SET007 Axioms: SET007+472.ax


%------------------------------------------------------------------------------
% File     : SET007+472 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Memory Handling for SCMFSA
% 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    : sf_mastr [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  101 (   6 unit)
%            Number of atoms       :  624 ( 195 equality)
%            Maximal formula depth :   20 (   8 average)
%            Number of connectives :  592 (  69 ~  ;  24  |; 204  &)
%                                         (  17 <=>; 278 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   22 (   1 propositional; 0-3 arity)
%            Number of functors    :   96 (  19 constant; 0-5 arity)
%            Number of variables   :  260 (   0 singleton; 237 !;  23 ?)
%            Maximal term depth    :    7 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_sf_mastr,axiom,(
    ! [A,B] :
      ( v1_finset_1(A)
     => ! [C] :
          ( m1_relset_1(C,A,B)
         => ( ( v1_funct_1(C)
              & v1_funct_2(C,A,B) )
           => ( v1_funct_1(C)
              & v1_finset_1(C)
              & v1_funct_2(C,A,B) ) ) ) ) )).

fof(fc1_sf_mastr,axiom,(
    ! [A,B,C] :
      ( ( v1_finset_1(A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,k5_finsub_1(B))
        & m1_relset_1(C,A,k5_finsub_1(B)) )
     => v1_finset_1(k3_card_3(C)) ) )).

fof(fc2_sf_mastr,axiom,(
    ~ v1_xboole_0(k2_scmfsa_2) )).

fof(fc3_sf_mastr,axiom,(
    ~ v1_xboole_0(k3_scmfsa_2) )).

fof(fc4_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => v1_finset_1(k2_sf_mastr(A)) ) )).

fof(fc5_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => v1_finset_1(k4_sf_mastr(A)) ) )).

fof(fc6_sf_mastr,axiom,(
    v1_sf_mastr(k4_scmfsa_2(np__0)) )).

fof(rc1_sf_mastr,axiom,(
    ? [A] :
      ( m1_scmfsa_2(A)
      & ~ v1_sf_mastr(A) ) )).

fof(fc7_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ~ v1_sf_mastr(k6_sf_mastr(A)) ) )).

fof(t1_sf_mastr,axiom,(
    ! [A,B,C,D] :
      ( ( v1_relat_1(D)
        & v1_funct_1(D) )
     => ( k1_funct_1(D,A) = k1_funct_1(D,B)
       => k1_funct_1(D,C) = k1_funct_1(k5_relat_1(k2_funct_7(k6_relat_1(k1_relat_1(D)),A,B),D),C) ) ) )).

fof(t2_sf_mastr,axiom,(
    ! [A,B,C] :
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ( ( r2_hidden(A,k1_relat_1(C))
         => ( r2_hidden(B,k1_relat_1(C))
            & k1_funct_1(C,A) = k1_funct_1(C,B) ) )
       => C = k5_relat_1(k2_funct_7(k6_relat_1(k1_relat_1(C)),A,B),C) ) ) )).

fof(t3_sf_mastr,axiom,(
    $true )).

fof(t4_sf_mastr,axiom,(
    $true )).

fof(t5_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ( k8_scmfsa_2(A,B) = k8_scmfsa_2(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t6_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ( k9_scmfsa_2(A,B) = k9_scmfsa_2(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t7_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ( k10_scmfsa_2(A,B) = k10_scmfsa_2(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t8_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ( k11_scmfsa_2(A,B) = k11_scmfsa_2(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t9_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ( k12_scmfsa_2(A,B) = k12_scmfsa_2(C,D)
                   => ( A = C
                      & B = D ) ) ) ) ) ) )).

fof(t10_sf_mastr,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] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ( k13_scmfsa_2(A) = k13_scmfsa_2(B)
           => A = B ) ) ) )).

fof(t11_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => ! [D] :
                  ( m1_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                 => ( k14_scmfsa_2(C,A) = k14_scmfsa_2(D,B)
                   => ( A = B
                      & C = D ) ) ) ) ) ) )).

