SET007 Axioms: SET007+634.ax


%------------------------------------------------------------------------------
% File     : SET007+634 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Construction and Computation of for-loop Programs for SCMPDS
% 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_7 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   87 (   1 unit)
%            Number of atoms       :  855 ( 119 equality)
%            Maximal formula depth :   23 (  11 average)
%            Number of connectives :  784 (  16 ~  ;  39  |; 359  &)
%                                         (   3 <=>; 367 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   25 (   1 propositional; 0-3 arity)
%            Number of functors    :   80 (  13 constant; 0-5 arity)
%            Number of variables   :  326 (   0 singleton; 326 !;   0 ?)
%            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(fc1_scmpds_7,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_relat_1(k2_scmpds_4(A))
        & v1_funct_1(k2_scmpds_4(A))
        & v1_finset_1(k2_scmpds_4(A))
        & v1_scmpds_3(k2_scmpds_4(A)) ) ) )).

fof(fc2_scmpds_7,axiom,(
    ! [A,B,C,D] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & m1_subset_1(D,k5_numbers) )
     => ( v1_relat_1(k1_scmpds_7(B,C,D,A))
        & v1_funct_1(k1_scmpds_7(B,C,D,A))
        & v1_finset_1(k1_scmpds_7(B,C,D,A))
        & v1_ami_3(k1_scmpds_7(B,C,D,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_7(B,C,D,A))
        & v3_scmpds_4(k1_scmpds_7(B,C,D,A)) ) ) )).

fof(fc3_scmpds_7,axiom,(
    ! [A,B,C,D] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_5(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & m1_subset_1(D,k5_numbers) )
     => ( v1_relat_1(k1_scmpds_7(B,C,D,A))
        & v1_funct_1(k1_scmpds_7(B,C,D,A))
        & v1_finset_1(k1_scmpds_7(B,C,D,A))
        & v1_ami_3(k1_scmpds_7(B,C,D,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_7(B,C,D,A))
        & v3_scmpds_5(k1_scmpds_7(B,C,D,A)) ) ) )).

fof(fc4_scmpds_7,axiom,(
    ! [A,B,C,D] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_4(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & m1_subset_1(D,k5_numbers) )
     => ( v1_relat_1(k2_scmpds_7(B,C,D,A))
        & v1_funct_1(k2_scmpds_7(B,C,D,A))
        & v1_finset_1(k2_scmpds_7(B,C,D,A))
        & v1_ami_3(k2_scmpds_7(B,C,D,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k2_scmpds_7(B,C,D,A))
        & v3_scmpds_4(k2_scmpds_7(B,C,D,A)) ) ) )).

fof(fc5_scmpds_7,axiom,(
    ! [A,B,C,D] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & v3_scmpds_5(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & m1_scmpds_2(B)
        & v1_int_1(C)
        & m1_subset_1(D,k5_numbers) )
     => ( v1_relat_1(k2_scmpds_7(B,C,D,A))
        & v1_funct_1(k2_scmpds_7(B,C,D,A))
        & v1_finset_1(k2_scmpds_7(B,C,D,A))
        & v1_ami_3(k2_scmpds_7(B,C,D,A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k2_scmpds_7(B,C,D,A))
        & v3_scmpds_5(k2_scmpds_7(B,C,D,A)) ) ) )).

fof(t1_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_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)
             => ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(B)
               => k19_scmpds_2(A,k6_xcmplx_0(C,B)) = k2_scmpds_3(C) ) ) ) ) )).

fof(t2_scmpds_7,axiom,(
    ! [A] :
      ( m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2)
     => ! [B] :
          ( m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2)
         => ( r1_tarski(A,B)
           => r1_tarski(k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A),k6_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B)) ) ) ) )).

fof(t3_scmpds_7,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_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( r1_tarski(A,B)
               => r1_tarski(k6_scmpds_3(A,C),k6_scmpds_3(B,C)) ) ) ) ) )).

fof(t4_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(np__0)
       => k1_scmpds_5(A) = A ) ) )).

fof(t5_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scmpds_3(np__0)
           => k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B)) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,B) ) ) ) )).

fof(t6_scmpds_7,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
         => k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),A),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) )).

fof(t7_scmpds_7,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)))
         => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
              & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2)
              & k7_relat_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
           => A = B ) ) ) )).

