SET007 Axioms: SET007+801.ax


%------------------------------------------------------------------------------
% File     : SET007+801 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : A Tree of Execution of a Macroinstruction
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : amistd_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   64 (   8 unit)
%            Number of atoms       :  503 (  38 equality)
%            Maximal formula depth :   22 (   9 average)
%            Number of connectives :  526 (  87 ~  ;   1  |; 310  &)
%                                         (   8 <=>; 120 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   53 (   1 propositional; 0-4 arity)
%            Number of functors    :   55 (   7 constant; 0-5 arity)
%            Number of variables   :  153 (   0 singleton; 147 !;   6 ?)
%            Maximal term depth    :    8 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_amistd_3,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & m1_relset_1(B,A,k5_numbers) )
     => ( v1_ordinal1(k1_funct_1(B,C))
        & v2_ordinal1(k1_funct_1(B,C))
        & v3_ordinal1(k1_funct_1(B,C))
        & v4_ordinal2(k1_funct_1(B,C))
        & v1_card_1(k1_funct_1(B,C))
        & v1_xreal_0(k1_funct_1(B,C))
        & v1_xcmplx_0(k1_funct_1(B,C)) ) ) )).

fof(fc2_amistd_3,axiom,(
    ! [A,B] :
      ( ( v1_relat_1(A)
        & v1_xboole_0(A) )
     => ( v1_relat_1(k7_relat_1(A,B))
        & v1_ordinal1(k7_relat_1(A,B))
        & v2_ordinal1(k7_relat_1(A,B))
        & v3_ordinal1(k7_relat_1(A,B))
        & v1_xboole_0(k7_relat_1(A,B))
        & v4_ordinal2(k7_relat_1(A,B))
        & v1_finset_1(k7_relat_1(A,B))
        & v1_card_1(k7_relat_1(A,B))
        & v1_xreal_0(k7_relat_1(A,B))
        & ~ v2_xreal_0(k7_relat_1(A,B))
        & ~ v3_xreal_0(k7_relat_1(A,B))
        & v1_setfam_1(k7_relat_1(A,B))
        & v1_xcmplx_0(k7_relat_1(A,B))
        & v1_membered(k7_relat_1(A,B))
        & v2_membered(k7_relat_1(A,B))
        & v3_membered(k7_relat_1(A,B))
        & v4_membered(k7_relat_1(A,B))
        & v5_membered(k7_relat_1(A,B)) ) ) )).

fof(fc3_amistd_3,axiom,(
    ! [A,B] :
      ( ~ v1_finset_1(A)
     => ( v1_relat_1(k2_funcop_1(A,B))
        & v1_funct_1(k2_funcop_1(A,B))
        & ~ v1_xboole_0(k2_funcop_1(A,B))
        & ~ v1_finset_1(k2_funcop_1(A,B))
        & v1_setfam_1(k2_funcop_1(A,B)) ) ) )).

fof(rc1_amistd_3,axiom,(
    ? [A] :
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & ~ v1_xboole_0(A)
      & ~ v1_finset_1(A)
      & v1_setfam_1(A) ) )).

fof(fc4_amistd_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k3_relat_1(A)) ) )).

fof(fc5_amistd_3,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & ~ v1_finset_1(A) )
     => ( ~ v1_xboole_0(k3_relat_1(A))
        & ~ v1_finset_1(k3_relat_1(A)) ) ) )).

