SET007 Axioms: SET007+550.ax


%------------------------------------------------------------------------------
% File     : SET007+550 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The While Macro Instructions of SCMFSA. Part II
% 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    : scmfsa9a [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   60 (   5 unit)
%            Number of atoms       :  517 (  75 equality)
%            Maximal formula depth :   21 (  10 average)
%            Number of connectives :  536 (  79 ~  ;  13  |; 224  &)
%                                         (   7 <=>; 213 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   36 (   1 propositional; 0-3 arity)
%            Number of functors    :   74 (  13 constant; 0-4 arity)
%            Number of variables   :  186 (   0 singleton; 180 !;   6 ?)
%            Maximal term depth    :   10 (   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(t1_scmfsa9a,axiom,(
    ! [A] :
      ( v4_ordinal2(A)
     => ( ~ ( ~ v1_abian(A)
            & ! [B] :
                ( m2_subset_1(B,k1_numbers,k5_numbers)
               => A != k1_nat_1(k2_nat_1(np__2,B),np__1) ) )
        & ~ ( ? [B] :
                ( m2_subset_1(B,k1_numbers,k5_numbers)
                & A = k1_nat_1(k2_nat_1(np__2,B),np__1) )
            & v1_abian(A) ) ) ) )).

fof(t2_scmfsa9a,axiom,(
    $true )).

fof(t3_scmfsa9a,axiom,(
    $true )).

fof(t4_scmfsa9a,axiom,(
    ! [A] :
      ( v1_int_1(A)
     => ! [B] :
          ( v1_int_1(B)
         => ~ ( ~ r1_xreal_0(A,np__0)
              & ~ r1_xreal_0(B,np__1)
              & r1_xreal_0(A,k5_int_1(A,B)) ) ) ) )).

fof(t5_scmfsa9a,axiom,(
    $true )).

fof(t6_scmfsa9a,axiom,(
    ! [A] :
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & ~ v2_ami_1(B,A)
            & v4_ami_1(B,A)
            & v5_ami_1(B,A)
            & v8_ami_1(B,A)
            & l1_ami_1(B,A) )
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( k8_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) = k5_ami_1(A,B)
                   => k11_ami_1(A,B,k10_ami_1(A,B,C),k2_scm_1(A,B,C)) = k11_ami_1(A,B,k10_ami_1(A,B,C),D) ) ) ) ) ) )).

fof(t7_scmfsa9a,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => k2_sf_mastr(k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k1_sf_mastr(B) ) ) )).

fof(t8_scmfsa9a,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => k4_sf_mastr(k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k3_sf_mastr(B) ) ) )).

fof(t9_scmfsa9a,axiom,(
    k2_sf_mastr(k5_scmfsa_4) = k1_xboole_0 )).

fof(t10_scmfsa9a,axiom,(
    k4_sf_mastr(k5_scmfsa_4) = k1_xboole_0 )).

fof(t11_scmfsa9a,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k2_sf_mastr(k2_scmfsa8a(A)) = k1_xboole_0 ) )).

fof(t12_scmfsa9a,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k4_sf_mastr(k2_scmfsa8a(A)) = k1_xboole_0 ) )).

fof(t13_scmfsa9a,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => k2_sf_mastr(k1_scmfsa8b(A,B,C)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_sfmastr1(A),k2_sf_mastr(B)),k2_sf_mastr(C)) ) ) ) )).

fof(t14_scmfsa9a,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(A)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( m1_scmfsa_2(C)
             => k4_sf_mastr(k1_scmfsa8b(C,A,B)) = k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(A),k4_sf_mastr(B)) ) ) ) )).

fof(t15_scmfsa9a,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => k2_sf_mastr(k2_scmfsa8b(A,B,C)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_sfmastr1(A),k2_sf_mastr(B)),k2_sf_mastr(C)) ) ) ) )).

fof(t16_scmfsa9a,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => k4_sf_mastr(k2_scmfsa8b(A,B,C)) = k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(B),k4_sf_mastr(C)) ) ) ) )).

fof(t17_scmfsa9a,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k2_sf_mastr(k1_scmfsa_9(A,B)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_sfmastr1(A),k2_sf_mastr(B)) ) ) )).

fof(t18_scmfsa9a,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k4_sf_mastr(k1_scmfsa_9(A,B)) = k4_sf_mastr(B) ) ) )).