fof(t8_scmpds_7,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ( r2_hidden(A,k1_relat_1(B))
          <=> r2_hidden(A,k1_relat_1(k2_scmpds_4(B))) ) ) ) )).

fof(t9_scmpds_7,axiom,(
    ! [A,B] :
      ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [C] :
          ( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [D] :
              ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(D)
                & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( r2_hidden(A,k1_relat_1(D))
               => k1_funct_1(D,A) = k1_funct_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C))),A) ) ) ) ) )).

fof(t10_scmpds_7,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] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( r2_hidden(B,k1_relat_1(C))
               => k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C)),B) = k1_funct_1(C,B) ) ) ) ) )).

fof(t11_scmpds_7,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_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k2_scmpds_2(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,C))),A) = k2_scmpds_2(B,A) ) ) ) ) )).

fof(t12_scmpds_7,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))
         => k1_funct_1(k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,B)),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = B ) ) )).

fof(t13_scmpds_7,axiom,(
    $true )).

fof(t14_scmpds_7,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] :
          ( m2_subset_1(B,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))
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => k1_funct_1(k5_scmpds_4(k5_scmpds_4(C,A),B),k2_scmpds_3(k4_card_1(C))) = A ) ) ) )).

fof(t15_scmpds_7,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] :
          ( m2_subset_1(B,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))
         => ! [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))
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k5_scmpds_4(k5_scmpds_4(k4_scmpds_4(A,D),B),C) = k4_scmpds_4(A,k5_scmpds_4(k5_scmpds_4(D,B),C)) ) ) ) ) )).

fof(t16_scmpds_7,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => r1_tarski(k6_scmpds_3(A,k4_card_1(B)),k3_scmpds_4(k3_scmpds_4(B,A),C)) ) ) ) )).

fof(t17_scmpds_7,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => r1_tarski(A,k8_scmpds_4(k3_scmpds_4(A,B))) ) ) )).

fof(t18_scmpds_7,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( r2_hidden(B,k1_relat_1(C))
               => k1_funct_1(k6_scmpds_3(k8_scmpds_4(C),A),k3_scmpds_3(B,A)) = k1_funct_1(k6_scmpds_3(C,A),k3_scmpds_3(B,A)) ) ) ) ) )).

fof(t19_scmpds_7,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ( ~ r1_xreal_0(k4_card_1(B),np__0)
           => k1_funct_1(k6_scmpds_3(k8_scmpds_4(B),A),k2_scmpds_3(A)) = k1_funct_1(k6_scmpds_3(B,A),k2_scmpds_3(A)) ) ) ) )).

fof(t20_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m2_subset_1(B,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))
         => ( r2_hidden(k1_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B),k2_enumset1(np__0,np__4,np__5,np__6))
           => k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A),k2_ami_2) = k7_relat_1(A,k2_ami_2) ) ) ) )).

fof(t21_scmpds_7,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(k1_funct_4(A,k7_relat_1(B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))),k2_ami_2) = k7_relat_1(A,k2_ami_2) ) ) )).

fof(t22_scmpds_7,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))
     => k2_relat_1(k1_scmpds_4(A)) = k1_tarski(A) ) )).

fof(t23_scmpds_7,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] :
              ( 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)
                  & k7_relat_1(B,k2_ami_2) = k7_relat_1(C,k2_ami_2) )
               => ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B)) = k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C))
                  & k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,B),k2_ami_2) = k7_relat_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C),k2_ami_2) ) ) ) ) ) )).

fof(t24_scmpds_7,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_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(C,A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
                  & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
               => ! [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,A),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,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,A),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))
                      & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),k2_ami_2) ) ) ) ) ) ) )).

fof(t25_scmpds_7,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_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(C,A)
                  & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(C)))),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(C)))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                      & 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(C)))),D)) ) ) ) ) ) ) )).

fof(t26_scmpds_7,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_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(C,A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
                  & r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
                      & 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,A),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)) ) ) ) ) ) ) )).

fof(t27_scmpds_7,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_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(C,A)
                  & r2_scmpds_6(C,A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
                  & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
               => k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,B) ) ) ) ) )).

