SET007 Axioms: SET007+646.ax


%------------------------------------------------------------------------------
% File     : SET007+646 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Standard Ordering of Instruction Locations
% 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_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  124 (   3 unit)
%            Number of atoms       : 1273 (  80 equality)
%            Maximal formula depth :   21 (  11 average)
%            Number of connectives : 1391 ( 242 ~  ;   5  |; 759  &)
%                                         (  30 <=>; 355 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   54 (   1 propositional; 0-4 arity)
%            Number of functors    :   73 (   5 constant; 0-4 arity)
%            Number of variables   :  400 (   0 singleton; 378 !;  22 ?)
%            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(rc1_amistd_1,axiom,(
    ? [A] :
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A)
      & ~ v1_realset1(A) ) )).

fof(cc1_amistd_1,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v1_relat_1(A)
        & v1_setfam_1(A) ) ) )).

fof(fc1_amistd_1,axiom,(
    ! [A,B] :
      ( v1_finset_1(A)
     => v1_finset_1(k2_funcop_1(A,B)) ) )).

fof(fc2_amistd_1,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(k3_cqc_lang(A,B))
      & v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B))
      & v1_realset1(k3_cqc_lang(A,B))
      & v1_setfam_1(k3_cqc_lang(A,B)) ) )).

fof(fc3_amistd_1,axiom,(
    ! [A,B] :
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( ~ v1_xboole_0(k3_graph_2(A,B))
        & v1_relat_1(k3_graph_2(A,B))
        & v1_funct_1(k3_graph_2(A,B))
        & v1_finset_1(k3_graph_2(A,B))
        & v1_finseq_1(k3_graph_2(A,B))
        & v1_setfam_1(k3_graph_2(A,B)) ) ) )).

fof(cc2_amistd_1,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => ( v1_xboole_0(C)
           => ( v1_relat_1(C)
              & v1_funct_1(C)
              & v1_finset_1(C)
              & v1_setfam_1(C)
              & v1_ami_3(C,A,B) ) ) ) ) )).

fof(rc2_amistd_1,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v2_funct_1(C)
          & v1_finset_1(C)
          & v1_realset1(C)
          & v1_setfam_1(C)
          & v1_ami_3(C,A,B)
          & v1_membered(C)
          & v2_membered(C)
          & v3_membered(C)
          & v4_membered(C)
          & v5_membered(C) ) ) )).

fof(rc3_amistd_1,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)
        & l1_ami_1(B,A) )
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_realset1(C)
          & v1_setfam_1(C)
          & v1_ami_3(C,A,B) ) ) )).

fof(fc4_amistd_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B))
        & m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) )
     => ( v1_relat_1(k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D))
        & v1_funct_1(k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D))
        & v1_setfam_1(k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D)) ) ) )).

fof(rc4_amistd_1,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v7_ami_1(B,A)
        & v8_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_realset1(C)
          & v1_setfam_1(C)
          & v11_ami_1(C,A,B)
          & v1_ami_3(C,A,B) ) ) )).

fof(cc3_amistd_1,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)
              & v7_ami_1(B,A)
              & v8_ami_1(B,A) )
           => ( ~ v3_struct_0(B)
              & ~ v2_ami_1(B,A)
              & v5_ami_1(B,A)
              & v8_ami_1(B,A)
              & v13_ami_1(B,A) ) ) ) ) )).

fof(fc5_amistd_1,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)
        & v10_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B))
        & m1_subset_1(D,u2_ami_1(A,B)) )
     => ~ v1_xboole_0(k1_amistd_1(A,B,D,C)) ) )).

fof(fc6_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ( ~ v1_xboole_0(u2_ami_1(A,k4_amistd_1(A)))
        & ~ v1_finset_1(u2_ami_1(A,k4_amistd_1(A)))
        & ~ v1_realset1(u2_ami_1(A,k4_amistd_1(A))) ) ) )).

fof(fc7_amistd_1,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) ) ) )).

fof(fc8_amistd_1,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)
        & 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) ) ) )).

fof(fc9_amistd_1,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)
        & 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)
        & v4_amistd_1(k4_amistd_1(A),A) ) ) )).

fof(fc10_amistd_1,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)
        & v4_amistd_1(k4_amistd_1(A),A) ) ) )).

fof(rc5_amistd_1,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)
          & v4_amistd_1(B,A) ) ) )).