fof(d1_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r1_scmfsa9a(A,B,C)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D),B) = np__0
                     => ( r5_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D))
                        & r6_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D)) ) ) ) ) ) ) ) )).

fof(d2_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r2_scmfsa9a(A,B,C)
              <=> ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
                    & m2_relset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ~ ( r1_xreal_0(k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),E)),k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),k1_nat_1(E,np__1))))
                            & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),E),B) = np__0 ) ) ) ) ) ) ) )).

fof(t19_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v2_scmfsa6b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => r1_scmfsa9a(A,B,C) ) ) ) )).

fof(t20_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r1_scmfsa9a(A,B,C)
                  & r2_scmfsa9a(A,B,C) )
               => ( r6_scmfsa7b(k1_scmfsa_9(B,C),A)
                  & r5_scmfsa7b(k1_scmfsa_9(B,C),A) ) ) ) ) ) )).

fof(t21_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v2_scmfsa6b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r2_scmfsa9a(A,B,C)
               => ( r6_scmfsa7b(k1_scmfsa_9(B,C),A)
                  & r5_scmfsa7b(k1_scmfsa_9(B,C),A) ) ) ) ) ) )).

fof(t22_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),A)
               => ( k20_scmfsa_2(A,B) = np__0
                  | ( k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__4
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) )).

fof(t23_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r5_scmfsa7b(C,A)
                  & r6_scmfsa7b(C,A)
                  & k20_scmfsa_2(A,B) = np__0 )
               => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__3)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) )).

fof(t24_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D),B) != np__0
                   => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),k1_nat_1(D,np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) )).

fof(t25_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D),B) = np__0
                      & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 )
                   => ( ( ~ ( r6_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D)))
                            & r5_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D))) )
                        & ~ v2_scmfsa6b(C) )
                      | k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),k1_nat_1(D,np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) )).

fof(t26_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
               => ( ( ~ r1_scmfsa9a(A,B,C)
                    & ~ v2_scmfsa6b(C) )
                  | ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) )).

fof(t27_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ! [D] :
                  ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                    & v1_scmfsa_4(D)
                    & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                 => ( ( r1_scmfsa9a(A,C,D)
                      & k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) )
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,D,C),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(B,D,C),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) )).

fof(d3_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r2_scmfsa9a(A,B,C)
               => ( ( ~ r1_scmfsa9a(A,B,C)
                    & ~ v2_scmfsa6b(C) )
                  | ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( D = k1_scmfsa9a(A,B,C)
                      <=> ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & D = E
                            & k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),E),B) != np__0
                            & ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),F),B) != np__0
                                 => r1_xreal_0(E,F) ) )
                            & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) )).

fof(t28_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
               => ( k20_scmfsa_2(A,B) = np__0
                  | k7_relat_1(k3_scmfsa6b(k1_scmfsa_9(B,C),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) )).

fof(t29_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r2_scmfsa9a(k1_scmfsa6c(A),B,C)
               => ( ( ~ r1_scmfsa9a(k1_scmfsa6c(A),B,C)
                    & ~ v2_scmfsa6b(C) )
                  | k7_relat_1(k3_scmfsa6b(k1_scmfsa_9(B,C),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(k1_scmfsa6c(A),C,B),k1_scmfsa9a(k1_scmfsa6c(A),B,C)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) )).

fof(t30_scmfsa9a,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k2_sf_mastr(k2_scmfsa_9(A,B)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_sfmastr1(A),k2_sf_mastr(B)) ) ) )).

fof(t31_scmfsa9a,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & v1_scmfsa_4(B)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => k4_sf_mastr(k2_scmfsa_9(A,B)) = k4_sf_mastr(B) ) ) )).

fof(d4_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r3_scmfsa9a(A,B,C)
              <=> ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( ~ r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),B),np__0)
                     => ( r5_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D))
                        & r6_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D)) ) ) ) ) ) ) ) )).

fof(d5_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r4_scmfsa9a(A,B,C)
              <=> ? [D] :
                    ( v1_funct_1(D)
                    & v1_funct_2(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
                    & m2_relset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
                    & ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ~ ( r1_xreal_0(k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E)),k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),k1_nat_1(E,np__1))))
                            & ~ r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),B),np__0) ) ) ) ) ) ) ) )).

