),A)
        & v4_amistd_1(k4_amistd_1(A),A)
        & v2_amistd_2(k4_amistd_1(A),A)
        & v5_amistd_2(k4_amistd_1(A),A)
        & v6_amistd_2(k4_amistd_1(A),A)
        & v7_amistd_2(k4_amistd_1(A),A)
        & v8_amistd_2(k4_amistd_1(A),A) ) ) )).

fof(rc4_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ? [B] :
          ( l1_ami_1(B,A)
          & ~ v3_struct_0(B)
          & ~ v2_ami_1(B,A)
          & v4_ami_1(B,A)
          & v5_ami_1(B,A)
          & v7_ami_1(B,A)
          & v8_ami_1(B,A)
          & v10_ami_1(B,A)
          & v13_ami_1(B,A)
          & v3_amistd_1(B,A)
          & v4_amistd_1(B,A)
          & v2_amistd_2(B,A)
          & v5_amistd_2(B,A)
          & v6_amistd_2(B,A)
          & v7_amistd_2(B,A)
          & v8_amistd_2(B,A) ) ) )).

fof(fc12_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u3_ami_1(A,B)) )
     => ( v1_fraenkel(k5_amistd_2(A,B,C))
        & v1_pralg_2(k5_amistd_2(A,B,C))
        & v1_amistd_2(k5_amistd_2(A,B,C)) ) ) )).

fof(fc13_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & v2_amistd_2(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u3_ami_1(A,B)) )
     => ( v1_fraenkel(k5_amistd_2(A,B,C))
        & v1_pralg_2(k5_amistd_2(A,B,C)) ) ) )).

fof(cc5_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v5_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( ~ v1_xboole_0(C)
            & v3_amistd_2(C,A,B) ) ) ) )).

fof(cc6_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v6_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( ~ v1_xboole_0(C)
            & v4_amistd_2(C,A,B) ) ) ) )).

fof(fc14_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v7_amistd_2(B,A)
        & l1_ami_1(B,A)
        & v3_ami_1(C,A,B)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => ( v1_relat_1(k2_amistd_1(A,B,C))
        & v1_xboole_0(k2_amistd_1(A,B,C))
        & v1_finset_1(k2_amistd_1(A,B,C))
        & v1_setfam_1(k2_amistd_1(A,B,C))
        & v1_membered(k2_amistd_1(A,B,C))
        & v2_membered(k2_amistd_1(A,B,C))
        & v3_membered(k2_amistd_1(A,B,C))
        & v4_membered(k2_amistd_1(A,B,C))
        & v5_membered(k2_amistd_1(A,B,C)) ) ) )).

fof(rc5_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v7_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_setfam_1(C)
          & v1_ami_3(C,A,B)
          & ~ v1_realset1(C) ) ) )).

fof(cc7_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => ( ( ~ v1_xboole_0(C)
              & v1_ami_3(C,A,B)
              & v1_realset1(C) )
           => ( v1_relat_1(C)
              & v1_funct_1(C)
              & ~ v1_xboole_0(C)
              & v1_finset_1(C)
              & v1_setfam_1(C)
              & v1_ami_3(C,A,B)
              & v11_amistd_1(C,A,B) ) ) ) ) )).

fof(cc8_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v6_amistd_2(B,A)
        & v7_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( v3_ami_1(C,A,B)
           => ( ~ v1_xboole_0(C)
              & v4_amistd_2(C,A,B)
              & v9_amistd_2(C,A,B) ) ) ) ) )).

fof(cc9_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v6_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( v5_amistd_1(C,A,B)
           => ( ~ v1_xboole_0(C)
              & v4_amistd_2(C,A,B)
              & v9_amistd_2(C,A,B) ) ) ) ) )).

fof(fc15_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A) )
     => ( v1_relat_1(k6_amistd_2(A,B))
        & v1_funct_1(k6_amistd_2(A,B))
        & ~ v1_xboole_0(k6_amistd_2(A,B))
        & v1_finset_1(k6_amistd_2(A,B))
        & v1_setfam_1(k6_amistd_2(A,B))
        & v1_ami_3(k6_amistd_2(A,B),A,B)
        & v9_amistd_1(k6_amistd_2(A,B),A,B)
        & v11_amistd_1(k6_amistd_2(A,B),A,B)
        & v1_realset1(k6_amistd_2(A,B)) ) ) )).

fof(fc16_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A) )
     => ( v1_relat_1(k6_amistd_2(A,B))
        & v1_funct_1(k6_amistd_2(A,B))
        & ~ v1_xboole_0(k6_amistd_2(A,B))
        & v1_finset_1(k6_amistd_2(A,B))
        & v1_setfam_1(k6_amistd_2(A,B))
        & v1_ami_3(k6_amistd_2(A,B),A,B)
        & v6_amistd_1(k6_amistd_2(A,B),A,B)
        & v9_amistd_1(k6_amistd_2(A,B),A,B)
        & v11_amistd_1(k6_amistd_2(A,B),A,B)
        & v1_realset1(k6_amistd_2(A,B)) ) ) )).

fof(fc17_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v7_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A) )
     => ( v1_relat_1(k6_amistd_2(A,B))
        & v1_funct_1(k6_amistd_2(A,B))
        & ~ v1_xboole_0(k6_amistd_2(A,B))
        & v1_finset_1(k6_amistd_2(A,B))
        & v1_setfam_1(k6_amistd_2(A,B))
        & v11_ami_1(k6_amistd_2(A,B),A,B)
        & v1_ami_3(k6_amistd_2(A,B),A,B)
        & v9_amistd_1(k6_amistd_2(A,B),A,B)
        & v11_amistd_1(k6_amistd_2(A,B),A,B)
        & v1_realset1(k6_amistd_2(A,B)) ) ) )).

fof(fc18_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A) )
     => ( v1_relat_1(k6_amistd_2(A,B))
        & v1_funct_1(k6_amistd_2(A,B))
        & ~ v1_xboole_0(k6_amistd_2(A,B))
        & v1_finset_1(k6_amistd_2(A,B))
        & v1_setfam_1(k6_amistd_2(A,B))
        & v1_ami_3(k6_amistd_2(A,B),A,B)
        & v9_amistd_1(k6_amistd_2(A,B),A,B)
        & v10_amistd_1(k6_amistd_2(A,B),A,B)
        & v11_amistd_1(k6_amistd_2(A,B),A,B)
        & v1_realset1(k6_amistd_2(A,B)) ) ) )).