fof(fc6_amistd_3,axiom,
    ( v1_relat_1(k1_wellord2(k1_xboole_0))
    & v1_ordinal1(k1_wellord2(k1_xboole_0))
    & v2_ordinal1(k1_wellord2(k1_xboole_0))
    & v3_ordinal1(k1_wellord2(k1_xboole_0))
    & v1_xboole_0(k1_wellord2(k1_xboole_0))
    & v4_ordinal2(k1_wellord2(k1_xboole_0))
    & v1_finset_1(k1_wellord2(k1_xboole_0))
    & v1_card_1(k1_wellord2(k1_xboole_0))
    & v1_xreal_0(k1_wellord2(k1_xboole_0))
    & ~ v2_xreal_0(k1_wellord2(k1_xboole_0))
    & ~ v3_xreal_0(k1_wellord2(k1_xboole_0))
    & v1_setfam_1(k1_wellord2(k1_xboole_0))
    & v1_xcmplx_0(k1_wellord2(k1_xboole_0))
    & v1_membered(k1_wellord2(k1_xboole_0))
    & v2_membered(k1_wellord2(k1_xboole_0))
    & v3_membered(k1_wellord2(k1_xboole_0))
    & v4_membered(k1_wellord2(k1_xboole_0))
    & v5_membered(k1_wellord2(k1_xboole_0)) )).

fof(fc7_amistd_3,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ( v1_relat_1(k1_wellord2(A))
        & ~ v1_xboole_0(k1_wellord2(A))
        & v1_setfam_1(k1_wellord2(A)) ) ) )).

fof(fc8_amistd_3,axiom,(
    ! [A] :
      ( v1_finset_1(A)
     => ( v1_relat_1(k1_wellord2(A))
        & v1_finset_1(k1_wellord2(A))
        & v1_setfam_1(k1_wellord2(A)) ) ) )).

fof(fc9_amistd_3,axiom,(
    ! [A] :
      ( ~ v1_finset_1(A)
     => ( v1_relat_1(k1_wellord2(A))
        & ~ v1_xboole_0(k1_wellord2(A))
        & ~ v1_finset_1(k1_wellord2(A))
        & v1_setfam_1(k1_wellord2(A)) ) ) )).

fof(fc10_amistd_3,axiom,
    ( v1_relat_1(k2_wellord2(k1_xboole_0))
    & v1_ordinal1(k2_wellord2(k1_xboole_0))
    & v2_ordinal1(k2_wellord2(k1_xboole_0))
    & v3_ordinal1(k2_wellord2(k1_xboole_0))
    & v1_xboole_0(k2_wellord2(k1_xboole_0))
    & v4_ordinal2(k2_wellord2(k1_xboole_0))
    & v1_finset_1(k2_wellord2(k1_xboole_0))
    & v1_card_1(k2_wellord2(k1_xboole_0))
    & v1_xreal_0(k2_wellord2(k1_xboole_0))
    & ~ v2_xreal_0(k2_wellord2(k1_xboole_0))
    & ~ v3_xreal_0(k2_wellord2(k1_xboole_0))
    & v1_setfam_1(k2_wellord2(k1_xboole_0))
    & v1_xcmplx_0(k2_wellord2(k1_xboole_0))
    & v1_membered(k2_wellord2(k1_xboole_0))
    & v2_membered(k2_wellord2(k1_xboole_0))
    & v3_membered(k2_wellord2(k1_xboole_0))
    & v4_membered(k2_wellord2(k1_xboole_0))
    & v5_membered(k2_wellord2(k1_xboole_0)) )).

fof(fc11_amistd_3,axiom,(
    ! [A,B,C] :
      ( ( v3_ordinal1(A)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ( v1_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(B))),k1_wellord2(B)),C))
        & v2_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(B))),k1_wellord2(B)),C))
        & v3_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(B))),k1_wellord2(B)),C)) ) ) )).

fof(fc12_amistd_3,axiom,(
    ! [A,B] :
      ( v5_membered(A)
     => ( v1_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
        & v2_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
        & v3_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
        & v4_ordinal2(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
        & v1_card_1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
        & v1_xreal_0(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B))
        & v1_xcmplx_0(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) ) ) )).

fof(fc13_amistd_3,axiom,
    ( ~ v1_xboole_0(k1_amistd_3)
    & v1_trees_1(k1_amistd_3) )).

fof(fc14_amistd_3,axiom,
    ( ~ v1_xboole_0(k1_amistd_3)
    & ~ v1_finset_1(k1_amistd_3)
    & v1_trees_1(k1_amistd_3) )).