fof(t12_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => ! [D] :
                  ( m1_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                 => ( k15_scmfsa_2(C,A) = k15_scmfsa_2(D,B)
                   => ( A = B
                      & C = D ) ) ) ) ) ) )).

fof(t13_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( m2_scmfsa_2(E)
                     => ! [F] :
                          ( m2_scmfsa_2(F)
                         => ( k16_scmfsa_2(A,B,E) = k16_scmfsa_2(C,D,F)
                           => ( B = D
                              & A = C
                              & E = F ) ) ) ) ) ) ) ) )).

fof(t14_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_scmfsa_2(C)
             => ! [D] :
                  ( m1_scmfsa_2(D)
                 => ! [E] :
                      ( m2_scmfsa_2(E)
                     => ! [F] :
                          ( m2_scmfsa_2(F)
                         => ( k17_scmfsa_2(B,A,E) = k17_scmfsa_2(D,C,F)
                           => ( A = C
                              & B = D
                              & E = F ) ) ) ) ) ) ) ) )).

fof(t15_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => ( k18_scmfsa_2(A,C) = k18_scmfsa_2(B,D)
                   => ( A = B
                      & C = D ) ) ) ) ) ) )).

fof(t16_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ! [D] :
                  ( m2_scmfsa_2(D)
                 => ( k19_scmfsa_2(A,C) = k19_scmfsa_2(B,D)
                   => ( A = B
                      & C = D ) ) ) ) ) ) )).

fof(d1_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(k2_scmfsa_2))
         => ( ( r2_hidden(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k3_enumset1(np__1,np__2,np__3,np__4,np__5))
             => ( B = k1_sf_mastr(A)
              <=> ? [C] :
                    ( m1_scmfsa_2(C)
                    & ? [D] :
                        ( m1_scmfsa_2(D)
                        & ~ ( A != k8_scmfsa_2(C,D)
                            & A != k9_scmfsa_2(C,D)
                            & A != k10_scmfsa_2(C,D)
                            & A != k11_scmfsa_2(C,D)
                            & A != k12_scmfsa_2(C,D) )
                        & B = k3_setwiseo(u1_struct_0(k1_scmfsa_2),C,D) ) ) ) )
            & ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__7
                | k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__8 )
             => ( B = k1_sf_mastr(A)
              <=> ? [C] :
                    ( m1_scmfsa_2(C)
                    & ? [D] :
                        ( m1_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
                        & ( A = k14_scmfsa_2(D,C)
                          | A = k15_scmfsa_2(D,C) )
                        & B = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),C) ) ) ) )
            & ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__9
                | k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__10 )
             => ( B = k1_sf_mastr(A)
              <=> ? [C] :
                    ( m1_scmfsa_2(C)
                    & ? [D] :
                        ( m1_scmfsa_2(D)
                        & ? [E] :
                            ( m2_scmfsa_2(E)
                            & ( A = k16_scmfsa_2(D,C,E)
                              | A = k17_scmfsa_2(D,C,E) )
                            & B = k3_setwiseo(u1_struct_0(k1_scmfsa_2),C,D) ) ) ) ) )
            & ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__11
                | k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__12 )
             => ( B = k1_sf_mastr(A)
              <=> ? [C] :
                    ( m1_scmfsa_2(C)
                    & ? [D] :
                        ( m2_scmfsa_2(D)
                        & ( A = k18_scmfsa_2(C,D)
                          | A = k19_scmfsa_2(C,D) )
                        & B = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),C) ) ) ) )
            & ~ ( ~ r2_hidden(k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k3_enumset1(np__1,np__2,np__3,np__4,np__5))
                & k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__7
                & k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__8
                & k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__9
                & k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__10
                & k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__11
                & k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__12
                & ~ ( B = k1_sf_mastr(A)
                  <=> B = k1_xboole_0 ) ) ) ) ) )).

fof(t17_sf_mastr,axiom,(
    k1_sf_mastr(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k1_xboole_0 )).

