SET007 Axioms: SET007+793.ax


%------------------------------------------------------------------------------
% File     : SET007+793 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : SCMPDS Is Not Standard
% 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    : scmpds_9 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   54 (   1 unit)
%            Number of atoms       :  329 (  41 equality)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :  305 (  30 ~  ;   0  |; 163  &)
%                                         (   2 <=>; 110 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   37 (   0 propositional; 1-4 arity)
%            Number of functors    :   59 (   8 constant; 0-4 arity)
%            Number of variables   :  146 (   0 singleton; 145 !;   1 ?)
%            Maximal term depth    :    7 (   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_scmpds_9,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v7_amistd_2(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(fc2_scmpds_9,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A))) ) ) )).

fof(fc3_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ( ~ v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A)))
        & ~ v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A)))
        & ~ v1_realset1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A))) ) ) )).

fof(fc4_scmpds_9,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B))) ) ) )).

fof(fc5_scmpds_9,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B))) ) ) )).

fof(fc6_scmpds_9,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C))) ) ) )).

fof(fc7_scmpds_9,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D))) ) ) )).

fof(fc8_scmpds_9,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C))) ) ) )).

fof(fc9_scmpds_9,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D))) ) ) )).

fof(fc10_scmpds_9,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D))) ) ) )).

fof(fc11_scmpds_9,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D))) ) ) )).

fof(fc12_scmpds_9,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D))) ) ) )).

fof(fc13_scmpds_9,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C))) ) ) )).

fof(fc14_scmpds_9,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C))) ) ) )).

fof(fc15_scmpds_9,axiom,(
    ! [A,B,C] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & v1_int_1(C) )
     => ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
        & v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C))) ) ) )).

fof(fc16_scmpds_9,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v3_amistd_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v7_amistd_2(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(fc17_scmpds_9,axiom,
    ( ~ v3_struct_0(k1_scmpds_2)
    & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v3_amistd_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & ~ v4_amistd_1(k1_scmpds_2,k1_tarski(k4_numbers))
    & v7_amistd_2(k1_scmpds_2,k1_tarski(k4_numbers)) )).

fof(t1_scmpds_9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => r1_xreal_0(np__0,k2_xcmplx_0(A,k18_complex1(A))) ) )).

fof(t2_scmpds_9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => r1_xreal_0(np__0,k2_xcmplx_0(k4_xcmplx_0(A),k18_complex1(A))) ) )).

fof(t3_scmpds_9,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ~ ( k18_complex1(A) = k18_complex1(B)
              & A != B
              & A != k4_xcmplx_0(B) ) ) ) )).

fof(t4_scmpds_9,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ! [B] :
          ( v4_ordinal2(B)
         => ~ ( ~ r1_xreal_0(B,A)
              & A != np__0
              & v1_int_1(k7_xcmplx_0(A,B)) ) ) ) )).

fof(t6_scmpds_9,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D] :
          ( B != D
         => k1_funct_1(k1_funct_4(A,k3_cqc_lang(B,C)),D) = k1_funct_1(A,D) ) ) )).

fof(t7_scmpds_9,axiom,(
    ! [A] :
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D,E] :
          ( B != C
         => ( k1_funct_1(k1_funct_4(A,k4_funct_4(B,C,D,E)),B) = D
            & k1_funct_1(k1_funct_4(A,k4_funct_4(B,C,D,E)),C) = E ) ) ) )).

fof(d1_scmpds_9,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( v4_ordinal2(B)
         => ( B = k2_scmpds_9(A)
          <=> k16_ami_3(B) = A ) ) ) )).

fof(t8_scmpds_9,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => A = k1_nat_1(k2_nat_1(np__2,k3_scmpds_9(A)),np__2) ) )).

fof(t9_scmpds_9,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ~ ( A != B
              & k3_scmpds_9(A) = k3_scmpds_9(B) ) ) ) )).

fof(t10_scmpds_9,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ~ ( A != B
              & k18_scmpds_2(A) = k18_scmpds_2(B) ) ) ) )).