fof(t28_scmpds_7,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_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(C,A)
                  & r2_scmpds_6(C,A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B)
                  & r1_funct_7(A,B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
               => ( k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,B)
                  & r1_funct_7(k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t29_scmpds_7,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_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(C,A)
                  & r2_scmpds_6(C,A)
                  & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
               => ( k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(C)))) = k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(C))))
                  & r1_funct_7(k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(C)))),k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(C)))),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t30_scmpds_7,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_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(C,A)
                  & r2_scmpds_6(C,A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
                  & r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),B) )
               => ( ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ~ r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),D),B,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) )
                  | r1_funct_7(k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t31_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ( r2_scmpds_6(B,A)
               => k2_scmpds_2(k9_scmpds_4(B,A),C) = k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B))))),C) ) ) ) ) )).

fof(t32_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v2_scmpds_4(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => k2_scmpds_2(k9_scmpds_4(B,A),C) = k2_scmpds_2(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B))))),C) ) ) ) )).

fof(t33_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ( ( r1_tarski(k2_scmpds_4(k8_scmpds_4(B)),A)
                  & r1_scmpds_6(B,A)
                  & r2_scmpds_6(B,A) )
               => ( r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),C)
                  | 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,A),C)),k1_relat_1(B)) ) ) ) ) ) )).

fof(t34_scmpds_7,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_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
                  & r1_scmpds_6(C,A)
                  & r2_scmpds_6(C,A) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r1_tarski(k6_scmpds_3(C,D),B)
                        & k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) = k2_scmpds_3(D)
                        & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
                     => ( r1_xreal_0(k4_card_1(C),np__0)
                        | ! [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                           => ( ~ r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E)
                             => ( k3_scmpds_3(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,A),E)),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,B),E))
                                & 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,A),E)) = 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),E))
                                & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),E),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),E),k2_ami_2) ) ) ) ) ) ) ) ) ) ) )).

fof(t35_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ~ ( r1_tarski(k2_scmpds_4(k8_scmpds_4(B)),A)
              & r2_scmpds_6(B,A)
              & ~ r1_xreal_0(k4_card_1(B),np__0)
              & r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A),np__0) ) ) ) )).

fof(t36_scmpds_7,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_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_tarski(k2_scmpds_4(k8_scmpds_4(C)),A)
                  & r1_scmpds_6(C,A)
                  & r2_scmpds_6(C,A) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ( r1_tarski(k6_scmpds_3(C,D),B)
                        & k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B) = k2_scmpds_3(D)
                        & k7_relat_1(A,k2_ami_2) = k7_relat_1(B,k2_ami_2) )
                     => ( r1_xreal_0(k4_card_1(C),np__0)
                        | ( 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),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A))) = k2_scmpds_3(k1_nat_1(k4_card_1(C),D))
                          & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A)),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,A)),k2_ami_2) ) ) ) ) ) ) ) ) )).

fof(t37_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m2_subset_1(C,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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B))),C)) = k2_scmpds_3(np__0)
               => k8_ami_5(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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B))),C),k2_scmpds_4(B)) = k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(B))),C) ) ) ) ) )).

fof(t38_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A)
                      & r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B))))) )
                   => r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k17_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_4(B,C),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(np__0))))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t39_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_tarski(B,C)
                      & r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A)
                      & r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B))))) )
                   => r1_funct_7(k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C))),D),k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),D),u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ) ) ) ) )).

fof(t40_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(D,k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))
                      & r1_tarski(B,C)
                      & r1_scmpds_6(B,A)
                      & r2_scmpds_6(B,A) )
                   => 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C))),D)),k1_relat_1(k8_scmpds_4(B))) ) ) ) ) ) )).

fof(t41_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ~ ( r1_tarski(B,C)
                  & r1_scmpds_6(B,A)
                  & r2_scmpds_6(B,A)
                  & 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))) != k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)
                  & 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))) != k2_scmpds_3(k4_card_1(B)) ) ) ) ) )).

fof(t42_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r2_scmpds_6(B,A)
                  & r1_scmpds_6(C,k9_scmpds_4(B,A))
                  & r2_scmpds_6(C,k9_scmpds_4(B,A)) )
               => ( r1_scmpds_6(C,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B))))))
                  & r2_scmpds_6(C,k11_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))) ) ) ) ) ) )).

fof(t43_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(B,A)
                  & r2_scmpds_6(B,A)
                  & r1_scmpds_6(C,k9_scmpds_4(B,A))
                  & r2_scmpds_6(C,k9_scmpds_4(B,A)) )
               => ( r1_scmpds_6(k3_scmpds_4(B,C),A)
                  & r2_scmpds_6(k3_scmpds_4(B,C),A) ) ) ) ) ) )).

