SET007 Axioms: SET007+606.ax


%------------------------------------------------------------------------------
% File     : SET007+606 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Computation and Program Shift in the SCMPDS Computer
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : scmpds_3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   60 (   5 unit)
%            Number of atoms       :  374 (  85 equality)
%            Maximal formula depth :   24 (   8 average)
%            Number of connectives :  358 (  44 ~  ;   4  |; 121  &)
%                                         (   9 <=>; 180 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-3 arity)
%            Number of functors    :   78 (  22 constant; 0-4 arity)
%            Number of variables   :  170 (   0 singleton; 163 !;   7 ?)
%            Maximal term depth    :    8 (   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(rc1_scmpds_3,axiom,(
    ? [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
      & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(fc1_scmpds_3,axiom,
    ( ~ v1_xboole_0(k5_scmpds_3)
    & v1_relat_1(k5_scmpds_3)
    & v1_funct_1(k5_scmpds_3)
    & v1_finset_1(k5_scmpds_3)
    & v1_ami_3(k5_scmpds_3,k1_tarski(k4_numbers),k1_scmpds_2)
    & v1_scmpds_3(k5_scmpds_3) )).

fof(rc2_scmpds_3,axiom,(
    ? [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
      & ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
      & v1_scmpds_3(A) ) )).

fof(t1_scmpds_3,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ~ ( r1_xreal_0(A,np__13)
          & A != np__0
          & A != np__1
          & A != np__2
          & A != np__3
          & A != np__4
          & A != np__5
          & A != np__6
          & A != np__7
          & A != np__8
          & A != np__9
          & A != np__10
          & A != np__11
          & A != np__12
          & A != np__13 ) ) )).

fof(t2_scmpds_3,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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,B) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C)
               => k19_scmpds_2(B,A) = k19_scmpds_2(C,A) ) ) ) ) )).

fof(t3_scmpds_3,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( m1_scmpds_2(B)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
                 => ( k7_relat_1(C,k2_ami_2) = k7_relat_1(D,k2_ami_2)
                   => k2_scmpds_2(C,k3_scmpds_2(k2_scmpds_2(C,B),A)) = k2_scmpds_2(D,k3_scmpds_2(k2_scmpds_2(D,B),A)) ) ) ) ) ) )).

fof(t4_scmpds_3,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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)))
             => ( k7_relat_1(B,k2_ami_2) = k7_relat_1(C,k2_ami_2)
               => k2_scmpds_2(B,A) = k2_scmpds_2(C,A) ) ) ) ) )).

fof(t5_scmpds_3,axiom,(
    u1_struct_0(k1_scmpds_2) = k2_xboole_0(k2_xboole_0(k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)),k2_ami_2),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )).

fof(t6_scmpds_3,axiom,(
    ~ r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k2_ami_2) )).

fof(t7_scmpds_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( k7_relat_1(A,k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) = k7_relat_1(B,k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))))
           => ! [C] :
                ( m2_subset_1(C,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))
               => k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,A),k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,B),k2_xboole_0(k2_ami_2,k1_struct_0(k1_scmpds_2,k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))) ) ) ) ) )).

fof(t8_scmpds_3,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_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k3_ami_2) = k7_relat_1(B,k3_ami_2) ) ) )).

fof(t9_scmpds_3,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => k7_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) = k7_relat_1(A,k2_ami_2) ) )).

fof(t10_scmpds_3,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => ( v1_ami_5(A,k1_tarski(k4_numbers),k1_scmpds_2)
      <=> r1_tarski(k1_relat_1(A),k2_ami_2) ) ) )).

fof(t11_scmpds_3,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => r1_tarski(k1_relat_1(k7_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)),k2_ami_2) ) )).

fof(t12_scmpds_3,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => r1_tarski(k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A)),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(t13_scmpds_3,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_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,C)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),C) ) ) ) )).

fof(t14_scmpds_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_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_scmpds_2(C)
             => k2_scmpds_2(A,C) = k2_scmpds_2(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B)),C) ) ) ) )).

fof(t15_scmpds_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => m1_subset_1(k1_funct_4(A,k7_relat_1(B,k2_ami_2)),k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) ) ) )).

fof(t16_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( k7_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A) != k1_xboole_0
       => r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_relat_1(A)) ) ) )).

fof(t17_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_relat_1(A)) ) )).

fof(t18_scmpds_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ! [C] :
              ( v1_int_1(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ~ ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
                          & C != D
                          & E = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)
                          & r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,C)))
                          & r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,D)))
                          & k19_scmpds_2(A,C) = k19_scmpds_2(B,D) ) ) ) ) ) ) )).

fof(t19_scmpds_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
                      & C != D
                      & k19_scmpds_2(A,C) = k19_scmpds_2(B,D) ) ) ) ) ) )).

fof(t20_scmpds_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) = k19_scmpds_2(A,np__1) ) )).