fof(t18_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_subset_1(C,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))
             => ( ~ ( C != k8_scmfsa_2(A,B)
                    & C != k9_scmfsa_2(A,B)
                    & C != k10_scmfsa_2(A,B)
                    & C != k11_scmfsa_2(A,B)
                    & C != k12_scmfsa_2(A,B) )
               => k1_sf_mastr(C) = k3_setwiseo(u1_struct_0(k1_scmfsa_2),A,B) ) ) ) ) )).

fof(t19_sf_mastr,axiom,(
    ! [A] :
      ( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => k1_sf_mastr(k13_scmfsa_2(A)) = k1_xboole_0 ) )).

fof(t20_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
         => ! [C] :
              ( m2_subset_1(C,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))
             => ( ( C = k14_scmfsa_2(B,A)
                  | C = k15_scmfsa_2(B,A) )
               => k1_sf_mastr(C) = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),A) ) ) ) ) )).

fof(t21_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ! [D] :
                  ( m2_subset_1(D,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))
                 => ( ( D = k16_scmfsa_2(A,B,C)
                      | D = k17_scmfsa_2(A,B,C) )
                   => k1_sf_mastr(D) = k3_setwiseo(u1_struct_0(k1_scmfsa_2),B,A) ) ) ) ) ) )).

fof(t22_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m2_scmfsa_2(B)
         => ! [C] :
              ( m2_subset_1(C,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))
             => ( ( C = k18_scmfsa_2(A,B)
                  | C = k19_scmfsa_2(A,B) )
               => k1_sf_mastr(C) = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),A) ) ) ) ) )).

fof(d2_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2))
         => ( B = k2_sf_mastr(A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k2_scmfsa_2))
                & m2_relset_1(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k2_scmfsa_2))
                & ! [D] :
                    ( m2_subset_1(D,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))
                   => k8_funct_2(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k2_scmfsa_2),C,D) = k1_sf_mastr(D) )
                & B = k3_card_3(k5_relat_1(A,C)) ) ) ) ) )).

fof(t23_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( r2_hidden(A,k2_relat_1(B))
           => r1_tarski(k1_sf_mastr(A),k2_sf_mastr(B)) ) ) ) )).

fof(t24_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & 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)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => r1_tarski(k2_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)),k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k2_sf_mastr(A),k2_sf_mastr(B))) ) ) )).

fof(t25_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & 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)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
           => k2_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k2_sf_mastr(A),k2_sf_mastr(B)) ) ) ) )).

fof(t26_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k2_sf_mastr(A) = k2_sf_mastr(k8_scmfsa_4(A,B)) ) ) )).

fof(t27_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k1_sf_mastr(A) = k1_sf_mastr(k4_scmfsa_4(A,B)) ) ) )).

fof(t28_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k2_sf_mastr(A) = k2_sf_mastr(k7_scmfsa_4(A,B)) ) ) )).

fof(t29_sf_mastr,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k2_sf_mastr(A) = k2_sf_mastr(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B))) ) ) )).

fof(t30_sf_mastr,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) )
     => k2_sf_mastr(A) = k2_sf_mastr(k1_scmfsa6a(A)) ) )).

fof(t31_sf_mastr,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) )
         => k2_sf_mastr(k4_scmfsa6a(A,B)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k2_sf_mastr(A),k2_sf_mastr(B)) ) ) )).

fof(t32_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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(k2_scmfsa6a(A)) = k1_sf_mastr(A) ) )).

fof(t33_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [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(k5_scmfsa6a(A,B)) = k2_xboole_0(k1_sf_mastr(A),k2_sf_mastr(B)) ) ) )).

fof(t34_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [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(k6_scmfsa6a(B,A)) = k2_xboole_0(k2_sf_mastr(B),k1_sf_mastr(A)) ) ) )).

fof(t35_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [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(k7_scmfsa6a(A,B)) = k5_setwiseo(k2_scmfsa_2,k1_sf_mastr(A),k1_sf_mastr(B)) ) ) )).