fof(fc19_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v6_amistd_2(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & v3_ami_1(C,A,B)
        & m1_subset_1(C,u4_ami_1(A,B))
        & v4_ordinal2(D) )
     => ( ~ v1_xboole_0(k8_amistd_2(A,B,C,D))
        & v3_ami_1(k8_amistd_2(A,B,C,D),A,B)
        & ~ v5_amistd_1(k8_amistd_2(A,B,C,D),A,B)
        & v4_amistd_2(k8_amistd_2(A,B,C,D),A,B)
        & v9_amistd_2(k8_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc20_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & v1_ami_3(C,A,B)
        & m1_ami_1(C,A,B)
        & v4_ordinal2(D) )
     => ( v1_relat_1(k9_amistd_2(A,B,C,D))
        & v1_funct_1(k9_amistd_2(A,B,C,D))
        & v1_finset_1(k9_amistd_2(A,B,C,D))
        & v1_setfam_1(k9_amistd_2(A,B,C,D))
        & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc21_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & m1_ami_1(C,A,B)
        & v4_ordinal2(D) )
     => ( v1_relat_1(k9_amistd_2(A,B,C,D))
        & v1_funct_1(k9_amistd_2(A,B,C,D))
        & v1_xboole_0(k9_amistd_2(A,B,C,D))
        & v1_finset_1(k9_amistd_2(A,B,C,D))
        & v1_setfam_1(k9_amistd_2(A,B,C,D))
        & v1_ami_3(k9_amistd_2(A,B,C,D),A,B)
        & v1_membered(k9_amistd_2(A,B,C,D))
        & v2_membered(k9_amistd_2(A,B,C,D))
        & v3_membered(k9_amistd_2(A,B,C,D))
        & v4_membered(k9_amistd_2(A,B,C,D))
        & v5_membered(k9_amistd_2(A,B,C,D))
        & v9_amistd_1(k9_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc22_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & m1_ami_1(C,A,B)
        & v4_ordinal2(D) )
     => ( v1_relat_1(k9_amistd_2(A,B,C,D))
        & v1_funct_1(k9_amistd_2(A,B,C,D))
        & ~ v1_xboole_0(k9_amistd_2(A,B,C,D))
        & v1_finset_1(k9_amistd_2(A,B,C,D))
        & v1_setfam_1(k9_amistd_2(A,B,C,D))
        & v1_ami_3(k9_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc23_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & v1_ami_3(C,A,B)
        & v9_amistd_1(C,A,B)
        & m1_ami_1(C,A,B)
        & v4_ordinal2(D) )
     => ( v1_relat_1(k9_amistd_2(A,B,C,D))
        & v1_funct_1(k9_amistd_2(A,B,C,D))
        & v1_finset_1(k9_amistd_2(A,B,C,D))
        & v1_setfam_1(k9_amistd_2(A,B,C,D))
        & v1_ami_3(k9_amistd_2(A,B,C,D),A,B)
        & v9_amistd_1(k9_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc24_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & m1_ami_1(C,A,B)
        & v4_ordinal2(D) )
     => ( v1_relat_1(k10_amistd_2(A,B,C,D))
        & v1_funct_1(k10_amistd_2(A,B,C,D))
        & v1_finset_1(k10_amistd_2(A,B,C,D))
        & v1_setfam_1(k10_amistd_2(A,B,C,D))
        & v1_ami_3(k10_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc25_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & v1_xboole_0(C)
        & m1_ami_1(C,A,B)
        & v4_ordinal2(D) )
     => ( v1_relat_1(k10_amistd_2(A,B,C,D))
        & v1_funct_1(k10_amistd_2(A,B,C,D))
        & v1_xboole_0(k10_amistd_2(A,B,C,D))
        & v1_finset_1(k10_amistd_2(A,B,C,D))
        & v1_setfam_1(k10_amistd_2(A,B,C,D))
        & v1_ami_3(k10_amistd_2(A,B,C,D),A,B)
        & v1_membered(k10_amistd_2(A,B,C,D))
        & v2_membered(k10_amistd_2(A,B,C,D))
        & v3_membered(k10_amistd_2(A,B,C,D))
        & v4_membered(k10_amistd_2(A,B,C,D))
        & v5_membered(k10_amistd_2(A,B,C,D))
        & v9_amistd_1(k10_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc26_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & m1_ami_1(C,A,B)
        & v4_ordinal2(D) )
     => ( v1_relat_1(k10_amistd_2(A,B,C,D))
        & v1_funct_1(k10_amistd_2(A,B,C,D))
        & ~ v1_xboole_0(k10_amistd_2(A,B,C,D))
        & v1_finset_1(k10_amistd_2(A,B,C,D))
        & v1_setfam_1(k10_amistd_2(A,B,C,D))
        & v1_ami_3(k10_amistd_2(A,B,C,D),A,B) ) ) )).

fof(cc10_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v6_amistd_2(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( v5_amistd_1(C,A,B)
           => ( ~ v1_xboole_0(C)
              & v4_amistd_2(C,A,B)
              & v10_amistd_2(C,A,B) ) ) ) ) )).

fof(cc11_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v6_amistd_2(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( v3_ami_1(C,A,B)
           => ( ~ v1_xboole_0(C)
              & v4_amistd_2(C,A,B)
              & v10_amistd_2(C,A,B) ) ) ) ) )).

fof(cc12_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( v3_ami_1(C,A,B)
           => ( ~ v1_xboole_0(C)
              & v12_amistd_2(C,A,B) ) ) ) ) )).

fof(fc27_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ( ~ v3_struct_0(k4_amistd_1(A))
        & v1_ami_1(k4_amistd_1(A),A)
        & ~ v2_ami_1(k4_amistd_1(A),A)
        & v4_ami_1(k4_amistd_1(A),A)
        & v5_ami_1(k4_amistd_1(A),A)
        & v6_ami_1(k4_amistd_1(A),A)
        & v7_ami_1(k4_amistd_1(A),A)
        & v8_ami_1(k4_amistd_1(A),A)
        & v10_ami_1(k4_amistd_1(A),A)
        & v13_ami_1(k4_amistd_1(A),A)
        & v3_amistd_1(k4_amistd_1(A),A)
        & v4_amistd_1(k4_amistd_1(A),A)
        & v2_amistd_2(k4_amistd_1(A),A)
        & v5_amistd_2(k4_amistd_1(A),A)
        & v6_amistd_2(k4_amistd_1(A),A)
        & v7_amistd_2(k4_amistd_1(A),A)
        & v8_amistd_2(k4_amistd_1(A),A)
        & v11_amistd_2(k4_amistd_1(A),A)
        & v13_amistd_2(k4_amistd_1(A),A) ) ) )).

fof(rc6_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ? [B] :
          ( l1_ami_1(B,A)
          & ~ v3_struct_0(B)
          & ~ v2_ami_1(B,A)
          & v4_ami_1(B,A)
          & v5_ami_1(B,A)
          & v7_ami_1(B,A)
          & v8_ami_1(B,A)
          & v10_ami_1(B,A)
          & v13_ami_1(B,A)
          & v3_amistd_1(B,A)
          & v4_amistd_1(B,A)
          & v2_amistd_2(B,A)
          & v5_amistd_2(B,A)
          & v6_amistd_2(B,A)
          & v7_amistd_2(B,A)
          & v8_amistd_2(B,A)
          & v11_amistd_2(B,A)
          & v13_amistd_2(B,A) ) ) )).