fof(t44_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_tarski(B,C)
                  & r1_scmpds_6(B,A)
                  & r2_scmpds_6(B,A) )
               => 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(C))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))))) = k2_scmpds_3(k4_card_1(B)) ) ) ) ) )).

fof(t45_scmpds_7,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & 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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ~ ( r2_scmpds_6(A,B)
                  & ~ r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A)))),C)
                  & 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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,B,k2_scmpds_4(k8_scmpds_4(A)))),C)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) )).

fof(t46_scmpds_7,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(A)
        & m1_ami_1(A,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,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)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ~ ( r1_scmpds_6(A,C)
                      & r2_scmpds_6(A,C)
                      & ~ r1_xreal_0(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(A)))),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,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,C,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(A,B))))),D)) = k5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ) ) ) ) )).

fof(t47_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(B,A)
                  & r2_scmpds_6(B,A)
                  & r1_scmpds_6(C,k9_scmpds_4(B,A))
                  & r2_scmpds_6(C,k9_scmpds_4(B,A)) )
               => k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(k3_scmpds_4(B,C))))) = k1_nat_1(k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scm_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k12_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k2_scmpds_4(k8_scmpds_4(B)))),k2_scmpds_4(k8_scmpds_4(C))))) ) ) ) ) )).

fof(t48_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_4(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ( ( r1_scmpds_6(B,A)
                  & r2_scmpds_6(B,A)
                  & r1_scmpds_6(C,k9_scmpds_4(B,A))
                  & r2_scmpds_6(C,k9_scmpds_4(B,A)) )
               => k9_scmpds_4(k3_scmpds_4(B,C),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,k9_scmpds_4(B,A)),k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k3_scmpds_3(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(C,k9_scmpds_4(B,A))),k4_card_1(B)))) ) ) ) ) )).

fof(t49_scmpds_7,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] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & v3_scmpds_4(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => ( ( r1_scmpds_6(C,B)
                      & r2_scmpds_6(C,B)
                      & r1_scmpds_6(D,k9_scmpds_4(C,B))
                      & r2_scmpds_6(D,k9_scmpds_4(C,B)) )
                   => k2_scmpds_2(k9_scmpds_4(k3_scmpds_4(C,D),B),A) = k2_scmpds_2(k9_scmpds_4(D,k9_scmpds_4(C,B)),A) ) ) ) ) ) )).

fof(t50_scmpds_7,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] :
              ( ( v1_ami_3(C,k1_tarski(k4_numbers),k1_scmpds_2)
                & v1_scmpds_3(C)
                & v3_scmpds_5(C)
                & m1_ami_1(C,k1_tarski(k4_numbers),k1_scmpds_2) )
             => ! [D] :
                  ( ( v4_scmpds_4(D)
                    & v2_scmpds_5(D)
                    & m2_subset_1(D,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)) )
                 => ( ( r1_scmpds_6(C,B)
                      & r2_scmpds_6(C,B) )
                   => k2_scmpds_2(k9_scmpds_4(k5_scmpds_4(C,D),B),A) = k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,D,k9_scmpds_4(C,B)),A) ) ) ) ) ) )).

fof(d1_scmpds_7,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k1_scmpds_7(A,B,C,D) = k5_scmpds_4(k5_scmpds_4(k4_scmpds_4(k10_scmpds_2(A,B,k1_nat_1(k4_card_1(D),np__3)),D),k12_scmpds_2(A,B,C)),k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(D),np__2)))) ) ) ) ) )).

fof(t51_scmpds_7,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k4_card_1(k1_scmpds_7(A,B,C,D)) = k1_nat_1(k4_card_1(D),np__3) ) ) ) ) )).

fof(t52_scmpds_7,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( v1_ami_3(E,k1_tarski(k4_numbers),k1_scmpds_2)
                        & v1_scmpds_3(E)
                        & m1_ami_1(E,k1_tarski(k4_numbers),k1_scmpds_2) )
                     => ( ~ r1_xreal_0(k1_nat_1(k4_card_1(E),np__3),D)
                      <=> r2_hidden(k2_scmpds_3(D),k1_relat_1(k1_scmpds_7(A,B,C,E))) ) ) ) ) ) ) )).