fof(cc4_amistd_1,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)
              & v3_amistd_1(B,A) ) ) ) ) )).

fof(cc5_amistd_1,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)
        & 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)
              & ~ v3_ami_1(C,A,B) ) ) ) ) )).

fof(cc6_amistd_1,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)
        & 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)
              & ~ v5_amistd_1(C,A,B) ) ) ) ) )).

fof(cc7_amistd_1,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & v5_ami_1(B,A)
        & v7_ami_1(B,A)
        & v8_ami_1(B,A)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => ( v6_amistd_1(C,A,B)
           => ( v1_relat_1(C)
              & v1_funct_1(C)
              & v1_finset_1(C)
              & v1_setfam_1(C)
              & v7_amistd_1(C,A,B) ) ) ) ) )).

fof(cc8_amistd_1,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)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => ( v1_xboole_0(C)
           => ( v1_relat_1(C)
              & v1_funct_1(C)
              & v1_finset_1(C)
              & v1_setfam_1(C)
              & v9_amistd_1(C,A,B) ) ) ) ) )).

fof(rc6_amistd_1,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)
        & l1_ami_1(B,A) )
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_realset1(C)
          & v1_setfam_1(C)
          & v1_ami_3(C,A,B)
          & v9_amistd_1(C,A,B) ) ) )).

fof(cc9_amistd_1,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_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) )
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => ( ( ~ v1_xboole_0(C)
              & v1_ami_3(C,A,B)
              & v7_amistd_1(C,A,B)
              & v9_amistd_1(C,A,B) )
           => ( v1_relat_1(C)
              & v1_funct_1(C)
              & v1_finset_1(C)
              & v1_setfam_1(C)
              & v8_amistd_1(C,A,B) ) ) ) ) )).

fof(rc7_amistd_1,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_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_realset1(C)
          & v1_setfam_1(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) ) ) )).

fof(rc8_amistd_1,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) )
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_realset1(C)
          & v1_setfam_1(C)
          & v1_ami_3(C,A,B)
          & v6_amistd_1(C,A,B)
          & v9_amistd_1(C,A,B) ) ) )).

fof(rc9_amistd_1,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) )
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_realset1(C)
          & v1_setfam_1(C)
          & v1_ami_3(C,A,B)
          & v6_amistd_1(C,A,B)
          & v9_amistd_1(C,A,B)
          & v10_amistd_1(C,A,B)
          & v11_amistd_1(C,A,B) ) ) )).

fof(rc10_amistd_1,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)
        & v10_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_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_realset1(C)
          & v1_setfam_1(C)
          & v11_ami_1(C,A,B)
          & v1_ami_3(C,A,B)
          & v6_amistd_1(C,A,B)
          & v7_amistd_1(C,A,B)
          & v8_amistd_1(C,A,B)
          & v9_amistd_1(C,A,B)
          & v10_amistd_1(C,A,B)
          & v11_amistd_1(C,A,B) ) ) )).

fof(rc11_amistd_1,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) )
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & ~ v1_xboole_0(C)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_finset_1(C)
          & v1_setfam_1(C)
          & v1_ami_3(C,A,B)
          & v6_amistd_1(C,A,B)
          & v9_amistd_1(C,A,B)
          & v10_amistd_1(C,A,B)
          & v11_amistd_1(C,A,B) ) ) )).

fof(t1_amistd_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => k1_pre_circ(k1_tarski(A)) = A ) )).

fof(t2_amistd_1,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k1_pre_circ(k6_domain_1(k5_numbers,A)) = A ) )).

fof(t3_amistd_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_realset1(B)
            & m2_finseq_1(B,A) )
         => ~ ( ~ v1_xboole_0(B)
              & ! [C] :
                  ( m1_subset_1(C,A)
                 => B != k13_binarith(A,C) ) ) ) ) )).

fof(t4_amistd_1,axiom,(
    $true )).

fof(t5_amistd_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m2_finseq_1(B,A) )
         => ! [C] :
              ( m2_finseq_1(C,A)
             => k4_finseq_4(k5_numbers,A,k4_graph_2(A,B,C),np__1) = k4_finseq_4(k5_numbers,A,B,np__1) ) ) ) )).