fof(fc15_amistd_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)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
     => ( v1_relat_1(k3_amistd_3(A,B,C))
        & v1_ordinal1(k3_amistd_3(A,B,C))
        & v2_ordinal1(k3_amistd_3(A,B,C))
        & v3_ordinal1(k3_amistd_3(A,B,C))
        & v1_xboole_0(k3_amistd_3(A,B,C))
        & v4_ordinal2(k3_amistd_3(A,B,C))
        & v1_finset_1(k3_amistd_3(A,B,C))
        & v1_card_1(k3_amistd_3(A,B,C))
        & v1_xreal_0(k3_amistd_3(A,B,C))
        & ~ v2_xreal_0(k3_amistd_3(A,B,C))
        & ~ v3_xreal_0(k3_amistd_3(A,B,C))
        & v1_setfam_1(k3_amistd_3(A,B,C))
        & v1_xcmplx_0(k3_amistd_3(A,B,C))
        & v1_membered(k3_amistd_3(A,B,C))
        & v2_membered(k3_amistd_3(A,B,C))
        & v3_membered(k3_amistd_3(A,B,C))
        & v4_membered(k3_amistd_3(A,B,C))
        & v5_membered(k3_amistd_3(A,B,C)) ) ) )).

fof(fc16_amistd_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)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & ~ v1_xboole_0(C)
        & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
     => ( ~ v1_xboole_0(k3_amistd_3(A,B,C))
        & v1_membered(k3_amistd_3(A,B,C))
        & v2_membered(k3_amistd_3(A,B,C))
        & v3_membered(k3_amistd_3(A,B,C))
        & v4_membered(k3_amistd_3(A,B,C))
        & v5_membered(k3_amistd_3(A,B,C)) ) ) )).

fof(fc17_amistd_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)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
     => ( v1_relat_1(k4_amistd_3(A,B,C))
        & v1_funct_1(k4_amistd_3(A,B,C))
        & v2_funct_1(k4_amistd_3(A,B,C))
        & v5_ordinal1(k4_amistd_3(A,B,C))
        & v1_setfam_1(k4_amistd_3(A,B,C)) ) ) )).

fof(t1_amistd_3,axiom,(
    ! [A,B,C] :
      ( v1_relat_1(C)
     => ( ( k1_relat_1(C) = k1_tarski(A)
          & k2_relat_1(C) = k1_tarski(B) )
       => C = k3_cqc_lang(A,B) ) ) )).

fof(t2_amistd_3,axiom,(
    ! [A] : k3_relat_1(k1_tarski(k4_tarski(A,A))) = k1_tarski(A) )).

fof(t3_amistd_3,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( v1_finset_1(k3_relat_1(A))
       => v1_finset_1(A) ) ) )).

fof(t4_amistd_3,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ( ( v1_finset_1(k1_relat_1(A))
          & v1_finset_1(k2_relat_1(A)) )
       => v1_finset_1(A) ) ) )).

fof(t5_amistd_3,axiom,(
    ! [A] : k1_wellord2(k1_tarski(A)) = k1_tarski(k4_tarski(A,A)) )).

fof(t6_amistd_3,axiom,(
    ! [A] : r1_tarski(k1_wellord2(A),k2_zfmisc_1(A,A)) )).

fof(t7_amistd_3,axiom,(
    ! [A] :
      ( v1_finset_1(k1_wellord2(A))
     => v1_finset_1(A) ) )).

fof(t8_amistd_3,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( ( r4_wellord1(A,B)
              & v2_wellord1(A) )
           => v2_wellord1(B) ) ) ) )).

fof(t9_amistd_3,axiom,(
    ! [A] :
      ( v1_relat_1(A)
     => ! [B] :
          ( v1_relat_1(B)
         => ( ( r4_wellord1(A,B)
              & v1_finset_1(A) )
           => v1_finset_1(B) ) ) ) )).

fof(t10_amistd_3,axiom,(
    ! [A,B] : r3_wellord1(k1_tarski(k4_tarski(A,A)),k1_tarski(k4_tarski(B,B)),k3_cqc_lang(A,B)) )).

