SET007 Axioms: SET007+378.ax


%------------------------------------------------------------------------------
% File     : SET007+378 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Some Remarks on the Simple Concrete Model of Computer
% 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_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  123 (  17 unit)
%            Number of atoms       :  659 ( 113 equality)
%            Maximal formula depth :   17 (   7 average)
%            Number of connectives :  633 (  97 ~  ;   1  |; 234  &)
%                                         (  16 <=>; 285 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   37 (   1 propositional; 0-4 arity)
%            Number of functors    :   89 (  26 constant; 0-8 arity)
%            Number of variables   :  302 (   0 singleton; 295 !;   7 ?)
%            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_3,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)) )).

fof(fc2_ami_3,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))
    & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) )).

fof(fc3_ami_3,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))
    & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) )).

fof(fc4_ami_3,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ~ v1_xboole_0(k14_ami_1(A,B)) ) )).

fof(rc1_ami_3,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_ami_3(C,A,B) ) ) )).

fof(fc5_ami_3,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)) )).

fof(d1_ami_3,axiom,(
    k1_ami_3 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,np__0,k3_ami_2,k1_gr_cy_1(np__9),k4_ami_2,k5_ami_2,k17_ami_2) )).

fof(t1_ami_3,axiom,(
    v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) )).

fof(t2_ami_3,axiom,(
    v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) )).

fof(d2_ami_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,u1_struct_0(k1_ami_3))
     => ( m1_ami_3(A)
      <=> r2_hidden(A,k2_ami_2) ) ) )).

fof(d3_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k3_ami_3(A,B) = k4_tarski(np__1,k10_finseq_1(A,B)) ) ) )).

fof(d4_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k4_ami_3(A,B) = k4_tarski(np__2,k10_finseq_1(A,B)) ) ) )).

fof(d5_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k5_ami_3(A,B) = k4_tarski(np__3,k10_finseq_1(A,B)) ) ) )).

fof(d6_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k6_ami_3(A,B) = k4_tarski(np__4,k10_finseq_1(A,B)) ) ) )).

fof(d7_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k7_ami_3(A,B) = k4_tarski(np__5,k10_finseq_1(A,B)) ) ) )).

fof(d8_ami_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => k8_ami_3(A) = k4_tarski(np__6,k12_finseq_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3),A)) ) )).

fof(d9_ami_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m1_ami_3(B)
         => k9_ami_3(A,B) = k4_tarski(np__7,k10_finseq_1(A,B)) ) ) )).

fof(d10_ami_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m1_ami_3(B)
         => k10_ami_3(A,B) = k4_tarski(np__8,k10_finseq_1(A,B)) ) ) )).

fof(t3_ami_3,axiom,(
    $true )).

fof(t4_ami_3,axiom,(
    k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) = np__0 )).

fof(t5_ami_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(k5_ami_2))
         => ( B = A
           => k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k6_ami_2(B) ) ) ) )).

fof(d11_ami_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ( B = k11_ami_3(A)
          <=> ? [C] :
                ( m2_subset_1(C,k5_numbers,k3_ami_2)
                & C = A
                & B = k15_ami_2(C) ) ) ) ) )).

fof(t6_ami_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m2_subset_1(B,k5_numbers,k3_ami_2)
         => ( B = A
           => k15_ami_2(B) = k11_ami_3(A) ) ) ) )).

fof(t7_ami_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
         => ! [C] :
              ( m1_subset_1(C,k4_ami_2)
             => ( C = A
               => ! [D] :
                    ( m1_subset_1(D,k4_card_3(k5_ami_2))
                   => ( D = B
                     => k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B) = k16_ami_2(C,D) ) ) ) ) ) ) )).