fof(t53_scmpds_7,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => ( k1_funct_1(k1_scmpds_7(A,B,C,D),k2_scmpds_3(np__0)) = k10_scmpds_2(A,B,k1_nat_1(k4_card_1(D),np__3))
                    & k1_funct_1(k1_scmpds_7(A,B,C,D),k2_scmpds_3(k1_nat_1(k4_card_1(D),np__1))) = k12_scmpds_2(A,B,C)
                    & k1_funct_1(k1_scmpds_7(A,B,C,D),k2_scmpds_3(k1_nat_1(k4_card_1(D),np__2))) = k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(D),np__2))) ) ) ) ) ) )).

fof(t54_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                       => ( r1_scmpds_6(k1_scmpds_7(C,D,E,B),A)
                          & r2_scmpds_6(k1_scmpds_7(C,D,E,B),A) ) ) ) ) ) ) ) )).

fof(t55_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
                           => k9_scmpds_4(k1_scmpds_7(C,E,F,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__3)))) ) ) ) ) ) ) ) )).

fof(t56_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                       => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k1_scmpds_7(C,D,E,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__3)) ) ) ) ) ) ) )).

fof(t57_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)))
                           => k2_scmpds_2(k9_scmpds_4(k1_scmpds_7(C,E,F,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ) )).

fof(t58_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ! [G] :
                              ( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
                             => ( ( ! [H] :
                                      ( m1_scmpds_2(H)
                                     => ( r2_hidden(H,F)
                                       => k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
                                  & k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
                               => ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
                                  & k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D)) = k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))
                                  & r1_scmpds_6(B,G)
                                  & r2_scmpds_6(B,G)
                                  & ! [H] :
                                      ( m1_scmpds_2(H)
                                     => ( r2_hidden(H,F)
                                       => k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) )
                         => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                            | r2_hidden(k3_scmpds_2(k2_scmpds_2(A,C),D),F)
                            | r1_xreal_0(E,np__0)
                            | r1_xreal_0(k4_card_1(B),np__0)
                            | C = k3_scmpds_2(k2_scmpds_2(A,C),D)
                            | ( r1_scmpds_6(k1_scmpds_7(C,D,E,B),A)
                              & r2_scmpds_6(k1_scmpds_7(C,D,E,B),A) ) ) ) ) ) ) ) ) )).

fof(t59_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ! [G] :
                              ( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
                             => ( ( ! [H] :
                                      ( m1_scmpds_2(H)
                                     => ( r2_hidden(H,F)
                                       => k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
                                  & k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
                               => ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
                                  & k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D)) = k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))
                                  & r1_scmpds_6(B,G)
                                  & r2_scmpds_6(B,G)
                                  & ! [H] :
                                      ( m1_scmpds_2(H)
                                     => ( r2_hidden(H,F)
                                       => k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) )
                         => ( r1_xreal_0(np__0,k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)))
                            | r2_hidden(k3_scmpds_2(k2_scmpds_2(A,C),D),F)
                            | r1_xreal_0(E,np__0)
                            | r1_xreal_0(k4_card_1(B),np__0)
                            | C = k3_scmpds_2(k2_scmpds_2(A,C),D)
                            | k9_scmpds_4(k1_scmpds_7(C,D,E,B),A) = k9_scmpds_4(k1_scmpds_7(C,D,E,B),k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,D,E)),A)) ) ) ) ) ) ) ) )).

fof(d2_scmpds_7,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k2_scmpds_7(A,B,C,D) = k5_scmpds_4(k5_scmpds_4(k4_scmpds_4(k9_scmpds_2(A,B,k1_nat_1(k4_card_1(D),np__3)),D),k12_scmpds_2(A,B,k4_xcmplx_0(C))),k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(D),np__2)))) ) ) ) ) )).

fof(t60_scmpds_7,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => k4_card_1(k2_scmpds_7(A,B,C,D)) = k1_nat_1(k4_card_1(D),np__3) ) ) ) ) )).

fof(t61_scmpds_7,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( ( v1_ami_3(E,k1_tarski(k4_numbers),k1_scmpds_2)
                        & v1_scmpds_3(E)
                        & m1_ami_1(E,k1_tarski(k4_numbers),k1_scmpds_2) )
                     => ( ~ r1_xreal_0(k1_nat_1(k4_card_1(E),np__3),D)
                      <=> r2_hidden(k2_scmpds_3(D),k1_relat_1(k2_scmpds_7(A,B,C,E))) ) ) ) ) ) ) )).