fof(t6_amistd_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_finseq_1(B,A)
         => ! [C] :
              ( ( ~ v1_realset1(C)
                & m2_finseq_1(C,A) )
             => k4_finseq_4(k5_numbers,A,k4_graph_2(A,B,C),k3_finseq_1(k4_graph_2(A,B,C))) = k4_finseq_4(k5_numbers,A,C,k3_finseq_1(C)) ) ) ) )).

fof(t7_amistd_1,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_graph_2(A,k1_xboole_0) = A ) )).

fof(t8_amistd_1,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k3_graph_2(B,k9_finseq_1(A)) = B ) )).

fof(t9_amistd_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ( ( r1_xreal_0(np__1,B)
                      & r1_xreal_0(B,k3_finseq_1(C)) )
                   => k4_finseq_4(k5_numbers,A,k4_graph_2(A,C,D),B) = k4_finseq_4(k5_numbers,A,C,B) ) ) ) ) ) )).

fof(t10_amistd_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_finseq_1(C,A)
             => ! [D] :
                  ( m2_finseq_1(D,A)
                 => ( r1_xreal_0(np__1,B)
                   => ( r1_xreal_0(k3_finseq_1(D),B)
                      | k4_finseq_4(k5_numbers,A,k4_graph_2(A,C,D),k1_nat_1(k3_finseq_1(C),B)) = k4_finseq_4(k5_numbers,A,D,k1_nat_1(B,np__1)) ) ) ) ) ) ) )).

fof(t11_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_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))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => m1_subset_1(k1_funct_4(D,k2_pre_circ(u2_ami_1(A,B),C)),k4_card_3(u5_ami_1(A,B))) ) ) ) ) )).

fof(t12_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_struct_0(C,B,u2_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))
                 => v11_ami_1(k14_ami_3(A,B,C,D),A,B) ) ) ) ) )).

fof(t13_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => v13_ami_1(B,A) ) ) )).

fof(d1_amistd_1,axiom,(
    $true )).

fof(d2_amistd_1,axiom,(
    $true )).

fof(d3_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,u3_ami_1(A,B))
             => ( v1_amistd_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m2_subset_1(F,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,F) = C
                             => ( E = k2_ami_1(A,B)
                                | k1_funct_1(k4_ami_1(A,B,F,D),E) = k1_funct_1(D,E) ) ) ) ) ) ) ) ) ) )).

fof(d4_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(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))
             => ( v2_amistd_1(C,A,B)
              <=> v1_amistd_1(k1_ami_5(A,B,C),A,B) ) ) ) ) )).

fof(t14_amistd_1,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))
             => ( ! [D] :
                    ( m1_struct_0(D,B,u2_ami_1(A,B))
                   => k1_amistd_1(A,B,D,C) = k1_struct_0(B,D) )
               => ( v1_realset1(u2_ami_1(A,B))
                  | v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) ) )).

fof(t15_amistd_1,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)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_struct_0(C,B,u2_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))
                 => ( v3_ami_1(D,A,B)
                   => k1_amistd_1(A,B,C,D) = k1_struct_0(B,C) ) ) ) ) ) )).

fof(d8_amistd_1,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] :
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r1_amistd_1(A,B,C,D)
                  <=> ? [E] :
                        ( ~ v1_xboole_0(E)
                        & m2_finseq_1(E,u2_ami_1(A,B))
                        & k4_finseq_4(k5_numbers,u2_ami_1(A,B),E,np__1) = C
                        & k4_finseq_4(k5_numbers,u2_ami_1(A,B),E,k3_finseq_1(E)) = D
                        & ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ( r1_xreal_0(np__1,F)
                             => ( r1_xreal_0(k3_finseq_1(E),F)
                                | r2_hidden(k4_finseq_4(k5_numbers,u2_ami_1(A,B),E,k1_nat_1(F,np__1)),k3_amistd_1(A,B,k4_finseq_4(k5_numbers,u2_ami_1(A,B),E,F))) ) ) ) ) ) ) ) ) ) )).

fof(t16_amistd_1,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] :
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ! [E] :
                      ( m1_struct_0(E,B,u2_ami_1(A,B))
                     => ( ( r1_amistd_1(A,B,C,D)
                          & r1_amistd_1(A,B,D,E) )
                       => r1_amistd_1(A,B,C,E) ) ) ) ) ) ) )).