fof(d3_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [B] :
          ( m1_subset_1(B,k5_finsub_1(k3_scmfsa_2))
         => ( ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__9
                | k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__10 )
             => ( B = k3_sf_mastr(A)
              <=> ? [C] :
                    ( m1_scmfsa_2(C)
                    & ? [D] :
                        ( m1_scmfsa_2(D)
                        & ? [E] :
                            ( m2_scmfsa_2(E)
                            & ( A = k16_scmfsa_2(D,C,E)
                              | A = k17_scmfsa_2(D,C,E) )
                            & B = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),E) ) ) ) ) )
            & ( ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__11
                | k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__12 )
             => ( B = k3_sf_mastr(A)
              <=> ? [C] :
                    ( m1_scmfsa_2(C)
                    & ? [D] :
                        ( m2_scmfsa_2(D)
                        & ( A = k18_scmfsa_2(C,D)
                          | A = k19_scmfsa_2(C,D) )
                        & B = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),D) ) ) ) )
            & ~ ( k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__9
                & k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__10
                & k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__11
                & k1_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) != np__12
                & ~ ( B = k3_sf_mastr(A)
                  <=> B = k1_xboole_0 ) ) ) ) ) )).

fof(t36_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
             => ! [D] :
                  ( m2_subset_1(D,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))
                 => ( ~ ( D != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                        & D != k8_scmfsa_2(A,B)
                        & D != k9_scmfsa_2(A,B)
                        & D != k10_scmfsa_2(A,B)
                        & D != k11_scmfsa_2(A,B)
                        & D != k12_scmfsa_2(A,B)
                        & D != k13_scmfsa_2(C)
                        & D != k14_scmfsa_2(C,A)
                        & D != k15_scmfsa_2(C,A) )
                   => k3_sf_mastr(D) = k1_xboole_0 ) ) ) ) ) )).

fof(t37_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ! [D] :
                  ( m2_subset_1(D,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))
                 => ( ( D = k16_scmfsa_2(A,B,C)
                      | D = k17_scmfsa_2(A,B,C) )
                   => k3_sf_mastr(D) = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),C) ) ) ) ) ) )).

fof(t38_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m2_scmfsa_2(B)
         => ! [C] :
              ( m2_subset_1(C,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))
             => ( ( C = k18_scmfsa_2(A,B)
                  | C = k19_scmfsa_2(A,B) )
               => k3_sf_mastr(C) = k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),B) ) ) ) ) )).

fof(d4_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k3_scmfsa_2))
         => ( B = k4_sf_mastr(A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k3_scmfsa_2))
                & m2_relset_1(C,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k3_scmfsa_2))
                & ! [D] :
                    ( m2_subset_1(D,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))
                   => k8_funct_2(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k5_finsub_1(k3_scmfsa_2),C,D) = k3_sf_mastr(D) )
                & B = k3_card_3(k5_relat_1(A,C)) ) ) ) ) )).

fof(t39_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [B] :
          ( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( r2_hidden(A,k2_relat_1(B))
           => r1_tarski(k3_sf_mastr(A),k4_sf_mastr(B)) ) ) ) )).

fof(t40_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & 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)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => r1_tarski(k4_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)),k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(A),k4_sf_mastr(B))) ) ) )).

fof(t41_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & 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)
            & m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
         => ( r1_xboole_0(k1_relat_1(A),k1_relat_1(B))
           => k4_sf_mastr(k1_scmfsa_4(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(A),k4_sf_mastr(B)) ) ) ) )).

fof(t42_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k4_sf_mastr(A) = k4_sf_mastr(k8_scmfsa_4(A,B)) ) ) )).

fof(t43_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k3_sf_mastr(A) = k3_sf_mastr(k4_scmfsa_4(A,B)) ) ) )).

fof(t44_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k4_sf_mastr(A) = k4_sf_mastr(k7_scmfsa_4(A,B)) ) ) )).