fof(t62_scmpds_7,axiom,(
    ! [A] :
      ( m1_scmpds_2(A)
     => ! [B] :
          ( v1_int_1(B)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( ( v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
                    & v1_scmpds_3(D)
                    & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
                 => ( k1_funct_1(k2_scmpds_7(A,B,C,D),k2_scmpds_3(np__0)) = k9_scmpds_2(A,B,k1_nat_1(k4_card_1(D),np__3))
                    & k1_funct_1(k2_scmpds_7(A,B,C,D),k2_scmpds_3(k1_nat_1(k4_card_1(D),np__1))) = k12_scmpds_2(A,B,k4_xcmplx_0(C))
                    & k1_funct_1(k2_scmpds_7(A,B,C,D),k2_scmpds_3(k1_nat_1(k4_card_1(D),np__2))) = k4_scmpds_2(k4_xcmplx_0(k1_nat_1(k4_card_1(D),np__2))) ) ) ) ) ) )).

fof(t63_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                       => ( r1_scmpds_6(k2_scmpds_7(C,D,E,B),A)
                          & r2_scmpds_6(k2_scmpds_7(C,D,E,B),A) ) ) ) ) ) ) ) )).

fof(t64_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
                           => k9_scmpds_4(k2_scmpds_7(C,E,F,B),A) = k8_ami_5(k1_tarski(k4_numbers),k1_scmpds_2,A,k12_ami_3(k1_tarski(k4_numbers),k1_scmpds_2,k2_scmpds_3(k1_nat_1(k4_card_1(B),np__3)))) ) ) ) ) ) ) ) )).

fof(t65_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                       => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_4(k2_scmpds_7(C,D,E,B),A)) = k2_scmpds_3(k1_nat_1(k4_card_1(B),np__3)) ) ) ) ) ) ) )).

fof(t66_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( m1_scmpds_2(D)
                 => ! [E] :
                      ( v1_int_1(E)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),E)),np__0)
                           => k2_scmpds_2(k9_scmpds_4(k2_scmpds_7(C,E,F,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ) )).

fof(t67_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ! [G] :
                              ( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
                             => ( ( ! [H] :
                                      ( m1_scmpds_2(H)
                                     => ( r2_hidden(H,F)
                                       => k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
                                  & k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
                               => ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
                                  & k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D)) = k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))
                                  & r1_scmpds_6(B,G)
                                  & r2_scmpds_6(B,G)
                                  & ! [H] :
                                      ( m1_scmpds_2(H)
                                     => ( r2_hidden(H,F)
                                       => k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) )
                         => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                            | r2_hidden(k3_scmpds_2(k2_scmpds_2(A,C),D),F)
                            | r1_xreal_0(E,np__0)
                            | r1_xreal_0(k4_card_1(B),np__0)
                            | C = k3_scmpds_2(k2_scmpds_2(A,C),D)
                            | ( r1_scmpds_6(k2_scmpds_7(C,D,E,B),A)
                              & r2_scmpds_6(k2_scmpds_7(C,D,E,B),A) ) ) ) ) ) ) ) ) )).

