SET007 Axioms: SET007+389.ax


%------------------------------------------------------------------------------
% File     : SET007+389 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Decomposition of the States of SCM
% 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_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  121 (  21 unit)
%            Number of atoms       :  618 ( 102 equality)
%            Maximal formula depth :   22 (   7 average)
%            Number of connectives :  592 (  95 ~  ;   4  |; 204  &)
%                                         (   5 <=>; 284 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   38 (   1 propositional; 0-3 arity)
%            Number of functors    :   77 (  17 constant; 0-4 arity)
%            Number of variables   :  284 (   0 singleton; 280 !;   4 ?)
%            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_5,axiom,
    ( ~ v1_xboole_0(k2_ami_2)
    & ~ v1_finset_1(k2_ami_2)
    & v1_membered(k2_ami_2)
    & v2_membered(k2_ami_2)
    & v3_membered(k2_ami_2)
    & v4_membered(k2_ami_2)
    & v5_membered(k2_ami_2) )).

fof(fc2_ami_5,axiom,
    ( ~ v1_xboole_0(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
    & ~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) )).

fof(fc3_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ( v4_ordinal2(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A))
        & v1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A))
        & v1_int_1(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A))
        & v1_xcmplx_0(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)) ) ) )).

fof(rc1_ami_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ? [C] :
          ( m1_ami_1(C,A,B)
          & v1_relat_1(C)
          & v1_funct_1(C)
          & v1_ami_5(C,A,B) ) ) )).

fof(rc2_ami_5,axiom,(
    ? [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
      & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3) ) )).

fof(t1_ami_5,axiom,(
    $true )).

fof(t2_ami_5,axiom,(
    $true )).

fof(t3_ami_5,axiom,(
    $true )).

fof(t4_ami_5,axiom,(
    $true )).

fof(t5_ami_5,axiom,(
    $true )).

fof(t6_ami_5,axiom,(
    $true )).

fof(t7_ami_5,axiom,(
    $true )).

fof(t8_ami_5,axiom,(
    $true )).

fof(t9_ami_5,axiom,(
    $true )).

fof(t10_ami_5,axiom,(
    $true )).

fof(t11_ami_5,axiom,(
    $true )).

fof(t12_ami_5,axiom,(
    $true )).

fof(t13_ami_5,axiom,(
    $true )).

fof(t14_ami_5,axiom,(
    $true )).

fof(t15_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [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,k7_ami_3(A,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))
            & k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A),B),A) = k6_int_1(k2_ami_3(B,A),k2_ami_3(B,A))
            & ! [C] :
                ( m1_ami_3(C)
               => ( C != A
                 => k2_ami_3(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,A),B),C) = k2_ami_3(B,C) ) ) ) ) ) )).

fof(t16_ami_5,axiom,(
    ! [A] :
      ( r2_hidden(A,k2_ami_2)
     => m1_ami_3(A) ) )).

fof(t17_ami_5,axiom,(
    $true )).

fof(t18_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k15_ami_3(B) ) ) )).

fof(t19_ami_5,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k16_ami_3(B) ) ) )).

fof(t20_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => A != k2_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) )).

fof(t21_ami_5,axiom,(
    $true )).

fof(t22_ami_5,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m1_ami_3(B)
         => A != B ) ) )).

fof(t23_ami_5,axiom,(
    u1_struct_0(k1_ami_3) = k2_xboole_0(k2_xboole_0(k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)),k2_ami_2),k3_ami_2) )).

fof(t24_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => ! [B] :
          ( m1_ami_3(B)
         => ! [C] :
              ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ( r2_hidden(B,k1_relat_1(A))
                & r2_hidden(C,k1_relat_1(A)) ) ) ) ) )).

fof(t25_ami_5,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)))
             => r2_hidden(k2_ami_1(A,B),k1_relat_1(C)) ) ) ) )).

fof(t26_ami_5,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(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
         => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,A) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,B)
              & ! [C] :
                  ( m1_ami_3(C)
                 => k2_ami_3(A,C) = k2_ami_3(B,C) )
              & ! [C] :
                  ( m1_struct_0(C,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                 => k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,C) = k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,B,C) ) )
           => A = B ) ) ) )).