fof(t11_amistd_3,axiom,(
    ! [A,B] : r4_wellord1(k1_tarski(k4_tarski(A,A)),k1_tarski(k4_tarski(B,B))) )).

fof(t12_amistd_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => k2_wellord2(k1_wellord2(A)) = A ) )).

fof(t13_amistd_3,axiom,(
    ! [A] :
      ( v3_ordinal1(A)
     => ! [B] :
          ( v1_finset_1(B)
         => ( r1_tarski(B,A)
           => k2_wellord2(k1_wellord2(B)) = k4_card_1(B) ) ) ) )).

fof(t14_amistd_3,axiom,(
    ! [A,B] :
      ( v3_ordinal1(B)
     => ( r1_tarski(k1_tarski(A),B)
       => k2_wellord2(k1_wellord2(k1_tarski(A))) = np__1 ) ) )).

fof(t15_amistd_3,axiom,(
    ! [A,B] :
      ( v3_ordinal1(B)
     => ( r1_tarski(k1_tarski(A),B)
       => k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(k1_tarski(A)))),k1_wellord2(k1_tarski(A))) = k3_cqc_lang(np__0,A) ) ) )).

fof(t16_amistd_3,axiom,(
    ! [A,B] :
      ( v4_ordinal2(B)
     => ! [C] :
          ( v4_ordinal2(C)
         => ( k2_finseq_2(B,A) = k2_finseq_2(C,A)
           => B = C ) ) ) )).

fof(t17_amistd_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ! [C] :
              ( m1_trees_1(C,B)
             => r2_hidden(k2_partfun1(k5_numbers,k5_numbers,C,k2_finseq_1(A)),B) ) ) ) )).

fof(t18_amistd_3,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_trees_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & v1_trees_1(B) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k2_trees_2(A,C) = k2_trees_2(B,C) )
           => A = B ) ) ) )).

fof(t19_amistd_3,axiom,(
    r2_wellord2(k5_numbers,k1_amistd_3) )).

fof(t20_amistd_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_trees_2(k1_amistd_3,A) = k1_tarski(k2_finseq_2(A,np__0)) ) )).

fof(t21_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => r2_hidden(k2_amistd_3(A,B,C),k1_relat_1(C)) ) ) ) )).

fof(t22_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & m1_ami_1(C,A,B) )
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ( r1_tarski(C,D)
                   => r1_amistd_1(A,B,k2_amistd_3(A,B,D),k2_amistd_3(A,B,C)) ) ) ) ) ) )).

fof(t23_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( ( ~ v1_xboole_0(D)
                    & v1_ami_3(D,A,B)
                    & m1_ami_1(D,A,B) )
                 => ( r2_hidden(C,k1_relat_1(D))
                   => r1_amistd_1(A,B,k2_amistd_3(A,B,D),C) ) ) ) ) ) )).

fof(t24_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( ( ~ v1_xboole_0(C)
                & v1_ami_3(C,A,B)
                & v9_amistd_1(C,A,B)
                & m1_ami_1(C,A,B) )
             => k2_amistd_3(A,B,C) = k5_amistd_1(A,B,np__0) ) ) ) )).

fof(t25_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u2_ami_1(A,B)))
                 => ( r2_hidden(k7_amistd_1(A,B,C),k3_amistd_3(A,B,D))
                  <=> r2_hidden(C,D) ) ) ) ) ) )).

fof(t26_amistd_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v4_amistd_1(C,B)
                & l1_ami_1(C,B) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u2_ami_1(B,C)))
                 => ( D = k1_struct_0(C,k5_amistd_1(B,C,A))
                   => k3_amistd_3(B,C,D) = k1_tarski(A) ) ) ) ) ) )).

fof(t27_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
             => r2_wellord2(C,k3_amistd_3(A,B,C)) ) ) ) )).

fof(t28_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
             => r1_ordinal1(k1_card_1(C),k2_wellord2(k1_wellord2(k3_amistd_3(A,B,C)))) ) ) ) )).