fof(t68_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( ( v1_ami_3(B,k1_tarski(k4_numbers),k1_scmpds_2)
            & v1_scmpds_3(B)
            & v3_scmpds_4(B)
            & v3_scmpds_5(B)
            & m1_ami_1(B,k1_tarski(k4_numbers),k1_scmpds_2) )
         => ! [C] :
              ( m1_scmpds_2(C)
             => ! [D] :
                  ( v1_int_1(D)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( ! [G] :
                              ( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
                             => ( ( ! [H] :
                                      ( m1_scmpds_2(H)
                                     => ( r2_hidden(H,F)
                                       => k2_scmpds_2(G,H) = k2_scmpds_2(A,H) ) )
                                  & k2_scmpds_2(G,C) = k2_scmpds_2(A,C) )
                               => ( k2_scmpds_2(k9_scmpds_4(B,G),C) = k2_scmpds_2(G,C)
                                  & k2_scmpds_2(k9_scmpds_4(B,G),k3_scmpds_2(k2_scmpds_2(A,C),D)) = k2_scmpds_2(G,k3_scmpds_2(k2_scmpds_2(A,C),D))
                                  & r1_scmpds_6(B,G)
                                  & r2_scmpds_6(B,G)
                                  & ! [H] :
                                      ( m1_scmpds_2(H)
                                     => ( r2_hidden(H,F)
                                       => k2_scmpds_2(k9_scmpds_4(B,G),H) = k2_scmpds_2(G,H) ) ) ) ) )
                         => ( r1_xreal_0(k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,C),D)),np__0)
                            | r2_hidden(k3_scmpds_2(k2_scmpds_2(A,C),D),F)
                            | r1_xreal_0(E,np__0)
                            | r1_xreal_0(k4_card_1(B),np__0)
                            | C = k3_scmpds_2(k2_scmpds_2(A,C),D)
                            | k9_scmpds_4(k2_scmpds_7(C,D,E,B),A) = k9_scmpds_4(k2_scmpds_7(C,D,E,B),k9_scmpds_4(k5_scmpds_4(B,k12_scmpds_2(C,D,k4_xcmplx_0(E))),A)) ) ) ) ) ) ) ) )).

fof(d3_scmpds_7,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k3_scmpds_7(A) = k3_scmpds_4(k5_scmpds_4(k6_scmpds_4(k6_scmpds_2(k2_scmp_gcd,np__0),k11_scmpds_2(k2_scmp_gcd,np__2,A)),k11_scmpds_2(k2_scmp_gcd,np__3,np__0)),k2_scmpds_7(k2_scmp_gcd,np__2,np__1,k1_scmpds_4(k12_scmpds_2(k2_scmp_gcd,np__3,np__1)))) ) )).

fof(t69_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ( k2_scmpds_2(A,k2_scmp_gcd) = np__0
       => ( r1_scmpds_6(k2_scmpds_7(k2_scmp_gcd,np__2,np__1,k1_scmpds_4(k12_scmpds_2(k2_scmp_gcd,np__3,np__1))),A)
          & r2_scmpds_6(k2_scmpds_7(k2_scmp_gcd,np__2,np__1,k1_scmpds_4(k12_scmpds_2(k2_scmp_gcd,np__3,np__1))),A) ) ) ) )).

fof(t70_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( ( k2_scmpds_2(A,k2_scmp_gcd) = np__0
              & k2_scmpds_2(A,k1_scmp_gcd(np__2)) = B
              & k2_scmpds_2(A,k1_scmp_gcd(np__3)) = np__0 )
           => k2_scmpds_2(k9_scmpds_4(k2_scmpds_7(k2_scmp_gcd,np__2,np__1,k1_scmpds_4(k12_scmpds_2(k2_scmp_gcd,np__3,np__1))),A),k1_scmp_gcd(np__3)) = B ) ) ) )).

fof(t71_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k2_scmpds_2(k9_scmpds_4(k3_scmpds_7(B),A),k1_scmp_gcd(np__3)) = B ) ) )).

fof(d4_scmpds_7,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => k4_scmpds_7(A,B,C,D,E) = k3_scmpds_4(k6_scmpds_4(k11_scmpds_2(k1_scmp_gcd(A),C,np__0),k6_scmpds_2(k1_scmp_gcd(D),E)),k2_scmpds_7(k1_scmp_gcd(A),B,np__1,k6_scmpds_4(k13_scmpds_2(k1_scmp_gcd(A),k1_scmp_gcd(E),C,np__0),k12_scmpds_2(k1_scmp_gcd(D),np__0,np__1)))) ) ) ) ) ) )).

fof(t72_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_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)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ( k2_scmpds_2(A,k1_scmp_gcd(E)) = F
                           => ( r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(B)),B)
                              | r1_xreal_0(D,C)
                              | r1_xreal_0(E,k2_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(B)),D))
                              | r1_xreal_0(F,E)
                              | r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(F)),F)
                              | ( r1_scmpds_6(k2_scmpds_7(k1_scmp_gcd(B),C,np__1,k6_scmpds_4(k13_scmpds_2(k1_scmp_gcd(B),k1_scmp_gcd(F),D,np__0),k12_scmpds_2(k1_scmp_gcd(E),np__0,np__1))),A)
                                & r2_scmpds_6(k2_scmpds_7(k1_scmp_gcd(B),C,np__1,k6_scmpds_4(k13_scmpds_2(k1_scmp_gcd(B),k1_scmp_gcd(F),D,np__0),k12_scmpds_2(k1_scmp_gcd(E),np__0,np__1))),A) ) ) ) ) ) ) ) ) ) )).

