SET007 Axioms: SET007+688.ax


%------------------------------------------------------------------------------
% File     : SET007+688 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Input and Output of Instructions
% 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    : ami_7 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   98 (   0 unit)
%            Number of atoms       :  670 (  78 equality)
%            Maximal formula depth :   23 (   9 average)
%            Number of connectives :  703 ( 131 ~  ;   2  |; 305  &)
%                                         (   9 <=>; 256 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   40 (   0 propositional; 1-3 arity)
%            Number of functors    :   47 (   3 constant; 0-5 arity)
%            Number of variables   :  272 (   0 singleton; 271 !;   1 ?)
%            Maximal term depth    :    6 (   2 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_ami_7,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)
        & v2_ami_7(k4_amistd_1(A),A) ) ) )).

fof(rc1_ami_7,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)
          & v1_ami_7(B,A)
          & v2_ami_7(B,A) ) ) )).

fof(cc1_ami_7,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( l1_ami_1(B,A)
         => ( ( ~ v3_struct_0(B)
              & ~ v2_ami_1(B,A)
              & v8_ami_1(B,A)
              & v2_ami_7(B,A) )
           => ( ~ v3_struct_0(B)
              & ~ v2_ami_1(B,A)
              & v8_ami_1(B,A)
              & v1_ami_7(B,A) ) ) ) ) )).

fof(cc2_ami_7,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( l1_ami_1(B,A)
         => ( ( ~ v3_struct_0(B)
              & v5_ami_1(B,A)
              & v2_ami_7(B,A) )
           => ( ~ v3_struct_0(B)
              & v5_ami_1(B,A)
              & v7_amistd_2(B,A) ) ) ) ) )).

fof(fc2_ami_7,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & v2_ami_7(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u1_struct_0(B)) )
     => ~ v1_realset1(k3_ami_1(A,B,C)) ) )).

fof(fc3_ami_7,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & v1_ami_7(B,A)
        & l1_ami_1(B,A) )
     => ( ~ v1_xboole_0(u4_ami_1(A,B))
        & v1_relat_1(u4_ami_1(A,B))
        & v1_setfam_1(u4_ami_1(A,B))
        & ~ v1_realset1(u4_ami_1(A,B)) ) ) )).

fof(fc4_ami_7,axiom,(
    ! [A,B] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & v5_ami_1(B,A)
        & v7_amistd_2(B,A)
        & l1_ami_1(B,A) )
     => ~ v1_realset1(k3_ami_1(A,B,k2_ami_1(A,B))) ) )).

fof(fc5_ami_7,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)
        & l1_ami_1(B,A)
        & v3_ami_1(C,A,B)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => v1_xboole_0(k5_ami_7(A,B,C)) ) )).

fof(fc6_ami_7,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)
        & l1_ami_1(B,A)
        & v3_ami_1(C,A,B)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => v1_xboole_0(k2_ami_7(A,B,C)) ) )).

fof(fc7_ami_7,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)
        & l1_ami_1(B,A)
        & v3_ami_1(C,A,B)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => v1_xboole_0(k4_ami_7(A,B,C)) ) )).

fof(fc8_ami_7,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)
        & v2_ami_7(B,A)
        & l1_ami_1(B,A)
        & v3_ami_1(C,A,B)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => v1_xboole_0(k3_ami_7(A,B,C)) ) )).

fof(fc9_ami_7,axiom,
    ( ~ v3_struct_0(k1_ami_3)
    & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v4_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v7_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v10_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v13_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v3_amistd_1(k1_ami_3,k1_tarski(k4_numbers))
    & v4_amistd_1(k1_ami_3,k1_tarski(k4_numbers))
    & v2_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
    & v5_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
    & v6_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
    & v7_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
    & v8_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
    & v11_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
    & v13_amistd_2(k1_ami_3,k1_tarski(k4_numbers))
    & v1_ami_7(k1_ami_3,k1_tarski(k4_numbers))
    & v2_ami_7(k1_ami_3,k1_tarski(k4_numbers)) )).

fof(t1_ami_7,axiom,(
    ! [A,B,C] :
      ~ ( A != B
        & A != C
        & k4_xboole_0(k1_enumset1(A,B,C),k1_tarski(A)) != k2_tarski(B,C) ) )).