fof(t8_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B),C),A) = k2_ami_3(C,B)
                & ! [D] :
                    ( m1_ami_3(D)
                   => ( D != A
                     => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t9_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B),C),A) = k2_xcmplx_0(k2_ami_3(C,A),k2_ami_3(C,B))
                & ! [D] :
                    ( m1_ami_3(D)
                   => ( D != A
                     => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t10_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B),C),A) = k6_xcmplx_0(k2_ami_3(C,A),k2_ami_3(C,B))
                & ! [D] :
                    ( m1_ami_3(D)
                   => ( D != A
                     => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t11_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B),C),A) = k3_xcmplx_0(k2_ami_3(C,A),k2_ami_3(C,B))
                & ! [D] :
                    ( m1_ami_3(D)
                   => ( D != A
                     => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B),C),D) = k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t12_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,C))
                & ( A != B
                 => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),A) = k5_int_1(k2_ami_3(C,A),k2_ami_3(C,B)) )
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),B) = k6_int_1(k2_ami_3(C,A),k2_ami_3(C,B))
                & ! [D] :
                    ( m1_ami_3(D)
                   => ~ ( D != A
                        & D != B
                        & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B),C),D) != k2_ami_3(C,D) ) ) ) ) ) ) )).

fof(t13_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(B),C),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = B
                & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(B),C),A) = k2_ami_3(C,A) ) ) ) ) )).

fof(t14_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ! [C] :
              ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
                 => ( ( k2_ami_3(D,A) = np__0
                     => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = C )
                    & ( k2_ami_3(D,A) != np__0
                     => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,D)) )
                    & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(C,A),D),B) = k2_ami_3(D,B) ) ) ) ) ) )).

fof(t15_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ! [C] :
              ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
                 => ( ( ~ r1_xreal_0(k2_ami_3(D,A),np__0)
                     => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = C )
                    & ( r1_xreal_0(k2_ami_3(D,A),np__0)
                     => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(C,A),D),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,D)) )
                    & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(C,A),D),B) = k2_ami_3(D,B) ) ) ) ) ) )).

fof(t16_ami_3,axiom,(
    $true )).

fof(t17_ami_3,axiom,(
    $true )).

fof(t18_ami_3,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => r1_int_1(k3_xcmplx_0(A,B),np__0,A) ) ) )).

fof(t19_ami_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v1_funct_1(C)
                & m2_relset_1(C,A,B) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & m2_relset_1(D,A,B) )
                 => ( ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,B)
                           => ( r2_hidden(k4_tarski(E,F),C)
                            <=> r2_hidden(k4_tarski(E,F),D) ) ) )
                   => C = D ) ) ) ) ) )).

fof(t20_ami_3,axiom,(
    $true )).

fof(t21_ami_3,axiom,(
    $true )).

fof(t22_ami_3,axiom,(
    $true )).

fof(t23_ami_3,axiom,(
    $true )).

fof(t24_ami_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] :
              ( ( k1_relat_1(A) = k1_relat_1(B)
                & k1_funct_1(A,C) = k1_funct_1(B,C) )
             => k7_relat_1(A,k1_tarski(C)) = k7_relat_1(B,k1_tarski(C)) ) ) ) )).

fof(t25_ami_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D] :
              ( ( k1_relat_1(A) = k1_relat_1(B)
                & k1_funct_1(A,C) = k1_funct_1(B,C)
                & k1_funct_1(A,D) = k1_funct_1(B,D) )
             => k7_relat_1(A,k2_tarski(C,D)) = k7_relat_1(B,k2_tarski(C,D)) ) ) ) )).

fof(t26_ami_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C,D,E] :
              ( ( k1_relat_1(A) = k1_relat_1(B)
                & k1_funct_1(A,C) = k1_funct_1(B,C)
                & k1_funct_1(A,D) = k1_funct_1(B,D)
                & k1_funct_1(A,E) = k1_funct_1(B,E) )
             => k7_relat_1(A,k1_enumset1(C,D,E)) = k7_relat_1(B,k1_enumset1(C,D,E)) ) ) ) )).