fof(t27_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => r1_tarski(k2_ami_2,k1_relat_1(A)) ) )).

fof(t28_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => r1_tarski(k3_ami_2,k1_relat_1(A)) ) )).

fof(t29_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => k1_relat_1(k7_relat_1(A,k2_ami_2)) = k2_ami_2 ) )).

fof(t30_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
     => k1_relat_1(k7_relat_1(A,k3_ami_2)) = k3_ami_2 ) )).

fof(t31_ami_5,axiom,(
    ~ v1_finset_1(k2_ami_2) )).

fof(t32_ami_5,axiom,(
    ~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) )).

fof(t33_ami_5,axiom,(
    r1_subset_1(k2_ami_2,k3_ami_2) )).

fof(t34_ami_5,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)))
             => k12_ami_3(A,B,k6_ami_1(A,B,C)) = k7_relat_1(C,k1_struct_0(B,k2_ami_1(A,B))) ) ) ) )).

fof(t35_ami_5,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) = k1_tarski(k1_domain_1(u1_struct_0(B),u2_ami_1(A,B),k2_ami_1(A,B),C)) ) ) ) )).

fof(d1_ami_5,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m1_subset_1(C,u4_ami_1(A,B))
         => k1_ami_5(A,B,C) = k1_mcart_1(C) ) ) )).

fof(d2_ami_5,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))
     => k2_ami_5(A) = A ) )).

fof(d3_ami_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k3_ami_2)
     => k3_ami_5(A) = A ) )).

fof(d4_ami_5,axiom,(
    ! [A] :
      ( m2_subset_1(A,k5_numbers,k2_ami_2)
     => k4_ami_5(A) = A ) )).

fof(t36_ami_5,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))
     => r1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A),np__8) ) )).

fof(t37_ami_5,axiom,(
    k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = np__0 )).

fof(t38_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k3_ami_3(A,B)) = np__1 ) ) )).

fof(t39_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k4_ami_3(A,B)) = np__2 ) ) )).

fof(t40_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k5_ami_3(A,B)) = np__3 ) ) )).

fof(t41_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_ami_3(A,B)) = np__4 ) ) )).

fof(t42_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_ami_3(B)
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k7_ami_3(A,B)) = np__5 ) ) )).

fof(t43_ami_5,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k8_ami_3(A)) = np__6 ) )).

fof(t44_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k9_ami_3(B,A)) = np__7 ) ) )).

fof(t45_ami_5,axiom,(
    ! [A] :
      ( m1_ami_3(A)
     => ! [B] :
          ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
         => k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k10_ami_3(B,A)) = np__8 ) ) )).

fof(t46_ami_5,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))
     => ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__0
       => A = k5_ami_1(k1_tarski(k4_numbers),k1_ami_3) ) ) )).

fof(t47_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__1
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k3_ami_3(B,C) ) ) ) ) )).

fof(t48_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__2
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k4_ami_3(B,C) ) ) ) ) )).

fof(t49_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__3
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k5_ami_3(B,C) ) ) ) ) )).

fof(t50_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__4
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k6_ami_3(B,C) ) ) ) ) )).

fof(t51_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__5
          & ! [B] :
              ( m1_ami_3(B)
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k7_ami_3(B,C) ) ) ) ) )).

fof(t52_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__6
          & ! [B] :
              ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => A != k8_ami_3(B) ) ) ) )).

fof(t53_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__7
          & ! [B] :
              ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k9_ami_3(B,C) ) ) ) ) )).

fof(t54_ami_5,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))
     => ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = np__8
          & ! [B] :
              ( m1_struct_0(B,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
             => ! [C] :
                  ( m1_ami_3(C)
                 => A != k10_ami_3(B,C) ) ) ) ) )).

fof(t55_ami_5,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => k11_ami_2(k2_ami_5(k8_ami_3(A))) = A ) )).

fof(t56_ami_5,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m1_ami_3(B)
         => ( k12_ami_2(k2_ami_5(k9_ami_3(A,B))) = A
            & k13_ami_2(k2_ami_5(k9_ami_3(A,B))) = B ) ) ) )).