fof(d9_amistd_1,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) )
         => ( v3_amistd_1(B,A)
          <=> ! [C] :
                ( m1_struct_0(C,B,u2_ami_1(A,B))
               => ! [D] :
                    ( m1_struct_0(D,B,u2_ami_1(A,B))
                   => ( ( r1_amistd_1(A,B,C,D)
                        & r1_amistd_1(A,B,D,C) )
                     => C = D ) ) ) ) ) ) )).

fof(d10_amistd_1,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) )
         => ( v4_amistd_1(B,A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u2_ami_1(A,B))
                & m2_relset_1(C,k5_numbers,u2_ami_1(A,B))
                & v3_funct_2(C,k5_numbers,u2_ami_1(A,B))
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r1_xreal_0(D,E)
                        <=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D),k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E)) ) ) ) ) ) ) ) )).

fof(t17_amistd_1,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u2_ami_1(A,B))
                & m2_relset_1(C,k5_numbers,u2_ami_1(A,B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,k5_numbers,u2_ami_1(A,B))
                    & m2_relset_1(D,k5_numbers,u2_ami_1(A,B)) )
                 => ( ( v3_funct_2(C,k5_numbers,u2_ami_1(A,B))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r1_xreal_0(E,F)
                              <=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E),k8_funct_2(k5_numbers,u2_ami_1(A,B),C,F)) ) ) )
                      & v3_funct_2(D,k5_numbers,u2_ami_1(A,B))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] :
                              ( m2_subset_1(F,k1_numbers,k5_numbers)
                             => ( r1_xreal_0(E,F)
                              <=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),D,E),k8_funct_2(k5_numbers,u2_ami_1(A,B),D,F)) ) ) ) )
                   => C = D ) ) ) ) ) )).

fof(t18_amistd_1,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] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u2_ami_1(A,B))
                & m2_relset_1(C,k5_numbers,u2_ami_1(A,B)) )
             => ( v3_funct_2(C,k5_numbers,u2_ami_1(A,B))
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(D,E)
                          <=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D),k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E)) ) ) )
                <=> ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(A,B),C,k1_nat_1(D,np__1)),k3_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D)))
                        & ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E),k3_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D)))
                             => r1_xreal_0(D,E) ) ) ) ) ) ) ) ) ) )).

fof(t19_amistd_1,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) )
         => ( v4_amistd_1(B,A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,k5_numbers,u2_ami_1(A,B))
                & m2_relset_1(C,k5_numbers,u2_ami_1(A,B))
                & v3_funct_2(C,k5_numbers,u2_ami_1(A,B))
                & ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(A,B),C,k1_nat_1(D,np__1)),k3_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D)))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(A,B),C,E),k3_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),C,D)))
                           => r1_xreal_0(D,E) ) ) ) ) ) ) ) ) )).

fof(d11_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( v1_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ( B = k4_amistd_1(A)
          <=> ( u1_struct_0(B) = k2_xboole_0(k5_numbers,k6_domain_1(k1_zfmisc_1(k1_numbers),k5_numbers))
              & u1_ami_1(A,B) = k5_numbers
              & u2_ami_1(A,B) = k5_numbers
              & u3_ami_1(A,B) = k7_domain_1(k5_numbers,np__0,np__1)
              & u4_ami_1(A,B) = k7_domain_1(k2_zfmisc_1(k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__0,np__0),k1_domain_1(k5_numbers,k5_numbers,np__1,np__0))
              & u5_ami_1(A,B) = k1_funct_4(k2_pre_circ(k5_numbers,k7_domain_1(k2_zfmisc_1(k5_numbers,k5_numbers),k1_domain_1(k5_numbers,k5_numbers,np__1,np__0),k1_domain_1(k5_numbers,k5_numbers,np__0,np__0))),k3_cqc_lang(k5_numbers,k5_numbers))
              & ? [C] :
                  ( v1_funct_1(C)
                  & v1_funct_2(C,k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))
                  & m2_relset_1(C,k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))
                  & ! [D] :
                      ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                     => k1_funct_1(C,D) = k1_funct_4(D,k3_cqc_lang(k5_numbers,k1_ordinal1(k1_funct_1(D,k5_numbers)))) )
                  & u6_ami_1(A,B) = k1_funct_4(k3_cqc_lang(k1_domain_1(k5_numbers,k5_numbers,np__1,np__0),C),k3_cqc_lang(k1_domain_1(k5_numbers,k5_numbers,np__0,np__0),k6_partfun1(k4_card_3(u5_ami_1(A,B))))) ) ) ) ) ) )).