fof(cc13_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & v11_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( ~ v1_xboole_0(C)
            & v10_amistd_2(C,A,B) ) ) ) )).

fof(cc14_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & v13_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => ( ~ v1_xboole_0(C)
            & v12_amistd_2(C,A,B) ) ) ) )).

fof(fc28_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & v1_realset1(C)
        & m1_ami_1(C,A,B) )
     => ( v1_relat_1(k11_amistd_2(A,B,C))
        & v1_funct_1(k11_amistd_2(A,B,C))
        & v1_xboole_0(k11_amistd_2(A,B,C))
        & v1_finset_1(k11_amistd_2(A,B,C))
        & v1_setfam_1(k11_amistd_2(A,B,C))
        & v1_ami_3(k11_amistd_2(A,B,C),A,B)
        & v1_membered(k11_amistd_2(A,B,C))
        & v2_membered(k11_amistd_2(A,B,C))
        & v3_membered(k11_amistd_2(A,B,C))
        & v4_membered(k11_amistd_2(A,B,C))
        & v5_membered(k11_amistd_2(A,B,C))
        & v9_amistd_1(k11_amistd_2(A,B,C),A,B) ) ) )).

fof(fc29_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & m1_ami_1(C,A,B) )
     => ( v1_relat_1(k11_amistd_2(A,B,C))
        & v1_funct_1(k11_amistd_2(A,B,C))
        & v1_finset_1(k11_amistd_2(A,B,C))
        & v1_setfam_1(k11_amistd_2(A,B,C))
        & v1_ami_3(k11_amistd_2(A,B,C),A,B) ) ) )).

fof(fc30_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & v9_amistd_1(C,A,B)
        & m1_ami_1(C,A,B) )
     => ( v1_relat_1(k11_amistd_2(A,B,C))
        & v1_funct_1(k11_amistd_2(A,B,C))
        & v1_finset_1(k11_amistd_2(A,B,C))
        & v1_setfam_1(k11_amistd_2(A,B,C))
        & v1_ami_3(k11_amistd_2(A,B,C),A,B)
        & v9_amistd_1(k11_amistd_2(A,B,C),A,B) ) ) )).

fof(fc31_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & m1_ami_1(C,A,B)
        & ~ v1_xboole_0(D)
        & v1_ami_3(D,A,B)
        & m1_ami_1(D,A,B) )
     => ( v1_relat_1(k12_amistd_2(A,B,C,D))
        & v1_funct_1(k12_amistd_2(A,B,C,D))
        & ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
        & v1_finset_1(k12_amistd_2(A,B,C,D))
        & v1_setfam_1(k12_amistd_2(A,B,C,D))
        & v1_ami_3(k12_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc32_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & v9_amistd_1(C,A,B)
        & m1_ami_1(C,A,B)
        & ~ v1_xboole_0(D)
        & v1_ami_3(D,A,B)
        & v9_amistd_1(D,A,B)
        & m1_ami_1(D,A,B) )
     => ( v1_relat_1(k12_amistd_2(A,B,C,D))
        & v1_funct_1(k12_amistd_2(A,B,C,D))
        & ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
        & v1_finset_1(k12_amistd_2(A,B,C,D))
        & v1_setfam_1(k12_amistd_2(A,B,C,D))
        & v1_ami_3(k12_amistd_2(A,B,C,D),A,B)
        & v9_amistd_1(k12_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc33_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v7_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v6_amistd_2(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & v9_amistd_1(C,A,B)
        & m1_ami_1(C,A,B)
        & ~ v1_xboole_0(D)
        & v1_ami_3(D,A,B)
        & v9_amistd_1(D,A,B)
        & v10_amistd_1(D,A,B)
        & m1_ami_1(D,A,B) )
     => ( v1_relat_1(k12_amistd_2(A,B,C,D))
        & v1_funct_1(k12_amistd_2(A,B,C,D))
        & ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
        & v1_finset_1(k12_amistd_2(A,B,C,D))
        & v1_setfam_1(k12_amistd_2(A,B,C,D))
        & v1_ami_3(k12_amistd_2(A,B,C,D),A,B)
        & v9_amistd_1(k12_amistd_2(A,B,C,D),A,B)
        & v10_amistd_1(k12_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc34_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v7_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v6_amistd_2(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & v9_amistd_1(C,A,B)
        & v10_amistd_1(C,A,B)
        & v11_amistd_1(C,A,B)
        & m1_ami_1(C,A,B)
        & ~ v1_xboole_0(D)
        & v1_ami_3(D,A,B)
        & v9_amistd_1(D,A,B)
        & v10_amistd_1(D,A,B)
        & v11_amistd_1(D,A,B)
        & m1_ami_1(D,A,B) )
     => ( v1_relat_1(k12_amistd_2(A,B,C,D))
        & v1_funct_1(k12_amistd_2(A,B,C,D))
        & ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
        & v1_finset_1(k12_amistd_2(A,B,C,D))
        & v1_setfam_1(k12_amistd_2(A,B,C,D))
        & v1_ami_3(k12_amistd_2(A,B,C,D),A,B)
        & v9_amistd_1(k12_amistd_2(A,B,C,D),A,B)
        & v10_amistd_1(k12_amistd_2(A,B,C,D),A,B)
        & v11_amistd_1(k12_amistd_2(A,B,C,D),A,B) ) ) )).

fof(fc35_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v7_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & v11_amistd_2(B,A)
        & v13_amistd_2(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & v6_amistd_1(C,A,B)
        & v9_amistd_1(C,A,B)
        & m1_ami_1(C,A,B)
        & ~ v1_xboole_0(D)
        & v1_ami_3(D,A,B)
        & v6_amistd_1(D,A,B)
        & v9_amistd_1(D,A,B)
        & m1_ami_1(D,A,B) )
     => ( v1_relat_1(k12_amistd_2(A,B,C,D))
        & v1_funct_1(k12_amistd_2(A,B,C,D))
        & ~ v1_xboole_0(k12_amistd_2(A,B,C,D))
        & v1_finset_1(k12_amistd_2(A,B,C,D))
        & v1_setfam_1(k12_amistd_2(A,B,C,D))
        & v1_ami_3(k12_amistd_2(A,B,C,D),A,B)
        & v6_amistd_1(k12_amistd_2(A,B,C,D),A,B)
        & v7_amistd_1(k12_amistd_2(A,B,C,D),A,B)
        & v8_amistd_1(k12_amistd_2(A,B,C,D),A,B)
        & v9_amistd_1(k12_amistd_2(A,B,C,D),A,B) ) ) )).