fof(t57_ami_5,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => ! [B] :
          ( m1_ami_3(B)
         => ( k12_ami_2(k2_ami_5(k10_ami_3(A,B))) = A
            & k13_ami_2(k2_ami_5(k10_ami_3(A,B))) = B ) ) ) )).

fof(t58_ami_5,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(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
         => ( k7_relat_1(A,k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) = k7_relat_1(B,k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3))))
           => ! [C] :
                ( m2_subset_1(C,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))
               => k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,A),k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,B),k2_xboole_0(k2_ami_2,k1_struct_0(k1_ami_3,k2_ami_1(k1_tarski(k4_numbers),k1_ami_3)))) ) ) ) ) )).

fof(t59_ami_5,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)))
         => k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),k3_ami_2) = k7_relat_1(B,k3_ami_2) ) ) )).

fof(t60_ami_5,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_subset_1(D,k4_card_3(u5_ami_1(A,B)))
                 => ( ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
                      & r1_tarski(C,D) )
                   => k13_ami_3(A,B,C) = k6_ami_1(A,B,D) ) ) ) ) ) )).

fof(d5_ami_5,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))
                 => ( r2_hidden(D,k1_relat_1(C))
                   => k5_ami_5(A,B,C,D) = k1_funct_1(C,D) ) ) ) ) ) )).

fof(t61_ami_5,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C,D] :
          ( m1_ami_1(D,A,B)
         => ( r1_tarski(C,D)
           => m1_ami_1(C,A,B) ) ) ) )).

fof(d6_ami_5,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => k6_ami_5(A,B,C) = k7_relat_1(C,u2_ami_1(A,B)) ) ) )).

fof(d7_ami_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => k7_ami_5(A,B,C) = k7_relat_1(C,k4_xboole_0(u1_struct_0(B),k4_subset_1(u1_struct_0(B),k1_struct_0(B,k2_ami_1(A,B)),u2_ami_1(A,B)))) ) ) )).

fof(d8_ami_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => ( v1_ami_5(C,A,B)
          <=> r1_xboole_0(k1_relat_1(C),k4_subset_1(u1_struct_0(B),k1_struct_0(B,k2_ami_1(A,B)),u2_ami_1(A,B))) ) ) ) )).

fof(t62_ami_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => r1_tarski(k7_ami_5(A,B,C),C) ) ) )).

fof(t63_ami_5,axiom,(
    ! [A,B] :
      ( l1_ami_1(B,A)
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => r1_tarski(k6_ami_5(A,B,C),C) ) ) )).

fof(t64_ami_5,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)
             => ! [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(k6_ami_5(A,B,C),k11_ami_1(A,B,k10_ami_1(A,B,D),E)) ) ) ) ) ) ) )).

fof(t65_ami_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => ~ r2_hidden(k2_ami_1(A,B),k1_relat_1(k7_ami_5(A,B,C))) ) ) )).

fof(t66_ami_5,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_ami_1(C,A,B)
             => ~ r2_hidden(k2_ami_1(A,B),k1_relat_1(k6_ami_5(A,B,C))) ) ) ) )).

fof(t67_ami_5,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A) )
     => ! [C] :
          ( m1_ami_1(C,A,B)
         => r1_xboole_0(k1_struct_0(B,k2_ami_1(A,B)),k1_relat_1(k7_ami_5(A,B,C))) ) ) )).

fof(t68_ami_5,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_ami_1(C,A,B)
             => r1_xboole_0(k1_struct_0(B,k2_ami_1(A,B)),k1_relat_1(k6_ami_5(A,B,C))) ) ) ) )).

fof(t69_ami_5,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => r1_tarski(k1_relat_1(k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)),k2_ami_2) ) )).

fof(t70_ami_5,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => r1_tarski(k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)),k3_ami_2) ) )).

fof(t71_ami_5,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_ami_1(D,A,B)
                 => r1_xboole_0(k1_relat_1(k7_ami_5(A,B,C)),k1_relat_1(k6_ami_5(A,B,D))) ) ) ) ) )).