fof(t29_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                 => ( ( v10_ami_1(B,A)
                      & v3_ami_1(D,A,B) )
                   => k3_amistd_3(A,B,k1_amistd_1(A,B,C,D)) = k15_cqc_sim1(k5_numbers,k7_amistd_1(A,B,C)) ) ) ) ) ) )).

fof(t30_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( m2_subset_1(D,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
                 => ( ( v10_ami_1(B,A)
                      & v5_amistd_1(D,A,B) )
                   => k3_amistd_3(A,B,k1_amistd_1(A,B,C,D)) = k15_cqc_sim1(k5_numbers,k7_amistd_1(A,B,k9_amistd_1(A,B,C))) ) ) ) ) ) )).

fof(d4_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
             => ! [D] :
                  ( m1_ordinal1(D,u2_ami_1(A,B))
                 => ( D = k4_amistd_3(A,B,C)
                  <=> ( k1_relat_1(D) = k1_card_1(C)
                      & ! [E] :
                          ( r2_hidden(E,k1_card_1(C))
                         => k1_funct_1(D,E) = k5_amistd_1(A,B,k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(k3_amistd_3(A,B,C)))),k1_wellord2(k3_amistd_3(A,B,C))),E)) ) ) ) ) ) ) ) )).

fof(t31_amistd_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v1_setfam_1(B)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & ~ v2_ami_1(C,B)
                & v5_ami_1(C,B)
                & v8_ami_1(C,B)
                & v4_amistd_1(C,B)
                & l1_ami_1(C,B) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u2_ami_1(B,C)))
                 => ( D = k1_struct_0(C,k5_amistd_1(B,C,A))
                   => k4_amistd_3(B,C,D) = k3_cqc_lang(np__0,k5_amistd_1(B,C,A)) ) ) ) ) ) )).

fof(t32_amistd_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)
            & v10_ami_1(B,A)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => k5_amistd_3(A,B,k7_amistd_2(A,B)) = k9_trees_2(u2_ami_1(A,B),k1_amistd_3,k5_amistd_1(A,B,np__0)) ) ) )).

fof(dt_k1_amistd_3,axiom,(
    $true )).

fof(dt_k2_amistd_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)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & m1_ami_1(C,A,B) )
     => m1_struct_0(k2_amistd_3(A,B,C),B,u2_ami_1(A,B)) ) )).

fof(dt_k3_amistd_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)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
     => m1_subset_1(k3_amistd_3(A,B,C),k1_zfmisc_1(k5_numbers)) ) )).

fof(dt_k4_amistd_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)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B))) )
     => m1_ordinal1(k4_amistd_3(A,B,C),u2_ami_1(A,B)) ) )).

fof(dt_k5_amistd_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)
        & v4_amistd_1(B,A)
        & l1_ami_1(B,A)
        & m1_ami_1(C,A,B) )
     => ( v1_funct_1(k5_amistd_3(A,B,C))
        & v3_trees_2(k5_amistd_3(A,B,C))
        & m3_trees_2(k5_amistd_3(A,B,C),u2_ami_1(A,B)) ) ) )).

fof(d1_amistd_3,axiom,(
    k1_amistd_3 = a_0_0_amistd_3 )).

fof(d2_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_ami_1(C,A,B)
             => ( v1_ami_3(C,A,B)
               => ( v1_xboole_0(C)
                  | ! [D] :
                      ( m1_struct_0(D,B,u2_ami_1(A,B))
                     => ( D = k2_amistd_3(A,B,C)
                      <=> ? [E] :
                            ( ~ v1_xboole_0(E)
                            & m1_subset_1(E,k1_zfmisc_1(k5_numbers))
                            & E = a_3_0_amistd_3(A,B,C)
                            & D = k5_amistd_1(A,B,k10_cqc_sim1(E)) ) ) ) ) ) ) ) ) )).

fof(d3_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u2_ami_1(A,B)))
             => k3_amistd_3(A,B,C) = a_3_1_amistd_3(A,B,C) ) ) ) )).