fof(t1_amistd_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( r2_tarski(k1_relat_1(A),k1_relat_1(B))
          <=> r2_tarski(A,B) ) ) ) )).

fof(t2_amistd_2,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finset_1(B) )
         => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
           => k4_card_1(k1_funct_4(A,B)) = k1_nat_1(k4_card_1(A),k4_card_1(B)) ) ) ) )).

fof(t3_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] :
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k4_xboole_0(k1_relat_1(B),k1_relat_1(C)))
           => k1_funct_1(k4_xboole_0(B,C),A) = k1_funct_1(B,A) ) ) ) )).

fof(t4_amistd_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A) )
     => k6_xcmplx_0(k4_card_1(A),np__1) = k5_binarith(k4_card_1(A),np__1) ) )).

fof(d1_amistd_2,axiom,(
    ! [A] :
      ( v1_fraenkel(A)
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( ~ v1_xboole_0(A)
             => ( B = k1_amistd_2(A)
              <=> ( ! [C] :
                      ( r2_hidden(C,k1_relat_1(B))
                    <=> ! [D] :
                          ( ( v1_relat_1(D)
                            & v1_funct_1(D) )
                         => ( r2_hidden(D,A)
                           => r2_hidden(C,k1_relat_1(D)) ) ) )
                  & ! [C] :
                      ( r2_hidden(C,k1_relat_1(B))
                     => k1_funct_1(B,C) = k5_card_3(C,A) ) ) ) )
            & ( v1_xboole_0(A)
             => ( B = k1_amistd_2(A)
              <=> B = k1_xboole_0 ) ) ) ) ) )).

fof(d2_amistd_2,axiom,(
    ! [A] :
      ( v1_amistd_2(A)
    <=> ? [B] :
          ( v1_relat_1(B)
          & v1_funct_1(B)
          & A = k4_card_3(B) ) ) )).

fof(t7_amistd_2,axiom,(
    ! [A] :
      ( ( v1_fraenkel(A)
        & v1_pralg_2(A) )
     => k1_relat_1(k1_amistd_2(A)) = k1_pralg_2(A) ) )).

fof(t8_amistd_2,axiom,(
    ! [A] :
      ( v1_fraenkel(A)
     => ! [B] :
          ( r2_hidden(B,k1_relat_1(k1_amistd_2(A)))
         => k1_funct_1(k1_amistd_2(A),B) = k5_card_3(B,A) ) ) )).

fof(t9_amistd_2,axiom,(
    ! [A] :
      ( ( v1_fraenkel(A)
        & v1_pralg_2(A) )
     => r1_tarski(A,k4_card_3(k1_amistd_2(A))) ) )).

fof(t10_amistd_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_amistd_2(A) )
     => A = k4_card_3(k1_amistd_2(A)) ) )).

fof(t11_amistd_2,axiom,(
    ! [A,B,C] :
      ( l1_ami_1(C,B)
     => ! [D] :
          ( m1_ami_1(D,B,C)
         => m1_ami_1(k4_xboole_0(D,A),B,C) ) ) )).

fof(t12_amistd_2,axiom,(
    ! [A,B] :
      ( v1_setfam_1(B)
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & ~ v2_ami_1(C,B)
            & v5_ami_1(C,B)
            & v8_ami_1(C,B)
            & l1_ami_1(C,B) )
         => ! [D] :
              ( ( v1_ami_3(D,B,C)
                & m1_ami_1(D,B,C) )
             => ( v1_ami_3(k4_xboole_0(D,A),B,C)
                & m1_ami_1(k4_xboole_0(D,A),B,C) ) ) ) ) )).

fof(t13_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ( k1_relat_1(C) = k1_relat_1(D)
                   => v9_amistd_1(D,A,B) ) ) ) ) ) )).

fof(t14_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ~ ( r2_hidden(D,k1_relat_1(C))
                      & r1_xreal_0(k4_card_1(C),k7_amistd_1(A,B,D)) ) ) ) ) ) )).

fof(d3_amistd_2,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
         => k3_amistd_2(A,B,C) = k3_domain_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B))),C) ) ) )).

fof(t16_amistd_2,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
         => ! [D] :
              ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( ( k1_ami_5(A,B,C) = k1_ami_5(A,B,D)
                  & k4_amistd_2(A,B,C) = k4_amistd_2(A,B,D) )
               => C = D ) ) ) ) )).

fof(d4_amistd_2,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ( v2_amistd_2(B,A)
      <=> ! [C] :
            ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
           => ! [D] :
                ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
               => ( k1_ami_5(A,B,C) = k1_ami_5(A,B,D)
                 => k4_finseq_1(k4_amistd_2(A,B,C)) = k4_finseq_1(k4_amistd_2(A,B,D)) ) ) ) ) ) )).

fof(t17_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(A,k4_amistd_1(A)),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(k4_amistd_1(A))))),u4_ami_1(A,k4_amistd_1(A)))
         => k4_amistd_2(A,k4_amistd_1(A),B) = np__0 ) ) )).

fof(d6_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v3_amistd_2(C,A,B)
              <=> ! [D] :
                    ~ ( r2_hidden(D,k2_amistd_1(A,B,C))
                      & ! [E] :
                          ~ ( r2_hidden(E,k4_finseq_1(k4_amistd_2(A,B,C)))
                            & D = k1_funct_1(k4_amistd_2(A,B,C),E)
                            & k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),E) = u2_ami_1(A,B) ) ) ) ) ) ) )).

fof(d7_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v4_amistd_2(C,A,B)
              <=> ! [D] :
                    ( ? [E] :
                        ( r2_hidden(E,k4_finseq_1(k4_amistd_2(A,B,C)))
                        & D = k1_funct_1(k4_amistd_2(A,B,C),E)
                        & k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),E) = u2_ami_1(A,B) )
                   => r2_hidden(D,k2_amistd_1(A,B,C)) ) ) ) ) ) )).

fof(d8_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ( v5_amistd_2(B,A)
          <=> ! [C] :
                ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
               => v3_amistd_2(C,A,B) ) ) ) ) )).

fof(d9_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ( v6_amistd_2(B,A)
          <=> ! [C] :
                ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
               => v4_amistd_2(C,A,B) ) ) ) ) )).

fof(d10_amistd_2,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ( v7_amistd_2(B,A)
      <=> ~ v1_realset1(u2_ami_1(A,B)) ) ) )).

fof(t18_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( ! [D] :
                    ( m1_struct_0(D,B,u2_ami_1(A,B))
                   => k1_amistd_1(A,B,D,C) = k1_struct_0(B,k9_amistd_1(A,B,D)) )
               => v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) )).

fof(d11_amistd_2,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ( v8_amistd_2(B,A)
      <=> ! [C] :
            ( m1_subset_1(C,u3_ami_1(A,B))
           => v1_amistd_2(k5_amistd_2(A,B,C)) ) ) ) )).