fof(t72_ami_5,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_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => k6_ami_5(A,B,C) = C ) ) ) )).

fof(t73_ami_5,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))
                 => ( r2_hidden(D,k1_relat_1(C))
                   => r2_hidden(D,k1_relat_1(k6_ami_5(A,B,C))) ) ) ) ) ) )).

fof(t74_ami_5,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_ami_5(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( m1_ami_1(D,A,B)
                 => ( r1_tarski(C,D)
                  <=> r1_tarski(C,k7_ami_5(A,B,D)) ) ) ) ) ) )).

fof(t75_ami_5,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_ami_1(C,A,B)
             => ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
               => C = k17_ami_1(A,B,k17_ami_1(A,B,k12_ami_3(A,B,k13_ami_3(A,B,C)),k6_ami_5(A,B,C)),k7_ami_5(A,B,C)) ) ) ) ) )).

fof(d9_ami_5,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)
                & m2_relset_1(C,k14_ami_1(A,B),k14_ami_1(A,B)) )
             => ( v2_ami_5(C,A,B)
              <=> ! [D] :
                    ( m1_ami_1(D,A,B)
                   => ( r2_hidden(D,k1_relat_1(C))
                     => ( v1_ami_5(D,A,B)
                        & ! [E] :
                            ( m1_ami_1(E,A,B)
                           => ( E = k1_funct_1(C,D)
                             => v1_ami_5(E,A,B) ) ) ) ) ) ) ) ) ) )).

fof(t76_ami_5,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_ami_1(C,A,B)
             => ~ ( r2_hidden(k2_ami_1(A,B),k1_relat_1(C))
                  & v1_ami_3(C,A,B) ) ) ) ) )).

fof(t77_ami_5,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] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_ami_3)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_ami_3) )
             => k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,B,C)) = k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,k4_ami_1(k1_tarski(k4_numbers),k1_ami_3,A,B),C) ) ) ) )).

fof(t78_ami_5,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))
               => r1_tarski(k12_ami_3(A,B,k13_ami_3(A,B,C)),C) ) ) ) ) )).

fof(t79_ami_5,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_struct_0(D,B,u2_ami_1(A,B))
                 => k6_ami_1(A,B,k8_ami_5(A,B,C,k12_ami_3(A,B,D))) = D ) ) ) ) )).

fof(t80_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_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))
         => ! [C] :
              ( m1_ami_3(C)
             => k2_ami_3(A,C) = k2_ami_3(k8_ami_5(k1_tarski(k4_numbers),k1_ami_3,A,k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,B)),C) ) ) ) )).

fof(t81_ami_5,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_struct_0(E,B,u2_ami_1(A,B))
                     => k13_ami_1(A,B,C,E) = k13_ami_1(A,B,k8_ami_5(A,B,C,k12_ami_3(A,B,D)),E) ) ) ) ) ) )).

fof(t82_ami_5,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,k4_card_3(u5_ami_1(A,B)))
                 => ! [E] : m1_subset_1(k1_funct_4(C,k7_relat_1(D,E)),k4_card_3(u5_ami_1(A,B))) ) ) ) ) )).

fof(t83_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
     => ( k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) != k1_xboole_0
       => r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A)) ) ) )).

fof(t84_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
     => r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A)) ) )).

fof(t85_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) )
     => ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A))
       => r2_hidden(k13_ami_3(k1_tarski(k4_numbers),k1_ami_3,A),k1_relat_1(A)) ) ) )).

fof(t86_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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)))
         => ( r1_tarski(A,B)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),C)),k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A))) ) ) ) ) )).

fof(t87_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,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))
                       => ( E = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                         => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D))
                            & E = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D)) ) ) ) ) ) ) ) ) )).

fof(t88_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m1_ami_3(E)
                       => ! [F] :
                            ( m1_ami_3(F)
                           => ! [G] :
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k3_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F) ) ) ) ) ) ) ) ) ) )).

fof(t89_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m1_ami_3(E)
                       => ! [F] :
                            ( m1_ami_3(F)
                           => ! [G] :
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k4_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => k2_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k2_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) )).