fof(t32_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v2_scmfsa6b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => r3_scmfsa9a(A,B,C) ) ) ) )).

fof(t33_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r3_scmfsa9a(A,B,C)
                  & r4_scmfsa9a(A,B,C) )
               => ( r6_scmfsa7b(k2_scmfsa_9(B,C),A)
                  & r5_scmfsa7b(k2_scmfsa_9(B,C),A) ) ) ) ) ) )).

fof(t34_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v2_scmfsa6b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r4_scmfsa9a(A,B,C)
               => ( r6_scmfsa7b(k2_scmfsa_9(B,C),A)
                  & r5_scmfsa7b(k2_scmfsa_9(B,C),A) ) ) ) ) ) )).

fof(t35_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),A)
                  & r1_xreal_0(k20_scmfsa_2(A,B),np__0) )
               => ( k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__4
                  & ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) )).

fof(t36_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( r5_scmfsa7b(C,A)
                  & r6_scmfsa7b(C,A) )
               => ( r1_xreal_0(k20_scmfsa_2(A,B),np__0)
                  | k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__3)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) )).

fof(t37_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),B),np__0)
                   => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),k1_nat_1(D,np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) )).

fof(t38_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),k4_scmfsa_2(np__0)) = np__1
                   => ( ( ~ ( r6_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D)))
                            & r5_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D))) )
                        & ~ v2_scmfsa6b(C) )
                      | r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),B),np__0)
                      | k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),k1_nat_1(D,np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) )).

fof(t39_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
               => ( ( ~ r3_scmfsa9a(A,B,C)
                    & ~ v2_scmfsa6b(C) )
                  | ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) )).

fof(t40_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ! [D] :
                  ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                    & v1_scmfsa_4(D)
                    & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                 => ( ( r3_scmfsa9a(A,C,D)
                      & k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) )
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,D,C),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(B,D,C),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) )).

fof(d6_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r4_scmfsa9a(A,B,C)
               => ( ( ~ r3_scmfsa9a(A,B,C)
                    & ~ v2_scmfsa6b(C) )
                  | ! [D] :
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( D = k2_scmfsa9a(A,B,C)
                      <=> ? [E] :
                            ( m2_subset_1(E,k1_numbers,k5_numbers)
                            & D = E
                            & r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),B),np__0)
                            & ! [F] :
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),F),B),np__0)
                                 => r1_xreal_0(E,F) ) )
                            & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) )).

fof(t41_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                  & r1_xreal_0(k20_scmfsa_2(A,B),np__0) )
               => k7_relat_1(k3_scmfsa6b(k2_scmfsa_9(B,C),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) )).

fof(t42_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( r4_scmfsa9a(k1_scmfsa6c(A),B,C)
               => ( ( ~ r3_scmfsa9a(k1_scmfsa6c(A),B,C)
                    & ~ v2_scmfsa6b(C) )
                  | k7_relat_1(k3_scmfsa6b(k2_scmfsa_9(B,C),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(k1_scmfsa6c(A),C,B),k2_scmfsa9a(k1_scmfsa6c(A),B,C)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) )).

fof(t43_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ! [D] :
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),B),np__0)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( r1_xreal_0(D,E)
                         => k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) )).

fof(t44_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ! [D] :
                  ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                    & v1_scmfsa_4(D)
                    & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                 => ( ( k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2))
                      & r3_scmfsa9a(A,C,D) )
                   => r3_scmfsa9a(B,C,D) ) ) ) ) ) )).

fof(t45_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                  & r3_scmfsa9a(A,B,C)
                  & r4_scmfsa9a(A,B,C) )
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ! [E] :
                        ( m2_subset_1(E,k1_numbers,k5_numbers)
                       => ( ( r1_xreal_0(D,k2_scmfsa9a(A,B,C))
                            & r1_xreal_0(E,k2_scmfsa9a(A,B,C)) )
                         => ( D = E
                            | ( k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D) != k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E)
                              & k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) != k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) ) )).

fof(d7_scmfsa9a,axiom,(
    ! [A] :
      ( ( v1_funct_1(A)
        & v1_funct_2(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
        & m2_relset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers) )
     => ( v1_scmfsa9a(A)
      <=> ! [B] :
            ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
           => ! [C] :
                ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
               => ( k7_relat_1(B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(C,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2))
                 => k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,A,B) = k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,A,C) ) ) ) ) ) )).