fof(t19_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( m1_subset_1(B,u3_ami_1(A,k4_amistd_1(A)))
         => k5_amistd_2(A,k4_amistd_1(A),B) = k6_domain_1(k5_numbers,np__0) ) ) )).

fof(t20_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v2_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ! [D] :
                  ( ( r2_hidden(D,k4_finseq_1(k4_amistd_2(A,B,C)))
                    & k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),D) = u2_ami_1(A,B) )
                 => m1_struct_0(k1_funct_1(k4_amistd_2(A,B,C),D),B,u2_ami_1(A,B)) ) ) ) ) )).

fof(t21_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & v7_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v3_ami_1(C,A,B)
               => v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) )).

fof(d12_amistd_2,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
         => ( v9_amistd_2(C,A,B)
          <=> ! [D] :
                ~ ( r2_hidden(D,k4_finseq_1(k4_amistd_2(A,B,C)))
                  & k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),D) = u2_ami_1(A,B) ) ) ) ) )).

fof(t22_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & v5_amistd_2(B,A)
            & v7_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v9_amistd_2(C,A,B)
               => v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) )).

fof(t23_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & v6_amistd_2(B,A)
            & v7_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v3_ami_1(C,A,B)
               => v9_amistd_2(C,A,B) ) ) ) ) )).

fof(t24_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v6_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v5_amistd_1(C,A,B)
               => v9_amistd_2(C,A,B) ) ) ) ) )).

fof(d13_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => k6_amistd_2(A,B) = k14_ami_3(A,B,k5_amistd_1(A,B,np__0),k5_ami_1(A,B)) ) ) )).

fof(t25_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => k4_card_1(k6_amistd_2(A,B)) = np__1 ) ) )).

fof(t26_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & v10_amistd_1(C,A,B)
                & v11_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ( k4_card_1(C) = np__1
               => C = k6_amistd_2(A,B) ) ) ) ) )).

fof(t27_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => k10_amistd_1(A,B,k6_amistd_2(A,B)) = k5_amistd_1(A,B,np__0) ) ) )).

fof(d14_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ! [D] :
                  ( v4_ordinal2(D)
                 => ! [E] :
                      ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                     => ( E = k8_amistd_2(A,B,C,D)
                      <=> ( k1_ami_5(A,B,E) = k1_ami_5(A,B,C)
                          & k4_finseq_1(k4_amistd_2(A,B,E)) = k4_finseq_1(k4_amistd_2(A,B,C))
                          & ! [F] :
                              ( r2_hidden(F,k4_finseq_1(k4_amistd_2(A,B,C)))
                             => ( ~ ( k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),F) = u2_ami_1(A,B)
                                    & ! [G] :
                                        ( m1_struct_0(G,B,u2_ami_1(A,B))
                                       => ~ ( G = k1_funct_1(k4_amistd_2(A,B,C),F)
                                            & k1_funct_1(k4_amistd_2(A,B,E),F) = k5_amistd_1(A,B,k2_xcmplx_0(D,k7_amistd_1(A,B,G))) ) ) )
                                & ( k1_funct_1(k1_amistd_2(k5_amistd_2(A,B,k1_ami_5(A,B,C))),F) != u2_ami_1(A,B)
                                 => k1_funct_1(k4_amistd_2(A,B,E),F) = k1_funct_1(k4_amistd_2(A,B,C),F) ) ) ) ) ) ) ) ) ) ) )).

fof(t28_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => k8_amistd_2(A,B,C,np__0) = C ) ) ) )).

fof(t29_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v4_amistd_1(C,B)
                & v8_amistd_2(C,B)
                & l1_ami_1(C,B) )
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
                 => ( v9_amistd_2(D,B,C)
                   => k8_amistd_2(B,C,D,A) = D ) ) ) ) ) )).

fof(t30_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v4_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v10_ami_1(C,B)
                & v4_amistd_1(C,B)
                & v6_amistd_2(C,B)
                & v8_amistd_2(C,B)
                & l1_ami_1(C,B) )
             => k8_amistd_2(B,C,k5_ami_1(B,C),A) = k5_ami_1(B,C) ) ) ) )).

fof(t31_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v4_amistd_1(C,B)
                & v8_amistd_2(C,B)
                & l1_ami_1(C,B) )
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
                 => k5_amistd_2(B,C,k1_ami_5(B,C,D)) = k5_amistd_2(B,C,k1_ami_5(B,C,k8_amistd_2(B,C,D,A))) ) ) ) ) )).

fof(t32_amistd_2,axiom,(
    ! [A,B] :
      ( v1_setfam_1(B)
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & ~ v2_ami_1(C,B)
            & v5_ami_1(C,B)
            & v8_ami_1(C,B)
            & v4_amistd_1(C,B)
            & v8_amistd_2(C,B)
            & l1_ami_1(C,B) )
         => ! [D] :
              ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
             => ! [E] :
                  ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
                 => ( k1_funct_1(k1_amistd_2(k5_amistd_2(B,C,k1_ami_5(B,C,D))),A) = u2_ami_1(B,C)
                   => ( ! [F] :
                          ( v4_ordinal2(F)
                         => k8_amistd_2(B,C,D,F) != k8_amistd_2(B,C,E,F) )
                      | k1_funct_1(k1_amistd_2(k5_amistd_2(B,C,k1_ami_5(B,C,E))),A) = u2_ami_1(B,C) ) ) ) ) ) ) )).

fof(t33_amistd_2,axiom,(
    ! [A,B] :
      ( v1_setfam_1(B)
     => ! [C] :
          ( ( ~ v3_struct_0(C)
            & ~ v2_ami_1(C,B)
            & v5_ami_1(C,B)
            & v8_ami_1(C,B)
            & v4_amistd_1(C,B)
            & v8_amistd_2(C,B)
            & l1_ami_1(C,B) )
         => ! [D] :
              ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
             => ! [E] :
                  ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
                 => ~ ( ? [F] :
                          ( v4_ordinal2(F)
                          & k8_amistd_2(B,C,D,F) = k8_amistd_2(B,C,E,F) )
                      & k1_funct_1(k1_amistd_2(k5_amistd_2(B,C,k1_ami_5(B,C,D))),A) != u2_ami_1(B,C)
                      & k1_funct_1(k1_amistd_2(k5_amistd_2(B,C,k1_ami_5(B,C,E))),A) = u2_ami_1(B,C) ) ) ) ) ) )).

fof(t34_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                 => ( ? [E] :
                        ( v4_ordinal2(E)
                        & k8_amistd_2(A,B,C,E) = k8_amistd_2(A,B,D,E) )
                   => C = D ) ) ) ) ) )).

fof(t35_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v4_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v10_ami_1(C,B)
                & v4_amistd_1(C,B)
                & v6_amistd_2(C,B)
                & v8_amistd_2(C,B)
                & l1_ami_1(C,B) )
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
                 => ( k8_amistd_2(B,C,D,A) = k5_ami_1(B,C)
                   => D = k5_ami_1(B,C) ) ) ) ) ) )).