fof(t45_sf_mastr,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k4_sf_mastr(A) = k4_sf_mastr(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(A,B))) ) ) )).

fof(t46_sf_mastr,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) )
     => k4_sf_mastr(A) = k4_sf_mastr(k1_scmfsa6a(A)) ) )).

fof(t47_sf_mastr,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) )
         => k4_sf_mastr(k4_scmfsa6a(A,B)) = k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(A),k4_sf_mastr(B)) ) ) )).

fof(t48_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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(k2_scmfsa6a(A)) = k3_sf_mastr(A) ) )).

fof(t49_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [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(k5_scmfsa6a(A,B)) = k2_xboole_0(k3_sf_mastr(A),k4_sf_mastr(B)) ) ) )).

fof(t50_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [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(k6_scmfsa6a(B,A)) = k2_xboole_0(k4_sf_mastr(B),k3_sf_mastr(A)) ) ) )).

fof(t51_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [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(k7_scmfsa6a(A,B)) = k5_setwiseo(k3_scmfsa_2,k3_sf_mastr(A),k3_sf_mastr(B)) ) ) )).

fof(d5_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ( v1_sf_mastr(A)
      <=> A = k4_scmfsa_2(np__0) ) ) )).

fof(t52_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
     => ~ r2_hidden(k5_sf_mastr(A),A) ) )).

fof(t53_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2)) )
             => ( k5_sf_mastr(C) = k4_scmfsa_2(A)
               => ( r2_hidden(k4_scmfsa_2(B),C)
                  | r1_xreal_0(A,B) ) ) ) ) ) )).

fof(d7_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ( B = k6_sf_mastr(A)
          <=> ? [C] :
                ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2))
                & C = k2_xboole_0(k2_sf_mastr(A),k15_cqc_sim1(u1_struct_0(k1_scmfsa_2),k4_scmfsa_2(np__0)))
                & B = k5_sf_mastr(C) ) ) ) ) )).

fof(t54_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ~ r2_hidden(k6_sf_mastr(A),k2_sf_mastr(A)) ) )).

fof(t55_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ( ~ ( ~ r2_hidden(k8_scmfsa_2(A,B),k2_relat_1(C))
                    & ~ r2_hidden(k9_scmfsa_2(A,B),k2_relat_1(C))
                    & ~ r2_hidden(k10_scmfsa_2(A,B),k2_relat_1(C))
                    & ~ r2_hidden(k11_scmfsa_2(A,B),k2_relat_1(C))
                    & ~ r2_hidden(k12_scmfsa_2(A,B),k2_relat_1(C)) )
               => ( k6_sf_mastr(C) != A
                  & k6_sf_mastr(C) != B ) ) ) ) ) )).

fof(t56_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(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)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ~ ( ( r2_hidden(k14_scmfsa_2(B,A),k2_relat_1(C))
                    | r2_hidden(k15_scmfsa_2(B,A),k2_relat_1(C)) )
                  & k6_sf_mastr(C) = A ) ) ) ) )).

fof(t57_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ! [D] :
                  ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                    & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                 => ( ( r2_hidden(k16_scmfsa_2(A,B,C),k2_relat_1(D))
                      | r2_hidden(k17_scmfsa_2(A,B,C),k2_relat_1(D)) )
                   => ( k6_sf_mastr(D) != B
                      & k6_sf_mastr(D) != A ) ) ) ) ) ) )).

fof(t58_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m2_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ~ ( ( r2_hidden(k18_scmfsa_2(A,B),k2_relat_1(C))
                    | r2_hidden(k19_scmfsa_2(A,B),k2_relat_1(C)) )
                  & k6_sf_mastr(C) = A ) ) ) ) )).

fof(t59_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) )
     => ~ r2_hidden(k7_sf_mastr(A),A) ) )).

fof(t60_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_scmfsa_2)) )
             => ( k7_sf_mastr(C) = k6_scmfsa_2(A)
               => ( r2_hidden(k6_scmfsa_2(B),C)
                  | r1_xreal_0(A,B) ) ) ) ) ) )).