fof(t11_scmpds_9,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => r1_tarski(k2_amistd_1(A,B,C),k1_amistd_1(A,B,D,C)) ) ) ) ) )).

fof(t12_scmpds_9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ( ! [C] :
                ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
               => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C) = B
                    & k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,B) = A )
                 => k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C)) ) )
           => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) )).

fof(t13_scmpds_9,axiom,(
    ! [A] :
      ( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ( ! [B] :
            ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
           => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) )
       => v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) ) ) )).

fof(t14_scmpds_9,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( v1_int_1(B)
         => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k4_scmpds_2(B)) = k1_tarski(k1_nat_1(k2_nat_1(np__2,k1_int_2(k2_xcmplx_0(B,k3_scmpds_9(A)))),np__2)) ) ) )).

fof(t16_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( v1_int_1(C)
             => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k7_scmpds_2(A,C)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) )).

fof(t17_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( v1_int_1(C)
             => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k6_scmpds_2(A,C)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) )).

fof(t18_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k11_scmpds_2(A,C,D)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) ) )).

fof(t19_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k17_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) )).

fof(t20_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_scmpds_2(A,C,D)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) ) )).

fof(t21_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k13_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) )).

fof(t22_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k14_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) )).

fof(t23_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k15_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) )).

fof(t24_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k16_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) )).

fof(t25_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k8_scmpds_2(A,C,D)) = k2_tarski(k18_scmpds_2(B),k1_nat_1(k1_int_2(k3_xcmplx_0(np__2,k2_xcmplx_0(D,k3_scmpds_9(B)))),np__2)) ) ) ) ) )).

fof(t26_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k9_scmpds_2(A,C,D)) = k2_tarski(k18_scmpds_2(B),k1_nat_1(k1_int_2(k3_xcmplx_0(np__2,k2_xcmplx_0(D,k3_scmpds_9(B)))),np__2)) ) ) ) ) )).

fof(t27_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k10_scmpds_2(A,C,D)) = k2_tarski(k18_scmpds_2(B),k1_nat_1(k1_int_2(k3_xcmplx_0(np__2,k2_xcmplx_0(D,k3_scmpds_9(B)))),np__2)) ) ) ) ) )).

fof(t29_scmpds_9,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => k3_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(t30_scmpds_9,axiom,(
    ! [A] :
      ( v1_setfam_1(A)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_struct_0(C,B,u2_ami_1(A,B))
             => ! [D] :
                  ( m1_struct_0(D,B,u2_ami_1(A,B))
                 => ( k3_amistd_1(A,B,C) = u2_ami_1(A,B)
                   => r1_amistd_1(A,B,C,D) ) ) ) ) ) )).

fof(dt_k1_scmpds_9,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => m1_ami_1(k1_scmpds_9(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(redefinition_k1_scmpds_9,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & v1_int_1(D) )
     => k1_scmpds_9(A,B,C,D) = k4_funct_4(A,B,C,D) ) )).

fof(dt_k2_scmpds_9,axiom,(
    ! [A] :
      ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => v4_ordinal2(k2_scmpds_9(A)) ) )).

fof(dt_k3_scmpds_9,axiom,(
    ! [A] :
      ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => m2_subset_1(k3_scmpds_9(A),k1_numbers,k5_numbers) ) )).

fof(redefinition_k3_scmpds_9,axiom,(
    ! [A] :
      ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => k3_scmpds_9(A) = k2_scmpds_9(A) ) )).

fof(t5_scmpds_9,axiom,(
    ~ v1_finset_1(a_0_0_scmpds_9) )).

fof(t15_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k5_scmpds_2(A)) = a_0_0_scmpds_9 ) ) )).

fof(t28_scmpds_9,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A)) = a_0_0_scmpds_9 ) )).

fof(fraenkel_a_0_0_scmpds_9,axiom,(
    ! [A] :
      ( r2_hidden(A,a_0_0_scmpds_9)
    <=> ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k2_nat_1(np__2,B)
          & ~ r1_xreal_0(B,np__1) ) ) )).
%------------------------------------------------------------------------------