fof(t2_ami_7,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,k4_card_3(u5_ami_1(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => r2_hidden(k1_funct_1(C,D),k3_ami_1(A,B,D)) ) ) ) ) )).

fof(t3_ami_7,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ! [E] :
                      ( m1_subset_1(E,k3_ami_1(A,B,k2_ami_1(A,B)))
                     => k1_funct_1(k2_funct_7(C,k2_ami_1(A,B),E),D) = k13_ami_1(A,B,C,D) ) ) ) ) ) )).

fof(t4_ami_7,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_struct_0(E,B,u2_ami_1(A,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))
                         => ! [G] :
                              ( m1_subset_1(G,k3_ami_1(A,B,D))
                             => ( E != D
                               => k13_ami_1(A,B,k4_ami_1(A,B,F,C),E) = k13_ami_1(A,B,k4_ami_1(A,B,F,k1_ami_7(A,B,C,D,G)),E) ) ) ) ) ) ) ) ) )).

fof(t5_ami_7,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_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,k3_ami_1(A,B,D))
                     => ( D != k2_ami_1(A,B)
                       => k6_ami_1(A,B,C) = k6_ami_1(A,B,k1_ami_7(A,B,C,D,E)) ) ) ) ) ) ) )).

fof(t6_ami_7,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_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,k3_ami_1(A,B,E))
                         => ( v5_amistd_1(C,A,B)
                           => ( E = k2_ami_1(A,B)
                              | k6_ami_1(A,B,k4_ami_1(A,B,C,D)) = k6_ami_1(A,B,k4_ami_1(A,B,C,k1_ami_7(A,B,D,E,F))) ) ) ) ) ) ) ) ) )).

fof(t7_ami_7,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_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,k3_ami_1(A,B,E))
                         => ( v5_amistd_1(C,A,B)
                           => ( E = k2_ami_1(A,B)
                              | k6_ami_1(A,B,k4_ami_1(A,B,C,k1_ami_7(A,B,D,E,F))) = k6_ami_1(A,B,k1_ami_7(A,B,k4_ami_1(A,B,C,D),E,F)) ) ) ) ) ) ) ) ) )).

fof(t8_ami_7,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] :
              ( 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)))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ! [F] :
                          ( m1_subset_1(F,k3_ami_1(A,B,E))
                         => ! [G] :
                              ( m1_struct_0(G,B,u2_ami_1(A,B))
                             => k13_ami_1(A,B,k4_ami_1(A,B,C,k1_ami_7(A,B,D,E,F)),G) = k13_ami_1(A,B,k1_ami_7(A,B,k4_ami_1(A,B,C,D),E,F),G) ) ) ) ) ) ) ) )).

fof(d1_ami_7,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ( v1_ami_7(B,A)
      <=> ~ v1_realset1(u4_ami_1(A,B)) ) ) )).

fof(d2_ami_7,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ( v2_ami_7(B,A)
      <=> ! [C] :
            ( m1_subset_1(C,u1_struct_0(B))
           => ~ v1_realset1(k3_ami_1(A,B,C)) ) ) ) )).

fof(d3_ami_7,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))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( D = k2_ami_7(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( r2_hidden(E,D)
                        <=> ~ ! [F] :
                                ( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
                               => k1_funct_1(F,E) = k1_funct_1(k4_ami_1(A,B,C,F),E) ) ) ) ) ) ) ) ) )).

fof(d4_ami_7,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_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( D = k3_ami_7(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( r2_hidden(E,D)
                        <=> ! [F] :
                              ( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
                             => ! [G] :
                                  ( m1_subset_1(G,k3_ami_1(A,B,E))
                                 => k4_ami_1(A,B,C,F) = k4_ami_1(A,B,C,k1_ami_7(A,B,F,E,G)) ) ) ) ) ) ) ) ) ) )).

fof(d5_ami_7,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_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                 => ( D = k4_ami_7(A,B,C)
                  <=> ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ( r2_hidden(E,D)
                        <=> ~ ! [F] :
                                ( m1_subset_1(F,k4_card_3(u5_ami_1(A,B)))
                               => ! [G] :
                                    ( m1_subset_1(G,k3_ami_1(A,B,E))
                                   => k4_ami_1(A,B,C,k1_ami_7(A,B,F,E,G)) = k1_ami_7(A,B,k4_ami_1(A,B,C,F),E,G) ) ) ) ) ) ) ) ) ) )).