fof(t20_amistd_1,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)))
         => ( k1_ami_5(A,k4_amistd_1(A),B) = np__0
           => v3_ami_1(B,A,k4_amistd_1(A)) ) ) ) )).

fof(t21_amistd_1,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)))
         => ~ ( k1_ami_5(A,k4_amistd_1(A),B) = np__1
              & v3_ami_1(B,A,k4_amistd_1(A)) ) ) ) )).

fof(t22_amistd_1,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)))
         => ( k1_ami_5(A,k4_amistd_1(A),B) = np__1
            | k1_ami_5(A,k4_amistd_1(A),B) = np__0 ) ) ) )).

fof(t23_amistd_1,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)))
         => v2_amistd_1(B,A,k4_amistd_1(A)) ) ) )).

fof(t24_amistd_1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( m1_struct_0(C,k4_amistd_1(B),u2_ami_1(B,k4_amistd_1(B)))
             => ( C = A
               => k3_amistd_1(B,k4_amistd_1(B),C) = k2_tarski(A,k2_xcmplx_0(A,np__1)) ) ) ) ) )).

fof(d12_amistd_1,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] :
              ( v4_ordinal2(C)
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( D = k5_amistd_1(A,B,C)
                  <=> ? [E] :
                        ( v1_funct_1(E)
                        & v1_funct_2(E,k5_numbers,u2_ami_1(A,B))
                        & m2_relset_1(E,k5_numbers,u2_ami_1(A,B))
                        & v3_funct_2(E,k5_numbers,u2_ami_1(A,B))
                        & ! [F] :
                            ( m2_subset_1(F,k1_numbers,k5_numbers)
                           => ! [G] :
                                ( m2_subset_1(G,k1_numbers,k5_numbers)
                               => ( r1_xreal_0(F,G)
                                <=> r1_amistd_1(A,B,k8_funct_2(k5_numbers,u2_ami_1(A,B),E,F),k8_funct_2(k5_numbers,u2_ami_1(A,B),E,G)) ) ) )
                        & D = k1_funct_1(E,C) ) ) ) ) ) ) )).

fof(t25_amistd_1,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] :
              ( v4_ordinal2(C)
             => ! [D] :
                  ( v4_ordinal2(D)
                 => ( k5_amistd_1(A,B,C) = k5_amistd_1(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t26_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => ? [D] :
                  ( v4_ordinal2(D)
                  & C = k5_amistd_1(A,B,D) ) ) ) ) )).

fof(d13_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( v4_ordinal2(D)
                 => ( D = k6_amistd_1(A,B,C)
                  <=> k5_amistd_1(A,B,D) = C ) ) ) ) ) )).

fof(t27_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( k7_amistd_1(A,B,C) = k7_amistd_1(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t28_amistd_1,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] :
              ( v4_ordinal2(C)
             => ! [D] :
                  ( v4_ordinal2(D)
                 => ( r1_amistd_1(A,B,k5_amistd_1(A,B,C),k5_amistd_1(A,B,D))
                  <=> r1_xreal_0(C,D) ) ) ) ) ) )).

fof(t29_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r1_xreal_0(k7_amistd_1(A,B,C),k7_amistd_1(A,B,D))
                  <=> r1_amistd_1(A,B,C,D) ) ) ) ) ) )).

fof(t30_amistd_1,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) )
         => ( v4_amistd_1(B,A)
           => v3_amistd_1(B,A) ) ) ) )).

fof(d14_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( v4_ordinal2(D)
                 => k8_amistd_1(A,B,C,D) = k5_amistd_1(A,B,k2_xcmplx_0(k7_amistd_1(A,B,C),D)) ) ) ) ) )).

fof(t31_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => k8_amistd_1(A,B,C,np__0) = C ) ) ) )).

fof(t32_amistd_1,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] :
                  ( m1_struct_0(D,C,u2_ami_1(B,C))
                 => ! [E] :
                      ( m1_struct_0(E,C,u2_ami_1(B,C))
                     => ( k8_amistd_1(B,C,D,A) = k8_amistd_1(B,C,E,A)
                       => D = E ) ) ) ) ) ) )).

fof(t33_amistd_1,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] :
                  ( m1_struct_0(D,C,u2_ami_1(B,C))
                 => k2_xcmplx_0(k7_amistd_1(B,C,D),A) = k7_amistd_1(B,C,k8_amistd_1(B,C,D,A)) ) ) ) ) )).