fof(t27_ami_3,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(A,k1_relat_1(C))
          & k1_funct_1(C,A) = B )
       => r1_tarski(k3_cqc_lang(A,B),C) ) ) )).

fof(t28_ami_3,axiom,(
    $true )).

fof(t29_ami_3,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_relat_1(E)
        & v1_funct_1(E) )
     => ( ( r2_hidden(A,k1_relat_1(E))
          & r2_hidden(C,k1_relat_1(E))
          & k1_funct_1(E,A) = B
          & k1_funct_1(E,C) = D )
       => r1_tarski(k4_funct_4(A,C,B,D),E) ) ) )).

fof(t30_ami_3,axiom,(
    $true )).

fof(t31_ami_3,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => r2_hidden(C,k14_ami_1(A,B)) ) ) )).

fof(t32_ami_3,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m2_subset_1(C,k7_ami_1(u5_ami_1(A,B)),k14_ami_1(A,B))
         => m1_ami_1(C,A,B) ) ) )).

fof(t33_ami_3,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( ( v1_funct_1(C)
            & m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
         => ! [D] :
              ( ( v1_funct_1(D)
                & m2_relset_1(D,k14_ami_1(A,B),k14_ami_1(A,B)) )
             => ( ! [E] :
                    ( m1_ami_1(E,A,B)
                   => ! [F] :
                        ( m1_ami_1(F,A,B)
                       => ( r2_hidden(k4_tarski(E,F),C)
                        <=> r2_hidden(k4_tarski(E,F),D) ) ) )
               => C = D ) ) ) ) )).

fof(d12_ami_3,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))
             => k12_ami_3(A,B,C) = k2_cat_3(u2_ami_1(A,B),k2_ami_1(A,B),C) ) ) ) )).

fof(t34_ami_3,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))
             => k1_relat_1(k12_ami_3(A,B,C)) = k1_struct_0(B,k2_ami_1(A,B)) ) ) ) )).

fof(d13_ami_3,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => ( v1_ami_3(C,A,B)
          <=> r1_tarski(k1_relat_1(C),u2_ami_1(A,B)) ) ) ) )).

fof(t35_ami_3,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( ( v1_ami_3(C,A,B)
            & m1_ami_1(C,A,B) )
         => ! [D] :
              ( ( v1_ami_3(D,A,B)
                & m1_ami_1(D,A,B) )
             => v1_ami_3(k17_ami_1(A,B,C,D),A,B) ) ) ) )).

fof(t36_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => k1_relat_1(C) = u1_struct_0(B) ) ) ) )).

fof(t37_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( l1_ami_1(B,A)
         => ! [C] :
              ( m1_ami_1(C,A,B)
             => r1_tarski(k1_relat_1(C),u1_struct_0(B)) ) ) ) )).

fof(t38_ami_3,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] :
              ( ( v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => ( r1_tarski(C,D)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => r1_tarski(C,k11_ami_1(A,B,k10_ami_1(A,B,D),E)) ) ) ) ) ) ) )).

fof(d14_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_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))
                 => ( r1_ami_3(A,B,C,D)
                  <=> k6_ami_1(A,B,C) = D ) ) ) ) ) )).

fof(d15_ami_3,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)
            & 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))
                 => ( r2_ami_3(A,B,C,D)
                  <=> k1_funct_1(C,D) = k5_ami_1(A,B) ) ) ) ) ) )).

fof(t39_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v2_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_ami_1(C,A,B)
             => ? [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                  & r1_tarski(C,D) ) ) ) ) )).

fof(d16_ami_3,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)
             => ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
               => k13_ami_3(A,B,C) = k1_funct_1(C,k2_ami_1(A,B)) ) ) ) ) )).

fof(d17_ami_3,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)
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r3_ami_3(A,B,C,D)
                  <=> ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
                      & k13_ami_3(A,B,C) = D ) ) ) ) ) ) )).