fof(d6_ami_7,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))
             => k5_ami_7(A,B,C) = k6_subset_1(u1_struct_0(B),k4_ami_7(A,B,C),k3_ami_7(A,B,C)) ) ) ) )).

fof(t9_ami_7,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))
             => r1_xboole_0(k3_ami_7(A,B,C),k5_ami_7(A,B,C)) ) ) ) )).

fof(t10_ami_7,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)
            & v2_ami_7(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))
             => r1_tarski(k3_ami_7(A,B,C),k2_ami_7(A,B,C)) ) ) ) )).

fof(t11_ami_7,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))
             => r1_tarski(k2_ami_7(A,B,C),k4_ami_7(A,B,C)) ) ) ) )).

fof(t12_ami_7,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))
             => r1_tarski(k5_ami_7(A,B,C),k4_ami_7(A,B,C)) ) ) ) )).

fof(t13_ami_7,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)
            & v2_ami_7(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))
             => k3_ami_7(A,B,C) = k6_subset_1(u1_struct_0(B),k2_ami_7(A,B,C),k5_ami_7(A,B,C)) ) ) ) )).

fof(t14_ami_7,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)
            & v2_ami_7(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))
             => k4_ami_7(A,B,C) = k4_subset_1(u1_struct_0(B),k2_ami_7(A,B,C),k5_ami_7(A,B,C)) ) ) ) )).

fof(t15_ami_7,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_subset_1(D,u1_struct_0(B))
                 => ~ ( v1_realset1(k3_ami_1(A,B,D))
                      & r2_hidden(D,k4_ami_7(A,B,C)) ) ) ) ) ) )).

fof(t16_ami_7,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_subset_1(D,u1_struct_0(B))
                 => ~ ( v1_realset1(k3_ami_1(A,B,D))
                      & r2_hidden(D,k5_ami_7(A,B,C)) ) ) ) ) ) )).

fof(t17_ami_7,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_subset_1(D,u1_struct_0(B))
                 => ~ ( v1_realset1(k3_ami_1(A,B,D))
                      & r2_hidden(D,k2_ami_7(A,B,C)) ) ) ) ) ) )).

fof(t18_ami_7,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_ami_1(C,A,B)
              <=> v1_xboole_0(k2_ami_7(A,B,C)) ) ) ) ) )).

fof(t19_ami_7,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)
            & v2_ami_7(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(k3_ami_7(A,B,C)) ) ) ) ) )).

fof(t20_ami_7,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_ami_1(C,A,B)
               => v1_xboole_0(k4_ami_7(A,B,C)) ) ) ) ) )).

fof(t21_ami_7,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_ami_1(C,A,B)
               => v1_xboole_0(k5_ami_7(A,B,C)) ) ) ) ) )).

fof(t22_ami_7,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)
            & v1_ami_7(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))
                 => ~ r2_hidden(C,k3_ami_7(A,B,D)) ) ) ) ) )).

fof(t23_ami_7,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)
                  & r2_hidden(k2_ami_1(A,B),k3_ami_7(A,B,C)) ) ) ) ) )).

fof(t24_ami_7,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_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)) = k6_ami_1(A,B,D) )
               => r2_hidden(k2_ami_1(A,B),k2_ami_7(A,B,C)) ) ) ) ) )).

fof(t25_ami_7,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)
               => r2_hidden(k2_ami_1(A,B),k2_ami_7(A,B,C)) ) ) ) ) )).

fof(t26_ami_7,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_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)) = k6_ami_1(A,B,D) )
               => r2_hidden(k2_ami_1(A,B),k4_ami_7(A,B,C)) ) ) ) ) )).

fof(t27_ami_7,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)
               => r2_hidden(k2_ami_1(A,B),k4_ami_7(A,B,C)) ) ) ) ) )).