fof(t36_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v4_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v10_ami_1(C,B)
                & v4_amistd_1(C,B)
                & v6_amistd_2(C,B)
                & v8_amistd_2(C,B)
                & l1_ami_1(C,B) )
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
                 => ( v5_amistd_1(D,B,C)
                   => v5_amistd_1(k8_amistd_2(B,C,D,A),B,C) ) ) ) ) ) )).

fof(t37_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v4_ordinal2(B)
         => ! [C] :
              ( v1_setfam_1(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & ~ v2_ami_1(D,C)
                    & v5_ami_1(D,C)
                    & v8_ami_1(D,C)
                    & v4_amistd_1(D,C)
                    & v8_amistd_2(D,C)
                    & l1_ami_1(D,C) )
                 => ! [E] :
                      ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(C,D),k13_finseq_1(k2_xboole_0(k3_tarski(C),u1_struct_0(D)))),u4_ami_1(C,D))
                     => k8_amistd_2(C,D,k8_amistd_2(C,D,E,A),B) = k8_amistd_2(C,D,E,k2_xcmplx_0(A,B)) ) ) ) ) ) )).

fof(d15_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( v4_ordinal2(D)
                 => ! [E] :
                      ( m1_ami_1(E,A,B)
                     => ( E = k9_amistd_2(A,B,C,D)
                      <=> ( k1_relat_1(E) = k1_relat_1(C)
                          & ! [F] :
                              ( v4_ordinal2(F)
                             => ( r2_hidden(k5_amistd_1(A,B,F),k1_relat_1(C))
                               => k1_funct_1(E,k5_amistd_1(A,B,F)) = k8_amistd_2(A,B,k5_ami_5(A,B,C,k5_amistd_1(A,B,F)),D) ) ) ) ) ) ) ) ) ) )).

fof(t38_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => k9_amistd_2(A,B,C,np__0) = C ) ) ) )).

fof(t39_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v4_ordinal2(B)
         => ! [C] :
              ( v1_setfam_1(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & ~ v2_ami_1(D,C)
                    & v5_ami_1(D,C)
                    & v8_ami_1(D,C)
                    & v4_amistd_1(D,C)
                    & v8_amistd_2(D,C)
                    & l1_ami_1(D,C) )
                 => ! [E] :
                      ( ( v1_ami_3(E,C,D)
                        & v9_amistd_1(E,C,D)
                        & m1_ami_1(E,C,D) )
                     => k9_amistd_2(C,D,k9_amistd_2(C,D,E,A),B) = k9_amistd_2(C,D,E,k2_xcmplx_0(A,B)) ) ) ) ) ) )).

fof(t40_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => k10_amistd_2(A,B,C,np__0) = C ) ) ) )).

fof(t41_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_ami_1(C,A,B)
             => ! [D] :
                  ( v4_ordinal2(D)
                 => ~ ( ~ r1_xreal_0(D,np__0)
                      & r2_hidden(k5_amistd_1(A,B,np__0),k1_relat_1(k10_amistd_2(A,B,C,D))) ) ) ) ) ) )).

fof(t42_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v4_ordinal2(B)
         => ! [C] :
              ( v1_setfam_1(C)
             => ! [D] :
                  ( ( ~ v3_struct_0(D)
                    & ~ v2_ami_1(D,C)
                    & v5_ami_1(D,C)
                    & v8_ami_1(D,C)
                    & v4_amistd_1(D,C)
                    & l1_ami_1(D,C) )
                 => ! [E] :
                      ( m1_ami_1(E,C,D)
                     => k10_amistd_2(C,D,k10_amistd_2(C,D,E,A),B) = k10_amistd_2(C,D,E,k2_xcmplx_0(A,B)) ) ) ) ) ) )).

fof(t43_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v4_amistd_1(C,B)
                & l1_ami_1(C,B) )
             => ! [D] :
                  ( ( v1_ami_3(D,B,C)
                    & m1_ami_1(D,B,C) )
                 => r2_tarski(k1_relat_1(D),k1_relat_1(k10_amistd_2(B,C,D,A))) ) ) ) ) )).

fof(d17_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v10_amistd_2(C,A,B)
              <=> ! [D] :
                    ( v4_ordinal2(D)
                   => ! [E] :
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
                       => ! [F] :
                            ( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
                           => ( F = k1_funct_4(E,k3_cqc_lang(k2_ami_1(A,B),k8_amistd_1(A,B,k6_ami_1(A,B,E),D)))
                             => k8_amistd_1(A,B,k6_ami_1(A,B,k4_ami_1(A,B,C,E)),D) = k6_ami_1(A,B,k4_ami_1(A,B,k8_amistd_2(A,B,C,D),F)) ) ) ) ) ) ) ) ) )).

fof(d18_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ( v11_amistd_2(B,A)
          <=> ! [C] :
                ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
               => v10_amistd_2(C,A,B) ) ) ) ) )).

fof(d19_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v12_amistd_2(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => ! [E] :
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
                       => ( r1_funct_7(D,E,u2_ami_1(A,B))
                         => r1_funct_7(k4_ami_1(A,B,C,D),k4_ami_1(A,B,C,E),u2_ami_1(A,B)) ) ) ) ) ) ) ) )).

fof(d20_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ( v13_amistd_2(B,A)
          <=> ! [C] :
                ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
               => v12_amistd_2(C,A,B) ) ) ) ) )).

fof(t44_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v6_amistd_2(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v5_amistd_1(C,A,B)
               => v10_amistd_2(C,A,B) ) ) ) ) )).

fof(t45_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v6_amistd_2(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v3_ami_1(C,A,B)
               => v10_amistd_2(C,A,B) ) ) ) ) )).

fof(t46_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ( v3_ami_1(C,A,B)
               => v12_amistd_2(C,A,B) ) ) ) ) )).

fof(d21_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => k11_amistd_2(A,B,C) = k4_xboole_0(C,k3_cqc_lang(k10_amistd_1(A,B,C),k1_funct_1(C,k10_amistd_1(A,B,C)))) ) ) ) )).

fof(t47_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => k1_relat_1(k11_amistd_2(A,B,C)) = k4_xboole_0(k1_relat_1(C),k1_struct_0(B,k10_amistd_1(A,B,C))) ) ) ) )).

fof(t48_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => k1_relat_1(C) = k2_xboole_0(k1_relat_1(k11_amistd_2(A,B,C)),k1_struct_0(B,k10_amistd_1(A,B,C))) ) ) ) )).

fof(t49_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => k4_card_1(k11_amistd_2(A,B,C)) = k6_xcmplx_0(k4_card_1(C),np__1) ) ) ) )).