fof(d18_ami_3,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)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_ami_1(C,A,B)
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r4_ami_3(A,B,C,D)
                  <=> ( r2_hidden(D,k1_relat_1(C))
                      & k1_funct_1(C,D) = k5_ami_1(A,B) ) ) ) ) ) ) )).

fof(t40_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( v9_ami_1(C,A,B)
              <=> ? [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) ) ) ) ) ) )).

fof(t41_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] :
                  ( m1_ami_1(D,A,B)
                 => ! [E] :
                      ( m1_struct_0(E,B,u2_ami_1(A,B))
                     => ( ( r1_tarski(D,C)
                          & r4_ami_3(A,B,D,E) )
                       => r2_ami_3(A,B,C,E) ) ) ) ) ) ) )).

fof(t42_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( v9_ami_1(C,A,B)
                   => ( k12_ami_1(A,B,C) = k11_ami_1(A,B,k10_ami_1(A,B,C),D)
                    <=> r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) ) ) ) ) ) ) )).

fof(t43_ami_3,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] :
                  ( ( v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_tarski(D,C)
                      <=> r1_tarski(D,k11_ami_1(A,B,k10_ami_1(A,B,C),E)) ) ) ) ) ) ) )).

fof(t44_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)))
                   => k12_ami_1(A,B,C) = k11_ami_1(A,B,k10_ami_1(A,B,C),D) ) ) ) ) ) )).

fof(t45_ami_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( v1_setfam_1(C)
             => ( r1_xreal_0(A,B)
               => ! [D] :
                    ( ( ~ v3_struct_0(D)
                      & ~ v2_ami_1(D,C)
                      & v4_ami_1(D,C)
                      & v5_ami_1(D,C)
                      & v7_ami_1(D,C)
                      & v8_ami_1(D,C)
                      & l1_ami_1(D,C) )
                   => ! [E] :
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(C,D)))
                       => ( r2_ami_3(C,D,E,k6_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),A)))
                         => r2_ami_3(C,D,E,k6_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),B))) ) ) ) ) ) ) ) )).

fof(t46_ami_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( v1_setfam_1(C)
             => ( r1_xreal_0(A,B)
               => ! [D] :
                    ( ( ~ v3_struct_0(D)
                      & ~ v2_ami_1(D,C)
                      & v4_ami_1(D,C)
                      & v5_ami_1(D,C)
                      & v7_ami_1(D,C)
                      & v8_ami_1(D,C)
                      & l1_ami_1(D,C) )
                   => ! [E] :
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(C,D)))
                       => ( r2_ami_3(C,D,E,k6_ami_1(C,D,k11_ami_1(C,D,k10_ami_1(C,D,E),A)))
                         => k11_ami_1(C,D,k10_ami_1(C,D,E),B) = k11_ami_1(C,D,k10_ami_1(C,D,E),A) ) ) ) ) ) ) ) )).

fof(t47_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ( ? [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & r2_ami_3(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => k12_ami_1(A,B,C) = k12_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) ) ) ) ) ) )).

fof(t48_ami_3,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v7_ami_1(B,A)
            & v8_ami_1(B,A)
            & 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] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r2_ami_3(A,B,C,D)
                      <=> r2_ami_3(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),E),D) ) ) ) ) ) ) )).

fof(t49_ami_3,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)
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( r3_ami_3(A,B,C,D)
                   => ! [E] :
                        ( m1_subset_1(E,k4_card_3(u5_ami_1(A,B)))
                       => ( r1_tarski(C,E)
                         => r1_ami_3(A,B,E,D) ) ) ) ) ) ) ) )).

fof(t50_ami_3,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))
             => k1_funct_1(k12_ami_3(A,B,C),k2_ami_1(A,B)) = C ) ) ) )).

fof(t51_ami_3,axiom,(
    v10_ami_1(k1_ami_3,k1_tarski(k4_numbers)) )).