fof(d5_amistd_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)
            & v4_amistd_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_ami_1(C,A,B)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v3_trees_2(D)
                    & m3_trees_2(D,u2_ami_1(A,B)) )
                 => ( D = k5_amistd_3(A,B,C)
                  <=> ( k1_funct_1(D,k1_xboole_0) = k2_amistd_3(A,B,C)
                      & ! [E] :
                          ( m1_trees_1(E,k1_relat_1(D))
                         => ( k1_trees_2(k1_relat_1(D),E) = a_5_0_amistd_3(A,B,C,D,E)
                            & ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ( r2_hidden(F,k1_card_1(k1_amistd_1(A,B,k3_trees_2(u2_ami_1(A,B),D,E),k5_ami_5(A,B,C,k3_trees_2(u2_ami_1(A,B),D,E)))))
                                 => k1_funct_1(D,k8_finseq_1(k5_numbers,E,k12_finseq_1(k5_numbers,F))) = k1_funct_1(k4_amistd_3(A,B,k1_amistd_1(A,B,k3_trees_2(u2_ami_1(A,B),D,E),k5_ami_5(A,B,C,k3_trees_2(u2_ami_1(A,B),D,E)))),F) ) ) ) ) ) ) ) ) ) ) )).

fof(fraenkel_a_0_0_amistd_3,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_amistd_3)
    <=> ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k2_finseq_2(B,np__0) ) ) )).

fof(fraenkel_a_3_0_amistd_3,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(B)
        & ~ v3_struct_0(C)
        & ~ v2_ami_1(C,B)
        & v5_ami_1(C,B)
        & v8_ami_1(C,B)
        & v4_amistd_1(C,B)
        & l1_ami_1(C,B)
        & m1_ami_1(D,B,C) )
     => ( r2_hidden(A,a_3_0_amistd_3(B,C,D))
      <=> ? [E] :
            ( m1_struct_0(E,C,u2_ami_1(B,C))
            & A = k7_amistd_1(B,C,E)
            & r2_hidden(E,k1_relat_1(D)) ) ) ) )).

fof(fraenkel_a_3_1_amistd_3,axiom,(
    ! [A,B,C,D] :
      ( ( v1_setfam_1(B)
        & ~ v3_struct_0(C)
        & ~ v2_ami_1(C,B)
        & v5_ami_1(C,B)
        & v8_ami_1(C,B)
        & v4_amistd_1(C,B)
        & l1_ami_1(C,B)
        & m1_subset_1(D,k1_zfmisc_1(u2_ami_1(B,C))) )
     => ( r2_hidden(A,a_3_1_amistd_3(B,C,D))
      <=> ? [E] :
            ( m1_struct_0(E,C,u2_ami_1(B,C))
            & A = k7_amistd_1(B,C,E)
            & r2_hidden(E,D) ) ) ) )).

fof(fraenkel_a_5_0_amistd_3,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( v1_setfam_1(B)
        & ~ v3_struct_0(C)
        & ~ v2_ami_1(C,B)
        & v5_ami_1(C,B)
        & v8_ami_1(C,B)
        & v4_amistd_1(C,B)
        & l1_ami_1(C,B)
        & m1_ami_1(D,B,C)
        & v1_funct_1(E)
        & v3_trees_2(E)
        & m3_trees_2(E,u2_ami_1(B,C))
        & m1_trees_1(F,k1_relat_1(E)) )
     => ( r2_hidden(A,a_5_0_amistd_3(B,C,D,E,F))
      <=> ? [G] :
            ( m2_subset_1(G,k1_numbers,k5_numbers)
            & A = k8_finseq_1(k5_numbers,F,k12_finseq_1(k5_numbers,G))
            & r2_hidden(G,k1_card_1(k1_amistd_1(B,C,k3_trees_2(u2_ami_1(B,C),E,F),k5_ami_5(B,C,D,k3_trees_2(u2_ami_1(B,C),E,F))))) ) ) ) )).
%------------------------------------------------------------------------------