fof(t50_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => r1_xboole_0(k1_relat_1(k11_amistd_2(A,B,C)),k1_relat_1(k10_amistd_2(A,B,k9_amistd_2(A,B,D,k5_binarith(k4_card_1(C),np__1)),k5_binarith(k4_card_1(C),np__1)))) ) ) ) ) )).

fof(t51_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & v11_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ~ ( r2_hidden(D,k1_relat_1(k11_amistd_2(A,B,C)))
                      & k1_funct_1(k11_amistd_2(A,B,C),D) = k5_ami_1(A,B) ) ) ) ) ) )).

fof(d22_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => k12_amistd_2(A,B,C,D) = k1_scmfsa_4(A,B,k11_amistd_2(A,B,C),k10_amistd_2(A,B,k9_amistd_2(A,B,D,k5_binarith(k4_card_1(C),np__1)),k5_binarith(k4_card_1(C),np__1))) ) ) ) ) )).

fof(t52_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ( k4_card_1(k12_amistd_2(A,B,C,D)) = k6_xcmplx_0(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__1)
                    & k4_card_1(k12_amistd_2(A,B,C,D)) = k5_binarith(k1_nat_1(k4_card_1(C),k4_card_1(D)),np__1) ) ) ) ) ) )).

fof(t53_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & v9_amistd_1(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => r1_tarski(k1_relat_1(C),k1_relat_1(k12_amistd_2(A,B,C,D))) ) ) ) ) )).

fof(t54_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & v9_amistd_1(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => r1_tarski(k11_amistd_2(A,B,C),k11_amistd_2(A,B,k12_amistd_2(A,B,C,D))) ) ) ) ) )).

fof(t55_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & v9_amistd_1(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => k1_funct_1(k12_amistd_2(A,B,C,D),k10_amistd_1(A,B,C)) = k1_funct_1(k9_amistd_2(A,B,D,k5_binarith(k4_card_1(C),np__1)),k5_amistd_1(A,B,np__0)) ) ) ) ) )).

fof(t56_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & v9_amistd_1(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ! [E] :
                      ( m1_struct_0(E,B,u2_ami_1(A,B))
                     => ( ~ r1_xreal_0(k6_xcmplx_0(k4_card_1(C),np__1),k7_amistd_1(A,B,E))
                       => k1_funct_1(k9_amistd_2(A,B,C,k5_binarith(k4_card_1(C),np__1)),E) = k1_funct_1(k9_amistd_2(A,B,k12_amistd_2(A,B,C,D),k5_binarith(k4_card_1(C),np__1)),E) ) ) ) ) ) ) )).

fof(t57_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v4_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v10_ami_1(C,B)
                & v4_amistd_1(C,B)
                & v6_amistd_2(C,B)
                & v8_amistd_2(C,B)
                & l1_ami_1(C,B) )
             => k9_amistd_2(B,C,k7_amistd_2(B,C),A) = k7_amistd_2(B,C) ) ) ) )).

fof(t58_amistd_2,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v4_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v4_amistd_1(C,B)
                & l1_ami_1(C,B) )
             => k10_amistd_2(B,C,k7_amistd_2(B,C),A) = k14_ami_3(B,C,k5_amistd_1(B,C,A),k5_ami_1(B,C)) ) ) ) )).

fof(t59_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v6_amistd_2(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & v10_amistd_1(C,A,B)
                & v11_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => k12_amistd_2(A,B,C,k7_amistd_2(A,B)) = C ) ) ) )).

fof(t60_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & v10_amistd_1(C,A,B)
                & v11_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => k12_amistd_2(A,B,k7_amistd_2(A,B),C) = C ) ) ) )).

fof(t61_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & v10_ami_1(B,A)
            & v4_amistd_1(B,A)
            & v6_amistd_2(B,A)
            & v8_amistd_2(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & v10_amistd_1(C,A,B)
                & v11_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & v9_amistd_1(D,A,B)
                    & v10_amistd_1(D,A,B)
                    & v11_amistd_1(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ! [E] :
                      ( ( ~ v1_xboole_0(E)
                        & v1_ami_3(E,A,B)
                        & v9_amistd_1(E,A,B)
                        & v10_amistd_1(E,A,B)
                        & v11_amistd_1(E,A,B)
                        & m1_ami_1(E,A,B) )
                     => k13_amistd_2(A,B,k13_amistd_2(A,B,C,D),E) = k13_amistd_2(A,B,C,k13_amistd_2(A,B,D,E)) ) ) ) ) ) )).

fof(dt_k1_amistd_2,axiom,(
    ! [A] :
      ( v1_fraenkel(A)
     => ( v1_relat_1(k1_amistd_2(A))
        & v1_funct_1(k1_amistd_2(A)) ) ) )).

fof(dt_k2_amistd_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u2_ami_1(A,B))
        & m1_subset_1(D,u2_ami_1(A,B))
        & m1_subset_1(E,u4_ami_1(A,B))
        & m1_subset_1(F,u4_ami_1(A,B)) )
     => m1_ami_1(k2_amistd_2(A,B,C,D,E,F),A,B) ) )).

fof(redefinition_k2_amistd_2,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u2_ami_1(A,B))
        & m1_subset_1(D,u2_ami_1(A,B))
        & m1_subset_1(E,u4_ami_1(A,B))
        & m1_subset_1(F,u4_ami_1(A,B)) )
     => k2_amistd_2(A,B,C,D,E,F) = k4_funct_4(C,D,E,F) ) )).

fof(dt_k3_amistd_2,axiom,(
    $true )).

fof(dt_k4_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => m2_finseq_1(k4_amistd_2(A,B,C),k2_xboole_0(k3_tarski(A),u1_struct_0(B))) ) )).

fof(redefinition_k4_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => k4_amistd_2(A,B,C) = k3_amistd_2(A,B,C) ) )).

fof(dt_k5_amistd_2,axiom,(
    $true )).

fof(dt_k6_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A) )
     => m1_ami_1(k6_amistd_2(A,B),A,B) ) )).

fof(dt_k7_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A) )
     => ( ~ v1_xboole_0(k7_amistd_2(A,B))
        & v1_ami_3(k7_amistd_2(A,B),A,B)
        & v9_amistd_1(k7_amistd_2(A,B),A,B)
        & v10_amistd_1(k7_amistd_2(A,B),A,B)
        & v11_amistd_1(k7_amistd_2(A,B),A,B)
        & m1_ami_1(k7_amistd_2(A,B),A,B) ) ) )).

fof(redefinition_k7_amistd_2,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A) )
     => k7_amistd_2(A,B) = k6_amistd_2(A,B) ) )).

fof(dt_k8_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B))
        & v4_ordinal2(D) )
     => m2_subset_1(k8_amistd_2(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) )).

fof(dt_k9_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & v1_ami_3(C,A,B)
        & m1_ami_1(C,A,B)
        & v4_ordinal2(D) )
     => m1_ami_1(k9_amistd_2(A,B,C,D),A,B) ) )).