fof(d15_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => k9_amistd_1(A,B,C) = k8_amistd_1(A,B,C,np__1) ) ) ) )).

fof(t34_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => k9_amistd_1(A,B,C) = k5_amistd_1(A,B,k1_nat_1(k7_amistd_1(A,B,C),np__1)) ) ) ) )).

fof(t35_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => C != k9_amistd_1(A,B,C) ) ) ) )).

fof(t36_amistd_1,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_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( k9_amistd_1(A,B,C) = k9_amistd_1(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t37_amistd_1,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => k5_amistd_1(B,k4_amistd_1(B),A) = A ) ) )).

fof(t38_amistd_1,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)))
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,k4_amistd_1(A))))
             => ( k1_ami_5(A,k4_amistd_1(A),B) = np__1
               => k1_funct_1(k4_ami_1(A,k4_amistd_1(A),B,C),k2_ami_1(A,k4_amistd_1(A))) = k9_amistd_1(A,k4_amistd_1(A),k6_ami_1(A,k4_amistd_1(A),C)) ) ) ) ) )).

fof(t39_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( m1_struct_0(B,k4_amistd_1(A),u2_ami_1(A,k4_amistd_1(A)))
         => ! [C] :
              ( m2_subset_1(C,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)))
             => ( k1_ami_5(A,k4_amistd_1(A),C) = np__1
               => k1_amistd_1(A,k4_amistd_1(A),B,C) = k1_struct_0(k4_amistd_1(A),k9_amistd_1(A,k4_amistd_1(A),B)) ) ) ) ) )).

fof(t40_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( m1_struct_0(B,k4_amistd_1(A),u2_ami_1(A,k4_amistd_1(A)))
         => k3_amistd_1(A,k4_amistd_1(A),B) = k2_struct_0(k4_amistd_1(A),B,k9_amistd_1(A,k4_amistd_1(A),B)) ) ) )).

fof(d16_amistd_1,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))
             => ( v5_amistd_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => k1_funct_1(k4_ami_1(A,B,C,D),k2_ami_1(A,B)) = k9_amistd_1(A,B,k6_ami_1(A,B,D)) ) ) ) ) ) )).

fof(t41_amistd_1,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)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_struct_0(C,B,u2_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))
                 => ( v5_amistd_1(D,A,B)
                   => k1_amistd_1(A,B,C,D) = k1_struct_0(B,k9_amistd_1(A,B,C)) ) ) ) ) ) )).

fof(t42_amistd_1,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)
            & 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)
                  & v3_ami_1(C,A,B) ) ) ) ) )).

fof(t43_amistd_1,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))
             => ~ ( ~ v1_xboole_0(k2_amistd_1(A,B,C))
                  & v5_amistd_1(C,A,B) ) ) ) ) )).

fof(d17_amistd_1,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] :
              ( m1_ami_1(C,A,B)
             => ( v6_amistd_1(C,A,B)
              <=> ! [D] :
                    ( m1_struct_0(D,B,u2_ami_1(A,B))
                   => ( r2_hidden(D,k1_relat_1(C))
                     => r1_tarski(k1_amistd_1(A,B,D,k5_ami_5(A,B,C,D)),k1_relat_1(C)) ) ) ) ) ) ) )).

fof(d18_amistd_1,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] :
              ( m1_ami_1(C,A,B)
             => ( v7_amistd_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => ( ( r1_tarski(C,D)
                        & r2_hidden(k6_ami_1(A,B,D),k1_relat_1(C)) )
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => r2_hidden(k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,D),E)),k1_relat_1(C)) ) ) ) ) ) ) ) )).

fof(d19_amistd_1,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)
             => ( v8_amistd_1(C,A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                   => ( ( r1_tarski(C,D)
                        & k6_ami_1(A,B,D) = k5_amistd_1(A,B,np__0) )
                     => ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => r2_hidden(k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,D),E)),k1_relat_1(C)) ) ) ) ) ) ) ) )).

fof(t44_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_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) )
         => ! [C] :
              ( m1_ami_1(C,A,B)
             => ( ( v7_amistd_1(C,A,B)
                  & r2_hidden(k5_amistd_1(A,B,np__0),k1_relat_1(C)) )
               => v8_amistd_1(C,A,B) ) ) ) ) )).