fof(t73_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_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)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( m1_trees_4(G,k1_numbers,k5_numbers)
                             => ( ( k2_scmpds_2(A,k1_scmp_gcd(E)) = F
                                  & k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),D)) = np__0
                                  & k3_finseq_1(G) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),C))
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( ~ r1_xreal_0(k3_finseq_1(G),H)
                                       => k3_wsierp_1(G,k1_nat_1(H,np__1)) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(F)),H)) ) ) )
                               => ( r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(B)),B)
                                  | r1_xreal_0(D,C)
                                  | r1_xreal_0(E,k2_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(B)),D))
                                  | r1_xreal_0(F,E)
                                  | r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(F)),F)
                                  | k2_scmpds_2(k9_scmpds_4(k2_scmpds_7(k1_scmp_gcd(B),C,np__1,k6_scmpds_4(k13_scmpds_2(k1_scmp_gcd(B),k1_scmp_gcd(F),D,np__0),k12_scmpds_2(k1_scmp_gcd(E),np__0,np__1))),A),k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),D)) = k9_wsierp_1(G) ) ) ) ) ) ) ) ) ) )).

fof(t74_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_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)
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ! [E] :
                      ( m2_subset_1(E,k1_numbers,k5_numbers)
                     => ! [F] :
                          ( m2_subset_1(F,k1_numbers,k5_numbers)
                         => ! [G] :
                              ( m1_trees_4(G,k1_numbers,k5_numbers)
                             => ( ( k3_finseq_1(G) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),C))
                                  & ! [H] :
                                      ( m2_subset_1(H,k1_numbers,k5_numbers)
                                     => ( ~ r1_xreal_0(k3_finseq_1(G),H)
                                       => k3_wsierp_1(G,k1_nat_1(H,np__1)) = k2_scmpds_2(A,k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(F)),H)) ) ) )
                               => ( r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(B)),B)
                                  | r1_xreal_0(D,C)
                                  | r1_xreal_0(E,k2_xcmplx_0(k2_scmpds_2(A,k1_scmp_gcd(B)),D))
                                  | r1_xreal_0(F,E)
                                  | r1_xreal_0(k2_scmpds_2(A,k1_scmp_gcd(F)),F)
                                  | k2_scmpds_2(k9_scmpds_4(k4_scmpds_7(B,C,D,E,F),A),k3_scmpds_2(k2_scmpds_2(A,k1_scmp_gcd(B)),D)) = k9_wsierp_1(G) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_scmpds_7,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & m1_subset_1(C,k5_numbers)
        & v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(D)
        & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k1_scmpds_7(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k1_scmpds_7(A,B,C,D))
        & m1_ami_1(k1_scmpds_7(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k2_scmpds_7,axiom,(
    ! [A,B,C,D] :
      ( ( m1_scmpds_2(A)
        & v1_int_1(B)
        & m1_subset_1(C,k5_numbers)
        & v1_ami_3(D,k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(D)
        & m1_ami_1(D,k1_tarski(k4_numbers),k1_scmpds_2) )
     => ( v1_ami_3(k2_scmpds_7(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k2_scmpds_7(A,B,C,D))
        & m1_ami_1(k2_scmpds_7(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k3_scmpds_7,axiom,(
    ! [A] :
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ami_3(k3_scmpds_7(A),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k3_scmpds_7(A))
        & m1_ami_1(k3_scmpds_7(A),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).

fof(dt_k4_scmpds_7,axiom,(
    ! [A,B,C,D,E] :
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,k5_numbers)
        & m1_subset_1(D,k5_numbers)
        & m1_subset_1(E,k5_numbers) )
     => ( v1_ami_3(k4_scmpds_7(A,B,C,D,E),k1_tarski(k4_numbers),k1_scmpds_2)
        & v1_scmpds_3(k4_scmpds_7(A,B,C,D,E))
        & m1_ami_1(k4_scmpds_7(A,B,C,D,E),k1_tarski(k4_numbers),k1_scmpds_2) ) ) )).
%------------------------------------------------------------------------------