fof(dt_k10_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & m1_ami_1(C,A,B)
        & v4_ordinal2(D) )
     => m1_ami_1(k10_amistd_2(A,B,C,D),A,B) ) )).

fof(dt_k11_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & m1_ami_1(C,A,B) )
     => m1_ami_1(k11_amistd_2(A,B,C),A,B) ) )).

fof(dt_k12_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v8_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & m1_ami_1(C,A,B)
        & ~ v1_xboole_0(D)
        & v1_ami_3(D,A,B)
        & m1_ami_1(D,A,B) )
     => m1_ami_1(k12_amistd_2(A,B,C,D),A,B) ) )).

fof(dt_k13_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v7_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v6_amistd_2(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & v9_amistd_1(C,A,B)
        & v10_amistd_1(C,A,B)
        & v11_amistd_1(C,A,B)
        & m1_ami_1(C,A,B)
        & ~ v1_xboole_0(D)
        & v1_ami_3(D,A,B)
        & v9_amistd_1(D,A,B)
        & v10_amistd_1(D,A,B)
        & v11_amistd_1(D,A,B)
        & m1_ami_1(D,A,B) )
     => ( ~ v1_xboole_0(k13_amistd_2(A,B,C,D))
        & v1_ami_3(k13_amistd_2(A,B,C,D),A,B)
        & v9_amistd_1(k13_amistd_2(A,B,C,D),A,B)
        & v10_amistd_1(k13_amistd_2(A,B,C,D),A,B)
        & v11_amistd_1(k13_amistd_2(A,B,C,D),A,B)
        & m1_ami_1(k13_amistd_2(A,B,C,D),A,B) ) ) )).

fof(redefinition_k13_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v4_ami_1(B,A)
        & v5_ami_1(B,A)
        & v7_ami_1(B,A)
        & v8_ami_1(B,A)
        & v10_ami_1(B,A)
        & v4_amistd_1(B,A)
        & v6_amistd_2(B,A)
        & v8_amistd_2(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & v1_ami_3(C,A,B)
        & v9_amistd_1(C,A,B)
        & v10_amistd_1(C,A,B)
        & v11_amistd_1(C,A,B)
        & m1_ami_1(C,A,B)
        & ~ v1_xboole_0(D)
        & v1_ami_3(D,A,B)
        & v9_amistd_1(D,A,B)
        & v10_amistd_1(D,A,B)
        & v11_amistd_1(D,A,B)
        & m1_ami_1(D,A,B) )
     => k13_amistd_2(A,B,C,D) = k12_amistd_2(A,B,C,D) ) )).

fof(t5_amistd_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A) )
     => k1_relat_1(k1_amistd_2(A)) = k1_setfam_1(a_1_0_amistd_2(A)) ) )).

fof(t6_amistd_2,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_fraenkel(A) )
     => ! [B] :
          ( r2_hidden(B,k1_relat_1(k1_amistd_2(A)))
         => k1_funct_1(k1_amistd_2(A),B) = a_2_0_amistd_2(A,B) ) ) )).

fof(t15_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => k1_relat_1(C) = a_3_0_amistd_2(A,B,C) ) ) ) )).

fof(d5_amistd_2,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,u3_ami_1(A,B))
         => k5_amistd_2(A,B,C) = a_3_1_amistd_2(A,B,C) ) ) )).

fof(d16_amistd_2,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_ami_1(C,A,B)
             => ! [D] :
                  ( v4_ordinal2(D)
                 => ! [E] :
                      ( m1_ami_1(E,A,B)
                     => ( E = k10_amistd_2(A,B,C,D)
                      <=> ( k1_relat_1(E) = a_4_0_amistd_2(A,B,C,D)
                          & ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r2_hidden(k5_amistd_1(A,B,F),k1_relat_1(C))
                               => k1_funct_1(E,k5_amistd_1(A,B,k2_xcmplx_0(F,D))) = k1_funct_1(C,k5_amistd_1(A,B,F)) ) ) ) ) ) ) ) ) ) )).

fof(fraenkel_a_1_0_amistd_2,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(B)
        & v1_fraenkel(B) )
     => ( r2_hidden(A,a_1_0_amistd_2(B))
      <=> ? [C] :
            ( m1_subset_1(C,B)
            & A = k1_relat_1(C) ) ) ) )).

fof(fraenkel_a_2_0_amistd_2,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(B)
        & v1_fraenkel(B) )
     => ( r2_hidden(A,a_2_0_amistd_2(B,C))
      <=> ? [D] :
            ( m1_subset_1(D,B)
            & A = k1_funct_1(D,C) ) ) ) )).

fof(fraenkel_a_3_0_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(B)
        & ~ v3_struct_0(C)
        & ~ v2_ami_1(C,B)
        & v5_ami_1(C,B)
        & v8_ami_1(C,B)
        & v4_amistd_1(C,B)
        & l1_ami_1(C,B)
        & v1_ami_3(D,B,C)
        & v9_amistd_1(D,B,C)
        & m1_ami_1(D,B,C) )
     => ( r2_hidden(A,a_3_0_amistd_2(B,C,D))
      <=> ? [E] :
            ( m2_subset_1(E,k1_numbers,k5_numbers)
            & A = k5_amistd_1(B,C,E)
            & ~ r1_xreal_0(k4_card_1(D),E) ) ) ) )).

fof(fraenkel_a_3_1_amistd_2,axiom,(
    ! [A,B,C,D] :
      ( ( l1_ami_1(C,B)
        & m1_subset_1(D,u3_ami_1(B,C)) )
     => ( r2_hidden(A,a_3_1_amistd_2(B,C,D))
      <=> ? [E] :
            ( m2_subset_1(E,k2_zfmisc_1(u3_ami_1(B,C),k13_finseq_1(k2_xboole_0(k3_tarski(B),u1_struct_0(C)))),u4_ami_1(B,C))
            & A = k4_amistd_2(B,C,E)
            & k1_ami_5(B,C,E) = D ) ) ) )).

fof(fraenkel_a_4_0_amistd_2,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_setfam_1(B)
        & ~ v3_struct_0(C)
        & ~ v2_ami_1(C,B)
        & v5_ami_1(C,B)
        & v8_ami_1(C,B)
        & v4_amistd_1(C,B)
        & l1_ami_1(C,B)
        & m1_ami_1(D,B,C)
        & v4_ordinal2(E) )
     => ( r2_hidden(A,a_4_0_amistd_2(B,C,D,E))
      <=> ? [F] :
            ( m2_subset_1(F,k1_numbers,k5_numbers)
            & A = k5_amistd_1(B,C,k2_xcmplx_0(F,E))
            & r2_hidden(k5_amistd_1(B,C,F),k1_relat_1(D)) ) ) ) )).
%------------------------------------------------------------------------------