fof(t45_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_ami_1(C,A,B)
             => ( v6_amistd_1(C,A,B)
               => v7_amistd_1(C,A,B) ) ) ) ) )).

fof(t46_amistd_1,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)
            & l1_ami_1(B,A) )
         => v6_amistd_1(k14_ami_3(A,B,k5_amistd_1(A,B,np__0),k5_ami_1(A,B)),A,B) ) ) )).

fof(d20_amistd_1,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] :
              ( m1_ami_1(C,A,B)
             => ( v9_amistd_1(C,A,B)
              <=> ! [D] :
                    ( m1_struct_0(D,B,u2_ami_1(A,B))
                   => ( r2_hidden(D,k1_relat_1(C))
                     => ! [E] :
                          ( m1_struct_0(E,B,u2_ami_1(A,B))
                         => ( r1_amistd_1(A,B,E,D)
                           => r2_hidden(E,k1_relat_1(C)) ) ) ) ) ) ) ) ) )).

fof(t47_amistd_1,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] :
              ( ( v1_xboole_0(C)
                & m1_ami_1(C,A,B) )
             => v9_amistd_1(C,A,B) ) ) ) )).

fof(t48_amistd_1,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))
             => v9_amistd_1(k14_ami_3(A,B,k5_amistd_1(A,B,np__0),C),A,B) ) ) ) )).

fof(t49_amistd_1,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)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => r2_hidden(k5_amistd_1(A,B,np__0),k1_relat_1(C)) ) ) ) )).

fof(t50_amistd_1,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)
                    & v9_amistd_1(D,B,C)
                    & m1_ami_1(D,B,C) )
                 => ( ~ r1_xreal_0(k4_card_1(D),A)
                  <=> r2_hidden(k5_amistd_1(B,C,A),k1_relat_1(D)) ) ) ) ) ) )).

fof(t51_amistd_1,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) )
             => r2_hidden(k10_amistd_1(A,B,C),k1_relat_1(C)) ) ) ) )).

fof(t52_amistd_1,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) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ( r1_tarski(C,D)
                   => r1_amistd_1(A,B,k10_amistd_1(A,B,C),k10_amistd_1(A,B,D)) ) ) ) ) ) )).

fof(t53_amistd_1,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) )
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r2_hidden(D,k1_relat_1(C))
                   => r1_amistd_1(A,B,D,k10_amistd_1(A,B,C)) ) ) ) ) ) )).

fof(t54_amistd_1,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)
                & 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_tarski(C,D)
                      & k10_amistd_1(A,B,C) = k10_amistd_1(A,B,D) )
                   => C = D ) ) ) ) ) )).

fof(t55_amistd_1,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)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => k10_amistd_1(A,B,C) = k5_amistd_1(A,B,k5_binarith(k4_card_1(C),np__1)) ) ) ) )).

fof(d22_amistd_1,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)
                & m1_ami_1(C,A,B) )
             => ( v10_amistd_1(C,A,B)
              <=> k1_funct_1(C,k10_amistd_1(A,B,C)) = k5_ami_1(A,B) ) ) ) ) )).

fof(d23_amistd_1,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)
                & m1_ami_1(C,A,B) )
             => ( v11_amistd_1(C,A,B)
              <=> ! [D] :
                    ( m1_struct_0(D,B,u2_ami_1(A,B))
                   => ( ( k1_funct_1(C,D) = k5_ami_1(A,B)
                        & r2_hidden(D,k1_relat_1(C)) )
                     => D = k10_amistd_1(A,B,C) ) ) ) ) ) ) )).

fof(reflexivity_r1_amistd_1,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)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u2_ami_1(A,B))
        & m1_subset_1(D,u2_ami_1(A,B)) )
     => r1_amistd_1(A,B,C,C) ) )).

fof(dt_k1_amistd_1,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)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u2_ami_1(A,B))
        & m1_subset_1(D,u4_ami_1(A,B)) )
     => m1_subset_1(k1_amistd_1(A,B,C,D),k1_zfmisc_1(u2_ami_1(A,B))) ) )).

fof(dt_k2_amistd_1,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)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => m1_subset_1(k2_amistd_1(A,B,C),k1_zfmisc_1(u2_ami_1(A,B))) ) )).

fof(dt_k3_amistd_1,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)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u2_ami_1(A,B)) )
     => m1_subset_1(k3_amistd_1(A,B,C),k1_zfmisc_1(u2_ami_1(A,B))) ) )).