fof(t46_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & v1_scmfsa_4(C)
                & v1_scmfsa7b(C)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                  & r3_scmfsa9a(A,B,C)
                  & r4_scmfsa9a(A,B,C)
                  & ! [D] :
                      ( ( v1_funct_1(D)
                        & v1_funct_2(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
                        & m2_relset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers) )
                     => ~ ( v1_scmfsa9a(D)
                          & ! [E] :
                              ( m2_subset_1(E,k1_numbers,k5_numbers)
                             => ~ ( r1_xreal_0(k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E)),k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),k1_nat_1(E,np__1))))
                                  & ~ r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),B),np__0) ) ) ) ) ) ) ) ) )).

fof(t47_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ! [D] :
                  ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                    & v1_scmfsa_4(D)
                    & v1_scmfsa7b(D)
                    & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                 => ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
                      & k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2))
                      & r3_scmfsa9a(A,C,D)
                      & r4_scmfsa9a(A,C,D) )
                   => r4_scmfsa9a(B,C,D) ) ) ) ) ) )).

fof(d8_scmfsa9a,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => k3_scmfsa9a(A,B) = k4_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k10_scmfsa_2(B,B),k8_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(A,B)),k4_scmfsa_2(np__0))),k8_scmfsa_2(k6_sfmastr1(np__2,k2_sfmastr1(A,B)),A)),k2_scmfsa_9(k6_sfmastr1(np__2,k2_sfmastr1(A,B)),k4_scmfsa6a(k6_scmfsa6a(k2_scmfsa_7(k6_sfmastr1(np__3,k2_sfmastr1(A,B)),np__2),k12_scmfsa_2(k6_sfmastr1(np__2,k2_sfmastr1(A,B)),k6_sfmastr1(np__3,k2_sfmastr1(A,B)))),k1_scmfsa8b(k6_sfmastr1(np__3,k2_sfmastr1(A,B)),k2_scmfsa6a(k9_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(A,B)),B)),k2_scmfsa6a(k9_scmfsa_2(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B)))))))) ) ) )).

fof(t48_scmfsa9a,axiom,(
    ! [A] :
      ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
     => ! [B] :
          ( ( ~ v1_sf_mastr(B)
            & m1_scmfsa_2(B) )
         => ! [C] :
              ( ( ~ v1_sf_mastr(C)
                & m1_scmfsa_2(C) )
             => ( B != C
               => ! [D] :
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( D = k20_scmfsa_2(A,B)
                     => ( k20_scmfsa_2(k3_scmfsa6b(k3_scmfsa9a(B,C),A),C) = k5_pre_ff(D)
                        & k20_scmfsa_2(k3_scmfsa6b(k3_scmfsa9a(B,C),A),B) = D ) ) ) ) ) ) ) )).

fof(s1_scmfsa9a,axiom,
    ( ! [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ~ ( r1_xreal_0(f1_s1_scmfsa9a(A),f1_s1_scmfsa9a(k1_nat_1(A,np__1)))
            & ~ p1_s1_scmfsa9a(A) ) )
   => ? [A] :
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & p1_s1_scmfsa9a(A)
        & ! [B] :
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( p1_s1_scmfsa9a(B)
             => r1_xreal_0(A,B) ) ) ) )).

fof(dt_k1_scmfsa9a,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
        & ~ v1_sf_mastr(B)
        & m1_scmfsa_2(B)
        & v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(C)
        & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => m2_subset_1(k1_scmfsa9a(A,B,C),k1_numbers,k5_numbers) ) )).

fof(dt_k2_scmfsa9a,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
        & ~ v1_sf_mastr(B)
        & m1_scmfsa_2(B)
        & v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(C)
        & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => m2_subset_1(k2_scmfsa9a(A,B,C),k1_numbers,k5_numbers) ) )).

fof(dt_k3_scmfsa9a,axiom,(
    ! [A,B] :
      ( ( m1_scmfsa_2(A)
        & m1_scmfsa_2(B) )
     => ( v1_ami_3(k3_scmfsa9a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & v1_scmfsa_4(k3_scmfsa9a(A,B))
        & m1_ami_1(k3_scmfsa9a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) )).
%------------------------------------------------------------------------------