fof(t21_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k1_relat_1(A))
       => r2_hidden(k13_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,A),k1_relat_1(A)) ) ) )).

fof(t22_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => ( r1_tarski(A,B)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => r2_hidden(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),C)),k1_relat_1(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A))) ) ) ) ) )).

fof(t23_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D))
                      & k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) = k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D)) ) ) ) ) ) ) )).

fof(t24_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( v1_int_1(E)
                       => ! [F] :
                            ( v1_int_1(F)
                           => ! [G] :
                                ( m1_scmpds_2(G)
                               => ! [H] :
                                    ( m1_scmpds_2(H)
                                   => ( ( k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) = k17_scmpds_2(G,H,E,F)
                                        & r2_hidden(G,k1_relat_1(A))
                                        & r2_hidden(k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E),k1_relat_1(A)) )
                                     => k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),H),F)) = k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),H),F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t25_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( v1_int_1(E)
                       => ! [F] :
                            ( v1_int_1(F)
                           => ! [G] :
                                ( m1_scmpds_2(G)
                               => ! [H] :
                                    ( m1_scmpds_2(H)
                                   => ( ( k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) = k13_scmpds_2(G,H,E,F)
                                        & r2_hidden(G,k1_relat_1(A))
                                        & r2_hidden(k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E),k1_relat_1(A)) )
                                     => k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),H),F)) = k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),H),F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t26_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( v1_int_1(E)
                       => ! [F] :
                            ( v1_int_1(F)
                           => ! [G] :
                                ( m1_scmpds_2(G)
                               => ! [H] :
                                    ( m1_scmpds_2(H)
                                   => ( ( k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) = k14_scmpds_2(G,H,E,F)
                                        & r2_hidden(G,k1_relat_1(A))
                                        & r2_hidden(k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E),k1_relat_1(A)) )
                                     => k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),H),F)) = k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),H),F)) ) ) ) ) ) ) ) ) ) ) )).

fof(t27_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( v1_int_1(E)
                       => ! [F] :
                            ( v1_int_1(F)
                           => ! [G] :
                                ( m1_scmpds_2(G)
                               => ! [H] :
                                    ( m1_scmpds_2(H)
                                   => ( ( k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) = k15_scmpds_2(G,H,E,F)
                                        & r2_hidden(G,k1_relat_1(A))
                                        & r2_hidden(k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E),k1_relat_1(A)) )
                                     => k3_xcmplx_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),G),E)),k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),H),F))) = k3_xcmplx_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),G),E)),k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),H),F))) ) ) ) ) ) ) ) ) ) ) )).

fof(t28_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ! [F] :
                            ( m1_scmpds_2(F)
                           => ! [G] :
                                ( v1_int_1(G)
                               => ! [H] :
                                    ( v1_int_1(H)
                                   => ( ( k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) = k8_scmpds_2(F,G,H)
                                        & E = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D))
                                        & r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,H))) )
                                     => ( H = np__1
                                        | ( k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G)) = np__0
                                        <=> k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G)) = np__0 ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t29_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ! [F] :
                            ( m1_scmpds_2(F)
                           => ! [G] :
                                ( v1_int_1(G)
                               => ! [H] :
                                    ( v1_int_1(H)
                                   => ( ( k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) = k9_scmpds_2(F,G,H)
                                        & E = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D))
                                        & r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,H))) )
                                     => ( H = np__1
                                        | ( ~ ( ~ r1_xreal_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G)),np__0)
                                              & r1_xreal_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G)),np__0) )
                                          & ~ ( ~ r1_xreal_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G)),np__0)
                                              & r1_xreal_0(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G)),np__0) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t30_scmpds_3,axiom,(
    ! [A] :
      ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_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)))
             => ( ( r1_tarski(A,B)
                  & r1_tarski(A,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ! [F] :
                            ( m1_scmpds_2(F)
                           => ! [G] :
                                ( v1_int_1(G)
                               => ! [H] :
                                    ( v1_int_1(H)
                                   => ( ( k8_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D)) = k10_scmpds_2(F,G,H)
                                        & E = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D))
                                        & r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(E,np__2),k3_xcmplx_0(np__2,H))) )
                                     => ( H = np__1
                                        | ( ~ ( ~ r1_xreal_0(np__0,k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G)))
                                              & r1_xreal_0(np__0,k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G))) )
                                          & ~ ( ~ r1_xreal_0(np__0,k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C),D),F),G)))
                                              & r1_xreal_0(np__0,k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k3_scmpds_2(k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),F),G))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d1_scmpds_3,axiom,(
    $true )).

fof(d2_scmpds_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k2_scmpds_3(A) = k16_ami_3(A) ) )).

fof(t31_scmpds_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( A != B
              & k2_scmpds_3(A) = k2_scmpds_3(B) ) ) ) )).

fof(t32_scmpds_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ? [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
          & A = k2_scmpds_3(B) ) ) )).