fof(dt_k4_amistd_1,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ( v1_ami_1(k4_amistd_1(A),A)
        & l1_ami_1(k4_amistd_1(A),A) ) ) )).

fof(dt_k5_amistd_1,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)
        & v4_ordinal2(C) )
     => m1_struct_0(k5_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) )).

fof(dt_k6_amistd_1,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)
        & m1_subset_1(C,u2_ami_1(A,B)) )
     => v4_ordinal2(k6_amistd_1(A,B,C)) ) )).

fof(dt_k7_amistd_1,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)
        & m1_subset_1(C,u2_ami_1(A,B)) )
     => m2_subset_1(k7_amistd_1(A,B,C),k1_numbers,k5_numbers) ) )).

fof(redefinition_k7_amistd_1,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)
        & m1_subset_1(C,u2_ami_1(A,B)) )
     => k7_amistd_1(A,B,C) = k6_amistd_1(A,B,C) ) )).

fof(dt_k8_amistd_1,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_subset_1(C,u2_ami_1(A,B))
        & v4_ordinal2(D) )
     => m1_struct_0(k8_amistd_1(A,B,C,D),B,u2_ami_1(A,B)) ) )).

fof(dt_k9_amistd_1,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)
        & m1_subset_1(C,u2_ami_1(A,B)) )
     => m1_struct_0(k9_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) )).

fof(dt_k10_amistd_1,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_struct_0(k10_amistd_1(A,B,C),B,u2_ami_1(A,B)) ) )).

fof(d5_amistd_1,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] :
              ( m1_struct_0(C,B,u2_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_amistd_1(A,B,C,D) = a_4_0_amistd_1(A,B,C,D) ) ) ) ) )).

fof(d6_amistd_1,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))
             => k2_amistd_1(A,B,C) = k1_setfam_1(a_3_0_amistd_1(A,B,C)) ) ) ) )).

fof(d7_amistd_1,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] :
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => k3_amistd_1(A,B,C) = k3_tarski(a_3_1_amistd_1(A,B,C)) ) ) ) )).

fof(d21_amistd_1,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) )
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( D = k10_amistd_1(A,B,C)
                  <=> ? [E] :
                        ( ~ v1_xboole_0(E)
                        & v1_finset_1(E)
                        & v5_membered(E)
                        & E = a_3_2_amistd_1(A,B,C)
                        & D = k5_amistd_1(A,B,k1_pre_circ(E)) ) ) ) ) ) ) )).

fof(fraenkel_a_4_0_amistd_1,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)
        & l1_ami_1(C,B)
        & m1_struct_0(D,C,u2_ami_1(B,C))
        & 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)) )
     => ( r2_hidden(A,a_4_0_amistd_1(B,C,D,E))
      <=> ? [F] :
            ( m1_subset_1(F,k4_card_3(u5_ami_1(B,C)))
            & A = k6_ami_1(B,C,k9_ami_1(B,C,F))
            & k6_ami_1(B,C,F) = D
            & k13_ami_1(B,C,F,D) = E ) ) ) )).

fof(fraenkel_a_3_0_amistd_1,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)
        & l1_ami_1(C,B)
        & 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)) )
     => ( r2_hidden(A,a_3_0_amistd_1(B,C,D))
      <=> ? [E] :
            ( m1_struct_0(E,C,u2_ami_1(B,C))
            & A = k1_amistd_1(B,C,E,D) ) ) ) )).

fof(fraenkel_a_3_1_amistd_1,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)
        & l1_ami_1(C,B)
        & m1_struct_0(D,C,u2_ami_1(B,C)) )
     => ( r2_hidden(A,a_3_1_amistd_1(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 = k6_subset_1(u2_ami_1(B,C),k1_amistd_1(B,C,D,E),k2_amistd_1(B,C,E)) ) ) ) )).

fof(fraenkel_a_3_2_amistd_1,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_xboole_0(D)
        & v1_ami_3(D,B,C)
        & m1_ami_1(D,B,C) )
     => ( r2_hidden(A,a_3_2_amistd_1(B,C,D))
      <=> ? [E] :
            ( m1_struct_0(E,C,u2_ami_1(B,C))
            & A = k7_amistd_1(B,C,E)
            & r2_hidden(E,k1_relat_1(D)) ) ) ) )).
%------------------------------------------------------------------------------