fof(t90_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m1_ami_3(E)
                       => ! [F] :
                            ( m1_ami_3(F)
                           => ! [G] :
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k5_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => k6_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k6_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) )).

fof(t91_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m1_ami_3(E)
                       => ! [F] :
                            ( m1_ami_3(F)
                           => ! [G] :
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k6_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => k3_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k3_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) )).

fof(t92_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m1_ami_3(E)
                       => ! [F] :
                            ( m1_ami_3(F)
                           => ! [G] :
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k7_ami_3(E,F)
                                    & r2_hidden(E,k1_relat_1(A)) )
                                 => ( E = F
                                    | k5_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k5_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t93_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m1_ami_3(E)
                       => ! [F] :
                            ( m1_ami_3(F)
                           => ! [G] :
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k7_ami_3(E,F)
                                    & r2_hidden(F,k1_relat_1(A)) )
                                 => ( E = F
                                    | k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),F)) = k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t94_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m1_ami_3(E)
                       => ! [F] :
                            ( m1_struct_0(F,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                           => ! [G] :
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k9_ami_3(F,E) )
                                 => ( F = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)))
                                    | ( k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E) = np__0
                                    <=> k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E) = np__0 ) ) ) ) ) ) ) ) ) ) ) )).

fof(t95_ami_5,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3)
        & m1_ami_1(A,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_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m1_ami_3(E)
                       => ! [F] :
                            ( m1_struct_0(F,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3))
                           => ! [G] :
                                ( m2_subset_1(G,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))
                               => ( ( G = k8_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D))
                                    & G = k10_ami_3(F,E) )
                                 => ( F = k11_ami_3(k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D)))
                                    | ( ~ ( ~ r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),np__0)
                                          & r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),np__0) )
                                      & ~ ( ~ r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),D),E),np__0)
                                          & r1_xreal_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),D),E),np__0) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t96_ami_5,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = k7_relat_1(A,k2_ami_2) ) )).

fof(t97_ami_5,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3)
     => ( v1_ami_5(A,k1_tarski(k4_numbers),k1_ami_3)
      <=> r1_tarski(k1_relat_1(A),k2_ami_2) ) ) )).

fof(dt_k1_ami_5,axiom,(
    ! [A,B,C] :
      ( ( l1_ami_1(B,A)
        & m1_subset_1(C,u4_ami_1(A,B)) )
     => m1_subset_1(k1_ami_5(A,B,C),u3_ami_1(A,B)) ) )).

fof(dt_k2_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))
     => m1_subset_1(k2_ami_5(A),k4_ami_2) ) )).

fof(dt_k3_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k3_ami_2)
     => m1_struct_0(k3_ami_5(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) )).

fof(dt_k4_ami_5,axiom,(
    ! [A] :
      ( m1_subset_1(A,k2_ami_2)
     => m1_ami_3(k4_ami_5(A)) ) )).

fof(dt_k5_ami_5,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_ami_1(C,A,B)
        & m1_subset_1(D,u2_ami_1(A,B)) )
     => m2_subset_1(k5_ami_5(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) )).

fof(dt_k6_ami_5,axiom,(
    ! [A,B,C] :
      ( ( l1_ami_1(B,A)
        & m1_ami_1(C,A,B) )
     => ( v1_ami_3(k6_ami_5(A,B,C),A,B)
        & m1_ami_1(k6_ami_5(A,B,C),A,B) ) ) )).

fof(dt_k7_ami_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(B)
        & l1_ami_1(B,A)
        & m1_ami_1(C,A,B) )
     => m1_ami_1(k7_ami_5(A,B,C),A,B) ) )).

fof(dt_k8_ami_5,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
        & m1_ami_1(D,A,B) )
     => m1_subset_1(k8_ami_5(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) )).

fof(idempotence_k8_ami_5,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
        & m1_ami_1(D,A,B) )
     => k8_ami_5(A,B,C,C) = C ) )).

fof(redefinition_k8_ami_5,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(A)
        & ~ v2_ami_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
        & m1_ami_1(D,A,B) )
     => k8_ami_5(A,B,C,D) = k1_funct_4(C,D) ) )).
%------------------------------------------------------------------------------