fof(d19_ami_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => k15_ami_3(A) = k2_xcmplx_0(k3_xcmplx_0(np__2,A),np__1) ) )).

fof(d20_ami_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => k16_ami_3(A) = k2_xcmplx_0(k3_xcmplx_0(np__2,A),np__2) ) )).

fof(t52_ami_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v4_ordinal2(B)
         => ~ ( A != B
              & k15_ami_3(A) = k15_ami_3(B) ) ) ) )).

fof(t53_ami_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v4_ordinal2(B)
         => ~ ( A != B
              & k16_ami_3(A) = k16_ami_3(B) ) ) ) )).

fof(t54_ami_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => k11_ami_3(k16_ami_3(A)) = k16_ami_3(k2_xcmplx_0(A,np__1)) ) )).

fof(t55_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => k3_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k4_numbers ) )).

fof(t56_ami_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v4_ordinal2(B)
         => k15_ami_3(A) != k16_ami_3(B) ) ) )).

fof(t57_ami_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ( k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k15_ami_3(A)
        & k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) != k16_ami_3(A) ) ) )).

fof(t58_ami_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ~ ( ? [B] :
              ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
              & k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B)) )
          & v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t59_ami_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ( A = k4_tarski(np__0,k1_xboole_0)
       => v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t60_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ~ v3_ami_1(k3_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t61_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ~ v3_ami_1(k4_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t62_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ~ v3_ami_1(k5_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t63_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ~ v3_ami_1(k6_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t64_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => ~ v3_ami_1(k7_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t65_ami_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ~ v3_ami_1(k8_ami_3(A),k1_tarski(k4_numbers),k1_ami_3) ) )).

fof(t66_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ~ v3_ami_1(k9_ami_3(B,A),k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t67_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => ~ v3_ami_1(k10_ami_3(B,A),k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t68_ami_3,axiom,(
    m2_subset_1(k4_tarski(np__0,k1_xboole_0),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)) )).

fof(t69_ami_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
    <=> ~ ( A != k4_tarski(np__0,k1_xboole_0)
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k3_ami_3(B,C) ) )
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k4_ami_3(B,C) ) )
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k5_ami_3(B,C) ) )
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k6_ami_3(B,C) ) )
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k7_ami_3(B,C) ) )
          & ! [B] :
              ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => A != k8_ami_3(B) )
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => A != k9_ami_3(C,B) ) )
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => A != k10_ami_3(C,B) ) ) ) ) )).

fof(t70_ami_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ( v3_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
       => A = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t71_ami_3,axiom,(
    k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) = k4_tarski(np__0,k1_xboole_0) )).

fof(s1_ami_3,axiom,
    ( ( p1_s1_ami_3(np__0)
      & ~ r1_xreal_0(f1_s1_ami_3,np__0)
      & ! [A] :
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ! [B] :
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => ( ( p1_s1_ami_3(k2_nat_1(f1_s1_ami_3,A))
                  & r1_xreal_0(B,f1_s1_ami_3) )
               => ( B = np__0
                  | p1_s1_ami_3(k1_nat_1(k2_nat_1(f1_s1_ami_3,A),B)) ) ) ) ) )
   => p1_s1_ami_3(f2_s1_ami_3) )).

fof(s2_ami_3,axiom,
    ( ( ! [A] :
          ( m1_ami_1(A,f1_s2_ami_3,f2_s2_ami_3)
         => ! [B] :
              ( m1_ami_1(B,f1_s2_ami_3,f2_s2_ami_3)
             => ( r2_hidden(k4_tarski(A,B),f3_s2_ami_3)
              <=> p1_s2_ami_3(A,B) ) ) )
      & ! [A] :
          ( m1_ami_1(A,f1_s2_ami_3,f2_s2_ami_3)
         => ! [B] :
              ( m1_ami_1(B,f1_s2_ami_3,f2_s2_ami_3)
             => ( r2_hidden(k4_tarski(A,B),f4_s2_ami_3)
              <=> p1_s2_ami_3(A,B) ) ) ) )
   => f3_s2_ami_3 = f4_s2_ami_3 )).