fof(d9_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ! [B] :
          ( m2_scmfsa_2(B)
         => ( B = k8_sf_mastr(A)
          <=> ? [C] :
                ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(k3_scmfsa_2))
                & C = k4_sf_mastr(A)
                & B = k7_sf_mastr(C) ) ) ) ) )).

fof(t61_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => ~ r2_hidden(k8_sf_mastr(A),k4_sf_mastr(A)) ) )).

fof(t62_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ! [C] :
              ( m2_scmfsa_2(C)
             => ! [D] :
                  ( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                    & m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
                 => ~ ( ( r2_hidden(k16_scmfsa_2(A,B,C),k2_relat_1(D))
                        | r2_hidden(k17_scmfsa_2(A,B,C),k2_relat_1(D)) )
                      & k8_sf_mastr(D) = C ) ) ) ) ) )).

fof(t63_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [B] :
          ( m2_scmfsa_2(B)
         => ! [C] :
              ( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
                & m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
             => ~ ( ( r2_hidden(k18_scmfsa_2(A,B),k2_relat_1(C))
                    | r2_hidden(k19_scmfsa_2(A,B),k2_relat_1(C)) )
                  & k8_sf_mastr(C) = B ) ) ) ) )).

fof(t64_sf_mastr,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r1_xboole_0(k1_relat_1(A),k1_relat_1(k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(B)))) ) ) )).

fof(t65_sf_mastr,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => r2_hidden(k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k1_relat_1(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(B))))) ) ) )).

fof(t66_sf_mastr,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k1_funct_1(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(B))),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k5_scmfsa_2(B) ) ) )).

fof(t67_sf_mastr,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(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,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(B))),C)
               => k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C) = k5_scmfsa_2(B) ) ) ) ) )).

fof(t68_sf_mastr,axiom,(
    ! [A] :
      ( m1_scmfsa_2(A)
     => ! [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))
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( ~ r2_hidden(A,k1_sf_mastr(B))
               => k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,C),A) = k20_scmfsa_2(C,A) ) ) ) ) )).

fof(t69_sf_mastr,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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(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,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),D)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(C,E)
                           => r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,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,D),E)),k1_relat_1(B)) ) ) )
                   => ( r2_hidden(A,k2_sf_mastr(B))
                      | k20_scmfsa_2(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,D),C),A) = k20_scmfsa_2(D,A) ) ) ) ) ) ) )).

fof(t70_sf_mastr,axiom,(
    ! [A] :
      ( m2_scmfsa_2(A)
     => ! [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))
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ( ~ r2_hidden(A,k3_sf_mastr(B))
               => k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,C),A) = k21_scmfsa_2(C,A) ) ) ) ) )).

fof(t71_sf_mastr,axiom,(
    ! [A] :
      ( m2_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] :
              ( m2_subset_1(C,k1_numbers,k5_numbers)
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(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,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),D)
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(C,E)
                           => r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,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,D),E)),k1_relat_1(B)) ) ) )
                   => ( r2_hidden(A,k4_sf_mastr(B))
                      | k21_scmfsa_2(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,D),C),A) = k21_scmfsa_2(D,A) ) ) ) ) ) ) )).

fof(t72_sf_mastr,axiom,(
    ! [A] :
      ( m2_subset_1(A,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))
     => ! [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_sf_mastr(A)) = k7_relat_1(C,k1_sf_mastr(A))
                  & k7_relat_1(B,k3_sf_mastr(A)) = k7_relat_1(C,k3_sf_mastr(A))
                  & k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C) )
               => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C))
                  & k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),k1_sf_mastr(A)) = k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C),k1_sf_mastr(A))
                  & k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),k3_sf_mastr(A)) = k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C),k3_sf_mastr(A)) ) ) ) ) ) )).