fof(t28_ami_7,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))
                 => ~ ( ! [E] :
                          ( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
                         => ! [F] :
                              ( ( v1_ami_3(F,A,B)
                                & m1_ami_1(F,A,B) )
                             => k4_ami_1(A,B,D,k8_ami_5(A,B,E,F)) = k8_ami_5(A,B,k4_ami_1(A,B,D,E),F) ) )
                      & r2_hidden(C,k4_ami_7(A,B,D)) ) ) ) ) ) )).

fof(t29_ami_7,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_subset_1(D,u1_struct_0(B))
                 => ( ( v2_amistd_1(C,A,B)
                      & r2_hidden(D,k2_ami_7(A,B,C)) )
                   => D = k2_ami_1(A,B) ) ) ) ) ) )).

fof(t30_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
         => ! [C] :
              ( m1_subset_1(C,k3_ami_1(k1_tarski(k4_numbers),k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => k2_ami_3(k1_ami_7(k1_tarski(k4_numbers),k1_ami_3,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),C),A) = k2_ami_3(B,A) ) ) ) )).

fof(t31_ami_7,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => A != k11_ami_3(A) ) )).

fof(t32_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,A)) = k1_xboole_0 ) )).

fof(t33_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ( A != B
           => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = k1_struct_0(k1_ami_3,A) ) ) ) )).

fof(t34_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = k1_xboole_0 ) ) )).

fof(t35_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,A)) = k1_struct_0(k1_ami_3,A) ) )).

fof(t36_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ( A != B
           => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = k1_xboole_0 ) ) ) )).

fof(t37_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = k1_xboole_0 ) ) )).

fof(t38_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A)) = k1_struct_0(k1_ami_3,A) ) )).

fof(t39_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ( A != B
           => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = k1_xboole_0 ) ) ) )).

fof(t40_ami_7,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(t41_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = k1_xboole_0 ) ) )).

fof(t42_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k3_ami_7(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = k1_xboole_0 ) ) )).

fof(t43_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(t44_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ( A != B
           => k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) )).

fof(t45_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t46_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t47_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t48_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t49_ami_7,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(t50_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t51_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k2_ami_7(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t52_ami_7,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ~ r2_hidden(A,k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,B)) ) ) )).

fof(t53_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(t54_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ( A != B
           => k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) )).

fof(t55_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t56_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t57_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t58_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t59_ami_7,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(t60_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t61_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k4_ami_7(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t62_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(t63_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ( A != B
           => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = k2_struct_0(k1_ami_3,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) )).

fof(t64_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t65_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(t66_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ( A != B
           => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) )).

fof(t67_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t68_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A)) = k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(t69_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ( A != B
           => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = k1_enumset1(A,B,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) ) )).

fof(t70_ami_7,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = k1_xboole_0 ) )).

fof(t71_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(t72_ami_7,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k5_ami_7(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = k2_struct_0(k1_ami_3,A,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ) )).

fof(dt_k1_ami_7,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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,k4_card_3(u5_ami_1(A,B)))
        & m1_subset_1(D,u1_struct_0(B))
        & m1_subset_1(E,k3_ami_1(A,B,D)) )
     => m1_subset_1(k1_ami_7(A,B,C,D,E),k4_card_3(u5_ami_1(A,B))) ) )).

fof(redefinition_k1_ami_7,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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,k4_card_3(u5_ami_1(A,B)))
        & m1_subset_1(D,u1_struct_0(B))
        & m1_subset_1(E,k3_ami_1(A,B,D)) )
     => k1_ami_7(A,B,C,D,E) = k2_funct_7(C,D,E) ) )).

fof(dt_k2_ami_7,axiom,(
    ! [A,B,C] :
      ( ( v1_setfam_1(A)
        & ~ v3_struct_0(B)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => m1_subset_1(k2_ami_7(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(dt_k3_ami_7,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(k3_ami_7(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(dt_k4_ami_7,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(k4_ami_7(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(dt_k5_ami_7,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(k5_ami_7(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) )).

fof(dt_k6_ami_7,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
        & m1_ami_3(B)
        & v1_int_1(C) )
     => m1_subset_1(k6_ami_7(A,B,C),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ) )).

fof(redefinition_k6_ami_7,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
        & m1_ami_3(B)
        & v1_int_1(C) )
     => k6_ami_7(A,B,C) = k2_funct_7(A,B,C) ) )).
%------------------------------------------------------------------------------