fof(d3_scmpds_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ( C = k3_scmpds_3(A,B)
              <=> ? [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & A = k2_scmpds_3(D)
                    & C = k2_scmpds_3(k1_nat_1(D,B)) ) ) ) ) ) )).

fof(d4_scmpds_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ( C = k4_scmpds_3(A,B)
              <=> ? [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                    & A = k2_scmpds_3(D)
                    & C = k2_scmpds_3(k5_binarith(D,B)) ) ) ) ) ) )).

fof(t33_scmpds_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k3_scmpds_3(k3_scmpds_3(A,B),C) = k3_scmpds_3(A,k1_nat_1(B,C)) ) ) ) )).

fof(t34_scmpds_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k4_scmpds_3(k3_scmpds_3(A,B),B) = A ) ) )).

fof(t35_scmpds_3,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))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(A,C)) = k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(B,C))
              <=> k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,A) = k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B) ) ) ) ) )).

fof(t36_scmpds_3,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))
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,A) = k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B)
               => k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_3(A,C)) = k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_3(B,C)) ) ) ) ) )).

fof(d5_scmpds_3,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => ( v1_scmpds_3(A)
      <=> ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => ( r2_hidden(k2_scmpds_3(C),k1_relat_1(A))
                 => ( r1_xreal_0(C,B)
                    | r2_hidden(k2_scmpds_3(B),k1_relat_1(A)) ) ) ) ) ) ) )).

fof(d6_scmpds_3,axiom,(
    k5_scmpds_3 = k14_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0),k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )).

fof(t37_scmpds_3,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( r2_hidden(A,k1_relat_1(C))
               => k1_funct_1(k6_scmpds_3(C,B),k3_scmpds_3(A,B)) = k1_funct_1(C,A) ) ) ) ) )).

fof(t39_scmpds_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k6_scmpds_3(k6_scmpds_3(C,A),B) = k6_scmpds_3(C,k1_nat_1(A,B)) ) ) ) )).

fof(t40_scmpds_3,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
            & m2_relset_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => k6_scmpds_3(k6_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,A,B),C) = k6_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_3(A,C),B) ) ) ) )).

fof(t41_scmpds_3,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k6_scmpds_3(k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,B,C),A) = k1_scmfsa_4(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_3(B,A),k6_scmpds_3(C,A)) ) ) ) )).

fof(dt_k1_scmpds_3,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => m1_ami_1(k1_scmpds_3(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) )).

fof(redefinition_k1_scmpds_3,axiom,(
    ! [A,B] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B) )
     => k1_scmpds_3(A,B) = k3_cqc_lang(A,B) ) )).

fof(dt_k2_scmpds_3,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => m1_struct_0(k2_scmpds_3(A),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k3_scmpds_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & m1_subset_1(B,k5_numbers) )
     => m1_struct_0(k3_scmpds_3(A,B),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k4_scmpds_3,axiom,(
    ! [A,B] :
      ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
        & m1_subset_1(B,k5_numbers) )
     => m1_struct_0(k4_scmpds_3(A,B),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) )).

fof(dt_k5_scmpds_3,axiom,(
    m1_ami_1(k5_scmpds_3,k1_tarski(k4_numbers),k1_scmpds_2) )).

fof(dt_k6_scmpds_3,axiom,(
    ! [A,B] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_subset_1(B,k5_numbers) )
     => ( v1_ami_3(k6_scmpds_3(A,B),k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(k6_scmpds_3(A,B),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(d7_scmpds_3,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( C = k6_scmpds_3(A,B)
              <=> ( k1_relat_1(C) = a_2_0_scmpds_3(A,B)
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(k2_scmpds_3(D),k1_relat_1(A))
                       => k1_funct_1(C,k2_scmpds_3(k1_nat_1(D,B))) = k1_funct_1(A,k2_scmpds_3(D)) ) ) ) ) ) ) ) )).

fof(t38_scmpds_3,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k1_relat_1(k6_scmpds_3(A,B)) = a_2_1_scmpds_3(A,B) ) ) )).

fof(fraenkel_a_2_0_scmpds_3,axiom,(
    ! [A,B,C] :
      ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_0_scmpds_3(B,C))
      <=> ? [D] :
            ( m2_subset_1(D,k1_numbers,k5_numbers)
            & A = k2_scmpds_3(k1_nat_1(D,C))
            & r2_hidden(k2_scmpds_3(D),k1_relat_1(B)) ) ) ) )).

fof(fraenkel_a_2_1_scmpds_3,axiom,(
    ! [A,B,C] :
      ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
        & m2_subset_1(C,k1_numbers,k5_numbers) )
     => ( r2_hidden(A,a_2_1_scmpds_3(B,C))
      <=> ? [D] :
            ( m1_struct_0(D,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
            & A = k3_scmpds_3(D,C)
            & r2_hidden(D,k1_relat_1(B)) ) ) ) )).
%------------------------------------------------------------------------------