fof(t73_sf_mastr,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] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(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,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),C)
                      & r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),D)
                      & k7_relat_1(C,k2_sf_mastr(A)) = k7_relat_1(D,k2_sf_mastr(A))
                      & k7_relat_1(C,k4_sf_mastr(A)) = k7_relat_1(D,k4_sf_mastr(A))
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(B,E)
                           => r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,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,C),E)),k1_relat_1(A)) ) ) )
                   => ( ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( ~ r1_xreal_0(B,E)
                           => r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,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,D),E)),k1_relat_1(A)) ) )
                      & ! [E] :
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ( r1_xreal_0(E,B)
                           => ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,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,C),E)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,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,D),E))
                              & ! [F] :
                                  ( m1_scmfsa_2(F)
                                 => ( r2_hidden(F,k2_sf_mastr(A))
                                   => k20_scmfsa_2(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,C),E),F) = k20_scmfsa_2(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,D),E),F) ) )
                              & ! [F] :
                                  ( m2_scmfsa_2(F)
                                 => ( r2_hidden(F,k4_sf_mastr(A))
                                   => k21_scmfsa_2(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,C),E),F) = k21_scmfsa_2(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,D),E),F) ) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_k1_sf_mastr,axiom,(
    ! [A] :
      ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => m1_subset_1(k1_sf_mastr(A),k5_finsub_1(k2_scmfsa_2)) ) )).

fof(dt_k2_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => m1_subset_1(k2_sf_mastr(A),k1_zfmisc_1(k2_scmfsa_2)) ) )).

fof(dt_k3_sf_mastr,axiom,(
    ! [A] :
      ( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
     => m1_subset_1(k3_sf_mastr(A),k5_finsub_1(k3_scmfsa_2)) ) )).

fof(dt_k4_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => m1_subset_1(k4_sf_mastr(A),k1_zfmisc_1(k3_scmfsa_2)) ) )).

fof(dt_k5_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
     => m1_scmfsa_2(k5_sf_mastr(A)) ) )).

fof(dt_k6_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => m1_scmfsa_2(k6_sf_mastr(A)) ) )).

fof(dt_k7_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) )
     => m2_scmfsa_2(k7_sf_mastr(A)) ) )).

fof(dt_k8_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
        & m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
     => m2_scmfsa_2(k8_sf_mastr(A)) ) )).

fof(d6_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
     => ! [B] :
          ( m1_scmfsa_2(B)
         => ( B = k5_sf_mastr(A)
          <=> ? [C] :
                ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k5_numbers))
                & B = k4_scmfsa_2(k10_cqc_sim1(C))
                & C = a_1_0_sf_mastr(A) ) ) ) ) )).

fof(d8_sf_mastr,axiom,(
    ! [A] :
      ( ( v1_finset_1(A)
        & m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) )
     => ! [B] :
          ( m2_scmfsa_2(B)
         => ( B = k7_sf_mastr(A)
          <=> ? [C] :
                ( ~ v1_xboole_0(C)
                & m1_subset_1(C,k1_zfmisc_1(k5_numbers))
                & B = k6_scmfsa_2(k10_cqc_sim1(C))
                & C = a_1_1_sf_mastr(A) ) ) ) ) )).

fof(fraenkel_a_1_0_sf_mastr,axiom,(
    ! [A,B] :
      ( ( v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) )
     => ( r2_hidden(A,a_1_0_sf_mastr(B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = C
            & ~ r2_hidden(k4_scmfsa_2(C),B) ) ) ) )).

fof(fraenkel_a_1_1_sf_mastr,axiom,(
    ! [A,B] :
      ( ( v1_finset_1(B)
        & m1_subset_1(B,k1_zfmisc_1(k3_scmfsa_2)) )
     => ( r2_hidden(A,a_1_1_sf_mastr(B))
      <=> ? [C] :
            ( m2_subset_1(C,k1_numbers,k5_numbers)
            & A = C
            & ~ r2_hidden(k6_scmfsa_2(C),B) ) ) ) )).
%------------------------------------------------------------------------------