fof(dt_m1_ami_3,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => m1_subset_1(A,u1_struct_0(k1_ami_3)) ) )).

fof(existence_m1_ami_3,axiom,(
    ? [A] : m1_ami_3(A) )).

fof(dt_k1_ami_3,axiom,
    ( v1_ami_1(k1_ami_3,k1_tarski(k4_numbers))
    & l1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) )).

fof(dt_k2_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
        & m1_ami_3(B) )
     => v1_int_1(k2_ami_3(A,B)) ) )).

fof(redefinition_k2_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
        & m1_ami_3(B) )
     => k2_ami_3(A,B) = k1_funct_1(A,B) ) )).

fof(dt_k3_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_ami_3(A)
        & m1_ami_3(B) )
     => m2_subset_1(k3_ami_3(A,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)) ) )).

fof(dt_k4_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_ami_3(A)
        & m1_ami_3(B) )
     => m2_subset_1(k4_ami_3(A,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)) ) )).

fof(dt_k5_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_ami_3(A)
        & m1_ami_3(B) )
     => m2_subset_1(k5_ami_3(A,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)) ) )).

fof(dt_k6_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_ami_3(A)
        & m1_ami_3(B) )
     => m2_subset_1(k6_ami_3(A,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)) ) )).

fof(dt_k7_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_ami_3(A)
        & m1_ami_3(B) )
     => m2_subset_1(k7_ami_3(A,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)) ) )).

fof(dt_k8_ami_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => m2_subset_1(k8_ami_3(A),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)) ) )).

fof(dt_k9_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
        & m1_ami_3(B) )
     => m2_subset_1(k9_ami_3(A,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)) ) )).

fof(dt_k10_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
        & m1_ami_3(B) )
     => m2_subset_1(k10_ami_3(A,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)) ) )).

fof(dt_k11_ami_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => m1_struct_0(k11_ami_3(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(dt_k12_ami_3,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_ami_1(k12_ami_3(A,B,C),A,B) ) )).

fof(dt_k13_ami_3,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_ami_1(C,A,B) )
     => m1_struct_0(k13_ami_3(A,B,C),B,u2_ami_1(A,B)) ) )).

fof(dt_k14_ami_3,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)) )
     => ( v1_ami_3(k14_ami_3(A,B,C,D),A,B)
        & m1_ami_1(k14_ami_3(A,B,C,D),A,B) ) ) )).

fof(redefinition_k14_ami_3,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)) )
     => k14_ami_3(A,B,C,D) = k3_cqc_lang(C,D) ) )).

fof(dt_k15_ami_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => m1_ami_3(k15_ami_3(A)) ) )).

fof(dt_k16_ami_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => m1_struct_0(k16_ami_3(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(dt_k17_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_ami_3(A)
        & v1_int_1(B) )
     => m1_ami_1(k17_ami_3(A,B),k1_tarski(k4_numbers),k1_ami_3) ) )).

fof(redefinition_k17_ami_3,axiom,(
    ! [A,B] :
      ( ( m1_ami_3(A)
        & v1_int_1(B) )
     => k17_ami_3(A,B) = k3_cqc_lang(A,B) ) )).

fof(dt_k18_ami_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_ami_3(A)
        & m1_ami_3(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => m1_ami_1(k18_ami_3(A,B,C,D),k1_tarski(k4_numbers),k1_ami_3) ) )).

fof(redefinition_k18_ami_3,axiom,(
    ! [A,B,C,D] :
      ( ( m1_ami_3(A)
        & m1_ami_3(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => k18_ami_3(A,B,C,D) = k4_funct_4(A,B,C,D) ) )).
%------------------------------------------------------------------------------